Finite Group Databasebeta

← #14908176

Subgroups — #14908176

Order 2816.

706 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
1C2×#10622806C211yesmaximal, characteristic, complemented
2#13079103C211yesmaximal, characteristic, complemented
3#13077533C211yesmaximal, characteristic, complemented
4#13070690C214yesmaximal, complemented
5#13070687C214yesmaximal, complemented
6#13070381C211yesmaximal, characteristic, complemented
7#13070365C211yesmaximal, characteristic, complemented
8C2×#10622154C211yesmaximal, characteristic, complemented
9C11×#3414C211yesmaximal, characteristic, complemented
10C2×C11×#135C2211yescharacteristic
11C2×C11×#135C2211yescharacteristic
12#10623361—21no—
13C2×#67002—21no—
14#10623350—21no—
15C22×D88C2211yescharacteristic
16C11×#510—21no—
17C11×#510C2212yescomplemented
18C11×#509—21no—
19C11×#509C2212yescomplemented
20C11×#508—22no—
21C2×C11×M32C2211yescharacteristic
22#10622849—21no—
23#10622810—22no—
24#10622809C2214yescomplemented
25#10622806—22no—
26#10622806C2214yes—
27#10622804C2212yescomplemented
28C2×#66892—21no—
29#10622789—22no—
30#10622764C2212yescomplemented
31C2×#66890—21no—
32C2×#66883C2211yescharacteristic
33#10622714C2211yescharacteristic
34C2×#66876C2211yescharacteristic
35#10622203C2212yescomplemented
36#10622201C2212yescomplemented
37#10622154C2214yescomplemented
38#10622149C2214yescomplemented
39C2×C11×#41—21no—
40C2×C11×#41—21no—
41C22×D44—21no—
42C11×#135—21no—
43C11×#135—21no—
44C11×#135—21no—
45C11×#135—21no—
46C11×#135—21no—
47C11×#135—21no—
48C11×#135D412yescomplemented
49C11×#135C2312yes—
50C2×C11×Q16D411yescharacteristic, complemented
51C2×C11×Q16C2311yescharacteristic
52C2×C11×SD16—21no—
53C2×C11×SD16—21no—
54C2×C11×D8D411yescharacteristic, complemented
55C2×C11×D8C2311yescharacteristic
56C22×C8×C11C2311yescharacteristic
57#67002—42no—
58#67002—42no—
59#67001—24no—
60#67001—42no—
61#67000—22no—
62C2×#4325—22no—
63#66993—22no—
64#66990—42no—
65C2×#4323—22no—
66#66983—42no—
67#66979D411yescharacteristic
68C2×#4318—21no—
69C2×#4318—42no—
70C2×#4318D411yescharacteristic
71C2×D88—21no—
72C2×D88—21no—
73C2×D88—21no—
74C2×D88—21no—
75C2×D88—21no—
76C2×D88C2312yes—
77C11×Q32—22no—
78C11×SD32—22no—
79C11×SD32—22no—
80C11×D16—22no—
81C11×M32—21no—
82C11×M32C2312yes—
83C2×C11×C16—21no—
84#66901—24no—
85#66892—24no—
86#66890—24no—
87#66883—21no—
88#66883C2312yes—
89#66879D412yes—
90C8×Dic11C2312yes—
91#66876—21no—
92#66876C2312yes—
93C2×C11⋊C16—21no—
94#33595—111nomaximal, Sylow
95C23×D11—41no—
96C11×#41—22no—
97C11×#41—22no—
98C11×#41—41no—
99C11×#41—41no—
100C11×#41—41no—
101C11×#41—41no—
102C11×#41—41no—
103C11×#41—41no—
104C2×Q8×C11—21no—
105C2×Q8×C11—21no—
106C2×D4×C11—21no—
107C2×D4×C11—21no—
108C2×D4×C11—41no—
109C2×D4×C11—41no—
110C22×C4×C11—41no—
111C22×C4×C11—41no—
112C22×C4×C11C2×D411yescharacteristic
113C2×C22⋊D11—44no—
114C2×D44—22no—
115C2×D44—41no—
116C2×D44—41no—
117C2×D44—41no—
118C2×D44—41no—
119C2×D44—41no—
120C11×Q16—21no—
121C11×Q16—21no—
122C11×Q16—21no—
123C11×Q16C2×D412yes—
124C11×SD16—22no—
125C11×SD16—22no—
126C11×SD16—41no—
127C11×SD16—41no—
128C11×D8—21no—
129C11×D8—21no—
130C11×D8—21no—
131C11×D8C2×D412yes—
132C2×C8×C11C2×D411yescharacteristic
133C2×C8×C11C2×D411yescharacteristic
134C2×C8×C11C2×D411yescharacteristic
135C2×C8×C11#4111yescharacteristic
136C2×C8×C11#4111yescharacteristic
137C2×C8×C11C2411yescharacteristic
138C22⋊Dic11—21no—
139#4325—44no—
140#4323—44no—
141(C2×D11)⋊C4—44no—
142C4⋊Dic11—21no—
143C4×Dic11C2×D412yes—
144#4318—22no—
145#4318—44no—
146#4318—41no—
147#4318D812yes—
148#4318D812yes—
149C2×C11⋊C8—44no—
150C2×C11⋊C8—41no—
151C2×C11⋊C8C2×D412yes—
152D88—22no—
153D88—22no—
154D88—41no—
155D88—41no—
156C11×C16—22no—
157C11⋊C16—22no—
158#3414D1111yescharacteristic, complemented
159C2×#509—111no—
160#3155—111no—
161#2957—111no—
162#2213—114no—
163#2212—114no—
164#2153—111no—
165#2148—111no—
166C2×#361—111no—
167C23×C11—41no—
168C23×C11—41no—
169C23×C11AGL(1,ℤ/8)11yescharacteristic
170C22×D11—42no—
171C22×D11—81no—
172C22×D11—81no—
173C22×D11—162no—
174Q8×C11—22no—
175Q8×C11—41no—
176Q8×C11—41no—
177Q8×C11—41no—
178D4×C11—22no—
179D4×C11—42no—
180D4×C11—42no—
181D4×C11—41no—
182D4×C11—41no—
183D4×C11—41no—
184D4×C11—81no—
185D4×C11—81no—
186C2×C4×C11—41no—
187C2×C4×C11—42no—
188C2×C4×C11—42no—
189C2×C4×C11—41no—
190C2×C4×C11—81no—
191C2×C4×C11—81no—
192C2×C4×C11#12111yescharacteristic
193C2×C4×C11#12111yescharacteristic
194C2×C4×C11C2×D811yescharacteristic
195C2×C4×C11C2×D811yescharacteristic
196C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
197C2×C4×C11C22×D411yescharacteristic
198C22⋊D11—164no—
199C2×Dic11—22no—
200D44—42no—
201D44—42no—
202D44—81no—
203D44—81no—
204C8×C11#12111yescharacteristic
205C8×C11#12111yescharacteristic
206C8×C11C22×D411yescharacteristic
207C8×C11C2×#4111yescharacteristic
208C11⋊C8—42no—
209C11⋊C8C2×D814yes—
210C2×AGL(1,ℤ/8)—221no—
211C2×#135C2×D1111yescharacteristic
212C2×#135C2×D1111yescharacteristic
213C22×D8—111no—
214#568—221no—
215#535—221no—
216#510—21no—
217#510C2×D1112yescomplemented
218#509—21no—
219#509—114no—
220#509—222no—
221#509C2×D1112yescomplemented
222#508—22no—
223C2×SD32—221no—
224C2×D16—221no—
225C2×M32—111no—
226C2×M32C2×D1111yescharacteristic
227#496—222no—
228#495—112no—
229#493—112no—
230#444—222no—
231#443—114no—
232C2×#108—111no—
233#421—221no—
234#405—111no—
235#364—114no—
236#362—112no—
237#361—112no—
238#361—114no—
239C22×C11—41no—
240C22×C11—42no—
241C22×C11—82no—
242C22×C11—81no—
243C22×C11—161no—
244C22×C11#45911yescharacteristic
245C22×C11#45911yescharacteristic
246C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
247C2×D11—84no—
248C2×D11—82no—
249C2×D11—162no—
250C2×D11—162no—
251C4×C11—42no—
252C4×C11—81no—
253C4×C11#45911yescharacteristic
254C4×C11#45911yescharacteristic
255C4×C11C2×#12111yescharacteristic
256C4×C11C22×D811yescharacteristic
257Dic11—42no—
258C2×#41—21no—
259C2×#41—21no—
260C22×D4—221no—
261AGL(1,ℤ/8)—442no—
262AGL(1,ℤ/8)—442no—
263#135—21no—
264#135—21no—
265#135—21no—
266#135—21no—
267#135—21no—
268#135—21no—
269#135C22⋊D1112yescomplemented
270#135C22×D1112yes—
271C2×Q16C22⋊D1111yescharacteristic, complemented
272C2×Q16C22×D1111yescharacteristic
273C2×SD16—21no—
274C2×SD16—21no—
275C2×SD16—222no—
276C2×D8—112no—
277C2×D8—222no—
278C2×D8—221no—
279C2×D8—221no—
280C2×D8—221no—
281C2×D8—221no—
282C2×D8—221no—
283C2×D8C22⋊D1111yescharacteristic, complemented
284C2×D8C22×D1111yescharacteristic
285#131—224no—
286#131—442no—
287C2×M16—111no—
288C2×M16—221no—
289C2×M16—442no—
290C22×C8C22×D1111yescharacteristic
291#127—222no—
292#124—222no—
293#121—442no—
294#120—442no—
295#117—111no—
296Q32—22no—
297SD32—22no—
298SD32—22no—
299SD32—224no—
300D16—22no—
301D16—224no—
302M32—21no—
303M32—112no—
304M32—221no—
305M32C22×D1112yes—
306C2×C16—21no—
307C2×C16—221no—
308#108—112no—
309#108—221no—
310#104—224no—
311#97—112no—
312C4×C8—112no—
313C2×C11—21no—
314C2×C11—21no—
315C2×C11—21no—
316C2×C11—82no—
317C2×C11—161no—
318C2×C11C2×#45911yescharacteristic
319D11—162no—
320C24—441no—
321#41—22no—
322#41—22no—
323#41—41no—
324#41—41no—
325#41—41no—
326#41—41no—
327#41—41no—
328#41—41no—
329C2×Q8—21no—
330C2×Q8—21no—
331C2×D4—21no—
332C2×D4—21no—
333C2×D4—41no—
334C2×D4—41no—
335C2×D4—222no—
336C2×D4—444no—
337C2×D4—441no—
338C2×D4—441no—
339C2×D4—441no—
340C2×D4—441no—
341C2×D4—441no—
342C22×C4—41no—
343C22×C4—41no—
344C22×C4D4×D1111yescharacteristic
345Q16—21no—
346Q16—21no—
347Q16—21no—
348Q16C2×C22⋊D1112yes—
349SD16—22no—
350SD16—22no—
351SD16—41no—
352SD16—41no—
353SD16—444no—
354D8—21no—
355D8—21no—
356D8—21no—
357D8—222no—
358D8—222no—
359D8—444no—
360D8—441no—
361D8—441no—
362D8C2×C22⋊D1112yes—
363M16—112no—
364M16—112no—
365M16—222no—
366M16—444no—
367M16—441no—
368C2×C8—112no—
369C2×C8—444no—
370C2×C8—441no—
371C2×C8D4×D1111yescharacteristic
372C2×C8#434111yescharacteristic
373C2×C8#434111yescharacteristic
374C2×C8C2×C22⋊D1111yescharacteristic
375C2×C8C2×C22⋊D1111yescharacteristic
376C2×C8C23×D1111yescharacteristic
377C4⋊C4—221no—
378C22⋊C4—221no—
379C22⋊C4—444no—
380C42—112no—
381C16—22no—
382C16—222no—
383C11#3359511yescharacteristic, complemented, Sylow
384C23—41no—
385C23—41no—
386C23—442no—
387C23—881no—
388C23—881no—
389C23—1762no—
390C23#6696411yescharacteristic
391Q8—22no—
392Q8—41no—
393Q8—41no—
394Q8—41no—
395D4—22no—
396D4—42no—
397D4—42no—
398D4—41no—
399D4—41no—
400D4—41no—
401D4—81no—
402D4—81no—
403D4—442no—
404D4—442no—
405D4—881no—
406D4—881no—
407D4—1764no—
408C2×C4—41no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—41no—
412C2×C4—81no—
413C2×C4—81no—
414C2×C4—222no—
415C2×C4D8×D1111yescharacteristic
416C2×C4D8×D1111yescharacteristic
417C2×C4#6696411yescharacteristic
418C2×C4#6699211yescharacteristic
419C2×C4#6699211yescharacteristic
420C2×C4C2×D4×D1111yescharacteristic
421C8—114no—
422C8—442no—
423C8#6699211yescharacteristic
424C8#6699211yescharacteristic
425C8C2×#434111yescharacteristic
426C8C22×C22⋊D1111yescharacteristic
427C22—41no—
428C22—42no—
429C22—82no—
430C22—81no—
431C22—161no—
432C22—884no—
433C22—882no—
434C22—1762no—
435C22—1762no—
436C22#1062276311yescharacteristic
437C22#1062276311yescharacteristic
438C22C2×#6696411yescharacteristic
439C4—42no—
440C4—81no—
441C4—442no—
442C4#1062276311yescharacteristic
443C4#1062276311yescharacteristic
444C4C2×D8×D1111yescharacteristic
445C4C2×#6699211yescharacteristic
446C2—21no—
447C2—21no—
448C2—21no—
449C2—82no—
450C2—161no—
451C2—1762no—
452C2C2×#1062276311yescharacteristic
subgroupG/H
centerC2C2×#10622763
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3414C2
socleC2×C11C2×#459
hypercenter#3414D11
hypocenterC11#33595
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C22×C4 ◁ C22×C8 ◁ #3414

Complements

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

NH ≅ G/Ntype
1. C2×#10622806C2semidirect
2. #13079103C2semidirect
3. #13077533C2semidirect
4. #13070690C2semidirect
5. #13070687C2semidirect
6. #13070381C2semidirect
7. #13070365C2semidirect
8. C2×#10622154C2semidirect
9. C11×#3414C2semidirect
17. C11×#510C22semidirect
19. C11×#509C22semidirect
24. #10622809C22semidirect
27. #10622804C22semidirect
30. #10622764C22semidirect
35. #10622203C22semidirect
36. #10622201C22semidirect
37. #10622154C22semidirect
38. #10622149C22semidirect
48. C11×#135D4semidirect
50. C2×C11×Q16D4semidirect
54. C2×C11×D8D4semidirect
158. #3414D11semidirect
217. #510C2×D11semidirect
221. #509C2×D11semidirect
269. #135C22⋊D11semidirect
271. C2×Q16C22⋊D11semidirect
283. C2×D8C22⋊D11semidirect
383. C11#33595semidirect

Maximal subgroups

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

subgroupindex
C2×#106228062
#130791032
#130775332
#130706902
#130706872
#130703812
#130703652
C2×#106221542
C11×#34142
#3359511