Finite Group Databasebeta

← C2×#22623617 #33993895

Subgroups — C2×#22623617 #33993895

Order 18688.

9502 conjugacy classes of subgroups.

The subgroup lattice has 1316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22623617C2132yesmaximal, direct product factor
2C2×#17989267C212yesmaximal, complemented
3C2×#17989265C212yesmaximal, complemented
4C2×#17989262C212yesmaximal, complemented
5C2×#17989262C212yesmaximal, complemented
6C2×#17989234C212yesmaximal, complemented
7C2×#17989230C212yesmaximal, complemented
8C2×#17989229C212yesmaximal, complemented
9C2×#17989226C212yesmaximal, complemented
10C2×#17989212C211yesmaximal, characteristic, complemented
11C2×#17989175C211yesmaximal, characteristic, complemented
12C2×#17989172C212yesmaximal, complemented
13C2×#17989145C211yesmaximal, characteristic, complemented
14C2×#17989100C211yesmaximal, characteristic, complemented
15C2×#17989097C211yesmaximal, characteristic, complemented
16C2×#17989096C212yesmaximal, complemented
17C2×#120×D73C212yesmaximal, complemented
18C2×#17989059C212yesmaximal, complemented
19C22×C22⋊C4×D73C211yesmaximal, characteristic, complemented
20C2×#538×C73C211yesmaximal, characteristic, complemented
21C25×D73C2211yescharacteristic
22C22×#11924029C2211yescharacteristic, complemented
23C22×#11924028C2212yescomplemented
24C22×#11924027C2211yescharacteristic, complemented
25C22×D4×D73C2212yes—
26C22×D4×D73C2212yescomplemented
27C22×D4×D73C2212yescomplemented
28C23×C4×D73C2211yescharacteristic, complemented
29C23×C4×D73C2211yescharacteristic, complemented
30#17989267C22132yescomplemented
31#17989265C22132yescomplemented
32#17989262C22132yescomplemented
33#17989262C22132yescomplemented
34#17989234C22132yescomplemented
35#17989230C22132yescomplemented
36#17989229C22132yescomplemented
37#17989226C22132yescomplemented
38#17989212C22116yescomplemented
39#17989175C22116yescomplemented
40#17989172C22132yescomplemented
41#17989145C22116yescomplemented
42C2×#14556584C2212yescomplemented
43C2×#14556584C2212yescomplemented
44C2×#14556584C2212yescomplemented
45C2×#14556578C2212yescomplemented
46C2×#14556577C2212yescomplemented
47C2×#14556577C2212yescomplemented
48#17989100C22116yescomplemented
49#17989097C22116yescomplemented
50#17989096C22132yescomplemented
51C2×#14556576C2212yescomplemented
52C2×#14556576C2212yescomplemented
53C2×#14556576C2212yescomplemented
54C2×#14556573C2212yescomplemented
55C2×#14556573C2212yescomplemented
56C2×#14556573C2212yescomplemented
57C2×#14556573C2212yescomplemented
58C2×#14556573C2212yescomplemented
59C2×#14556572C2212yescomplemented
60C2×#14556571C2212yescomplemented
61C2×#14556571C2211yescharacteristic, complemented
62C2×#14556570C2211yescharacteristic, complemented
63C2×#14556569C2212yescomplemented
64C2×#14556569C2212yescomplemented
65C2×#14556569C2212yescomplemented
66C2×#14556568C2212yescomplemented
67C2×#14556567C2212yescomplemented
68C2×#14556567C2211yescharacteristic, complemented
69C2×#14556566C2211yescharacteristic, complemented
70C2×#14556565C2211yescharacteristic, complemented
71C2×#14556564C2212yescomplemented
72C2×#14556564C2212yescomplemented
73C2×#14556563C2212yescomplemented
74C2×#14556563C2212yescomplemented
75C2×#14556562C2212yescomplemented
76C2×#14556562C2211yescharacteristic, complemented
77C2×#14556561C2212yes—
78C2×#14556561C2212yes—
79C2×#14556561C2212yescomplemented
80C2×#14556561C2212yescomplemented
81C2×#14556560C2212yescomplemented
82C2×#14556559C2212yes—
83C2×#14556559C2212yes—
84C2×#14556559C2212yescomplemented
85C2×#14556559C2212yescomplemented
86#120×D73C22132yescomplemented
87#17989059C22132yescomplemented
88C2×C4×D292C2212yescomplemented
89C2×C4×D292C2212yescomplemented
90C2×D4×Dic73C2212yescomplemented
91C2×#14556553C2212yescomplemented
92C2×#14556553C2212yescomplemented
93C2×C4×C22⋊D73C2212yescomplemented
94C2×C4×C22⋊D73C2212yescomplemented
95C2×C4×C22⋊D73C2212yescomplemented
96C2×#14556551C2212yescomplemented
97C2×#14556551C2212yescomplemented
98C2×#14556551C2212yescomplemented
99C2×#14556549C2212yescomplemented
100C2×#14556549C2211yescharacteristic, complemented
101C2×#14556549C2211yescharacteristic, complemented
102C2×#14556548C2212yescomplemented
103C2×#14556548C2212yescomplemented
104C22×C22⋊Dic73C2211yescharacteristic, complemented
105C22×#11924005C2211yescharacteristic
106C22×#11924005C2211yescharacteristic
107C22×#11924005C2212yescomplemented
108C2×C22⋊C4×D73C2212yes—
109C2×C22⋊C4×D73C2212yescomplemented
110C2×C22⋊C4×D73C2212yescomplemented
111C2×C22⋊C4×D73C2212yescomplemented
112C2×C22⋊C4×D73C2212yescomplemented
113C2×C22⋊C4×D73C2212yescomplemented
114C2×C22⋊C4×D73C2212yescomplemented
115C2×C22⋊C4×D73C22116yescomplemented
116C2×C22⋊C4×D73C2212yescomplemented
117#538×C73C22116yescomplemented
118C2×#126×C73C2212yescomplemented
119C2×#124×C73C2212yescomplemented
120C2×#123×C73C2212yescomplemented
121C2×C22⋊Q8×C73C2211yescharacteristic, complemented
122C2×#121×C73C2212yescomplemented
123C2×#121×C73C2211yescharacteristic, complemented
124C2×#120×C73C2212yescomplemented
125C2×C4×D4×C73C2212yescomplemented
126C22×C22⋊C4×C73C2211yescharacteristic, complemented
127C24×D73—28no—
128C24×D73—44no—
129C24×D73—44no—
130C24×D73C2311yescharacteristic
131C24×D73C2312yes—
132C24×D73C2312yes—
133C24×D73C2312yes—
134C24×D73C2318yes—
135C24×D73C2311yescharacteristic
136C2×#11924029—44no—
137C2×#11924029C2318yescomplemented
138C2×#11924028—48no—
139C2×#11924028C23116yescomplemented
140C2×#11924027—44no—
141C2×#11924027C2318yescomplemented
142C22×Dic146C2311yescharacteristic, complemented
143C22×Dic146C2312yescomplemented
144C22×D292C2312yes—
145C22×D292C2312yes—
146C22×D292C2312yes—
147C22×D292C2311yescharacteristic, complemented
148C22×C22⋊D73C2312yes—
149C22×C22⋊D73C2312yes—
150C22×C22⋊D73C2312yes—
151C22×C22⋊D73C2312yes—
152C22×C22⋊D73C2312yes—
153C22×C22⋊D73C2312yes—
154C22×C22⋊D73C2312yescomplemented
155C2×D4×D73—216no—
156C2×D4×D73—48no—
157C2×D4×D73—48no—
158C2×D4×D73C23116yes—
159C2×D4×D73C23116yescomplemented
160C2×D4×D73C23116yescomplemented
161C23×Dic73C2311yescharacteristic
162C23×Dic73C2311yescharacteristic
163C23×Dic73C2312yescomplemented
164C22×C4×D73—44no—
165C22×C4×D73—44no—
166C22×C4×D73C2311yescharacteristic
167C22×C4×D73C2312yes—
168C22×C4×D73C2311yescharacteristic
169C22×C4×D73C2312yes—
170C22×C4×D73C2311yescharacteristic
171C22×C4×D73C2312yes—
172C22×C4×D73C2311yescharacteristic
173C22×C4×D73C2312yes—
174C22×C4×D73C2312yes—
175C22×C4×D73C2318yescomplemented
176C22×C4×D73C2318yescomplemented
177C22×C4×D73C2312yescomplemented
178C22×C4×D73C2312yescomplemented
179#14556584C23116yescomplemented
180#14556584C23116yescomplemented
181#14556584C23116yescomplemented
182#14556578C23116yescomplemented
183#14556577C23116yescomplemented
184#14556577C23116yescomplemented
185#14556576C23116yescomplemented
186#14556576C23116yescomplemented
187#14556576C23116yescomplemented
188#14556573C23116yescomplemented
189#14556573C23116yescomplemented
190#14556573C23116yescomplemented
191#14556573C23116yescomplemented
192#14556573C23116yescomplemented
193#14556572C23116yescomplemented
194#14556571C23116yescomplemented
195#14556571C2318yescomplemented
196#14556570C2318yescomplemented
197#14556569C23116yescomplemented
198#14556569C23116yescomplemented
199#14556569C23116yescomplemented
200#14556568C23116yescomplemented
201#14556567C23116yescomplemented
202#14556567C2318yescomplemented
203#14556566C2318yescomplemented
204#14556565C2318yescomplemented
205#14556564C23116yescomplemented
206#14556564C23116yescomplemented
207#14556563C23116yescomplemented
208#14556563C23116yescomplemented
209#14556562C23116yescomplemented
210#14556562C2318yescomplemented
211#14556561C23116yes—
212#14556561C23116yes—
213#14556561C23116yescomplemented
214#14556561C23116yescomplemented
215#14556560C23116yescomplemented
216#14556559C23116yes—
217#14556559C23116yes—
218#14556559C23116yescomplemented
219#14556559C23116yescomplemented
220C4×D292C23116yescomplemented
221C4×D292C23116yescomplemented
222D4×Dic73C23116yescomplemented
223#14556553C23116yescomplemented
224#14556553C23116yescomplemented
225C4×C22⋊D73C23116yescomplemented
226C4×C22⋊D73C23116yescomplemented
227C4×C22⋊D73C23116yescomplemented
228#14556551C23116yescomplemented
229#14556551C23116yescomplemented
230#14556551C23116yescomplemented
231#14556549C2318yescomplemented
232#14556549C23116yescomplemented
233#14556549C2318yescomplemented
234#14556548C23116yescomplemented
235#14556548C23116yescomplemented
236C2×C4⋊Dic73C2312yescomplemented
237C2×C4⋊Dic73C2311yescharacteristic, complemented
238C2×C4⋊Dic73C2311yescharacteristic, complemented
239C2×C4⋊Dic73C2312yescomplemented
240C2×#11924007C2312yescomplemented
241C2×#11924007C2312yescomplemented
242C2×#11924007C2312yescomplemented
243C2×#11924007C2312yescomplemented
244C2×#11924007C2312yescomplemented
245C2×#11924007C2312yescomplemented
246C2×C22⋊Dic73C2312yes—
247C2×C22⋊Dic73C2312yes—
248C2×C22⋊Dic73C2312yes—
249C2×C22⋊Dic73C2312yes—
250C2×C22⋊Dic73C2312yes—
251C2×C22⋊Dic73C2318yescomplemented
252C2×C22⋊Dic73C2312yescomplemented
253C2×C22⋊Dic73C2312yescomplemented
254C2×#11924005C2318yes—
255C2×#11924005C2312yes—
256C2×#11924005C2312yes—
257C2×#11924005C2312yes—
258C2×#11924005C2312yes—
259C2×#11924005C2318yes—
260C2×#11924005C2312yes—
261C2×#11924005C2312yes—
262C2×#11924005C2312yes—
263C2×#11924005C2312yes—
264C2×#11924005C2312yes—
265C2×#11924005C2312yes—
266C2×#11924005C2312yescomplemented
267C2×#11924005C2312yescomplemented
268C2×#11924005C2312yescomplemented
269C2×#11924005C2312yescomplemented
270C2×#11924005C23116yescomplemented
271C22⋊C4×D73C23116yes—
272C22⋊C4×D73C23116yescomplemented
273C22⋊C4×D73C23116yescomplemented
274C22⋊C4×D73C23116yescomplemented
275C22⋊C4×D73C23116yescomplemented
276C22⋊C4×D73C23116yescomplemented
277C22⋊C4×D73C23116yescomplemented
278C22⋊C4×D73C23116yescomplemented
279C2×C4×Dic73C2312yescomplemented
280C2×C4×Dic73C2312yescomplemented
281C2×C4×Dic73C2312yescomplemented
282C25×C73C2311yescharacteristic
283C22×Q8×C73C2311yescharacteristic, complemented
284C22×D4×C73C2312yes—
285C22×D4×C73C2312yes—
286C22×D4×C73C2312yes—
287C22×D4×C73C2311yescharacteristic, complemented
288C23×C4×C73C2311yescharacteristic
289C23×C4×C73C2311yescharacteristic
290C23×C4×C73C2312yescomplemented
291#126×C73C23116yescomplemented
292#124×C73C23116yescomplemented
293#123×C73C23116yescomplemented
294C22⋊Q8×C73C2318yescomplemented
295#121×C73C23116yescomplemented
296#121×C73C2318yescomplemented
297#120×C73C23116yescomplemented
298C4×D4×C73C23116yescomplemented
299C2×C4⋊C4×C73C2312yescomplemented
300C2×C4⋊C4×C73C2312yescomplemented
301C2×C4⋊C4×C73C2311yescharacteristic, complemented
302C2×C4⋊C4×C73C2311yescharacteristic, complemented
303C2×C22⋊C4×C73C2312yes—
304C2×C22⋊C4×C73C2312yes—
305C2×C22⋊C4×C73C2312yes—
306C2×C22⋊C4×C73C2312yes—
307C2×C22⋊C4×C73C2312yes—
308C2×C22⋊C4×C73C2318yescomplemented
309C2×C22⋊C4×C73C2312yescomplemented
310C2×C22⋊C4×C73C2312yescomplemented
311C2×C42×C73C2312yescomplemented
312C23×D73—24no—
313C23×D73—24no—
314C23×D73—24no—
315C23×D73—28no—
316C23×D73—28no—
317C23×D73—232no—
318C23×D73—28no—
319C23×D73—28no—
320C23×D73—28no—
321C23×D73—416no—
322C23×D73—416no—
323C23×D73—44no—
324C23×D73—44no—
325C23×D73—42no—
326C23×D73—42no—
327C23×D73—44no—
328C23×D73—44no—
329C23×D73—464no—
330C23×D73#4118yescomplemented
331C23×D73C2412yes—
332C23×D73C2414yes—
333C23×D73C2418yes—
334C23×D73C2418yes—
335C23×D73C2412yes—
336C23×D73C2411yescharacteristic
337C23×D73C2411yescharacteristic
338C23×D73C2418yes—
339C23×D73C2414yes—
340#11924029—416no—
341#11924028—432no—
342#11924027—416no—
343C2×Dic146—42no—
344C2×Dic146—44no—
345C2×Dic146C2418yescomplemented
346C2×Dic146C2414yescomplemented
347C2×D292—28no—
348C2×D292—28no—
349C2×D292—28no—
350C2×D292—42no—
351C2×D292C2418yes—
352C2×D292C2418yes—
353C2×D292C2418yes—
354C2×D292C2414yescomplemented
355C2×C22⋊D73—28no—
356C2×C22⋊D73—28no—
357C2×C22⋊D73—28no—
358C2×C22⋊D73—28no—
359C2×C22⋊D73—44no—
360C2×C22⋊D73—44no—
361C2×C22⋊D73—44no—
362C2×C22⋊D73C2418yes—
363C2×C22⋊D73C2418yes—
364C2×C22⋊D73C2418yes—
365C2×C22⋊D73C2418yes—
366C2×C22⋊D73C2418yes—
367C2×C22⋊D73C2418yes—
368C2×C22⋊D73C2418yescomplemented
369D4×D73—264no—
370D4×D73—432no—
371D4×D73—432no—
372C22×Dic73—42no—
373C22×Dic73—42no—
374C22×Dic73—44no—
375C22×Dic73C2411yescharacteristic
376C22×Dic73C2412yes—
377C22×Dic73C2411yescharacteristic
378C22×Dic73C2412yes—
379C22×Dic73C2412yes—
380C22×Dic73C2412yes—
381C22×Dic73C2414yes—
382C22×Dic73C2414yes—
383C22×Dic73C2418yescomplemented
384C2×C4×D73—28no—
385C2×C4×D73—24no—
386C2×C4×D73—28no—
387C2×C4×D73—24no—
388C2×C4×D73—416no—
389C2×C4×D73—416no—
390C2×C4×D73—42no—
391C2×C4×D73—42no—
392C2×C4×D73—44no—
393C2×C4×D73—44no—
394C2×C4×D73—44no—
395C2×C4×D73—44no—
396C2×C4×D73—44no—
397C2×C4×D73C2418yes—
398C2×C4×D73C2418yes—
399C2×C4×D73C2414yes—
400C2×C4×D73C2414yes—
401C2×C4×D73C2418yes—
402C2×C4×D73C2418yes—
403C2×C4×D73C2414yes—
404C2×C4×D73C2418yes—
405C2×C4×D73C2414yes—
406C2×C4×D73C2418yescomplemented
407C2×C4×D73C2418yescomplemented
408C4⋊Dic73C2418yescomplemented
409C4⋊Dic73C2414yescomplemented
410C4⋊Dic73C2414yescomplemented
411C4⋊Dic73C2418yescomplemented
412#11924007C2418yescomplemented
413#11924007C2418yescomplemented
414#11924007C2418yescomplemented
415#11924007C2418yescomplemented
416#11924007C2418yescomplemented
417#11924007C2418yescomplemented
418C22⋊Dic73C2418yes—
419C22⋊Dic73C2418yes—
420C22⋊Dic73C2418yes—
421C22⋊Dic73C2418yes—
422C22⋊Dic73C2418yes—
423C22⋊Dic73C2418yescomplemented
424C22⋊Dic73C2418yescomplemented
425#11924005C2418yes—
426#11924005C2418yes—
427#11924005C2418yes—
428#11924005C2418yes—
429#11924005C2418yes—
430#11924005C2418yes—
431#11924005C2418yes—
432#11924005C2418yes—
433#11924005C2418yes—
434#11924005C2418yes—
435#11924005C2418yescomplemented
436#11924005C2418yescomplemented
437#11924005C2418yescomplemented
438#11924005C2418yescomplemented
439C4×Dic73C2418yescomplemented
440C4×Dic73C2418yescomplemented
441C4×Dic73C2418yescomplemented
442C24×C73—24no—
443C24×C73—42no—
444C24×C73—42no—
445C24×C73C2412yes—
446C24×C73C2412yes—
447C24×C73C2411yescharacteristic
448C24×C73C2414yes—
449C2×Q8×C73—42no—
450C2×Q8×C73C2414yescomplemented
451C2×D4×C73—28no—
452C2×D4×C73—44no—
453C2×D4×C73—44no—
454C2×D4×C73—42no—
455C2×D4×C73C2418yes—
456C2×D4×C73C2418yes—
457C2×D4×C73C2418yes—
458C2×D4×C73C2414yescomplemented
459C22×C4×C73—42no—
460C22×C4×C73—42no—
461C22×C4×C73—44no—
462C22×C4×C73C2412yes—
463C22×C4×C73C2412yes—
464C22×C4×C73C2412yes—
465C22×C4×C73C2411yescharacteristic
466C22×C4×C73C2411yescharacteristic
467C22×C4×C73C2412yes—
468C22×C4×C73C2414yes—
469C22×C4×C73C2414yes—
470C22×C4×C73C2418yescomplemented
471C4⋊C4×C73C2418yescomplemented
472C4⋊C4×C73C2418yescomplemented
473C4⋊C4×C73C2414yescomplemented
474C4⋊C4×C73C2414yescomplemented
475C22⋊C4×C73C2418yes—
476C22⋊C4×C73C2418yes—
477C22⋊C4×C73C2418yes—
478C22⋊C4×C73C2418yes—
479C22⋊C4×C73C2418yes—
480C22⋊C4×C73C2418yescomplemented
481C22⋊C4×C73C2418yescomplemented
482C42×C73C2418yescomplemented
483C23×C73—22no—
484C23×C73—22no—
485C23×C73—24no—
486C23×C73—28no—
487C23×C73—24no—
488C23×C73—24no—
489C23×C73—24no—
490C23×C73—24no—
491C23×C73—24no—
492C23×C73—44no—
493C23×C73—44no—
494C23×C73—416no—
495C23×C73C2×#4114yes—
496C23×C73C2514yes—
497C23×C73C2514yes—
498C23×C73C2512yes—
499C23×C73C2511yescharacteristic
500C22×D73—232no—
501C22×D73—28no—
502C22×D73—22no—
503C22×D73—22no—
504C22×D73—22no—
505C22×D73—22no—
506C22×D73—24no—
507C22×D73—24no—
508C22×D73—28no—
509C22×D73—28no—
510C22×D73—24no—
511C22×D73—24no—
512C22×D73—24no—
513C22×D73—216no—
514C22×D73—216no—
515C22×D73—216no—
516C22×D73—216no—
517C22×D73—216no—
518C22×D73—416no—
519C22×D73—48no—
520C22×D73—48no—
521C22×D73—44no—
522C22×D73—44no—
523C22×D73—432no—
524C22×D73—432no—
525C22×D73—48no—
526C22×D73—48no—
527C22×D73—4128no—
528C22×D73—816no—
529C22×D73C2×#4118yes—
530C22×D73C2×#41116yescomplemented
531C22×D73H(5,𝔽2)14yes—
532C22×D73H(5,𝔽2)14yes—
533C22×D73C2514yes—
534C22×D73C2514yes—
535C22×D73C2512yes—
536C22×D73C2512yes—
537Q8×C73—44no—
538D4×C73—216no—
539D4×C73—48no—
540D4×C73—48no—
541D4×C73—44no—
542C2×C4×C73—24no—
543C2×C4×C73—24no—
544C2×C4×C73—22no—
545C2×C4×C73—24no—
546C2×C4×C73—22no—
547C2×C4×C73—24no—
548C2×C4×C73—44no—
549C2×C4×C73—44no—
550C2×C4×C73—48no—
551C2×C4×C73C2514yes—
552C2×C4×C73C2514yes—
553C2×C4×C73C2514yes—
554C2×C4×C73C2512yes—
555C2×C4×C73C2512yes—
556C2×C4×C73C2514yes—
557C22⋊D73—216no—
558C22⋊D73—216no—
559C22⋊D73—216no—
560C22⋊D73—216no—
561C22⋊D73—48no—
562C22⋊D73—48no—
563C22⋊D73—48no—
564C2×Dic73—24no—
565C2×Dic73—22no—
566C2×Dic73—22no—
567C2×Dic73—24no—
568C2×Dic73—24no—
569C2×Dic73—24no—
570C2×Dic73—44no—
571C2×Dic73—44no—
572C2×Dic73—48no—
573C2×Dic73C2512yes—
574C2×Dic73C2514yes—
575C2×Dic73C2512yes—
576C2×Dic73C2514yes—
577C2×Dic73C2514yes—
578C2×Dic73C2514yes—
579D292—216no—
580D292—216no—
581D292—216no—
582D292—44no—
583C4×D73—216no—
584C4×D73—28no—
585C4×D73—216no—
586C4×D73—28no—
587C4×D73—48no—
588C4×D73—44no—
589C4×D73—44no—
590C4×D73—48no—
591C4×D73—48no—
592C4×D73—48no—
593C4×D73—48no—
594Dic146—44no—
595Dic146—48no—
596C22×C73—22no—
597C22×C73—22no—
598C22×C73—28no—
599C22×C73—24no—
600C22×C73—24no—
601C22×C73—24no—
602C22×C73—24no—
603C22×C73—24no—
604C22×C73—24no—
605C22×C73—416no—
606C22×C73—48no—
607C22×C73—48no—
608C22×C73C22×#4114yes—
609C22×C73C22×#4112yes—
610C22×C73C2×H(5,𝔽2)12yes—
611C22×C73C2×H(5,𝔽2)12yes—
612C22×C73C2611yescharacteristic
613C2×D73—232no—
614C2×D73—22no—
615C2×D73—22no—
616C2×D73—22no—
617C2×D73—22no—
618C2×D73—24no—
619C2×D73—24no—
620C2×D73—28no—
621C2×D73—28no—
622C2×D73—216no—
623C2×D73—24no—
624C2×D73—24no—
625C2×D73—24no—
626C2×D73—416no—
627C2×D73—432no—
628C2×D73—432no—
629C2×D73—48no—
630C2×D73—816no—
631C2×D73C22×#4118yes—
632C2×D73C2×H(5,𝔽2)14yes—
633C2×D73C2×H(5,𝔽2)14yes—
634C4×C73—24no—
635C4×C73—22no—
636C4×C73—24no—
637C4×C73—24no—
638C4×C73—22no—
639C4×C73—24no—
640Dic73—24no—
641Dic73—24no—
642Dic73—24no—
643Dic73—24no—
644Dic73—22no—
645Dic73—22no—
646C2×#3490—731nomaximal, Sylow
647C2×C73—24no—
648C2×C73—44no—
649C2×C73—44no—
650C2×C73#349014yescomplemented
651C2×C73C23×#4111yescharacteristic
652C2×C73C22×H(5,𝔽2)11yescharacteristic
653C2×C73C22×H(5,𝔽2)11yescharacteristic
654D73—24no—
655D73—24no—
656D73—28no—
657D73—44no—
658#3490—7332no—
659C2×#551—732no—
660C2×#551—732no—
661C2×#551—732no—
662C2×#551—732no—
663C2×#546—732no—
664C2×#546—732no—
665C2×#546—732no—
666C2×#546—732no—
667C2×#543—731no—
668C2×#538—732no—
669C2×#538—731no—
670C2×#538D7311yescharacteristic, complemented
671C2×#534—731no—
672C2×#525—731no—
673C2×#525—731no—
674C2×#525—732no—
675C22×#120—732no—
676C2×#518—732no—
677C23×C22⋊C4—731no—
678C73C2×#349011yescharacteristic, complemented, Sylow
679C26—731no—
680C22×#41—731no—
681C22×#41—731no—
682C22×#41—732no—
683C23×D4—732no—
684C23×D4—732no—
685C23×D4—732no—
686C24×C4—731no—
687C24×C4—731no—
688#551—7332no—
689#551—7332no—
690#551—7332no—
691#551—7332no—
692#546—7332no—
693#546—7332no—
694#546—7332no—
695#546—7332no—
696#543—7316no—
697#538—7332no—
698#538—7316no—
699#538C2×D73116yescomplemented
700#534—7316no—
701C2×#126—732no—
702C2×#126—732no—
703C2×#126—732no—
704C2×#126C2×D7312yescomplemented
705C2×#124—732no—
706C2×#124—732no—
707C2×#124—732no—
708C2×#124C2×D7312yescomplemented
709#525—7316no—
710#525—7316no—
711#525—7332no—
712C2×#123—732no—
713C2×#123—732no—
714C2×#123—732no—
715C2×#123—732no—
716C2×#123—732no—
717C2×#123—732no—
718C2×#123—732no—
719C2×#123—732no—
720C2×#123—732no—
721C2×#123C2×D7312yescomplemented
722C2×C22⋊Q8—731no—
723C2×C22⋊Q8—732no—
724C2×C22⋊Q8—731no—
725C2×C22⋊Q8—732no—
726C2×C22⋊Q8—731no—
727C2×C22⋊Q8—732no—
728C2×C22⋊Q8—732no—
729C2×C22⋊Q8—732no—
730C2×C22⋊Q8—732no—
731C2×C22⋊Q8C2×D7311yescharacteristic, complemented
732C2×#121—732no—
733C2×#121—732no—
734C2×#121—732no—
735C2×#121—731no—
736C2×#121—731no—
737C2×#121—731no—
738C2×#121—732no—
739C2×#121—732no—
740C2×#121C2×D7312yescomplemented
741C2×#121C2×D7311yescharacteristic, complemented
742C2×#120—732no—
743C2×#120—732no—
744C2×#120—732no—
745C2×#120—732no—
746C2×#120—732no—
747C2×#120—7332no—
748C2×#120—732no—
749C2×#120—732no—
750C2×#120—732no—
751C2×#120—732no—
752C2×#120C2×D7312yescomplemented
753#518—7332no—
754C2×C4×D4—732no—
755C2×C4×D4—732no—
756C2×C4×D4—732no—
757C2×C4×D4—732no—
758C2×C4×D4—732no—
759C2×C4×D4—732no—
760C2×C4×D4—732no—
761C2×C4×D4—732no—
762C2×C4×D4—732no—
763C2×C4×D4—732no—
764C2×C4×D4—732no—
765C2×C4×D4C2×D7312yescomplemented
766C2×#117—732no—
767C2×#117—731no—
768C2×#117—731no—
769C2×#117—732no—
770C2×#117—732no—
771C22×C22⋊C4—731no—
772C22×C22⋊C4—731no—
773C22×C22⋊C4—731no—
774C22×C22⋊C4—732no—
775C22×C22⋊C4—732no—
776C22×C22⋊C4—732no—
777C22×C22⋊C4—732no—
778C22×C22⋊C4—732no—
779C22×C22⋊C4—732no—
780C22×C22⋊C4—732no—
781C22×C22⋊C4—732no—
782C22×C22⋊C4—7316no—
783C22×C22⋊C4—732no—
784C22×C22⋊C4C2×D7311yescharacteristic, complemented
785C25—2924no—
786C25—2924no—
787C25—731no—
788C25—738no—
789C25—732no—
790C25—732no—
791C25—732no—
792C25—731no—
793C25—1468no—
794C25C22×D7311yescharacteristic
795C2×#41—2928no—
796C2×#41—2924no—
797C2×#41—2924no—
798C2×#41—738no—
799C2×#41—738no—
800C2×#41—7316no—
801C22×Q8—731no—
802C22×Q8—732no—
803C22×Q8C22×D7311yescharacteristic, complemented
804C22×D4—2928no—
805C22×D4—2928no—
806C22×D4—732no—
807C22×D4—732no—
808C22×D4—732no—
809C22×D4—7316no—
810C22×D4—7316no—
811C22×D4—732no—
812C22×D4—732no—
813C22×D4—732no—
814C22×D4—732no—
815C22×D4—7316no—
816C22×D4—731no—
817C22×D4—732no—
818C22×D4—732no—
819C22×D4—732no—
820C22×D4—14616no—
821C22×D4C22×D7312yes—
822C22×D4C22×D7312yes—
823C22×D4C22×D7312yes—
824C22×D4C22×D7311yescharacteristic, complemented
825C23×C4—2924no—
826C23×C4—2924no—
827C23×C4—731no—
828C23×C4—731no—
829C23×C4—732no—
830C23×C4—731no—
831C23×C4—731no—
832C23×C4—732no—
833C23×C4—732no—
834C23×C4—732no—
835C23×C4—738no—
836C23×C4—738no—
837C23×C4—732no—
838C23×C4—732no—
839C23×C4—732no—
840C23×C4—731no—
841C23×C4—731no—
842C23×C4—732no—
843C23×C4C22×D7311yescharacteristic
844C23×C4C22×D7311yescharacteristic
845C23×C4C22×D7312yescomplemented
846#126—7316no—
847#126—7316no—
848#126—7316no—
849#126C22×D73116yescomplemented
850#124—7316no—
851#124—7316no—
852#124—7316no—
853#124C22×D73116yescomplemented
854#123—7316no—
855#123—7316no—
856#123—7316no—
857#123—7316no—
858#123—7316no—
859#123—7316no—
860#123—7316no—
861#123—7316no—
862#123—7316no—
863#123C22×D73116yescomplemented
864C22⋊Q8—738no—
865C22⋊Q8—7316no—
866C22⋊Q8—738no—
867C22⋊Q8—7316no—
868C22⋊Q8—738no—
869C22⋊Q8—7316no—
870C22⋊Q8—7316no—
871C22⋊Q8—7316no—
872C22⋊Q8—7316no—
873C22⋊Q8C22×D7318yescomplemented
874#121—7316no—
875#121—7316no—
876#121—7316no—
877#121—738no—
878#121—738no—
879#121—738no—
880#121—7316no—
881#121—7316no—
882#121C22×D73116yescomplemented
883#121C22×D7318yescomplemented
884#120—7316no—
885#120—7316no—
886#120—7316no—
887#120—7316no—
888#120—7316no—
889#120—7316no—
890#120—7316no—
891#120—7316no—
892#120—7316no—
893#120C22×D73116yescomplemented
894C4×D4—7316no—
895C4×D4—7316no—
896C4×D4—7316no—
897C4×D4—7316no—
898C4×D4—7316no—
899C4×D4—7316no—
900C4×D4—7316no—
901C4×D4—7316no—
902C4×D4—7316no—
903C4×D4—7316no—
904C4×D4—7316no—
905C4×D4C22×D73116yescomplemented
906#117—7316no—
907#117—738no—
908#117—738no—
909#117—7316no—
910#117—7316no—
911C2×C4⋊C4—732no—
912C2×C4⋊C4—732no—
913C2×C4⋊C4—732no—
914C2×C4⋊C4—732no—
915C2×C4⋊C4—731no—
916C2×C4⋊C4—732no—
917C2×C4⋊C4—731no—
918C2×C4⋊C4—732no—
919C2×C4⋊C4—732no—
920C2×C4⋊C4—732no—
921C2×C4⋊C4C22×D7312yescomplemented
922C2×C4⋊C4C22×D7311yescharacteristic, complemented
923C2×C4⋊C4C22×D7311yescharacteristic, complemented
924C2×C4⋊C4C22×D7312yescomplemented
925C2×C22⋊C4—732no—
926C2×C22⋊C4—732no—
927C2×C22⋊C4—738no—
928C2×C22⋊C4—732no—
929C2×C22⋊C4—732no—
930C2×C22⋊C4—732no—
931C2×C22⋊C4—732no—
932C2×C22⋊C4—732no—
933C2×C22⋊C4—732no—
934C2×C22⋊C4—732no—
935C2×C22⋊C4—738no—
936C2×C22⋊C4—732no—
937C2×C22⋊C4—732no—
938C2×C22⋊C4—738no—
939C2×C22⋊C4—732no—
940C2×C22⋊C4—732no—
941C2×C22⋊C4—732no—
942C2×C22⋊C4—732no—
943C2×C22⋊C4—732no—
944C2×C22⋊C4—732no—
945C2×C22⋊C4—732no—
946C2×C22⋊C4—732no—
947C2×C22⋊C4—732no—
948C2×C22⋊C4—732no—
949C2×C22⋊C4—7316no—
950C2×C22⋊C4—7316no—
951C2×C22⋊C4—7316no—
952C2×C22⋊C4—7316no—
953C2×C22⋊C4—7316no—
954C2×C22⋊C4—7316no—
955C2×C22⋊C4—7316no—
956C2×C22⋊C4—7316no—
957C2×C22⋊C4—7316no—
958C2×C22⋊C4C22×D7312yes—
959C2×C22⋊C4C22×D7312yes—
960C2×C22⋊C4C22×D7312yes—
961C2×C22⋊C4C22×D7312yes—
962C2×C22⋊C4C22×D7312yes—
963C2×C22⋊C4C22×D7318yescomplemented
964C2×C22⋊C4C22×D7312yescomplemented
965C2×C22⋊C4C22×D7312yescomplemented
966C2×C42—732no—
967C2×C42—732no—
968C2×C42—732no—
969C2×C42C22×D7312yescomplemented
970C24—24no—
971C24—42no—
972C24—42no—
973C24—2922no—
974C24—2922no—
975C24—2924no—
976C24—2924no—
977C24—2924no—
978C24—2924no—
979C24—29264no—
980C24—29216no—
981C24—29216no—
982C24—738no—
983C24—734no—
984C24—738no—
985C24—738no—
986C24—738no—
987C24—732no—
988C24—731no—
989C24—731no—
990C24—734no—
991C24—732no—
992C24—1468no—
993C24—1468no—
994C24—14632no—
995C24—1468no—
996C24—1468no—
997C24—1468no—
998C24—1464no—
999C24—1464no—
1000C24—1464no—
1001C24C23×D7312yes—
1002C24C23×D7312yes—
1003C24C23×D7311yescharacteristic
1004C24C23×D7314yes—
1005#41—29232no—
1006#41—29216no—
1007#41—29216no—
1008C2×Q8—42no—
1009C2×Q8—2922no—
1010C2×Q8—2924no—
1011C2×Q8—734no—
1012C2×Q8—738no—
1013C2×Q8C23×D7314yescomplemented
1014C2×D4—28no—
1015C2×D4—44no—
1016C2×D4—44no—
1017C2×D4—42no—
1018C2×D4—2922no—
1019C2×D4—29232no—
1020C2×D4—29232no—
1021C2×D4—2924no—
1022C2×D4—2924no—
1023C2×D4—2924no—
1024C2×D4—738no—
1025C2×D4—738no—
1026C2×D4—738no—
1027C2×D4—738no—
1028C2×D4—738no—
1029C2×D4—738no—
1030C2×D4—738no—
1031C2×D4—734no—
1032C2×D4—738no—
1033C2×D4—738no—
1034C2×D4—738no—
1035C2×D4—1468no—
1036C2×D4—1468no—
1037C2×D4—1468no—
1038C2×D4—14664no—
1039C2×D4—1468no—
1040C2×D4—1468no—
1041C2×D4—1468no—
1042C2×D4—1468no—
1043C2×D4C23×D7318yes—
1044C2×D4C23×D7318yes—
1045C2×D4C23×D7318yes—
1046C2×D4C23×D7314yescomplemented
1047C22×C4—42no—
1048C22×C4—42no—
1049C22×C4—44no—
1050C22×C4—2924no—
1051C22×C4—2922no—
1052C22×C4—2922no—
1053C22×C4—2924no—
1054C22×C4—2924no—
1055C22×C4—2924no—
1056C22×C4—2924no—
1057C22×C4—29216no—
1058C22×C4—29216no—
1059C22×C4—2922no—
1060C22×C4—2922no—
1061C22×C4—2924no—
1062C22×C4—734no—
1063C22×C4—734no—
1064C22×C4—738no—
1065C22×C4—734no—
1066C22×C4—734no—
1067C22×C4—738no—
1068C22×C4—738no—
1069C22×C4—738no—
1070C22×C4—738no—
1071C22×C4—738no—
1072C22×C4—732no—
1073C22×C4—731no—
1074C22×C4—731no—
1075C22×C4—732no—
1076C22×C4—732no—
1077C22×C4—732no—
1078C22×C4—738no—
1079C22×C4—734no—
1080C22×C4—734no—
1081C22×C4—738no—
1082C22×C4—1468no—
1083C22×C4—1464no—
1084C22×C4—1464no—
1085C22×C4—1468no—
1086C22×C4C23×D7312yes—
1087C22×C4C23×D7312yes—
1088C22×C4C23×D7312yes—
1089C22×C4C23×D7312yes—
1090C22×C4C23×D7311yescharacteristic
1091C22×C4C23×D7311yescharacteristic
1092C22×C4C23×D7314yes—
1093C22×C4C23×D7314yes—
1094C22×C4C23×D7318yescomplemented
1095C4⋊C4—738no—
1096C4⋊C4—738no—
1097C4⋊C4—738no—
1098C4⋊C4—738no—
1099C4⋊C4—738no—
1100C4⋊C4—738no—
1101C4⋊C4—738no—
1102C4⋊C4—734no—
1103C4⋊C4—734no—
1104C4⋊C4—738no—
1105C4⋊C4C23×D7318yescomplemented
1106C4⋊C4C23×D7314yescomplemented
1107C4⋊C4C23×D7314yescomplemented
1108C4⋊C4C23×D7318yescomplemented
1109C22⋊C4—738no—
1110C22⋊C4—738no—
1111C22⋊C4—738no—
1112C22⋊C4—738no—
1113C22⋊C4—738no—
1114C22⋊C4—738no—
1115C22⋊C4—738no—
1116C22⋊C4—738no—
1117C22⋊C4—738no—
1118C22⋊C4—738no—
1119C22⋊C4—738no—
1120C22⋊C4—738no—
1121C22⋊C4—738no—
1122C22⋊C4—738no—
1123C22⋊C4—738no—
1124C22⋊C4—738no—
1125C22⋊C4—738no—
1126C22⋊C4—738no—
1127C22⋊C4—738no—
1128C22⋊C4—738no—
1129C22⋊C4—738no—
1130C22⋊C4C23×D7318yes—
1131C22⋊C4C23×D7318yes—
1132C22⋊C4C23×D7318yes—
1133C22⋊C4C23×D7318yes—
1134C22⋊C4C23×D7318yes—
1135C22⋊C4C23×D7318yescomplemented
1136C22⋊C4C23×D7318yescomplemented
1137C42—738no—
1138C42—738no—
1139C42—738no—
1140C42C23×D7318yescomplemented
1141C23—22no—
1142C23—22no—
1143C23—24no—
1144C23—28no—
1145C23—24no—
1146C23—24no—
1147C23—24no—
1148C23—24no—
1149C23—24no—
1150C23—44no—
1151C23—44no—
1152C23—416no—
1153C23—29216no—
1154C23—2924no—
1155C23—2924no—
1156C23—2928no—
1157C23—2928no—
1158C23—2928no—
1159C23—2928no—
1160C23—292128no—
1161C23—29232no—
1162C23—29232no—
1163C23—58416no—
1164C23—7316no—
1165C23—738no—
1166C23—734no—
1167C23—734no—
1168C23—734no—
1169C23—732no—
1170C23—732no—
1171C23—734no—
1172C23—14616no—
1173C23—14616no—
1174C23—14616no—
1175C23—14616no—
1176C23—14616no—
1177C23—1468no—
1178C23—1468no—
1179C23—14632no—
1180C23—1464no—
1181C23—1464no—
1182C23—1464no—
1183C23—1468no—
1184C23—1462no—
1185C23—1462no—
1186C23—1462no—
1187C23—1462no—
1188C23—1464no—
1189C23—1464no—
1190C23#41×D7314yes—
1191C23C24×D7314yes—
1192C23C24×D7314yes—
1193C23C24×D7312yes—
1194C23C24×D7311yescharacteristic
1195Q8—44no—
1196Q8—2924no—
1197Q8—2928no—
1198D4—216no—
1199D4—48no—
1200D4—48no—
1201D4—44no—
1202D4—2924no—
1203D4—2928no—
1204D4—2928no—
1205D4—2928no—
1206D4—14616no—
1207D4—14616no—
1208D4—14616no—
1209D4—14616no—
1210D4—14616no—
1211D4—14616no—
1212D4—14616no—
1213C2×C4—24no—
1214C2×C4—24no—
1215C2×C4—22no—
1216C2×C4—22no—
1217C2×C4—24no—
1218C2×C4—24no—
1219C2×C4—44no—
1220C2×C4—44no—
1221C2×C4—48no—
1222C2×C4—2928no—
1223C2×C4—2924no—
1224C2×C4—2924no—
1225C2×C4—2928no—
1226C2×C4—2928no—
1227C2×C4—2928no—
1228C2×C4—2928no—
1229C2×C4—2924no—
1230C2×C4—2924no—
1231C2×C4—2928no—
1232C2×C4—734no—
1233C2×C4—732no—
1234C2×C4—732no—
1235C2×C4—734no—
1236C2×C4—734no—
1237C2×C4—734no—
1238C2×C4—14616no—
1239C2×C4—1468no—
1240C2×C4—1468no—
1241C2×C4—14616no—
1242C2×C4—1464no—
1243C2×C4—1462no—
1244C2×C4—1462no—
1245C2×C4—1464no—
1246C2×C4—1464no—
1247C2×C4—1464no—
1248C2×C4C24×D7314yes—
1249C2×C4C24×D7314yes—
1250C2×C4C24×D7314yes—
1251C2×C4C24×D7314yes—
1252C2×C4C24×D7312yes—
1253C2×C4C24×D7312yes—
1254C22—28no—
1255C22—22no—
1256C22—22no—
1257C22—24no—
1258C22—24no—
1259C22—24no—
1260C22—24no—
1261C22—24no—
1262C22—24no—
1263C22—416no—
1264C22—48no—
1265C22—48no—
1266C22—29216no—
1267C22—29232no—
1268C22—29232no—
1269C22—2928no—
1270C22—58416no—
1271C22—738no—
1272C22—734no—
1273C22—734no—
1274C22—14632no—
1275C22—1464no—
1276C22—1464no—
1277C22—1464no—
1278C22—14616no—
1279C22—1468no—
1280C22—1468no—
1281C22—1462no—
1282C22—1462no—
1283C22—1462no—
1284C22—1462no—
1285C22—1464no—
1286C22—1464no—
1287C22C2×#41×D7314yes—
1288C22C2×#41×D7312yes—
1289C22H(5,𝔽2)×D7312yes—
1290C22H(5,𝔽2)×D7312yes—
1291C22C25×D7311yescharacteristic
1292C4—24no—
1293C4—24no—
1294C4—22no—
1295C4—22no—
1296C4—24no—
1297C4—24no—
1298C4—1464no—
1299C4—1462no—
1300C4—1462no—
1301C4—1464no—
1302C4—1464no—
1303C4—1464no—
1304C2—24no—
1305C2—44no—
1306C2—44no—
1307C2—2924no—
1308C2—1468no—
1309C2—1464no—
1310C2—1464no—
1311C2#2262361714yesdirect product factor
1312C2C22×#41×D7311yescharacteristic
1313C2C2×H(5,𝔽2)×D7311yescharacteristic
1314C2C2×H(5,𝔽2)×D7311yescharacteristic
subgroupG/H
centerC23C24×D73
commutator, cosocleC22×C73C26
FrattiniC22C25×D73
FittingC2×#538×C73C2
socleC23×C73C25
hypercenterC2×#538D73
hypocenterC73C2×#3490
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#538

Complements

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

NH ≅ G/Ntype
1. #22623617C2direct (N × H)
2. C2×#17989267C2semidirect
3. C2×#17989265C2semidirect
4. C2×#17989262C2semidirect
5. C2×#17989262C2semidirect
6. C2×#17989234C2semidirect
7. C2×#17989230C2semidirect
8. C2×#17989229C2semidirect
9. C2×#17989226C2semidirect
10. C2×#17989212C2semidirect
11. C2×#17989175C2semidirect
12. C2×#17989172C2semidirect
13. C2×#17989145C2semidirect
14. C2×#17989100C2semidirect
15. C2×#17989097C2semidirect
16. C2×#17989096C2semidirect
17. C2×#120×D73C2semidirect
18. C2×#17989059C2semidirect
19. C22×C22⋊C4×D73C2semidirect
20. C2×#538×C73C2semidirect
22. C22×#11924029C22semidirect
23. C22×#11924028C22semidirect
24. C22×#11924027C22semidirect
26. C22×D4×D73C22semidirect
27. C22×D4×D73C22semidirect
28. C23×C4×D73C22semidirect
29. C23×C4×D73C22semidirect
30. #17989267C22semidirect
31. #17989265C22semidirect
32. #17989262C22semidirect
33. #17989262C22semidirect
34. #17989234C22semidirect
35. #17989230C22semidirect
36. #17989229C22semidirect
37. #17989226C22semidirect
38. #17989212C22semidirect
39. #17989175C22semidirect
40. #17989172C22semidirect
41. #17989145C22semidirect
42. C2×#14556584C22semidirect
43. C2×#14556584C22semidirect
44. C2×#14556584C22semidirect
45. C2×#14556578C22semidirect
46. C2×#14556577C22semidirect
47. C2×#14556577C22semidirect
48. #17989100C22semidirect
49. #17989097C22semidirect
50. #17989096C22semidirect
51. C2×#14556576C22semidirect
52. C2×#14556576C22semidirect
53. C2×#14556576C22semidirect
54. C2×#14556573C22semidirect
55. C2×#14556573C22semidirect
56. C2×#14556573C22semidirect
57. C2×#14556573C22semidirect
58. C2×#14556573C22semidirect
59. C2×#14556572C22semidirect
60. C2×#14556571C22semidirect
61. C2×#14556571C22semidirect
62. C2×#14556570C22semidirect
63. C2×#14556569C22semidirect
64. C2×#14556569C22semidirect
65. C2×#14556569C22semidirect
66. C2×#14556568C22semidirect
67. C2×#14556567C22semidirect
68. C2×#14556567C22semidirect
69. C2×#14556566C22semidirect
70. C2×#14556565C22semidirect
71. C2×#14556564C22semidirect
72. C2×#14556564C22semidirect
73. C2×#14556563C22semidirect
74. C2×#14556563C22semidirect
75. C2×#14556562C22semidirect
76. C2×#14556562C22semidirect
79. C2×#14556561C22semidirect
80. C2×#14556561C22semidirect
81. C2×#14556560C22semidirect
84. C2×#14556559C22semidirect
85. C2×#14556559C22semidirect
86. #120×D73C22semidirect
87. #17989059C22semidirect
88. C2×C4×D292C22semidirect
89. C2×C4×D292C22semidirect
90. C2×D4×Dic73C22semidirect
91. C2×#14556553C22semidirect
92. C2×#14556553C22semidirect
93. C2×C4×C22⋊D73C22semidirect
94. C2×C4×C22⋊D73C22semidirect
95. C2×C4×C22⋊D73C22semidirect
96. C2×#14556551C22semidirect
97. C2×#14556551C22semidirect
98. C2×#14556551C22semidirect
99. C2×#14556549C22semidirect
100. C2×#14556549C22semidirect
101. C2×#14556549C22semidirect
102. C2×#14556548C22semidirect
103. C2×#14556548C22semidirect
104. C22×C22⋊Dic73C22semidirect
107. C22×#11924005C22semidirect
109. C2×C22⋊C4×D73C22semidirect
110. C2×C22⋊C4×D73C22semidirect
111. C2×C22⋊C4×D73C22semidirect
112. C2×C22⋊C4×D73C22semidirect
113. C2×C22⋊C4×D73C22semidirect
114. C2×C22⋊C4×D73C22semidirect
115. C2×C22⋊C4×D73C22semidirect
116. C2×C22⋊C4×D73C22semidirect
117. #538×C73C22semidirect
118. C2×#126×C73C22semidirect
119. C2×#124×C73C22semidirect
120. C2×#123×C73C22semidirect
121. C2×C22⋊Q8×C73C22semidirect
122. C2×#121×C73C22semidirect
123. C2×#121×C73C22semidirect
124. C2×#120×C73C22semidirect
125. C2×C4×D4×C73C22semidirect
126. C22×C22⋊C4×C73C22semidirect
137. C2×#11924029C23semidirect
139. C2×#11924028C23semidirect
141. C2×#11924027C23semidirect
142. C22×Dic146C23semidirect
143. C22×Dic146C23semidirect
147. C22×D292C23semidirect
154. C22×C22⋊D73C23semidirect
159. C2×D4×D73C23semidirect
160. C2×D4×D73C23semidirect
163. C23×Dic73C23semidirect
175. C22×C4×D73C23semidirect
176. C22×C4×D73C23semidirect
177. C22×C4×D73C23semidirect
178. C22×C4×D73C23semidirect
179. #14556584C23semidirect
180. #14556584C23semidirect
181. #14556584C23semidirect
182. #14556578C23semidirect
183. #14556577C23semidirect
184. #14556577C23semidirect
185. #14556576C23semidirect
186. #14556576C23semidirect
187. #14556576C23semidirect
188. #14556573C23semidirect
189. #14556573C23semidirect
190. #14556573C23semidirect
191. #14556573C23semidirect
192. #14556573C23semidirect
193. #14556572C23semidirect
194. #14556571C23semidirect
195. #14556571C23semidirect
196. #14556570C23semidirect
197. #14556569C23semidirect
198. #14556569C23semidirect
199. #14556569C23semidirect
200. #14556568C23semidirect
201. #14556567C23semidirect
202. #14556567C23semidirect
203. #14556566C23semidirect
204. #14556565C23semidirect
205. #14556564C23semidirect
206. #14556564C23semidirect
207. #14556563C23semidirect
208. #14556563C23semidirect
209. #14556562C23semidirect
210. #14556562C23semidirect
213. #14556561C23semidirect
214. #14556561C23semidirect
215. #14556560C23semidirect
218. #14556559C23semidirect
219. #14556559C23semidirect
220. C4×D292C23semidirect
221. C4×D292C23semidirect
222. D4×Dic73C23semidirect
223. #14556553C23semidirect
224. #14556553C23semidirect
225. C4×C22⋊D73C23semidirect
226. C4×C22⋊D73C23semidirect
227. C4×C22⋊D73C23semidirect
228. #14556551C23semidirect
229. #14556551C23semidirect
230. #14556551C23semidirect
231. #14556549C23semidirect
232. #14556549C23semidirect
233. #14556549C23semidirect
234. #14556548C23semidirect
235. #14556548C23semidirect
236. C2×C4⋊Dic73C23semidirect
237. C2×C4⋊Dic73C23semidirect
238. C2×C4⋊Dic73C23semidirect
239. C2×C4⋊Dic73C23semidirect
240. C2×#11924007C23semidirect
241. C2×#11924007C23semidirect
242. C2×#11924007C23semidirect
243. C2×#11924007C23semidirect
244. C2×#11924007C23semidirect
245. C2×#11924007C23semidirect
251. C2×C22⋊Dic73C23semidirect
252. C2×C22⋊Dic73C23semidirect
253. C2×C22⋊Dic73C23semidirect
266. C2×#11924005C23semidirect
267. C2×#11924005C23semidirect
268. C2×#11924005C23semidirect
269. C2×#11924005C23semidirect
270. C2×#11924005C23semidirect
272. C22⋊C4×D73C23semidirect
273. C22⋊C4×D73C23semidirect
274. C22⋊C4×D73C23semidirect
275. C22⋊C4×D73C23semidirect
276. C22⋊C4×D73C23semidirect
277. C22⋊C4×D73C23semidirect
278. C22⋊C4×D73C23semidirect
279. C2×C4×Dic73C23semidirect
280. C2×C4×Dic73C23semidirect
281. C2×C4×Dic73C23semidirect
283. C22×Q8×C73C23semidirect
287. C22×D4×C73C23semidirect
290. C23×C4×C73C23semidirect
291. #126×C73C23semidirect
292. #124×C73C23semidirect
293. #123×C73C23semidirect
294. C22⋊Q8×C73C23semidirect
295. #121×C73C23semidirect
296. #121×C73C23semidirect
297. #120×C73C23semidirect
298. C4×D4×C73C23semidirect
299. C2×C4⋊C4×C73C23semidirect
300. C2×C4⋊C4×C73C23semidirect
301. C2×C4⋊C4×C73C23semidirect
302. C2×C4⋊C4×C73C23semidirect
308. C2×C22⋊C4×C73C23semidirect
309. C2×C22⋊C4×C73C23semidirect
310. C2×C22⋊C4×C73C23semidirect
311. C2×C42×C73C23semidirect
330. C23×D73#41semidirect
345. C2×Dic146C24semidirect
346. C2×Dic146C24semidirect
354. C2×D292C24semidirect
368. C2×C22⋊D73C24semidirect
383. C22×Dic73C24semidirect
406. C2×C4×D73C24semidirect
407. C2×C4×D73C24semidirect
408. C4⋊Dic73C24semidirect
409. C4⋊Dic73C24semidirect
410. C4⋊Dic73C24semidirect
411. C4⋊Dic73C24semidirect
412. #11924007C24semidirect
413. #11924007C24semidirect
414. #11924007C24semidirect
415. #11924007C24semidirect
416. #11924007C24semidirect
417. #11924007C24semidirect
423. C22⋊Dic73C24semidirect
424. C22⋊Dic73C24semidirect
435. #11924005C24semidirect
436. #11924005C24semidirect
437. #11924005C24semidirect
438. #11924005C24semidirect
439. C4×Dic73C24semidirect
440. C4×Dic73C24semidirect
441. C4×Dic73C24semidirect
450. C2×Q8×C73C24semidirect
458. C2×D4×C73C24semidirect
470. C22×C4×C73C24semidirect
471. C4⋊C4×C73C24semidirect
472. C4⋊C4×C73C24semidirect
473. C4⋊C4×C73C24semidirect
474. C4⋊C4×C73C24semidirect
480. C22⋊C4×C73C24semidirect
481. C22⋊C4×C73C24semidirect
482. C42×C73C24semidirect
530. C22×D73C2×#41semidirect
650. C2×C73#3490semidirect
670. C2×#538D73semidirect
678. C73C2×#3490semidirect
699. #538C2×D73semidirect
704. C2×#126C2×D73semidirect
708. C2×#124C2×D73semidirect
721. C2×#123C2×D73semidirect
731. C2×C22⋊Q8C2×D73semidirect
740. C2×#121C2×D73semidirect
741. C2×#121C2×D73semidirect
752. C2×#120C2×D73semidirect
765. C2×C4×D4C2×D73semidirect
784. C22×C22⋊C4C2×D73semidirect
803. C22×Q8C22×D73semidirect
824. C22×D4C22×D73semidirect
845. C23×C4C22×D73semidirect
849. #126C22×D73semidirect
853. #124C22×D73semidirect
863. #123C22×D73semidirect
873. C22⋊Q8C22×D73semidirect
882. #121C22×D73semidirect
883. #121C22×D73semidirect
893. #120C22×D73semidirect
905. C4×D4C22×D73semidirect
921. C2×C4⋊C4C22×D73semidirect
922. C2×C4⋊C4C22×D73semidirect
923. C2×C4⋊C4C22×D73semidirect
924. C2×C4⋊C4C22×D73semidirect
963. C2×C22⋊C4C22×D73semidirect
964. C2×C22⋊C4C22×D73semidirect
965. C2×C22⋊C4C22×D73semidirect
969. C2×C42C22×D73semidirect
1013. C2×Q8C23×D73semidirect
1046. C2×D4C23×D73semidirect
1094. C22×C4C23×D73semidirect
1105. C4⋊C4C23×D73semidirect
1106. C4⋊C4C23×D73semidirect
1107. C4⋊C4C23×D73semidirect
1108. C4⋊C4C23×D73semidirect
1135. C22⋊C4C23×D73semidirect
1136. C22⋊C4C23×D73semidirect
1140. C42C23×D73semidirect
1311. C2#22623617direct (N × H)

Maximal subgroups

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

subgroupindex
#226236172
C2×#179892672
C2×#179892652
C2×#179892622
C2×#179892342
C2×#179892302
C2×#179892292
C2×#179892262
C2×#179892122
C2×#179891752
C2×#179891722
C2×#179891452
C2×#179891002
C2×#179890972
C2×#179890962
C2×#120×D732
C2×#179890592
C22×C22⋊C4×D732
C2×#538×C732
C2×#349073