Finite Group Databasebeta

← #13080207

Subgroups — #13080207

Order 1408.

488 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66971C211yesmaximal, characteristic, complemented
2C2×#66969C211yesmaximal, characteristic, complemented
3#10623208C211yesmaximal, characteristic, complemented
4#10623108C211yesmaximal, characteristic, complemented
5C11×#464C211yesmaximal, characteristic, complemented
6#10622800C211yesmaximal, characteristic, complemented
7#10622785C211yesmaximal, characteristic, complemented
8#10622671C211yesmaximal, characteristic, complemented
9#10622643C211yesmaximal, characteristic, complemented
10#10622461C211yesmaximal, characteristic, complemented
11#10622449C211yesmaximal, characteristic, complemented
12#10622420C211yesmaximal, characteristic, complemented
13#10622419C211yesmaximal, characteristic, complemented
14#10622395C211yesmaximal, characteristic, complemented
15#10622394C211yesmaximal, characteristic, complemented
16C2×#4343C2211yescharacteristic
17C2×#4343C2211yescharacteristic
18C2×Q8×D11C2211yescharacteristic
19C2×#4341C2211yescharacteristic
20C2×C11×Q16C2211yescharacteristic
21C2×C11×SD16C2211yescharacteristic
22C11×#124C2211yescharacteristic
23C4×Q8×C11C2211yescharacteristic
24#66999C2211yescharacteristic
25C2×#4326C2211yescharacteristic
26C2×#4325C2211yescharacteristic
27C2×#4325C2211yescharacteristic
28#66991C2211yescharacteristic
29C2×#4323C2211yescharacteristic
30C2×#4323C2211yescharacteristic
31#66971—24no—
32#66969—24no—
33C2×#4314C2211yescharacteristic
34C2×#4314C2211yescharacteristic
35C2×#4313C2211yescharacteristic
36C2×C8×D11C2211yescharacteristic
37#66948—21no—
38#66948—21no—
39#66948C2211yescharacteristic
40#66948C2211yescharacteristic
41#66938—21no—
42#66937—21no—
43(C22⋊D11)⋊C4—21no—
44#66931—21no—
45#66927—21no—
46#66927C2211yescharacteristic
47C4×D44—21no—
48C4×D44C2211yescharacteristic
49C4×Dic22C2211yescharacteristic
50C11×C4⋊C8C2211yescharacteristic
51C11×#103C2211yescharacteristic
52C11×#102C2211yescharacteristic
53#66899C2211yescharacteristic
54#66885C2211yescharacteristic
55#66885C2211yescharacteristic
56(C2×D11)⋊C8C2211yescharacteristic
57(C2×D11)⋊C8C2211yescharacteristic
58#66874C2211yescharacteristic
59#66872C2211yescharacteristic
60#66867C2211yescharacteristic
61C2×Q8×C11C2311yescharacteristic
62C2×Q8×C11C2311yescharacteristic
63C2×D4×C11C2311yescharacteristic
64C2×C22⋊D11—21no—
65C2×C22⋊D11—21no—
66C22×Dic11—21no—
67#4343—22no—
68#4343—22no—
69#4343—41no—
70#4343—41no—
71Q8×D11—22no—
72Q8×D11—41no—
73#4341—22no—
74#4341—41no—
75C2×D44—21no—
76C2×D44—21no—
77C2×D44—21no—
78C2×D44—21no—
79C2×D44—21no—
80C2×D44—21no—
81C2×D44D411yescharacteristic
82C2×D44C2311yescharacteristic
83C2×D44C2311yescharacteristic
84C2×C4×D11—21no—
85C2×C4×D11—21no—
86C2×C4×D11—21no—
87C2×C4×D11C2311yescharacteristic
88C2×C4×D11C2311yescharacteristic
89C2×Dic22—21no—
90C2×Dic22C2311yescharacteristic
91C11×Q16—22no—
92C11×SD16—22no—
93C2×C8×C11C2311yescharacteristic
94C2×C8×C11C2311yescharacteristic
95C11×C4⋊C4—21no—
96C11×C4⋊C4C2311yescharacteristic
97C11×C22⋊C4—21no—
98C11×C22⋊C4—21no—
99C42×C11—21no—
100C42×C11C2311yescharacteristic
101C22⋊Dic11—21no—
102#4326D414yescomplemented
103#4325—22no—
104#4325—41no—
105#4323—22no—
106#4323—41no—
107(C2×D11)⋊C4—21no—
108(C2×D11)⋊C4—21no—
109(C2×D11)⋊C4—21no—
110(C2×D11)⋊C4D411yescharacteristic
111(C2×D11)⋊C4D411yescharacteristic
112C4⋊Dic11D411yescharacteristic
113C4⋊Dic11C2311yescharacteristic
114Dic11⋊C4—21no—
115Dic11⋊C4—21no—
116C4×Dic11—21no—
117C2×C11⋊C8C2311yescharacteristic
118C2×C11⋊C8C2311yescharacteristic
119#4314—22no—
120#4314—22no—
121#4313—22no—
122C8×D11—22no—
123#3271—111nomaximal, Sylow
124C23×C11—21no—
125C22×D11—21no—
126C22×D11—21no—
127C22×D11C2×D411yescharacteristic
128C22×D11C2×D411yescharacteristic
129Q8×C11—21no—
130Q8×C11—21no—
131Q8×C11—21no—
132Q8×C11C2×D412yes—
133D4×C11—21no—
134D4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11C2×D411yescharacteristic
139C2×C4×C11C2×D411yescharacteristic
140C2×C4×C11C2411yescharacteristic
141C22⋊D11—42no—
142C22⋊D11—42no—
143C2×Dic11—21no—
144C2×Dic11—21no—
145C2×Dic11—42no—
146C2×Dic11C2×D411yescharacteristic
147C2×Dic11C2×D411yescharacteristic
148D44—21no—
149D44—21no—
150D44—21no—
151D44—21no—
152D44—41no—
153D44—42no—
154D44—42no—
155D44—42no—
156D44—81no—
157D44—81no—
158D44—81no—
159C4×D11—21no—
160C4×D11—21no—
161C4×D11—21no—
162C4×D11—21no—
163C4×D11—42no—
164C4×D11—42no—
165C4×D11—42no—
166Dic22—21no—
167Dic22—42no—
168Dic22C2×D412yes—
169C8×C11—21no—
170C8×C11—21no—
171C11⋊C8—21no—
172C11⋊C8C2×D412yes—
173C2×#137—111no—
174C2×#135—111no—
175#550—111no—
176#548—111no—
177#496—111no—
178#469—111no—
179#465—111no—
180#464D1111yescharacteristic, complemented
181#460—111no—
182#452—111no—
183#449—111no—
184#449—111no—
185#448—111no—
186#441—111no—
187#435—111no—
188C22×C11—41no—
189C22×C11—41no—
190C22×C11—41no—
191C22×C11C22×D411yescharacteristic
192C2×D11—21no—
193C2×D11—21no—
194C2×D11—21no—
195C2×D11—21no—
196C2×D11—21no—
197C2×D11—21no—
198C2×D11—41no—
199C2×D11—41no—
200C2×D11—41no—
201C2×D11—41no—
202C2×D11—41no—
203C2×D11—41no—
204C4×C11—22no—
205C4×C11—21no—
206C4×C11—21no—
207C4×C11—41no—
208C4×C11—41no—
209C4×C11C22×D411yescharacteristic
210C4×C11H(5,𝔽2)11yescharacteristic
211Dic11—22no—
212Dic11—21no—
213Dic11—21no—
214Dic11—41no—
215C2×#41—111no—
216C2×#41—111no—
217C2×#41—111no—
218C22×Q8—111no—
219#137—224no—
220#135—224no—
221C2×Q16—111no—
222C2×Q16C2×D1111yescharacteristic
223C2×SD16—111no—
224C2×SD16—111no—
225C2×SD16—111no—
226C2×SD16—111no—
227C2×SD16C2×D1111yescharacteristic
228C2×D8—111no—
229C2×D8—111no—
230C2×M16—111no—
231C22×C8—111no—
232#127—111no—
233#127—221no—
234#124—221no—
235#124C2×D1111yescharacteristic
236C22⋊Q8—111no—
237C22⋊Q8—221no—
238#121—111no—
239#121—111no—
240#121—111no—
241#121—221no—
242#121—221no—
243#121—221no—
244C4×Q8—111no—
245C4×Q8C2×D1111yescharacteristic
246C4×D4—111no—
247C4×D4—221no—
248C4×D4—221no—
249#106—111no—
250C4⋊C8C2×D1111yescharacteristic
251#103—111no—
252#103—111no—
253#103C2×D1111yescharacteristic
254#102—111no—
255#102—111no—
256#102C2×D1111yescharacteristic
257C22⋊C8—111no—
258C22⋊C8—111no—
259#97—111no—
260C2×C11—81no—
261C2×C11D4211yescharacteristic
262C2×C11#57511yescharacteristic
263C2×C11#57711yescharacteristic
264D11—41no—
265D11—41no—
266D11—81no—
267D11—81no—
268#41—222no—
269#41—222no—
270#41—222no—
271#41—441no—
272#41—441no—
273#41—441no—
274C2×Q8—111no—
275C2×Q8—221no—
276C2×Q8—222no—
277C2×Q8—441no—
278C2×Q8C22×D1111yescharacteristic
279C2×Q8C22×D1111yescharacteristic
280C2×D4—111no—
281C2×D4—111no—
282C2×D4—111no—
283C2×D4—221no—
284C2×D4—221no—
285C2×D4—221no—
286C2×D4—221no—
287C2×D4—221no—
288C2×D4—221no—
289C2×D4—221no—
290C2×D4—221no—
291C2×D4C22×D1111yescharacteristic
292C22×C4—111no—
293C22×C4—111no—
294C22×C4—221no—
295C22×C4—221no—
296C22×C4—221no—
297C22×C4—221no—
298Q16—22no—
299Q16—114no—
300SD16—22no—
301SD16—222no—
302SD16—222no—
303SD16—222no—
304SD16—441no—
305D8—222no—
306D8—441no—
307M16—222no—
308C2×C8—111no—
309C2×C8—111no—
310C2×C8—222no—
311C2×C8C22×D1111yescharacteristic
312C2×C8C22×D1111yescharacteristic
313C4⋊C4—21no—
314C4⋊C4—111no—
315C4⋊C4—111no—
316C4⋊C4—221no—
317C4⋊C4—221no—
318C4⋊C4C22×D1111yescharacteristic
319C22⋊C4—21no—
320C22⋊C4—21no—
321C22⋊C4—111no—
322C22⋊C4—111no—
323C22⋊C4—221no—
324C22⋊C4—221no—
325C22⋊C4—221no—
326C22⋊C4—221no—
327C42—21no—
328C42—221no—
329C42C22×D1111yescharacteristic
330C11#327111yescharacteristic, complemented, Sylow
331C23—21no—
332C23—111no—
333C23—111no—
334C23—221no—
335C23—221no—
336Q8—21no—
337Q8—21no—
338Q8—21no—
339Q8—112no—
340Q8—221no—
341Q8—442no—
342Q8D4×D1112yes—
343D4—21no—
344D4—21no—
345D4—221no—
346D4—221no—
347D4—221no—
348D4—221no—
349D4—441no—
350D4—442no—
351D4—442no—
352D4—442no—
353D4—442no—
354D4—442no—
355D4—881no—
356D4—881no—
357D4—881no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—111no—
362C2×C4—111no—
363C2×C4—221no—
364C2×C4—221no—
365C2×C4—221no—
366C2×C4—221no—
367C2×C4—221no—
368C2×C4—221no—
369C2×C4—442no—
370C2×C4—442no—
371C2×C4—442no—
372C2×C4—442no—
373C2×C4D4×D1111yescharacteristic
374C2×C4D4×D1111yescharacteristic
375C2×C4C23×D1111yescharacteristic
376C8—21no—
377C8—21no—
378C8—112no—
379C8—221no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22—221no—
384C22—221no—
385C22—221no—
386C22—221no—
387C22—221no—
388C22—221no—
389C22—441no—
390C22—441no—
391C22—441no—
392C22—441no—
393C22—441no—
394C22—441no—
395C22C2×D4×D1111yescharacteristic
396C4—21no—
397C4—21no—
398C4—22no—
399C4—41no—
400C4—41no—
401C4—221no—
402C4—221no—
403C4—222no—
404C4—441no—
405C4C2×D4×D1111yescharacteristic
406C4#6704211yescharacteristic
407C2—81no—
408C2—441no—
409C2—441no—
410C2—881no—
411C2—881no—
412C2#1062314011yescharacteristic
413C2#1062330111yescharacteristic
414C2#1062330811yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#464C2
socleC22×C11C22×D4
hypercenter#464D11
hypocenterC11#3271
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. C2×#66971C2semidirect
2. C2×#66969C2semidirect
3. #10623208C2semidirect
4. #10623108C2semidirect
5. C11×#464C2semidirect
6. #10622800C2semidirect
7. #10622785C2semidirect
8. #10622671C2semidirect
9. #10622643C2semidirect
10. #10622461C2semidirect
11. #10622449C2semidirect
12. #10622420C2semidirect
13. #10622419C2semidirect
14. #10622395C2semidirect
15. #10622394C2semidirect
102. #4326D4semidirect
180. #464D11semidirect
330. C11#3271semidirect

Maximal subgroups

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

subgroupindex
C2×#669712
C2×#669692
#106232082
#106231082
C11×#4642
#106228002
#106227852
#106226712
#106226432
#106224612
#106224492
#106224202
#106224192
#106223952
#106223942
#327111