Finite Group Databasebeta

← #33108073

Subgroups — #33108073

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#22619721C211yesmaximal, characteristic
2#22618878C211yesmaximal, characteristic, complemented
3#22618500C211yesmaximal, characteristic
4#22610911C211yesmaximal, characteristic, complemented
5#22610682C211yesmaximal, characteristic, complemented
6#22610677C211yesmaximal, characteristic, complemented
7#22610529C211yesmaximal, characteristic, complemented
8#22610529C211yesmaximal, characteristic, complemented
9#22610203C211yesmaximal, characteristic
10#22610203C211yesmaximal, characteristic
11#22609790C211yesmaximal, characteristic, complemented
12#22609774C211yesmaximal, characteristic
13#22609767C211yesmaximal, characteristic
14#22609744C211yesmaximal, characteristic
15C73×#1950C211yesmaximal, characteristic, complemented
16C2×#14556599C2211yescharacteristic
17C2×#14556599C2211yescharacteristic
18#17989144C2211yescharacteristic
19C4×#11924028C2211yescharacteristic
20#17988895C411yescharacteristic, complemented
21#17988895C411yescharacteristic, complemented
22#17988888C411yescharacteristic, complemented
23#17988888C411yescharacteristic, complemented
24#17988883C411yescharacteristic, complemented
25#17988878C411yescharacteristic, complemented
26#17988873C411yescharacteristic, complemented
27#17988868C411yescharacteristic, complemented
28#17988717—21no—
29#17988715—21no—
30#17988715—21no—
31C8×Dic146—21no—
32#17988625C2211yescharacteristic
33#17988625C2211yescharacteristic
34#17988615C2211yescharacteristic
35#17988615C2211yescharacteristic
36#17988615C2211yescharacteristic
37#17988615C2211yescharacteristic
38#17988612—21no—
39#17988612—21no—
40#17988609—21no—
41C2×C4⋊#10596831C2211yescharacteristic
42C4⋊C8×D73—21no—
43C2×#14556517C2211yescharacteristic
44C2×#14556517C2211yescharacteristic
45#17988584C2211yescharacteristic
46#17988584C2211yescharacteristic
47#17988545C2211yescharacteristic
48#17988545C2211yescharacteristic
49C2×#14556501C2211yescharacteristic
50C2×C8×Dic73C2211yescharacteristic
51#17988433C2211yescharacteristic
52#17988348C2211yescharacteristic
53#17988348C2211yescharacteristic
54#17988348C2211yescharacteristic
55#17988348C2211yescharacteristic
56#17988348C2211yescharacteristic
57#17988348C2211yescharacteristic
58#17988341C2211yescharacteristic
59#17988341C2211yescharacteristic
60C2×#108×C73C2211yescharacteristic
61C2×#108×C73C2211yescharacteristic
62#423×C73C2211yescharacteristic
63C2×C4⋊C8×C73C2211yescharacteristic
64C4×M16×C73C2211yescharacteristic
65#341×C73C2211yescharacteristic
66#341×C73C2211yescharacteristic
67C2×#11924028C2311yescharacteristic
68#14556599—22no—
69#14556599—22no—
70#14556599—41no—
71#14556599—41no—
72C2×#11924011—21no—
73C2×#11924011—21no—
74C22×#10596831C2311yescharacteristic
75C22×#10596831C2311yescharacteristic
76C2×C8×D73—21no—
77C2×C8×D73—21no—
78#14556591C2×C411yescharacteristic
79#14556591C2×C411yescharacteristic
80#14556583C2×C411yescharacteristic
81#14556583C2×C411yescharacteristic
82#14556570—21no—
83#14556570—21no—
84C4×Dic146—21no—
85C4×Dic146—21no—
86C4×Dic146C2×C411yescharacteristic
87C4×Dic146C2×C411yescharacteristic
88C4×D292C2×C411yescharacteristic
89C4×D292C2×C411yescharacteristic
90C4×C22⋊D73—21no—
91C4×C22⋊D73—21no—
92#14556550C2311yescharacteristic
93#14556550C2311yescharacteristic
94#14556550C2311yescharacteristic
95#14556548—21no—
96C2×C4×Dic73C2311yescharacteristic
97C2×C4×Dic73C2311yescharacteristic
98C42×D73—21no—
99#14556525C2×C411yescharacteristic
100#14556525C2×C411yescharacteristic
101#14556525C2×C411yescharacteristic
102#14556525C2×C411yescharacteristic
103#14556523C2×C411yescharacteristic
104#14556523C2×C411yescharacteristic
105#14556523C2×C411yescharacteristic
106#14556523C2×C411yescharacteristic
107C4⋊#10596831D411yescharacteristic
108C4⋊#10596831D411yescharacteristic
109C4⋊#10596831D411yescharacteristic
110C4⋊#10596831D411yescharacteristic
111#14556520—21no—
112#14556520—21no—
113#14556520—21no—
114#14556520—21no—
115#14556520—21no—
116#14556520—21no—
117#14556520—21no—
118#14556520—21no—
119#14556517—22no—
120#14556517Q814yescomplemented
121#14556516C2×C411yescharacteristic
122#14556516C2×C411yescharacteristic
123#14556516C2×C411yescharacteristic
124#14556516C2×C411yescharacteristic
125#14556513C2×C411yescharacteristic
126#14556513C2×C411yescharacteristic
127#14556513C2×C411yescharacteristic
128#14556513C2×C411yescharacteristic
129#14556501—21no—
130#14556501—21no—
131#14556501—41no—
132C8×Dic73—21no—
133C8×Dic73—21no—
134C8×Dic73—41no—
135#14556498—21no—
136#14556498—21no—
137C2×M16×C73C2311yescharacteristic
138C2×M16×C73C2311yescharacteristic
139C2×M16×C73C2311yescharacteristic
140C2×M16×C73C2311yescharacteristic
141C22×C8×C73C2311yescharacteristic
142C22×C8×C73C2311yescharacteristic
143C2×C42×C73C2311yescharacteristic
144#108×C73—41no—
145#108×C73—41no—
146C4⋊C8×C73—21no—
147C4⋊C8×C73—21no—
148C4⋊C8×C73C2×C411yescharacteristic
149C4⋊C8×C73C2×C411yescharacteristic
150C4⋊C8×C73C2×C411yescharacteristic
151C4⋊C8×C73C2×C411yescharacteristic
152#97×C73—21no—
153C4×C8×C73—21no—
154#11924028—21no—
155#11924028—21no—
156#11924028C2×Q812yes—
157#11924028#4112yes—
158C2×Dic146—21no—
159C2×Dic146—21no—
160C2×Dic146C22×C411yescharacteristic
161C2×D292C22×C411yescharacteristic
162C2×C22⋊D73—21no—
163C22×Dic73—21no—
164C22×Dic73—21no—
165C2×C4×D73—21no—
166C2×C4×D73—21no—
167C2×C4×D73—21no—
168#11924011—42no—
169#11924011—42no—
170C2×#10596831—21no—
171C2×#10596831—21no—
172C2×#10596831—21no—
173C2×#10596831—21no—
174C2×#10596831C2×D411yescharacteristic
175C2×#10596831C2×D411yescharacteristic
176C2×#10596831C2×D411yescharacteristic
177C2×#10596831C2×D411yescharacteristic
178C8×D73—42no—
179C8×D73—42no—
180C4⋊Dic73—21no—
181C4⋊Dic73—21no—
182C4⋊Dic73C22×C411yescharacteristic
183C4⋊Dic73C22×C411yescharacteristic
184C4⋊Dic73C22×C411yescharacteristic
185C4⋊Dic73C22×C411yescharacteristic
186C4⋊Dic73C22×C411yescharacteristic
187C4⋊Dic73C22×C411yescharacteristic
188#11924007—21no—
189#11924007—21no—
190#11924007—21no—
191#11924007—21no—
192#11924007—21no—
193#11924007—21no—
194C22⋊Dic73—21no—
195C22⋊Dic73—21no—
196C22⋊Dic73—21no—
197#11924005—21no—
198#11924005—21no—
199C4×Dic73—21no—
200C4×Dic73—21no—
201C4×Dic73—21no—
202C4×Dic73—21no—
203C4×Dic73—21no—
204C4×Dic73—21no—
205C4×Dic73—21no—
206C4×Dic73—21no—
207C4×Dic73C2×Q812yes—
208C22×C4×C73#4111yescharacteristic
209C22×C4×C73#4111yescharacteristic
210C22×C4×C73C2411yescharacteristic
211M16×C73—21no—
212M16×C73—21no—
213M16×C73—21no—
214M16×C73—21no—
215M16×C73—21no—
216M16×C73—21no—
217M16×C73—21no—
218M16×C73C2×Q812yes—
219C2×C8×C73—21no—
220C2×C8×C73—21no—
221C2×C8×C73—21no—
222C2×C8×C73—21no—
223C2×C8×C73—21no—
224C2×C8×C73—21no—
225C2×C8×C73—21no—
226C2×C8×C73—21no—
227C2×C8×C73C22×C411yescharacteristic
228C2×C8×C73C22×C411yescharacteristic
229C2×C8×C73C22×C411yescharacteristic
230C2×C8×C73C22×C411yescharacteristic
231C42×C73C22×C411yescharacteristic
232C42×C73C22×C411yescharacteristic
233C42×C73C2×D411yescharacteristic
234C42×C73C2×D411yescharacteristic
235C23×C73C2×#4111yescharacteristic
236C22×D73—21no—
237C2×C4×C73—41no—
238C2×C4×C73—41no—
239C2×C4×C73C4×D411yescharacteristic
240C2×C4×C73C4×D411yescharacteristic
241C2×C4×C73C4×D411yescharacteristic
242C2×C4×C73C4×D411yescharacteristic
243C2×C4×C73C23×C411yescharacteristic
244C2×C4×C73C22×D411yescharacteristic
245C2×C4×C73C22×Q811yescharacteristic
246C2×C4×C73C2×#4111yescharacteristic
247C2×C4×C73H(5,𝔽2)11yescharacteristic
248C2×C4×C732−1+411yescharacteristic
249C22⋊D73—22no—
250C22⋊D73—22no—
251C2×Dic73—21no—
252C2×Dic73—21no—
253C2×Dic73—21no—
254C2×Dic73—21no—
255C2×Dic73—21no—
256C2×Dic73—21no—
257C2×Dic73—21no—
258C2×Dic73—22no—
259C2×Dic73—41no—
260C2×Dic73—41no—
261C2×Dic73—41no—
262C2×Dic73—41no—
263C2×Dic73—41no—
264D292—21no—
265D292C4×Q812yes—
266C4×D73—22no—
267C4×D73—22no—
268C4×D73—42no—
269C4×D73—81no—
270Dic146—21no—
271Dic146—42no—
272Dic146—81no—
273Dic146C4×Q812yes—
274C8×C73—21no—
275C8×C73—21no—
276C8×C73—21no—
277C8×C73—21no—
278C8×C73—22no—
279C8×C73—41no—
280C8×C73—41no—
281C8×C73—41no—
282#10596831—21no—
283#10596831—21no—
284#10596831—21no—
285#10596831—21no—
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×C73C2×C4×Q811yescharacteristic
299C4×C73#52011yescharacteristic
300C4×C73#54611yescharacteristic
301C4×C73D4×Q811yescharacteristic
302Dic73—22no—
303Dic73—42no—
304Dic73—41no—
305Dic73—41no—
306Dic73—41no—
307Dic73—41no—
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#2962—731no—
320#2906—731no—
321#1995—731no—
322#1950D7311yescharacteristic, complemented
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#533—731no—
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—1461no—
347#446—1461no—
348#446—1461no—
349C8×Q8—1461no—
350C2×#108C2×D7311yescharacteristic
351C2×#108C2×D7311yescharacteristic
352#427—731no—
353#427—731no—
354#424—731no—
355#424—731no—
356#424—731no—
357#424—731no—
358#424—1461no—
359#424—1461no—
360#423—1461no—
361#423C2×D7311yescharacteristic
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#405—731no—
370#405—731no—
371C4×M16C2×D7311yescharacteristic
372C2×#97—731no—
373C2×C4×C8—731no—
374#376—731no—
375#341C2×D7311yescharacteristic
376#341C2×D7311yescharacteristic
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—1461no—
391C2×M16—1461no—
392C2×M16C22×D7311yescharacteristic
393C2×M16C22×D7311yescharacteristic
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⋊Q8—731no—
403C4⋊Q8—731no—
404#125—731no—
405#125—731no—
406C22⋊Q8—1461no—
407C22⋊Q8—1461no—
408C4×Q8—731no—
409C4×Q8—731no—
410C4×Q8—1461no—
411C4×Q8—1461no—
412C4×D4—731no—
413C4×D4—731no—
414C4×D4—1461no—
415C4×D4—1461no—
416#117—731no—
417#117—731no—
418#117—731no—
419#117—1461no—
420C2×C42—731no—
421C2×C42—731no—
422C2×C42—1461no—
423C2×C42C22×D7311yescharacteristic
424#108—41no—
425#108—41no—
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—731no—
437C4⋊C8—731no—
438C4⋊C8—731no—
439C4⋊C8—731no—
440C4⋊C8—1461no—
441C4⋊C8—1461no—
442C4⋊C8—1461no—
443C4⋊C8—1461no—
444C4⋊C8—1461no—
445C4⋊C8—1461no—
446C4⋊C8—1461no—
447C4⋊C8—1461no—
448C4⋊C8C4×D7311yescharacteristic
449C4⋊C8C4×D7311yescharacteristic
450C4⋊C8C4×D7311yescharacteristic
451C4⋊C8C4×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—2921no—
464#97—1461no—
465#97—1461no—
466C4×C8—21no—
467C4×C8—2921no—
468C4×C8—1461no—
469C4×C8—1461no—
470#95—1461no—
471#95—1461no—
472#41—732no—
473#41—732no—
474#41—1461no—
475#41—1461no—
476C2×Q8—731no—
477C2×Q8—1461no—
478C2×Q8—1461no—
479C2×D4—731no—
480C2×D4—1461no—
481C22×C4—1461no—
482C22×C4—1461no—
483C22×C4—1461no—
484C22×C4—1461no—
485C22×C4—1461no—
486C22×C4#1192402911yescharacteristic
487C22×C4#1192402911yescharacteristic
488C22×C4C23×D7311yescharacteristic
489M16—21no—
490M16—21no—
491M16—21no—
492M16—21no—
493M16—21no—
494M16—21no—
495M16—21no—
496M16—2922no—
497M16—2922no—
498M16Q8×D7312yes—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—2922no—
508C2×C8—2922no—
509C2×C8—731no—
510C2×C8—731no—
511C2×C8—731no—
512C2×C8—731no—
513C2×C8—1461no—
514C2×C8—1461no—
515C2×C8—1461no—
516C2×C8—1461no—
517C2×C8C2×C4×D7311yescharacteristic
518C2×C8C2×C4×D7311yescharacteristic
519C2×C8C2×C4×D7311yescharacteristic
520C2×C8C2×C4×D7311yescharacteristic
521C4⋊C4—731no—
522C4⋊C4—731no—
523C4⋊C4—731no—
524C4⋊C4—731no—
525C4⋊C4—731no—
526C4⋊C4—731no—
527C4⋊C4—1461no—
528C4⋊C4—1461no—
529C4⋊C4—1461no—
530C4⋊C4—1461no—
531C4⋊C4—1461no—
532C4⋊C4—1461no—
533C4⋊C4—1461no—
534C4⋊C4—1461no—
535C22⋊C4—1461no—
536C22⋊C4—1461no—
537C22⋊C4—1461no—
538C22⋊C4—1461no—
539C22⋊C4—1461no—
540C42—732no—
541C42—1461no—
542C42—1461no—
543C42—1461no—
544C42—1461no—
545C42—1461no—
546C42—1461no—
547C42—1461no—
548C42—1461no—
549C42C2×C4×D7311yescharacteristic
550C42C2×C4×D7311yescharacteristic
551C42D4×D7311yescharacteristic
552C42D4×D7311yescharacteristic
553C23—1461no—
554C23C2×#1192402911yescharacteristic
555Q8—2922no—
556Q8—5841no—
557Q8—732no—
558Q8—1461no—
559D4—732no—
560D4—1462no—
561D4—1462no—
562D4—1461no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—2922no—
566C2×C4—2921no—
567C2×C4—2921no—
568C2×C4—2921no—
569C2×C4—2921no—
570C2×C4—2921no—
571C2×C4—5841no—
572C2×C4—1462no—
573C2×C4—1461no—
574C2×C4—1461no—
575C2×C4—1461no—
576C2×C4—1461no—
577C2×C4—1461no—
578C2×C4—1461no—
579C2×C4—1461no—
580C2×C4—1462no—
581C2×C4—1462no—
582C2×C4#1455655311yescharacteristic
583C2×C4#1455655311yescharacteristic
584C2×C4#1455655311yescharacteristic
585C2×C4#1455655311yescharacteristic
586C2×C4C22×C4×D7311yescharacteristic
587C2×C4C2×D4×D7311yescharacteristic
588C2×C4C2×Q8×D7311yescharacteristic
589C2×C4#41×D7311yescharacteristic
590C2×C4#1455663611yescharacteristic
591C2×C4#1455663811yescharacteristic
592C8—22no—
593C8—21no—
594C8—21no—
595C8—21no—
596C8—21no—
597C8—41no—
598C8—41no—
599C8—41no—
600C8—1461no—
601C8—1461no—
602C8—1461no—
603C8—1461no—
604C22—21no—
605C22—21no—
606C22—2921no—
607C22—2921no—
608C22—1462no—
609C22C2×#1455655311yescharacteristic
610C22#1798927511yescharacteristic
611C22#1798929811yescharacteristic
612C4—21no—
613C4—21no—
614C4—21no—
615C4—21no—
616C4—2922no—
617C4—2921no—
618C4—2921no—
619C4—2921no—
620C4—2921no—
621C4—2921no—
622C4—2921no—
623C4—5841no—
624C4—1462no—
625C4C4×Q8×D7311yescharacteristic
626C4#1798906611yescharacteristic
627C4#1798923411yescharacteristic
628C4#1798925011yescharacteristic
629C2—21no—
630C2—21no—
631C2—2922no—
632C2#2261293511yescharacteristic
633C2#2261883311yescharacteristic
634C2#2261884711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#1950C2
socleC22×C73C2×C4×D4
prime radicalC2×#11924028C23
cosocleC22×C4×C73C24
hypercenter#1950D73
hypocenterC73#22984
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1950

Complements

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

NH ≅ G/Ntype
2. #22618878C2semidirect
4. #22610911C2semidirect
5. #22610682C2semidirect
6. #22610677C2semidirect
7. #22610529C2semidirect
8. #22610529C2semidirect
11. #22609790C2semidirect
15. C73×#1950C2semidirect
20. #17988895C4semidirect
21. #17988895C4semidirect
22. #17988888C4semidirect
23. #17988888C4semidirect
24. #17988883C4semidirect
25. #17988878C4semidirect
26. #17988873C4semidirect
27. #17988868C4semidirect
120. #14556517Q8semidirect
322. #1950D73semidirect
333. C73#22984semidirect

Maximal subgroups

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

subgroupindex
#226197212
#226188782
#226185002
#226109112
#226106822
#226106772
#226105292
#226102032
#226097902
#226097742
#226097672
#226097442
C73×#19502
#2298473