Finite Group Databasebeta

← #13080331

Subgroups — #13080331

Order 1408.

484 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623355C211yesmaximal, characteristic, complemented
2C2×#67003C211yesmaximal, characteristic, complemented
3C2×#66969C211yesmaximal, characteristic, complemented
4#10623162C211yesmaximal, characteristic, complemented
5C11×#452C211yesmaximal, characteristic, complemented
6#10622800C211yesmaximal, characteristic, complemented
7#10622794C211yesmaximal, characteristic, complemented
8#10622775C211yesmaximal, characteristic, complemented
9#10622664C211yesmaximal, characteristic, complemented
10#10622431C211yesmaximal, characteristic, complemented
11#10622426C211yesmaximal, characteristic, complemented
12#10622396C211yesmaximal, characteristic, complemented
13#10622369C211yesmaximal, characteristic, complemented
14#10622346C211yesmaximal, characteristic, complemented
15(C22⋊D11)⋊C8C211yesmaximal, characteristic, complemented
16C2×C11×#41C2211yescharacteristic
17C2×#4343C2211yescharacteristic
18C2×#4341C2211yescharacteristic
19C2×#4339C2211yescharacteristic
20C2×C11×Q16C2211yescharacteristic
21C2×C11×SD16C2211yescharacteristic
22C11×C22⋊Q8C2211yescharacteristic
23#67003—24no—
24#66999C2211yescharacteristic
25#66997C2211yescharacteristic
26#66997C2211yescharacteristic
27C2×#4326C2211yescharacteristic
28C2×#4326C2211yescharacteristic
29C2×#4325C2211yescharacteristic
30#66992—21no—
31#66988—21no—
32D4×Dic11C2211yescharacteristic
33C2×#4324C2211yescharacteristic
34C2×#4323C2211yescharacteristic
35#66982—21no—
36C4×C22⋊D11C2211yescharacteristic
37#66977C2211yescharacteristic
38C2×Dic11⋊C4—21no—
39C22×C11⋊C8C2211yescharacteristic
40#66969—24no—
41C2×Dic44C2211yescharacteristic
42C2×#4314C2211yescharacteristic
43C2×C8×D11C2211yescharacteristic
44#66950C2211yescharacteristic
45#66947—21no—
46#66946C2211yescharacteristic
47C4⋊C4×D11—21no—
48#66937—21no—
49#66936—21no—
50C11×#103C2211yescharacteristic
51C11×#102C2211yescharacteristic
52C11×C22⋊C8C2211yescharacteristic
53#66899C2211yescharacteristic
54#66885C2211yescharacteristic
55(C2×D11)⋊C8C2211yescharacteristic
56#66880C2211yescharacteristic
57Dic11⋊C8C2211yescharacteristic
58C8×Dic11C2211yescharacteristic
59#66874C2211yescharacteristic
60#66871C2211yescharacteristic
61C11×#41—22no—
62C11×#41—41no—
63C2×Q8×C11C2311yescharacteristic
64C2×Q8×C11C2311yescharacteristic
65C2×D4×C11—21no—
66C2×D4×C11C2311yescharacteristic
67C22×C4×C11—21no—
68C22×C4×C11C2311yescharacteristic
69C2×C22⋊D11—21no—
70C2×C22⋊D11—21no—
71C2×C22⋊D11D411yescharacteristic
72C22×Dic11—21no—
73C22×Dic11—21no—
74#4343—22no—
75#4343—41no—
76#4341—22no—
77#4341—41no—
78#4339—22no—
79#4339—41no—
80C2×D44—21no—
81C2×D44C2311yescharacteristic
82C2×C4×D11—21no—
83C2×C4×D11—21no—
84C2×C4×D11—21no—
85C2×C4×D11C2311yescharacteristic
86C2×Dic22C2311yescharacteristic
87C2×Dic22C2311yescharacteristic
88C11×Q16—41no—
89C11×SD16—22no—
90C2×C8×C11C2311yescharacteristic
91C2×C8×C11C2311yescharacteristic
92C11×C4⋊C4—21no—
93C11×C4⋊C4C2311yescharacteristic
94C11×C22⋊C4—21no—
95C22⋊Dic11—21no—
96C22⋊Dic11—21no—
97C22⋊Dic11D411yescharacteristic
98#4326—22no—
99#4326—22no—
100#4325—22no—
101#4324—22no—
102#4323D414yescomplemented
103(C2×D11)⋊C4—21no—
104(C2×D11)⋊C4—21no—
105(C2×D11)⋊C4—21no—
106(C2×D11)⋊C4D411yescharacteristic
107C4⋊Dic11—21no—
108C4⋊Dic11C2311yescharacteristic
109Dic11⋊C4—21no—
110Dic11⋊C4—21no—
111Dic11⋊C4—21no—
112Dic11⋊C4—21no—
113Dic11⋊C4—21no—
114Dic11⋊C4—21no—
115Dic11⋊C4D411yescharacteristic
116C4×Dic11C2311yescharacteristic
117C2×C11⋊C8—22no—
118C2×C11⋊C8C2311yescharacteristic
119C2×C11⋊C8C2311yescharacteristic
120Dic44—41no—
121#4314—22no—
122C8×D11—22no—
123#3283—111nomaximal, Sylow
124C23×C11—21no—
125C23×C11C2×D411yescharacteristic
126C22×D11—21no—
127C22×D11C2×D411yescharacteristic
128Q8×C11—21no—
129Q8×C11—21no—
130Q8×C11—21no—
131Q8×C11—21no—
132D4×C11—21no—
133D4×C11—42no—
134D4×C11C2×D412yes—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—21no—
140C2×C4×C11—42no—
141C2×C4×C11C2×D411yescharacteristic
142C2×C4×C11C2411yescharacteristic
143C22⋊D11—22no—
144C22⋊D11—42no—
145C22⋊D11—42no—
146C2×Dic11—21no—
147C2×Dic11—21no—
148C2×Dic11—21no—
149C2×Dic11—42no—
150C2×Dic11—42no—
151C2×Dic11C2×D411yescharacteristic
152C2×Dic11C2×D411yescharacteristic
153C2×Dic11C2×D411yescharacteristic
154D44—21no—
155D44—42no—
156D44C2×D412yes—
157C4×D11—21no—
158C4×D11—21no—
159C4×D11—42no—
160C4×D11—42no—
161C4×D11—42no—
162Dic22—21no—
163Dic22—21no—
164Dic22—21no—
165Dic22—21no—
166C8×C11—21no—
167C8×C11—21no—
168C11⋊C8—21no—
169C11⋊C8C2×D412yes—
170C2×#135—111no—
171C2×#135—111no—
172#547—111no—
173#547—111no—
174#494—111no—
175#467—111no—
176#467—111no—
177#461—111no—
178#461—111no—
179#452—111no—
180#452—111no—
181#452—111no—
182#452D1111yescharacteristic, complemented
183C4×D8—111no—
184C8×D4—111no—
185C22×C11—21no—
186C22×C11—22no—
187C22×C11—21no—
188C22×C11—21no—
189C22×C11—41no—
190C22×C11—41no—
191C22×C11C22×D411yescharacteristic
192C2×D11—22no—
193C2×D11—21no—
194C2×D11—21no—
195C2×D11—21no—
196C2×D11—41no—
197C2×D11—41no—
198C4×C11—21no—
199C4×C11—41no—
200C4×C11—41no—
201C4×C11—41no—
202C4×C11C22×D411yescharacteristic
203C4×C11H(5,𝔽2)11yescharacteristic
204Dic11—21no—
205Dic11—21no—
206Dic11—41no—
207Dic11—41no—
208Dic11—41no—
209Dic11#13512yescomplemented
210C2×#41—111no—
211C2×#41—111no—
212C2×#41—111no—
213C2×#41C2×D1111yescharacteristic
214#135—224no—
215#135—224no—
216C2×Q16—111no—
217C2×Q16—111no—
218C2×Q16—111no—
219C2×Q16C2×D1111yescharacteristic
220C2×SD16—111no—
221C2×SD16—111no—
222C2×SD16—111no—
223C2×SD16C2×D1111yescharacteristic
224C2×D8—111no—
225C22×C8—111no—
226C22×C8—111no—
227C4⋊Q8—111no—
228C4⋊Q8—111no—
229#123—221no—
230#123—221no—
231#123—221no—
232#123—221no—
233C22⋊Q8—111no—
234C22⋊Q8—111no—
235C22⋊Q8—111no—
236C22⋊Q8C2×D1111yescharacteristic
237#121—221no—
238#121—221no—
239C4×D4—111no—
240C4×D4—111no—
241C4×D4—111no—
242C2×C4⋊C4—221no—
243C2×C4⋊C4—221no—
244#107—111no—
245C4⋊C8—111no—
246#103—111no—
247#103—111no—
248#103—111no—
249#103C2×D1111yescharacteristic
250#102—111no—
251#102C2×D1111yescharacteristic
252C22⋊C8—111no—
253C22⋊C8C2×D1111yescharacteristic
254C4×C8—111no—
255C2×C11—41no—
256C2×C11—42no—
257C2×C11D4211yescharacteristic
258C2×C11C2×#13511yescharacteristic
259C2×C11#57811yescharacteristic
260D11—41no—
261D11—42no—
262#41—22no—
263#41—41no—
264#41—222no—
265#41—222no—
266#41—222no—
267#41—441no—
268#41—441no—
269#41—441no—
270C2×Q8—111no—
271C2×Q8—111no—
272C2×Q8C22×D1111yescharacteristic
273C2×Q8C22×D1111yescharacteristic
274C2×D4—21no—
275C2×D4—111no—
276C2×D4—111no—
277C2×D4—221no—
278C2×D4—221no—
279C2×D4—221no—
280C2×D4C22×D1111yescharacteristic
281C22×C4—21no—
282C22×C4—111no—
283C22×C4—221no—
284C22×C4—221no—
285C22×C4—221no—
286C22×C4—221no—
287C22×C4—221no—
288C22×C4C22×D1111yescharacteristic
289Q16—41no—
290Q16—222no—
291Q16—222no—
292Q16—441no—
293SD16—22no—
294SD16—222no—
295SD16—222no—
296SD16—222no—
297D8—114no—
298C2×C8—111no—
299C2×C8—111no—
300C2×C8—222no—
301C2×C8—222no—
302C2×C8C22×D1111yescharacteristic
303C2×C8C22×D1111yescharacteristic
304C4⋊C4—21no—
305C4⋊C4—111no—
306C4⋊C4—111no—
307C4⋊C4—221no—
308C4⋊C4—221no—
309C4⋊C4—221no—
310C4⋊C4—221no—
311C4⋊C4—221no—
312C4⋊C4—221no—
313C4⋊C4—221no—
314C4⋊C4C22×D1111yescharacteristic
315C22⋊C4—21no—
316C22⋊C4—111no—
317C22⋊C4—111no—
318C22⋊C4—221no—
319C22⋊C4—221no—
320C22⋊C4—221no—
321C22⋊C4—221no—
322C22⋊C4—221no—
323C42—111no—
324C11#328311yescharacteristic, complemented, Sylow
325C23—21no—
326C23—111no—
327C23—221no—
328C23D4×D1111yescharacteristic
329Q8—21no—
330Q8—21no—
331Q8—21no—
332Q8—21no—
333Q8—221no—
334Q8—221no—
335Q8—221no—
336Q8—221no—
337D4—21no—
338D4—42no—
339D4—112no—
340D4—222no—
341D4—221no—
342D4—442no—
343D4—442no—
344D4—442no—
345D4D4×D1112yes—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—42no—
352C2×C4—111no—
353C2×C4—111no—
354C2×C4—111no—
355C2×C4—221no—
356C2×C4—221no—
357C2×C4—221no—
358C2×C4—221no—
359C2×C4—221no—
360C2×C4—442no—
361C2×C4—442no—
362C2×C4—442no—
363C2×C4—442no—
364C2×C4—442no—
365C2×C4D4×D1111yescharacteristic
366C2×C4C23×D1111yescharacteristic
367C8—21no—
368C8—21no—
369C8—112no—
370C8—221no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—22no—
375C22—41no—
376C22—41no—
377C22—221no—
378C22—221no—
379C22—221no—
380C22—222no—
381C22—441no—
382C22—441no—
383C22C2×D4×D1111yescharacteristic
384C4—21no—
385C4—41no—
386C4—41no—
387C4—41no—
388C4—112no—
389C4—221no—
390C4—221no—
391C4—441no—
392C4—441no—
393C4—441no—
394C4C2×D4×D1111yescharacteristic
395C4#6703711yescharacteristic
396C2—41no—
397C2—42no—
398C2—441no—
399C2—442no—
400C2#1062312111yescharacteristic
401C2D11×#13511yescharacteristic
402C2#1062331011yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#452C2
socleC22×C11C22×D4
hypercenter#452D11
hypocenterC11#3283
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. #10623355C2semidirect
2. C2×#67003C2semidirect
3. C2×#66969C2semidirect
4. #10623162C2semidirect
5. C11×#452C2semidirect
6. #10622800C2semidirect
7. #10622794C2semidirect
8. #10622775C2semidirect
9. #10622664C2semidirect
10. #10622431C2semidirect
11. #10622426C2semidirect
12. #10622396C2semidirect
13. #10622369C2semidirect
14. #10622346C2semidirect
15. (C22⋊D11)⋊C8C2semidirect
102. #4323D4semidirect
182. #452D11semidirect
209. Dic11#135semidirect
324. C11#3283semidirect

Maximal subgroups

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

subgroupindex
#106233552
C2×#670032
C2×#669692
#106231622
C11×#4522
#106228002
#106227942
#106227752
#106226642
#106224312
#106224262
#106223962
#106223692
#106223462
(C22⋊D11)⋊C82
#328311