Finite Group Databasebeta

← #14723878

Subgroups — #14723878

Order 2816.

598 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078687C211yesmaximal, characteristic
2#13077710C211yesmaximal, characteristic, complemented
3#13067487C211yesmaximal, characteristic, complemented
4#13067473C211yesmaximal, characteristic, complemented
5#13067466C211yesmaximal, characteristic, complemented
6#13067452C211yesmaximal, characteristic, complemented
7#13067433C211yesmaximal, characteristic, complemented
8#13067428C211yesmaximal, characteristic, complemented
9C8×#4326C211yesmaximal, characteristic, complemented
10C8×#4324C211yesmaximal, characteristic, complemented
11#13067399C211yesmaximal, characteristic, complemented
12#13067050C211yesmaximal, characteristic
13#13067018C211yesmaximal, characteristic, complemented
14#13066916C211yesmaximal, characteristic, complemented
15C11×#2988C211yesmaximal, characteristic
16C4×C11×#41C2211yescharacteristic
17#10623001C2211yescharacteristic
18C8×Q8×C11C2211yescharacteristic
19C8×Q8×C11C2211yescharacteristic
20C8×D4×C11—21no—
21C8×D4×C11—21no—
22C8×D4×C11C2211yescharacteristic
23C8×D4×C11C2211yescharacteristic
24C11×#431—21no—
25C11×#431C2211yescharacteristic
26C2×C11×C4⋊C8—21no—
27C2×C11×C4⋊C8C2211yescharacteristic
28#10622852C411yescharacteristic
29#10622852C411yescharacteristic
30#10622644C411yescharacteristic
31C4×#4326C2211yescharacteristic
32C4×#4326C2211yescharacteristic
33#10622633C411yescharacteristic
34#10622632C411yescharacteristic
35C4×#4324C2211yescharacteristic
36C4×#4324C2211yescharacteristic
37#10622620C411yescharacteristic
38#10622609C411yescharacteristic
39#10622609C411yescharacteristic
40#10622539C2211yescharacteristic
41#10622538C2211yescharacteristic
42#10622538C2211yescharacteristic
43#10622441—21no—
44#10622441—21no—
45#10622333—21no—
46#10622333—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
68C22×C8×C11—21no—
69C22×C8×C11—21no—
70C22×C8×C11—21no—
71C4×Q8×C11C2×C411yescharacteristic
72C4×Q8×C11C2311yescharacteristic
73C4×D4×C11—21no—
74C4×D4×C11—21no—
75C4×D4×C11C2×C411yescharacteristic
76C4×D4×C11C2311yescharacteristic
77C11×#117—21no—
78C11×#117C2×C411yescharacteristic
79C2×C42×C11—21no—
80C2×C42×C11C2311yescharacteristic
81C2×#4326C2×C411yescharacteristic
82C2×#4326C2×C411yescharacteristic
83C2×#4324C2×C411yescharacteristic
84C2×#4324C2×C411yescharacteristic
85#66979—21no—
86#66977—21no—
87#66977C2×C411yescharacteristic
88#66977C2×C411yescharacteristic
89#66923—21no—
90#66922C2×C411yescharacteristic
91#66922C2×C411yescharacteristic
92C4×Dic22—21no—
93C4×Dic22C2311yescharacteristic
94C4×Dic22C2311yescharacteristic
95C11×C4⋊C8—21no—
96C11×C4⋊C8—21no—
97C11×C4⋊C8—21no—
98C11×C4⋊C8D411yescharacteristic
99C11×C4⋊C8D411yescharacteristic
100C11×C4⋊C8C2311yescharacteristic
101C11×C4⋊C8C2311yescharacteristic
102C11×C22⋊C8—21no—
103C11×C22⋊C8—21no—
104C11×C22⋊C8D411yescharacteristic
105C11×C22⋊C8D411yescharacteristic
106C4×C8×C11—21no—
107C4×C8×C11—21no—
108C4×C8×C11C2311yescharacteristic
109C4×C8×C11C2311yescharacteristic
110#66899C2×C411yescharacteristic
111#66899C2×C411yescharacteristic
112#66896C2×C411yescharacteristic
113#66896C2×C411yescharacteristic
114C22⋊(C11⋊C8)—21no—
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)C2×C411yescharacteristic
136C4⋊(C11⋊C8)C2×C411yescharacteristic
137C4⋊(C11⋊C8)C2311yescharacteristic
138C4⋊(C11⋊C8)C2311yescharacteristic
139#66867—21no—
140C4×C11⋊C8C2311yescharacteristic
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#17921—111nomaximal, Sylow
145C11×#41—22no—
146C11×#41—22no—
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
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11—81no—
162C2×C8×C11—81no—
163C2×C8×C11—81no—
164C2×C8×C11C2×D411yescharacteristic
165C2×C8×C11C2×D411yescharacteristic
166C2×C8×C11C2×D411yescharacteristic
167C2×C8×C11C2×D411yescharacteristic
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4C22×C411yescharacteristic
171C11×C4⋊C4C22×C411yescharacteristic
172C11×C22⋊C4—21no—
173C11×C22⋊C4—21no—
174C11×C22⋊C4—21no—
175C42×C11—21no—
176C42×C11—21no—
177C42×C11—21no—
178C42×C11C22×C411yescharacteristic
179C42×C11C2×D411yescharacteristic
180C42×C11#4111yescharacteristic
181C42×C11C2411yescharacteristic
182C22⋊Dic11—21no—
183C22⋊Dic11—21no—
184#4326—22no—
185#4326—22no—
186#4324—22no—
187#4324—22no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11C22×C411yescharacteristic
192C4⋊Dic11C22×C411yescharacteristic
193Dic11⋊C4—21no—
194Dic11⋊C4—21no—
195Dic11⋊C4—21no—
196Dic11⋊C4—21no—
197C4×Dic11—21no—
198C4×Dic11—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8C22×C411yescharacteristic
204C2×C11⋊C8C22×C411yescharacteristic
205C2×C11⋊C8C22×C411yescharacteristic
206C2×C11⋊C8C22×C411yescharacteristic
207#3107—111no—
208#2988D1111yescharacteristic
209#2985—111no—
210#1587—111no—
211#1585—111no—
212#1584—111no—
213#1582—111no—
214#1579—111no—
215SD16⋊C8—111no—
216C8×Q16—111no—
217C8×SD16—111no—
218#1573—111no—
219#1488—111no—
220#1481—111no—
221#1454—111no—
222C23×C11—21no—
223C23×C11C4×D411yescharacteristic
224Q8×C11—21no—
225Q8×C11#13112yes—
226D4×C11—24no—
227D4×C11—21no—
228D4×C11#13112yes—
229C2×C4×C11—24no—
230C2×C4×C11—21no—
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—41no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—81no—
241C2×C4×C11C4×D411yescharacteristic
242C2×C4×C11C4×D411yescharacteristic
243C2×C4×C11C4×D411yescharacteristic
244C2×C4×C11C23×C411yescharacteristic
245C2×C4×C11C22×D411yescharacteristic
246C2×C4×C11C2×#4111yescharacteristic
247C2×Dic11—21no—
248C2×Dic11—21no—
249C2×Dic11—21no—
250C2×Dic11—21no—
251Dic22—21no—
252Dic22—21no—
253Dic22—21no—
254Dic22—21no—
255Dic22—81no—
256C8×C11—21no—
257C8×C11—21no—
258C8×C11—21no—
259C8×C11—21no—
260C8×C11—41no—
261C8×C11—41no—
262C11⋊C8—21no—
263C11⋊C8—21no—
264C11⋊C8—21no—
265C11⋊C8—21no—
266C11⋊C8—41no—
267C11⋊C8—41no—
268C11⋊C8—41no—
269C11⋊C8—41no—
270#533—111no—
271C4×#41C2×D1111yescharacteristic
272#485—111no—
273#485—111no—
274#475—111no—
275#474—111no—
276#462—111no—
277#461—111no—
278#452—111no—
279#452—111no—
280#446—111no—
281#446—111no—
282#446—221no—
283#446—221no—
284C8×Q8—111no—
285C8×Q8—111no—
286C8×Q8C2×D1111yescharacteristic
287C8×Q8C2×D1111yescharacteristic
288C4×Q16—111no—
289C4×Q16—111no—
290C4×SD16—111no—
291C4×SD16—111no—
292C8×D4—21no—
293C8×D4—21no—
294C8×D4C2×D1111yescharacteristic
295C8×D4C2×D1111yescharacteristic
296#433—221no—
297#433—221no—
298#432—111no—
299#431—21no—
300#431—111no—
301#431—111no—
302#431C2×D1111yescharacteristic
303C2×C4⋊C8—21no—
304C2×C4⋊C8C2×D1111yescharacteristic
305#335—111no—
306#335—111no—
307#334—111no—
308#334—111no—
309Q8⋊C8—111no—
310Q8⋊C8—111no—
311Q8⋊C8—111no—
312Q8⋊C8—111no—
313Q8⋊C8—111no—
314Q8⋊C8—111no—
315D4⋊C8—111no—
316D4⋊C8—111no—
317#322—111no—
318#322—111no—
319#322—111no—
320C82—111no—
321C22×C11—21no—
322C22×C11—22no—
323C22×C11—21no—
324C22×C11—21no—
325C22×C11—41no—
326C22×C11—41no—
327C22×C11C2×C4×D411yescharacteristic
328C4×C11—21no—
329C4×C11—22no—
330C4×C11—21no—
331C4×C11—21no—
332C4×C11—21no—
333C4×C11—41no—
334C4×C11—41no—
335C4×C11C2×#13111yescharacteristic
336C4×C11C2×#13111yescharacteristic
337C4×C11#57711yescharacteristic
338C4×C11#57811yescharacteristic
339Dic11—41no—
340Dic11—41no—
341Dic11—41no—
342Dic11—41no—
343C2×#41C4×D1111yescharacteristic
344C2×Q16—111no—
345C2×Q16—111no—
346C2×SD16—111no—
347C2×SD16—111no—
348C22×C8—21no—
349C22×C8—21no—
350C22×C8—21no—
351C4⋊Q8—111no—
352C4⋊Q8—111no—
353#125—221no—
354C22⋊Q8—111no—
355C22⋊Q8—111no—
356C22⋊Q8—221no—
357C4×Q8—111no—
358C4×Q8—111no—
359C4×Q8—221no—
360C4×Q8C4×D1111yescharacteristic
361C4×Q8C22×D1111yescharacteristic
362C4×D4—21no—
363C4×D4—21no—
364C4×D4C4×D1111yescharacteristic
365C4×D4C22×D1111yescharacteristic
366#117—21no—
367#117—221no—
368#117C4×D1111yescharacteristic
369C2×C42—21no—
370C2×C42C22×D1111yescharacteristic
371#107—111no—
372#107—111no—
373#106—111no—
374#106—111no—
375C4⋊C8—21no—
376C4⋊C8—21no—
377C4⋊C8—21no—
378C4⋊C8—111no—
379C4⋊C8—111no—
380C4⋊C8—111no—
381C4⋊C8—111no—
382C4⋊C8—221no—
383C4⋊C8—221no—
384C4⋊C8—221no—
385C4⋊C8—221no—
386C4⋊C8—221no—
387C4⋊C8C22⋊D1111yescharacteristic
388C4⋊C8C22⋊D1111yescharacteristic
389C4⋊C8C22×D1111yescharacteristic
390C4⋊C8C22×D1111yescharacteristic
391#103—111no—
392#103—111no—
393#103—111no—
394#103—111no—
395#103—111no—
396#103—111no—
397#102—111no—
398#102—111no—
399C22⋊C8—21no—
400C22⋊C8—21no—
401C22⋊C8—111no—
402C22⋊C8—111no—
403C22⋊C8—221no—
404C22⋊C8—221no—
405C22⋊C8C22⋊D1111yescharacteristic
406C22⋊C8C22⋊D1111yescharacteristic
407#97—221no—
408#97—221no—
409#97—221no—
410C4×C8—21no—
411C4×C8—21no—
412C4×C8—111no—
413C4×C8—111no—
414C4×C8—111no—
415C4×C8—111no—
416C4×C8—221no—
417C4×C8—221no—
418C4×C8C22×D1111yescharacteristic
419C4×C8C22×D1111yescharacteristic
420C2×C11—41no—
421C2×C11—42no—
422C2×C11#292911yescharacteristic
423C2×C11#294711yescharacteristic
424C2×C11#295711yescharacteristic
425#41—22no—
426#41—22no—
427C2×Q8—111no—
428C2×Q8—111no—
429C2×Q8—221no—
430C2×Q8C2×C4×D1111yescharacteristic
431C2×D4—21no—
432C2×D4C2×C4×D1111yescharacteristic
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4C2×C4×D1111yescharacteristic
437C22×C4#433911yescharacteristic
438C22×C4C2×C22⋊D1111yescharacteristic
439Q16—222no—
440Q16—222no—
441SD16—222no—
442SD16—222no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—81no—
446C2×C8—81no—
447C2×C8—81no—
448C2×C8—111no—
449C2×C8—111no—
450C2×C8—111no—
451C2×C8—111no—
452C2×C8—221no—
453C2×C8—221no—
454C2×C8—221no—
455C2×C8—221no—
456C2×C8C2×C22⋊D1111yescharacteristic
457C2×C8C2×C22⋊D1111yescharacteristic
458C2×C8C2×C22⋊D1111yescharacteristic
459C2×C8C2×C22⋊D1111yescharacteristic
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—111no—
463C4⋊C4—111no—
464C4⋊C4—221no—
465C4⋊C4—221no—
466C4⋊C4—221no—
467C4⋊C4—221no—
468C4⋊C4—221no—
469C4⋊C4—221no—
470C4⋊C4—221no—
471C4⋊C4C2×C4×D1111yescharacteristic
472C4⋊C4C2×C4×D1111yescharacteristic
473C22⋊C4—21no—
474C22⋊C4—21no—
475C22⋊C4—21no—
476C22⋊C4—221no—
477C22⋊C4—221no—
478C42—21no—
479C42—21no—
480C42—21no—
481C42—221no—
482C42—221no—
483C42C2×C4×D1111yescharacteristic
484C42#433911yescharacteristic
485C42C2×C22⋊D1111yescharacteristic
486C42C23×D1111yescharacteristic
487C11#1792111yescharacteristic, complemented, Sylow
488C23—21no—
489C23C4×C22⋊D1111yescharacteristic
490Q8—21no—
491Q8—221no—
492Q8—221no—
493Q8—221no—
494Q8—221no—
495Q8—881no—
496Q8#6695412yes—
497D4—24no—
498D4—21no—
499D4#6695412yes—
500C2×C4—24no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—81no—
512C2×C4—221no—
513C2×C4—221no—
514C2×C4—221no—
515C2×C4—221no—
516C2×C4C4×C22⋊D1111yescharacteristic
517C2×C4C4×C22⋊D1111yescharacteristic
518C2×C4C4×C22⋊D1111yescharacteristic
519C2×C4C22×C4×D1111yescharacteristic
520C2×C4C2×#433911yescharacteristic
521C2×C4C22×C22⋊D1111yescharacteristic
522C8—21no—
523C8—21no—
524C8—21no—
525C8—21no—
526C8—41no—
527C8—41no—
528C8—221no—
529C8—221no—
530C8—221no—
531C8—221no—
532C8—441no—
533C8—441no—
534C8—441no—
535C8—441no—
536C22—21no—
537C22—21no—
538C22—22no—
539C22—21no—
540C22—41no—
541C22—41no—
542C22C2×C4×C22⋊D1111yescharacteristic
543C4—21no—
544C4—21no—
545C4—21no—
546C4—22no—
547C4—21no—
548C4—41no—
549C4—41no—
550C4—441no—
551C4—441no—
552C4—441no—
553C4—441no—
554C4C2×#6695411yescharacteristic
555C4C2×#6695411yescharacteristic
556C4#1062336711yescharacteristic
557C4#1062336911yescharacteristic
558C2—41no—
559C2—42no—
560C2#1307731011yescharacteristic
561C2#1307745511yescharacteristic
562C2#1307753111yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#2988C2
socleC22×C11C2×C4×D4
prime radicalC2×C11×#41C2×C4
cosocleC42×C11C24
hypercenter#2988D11
hypocenterC11#17921
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2988

Complements

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

NH ≅ G/Ntype
2. #13077710C2semidirect
3. #13067487C2semidirect
4. #13067473C2semidirect
5. #13067466C2semidirect
6. #13067452C2semidirect
7. #13067433C2semidirect
8. #13067428C2semidirect
9. C8×#4326C2semidirect
10. C8×#4324C2semidirect
11. #13067399C2semidirect
13. #13067018C2semidirect
14. #13066916C2semidirect
487. C11#17921semidirect

Maximal subgroups

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

subgroupindex
#130786872
#130777102
#130674872
#130674732
#130674662
#130674522
#130674332
#130674282
C8×#43262
C8×#43242
#130673992
#130670502
#130670182
#130669162
C11×#29882
#1792111