Finite Group Databasebeta

← C2×#22624085 #33993103

Subgroups — C2×#22624085 #33993103

Order 18688.

9542 conjugacy classes of subgroups.

The subgroup lattice has 1336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22624085C2132yesmaximal, direct product factor
2C2×#17989329C211yesmaximal, characteristic, complemented
3C2×#17989325C212yesmaximal, complemented
4C2×#17989324C211yesmaximal, characteristic, complemented
5C2×#17989267C211yesmaximal, characteristic, complemented
6C2×#17989261C212yesmaximal, complemented
7C2×#17989226C212yesmaximal, complemented
8C2×#17989225C212yesmaximal, complemented
9C2×#17989224C212yesmaximal, complemented
10C2×#17989222C211yesmaximal, characteristic, complemented
11C2×#17989219C212yesmaximal, complemented
12C2×#17989172C212yesmaximal, complemented
13C2×#17989171C212yesmaximal, complemented
14C2×#17989169C212yesmaximal, complemented
15C2×#17989150C212yesmaximal, complemented
16C2×#17989146C211yesmaximal, characteristic, complemented
17C2×#17989145C212yesmaximal, complemented
18C22×#14556559C211yesmaximal, characteristic, complemented
19C2×#120×D73C212yesmaximal, complemented
20C2×#535×C73C211yesmaximal, characteristic, complemented
21C25×D73C2211yescharacteristic, complemented
22C22×#11924027C2212yescomplemented
23C23×C22⋊D73C2212yescomplemented
24C23×C22⋊D73C2211yescharacteristic, complemented
25C22×D4×D73C2212yescomplemented
26C22×D4×D73C2212yescomplemented
27C22×D4×D73C2212yescomplemented
28C22×D4×D73C2212yescomplemented
29#17989329C22116yescomplemented
30#17989325C22132yescomplemented
31#17989324C22116yescomplemented
32#17989267C22116yescomplemented
33#17989261C22132yescomplemented
34#17989226C22132yescomplemented
35#17989225C22132yescomplemented
36#17989224C22132yescomplemented
37#17989222C22116yescomplemented
38#17989219C22132yescomplemented
39#17989172C22132yescomplemented
40#17989171C22132yescomplemented
41#17989169C22132yescomplemented
42#17989150C22132yescomplemented
43#17989146C22116yescomplemented
44#17989145C22132yescomplemented
45C2×#14556587C2212yescomplemented
46C2×#14556586C2212yescomplemented
47C2×#14556585C2212yescomplemented
48C2×#14556584C2212yescomplemented
49C2×#14556584C2212yescomplemented
50C2×#14556580C2212yescomplemented
51C2×#14556579C2212yescomplemented
52C2×#14556578C2212yescomplemented
53C2×#14556577C2212yescomplemented
54C2×#14556577C2212yescomplemented
55C2×#14556576C2212yescomplemented
56C2×#14556576C2212yescomplemented
57C2×#14556575C2212yescomplemented
58C2×#14556574C2212yescomplemented
59C2×#14556574C2212yescomplemented
60C2×#14556573C2212yescomplemented
61C2×#14556573C2212yescomplemented
62C2×#14556572C2211yescharacteristic, complemented
63C2×#14556572C2212yescomplemented
64C2×#14556572C2211yescharacteristic, complemented
65C2×#14556569C2212yescomplemented
66C2×#14556568C2212yescomplemented
67C2×#14556567C2212yescomplemented
68C2×#14556565C2212yescomplemented
69C2×#14556564C2212yescomplemented
70C2×#14556564C2212yescomplemented
71C2×#14556563C2212yescomplemented
72C2×#14556563C2212yescomplemented
73C2×#14556563C2212yescomplemented
74C2×#14556563C2212yescomplemented
75C2×#14556563C2212yescomplemented
76C2×#14556563C2212yescomplemented
77C2×#14556563C2212yescomplemented
78C2×#14556563C2212yescomplemented
79C2×#14556562C2212yescomplemented
80C2×#14556562C2212yescomplemented
81C2×#14556561C2212yes—
82C2×#14556561C2212yescomplemented
83C2×#14556561C2212yescomplemented
84C2×#14556561C2212yescomplemented
85C2×#14556560C2212yescomplemented
86C2×#14556559C2211yescharacteristic
87C2×#14556559C2212yescomplemented
88C2×#14556559C2212yescomplemented
89C2×#14556559C2212yescomplemented
90C2×#14556559C2212yescomplemented
91C2×#14556559C2211yescharacteristic, complemented
92C2×#14556559C2211yescharacteristic, complemented
93C2×#14556559C2212yescomplemented
94C2×#14556559C2211yescharacteristic, complemented
95C2×#14556559C2211yescharacteristic, complemented
96C2×#14556559C2211yescharacteristic, complemented
97C2×#14556559C2212yescomplemented
98C2×#14556559C2212yescomplemented
99C2×#14556559C22116yescomplemented
100#120×D73C22132yescomplemented
101C2×C4×D292C2212yescomplemented
102C2×D4×Dic73C2212yescomplemented
103C2×C4×C22⋊D73C2212yescomplemented
104C2×#14556551C2212yescomplemented
105C2×#14556551C2212yescomplemented
106C2×#14556551C2212yescomplemented
107C2×#14556548C2212yescomplemented
108C22×C22⋊Dic73C2211yescharacteristic, complemented
109C22×C22⋊Dic73C2211yescharacteristic, complemented
110C22×#11924005C2212yescomplemented
111C22×#11924005C2212yescomplemented
112C2×C22⋊C4×D73C2212yescomplemented
113C2×C22⋊C4×D73C2212yescomplemented
114C2×C22⋊C4×D73C2212yescomplemented
115C22×#41×C73C2211yescharacteristic, complemented
116C23×D4×C73C2211yescharacteristic, complemented
117#535×C73C22116yescomplemented
118C2×#127×C73C2211yescharacteristic, complemented
119C2×#127×C73C2211yescharacteristic, complemented
120C2×#124×C73C2211yescharacteristic, complemented
121C2×#124×C73C2211yescharacteristic, complemented
122C2×#121×C73C2212yescomplemented
123C2×#121×C73C2212yescomplemented
124C2×#120×C73C2212yescomplemented
125C2×#120×C73C2212yescomplemented
126C2×#117×C73C2211yescharacteristic, complemented
127C24×D73—44no—
128C24×D73—48no—
129C24×D73C2311yescharacteristic
130C24×D73C2312yes—
131C24×D73C2312yes—
132C24×D73C2312yes—
133C24×D73C2311yescharacteristic
134C24×D73C2318yescomplemented
135C24×D73C2311yescharacteristic, complemented
136C2×#11924027—48no—
137C2×#11924027C23116yescomplemented
138C22×Dic146C2312yescomplemented
139C22×D292C2312yes—
140C22×D292C2312yes—
141C22×D292C2312yes—
142C22×C22⋊D73—44no—
143C22×C22⋊D73—48no—
144C22×C22⋊D73C2312yes—
145C22×C22⋊D73C2312yes—
146C22×C22⋊D73C2312yes—
147C22×C22⋊D73C2312yes—
148C22×C22⋊D73C2312yes—
149C22×C22⋊D73C2312yes—
150C22×C22⋊D73C2312yes—
151C22×C22⋊D73C2312yes—
152C22×C22⋊D73C2312yes—
153C22×C22⋊D73C2312yes—
154C22×C22⋊D73C23116yescomplemented
155C22×C22⋊D73C2312yescomplemented
156C22×C22⋊D73C2312yescomplemented
157C22×C22⋊D73C2318yescomplemented
158C2×D4×D73—48no—
159C2×D4×D73—48no—
160C2×D4×D73—48no—
161C2×D4×D73—48no—
162C2×D4×D73C23116yescomplemented
163C2×D4×D73C23116yescomplemented
164C2×D4×D73C23116yescomplemented
165C2×D4×D73C23116yescomplemented
166C23×Dic73C2312yes—
167C23×Dic73C2311yescharacteristic, complemented
168C23×Dic73C2312yescomplemented
169C23×Dic73C2312yescomplemented
170C22×C4×D73C2312yes—
171C22×C4×D73C2312yes—
172C22×C4×D73C2312yes—
173C22×C4×D73C2312yescomplemented
174#14556587C23116yescomplemented
175#14556586C23116yescomplemented
176#14556585C23116yescomplemented
177#14556584C23116yescomplemented
178#14556584C23116yescomplemented
179#14556580C23116yescomplemented
180#14556579C23116yescomplemented
181#14556578C23116yescomplemented
182#14556577C23116yescomplemented
183#14556577C23116yescomplemented
184#14556576C23116yescomplemented
185#14556576C23116yescomplemented
186#14556575C23116yescomplemented
187#14556574C23116yescomplemented
188#14556574C23116yescomplemented
189#14556573C23116yescomplemented
190#14556573C23116yescomplemented
191#14556572C2318yescomplemented
192#14556572C2318yescomplemented
193#14556572C23116yescomplemented
194#14556569C23116yescomplemented
195#14556568C23116yescomplemented
196#14556567C23116yescomplemented
197#14556565C23116yescomplemented
198#14556564C23116yescomplemented
199#14556564C23116yescomplemented
200#14556563C23116yescomplemented
201#14556563C23116yescomplemented
202#14556563C23116yescomplemented
203#14556563C23116yescomplemented
204#14556563C23116yescomplemented
205#14556563C23116yescomplemented
206#14556563C23116yescomplemented
207#14556563C23116yescomplemented
208#14556562C23116yescomplemented
209#14556562C23116yescomplemented
210#14556561C23116yes—
211#14556561C23116yescomplemented
212#14556561C23116yescomplemented
213#14556561C23116yescomplemented
214#14556560C23116yescomplemented
215#14556559C2318yes—
216#14556559C23116yescomplemented
217#14556559C23116yescomplemented
218#14556559C23116yescomplemented
219#14556559C23116yescomplemented
220#14556559C2318yescomplemented
221#14556559C23116yescomplemented
222#14556559C2318yescomplemented
223#14556559C2318yescomplemented
224#14556559C2318yescomplemented
225#14556559C2318yescomplemented
226#14556559C23116yescomplemented
227#14556559C23116yescomplemented
228C4×D292C23116yescomplemented
229D4×Dic73C23116yescomplemented
230C4×C22⋊D73C23116yescomplemented
231#14556551C23116yescomplemented
232#14556551C23116yescomplemented
233#14556551C23116yescomplemented
234#14556548C23116yescomplemented
235C2×C4⋊Dic73C2312yescomplemented
236C2×C4⋊Dic73C2312yescomplemented
237C2×#11924007C2312yescomplemented
238C2×#11924007C2312yescomplemented
239C2×#11924007C2312yescomplemented
240C2×#11924007C2312yescomplemented
241C2×#11924007C2312yescomplemented
242C2×#11924007C2312yescomplemented
243C2×C22⋊Dic73C2312yes—
244C2×C22⋊Dic73C2312yes—
245C2×C22⋊Dic73C2312yes—
246C2×C22⋊Dic73C2311yescharacteristic
247C2×C22⋊Dic73C2312yes—
248C2×C22⋊Dic73C2311yescharacteristic
249C2×C22⋊Dic73C2318yescomplemented
250C2×C22⋊Dic73C2318yescomplemented
251C2×C22⋊Dic73C2311yescharacteristic, complemented
252C2×C22⋊Dic73C2311yescharacteristic, complemented
253C2×C22⋊Dic73C2312yescomplemented
254C2×C22⋊Dic73C2312yescomplemented
255C2×#11924005C2312yes—
256C2×#11924005C2312yes—
257C2×#11924005C2312yes—
258C2×#11924005C2312yes—
259C2×#11924005C2312yes—
260C2×#11924005C2312yes—
261C2×#11924005C2312yes—
262C2×#11924005C2312yes—
263C2×#11924005C2312yes—
264C2×#11924005C2312yes—
265C2×#11924005C23116yescomplemented
266C2×#11924005C2312yescomplemented
267C2×#11924005C2312yescomplemented
268C2×#11924005C2312yescomplemented
269C2×#11924005C2312yescomplemented
270C2×#11924005C23116yescomplemented
271C22⋊C4×D73C23116yescomplemented
272C22⋊C4×D73C23116yescomplemented
273C22⋊C4×D73C23116yescomplemented
274C2×C4×Dic73C2312yescomplemented
275C2×C4×Dic73C2312yescomplemented
276C25×C73C2311yescharacteristic
277C25×C73C2311yescharacteristic
278C2×#41×C73—44no—
279C2×#41×C73C2318yescomplemented
280C22×Q8×C73C2311yescharacteristic, complemented
281C22×D4×C73—44no—
282C22×D4×C73C2312yes—
283C22×D4×C73C2312yes—
284C22×D4×C73C2312yes—
285C22×D4×C73C2311yescharacteristic
286C22×D4×C73C2311yescharacteristic
287C22×D4×C73C2311yescharacteristic
288C22×D4×C73C2311yescharacteristic
289C22×D4×C73C2318yescomplemented
290C22×D4×C73C2312yescomplemented
291C22×D4×C73C2312yescomplemented
292C22×D4×C73C2311yescharacteristic, complemented
293C23×C4×C73C2311yescharacteristic
294C23×C4×C73C2312yescomplemented
295#127×C73C2318yescomplemented
296#127×C73C2318yescomplemented
297#124×C73C2318yescomplemented
298#124×C73C2318yescomplemented
299#121×C73C23116yescomplemented
300#121×C73C23116yescomplemented
301#120×C73C23116yescomplemented
302#120×C73C23116yescomplemented
303#117×C73C2318yescomplemented
304C2×C4⋊C4×C73C2312yescomplemented
305C2×C22⋊C4×C73C2312yes—
306C2×C22⋊C4×C73C2312yes—
307C2×C22⋊C4×C73C2312yes—
308C2×C22⋊C4×C73C2312yescomplemented
309C2×C22⋊C4×C73C2312yescomplemented
310C2×C42×C73C2311yescharacteristic, complemented
311C2×C42×C73C2311yescharacteristic, complemented
312C23×D73—28no—
313C23×D73—28no—
314C23×D73—28no—
315C23×D73—28no—
316C23×D73—28no—
317C23×D73—432no—
318C23×D73—42no—
319C23×D73—44no—
320C23×D73—44no—
321C23×D73—44no—
322C23×D73—44no—
323C23×D73—42no—
324C23×D73—416no—
325C23×D73—44no—
326C23×D73—44no—
327C23×D73—44no—
328C23×D73—42no—
329C23×D73—464no—
330C23×D73C2412yes—
331C23×D73C2412yes—
332C23×D73C2414yes—
333C23×D73C2418yes—
334C23×D73C2412yes—
335C23×D73C2418yes—
336C23×D73C2418yes—
337C23×D73C2414yes—
338C23×D73C2414yescomplemented
339#11924027—432no—
340C2×Dic146—44no—
341C2×Dic146C2418yescomplemented
342C2×D292—28no—
343C2×D292—44no—
344C2×D292—44no—
345C2×D292C2418yes—
346C2×D292C2418yes—
347C2×D292C2418yes—
348C2×C22⋊D73—28no—
349C2×C22⋊D73—28no—
350C2×C22⋊D73—28no—
351C2×C22⋊D73—28no—
352C2×C22⋊D73—44no—
353C2×C22⋊D73—44no—
354C2×C22⋊D73—44no—
355C2×C22⋊D73—44no—
356C2×C22⋊D73—44no—
357C2×C22⋊D73—44no—
358C2×C22⋊D73—44no—
359C2×C22⋊D73—44no—
360C2×C22⋊D73—432no—
361C2×C22⋊D73—416no—
362C2×C22⋊D73C2418yes—
363C2×C22⋊D73C2418yes—
364C2×C22⋊D73C2418yes—
365C2×C22⋊D73C2418yes—
366C2×C22⋊D73C2418yes—
367C2×C22⋊D73C2418yes—
368C2×C22⋊D73C2418yes—
369C2×C22⋊D73C2418yes—
370C2×C22⋊D73C2418yes—
371C2×C22⋊D73C2418yes—
372C2×C22⋊D73C2418yescomplemented
373C2×C22⋊D73C2418yescomplemented
374D4×D73—432no—
375D4×D73—432no—
376D4×D73—432no—
377D4×D73—432no—
378C22×Dic73—44no—
379C22×Dic73—42no—
380C22×Dic73—44no—
381C22×Dic73—44no—
382C22×Dic73C2412yes—
383C22×Dic73C2412yes—
384C22×Dic73C2412yes—
385C22×Dic73C2412yes—
386C22×Dic73C2412yes—
387C22×Dic73C2418yes—
388C22×Dic73C2418yescomplemented
389C22×Dic73C2418yescomplemented
390C22×Dic73C2414yescomplemented
391C2×C4×D73—28no—
392C2×C4×D73—44no—
393C2×C4×D73—44no—
394C2×C4×D73—44no—
395C2×C4×D73C2418yes—
396C2×C4×D73C2418yes—
397C2×C4×D73C2418yes—
398C2×C4×D73C2418yescomplemented
399C4⋊Dic73C2418yescomplemented
400C4⋊Dic73C2418yescomplemented
401#11924007C2418yescomplemented
402#11924007C2418yescomplemented
403#11924007C2418yescomplemented
404#11924007C2418yescomplemented
405#11924007C2418yescomplemented
406#11924007C2418yescomplemented
407C22⋊Dic73C2418yes—
408C22⋊Dic73C2418yes—
409C22⋊Dic73C2418yes—
410C22⋊Dic73C2414yes—
411C22⋊Dic73C2418yes—
412C22⋊Dic73C2414yes—
413C22⋊Dic73C2414yescomplemented
414C22⋊Dic73C2414yescomplemented
415C22⋊Dic73C2418yescomplemented
416C22⋊Dic73C2418yescomplemented
417#11924005C2418yes—
418#11924005C2418yes—
419#11924005C2418yes—
420#11924005C2418yes—
421#11924005C2418yes—
422#11924005C2418yes—
423#11924005C2418yes—
424#11924005C2418yes—
425#11924005C2418yes—
426#11924005C2418yes—
427#11924005C2418yescomplemented
428#11924005C2418yescomplemented
429#11924005C2418yescomplemented
430#11924005C2418yescomplemented
431C4×Dic73C2418yescomplemented
432C4×Dic73C2418yescomplemented
433C24×C73—24no—
434C24×C73—24no—
435C24×C73—44no—
436C24×C73—44no—
437C24×C73C2411yescharacteristic
438C24×C73C2411yescharacteristic
439C24×C73C2411yescharacteristic
440C24×C73C2411yescharacteristic
441C24×C73C2412yes—
442C24×C73C2411yescharacteristic
443C24×C73C2414yes—
444C24×C73C2414yes—
445#41×C73—416no—
446C2×Q8×C73—42no—
447C2×Q8×C73C2414yescomplemented
448C2×D4×C73—28no—
449C2×D4×C73—42no—
450C2×D4×C73—42no—
451C2×D4×C73—42no—
452C2×D4×C73—42no—
453C2×D4×C73—416no—
454C2×D4×C73—44no—
455C2×D4×C73—44no—
456C2×D4×C73—42no—
457C2×D4×C73—44no—
458C2×D4×C73—44no—
459C2×D4×C73C2418yes—
460C2×D4×C73C2418yes—
461C2×D4×C73C2418yes—
462C2×D4×C73C2414yes—
463C2×D4×C73C2414yes—
464C2×D4×C73C2414yes—
465C2×D4×C73C2414yes—
466C2×D4×C73C2418yescomplemented
467C2×D4×C73C2418yescomplemented
468C2×D4×C73C2414yescomplemented
469C22×C4×C73—24no—
470C22×C4×C73—44no—
471C22×C4×C73C2411yescharacteristic
472C22×C4×C73C2412yes—
473C22×C4×C73C2412yes—
474C22×C4×C73C2412yes—
475C22×C4×C73C2411yescharacteristic
476C22×C4×C73C2414yes—
477C22×C4×C73C2418yescomplemented
478C4⋊C4×C73C2418yescomplemented
479C22⋊C4×C73C2418yes—
480C22⋊C4×C73C2418yes—
481C22⋊C4×C73C2418yes—
482C22⋊C4×C73C2418yescomplemented
483C22⋊C4×C73C2418yescomplemented
484C42×C73C2414yescomplemented
485C42×C73C2414yescomplemented
486C23×C73—24no—
487C23×C73—24no—
488C23×C73—22no—
489C23×C73—22no—
490C23×C73—28no—
491C23×C73—22no—
492C23×C73—22no—
493C23×C73—24no—
494C23×C73—24no—
495C23×C73—24no—
496C23×C73—24no—
497C23×C73—24no—
498C23×C73—24no—
499C23×C73—28no—
500C23×C73—48no—
501C23×C73—48no—
502C23×C73—416no—
503C23×C73—88no—
504C23×C73H(5,𝔽2)14yes—
505C23×C73C2512yes—
506C23×C73C2512yes—
507C23×C73C2512yes—
508C23×C73C2512yes—
509C23×C73C2514yes—
510C23×C73C2512yes—
511C23×C73C2511yescharacteristic
512C22×D73—24no—
513C22×D73—24no—
514C22×D73—24no—
515C22×D73—216no—
516C22×D73—24no—
517C22×D73—24no—
518C22×D73—24no—
519C22×D73—24no—
520C22×D73—24no—
521C22×D73—216no—
522C22×D73—216no—
523C22×D73—216no—
524C22×D73—216no—
525C22×D73—44no—
526C22×D73—48no—
527C22×D73—48no—
528C22×D73—48no—
529C22×D73—44no—
530C22×D73—48no—
531C22×D73—416no—
532C22×D73—48no—
533C22×D73—48no—
534C22×D73—48no—
535C22×D73—44no—
536C22×D73—432no—
537C22×D73—432no—
538C22×D73—4128no—
539C22×D73—416no—
540C22×D73—816no—
541C22×D73—88no—
542C22×D73H(5,𝔽2)18yes—
543C22×D73C2514yes—
544C22×D73C2514yes—
545C22×D73C2514yes—
546Q8×C73—44no—
547D4×C73—216no—
548D4×C73—44no—
549D4×C73—44no—
550D4×C73—44no—
551D4×C73—44no—
552D4×C73—48no—
553D4×C73—48no—
554D4×C73—44no—
555D4×C73—48no—
556D4×C73—48no—
557C2×C4×C73—22no—
558C2×C4×C73—22no—
559C2×C4×C73—28no—
560C2×C4×C73—24no—
561C2×C4×C73—24no—
562C2×C4×C73—24no—
563C2×C4×C73—48no—
564C2×C4×C73C2512yes—
565C2×C4×C73C2514yes—
566C2×C4×C73C2514yes—
567C2×C4×C73C2514yes—
568C2×C4×C73C2512yes—
569C22⋊D73—216no—
570C22⋊D73—216no—
571C22⋊D73—216no—
572C22⋊D73—216no—
573C22⋊D73—48no—
574C22⋊D73—48no—
575C22⋊D73—48no—
576C22⋊D73—48no—
577C22⋊D73—48no—
578C22⋊D73—48no—
579C22⋊D73—48no—
580C22⋊D73—48no—
581C2×Dic73—24no—
582C2×Dic73—24no—
583C2×Dic73—24no—
584C2×Dic73—24no—
585C2×Dic73—24no—
586C2×Dic73—48no—
587C2×Dic73—44no—
588C2×Dic73—48no—
589C2×Dic73—48no—
590C2×Dic73C2514yes—
591C2×Dic73C2514yes—
592C2×Dic73C2514yes—
593C2×Dic73C2514yes—
594C2×Dic73C2514yes—
595D292—216no—
596D292—48no—
597D292—48no—
598C4×D73—216no—
599C4×D73—48no—
600C4×D73—48no—
601C4×D73—48no—
602Dic146—48no—
603C22×C73—24no—
604C22×C73—28no—
605C22×C73—24no—
606C22×C73—24no—
607C22×C73—22no—
608C22×C73—24no—
609C22×C73—24no—
610C22×C73—22no—
611C22×C73—24no—
612C22×C73—24no—
613C22×C73—24no—
614C22×C73—22no—
615C22×C73—22no—
616C22×C73—416no—
617C22×C73—44no—
618C22×C73—44no—
619C22×C73—48no—
620C22×C73—44no—
621C22×C73—44no—
622C22×C73—88no—
623C22×C73C2×H(5,𝔽2)14yes—
624C22×C73C2×H(5,𝔽2)14yes—
625C22×C73C2×H(5,𝔽2)12yes—
626C22×C73C2611yescharacteristic
627C2×D73—24no—
628C2×D73—24no—
629C2×D73—216no—
630C2×D73—24no—
631C2×D73—24no—
632C2×D73—24no—
633C2×D73—24no—
634C2×D73—24no—
635C2×D73—24no—
636C2×D73—416no—
637C2×D73—432no—
638C2×D73—432no—
639C2×D73—416no—
640C2×D73—48no—
641C2×D73—48no—
642C2×D73—816no—
643C2×D73—88no—
644C2×D73C2×H(5,𝔽2)18yes—
645C4×C73—24no—
646C4×C73—24no—
647C4×C73—24no—
648C4×C73—22no—
649C4×C73—22no—
650Dic73—24no—
651Dic73—24no—
652Dic73—24no—
653Dic73—24no—
654Dic73—24no—
655C2×#3532—731nomaximal, Sylow
656C2×C73—24no—
657C2×C73—42no—
658C2×C73—42no—
659C2×C73—44no—
660C2×C73—42no—
661C2×C73—42no—
662C2×C73#353214yescomplemented
663C2×C73C22×H(5,𝔽2)12yes—
664C2×C73C22×H(5,𝔽2)11yescharacteristic
665D73—28no—
666D73—44no—
667D73—44no—
668#3532—7332no—
669C2×H(3,𝔽4)—731no—
670C2×#560—731no—
671C2×#560—732no—
672C2×#551—731no—
673C2×#551—732no—
674C2×#546—732no—
675C2×#546—732no—
676C2×#546—732no—
677C2×D42—731no—
678C2×D42—732no—
679C2×#538—732no—
680C2×#538—732no—
681C2×#538—732no—
682C2×#535—732no—
683C2×#535D7311yescharacteristic, complemented
684C2×#534—731no—
685C2×#534—732no—
686C22×#120—731no—
687C22×#120—732no—
688C73C2×#353211yescharacteristic, complemented, Sylow
689C26—731no—
690C22×#41—732no—
691C22×#41C2×D7311yescharacteristic, complemented
692C23×D4—732no—
693C23×D4—731no—
694C23×D4—732no—
695C23×D4—732no—
696C23×D4—732no—
697C23×D4—732no—
698C23×D4C2×D7311yescharacteristic, complemented
699H(3,𝔽4)—7316no—
700#560—7316no—
701#560—7332no—
702#551—7316no—
703#551—7332no—
704#546—7332no—
705#546—7332no—
706#546—7332no—
707D42—7316no—
708D42—7332no—
709#538—7332no—
710#538—7332no—
711#538—7332no—
712#535—7332no—
713#535C2×D73116yescomplemented
714#534—7316no—
715#534—7332no—
716C2×#127—732no—
717C2×#127C2×D7311yescharacteristic, complemented
718C2×#127C2×D7311yescharacteristic, complemented
719C2×#126—732no—
720C2×#126—732no—
721C2×#126—732no—
722C2×#126—732no—
723C2×#124—732no—
724C2×#124—732no—
725C2×#124—732no—
726C2×#124—732no—
727C2×#124—732no—
728C2×#124C2×D7311yescharacteristic, complemented
729C2×#124C2×D7311yescharacteristic, complemented
730C2×#123—731no—
731C2×#123—731no—
732C2×#123—732no—
733C2×#123—732no—
734C2×#123—732no—
735C2×#123—732no—
736C2×#123—732no—
737C2×#123—732no—
738C2×#123—732no—
739C2×#123—732no—
740C2×C22⋊Q8—732no—
741C2×C22⋊Q8—732no—
742C2×C22⋊Q8—732no—
743C2×#121—732no—
744C2×#121—732no—
745C2×#121—732no—
746C2×#121—732no—
747C2×#121—732no—
748C2×#121—732no—
749C2×#121—732no—
750C2×#121—732no—
751C2×#121—732no—
752C2×#121—732no—
753C2×#121—732no—
754C2×#121—732no—
755C2×#121—732no—
756C2×#121C2×D7312yescomplemented
757C2×#121C2×D7312yescomplemented
758C2×#120—732no—
759C2×#120—732no—
760C2×#120—732no—
761C2×#120—732no—
762C2×#120—731no—
763C2×#120—732no—
764C2×#120—731no—
765C2×#120—731no—
766C2×#120—732no—
767C2×#120—731no—
768C2×#120—731no—
769C2×#120—731no—
770C2×#120—7316no—
771C2×#120—732no—
772C2×#120—732no—
773C2×#120—7332no—
774C2×#120—732no—
775C2×#120—732no—
776C2×#120—732no—
777C2×#120—732no—
778C2×#120C2×D7312yescomplemented
779C2×#120C2×D7312yescomplemented
780C2×C4×D4—732no—
781C2×C4×D4—732no—
782C2×C4×D4—732no—
783C2×C4×D4—732no—
784C2×C4×D4—732no—
785C2×C4×D4—732no—
786C2×#117—732no—
787C2×#117C2×D7311yescharacteristic, complemented
788C22×C22⋊C4—731no—
789C22×C22⋊C4—731no—
790C22×C22⋊C4—732no—
791C22×C22⋊C4—732no—
792C22×C22⋊C4—732no—
793C22×C22⋊C4—732no—
794C22×C22⋊C4—732no—
795C25—2924no—
796C25—2928no—
797C25—731no—
798C25—738no—
799C25—731no—
800C25—732no—
801C25—732no—
802C25—731no—
803C25—732no—
804C25C22×D7311yescharacteristic
805C25C22×D7311yescharacteristic
806C2×#41—44no—
807C2×#41—2928no—
808C2×#41—7316no—
809C2×#41C22×D7318yescomplemented
810C22×Q8—732no—
811C22×Q8C22×D7311yescharacteristic, complemented
812C22×D4—44no—
813C22×D4—2928no—
814C22×D4—2928no—
815C22×D4—2928no—
816C22×D4—2924no—
817C22×D4—2928no—
818C22×D4—2928no—
819C22×D4—732no—
820C22×D4—732no—
821C22×D4—732no—
822C22×D4—732no—
823C22×D4—732no—
824C22×D4—732no—
825C22×D4—7316no—
826C22×D4—732no—
827C22×D4—732no—
828C22×D4—738no—
829C22×D4—7316no—
830C22×D4—7316no—
831C22×D4—7316no—
832C22×D4—7316no—
833C22×D4—732no—
834C22×D4—732no—
835C22×D4—732no—
836C22×D4—732no—
837C22×D4—732no—
838C22×D4—732no—
839C22×D4—732no—
840C22×D4C22×D7312yes—
841C22×D4C22×D7311yescharacteristic
842C22×D4C22×D7311yescharacteristic
843C22×D4C22×D7311yescharacteristic
844C22×D4C22×D7311yescharacteristic
845C22×D4C22×D7312yes—
846C22×D4C22×D7312yes—
847C22×D4C22×D7318yescomplemented
848C22×D4C22×D7311yescharacteristic, complemented
849C22×D4C22×D7312yescomplemented
850C22×D4C22×D7312yescomplemented
851C23×C4—732no—
852C23×C4—732no—
853C23×C4—732no—
854C23×C4—731no—
855C23×C4—732no—
856C23×C4—732no—
857C23×C4—732no—
858C23×C4—732no—
859C23×C4C22×D7311yescharacteristic
860C23×C4C22×D7312yescomplemented
861#127—7316no—
862#127C22×D7318yescomplemented
863#127C22×D7318yescomplemented
864#126—7316no—
865#126—7316no—
866#126—7316no—
867#126—7316no—
868#124—7316no—
869#124—7316no—
870#124—7316no—
871#124—7316no—
872#124—7316no—
873#124C22×D7318yescomplemented
874#124C22×D7318yescomplemented
875#123—738no—
876#123—738no—
877#123—7316no—
878#123—7316no—
879#123—7316no—
880#123—7316no—
881#123—7316no—
882#123—7316no—
883#123—7316no—
884#123—7316no—
885C22⋊Q8—7316no—
886C22⋊Q8—7316no—
887C22⋊Q8—7316no—
888#121—7316no—
889#121—7316no—
890#121—7316no—
891#121—7316no—
892#121—7316no—
893#121—7316no—
894#121—7316no—
895#121—7316no—
896#121—7316no—
897#121—7316no—
898#121—7316no—
899#121—7316no—
900#121—7316no—
901#121C22×D73116yescomplemented
902#121C22×D73116yescomplemented
903#120—7316no—
904#120—7316no—
905#120—7316no—
906#120—7316no—
907#120—738no—
908#120—7316no—
909#120—738no—
910#120—738no—
911#120—7316no—
912#120—738no—
913#120—738no—
914#120—738no—
915#120—7316no—
916#120—7316no—
917#120—7316no—
918#120—7316no—
919#120—7316no—
920#120—7316no—
921#120C22×D73116yescomplemented
922#120C22×D73116yescomplemented
923C4×D4—7316no—
924C4×D4—7316no—
925C4×D4—7316no—
926C4×D4—7316no—
927C4×D4—7316no—
928C4×D4—7316no—
929#117—7316no—
930#117C22×D7318yescomplemented
931C2×C4⋊C4—732no—
932C2×C4⋊C4—732no—
933C2×C4⋊C4—732no—
934C2×C4⋊C4—732no—
935C2×C4⋊C4—732no—
936C2×C4⋊C4—732no—
937C2×C4⋊C4—732no—
938C2×C4⋊C4—732no—
939C2×C4⋊C4C22×D7312yescomplemented
940C2×C22⋊C4—732no—
941C2×C22⋊C4—731no—
942C2×C22⋊C4—732no—
943C2×C22⋊C4—732no—
944C2×C22⋊C4—732no—
945C2×C22⋊C4—731no—
946C2×C22⋊C4—738no—
947C2×C22⋊C4—731no—
948C2×C22⋊C4—731no—
949C2×C22⋊C4—738no—
950C2×C22⋊C4—732no—
951C2×C22⋊C4—732no—
952C2×C22⋊C4—732no—
953C2×C22⋊C4—732no—
954C2×C22⋊C4—732no—
955C2×C22⋊C4—732no—
956C2×C22⋊C4—732no—
957C2×C22⋊C4—732no—
958C2×C22⋊C4—732no—
959C2×C22⋊C4—732no—
960C2×C22⋊C4—732no—
961C2×C22⋊C4—732no—
962C2×C22⋊C4—7316no—
963C2×C22⋊C4—732no—
964C2×C22⋊C4—732no—
965C2×C22⋊C4—732no—
966C2×C22⋊C4—732no—
967C2×C22⋊C4—7316no—
968C2×C22⋊C4—7316no—
969C2×C22⋊C4—7316no—
970C2×C22⋊C4—7316no—
971C2×C22⋊C4C22×D7312yes—
972C2×C22⋊C4C22×D7312yes—
973C2×C22⋊C4C22×D7312yes—
974C2×C22⋊C4C22×D7312yescomplemented
975C2×C22⋊C4C22×D7312yescomplemented
976C2×C42—732no—
977C2×C42—732no—
978C2×C42C22×D7311yescharacteristic, complemented
979C2×C42C22×D7311yescharacteristic, complemented
980C24—24no—
981C24—24no—
982C24—44no—
983C24—44no—
984C24—2924no—
985C24—2924no—
986C24—2924no—
987C24—2922no—
988C24—29216no—
989C24—2924no—
990C24—2922no—
991C24—2924no—
992C24—2924no—
993C24—2924no—
994C24—2922no—
995C24—29264no—
996C24—29232no—
997C24—734no—
998C24—734no—
999C24—738no—
1000C24—738no—
1001C24—734no—
1002C24—738no—
1003C24—732no—
1004C24—732no—
1005C24—732no—
1006C24—1468no—
1007C24—1468no—
1008C24—1468no—
1009C24—1468no—
1010C24—1468no—
1011C24C23×D7311yescharacteristic
1012C24C23×D7311yescharacteristic
1013C24C23×D7311yescharacteristic
1014C24C23×D7312yes—
1015C24C23×D7311yescharacteristic
1016C24C23×D7311yescharacteristic
1017C24C23×D7314yes—
1018C24C23×D7314yes—
1019#41—416no—
1020#41—29232no—
1021C2×Q8—42no—
1022C2×Q8—2924no—
1023C2×Q8—738no—
1024C2×Q8C23×D7314yescomplemented
1025C2×D4—28no—
1026C2×D4—42no—
1027C2×D4—42no—
1028C2×D4—42no—
1029C2×D4—42no—
1030C2×D4—416no—
1031C2×D4—44no—
1032C2×D4—44no—
1033C2×D4—44no—
1034C2×D4—42no—
1035C2×D4—44no—
1036C2×D4—2924no—
1037C2×D4—2924no—
1038C2×D4—29232no—
1039C2×D4—29232no—
1040C2×D4—29232no—
1041C2×D4—29216no—
1042C2×D4—29232no—
1043C2×D4—29232no—
1044C2×D4—2924no—
1045C2×D4—2924no—
1046C2×D4—2924no—
1047C2×D4—2924no—
1048C2×D4—2924no—
1049C2×D4—2924no—
1050C2×D4—2924no—
1051C2×D4—2924no—
1052C2×D4—738no—
1053C2×D4—738no—
1054C2×D4—738no—
1055C2×D4—738no—
1056C2×D4—738no—
1057C2×D4—738no—
1058C2×D4—738no—
1059C2×D4—738no—
1060C2×D4—738no—
1061C2×D4—738no—
1062C2×D4—738no—
1063C2×D4—738no—
1064C2×D4—738no—
1065C2×D4—738no—
1066C2×D4—738no—
1067C2×D4—1468no—
1068C2×D4—1468no—
1069C2×D4—1468no—
1070C2×D4—1468no—
1071C2×D4—1468no—
1072C2×D4C23×D7318yes—
1073C2×D4C23×D7314yes—
1074C2×D4C23×D7314yes—
1075C2×D4C23×D7314yes—
1076C2×D4C23×D7314yes—
1077C2×D4C23×D7318yes—
1078C2×D4C23×D7318yes—
1079C2×D4C23×D7314yescomplemented
1080C2×D4C23×D7318yescomplemented
1081C2×D4C23×D7318yescomplemented
1082C22×C4—24no—
1083C22×C4—44no—
1084C22×C4—2924no—
1085C22×C4—2924no—
1086C22×C4—2924no—
1087C22×C4—2924no—
1088C22×C4—2922no—
1089C22×C4—2924no—
1090C22×C4—2924no—
1091C22×C4—738no—
1092C22×C4—738no—
1093C22×C4—738no—
1094C22×C4—734no—
1095C22×C4—738no—
1096C22×C4—738no—
1097C22×C4—738no—
1098C22×C4—732no—
1099C22×C4—732no—
1100C22×C4—732no—
1101C22×C4—732no—
1102C22×C4—732no—
1103C22×C4—738no—
1104C22×C4—1468no—
1105C22×C4C23×D7314yes—
1106C22×C4C23×D7312yes—
1107C22×C4C23×D7312yes—
1108C22×C4C23×D7311yescharacteristic
1109C22×C4C23×D7312yes—
1110C22×C4C23×D7311yescharacteristic
1111C22×C4C23×D7318yescomplemented
1112C4⋊C4—738no—
1113C4⋊C4—738no—
1114C4⋊C4—738no—
1115C4⋊C4—738no—
1116C4⋊C4—738no—
1117C4⋊C4—738no—
1118C4⋊C4—738no—
1119C4⋊C4—738no—
1120C4⋊C4C23×D7318yescomplemented
1121C22⋊C4—738no—
1122C22⋊C4—734no—
1123C22⋊C4—738no—
1124C22⋊C4—738no—
1125C22⋊C4—738no—
1126C22⋊C4—734no—
1127C22⋊C4—734no—
1128C22⋊C4—734no—
1129C22⋊C4—738no—
1130C22⋊C4—738no—
1131C22⋊C4—738no—
1132C22⋊C4—738no—
1133C22⋊C4—738no—
1134C22⋊C4—738no—
1135C22⋊C4—738no—
1136C22⋊C4—738no—
1137C22⋊C4—738no—
1138C22⋊C4—738no—
1139C22⋊C4—738no—
1140C22⋊C4—738no—
1141C22⋊C4—738no—
1142C22⋊C4—738no—
1143C22⋊C4—738no—
1144C22⋊C4—738no—
1145C22⋊C4C23×D7318yes—
1146C22⋊C4C23×D7318yes—
1147C22⋊C4C23×D7318yes—
1148C22⋊C4C23×D7318yescomplemented
1149C22⋊C4C23×D7318yescomplemented
1150C42—738no—
1151C42—738no—
1152C42C23×D7314yescomplemented
1153C42C23×D7314yescomplemented
1154C23—24no—
1155C23—24no—
1156C23—24no—
1157C23—24no—
1158C23—24no—
1159C23—24no—
1160C23—24no—
1161C23—24no—
1162C23—22no—
1163C23—22no—
1164C23—28no—
1165C23—22no—
1166C23—22no—
1167C23—28no—
1168C23—48no—
1169C23—48no—
1170C23—416no—
1171C23—88no—
1172C23—29232no—
1173C23—2928no—
1174C23—2928no—
1175C23—2928no—
1176C23—2924no—
1177C23—2928no—
1178C23—2924no—
1179C23—2928no—
1180C23—2928no—
1181C23—2928no—
1182C23—2924no—
1183C23—292128no—
1184C23—29216no—
1185C23—29232no—
1186C23—29216no—
1187C23—5848no—
1188C23—58416no—
1189C23—738no—
1190C23—734no—
1191C23—734no—
1192C23—734no—
1193C23—14616no—
1194C23—14616no—
1195C23—14616no—
1196C23—14616no—
1197C23—1464no—
1198C23—1464no—
1199C23—1464no—
1200C23—1464no—
1201C23—1464no—
1202C23—14616no—
1203C23—1464no—
1204C23—1464no—
1205C23—1464no—
1206C23#1455663614yes—
1207C23C24×D7312yes—
1208C23C24×D7312yes—
1209C23C24×D7312yes—
1210C23C24×D7314yes—
1211C23C24×D7312yes—
1212C23C24×D7312yes—
1213C23C24×D7311yescharacteristic
1214Q8—44no—
1215Q8—2928no—
1216D4—216no—
1217D4—44no—
1218D4—44no—
1219D4—44no—
1220D4—44no—
1221D4—48no—
1222D4—48no—
1223D4—48no—
1224D4—44no—
1225D4—48no—
1226D4—2928no—
1227D4—2928no—
1228D4—2928no—
1229D4—2928no—
1230D4—2928no—
1231D4—2928no—
1232D4—2928no—
1233D4—2928no—
1234D4—2928no—
1235D4—2928no—
1236D4—14616no—
1237D4—14616no—
1238D4—14616no—
1239D4—14616no—
1240D4—14616no—
1241C2×C4—24no—
1242C2×C4—24no—
1243C2×C4—22no—
1244C2×C4—22no—
1245C2×C4—28no—
1246C2×C4—24no—
1247C2×C4—48no—
1248C2×C4—2928no—
1249C2×C4—2928no—
1250C2×C4—2928no—
1251C2×C4—2928no—
1252C2×C4—2924no—
1253C2×C4—2928no—
1254C2×C4—2928no—
1255C2×C4—734no—
1256C2×C4—734no—
1257C2×C4—734no—
1258C2×C4—734no—
1259C2×C4—734no—
1260C2×C4—14616no—
1261C2×C4—1464no—
1262C2×C4—1464no—
1263C2×C4—1464no—
1264C2×C4—1464no—
1265C2×C4—1464no—
1266C2×C4C24×D7314yes—
1267C2×C4C24×D7314yes—
1268C2×C4C24×D7312yes—
1269C2×C4C24×D7314yes—
1270C2×C4C24×D7312yes—
1271C22—28no—
1272C22—24no—
1273C22—24no—
1274C22—24no—
1275C22—24no—
1276C22—24no—
1277C22—24no—
1278C22—24no—
1279C22—24no—
1280C22—22no—
1281C22—22no—
1282C22—22no—
1283C22—22no—
1284C22—416no—
1285C22—44no—
1286C22—44no—
1287C22—44no—
1288C22—44no—
1289C22—48no—
1290C22—88no—
1291C22—29232no—
1292C22—29216no—
1293C22—29232no—
1294C22—29216no—
1295C22—2928no—
1296C22—2928no—
1297C22—5848no—
1298C22—58416no—
1299C22—738no—
1300C22—1464no—
1301C22—1464no—
1302C22—1464no—
1303C22—1464no—
1304C22—1464no—
1305C22—1464no—
1306C22—14616no—
1307C22—1464no—
1308C22—1464no—
1309C22H(5,𝔽2)×D7314yes—
1310C22C2×#1455663614yes—
1311C22C2×#1455663612yes—
1312C22C25×D7311yescharacteristic
1313C4—24no—
1314C4—24no—
1315C4—22no—
1316C4—22no—
1317C4—24no—
1318C4—1464no—
1319C4—1464no—
1320C4—1464no—
1321C4—1464no—
1322C4—1464no—
1323C2—24no—
1324C2—42no—
1325C2—42no—
1326C2—42no—
1327C2—42no—
1328C2—44no—
1329C2—2924no—
1330C2—2924no—
1331C2—1468no—
1332C2#2262408514yesdirect product factor
1333C2C2×H(5,𝔽2)×D7312yes—
1334C2C22×#1455663611yescharacteristic
subgroupG/H
centerC23C24×D73
commutator, cosocleC22×C73C26
FrattiniC22C25×D73
FittingC2×#535×C73C2
socleC23×C73C25
hypercenterC2×#535D73
hypocenterC73C2×#3532
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#535

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #22624085C2direct (N × H)
2. C2×#17989329C2semidirect
3. C2×#17989325C2semidirect
4. C2×#17989324C2semidirect
5. C2×#17989267C2semidirect
6. C2×#17989261C2semidirect
7. C2×#17989226C2semidirect
8. C2×#17989225C2semidirect
9. C2×#17989224C2semidirect
10. C2×#17989222C2semidirect
11. C2×#17989219C2semidirect
12. C2×#17989172C2semidirect
13. C2×#17989171C2semidirect
14. C2×#17989169C2semidirect
15. C2×#17989150C2semidirect
16. C2×#17989146C2semidirect
17. C2×#17989145C2semidirect
18. C22×#14556559C2semidirect
19. C2×#120×D73C2semidirect
20. C2×#535×C73C2semidirect
21. C25×D73C22semidirect
22. C22×#11924027C22semidirect
23. C23×C22⋊D73C22semidirect
24. C23×C22⋊D73C22semidirect
25. C22×D4×D73C22semidirect
26. C22×D4×D73C22semidirect
27. C22×D4×D73C22semidirect
28. C22×D4×D73C22semidirect
29. #17989329C22semidirect
30. #17989325C22semidirect
31. #17989324C22semidirect
32. #17989267C22semidirect
33. #17989261C22semidirect
34. #17989226C22semidirect
35. #17989225C22semidirect
36. #17989224C22semidirect
37. #17989222C22semidirect
38. #17989219C22semidirect
39. #17989172C22semidirect
40. #17989171C22semidirect
41. #17989169C22semidirect
42. #17989150C22semidirect
43. #17989146C22semidirect
44. #17989145C22semidirect
45. C2×#14556587C22semidirect
46. C2×#14556586C22semidirect
47. C2×#14556585C22semidirect
48. C2×#14556584C22semidirect
49. C2×#14556584C22semidirect
50. C2×#14556580C22semidirect
51. C2×#14556579C22semidirect
52. C2×#14556578C22semidirect
53. C2×#14556577C22semidirect
54. C2×#14556577C22semidirect
55. C2×#14556576C22semidirect
56. C2×#14556576C22semidirect
57. C2×#14556575C22semidirect
58. C2×#14556574C22semidirect
59. C2×#14556574C22semidirect
60. C2×#14556573C22semidirect
61. C2×#14556573C22semidirect
62. C2×#14556572C22semidirect
63. C2×#14556572C22semidirect
64. C2×#14556572C22semidirect
65. C2×#14556569C22semidirect
66. C2×#14556568C22semidirect
67. C2×#14556567C22semidirect
68. C2×#14556565C22semidirect
69. C2×#14556564C22semidirect
70. C2×#14556564C22semidirect
71. C2×#14556563C22semidirect
72. C2×#14556563C22semidirect
73. C2×#14556563C22semidirect
74. C2×#14556563C22semidirect
75. C2×#14556563C22semidirect
76. C2×#14556563C22semidirect
77. C2×#14556563C22semidirect
78. C2×#14556563C22semidirect
79. C2×#14556562C22semidirect
80. C2×#14556562C22semidirect
82. C2×#14556561C22semidirect
83. C2×#14556561C22semidirect
84. C2×#14556561C22semidirect
85. C2×#14556560C22semidirect
87. C2×#14556559C22semidirect
88. C2×#14556559C22semidirect
89. C2×#14556559C22semidirect
90. C2×#14556559C22semidirect
91. C2×#14556559C22semidirect
92. C2×#14556559C22semidirect
93. C2×#14556559C22semidirect
94. C2×#14556559C22semidirect
95. C2×#14556559C22semidirect
96. C2×#14556559C22semidirect
97. C2×#14556559C22semidirect
98. C2×#14556559C22semidirect
99. C2×#14556559C22semidirect
100. #120×D73C22semidirect
101. C2×C4×D292C22semidirect
102. C2×D4×Dic73C22semidirect
103. C2×C4×C22⋊D73C22semidirect
104. C2×#14556551C22semidirect
105. C2×#14556551C22semidirect
106. C2×#14556551C22semidirect
107. C2×#14556548C22semidirect
108. C22×C22⋊Dic73C22semidirect
109. C22×C22⋊Dic73C22semidirect
110. C22×#11924005C22semidirect
111. C22×#11924005C22semidirect
112. C2×C22⋊C4×D73C22semidirect
113. C2×C22⋊C4×D73C22semidirect
114. C2×C22⋊C4×D73C22semidirect
115. C22×#41×C73C22semidirect
116. C23×D4×C73C22semidirect
117. #535×C73C22semidirect
118. C2×#127×C73C22semidirect
119. C2×#127×C73C22semidirect
120. C2×#124×C73C22semidirect
121. C2×#124×C73C22semidirect
122. C2×#121×C73C22semidirect
123. C2×#121×C73C22semidirect
124. C2×#120×C73C22semidirect
125. C2×#120×C73C22semidirect
126. C2×#117×C73C22semidirect
134. C24×D73C23semidirect
135. C24×D73C23semidirect
137. C2×#11924027C23semidirect
138. C22×Dic146C23semidirect
154. C22×C22⋊D73C23semidirect
155. C22×C22⋊D73C23semidirect
156. C22×C22⋊D73C23semidirect
157. C22×C22⋊D73C23semidirect
162. C2×D4×D73C23semidirect
163. C2×D4×D73C23semidirect
164. C2×D4×D73C23semidirect
165. C2×D4×D73C23semidirect
167. C23×Dic73C23semidirect
168. C23×Dic73C23semidirect
169. C23×Dic73C23semidirect
173. C22×C4×D73C23semidirect
174. #14556587C23semidirect
175. #14556586C23semidirect
176. #14556585C23semidirect
177. #14556584C23semidirect
178. #14556584C23semidirect
179. #14556580C23semidirect
180. #14556579C23semidirect
181. #14556578C23semidirect
182. #14556577C23semidirect
183. #14556577C23semidirect
184. #14556576C23semidirect
185. #14556576C23semidirect
186. #14556575C23semidirect
187. #14556574C23semidirect
188. #14556574C23semidirect
189. #14556573C23semidirect
190. #14556573C23semidirect
191. #14556572C23semidirect
192. #14556572C23semidirect
193. #14556572C23semidirect
194. #14556569C23semidirect
195. #14556568C23semidirect
196. #14556567C23semidirect
197. #14556565C23semidirect
198. #14556564C23semidirect
199. #14556564C23semidirect
200. #14556563C23semidirect
201. #14556563C23semidirect
202. #14556563C23semidirect
203. #14556563C23semidirect
204. #14556563C23semidirect
205. #14556563C23semidirect
206. #14556563C23semidirect
207. #14556563C23semidirect
208. #14556562C23semidirect
209. #14556562C23semidirect
211. #14556561C23semidirect
212. #14556561C23semidirect
213. #14556561C23semidirect
214. #14556560C23semidirect
216. #14556559C23semidirect
217. #14556559C23semidirect
218. #14556559C23semidirect
219. #14556559C23semidirect
220. #14556559C23semidirect
221. #14556559C23semidirect
222. #14556559C23semidirect
223. #14556559C23semidirect
224. #14556559C23semidirect
225. #14556559C23semidirect
226. #14556559C23semidirect
227. #14556559C23semidirect
228. C4×D292C23semidirect
229. D4×Dic73C23semidirect
230. C4×C22⋊D73C23semidirect
231. #14556551C23semidirect
232. #14556551C23semidirect
233. #14556551C23semidirect
234. #14556548C23semidirect
235. C2×C4⋊Dic73C23semidirect
236. C2×C4⋊Dic73C23semidirect
237. C2×#11924007C23semidirect
238. C2×#11924007C23semidirect
239. C2×#11924007C23semidirect
240. C2×#11924007C23semidirect
241. C2×#11924007C23semidirect
242. C2×#11924007C23semidirect
249. C2×C22⋊Dic73C23semidirect
250. C2×C22⋊Dic73C23semidirect
251. C2×C22⋊Dic73C23semidirect
252. C2×C22⋊Dic73C23semidirect
253. C2×C22⋊Dic73C23semidirect
254. C2×C22⋊Dic73C23semidirect
265. C2×#11924005C23semidirect
266. C2×#11924005C23semidirect
267. C2×#11924005C23semidirect
268. C2×#11924005C23semidirect
269. C2×#11924005C23semidirect
270. C2×#11924005C23semidirect
271. C22⋊C4×D73C23semidirect
272. C22⋊C4×D73C23semidirect
273. C22⋊C4×D73C23semidirect
274. C2×C4×Dic73C23semidirect
275. C2×C4×Dic73C23semidirect
279. C2×#41×C73C23semidirect
280. C22×Q8×C73C23semidirect
289. C22×D4×C73C23semidirect
290. C22×D4×C73C23semidirect
291. C22×D4×C73C23semidirect
292. C22×D4×C73C23semidirect
294. C23×C4×C73C23semidirect
295. #127×C73C23semidirect
296. #127×C73C23semidirect
297. #124×C73C23semidirect
298. #124×C73C23semidirect
299. #121×C73C23semidirect
300. #121×C73C23semidirect
301. #120×C73C23semidirect
302. #120×C73C23semidirect
303. #117×C73C23semidirect
304. C2×C4⋊C4×C73C23semidirect
308. C2×C22⋊C4×C73C23semidirect
309. C2×C22⋊C4×C73C23semidirect
310. C2×C42×C73C23semidirect
311. C2×C42×C73C23semidirect
338. C23×D73C24semidirect
341. C2×Dic146C24semidirect
372. C2×C22⋊D73C24semidirect
373. C2×C22⋊D73C24semidirect
388. C22×Dic73C24semidirect
389. C22×Dic73C24semidirect
390. C22×Dic73C24semidirect
398. C2×C4×D73C24semidirect
399. C4⋊Dic73C24semidirect
400. C4⋊Dic73C24semidirect
401. #11924007C24semidirect
402. #11924007C24semidirect
403. #11924007C24semidirect
404. #11924007C24semidirect
405. #11924007C24semidirect
406. #11924007C24semidirect
413. C22⋊Dic73C24semidirect
414. C22⋊Dic73C24semidirect
415. C22⋊Dic73C24semidirect
416. C22⋊Dic73C24semidirect
427. #11924005C24semidirect
428. #11924005C24semidirect
429. #11924005C24semidirect
430. #11924005C24semidirect
431. C4×Dic73C24semidirect
432. C4×Dic73C24semidirect
447. C2×Q8×C73C24semidirect
466. C2×D4×C73C24semidirect
467. C2×D4×C73C24semidirect
468. C2×D4×C73C24semidirect
477. C22×C4×C73C24semidirect
478. C4⋊C4×C73C24semidirect
482. C22⋊C4×C73C24semidirect
483. C22⋊C4×C73C24semidirect
484. C42×C73C24semidirect
485. C42×C73C24semidirect
662. C2×C73#3532semidirect
683. C2×#535D73semidirect
688. C73C2×#3532semidirect
691. C22×#41C2×D73semidirect
698. C23×D4C2×D73semidirect
713. #535C2×D73semidirect
717. C2×#127C2×D73semidirect
718. C2×#127C2×D73semidirect
728. C2×#124C2×D73semidirect
729. C2×#124C2×D73semidirect
756. C2×#121C2×D73semidirect
757. C2×#121C2×D73semidirect
778. C2×#120C2×D73semidirect
779. C2×#120C2×D73semidirect
787. C2×#117C2×D73semidirect
809. C2×#41C22×D73semidirect
811. C22×Q8C22×D73semidirect
847. C22×D4C22×D73semidirect
848. C22×D4C22×D73semidirect
849. C22×D4C22×D73semidirect
850. C22×D4C22×D73semidirect
860. C23×C4C22×D73semidirect
862. #127C22×D73semidirect
863. #127C22×D73semidirect
873. #124C22×D73semidirect
874. #124C22×D73semidirect
901. #121C22×D73semidirect
902. #121C22×D73semidirect
921. #120C22×D73semidirect
922. #120C22×D73semidirect
930. #117C22×D73semidirect
939. C2×C4⋊C4C22×D73semidirect
974. C2×C22⋊C4C22×D73semidirect
975. C2×C22⋊C4C22×D73semidirect
978. C2×C42C22×D73semidirect
979. C2×C42C22×D73semidirect
1024. C2×Q8C23×D73semidirect
1079. C2×D4C23×D73semidirect
1080. C2×D4C23×D73semidirect
1081. C2×D4C23×D73semidirect
1111. C22×C4C23×D73semidirect
1120. C4⋊C4C23×D73semidirect
1148. C22⋊C4C23×D73semidirect
1149. C22⋊C4C23×D73semidirect
1152. C42C23×D73semidirect
1153. C42C23×D73semidirect
1332. C2#22624085direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#226240852
C2×#179893292
C2×#179893252
C2×#179893242
C2×#179892672
C2×#179892612
C2×#179892262
C2×#179892252
C2×#179892242
C2×#179892222
C2×#179892192
C2×#179891722
C2×#179891712
C2×#179891692
C2×#179891502
C2×#179891462
C2×#179891452
C22×#145565592
C2×#120×D732
C2×#535×C732
C2×#353273