Finite Group Databasebeta

← #14738548

Subgroups — #14738548

Order 2816.

678 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079978C212yesmaximal, complemented
2#13079044C211yesmaximal, characteristic, complemented
3#13068110C211yesmaximal, characteristic, complemented
4#13068105C211yesmaximal, characteristic, complemented
5#13068100C211yesmaximal, characteristic, complemented
6#13068095C211yesmaximal, characteristic, complemented
7#13067964C212yesmaximal, complemented
8#13067957C212yesmaximal, complemented
9#13067372C211yesmaximal, 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#10622095C2211yescharacteristic
45#10622095C2211yescharacteristic
46#10622095C2212yes—
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#19355—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#1690—111no—
165#1689—111no—
166#1688—111no—
167#1687—111no—
168#1666—112no—
169#1665—112no—
170#1566—111no—
171#1557—112no—
172C23×C11—21no—
173C23×C11#12111yescharacteristic
174C22×D11—42no—
175Q8×C11—22no—
176D4×C11—22no—
177D4×C11—42no—
178C2×C4×C11—21no—
179C2×C4×C11—21no—
180C2×C4×C11—22no—
181C2×C4×C11—21no—
182C2×C4×C11—21no—
183C2×C4×C11—21no—
184C2×C4×C11—41no—
185C2×C4×C11—41no—
186C2×C4×C11—41no—
187C2×C4×C11#12111yescharacteristic
188C2×C4×C11#12111yescharacteristic
189C2×C4×C11#12111yescharacteristic
190C2×C4×C11C22×D411yescharacteristic
191C2×C4×C11C22×D411yescharacteristic
192C2×C4×C11C2×#4111yescharacteristic
193C22⋊D11—84no—
194C2×Dic11—42no—
195D44—42no—
196D44—42no—
197D44—42no—
198D44—42no—
199D44—82no—
200C4×D11—84no—
201Dic22—42no—
202Dic22—42no—
203C8×C11—21no—
204C8×C11—21no—
205C8×C11—41no—
206C8×C11—41no—
207C8×C11AGL(1,ℤ/8)12yes—
208C8×C11AGL(1,ℤ/8)12yes—
209C11⋊C8—42no—
210C11⋊C8—42no—
211C2×#135—221no—
212C2×#135—221no—
213#532—112no—
214#529C2×D1111yescharacteristic
215#495—221no—
216#495—221no—
217#494—111no—
218#493—111no—
219#492—112no—
220#478—222no—
221#475—112no—
222#474—112no—
223#469—222no—
224#468—222no—
225#463—222no—
226#460—112no—
227#459—112no—
228#446C2×D1111yescharacteristic
229C8×Q8C2×D1111yescharacteristic
230#436C2×D1111yescharacteristic
231#435—21no—
232C8×D4—21no—
233C8×D4C2×D1111yescharacteristic
234#433—21no—
235#432C2×D1111yescharacteristic
236#423—112no—
237#405—21no—
238C2×C4×C8C2×D1111yescharacteristic
239#334—112no—
240#334—111no—
241#334—111no—
242#332—112no—
243#332—112no—
244#331—112no—
245#331—112no—
246C22×C11—21no—
247C22×C11—21no—
248C22×C11—21no—
249C22×C11—41no—
250C22×C11—41no—
251C22×C11—41no—
252C22×C11C2×#12111yescharacteristic
253C2×D11—82no—
254C2×D11—82no—
255C2×D11—82no—
256C4×C11—21no—
257C4×C11—21no—
258C4×C11—21no—
259C4×C11—21no—
260C4×C11—41no—
261C4×C11—41no—
262C4×C11—41no—
263C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
264C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
265C4×C11#57712yes—
266Dic11—82no—
267C2×#41—222no—
268#135—444no—
269#135—444no—
270C2×Q16—221no—
271C2×Q16—221no—
272C2×SD16—222no—
273C2×SD16—222no—
274C2×SD16—222no—
275C2×D8—222no—
276C2×D8—221no—
277C2×D8—221no—
278C2×M16—21no—
279C2×M16—222no—
280C22×C8—21no—
281C22×C8C22⋊D1111yescharacteristic
282C22×C8C22⋊D1111yescharacteristic
283C4⋊Q8—112no—
284#127—112no—
285#126—21no—
286#125D4411yescharacteristic
287#124—222no—
288#124D4411yescharacteristic
289#123—21no—
290C22⋊Q8D4411yescharacteristic
291#121—222no—
292#121—222no—
293#121D4411yescharacteristic
294C4×Q8C22×D1111yescharacteristic
295C4×D4—21no—
296C4×D4—222no—
297C4×D4—222no—
298C4×D4C22×D1111yescharacteristic
299#117—21no—
300C2×C42C22×D1111yescharacteristic
301#107—222no—
302#106—222no—
303C4⋊C8—21no—
304C4⋊C8—21no—
305C4⋊C8—112no—
306C4⋊C8—112no—
307C4⋊C8—222no—
308C4⋊C8C22×D1111yescharacteristic
309C4⋊C8C22×D1111yescharacteristic
310#103—222no—
311#102—222no—
312#102—222no—
313#102—222no—
314C22⋊C8—21no—
315C22⋊C8—21no—
316C22⋊C8—21no—
317#97—21no—
318#97—21no—
319C4×C8—21no—
320C4×C8C22⋊D1111yescharacteristic
321C4×C8C22⋊D1111yescharacteristic
322C4×C8C22×D1111yescharacteristic
323C4×C8C22×D1111yescharacteristic
324C2×C11—41no—
325C2×C11—81no—
326C2×C11#303811yescharacteristic
327C2×C11#306011yescharacteristic
328C2×C11#306711yescharacteristic
329D11—162no—
330#41—444no—
331#41—444no—
332C2×Q8—222no—
333C2×Q8C2×D4411yescharacteristic
334C2×D4—21no—
335C2×D4—222no—
336C2×D4—222no—
337C2×D4—222no—
338C2×D4—442no—
339C2×D4C2×D4411yescharacteristic
340C22×C4—21no—
341C22×C4—442no—
342C22×C4C2×D4411yescharacteristic
343C22×C4#433911yescharacteristic
344C22×C4C2×C22⋊D1111yescharacteristic
345Q16—442no—
346Q16—442no—
347SD16—444no—
348SD16—444no—
349SD16—882no—
350D8—442no—
351D8—442no—
352D8—882no—
353M16—42no—
354M16—882no—
355C2×C8—22no—
356C2×C8—22no—
357C2×C8—21no—
358C2×C8—21no—
359C2×C8—42no—
360C2×C8—222no—
361C2×C8—222no—
362C2×C8C2×C22⋊D1111yescharacteristic
363C2×C8C2×C22⋊D1111yescharacteristic
364C2×C8C2×C22⋊D1111yescharacteristic
365C2×C8C2×C22⋊D1111yescharacteristic
366C4⋊C4—21no—
367C4⋊C4—21no—
368C4⋊C4—21no—
369C4⋊C4—21no—
370C4⋊C4—222no—
371C4⋊C4—222no—
372C4⋊C4C2×D4411yescharacteristic
373C4⋊C4C2×D4411yescharacteristic
374C22⋊C4—21no—
375C22⋊C4—21no—
376C22⋊C4—21no—
377C22⋊C4—21no—
378C22⋊C4—21no—
379C22⋊C4—442no—
380C22⋊C4—442no—
381C42—21no—
382C42C2×D4411yescharacteristic
383C42#433911yescharacteristic
384C42C2×C22⋊D1111yescharacteristic
385C42C23×D1111yescharacteristic
386C11#1935511yescharacteristic, complemented, Sylow
387C23—21no—
388C23—442no—
389C23#6698311yescharacteristic
390Q8—22no—
391Q8—442no—
392Q8—442no—
393D4—22no—
394D4—42no—
395D4—442no—
396D4—442no—
397D4—442no—
398D4—442no—
399D4—882no—
400D4—884no—
401C2×C4—22no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—442no—
411C2×C4—884no—
412C2×C4#6698311yescharacteristic
413C2×C4#6698311yescharacteristic
414C2×C4#6698311yescharacteristic
415C2×C4C22×D4411yescharacteristic
416C2×C4C2×#433911yescharacteristic
417C2×C4C22×C22⋊D1111yescharacteristic
418C8—21no—
419C8—21no—
420C8—41no—
421C8—41no—
422C8—442no—
423C8—442no—
424C8#6700212yes—
425C8#6700212yes—
426C22—21no—
427C22—21no—
428C22—21no—
429C22—41no—
430C22—41no—
431C22—41no—
432C22—882no—
433C22—882no—
434C22—882no—
435C22C2×#6698311yescharacteristic
436C4—21no—
437C4—21no—
438C4—21no—
439C4—21no—
440C4—41no—
441C4—41no—
442C4—41no—
443C4—882no—
444C4#1062328212yes—
445C4C2×#6700211yescharacteristic
446C4C2×#6700211yescharacteristic
447C2—41no—
448C2—81no—
449C2—1762no—
450C2#1307809611yescharacteristic
451C2#1307827811yescharacteristic
452C2#1307833611yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#2966C2
socleC22×C11C2×#121
hypercenter#2966D11
hypocenterC11#19355
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. #13068110C2semidirect
4. #13068105C2semidirect
5. #13068100C2semidirect
6. #13068095C2semidirect
7. #13067964C2semidirect
8. #13067957C2semidirect
9. #13067372C2semidirect
10. #13067339C2semidirect
11. C11×#2966C2semidirect
163. #2966D11semidirect
386. C11#19355semidirect

Maximal subgroups

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

subgroupindex
#130799782
#130790442
#130681102
#130681052
#130681002
#130680952
#130679642
#130679572
#130673722
#130673392
C11×#29662
#1935511