Finite Group Databasebeta

← #33057140

Subgroups — #33057140

Order 18688.

650 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22619978C211yesmaximal, characteristic
2#22619093C211yesmaximal, characteristic, complemented
3#22608819C211yesmaximal, characteristic, complemented
4#22608814C211yesmaximal, characteristic, complemented
5#22608807C211yesmaximal, characteristic, complemented
6#22608795C211yesmaximal, characteristic, complemented
7#22608793C211yesmaximal, characteristic, complemented
8#22608788C211yesmaximal, characteristic, complemented
9C8×#11924016C211yesmaximal, characteristic, complemented
10C8×#11924013C211yesmaximal, characteristic, complemented
11#22608717C211yesmaximal, characteristic, complemented
12#22608389C211yesmaximal, characteristic, complemented
13C2×D4⋊#10596831C211yesmaximal, characteristic, complemented
14#22608215C211yesmaximal, characteristic, complemented
15C73×#2974C211yesmaximal, characteristic, complemented
16#17989121C2211yescharacteristic
17#17988922C411yescharacteristic
18#17988905C411yescharacteristic
19#17988887C411yescharacteristic
20#17988887C411yescharacteristic
21#17988802C411yescharacteristic
22#17988802C411yescharacteristic
23#17988738C411yescharacteristic
24#17988721C411yescharacteristic
25#17988717C2211yescharacteristic, complemented
26C8×Dic146C2211yescharacteristic, complemented
27C4×#11924016C2211yescharacteristic
28C4×#11924016C2211yescharacteristic
29C4×#11924013C2211yescharacteristic
30C4×#11924013C2211yescharacteristic
31#17988666C2211yescharacteristic, complemented
32#17988655—21no—
33C8×D292C2211yescharacteristic, complemented
34#17988650—21no—
35#17988647—21no—
36#17988640C2211yescharacteristic
37#17988612—21no—
38C2×C4⋊#10596831C2211yescharacteristic
39C2×C4×#10596831C2211yescharacteristic
40#17988339C2211yescharacteristic, complemented
41#17988339C2211yescharacteristic, complemented
42#17988337C2211yescharacteristic, complemented
43#17988337C2211yescharacteristic, complemented
44#17988317C2211yescharacteristic, complemented
45#17988317C2211yescharacteristic, complemented
46D4⋊#10596831C2211yescharacteristic
47D4⋊#10596831C2211yescharacteristic
48D4⋊#10596831C2211yescharacteristic
49D4⋊#10596831C2211yescharacteristic
50#17988314C2211yescharacteristic, complemented
51#17988314C2211yescharacteristic, complemented
52#17988309C2211yescharacteristic, complemented
53#17988309C2211yescharacteristic, complemented
54C8×#10596831C2211yescharacteristic, complemented
55C8×#10596831C2211yescharacteristic, complemented
56C2×C4×D4×C73C2211yescharacteristic
57#436×C73C2211yescharacteristic
58#436×C73C2211yescharacteristic
59#435×C73—21no—
60#435×C73—21no—
61C8×D4×C73C2211yescharacteristic
62C8×D4×C73C2211yescharacteristic
63#432×C73C2211yescharacteristic
64#431×C73C2211yescharacteristic
65#407×C73—21no—
66C2×C22⋊C8×C73—21no—
67C2×#11924016C2×C411yescharacteristic
68C2×#11924016C2×C411yescharacteristic
69C2×#11924013C2×C411yescharacteristic
70C2×#11924013C2×C411yescharacteristic
71C2×#11924011—21no—
72C22×#10596831—21no—
73C22×#10596831—21no—
74C2×C8×D73—21no—
75#14556585—21no—
76#14556583C2×C411yescharacteristic
77#14556579C2×C411yescharacteristic
78#14556574—21no—
79#14556570C2×C411yescharacteristic
80#14556565C2×C411yescharacteristic
81C4×Dic146C2311yescharacteristic
82C4×D292C2311yescharacteristic
83C4×C22⋊D73—21no—
84#14556548—21no—
85#14556524C2×C411yescharacteristic
86#14556524C2×C411yescharacteristic
87#14556522C2×C411yescharacteristic
88#14556522C2×C411yescharacteristic
89C4⋊#10596831—21no—
90C4⋊#10596831C2×C411yescharacteristic
91C4⋊#10596831C2×C411yescharacteristic
92C4⋊#10596831C2311yescharacteristic
93C4⋊#10596831C2311yescharacteristic
94#14556520—21no—
95#14556520—21no—
96#14556514C2×C411yescharacteristic
97#14556514C2×C411yescharacteristic
98#14556512C2×C411yescharacteristic
99#14556512C2×C411yescharacteristic
100#14556512C2×C411yescharacteristic
101#14556512C2×C411yescharacteristic
102#14556511C2×C411yescharacteristic
103#14556511C2×C411yescharacteristic
104C22⋊#10596831C2×C411yescharacteristic
105C22⋊#10596831C2×C411yescharacteristic
106#14556503—21no—
107#14556503—21no—
108#14556501—21no—
109C4×#10596831—21no—
110C4×#10596831C2311yescharacteristic
111C4×#10596831C2311yescharacteristic
112C4×#10596831C2311yescharacteristic
113C4×#10596831C2311yescharacteristic
114C8×Dic73—21no—
115C22×D4×C73C2×C411yescharacteristic
116C23×C4×C73—21no—
117C2×M16×C73—21no—
118C2×M16×C73—21no—
119C22×C8×C73—21no—
120C22×C8×C73—21no—
121C4×D4×C73—21no—
122C4×D4×C73—21no—
123C4×D4×C73C2×C411yescharacteristic
124C4×D4×C73C2×C411yescharacteristic
125C4×D4×C73C2311yescharacteristic
126C4×D4×C73C2311yescharacteristic
127C2×C4⋊C4×C73C2×C411yescharacteristic
128C2×C22⋊C4×C73—21no—
129C2×C42×C73C2311yescharacteristic
130C4⋊C8×C73D411yescharacteristic
131C4⋊C8×C73D411yescharacteristic
132C4⋊C8×C73C2311yescharacteristic
133C4⋊C8×C73C2311yescharacteristic
134C22⋊C8×C73—21no—
135C22⋊C8×C73—21no—
136C22⋊C8×C73—21no—
137C22⋊C8×C73—21no—
138C22⋊C8×C73—21no—
139C22⋊C8×C73D411yescharacteristic
140C22⋊C8×C73D411yescharacteristic
141#97×C73—21no—
142C4×C8×C73C2311yescharacteristic
143C4×C8×C73C2311yescharacteristic
144C2×Dic146C22×C411yescharacteristic
145C2×D292C22×C411yescharacteristic
146C2×C22⋊D73—21no—
147C2×C4×D73—21no—
148#11924016—22no—
149#11924016—41no—
150#11924013—22no—
151#11924013—41no—
152#11924011—81no—
153C2×#10596831—24no—
154C2×#10596831—21no—
155C2×#10596831—21no—
156C2×#10596831—21no—
157C2×#10596831—21no—
158C2×#10596831—81no—
159C2×#10596831C22×C411yescharacteristic
160C2×#10596831C22×C411yescharacteristic
161C2×#10596831C22×C411yescharacteristic
162C2×#10596831C22×C411yescharacteristic
163C8×D73—81no—
164C4⋊Dic73C22×C411yescharacteristic
165C4⋊Dic73C22×C411yescharacteristic
166#11924007—21no—
167#11924007—21no—
168#11924007—21no—
169#11924007—21no—
170C22⋊Dic73—21no—
171#11924005—21no—
172#11924005—21no—
173#11924005—21no—
174#11924005—21no—
175C4×Dic73—21no—
176C24×C73—21no—
177C2×D4×C73—22no—
178C2×D4×C73—21no—
179C2×D4×C73—41no—
180C2×D4×C73C22×C411yescharacteristic
181C2×D4×C73C22×C411yescharacteristic
182C22×C4×C73—21no—
183C22×C4×C73—21no—
184C22×C4×C73—21no—
185C22×C4×C73—21no—
186C22×C4×C73—21no—
187C22×C4×C73—81no—
188C22×C4×C73—81no—
189C22×C4×C73C22×C411yescharacteristic
190C22×C4×C73C2×D411yescharacteristic
191C22×C4×C73#4111yescharacteristic
192M16×C73—81no—
193M16×C73—81no—
194C2×C8×C73—21no—
195C2×C8×C73—21no—
196C2×C8×C73—81no—
197C2×C8×C73—81no—
198C2×C8×C73C2×D411yescharacteristic
199C2×C8×C73C2×D411yescharacteristic
200C2×C8×C73C2×D411yescharacteristic
201C2×C8×C73C2×D411yescharacteristic
202C4⋊C4×C73—21no—
203C4⋊C4×C73C22×C411yescharacteristic
204C4⋊C4×C73C22×C411yescharacteristic
205C22⋊C4×C73—21no—
206C22⋊C4×C73—21no—
207C22⋊C4×C73—21no—
208C22⋊C4×C73—21no—
209C42×C73C22×C411yescharacteristic
210C42×C73C2×D411yescharacteristic
211C42×C73#4111yescharacteristic
212C42×C73C2411yescharacteristic
213C23×C73—21no—
214C23×C73—21no—
215C23×C73—42no—
216C23×C73—42no—
217C23×C73—81no—
218C23×C73C4×D411yescharacteristic
219C22×D73—21no—
220D4×C73—21no—
221D4×C73—21no—
222D4×C73—21no—
223D4×C73—42no—
224D4×C73#13112yes—
225C2×C4×C73—22no—
226C2×C4×C73—21no—
227C2×C4×C73—21no—
228C2×C4×C73—21no—
229C2×C4×C73—21no—
230C2×C4×C73—21no—
231C2×C4×C73—21no—
232C2×C4×C73—41no—
233C2×C4×C73—41no—
234C2×C4×C73—41no—
235C2×C4×C73—41no—
236C2×C4×C73—81no—
237C2×C4×C73—81no—
238C2×C4×C73—81no—
239C2×C4×C73C4×D411yescharacteristic
240C2×C4×C73C4×D411yescharacteristic
241C2×C4×C73C4×D411yescharacteristic
242C2×C4×C73C23×C411yescharacteristic
243C2×C4×C73C22×D411yescharacteristic
244C2×C4×C73C2×#4111yescharacteristic
245C22⋊D73—42no—
246C2×Dic73—21no—
247C2×Dic73—21no—
248C2×Dic73—21no—
249D292—21no—
250D292—21no—
251C4×D73—41no—
252C4×D73—41no—
253Dic146—21no—
254Dic146—21no—
255C8×C73—21no—
256C8×C73—21no—
257C8×C73—21no—
258C8×C73—21no—
259C8×C73—41no—
260C8×C73—41no—
261#10596831—22no—
262#10596831—22no—
263#10596831—21no—
264#10596831—21no—
265#10596831—21no—
266#10596831—21no—
267#10596831—41no—
268#10596831—41no—
269C22×C73—21no—
270C22×C73—21no—
271C22×C73—22no—
272C22×C73—41no—
273C22×C73—41no—
274C22×C73—41no—
275C22×C73—41no—
276C22×C73—41no—
277C22×C73—84no—
278C22×C73#44312yes—
279C22×C73C2×C4×D411yescharacteristic
280C2×D73—41no—
281C2×D73—41no—
282C2×D73—41no—
283C4×C73—21no—
284C4×C73—21no—
285C4×C73—21no—
286C4×C73—21no—
287C4×C73—41no—
288C4×C73—41no—
289C4×C73C2×#13111yescharacteristic
290C4×C73#56811yescharacteristic
291C4×C73#57611yescharacteristic
292C4×C73#57711yescharacteristic
293Dic73—41no—
294Dic73—41no—
295Dic73—41no—
296#18014—731nomaximal, Sylow
297C2×C73—22no—
298C2×C73—42no—
299C2×C73—81no—
300C2×C73#293311yescharacteristic
301C2×C73#294611yescharacteristic
302C2×C73C2×#44311yescharacteristic
303D73—81no—
304#3105—731no—
305#2994—731no—
306#2974D7311yescharacteristic, complemented
307#1590—731no—
308#1589—731no—
309#1588—731no—
310#1586—731no—
311#1586—731no—
312#1585—731no—
313C8×SD16—731no—
314C8×D8—731no—
315#1573—731no—
316#1494—731no—
317C2×D4⋊C8—731no—
318#1450—731no—
319C73#1801411yescharacteristic, complemented, Sylow
320#529—731no—
321C2×C4×D4C2×D7311yescharacteristic
322#484—731no—
323#481—731no—
324#478—731no—
325#478—731no—
326#463—731no—
327#463—731no—
328#450—731no—
329#447—731no—
330#446—731no—
331C8×Q8—731no—
332C4×SD16—731no—
333C4×SD16—731no—
334C4×D8—731no—
335C4×D8—731no—
336#436—731no—
337#436C2×D7311yescharacteristic
338#436C2×D7311yescharacteristic
339#435—21no—
340#435—21no—
341#435—1461no—
342C8×D4—731no—
343C8×D4—1461no—
344C8×D4C2×D7311yescharacteristic
345C8×D4C2×D7311yescharacteristic
346#433—1461no—
347#432C2×D7311yescharacteristic
348#431—731no—
349#431C2×D7311yescharacteristic
350#424—1461no—
351C2×C4⋊C8—731no—
352#407—21no—
353C2×C22⋊C8—21no—
354C2×C4×C8—731no—
355#335—731no—
356#335—731no—
357#334—731no—
358#334—731no—
359Q8⋊C8—731no—
360Q8⋊C8—731no—
361D4⋊C8—731no—
362D4⋊C8—731no—
363D4⋊C8—731no—
364D4⋊C8—731no—
365D4⋊C8—731no—
366D4⋊C8—731no—
367#322—731no—
368#322—731no—
369C82—731no—
370C82—731no—
371C22×D4C4×D7311yescharacteristic
372C23×C4—21no—
373C2×SD16—731no—
374C2×SD16—731no—
375C2×D8—731no—
376C2×D8—731no—
377C2×M16—21no—
378C2×M16—21no—
379C2×M16—1461no—
380C22×C8—21no—
381C22×C8—21no—
382C22×C8—1461no—
383C22×C8—1461no—
384C22×C8—1461no—
385#126—1461no—
386#125—731no—
387#124—731no—
388#123—1461no—
389C22⋊Q8—731no—
390#121—731no—
391C4×Q8—731no—
392C4×D4—21no—
393C4×D4—21no—
394C4×D4—731no—
395C4×D4—1461no—
396C4×D4C4×D7311yescharacteristic
397C4×D4C4×D7311yescharacteristic
398C4×D4C22×D7311yescharacteristic
399C4×D4C22×D7311yescharacteristic
400#117—1461no—
401C2×C4⋊C4C4×D7311yescharacteristic
402C2×C22⋊C4—21no—
403C2×C42C22×D7311yescharacteristic
404#107—731no—
405#107—731no—
406#106—731no—
407#106—731no—
408C4⋊C8—731no—
409C4⋊C8—731no—
410C4⋊C8—731no—
411C4⋊C8—731no—
412C4⋊C8—1461no—
413C4⋊C8—1461no—
414C4⋊C8—1461no—
415C4⋊C8C22⋊D7311yescharacteristic
416C4⋊C8C22⋊D7311yescharacteristic
417C4⋊C8C22×D7311yescharacteristic
418C4⋊C8C22×D7311yescharacteristic
419#103—731no—
420#103—731no—
421#102—731no—
422#102—731no—
423#102—731no—
424#102—731no—
425#102—731no—
426#102—731no—
427C22⋊C8—21no—
428C22⋊C8—21no—
429C22⋊C8—21no—
430C22⋊C8—21no—
431C22⋊C8—21no—
432C22⋊C8—731no—
433C22⋊C8—731no—
434C22⋊C8—1461no—
435C22⋊C8—1461no—
436C22⋊C8C22⋊D7311yescharacteristic
437C22⋊C8C22⋊D7311yescharacteristic
438#97—21no—
439#97—1461no—
440C4×C8—731no—
441C4×C8—731no—
442C4×C8—731no—
443C4×C8—731no—
444C4×C8—1461no—
445C4×C8—1461no—
446C4×C8C22×D7311yescharacteristic
447C4×C8C22×D7311yescharacteristic
448C24—21no—
449C2×Q8—731no—
450C2×D4—22no—
451C2×D4—21no—
452C2×D4—41no—
453C2×D4—731no—
454C2×D4—1461no—
455C2×D4C2×C4×D7311yescharacteristic
456C2×D4C2×C4×D7311yescharacteristic
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—81no—
463C22×C4—81no—
464C22×C4—1461no—
465C22×C4C2×C4×D7311yescharacteristic
466C22×C4C2×C22⋊D7311yescharacteristic
467C22×C4#1192402811yescharacteristic
468SD16—2921no—
469SD16—1462no—
470D8—2921no—
471D8—1462no—
472M16—81no—
473M16—81no—
474M16—5841no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—81no—
478C2×C8—81no—
479C2×C8—5841no—
480C2×C8—5841no—
481C2×C8—731no—
482C2×C8—731no—
483C2×C8—731no—
484C2×C8—731no—
485C2×C8—1461no—
486C2×C8—1461no—
487C2×C8—1464no—
488C2×C8—1461no—
489C2×C8—1461no—
490C2×C8C2×C22⋊D7311yescharacteristic
491C2×C8C2×C22⋊D7311yescharacteristic
492C2×C8C2×C22⋊D7311yescharacteristic
493C2×C8C2×C22⋊D7311yescharacteristic
494C4⋊C4—21no—
495C4⋊C4—731no—
496C4⋊C4—731no—
497C4⋊C4—1461no—
498C4⋊C4—1461no—
499C4⋊C4—1461no—
500C4⋊C4—1461no—
501C4⋊C4C2×C4×D7311yescharacteristic
502C4⋊C4C2×C4×D7311yescharacteristic
503C22⋊C4—21no—
504C22⋊C4—21no—
505C22⋊C4—21no—
506C22⋊C4—21no—
507C22⋊C4—1461no—
508C22⋊C4—1461no—
509C22⋊C4—1461no—
510C22⋊C4—1461no—
511C22⋊C4—1461no—
512C42—1461no—
513C42C2×C4×D7311yescharacteristic
514C42C2×C22⋊D7311yescharacteristic
515C42#1192402811yescharacteristic
516C42C23×D7311yescharacteristic
517C23—21no—
518C23—21no—
519C23—42no—
520C23—42no—
521C23—81no—
522C23—1461no—
523C23C4×C22⋊D7311yescharacteristic
524Q8—1461no—
525Q8—1461no—
526D4—21no—
527D4—21no—
528D4—21no—
529D4—42no—
530D4—2922no—
531D4—1461no—
532D4—1461no—
533D4#1455659912yes—
534C2×C4—22no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—81no—
546C2×C4—81no—
547C2×C4—81no—
548C2×C4—2921no—
549C2×C4—2921no—
550C2×C4—1461no—
551C2×C4—1461no—
552C2×C4—1461no—
553C2×C4C4×C22⋊D7311yescharacteristic
554C2×C4C4×C22⋊D7311yescharacteristic
555C2×C4C4×C22⋊D7311yescharacteristic
556C2×C4C22×C4×D7311yescharacteristic
557C2×C4C22×C22⋊D7311yescharacteristic
558C2×C4C2×#1192402811yescharacteristic
559C8—21no—
560C8—21no—
561C8—21no—
562C8—21no—
563C8—41no—
564C8—41no—
565C8—2921no—
566C8—2921no—
567C8—1462no—
568C8—1462no—
569C8—1461no—
570C8—1461no—
571C8—1461no—
572C8—1461no—
573C22—21no—
574C22—21no—
575C22—22no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—84no—
582C22—2921no—
583C22—2921no—
584C22—2921no—
585C22#1798870212yes—
586C22C2×C4×C22⋊D7311yescharacteristic
587C4—21no—
588C4—21no—
589C4—21no—
590C4—21no—
591C4—41no—
592C4—41no—
593C4—2921no—
594C4—2921no—
595C4—2921no—
596C4C2×#1455659911yescharacteristic
597C4#1798935311yescharacteristic
598C4#1798939011yescharacteristic
599C4#1798939811yescharacteristic
600C2—22no—
601C2—42no—
602C2—81no—
603C2—5841no—
604C2#2261865611yescharacteristic
605C2#2261876311yescharacteristic
606C2C2×#1798870211yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#2974C2
socleC22×C73C2×C4×D4
prime radical#17988721C4
cosocleC42×C73C24
hypercenter#2974D73
hypocenterC73#18014
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2974

Complements

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

NH ≅ G/Ntype
2. #22619093C2semidirect
3. #22608819C2semidirect
4. #22608814C2semidirect
5. #22608807C2semidirect
6. #22608795C2semidirect
7. #22608793C2semidirect
8. #22608788C2semidirect
9. C8×#11924016C2semidirect
10. C8×#11924013C2semidirect
11. #22608717C2semidirect
12. #22608389C2semidirect
13. C2×D4⋊#10596831C2semidirect
14. #22608215C2semidirect
15. C73×#2974C2semidirect
25. #17988717C22semidirect
26. C8×Dic146C22semidirect
31. #17988666C22semidirect
33. C8×D292C22semidirect
40. #17988339C22semidirect
41. #17988339C22semidirect
42. #17988337C22semidirect
43. #17988337C22semidirect
44. #17988317C22semidirect
45. #17988317C22semidirect
50. #17988314C22semidirect
51. #17988314C22semidirect
52. #17988309C22semidirect
53. #17988309C22semidirect
54. C8×#10596831C22semidirect
55. C8×#10596831C22semidirect
306. #2974D73semidirect
319. C73#18014semidirect

Maximal subgroups

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

subgroupindex
#226199782
#226190932
#226088192
#226088142
#226088072
#226087952
#226087932
#226087882
C8×#119240162
C8×#119240132
#226087172
#226083892
C2×D4⋊#105968312
#226082152
C73×#29742
#1801473