Finite Group Databasebeta

← C2×#22624302 #33993621

Subgroups — C2×#22624302 #33993621

Order 18688.

8046 conjugacy classes of subgroups.

The subgroup lattice has 1440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22624302C2132yesmaximal, direct product factor
2C2×#17989328C212yesmaximal, complemented
3C2×#17989325C212yesmaximal, complemented
4C2×#17989305C211yesmaximal, characteristic, complemented
5C2×#17989290C211yesmaximal, characteristic, complemented
6C2×#17989258C212yesmaximal, complemented
7C2×#17989255C211yesmaximal, characteristic, complemented
8C2×#17989238C211yesmaximal, characteristic, complemented
9C2×#17989233C211yesmaximal, characteristic, complemented
10C2×#17989232C211yesmaximal, characteristic, complemented
11C2×#17989229C212yesmaximal, complemented
12C2×#17989221C211yesmaximal, characteristic, complemented
13C2×#17989203C212yesmaximal, complemented
14C2×#17989173C212yesmaximal, complemented
15C2×#17989170C212yesmaximal, complemented
16C2×#17989168C211yesmaximal, characteristic, complemented
17C2×#17989166C211yesmaximal, characteristic, complemented
18C2×#17989156C211yesmaximal, characteristic, complemented
19C2×#17989153C212yesmaximal, complemented
20C2×#17989153C211yesmaximal, characteristic, complemented
21C2×#17989134C211yesmaximal, characteristic, complemented
22C2×#17989134C211yesmaximal, characteristic, complemented
23C2×#17989122C211yesmaximal, characteristic, complemented
24C2×#553×C73C211yesmaximal, characteristic, complemented
25C22×#11924028C2211yescharacteristic, complemented
26C22×#11924028C2212yescomplemented
27C22×#11924028C2211yescharacteristic, complemented
28C22×#11924028C2211yescharacteristic, complemented
29C22×#11924028C2212yescomplemented
30C22×#11924027C2211yescharacteristic, complemented
31C23×D292C2211yescharacteristic
32C22×D4×D73C2212yes—
33C22×D4×D73C2211yescharacteristic
34#17989328C22132yescomplemented
35#17989325C22132yescomplemented
36#17989305C22116yescomplemented
37#17989290C22116yescomplemented
38#17989258C22132yescomplemented
39#17989255C22116yescomplemented
40#17989238C22116yescomplemented
41#17989233C22116yescomplemented
42#17989232C22116yescomplemented
43#17989229C22132yescomplemented
44#17989221C22116yescomplemented
45#17989203C22132yescomplemented
46#17989173C22132yescomplemented
47#17989170C22132yescomplemented
48#17989168C22116yescomplemented
49#17989166C22116yescomplemented
50#17989156C22116yescomplemented
51#17989153C22116yescomplemented
52#17989153C22132yescomplemented
53#17989134C22116yescomplemented
54#17989134C22116yescomplemented
55C2×#14556590C2211yescharacteristic, complemented
56C2×#14556590C2211yescharacteristic, complemented
57C2×#14556588C2212yescomplemented
58C2×#14556587C2211yescharacteristic
59C2×#14556587C2211yescharacteristic
60C2×#14556587C2212yescomplemented
61C2×#14556587C2212yescomplemented
62#17989122C22116yescomplemented
63C2×#14556586C2212yescomplemented
64C2×#14556586C2212yescomplemented
65C2×#14556585C2212yescomplemented
66C2×#14556584C2212yescomplemented
67C2×#14556579C2211yescharacteristic
68C2×#14556579C2212yescomplemented
69C2×#14556577C2212yes—
70C2×#14556577C2212yescomplemented
71C2×#14556577C2212yescomplemented
72C2×#14556577C2211yescharacteristic, complemented
73C2×#14556577C2211yescharacteristic, complemented
74C2×#14556576C2212yescomplemented
75C2×#14556576C2212yescomplemented
76C2×#14556576C2212yescomplemented
77C2×#14556576C2212yescomplemented
78C2×#14556575C2212yescomplemented
79C2×#14556574C2212yescomplemented
80C2×#14556571C2211yescharacteristic, complemented
81C2×#14556571C2212yescomplemented
82C2×#14556571C2211yescharacteristic, complemented
83C2×#14556570C2211yescharacteristic, complemented
84C2×#14556569C2212yescomplemented
85C2×#14556568C2212yescomplemented
86C2×#14556566C2211yescharacteristic
87C2×#14556566C2211yescharacteristic
88C2×#14556566C2211yescharacteristic
89C2×#14556566C2212yescomplemented
90C2×#14556566C2211yescharacteristic, complemented
91C2×#14556566C2211yescharacteristic, complemented
92C2×#14556566C2212yescomplemented
93C2×#14556566C2211yescharacteristic, complemented
94C2×#14556565C2211yescharacteristic
95C2×#14556565C2212yescomplemented
96C2×#14556565C2212yescomplemented
97C2×#14556565C2212yescomplemented
98C2×#14556564C2212yes—
99C2×#14556564C2211yescharacteristic
100C2×#14556564C2212yescomplemented
101C2×#14556564C2212yescomplemented
102C2×#14556564C2212yescomplemented
103C2×#14556564C2212yescomplemented
104C2×#14556564C2211yescharacteristic, complemented
105C2×#14556563C2212yescomplemented
106C2×#14556563C2212yescomplemented
107C2×#14556562C2212yescomplemented
108C2×#14556562C2211yescharacteristic, complemented
109C2×#14556562C2211yescharacteristic, complemented
110C2×#14556561C2212yes—
111C2×#14556561C2212yescomplemented
112C2×#14556561C2212yescomplemented
113C2×#14556561C2212yescomplemented
114C2×#14556561C2212yescomplemented
115C2×#14556559C2212yes—
116C2×#14556559C2212yescomplemented
117C2×#14556559C2212yescomplemented
118C2×C4×Dic146C2212yescomplemented
119C2×#14556556C2211yescharacteristic, complemented
120C2×C4×D292C2211yescharacteristic, complemented
121C2×C4×D292C2211yescharacteristic, complemented
122C2×#14556553C2211yescharacteristic
123C2×#14556553C2212yescomplemented
124C2×#14556553C2212yescomplemented
125C2×C4×C22⋊D73C2211yescharacteristic
126C2×C4×C22⋊D73C2212yescomplemented
127C2×C4×C22⋊D73C2211yescharacteristic, complemented
128C2×#14556551C2212yescomplemented
129C2×#14556549C2212yescomplemented
130C2×#14556549C2211yescharacteristic, complemented
131C2×C4⋊C4×D73C2211yescharacteristic, complemented
132C22×#11924005C2212yescomplemented
133C2×C22⋊C4×D73C2212yescomplemented
134C2×C42×D73C2211yescharacteristic, complemented
135#553×C73C22116yescomplemented
136C2×#126×C73C2212yescomplemented
137C2×#125×C73C2211yescharacteristic, complemented
138C2×#123×C73C2212yescomplemented
139C2×#121×C73C2211yescharacteristic
140C2×#121×C73C2212yescomplemented
141C2×#121×C73C2211yescharacteristic, complemented
142C2×C4×D4×C73C2212yescomplemented
143C2×C4×D4×C73C2211yescharacteristic, complemented
144C2×C4×D4×C73C2211yescharacteristic, complemented
145C2×#117×C73C2211yescharacteristic, complemented
146C22×C4⋊C4×C73C2211yescharacteristic, complemented
147C24×D73C2312yes—
148C24×D73C2312yes—
149C2×#11924028—44no—
150C2×#11924028—44no—
151C2×#11924028—44no—
152C2×#11924028—48no—
153C2×#11924028—48no—
154C2×#11924028C2318yescomplemented
155C2×#11924028C2318yescomplemented
156C2×#11924028C23116yescomplemented
157C2×#11924028C23116yescomplemented
158C2×#11924028C2318yescomplemented
159C2×#11924027—44no—
160C2×#11924027C2318yescomplemented
161C22×Dic146C2312yes—
162C22×Dic146C2311yescharacteristic
163C22×Dic146C2311yescharacteristic
164C22×Dic146C2311yescharacteristic
165C22×D292—44no—
166C22×D292C2311yescharacteristic
167C22×D292C2311yescharacteristic
168C22×D292C2311yescharacteristic
169C22×D292C2312yes—
170C22×D292C2312yes—
171C22×D292C2311yescharacteristic
172C22×D292C2312yes—
173C22×D292C2312yes—
174C22×D292C2312yes—
175C22×D292C2312yes—
176C22×D292C2318yes—
177C22×D292C2311yescharacteristic
178C22×C22⋊D73C2311yescharacteristic
179C22×C22⋊D73C2312yes—
180C22×C22⋊D73C2311yescharacteristic
181C22×C22⋊D73C2311yescharacteristic
182C22×C22⋊D73C2311yescharacteristic
183C22×C22⋊D73C2312yes—
184C22×C22⋊D73C2311yescharacteristic
185C22×C22⋊D73C2312yes—
186C22×C22⋊D73C2312yes—
187C22×C22⋊D73C2312yes—
188C22×C22⋊D73C2312yes—
189C22×C22⋊D73C2312yes—
190C22×C22⋊D73C2311yescharacteristic
191C2×D4×D73—44no—
192C2×D4×D73—48no—
193C2×D4×D73C23116yes—
194C2×D4×D73C2318yes—
195C23×Dic73C2312yes—
196C22×C4×D73C2311yescharacteristic
197C22×C4×D73C2312yes—
198C22×C4×D73C2311yescharacteristic
199C22×C4×D73C2311yescharacteristic
200C22×C4×D73C2311yescharacteristic
201C22×C4×D73C2312yes—
202C22×C4×D73C2312yes—
203C22×C4×D73C2312yes—
204C22×C4×D73C2311yescharacteristic
205#14556590C2318yescomplemented
206#14556590C2318yescomplemented
207#14556588C23116yescomplemented
208#14556587C2318yes—
209#14556587C2318yes—
210#14556587C23116yescomplemented
211#14556587C23116yescomplemented
212#14556586C23116yescomplemented
213#14556586C23116yescomplemented
214#14556585C23116yescomplemented
215#14556584C23116yescomplemented
216#14556579C2318yes—
217#14556579C23116yescomplemented
218#14556577C23116yes—
219#14556577C23116yescomplemented
220#14556577C2318yescomplemented
221#14556577C2318yescomplemented
222#14556577C23116yescomplemented
223#14556576C23116yescomplemented
224#14556576C23116yescomplemented
225#14556576C23116yescomplemented
226#14556576C23116yescomplemented
227#14556575C23116yescomplemented
228#14556574C23116yescomplemented
229#14556571C2318yescomplemented
230#14556571C23116yescomplemented
231#14556571C2318yescomplemented
232#14556570C2318yescomplemented
233#14556569C23116yescomplemented
234#14556568C23116yescomplemented
235#14556566C2318yes—
236#14556566C2318yes—
237#14556566C2318yes—
238#14556566C2318yescomplemented
239#14556566C2318yescomplemented
240#14556566C23116yescomplemented
241#14556566C2318yescomplemented
242#14556566C23116yescomplemented
243#14556565C2318yes—
244#14556565C23116yescomplemented
245#14556565C23116yescomplemented
246#14556565C23116yescomplemented
247#14556564C2318yes—
248#14556564C23116yes—
249#14556564C2318yescomplemented
250#14556564C23116yescomplemented
251#14556564C23116yescomplemented
252#14556564C23116yescomplemented
253#14556564C23116yescomplemented
254#14556563C23116yescomplemented
255#14556563C23116yescomplemented
256#14556562C2318yescomplemented
257#14556562C2318yescomplemented
258#14556562C23116yescomplemented
259#14556561C23116yes—
260#14556561C23116yescomplemented
261#14556561C23116yescomplemented
262#14556561C23116yescomplemented
263#14556561C23116yescomplemented
264#14556559C23116yes—
265#14556559C23116yescomplemented
266#14556559C23116yescomplemented
267C4×Dic146C23116yescomplemented
268#14556556C2318yescomplemented
269C4×D292C2318yescomplemented
270C4×D292C2318yescomplemented
271#14556553C2318yes—
272#14556553C23116yescomplemented
273#14556553C23116yescomplemented
274C4×C22⋊D73C2318yes—
275C4×C22⋊D73C23116yescomplemented
276C4×C22⋊D73C2318yescomplemented
277#14556551C23116yescomplemented
278#14556549C23116yescomplemented
279#14556549C2318yescomplemented
280C2×C4⋊Dic73C2311yescharacteristic
281C2×C4⋊Dic73C2311yescharacteristic
282C2×C4⋊Dic73C2312yes—
283C2×C4⋊Dic73C2312yes—
284C2×#11924007C2311yescharacteristic
285C2×#11924007C2311yescharacteristic
286C2×#11924007C2312yes—
287C2×#11924007C2312yes—
288C2×#11924007C2312yes—
289C2×#11924007C2312yes—
290C4⋊C4×D73C2318yescomplemented
291C2×C22⋊Dic73C2312yes—
292C2×C22⋊Dic73C2311yescharacteristic
293C2×C22⋊Dic73C2312yes—
294C2×C22⋊Dic73C2311yescharacteristic
295C2×#11924005C2312yes—
296C2×#11924005C2312yes—
297C2×#11924005C2311yescharacteristic
298C2×#11924005C2312yes—
299C2×#11924005C2312yes—
300C2×#11924005C2312yes—
301C2×#11924005C2312yes—
302C2×#11924005C2312yes—
303C2×#11924005C2312yes—
304C2×#11924005C2311yescharacteristic
305C2×#11924005C2312yes—
306C2×#11924005C2311yescharacteristic
307C2×#11924005C2312yes—
308C2×#11924005C2311yescharacteristic
309C2×#11924005C2312yes—
310C2×#11924005C2312yes—
311C2×#11924005C2312yes—
312C2×#11924005C23116yescomplemented
313C22⋊C4×D73C23116yescomplemented
314C2×C4×Dic73C2311yescharacteristic
315C2×C4×Dic73C2311yescharacteristic
316C2×C4×Dic73C2312yes—
317C2×C4×Dic73C2312yes—
318C2×C4×Dic73C2311yescharacteristic
319C42×D73C2318yescomplemented
320C22×D4×C73C2311yescharacteristic
321C22×D4×C73C2311yescharacteristic
322C22×D4×C73C2312yes—
323C22×D4×C73C2312yes—
324C23×C4×C73C2311yescharacteristic
325C23×C4×C73C2311yescharacteristic
326C23×C4×C73C2312yes—
327C23×C4×C73C2312yes—
328#126×C73C23116yescomplemented
329#125×C73C2318yescomplemented
330#123×C73C23116yescomplemented
331#121×C73C2318yes—
332#121×C73C2318yescomplemented
333#121×C73C23116yescomplemented
334C4×D4×C73C2318yescomplemented
335C4×D4×C73C2318yescomplemented
336C4×D4×C73C23116yescomplemented
337#117×C73C2318yescomplemented
338C2×C4⋊C4×C73C2311yescharacteristic
339C2×C4⋊C4×C73C2311yescharacteristic
340C2×C4⋊C4×C73C2311yescharacteristic
341C2×C4⋊C4×C73C2312yes—
342C2×C4⋊C4×C73C2311yescharacteristic
343C2×C4⋊C4×C73C2312yes—
344C2×C4⋊C4×C73C2312yes—
345C2×C4⋊C4×C73C2318yescomplemented
346C2×C22⋊C4×C73C2312yes—
347C2×C22⋊C4×C73C2311yescharacteristic
348C2×C22⋊C4×C73C2312yes—
349C2×C22⋊C4×C73C2312yes—
350C2×C22⋊C4×C73C2311yescharacteristic
351C2×C22⋊C4×C73C2312yes—
352C2×C42×C73C2312yes—
353C2×C42×C73C2311yescharacteristic
354C23×D73—44no—
355C23×D73—44no—
356C23×D73—44no—
357C23×D73—44no—
358C23×D73—44no—
359C23×D73—44no—
360C23×D73C2411yescharacteristic
361C23×D73C2412yes—
362C23×D73C2412yes—
363C23×D73C2411yescharacteristic
364C23×D73C2411yescharacteristic
365C23×D73C2418yes—
366C23×D73C2418yes—
367#11924028—432no—
368#11924028—432no—
369#11924028—416no—
370#11924028—416no—
371#11924028—416no—
372#11924027—416no—
373C2×Dic146—24no—
374C2×Dic146—28no—
375C2×Dic146—42no—
376C2×Dic146—42no—
377C2×Dic146C2414yes—
378C2×Dic146C2418yes—
379C2×Dic146C2414yes—
380C2×Dic146C2414yes—
381C2×D292—24no—
382C2×D292—24no—
383C2×D292—416no—
384C2×D292—44no—
385C2×D292—44no—
386C2×D292—42no—
387C2×D292—44no—
388C2×D292—44no—
389C2×D292—42no—
390C2×D292—42no—
391C2×D292—44no—
392C2×D292—44no—
393C2×D292C2414yes—
394C2×D292C2414yes—
395C2×D292C2418yes—
396C2×D292C2418yes—
397C2×D292C2414yes—
398C2×D292C2418yes—
399C2×D292C2418yes—
400C2×D292C2414yes—
401C2×D292C2418yes—
402C2×D292C2418yes—
403C2×D292C2414yes—
404C2×C22⋊D73—24no—
405C2×C22⋊D73—28no—
406C2×C22⋊D73—24no—
407C2×C22⋊D73—44no—
408C2×C22⋊D73—44no—
409C2×C22⋊D73—44no—
410C2×C22⋊D73—42no—
411C2×C22⋊D73—42no—
412C2×C22⋊D73—42no—
413C2×C22⋊D73—42no—
414C2×C22⋊D73—44no—
415C2×C22⋊D73—44no—
416C2×C22⋊D73—44no—
417C2×C22⋊D73C2418yes—
418C2×C22⋊D73C2414yes—
419C2×C22⋊D73C2414yes—
420C2×C22⋊D73C2418yes—
421C2×C22⋊D73C2418yes—
422C2×C22⋊D73C2418yes—
423C2×C22⋊D73C2414yes—
424C2×C22⋊D73C2418yes—
425C2×C22⋊D73C2414yes—
426C2×C22⋊D73C2414yes—
427C2×C22⋊D73C2418yes—
428C2×C22⋊D73C2418yes—
429C2×C22⋊D73C2414yes—
430D4×D73—416no—
431D4×D73—432no—
432C22×Dic73—44no—
433C22×Dic73C2411yescharacteristic
434C22×Dic73C2411yescharacteristic
435C22×Dic73C2411yescharacteristic
436C22×Dic73C2412yes—
437C22×Dic73C2412yes—
438C22×Dic73C2411yescharacteristic
439C22×Dic73C2418yes—
440C22×Dic73C2411yescharacteristic
441C2×C4×D73—24no—
442C2×C4×D73—24no—
443C2×C4×D73—24no—
444C2×C4×D73—28no—
445C2×C4×D73—24no—
446C2×C4×D73—42no—
447C2×C4×D73—44no—
448C2×C4×D73—44no—
449C2×C4×D73—44no—
450C2×C4×D73C2414yes—
451C2×C4×D73C2414yes—
452C2×C4×D73C2414yes—
453C2×C4×D73C2414yes—
454C2×C4×D73C2418yes—
455C2×C4×D73C2414yes—
456C2×C4×D73C2418yes—
457C2×C4×D73C2418yes—
458C2×C4×D73C2418yes—
459C4⋊Dic73C2414yes—
460C4⋊Dic73C2418yes—
461C4⋊Dic73C2414yes—
462C4⋊Dic73C2418yes—
463#11924007C2418yes—
464#11924007C2414yes—
465#11924007C2414yes—
466#11924007C2418yes—
467#11924007C2418yes—
468#11924007C2418yes—
469C22⋊Dic73C2418yes—
470C22⋊Dic73C2414yes—
471C22⋊Dic73C2418yes—
472C22⋊Dic73C2414yes—
473#11924005C2418yes—
474#11924005C2418yes—
475#11924005C2414yes—
476#11924005C2418yes—
477#11924005C2418yes—
478#11924005C2418yes—
479#11924005C2418yes—
480#11924005C2418yes—
481#11924005C2418yes—
482#11924005C2414yes—
483#11924005C2418yes—
484#11924005C2414yes—
485#11924005C2418yes—
486#11924005C2414yes—
487#11924005C2418yes—
488#11924005C2418yes—
489#11924005C2418yes—
490C4×Dic73C2414yes—
491C4×Dic73C2414yes—
492C4×Dic73C2414yes—
493C4×Dic73C2418yes—
494C4×Dic73C2418yes—
495C24×C73C2411yescharacteristic
496C24×C73C2412yes—
497C24×C73C2411yescharacteristic
498C2×D4×C73—24no—
499C2×D4×C73—42no—
500C2×D4×C73—44no—
501C2×D4×C73—44no—
502C2×D4×C73C2414yes—
503C2×D4×C73C2414yes—
504C2×D4×C73C2418yes—
505C2×D4×C73C2418yes—
506C22×C4×C73—24no—
507C22×C4×C73—24no—
508C22×C4×C73—44no—
509C22×C4×C73—44no—
510C22×C4×C73C2411yescharacteristic
511C22×C4×C73C2412yes—
512C22×C4×C73C2411yescharacteristic
513C22×C4×C73C2411yescharacteristic
514C22×C4×C73C2412yes—
515C22×C4×C73C2411yescharacteristic
516C22×C4×C73C2412yes—
517C22×C4×C73C2414yes—
518C22×C4×C73C2414yes—
519C22×C4×C73C2418yes—
520C22×C4×C73C2418yes—
521C22×C4×C73C2411yescharacteristic
522C4⋊C4×C73C2414yes—
523C4⋊C4×C73C2414yes—
524C4⋊C4×C73C2418yes—
525C4⋊C4×C73C2414yes—
526C4⋊C4×C73C2418yes—
527C4⋊C4×C73C2414yes—
528C4⋊C4×C73C2418yes—
529C22⋊C4×C73C2418yes—
530C22⋊C4×C73C2414yes—
531C22⋊C4×C73C2418yes—
532C22⋊C4×C73C2418yes—
533C22⋊C4×C73C2414yes—
534C22⋊C4×C73C2418yes—
535C42×C73C2418yes—
536C42×C73C2414yes—
537C23×C73—22no—
538C23×C73—22no—
539C23×C73—22no—
540C23×C73—24no—
541C23×C73—24no—
542C23×C73—22no—
543C23×C73—22no—
544C23×C73—24no—
545C23×C73—22no—
546C23×C73C2512yes—
547C23×C73C2514yes—
548C23×C73C2512yes—
549C23×C73C2511yescharacteristic
550C22×D73—22no—
551C22×D73—22no—
552C22×D73—22no—
553C22×D73—24no—
554C22×D73—22no—
555C22×D73—22no—
556C22×D73—24no—
557C22×D73—24no—
558C22×D73—22no—
559C22×D73—24no—
560C22×D73—22no—
561C22×D73—24no—
562C22×D73—22no—
563C22×D73—22no—
564C22×D73—24no—
565C22×D73—48no—
566C22×D73—48no—
567C22×D73—48no—
568C22×D73—48no—
569C22×D73—48no—
570C22×D73—48no—
571C22×D73—816no—
572C22×D73—816no—
573C22×D73C2514yes—
574C22×D73C2512yes—
575C22×D73C2514yes—
576C22×D73C2512yes—
577C22×D73C2512yes—
578D4×C73—28no—
579D4×C73—44no—
580D4×C73—48no—
581D4×C73—48no—
582C2×C4×C73—22no—
583C2×C4×C73—22no—
584C2×C4×C73—22no—
585C2×C4×C73—24no—
586C2×C4×C73—24no—
587C2×C4×C73—22no—
588C2×C4×C73—24no—
589C2×C4×C73—28no—
590C2×C4×C73—28no—
591C2×C4×C73—48no—
592C2×C4×C73—48no—
593C2×C4×C73H(5,𝔽2)14yes—
594C2×C4×C73C2512yes—
595C2×C4×C73C2514yes—
596C2×C4×C73C2512yes—
597C2×C4×C73C2512yes—
598C2×C4×C73C2514yes—
599C2×C4×C73C2512yes—
600C2×C4×C73C2514yes—
601C2×C4×C73C2512yes—
602C22⋊D73—28no—
603C22⋊D73—216no—
604C22⋊D73—28no—
605C22⋊D73—48no—
606C22⋊D73—48no—
607C22⋊D73—48no—
608C22⋊D73—48no—
609C22⋊D73—48no—
610C22⋊D73—48no—
611C22⋊D73—44no—
612C22⋊D73—44no—
613C22⋊D73—44no—
614C22⋊D73—44no—
615C2×Dic73—22no—
616C2×Dic73—22no—
617C2×Dic73—22no—
618C2×Dic73—24no—
619C2×Dic73—24no—
620C2×Dic73—22no—
621C2×Dic73—48no—
622C2×Dic73H(5,𝔽2)14yes—
623C2×Dic73C2512yes—
624C2×Dic73C2512yes—
625C2×Dic73C2512yes—
626C2×Dic73C2514yes—
627C2×Dic73C2514yes—
628C2×Dic73C2512yes—
629C2×Dic73C2512yes—
630D292—28no—
631D292—28no—
632D292—48no—
633D292—48no—
634D292—44no—
635D292—48no—
636D292—48no—
637D292—48no—
638D292—48no—
639D292—44no—
640D292—44no—
641C4×D73—28no—
642C4×D73—28no—
643C4×D73—28no—
644C4×D73—216no—
645C4×D73—28no—
646C4×D73—44no—
647C4×D73—48no—
648C4×D73—48no—
649C4×D73—48no—
650Dic146—28no—
651Dic146—216no—
652Dic146—44no—
653Dic146—44no—
654C22×C73—24no—
655C22×C73—22no—
656C22×C73—24no—
657C22×C73—22no—
658C22×C73—22no—
659C22×C73—22no—
660C22×C73—24no—
661C22×C73—22no—
662C22×C73—22no—
663C22×C73—44no—
664C22×C73—48no—
665C22×C73—44no—
666C22×C73C2×H(5,𝔽2)12yes—
667C22×C73C2×H(5,𝔽2)12yes—
668C22×C73#58512yes—
669C22×C73C2611yescharacteristic
670C2×D73—22no—
671C2×D73—22no—
672C2×D73—22no—
673C2×D73—24no—
674C2×D73—22no—
675C2×D73—22no—
676C2×D73—24no—
677C2×D73—24no—
678C2×D73—24no—
679C2×D73—22no—
680C2×D73—22no—
681C2×D73—22no—
682C2×D73—24no—
683C2×D73—24no—
684C2×D73—22no—
685C2×D73—44no—
686C2×D73—44no—
687C2×D73—48no—
688C2×D73—44no—
689C2×D73—48no—
690C2×D73—816no—
691C2×D73—816no—
692C4×C73—24no—
693C4×C73—22no—
694C4×C73—22no—
695C4×C73—22no—
696C4×C73—24no—
697C4×C73—22no—
698C4×C73—24no—
699C4×C73C2×H(5,𝔽2)14yes—
700Dic73—24no—
701Dic73—24no—
702Dic73—22no—
703Dic73—22no—
704Dic73—22no—
705Dic73—22no—
706Dic73C2×H(5,𝔽2)14yes—
707C2×#3546—731nomaximal, Sylow
708C2×C73—42no—
709C2×C73—44no—
710C2×C73—42no—
711C2×C73#354614yescomplemented
712C2×C73C22×H(5,𝔽2)11yescharacteristic
713C2×C73C22×H(5,𝔽2)11yescharacteristic
714C2×C73C2×#58511yescharacteristic
715D73—42no—
716D73—42no—
717D73—44no—
718D73—44no—
719D73—42no—
720#3546—7332no—
721C2×#560—732no—
722C2×#560—732no—
723C2×#556—731no—
724C2×#553—731no—
725C2×#553D7311yescharacteristic, complemented
726C2×#550—731no—
727C2×#550—732no—
728C2×#547—731no—
729C2×#546—732no—
730C2×#546—731no—
731C2×#546—731no—
732C2×D42—731no—
733C2×#542—732no—
734C2×#538—732no—
735C2×#538—732no—
736C2×#537—731no—
737C2×#537—731no—
738C2×#535—732no—
739C2×#535—731no—
740C2×#535—731no—
741C2×#532—731no—
742C2×#532—731no—
743C2×#529—731no—
744C73C2×#354611yescharacteristic, complemented, Sylow
745C22×#41—731no—
746C22×#41—731no—
747C22×#41—731no—
748C22×#41—732no—
749C22×#41—732no—
750C22×#41—731no—
751C23×D4—731no—
752C23×D4—732no—
753C23×D4—731no—
754#560—7332no—
755#560—7332no—
756#556—7316no—
757#553—7316no—
758#553C2×D73116yescomplemented
759#550—7316no—
760#550—7332no—
761#547—7316no—
762#546—7332no—
763#546—7316no—
764#546—7316no—
765D42—7316no—
766#542—7332no—
767#538—7332no—
768#538—7332no—
769#537—7316no—
770#537—7316no—
771#535—7332no—
772#535—7316no—
773#535—7316no—
774#532—7316no—
775#532—7316no—
776C2×C4⋊Q8—731no—
777C2×C4⋊Q8—731no—
778C2×#127—731no—
779C2×#127—731no—
780C2×#127—732no—
781C2×#127—732no—
782C2×#127—732no—
783#529—7316no—
784C2×#126—732no—
785C2×#126—732no—
786C2×#126—732no—
787C2×#126—732no—
788C2×#126C2×D7312yescomplemented
789C2×#125C2×D7311yescharacteristic, complemented
790C2×#124—732no—
791C2×#124—731no—
792C2×#124—731no—
793C2×#124—732no—
794C2×#124—732no—
795C2×#124—731no—
796C2×#124—732no—
797C2×#123—732no—
798C2×#123—732no—
799C2×#123—732no—
800C2×#123—732no—
801C2×#123—732no—
802C2×#123—732no—
803C2×#123C2×D7312yescomplemented
804C2×C22⋊Q8—731no—
805C2×C22⋊Q8—731no—
806C2×C22⋊Q8—732no—
807C2×C22⋊Q8—731no—
808C2×C22⋊Q8—732no—
809C2×C22⋊Q8—732no—
810C2×#121—731no—
811C2×#121—731no—
812C2×#121—732no—
813C2×#121—732no—
814C2×#121—732no—
815C2×#121—732no—
816C2×#121—731no—
817C2×#121—732no—
818C2×#121—732no—
819C2×#121—731no—
820C2×#121—731no—
821C2×#121—731no—
822C2×#121—731no—
823C2×#121—731no—
824C2×#121—732no—
825C2×#121—731no—
826C2×#121—732no—
827C2×#121—731no—
828C2×#121—731no—
829C2×#121—732no—
830C2×#121—732no—
831C2×#121—732no—
832C2×#121—732no—
833C2×#121—732no—
834C2×#121C2×D7311yescharacteristic
835C2×#121C2×D7311yescharacteristic, complemented
836C2×#121C2×D7312yescomplemented
837C2×#120—732no—
838C2×#120—732no—
839C2×#120—732no—
840C2×#120—732no—
841C2×#120—732no—
842C2×#120—732no—
843C2×#120—732no—
844C2×#120—732no—
845C2×C4×Q8—731no—
846C2×C4×Q8—732no—
847C2×C4×D4—732no—
848C2×C4×D4—731no—
849C2×C4×D4—731no—
850C2×C4×D4—731no—
851C2×C4×D4—732no—
852C2×C4×D4—732no—
853C2×C4×D4—732no—
854C2×C4×D4—731no—
855C2×C4×D4—731no—
856C2×C4×D4C2×D7311yescharacteristic, complemented
857C2×C4×D4C2×D7311yescharacteristic, complemented
858C2×C4×D4C2×D7312yescomplemented
859C2×#117—732no—
860C2×#117—731no—
861C2×#117C2×D7311yescharacteristic, complemented
862C22×C4⋊C4—731no—
863C22×C4⋊C4C2×D7311yescharacteristic, complemented
864C22×C22⋊C4—732no—
865C22×C22⋊C4—732no—
866C22×C42—731no—
867C25—732no—
868C25—732no—
869C2×#41—2924no—
870C2×#41—2924no—
871C2×#41—2924no—
872C2×#41—2928no—
873C2×#41—2928no—
874C2×#41—2924no—
875C2×#41—738no—
876C2×#41—738no—
877C2×#41—738no—
878C2×#41—7316no—
879C2×#41—7316no—
880C2×#41—738no—
881C22×Q8—731no—
882C22×Q8—731no—
883C22×Q8—731no—
884C22×Q8—732no—
885C22×D4—2924no—
886C22×D4—2924no—
887C22×D4—2928no—
888C22×D4—732no—
889C22×D4—731no—
890C22×D4—732no—
891C22×D4—731no—
892C22×D4—731no—
893C22×D4—732no—
894C22×D4—732no—
895C22×D4—732no—
896C22×D4—732no—
897C22×D4—731no—
898C22×D4—738no—
899C22×D4—7316no—
900C22×D4—731no—
901C22×D4—732no—
902C22×D4—731no—
903C22×D4—731no—
904C22×D4—732no—
905C22×D4—732no—
906C22×D4—731no—
907C22×D4—732no—
908C22×D4—732no—
909C22×D4—732no—
910C22×D4—732no—
911C22×D4—731no—
912C22×D4—738no—
913C22×D4—731no—
914C22×D4—731no—
915C22×D4C22×D7311yescharacteristic
916C22×D4C22×D7311yescharacteristic
917C22×D4C22×D7312yes—
918C22×D4C22×D7312yes—
919C23×C4—732no—
920C23×C4—732no—
921C23×C4—732no—
922C23×C4—732no—
923C23×C4—731no—
924C23×C4—731no—
925C23×C4—732no—
926C23×C4—731no—
927C23×C4—731no—
928C23×C4—731no—
929C23×C4C22×D7311yescharacteristic
930C23×C4C22×D7311yescharacteristic
931C23×C4C22×D7312yes—
932C23×C4C22×D7312yes—
933C4⋊Q8—738no—
934C4⋊Q8—738no—
935#127—738no—
936#127—738no—
937#127—7316no—
938#127—7316no—
939#127—7316no—
940#126—7316no—
941#126—7316no—
942#126—7316no—
943#126—7316no—
944#126C22×D73116yescomplemented
945#125C22×D7318yescomplemented
946#124—7316no—
947#124—738no—
948#124—738no—
949#124—7316no—
950#124—7316no—
951#124—738no—
952#124—7316no—
953#123—7316no—
954#123—7316no—
955#123—7316no—
956#123—7316no—
957#123—7316no—
958#123—7316no—
959#123C22×D73116yescomplemented
960C22⋊Q8—738no—
961C22⋊Q8—738no—
962C22⋊Q8—7316no—
963C22⋊Q8—738no—
964C22⋊Q8—7316no—
965C22⋊Q8—7316no—
966#121—738no—
967#121—738no—
968#121—7316no—
969#121—7316no—
970#121—7316no—
971#121—7316no—
972#121—738no—
973#121—7316no—
974#121—7316no—
975#121—738no—
976#121—738no—
977#121—738no—
978#121—738no—
979#121—738no—
980#121—7316no—
981#121—738no—
982#121—7316no—
983#121—738no—
984#121—738no—
985#121—7316no—
986#121—7316no—
987#121—7316no—
988#121—7316no—
989#121—7316no—
990#121C22×D7318yes—
991#121C22×D7318yescomplemented
992#121C22×D73116yescomplemented
993#120—7316no—
994#120—7316no—
995#120—7316no—
996#120—7316no—
997#120—7316no—
998#120—7316no—
999#120—7316no—
1000#120—7316no—
1001C4×Q8—738no—
1002C4×Q8—7316no—
1003C4×D4—7316no—
1004C4×D4—738no—
1005C4×D4—738no—
1006C4×D4—738no—
1007C4×D4—7316no—
1008C4×D4—7316no—
1009C4×D4—7316no—
1010C4×D4—738no—
1011C4×D4—738no—
1012C4×D4C22×D7318yescomplemented
1013C4×D4C22×D7318yescomplemented
1014C4×D4C22×D73116yescomplemented
1015#117—7316no—
1016#117—738no—
1017#117C22×D7318yescomplemented
1018C2×C4⋊C4—731no—
1019C2×C4⋊C4—732no—
1020C2×C4⋊C4—732no—
1021C2×C4⋊C4—731no—
1022C2×C4⋊C4—731no—
1023C2×C4⋊C4—732no—
1024C2×C4⋊C4—731no—
1025C2×C4⋊C4—732no—
1026C2×C4⋊C4—732no—
1027C2×C4⋊C4—732no—
1028C2×C4⋊C4—738no—
1029C2×C4⋊C4C22×D7311yescharacteristic
1030C2×C4⋊C4C22×D7311yescharacteristic
1031C2×C4⋊C4C22×D7312yes—
1032C2×C4⋊C4C22×D7311yescharacteristic
1033C2×C4⋊C4C22×D7312yes—
1034C2×C4⋊C4C22×D7312yes—
1035C2×C4⋊C4C22×D7311yescharacteristic
1036C2×C4⋊C4C22×D7318yescomplemented
1037C2×C22⋊C4—732no—
1038C2×C22⋊C4—731no—
1039C2×C22⋊C4—732no—
1040C2×C22⋊C4—731no—
1041C2×C22⋊C4—732no—
1042C2×C22⋊C4—731no—
1043C2×C22⋊C4—732no—
1044C2×C22⋊C4—732no—
1045C2×C22⋊C4—732no—
1046C2×C22⋊C4—7316no—
1047C2×C22⋊C4—732no—
1048C2×C22⋊C4—732no—
1049C2×C22⋊C4—732no—
1050C2×C22⋊C4—731no—
1051C2×C22⋊C4—731no—
1052C2×C22⋊C4—732no—
1053C2×C22⋊C4—732no—
1054C2×C22⋊C4—732no—
1055C2×C22⋊C4—732no—
1056C2×C22⋊C4—732no—
1057C2×C22⋊C4—732no—
1058C2×C22⋊C4—731no—
1059C2×C22⋊C4—7316no—
1060C2×C22⋊C4C22×D7311yescharacteristic
1061C2×C22⋊C4C22×D7312yes—
1062C2×C22⋊C4C22×D7312yes—
1063C2×C22⋊C4C22×D7311yescharacteristic
1064C2×C22⋊C4C22×D7312yes—
1065C2×C22⋊C4C22×D7312yes—
1066C2×C42—731no—
1067C2×C42—732no—
1068C2×C42—732no—
1069C2×C42—731no—
1070C2×C42—731no—
1071C2×C42—738no—
1072C2×C42C22×D7312yes—
1073C2×C42C22×D7311yescharacteristic
1074C24—2924no—
1075C24—2924no—
1076C24—2924no—
1077C24—2924no—
1078C24—2924no—
1079C24—2924no—
1080C24—738no—
1081C24—738no—
1082C24—732no—
1083C24—731no—
1084C24—732no—
1085C24—731no—
1086C24—731no—
1087C24C23×D7311yescharacteristic
1088C24C23×D7312yes—
1089C24C23×D7311yescharacteristic
1090#41—29216no—
1091#41—29216no—
1092#41—29216no—
1093#41—29232no—
1094#41—29232no—
1095#41—29216no—
1096C2×Q8—2922no—
1097C2×Q8—2922no—
1098C2×Q8—734no—
1099C2×Q8—734no—
1100C2×Q8—734no—
1101C2×Q8—738no—
1102C2×Q8—1468no—
1103C2×Q8—1464no—
1104C2×D4—24no—
1105C2×D4—44no—
1106C2×D4—42no—
1107C2×D4—44no—
1108C2×D4—2924no—
1109C2×D4—2924no—
1110C2×D4—2922no—
1111C2×D4—2924no—
1112C2×D4—2924no—
1113C2×D4—2924no—
1114C2×D4—2924no—
1115C2×D4—2922no—
1116C2×D4—2922no—
1117C2×D4—29216no—
1118C2×D4—29216no—
1119C2×D4—29232no—
1120C2×D4—2924no—
1121C2×D4—2924no—
1122C2×D4—2924no—
1123C2×D4—2924no—
1124C2×D4—2922no—
1125C2×D4—2924no—
1126C2×D4—2924no—
1127C2×D4—2922no—
1128C2×D4—2922no—
1129C2×D4—2922no—
1130C2×D4—738no—
1131C2×D4—734no—
1132C2×D4—738no—
1133C2×D4—734no—
1134C2×D4—734no—
1135C2×D4—738no—
1136C2×D4—738no—
1137C2×D4—738no—
1138C2×D4—738no—
1139C2×D4—734no—
1140C2×D4—734no—
1141C2×D4—738no—
1142C2×D4—734no—
1143C2×D4—734no—
1144C2×D4—738no—
1145C2×D4—738no—
1146C2×D4—734no—
1147C2×D4—738no—
1148C2×D4—738no—
1149C2×D4—738no—
1150C2×D4—738no—
1151C2×D4—734no—
1152C2×D4—734no—
1153C2×D4—734no—
1154C2×D4—1464no—
1155C2×D4—1468no—
1156C2×D4—1464no—
1157C2×D4—1464no—
1158C2×D4—1464no—
1159C2×D4C23×D7314yes—
1160C2×D4C23×D7314yes—
1161C2×D4C23×D7318yes—
1162C2×D4C23×D7318yes—
1163C22×C4—24no—
1164C22×C4—24no—
1165C22×C4—44no—
1166C22×C4—44no—
1167C22×C4—2922no—
1168C22×C4—2924no—
1169C22×C4—2924no—
1170C22×C4—2924no—
1171C22×C4—2924no—
1172C22×C4—738no—
1173C22×C4—734no—
1174C22×C4—738no—
1175C22×C4—738no—
1176C22×C4—738no—
1177C22×C4—731no—
1178C22×C4—731no—
1179C22×C4—731no—
1180C22×C4—731no—
1181C22×C4—732no—
1182C22×C4—732no—
1183C22×C4—731no—
1184C22×C4—734no—
1185C22×C4—734no—
1186C22×C4—734no—
1187C22×C4—738no—
1188C22×C4—734no—
1189C22×C4—1468no—
1190C22×C4—1464no—
1191C22×C4—1464no—
1192C22×C4—1464no—
1193C22×C4—1464no—
1194C22×C4C23×D7314yes—
1195C22×C4C23×D7314yes—
1196C22×C4C23×D7312yes—
1197C22×C4C23×D7311yescharacteristic
1198C22×C4C23×D7311yescharacteristic
1199C22×C4C23×D7311yescharacteristic
1200C22×C4C23×D7312yes—
1201C22×C4C23×D7311yescharacteristic
1202C22×C4C23×D7312yes—
1203C22×C4C23×D7318yes—
1204C22×C4C23×D7318yes—
1205C22×C4C23×D7311yescharacteristic
1206C4⋊C4—738no—
1207C4⋊C4—734no—
1208C4⋊C4—734no—
1209C4⋊C4—738no—
1210C4⋊C4—738no—
1211C4⋊C4—738no—
1212C4⋊C4—734no—
1213C4⋊C4—738no—
1214C4⋊C4—734no—
1215C4⋊C4—738no—
1216C4⋊C4C23×D7314yes—
1217C4⋊C4C23×D7314yes—
1218C4⋊C4C23×D7318yes—
1219C4⋊C4C23×D7314yes—
1220C4⋊C4C23×D7318yes—
1221C4⋊C4C23×D7318yes—
1222C4⋊C4C23×D7314yes—
1223C22⋊C4—738no—
1224C22⋊C4—734no—
1225C22⋊C4—738no—
1226C22⋊C4—734no—
1227C22⋊C4—738no—
1228C22⋊C4—734no—
1229C22⋊C4—738no—
1230C22⋊C4—738no—
1231C22⋊C4—738no—
1232C22⋊C4—738no—
1233C22⋊C4—738no—
1234C22⋊C4—738no—
1235C22⋊C4—734no—
1236C22⋊C4—734no—
1237C22⋊C4—738no—
1238C22⋊C4—738no—
1239C22⋊C4—738no—
1240C22⋊C4—738no—
1241C22⋊C4—738no—
1242C22⋊C4—738no—
1243C22⋊C4—734no—
1244C22⋊C4C23×D7314yes—
1245C22⋊C4C23×D7318yes—
1246C22⋊C4C23×D7318yes—
1247C22⋊C4C23×D7314yes—
1248C22⋊C4C23×D7318yes—
1249C22⋊C4C23×D7318yes—
1250C42—734no—
1251C42—734no—
1252C42—734no—
1253C42—738no—
1254C42—738no—
1255C42C23×D7314yes—
1256C42C23×D7318yes—
1257C23—22no—
1258C23—24no—
1259C23—22no—
1260C23—22no—
1261C23—22no—
1262C23—24no—
1263C23—22no—
1264C23—24no—
1265C23—22no—
1266C23—2928no—
1267C23—2928no—
1268C23—2928no—
1269C23—2928no—
1270C23—2928no—
1271C23—2928no—
1272C23—58416no—
1273C23—58416no—
1274C23—734no—
1275C23—732no—
1276C23—734no—
1277C23—732no—
1278C23—732no—
1279C23—1462no—
1280C23—1464no—
1281C23—1462no—
1282C23—1464no—
1283C23—1462no—
1284C23—1464no—
1285C23—1462no—
1286C23—1462no—
1287C23—1462no—
1288C23—1464no—
1289C23—1462no—
1290C23—1462no—
1291C23—1464no—
1292C23—1464no—
1293C23—1462no—
1294C23C24×D7312yes—
1295C23C24×D7314yes—
1296C23C24×D7312yes—
1297C23C24×D7311yescharacteristic
1298Q8—2924no—
1299Q8—2924no—
1300Q8—14616no—
1301Q8—1468no—
1302D4—28no—
1303D4—48no—
1304D4—44no—
1305D4—48no—
1306D4—2928no—
1307D4—2928no—
1308D4—2928no—
1309D4—2928no—
1310D4—2924no—
1311D4—2924no—
1312D4—2924no—
1313D4—2928no—
1314D4—2928no—
1315D4—2928no—
1316D4—2928no—
1317D4—2928no—
1318D4—2924no—
1319D4—2928no—
1320D4—2928no—
1321D4—2924no—
1322D4—2924no—
1323D4—2924no—
1324D4—2928no—
1325D4—1468no—
1326D4—14616no—
1327D4—1468no—
1328D4—1468no—
1329D4—1468no—
1330C2×C4—22no—
1331C2×C4—24no—
1332C2×C4—24no—
1333C2×C4—22no—
1334C2×C4—22no—
1335C2×C4—22no—
1336C2×C4—24no—
1337C2×C4—28no—
1338C2×C4—28no—
1339C2×C4—48no—
1340C2×C4—48no—
1341C2×C4—2928no—
1342C2×C4—2928no—
1343C2×C4—2928no—
1344C2×C4—2924no—
1345C2×C4—2928no—
1346C2×C4—734no—
1347C2×C4—732no—
1348C2×C4—732no—
1349C2×C4—732no—
1350C2×C4—732no—
1351C2×C4—734no—
1352C2×C4—734no—
1353C2×C4—732no—
1354C2×C4—14616no—
1355C2×C4—1468no—
1356C2×C4—1464no—
1357C2×C4—1462no—
1358C2×C4—1464no—
1359C2×C4—1462no—
1360C2×C4—1462no—
1361C2×C4—1462no—
1362C2×C4—1468no—
1363C2×C4—1468no—
1364C2×C4—1468no—
1365C2×C4#1455663714yes—
1366C2×C4C24×D7314yes—
1367C2×C4C24×D7312yes—
1368C2×C4C24×D7312yes—
1369C2×C4C24×D7312yes—
1370C2×C4C24×D7314yes—
1371C2×C4C24×D7312yes—
1372C2×C4C24×D7314yes—
1373C2×C4C24×D7312yes—
1374C22—22no—
1375C22—24no—
1376C22—22no—
1377C22—22no—
1378C22—22no—
1379C22—24no—
1380C22—22no—
1381C22—24no—
1382C22—22no—
1383C22—44no—
1384C22—48no—
1385C22—44no—
1386C22—2928no—
1387C22—2924no—
1388C22—2928no—
1389C22—2924no—
1390C22—2924no—
1391C22—58416no—
1392C22—58416no—
1393C22—1462no—
1394C22—1464no—
1395C22—1462no—
1396C22—1464no—
1397C22—1462no—
1398C22—1464no—
1399C22—1462no—
1400C22—1462no—
1401C22—1462no—
1402C22—1464no—
1403C22—1462no—
1404C22—1462no—
1405C22—1464no—
1406C22—1464no—
1407C22—1462no—
1408C22H(5,𝔽2)×D7312yes—
1409C22C2×#1455663712yes—
1410C22#1798942312yes—
1411C22C25×D7311yescharacteristic
1412C4—22no—
1413C4—24no—
1414C4—24no—
1415C4—22no—
1416C4—22no—
1417C4—22no—
1418C4—24no—
1419C4—734no—
1420C4—1464no—
1421C4—1462no—
1422C4—1464no—
1423C4—1462no—
1424C4—1462no—
1425C4—1462no—
1426C4C2×#1455663714yes—
1427C2—42no—
1428C2—44no—
1429C2—42no—
1430C2—2924no—
1431C2—2922no—
1432C2—2924no—
1433C2—2922no—
1434C2—2922no—
1435C2#2262430214yesdirect product factor
1436C2C2×H(5,𝔽2)×D7311yescharacteristic
1437C2C22×#1455663711yescharacteristic
1438C2C2×#1798942311yescharacteristic
subgroupG/H
centerC23C24×D73
commutator, cosocleC22×C73C26
FrattiniC22C25×D73
FittingC2×#553×C73C2
socleC23×C73C25
hypercenterC2×#553D73
hypocenterC73C2×#3546
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#553

Complements

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

NH ≅ G/Ntype
1. #22624302C2direct (N × H)
2. C2×#17989328C2semidirect
3. C2×#17989325C2semidirect
4. C2×#17989305C2semidirect
5. C2×#17989290C2semidirect
6. C2×#17989258C2semidirect
7. C2×#17989255C2semidirect
8. C2×#17989238C2semidirect
9. C2×#17989233C2semidirect
10. C2×#17989232C2semidirect
11. C2×#17989229C2semidirect
12. C2×#17989221C2semidirect
13. C2×#17989203C2semidirect
14. C2×#17989173C2semidirect
15. C2×#17989170C2semidirect
16. C2×#17989168C2semidirect
17. C2×#17989166C2semidirect
18. C2×#17989156C2semidirect
19. C2×#17989153C2semidirect
20. C2×#17989153C2semidirect
21. C2×#17989134C2semidirect
22. C2×#17989134C2semidirect
23. C2×#17989122C2semidirect
24. C2×#553×C73C2semidirect
25. C22×#11924028C22semidirect
26. C22×#11924028C22semidirect
27. C22×#11924028C22semidirect
28. C22×#11924028C22semidirect
29. C22×#11924028C22semidirect
30. C22×#11924027C22semidirect
34. #17989328C22semidirect
35. #17989325C22semidirect
36. #17989305C22semidirect
37. #17989290C22semidirect
38. #17989258C22semidirect
39. #17989255C22semidirect
40. #17989238C22semidirect
41. #17989233C22semidirect
42. #17989232C22semidirect
43. #17989229C22semidirect
44. #17989221C22semidirect
45. #17989203C22semidirect
46. #17989173C22semidirect
47. #17989170C22semidirect
48. #17989168C22semidirect
49. #17989166C22semidirect
50. #17989156C22semidirect
51. #17989153C22semidirect
52. #17989153C22semidirect
53. #17989134C22semidirect
54. #17989134C22semidirect
55. C2×#14556590C22semidirect
56. C2×#14556590C22semidirect
57. C2×#14556588C22semidirect
60. C2×#14556587C22semidirect
61. C2×#14556587C22semidirect
62. #17989122C22semidirect
63. C2×#14556586C22semidirect
64. C2×#14556586C22semidirect
65. C2×#14556585C22semidirect
66. C2×#14556584C22semidirect
68. C2×#14556579C22semidirect
70. C2×#14556577C22semidirect
71. C2×#14556577C22semidirect
72. C2×#14556577C22semidirect
73. C2×#14556577C22semidirect
74. C2×#14556576C22semidirect
75. C2×#14556576C22semidirect
76. C2×#14556576C22semidirect
77. C2×#14556576C22semidirect
78. C2×#14556575C22semidirect
79. C2×#14556574C22semidirect
80. C2×#14556571C22semidirect
81. C2×#14556571C22semidirect
82. C2×#14556571C22semidirect
83. C2×#14556570C22semidirect
84. C2×#14556569C22semidirect
85. C2×#14556568C22semidirect
89. C2×#14556566C22semidirect
90. C2×#14556566C22semidirect
91. C2×#14556566C22semidirect
92. C2×#14556566C22semidirect
93. C2×#14556566C22semidirect
95. C2×#14556565C22semidirect
96. C2×#14556565C22semidirect
97. C2×#14556565C22semidirect
100. C2×#14556564C22semidirect
101. C2×#14556564C22semidirect
102. C2×#14556564C22semidirect
103. C2×#14556564C22semidirect
104. C2×#14556564C22semidirect
105. C2×#14556563C22semidirect
106. C2×#14556563C22semidirect
107. C2×#14556562C22semidirect
108. C2×#14556562C22semidirect
109. C2×#14556562C22semidirect
111. C2×#14556561C22semidirect
112. C2×#14556561C22semidirect
113. C2×#14556561C22semidirect
114. C2×#14556561C22semidirect
116. C2×#14556559C22semidirect
117. C2×#14556559C22semidirect
118. C2×C4×Dic146C22semidirect
119. C2×#14556556C22semidirect
120. C2×C4×D292C22semidirect
121. C2×C4×D292C22semidirect
123. C2×#14556553C22semidirect
124. C2×#14556553C22semidirect
126. C2×C4×C22⋊D73C22semidirect
127. C2×C4×C22⋊D73C22semidirect
128. C2×#14556551C22semidirect
129. C2×#14556549C22semidirect
130. C2×#14556549C22semidirect
131. C2×C4⋊C4×D73C22semidirect
132. C22×#11924005C22semidirect
133. C2×C22⋊C4×D73C22semidirect
134. C2×C42×D73C22semidirect
135. #553×C73C22semidirect
136. C2×#126×C73C22semidirect
137. C2×#125×C73C22semidirect
138. C2×#123×C73C22semidirect
140. C2×#121×C73C22semidirect
141. C2×#121×C73C22semidirect
142. C2×C4×D4×C73C22semidirect
143. C2×C4×D4×C73C22semidirect
144. C2×C4×D4×C73C22semidirect
145. C2×#117×C73C22semidirect
146. C22×C4⋊C4×C73C22semidirect
154. C2×#11924028C23semidirect
155. C2×#11924028C23semidirect
156. C2×#11924028C23semidirect
157. C2×#11924028C23semidirect
158. C2×#11924028C23semidirect
160. C2×#11924027C23semidirect
205. #14556590C23semidirect
206. #14556590C23semidirect
207. #14556588C23semidirect
210. #14556587C23semidirect
211. #14556587C23semidirect
212. #14556586C23semidirect
213. #14556586C23semidirect
214. #14556585C23semidirect
215. #14556584C23semidirect
217. #14556579C23semidirect
219. #14556577C23semidirect
220. #14556577C23semidirect
221. #14556577C23semidirect
222. #14556577C23semidirect
223. #14556576C23semidirect
224. #14556576C23semidirect
225. #14556576C23semidirect
226. #14556576C23semidirect
227. #14556575C23semidirect
228. #14556574C23semidirect
229. #14556571C23semidirect
230. #14556571C23semidirect
231. #14556571C23semidirect
232. #14556570C23semidirect
233. #14556569C23semidirect
234. #14556568C23semidirect
238. #14556566C23semidirect
239. #14556566C23semidirect
240. #14556566C23semidirect
241. #14556566C23semidirect
242. #14556566C23semidirect
244. #14556565C23semidirect
245. #14556565C23semidirect
246. #14556565C23semidirect
249. #14556564C23semidirect
250. #14556564C23semidirect
251. #14556564C23semidirect
252. #14556564C23semidirect
253. #14556564C23semidirect
254. #14556563C23semidirect
255. #14556563C23semidirect
256. #14556562C23semidirect
257. #14556562C23semidirect
258. #14556562C23semidirect
260. #14556561C23semidirect
261. #14556561C23semidirect
262. #14556561C23semidirect
263. #14556561C23semidirect
265. #14556559C23semidirect
266. #14556559C23semidirect
267. C4×Dic146C23semidirect
268. #14556556C23semidirect
269. C4×D292C23semidirect
270. C4×D292C23semidirect
272. #14556553C23semidirect
273. #14556553C23semidirect
275. C4×C22⋊D73C23semidirect
276. C4×C22⋊D73C23semidirect
277. #14556551C23semidirect
278. #14556549C23semidirect
279. #14556549C23semidirect
290. C4⋊C4×D73C23semidirect
312. C2×#11924005C23semidirect
313. C22⋊C4×D73C23semidirect
319. C42×D73C23semidirect
328. #126×C73C23semidirect
329. #125×C73C23semidirect
330. #123×C73C23semidirect
332. #121×C73C23semidirect
333. #121×C73C23semidirect
334. C4×D4×C73C23semidirect
335. C4×D4×C73C23semidirect
336. C4×D4×C73C23semidirect
337. #117×C73C23semidirect
345. C2×C4⋊C4×C73C23semidirect
711. C2×C73#3546semidirect
725. C2×#553D73semidirect
744. C73C2×#3546semidirect
758. #553C2×D73semidirect
788. C2×#126C2×D73semidirect
789. C2×#125C2×D73semidirect
803. C2×#123C2×D73semidirect
835. C2×#121C2×D73semidirect
836. C2×#121C2×D73semidirect
856. C2×C4×D4C2×D73semidirect
857. C2×C4×D4C2×D73semidirect
858. C2×C4×D4C2×D73semidirect
861. C2×#117C2×D73semidirect
863. C22×C4⋊C4C2×D73semidirect
944. #126C22×D73semidirect
945. #125C22×D73semidirect
959. #123C22×D73semidirect
991. #121C22×D73semidirect
992. #121C22×D73semidirect
1012. C4×D4C22×D73semidirect
1013. C4×D4C22×D73semidirect
1014. C4×D4C22×D73semidirect
1017. #117C22×D73semidirect
1036. C2×C4⋊C4C22×D73semidirect
1435. C2#22624302direct (N × H)

Maximal subgroups

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

subgroupindex
#226243022
C2×#179893282
C2×#179893252
C2×#179893052
C2×#179892902
C2×#179892582
C2×#179892552
C2×#179892382
C2×#179892332
C2×#179892322
C2×#179892292
C2×#179892212
C2×#179892032
C2×#179891732
C2×#179891702
C2×#179891682
C2×#179891662
C2×#179891562
C2×#179891532
C2×#179891342
C2×#179891222
C2×#553×C732
C2×#354673