Finite Group Databasebeta

← #33098315

Subgroups — #33098315

Order 18688.

628 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22619721C211yesmaximal, characteristic
2#22618871C211yesmaximal, characteristic, complemented
3#22618580C211yesmaximal, characteristic
4#22610874C211yesmaximal, characteristic, complemented
5#22610707C211yesmaximal, characteristic, complemented
6#22610684C211yesmaximal, characteristic, complemented
7#22610679C211yesmaximal, characteristic, complemented
8#22610642C211yesmaximal, characteristic
9#22610635C211yesmaximal, characteristic
10#22610580C211yesmaximal, characteristic
11#22610580C211yesmaximal, characteristic
12#22610531C211yesmaximal, characteristic, complemented
13#22610531C211yesmaximal, characteristic, complemented
14#22609952C211yesmaximal, characteristic
15C73×#1771C211yesmaximal, characteristic, complemented
16#17989144C2211yescharacteristic
17C4×#11924028C2211yescharacteristic
18#17988895C411yescharacteristic, complemented
19#17988895C411yescharacteristic, complemented
20#17988888C411yescharacteristic, complemented
21#17988888C411yescharacteristic, complemented
22#17988883C411yescharacteristic, complemented
23#17988878C411yescharacteristic, complemented
24#17988873C411yescharacteristic, complemented
25#17988868C411yescharacteristic, complemented
26#17988715—21no—
27#17988715—21no—
28#17988715—21no—
29#17988715—21no—
30#17988649—21no—
31#17988649—21no—
32#17988642—21no—
33#17988642—21no—
34C2×#14556527C2211yescharacteristic
35C2×#14556527C2211yescharacteristic
36#17988625C2211yescharacteristic
37#17988625C2211yescharacteristic
38#17988613C2211yescharacteristic
39#17988613C2211yescharacteristic
40#17988613C2211yescharacteristic
41#17988613C2211yescharacteristic
42#17988611C2211yescharacteristic
43C2×#14556519C2211yescharacteristic
44C2×#14556519C2211yescharacteristic
45#17988584C2211yescharacteristic
46#17988584C2211yescharacteristic
47#17988553C2211yescharacteristic
48#17988553C2211yescharacteristic
49#17988542C2211yescharacteristic
50#17988542C2211yescharacteristic
51C4×#11924012C2211yescharacteristic
52#17988352C2211yescharacteristic
53#17988352C2211yescharacteristic
54#17988347C2211yescharacteristic
55#17988347C2211yescharacteristic
56#17988347C2211yescharacteristic
57#17988347C2211yescharacteristic
58#17988347C2211yescharacteristic
59#17988347C2211yescharacteristic
60C2×C4⋊C8×C73C2211yescharacteristic
61C2×#97×C73C2211yescharacteristic
62C2×#97×C73C2211yescharacteristic
63C2×C4×C8×C73C2211yescharacteristic
64C4×C4⋊C4×C73C2211yescharacteristic
65#336×C73C2211yescharacteristic
66#336×C73C2211yescharacteristic
67C2×#11924028C2311yescharacteristic
68C2×#11924012C2311yescharacteristic
69C2×#11924012C2311yescharacteristic
70C2×#11924012C2311yescharacteristic
71C2×#11924012C2311yescharacteristic
72#14556591C2×C411yescharacteristic
73#14556591C2×C411yescharacteristic
74#14556583C2×C411yescharacteristic
75#14556583C2×C411yescharacteristic
76#14556570—21no—
77#14556570—21no—
78C4×Dic146—21no—
79C4×Dic146—21no—
80C4×Dic146C2×C411yescharacteristic
81C4×Dic146C2×C411yescharacteristic
82C4×D292C2×C411yescharacteristic
83C4×D292C2×C411yescharacteristic
84C4×C22⋊D73—21no—
85C4×C22⋊D73—21no—
86#14556550C2311yescharacteristic
87#14556550C2311yescharacteristic
88#14556550C2311yescharacteristic
89#14556548—21no—
90C42×D73—21no—
91#14556527—41no—
92#14556527—41no—
93#14556525C2×C411yescharacteristic
94#14556525C2×C411yescharacteristic
95#14556525C2×C411yescharacteristic
96#14556525C2×C411yescharacteristic
97#14556523C2×C411yescharacteristic
98#14556523C2×C411yescharacteristic
99#14556523C2×C411yescharacteristic
100#14556523C2×C411yescharacteristic
101C4⋊#10596831—21no—
102C4⋊#10596831—21no—
103#14556520—21no—
104#14556520—21no—
105#14556520—21no—
106#14556520—21no—
107#14556520—21no—
108#14556520—21no—
109#14556520—21no—
110#14556520—21no—
111#14556519—41no—
112#14556519—41no—
113#14556516C2×C411yescharacteristic
114#14556516C2×C411yescharacteristic
115#14556516C2×C411yescharacteristic
116#14556516C2×C411yescharacteristic
117#14556513C2×C411yescharacteristic
118#14556513C2×C411yescharacteristic
119#14556513C2×C411yescharacteristic
120#14556513C2×C411yescharacteristic
121#14556503—21no—
122#14556503—21no—
123#14556503—21no—
124#14556503—21no—
125#14556502—21no—
126#14556501—21no—
127#14556501—21no—
128C4×#10596831—21no—
129C8×Dic73—21no—
130C8×Dic73—21no—
131C22×C8×C73C2311yescharacteristic
132C22×C8×C73C2311yescharacteristic
133C22×C8×C73C2311yescharacteristic
134C22×C8×C73C2311yescharacteristic
135C2×C4⋊C4×C73—21no—
136C2×C42×C73C2311yescharacteristic
137C2×C42×C73C2311yescharacteristic
138C2×C42×C73C2311yescharacteristic
139C4⋊C8×C73C2×C411yescharacteristic
140C4⋊C8×C73C2×C411yescharacteristic
141C4⋊C8×C73C2×C411yescharacteristic
142C4⋊C8×C73C2×C411yescharacteristic
143#97×C73—41no—
144#97×C73D411yescharacteristic
145#97×C73D411yescharacteristic
146#97×C73D411yescharacteristic
147#97×C73D411yescharacteristic
148C4×C8×C73—41no—
149#95×C73—21no—
150#11924028—21no—
151#11924028—21no—
152#11924028—21no—
153#11924028—21no—
154C2×Dic146—21no—
155C2×Dic146—21no—
156C2×Dic146C22×C411yescharacteristic
157C2×D292C22×C411yescharacteristic
158C2×C22⋊D73—21no—
159C2×C4×D73—21no—
160C2×C4×D73—21no—
161C2×C4×D73—21no—
162#11924012—21no—
163#11924012—21no—
164#11924012—21no—
165#11924012—21no—
166#11924012—21no—
167#11924012—21no—
168#11924012—21no—
169#11924012—21no—
170C2×#10596831—21no—
171C2×#10596831—21no—
172C2×#10596831—21no—
173C2×#10596831—21no—
174C4⋊Dic73—21no—
175C4⋊Dic73—21no—
176C4⋊Dic73C22×C411yescharacteristic
177C4⋊Dic73C22×C411yescharacteristic
178C4⋊Dic73C22×C411yescharacteristic
179C4⋊Dic73C22×C411yescharacteristic
180C4⋊Dic73C22×C411yescharacteristic
181C4⋊Dic73C22×C411yescharacteristic
182#11924007—21no—
183#11924007—21no—
184#11924007—21no—
185#11924007—21no—
186#11924007—21no—
187#11924007—21no—
188C22⋊Dic73—21no—
189C22⋊Dic73—21no—
190C22⋊Dic73—21no—
191#11924005—21no—
192#11924005—21no—
193C4×Dic73—21no—
194C4×Dic73—21no—
195C4×Dic73—21no—
196C4×Dic73—21no—
197C4×Dic73—21no—
198C22×C4×C73—21no—
199C22×C4×C73—21no—
200C22×C4×C73#4111yescharacteristic
201C22×C4×C73#4111yescharacteristic
202C22×C4×C73C2411yescharacteristic
203C2×C8×C73—21no—
204C2×C8×C73—21no—
205C2×C8×C73—21no—
206C2×C8×C73—21no—
207C2×C8×C73—21no—
208C2×C8×C73—21no—
209C2×C8×C73—21no—
210C2×C8×C73—21no—
211C2×C8×C73C22×C411yescharacteristic
212C2×C8×C73C22×C411yescharacteristic
213C2×C8×C73C22×C411yescharacteristic
214C2×C8×C73C22×C411yescharacteristic
215C2×C8×C73C2×D411yescharacteristic
216C2×C8×C73C2×D411yescharacteristic
217C2×C8×C73C2×D411yescharacteristic
218C2×C8×C73C2×D411yescharacteristic
219C4⋊C4×C73—42no—
220C42×C73—21no—
221C42×C73—21no—
222C42×C73—21no—
223C42×C73—21no—
224C42×C73C22×C411yescharacteristic
225C42×C73C22×C411yescharacteristic
226C42×C73C2×D411yescharacteristic
227C42×C73C2×D411yescharacteristic
228C23×C73C2×#4111yescharacteristic
229C22×D73—21no—
230C2×C4×C73—22no—
231C2×C4×C73—41no—
232C2×C4×C73—41no—
233C2×C4×C73—41no—
234C2×C4×C73—41no—
235C2×C4×C73—41no—
236C2×C4×C73—41no—
237C2×C4×C73—41no—
238C2×C4×C73C4×D411yescharacteristic
239C2×C4×C73C4×D411yescharacteristic
240C2×C4×C73C4×D411yescharacteristic
241C2×C4×C73C4×D411yescharacteristic
242C2×C4×C73C23×C411yescharacteristic
243C2×C4×C73C22×D411yescharacteristic
244C2×C4×C73H(5,𝔽2)11yescharacteristic
245C2×C4×C732−1+411yescharacteristic
246C2×C4×C732−1+411yescharacteristic
247C2×C4×C732−1+411yescharacteristic
248C22⋊D73—41no—
249C22⋊D73—41no—
250C2×Dic73—21no—
251C2×Dic73—21no—
252C2×Dic73—21no—
253C2×Dic73—21no—
254C2×Dic73—21no—
255C2×Dic73—21no—
256C2×Dic73—21no—
257D292—21no—
258D292—21no—
259C4×D73—41no—
260C4×D73—41no—
261C4×D73—81no—
262C4×D73—81no—
263Dic146—21no—
264Dic146—21no—
265Dic146—81no—
266Dic146—81no—
267C8×C73—21no—
268C8×C73—21no—
269C8×C73—21no—
270C8×C73—21no—
271C8×C73—21no—
272C8×C73—21no—
273C8×C73—21no—
274C8×C73—21no—
275#10596831—41no—
276#10596831—41no—
277#10596831—41no—
278#10596831—41no—
279C22×C73—21no—
280C22×C73—21no—
281C22×C73C2×C4×D411yescharacteristic
282C22×C73#54111yescharacteristic
283C22×C73#54211yescharacteristic
284C2×D73—41no—
285C2×D73—41no—
286C2×D73—41no—
287C4×C73—21no—
288C4×C73—21no—
289C4×C73—21no—
290C4×C73—21no—
291C4×C73—42no—
292C4×C73—81no—
293C4×C73#51911yescharacteristic
294C4×C73#52011yescharacteristic
295C4×C73#53611yescharacteristic
296C4×C73#53711yescharacteristic
297Dic73—41no—
298Dic73—41no—
299Dic73—41no—
300Dic73—41no—
301Dic73—41no—
302Dic73—41no—
303Dic73—41no—
304#22132—731nomaximal, Sylow
305C2×C73—21no—
306C2×C73—21no—
307C2×C73#232311yescharacteristic
308C2×C73#295611yescharacteristic
309C2×C73#295711yescharacteristic
310D73—81no—
311#3076—731no—
312#2961—731no—
313#2923—731no—
314#1986—731no—
315#1950—731no—
316#1946—731no—
317#1945—731no—
318#1938—731no—
319#1937—731no—
320#1929—731no—
321#1929—731no—
322#1922—731no—
323#1922—731no—
324#1806—731no—
325#1771D7311yescharacteristic, complemented
326C73#2213211yescharacteristic, complemented, Sylow
327#533—731no—
328C4×#41—731no—
329#479—731no—
330#479—731no—
331#478—731no—
332#478—731no—
333#477—731no—
334#476—731no—
335#475—731no—
336#474—731no—
337#446—1461no—
338#446—1461no—
339#446—1461no—
340#446—1461no—
341#433—1461no—
342#433—1461no—
343#432—1461no—
344#432—1461no—
345C2×#108—731no—
346C2×#108—731no—
347#427—731no—
348#427—731no—
349#424—731no—
350#424—731no—
351#424—731no—
352#424—731no—
353#423—731no—
354C2×C4⋊C8C2×D7311yescharacteristic
355C2×#104—731no—
356C2×#104—731no—
357#416—731no—
358#416—731no—
359#408—731no—
360#408—731no—
361#405—731no—
362#405—731no—
363C4×M16—731no—
364C2×#97C2×D7311yescharacteristic
365C2×#97C2×D7311yescharacteristic
366C2×C4×C8C2×D7311yescharacteristic
367C4×C4⋊C4C2×D7311yescharacteristic
368#341—731no—
369#341—731no—
370#339—731no—
371#339—731no—
372#339—731no—
373#339—731no—
374#339—731no—
375#339—731no—
376#336C2×D7311yescharacteristic
377#336C2×D7311yescharacteristic
378C2×#41—731no—
379C2×M16—731no—
380C2×M16—731no—
381C2×M16—731no—
382C2×M16—731no—
383C22×C8C22×D7311yescharacteristic
384C22×C8C22×D7311yescharacteristic
385C22×C8C22×D7311yescharacteristic
386C22×C8C22×D7311yescharacteristic
387C4⋊Q8—731no—
388C4⋊Q8—731no—
389#125—731no—
390#125—731no—
391C22⋊Q8—1461no—
392C22⋊Q8—1461no—
393C4×Q8—731no—
394C4×Q8—731no—
395C4×Q8—1461no—
396C4×Q8—1461no—
397C4×D4—731no—
398C4×D4—731no—
399C4×D4—1461no—
400C4×D4—1461no—
401#117—731no—
402#117—731no—
403#117—731no—
404#117—1461no—
405C2×C4⋊C4—21no—
406C2×C42—1461no—
407C2×C42C22×D7311yescharacteristic
408C2×C42C22×D7311yescharacteristic
409C2×C42C22×D7311yescharacteristic
410#108—2921no—
411#108—2921no—
412#107—731no—
413#107—731no—
414#107—731no—
415#107—731no—
416#106—731no—
417#106—731no—
418#106—731no—
419#106—731no—
420C4⋊C8—1461no—
421C4⋊C8—1461no—
422C4⋊C8—1461no—
423C4⋊C8—1461no—
424C4⋊C8—1461no—
425C4⋊C8—1461no—
426C4⋊C8—1461no—
427C4⋊C8—1461no—
428C4⋊C8—1461no—
429C4⋊C8—1461no—
430C4⋊C8C4×D7311yescharacteristic
431C4⋊C8C4×D7311yescharacteristic
432C4⋊C8C4×D7311yescharacteristic
433C4⋊C8C4×D7311yescharacteristic
434#104—2921no—
435#104—2921no—
436#103—731no—
437#103—731no—
438#103—731no—
439#103—731no—
440#102—731no—
441#102—731no—
442#102—731no—
443#102—731no—
444C22⋊C8—1461no—
445C22⋊C8—1461no—
446C22⋊C8—1461no—
447C22⋊C8—1461no—
448#97—41no—
449#97—1461no—
450#97—1461no—
451#97—1461no—
452#97D29211yescharacteristic
453#97D29211yescharacteristic
454#97D29211yescharacteristic
455#97D29211yescharacteristic
456C4×C8—41no—
457C4×C8—1461no—
458C4×C8—1461no—
459C4×C8—1461no—
460#95—21no—
461#41—1461no—
462#41—1461no—
463#41—1461no—
464#41—1461no—
465C2×Q8—731no—
466C2×Q8—1461no—
467C2×Q8—1461no—
468C2×D4—731no—
469C2×D4—1461no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—1461no—
473C22×C4—1461no—
474C22×C4—1461no—
475C22×C4#1192402811yescharacteristic
476C22×C4#1192402811yescharacteristic
477C22×C4C23×D7311yescharacteristic
478M16—1461no—
479M16—1461no—
480M16—1461no—
481M16—1461no—
482M16—1461no—
483M16—1461no—
484M16—1461no—
485M16—1461no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—1461no—
495C2×C8—1461no—
496C2×C8—1461no—
497C2×C8—1461no—
498C2×C8C2×C4×D7311yescharacteristic
499C2×C8C2×C4×D7311yescharacteristic
500C2×C8C2×C4×D7311yescharacteristic
501C2×C8C2×C4×D7311yescharacteristic
502C2×C8C2×D29211yescharacteristic
503C2×C8C2×D29211yescharacteristic
504C2×C8C2×D29211yescharacteristic
505C2×C8C2×D29211yescharacteristic
506C4⋊C4—42no—
507C4⋊C4—731no—
508C4⋊C4—731no—
509C4⋊C4—731no—
510C4⋊C4—731no—
511C4⋊C4—731no—
512C4⋊C4—731no—
513C4⋊C4—1461no—
514C4⋊C4—1461no—
515C4⋊C4—1461no—
516C4⋊C4—1461no—
517C4⋊C4—1461no—
518C4⋊C4—1461no—
519C4⋊C4—1461no—
520C4⋊C4—1461no—
521C22⋊C4—1461no—
522C22⋊C4—1461no—
523C22⋊C4—1461no—
524C22⋊C4—1461no—
525C22⋊C4—1461no—
526C42—21no—
527C42—21no—
528C42—21no—
529C42—21no—
530C42—1461no—
531C42—1461no—
532C42—1461no—
533C42—1461no—
534C42—1461no—
535C42C2×C4×D7311yescharacteristic
536C42C2×C4×D7311yescharacteristic
537C42C2×D29211yescharacteristic
538C42C2×D29211yescharacteristic
539C23—1461no—
540C23C2×#1192402811yescharacteristic
541Q8—5841no—
542Q8—5841no—
543Q8—1461no—
544Q8—1461no—
545D4—2921no—
546D4—2921no—
547D4—1461no—
548D4—1461no—
549C2×C4—22no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—2921no—
558C2×C4—2921no—
559C2×C4—5841no—
560C2×C4—5841no—
561C2×C4—1461no—
562C2×C4—1461no—
563C2×C4—1461no—
564C2×C4—1461no—
565C2×C4—1461no—
566C2×C4—1461no—
567C2×C4—1461no—
568C2×C4C4×D29211yescharacteristic
569C2×C4C4×D29211yescharacteristic
570C2×C4C4×D29211yescharacteristic
571C2×C4C4×D29211yescharacteristic
572C2×C4C22×C4×D7311yescharacteristic
573C2×C4C22×D29211yescharacteristic
574C2×C4#1455663611yescharacteristic
575C2×C4#1455663811yescharacteristic
576C2×C4#1455663811yescharacteristic
577C2×C4#1455663911yescharacteristic
578C8—21no—
579C8—21no—
580C8—21no—
581C8—21no—
582C8—21no—
583C8—21no—
584C8—21no—
585C8—21no—
586C8—2921no—
587C8—2921no—
588C8—2921no—
589C8—2921no—
590C22—21no—
591C22—21no—
592C22—2921no—
593C22—2921no—
594C22—2921no—
595C22C2×C4×D29211yescharacteristic
596C22#1798919511yescharacteristic
597C22#1798920211yescharacteristic
598C4—21no—
599C4—21no—
600C4—21no—
601C4—21no—
602C4—42no—
603C4—81no—
604C4—2921no—
605C4—2921no—
606C4—2921no—
607C4—2921no—
608C4—2921no—
609C4—2921no—
610C4—2921no—
611C4#1798906311yescharacteristic
612C4#1798906611yescharacteristic
613C4#1798916311yescharacteristic
614C4#1798916811yescharacteristic
615C2—21no—
616C2—21no—
617C2—5841no—
618C2#2261261411yescharacteristic
619C2#2261884211yescharacteristic
620C2#2261884911yescharacteristic
subgroupG/H
centerC2×C4C22×D292
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#1771C2
socleC22×C73C2×C4×D4
prime radicalC2×#11924028C23
cosocleC22×C4×C73C24
hypercenter#1771D73
hypocenterC73#22132
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×#97 ◁ #1771

Complements

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

NH ≅ G/Ntype
2. #22618871C2semidirect
4. #22610874C2semidirect
5. #22610707C2semidirect
6. #22610684C2semidirect
7. #22610679C2semidirect
12. #22610531C2semidirect
13. #22610531C2semidirect
15. C73×#1771C2semidirect
18. #17988895C4semidirect
19. #17988895C4semidirect
20. #17988888C4semidirect
21. #17988888C4semidirect
22. #17988883C4semidirect
23. #17988878C4semidirect
24. #17988873C4semidirect
25. #17988868C4semidirect
325. #1771D73semidirect
326. C73#22132semidirect

Maximal subgroups

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

subgroupindex
#226197212
#226188712
#226185802
#226108742
#226107072
#226106842
#226106792
#226106422
#226106352
#226105802
#226105312
#226099522
C73×#17712
#2213273