Finite Group Databasebeta

← #33956757

Subgroups — #33956757

Order 18688.

2362 conjugacy classes of subgroups.

The subgroup lattice has 1182 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989098C211yesmaximal, characteristic, complemented
2#22620768C214yesmaximal, complemented
3#22620757C212yesmaximal, complemented
4#22620741C212yesmaximal, complemented
5#22620719C214yesmaximal, complemented
6#22620708C212yesmaximal, complemented
7#22620692C212yesmaximal, complemented
8#22619875C211yesmaximal, characteristic, complemented
9#22619867C211yesmaximal, characteristic, complemented
10#22619862C212yesmaximal, complemented
11#22619557C212yesmaximal, complemented
12#22619546C212yesmaximal, complemented
13#22619189C211yesmaximal, characteristic, complemented
14#22619181C211yesmaximal, characteristic, complemented
15#22619173C212yesmaximal, complemented
16C2×#17988551C211yesmaximal, characteristic, complemented
17C2×#525×C73C211yesmaximal, characteristic, complemented
18C22×#11924028C2211yescharacteristic
19C2×#14556622C2212yescomplemented
20C2×#14556617C2212yescomplemented
21C22×#11924012C2212yescomplemented
22#17989098—21no—
23#17989098—21no—
24#17989098—21no—
25#17989098—21no—
26#17989098C2212yes—
27#17989098C2212yes—
28#17989098C2212yescomplemented
29#17989098C2212yescomplemented
30C2×#14556574—21no—
31C2×#14556570C2211yescharacteristic, complemented
32C2×#14556570C2211yescharacteristic, complemented
33C2×#14556565C2211yescharacteristic, complemented
34C2×#14556565C2211yescharacteristic, complemented
35C2×#14556560—21no—
36C2×C4×C22⋊D73—21no—
37C2×C4×C22⋊D73—21no—
38C2×#14556550C2211yescharacteristic
39#17988928C2214yescomplemented
40#17988928C2214yescomplemented
41#17988925C2214yescomplemented
42#17988920C2212yescomplemented
43#17988915C2212yescomplemented
44#17988911C2214yescomplemented
45#17988911C2214yescomplemented
46#17988908C2214yescomplemented
47#17988903C2212yescomplemented
48#17988898C2212yescomplemented
49#17988843C2214yescomplemented
50#17988838C2214yescomplemented
51#17988835C2214yescomplemented
52#17988831C2214yescomplemented
53#17988826C2214yescomplemented
54#17988821C2214yescomplemented
55#17988818C2214yescomplemented
56#17988814C2214yescomplemented
57#17988749C2214yescomplemented
58#17988749C2214yescomplemented
59#17988747C2214yescomplemented
60#17988742C2212yescomplemented
61#17988737C2212yescomplemented
62#17988732C2214yescomplemented
63#17988732C2214yescomplemented
64#17988730C2214yescomplemented
65#17988725C2212yescomplemented
66#17988720C2212yescomplemented
67#17988627C2212yescomplemented
68#17988627C2212yescomplemented
69#17988596C2212yescomplemented
70#17988592C2212yescomplemented
71#17988586C2212yescomplemented
72#17988586C2212yescomplemented
73#17988551C2211yescharacteristic
74#17988551C2211yescharacteristic
75#17988551C2212yescomplemented
76#17988551C2212yescomplemented
77#17988551C2212yescomplemented
78C2×C22⋊#10596831C2212yescomplemented
79C2×C22⋊#10596831C2212yescomplemented
80C22×#41×C73C2211yescharacteristic, complemented
81C24×C4×C73C2211yescharacteristic
82#525×C73—21no—
83#525×C73—21no—
84#525×C73—21no—
85#525×C73—21no—
86#525×C73C2212yes—
87#525×C73C2212yes—
88#525×C73C2212yescomplemented
89#525×C73C2212yescomplemented
90C2×#123×C73—21no—
91C2×C22⋊Q8×C73C2211yescharacteristic
92C2×C22⋊Q8×C73C2211yescharacteristic, complemented
93C2×#121×C73C2211yescharacteristic
94C2×#121×C73C2211yescharacteristic, complemented
95C2×#120×C73—21no—
96C2×C4×D4×C73—21no—
97C2×C4×D4×C73—21no—
98C2×#117×C73C2211yescharacteristic, complemented
99C2×#11924028—21no—
100C2×#11924028—21no—
101C2×#11924028—44no—
102C2×#11924028C2312yes—
103C2×#11924028C2312yes—
104C22×Dic146C2311yescharacteristic
105C22×D292C2311yescharacteristic
106C22×C22⋊D73—21no—
107C22×C22⋊D73—21no—
108C22×C22⋊D73—21no—
109C22×C4×D73—21no—
110#14556622—44no—
111#14556617—44no—
112C2×#11924018C2314yescomplemented
113C2×#11924016C2314yescomplemented
114C2×#11924015C2314yescomplemented
115C2×#11924013C2314yescomplemented
116C2×#11924012—44no—
117C2×#11924012C2312yes—
118C2×#11924012C2312yes—
119C2×#11924012C2314yes—
120C22×#10596831C2314yes—
121#14556574—22no—
122#14556574—22no—
123#14556574—22no—
124#14556574—22no—
125#14556570—21no—
126#14556570—21no—
127#14556570—21no—
128#14556570—21no—
129#14556570C2312yes—
130#14556570C2312yes—
131#14556570C2312yes—
132#14556570C2312yes—
133#14556565—21no—
134#14556565—21no—
135#14556565—21no—
136#14556565—21no—
137#14556565C2312yes—
138#14556565C2312yes—
139#14556565C2312yes—
140#14556565C2312yes—
141#14556560—22no—
142#14556560—22no—
143#14556560—22no—
144#14556560—22no—
145C4×C22⋊D73—22no—
146C4×C22⋊D73—22no—
147C4×C22⋊D73—22no—
148C4×C22⋊D73—22no—
149C4×C22⋊D73—22no—
150C4×C22⋊D73—22no—
151C4×C22⋊D73—22no—
152C4×C22⋊D73—22no—
153#14556550—21no—
154#14556550—21no—
155#14556550C2312yes—
156#14556550C2312yes—
157C2×C4⋊Dic73C2311yescharacteristic
158C2×C4⋊Dic73C2311yescharacteristic
159C2×#11924007—21no—
160C2×#11924007—21no—
161C2×C22⋊Dic73—21no—
162C2×C22⋊Dic73—21no—
163C2×C22⋊Dic73—21no—
164C2×#11924005—21no—
165C2×#11924005—21no—
166C2×C4×Dic73—21no—
167#14556524C2314yescomplemented
168#14556524C2314yescomplemented
169#14556522C2314yescomplemented
170#14556522C2314yescomplemented
171#14556515C2314yescomplemented
172#14556515C2314yescomplemented
173#14556514C2314yescomplemented
174#14556514C2314yescomplemented
175#14556512C2314yescomplemented
176#14556512C2314yescomplemented
177#14556511C2314yescomplemented
178#14556511C2314yescomplemented
179C22⋊#10596831C2312yes—
180C22⋊#10596831C2312yes—
181C22⋊#10596831C2314yes—
182C22⋊#10596831C2314yes—
183C22⋊#10596831C2312yes—
184C22⋊#10596831C2312yes—
185C25×C73D411yescharacteristic
186C2×#41×C73—21no—
187C2×#41×C73—21no—
188C2×#41×C73—44no—
189C2×#41×C73C2312yes—
190C2×#41×C73C2312yes—
191C22×Q8×C73C2311yescharacteristic
192C22×D4×C73—21no—
193C22×D4×C73—21no—
194C22×D4×C73—21no—
195C22×D4×C73C2311yescharacteristic
196C23×C4×C73—21no—
197C23×C4×C73—44no—
198C23×C4×C73D411yescharacteristic
199C23×C4×C73D411yescharacteristic
200C23×C4×C73D411yescharacteristic
201C23×C4×C73D411yescharacteristic
202C23×C4×C73D411yescharacteristic
203C23×C4×C73D411yescharacteristic
204C23×C4×C73D411yescharacteristic
205C23×C4×C73C2311yescharacteristic
206C23×C4×C73C2311yescharacteristic
207C23×C4×C73C2311yescharacteristic
208C23×C4×C73C2311yescharacteristic
209C23×C4×C73C2311yescharacteristic
210C23×C4×C73C2311yescharacteristic
211C23×C4×C73C2311yescharacteristic
212#123×C73—22no—
213#123×C73—22no—
214#123×C73—22no—
215#123×C73—22no—
216C22⋊Q8×C73—21no—
217C22⋊Q8×C73—21no—
218C22⋊Q8×C73—21no—
219C22⋊Q8×C73—21no—
220C22⋊Q8×C73C2312yes—
221C22⋊Q8×C73C2312yes—
222C22⋊Q8×C73C2312yes—
223C22⋊Q8×C73C2312yes—
224#121×C73—21no—
225#121×C73—21no—
226#121×C73—21no—
227#121×C73—21no—
228#121×C73C2312yes—
229#121×C73C2312yes—
230#121×C73C2312yes—
231#121×C73C2312yes—
232#120×C73—22no—
233#120×C73—22no—
234#120×C73—22no—
235#120×C73—22no—
236C4×D4×C73—22no—
237C4×D4×C73—22no—
238C4×D4×C73—22no—
239C4×D4×C73—22no—
240C4×D4×C73—22no—
241C4×D4×C73—22no—
242C4×D4×C73—22no—
243C4×D4×C73—22no—
244#117×C73—21no—
245#117×C73—21no—
246#117×C73C2312yes—
247#117×C73C2312yes—
248C2×C4⋊C4×C73—21no—
249C2×C4⋊C4×C73—21no—
250C2×C4⋊C4×C73C2311yescharacteristic
251C2×C4⋊C4×C73C2311yescharacteristic
252C2×C22⋊C4×C73—21no—
253C2×C22⋊C4×C73—21no—
254C2×C22⋊C4×C73—21no—
255C2×C22⋊C4×C73—21no—
256C2×C22⋊C4×C73—21no—
257C2×C42×C73—21no—
258C23×D73—21no—
259#11924028—24no—
260#11924028—24no—
261#11924028—42no—
262#11924028—42no—
263#11924028—44no—
264#11924028—44no—
265C2×Dic146—21no—
266C2×Dic146—42no—
267C2×Dic146C2412yes—
268C2×D292—21no—
269C2×D292—42no—
270C2×D292C2412yes—
271C2×C22⋊D73—22no—
272C2×C22⋊D73—22no—
273C2×C22⋊D73—22no—
274C2×C22⋊D73—22no—
275C2×C22⋊D73—22no—
276C2×C22⋊D73—22no—
277C2×C22⋊D73—44no—
278C2×C22⋊D73—44no—
279C2×C22⋊D73—44no—
280C22×Dic73—21no—
281C22×Dic73—21no—
282C22×Dic73—21no—
283C2×C4×D73—22no—
284C2×C4×D73—22no—
285C2×C4×D73—44no—
286#11924018—44no—
287#11924016—44no—
288#11924015—44no—
289#11924013—44no—
290#11924012—24no—
291#11924012—24no—
292#11924012—44no—
293C2×#10596831—44no—
294C2×#10596831C2414yes—
295C2×#10596831C2414yes—
296C4⋊Dic73—21no—
297C4⋊Dic73—21no—
298C4⋊Dic73C2412yes—
299C4⋊Dic73C2412yes—
300#11924007—22no—
301#11924007—22no—
302#11924007—22no—
303#11924007—22no—
304C22⋊Dic73—22no—
305C22⋊Dic73—22no—
306C22⋊Dic73—22no—
307C22⋊Dic73—22no—
308C22⋊Dic73—22no—
309C22⋊Dic73—22no—
310#11924005—22no—
311#11924005—22no—
312#11924005—22no—
313#11924005—22no—
314C4×Dic73—22no—
315C4×Dic73—22no—
316C24×C73—21no—
317C24×C73—42no—
318C24×C73—42no—
319C24×C73—42no—
320C24×C73C2×D411yescharacteristic
321C24×C73C2×D411yescharacteristic
322C24×C73C2×D411yescharacteristic
323C24×C73C2×D411yescharacteristic
324C24×C73C2×D411yescharacteristic
325C24×C73C2×D411yescharacteristic
326C24×C73C2×D411yescharacteristic
327#41×C73—44no—
328#41×C73—44no—
329#41×C73—44no—
330#41×C73—44no—
331C2×Q8×C73—21no—
332C2×Q8×C73—24no—
333C2×Q8×C73C2412yes—
334C2×D4×C73—22no—
335C2×D4×C73—22no—
336C2×D4×C73—22no—
337C2×D4×C73—22no—
338C2×D4×C73—22no—
339C2×D4×C73—22no—
340C2×D4×C73—21no—
341C2×D4×C73—24no—
342C2×D4×C73—44no—
343C2×D4×C73—44no—
344C2×D4×C73—44no—
345C2×D4×C73C2412yes—
346C22×C4×C73—24no—
347C22×C4×C73—24no—
348C22×C4×C73—24no—
349C22×C4×C73—21no—
350C22×C4×C73—21no—
351C22×C4×C73—21no—
352C22×C4×C73—22no—
353C22×C4×C73—22no—
354C22×C4×C73—42no—
355C22×C4×C73—42no—
356C22×C4×C73—42no—
357C22×C4×C73—42no—
358C22×C4×C73—42no—
359C22×C4×C73—42no—
360C22×C4×C73—42no—
361C22×C4×C73—42no—
362C22×C4×C73—42no—
363C22×C4×C73—42no—
364C22×C4×C73—42no—
365C22×C4×C73—44no—
366C22×C4×C73C2×D411yescharacteristic
367C22×C4×C73C2×D411yescharacteristic
368C22×C4×C73C2×D411yescharacteristic
369C22×C4×C73C2×D411yescharacteristic
370C22×C4×C73C2×D411yescharacteristic
371C22×C4×C73C2×D411yescharacteristic
372C22×C4×C73C2×D411yescharacteristic
373C22×C4×C73C2×D411yescharacteristic
374C22×C4×C73C2×D411yescharacteristic
375C22×C4×C73C2×D411yescharacteristic
376C22×C4×C73C2×D411yescharacteristic
377C22×C4×C73C2×D411yescharacteristic
378C22×C4×C73C2×D411yescharacteristic
379C22×C4×C73C2×D411yescharacteristic
380C22×C4×C73C2×D411yescharacteristic
381C22×C4×C73C2×D411yescharacteristic
382C22×C4×C73C2×D411yescharacteristic
383C22×C4×C73C2×D411yescharacteristic
384C22×C4×C73C2×D411yescharacteristic
385C22×C4×C73C2×D411yescharacteristic
386C22×C4×C73C2×D411yescharacteristic
387C22×C4×C73C2411yescharacteristic
388C22×C4×C73C2411yescharacteristic
389C22×C4×C73C2411yescharacteristic
390C22×C4×C73C2411yescharacteristic
391C22×C4×C73C2411yescharacteristic
392C22×C4×C73C2411yescharacteristic
393C22×C4×C73C2411yescharacteristic
394C4⋊C4×C73—22no—
395C4⋊C4×C73—22no—
396C4⋊C4×C73—22no—
397C4⋊C4×C73—22no—
398C4⋊C4×C73—21no—
399C4⋊C4×C73—21no—
400C4⋊C4×C73C2412yes—
401C4⋊C4×C73C2412yes—
402C22⋊C4×C73—22no—
403C22⋊C4×C73—22no—
404C22⋊C4×C73—22no—
405C22⋊C4×C73—22no—
406C22⋊C4×C73—22no—
407C22⋊C4×C73—22no—
408C22⋊C4×C73—22no—
409C22⋊C4×C73—22no—
410C22⋊C4×C73—22no—
411C22⋊C4×C73—22no—
412C42×C73—22no—
413C42×C73—22no—
414C23×C73—22no—
415C23×C73—22no—
416C23×C73—22no—
417C23×C73—22no—
418C23×C73—22no—
419C23×C73—22no—
420C23×C73—22no—
421C23×C73—22no—
422C23×C73—22no—
423C23×C73—22no—
424C23×C73—41no—
425C23×C73—41no—
426C23×C73—41no—
427C23×C73—41no—
428C23×C73—41no—
429C23×C73—41no—
430C23×C73—41no—
431C23×C73—41no—
432C23×C73—41no—
433C23×C73—41no—
434C23×C73—41no—
435C23×C73—41no—
436C23×C73—42no—
437C23×C73—42no—
438C23×C73—416no—
439C23×C73—42no—
440C23×C73C22×D411yescharacteristic
441C23×C73C22×D411yescharacteristic
442C23×C73C22×D411yescharacteristic
443C23×C73C22×D411yescharacteristic
444C23×C73C22×D411yescharacteristic
445C23×C73C22×D411yescharacteristic
446C23×C73C22×D411yescharacteristic
447C22×D73—22no—
448C22×D73—42no—
449C22×D73—42no—
450C22×D73—42no—
451Q8×C73—24no—
452Q8×C73—42no—
453D4×C73—24no—
454D4×C73—44no—
455D4×C73—44no—
456D4×C73—44no—
457D4×C73—44no—
458D4×C73—44no—
459D4×C73—44no—
460D4×C73—42no—
461C2×C4×C73—22no—
462C2×C4×C73—22no—
463C2×C4×C73—22no—
464C2×C4×C73—22no—
465C2×C4×C73—22no—
466C2×C4×C73—22no—
467C2×C4×C73—22no—
468C2×C4×C73—22no—
469C2×C4×C73—22no—
470C2×C4×C73—22no—
471C2×C4×C73—22no—
472C2×C4×C73—22no—
473C2×C4×C73—22no—
474C2×C4×C73—22no—
475C2×C4×C73—22no—
476C2×C4×C73—22no—
477C2×C4×C73—22no—
478C2×C4×C73—22no—
479C2×C4×C73—41no—
480C2×C4×C73—41no—
481C2×C4×C73—41no—
482C2×C4×C73—41no—
483C2×C4×C73—41no—
484C2×C4×C73—41no—
485C2×C4×C73—41no—
486C2×C4×C73—41no—
487C2×C4×C73—41no—
488C2×C4×C73—41no—
489C2×C4×C73—41no—
490C2×C4×C73—41no—
491C2×C4×C73—44no—
492C2×C4×C73—44no—
493C2×C4×C73—42no—
494C2×C4×C73—42no—
495C2×C4×C73—42no—
496C2×C4×C73C22×D411yescharacteristic
497C2×C4×C73C22×D411yescharacteristic
498C2×C4×C73C22×D411yescharacteristic
499C2×C4×C73C22×D411yescharacteristic
500C2×C4×C73C22×D411yescharacteristic
501C2×C4×C73C22×D411yescharacteristic
502C2×C4×C73C22×D411yescharacteristic
503C2×C4×C73H(5,𝔽2)14yes—
504C2×C4×C73C2511yescharacteristic
505C22⋊D73—44no—
506C22⋊D73—44no—
507C22⋊D73—44no—
508C22⋊D73—44no—
509C22⋊D73—44no—
510C22⋊D73—44no—
511C2×Dic73—22no—
512C2×Dic73—22no—
513C2×Dic73—22no—
514C2×Dic73—42no—
515C2×Dic73—42no—
516C2×Dic73—42no—
517D292—22no—
518D292—22no—
519D292—42no—
520C4×D73—44no—
521C4×D73—44no—
522Dic146—22no—
523Dic146—22no—
524Dic146—42no—
525#10596831—24no—
526#10596831—24no—
527C22×C73—21no—
528C22×C73—21no—
529C22×C73—21no—
530C22×C73—21no—
531C22×C73—21no—
532C22×C73—21no—
533C22×C73—21no—
534C22×C73—21no—
535C22×C73—21no—
536C22×C73—21no—
537C22×C73—21no—
538C22×C73—21no—
539C22×C73—21no—
540C22×C73—21no—
541C22×C73—21no—
542C22×C73—21no—
543C22×C73—21no—
544C22×C73—21no—
545C22×C73—44no—
546C22×C73—44no—
547C22×C73—44no—
548C22×C73—44no—
549C22×C73—44no—
550C22×C73—44no—
551C22×C73—44no—
552C22×C73—42no—
553C22×C73—42no—
554C22×C73—42no—
555C22×C73—84no—
556C22×C73#53412yes—
557C22×C73#57512yes—
558C22×C73#57512yes—
559C22×C73C23×D411yescharacteristic
560C2×D73—42no—
561C2×D73—42no—
562C2×D73—42no—
563C2×D73—84no—
564C4×C73—21no—
565C4×C73—21no—
566C4×C73—21no—
567C4×C73—21no—
568C4×C73—21no—
569C4×C73—21no—
570C4×C73—42no—
571C4×C73—42no—
572C4×C73—42no—
573C4×C73#53412yes—
574C4×C73C2×H(5,𝔽2)12yes—
575Dic73—42no—
576Dic73—42no—
577Dic73—42no—
578#60752—731nomaximal, Sylow
579C2×C73—22no—
580C2×C73—22no—
581C2×C73—22no—
582C2×C73—41no—
583C2×C73—41no—
584C2×C73—41no—
585C2×C73—41no—
586C2×C73—82no—
587C2×C73C2×#53411yescharacteristic
588C2×C73C2×#57511yescharacteristic
589C2×C73C2×#57511yescharacteristic
590D73—82no—
591C2×#525—731no—
592C2×#525D7311yescharacteristic, complemented
593#3197—734no—
594#3196—732no—
595#3194—732no—
596#3191—734no—
597#3190—732no—
598#3188—732no—
599#3095—731no—
600#3094—731no—
601#3093—732no—
602#3056—732no—
603#3055—732no—
604#3007—731no—
605#3006—731no—
606#3005—732no—
607C2×#407—731no—
608C73#6075211yescharacteristic, complemented, Sylow
609C22×#41—731no—
610C22×#41C2×D7311yescharacteristic, complemented
611C24×C4C2×D7311yescharacteristic
612C2×#137—732no—
613C2×AGL(1,ℤ/8)—732no—
614C22×M16—732no—
615#525—21no—
616#525—21no—
617#525—21no—
618#525—21no—
619#525—732no—
620#525—732no—
621#525—732no—
622#525—732no—
623#525—1461no—
624#525—1461no—
625#525—1461no—
626#525—1461no—
627#525C2×D7312yes—
628#525C2×D7312yes—
629#525C2×D7312yescomplemented
630#525C2×D7312yescomplemented
631C2×#123—21no—
632C2×#123—1461no—
633C2×C22⋊Q8—731no—
634C2×C22⋊Q8—731no—
635C2×C22⋊Q8C2×D7311yescharacteristic
636C2×C22⋊Q8C2×D7311yescharacteristic, complemented
637C2×#121—731no—
638C2×#121—731no—
639C2×#121C2×D7311yescharacteristic
640C2×#121C2×D7311yescharacteristic, complemented
641C2×#120—21no—
642C2×#120—1461no—
643C2×C4×D4—21no—
644C2×C4×D4—21no—
645C2×C4×D4—1461no—
646C2×C4×D4—1461no—
647C2×#117—731no—
648C2×#117C2×D7311yescharacteristic, complemented
649#485—734no—
650#485—734no—
651#485—734no—
652#484—732no—
653#483—732no—
654#482—734no—
655#482—734no—
656#482—734no—
657#481—732no—
658#480—732no—
659#470—734no—
660#469—734no—
661#468—734no—
662#468—734no—
663#467—734no—
664#466—734no—
665#465—734no—
666#465—734no—
667#452—734no—
668#452—734no—
669#452—734no—
670#451—732no—
671#450—732no—
672#449—734no—
673#449—734no—
674#449—734no—
675#448—732no—
676#447—732no—
677#428—732no—
678#428—732no—
679#419—732no—
680#418—732no—
681#417—732no—
682#417—732no—
683#407—732no—
684#407—731no—
685#407—731no—
686#407—732no—
687#407—732no—
688C2×C22⋊C8—732no—
689C2×C22⋊C8—732no—
690C25C22⋊D7311yescharacteristic
691C2×#41—21no—
692C2×#41—21no—
693C2×#41—44no—
694C2×#41—2924no—
695C2×#41—732no—
696C2×#41—732no—
697C2×#41—1461no—
698C2×#41—1461no—
699C2×#41C22×D7312yes—
700C2×#41C22×D7312yes—
701C22×Q8—731no—
702C22×Q8C22×D7311yescharacteristic
703C22×D4—21no—
704C22×D4—21no—
705C22×D4—21no—
706C22×D4—731no—
707C22×D4—1461no—
708C22×D4—1461no—
709C22×D4—1461no—
710C22×D4C22×D7311yescharacteristic
711C23×C4—21no—
712C23×C4—44no—
713C23×C4—1461no—
714C23×C4C22⋊D7311yescharacteristic
715C23×C4C22⋊D7311yescharacteristic
716C23×C4C22⋊D7311yescharacteristic
717C23×C4C22⋊D7311yescharacteristic
718C23×C4C22⋊D7311yescharacteristic
719C23×C4C22⋊D7311yescharacteristic
720C23×C4C22⋊D7311yescharacteristic
721C23×C4C22×D7311yescharacteristic
722C23×C4C22×D7311yescharacteristic
723C23×C4C22×D7311yescharacteristic
724C23×C4C22×D7311yescharacteristic
725C23×C4C22×D7311yescharacteristic
726C23×C4C22×D7311yescharacteristic
727C23×C4C22×D7311yescharacteristic
728#137—2924no—
729AGL(1,ℤ/8)—2924no—
730C2×Q16—734no—
731C2×SD16—734no—
732C2×SD16—734no—
733C2×D8—734no—
734C2×M16—2924no—
735C2×M16—734no—
736C2×M16—732no—
737C2×M16—732no—
738C22×C8—734no—
739#123—22no—
740#123—22no—
741#123—22no—
742#123—22no—
743#123—1462no—
744#123—1462no—
745#123—1462no—
746#123—1462no—
747C22⋊Q8—21no—
748C22⋊Q8—21no—
749C22⋊Q8—21no—
750C22⋊Q8—21no—
751C22⋊Q8—732no—
752C22⋊Q8—732no—
753C22⋊Q8—732no—
754C22⋊Q8—732no—
755C22⋊Q8—1461no—
756C22⋊Q8—1461no—
757C22⋊Q8—1461no—
758C22⋊Q8—1461no—
759C22⋊Q8C22×D7312yes—
760C22⋊Q8C22×D7312yes—
761C22⋊Q8C22×D7312yes—
762C22⋊Q8C22×D7312yes—
763#121—21no—
764#121—21no—
765#121—21no—
766#121—21no—
767#121—732no—
768#121—732no—
769#121—732no—
770#121—732no—
771#121—1461no—
772#121—1461no—
773#121—1461no—
774#121—1461no—
775#121C22×D7312yes—
776#121C22×D7312yes—
777#121C22×D7312yes—
778#121C22×D7312yes—
779#120—22no—
780#120—22no—
781#120—22no—
782#120—22no—
783#120—1462no—
784#120—1462no—
785#120—1462no—
786#120—1462no—
787C4×D4—22no—
788C4×D4—22no—
789C4×D4—22no—
790C4×D4—22no—
791C4×D4—22no—
792C4×D4—22no—
793C4×D4—22no—
794C4×D4—22no—
795C4×D4—1462no—
796C4×D4—1462no—
797C4×D4—1462no—
798C4×D4—1462no—
799C4×D4—1462no—
800C4×D4—1462no—
801C4×D4—1462no—
802C4×D4—1462no—
803#117—21no—
804#117—21no—
805#117—732no—
806#117—732no—
807#117—1461no—
808#117—1461no—
809#117C22×D7312yes—
810#117C22×D7312yes—
811C2×C4⋊C4—21no—
812C2×C4⋊C4—21no—
813C2×C4⋊C4—731no—
814C2×C4⋊C4—731no—
815C2×C4⋊C4—1461no—
816C2×C4⋊C4—1461no—
817C2×C4⋊C4C22×D7311yescharacteristic
818C2×C4⋊C4C22×D7311yescharacteristic
819C2×C22⋊C4—21no—
820C2×C22⋊C4—21no—
821C2×C22⋊C4—21no—
822C2×C22⋊C4—21no—
823C2×C22⋊C4—21no—
824C2×C22⋊C4—1461no—
825C2×C22⋊C4—1461no—
826C2×C22⋊C4—1461no—
827C2×C22⋊C4—1461no—
828C2×C22⋊C4—1461no—
829C2×C42—21no—
830C2×C42—1461no—
831#107—734no—
832#107—734no—
833#106—734no—
834#106—734no—
835#103—734no—
836#103—734no—
837#103—734no—
838#103—734no—
839#102—734no—
840#102—734no—
841#102—734no—
842#102—734no—
843C22⋊C8—732no—
844C22⋊C8—732no—
845C22⋊C8—734no—
846C22⋊C8—734no—
847C22⋊C8—732no—
848C22⋊C8—732no—
849C24—21no—
850C24—42no—
851C24—42no—
852C24—42no—
853C24—1461no—
854C24C2×C22⋊D7311yescharacteristic
855C24C2×C22⋊D7311yescharacteristic
856C24C2×C22⋊D7311yescharacteristic
857C24C2×C22⋊D7311yescharacteristic
858C24C2×C22⋊D7311yescharacteristic
859C24C2×C22⋊D7311yescharacteristic
860C24C2×C22⋊D7311yescharacteristic
861#41—44no—
862#41—44no—
863#41—44no—
864#41—44no—
865#41—2924no—
866#41—2924no—
867#41—2922no—
868#41—2922no—
869#41—1464no—
870#41—1464no—
871C2×Q8—21no—
872C2×Q8—24no—
873C2×Q8—2922no—
874C2×Q8—732no—
875C2×Q8—1461no—
876C2×Q8C23×D7312yes—
877C2×D4—22no—
878C2×D4—22no—
879C2×D4—22no—
880C2×D4—22no—
881C2×D4—22no—
882C2×D4—22no—
883C2×D4—21no—
884C2×D4—24no—
885C2×D4—44no—
886C2×D4—44no—
887C2×D4—44no—
888C2×D4—2922no—
889C2×D4—2924no—
890C2×D4—2924no—
891C2×D4—2924no—
892C2×D4—732no—
893C2×D4—1462no—
894C2×D4—1462no—
895C2×D4—1462no—
896C2×D4—1462no—
897C2×D4—1462no—
898C2×D4—1462no—
899C2×D4—1461no—
900C2×D4C23×D7312yes—
901C22×C4—24no—
902C22×C4—24no—
903C22×C4—24no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—22no—
908C22×C4—22no—
909C22×C4—42no—
910C22×C4—42no—
911C22×C4—42no—
912C22×C4—42no—
913C22×C4—42no—
914C22×C4—42no—
915C22×C4—42no—
916C22×C4—42no—
917C22×C4—42no—
918C22×C4—42no—
919C22×C4—42no—
920C22×C4—44no—
921C22×C4—2924no—
922C22×C4—1461no—
923C22×C4—1461no—
924C22×C4—1461no—
925C22×C4—1462no—
926C22×C4—1462no—
927C22×C4C2×C22⋊D7311yescharacteristic
928C22×C4C2×C22⋊D7311yescharacteristic
929C22×C4C2×C22⋊D7311yescharacteristic
930C22×C4C2×C22⋊D7311yescharacteristic
931C22×C4C2×C22⋊D7311yescharacteristic
932C22×C4C2×C22⋊D7311yescharacteristic
933C22×C4C2×C22⋊D7311yescharacteristic
934C22×C4C2×C22⋊D7311yescharacteristic
935C22×C4C2×C22⋊D7311yescharacteristic
936C22×C4C2×C22⋊D7311yescharacteristic
937C22×C4C2×C22⋊D7311yescharacteristic
938C22×C4C2×C22⋊D7311yescharacteristic
939C22×C4C2×C22⋊D7311yescharacteristic
940C22×C4C2×C22⋊D7311yescharacteristic
941C22×C4C2×C22⋊D7311yescharacteristic
942C22×C4C2×C22⋊D7311yescharacteristic
943C22×C4C2×C22⋊D7311yescharacteristic
944C22×C4C2×C22⋊D7311yescharacteristic
945C22×C4C2×C22⋊D7311yescharacteristic
946C22×C4C2×C22⋊D7311yescharacteristic
947C22×C4C2×C22⋊D7311yescharacteristic
948C22×C4C23×D7311yescharacteristic
949C22×C4C23×D7311yescharacteristic
950C22×C4C23×D7311yescharacteristic
951C22×C4C23×D7311yescharacteristic
952C22×C4C23×D7311yescharacteristic
953C22×C4C23×D7311yescharacteristic
954C22×C4C23×D7311yescharacteristic
955Q16—2924no—
956SD16—2924no—
957SD16—2924no—
958D8—2924no—
959M16—2924no—
960M16—1464no—
961M16—1464no—
962C2×C8—2924no—
963C2×C8—734no—
964C2×C8—734no—
965C4⋊C4—22no—
966C4⋊C4—22no—
967C4⋊C4—22no—
968C4⋊C4—22no—
969C4⋊C4—21no—
970C4⋊C4—21no—
971C4⋊C4—732no—
972C4⋊C4—732no—
973C4⋊C4—1462no—
974C4⋊C4—1462no—
975C4⋊C4—1462no—
976C4⋊C4—1462no—
977C4⋊C4—1461no—
978C4⋊C4—1461no—
979C4⋊C4C23×D7312yes—
980C4⋊C4C23×D7312yes—
981C22⋊C4—22no—
982C22⋊C4—22no—
983C22⋊C4—22no—
984C22⋊C4—22no—
985C22⋊C4—22no—
986C22⋊C4—22no—
987C22⋊C4—22no—
988C22⋊C4—22no—
989C22⋊C4—22no—
990C22⋊C4—22no—
991C22⋊C4—1462no—
992C22⋊C4—1462no—
993C22⋊C4—1462no—
994C22⋊C4—1462no—
995C22⋊C4—1462no—
996C22⋊C4—1462no—
997C22⋊C4—1462no—
998C22⋊C4—1462no—
999C22⋊C4—1462no—
1000C22⋊C4—1462no—
1001C42—22no—
1002C42—22no—
1003C42—1462no—
1004C42—1462no—
1005C23—22no—
1006C23—22no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—22no—
1011C23—22no—
1012C23—22no—
1013C23—22no—
1014C23—22no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23—41no—
1027C23—42no—
1028C23—42no—
1029C23—416no—
1030C23—42no—
1031C23—2922no—
1032C23—2922no—
1033C23—2922no—
1034C23—1462no—
1035C23C22×C22⋊D7311yescharacteristic
1036C23C22×C22⋊D7311yescharacteristic
1037C23C22×C22⋊D7311yescharacteristic
1038C23C22×C22⋊D7311yescharacteristic
1039C23C22×C22⋊D7311yescharacteristic
1040C23C22×C22⋊D7311yescharacteristic
1041C23C22×C22⋊D7311yescharacteristic
1042Q8—24no—
1043Q8—42no—
1044Q8—2922no—
1045Q8—1462no—
1046Q8—1462no—
1047D4—24no—
1048D4—44no—
1049D4—44no—
1050D4—44no—
1051D4—44no—
1052D4—44no—
1053D4—44no—
1054D4—42no—
1055D4—2922no—
1056D4—2924no—
1057D4—2924no—
1058D4—2924no—
1059D4—2924no—
1060D4—2924no—
1061D4—2924no—
1062D4—1462no—
1063D4—1462no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—22no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—44no—
1095C2×C4—44no—
1096C2×C4—42no—
1097C2×C4—42no—
1098C2×C4—42no—
1099C2×C4—2924no—
1100C2×C4—2922no—
1101C2×C4—2922no—
1102C2×C4—2922no—
1103C2×C4—2924no—
1104C2×C4—1462no—
1105C2×C4—1462no—
1106C2×C4—1462no—
1107C2×C4C22×C22⋊D7311yescharacteristic
1108C2×C4C22×C22⋊D7311yescharacteristic
1109C2×C4C22×C22⋊D7311yescharacteristic
1110C2×C4C22×C22⋊D7311yescharacteristic
1111C2×C4C22×C22⋊D7311yescharacteristic
1112C2×C4C22×C22⋊D7311yescharacteristic
1113C2×C4C22×C22⋊D7311yescharacteristic
1114C2×C4#1455663614yes—
1115C2×C4C24×D7311yescharacteristic
1116C8—1464no—
1117C8—1464no—
1118C22—21no—
1119C22—21no—
1120C22—21no—
1121C22—21no—
1122C22—21no—
1123C22—21no—
1124C22—21no—
1125C22—21no—
1126C22—21no—
1127C22—21no—
1128C22—21no—
1129C22—21no—
1130C22—21no—
1131C22—21no—
1132C22—21no—
1133C22—21no—
1134C22—21no—
1135C22—21no—
1136C22—44no—
1137C22—44no—
1138C22—44no—
1139C22—44no—
1140C22—44no—
1141C22—44no—
1142C22—44no—
1143C22—42no—
1144C22—42no—
1145C22—42no—
1146C22—84no—
1147C22—2922no—
1148C22—2922no—
1149C22—2922no—
1150C22—5844no—
1151C22#1798914612yes—
1152C22#1798938512yes—
1153C22#1798938512yes—
1154C22C23×C22⋊D7311yescharacteristic
1155C4—21no—
1156C4—21no—
1157C4—21no—
1158C4—21no—
1159C4—21no—
1160C4—21no—
1161C4—42no—
1162C4—42no—
1163C4—42no—
1164C4—2922no—
1165C4—2922no—
1166C4—2922no—
1167C4#1798914612yes—
1168C4C2×#1455663612yes—
1169C2—22no—
1170C2—22no—
1171C2—22no—
1172C2—41no—
1173C2—41no—
1174C2—41no—
1175C2—41no—
1176C2—82no—
1177C2—5842no—
1178C2C2×#1798914611yescharacteristic
1179C2C2×#1798938511yescharacteristic
1180C2C2×#1798938511yescharacteristic
subgroupG/H
centerC22C23×C22⋊D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#525×C73C2
socleC22×C73C23×D4
hypercenterC2×#525D73
hypocenterC73#60752
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C24×C4 ◁ C2×#525

Complements

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

NH ≅ G/Ntype
1. C2×#17989098C2semidirect
2. #22620768C2semidirect
3. #22620757C2semidirect
4. #22620741C2semidirect
5. #22620719C2semidirect
6. #22620708C2semidirect
7. #22620692C2semidirect
8. #22619875C2semidirect
9. #22619867C2semidirect
10. #22619862C2semidirect
11. #22619557C2semidirect
12. #22619546C2semidirect
13. #22619189C2semidirect
14. #22619181C2semidirect
15. #22619173C2semidirect
16. C2×#17988551C2semidirect
17. C2×#525×C73C2semidirect
19. C2×#14556622C22semidirect
20. C2×#14556617C22semidirect
21. C22×#11924012C22semidirect
28. #17989098C22semidirect
29. #17989098C22semidirect
31. C2×#14556570C22semidirect
32. C2×#14556570C22semidirect
33. C2×#14556565C22semidirect
34. C2×#14556565C22semidirect
39. #17988928C22semidirect
40. #17988928C22semidirect
41. #17988925C22semidirect
42. #17988920C22semidirect
43. #17988915C22semidirect
44. #17988911C22semidirect
45. #17988911C22semidirect
46. #17988908C22semidirect
47. #17988903C22semidirect
48. #17988898C22semidirect
49. #17988843C22semidirect
50. #17988838C22semidirect
51. #17988835C22semidirect
52. #17988831C22semidirect
53. #17988826C22semidirect
54. #17988821C22semidirect
55. #17988818C22semidirect
56. #17988814C22semidirect
57. #17988749C22semidirect
58. #17988749C22semidirect
59. #17988747C22semidirect
60. #17988742C22semidirect
61. #17988737C22semidirect
62. #17988732C22semidirect
63. #17988732C22semidirect
64. #17988730C22semidirect
65. #17988725C22semidirect
66. #17988720C22semidirect
67. #17988627C22semidirect
68. #17988627C22semidirect
69. #17988596C22semidirect
70. #17988592C22semidirect
71. #17988586C22semidirect
72. #17988586C22semidirect
75. #17988551C22semidirect
76. #17988551C22semidirect
77. #17988551C22semidirect
78. C2×C22⋊#10596831C22semidirect
79. C2×C22⋊#10596831C22semidirect
80. C22×#41×C73C22semidirect
88. #525×C73C22semidirect
89. #525×C73C22semidirect
92. C2×C22⋊Q8×C73C22semidirect
94. C2×#121×C73C22semidirect
98. C2×#117×C73C22semidirect
112. C2×#11924018C23semidirect
113. C2×#11924016C23semidirect
114. C2×#11924015C23semidirect
115. C2×#11924013C23semidirect
167. #14556524C23semidirect
168. #14556524C23semidirect
169. #14556522C23semidirect
170. #14556522C23semidirect
171. #14556515C23semidirect
172. #14556515C23semidirect
173. #14556514C23semidirect
174. #14556514C23semidirect
175. #14556512C23semidirect
176. #14556512C23semidirect
177. #14556511C23semidirect
178. #14556511C23semidirect
592. C2×#525D73semidirect
608. C73#60752semidirect
610. C22×#41C2×D73semidirect
629. #525C2×D73semidirect
630. #525C2×D73semidirect
636. C2×C22⋊Q8C2×D73semidirect
640. C2×#121C2×D73semidirect
648. C2×#117C2×D73semidirect

Maximal subgroups

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

subgroupindex
C2×#179890982
#226207682
#226207572
#226207412
#226207192
#226207082
#226206922
#226198752
#226198672
#226198622
#226195572
#226195462
#226191892
#226191812
#226191732
C2×#179885512
C2×#525×C732
#6075273