Finite Group Databasebeta

← #33108069

Subgroups — #33108069

Order 18688.

692 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22619713C211yesmaximal, characteristic
2#22618496C211yesmaximal, characteristic
3#22610913C211yesmaximal, characteristic, complemented
4#22610706C211yesmaximal, characteristic, complemented
5#22610681C211yesmaximal, characteristic, complemented
6#22610676C211yesmaximal, characteristic, complemented
7#22610530C211yesmaximal, characteristic, complemented
8#22610530C211yesmaximal, characteristic, complemented
9#22610205C211yesmaximal, characteristic
10#22610205C211yesmaximal, characteristic
11#22609790C211yesmaximal, characteristic, complemented
12#22609777C211yesmaximal, characteristic
13#22609770C211yesmaximal, characteristic
14#22609744C211yesmaximal, characteristic
15C73×#2962C211yesmaximal, characteristic, complemented
16C2×#14556597C2211yescharacteristic
17C2×#14556597C2211yescharacteristic
18C4×#11924028C2211yescharacteristic
19#17988891C411yescharacteristic, complemented
20#17988891C411yescharacteristic, complemented
21#17988884C411yescharacteristic, complemented
22#17988884C411yescharacteristic, complemented
23#17988879C411yescharacteristic, complemented
24#17988874C411yescharacteristic, complemented
25#17988869C411yescharacteristic, complemented
26#17988864C411yescharacteristic, complemented
27C2×#14556526C2211yescharacteristic
28C2×#14556526C2211yescharacteristic
29#17988623C2211yescharacteristic
30#17988623C2211yescharacteristic
31#17988613C2211yescharacteristic
32#17988613C2211yescharacteristic
33#17988612—21no—
34#17988612—21no—
35#17988611C2211yescharacteristic
36#17988609—21no—
37C2×C4⋊#10596831C2211yescharacteristic
38C4⋊C8×D73—21no—
39C2×#14556517C2211yescharacteristic
40C2×#14556517C2211yescharacteristic
41#17988581C2211yescharacteristic
42#17988581C2211yescharacteristic
43C2×#14556501C2211yescharacteristic
44C2×C8×Dic73C2211yescharacteristic
45#17988433C2211yescharacteristic
46#17988351C2211yescharacteristic
47#17988351C2211yescharacteristic
48#17988348C2211yescharacteristic
49#17988348C2211yescharacteristic
50#17988346C2211yescharacteristic
51#17988346C2211yescharacteristic
52#17988346C2211yescharacteristic
53#17988346C2211yescharacteristic
54#17988341C2211yescharacteristic
55#17988341C2211yescharacteristic
56#533×C73C2211yescharacteristic
57#446×C73—21no—
58#446×C73—21no—
59#446×C73—21no—
60C8×Q8×C73—21no—
61#424×C73C2211yescharacteristic
62#424×C73C2211yescharacteristic
63C2×C4⋊C8×C73C2211yescharacteristic
64#405×C73C2211yescharacteristic
65#405×C73C2211yescharacteristic
66C4×M16×C73C2211yescharacteristic
67C2×#11924028C2311yescharacteristic
68#14556597—22no—
69#14556597—22no—
70#14556597—41no—
71#14556597—41no—
72C2×#11924012C2311yescharacteristic
73C2×#11924012C2311yescharacteristic
74C2×#11924011—21no—
75C2×#11924011—21no—
76C22×#10596831C2311yescharacteristic
77C22×#10596831C2311yescharacteristic
78C2×C8×D73—21no—
79C2×C8×D73—21no—
80C4×Dic146C2×C411yescharacteristic
81C4×Dic146C2×C411yescharacteristic
82C4×D292C2×C411yescharacteristic
83C4×D292C2×C411yescharacteristic
84C4×C22⋊D73—21no—
85C4×C22⋊D73—21no—
86#14556550C2311yescharacteristic
87#14556548—21no—
88C2×C4×Dic73C2311yescharacteristic
89C2×C4×Dic73C2311yescharacteristic
90C42×D73—21no—
91#14556526—41no—
92#14556526—41no—
93#14556524C2×C411yescharacteristic
94#14556524C2×C411yescharacteristic
95#14556524C2×C411yescharacteristic
96#14556524C2×C411yescharacteristic
97#14556522C2×C411yescharacteristic
98#14556522C2×C411yescharacteristic
99#14556522C2×C411yescharacteristic
100#14556522C2×C411yescharacteristic
101C4⋊#10596831—21no—
102C4⋊#10596831—21no—
103C4⋊#10596831C2×C411yescharacteristic
104C4⋊#10596831C2×C411yescharacteristic
105C4⋊#10596831C2×C411yescharacteristic
106C4⋊#10596831C2×C411yescharacteristic
107#14556520—21no—
108#14556520—21no—
109#14556520—21no—
110#14556520—21no—
111#14556517—22no—
112#14556517Q814yescomplemented
113#14556514C2×C411yescharacteristic
114#14556514C2×C411yescharacteristic
115#14556514C2×C411yescharacteristic
116#14556514C2×C411yescharacteristic
117#14556511C2×C411yescharacteristic
118#14556511C2×C411yescharacteristic
119#14556511C2×C411yescharacteristic
120#14556511C2×C411yescharacteristic
121#14556501—41no—
122C8×Dic73—41no—
123#14556498—21no—
124#14556498—21no—
125C2×M16×C73C2311yescharacteristic
126C2×M16×C73C2311yescharacteristic
127C22×C8×C73C2311yescharacteristic
128C22×C8×C73C2311yescharacteristic
129C4⋊Q8×C73C2×C411yescharacteristic
130C4⋊Q8×C73C2×C411yescharacteristic
131#125×C73C2×C411yescharacteristic
132#125×C73C2×C411yescharacteristic
133C22⋊Q8×C73—21no—
134C22⋊Q8×C73—21no—
135C4×Q8×C73—21no—
136C4×Q8×C73—21no—
137#117×C73C2311yescharacteristic
138#117×C73C2311yescharacteristic
139C2×C42×C73C2311yescharacteristic
140C4⋊C8×C73—21no—
141C4⋊C8×C73—21no—
142C4⋊C8×C73—21no—
143C4⋊C8×C73—21no—
144C4⋊C8×C73D411yescharacteristic
145C4⋊C8×C73D411yescharacteristic
146C4⋊C8×C73D411yescharacteristic
147C4⋊C8×C73D411yescharacteristic
148#97×C73—21no—
149#97×C73—21no—
150#97×C73—21no—
151C4×C8×C73—21no—
152C4×C8×C73—21no—
153C4×C8×C73—21no—
154#11924028—21no—
155#11924028—21no—
156#11924028C2×Q812yes—
157#11924028#4112yes—
158C2×Dic146C22×C411yescharacteristic
159C2×D292C22×C411yescharacteristic
160C2×C22⋊D73—21no—
161C22×Dic73—21no—
162C22×Dic73—21no—
163C2×C4×D73—21no—
164C2×C4×D73—21no—
165C2×C4×D73—21no—
166#11924012—21no—
167#11924012—21no—
168#11924012—21no—
169#11924012—21no—
170#11924011—42no—
171#11924011—42no—
172C2×#10596831—21no—
173C2×#10596831—21no—
174C2×#10596831—21no—
175C2×#10596831—21no—
176C2×#10596831—21no—
177C2×#10596831—21no—
178C2×#10596831C22×C411yescharacteristic
179C2×#10596831C22×C411yescharacteristic
180C2×#10596831C22×C411yescharacteristic
181C2×#10596831C22×C411yescharacteristic
182C8×D73—42no—
183C8×D73—42no—
184C4⋊Dic73C22×C411yescharacteristic
185C4⋊Dic73C22×C411yescharacteristic
186#11924007—21no—
187#11924007—21no—
188C22⋊Dic73—21no—
189#11924005—21no—
190#11924005—21no—
191C4×Dic73—21no—
192C4×Dic73—21no—
193C4×Dic73—21no—
194C4×Dic73—21no—
195C4×Dic73—21no—
196C4×Dic73—21no—
197C4×Dic73C2×Q812yes—
198C2×Q8×C73—21no—
199C2×Q8×C73—21no—
200C22×C4×C73#4111yescharacteristic
201C22×C4×C73#4111yescharacteristic
202C22×C4×C73C2411yescharacteristic
203M16×C73—21no—
204M16×C73—21no—
205M16×C73—21no—
206M16×C73C2×Q812yes—
207C2×C8×C73—21no—
208C2×C8×C73—21no—
209C2×C8×C73—21no—
210C2×C8×C73—21no—
211C2×C8×C73—21no—
212C2×C8×C73—21no—
213C2×C8×C73C2×D411yescharacteristic
214C2×C8×C73C2×D411yescharacteristic
215C2×C8×C73C2×D411yescharacteristic
216C2×C8×C73C2×D411yescharacteristic
217C4⋊C4×C73—21no—
218C4⋊C4×C73—21no—
219C4⋊C4×C73—21no—
220C4⋊C4×C73—21no—
221C4⋊C4×C73—21no—
222C4⋊C4×C73—21no—
223C4⋊C4×C73C22×C411yescharacteristic
224C4⋊C4×C73C22×C411yescharacteristic
225C4⋊C4×C73C22×C411yescharacteristic
226C4⋊C4×C73C22×C411yescharacteristic
227C22⋊C4×C73—21no—
228C22⋊C4×C73—21no—
229C42×C73—21no—
230C42×C73—21no—
231C42×C73C22×C411yescharacteristic
232C42×C73C22×C411yescharacteristic
233C42×C73C2×D411yescharacteristic
234C42×C73C2×D411yescharacteristic
235C23×C73C2×#4111yescharacteristic
236C22×D73—21no—
237Q8×C73—42no—
238Q8×C73—81no—
239C2×C4×C73—21no—
240C2×C4×C73—21no—
241C2×C4×C73—21no—
242C2×C4×C73—21no—
243C2×C4×C73—41no—
244C2×C4×C73—41no—
245C2×C4×C73C4×D411yescharacteristic
246C2×C4×C73C4×D411yescharacteristic
247C2×C4×C73C4×D411yescharacteristic
248C2×C4×C73C4×D411yescharacteristic
249C2×C4×C73C23×C411yescharacteristic
250C2×C4×C73C22×D411yescharacteristic
251C2×C4×C73C22×Q811yescharacteristic
252C2×C4×C73C2×#4111yescharacteristic
253C2×C4×C73H(5,𝔽2)11yescharacteristic
254C2×C4×C732−1+411yescharacteristic
255C22⋊D73—22no—
256C22⋊D73—22no—
257C2×Dic73—21no—
258C2×Dic73—21no—
259C2×Dic73—21no—
260C2×Dic73—22no—
261C2×Dic73—41no—
262C2×Dic73—41no—
263C2×Dic73—41no—
264C2×Dic73—41no—
265C2×Dic73—41no—
266D292—21no—
267D292C4×Q812yes—
268C4×D73—22no—
269C4×D73—22no—
270C4×D73—42no—
271C4×D73—81no—
272Dic146—21no—
273Dic146C4×Q812yes—
274C8×C73—21no—
275C8×C73—21no—
276C8×C73—21no—
277C8×C73—21no—
278C8×C73—22no—
279C8×C73—41no—
280#10596831—21no—
281#10596831—21no—
282#10596831—21no—
283#10596831—21no—
284#10596831—41no—
285#10596831—41no—
286C22×C73—21no—
287C22×C73—21no—
288C22×C73C2×C4×D411yescharacteristic
289C22×C73#55211yescharacteristic
290C22×C73#55411yescharacteristic
291C2×D73—22no—
292C2×D73—41no—
293C2×D73—41no—
294C4×C73—21no—
295C4×C73—21no—
296C4×C73—21no—
297C4×C73—21no—
298C4×C73—41no—
299C4×C73—41no—
300C4×C73—41no—
301C4×C73—41no—
302C4×C73C2×C4×Q811yescharacteristic
303C4×C73#52011yescharacteristic
304C4×C73#54611yescharacteristic
305C4×C73D4×Q811yescharacteristic
306Dic73—22no—
307Dic73—42no—
308Dic73—41no—
309Dic73—41no—
310Dic73—81no—
311#22984—731nomaximal, Sylow
312C2×C73—21no—
313C2×C73—21no—
314C2×C73#236011yescharacteristic
315C2×C73#295511yescharacteristic
316C2×C73#295711yescharacteristic
317D73—42no—
318#3076—731no—
319#2962D7311yescharacteristic, complemented
320#2906—731no—
321#1995—731no—
322#1950—731no—
323#1946—731no—
324#1945—731no—
325#1922—731no—
326#1922—731no—
327#1866—731no—
328#1866—731no—
329#1768—731no—
330#1765—731no—
331#1764—731no—
332#1759—731no—
333C73#2298411yescharacteristic, complemented, Sylow
334C2×#131—731no—
335C2×#131—731no—
336#533C2×D7311yescharacteristic
337C4×#41—731no—
338#479—731no—
339#479—731no—
340#478—731no—
341#478—731no—
342#477—731no—
343#476—731no—
344#475—731no—
345#474—731no—
346#446—21no—
347#446—21no—
348#446—21no—
349C8×Q8—21no—
350C2×#108—731no—
351C2×#108—731no—
352#427—731no—
353#427—731no—
354#424—731no—
355#424—731no—
356#424—1461no—
357#424—1461no—
358#424C2×D7311yescharacteristic
359#424C2×D7311yescharacteristic
360#423—731no—
361#423—1461no—
362C2×C4⋊C8—731no—
363C2×C4⋊C8—1461no—
364C2×C4⋊C8C2×D7311yescharacteristic
365C2×#104—731no—
366C2×#104—731no—
367#416—731no—
368#416—731no—
369#405C2×D7311yescharacteristic
370#405C2×D7311yescharacteristic
371C4×M16C2×D7311yescharacteristic
372C2×#97—731no—
373C2×C4×C8—731no—
374#376—731no—
375#341—731no—
376#341—731no—
377#339—731no—
378#339—731no—
379#339—731no—
380#339—731no—
381#339—731no—
382#339—731no—
383#336—731no—
384#336—731no—
385C2×#41—731no—
386#131—2921no—
387#131—2921no—
388#131—1462no—
389#131—1462no—
390C2×M16—731no—
391C2×M16—731no—
392C2×M16—1461no—
393C2×M16—1461no—
394C2×M16C22×D7311yescharacteristic
395C2×M16C22×D7311yescharacteristic
396C22×C8—731no—
397C22×C8—731no—
398C22×C8—1461no—
399C22×C8—1461no—
400C22×C8C22×D7311yescharacteristic
401C22×C8C22×D7311yescharacteristic
402C4⋊Q8C4×D7311yescharacteristic
403C4⋊Q8C4×D7311yescharacteristic
404#125C4×D7311yescharacteristic
405#125C4×D7311yescharacteristic
406C22⋊Q8—21no—
407C22⋊Q8—21no—
408C4×Q8—21no—
409C4×Q8—21no—
410C4×Q8—731no—
411C4×Q8—731no—
412C4×D4—731no—
413C4×D4—731no—
414C4×D4—1461no—
415C4×D4—1461no—
416#117—731no—
417#117—1461no—
418#117C22×D7311yescharacteristic
419#117C22×D7311yescharacteristic
420C2×C42—731no—
421C2×C42—731no—
422C2×C42—1461no—
423C2×C42C22×D7311yescharacteristic
424#108—2921no—
425#108—2921no—
426#107—731no—
427#107—731no—
428#107—731no—
429#107—731no—
430#106—731no—
431#106—731no—
432#106—731no—
433#106—731no—
434C4⋊C8—21no—
435C4⋊C8—21no—
436C4⋊C8—21no—
437C4⋊C8—21no—
438C4⋊C8—731no—
439C4⋊C8—731no—
440C4⋊C8—731no—
441C4⋊C8—731no—
442C4⋊C8—1461no—
443C4⋊C8—1461no—
444C4⋊C8—1461no—
445C4⋊C8—1461no—
446C4⋊C8—1461no—
447C4⋊C8—1461no—
448C4⋊C8C22⋊D7311yescharacteristic
449C4⋊C8C22⋊D7311yescharacteristic
450C4⋊C8C22⋊D7311yescharacteristic
451C4⋊C8C22⋊D7311yescharacteristic
452#104—734no—
453#104—1462no—
454#103—731no—
455#103—731no—
456#103—731no—
457#103—731no—
458#102—731no—
459#102—731no—
460#102—731no—
461#102—731no—
462#97—21no—
463#97—21no—
464#97—21no—
465#97—2921no—
466C4×C8—21no—
467C4×C8—21no—
468C4×C8—21no—
469C4×C8—2921no—
470#95—1461no—
471#95—1461no—
472#41—732no—
473#41—732no—
474#41—1461no—
475#41—1461no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—731no—
479C2×D4—731no—
480C2×D4—1461no—
481C22×C4—1461no—
482C22×C4—1461no—
483C22×C4—1461no—
484C22×C4—1461no—
485C22×C4—1461no—
486C22×C4#1192402811yescharacteristic
487C22×C4#1192402811yescharacteristic
488C22×C4C23×D7311yescharacteristic
489M16—21no—
490M16—21no—
491M16—21no—
492M16—2922no—
493M16—2922no—
494M16—1461no—
495M16—1461no—
496M16—1461no—
497M16—1461no—
498M16Q8×D7312yes—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—2922no—
506C2×C8—2922no—
507C2×C8—731no—
508C2×C8—731no—
509C2×C8—731no—
510C2×C8—731no—
511C2×C8—1461no—
512C2×C8—1461no—
513C2×C8—1461no—
514C2×C8—1461no—
515C2×C8—1461no—
516C2×C8—1461no—
517C2×C8C2×C22⋊D7311yescharacteristic
518C2×C8C2×C22⋊D7311yescharacteristic
519C2×C8C2×C22⋊D7311yescharacteristic
520C2×C8C2×C22⋊D7311yescharacteristic
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—731no—
528C4⋊C4—731no—
529C4⋊C4—1461no—
530C4⋊C4—1461no—
531C4⋊C4C2×C4×D7311yescharacteristic
532C4⋊C4C2×C4×D7311yescharacteristic
533C4⋊C4C2×C4×D7311yescharacteristic
534C4⋊C4C2×C4×D7311yescharacteristic
535C22⋊C4—21no—
536C22⋊C4—21no—
537C22⋊C4—1461no—
538C22⋊C4—1461no—
539C22⋊C4—1461no—
540C42—21no—
541C42—21no—
542C42—732no—
543C42—1461no—
544C42—1461no—
545C42—1461no—
546C42—1461no—
547C42—1461no—
548C42—1461no—
549C42C2×C4×D7311yescharacteristic
550C42C2×C4×D7311yescharacteristic
551C42C2×C22⋊D7311yescharacteristic
552C42C2×C22⋊D7311yescharacteristic
553C23—1461no—
554C23C2×#1192402811yescharacteristic
555Q8—42no—
556Q8—81no—
557Q8—732no—
558Q8—1461no—
559D4—732no—
560D4—1462no—
561D4—1462no—
562D4—1461no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—2922no—
570C2×C4—2921no—
571C2×C4—2921no—
572C2×C4—2921no—
573C2×C4—2921no—
574C2×C4—2921no—
575C2×C4—5841no—
576C2×C4—1462no—
577C2×C4—1461no—
578C2×C4—1461no—
579C2×C4—1461no—
580C2×C4—1462no—
581C2×C4—1462no—
582C2×C4C4×C22⋊D7311yescharacteristic
583C2×C4C4×C22⋊D7311yescharacteristic
584C2×C4C4×C22⋊D7311yescharacteristic
585C2×C4C4×C22⋊D7311yescharacteristic
586C2×C4C22×C4×D7311yescharacteristic
587C2×C4C22×C22⋊D7311yescharacteristic
588C2×C4C2×Q8×D7311yescharacteristic
589C2×C4#41×D7311yescharacteristic
590C2×C4#1455663711yescharacteristic
591C2×C4#1455663911yescharacteristic
592C8—21no—
593C8—21no—
594C8—21no—
595C8—21no—
596C8—22no—
597C8—41no—
598C8—2921no—
599C8—2921no—
600C8—1461no—
601C8—1461no—
602C8—1461no—
603C8—1461no—
604C22—21no—
605C22—21no—
606C22—2921no—
607C22—2921no—
608C22—1462no—
609C22C2×C4×C22⋊D7311yescharacteristic
610C22#1798927811yescharacteristic
611C22#1798929711yescharacteristic
612C4—21no—
613C4—21no—
614C4—21no—
615C4—21no—
616C4—41no—
617C4—41no—
618C4—41no—
619C4—41no—
620C4—2922no—
621C4—2921no—
622C4—2921no—
623C4—5841no—
624C4—1462no—
625C4C4×Q8×D7311yescharacteristic
626C4#1798906911yescharacteristic
627C4#1798922511yescharacteristic
628C4Q8×C22⋊D7311yescharacteristic
629C2—21no—
630C2—21no—
631C2—2922no—
632C2#2261293211yescharacteristic
633C2#2261883211yescharacteristic
634C2#2261884611yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#2962C2
socleC22×C73C2×C4×D4
prime radicalC2×#11924028C23
cosocleC22×C4×C73C24
hypercenter#2962D73
hypocenterC73#22984
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C4⋊C8 ◁ #2962

Complements

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

NH ≅ G/Ntype
3. #22610913C2semidirect
4. #22610706C2semidirect
5. #22610681C2semidirect
6. #22610676C2semidirect
7. #22610530C2semidirect
8. #22610530C2semidirect
11. #22609790C2semidirect
15. C73×#2962C2semidirect
19. #17988891C4semidirect
20. #17988891C4semidirect
21. #17988884C4semidirect
22. #17988884C4semidirect
23. #17988879C4semidirect
24. #17988874C4semidirect
25. #17988869C4semidirect
26. #17988864C4semidirect
112. #14556517Q8semidirect
319. #2962D73semidirect
333. C73#22984semidirect

Maximal subgroups

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

subgroupindex
#226197132
#226184962
#226109132
#226107062
#226106812
#226106762
#226105302
#226102052
#226097902
#226097772
#226097702
#226097442
C73×#29622
#2298473