Finite Group Databasebeta

← #14738559

Subgroups — #14738559

Order 2816.

678 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079978C212yesmaximal, complemented
2#13079044C211yesmaximal, characteristic, complemented
3#13068088C212yesmaximal, complemented
4#13068081C212yesmaximal, complemented
5#13067986C211yesmaximal, characteristic, complemented
6#13067981C211yesmaximal, characteristic, complemented
7#13067976C211yesmaximal, characteristic, complemented
8#13067971C211yesmaximal, characteristic, complemented
9#13067375C211yesmaximal, characteristic, complemented
10#13067339C212yesmaximal, complemented
11C11×#2966C211yesmaximal, characteristic, complemented
12C11×#529C2211yescharacteristic
13C2×#66957—21no—
14C2×#66957—21no—
15#10623008C2212yes—
16C11×#446C2211yescharacteristic
17C8×Q8×C11C2211yescharacteristic
18C11×#436C2211yescharacteristic
19C11×#435—21no—
20C8×D4×C11—21no—
21C8×D4×C11C2211yescharacteristic
22C11×#433—21no—
23C11×#432C2211yescharacteristic
24C11×#405—21no—
25C2×C4×C8×C11C2211yescharacteristic
26#10622679—22no—
27#10622670—22no—
28#10622662—22no—
29#10622652—22no—
30#10622640C2212yes—
31#10622633C2212yes—
32#10622628C2212yes—
33#10622620C2212yes—
34#10622537C2212yes—
35#10622312C2211yescharacteristic
36#10622309—21no—
37#10622309—21no—
38#10622308C2211yescharacteristic
39#10622306C2212yes—
40#10622123C2212yes—
41#10622123C2212yes—
42#10622120C2212yes—
43#10622120C2212yes—
44#10622096C2212yes—
45#10622096C2211yescharacteristic
46#10622096C2211yescharacteristic
47C2×#4339—22no—
48C2×C11×M16—21no—
49C22×C8×C11—21no—
50C22×C8×C11D411yescharacteristic
51C22×C8×C11D411yescharacteristic
52C11×#126—21no—
53C11×#125D411yescharacteristic
54C11×#124D411yescharacteristic
55C11×#123—21no—
56C11×C22⋊Q8D411yescharacteristic
57C11×#121D411yescharacteristic
58C4×Q8×C11C2311yescharacteristic
59C4×D4×C11—21no—
60C4×D4×C11C2311yescharacteristic
61C11×#117—21no—
62C2×C42×C11C2311yescharacteristic
63C2×#4325—22no—
64C2×#4323—22no—
65#66983—22no—
66#66983—22no—
67C2×#4318—22no—
68C2×Dic44—21no—
69C2×Dic44—21no—
70#66957—44no—
71#66957—44no—
72C2×D88—21no—
73C2×D88—21no—
74C2×#4314—22no—
75C2×#4314—22no—
76#66928—22no—
77#66927C2312yes—
78C4×D44—22no—
79C4×D44—22no—
80#66922C2312yes—
81C11×C4⋊C8—21no—
82C11×C4⋊C8—21no—
83C11×C4⋊C8C2311yescharacteristic
84C11×C4⋊C8C2311yescharacteristic
85C11×C22⋊C8—21no—
86C11×C22⋊C8—21no—
87C11×C22⋊C8—21no—
88C11×#97—21no—
89C11×#97—21no—
90C4×C8×C11—21no—
91C4×C8×C11D411yescharacteristic
92C4×C8×C11D411yescharacteristic
93C4×C8×C11C2311yescharacteristic
94C4×C8×C11C2311yescharacteristic
95#66899—22no—
96#66896—22no—
97#66873—22no—
98#66873—22no—
99#66872—22no—
100#66871—22no—
101C4⋊(C11⋊C8)—22no—
102C4⋊(C11⋊C8)C2312yes—
103C4⋊(C11⋊C8)C2312yes—
104#19356—111nomaximal, Sylow
105C2×Q8×C11C2×D411yescharacteristic
106C2×D4×C11—21no—
107C2×D4×C11C2×D411yescharacteristic
108C22×C4×C11—21no—
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11#4111yescharacteristic
112C2×C22⋊D11—42no—
113#4339—44no—
114#4339—44no—
115C2×D44—22no—
116C2×D44—22no—
117C2×D44—22no—
118C2×C4×D11—42no—
119C2×Dic22—22no—
120C11×M16—42no—
121C2×C8×C11—22no—
122C2×C8×C11—22no—
123C2×C8×C11—21no—
124C2×C8×C11—21no—
125C2×C8×C11—42no—
126C2×C8×C11C2×D411yescharacteristic
127C2×C8×C11C2×D411yescharacteristic
128C2×C8×C11C2×D411yescharacteristic
129C2×C8×C11C2×D411yescharacteristic
130C11×C4⋊C4—21no—
131C11×C4⋊C4—21no—
132C11×C4⋊C4—21no—
133C11×C4⋊C4—21no—
134C11×C4⋊C4C2×D411yescharacteristic
135C11×C4⋊C4C2×D411yescharacteristic
136C11×C22⋊C4—21no—
137C11×C22⋊C4—21no—
138C11×C22⋊C4—21no—
139C11×C22⋊C4—21no—
140C11×C22⋊C4—21no—
141C42×C11—21no—
142C42×C11C2×D411yescharacteristic
143C42×C11C2×D411yescharacteristic
144C42×C11#4111yescharacteristic
145C42×C11C2411yescharacteristic
146#4325—82no—
147#4323—82no—
148(C2×D11)⋊C4—42no—
149(C2×D11)⋊C4—42no—
150C4⋊Dic11—22no—
151C4⋊Dic11—22no—
152#4318—82no—
153C2×C11⋊C8—22no—
154C2×C11⋊C8—22no—
155Dic44—42no—
156Dic44—42no—
157D88—42no—
158D88—42no—
159#4314—44no—
160#4314—44no—
161#3251—112no—
162#3147—111no—
163#2966D1111yescharacteristic, complemented
164#1686—112no—
165#1685—112no—
166#1670—111no—
167#1669—111no—
168#1668—111no—
169#1667—111no—
170#1567—111no—
171#1557—112no—
172C23×C11—21no—
173C23×C11#12111yescharacteristic
174C22×D11—42no—
175Q8×C11—21no—
176Q8×C11—21no—
177D4×C11—21no—
178D4×C11—21no—
179D4×C11—42no—
180C2×C4×C11—21no—
181C2×C4×C11—21no—
182C2×C4×C11—21no—
183C2×C4×C11—21no—
184C2×C4×C11—21no—
185C2×C4×C11—21no—
186C2×C4×C11—21no—
187C2×C4×C11—41no—
188C2×C4×C11—41no—
189C2×C4×C11—41no—
190C2×C4×C11#12111yescharacteristic
191C2×C4×C11#12111yescharacteristic
192C2×C4×C11#12111yescharacteristic
193C2×C4×C11C22×D411yescharacteristic
194C2×C4×C11C22×D411yescharacteristic
195C2×C4×C11C2×#4111yescharacteristic
196C22⋊D11—84no—
197C2×Dic11—42no—
198D44—42no—
199D44—42no—
200D44—42no—
201D44—42no—
202D44—82no—
203C4×D11—84no—
204Dic22—42no—
205Dic22—42no—
206C8×C11—21no—
207C8×C11—21no—
208C8×C11—41no—
209C8×C11—41no—
210C8×C11AGL(1,ℤ/8)12yes—
211C8×C11AGL(1,ℤ/8)12yes—
212C11⋊C8—42no—
213C11⋊C8—42no—
214C2×#135—221no—
215C2×#135—221no—
216#532—112no—
217#529C2×D1111yescharacteristic
218#495—221no—
219#495—221no—
220#494—111no—
221#493—111no—
222#492—112no—
223#478—222no—
224#475—112no—
225#474—112no—
226#469—222no—
227#468—222no—
228#463—222no—
229#460—112no—
230#459—112no—
231#446C2×D1111yescharacteristic
232C8×Q8C2×D1111yescharacteristic
233#436C2×D1111yescharacteristic
234#435—21no—
235C8×D4—21no—
236C8×D4C2×D1111yescharacteristic
237#433—21no—
238#432C2×D1111yescharacteristic
239#423—112no—
240#405—21no—
241C2×C4×C8C2×D1111yescharacteristic
242#335—111no—
243#335—111no—
244#335—112no—
245#332—112no—
246#332—112no—
247#331—112no—
248#331—112no—
249C22×C11—21no—
250C22×C11—21no—
251C22×C11—21no—
252C22×C11—41no—
253C22×C11—41no—
254C22×C11—41no—
255C22×C11C2×#12111yescharacteristic
256C2×D11—82no—
257C2×D11—82no—
258C2×D11—82no—
259C4×C11—21no—
260C4×C11—21no—
261C4×C11—21no—
262C4×C11—21no—
263C4×C11—41no—
264C4×C11—41no—
265C4×C11—41no—
266C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
267C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
268C4×C11#57611yescharacteristic
269C4×C11#57811yescharacteristic
270Dic11—82no—
271C2×#41—222no—
272#135—444no—
273#135—444no—
274C2×Q16—221no—
275C2×Q16—221no—
276C2×SD16—222no—
277C2×SD16—222no—
278C2×SD16—222no—
279C2×D8—222no—
280C2×D8—221no—
281C2×D8—221no—
282C2×M16—21no—
283C2×M16—222no—
284C22×C8—21no—
285C22×C8C22⋊D1111yescharacteristic
286C22×C8C22⋊D1111yescharacteristic
287C4⋊Q8—112no—
288#127—112no—
289#126—21no—
290#125D4411yescharacteristic
291#124—222no—
292#124D4411yescharacteristic
293#123—21no—
294C22⋊Q8D4411yescharacteristic
295#121—222no—
296#121—222no—
297#121D4411yescharacteristic
298C4×Q8C22×D1111yescharacteristic
299C4×D4—21no—
300C4×D4—222no—
301C4×D4—222no—
302C4×D4C22×D1111yescharacteristic
303#117—21no—
304C2×C42C22×D1111yescharacteristic
305#107—222no—
306#106—222no—
307C4⋊C8—21no—
308C4⋊C8—21no—
309C4⋊C8—112no—
310C4⋊C8—112no—
311C4⋊C8—222no—
312C4⋊C8C22×D1111yescharacteristic
313C4⋊C8C22×D1111yescharacteristic
314#103—222no—
315#102—222no—
316#102—222no—
317#102—222no—
318C22⋊C8—21no—
319C22⋊C8—21no—
320C22⋊C8—21no—
321#97—21no—
322#97—21no—
323C4×C8—21no—
324C4×C8C22⋊D1111yescharacteristic
325C4×C8C22⋊D1111yescharacteristic
326C4×C8C22×D1111yescharacteristic
327C4×C8C22×D1111yescharacteristic
328C2×C11—41no—
329C2×C11—81no—
330C2×C11#303811yescharacteristic
331C2×C11#306111yescharacteristic
332C2×C11#306711yescharacteristic
333D11—162no—
334#41—444no—
335#41—444no—
336C2×Q8—222no—
337C2×Q8C2×D4411yescharacteristic
338C2×D4—21no—
339C2×D4—222no—
340C2×D4—222no—
341C2×D4—222no—
342C2×D4—442no—
343C2×D4C2×D4411yescharacteristic
344C22×C4—21no—
345C22×C4—442no—
346C22×C4C2×D4411yescharacteristic
347C22×C4#433911yescharacteristic
348C22×C4C2×C22⋊D1111yescharacteristic
349Q16—442no—
350Q16—442no—
351SD16—444no—
352SD16—444no—
353SD16—882no—
354D8—442no—
355D8—442no—
356D8—882no—
357M16—42no—
358M16—882no—
359C2×C8—22no—
360C2×C8—22no—
361C2×C8—21no—
362C2×C8—21no—
363C2×C8—42no—
364C2×C8—222no—
365C2×C8—222no—
366C2×C8C2×C22⋊D1111yescharacteristic
367C2×C8C2×C22⋊D1111yescharacteristic
368C2×C8C2×C22⋊D1111yescharacteristic
369C2×C8C2×C22⋊D1111yescharacteristic
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—21no—
374C4⋊C4—222no—
375C4⋊C4—222no—
376C4⋊C4C2×D4411yescharacteristic
377C4⋊C4C2×D4411yescharacteristic
378C22⋊C4—21no—
379C22⋊C4—21no—
380C22⋊C4—21no—
381C22⋊C4—21no—
382C22⋊C4—21no—
383C22⋊C4—442no—
384C22⋊C4—442no—
385C42—21no—
386C42C2×D4411yescharacteristic
387C42#433911yescharacteristic
388C42C2×C22⋊D1111yescharacteristic
389C42C23×D1111yescharacteristic
390C11#1935611yescharacteristic, complemented, Sylow
391C23—21no—
392C23—442no—
393C23#6698311yescharacteristic
394Q8—21no—
395Q8—21no—
396Q8—442no—
397Q8—442no—
398D4—21no—
399D4—21no—
400D4—42no—
401D4—442no—
402D4—442no—
403D4—442no—
404D4—442no—
405D4—882no—
406D4—884no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—442no—
418C2×C4—884no—
419C2×C4#6698311yescharacteristic
420C2×C4#6698311yescharacteristic
421C2×C4#6698311yescharacteristic
422C2×C4C22×D4411yescharacteristic
423C2×C4C2×#433911yescharacteristic
424C2×C4C22×C22⋊D1111yescharacteristic
425C8—21no—
426C8—21no—
427C8—41no—
428C8—41no—
429C8—442no—
430C8—442no—
431C8#6700212yes—
432C8#6700212yes—
433C22—21no—
434C22—21no—
435C22—21no—
436C22—41no—
437C22—41no—
438C22—41no—
439C22—882no—
440C22—882no—
441C22—882no—
442C22C2×#6698311yescharacteristic
443C4—21no—
444C4—21no—
445C4—21no—
446C4—21no—
447C4—41no—
448C4—41no—
449C4—41no—
450C4—882no—
451C4#1062328311yescharacteristic
452C4#1062328411yescharacteristic
453C4C2×#6700211yescharacteristic
454C4C2×#6700211yescharacteristic
455C2—41no—
456C2—81no—
457C2—1762no—
458C2#1307809611yescharacteristic
459C2#1307828611yescharacteristic
460C2#1307833611yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#2966C2
socleC22×C11C2×#121
hypercenter#2966D11
hypocenterC11#19356
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2966

Complements

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

NH ≅ G/Ntype
1. #13079978C2semidirect
2. #13079044C2semidirect
3. #13068088C2semidirect
4. #13068081C2semidirect
5. #13067986C2semidirect
6. #13067981C2semidirect
7. #13067976C2semidirect
8. #13067971C2semidirect
9. #13067375C2semidirect
10. #13067339C2semidirect
11. C11×#2966C2semidirect
163. #2966D11semidirect
390. C11#19356semidirect

Maximal subgroups

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

subgroupindex
#130799782
#130790442
#130680882
#130680812
#130679862
#130679812
#130679762
#130679712
#130673752
#130673392
C11×#29662
#1935611