Finite Group Databasebeta

← #14724914

Subgroups — #14724914

Order 2816.

592 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078687C211yesmaximal, characteristic
2#13077563C211yesmaximal, characteristic, complemented
3#13067518C211yesmaximal, characteristic, complemented
4#13067504C211yesmaximal, characteristic, complemented
5#13067492C211yesmaximal, characteristic, complemented
6#13067487C211yesmaximal, characteristic, complemented
7#13067466C211yesmaximal, characteristic, complemented
8#13067457C211yesmaximal, characteristic, complemented
9#13067433C211yesmaximal, characteristic, complemented
10C8×#4326C211yesmaximal, characteristic, complemented
11#13067402C211yesmaximal, characteristic, complemented
12#13067088C211yesmaximal, characteristic, complemented
13#13067003C211yesmaximal, characteristic
14#13066913C211yesmaximal, characteristic, complemented
15C11×#2971C211yesmaximal, characteristic
16C4×C11×#41C2211yescharacteristic
17#10623001C2211yescharacteristic
18C8×Q8×C11C2211yescharacteristic
19C8×Q8×C11C2211yescharacteristic
20C11×#436—21no—
21C11×#436—21no—
22C11×#436C2211yescharacteristic
23C11×#436C2211yescharacteristic
24C11×#432—21no—
25C11×#432C2211yescharacteristic
26C4×C11×M16—21no—
27C4×C11×M16C2211yescharacteristic
28#10622852C411yescharacteristic
29#10622852C411yescharacteristic
30#10622735—21no—
31#10622732—21no—
32#10622644C411yescharacteristic
33C4×#4326C2211yescharacteristic
34C4×#4326C2211yescharacteristic
35#10622633C411yescharacteristic
36#10622632C411yescharacteristic
37C4×#4324C2211yescharacteristic
38C4×#4324C2211yescharacteristic
39#10622620C411yescharacteristic
40#10622609C411yescharacteristic
41#10622609C411yescharacteristic
42#10622538C2211yescharacteristic
43#10622538C2211yescharacteristic
44C2×C4⋊(C11⋊C8)C2211yescharacteristic
45#10622314—21no—
46#10622314—21no—
47#10622292C2211yescharacteristic
48#10622292C2211yescharacteristic
49C8×Dic22C2211yescharacteristic
50C8×Dic22C2211yescharacteristic
51Q8⋊(C11⋊C8)C2211yescharacteristic
52Q8⋊(C11⋊C8)C2211yescharacteristic
53D4⋊(C11⋊C8)C2211yescharacteristic
54D4⋊(C11⋊C8)C2211yescharacteristic
55#10622122C2211yescharacteristic
56#10622122C2211yescharacteristic
57#10622122C2211yescharacteristic
58#10622122C2211yescharacteristic
59#10622118C2211yescharacteristic
60#10622118C2211yescharacteristic
61#10622117C2211yescharacteristic
62#10622117C2211yescharacteristic
63#10622093C2211yescharacteristic
64#10622092C2211yescharacteristic
65#10622092C2211yescharacteristic
66C8×C11⋊C8C2211yescharacteristic
67C2×C11×#41C2×C411yescharacteristic
68C2×C11×M16—21no—
69C2×C11×M16—21no—
70C2×C11×M16D411yescharacteristic
71C2×C11×M16D411yescharacteristic
72C4×Q8×C11C2×C411yescharacteristic
73C4×Q8×C11C2311yescharacteristic
74C4×D4×C11—21no—
75C4×D4×C11—21no—
76C4×D4×C11C2×C411yescharacteristic
77C4×D4×C11C2311yescharacteristic
78C11×#117—21no—
79C11×#117C2×C411yescharacteristic
80C2×C42×C11—21no—
81C2×C42×C11C2311yescharacteristic
82C2×#4326C2×C411yescharacteristic
83C2×#4326C2×C411yescharacteristic
84C2×#4324C2×C411yescharacteristic
85C2×#4324C2×C411yescharacteristic
86#66979—21no—
87#66977—21no—
88#66977C2×C411yescharacteristic
89#66977C2×C411yescharacteristic
90C22×C11⋊C8—21no—
91#66923—21no—
92#66922C2×C411yescharacteristic
93#66922C2×C411yescharacteristic
94C4×Dic22—21no—
95C4×Dic22C2311yescharacteristic
96C4×Dic22C2311yescharacteristic
97C11×C4⋊C8—21no—
98C11×C4⋊C8—21no—
99C11×C4⋊C8C2311yescharacteristic
100C11×C4⋊C8C2311yescharacteristic
101C11×C22⋊C8—21no—
102C11×C22⋊C8—21no—
103C11×C22⋊C8—21no—
104C11×#97—21no—
105C11×#97D411yescharacteristic
106C11×#97D411yescharacteristic
107C4×C8×C11—21no—
108C4×C8×C11—21no—
109C4×C8×C11C2311yescharacteristic
110C4×C8×C11C2311yescharacteristic
111#66899C2×C411yescharacteristic
112#66899C2×C411yescharacteristic
113#66896C2×C411yescharacteristic
114#66896C2×C411yescharacteristic
115C22⋊(C11⋊C8)—21no—
116C22⋊(C11⋊C8)C2×C411yescharacteristic
117C22⋊(C11⋊C8)C2×C411yescharacteristic
118#66879—21no—
119#66879—21no—
120Dic11⋊C8—21no—
121Dic11⋊C8—21no—
122Dic11⋊C8—21no—
123Dic11⋊C8—21no—
124C8×Dic11—21no—
125C8×Dic11—21no—
126#66874C2×C411yescharacteristic
127#66874C2×C411yescharacteristic
128#66874C2×C411yescharacteristic
129#66874C2×C411yescharacteristic
130#66872C2×C411yescharacteristic
131#66872C2×C411yescharacteristic
132#66871C2×C411yescharacteristic
133#66871C2×C411yescharacteristic
134C4⋊(C11⋊C8)—21no—
135C4⋊(C11⋊C8)—21no—
136C4⋊(C11⋊C8)C2×C411yescharacteristic
137C4⋊(C11⋊C8)C2×C411yescharacteristic
138C4⋊(C11⋊C8)C2311yescharacteristic
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4×C11⋊C8C2311yescharacteristic
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#18013—111nomaximal, Sylow
145C11×#41—22no—
146C11×#41—41no—
147C2×Q8×C11C22×C411yescharacteristic
148C2×D4×C11—21no—
149C2×D4×C11C22×C411yescharacteristic
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11C22×C411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11#4111yescharacteristic
156C2×Dic22—21no—
157C2×Dic22C22×C411yescharacteristic
158C2×Dic22C22×C411yescharacteristic
159C11×M16—22no—
160C11×M16—41no—
161C11×M16—42no—
162C11×M16—42no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11C2×D411yescharacteristic
166C2×C8×C11C2×D411yescharacteristic
167C2×C8×C11C2×D411yescharacteristic
168C2×C8×C11C2×D411yescharacteristic
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4C22×C411yescharacteristic
172C11×C4⋊C4C22×C411yescharacteristic
173C11×C22⋊C4—21no—
174C11×C22⋊C4—21no—
175C11×C22⋊C4—21no—
176C42×C11—21no—
177C42×C11—21no—
178C42×C11—21no—
179C42×C11C22×C411yescharacteristic
180C42×C11C2×D411yescharacteristic
181C42×C11#4111yescharacteristic
182C42×C11C2411yescharacteristic
183C22⋊Dic11—21no—
184C22⋊Dic11—21no—
185#4326—22no—
186#4326—22no—
187#4324—41no—
188#4324—41no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11C22×C411yescharacteristic
193C4⋊Dic11C22×C411yescharacteristic
194Dic11⋊C4—21no—
195Dic11⋊C4—21no—
196Dic11⋊C4—21no—
197Dic11⋊C4—21no—
198C4×Dic11—21no—
199C4×Dic11—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—42no—
205C2×C11⋊C8C22×C411yescharacteristic
206C2×C11⋊C8C22×C411yescharacteristic
207C2×C11⋊C8C22×C411yescharacteristic
208C2×C11⋊C8C22×C411yescharacteristic
209#3107—111no—
210#2971D1111yescharacteristic
211#2962—111no—
212#1592—111no—
213#1590—111no—
214#1588—111no—
215#1587—111no—
216#1584—111no—
217#1583—111no—
218#1579—111no—
219C8×Q16—111no—
220#1573—111no—
221#1497—111no—
222#1477—111no—
223#1453—111no—
224C23×C11—21no—
225C23×C11C4×D411yescharacteristic
226Q8×C11—21no—
227Q8×C11#13112yes—
228D4×C11—21no—
229D4×C11—21no—
230D4×C11—42no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—41no—
239C2×C4×C11—42no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—81no—
243C2×C4×C11C4×D411yescharacteristic
244C2×C4×C11C4×D411yescharacteristic
245C2×C4×C11C4×D411yescharacteristic
246C2×C4×C11C23×C411yescharacteristic
247C2×C4×C11C22×D411yescharacteristic
248C2×C4×C11C2×#4111yescharacteristic
249C2×Dic11—21no—
250C2×Dic11—21no—
251C2×Dic11—21no—
252C2×Dic11—21no—
253Dic22—21no—
254Dic22—21no—
255Dic22—21no—
256Dic22—21no—
257Dic22—81no—
258C8×C11—21no—
259C8×C11—21no—
260C8×C11—21no—
261C8×C11—41no—
262C8×C11—41no—
263C8×C11#13712yes—
264C11⋊C8—21no—
265C11⋊C8—21no—
266C11⋊C8—21no—
267C11⋊C8—21no—
268C11⋊C8—41no—
269C11⋊C8—41no—
270C11⋊C8—41no—
271C11⋊C8—41no—
272#533—111no—
273C4×#41C2×D1111yescharacteristic
274#485—111no—
275#485—111no—
276#475—111no—
277#474—111no—
278#462—111no—
279#461—111no—
280#452—111no—
281#452—111no—
282#446—111no—
283#446—111no—
284#446—221no—
285#446—221no—
286C8×Q8—111no—
287C8×Q8—111no—
288C8×Q8C2×D1111yescharacteristic
289C8×Q8C2×D1111yescharacteristic
290C4×Q16—111no—
291C4×Q16—111no—
292C4×SD16—111no—
293C4×SD16—111no—
294#436—21no—
295#436—21no—
296#436C2×D1111yescharacteristic
297#436C2×D1111yescharacteristic
298#432—21no—
299#432C2×D1111yescharacteristic
300#431—111no—
301#431—111no—
302#424—221no—
303C2×C4⋊C8—111no—
304#405—221no—
305C4×M16—21no—
306C4×M16C2×D1111yescharacteristic
307#335—111no—
308#335—111no—
309#334—111no—
310#334—111no—
311Q8⋊C8—111no—
312Q8⋊C8—111no—
313Q8⋊C8—111no—
314Q8⋊C8—111no—
315Q8⋊C8—111no—
316Q8⋊C8—111no—
317D4⋊C8—111no—
318D4⋊C8—111no—
319#322—111no—
320#322—111no—
321#322—111no—
322C82—111no—
323C22×C11—21no—
324C22×C11—21no—
325C22×C11—21no—
326C22×C11—41no—
327C22×C11—41no—
328C22×C11—41no—
329C22×C11C2×C4×D411yescharacteristic
330C4×C11—21no—
331C4×C11—22no—
332C4×C11—21no—
333C4×C11—21no—
334C4×C11—21no—
335C4×C11—41no—
336C4×C11—41no—
337C4×C11C2×#13111yescharacteristic
338C4×C11#56811yescharacteristic
339C4×C11C2×#13711yescharacteristic
340C4×C11#57511yescharacteristic
341Dic11—41no—
342Dic11—41no—
343Dic11—41no—
344Dic11—41no—
345C2×#41C4×D1111yescharacteristic
346C2×Q16—111no—
347C2×Q16—111no—
348C2×SD16—111no—
349C2×SD16—111no—
350C2×M16—21no—
351C2×M16—21no—
352C2×M16C22⋊D1111yescharacteristic
353C2×M16C22⋊D1111yescharacteristic
354C22×C8—221no—
355C4⋊Q8—111no—
356C4⋊Q8—111no—
357#125—221no—
358C22⋊Q8—111no—
359C22⋊Q8—111no—
360C22⋊Q8—221no—
361C4×Q8—111no—
362C4×Q8—111no—
363C4×Q8—221no—
364C4×Q8C4×D1111yescharacteristic
365C4×Q8C22×D1111yescharacteristic
366C4×D4—21no—
367C4×D4—21no—
368C4×D4C4×D1111yescharacteristic
369C4×D4C22×D1111yescharacteristic
370#117—21no—
371#117—221no—
372#117C4×D1111yescharacteristic
373C2×C42—21no—
374C2×C42C22×D1111yescharacteristic
375#107—111no—
376#107—111no—
377#106—111no—
378#106—111no—
379C4⋊C8—21no—
380C4⋊C8—21no—
381C4⋊C8—111no—
382C4⋊C8—111no—
383C4⋊C8—111no—
384C4⋊C8—111no—
385C4⋊C8—221no—
386C4⋊C8—221no—
387C4⋊C8—221no—
388C4⋊C8—221no—
389C4⋊C8—221no—
390C4⋊C8—221no—
391C4⋊C8C22×D1111yescharacteristic
392C4⋊C8C22×D1111yescharacteristic
393#103—111no—
394#103—111no—
395#103—111no—
396#103—111no—
397#103—111no—
398#103—111no—
399#102—111no—
400#102—111no—
401C22⋊C8—21no—
402C22⋊C8—21no—
403C22⋊C8—21no—
404C22⋊C8—111no—
405C22⋊C8—111no—
406C22⋊C8—221no—
407#97—21no—
408#97—221no—
409#97—221no—
410#97C22⋊D1111yescharacteristic
411#97C22⋊D1111yescharacteristic
412C4×C8—21no—
413C4×C8—21no—
414C4×C8—111no—
415C4×C8—111no—
416C4×C8—111no—
417C4×C8—111no—
418C4×C8—221no—
419C4×C8—221no—
420C4×C8C22×D1111yescharacteristic
421C4×C8C22×D1111yescharacteristic
422C2×C11—41no—
423C2×C11—81no—
424C2×C11#293311yescharacteristic
425C2×C11C4×#13711yescharacteristic
426C2×C11#295711yescharacteristic
427#41—22no—
428#41—41no—
429C2×Q8—111no—
430C2×Q8—111no—
431C2×Q8—221no—
432C2×Q8C2×C4×D1111yescharacteristic
433C2×D4—21no—
434C2×D4C2×C4×D1111yescharacteristic
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4C2×C4×D1111yescharacteristic
439C22×C4#433911yescharacteristic
440C22×C4C2×C22⋊D1111yescharacteristic
441Q16—222no—
442Q16—222no—
443SD16—441no—
444SD16—441no—
445M16—22no—
446M16—41no—
447M16—42no—
448M16—42no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—111no—
452C2×C8—111no—
453C2×C8—111no—
454C2×C8—111no—
455C2×C8—221no—
456C2×C8—221no—
457C2×C8—221no—
458C2×C8—221no—
459C2×C8—442no—
460C2×C8C2×C22⋊D1111yescharacteristic
461C2×C8C2×C22⋊D1111yescharacteristic
462C2×C8C2×C22⋊D1111yescharacteristic
463C2×C8C2×C22⋊D1111yescharacteristic
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—111no—
467C4⋊C4—111no—
468C4⋊C4—221no—
469C4⋊C4—221no—
470C4⋊C4—221no—
471C4⋊C4—221no—
472C4⋊C4—221no—
473C4⋊C4—221no—
474C4⋊C4—221no—
475C4⋊C4C2×C4×D1111yescharacteristic
476C4⋊C4C2×C4×D1111yescharacteristic
477C22⋊C4—21no—
478C22⋊C4—21no—
479C22⋊C4—21no—
480C22⋊C4—221no—
481C22⋊C4—221no—
482C42—21no—
483C42—21no—
484C42—21no—
485C42—221no—
486C42—221no—
487C42C2×C4×D1111yescharacteristic
488C42#433911yescharacteristic
489C42C2×C22⋊D1111yescharacteristic
490C42C23×D1111yescharacteristic
491C11#1801311yescharacteristic, complemented, Sylow
492C23—21no—
493C23C4×C22⋊D1111yescharacteristic
494Q8—21no—
495Q8—221no—
496Q8—221no—
497Q8—221no—
498Q8—221no—
499Q8—881no—
500Q8#6696012yes—
501D4—21no—
502D4—21no—
503D4—42no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—41no—
512C2×C4—42no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—81no—
516C2×C4—221no—
517C2×C4—221no—
518C2×C4—221no—
519C2×C4—221no—
520C2×C4C4×C22⋊D1111yescharacteristic
521C2×C4C4×C22⋊D1111yescharacteristic
522C2×C4C4×C22⋊D1111yescharacteristic
523C2×C4C22×C4×D1111yescharacteristic
524C2×C4C2×#433911yescharacteristic
525C2×C4C22×C22⋊D1111yescharacteristic
526C8—21no—
527C8—21no—
528C8—21no—
529C8—41no—
530C8—41no—
531C8—221no—
532C8—221no—
533C8—221no—
534C8—221no—
535C8—441no—
536C8—441no—
537C8—441no—
538C8—441no—
539C8#6700412yes—
540C22—21no—
541C22—21no—
542C22—21no—
543C22—41no—
544C22—41no—
545C22—41no—
546C22C2×C4×C22⋊D1111yescharacteristic
547C4—21no—
548C4—21no—
549C4—21no—
550C4—22no—
551C4—21no—
552C4—41no—
553C4—41no—
554C4—441no—
555C4—441no—
556C4—441no—
557C4—441no—
558C4C2×#6696011yescharacteristic
559C4#1062327611yescharacteristic
560C4#1062335311yescharacteristic
561C4C2×#6700411yescharacteristic
562C2—41no—
563C2—81no—
564C2#1307734111yescharacteristic
565C2C4×#6700411yescharacteristic
566C2#1307753111yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#2971C2
socleC22×C11C2×C4×D4
prime radicalC2×C11×#41C2×C4
cosocleC42×C11C24
hypercenter#2971D11
hypocenterC11#18013
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×M16 ◁ #2971

Complements

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

NH ≅ G/Ntype
2. #13077563C2semidirect
3. #13067518C2semidirect
4. #13067504C2semidirect
5. #13067492C2semidirect
6. #13067487C2semidirect
7. #13067466C2semidirect
8. #13067457C2semidirect
9. #13067433C2semidirect
10. C8×#4326C2semidirect
11. #13067402C2semidirect
12. #13067088C2semidirect
14. #13066913C2semidirect
491. C11#18013semidirect

Maximal subgroups

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

subgroupindex
#130786872
#130775632
#130675182
#130675042
#130674922
#130674872
#130674662
#130674572
#130674332
C8×#43262
#130674022
#130670882
#130670032
#130669132
C11×#29712
#1801311