Finite Group Databasebeta

← #13080783

Subgroups — #13080783

Order 1408.

388 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×C22⋊D11C211yesmaximal, characteristic, complemented
2#10623045C211yesmaximal, characteristic
3C2×C11×#103C211yesmaximal, characteristic, complemented
4#10622840C211yesmaximal, characteristic, complemented
5#10622727C211yesmaximal, characteristic, complemented
6#10622724C211yesmaximal, characteristic, complemented
7#10622583C211yesmaximal, characteristic, complemented
8#10622431C211yesmaximal, characteristic, complemented
9#10622430C211yesmaximal, characteristic, complemented
10#10622428C211yesmaximal, characteristic, complemented
11#10622425C211yesmaximal, characteristic, complemented
12#10622419C211yesmaximal, characteristic, complemented
13#10622415C211yesmaximal, characteristic, complemented
14#10622412C211yesmaximal, characteristic, complemented
15#10622410C211yesmaximal, characteristic, complemented
16C22×Q8×C11C2211yescharacteristic
17C2×Q8×D11C2211yescharacteristic
18C22×C8×C11C2211yescharacteristic
19C2×C11×C4⋊C4C2211yescharacteristic
20#66999—21no—
21#66999C2211yescharacteristic
22Q8×Dic11C2211yescharacteristic
23#66997—21no—
24#66997C2211yescharacteristic
25C2×#4325C2211yescharacteristic
26C2×#4325C2211yescharacteristic
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#66951—21no—
37#66948C2211yescharacteristic
38#66947—21no—
39#66946C2211yescharacteristic
40#66945C2211yescharacteristic
41#66943C2211yescharacteristic
42C11×#103C2211yescharacteristic
43C11×#103C2211yescharacteristic
44C11×#103C2211yescharacteristic
45C11×#103C2211yescharacteristic
46#66899C2211yescharacteristic
47#66899C2211yescharacteristic
48C22⋊(C11⋊C8)C2211yescharacteristic
49#66885C2211yescharacteristic
50(C2×D11)⋊C8C2211yescharacteristic
51#66881C2211yescharacteristic
52#66880C2211yescharacteristic
53#66879C2211yescharacteristic
54Dic11⋊C8C2211yescharacteristic
55#66874C2211yescharacteristic
56#66874C2211yescharacteristic
57#66871C2211yescharacteristic
58#66871C2211yescharacteristic
59C2×Q8×C11—21no—
60C2×Q8×C11—22no—
61C2×Q8×C11—41no—
62C2×Q8×C11C2311yescharacteristic
63C2×Q8×C11C2311yescharacteristic
64C22×C4×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11C2311yescharacteristic
67C2×C22⋊D11—21no—
68C2×C22⋊D11D411yescharacteristic
69Q8×D11—22no—
70Q8×D11—41no—
71C2×D44—21no—
72C2×D44C2311yescharacteristic
73C2×C4×D11—21no—
74C2×C4×D11—21no—
75C2×C4×D11C2311yescharacteristic
76C2×Dic22—21no—
77C2×Dic22C2311yescharacteristic
78C2×C8×C11—41no—
79C2×C8×C11C2311yescharacteristic
80C2×C8×C11C2311yescharacteristic
81C11×C4⋊C4—21no—
82C11×C4⋊C4C2311yescharacteristic
83C11×C4⋊C4C2311yescharacteristic
84C22⋊Dic11—21no—
85C22⋊Dic11D411yescharacteristic
86#4325—22no—
87#4325—41no—
88(C2×D11)⋊C4—21no—
89(C2×D11)⋊C4—21no—
90(C2×D11)⋊C4—21no—
91(C2×D11)⋊C4—21no—
92(C2×D11)⋊C4—21no—
93(C2×D11)⋊C4D411yescharacteristic
94C4⋊Dic11—21no—
95C4⋊Dic11—21no—
96C4⋊Dic11C2311yescharacteristic
97C4⋊Dic11C2311yescharacteristic
98Dic11⋊C4—21no—
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#3320—111nomaximal, Sylow
112C23×C11C2×D411yescharacteristic
113C22×D11—21no—
114C22×D11C2×D411yescharacteristic
115Q8×C11—21no—
116Q8×C11—21no—
117Q8×C11—21no—
118Q8×C11—42no—
119Q8×C11#4112yes—
120C2×C4×C11—21no—
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—
132C2×Dic11—21no—
133C2×Dic11—21no—
134C2×Dic11—21no—
135C2×Dic11C2×D411yescharacteristic
136C2×Dic11C2×D411yescharacteristic
137C2×Dic11C2×D411yescharacteristic
138D44—21no—
139D44—21no—
140D44—81no—
141C4×D11—21no—
142C4×D11—21no—
143C4×D11—42no—
144C4×D11—81no—
145Dic22—21no—
146Dic22—21no—
147Dic22—42no—
148C8×C11—21no—
149C8×C11—21no—
150C11⋊C8—21no—
151C11⋊C8—21no—
152#553—111no—
153D4×Q8—111no—
154#491—111no—
155#485—111no—
156#484—111no—
157#479—111no—
158#468—111no—
159#465—111no—
160#461—111no—
161#448—111no—
162#448—111no—
163#440—111no—
164#435—111no—
165#419—111no—
166C2×#103D1111yescharacteristic, complemented
167C22×C11—21no—
168C22×C11—21no—
169C22×C11#13712yes—
170C22×C11C22×D411yescharacteristic
171C2×D11—21no—
172C2×D11—21no—
173C2×D11—21no—
174C2×D11—41no—
175C2×D11—41no—
176C2×D11—41no—
177C4×C11—21no—
178C4×C11—22no—
179C4×C11—41no—
180C4×C11—41no—
181C4×C11—41no—
182C4×C11C2×#4111yescharacteristic
183C4×C11H(5,𝔽2)11yescharacteristic
184Dic11—21no—
185Dic11—21no—
186Dic11—21no—
187Dic11—41no—
188Dic11—41no—
189Dic11—41no—
190C22×Q8—111no—
191C22×Q8C2×D1111yescharacteristic
192C2×SD16—111no—
193C2×SD16—111no—
194C2×SD16—111no—
195C2×M16—111no—
196C22×C8C2×D1111yescharacteristic
197C4⋊Q8—111no—
198C4⋊Q8—221no—
199#126—221no—
200#125—111no—
201#123—221no—
202C22⋊Q8—111no—
203C22⋊Q8—111no—
204C22⋊Q8—221no—
205C22⋊Q8—221no—
206#121—111no—
207#121—111no—
208#121—221no—
209C4×Q8—111no—
210C4×D4—111no—
211C4×D4—111no—
212C4×D4—221no—
213C4×D4—221no—
214#117—111no—
215C2×C4⋊C4C2×D1111yescharacteristic
216#107—111no—
217#107—111no—
218#106—111no—
219C4⋊C8—111no—
220#103—111no—
221#103—111no—
222#103—111no—
223#103—111no—
224#103—111no—
225#103C2×D1111yescharacteristic
226#103C2×D1111yescharacteristic
227#103C2×D1111yescharacteristic
228#103C2×D1111yescharacteristic
229#102—111no—
230C22⋊C8—111no—
231C22⋊C8—111no—
232#97—111no—
233C2×C11—22no—
234C2×C11#54611yescharacteristic
235C2×C11C2×#13711yescharacteristic
236C2×C11#57711yescharacteristic
237D11—41no—
238D11—81no—
239C2×Q8—21no—
240C2×Q8—22no—
241C2×Q8—41no—
242C2×Q8—111no—
243C2×Q8—221no—
244C2×Q8—222no—
245C2×Q8—441no—
246C2×Q8C22×D1111yescharacteristic
247C2×Q8C22×D1111yescharacteristic
248C2×D4—111no—
249C2×D4—111no—
250C2×D4—221no—
251C2×D4—221no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—111no—
255C22×C4—221no—
256C22×C4—221no—
257C22×C4C22×D1111yescharacteristic
258SD16—222no—
259SD16—441no—
260SD16—441no—
261M16—441no—
262C2×C8—41no—
263C2×C8—111no—
264C2×C8—111no—
265C2×C8C22×D1111yescharacteristic
266C2×C8C22×D1111yescharacteristic
267C4⋊C4—21no—
268C4⋊C4—111no—
269C4⋊C4—111no—
270C4⋊C4—111no—
271C4⋊C4—221no—
272C4⋊C4—221no—
273C4⋊C4—221no—
274C4⋊C4—221no—
275C4⋊C4—221no—
276C4⋊C4—221no—
277C4⋊C4—221no—
278C4⋊C4C22×D1111yescharacteristic
279C4⋊C4C22×D1111yescharacteristic
280C22⋊C4—111no—
281C22⋊C4—111no—
282C22⋊C4—221no—
283C22⋊C4—221no—
284C22⋊C4—221no—
285C22⋊C4—221no—
286C22⋊C4—221no—
287C22⋊C4—221no—
288C42—111no—
289C42—221no—
290C42—221no—
291C11#332011yescharacteristic, complemented, Sylow
292C23—111no—
293C23—221no—
294C23D4×D1111yescharacteristic
295Q8—21no—
296Q8—21no—
297Q8—21no—
298Q8—42no—
299Q8—221no—
300Q8—221no—
301Q8—442no—
302Q8#433912yes—
303D4—222no—
304D4—221no—
305D4—221no—
306D4—442no—
307D4—881no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—42no—
315C2×C4—81no—
316C2×C4—111no—
317C2×C4—111no—
318C2×C4—111no—
319C2×C4—221no—
320C2×C4—221no—
321C2×C4—221no—
322C2×C4—221no—
323C2×C4—221no—
324C2×C4—442no—
325C2×C4—881no—
326C2×C4D4×D1111yescharacteristic
327C2×C4C23×D1111yescharacteristic
328C8—21no—
329C8—21no—
330C8—221no—
331C8—221no—
332C22—21no—
333C22—21no—
334C22—221no—
335C22—221no—
336C22—221no—
337C22—441no—
338C22—441no—
339C22—441no—
340C22#6697112yes—
341C22C2×D4×D1111yescharacteristic
342C4—21no—
343C4—22no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4—221no—
348C4—221no—
349C4—221no—
350C4—441no—
351C4—441no—
352C4—441no—
353C4C2×#433911yescharacteristic
354C4#6703711yescharacteristic
355C2—22no—
356C2—441no—
357C2—881no—
358C2#1062302111yescharacteristic
359C2#1062329311yescharacteristic
360C2C2×#6697111yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC2×C11×#103C2
socleC22×C11C22×D4
prime radical#10623045C2
hypercenterC2×#103D11
hypocenterC11#3320
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
1. Q8×C22⋊D11C2semidirect
3. C2×C11×#103C2semidirect
4. #10622840C2semidirect
5. #10622727C2semidirect
6. #10622724C2semidirect
7. #10622583C2semidirect
8. #10622431C2semidirect
9. #10622430C2semidirect
10. #10622428C2semidirect
11. #10622425C2semidirect
12. #10622419C2semidirect
13. #10622415C2semidirect
14. #10622412C2semidirect
15. #10622410C2semidirect
166. C2×#103D11semidirect
291. C11#3320semidirect

Maximal subgroups

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

subgroupindex
Q8×C22⋊D112
#106230452
C2×C11×#1032
#106228402
#106227272
#106227242
#106225832
#106224312
#106224302
#106224282
#106224252
#106224192
#106224152
#106224122
#106224102
#332011