Finite Group Databasebeta

← #33057312

Subgroups — #33057312

Order 18688.

616 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22619939C211yesmaximal, characteristic
2#22619032C211yesmaximal, characteristic, complemented
3#22618966C211yesmaximal, characteristic
4#22608830C211yesmaximal, characteristic, complemented
5#22608824C211yesmaximal, characteristic, complemented
6#22608812C211yesmaximal, characteristic, complemented
7#22608785C211yesmaximal, characteristic, complemented
8#22608777C211yesmaximal, characteristic, complemented
9#22608764C211yesmaximal, characteristic, complemented
10#22608740C211yesmaximal, characteristic, complemented
11#22608734C211yesmaximal, characteristic, complemented
12#22608709C211yesmaximal, characteristic, complemented
13#22608405C211yesmaximal, characteristic, complemented
14#22608231C211yesmaximal, characteristic, complemented
15C73×#1478C211yesmaximal, characteristic
16#17989144C2211yescharacteristic
17#17988917C411yescharacteristic
18#17988917C411yescharacteristic
19#17988877C411yescharacteristic
20#17988877C411yescharacteristic
21#17988792C411yescharacteristic
22#17988792C411yescharacteristic
23#17988738C411yescharacteristic
24#17988738C411yescharacteristic
25#17988717—21no—
26#17988714C2211yescharacteristic, complemented
27#17988714C2211yescharacteristic, complemented
28C8×Dic146—21no—
29#17988711C2211yescharacteristic, complemented
30#17988711C2211yescharacteristic, complemented
31C4×#11924016C2211yescharacteristic
32C4×#11924016C2211yescharacteristic
33C4×#11924016C2211yescharacteristic
34C4×#11924016C2211yescharacteristic
35#17988665C2211yescharacteristic
36#17988665C2211yescharacteristic
37#17988659—21no—
38#17988659—21no—
39D4×#10596831C2211yescharacteristic
40D4×#10596831C2211yescharacteristic
41#17988645—21no—
42#17988645—21no—
43#17988644C2211yescharacteristic
44#17988640C2211yescharacteristic
45#17988640C2211yescharacteristic
46#17988551—21no—
47C2×C22⋊#10596831—21no—
48#17988339C2211yescharacteristic, complemented
49#17988339C2211yescharacteristic, complemented
50#17988337C2211yescharacteristic, complemented
51#17988337C2211yescharacteristic, complemented
52#17988319C2211yescharacteristic, complemented
53#17988319C2211yescharacteristic, complemented
54#17988319C2211yescharacteristic, complemented
55#17988319C2211yescharacteristic, complemented
56#17988309C2211yescharacteristic, complemented
57#17988309C2211yescharacteristic, complemented
58#17988308C2211yescharacteristic, complemented
59C8×#10596831C2211yescharacteristic, complemented
60C2×C4×D4×C73C2211yescharacteristic
61#431×C73C2211yescharacteristic
62#431×C73C2211yescharacteristic
63D4⋊C8×C73C2211yescharacteristic
64D4⋊C8×C73C2211yescharacteristic
65D4⋊C8×C73C2211yescharacteristic
66D4⋊C8×C73C2211yescharacteristic
67C2×#11924016C2×C411yescharacteristic
68C2×#11924016C2×C411yescharacteristic
69C2×#11924016C2×C411yescharacteristic
70C2×#11924016C2×C411yescharacteristic
71C2×#11924012—21no—
72C2×#11924012—21no—
73C22×#10596831—21no—
74C22×#10596831—21no—
75#14556591C2×C411yescharacteristic
76#14556591C2×C411yescharacteristic
77#14556583—21no—
78#14556570—21no—
79#14556570C2×C411yescharacteristic
80#14556570C2×C411yescharacteristic
81C4×Dic146—21no—
82C4×Dic146C2311yescharacteristic
83C4×Dic146C2311yescharacteristic
84#14556550—21no—
85#14556522C2×C411yescharacteristic
86#14556522C2×C411yescharacteristic
87#14556522C2×C411yescharacteristic
88#14556522C2×C411yescharacteristic
89C4⋊#10596831C2×C411yescharacteristic
90C4⋊#10596831C2×C411yescharacteristic
91C4⋊#10596831D411yescharacteristic
92C4⋊#10596831D411yescharacteristic
93C4⋊#10596831C2311yescharacteristic
94C4⋊#10596831C2311yescharacteristic
95#14556520—21no—
96#14556520—21no—
97#14556520—21no—
98#14556520—21no—
99#14556514C2×C411yescharacteristic
100#14556514C2×C411yescharacteristic
101#14556514C2×C411yescharacteristic
102#14556514C2×C411yescharacteristic
103#14556512C2×C411yescharacteristic
104#14556512C2×C411yescharacteristic
105#14556512C2×C411yescharacteristic
106#14556512C2×C411yescharacteristic
107C22⋊#10596831—21no—
108C22⋊#10596831—21no—
109C22⋊#10596831—21no—
110C22⋊#10596831—21no—
111C22⋊#10596831—21no—
112C22⋊#10596831C2×C411yescharacteristic
113C22⋊#10596831C2×C411yescharacteristic
114C22⋊#10596831D411yescharacteristic
115C22⋊#10596831D411yescharacteristic
116#14556502—21no—
117#14556501—21no—
118#14556501—21no—
119C4×#10596831C2311yescharacteristic
120C4×#10596831C2311yescharacteristic
121C4×#10596831C2311yescharacteristic
122C4×#10596831C2311yescharacteristic
123C8×Dic73—21no—
124C8×Dic73—21no—
125C22×D4×C73C2×C411yescharacteristic
126C23×C4×C73—21no—
127C4×D4×C73—21no—
128C4×D4×C73—21no—
129C4×D4×C73C2×C411yescharacteristic
130C4×D4×C73C2×C411yescharacteristic
131C4×D4×C73C2311yescharacteristic
132C4×D4×C73C2311yescharacteristic
133C2×C4⋊C4×C73C2×C411yescharacteristic
134C2×C22⋊C4×C73—21no—
135C2×C42×C73C2311yescharacteristic
136C4⋊C8×C73—21no—
137C4⋊C8×C73C2311yescharacteristic
138C4⋊C8×C73C2311yescharacteristic
139C22⋊C8×C73—21no—
140C22⋊C8×C73—21no—
141C4×C8×C73—21no—
142C4×C8×C73C2311yescharacteristic
143C4×C8×C73C2311yescharacteristic
144C2×Dic146—21no—
145C2×Dic146C22×C411yescharacteristic
146C2×Dic146C22×C411yescharacteristic
147#11924016—22no—
148#11924016—22no—
149#11924016—41no—
150#11924016—41no—
151#11924012—81no—
152#11924012—81no—
153C2×#10596831—21no—
154C2×#10596831—21no—
155C2×#10596831—81no—
156C2×#10596831—81no—
157C2×#10596831C22×C411yescharacteristic
158C2×#10596831C22×C411yescharacteristic
159C2×#10596831C22×C411yescharacteristic
160C2×#10596831C22×C411yescharacteristic
161C2×#10596831C2×D411yescharacteristic
162C2×#10596831C2×D411yescharacteristic
163C2×#10596831C2×D411yescharacteristic
164C2×#10596831C2×D411yescharacteristic
165C4⋊Dic73—21no—
166C4⋊Dic73—21no—
167C4⋊Dic73—21no—
168C4⋊Dic73C22×C411yescharacteristic
169C4⋊Dic73C22×C411yescharacteristic
170#11924007—21no—
171#11924007—21no—
172#11924007—21no—
173#11924007—21no—
174C22⋊Dic73—21no—
175C22⋊Dic73—21no—
176C4×Dic73—21no—
177C4×Dic73—21no—
178C24×C73—21no—
179C2×D4×C73—22no—
180C2×D4×C73—21no—
181C2×D4×C73—41no—
182C2×D4×C73C22×C411yescharacteristic
183C2×D4×C73C22×C411yescharacteristic
184C22×C4×C73—21no—
185C22×C4×C73—21no—
186C22×C4×C73—21no—
187C22×C4×C73—21no—
188C22×C4×C73—21no—
189C22×C4×C73—81no—
190C22×C4×C73—81no—
191C22×C4×C73C22×C411yescharacteristic
192C22×C4×C73C2×D411yescharacteristic
193C22×C4×C73#4111yescharacteristic
194C2×C8×C73—21no—
195C2×C8×C73—21no—
196C2×C8×C73—21no—
197C2×C8×C73—21no—
198C4⋊C4×C73—21no—
199C4⋊C4×C73C22×C411yescharacteristic
200C4⋊C4×C73C22×C411yescharacteristic
201C22⋊C4×C73—21no—
202C22⋊C4×C73—21no—
203C22⋊C4×C73—21no—
204C22⋊C4×C73—21no—
205C42×C73C22×C411yescharacteristic
206C42×C73C2×D411yescharacteristic
207C42×C73#4111yescharacteristic
208C42×C73C2411yescharacteristic
209C23×C73—21no—
210C23×C73—21no—
211C23×C73—42no—
212C23×C73—42no—
213C23×C73—81no—
214C23×C73C4×D411yescharacteristic
215D4×C73—21no—
216D4×C73—21no—
217D4×C73—21no—
218D4×C73—42no—
219D4×C73#13112yes—
220C2×C4×C73—21no—
221C2×C4×C73—21no—
222C2×C4×C73—21no—
223C2×C4×C73—21no—
224C2×C4×C73—21no—
225C2×C4×C73—21no—
226C2×C4×C73—41no—
227C2×C4×C73—41no—
228C2×C4×C73—41no—
229C2×C4×C73—41no—
230C2×C4×C73—41no—
231C2×C4×C73—81no—
232C2×C4×C73—81no—
233C2×C4×C73—81no—
234C2×C4×C73C4×D411yescharacteristic
235C2×C4×C73C4×D411yescharacteristic
236C2×C4×C73C4×D411yescharacteristic
237C2×C4×C73C23×C411yescharacteristic
238C2×C4×C73C22×D411yescharacteristic
239C2×C4×C73C2×#4111yescharacteristic
240C2×Dic73—21no—
241C2×Dic73—21no—
242C2×Dic73—21no—
243C2×Dic73—21no—
244Dic146—21no—
245Dic146—21no—
246Dic146—21no—
247Dic146—21no—
248Dic146—42no—
249C8×C73—41no—
250C8×C73—41no—
251C8×C73—41no—
252C8×C73—41no—
253#10596831—21no—
254#10596831—21no—
255#10596831—21no—
256#10596831—21no—
257#10596831—21no—
258#10596831—21no—
259#10596831—21no—
260#10596831—21no—
261#10596831—41no—
262#10596831—41no—
263C22×C73—21no—
264C22×C73—22no—
265C22×C73—21no—
266C22×C73—21no—
267C22×C73—41no—
268C22×C73—41no—
269C22×C73—41no—
270C22×C73—41no—
271C22×C73—41no—
272C22×C73—84no—
273C22×C73C2×C4×D411yescharacteristic
274C4×C73—21no—
275C4×C73—21no—
276C4×C73—21no—
277C4×C73—21no—
278C4×C73—41no—
279C4×C73—41no—
280C4×C73C2×#13111yescharacteristic
281C4×C73#56811yescharacteristic
282C4×C73#57711yescharacteristic
283C4×C73#57711yescharacteristic
284Dic73—41no—
285Dic73—41no—
286Dic73—41no—
287Dic73—41no—
288#18028—731nomaximal, Sylow
289C2×C73—41no—
290C2×C73—42no—
291C2×C73—81no—
292C2×C73#293311yescharacteristic
293C2×C73#294911yescharacteristic
294C2×C73#295511yescharacteristic
295#3101—731no—
296#2986—731no—
297#2974—731no—
298#1592—731no—
299#1590—731no—
300#1588—731no—
301#1585—731no—
302#1583—731no—
303#1582—731no—
304SD16⋊C8—731no—
305C8×SD16—731no—
306#1572—731no—
307#1497—731no—
308#1478D7311yescharacteristic
309#1454—731no—
310C73#1802811yescharacteristic, complemented, Sylow
311#533—731no—
312C2×C4×D4C2×D7311yescharacteristic
313#483—731no—
314#483—731no—
315#476—731no—
316#476—731no—
317#461—731no—
318#461—731no—
319#450—731no—
320#450—731no—
321#446—731no—
322#446—731no—
323#446—1461no—
324C8×Q8—731no—
325C8×Q8—731no—
326C8×Q8—1461no—
327C4×SD16—731no—
328C4×SD16—731no—
329C4×SD16—731no—
330C4×SD16—731no—
331#436—731no—
332#436—731no—
333#435—1461no—
334#435—1461no—
335C8×D4—731no—
336C8×D4—731no—
337#433—1461no—
338#433—1461no—
339#432—731no—
340#431—731no—
341#431—731no—
342#431C2×D7311yescharacteristic
343#431C2×D7311yescharacteristic
344#407—1461no—
345C2×C22⋊C8—1461no—
346#335—731no—
347#335—731no—
348#334—731no—
349#334—731no—
350Q8⋊C8—731no—
351Q8⋊C8—731no—
352Q8⋊C8—731no—
353Q8⋊C8—731no—
354D4⋊C8C2×D7311yescharacteristic
355D4⋊C8C2×D7311yescharacteristic
356D4⋊C8C2×D7311yescharacteristic
357D4⋊C8C2×D7311yescharacteristic
358#322—731no—
359#322—731no—
360#322—731no—
361C82—731no—
362C22×D4C4×D7311yescharacteristic
363C23×C4—21no—
364C2×SD16—731no—
365C2×SD16—731no—
366C2×SD16—731no—
367C2×SD16—731no—
368C2×M16—1461no—
369C2×M16—1461no—
370C22×C8—1461no—
371C22×C8—1461no—
372C4⋊Q8—731no—
373C4⋊Q8—731no—
374#125—1461no—
375C22⋊Q8—731no—
376C22⋊Q8—731no—
377C22⋊Q8—1461no—
378C4×Q8—731no—
379C4×Q8—731no—
380C4×Q8—1461no—
381C4×D4—21no—
382C4×D4—21no—
383C4×D4C4×D7311yescharacteristic
384C4×D4C4×D7311yescharacteristic
385C4×D4C22×D7311yescharacteristic
386C4×D4C22×D7311yescharacteristic
387#117—1461no—
388C2×C4⋊C4C4×D7311yescharacteristic
389C2×C22⋊C4—21no—
390C2×C42C22×D7311yescharacteristic
391#106—731no—
392#106—731no—
393#106—731no—
394#106—731no—
395C4⋊C8—21no—
396C4⋊C8—731no—
397C4⋊C8—731no—
398C4⋊C8—731no—
399C4⋊C8—731no—
400C4⋊C8—731no—
401C4⋊C8—731no—
402C4⋊C8—1461no—
403C4⋊C8—1461no—
404C4⋊C8—1461no—
405C4⋊C8—1461no—
406C4⋊C8C22×D7311yescharacteristic
407C4⋊C8C22×D7311yescharacteristic
408#103—731no—
409#103—731no—
410#103—731no—
411#103—731no—
412#102—731no—
413#102—731no—
414#102—731no—
415#102—731no—
416C22⋊C8—21no—
417C22⋊C8—21no—
418C22⋊C8—731no—
419C22⋊C8—731no—
420C22⋊C8—731no—
421C22⋊C8—731no—
422C22⋊C8—1461no—
423C22⋊C8—1461no—
424C22⋊C8—1461no—
425C22⋊C8—1461no—
426C22⋊C8—1461no—
427#97—1461no—
428#97—1461no—
429#97—1461no—
430C4×C8—21no—
431C4×C8—731no—
432C4×C8—731no—
433C4×C8—731no—
434C4×C8—731no—
435C4×C8—1461no—
436C4×C8—1461no—
437C4×C8C22×D7311yescharacteristic
438C4×C8C22×D7311yescharacteristic
439C24—21no—
440C2×Q8—731no—
441C2×Q8—731no—
442C2×Q8—1461no—
443C2×D4—22no—
444C2×D4—21no—
445C2×D4—41no—
446C2×D4C2×C4×D7311yescharacteristic
447C2×D4C2×C4×D7311yescharacteristic
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—81no—
454C22×C4—81no—
455C22×C4C2×C4×D7311yescharacteristic
456C22×C4D4×D7311yescharacteristic
457C22×C4#1192402711yescharacteristic
458SD16—2921no—
459SD16—2921no—
460SD16—1462no—
461SD16—1462no—
462M16—5841no—
463M16—5841no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—5841no—
469C2×C8—5841no—
470C2×C8—731no—
471C2×C8—731no—
472C2×C8—731no—
473C2×C8—731no—
474C2×C8—731no—
475C2×C8—731no—
476C2×C8—731no—
477C2×C8—731no—
478C2×C8—1461no—
479C2×C8—1461no—
480C4⋊C4—21no—
481C4⋊C4—731no—
482C4⋊C4—731no—
483C4⋊C4—1461no—
484C4⋊C4—1461no—
485C4⋊C4—1461no—
486C4⋊C4—1461no—
487C4⋊C4—1461no—
488C4⋊C4—1461no—
489C4⋊C4—1461no—
490C4⋊C4C2×C4×D7311yescharacteristic
491C4⋊C4C2×C4×D7311yescharacteristic
492C22⋊C4—21no—
493C22⋊C4—21no—
494C22⋊C4—21no—
495C22⋊C4—21no—
496C22⋊C4—1461no—
497C22⋊C4—1461no—
498C42—1461no—
499C42—1461no—
500C42C2×C4×D7311yescharacteristic
501C42D4×D7311yescharacteristic
502C42#1192402711yescharacteristic
503C42C23×D7311yescharacteristic
504C23—21no—
505C23—21no—
506C23—42no—
507C23—42no—
508C23—81no—
509C23#1455655111yescharacteristic
510Q8—2922no—
511Q8—1461no—
512Q8—1461no—
513Q8—1461no—
514Q8—1461no—
515D4—21no—
516D4—21no—
517D4—21no—
518D4—42no—
519D4#1455659712yes—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—81no—
532C2×C4—81no—
533C2×C4—81no—
534C2×C4—1461no—
535C2×C4—1461no—
536C2×C4—1461no—
537C2×C4—1461no—
538C2×C4#1455655111yescharacteristic
539C2×C4#1455655111yescharacteristic
540C2×C4#1455655111yescharacteristic
541C2×C4C22×C4×D7311yescharacteristic
542C2×C4C2×D4×D7311yescharacteristic
543C2×C4C2×#1192402711yescharacteristic
544C8—41no—
545C8—41no—
546C8—41no—
547C8—41no—
548C8—2921no—
549C8—2921no—
550C8—1461no—
551C8—1461no—
552C8—1461no—
553C8—1461no—
554C8—1461no—
555C8—1461no—
556C8—1461no—
557C8—1461no—
558C22—21no—
559C22—22no—
560C22—21no—
561C22—21no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22—84no—
568C22C2×#1455655111yescharacteristic
569C4—21no—
570C4—21no—
571C4—21no—
572C4—21no—
573C4—41no—
574C4—41no—
575C4—2921no—
576C4—2921no—
577C4—2921no—
578C4—2921no—
579C4C2×#1455659711yescharacteristic
580C4#1798935311yescharacteristic
581C4#1798939711yescharacteristic
582C4#1798939711yescharacteristic
583C2—41no—
584C2—42no—
585C2—81no—
586C2#2261865211yescharacteristic
587C2#2261879311yescharacteristic
588C2#2261883011yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#1478C2
socleC22×C73C2×C4×D4
prime radicalC22×D4×C73C2×C4
cosocleC42×C73C24
hypercenter#1478D73
hypocenterC73#18028
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1478

Complements

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

NH ≅ G/Ntype
2. #22619032C2semidirect
4. #22608830C2semidirect
5. #22608824C2semidirect
6. #22608812C2semidirect
7. #22608785C2semidirect
8. #22608777C2semidirect
9. #22608764C2semidirect
10. #22608740C2semidirect
11. #22608734C2semidirect
12. #22608709C2semidirect
13. #22608405C2semidirect
14. #22608231C2semidirect
26. #17988714C22semidirect
27. #17988714C22semidirect
29. #17988711C22semidirect
30. #17988711C22semidirect
48. #17988339C22semidirect
49. #17988339C22semidirect
50. #17988337C22semidirect
51. #17988337C22semidirect
52. #17988319C22semidirect
53. #17988319C22semidirect
54. #17988319C22semidirect
55. #17988319C22semidirect
56. #17988309C22semidirect
57. #17988309C22semidirect
58. #17988308C22semidirect
59. C8×#10596831C22semidirect
310. C73#18028semidirect

Maximal subgroups

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

subgroupindex
#226199392
#226190322
#226189662
#226088302
#226088242
#226088122
#226087852
#226087772
#226087642
#226087402
#226087342
#226087092
#226084052
#226082312
C73×#14782
#1802873