Finite Group Databasebeta

← #14775851

Subgroups — #14775851

Order 2816.

708 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078404C211yesmaximal, characteristic
2#13077559C211yesmaximal, characteristic, complemented
3#13069592C211yesmaximal, characteristic, complemented
4#13069389C211yesmaximal, characteristic, complemented
5#13069366C212yesmaximal, complemented
6#13069212C212yesmaximal, complemented
7#13068891C212yesmaximal
8#13068471C211yesmaximal, characteristic, complemented
9#13068458C212yesmaximal
10C4×#66901C211yesmaximal, characteristic
11C11×#2906C211yesmaximal, characteristic
12C2×C11×#131C2212yes—
13C4×C11×#41C2211yescharacteristic
14#10623001C2211yescharacteristic
15C11×#424—22no—
16C11×#424C2212yes—
17C11×#423—21no—
18C11×#423C2211yescharacteristic
19C2×C11×C4⋊C8—21no—
20C2×C11×C4⋊C8C2211yescharacteristic
21C2×#66901C2211yescharacteristic
22C2×#66901C2211yescharacteristic
23#10622846C2212yes—
24C2×#66886C2212yes—
25#10622715C2212yes—
26#10622714C2212yes—
27C2×#66879C2212yes—
28#10622635C412yescomplemented
29#10622634C411yescharacteristic, complemented
30#10622633C411yescharacteristic, complemented
31#10622622C412yescomplemented
32#10622621C411yescharacteristic, complemented
33#10622620C411yescharacteristic, complemented
34#10622611C2212yes—
35C42×Dic11C2211yescharacteristic
36C2×C4⋊(C11⋊C8)C2211yescharacteristic
37C4×#4318C2211yescharacteristic
38#10622444—21no—
39#10622443—21no—
40#10622441—22no—
41#10622196C2212yes—
42#10622193C2212yes—
43#10622193C2212yes—
44#10622188C2212yes—
45#10622170C2211yescharacteristic
46#10622170C2211yescharacteristic
47C2×C11×#41C2311yescharacteristic
48C11×#131—24no—
49C11×#131—42no—
50C2×C11×M16—22no—
51C2×C11×M16C2312yes—
52C22×C8×C11—22no—
53C22×C8×C11C2312yes—
54C4×Q8×C11C2×C411yescharacteristic
55C4×Q8×C11C2×C411yescharacteristic
56C4×D4×C11—21no—
57C4×D4×C11—21no—
58C4×D4×C11C2×C411yescharacteristic
59C4×D4×C11C2×C411yescharacteristic
60C11×#117—21no—
61C11×#117C2311yescharacteristic
62C2×C42×C11—21no—
63C2×C42×C11C2311yescharacteristic
64#66979C2312yes—
65#66977—21no—
66#66977—21no—
67C2×C4×Dic11—21no—
68C2×C4×Dic11—21no—
69C2×C4×Dic11C2311yescharacteristic
70C2×C4×Dic11C2311yescharacteristic
71C2×#4318C2311yescharacteristic
72C2×#4318C2311yescharacteristic
73C22×C11⋊C8C2312yes—
74#66923C2×C412yes—
75#66922C2×C411yescharacteristic
76#66922C2×C411yescharacteristic
77C4×Dic22—21no—
78C4×Dic22—21no—
79C11×C4⋊C8—22no—
80C11×C4⋊C8—22no—
81C11×C4⋊C8—21no—
82C11×C4⋊C8—21no—
83C11×C4⋊C8D411yescharacteristic
84C11×C4⋊C8D411yescharacteristic
85C11×C4⋊C8D412yes—
86#66901—22no—
87#66901Q814yescomplemented
88#66899C2×C412yes—
89#66899C2×C412yes—
90#66896C2×C412yes—
91#66896C2×C412yes—
92#66886—42no—
93#66879—22no—
94#66879—42no—
95Dic11⋊C8—22no—
96Dic11⋊C8—22no—
97C8×Dic11—22no—
98#66872C2×C412yes—
99#66872C2×C412yes—
100#66871C2×C412yes—
101#66871C2×C412yes—
102C4⋊(C11⋊C8)C2×C411yescharacteristic
103C4⋊(C11⋊C8)C2×C411yescharacteristic
104C4⋊(C11⋊C8)C2×C412yes—
105#66867—21no—
106C4×C11⋊C8—21no—
107#22983—111nomaximal, Sylow
108C11×#41—21no—
109C11×#41—21no—
110C11×#41C2×Q812yes—
111C11×#41#4112yes—
112C2×Q8×C11C22×C411yescharacteristic
113C2×D4×C11—21no—
114C2×D4×C11C22×C411yescharacteristic
115C22×C4×C11—21no—
116C22×C4×C11—21no—
117C22×C4×C11—21no—
118C22×C4×C11#4111yescharacteristic
119C22×C4×C11#4111yescharacteristic
120C22×C4×C11C2411yescharacteristic
121C22×Dic11—21no—
122C22×Dic11—21no—
123C2×Dic22—21no—
124C2×Dic22—21no—
125C11×M16—22no—
126C11×M16—22no—
127C11×M16—44no—
128C2×C8×C11—22no—
129C2×C8×C11—22no—
130C2×C8×C11—22no—
131C2×C8×C11—44no—
132C2×C8×C11C2×D412yes—
133C2×C8×C11C2×D412yes—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4C22×C411yescharacteristic
137C11×C4⋊C4C22×C411yescharacteristic
138C11×C22⋊C4—21no—
139C11×C22⋊C4—21no—
140C11×C22⋊C4—21no—
141C42×C11—21no—
142C42×C11—21no—
143C42×C11—21no—
144C42×C11C22×C411yescharacteristic
145C42×C11C22×C411yescharacteristic
146C42×C11C2×D411yescharacteristic
147C42×C11C2×D411yescharacteristic
148C22⋊Dic11—22no—
149C4⋊Dic11—21no—
150C4⋊Dic11—21no—
151C4⋊Dic11C22×C412yes—
152C4⋊Dic11C22×C412yes—
153Dic11⋊C4—22no—
154Dic11⋊C4—22no—
155C4×Dic11—22no—
156C4×Dic11—21no—
157C4×Dic11—21no—
158C4×Dic11—21no—
159C4×Dic11—42no—
160C4×Dic11—42no—
161C4×Dic11C2×Q812yes—
162#4318—21no—
163#4318—21no—
164#4318—21no—
165#4318C2×Q812yes—
166C2×C11⋊C8—21no—
167C2×C11⋊C8—21no—
168C2×C11⋊C8—22no—
169C2×C11⋊C8—22no—
170C2×C11⋊C8C22×C412yes—
171C2×C11⋊C8C22×C412yes—
172#3076—111no—
173#2962—111no—
174#2906D1111yescharacteristic
175#1994—111no—
176#1950—111no—
177#1946—112no—
178#1922—112no—
179#1866—112no—
180#1767—111no—
181#1765—112no—
182C4×#104—111no—
183C23×C11—21no—
184C23×C11C2×#4111yescharacteristic
185Q8×C11—21no—
186Q8×C11C4×Q812yes—
187D4×C11—22no—
188D4×C11—22no—
189D4×C11—21no—
190D4×C11C4×Q812yes—
191C2×C4×C11—21no—
192C2×C4×C11—22no—
193C2×C4×C11—22no—
194C2×C4×C11—22no—
195C2×C4×C11—21no—
196C2×C4×C11—21no—
197C2×C4×C11—41no—
198C2×C4×C11—42no—
199C2×C4×C11—81no—
200C2×C4×C11C4×D411yescharacteristic
201C2×C4×C11C4×D411yescharacteristic
202C2×C4×C11C4×D411yescharacteristic
203C2×C4×C11C4×D411yescharacteristic
204C2×C4×C11C23×C411yescharacteristic
205C2×C4×C11C22×D411yescharacteristic
206C2×C4×C11C22×Q811yescharacteristic
207C2×C4×C11C2×#4111yescharacteristic
208C2×C4×C11H(5,𝔽2)11yescharacteristic
209C2×C4×C112−1+411yescharacteristic
210C2×Dic11—22no—
211C2×Dic11—22no—
212C2×Dic11—22no—
213C2×Dic11—22no—
214C2×Dic11—41no—
215C2×Dic11—41no—
216C2×Dic11—41no—
217C2×Dic11—41no—
218Dic22—42no—
219Dic22—81no—
220C8×C11—22no—
221C8×C11—22no—
222C8×C11—42no—
223C11⋊C8—22no—
224C11⋊C8—22no—
225C11⋊C8—22no—
226C11⋊C8—41no—
227C2×#131C2×D1112yes—
228#533—111no—
229C4×#41C2×D1111yescharacteristic
230#479—112no—
231#478—112no—
232#477—111no—
233#476—111no—
234#475—111no—
235#474—111no—
236#446—222no—
237#446—221no—
238C8×Q8—221no—
239C2×#108—112no—
240#427—112no—
241#424—22no—
242#424—112no—
243#424C2×D1112yes—
244#423—21no—
245#423C2×D1111yescharacteristic
246C2×C4⋊C8—21no—
247C2×C4⋊C8—111no—
248C2×C4⋊C8C2×D1111yescharacteristic
249C2×#104—111no—
250C2×#104—111no—
251#416—112no—
252#405—112no—
253C4×M16—111no—
254C2×#97—112no—
255C43—111no—
256#341—112no—
257#339—112no—
258#339—112no—
259#339—111no—
260#339—111no—
261#336—112no—
262C22×C11—21no—
263C22×C11—21no—
264C22×C11—22no—
265C22×C11—41no—
266C22×C11—41no—
267C22×C11C2×C4×D411yescharacteristic
268C22×C11#55211yescharacteristic
269C22×C11#55411yescharacteristic
270C4×C11—22no—
271C4×C11—21no—
272C4×C11—21no—
273C4×C11—21no—
274C4×C11—41no—
275C4×C11—41no—
276C4×C11#44412yes—
277C4×C11C2×C4×Q811yescharacteristic
278C4×C11#52011yescharacteristic
279C4×C11#54611yescharacteristic
280C4×C11D4×Q811yescharacteristic
281Dic11—42no—
282Dic11—42no—
283Dic11—42no—
284Dic11—42no—
285C2×#41C22×D1111yescharacteristic
286#131—24no—
287#131—42no—
288C2×M16—22no—
289C2×M16—111no—
290C2×M16—111no—
291C2×M16C22×D1112yes—
292C22×C8—22no—
293C22×C8—112no—
294C22×C8C22×D1112yes—
295C4⋊Q8—111no—
296C4⋊Q8—111no—
297#125—112no—
298C22⋊Q8—221no—
299C22⋊Q8—221no—
300C4×Q8—221no—
301C4×Q8—221no—
302C4×Q8C4×D1111yescharacteristic
303C4×Q8C4×D1111yescharacteristic
304C4×D4—21no—
305C4×D4—21no—
306C4×D4C4×D1111yescharacteristic
307C4×D4C4×D1111yescharacteristic
308#117—21no—
309#117—112no—
310#117C22×D1111yescharacteristic
311C2×C42—21no—
312C2×C42—111no—
313C2×C42—111no—
314C2×C42—221no—
315C2×C42—221no—
316C2×C42C22×D1111yescharacteristic
317#108—442no—
318#107—112no—
319#107—112no—
320#106—112no—
321#106—112no—
322C4⋊C8—22no—
323C4⋊C8—22no—
324C4⋊C8—21no—
325C4⋊C8—21no—
326C4⋊C8—111no—
327C4⋊C8—111no—
328C4⋊C8—112no—
329C4⋊C8—222no—
330C4⋊C8—222no—
331C4⋊C8C22⋊D1111yescharacteristic
332C4⋊C8C22⋊D1111yescharacteristic
333C4⋊C8C22⋊D1112yes—
334#104—114no—
335#104—222no—
336#103—112no—
337#103—112no—
338#102—112no—
339#102—112no—
340#97—222no—
341#97—221no—
342#97—442no—
343C4×C8—222no—
344C4×C8—221no—
345C2×C11—21no—
346C2×C11—21no—
347C2×C11—42no—
348C2×C11#236011yescharacteristic
349C2×C11C2×#44411yescharacteristic
350C2×C11#295611yescharacteristic
351#41—21no—
352#41—21no—
353#41#434112yes—
354#41Q8×D1112yes—
355C2×Q8—221no—
356C2×Q8—221no—
357C2×Q8C2×C4×D1111yescharacteristic
358C2×D4—21no—
359C2×D4C2×C4×D1111yescharacteristic
360C22×C4—21no—
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—221no—
364C22×C4—221no—
365C22×C4#433911yescharacteristic
366C22×C4#433911yescharacteristic
367C22×C4C23×D1111yescharacteristic
368M16—22no—
369M16—22no—
370M16—44no—
371M16—112no—
372M16—221no—
373M16—221no—
374M16—221no—
375C2×C8—22no—
376C2×C8—22no—
377C2×C8—22no—
378C2×C8—44no—
379C2×C8—112no—
380C2×C8—112no—
381C2×C8—222no—
382C2×C8—222no—
383C2×C8—221no—
384C2×C8—221no—
385C2×C8C2×C22⋊D1112yes—
386C2×C8C2×C22⋊D1112yes—
387C4⋊C4—21no—
388C4⋊C4—21no—
389C4⋊C4—112no—
390C4⋊C4—112no—
391C4⋊C4—222no—
392C4⋊C4—222no—
393C4⋊C4—221no—
394C4⋊C4—221no—
395C4⋊C4C2×C4×D1111yescharacteristic
396C4⋊C4C2×C4×D1111yescharacteristic
397C22⋊C4—21no—
398C22⋊C4—21no—
399C22⋊C4—21no—
400C22⋊C4—222no—
401C42—21no—
402C42—21no—
403C42—21no—
404C42—112no—
405C42—221no—
406C42—222no—
407C42—221no—
408C42—221no—
409C42—442no—
410C42—442no—
411C42C2×C4×D1111yescharacteristic
412C42C2×C4×D1111yescharacteristic
413C42C2×C22⋊D1111yescharacteristic
414C42C2×C22⋊D1111yescharacteristic
415C11#2298311yescharacteristic, complemented, Sylow
416C23—21no—
417C23C2×#433911yescharacteristic
418Q8—21no—
419Q8—442no—
420Q8—881no—
421Q8#6694012yes—
422D4—22no—
423D4—22no—
424D4—21no—
425D4#6694012yes—
426C2×C4—21no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—41no—
433C2×C4—42no—
434C2×C4—81no—
435C2×C4—222no—
436C2×C4—222no—
437C2×C4—222no—
438C2×C4—222no—
439C2×C4—441no—
440C2×C4—441no—
441C2×C4—441no—
442C2×C4—441no—
443C2×C4C4×C22⋊D1111yescharacteristic
444C2×C4C4×C22⋊D1111yescharacteristic
445C2×C4C4×C22⋊D1111yescharacteristic
446C2×C4C4×C22⋊D1111yescharacteristic
447C2×C4C22×C4×D1111yescharacteristic
448C2×C4C2×#434111yescharacteristic
449C2×C4#6703711yescharacteristic
450C2×C4C2×Q8×D1111yescharacteristic
451C2×C4#6704011yescharacteristic
452C2×C4C22×C22⋊D1111yescharacteristic
453C8—22no—
454C8—22no—
455C8—42no—
456C8—222no—
457C8—222no—
458C8—222no—
459C8—441no—
460C22—21no—
461C22—21no—
462C22—22no—
463C22—41no—
464C22—41no—
465C22#1062304211yescharacteristic
466C22#1062304411yescharacteristic
467C22C2×C4×C22⋊D1111yescharacteristic
468C4—22no—
469C4—21no—
470C4—21no—
471C4—21no—
472C4—41no—
473C4—41no—
474C4—442no—
475C4—442no—
476C4—442no—
477C4—442no—
478C4#1062275812yes—
479C4C2×#6694011yescharacteristic
480C4#1062303511yescharacteristic
481C4#1062333711yescharacteristic
482C4Q8×C22⋊D1111yescharacteristic
483C2—21no—
484C2—21no—
485C2—42no—
486C2#1307162111yescharacteristic
487C2C2×#1062275811yescharacteristic
488C2#1307752311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2906C2
socleC22×C11C2×C4×D4
prime radicalC2×C11×#41C23
cosocleC22×C4×C11C24
hypercenter#2906D11
hypocenterC11#22983
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C4⋊C8 ◁ #2906

Complements

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

NH ≅ G/Ntype
2. #13077559C2semidirect
3. #13069592C2semidirect
4. #13069389C2semidirect
5. #13069366C2semidirect
6. #13069212C2semidirect
8. #13068471C2semidirect
28. #10622635C4semidirect
29. #10622634C4semidirect
30. #10622633C4semidirect
31. #10622622C4semidirect
32. #10622621C4semidirect
33. #10622620C4semidirect
87. #66901Q8semidirect
415. C11#22983semidirect

Maximal subgroups

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

subgroupindex
#130784042
#130775592
#130695922
#130693892
#130693662
#130692122
#130688912
#130684712
#130684582
C4×#669012
C11×#29062
#2298311