Finite Group Databasebeta

← #15626377

Subgroups — #15626377

Order 2816.

1622 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082503C211yesmaximal, characteristic
2#13082437C211yesmaximal, characteristic
3#13079885C218yesmaximal, complemented
4#13079831C214yesmaximal, complemented
5#13079823C214yesmaximal, complemented
6#13079169C211yesmaximal, characteristic, complemented
7#13078998C211yesmaximal, characteristic, complemented
8C2×#10622316C211yesmaximal, characteristic, complemented
9#13078588C214yesmaximal
10#13078461C214yesmaximal, complemented
11#13077265C211yesmaximal, characteristic
12C11×#3162C211yesmaximal, characteristic, complemented
13C11×#533C2211yescharacteristic
14C11×#533C2211yescharacteristic
15#10623260C2214yes—
16#10623259C2214yes—
17#10623228C2214yes—
18#10623219C2212yes—
19D11×#125C2212yes—
20#10623173—24no—
21#10623167—24no—
22#10623115—22no—
23#10623110—22no—
24#10623101—22no—
25#10623098—22no—
26#10623057C2212yes—
27#10623054C2212yes—
28#10623050C2212yes—
29#10623047C2212yes—
30C4×#4339C2211yescharacteristic
31C2×#66923C2211yescharacteristic
32C2×#66922C2211yescharacteristic
33C11×#501C2212yes—
34C11×#501C2212yes—
35C11×#501C2214yes—
36C11×#427C2214yes—
37C2×C11×#97C2211yescharacteristic
38#10622723C2212yes—
39C2×#66880C2214yes—
40#10622715C2212yes—
41#10622706C2214yes—
42#10622693C2214yes—
43#10622682C2212yes—
44#10622682C2212yes—
45#10622677C2214yes—
46#10622617C2214yes—
47#10622608C2214yes—
48C4×#4318C2211yescharacteristic
49#10622501C2218yes—
50#10622497C2218yes—
51#10622490C2218yes—
52#10622488C2218yes—
53#10622480C2218yes—
54#10622475C2218yes—
55#10622470C2218yes—
56#10622467C2218yes—
57#10622322C2214yes—
58#10622318C2214yes—
59#10622316C2214yes—
60#10622316C2214yes—
61C2×#4339C2311yescharacteristic
62C22×Dic22C2312yes—
63C22×C8×C11C2312yes—
64C11×C4⋊Q8C2312yes—
65C11×C4⋊Q8C2312yes—
66C11×#125C2312yes—
67C11×#125C2311yescharacteristic
68C11×#125C2311yescharacteristic
69C11×C22⋊Q8—22no—
70C11×C22⋊Q8—22no—
71C4×Q8×C11—22no—
72C4×Q8×C11—22no—
73C11×#117C2312yes—
74C11×#117C2312yes—
75C2×C42×C11C2311yescharacteristic
76#66999—24no—
77#66999—24no—
78Q8×Dic11—24no—
79#66997—24no—
80C4×C22⋊D11D414yes—
81#66979C2311yescharacteristic
82C2×C4⋊Dic11—22no—
83C2×C4⋊Dic11C2312yes—
84C2×Dic11⋊C4—22no—
85C2×#4318C2312yes—
86#66951—28no—
87#66950C2318yes—
88#66949—24no—
89#66949—24no—
90#66945—24no—
91#66945C2314yes—
92C4⋊C4×D11—24no—
93C4⋊C4×D11C2314yes—
94#66943—28no—
95#66943—24no—
96#66943C2314yes—
97#66942—24no—
98#66942—24no—
99#66941C2314yes—
100#66940—24no—
101#66940C2318yes—
102#66939—24no—
103(C22⋊D11)⋊C4—24no—
104#66931—24no—
105#66930—24no—
106#66928—22no—
107C4×D44—22no—
108C4×D44D412yes—
109#66925C2312yes—
110C42×D11C2312yes—
111#66923—22no—
112#66923—22no—
113#66923C2312yes—
114#66923C2312yes—
115#66922—22no—
116#66922—22no—
117#66922—22no—
118#66922C2312yes—
119#66922C2312yes—
120C4×Dic22—22no—
121C4×Dic22—24no—
122C4×Dic22D412yes—
123C11×#107C2314yes—
124C11×#107C2314yes—
125C11×#106C2314yes—
126C11×#106C2314yes—
127C11×#97C2312yes—
128C11×#97C2312yes—
129(C2×D11)⋊C8C2318yes—
130#66880C2318yes—
131#66880C2318yes—
132Dic11⋊C8C2318yes—
133#66874C2318yes—
134#66874C2318yes—
135#66872C2318yes—
136#66871C2318yes—
137#66867C2312yes—
138C4×C11⋊C8C2312yes—
139#60884—111nomaximal, Sylow
140C2×Q8×C11—22no—
141C2×Q8×C11—22no—
142C22×C4×C11C2×D412yes—
143C22×C4×C11C2411yescharacteristic
144C2×C22⋊D11C2×D412yes—
145C22×Dic11—22no—
146C22×Dic11—22no—
147#4339—24no—
148C2×D44C2×D411yescharacteristic
149C2×C4×D11—24no—
150C2×C4×D11C2×D414yes—
151C2×C4×D11C2412yes—
152C2×Dic22—24no—
153C2×Dic22—22no—
154C2×Dic22—28no—
155C2×Dic22C2×D411yescharacteristic
156C2×Dic22C2414yes—
157C2×C8×C11—24no—
158C2×C8×C11C2414yes—
159C11×C4⋊C4—22no—
160C11×C4⋊C4—22no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4—24no—
164C11×C4⋊C4C2414yes—
165C11×C4⋊C4C2412yes—
166C11×C4⋊C4C2412yes—
167C11×C22⋊C4—22no—
168C11×C22⋊C4—22no—
169C42×C11—22no—
170C42×C11—22no—
171C42×C11C2×D412yes—
172C42×C11C2411yescharacteristic
173C42×C11C2411yescharacteristic
174C22⋊Dic11C2×D412yes—
175(C2×D11)⋊C4—24no—
176(C2×D11)⋊C4—28no—
177(C2×D11)⋊C4C2×D414yes—
178C4⋊Dic11—24no—
179C4⋊Dic11—28no—
180C4⋊Dic11—22no—
181C4⋊Dic11—24no—
182C4⋊Dic11—24no—
183C4⋊Dic11C2×D412yes—
184C4⋊Dic11C2414yes—
185Dic11⋊C4—28no—
186Dic11⋊C4—24no—
187Dic11⋊C4—24no—
188Dic11⋊C4—24no—
189Dic11⋊C4—24no—
190Dic11⋊C4—24no—
191Dic11⋊C4C2×D414yes—
192C4×Dic11—28no—
193C4×Dic11—24no—
194C4×Dic11C2×D414yes—
195C4×Dic11C2412yes—
196#4318—24no—
197C2×C11⋊C8C2414yes—
198#3509—111no—
199#3504—111no—
200#3242—118no—
201#3237—114no—
202#3236—114no—
203#3166—111no—
204#3162D1111yescharacteristic, complemented
205#3139—111no—
206C2×#491—111no—
207#3097—114no—
208#3082—114no—
209#2923—111no—
210C23×C11C22×D411yescharacteristic
211C22×D11C22×D412yes—
212Q8×C11—44no—
213Q8×C11—82no—
214C2×C4×C11—24no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—42no—
218C2×C4×C11C22×D412yes—
219C2×C4×C11C22×D412yes—
220C2×C4×C11C22×D411yescharacteristic
221C2×C4×C112−1+414yes—
222C2×C4×C11C2511yescharacteristic
223C22⋊D11—24no—
224C2×Dic11—24no—
225C2×Dic11—24no—
226C2×Dic11—44no—
227C2×Dic11—82no—
228C2×Dic11C22×D412yes—
229C2×Dic11C22×D414yes—
230D44—22no—
231C4×D11—24no—
232C4×D11—44no—
233C4×D11—84no—
234Dic22—22no—
235Dic22—28no—
236Dic22—44no—
237Dic22—84no—
238C8×C11—24no—
239C11⋊C8—24no—
240#557—222no—
241#557—222no—
242#556—222no—
243#554—222no—
244#554—224no—
245#552—224no—
246#544—114no—
247#544—112no—
248#541—114no—
249#536—112no—
250#533—112no—
251#533—114no—
252#533C2×D1111yescharacteristic
253#533C2×D1111yescharacteristic
254C2×C4⋊Q8—111no—
255C2×#125—112no—
256C2×#125—111no—
257#520—112no—
258#519—112no—
259C4×#41—111no—
260#501—114no—
261#501C2×D1112yes—
262#501C2×D1112yes—
263#501C2×D1114yes—
264#499—114no—
265#491—112no—
266#491—112no—
267#491—114no—
268#491—114no—
269#487—114no—
270#485—118no—
271#485—118no—
272#484—118no—
273#483—118no—
274#479—118no—
275#479—118no—
276#477—118no—
277#475—118no—
278#433—114no—
279#432—114no—
280#428—114no—
281#427C2×D1114yes—
282#424—112no—
283#419—114no—
284C2×#103—114no—
285#408—112no—
286C4×M16—111no—
287C2×#97C2×D1111yescharacteristic
288C22×C11—22no—
289C22×C11#53612yes—
290C22×C11C23×D411yescharacteristic
291C2×D11—24no—
292C2×D11—22no—
293C4×C11—22no—
294C4×C11—22no—
295C4×C11—44no—
296C4×C11—42no—
297C4×C11—42no—
298C4×C11#53612yes—
299C4×C11C2×2−1+412yes—
300Dic11—24no—
301Dic11—22no—
302Dic11—44no—
303Dic11—44no—
304C2×#41—111no—
305C22×Q8—112no—
306C2×M16—112no—
307C22×C8C22×D1112yes—
308C4⋊Q8—114no—
309C4⋊Q8—112no—
310C4⋊Q8—112no—
311C4⋊Q8—222no—
312C4⋊Q8—222no—
313C4⋊Q8—224no—
314C4⋊Q8—222no—
315C4⋊Q8C22×D1112yes—
316C4⋊Q8C22×D1112yes—
317#126—228no—
318#125—114no—
319#125—112no—
320#125—112no—
321#125—222no—
322#125—224no—
323#125—224no—
324#125—228no—
325#125—224no—
326#125—222no—
327#125C22×D1111yescharacteristic
328#125C22×D1111yescharacteristic
329#125C22×D1112yes—
330#124—222no—
331#123—224no—
332C22⋊Q8—22no—
333C22⋊Q8—22no—
334C22⋊Q8—118no—
335C22⋊Q8—224no—
336C22⋊Q8—224no—
337C22⋊Q8—224no—
338C22⋊Q8—224no—
339C22⋊Q8—224no—
340C4×Q8—22no—
341C4×Q8—22no—
342C4×Q8—112no—
343C4×Q8—118no—
344C4×Q8—224no—
345C4×Q8—222no—
346C4×Q8—224no—
347C4×Q8—224no—
348C4×D4—114no—
349C4×D4—112no—
350C4×D4—222no—
351C4×D4—224no—
352#117—111no—
353#117—112no—
354#117—114no—
355#117—224no—
356#117—224no—
357#117C22×D1112yes—
358#117C22×D1112yes—
359C2×C4⋊C4—112no—
360C2×C4⋊C4—114no—
361C2×C4⋊C4—224no—
362C2×C4⋊C4—222no—
363C2×C4⋊C4—222no—
364C2×C42—112no—
365C2×C42C22×D1111yescharacteristic
366#107—118no—
367#107C22×D1114yes—
368#107C22×D1114yes—
369#106—118no—
370#106C22×D1114yes—
371#106C22×D1114yes—
372C4⋊C8—118no—
373#103—118no—
374#103—118no—
375#103—118no—
376#103—118no—
377C22⋊C8—118no—
378#97—112no—
379#97C22×D1112yes—
380#97C22×D1112yes—
381C4×C8—112no—
382C2×C11—22no—
383C2×C11C2×#53611yescharacteristic
384C2×C11#358612yes—
385D11—42no—
386#41—224no—
387C2×Q8—22no—
388C2×Q8—22no—
389C2×Q8—111no—
390C2×Q8—114no—
391C2×Q8—224no—
392C2×Q8—222no—
393C2×Q8—228no—
394C2×D4—112no—
395C2×D4—111no—
396C22×C4—112no—
397C22×C4—114no—
398C22×C4—224no—
399C22×C4—222no—
400C22×C4—222no—
401C22×C4D4×D1112yes—
402C22×C4C23×D1111yescharacteristic
403M16—224no—
404C2×C8—24no—
405C2×C8—114no—
406C2×C8C23×D1114yes—
407C4⋊C4—22no—
408C4⋊C4—22no—
409C4⋊C4—22no—
410C4⋊C4—22no—
411C4⋊C4—24no—
412C4⋊C4—112no—
413C4⋊C4—114no—
414C4⋊C4—114no—
415C4⋊C4—224no—
416C4⋊C4—224no—
417C4⋊C4—224no—
418C4⋊C4—228no—
419C4⋊C4—228no—
420C4⋊C4—224no—
421C4⋊C4—222no—
422C4⋊C4—224no—
423C4⋊C4—224no—
424C4⋊C4—224no—
425C4⋊C4—224no—
426C4⋊C4C23×D1112yes—
427C4⋊C4C23×D1112yes—
428C4⋊C4C23×D1114yes—
429C22⋊C4—22no—
430C22⋊C4—22no—
431C22⋊C4—112no—
432C22⋊C4—114no—
433C22⋊C4—224no—
434C22⋊C4—228no—
435C42—22no—
436C42—22no—
437C42—114no—
438C42—112no—
439C42—224no—
440C42—228no—
441C42D4×D1112yes—
442C42C23×D1111yescharacteristic
443C42C23×D1111yescharacteristic
444C11#6088411yescharacteristic, complemented, Sylow
445C23—112no—
446C23C2×D4×D1111yescharacteristic
447Q8—44no—
448Q8—82no—
449Q8—222no—
450Q8—228no—
451Q8—444no—
452Q8—884no—
453D4—224no—
454D4—222no—
455C2×C4—24no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—42no—
459C2×C4—114no—
460C2×C4—112no—
461C2×C4—224no—
462C2×C4—224no—
463C2×C4—224no—
464C2×C4—444no—
465C2×C4—444no—
466C2×C4—884no—
467C2×C4—882no—
468C2×C4C2×D4×D1112yes—
469C2×C4C2×D4×D1112yes—
470C2×C4C2×D4×D1111yescharacteristic
471C2×C4#6704014yes—
472C2×C4C24×D1111yescharacteristic
473C8—24no—
474C8—224no—
475C22—22no—
476C22—224no—
477C22—222no—
478C22#1062325512yes—
479C22C22×D4×D1111yescharacteristic
480C4—22no—
481C4—22no—
482C4—42no—
483C4—44no—
484C4—42no—
485C4—224no—
486C4—222no—
487C4—444no—
488C4—444no—
489C4#1062325512yes—
490C4C2×#6704012yes—
491C2—22no—
492C2—442no—
493C2C2×#1062325511yescharacteristic
494C2#1308340012yes—
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3162C2
socleC22×C11C23×D4
prime radicalC2×#4339C23
hypercenter#3162D11
hypocenterC11#60884
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3162

Complements

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

NH ≅ G/Ntype
3. #13079885C2semidirect
4. #13079831C2semidirect
5. #13079823C2semidirect
6. #13079169C2semidirect
7. #13078998C2semidirect
8. C2×#10622316C2semidirect
10. #13078461C2semidirect
12. C11×#3162C2semidirect
204. #3162D11semidirect
444. C11#60884semidirect

Maximal subgroups

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

subgroupindex
#130825032
#130824372
#130798852
#130798312
#130798232
#130791692
#130789982
C2×#106223162
#130785882
#130784612
#130772652
C11×#31622
#6088411