Finite Group Databasebeta

← #13080201

Subgroups — #13080201

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×C11×#135C211yesmaximal, characteristic, complemented
2#10623365C211yesmaximal, characteristic, complemented
3#10623362C211yesmaximal, characteristic, complemented
4C2×#66971C211yesmaximal, characteristic, complemented
5#10622852C211yesmaximal, characteristic, complemented
6#10622851C211yesmaximal, characteristic, complemented
7#10622797C211yesmaximal, characteristic, complemented
8#10622785C211yesmaximal, characteristic, complemented
9#10622783C211yesmaximal, characteristic, complemented
10#10622779C211yesmaximal, characteristic, complemented
11#10622776C211yesmaximal, characteristic, complemented
12#10622772C211yesmaximal, characteristic, complemented
13#10622767C211yesmaximal, characteristic, complemented
14#10622727C211yesmaximal, characteristic, complemented
15#10622724C211yesmaximal, characteristic, complemented
16C2×C11×#41C2211yescharacteristic
17C2×C11×#41C2211yescharacteristic
18C2×#4343C2211yescharacteristic
19C2×Q8×D11C2211yescharacteristic
20C11×#135—24no—
21C2×C11×Q16C2211yescharacteristic
22C2×C11×SD16C2211yescharacteristic
23C2×C11×SD16C2211yescharacteristic
24C2×C11×D8C2211yescharacteristic
25C22×C8×C11C2211yescharacteristic
26Q8×Dic11C2211yescharacteristic
27Q8×Dic11C2211yescharacteristic
28C2×#4326C2211yescharacteristic
29C2×#4325C2211yescharacteristic
30#66993—21no—
31#66993C2211yescharacteristic
32#66991—21no—
33#66991—21no—
34#66991C2211yescharacteristic
35#66991C2211yescharacteristic
36#66989—21no—
37#66989C2211yescharacteristic
38C2×#4324C2211yescharacteristic
39C2×#4323C2211yescharacteristic
40#66983—21no—
41#66983C2211yescharacteristic
42C4×C22⋊D11—21no—
43C4×C22⋊D11—21no—
44C4×C22⋊D11C2211yescharacteristic
45#66977—21no—
46#66977C2211yescharacteristic
47#66971—24no—
48C2×#4314C2211yescharacteristic
49C2×#4313C2211yescharacteristic
50#66899C2211yescharacteristic
51#66899C2211yescharacteristic
52#66896C2211yescharacteristic
53#66896C2211yescharacteristic
54C22⋊(C11⋊C8)C2211yescharacteristic
55#66885C2211yescharacteristic
56(C2×D11)⋊C8C2211yescharacteristic
57#66881C2211yescharacteristic
58#66880C2211yescharacteristic
59#66879C2211yescharacteristic
60Dic11⋊C8C2211yescharacteristic
61C11×#41—22no—
62C11×#41—22no—
63C11×#41—41no—
64C11×#41—41no—
65C2×Q8×C11C2311yescharacteristic
66C2×Q8×C11C2311yescharacteristic
67C2×D4×C11—21no—
68C2×D4×C11—21no—
69C2×D4×C11C2311yescharacteristic
70C2×D4×C11C2311yescharacteristic
71C22×C4×C11—21no—
72C22×C4×C11—21no—
73C22×C4×C11C2311yescharacteristic
74C2×C22⋊D11—21no—
75C2×C22⋊D11—21no—
76C2×C22⋊D11—21no—
77C2×C22⋊D11—21no—
78C2×C22⋊D11—21no—
79C2×C22⋊D11D411yescharacteristic
80#4343—22no—
81#4343—41no—
82Q8×D11—22no—
83Q8×D11—41no—
84C2×D44—21no—
85C2×D44C2311yescharacteristic
86C2×C4×D11—21no—
87C2×C4×D11—21no—
88C2×C4×D11C2311yescharacteristic
89C2×Dic22—21no—
90C2×Dic22C2311yescharacteristic
91C11×Q16D414yescomplemented
92C11×SD16—22no—
93C11×SD16—22no—
94C11×D8—22no—
95C2×C8×C11—22no—
96C2×C8×C11C2311yescharacteristic
97C2×C8×C11C2311yescharacteristic
98C22⋊Dic11—21no—
99C22⋊Dic11—21no—
100C22⋊Dic11—21no—
101C22⋊Dic11—21no—
102C22⋊Dic11—21no—
103C22⋊Dic11D411yescharacteristic
104#4326—22no—
105#4325—22no—
106#4324—41no—
107#4323—41no—
108(C2×D11)⋊C4—21no—
109(C2×D11)⋊C4D411yescharacteristic
110C4⋊Dic11—21no—
111C4⋊Dic11—21no—
112C4⋊Dic11C2311yescharacteristic
113C4⋊Dic11C2311yescharacteristic
114Dic11⋊C4—21no—
115Dic11⋊C4D411yescharacteristic
116C4×Dic11—21no—
117C4×Dic11—21no—
118C4×Dic11C2311yescharacteristic
119C2×C11⋊C8C2311yescharacteristic
120C2×C11⋊C8C2311yescharacteristic
121#4314—22no—
122#4313—22no—
123#3271—111nomaximal, Sylow
124C23×C11—21no—
125C23×C11—21no—
126C23×C11C2×D411yescharacteristic
127C22×D11—21no—
128C22×D11C2×D411yescharacteristic
129Q8×C11—21no—
130Q8×C11—21no—
131Q8×C11C2×D412yes—
132Q8×C11C2×D412yes—
133D4×C11—21no—
134D4×C11—21no—
135D4×C11—21no—
136D4×C11—21no—
137D4×C11—42no—
138D4×C11—42no—
139C2×C4×C11—21no—
140C2×C4×C11—21no—
141C2×C4×C11—21no—
142C2×C4×C11—21no—
143C2×C4×C11—42no—
144C2×C4×C11—42no—
145C2×C4×C11C2×D411yescharacteristic
146C2×C4×C11C2411yescharacteristic
147C22⋊D11—41no—
148C22⋊D11—42no—
149C22⋊D11—42no—
150C22⋊D11—81no—
151C22⋊D11—81no—
152C22⋊D11—81no—
153C2×Dic11—21no—
154C2×Dic11—21no—
155C2×Dic11—21no—
156C2×Dic11C2×D411yescharacteristic
157C2×Dic11C2×D411yescharacteristic
158C2×Dic11C2×D411yescharacteristic
159D44—21no—
160D44—21no—
161D44—42no—
162C4×D11—21no—
163C4×D11—21no—
164C4×D11—42no—
165C4×D11—42no—
166Dic22—21no—
167Dic22—21no—
168Dic22—42no—
169C8×C11—21no—
170C8×C11C2×D412yes—
171C11⋊C8—21no—
172C11⋊C8—21no—
173C2×#137—111no—
174C2×#135D1111yescharacteristic, complemented
175#550—111no—
176#548—111no—
177#496—111no—
178#469—111no—
179#465—111no—
180#464—111no—
181#460—111no—
182#452—111no—
183#449—111no—
184#449—111no—
185#448—111no—
186#441—111no—
187#435—111no—
188C22×C11—21no—
189C22×C11—21no—
190C22×C11—21no—
191C22×C11—41no—
192C22×C11—41no—
193C22×C11—41no—
194C22×C11—41no—
195C22×C11—41no—
196C22×C11—41no—
197C22×C11C22×D411yescharacteristic
198C2×D11—21no—
199C2×D11—21no—
200C2×D11—21no—
201C2×D11—41no—
202C2×D11—41no—
203C2×D11—41no—
204C4×C11—21no—
205C4×C11—22no—
206C4×C11—22no—
207C4×C11C22×D411yescharacteristic
208C4×C11H(5,𝔽2)11yescharacteristic
209Dic11—21no—
210Dic11—21no—
211Dic11—21no—
212Dic11—41no—
213Dic11—41no—
214Dic11—41no—
215C2×#41—111no—
216C2×#41C2×D1111yescharacteristic
217C2×#41C2×D1111yescharacteristic
218C22×Q8—111no—
219#137—224no—
220#135—24no—
221C2×Q16—111no—
222C2×Q16C2×D1111yescharacteristic
223C2×SD16—111no—
224C2×SD16—111no—
225C2×SD16—111no—
226C2×SD16C2×D1111yescharacteristic
227C2×SD16C2×D1111yescharacteristic
228C2×D8—111no—
229C2×D8C2×D1111yescharacteristic
230C2×M16—111no—
231C22×C8C2×D1111yescharacteristic
232#127—111no—
233#127—221no—
234#124—111no—
235#124—221no—
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×Q8—111no—
246C4×D4—111no—
247C4×D4—221no—
248C4×D4—221no—
249#106—111no—
250C4⋊C8—111no—
251#103—111no—
252#103—111no—
253#103—111no—
254#102—111no—
255#102—111no—
256#102—111no—
257C22⋊C8—111no—
258C22⋊C8—111no—
259#97—111no—
260C2×C11—41no—
261C2×C11—81no—
262C2×C11—81no—
263C2×C11D4211yescharacteristic
264C2×C11#57511yescharacteristic
265C2×C11#57711yescharacteristic
266D11—41no—
267D11—81no—
268#41—22no—
269#41—22no—
270#41—41no—
271#41—41no—
272#41—222no—
273#41—441no—
274C2×Q8—111no—
275C2×Q8—221no—
276C2×Q8—222no—
277C2×Q8—441no—
278C2×Q8C22×D1111yescharacteristic
279C2×Q8C22×D1111yescharacteristic
280C2×D4—21no—
281C2×D4—21no—
282C2×D4—111no—
283C2×D4—111no—
284C2×D4—221no—
285C2×D4—221no—
286C2×D4—221no—
287C2×D4—221no—
288C2×D4—221no—
289C2×D4—221no—
290C2×D4C22×D1111yescharacteristic
291C2×D4C22×D1111yescharacteristic
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—111no—
295C22×C4—221no—
296C22×C4—221no—
297C22×C4C22×D1111yescharacteristic
298Q16—222no—
299Q16C22⋊D1114yescomplemented
300SD16—22no—
301SD16—22no—
302SD16—222no—
303SD16—222no—
304SD16—441no—
305D8—22no—
306D8—441no—
307M16—222no—
308C2×C8—22no—
309C2×C8—111no—
310C2×C8—111no—
311C2×C8C22×D1111yescharacteristic
312C2×C8C22×D1111yescharacteristic
313C4⋊C4—111no—
314C4⋊C4—111no—
315C4⋊C4—111no—
316C4⋊C4—221no—
317C4⋊C4—221no—
318C4⋊C4—221no—
319C22⋊C4—111no—
320C22⋊C4—111no—
321C22⋊C4—221no—
322C22⋊C4—221no—
323C22⋊C4—221no—
324C22⋊C4—221no—
325C22⋊C4—221no—
326C22⋊C4—221no—
327C42—111no—
328C42—221no—
329C42—221no—
330C11#327111yescharacteristic, complemented, Sylow
331C23—21no—
332C23—21no—
333C23—111no—
334C23—221no—
335C23D4×D1111yescharacteristic
336Q8—21no—
337Q8—21no—
338Q8—221no—
339Q8—221no—
340Q8—442no—
341Q8C2×C22⋊D1112yes—
342Q8C2×C22⋊D1112yes—
343D4—21no—
344D4—21no—
345D4—21no—
346D4—21no—
347D4—42no—
348D4—42no—
349D4—221no—
350D4—221no—
351D4—442no—
352D4—441no—
353D4—442no—
354D4—442no—
355D4—881no—
356D4—881no—
357D4—881no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—42no—
363C2×C4—42no—
364C2×C4—111no—
365C2×C4—111no—
366C2×C4—111no—
367C2×C4—221no—
368C2×C4—221no—
369C2×C4—221no—
370C2×C4—221no—
371C2×C4—221no—
372C2×C4—442no—
373C2×C4—442no—
374C2×C4D4×D1111yescharacteristic
375C2×C4C23×D1111yescharacteristic
376C8—21no—
377C8—221no—
378C8—221no—
379C8C2×C22⋊D1112yes—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—221no—
390C22—221no—
391C22—221no—
392C22—441no—
393C22—441no—
394C22—441no—
395C22C2×D4×D1111yescharacteristic
396C4—21no—
397C4—22no—
398C4—22no—
399C4—221no—
400C4—221no—
401C4—221no—
402C4—441no—
403C4—441no—
404C4—441no—
405C4#6703711yescharacteristic
406C4C22×C22⋊D1111yescharacteristic
407C2—41no—
408C2—81no—
409C2—81no—
410C2—441no—
411C2—881no—
412C2#1062329911yescharacteristic
413C2#1062330111yescharacteristic
414C2D4×C22⋊D1111yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC2×C11×#135C2
socleC22×C11C22×D4
hypercenterC2×#135D11
hypocenterC11#3271
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C2×C11×#135C2semidirect
2. #10623365C2semidirect
3. #10623362C2semidirect
4. C2×#66971C2semidirect
5. #10622852C2semidirect
6. #10622851C2semidirect
7. #10622797C2semidirect
8. #10622785C2semidirect
9. #10622783C2semidirect
10. #10622779C2semidirect
11. #10622776C2semidirect
12. #10622772C2semidirect
13. #10622767C2semidirect
14. #10622727C2semidirect
15. #10622724C2semidirect
91. C11×Q16D4semidirect
174. C2×#135D11semidirect
299. Q16C22⋊D11semidirect
330. C11#3271semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1352
#106233652
#106233622
C2×#669712
#106228522
#106228512
#106227972
#106227852
#106227832
#106227792
#106227762
#106227722
#106227672
#106227272
#106227242
#327111