Finite Group Databasebeta

← #13080950

Subgroups — #13080950

Order 1408.

398 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623365C211yesmaximal, characteristic
2#10623042C211yesmaximal, characteristic, complemented
3C11×#417C211yesmaximal, characteristic, complemented
4#10622852C211yesmaximal, characteristic, complemented
5#10622747C211yesmaximal, characteristic, complemented
6#10622741C211yesmaximal, characteristic, complemented
7#10622580C211yesmaximal, characteristic, complemented
8#10622423C211yesmaximal, characteristic, complemented
9#10622416C211yesmaximal, characteristic, complemented
10#10622407C211yesmaximal, characteristic, complemented
11#10622403C211yesmaximal, characteristic, complemented
12#10622393C211yesmaximal, characteristic, complemented
13#10622387C211yesmaximal, characteristic, complemented
14#10622375C211yesmaximal, characteristic, complemented
15#10622373C211yesmaximal, characteristic, complemented
16C2×C11×#41C2211yescharacteristic
17C2×#4343C2211yescharacteristic
18C2×C11×M16C2211yescharacteristic
19C2×C11×C4⋊C4C2211yescharacteristic
20Q8×Dic11C2211yescharacteristic
21C2×#4326C2211yescharacteristic
22#66993—21no—
23#66993C2211yescharacteristic
24#66991—21no—
25#66991C2211yescharacteristic
26C2×#4324C2211yescharacteristic
27#66983—21no—
28#66983C2211yescharacteristic
29C4×C22⋊D11—21no—
30C4×C22⋊D11—21no—
31C4×C22⋊D11C2211yescharacteristic
32#66977—21no—
33#66977C2211yescharacteristic
34C2×#4314C2211yescharacteristic
35C2×#4313C2211yescharacteristic
36#66950C2211yescharacteristic
37#66949—21no—
38C4⋊C4×D11C2211yescharacteristic
39#66942—21no—
40#66941C2211yescharacteristic
41#66940C2211yescharacteristic
42C11×#103C2211yescharacteristic
43C11×#103C2211yescharacteristic
44C11×#102C2211yescharacteristic
45C11×#102C2211yescharacteristic
46#66899C2211yescharacteristic
47#66896C2211yescharacteristic
48C22⋊(C11⋊C8)C2211yescharacteristic
49#66885C2211yescharacteristic
50(C2×D11)⋊C8C2211yescharacteristic
51#66882C2211yescharacteristic
52#66880C2211yescharacteristic
53Dic11⋊C8C2211yescharacteristic
54C8×Dic11C2211yescharacteristic
55#66873C2211yescharacteristic
56#66873C2211yescharacteristic
57#66871C2211yescharacteristic
58#66871C2211yescharacteristic
59C11×#41—22no—
60C11×#41—41no—
61C2×Q8×C11C2311yescharacteristic
62C2×D4×C11—21no—
63C2×D4×C11C2311yescharacteristic
64C22×C4×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11C2311yescharacteristic
67C2×C22⋊D11—21no—
68C2×C22⋊D11—21no—
69C2×C22⋊D11—21no—
70C2×C22⋊D11—21no—
71C2×C22⋊D11D411yescharacteristic
72#4343—22no—
73#4343—41no—
74C2×D44—21no—
75C2×D44C2311yescharacteristic
76C2×C4×D11—21no—
77C2×C4×D11—21no—
78C2×C4×D11C2311yescharacteristic
79C2×Dic22—21no—
80C2×Dic22C2311yescharacteristic
81C11×M16—41no—
82C2×C8×C11C2311yescharacteristic
83C2×C8×C11C2311yescharacteristic
84C11×C4⋊C4—21no—
85C11×C4⋊C4C2311yescharacteristic
86C11×C4⋊C4C2311yescharacteristic
87C22⋊Dic11—21no—
88C22⋊Dic11—21no—
89C22⋊Dic11D411yescharacteristic
90#4326—22no—
91#4324—41no—
92(C2×D11)⋊C4—21no—
93(C2×D11)⋊C4—21no—
94(C2×D11)⋊C4D411yescharacteristic
95C4⋊Dic11—21no—
96C4⋊Dic11—21no—
97C4⋊Dic11C2311yescharacteristic
98C4⋊Dic11C2311yescharacteristic
99Dic11⋊C4—21no—
100Dic11⋊C4—21no—
101Dic11⋊C4—21no—
102Dic11⋊C4—21no—
103Dic11⋊C4D411yescharacteristic
104C4×Dic11—21no—
105C4×Dic11—21no—
106C4×Dic11C2311yescharacteristic
107C2×C11⋊C8C2311yescharacteristic
108C2×C11⋊C8C2311yescharacteristic
109#4314—41no—
110#4313—41no—
111#3333—111nomaximal, Sylow
112C23×C11—21no—
113C23×C11C2×D411yescharacteristic
114C22×D11—21no—
115C22×D11C2×D411yescharacteristic
116Q8×C11—21no—
117Q8×C11#4112yes—
118D4×C11—21no—
119D4×C11—21no—
120D4×C11—42no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—42no—
127C2×C4×C11—81no—
128C2×C4×C11C2×D411yescharacteristic
129C2×C4×C11C2411yescharacteristic
130C22⋊D11—22no—
131C22⋊D11—42no—
132C22⋊D11—81no—
133C22⋊D11—81no—
134C22⋊D11—81no—
135C2×Dic11—21no—
136C2×Dic11—21no—
137C2×Dic11—21no—
138C2×Dic11C2×D411yescharacteristic
139C2×Dic11C2×D411yescharacteristic
140C2×Dic11C2×D411yescharacteristic
141D44—21no—
142D44—21no—
143D44—42no—
144C4×D11—21no—
145C4×D11—21no—
146C4×D11—42no—
147C4×D11—81no—
148Dic22—21no—
149Dic22—21no—
150Dic22—81no—
151C8×C11—21no—
152C8×C11—21no—
153C11⋊C8—21no—
154C11⋊C8—21no—
155#554—111no—
156#550—111no—
157#486—111no—
158#480—111no—
159#480—111no—
160#477—111no—
161#468—111no—
162#468—111no—
163#460—111no—
164#452—111no—
165#452—111no—
166C4×Q16—111no—
167#436—111no—
168#417—111no—
169#417D1111yescharacteristic, complemented
170C22×C11—21no—
171C22×C11—21no—
172C22×C11—21no—
173C22×C11—41no—
174C22×C11—41no—
175C22×C11—41no—
176C22×C11C22×D411yescharacteristic
177C2×D11—21no—
178C2×D11—21no—
179C2×D11—21no—
180C2×D11—41no—
181C2×D11—41no—
182C2×D11—41no—
183C4×C11—21no—
184C4×C11—22no—
185C4×C11—41no—
186C4×C11—41no—
187C4×C11C2×#4111yescharacteristic
188C4×C11H(5,𝔽2)11yescharacteristic
189Dic11—21no—
190Dic11—21no—
191Dic11—41no—
192Dic11—41no—
193Dic11—41no—
194Dic11#13712yes—
195C2×#41—111no—
196C2×#41C2×D1111yescharacteristic
197C2×Q16—111no—
198C2×SD16—111no—
199C2×SD16—111no—
200C2×M16—111no—
201C2×M16C2×D1111yescharacteristic
202C4⋊Q8—111no—
203#127—111no—
204#127—221no—
205#125—221no—
206C22⋊Q8—111no—
207C22⋊Q8—111no—
208C22⋊Q8—221no—
209C22⋊Q8—221no—
210#121—111no—
211#121—111no—
212#121—221no—
213#121—221no—
214C4×Q8—111no—
215C4×Q8—111no—
216C4×D4—111no—
217C4×D4—221no—
218C4×D4—221no—
219C2×C4⋊C4—111no—
220C2×C4⋊C4C2×D1111yescharacteristic
221#107—111no—
222#107—111no—
223#107—111no—
224C4⋊C8—111no—
225#103—111no—
226#103—111no—
227#103C2×D1111yescharacteristic
228#103C2×D1111yescharacteristic
229#102—111no—
230#102—111no—
231#102—111no—
232#102—111no—
233#102C2×D1111yescharacteristic
234#102C2×D1111yescharacteristic
235C22⋊C8—111no—
236C22⋊C8—111no—
237C4×C8—111no—
238C2×C11—41no—
239C2×C11—81no—
240C2×C11#54611yescharacteristic
241C2×C11C2×#13711yescharacteristic
242C2×C11#57611yescharacteristic
243D11—41no—
244D11—81no—
245#41—22no—
246#41—41no—
247#41—222no—
248#41—441no—
249C2×Q8—111no—
250C2×Q8—221no—
251C2×Q8C22×D1111yescharacteristic
252C2×D4—21no—
253C2×D4—111no—
254C2×D4—111no—
255C2×D4—221no—
256C2×D4—221no—
257C2×D4—221no—
258C2×D4—221no—
259C2×D4—221no—
260C2×D4C22×D1111yescharacteristic
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—111no—
264C22×C4—221no—
265C22×C4—221no—
266C22×C4C22×D1111yescharacteristic
267Q16—222no—
268SD16—441no—
269SD16—441no—
270M16—41no—
271M16—441no—
272C2×C8—111no—
273C2×C8—111no—
274C2×C8C22×D1111yescharacteristic
275C2×C8C22×D1111yescharacteristic
276C4⋊C4—21no—
277C4⋊C4—111no—
278C4⋊C4—111no—
279C4⋊C4—111no—
280C4⋊C4—221no—
281C4⋊C4—221no—
282C4⋊C4—221no—
283C4⋊C4—221no—
284C4⋊C4—221no—
285C4⋊C4—221no—
286C4⋊C4C22×D1111yescharacteristic
287C4⋊C4C22×D1111yescharacteristic
288C22⋊C4—111no—
289C22⋊C4—111no—
290C22⋊C4—221no—
291C22⋊C4—221no—
292C22⋊C4—221no—
293C22⋊C4—221no—
294C42—111no—
295C42—221no—
296C42—221no—
297C11#333311yescharacteristic, complemented, Sylow
298C23—21no—
299C23—111no—
300C23—221no—
301C23D4×D1111yescharacteristic
302Q8—21no—
303Q8—221no—
304Q8—221no—
305Q8—881no—
306Q8#433912yes—
307D4—21no—
308D4—21no—
309D4—42no—
310D4—222no—
311D4—221no—
312D4—221no—
313D4—442no—
314D4—442no—
315D4—881no—
316D4—881no—
317D4—881no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—42no—
324C2×C4—81no—
325C2×C4—111no—
326C2×C4—111no—
327C2×C4—111no—
328C2×C4—221no—
329C2×C4—221no—
330C2×C4—221no—
331C2×C4—221no—
332C2×C4—221no—
333C2×C4—442no—
334C2×C4—881no—
335C2×C4D4×D1111yescharacteristic
336C2×C4C23×D1111yescharacteristic
337C8—21no—
338C8—21no—
339C8—221no—
340C8—221no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—221no—
348C22—221no—
349C22—221no—
350C22—441no—
351C22—441no—
352C22—441no—
353C22C2×D4×D1111yescharacteristic
354C4—21no—
355C4—22no—
356C4—41no—
357C4—41no—
358C4—112no—
359C4—221no—
360C4—221no—
361C4—441no—
362C4—441no—
363C4—441no—
364C4C2×#433911yescharacteristic
365C4#6703711yescharacteristic
366C2—41no—
367C2—81no—
368C2—441no—
369C2—881no—
370C2#1062302111yescharacteristic
371C2#1062330511yescharacteristic
372C2D11×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#417C2
socleC22×C11C22×D4
prime radical#10623365C2
hypercenter#417D11
hypocenterC11#3333
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
2. #10623042C2semidirect
3. C11×#417C2semidirect
4. #10622852C2semidirect
5. #10622747C2semidirect
6. #10622741C2semidirect
7. #10622580C2semidirect
8. #10622423C2semidirect
9. #10622416C2semidirect
10. #10622407C2semidirect
11. #10622403C2semidirect
12. #10622393C2semidirect
13. #10622387C2semidirect
14. #10622375C2semidirect
15. #10622373C2semidirect
169. #417D11semidirect
297. C11#3333semidirect

Maximal subgroups

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

subgroupindex
#106233652
#106230422
C11×#4172
#106228522
#106227472
#106227412
#106225802
#106224232
#106224162
#106224072
#106224032
#106223932
#106223872
#106223752
#106223732
#333311