Finite Group Databasebeta

← #14738553

Subgroups — #14738553

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#13079972C212yesmaximal, complemented
2#13077591C211yesmaximal, characteristic, complemented
3#13068085C212yesmaximal, complemented
4#13068078C212yesmaximal, complemented
5#13067983C211yesmaximal, characteristic, complemented
6#13067978C211yesmaximal, characteristic, complemented
7#13067973C211yesmaximal, characteristic, complemented
8#13067968C211yesmaximal, characteristic, complemented
9#13067375C211yesmaximal, characteristic, complemented
10#13067338C212yesmaximal, complemented
11C11×#3147C211yesmaximal, characteristic, complemented
12C2×C11×#135—21no—
13C2×C11×#135—21no—
14C11×#532C2212yes—
15#10623010C2211yescharacteristic
16C11×#495—21no—
17C11×#495—21no—
18C11×#494C2211yescharacteristic
19C11×#493C2211yescharacteristic
20C11×#492C2212yes—
21C2×C4×C8×C11C2211yescharacteristic
22#10622724—21no—
23C8×C22⋊D11—21no—
24#10622707C2212yes—
25#10622700C2212yes—
26#10622688C2212yes—
27#10622685C2212yes—
28#10622655—22no—
29#10622652—22no—
30#10622629—22no—
31#10622622—22no—
32#10622539C2211yescharacteristic
33#10622537C2212yes—
34#10622303—21no—
35#10622302—21no—
36#10622301C2211yescharacteristic
37C8×D44C2211yescharacteristic
38#10622292C2211yescharacteristic
39C8×Dic22C2211yescharacteristic
40#10622185C2212yes—
41#10622185C2212yes—
42#10622182C2212yes—
43#10622182C2212yes—
44#10622096C2212yes—
45#10622096C2211yescharacteristic
46#10622096C2211yescharacteristic
47C2×C11×#41—22no—
48C11×#135—44no—
49C11×#135—44no—
50C2×C11×Q16—21no—
51C2×C11×Q16—21no—
52C2×C11×SD16—22no—
53C2×C11×SD16—22no—
54C2×C11×D8—21no—
55C2×C11×D8—21no—
56C22×C8×C11D411yescharacteristic
57C22×C8×C11D411yescharacteristic
58C11×C4⋊Q8C2312yes—
59C11×#127C2312yes—
60C11×#124—22no—
61C11×#121—22no—
62C11×#121—22no—
63C4×D4×C11—22no—
64C4×D4×C11—22no—
65C2×C42×C11C2311yescharacteristic
66C2×#4324—22no—
67C2×#4323—22no—
68#66983D411yescharacteristic
69#66982—21no—
70C4×C22⋊D11—21no—
71#66977D411yescharacteristic
72C2×#4318—22no—
73C2×#4313—21no—
74C2×C8×D11—21no—
75#66929—21no—
76#66928D411yescharacteristic
77C4×D44C2311yescharacteristic
78#66925—21no—
79#66923D411yescharacteristic
80C4×Dic22C2311yescharacteristic
81C4×C8×C11D411yescharacteristic
82C4×C8×C11D411yescharacteristic
83C4×C8×C11C2311yescharacteristic
84C4×C8×C11C2311yescharacteristic
85#66896—22no—
86#66896—22no—
87C22⋊(C11⋊C8)—21no—
88(C2×D11)⋊C8—21no—
89(C2×D11)⋊C8—21no—
90#66879—21no—
91Dic11⋊C8—21no—
92Dic11⋊C8—21no—
93C8×Dic11—21no—
94#66874—22no—
95#66873—22no—
96#66872—22no—
97#66871—22no—
98C4⋊(C11⋊C8)—22no—
99C4⋊(C11⋊C8)C2312yes—
100C4⋊(C11⋊C8)C2312yes—
101C4⋊(C11⋊C8)C2311yescharacteristic
102C4⋊(C11⋊C8)C2311yescharacteristic
103#66867—21no—
104#19356—111nomaximal, Sylow
105C11×#41—44no—
106C11×#41—44no—
107C2×Q8×C11—22no—
108C2×D4×C11—22no—
109C2×D4×C11—22no—
110C2×D4×C11—22no—
111C2×D4×C11—42no—
112C22×C4×C11—42no—
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11#4111yescharacteristic
116C2×C22⋊D11—21no—
117C2×D44C2×D411yescharacteristic
118C2×C4×D11—21no—
119C2×Dic22C2×D411yescharacteristic
120C11×Q16—42no—
121C11×Q16—42no—
122C11×SD16—44no—
123C11×SD16—44no—
124C11×D8—42no—
125C11×D8—42no—
126C2×C8×C11—22no—
127C2×C8×C11—22no—
128C2×C8×C11C2×D411yescharacteristic
129C2×C8×C11C2×D411yescharacteristic
130C2×C8×C11C2×D411yescharacteristic
131C2×C8×C11C2×D411yescharacteristic
132C11×C4⋊C4—22no—
133C11×C4⋊C4—22no—
134C11×C22⋊C4—42no—
135C11×C22⋊C4—42no—
136C42×C11C2×D411yescharacteristic
137C42×C11C2×D411yescharacteristic
138C42×C11#4111yescharacteristic
139C42×C11C2411yescharacteristic
140C22⋊Dic11—21no—
141#4324—82no—
142#4323—82no—
143(C2×D11)⋊C4—21no—
144(C2×D11)⋊C4—21no—
145(C2×D11)⋊C4—21no—
146(C2×D11)⋊C4—21no—
147C4⋊Dic11C2×D411yescharacteristic
148C4⋊Dic11C2×D411yescharacteristic
149Dic11⋊C4—21no—
150Dic11⋊C4—21no—
151Dic11⋊C4—21no—
152Dic11⋊C4—21no—
153C4×Dic11—21no—
154#4318—82no—
155C2×C11⋊C8—21no—
156C2×C11⋊C8—21no—
157C2×C11⋊C8—22no—
158C2×C11⋊C8—22no—
159#4313—42no—
160C8×D11—42no—
161#3251—112no—
162#3147D1111yescharacteristic, complemented
163#2966—111no—
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—42no—
173C23×C11#12111yescharacteristic
174C22×D11—21no—
175Q8×C11—42no—
176Q8×C11—42no—
177D4×C11—42no—
178D4×C11—42no—
179D4×C11—42no—
180D4×C11—42no—
181D4×C11—82no—
182D4×C11—84no—
183C2×C4×C11—21no—
184C2×C4×C11—21no—
185C2×C4×C11—21no—
186C2×C4×C11—21no—
187C2×C4×C11—41no—
188C2×C4×C11—42no—
189C2×C4×C11—84no—
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—42no—
197C2×Dic11—21no—
198C2×Dic11—21no—
199C2×Dic11—21no—
200D44—21no—
201D44—21no—
202C4×D11—41no—
203C4×D11—41no—
204Dic22—21no—
205Dic22—21no—
206C8×C11—21no—
207C8×C11—21no—
208C8×C11AGL(1,ℤ/8)12yes—
209C8×C11AGL(1,ℤ/8)12yes—
210C11⋊C8—41no—
211C11⋊C8—41no—
212C11⋊C8—42no—
213C11⋊C8—42no—
214C2×#135—21no—
215C2×#135—21no—
216#532C2×D1112yes—
217#529—111no—
218#495—21no—
219#495—21no—
220#494C2×D1111yescharacteristic
221#493C2×D1111yescharacteristic
222#492C2×D1112yes—
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#446—111no—
232C8×Q8—111no—
233#436—111no—
234#435—221no—
235C8×D4—111no—
236C8×D4—221no—
237#433—221no—
238#432—111no—
239#423—112no—
240#405—221no—
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—82no—
253C22×C11—82no—
254C22×C11—82no—
255C22×C11C2×#12111yescharacteristic
256C2×D11—41no—
257C2×D11—41no—
258C2×D11—41no—
259C4×C11—21no—
260C4×C11—21no—
261C4×C11—21no—
262C4×C11—21no—
263C4×C11—82no—
264C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
265C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
266C4×C11#57611yescharacteristic
267C4×C11#57811yescharacteristic
268Dic11—41no—
269Dic11—41no—
270Dic11—41no—
271C2×#41—22no—
272#135—44no—
273#135—44no—
274C2×Q16—21no—
275C2×Q16—21no—
276C2×SD16—22no—
277C2×SD16—22no—
278C2×SD16—222no—
279C2×D8—21no—
280C2×D8—21no—
281C2×D8—222no—
282C2×M16—222no—
283C2×M16—221no—
284C22×C8—221no—
285C22×C8C22⋊D1111yescharacteristic
286C22×C8C22⋊D1111yescharacteristic
287C4⋊Q8C22×D1112yes—
288#127C22×D1112yes—
289#126—221no—
290#125—111no—
291#124—22no—
292#124—111no—
293#123—221no—
294C22⋊Q8—111no—
295#121—22no—
296#121—22no—
297#121—111no—
298C4×Q8—111no—
299C4×D4—22no—
300C4×D4—22no—
301C4×D4—111no—
302C4×D4—221no—
303#117—221no—
304C2×C42C22×D1111yescharacteristic
305#107—222no—
306#106—222no—
307C4⋊C8—111no—
308C4⋊C8—111no—
309C4⋊C8—112no—
310C4⋊C8—112no—
311C4⋊C8—221no—
312C4⋊C8—221no—
313C4⋊C8—222no—
314#103—222no—
315#102—222no—
316#102—222no—
317#102—222no—
318C22⋊C8—221no—
319C22⋊C8—221no—
320C22⋊C8—221no—
321#97—221no—
322#97—221no—
323C4×C8—221no—
324C4×C8C22⋊D1111yescharacteristic
325C4×C8C22⋊D1111yescharacteristic
326C4×C8C22×D1111yescharacteristic
327C4×C8C22×D1111yescharacteristic
328C2×C11—41no—
329C2×C11—162no—
330C2×C11#303811yescharacteristic
331C2×C11#306111yescharacteristic
332C2×C11#306711yescharacteristic
333D11—81no—
334#41—44no—
335#41—44no—
336C2×Q8—22no—
337C2×Q8—111no—
338C2×D4—22no—
339C2×D4—22no—
340C2×D4—22no—
341C2×D4—42no—
342C2×D4—111no—
343C2×D4—221no—
344C22×C4—42no—
345C22×C4—221no—
346C22×C4D4×D1111yescharacteristic
347C22×C4#434111yescharacteristic
348C22×C4C2×C22⋊D1111yescharacteristic
349Q16—42no—
350Q16—42no—
351SD16—44no—
352SD16—44no—
353SD16—882no—
354D8—42no—
355D8—42no—
356D8—882no—
357M16—442no—
358M16—882no—
359C2×C8—22no—
360C2×C8—22no—
361C2×C8—222no—
362C2×C8—222no—
363C2×C8—221no—
364C2×C8—221no—
365C2×C8—442no—
366C2×C8C2×C22⋊D1111yescharacteristic
367C2×C8C2×C22⋊D1111yescharacteristic
368C2×C8C2×C22⋊D1111yescharacteristic
369C2×C8C2×C22⋊D1111yescharacteristic
370C4⋊C4—22no—
371C4⋊C4—22no—
372C4⋊C4—111no—
373C4⋊C4—111no—
374C4⋊C4—221no—
375C4⋊C4—221no—
376C4⋊C4—221no—
377C4⋊C4—221no—
378C22⋊C4—42no—
379C22⋊C4—42no—
380C22⋊C4—221no—
381C22⋊C4—221no—
382C22⋊C4—221no—
383C22⋊C4—221no—
384C22⋊C4—221no—
385C42—221no—
386C42D4×D1111yescharacteristic
387C42#434111yescharacteristic
388C42C2×C22⋊D1111yescharacteristic
389C42C23×D1111yescharacteristic
390C11#1935611yescharacteristic, complemented, Sylow
391C23—42no—
392C23—221no—
393C23#6699111yescharacteristic
394Q8—42no—
395Q8—42no—
396Q8—221no—
397Q8—221no—
398D4—42no—
399D4—42no—
400D4—42no—
401D4—42no—
402D4—82no—
403D4—84no—
404D4—221no—
405D4—221no—
406D4—442no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—41no—
412C2×C4—42no—
413C2×C4—84no—
414C2×C4—221no—
415C2×C4—221no—
416C2×C4—221no—
417C2×C4—441no—
418C2×C4—441no—
419C2×C4#6699111yescharacteristic
420C2×C4#6699111yescharacteristic
421C2×C4#6699111yescharacteristic
422C2×C4C2×D4×D1111yescharacteristic
423C2×C4C2×#434111yescharacteristic
424C2×C4C22×C22⋊D1111yescharacteristic
425C8—21no—
426C8—21no—
427C8—442no—
428C8—442no—
429C8—441no—
430C8—441no—
431C8#6698512yes—
432C8#6698512yes—
433C22—21no—
434C22—21no—
435C22—21no—
436C22—82no—
437C22—82no—
438C22—82no—
439C22—441no—
440C22—441no—
441C22—441no—
442C22C2×#6699111yescharacteristic
443C4—21no—
444C4—21no—
445C4—21no—
446C4—21no—
447C4—82no—
448C4—441no—
449C4—441no—
450C4—441no—
451C4#1062330011yescharacteristic
452C4#1062330211yescharacteristic
453C4C2×#6698511yescharacteristic
454C4C2×#6698511yescharacteristic
455C2—41no—
456C2—162no—
457C2—881no—
458C2#1307809211yescharacteristic
459C2#1307828211yescharacteristic
460C2#1307833211yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3147C2
socleC22×C11C2×#121
hypercenter#3147D11
hypocenterC11#19356
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3147

Complements

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

NH ≅ G/Ntype
1. #13079972C2semidirect
2. #13077591C2semidirect
3. #13068085C2semidirect
4. #13068078C2semidirect
5. #13067983C2semidirect
6. #13067978C2semidirect
7. #13067973C2semidirect
8. #13067968C2semidirect
9. #13067375C2semidirect
10. #13067338C2semidirect
11. C11×#3147C2semidirect
162. #3147D11semidirect
390. C11#19356semidirect

Maximal subgroups

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

subgroupindex
#130799722
#130775912
#130680852
#130680782
#130679832
#130679782
#130679732
#130679682
#130673752
#130673382
C11×#31472
#1935611