Finite Group Databasebeta

← #13079652

Subgroups — #13079652

Order 1408.

396 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623199C211yesmaximal, characteristic, complemented
2#10623088C211yesmaximal, characteristic, complemented
3C11×#463C211yesmaximal, characteristic, complemented
4#10622785C211yesmaximal, characteristic, complemented
5#10622780C211yesmaximal, characteristic, complemented
6#10622771C211yesmaximal, characteristic, complemented
7#10622767C211yesmaximal, characteristic, complemented
8#10622667C211yesmaximal, characteristic, complemented
9#10622629C211yesmaximal, characteristic, complemented
10#10622458C211yesmaximal, characteristic, complemented
11#10622448C211yesmaximal, characteristic, complemented
12#10622423C211yesmaximal, characteristic, complemented
13#10622410C211yesmaximal, characteristic, complemented
14#10622396C211yesmaximal, characteristic, complemented
15#10622377C211yesmaximal, characteristic, complemented
16C2×#4343C2211yescharacteristic
17C2×#4341C2211yescharacteristic
18C2×C11×SD16C2211yescharacteristic
19C2×C11×D8C2211yescharacteristic
20C11×#124C2211yescharacteristic
21C4×D4×C11C2211yescharacteristic
22#66997C2211yescharacteristic
23C2×#4326C2211yescharacteristic
24#66993C2211yescharacteristic
25#66991C2211yescharacteristic
26#66989C2211yescharacteristic
27C2×#4324C2211yescharacteristic
28C2×#4324C2211yescharacteristic
29C2×#4323C2211yescharacteristic
30C4×C22⋊D11—21no—
31#66979—21no—
32C2×Dic44C2211yescharacteristic
33C2×#4314C2211yescharacteristic
34#66950C2211yescharacteristic
35#66943C2211yescharacteristic
36#66937—21no—
37#66937—21no—
38#66936—21no—
39(C22⋊D11)⋊C4—21no—
40(C22⋊D11)⋊C4—21no—
41#66932—21no—
42#66928C2211yescharacteristic
43C42×D11C2211yescharacteristic
44C4×Dic22C2211yescharacteristic
45C11×C4⋊C8C2211yescharacteristic
46C11×#103C2211yescharacteristic
47C11×#102C2211yescharacteristic
48#66899C2211yescharacteristic
49#66896C2211yescharacteristic
50#66885C2211yescharacteristic
51(C2×D11)⋊C8C2211yescharacteristic
52(C2×D11)⋊C8C2211yescharacteristic
53#66880C2211yescharacteristic
54#66879C2211yescharacteristic
55#66879C2211yescharacteristic
56#66874C2211yescharacteristic
57#66873C2211yescharacteristic
58C4⋊(C11⋊C8)C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C2×D4×C11C2311yescharacteristic
61C2×D4×C11C2311yescharacteristic
62C22×C4×C11—21no—
63C2×C22⋊D11—21no—
64C2×C22⋊D11—21no—
65C2×C22⋊D11—21no—
66C2×C22⋊D11—21no—
67C22×Dic11—21no—
68#4343—41no—
69#4343—41no—
70#4341—41no—
71#4341—41no—
72C2×D44—21no—
73C2×D44C2311yescharacteristic
74C2×C4×D11—21no—
75C2×C4×D11D411yescharacteristic
76C2×C4×D11D411yescharacteristic
77C2×C4×D11C2311yescharacteristic
78C2×Dic22C2311yescharacteristic
79C2×Dic22C2311yescharacteristic
80C11×SD16—41no—
81C11×D8—41no—
82C2×C8×C11C2311yescharacteristic
83C2×C8×C11C2311yescharacteristic
84C11×C4⋊C4C2311yescharacteristic
85C11×C22⋊C4—21no—
86C11×C22⋊C4—21no—
87C11×C22⋊C4—21no—
88C42×C11C2311yescharacteristic
89C22⋊Dic11—21no—
90C22⋊Dic11—21no—
91C22⋊Dic11—21no—
92#4326—41no—
93#4324—41no—
94#4324—41no—
95#4323—41no—
96(C2×D11)⋊C4—21no—
97(C2×D11)⋊C4—21no—
98(C2×D11)⋊C4—21no—
99C4⋊Dic11—21no—
100C4⋊Dic11—21no—
101C4⋊Dic11C2311yescharacteristic
102Dic11⋊C4—21no—
103Dic11⋊C4—21no—
104Dic11⋊C4—21no—
105Dic11⋊C4—21no—
106C4×Dic11—21no—
107C4×Dic11D411yescharacteristic
108C4×Dic11D411yescharacteristic
109C4×Dic11C2311yescharacteristic
110C2×C11⋊C8C2311yescharacteristic
111C2×C11⋊C8C2311yescharacteristic
112Dic44—41no—
113#4314—41no—
114#3219—111nomaximal, Sylow
115C23×C11—21no—
116C23×C11—21no—
117C22×D11—21no—
118C22×D11C2×D411yescharacteristic
119Q8×C11—21no—
120Q8×C11—21no—
121D4×C11—21no—
122D4×C11—21no—
123D4×C11—21no—
124D4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—42no—
128C2×C4×C11C2×D411yescharacteristic
129C2×C4×C11C2×D411yescharacteristic
130C2×C4×C11C2411yescharacteristic
131C22⋊D11—42no—
132C22⋊D11—42no—
133C22⋊D11—42no—
134C22⋊D11—42no—
135C2×Dic11—21no—
136C2×Dic11—21no—
137C2×Dic11—21no—
138C2×Dic11—42no—
139C2×Dic11C2×D411yescharacteristic
140C2×Dic11C2×D411yescharacteristic
141C2×Dic11C2×D411yescharacteristic
142D44—21no—
143D44—21no—
144D44—42no—
145C4×D11—21no—
146C4×D11—21no—
147C4×D11—41no—
148C4×D11—41no—
149C4×D11—42no—
150Dic22—21no—
151Dic22—21no—
152Dic22—21no—
153Dic22—21no—
154C8×C11—21no—
155C8×C11—21no—
156C11⋊C8—21no—
157C11⋊C8—21no—
158#532—111no—
159#529—111no—
160#497—111no—
161#496—111no—
162#491—111no—
163#490—111no—
164#464—111no—
165#464—111no—
166#463—111no—
167#463D1111yescharacteristic, complemented
168#452—111no—
169#452—111no—
170#449—111no—
171#449—111no—
172#432—111no—
173C22×C11—41no—
174C22×C11—41no—
175C22×C11—41no—
176C22×C11—41no—
177C22×C11—41no—
178C22×C11—41no—
179C22×C11C22×D411yescharacteristic
180C2×D11—21no—
181C2×D11—21no—
182C2×D11—21no—
183C2×D11—41no—
184C2×D11—41no—
185C2×D11—41no—
186C4×C11—21no—
187C4×C11—21no—
188C4×C11—41no—
189C4×C11—41no—
190C4×C11H(5,𝔽2)11yescharacteristic
191C4×C11H(5,𝔽2)11yescharacteristic
192Dic11—21no—
193Dic11—21no—
194Dic11—21no—
195Dic11—41no—
196Dic11—41no—
197Dic11—41no—
198C2×#41—111no—
199C2×#41—111no—
200C2×Q16—111no—
201C2×Q16—111no—
202C2×SD16—111no—
203C2×SD16—111no—
204C2×SD16—111no—
205C2×SD16C2×D1111yescharacteristic
206C2×D8—111no—
207C2×D8C2×D1111yescharacteristic
208C4⋊Q8—111no—
209#127—111no—
210#126—221no—
211#125—111no—
212#124—111no—
213#124—111no—
214#124C2×D1111yescharacteristic
215#123—221no—
216C22⋊Q8—111no—
217#121—111no—
218#121—221no—
219#121—221no—
220C4×Q8—111no—
221C4×D4—221no—
222C4×D4—221no—
223C4×D4—221no—
224C4×D4C2×D1111yescharacteristic
225#117—221no—
226C2×C42—111no—
227C4⋊C8—111no—
228C4⋊C8C2×D1111yescharacteristic
229#103—111no—
230#103—111no—
231#103—111no—
232#103C2×D1111yescharacteristic
233#102—111no—
234#102—111no—
235#102—111no—
236#102C2×D1111yescharacteristic
237C22⋊C8—111no—
238C22⋊C8—111no—
239#97—111no—
240#97—111no—
241C2×C11—81no—
242C2×C11—81no—
243C2×C11#53511yescharacteristic
244C2×C11#57511yescharacteristic
245C2×C11#57511yescharacteristic
246D11—41no—
247D11—81no—
248#41—441no—
249#41—441no—
250#41—441no—
251#41—441no—
252C2×Q8—111no—
253C2×Q8—111no—
254C2×Q8C22×D1111yescharacteristic
255C2×D4—111no—
256C2×D4—221no—
257C2×D4—221no—
258C2×D4—221no—
259C2×D4—221no—
260C2×D4—221no—
261C2×D4C22×D1111yescharacteristic
262C2×D4C22×D1111yescharacteristic
263C22×C4—21no—
264C22×C4—111no—
265C22×C4—111no—
266C22×C4—111no—
267C22×C4—221no—
268C22×C4—221no—
269Q16—441no—
270Q16—441no—
271SD16—41no—
272SD16—441no—
273SD16—441no—
274SD16—441no—
275D8—41no—
276D8—441no—
277C2×C8—111no—
278C2×C8—111no—
279C2×C8C22×D1111yescharacteristic
280C2×C8C22×D1111yescharacteristic
281C4⋊C4—111no—
282C4⋊C4—221no—
283C4⋊C4—221no—
284C4⋊C4—221no—
285C4⋊C4—221no—
286C4⋊C4—221no—
287C4⋊C4—221no—
288C4⋊C4C22×D1111yescharacteristic
289C22⋊C4—21no—
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—221no—
293C22⋊C4—221no—
294C22⋊C4—221no—
295C22⋊C4—221no—
296C22⋊C4—221no—
297C22⋊C4—221no—
298C42—111no—
299C42—111no—
300C42—111no—
301C42—221no—
302C42C22×D1111yescharacteristic
303C11#321911yescharacteristic, complemented, Sylow
304C23—21no—
305C23—21no—
306C23—111no—
307C23—221no—
308Q8—21no—
309Q8—21no—
310Q8—221no—
311Q8—221no—
312Q8—221no—
313Q8—221no—
314D4—21no—
315D4—21no—
316D4—21no—
317D4—21no—
318D4—221no—
319D4—221no—
320D4—442no—
321D4—442no—
322D4—442no—
323D4—442no—
324D4—442no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—42no—
328C2×C4—111no—
329C2×C4—111no—
330C2×C4—111no—
331C2×C4—221no—
332C2×C4—221no—
333C2×C4—221no—
334C2×C4—221no—
335C2×C4—221no—
336C2×C4—441no—
337C2×C4—441no—
338C2×C4—442no—
339C2×C4—442no—
340C2×C4D4×D1111yescharacteristic
341C2×C4D4×D1111yescharacteristic
342C2×C4C23×D1111yescharacteristic
343C8—21no—
344C8—21no—
345C8—221no—
346C8—221no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—221no—
354C22—221no—
355C22—221no—
356C22—441no—
357C22—441no—
358C22—441no—
359C22C2×D4×D1111yescharacteristic
360C4—21no—
361C4—21no—
362C4—41no—
363C4—41no—
364C4—221no—
365C4—221no—
366C4—221no—
367C4—441no—
368C4—441no—
369C4—441no—
370C4#6703711yescharacteristic
371C4#6704211yescharacteristic
372C2—81no—
373C2—81no—
374C2—441no—
375C2—881no—
376C2#1062313811yescharacteristic
377C2#1062329911yescharacteristic
378C2#1062330411yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#463C2
socleC22×C11C22×D4
hypercenter#463D11
hypocenterC11#3219
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. #10623199C2semidirect
2. #10623088C2semidirect
3. C11×#463C2semidirect
4. #10622785C2semidirect
5. #10622780C2semidirect
6. #10622771C2semidirect
7. #10622767C2semidirect
8. #10622667C2semidirect
9. #10622629C2semidirect
10. #10622458C2semidirect
11. #10622448C2semidirect
12. #10622423C2semidirect
13. #10622410C2semidirect
14. #10622396C2semidirect
15. #10622377C2semidirect
167. #463D11semidirect
303. C11#3219semidirect

Maximal subgroups

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

subgroupindex
#106231992
#106230882
C11×#4632
#106227852
#106227802
#106227712
#106227672
#106226672
#106226292
#106224582
#106224482
#106224232
#106224102
#106223962
#106223772
#321911