Finite Group Databasebeta

← #13077839

Subgroups — #13077839

Order 1408.

764 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 764 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4343C211yesmaximal, characteristic, complemented
2C2×#66972C212yesmaximal, complemented
3#10623158C211yesmaximal, characteristic, complemented
4C11×#451C211yesmaximal, characteristic, complemented
5#10622840C211yesmaximal, characteristic, complemented
6#10622800C212yesmaximal, complemented
7#10622659C211yesmaximal, characteristic, complemented
8#10622424C212yesmaximal, complemented
9#10622417C212yesmaximal, complemented
10#10622345C211yesmaximal, characteristic, complemented
11D11×C22⋊C8C211yesmaximal, characteristic, complemented
12C22×Q8×C11C2211yescharacteristic
13C2×#4343—28no—
14C2×#4343—21no—
15C2×#4343—21no—
16C2×#4343C2212yes—
17C2×#4343C2212yes—
18C2×#4343C2211yescharacteristic, complemented
19C22×D44—21no—
20C22×D44C2211yescharacteristic
21C22×C4×D11—21no—
22C22×C4×D11C2211yescharacteristic
23C2×C11×Q16C2212yescomplemented
24C11×C22⋊Q8C2211yescharacteristic
25#66999C2211yescharacteristic, complemented
26C2×#4325C2212yescomplemented
27C2×#4325C2212yescomplemented
28#66983C2211yescharacteristic
29#66972—28no—
30C2×D88C2212yescomplemented
31C2×C8×D11C2212yescomplemented
32#66948C2211yescharacteristic, complemented
33#66947—21no—
34#66946—21no—
35#66945C2211yescharacteristic, complemented
36#66935—21no—
37(C22⋊D11)⋊C4—21no—
38C11×#103C2212yescomplemented
39C11×C22⋊C8C2211yescharacteristic
40#66899C2212yescomplemented
41C22⋊(C11⋊C8)C2211yescharacteristic
42#66885C2212yescomplemented
43(C2×D11)⋊C8C2212yescomplemented
44#66873C2212yescomplemented
45C23×D11—21no—
46C23×D11D411yescharacteristic
47C2×Q8×C11—24no—
48C2×Q8×C11—21no—
49C2×Q8×C11C2311yescharacteristic
50C2×Q8×C11C2312yes—
51C22×C4×C11—21no—
52C22×C4×C11C2311yescharacteristic
53C2×C22⋊D11—21no—
54C22×Dic11D411yescharacteristic
55#4343—28no—
56#4343—28no—
57#4343—24no—
58#4343—24no—
59#4343—24no—
60#4343—24no—
61#4343D418yescomplemented
62C2×D44—28no—
63C2×D44—24no—
64C2×D44—22no—
65C2×D44—22no—
66C2×D44—21no—
67C2×D44—21no—
68C2×D44—21no—
69C2×D44C2311yescharacteristic
70C2×D44C2312yes—
71C2×C4×D11—28no—
72C2×C4×D11—22no—
73C2×C4×D11—22no—
74C2×C4×D11—24no—
75C2×C4×D11—21no—
76C2×C4×D11D411yescharacteristic
77C2×C4×D11D411yescharacteristic
78C2×C4×D11C2311yescharacteristic
79C2×C4×D11C2311yescharacteristic
80C11×Q16—24no—
81C2×C8×C11C2312yes—
82C11×C4⋊C4—21no—
83C11×C4⋊C4C2311yescharacteristic
84C11×C22⋊C4—21no—
85#4325—24no—
86#4325—24no—
87(C2×D11)⋊C4—21no—
88(C2×D11)⋊C4—21no—
89(C2×D11)⋊C4—21no—
90(C2×D11)⋊C4—21no—
91C4⋊Dic11C2311yescharacteristic
92Dic11⋊C4—21no—
93C4×Dic11—21no—
94C2×C11⋊C8C2312yes—
95D88—24no—
96C8×D11—24no—
97#3002—111nomaximal, Sylow
98C23×C11C2×D411yescharacteristic
99C22×D11—24no—
100C22×D11—22no—
101C22×D11—22no—
102C22×D11—22no—
103C22×D11—21no—
104C22×D11—41no—
105C22×D11—42no—
106C22×D11—42no—
107C22×D11C2×D411yescharacteristic
108C22×D11C2×D411yescharacteristic
109Q8×C11—24no—
110Q8×C11—22no—
111Q8×C11—22no—
112Q8×C11C2×D414yes—
113C2×C4×C11—24no—
114C2×C4×C11—22no—
115C2×C4×C11—22no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11C2×D411yescharacteristic
119C2×C4×C11C2411yescharacteristic
120C22⋊D11—42no—
121C2×Dic11—22no—
122C2×Dic11—21no—
123C2×Dic11C2×D411yescharacteristic
124C2×Dic11C2×D411yescharacteristic
125D44—28no—
126D44—24no—
127D44—28no—
128D44—22no—
129D44—22no—
130D44—42no—
131D44—42no—
132D44C2×D414yes—
133C4×D11—28no—
134C4×D11—22no—
135C4×D11—22no—
136C4×D11—28no—
137C4×D11—22no—
138C4×D11—42no—
139C4×D11C2×D414yes—
140C8×C11—22no—
141C11⋊C8—22no—
142C22×#41—111no—
143C2×#135—112no—
144#525—111no—
145#452—112no—
146#451D1111yescharacteristic, complemented
147#450—111no—
148#449—112no—
149#448—111no—
150#447—111no—
151#416—112no—
152C2×C22⋊C8—111no—
153C22×C11—21no—
154C22×C11—21no—
155C22×C11#13512yescomplemented
156C22×C11C22×D411yescharacteristic
157C2×D11—21no—
158C2×D11—21no—
159C2×D11—24no—
160C2×D11—21no—
161C2×D11—21no—
162C2×D11—21no—
163C2×D11—44no—
164C2×D11—48no—
165C2×D11—42no—
166C2×D11—42no—
167C2×D11—41no—
168C2×D11—41no—
169C2×D11—41no—
170C2×D11#12012yes—
171C4×C11—24no—
172C4×C11—21no—
173C4×C11—41no—
174C4×C11—41no—
175C4×C11C22×D412yes—
176Dic11—21no—
177Dic11—41no—
178Dic11#12012yes—
179C2×#41—112no—
180C2×#41—111no—
181C2×#41—112no—
182C2×#41—221no—
183C2×#41—221no—
184C2×#41—228no—
185C22×Q8C2×D1111yescharacteristic
186C22×D4—111no—
187C22×D4—221no—
188C23×C4—111no—
189C23×C4—221no—
190#135—228no—
191C2×Q16C2×D1112yescomplemented
192C2×SD16—112no—
193C2×SD16—112no—
194C2×D8—112no—
195C22×C8—112no—
196#123—221no—
197C22⋊Q8—111no—
198C22⋊Q8C2×D1111yescharacteristic
199#121—111no—
200#121—111no—
201#120—221no—
202C4×D4—221no—
203C4×D4—221no—
204#117—111no—
205#103—112no—
206#103C2×D1112yescomplemented
207#102—112no—
208#102—112no—
209C22⋊C8—111no—
210C22⋊C8—112no—
211C22⋊C8C2×D1111yescharacteristic
212C2×C11—22no—
213C2×C11C2×#12011yescharacteristic
214C2×C11C2×#13511yescharacteristic
215C2×C11#57511yescharacteristic
216D11—22no—
217D11—41no—
218D11—44no—
219D11—81no—
220C24—111no—
221C24—221no—
222#41—118no—
223#41—224no—
224#41—224no—
225#41—224no—
226#41—228no—
227#41—228no—
228#41—224no—
229C2×Q8—24no—
230C2×Q8—21no—
231C2×Q8C22×D1111yescharacteristic
232C2×Q8C22×D1112yes—
233C2×D4—112no—
234C2×D4—111no—
235C2×D4—224no—
236C2×D4—222no—
237C2×D4—222no—
238C2×D4—228no—
239C2×D4—221no—
240C2×D4—221no—
241C2×D4—221no—
242C2×D4—221no—
243C22×C4—21no—
244C22×C4—111no—
245C22×C4—111no—
246C22×C4—111no—
247C22×C4—111no—
248C22×C4—111no—
249C22×C4—224no—
250C22×C4—222no—
251C22×C4—222no—
252C22×C4—221no—
253C22×C4—228no—
254C22×C4C22×D1111yescharacteristic
255Q16—24no—
256SD16—224no—
257SD16—224no—
258D8—224no—
259C2×C8—112no—
260C2×C8—224no—
261C2×C8C22×D1112yes—
262C4⋊C4—21no—
263C4⋊C4—111no—
264C4⋊C4—221no—
265C4⋊C4C22×D1111yescharacteristic
266C22⋊C4—21no—
267C22⋊C4—221no—
268C22⋊C4—221no—
269C22⋊C4—221no—
270C22⋊C4—221no—
271C42—221no—
272C11#300211yescharacteristic, complemented, Sylow
273C23—111no—
274C23—111no—
275C23—222no—
276C23—224no—
277C23—222no—
278C23—222no—
279C23—221no—
280C23—441no—
281C23—442no—
282C23—442no—
283C23D4×D1111yescharacteristic
284Q8—24no—
285Q8—22no—
286Q8—22no—
287Q8D4×D1114yes—
288D4—114no—
289D4—228no—
290D4—228no—
291D4—224no—
292D4—222no—
293D4—222no—
294D4—442no—
295D4—442no—
296D4—442no—
297C2×C4—24no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—111no—
303C2×C4—114no—
304C2×C4—111no—
305C2×C4—222no—
306C2×C4—228no—
307C2×C4—222no—
308C2×C4—228no—
309C2×C4—222no—
310C2×C4—222no—
311C2×C4—221no—
312C2×C4—442no—
313C2×C4D4×D1111yescharacteristic
314C2×C4C23×D1111yescharacteristic
315C8—22no—
316C8—222no—
317C22—21no—
318C22—21no—
319C22—112no—
320C22—221no—
321C22—221no—
322C22—221no—
323C22—221no—
324C22—224no—
325C22—221no—
326C22—444no—
327C22—448no—
328C22—442no—
329C22—442no—
330C22—441no—
331C22—441no—
332C22—441no—
333C22#6697212yescomplemented
334C22C2×D4×D1111yescharacteristic
335C4—24no—
336C4—21no—
337C4—41no—
338C4—41no—
339C4—112no—
340C4—221no—
341C4—441no—
342C4C2×D4×D1112yes—
343C2—22no—
344C2—222no—
345C2—441no—
346C2—444no—
347C2—881no—
348C2D11×#12011yescharacteristic
349C2C2×#6697211yescharacteristic
350C2#1062330811yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#451C2
socleC22×C11C22×D4
hypercenter#451D11
hypocenterC11#3002
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
1. C22×#4343C2semidirect
2. C2×#66972C2semidirect
3. #10623158C2semidirect
4. C11×#451C2semidirect
5. #10622840C2semidirect
6. #10622800C2semidirect
7. #10622659C2semidirect
8. #10622424C2semidirect
9. #10622417C2semidirect
10. #10622345C2semidirect
11. D11×C22⋊C8C2semidirect
18. C2×#4343C22semidirect
23. C2×C11×Q16C22semidirect
25. #66999C22semidirect
26. C2×#4325C22semidirect
27. C2×#4325C22semidirect
30. C2×D88C22semidirect
31. C2×C8×D11C22semidirect
32. #66948C22semidirect
35. #66945C22semidirect
38. C11×#103C22semidirect
40. #66899C22semidirect
42. #66885C22semidirect
43. (C2×D11)⋊C8C22semidirect
44. #66873C22semidirect
61. #4343D4semidirect
146. #451D11semidirect
155. C22×C11#135semidirect
191. C2×Q16C2×D11semidirect
206. #103C2×D11semidirect
272. C11#3002semidirect
333. C22#66972semidirect

Maximal subgroups

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

subgroupindex
C22×#43432
C2×#669722
#106231582
C11×#4512
#106228402
#106228002
#106226592
#106224242
#106224172
#106223452
D11×C22⋊C82
#300211