Finite Group Databasebeta

← #14795088

Subgroups — #14795088

Order 2816.

828 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622633C211yesmaximal, characteristic, complemented
2C2×#10622539C211yesmaximal, characteristic
3#13076968C211yesmaximal, characteristic
4#13070052C212yesmaximal
5#13069816C212yesmaximal
6#13069568C211yesmaximal, characteristic, complemented
7#13069374C211yesmaximal, characteristic, complemented
8#13069351C212yesmaximal, complemented
9#13069309C212yesmaximal, complemented
10#13068621C211yesmaximal, characteristic, complemented
11C4×C11×C22⋊Q8C211yesmaximal, characteristic
12C2×C11×C22⋊Q8C2211yescharacteristic
13C2×C4×Q8×C11C2211yescharacteristic
14C22×C42×C11C2211yescharacteristic
15C2×#66977—21no—
16C2×#66922C2211yescharacteristic
17C11×#391C2211yescharacteristic
18C11×#389C2211yescharacteristic
19C11×#387—21no—
20C11×#385—21no—
21C11×#380C2211yescharacteristic
22C4×C11×C4⋊C4—21no—
23C4×C11×C4⋊C4C2211yescharacteristic
24C4×C11×C22⋊C4—21no—
25C2×#66899C2212yes—
26C2×#66899C2212yes—
27#10622825—21no—
28#10622825C2212yes—
29C2×C22⋊(C11⋊C8)C2212yes—
30#10622633—24no—
31C2×#66872C2212yes—
32C2×#66871C2212yes—
33#10622548C2211yescharacteristic
34#10622542—21no—
35#10622541—21no—
36#10622541C2212yes—
37#10622539—24no—
38C2×C4⋊(C11⋊C8)C2211yescharacteristic
39C2×C4⋊(C11⋊C8)C2211yescharacteristic
40C2×#66867C2212yes—
41#10622167C2212yes—
42#10622167C2212yes—
43#10622167C2212yes—
44#10622167C2212yes—
45C22×Q8×C11C2311yescharacteristic
46C23×C4×C11D411yescharacteristic
47C23×C4×C11D411yescharacteristic
48C23×C4×C11C2311yescharacteristic
49C22×Dic22—21no—
50C11×C22⋊Q8—22no—
51C11×C22⋊Q8—22no—
52C4×Q8×C11—22no—
53C4×Q8×C11—22no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4C2311yescharacteristic
58C2×C11×C4⋊C4C2311yescharacteristic
59C2×C11×C4⋊C4C2311yescharacteristic
60C2×C11×C22⋊C4—21no—
61C2×C11×C22⋊C4—21no—
62C2×C42×C11—22no—
63C2×C42×C11—22no—
64C2×C42×C11—21no—
65C2×C42×C11—21no—
66C2×C42×C11D411yescharacteristic
67C2×C42×C11D411yescharacteristic
68C2×C42×C11C2311yescharacteristic
69C2×C42×C11C2311yescharacteristic
70C2×C22⋊Dic11—22no—
71C2×C4⋊Dic11—21no—
72C2×C4⋊Dic11—21no—
73C2×C4⋊Dic11—21no—
74C2×C4⋊Dic11C2312yes—
75C2×C4⋊Dic11C2312yes—
76#66977—44no—
77C2×Dic11⋊C4—22no—
78C22×C11⋊C8C2312yes—
79C22×C11⋊C8C2312yes—
80#66922—22no—
81#66922—22no—
82C11×#95—21no—
83C11×#95—21no—
84C11×#95—21no—
85C11×#95—21no—
86C11×#95—21no—
87#66899—24no—
88#66899—24no—
89C11⋊#95—22no—
90C11⋊#95—22no—
91C22⋊(C11⋊C8)—24no—
92#66872—24no—
93#66871—24no—
94C4⋊(C11⋊C8)—22no—
95C4⋊(C11⋊C8)D414yes—
96#66867—24no—
97#24710—111nomaximal, Sylow
98C24×C11C2×D411yescharacteristic
99C2×Q8×C11—21no—
100C2×Q8×C11—21no—
101C2×Q8×C11—21no—
102C2×Q8×C11—21no—
103C2×Q8×C11—21no—
104C2×Q8×C11#4112yes—
105C22×C4×C11—22no—
106C22×C4×C11—21no—
107C22×C4×C11—21no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—21no—
113C22×C4×C11—21no—
114C22×C4×C11—21no—
115C22×C4×C11—21no—
116C22×C4×C11—21no—
117C22×C4×C11—21no—
118C22×C4×C11—21no—
119C22×C4×C11—21no—
120C22×C4×C11—41no—
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2411yescharacteristic
127C22×Dic11—22no—
128C22×Dic11—22no—
129C2×Dic22—42no—
130C2×Dic22—42no—
131C2×Dic22—42no—
132C11×C4⋊C4—24no—
133C11×C4⋊C4—21no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4—21no—
137C11×C4⋊C4—21no—
138C11×C4⋊C4—42no—
139C11×C4⋊C4—42no—
140C11×C4⋊C4#4112yes—
141C11×C22⋊C4—24no—
142C11×C22⋊C4—42no—
143C42×C11—22no—
144C42×C11—22no—
145C42×C11—21no—
146C42×C11—21no—
147C42×C11—42no—
148C42×C11—42no—
149C42×C11C2×D412yes—
150C42×C11#4112yes—
151C22⋊Dic11—44no—
152C4⋊Dic11—22no—
153C4⋊Dic11—22no—
154C4⋊Dic11—22no—
155C4⋊Dic11—22no—
156C4⋊Dic11—42no—
157C4⋊Dic11—42no—
158C4⋊Dic11—42no—
159Dic11⋊C4—44no—
160C2×C11⋊C8—22no—
161C2×C11⋊C8—22no—
162C2×C11⋊C8—22no—
163C2×C11⋊C8—22no—
164C2×C11⋊C8—22no—
165C2×C11⋊C8C2×D414yes—
166C2×#475—111no—
167C2×#432—111no—
168#2857—111no—
169C4×C22⋊Q8D1111yescharacteristic
170#2077—112no—
171#2036—112no—
172#1988—111no—
173#1947—111no—
174#1943—112no—
175#1935—112no—
176#1803—111no—
177C23×C11—21no—
178C23×C11—21no—
179C23×C11—21no—
180C23×C11—21no—
181C23×C11—21no—
182C23×C11—21no—
183C23×C11#13712yes—
184C23×C11C22×D411yescharacteristic
185Q8×C11—22no—
186Q8×C11—22no—
187Q8×C11—41no—
188Q8×C11—41no—
189C2×C4×C11—21no—
190C2×C4×C11—21no—
191C2×C4×C11—21no—
192C2×C4×C11—21no—
193C2×C4×C11—21no—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—21no—
197C2×C4×C11—21no—
198C2×C4×C11—21no—
199C2×C4×C11—21no—
200C2×C4×C11—21no—
201C2×C4×C11—21no—
202C2×C4×C11—44no—
203C2×C4×C11—41no—
204C2×C4×C11—41no—
205C2×C4×C11—41no—
206C2×C4×C11—41no—
207C2×C4×C11—41no—
208C2×C4×C11—41no—
209C2×C4×C11—41no—
210C2×C4×C11—41no—
211C2×C4×C11—44no—
212C2×C4×C11—41no—
213C2×C4×C11—41no—
214C2×C4×C11—41no—
215C2×C4×C11—41no—
216C2×C4×C11—41no—
217C2×C4×C11—41no—
218C2×C4×C11#12112yes—
219C2×C4×C11#12112yes—
220C2×C4×C11AGL(1,ℤ/8)12yes—
221C2×C4×C11#13712yes—
222C2×C4×C11C22×D411yescharacteristic
223C2×C4×C11C2×#4111yescharacteristic
224C2×C4×C11C2×#4111yescharacteristic
225C2×C4×C11C2×#4111yescharacteristic
226C2×C4×C112−1+411yescharacteristic
227C2×C4×C112−1+411yescharacteristic
228C2×Dic11—42no—
229C2×Dic11—42no—
230C2×Dic11—42no—
231C2×Dic11—42no—
232C2×Dic11—42no—
233C2×Dic11—42no—
234Dic22—84no—
235C11⋊C8—24no—
236C11⋊C8—42no—
237C2×C4⋊Q8—111no—
238C2×C22⋊Q8—221no—
239C2×C22⋊Q8C2×D1111yescharacteristic
240C2×C4×Q8C2×D1111yescharacteristic
241C22×C42C2×D1111yescharacteristic
242#475—224no—
243#432—224no—
244C2×#107—112no—
245C2×#106—112no—
246C2×C4⋊C8—111no—
247C2×C4⋊C8—111no—
248C2×#103—112no—
249C2×#103—112no—
250C2×C22⋊C8—112no—
251C2×#97—112no—
252#391—221no—
253#391C2×D1111yescharacteristic
254#389—112no—
255#389—221no—
256#389C2×D1111yescharacteristic
257#387—21no—
258#385—21no—
259#384—111no—
260#380—112no—
261#380—221no—
262#380C2×D1111yescharacteristic
263C4×C4⋊C4—21no—
264C4×C4⋊C4C2×D1111yescharacteristic
265C4×C22⋊C4—21no—
266#340—112no—
267#340—112no—
268#340—112no—
269#340—112no—
270C22×C11—22no—
271C22×C11—22no—
272C22×C11—22no—
273C22×C11—41no—
274C22×C11—41no—
275C22×C11—41no—
276C22×C11—41no—
277C22×C11C2×#12111yescharacteristic
278C22×C11#52511yescharacteristic
279C22×C11#53611yescharacteristic
280C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
281C22×C11C2×#13711yescharacteristic
282C22×C11C2×#13711yescharacteristic
283C22×C11#57511yescharacteristic
284C4×C11—22no—
285C4×C11—42no—
286C4×C11—41no—
287C4×C11—42no—
288C4×C11—41no—
289C4×C11—41no—
290C4×C11—81no—
291C4×C11—81no—
292C4×C11#46814yes—
293C4×C11#54711yescharacteristic
294C4×C11#54811yescharacteristic
295C4×C11#55211yescharacteristic
296C4×C11#55611yescharacteristic
297Dic11—82no—
298Dic11—82no—
299C22×Q8—221no—
300C22×Q8C22×D1111yescharacteristic
301C23×C4C22⋊D1111yescharacteristic
302C23×C4C22⋊D1111yescharacteristic
303C23×C4C22×D1111yescharacteristic
304C22×C8—112no—
305C22×C8—112no—
306C4⋊Q8—222no—
307C4⋊Q8—222no—
308C22⋊Q8—22no—
309C22⋊Q8—22no—
310C22⋊Q8—444no—
311C4×Q8—22no—
312C4×Q8—22no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—112no—
317C2×C4⋊C4—112no—
318C2×C4⋊C4—221no—
319C2×C4⋊C4—222no—
320C2×C4⋊C4—221no—
321C2×C4⋊C4—221no—
322C2×C4⋊C4C22×D1111yescharacteristic
323C2×C4⋊C4C22×D1111yescharacteristic
324C2×C4⋊C4C22×D1111yescharacteristic
325C2×C22⋊C4—21no—
326C2×C22⋊C4—21no—
327C2×C22⋊C4—222no—
328C2×C42—22no—
329C2×C42—22no—
330C2×C42—21no—
331C2×C42—21no—
332C2×C42C22⋊D1111yescharacteristic
333C2×C42C22⋊D1111yescharacteristic
334C2×C42C22×D1111yescharacteristic
335C2×C42C22×D1111yescharacteristic
336#107—224no—
337#106—224no—
338C4⋊C8—114no—
339C4⋊C8—222no—
340#103—224no—
341#103—224no—
342C22⋊C8—224no—
343#97—224no—
344#95—21no—
345#95—21no—
346#95—21no—
347#95—21no—
348#95—21no—
349#95—222no—
350#95—222no—
351C2×C11—42no—
352C2×C11#241511yescharacteristic
353C2×C11C2×#46811yescharacteristic
354C2×C11#305611yescharacteristic
355C2×C11#311311yescharacteristic
356C2×C11#311511yescharacteristic
357C2×C11#323711yescharacteristic
358C2×C11#323911yescharacteristic
359C24C2×C22⋊D1111yescharacteristic
360C2×Q8—21no—
361C2×Q8—21no—
362C2×Q8—21no—
363C2×Q8—21no—
364C2×Q8—21no—
365C2×Q8—442no—
366C2×Q8—442no—
367C2×Q8—442no—
368C2×Q8#433912yes—
369C22×C4—22no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—41no—
385C22×C4—222no—
386C22×C4—222no—
387C22×C4C2×C22⋊D1111yescharacteristic
388C22×C4C2×C22⋊D1111yescharacteristic
389C22×C4C2×C22⋊D1111yescharacteristic
390C22×C4C2×C22⋊D1111yescharacteristic
391C22×C4C2×C22⋊D1111yescharacteristic
392C22×C4C23×D1111yescharacteristic
393C2×C8—114no—
394C2×C8—222no—
395C2×C8—222no—
396C2×C8—222no—
397C2×C8—222no—
398C2×C8—222no—
399C4⋊C4—24no—
400C4⋊C4—21no—
401C4⋊C4—21no—
402C4⋊C4—21no—
403C4⋊C4—21no—
404C4⋊C4—21no—
405C4⋊C4—42no—
406C4⋊C4—42no—
407C4⋊C4—222no—
408C4⋊C4—222no—
409C4⋊C4—222no—
410C4⋊C4—222no—
411C4⋊C4—444no—
412C4⋊C4—442no—
413C4⋊C4—442no—
414C4⋊C4—442no—
415C4⋊C4#433912yes—
416C22⋊C4—24no—
417C22⋊C4—42no—
418C22⋊C4—444no—
419C42—22no—
420C42—22no—
421C42—21no—
422C42—21no—
423C42—42no—
424C42—42no—
425C42D4×D1112yes—
426C42#434112yes—
427C11#2471011yescharacteristic, complemented, Sylow
428C23—21no—
429C23—21no—
430C23—21no—
431C23—21no—
432C23—21no—
433C23—21no—
434C23#6700412yes—
435C23C22×C22⋊D1111yescharacteristic
436Q8—22no—
437Q8—22no—
438Q8—41no—
439Q8—41no—
440Q8—884no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—44no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—44no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—442no—
471C2×C4—442no—
472C2×C4—442no—
473C2×C4—442no—
474C2×C4—442no—
475C2×C4—442no—
476C2×C4#6699212yes—
477C2×C4#6699212yes—
478C2×C4#6699512yes—
479C2×C4#6700212yes—
480C2×C4C2×#433911yescharacteristic
481C2×C4C2×#433911yescharacteristic
482C2×C4C2×D4×D1111yescharacteristic
483C2×C4C2×#434111yescharacteristic
484C2×C4#6704311yescharacteristic
485C2×C4#6704311yescharacteristic
486C8—224no—
487C8—442no—
488C22—22no—
489C22—22no—
490C22—22no—
491C22—41no—
492C22—41no—
493C22—41no—
494C22—41no—
495C22#1062332211yescharacteristic
496C22C2×#6699211yescharacteristic
497C22C2×#6699511yescharacteristic
498C22C2×#6700211yescharacteristic
499C22#1062335311yescharacteristic
500C22C2×#6700411yescharacteristic
501C22#1062335611yescharacteristic
502C4—22no—
503C4—41no—
504C4—42no—
505C4—41no—
506C4—41no—
507C4—42no—
508C4—81no—
509C4—81no—
510C4—882no—
511C4—882no—
512C4#1062266214yes—
513C4#1062307211yescharacteristic
514C4#1062307311yescharacteristic
515C4#1062308211yescharacteristic
516C4#1062308311yescharacteristic
517C2—42no—
518C2#1307204511yescharacteristic
519C2C2×#1062266211yescharacteristic
520C2#1307824811yescharacteristic
521C2#1307874611yescharacteristic
522C2#1307876711yescharacteristic
523C2#1307982611yescharacteristic
524C2#1307984311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC4×C11×C22⋊Q8C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenterC4×C22⋊Q8D11
hypocenterC11#24710
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×#10622633C2semidirect
6. #13069568C2semidirect
7. #13069374C2semidirect
8. #13069351C2semidirect
9. #13069309C2semidirect
10. #13068621C2semidirect
427. C11#24710semidirect

Maximal subgroups

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

subgroupindex
C2×#106226332
C2×#106225392
#130769682
#130700522
#130698162
#130695682
#130693742
#130693512
#130693092
#130686212
C4×C11×C22⋊Q82
#2471011