Finite Group Databasebeta

← #33093837

Subgroups — #33093837

Order 18688.

730 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22618872C211yesmaximal, characteristic, complemented
2#22618359C211yesmaximal, characteristic
3#22610876C211yesmaximal, characteristic, complemented
4#22610707C211yesmaximal, characteristic, complemented
5#22610532C211yesmaximal, characteristic, complemented
6#22610532C211yesmaximal, characteristic, complemented
7#22610208C211yesmaximal, characteristic
8#22610208C211yesmaximal, characteristic
9#22609951C211yesmaximal, characteristic
10#22609817C211yesmaximal, characteristic, complemented
11#22609812C211yesmaximal, characteristic, complemented
12#22609808C211yesmaximal, characteristic, complemented
13#22609778C211yesmaximal, characteristic
14#22609771C211yesmaximal, characteristic
15C73×#3076C211yesmaximal, characteristic
16C2×#14556598C2211yescharacteristic
17C2×#14556598C2211yescharacteristic
18#17988718—21no—
19#17988718—21no—
20#17988718—21no—
21#17988718—21no—
22C2×#14556527C2211yescharacteristic
23C2×#14556527C2211yescharacteristic
24#17988614C2211yescharacteristic
25#17988614C2211yescharacteristic
26#17988611C2211yescharacteristic
27C2×#14556518C2211yescharacteristic
28C2×#14556518C2211yescharacteristic
29#17988543—21no—
30#17988543—21no—
31#17988543C2211yescharacteristic
32#17988543C2211yescharacteristic
33#17988543C2211yescharacteristic
34#17988543C2211yescharacteristic
35C4×#11924012—21no—
36C4×#11924012C2211yescharacteristic
37C2×#14556502—21no—
38C2×#14556502C2211yescharacteristic
39C2×#14556501C2211yescharacteristic
40C2×C8×Dic73C2211yescharacteristic
41C4×C4⋊Dic73C2211yescharacteristic
42#17988352C2211yescharacteristic
43#17988352C2211yescharacteristic
44#17988346C2211yescharacteristic
45#17988346C2211yescharacteristic
46#17988346C2211yescharacteristic
47#17988346C2211yescharacteristic
48#17988346C2211yescharacteristic
49#17988346C2211yescharacteristic
50#17988341C2211yescharacteristic
51#17988341C2211yescharacteristic
52#533×C73C2211yescharacteristic
53C4×#41×C73C2211yescharacteristic
54#479×C73C411yescharacteristic, complemented
55#479×C73C411yescharacteristic, complemented
56#478×C73C411yescharacteristic, complemented
57#478×C73C411yescharacteristic, complemented
58#477×C73C411yescharacteristic, complemented
59#476×C73C411yescharacteristic, complemented
60#475×C73C411yescharacteristic, complemented
61#474×C73C411yescharacteristic, complemented
62#427×C73C2211yescharacteristic
63#427×C73C2211yescharacteristic
64C2×C4⋊C8×C73C2211yescharacteristic
65#416×C73C2211yescharacteristic
66#416×C73C2211yescharacteristic
67#14556598—22no—
68#14556598—22no—
69#14556598—22no—
70#14556598Q814yescomplemented
71C2×#11924012—21no—
72C2×#11924012—21no—
73C2×#11924012C2311yescharacteristic
74C2×#11924012C2311yescharacteristic
75C2×#11924012C2311yescharacteristic
76C2×#11924012C2311yescharacteristic
77C22×#10596831—21no—
78C22×#10596831—21no—
79C22×#10596831C2311yescharacteristic
80C22×#10596831C2311yescharacteristic
81C2×C4⋊Dic73—21no—
82C2×C4×Dic73C2311yescharacteristic
83C2×C4×Dic73C2311yescharacteristic
84#14556527—22no—
85#14556527—22no—
86C4⋊#10596831—21no—
87C4⋊#10596831—21no—
88C4⋊#10596831—21no—
89C4⋊#10596831—21no—
90C4⋊#10596831—21no—
91C4⋊#10596831—21no—
92#14556518—22no—
93#14556518—22no—
94#14556502—21no—
95#14556502—21no—
96#14556502—21no—
97#14556502—21no—
98#14556502—21no—
99#14556502D411yescharacteristic
100#14556502D411yescharacteristic
101#14556502D411yescharacteristic
102#14556502D411yescharacteristic
103#14556501—22no—
104C4×#10596831—21no—
105C4×#10596831—21no—
106C4×#10596831—21no—
107C4×#10596831—21no—
108C4×#10596831—21no—
109C8×Dic73—22no—
110#14556498—21no—
111C2×#41×C73C2311yescharacteristic
112C22×C8×C73C2311yescharacteristic
113C22×C8×C73C2311yescharacteristic
114C4⋊Q8×C73C2×C411yescharacteristic
115C4⋊Q8×C73C2×C411yescharacteristic
116#125×C73C2×C411yescharacteristic
117#125×C73C2×C411yescharacteristic
118C22⋊Q8×C73—21no—
119C22⋊Q8×C73—21no—
120C4×Q8×C73—21no—
121C4×Q8×C73—21no—
122C4×Q8×C73C2×C411yescharacteristic
123C4×Q8×C73C2×C411yescharacteristic
124C4×D4×C73—21no—
125C4×D4×C73—21no—
126C4×D4×C73C2×C411yescharacteristic
127C4×D4×C73C2×C411yescharacteristic
128#117×C73—21no—
129#117×C73C2311yescharacteristic
130#117×C73C2311yescharacteristic
131#117×C73C2311yescharacteristic
132C2×C42×C73—21no—
133C2×C42×C73C2311yescharacteristic
134#107×C73C2×C411yescharacteristic
135#107×C73C2×C411yescharacteristic
136#107×C73C2×C411yescharacteristic
137#107×C73C2×C411yescharacteristic
138#106×C73C2×C411yescharacteristic
139#106×C73C2×C411yescharacteristic
140#106×C73C2×C411yescharacteristic
141#106×C73C2×C411yescharacteristic
142C4⋊C8×C73C2×C411yescharacteristic
143C4⋊C8×C73C2×C411yescharacteristic
144C4⋊C8×C73C2×C411yescharacteristic
145C4⋊C8×C73C2×C411yescharacteristic
146#103×C73C2×C411yescharacteristic
147#103×C73C2×C411yescharacteristic
148#103×C73C2×C411yescharacteristic
149#103×C73C2×C411yescharacteristic
150#102×C73C2×C411yescharacteristic
151#102×C73C2×C411yescharacteristic
152#102×C73C2×C411yescharacteristic
153#102×C73C2×C411yescharacteristic
154C22×Dic73—21no—
155C22×Dic73—21no—
156#11924012—24no—
157#11924012—21no—
158#11924012—21no—
159#11924012—24no—
160#11924012—21no—
161#11924012—21no—
162#11924012—21no—
163#11924012—21no—
164#11924012C2×Q812yes—
165#11924012#4112yes—
166C2×#10596831—24no—
167C2×#10596831—21no—
168C2×#10596831—21no—
169C2×#10596831—21no—
170C2×#10596831—21no—
171C2×#10596831—24no—
172C2×#10596831—21no—
173C2×#10596831—21no—
174C2×#10596831C2×D411yescharacteristic
175C2×#10596831C2×D411yescharacteristic
176C2×#10596831C2×D411yescharacteristic
177C2×#10596831C2×D411yescharacteristic
178C2×#10596831C2×Q812yes—
179C2×#10596831#4112yes—
180C4⋊Dic73—42no—
181C4×Dic73—21no—
182C4×Dic73—21no—
183C4×Dic73—21no—
184C4×Dic73—21no—
185#41×C73—21no—
186#41×C73—21no—
187#41×C73C2×Q812yes—
188#41×C73#4112yes—
189C2×Q8×C73—21no—
190C2×Q8×C73—21no—
191C2×Q8×C73C22×C411yescharacteristic
192C2×D4×C73—21no—
193C2×D4×C73C22×C411yescharacteristic
194C22×C4×C73—21no—
195C22×C4×C73—21no—
196C22×C4×C73—21no—
197C22×C4×C73#4111yescharacteristic
198C22×C4×C73#4111yescharacteristic
199C22×C4×C73C2411yescharacteristic
200C2×C8×C73—21no—
201C2×C8×C73—21no—
202C2×C8×C73—21no—
203C2×C8×C73—21no—
204C2×C8×C73C22×C411yescharacteristic
205C2×C8×C73C22×C411yescharacteristic
206C2×C8×C73C22×C411yescharacteristic
207C2×C8×C73C22×C411yescharacteristic
208C4⋊C4×C73—21no—
209C4⋊C4×C73—21no—
210C4⋊C4×C73—21no—
211C4⋊C4×C73—21no—
212C4⋊C4×C73—21no—
213C4⋊C4×C73—21no—
214C4⋊C4×C73—21no—
215C4⋊C4×C73—21no—
216C4⋊C4×C73C22×C411yescharacteristic
217C4⋊C4×C73C22×C411yescharacteristic
218C4⋊C4×C73C22×C411yescharacteristic
219C4⋊C4×C73C22×C411yescharacteristic
220C4⋊C4×C73C22×C411yescharacteristic
221C4⋊C4×C73C22×C411yescharacteristic
222C22⋊C4×C73—21no—
223C22⋊C4×C73—21no—
224C22⋊C4×C73—21no—
225C22⋊C4×C73—21no—
226C22⋊C4×C73—21no—
227C42×C73—21no—
228C42×C73—21no—
229C42×C73—21no—
230C42×C73—21no—
231C42×C73—21no—
232C42×C73C22×C411yescharacteristic
233C42×C73C22×C411yescharacteristic
234C42×C73C2×D411yescharacteristic
235C42×C73C2×D411yescharacteristic
236C23×C73—21no—
237C23×C73C2×#4111yescharacteristic
238Q8×C73—21no—
239Q8×C73—81no—
240Q8×C73—81no—
241Q8×C73C4×Q812yes—
242D4×C73—22no—
243D4×C73—22no—
244D4×C73—21no—
245D4×C73C4×Q812yes—
246C2×C4×C73—21no—
247C2×C4×C73—22no—
248C2×C4×C73—22no—
249C2×C4×C73—21no—
250C2×C4×C73—21no—
251C2×C4×C73—21no—
252C2×C4×C73—21no—
253C2×C4×C73—21no—
254C2×C4×C73—21no—
255C2×C4×C73—41no—
256C2×C4×C73—41no—
257C2×C4×C73—81no—
258C2×C4×C73—81no—
259C2×C4×C73C4×D411yescharacteristic
260C2×C4×C73C4×D411yescharacteristic
261C2×C4×C73C4×D411yescharacteristic
262C2×C4×C73C4×D411yescharacteristic
263C2×C4×C73C23×C411yescharacteristic
264C2×C4×C73C22×D411yescharacteristic
265C2×C4×C73C22×Q811yescharacteristic
266C2×C4×C73C2×#4111yescharacteristic
267C2×C4×C73C2×#4111yescharacteristic
268C2×C4×C73C2×#4111yescharacteristic
269C2×Dic73—22no—
270C2×Dic73—41no—
271C2×Dic73—41no—
272C2×Dic73—41no—
273C2×Dic73—41no—
274C2×Dic73—41no—
275C8×C73—21no—
276C8×C73—21no—
277C8×C73—21no—
278C8×C73—21no—
279#10596831—22no—
280#10596831—21no—
281#10596831—22no—
282#10596831—21no—
283#10596831—41no—
284#10596831—41no—
285#10596831C22⋊Q812yes—
286#10596831C22⋊Q812yes—
287C22×C73—21no—
288C22×C73—21no—
289C22×C73—22no—
290C22×C73—41no—
291C22×C73—41no—
292C22×C73C2×C4×D411yescharacteristic
293C22×C73#52911yescharacteristic
294C22×C73#53311yescharacteristic
295C4×C73—21no—
296C4×C73—21no—
297C4×C73—21no—
298C4×C73—21no—
299C4×C73—22no—
300C4×C73—41no—
301C4×C73—41no—
302C4×C73—41no—
303C4×C73—41no—
304C4×C73—41no—
305C4×C73—41no—
306C4×C73C2×C4×Q811yescharacteristic
307C4×C73C4×#4111yescharacteristic
308C4×C73C2×C22⋊Q811yescharacteristic
309C4×C73#52511yescharacteristic
310Dic73—42no—
311Dic73—81no—
312#21629—731nomaximal, Sylow
313C2×C73—21no—
314C2×C73—21no—
315C2×C73—42no—
316C2×C73C4×C22⋊Q811yescharacteristic
317C2×C73#295611yescharacteristic
318C2×C73#295711yescharacteristic
319#3076D7311yescharacteristic
320#2961—731no—
321#2875—731no—
322#1986—731no—
323#1950—731no—
324#1922—731no—
325#1922—731no—
326#1866—731no—
327#1866—731no—
328#1806—731no—
329#1773—731no—
330#1772—731no—
331#1771—731no—
332#1765—731no—
333#1764—731no—
334C73#2162911yescharacteristic, complemented, Sylow
335C2×#131—731no—
336C2×#131—731no—
337#533C2×D7311yescharacteristic
338C4×#41C2×D7311yescharacteristic
339#479Dic7311yescharacteristic, complemented
340#479Dic7311yescharacteristic, complemented
341#478Dic7311yescharacteristic, complemented
342#478Dic7311yescharacteristic, complemented
343#477Dic7311yescharacteristic, complemented
344#476Dic7311yescharacteristic, complemented
345#475Dic7311yescharacteristic, complemented
346#474Dic7311yescharacteristic, complemented
347#446—1461no—
348#446—1461no—
349#446—1461no—
350#446—1461no—
351C2×#108—731no—
352C2×#108—731no—
353#427C2×D7311yescharacteristic
354#427C2×D7311yescharacteristic
355#424—731no—
356#424—731no—
357#423—731no—
358C2×C4⋊C8C2×D7311yescharacteristic
359C2×#104—731no—
360C2×#104—731no—
361#416C2×D7311yescharacteristic
362#416C2×D7311yescharacteristic
363#405—731no—
364#405—731no—
365#405—731no—
366#405—731no—
367#405—1461no—
368#405—1461no—
369C4×M16—731no—
370C4×M16—1461no—
371C2×#97—731no—
372C2×#97—731no—
373C2×#97—1461no—
374C2×C4×C8—731no—
375C4×C4⋊C4—731no—
376#341—731no—
377#341—731no—
378#339—731no—
379#339—731no—
380#339—731no—
381#339—731no—
382#339—731no—
383#339—731no—
384#336—731no—
385#336—731no—
386C2×#41C22×D7311yescharacteristic
387#131—734no—
388#131—1462no—
389#131—1462no—
390#131—1462no—
391C2×M16—731no—
392C2×M16—731no—
393C2×M16—731no—
394C2×M16—731no—
395C2×M16—1461no—
396C2×M16—1461no—
397C22×C8—731no—
398C22×C8—731no—
399C22×C8—1461no—
400C22×C8—1461no—
401C22×C8C22×D7311yescharacteristic
402C22×C8C22×D7311yescharacteristic
403C4⋊Q8C2×Dic7311yescharacteristic
404C4⋊Q8C2×Dic7311yescharacteristic
405#125C2×Dic7311yescharacteristic
406#125C2×Dic7311yescharacteristic
407C22⋊Q8—21no—
408C22⋊Q8—21no—
409C4×Q8—21no—
410C4×Q8—21no—
411C4×Q8C2×Dic7311yescharacteristic
412C4×Q8C2×Dic7311yescharacteristic
413C4×D4—21no—
414C4×D4—21no—
415C4×D4C2×Dic7311yescharacteristic
416C4×D4C2×Dic7311yescharacteristic
417#117—21no—
418#117C22×D7311yescharacteristic
419#117C22×D7311yescharacteristic
420#117C22×D7311yescharacteristic
421C2×C4⋊C4—1461no—
422C2×C42—21no—
423C2×C42—731no—
424C2×C42—731no—
425C2×C42C22×D7311yescharacteristic
426#108—1462no—
427#108—1462no—
428#107C2×Dic7311yescharacteristic
429#107C2×Dic7311yescharacteristic
430#107C2×Dic7311yescharacteristic
431#107C2×Dic7311yescharacteristic
432#106C2×Dic7311yescharacteristic
433#106C2×Dic7311yescharacteristic
434#106C2×Dic7311yescharacteristic
435#106C2×Dic7311yescharacteristic
436C4⋊C8—1461no—
437C4⋊C8—1461no—
438C4⋊C8—1461no—
439C4⋊C8—1461no—
440C4⋊C8—1461no—
441C4⋊C8—1461no—
442C4⋊C8C2×Dic7311yescharacteristic
443C4⋊C8C2×Dic7311yescharacteristic
444C4⋊C8C2×Dic7311yescharacteristic
445C4⋊C8C2×Dic7311yescharacteristic
446#104—1462no—
447#104—1462no—
448#103C2×Dic7311yescharacteristic
449#103C2×Dic7311yescharacteristic
450#103C2×Dic7311yescharacteristic
451#103C2×Dic7311yescharacteristic
452#102C2×Dic7311yescharacteristic
453#102C2×Dic7311yescharacteristic
454#102C2×Dic7311yescharacteristic
455#102C2×Dic7311yescharacteristic
456#97—731no—
457#97—731no—
458#97—731no—
459#97—731no—
460#97—1461no—
461#97—1461no—
462#97—1461no—
463#97—1461no—
464#97—1462no—
465#97—1461no—
466C4×C8—1461no—
467C4×C8—1461no—
468C4×C8—1461no—
469C4×C8—1461no—
470C4×C8—1462no—
471C4×C8—1461no—
472#95—1461no—
473#41—21no—
474#41—21no—
475#41Q8×D7312yes—
476#41#1192402912yes—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8C22×Dic7311yescharacteristic
480C2×D4—21no—
481C2×D4C22×Dic7311yescharacteristic
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—1461no—
486C22×C4—1461no—
487C22×C4#1192402711yescharacteristic
488C22×C4#1192402711yescharacteristic
489C22×C4C23×D7311yescharacteristic
490M16—732no—
491M16—732no—
492M16—1461no—
493M16—1461no—
494M16—1461no—
495M16—1461no—
496M16—1464no—
497M16—1464no—
498M16—1461no—
499M16—1461no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—731no—
505C2×C8—731no—
506C2×C8—732no—
507C2×C8—732no—
508C2×C8—731no—
509C2×C8—731no—
510C2×C8—1461no—
511C2×C8—1461no—
512C2×C8—1464no—
513C2×C8—1464no—
514C2×C8—1461no—
515C2×C8—1461no—
516C2×C8—1461no—
517C2×C8—1461no—
518C2×C8C22×Dic7311yescharacteristic
519C2×C8C22×Dic7311yescharacteristic
520C2×C8C22×Dic7311yescharacteristic
521C2×C8C22×Dic7311yescharacteristic
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—2922no—
531C4⋊C4C22×Dic7311yescharacteristic
532C4⋊C4C22×Dic7311yescharacteristic
533C4⋊C4C22×Dic7311yescharacteristic
534C4⋊C4C22×Dic7311yescharacteristic
535C4⋊C4C22×Dic7311yescharacteristic
536C4⋊C4C22×Dic7311yescharacteristic
537C22⋊C4—21no—
538C22⋊C4—21no—
539C22⋊C4—21no—
540C22⋊C4—21no—
541C22⋊C4—21no—
542C42—21no—
543C42—21no—
544C42—21no—
545C42—21no—
546C42—21no—
547C42—1461no—
548C42—1461no—
549C42—1461no—
550C42—1461no—
551C42C22×Dic7311yescharacteristic
552C42C22×Dic7311yescharacteristic
553C42D4×D7311yescharacteristic
554C42D4×D7311yescharacteristic
555C23—21no—
556C23C2×#1192402711yescharacteristic
557Q8—21no—
558Q8—81no—
559Q8—81no—
560Q8Q8×Dic7312yes—
561D4—22no—
562D4—22no—
563D4—21no—
564D4Q8×Dic7312yes—
565C2×C4—21no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—81no—
577C2×C4—81no—
578C2×C4—2921no—
579C2×C4—2921no—
580C2×C4—2921no—
581C2×C4—2921no—
582C2×C4—2921no—
583C2×C4—1462no—
584C2×C4D4×Dic7311yescharacteristic
585C2×C4D4×Dic7311yescharacteristic
586C2×C4D4×Dic7311yescharacteristic
587C2×C4D4×Dic7311yescharacteristic
588C2×C4C23×Dic7311yescharacteristic
589C2×C4C2×D4×D7311yescharacteristic
590C2×C4C2×Q8×D7311yescharacteristic
591C2×C4#41×D7311yescharacteristic
592C2×C4#41×D7311yescharacteristic
593C2×C4C2×#1192402911yescharacteristic
594C8—21no—
595C8—21no—
596C8—21no—
597C8—21no—
598C8—2921no—
599C8—2921no—
600C8—732no—
601C8—732no—
602C8—1462no—
603C8—1461no—
604C8—1461no—
605C8—1462no—
606C22—21no—
607C22—21no—
608C22—22no—
609C22—41no—
610C22—41no—
611C22C2×D4×Dic7311yescharacteristic
612C22#1798912311yescharacteristic
613C22#1798913911yescharacteristic
614C4—21no—
615C4—21no—
616C4—21no—
617C4—21no—
618C4—22no—
619C4—41no—
620C4—41no—
621C4—41no—
622C4—41no—
623C4—41no—
624C4—41no—
625C4—2922no—
626C4—5841no—
627C4C2×Q8×Dic7311yescharacteristic
628C4#41×Dic7311yescharacteristic
629C4C22⋊Q8×D7311yescharacteristic
630C4#1798910011yescharacteristic
631C2—21no—
632C2—21no—
633C2—42no—
634C2C22⋊Q8×Dic7311yescharacteristic
635C2#2261884111yescharacteristic
636C2#2261884811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#3076C2
socleC22×C73C2×C4×D4
prime radicalC2×#41×C73C23
cosocleC22×C4×C73C24
hypercenter#3076D73
hypocenterC73#21629
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3076

Complements

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

NH ≅ G/Ntype
1. #22618872C2semidirect
3. #22610876C2semidirect
4. #22610707C2semidirect
5. #22610532C2semidirect
6. #22610532C2semidirect
10. #22609817C2semidirect
11. #22609812C2semidirect
12. #22609808C2semidirect
54. #479×C73C4semidirect
55. #479×C73C4semidirect
56. #478×C73C4semidirect
57. #478×C73C4semidirect
58. #477×C73C4semidirect
59. #476×C73C4semidirect
60. #475×C73C4semidirect
61. #474×C73C4semidirect
70. #14556598Q8semidirect
334. C73#21629semidirect
339. #479Dic73semidirect
340. #479Dic73semidirect
341. #478Dic73semidirect
342. #478Dic73semidirect
343. #477Dic73semidirect
344. #476Dic73semidirect
345. #475Dic73semidirect
346. #474Dic73semidirect

Maximal subgroups

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

subgroupindex
#226188722
#226183592
#226108762
#226107072
#226105322
#226102082
#226099512
#226098172
#226098122
#226098082
#226097782
#226097712
C73×#30762
#2162973