Finite Group Databasebeta

← #13080794

Subgroups — #13080794

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
1#10623258C211yesmaximal, characteristic, complemented
2#10623089C211yesmaximal, characteristic
3C11×#461C211yesmaximal, characteristic, complemented
4#10622787C211yesmaximal, characteristic, complemented
5#10622784C211yesmaximal, characteristic, complemented
6#10622783C211yesmaximal, characteristic, complemented
7#10622783C211yesmaximal, characteristic, complemented
8#10622695C211yesmaximal, characteristic, complemented
9#10622631C211yesmaximal, characteristic, complemented
10#10622449C211yesmaximal, characteristic, complemented
11#10622442C211yesmaximal, characteristic, complemented
12#10622428C211yesmaximal, characteristic, complemented
13#10622422C211yesmaximal, characteristic, complemented
14#10622415C211yesmaximal, characteristic, complemented
15D11×#103C211yesmaximal, characteristic, complemented
16C2×Q8×D11C2211yescharacteristic
17C2×Q8×D11C2211yescharacteristic
18C2×C11×SD16C2211yescharacteristic
19C2×C11×SD16C2211yescharacteristic
20C11×C4⋊Q8C2211yescharacteristic
21C4×D4×C11C2211yescharacteristic
22#66999C2211yescharacteristic
23#66999C2211yescharacteristic
24#66991C2211yescharacteristic
25#66991C2211yescharacteristic
26C2×#4324C2211yescharacteristic
27#66982—21no—
28C4×C22⋊D11—21no—
29C2×#4313C2211yescharacteristic
30C2×C8×D11C2211yescharacteristic
31#66949—21no—
32#66949—21no—
33#66946—21no—
34#66945C2211yescharacteristic
35C4⋊C4×D11C2211yescharacteristic
36#66941—21no—
37#66937—21no—
38#66932—21no—
39C4×D44C2211yescharacteristic
40#66923C2211yescharacteristic
41C4×Dic22C2211yescharacteristic
42C11×C4⋊C8C2211yescharacteristic
43C11×#103C2211yescharacteristic
44C11×#103C2211yescharacteristic
45#66899C2211yescharacteristic
46#66899C2211yescharacteristic
47#66899C2211yescharacteristic
48#66899C2211yescharacteristic
49#66896C2211yescharacteristic
50(C2×D11)⋊C8C2211yescharacteristic
51(C2×D11)⋊C8C2211yescharacteristic
52#66882C2211yescharacteristic
53#66881C2211yescharacteristic
54#66880C2211yescharacteristic
55#66880C2211yescharacteristic
56#66874C2211yescharacteristic
57#66871C2211yescharacteristic
58#66867C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C2×Q8×C11C2311yescharacteristic
61C2×D4×C11C2311yescharacteristic
62C22×C4×C11—21no—
63C2×C22⋊D11—21no—
64C2×C22⋊D11—21no—
65Q8×D11—22no—
66Q8×D11—22no—
67Q8×D11—41no—
68Q8×D11—41no—
69C2×D44D411yescharacteristic
70C2×C4×D11—21no—
71C2×C4×D11—21no—
72C2×C4×D11—21no—
73C2×C4×D11C2311yescharacteristic
74C2×C4×D11C2311yescharacteristic
75C2×Dic22—21no—
76C2×Dic22—21no—
77C2×Dic22C2311yescharacteristic
78C11×SD16—41no—
79C11×SD16—41no—
80C2×C8×C11C2311yescharacteristic
81C2×C8×C11C2311yescharacteristic
82C11×C4⋊C4—21no—
83C11×C4⋊C4—21no—
84C11×C4⋊C4C2311yescharacteristic
85C11×C22⋊C4—21no—
86C42×C11C2311yescharacteristic
87C22⋊Dic11—21no—
88C22⋊Dic11—21no—
89#4324—22no—
90(C2×D11)⋊C4—21no—
91(C2×D11)⋊C4—21no—
92(C2×D11)⋊C4—21no—
93(C2×D11)⋊C4D411yescharacteristic
94(C2×D11)⋊C4D411yescharacteristic
95C4⋊Dic11D411yescharacteristic
96C4⋊Dic11C2311yescharacteristic
97C4⋊Dic11C2311yescharacteristic
98C4⋊Dic11C2311yescharacteristic
99Dic11⋊C4—21no—
100Dic11⋊C4—21no—
101Dic11⋊C4—21no—
102Dic11⋊C4—21no—
103Dic11⋊C4—21no—
104Dic11⋊C4—21no—
105C4×Dic11—21no—
106C4×Dic11—21no—
107C2×C11⋊C8C2311yescharacteristic
108C2×C11⋊C8C2311yescharacteristic
109#4313—41no—
110C8×D11—41no—
111#3320—111nomaximal, Sylow
112C23×C11—21no—
113C22×D11C2×D411yescharacteristic
114C22×D11C2×D411yescharacteristic
115Q8×C11—21no—
116Q8×C11—21no—
117Q8×C11—21no—
118Q8×C11—21no—
119D4×C11—21no—
120D4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—81no—
125C2×C4×C11C2×D411yescharacteristic
126C2×C4×C11C2×D411yescharacteristic
127C2×C4×C11C2411yescharacteristic
128C22⋊D11—42no—
129C22⋊D11—81no—
130C2×Dic11—21no—
131C2×Dic11—21no—
132C2×Dic11—21no—
133C2×Dic11—21no—
134C2×Dic11C2×D411yescharacteristic
135C2×Dic11C2×D411yescharacteristic
136D44—22no—
137C4×D11—21no—
138C4×D11—21no—
139C4×D11—21no—
140C4×D11—21no—
141C4×D11—42no—
142C4×D11—42no—
143C4×D11—81no—
144Dic22—21no—
145Dic22—42no—
146Dic22—42no—
147Dic22#4112yes—
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#461D1111yescharacteristic, complemented
161#448—111no—
162#448—111no—
163#440—111no—
164#435—111no—
165#419—111no—
166C2×#103—111no—
167C22×C11—41no—
168C22×C11—41no—
169C22×C11—41no—
170C22×C11C22×D411yescharacteristic
171C2×D11—21no—
172C2×D11—21no—
173C2×D11—21no—
174C2×D11—21no—
175C2×D11—21no—
176C2×D11#13712yes—
177C4×C11—21no—
178C4×C11—21no—
179C4×C11—41no—
180C4×C11—41no—
181C4×C11—41no—
182C4×C11C2×#4111yescharacteristic
183C4×C11H(5,𝔽2)11yescharacteristic
184Dic11—22no—
185Dic11—21no—
186Dic11—21no—
187Dic11—41no—
188Dic11—41no—
189Dic11—41no—
190C22×Q8—111no—
191C22×Q8—111no—
192C2×SD16—111no—
193C2×SD16C2×D1111yescharacteristic
194C2×SD16C2×D1111yescharacteristic
195C2×M16—111no—
196C22×C8—111no—
197C4⋊Q8—221no—
198C4⋊Q8C2×D1111yescharacteristic
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—221no—
212C4×D4—221no—
213C4×D4C2×D1111yescharacteristic
214#117—111no—
215C2×C4⋊C4—111no—
216#107—111no—
217#107—111no—
218#106—111no—
219C4⋊C8C2×D1111yescharacteristic
220#103—111no—
221#103—111no—
222#103—111no—
223#103—111no—
224#103—111no—
225#103—111no—
226#103—111no—
227#103C2×D1111yescharacteristic
228#103C2×D1111yescharacteristic
229#102—111no—
230C22⋊C8—111no—
231C22⋊C8—111no—
232#97—111no—
233C2×C11—81no—
234C2×C11#54611yescharacteristic
235C2×C11C2×#13711yescharacteristic
236C2×C11#57711yescharacteristic
237D11—22no—
238D11—41no—
239C2×Q8—111no—
240C2×Q8—221no—
241C2×Q8—221no—
242C2×Q8—222no—
243C2×Q8—222no—
244C2×Q8—441no—
245C2×Q8—441no—
246C2×Q8C22×D1111yescharacteristic
247C2×Q8C22×D1111yescharacteristic
248C2×D4—111no—
249C2×D4—221no—
250C2×D4—221no—
251C2×D4C22×D1111yescharacteristic
252C22×C4—21no—
253C22×C4—111no—
254C22×C4—111no—
255C22×C4—221no—
256C22×C4—221no—
257C22×C4—221no—
258SD16—41no—
259SD16—41no—
260SD16—222no—
261M16—441no—
262C2×C8—111no—
263C2×C8—111no—
264C2×C8—441no—
265C2×C8C22×D1111yescharacteristic
266C2×C8C22×D1111yescharacteristic
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—111no—
270C4⋊C4—111no—
271C4⋊C4—111no—
272C4⋊C4—111no—
273C4⋊C4—221no—
274C4⋊C4—221no—
275C4⋊C4—221no—
276C4⋊C4—221no—
277C4⋊C4—221no—
278C4⋊C4—221no—
279C4⋊C4C22×D1111yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—111no—
282C22⋊C4—111no—
283C22⋊C4—221no—
284C22⋊C4—221no—
285C22⋊C4—221no—
286C22⋊C4—221no—
287C22⋊C4—221no—
288C42—221no—
289C42—221no—
290C42C22×D1111yescharacteristic
291C11#332011yescharacteristic, complemented, Sylow
292C23—21no—
293C23—111no—
294C23—111no—
295Q8—21no—
296Q8—21no—
297Q8—21no—
298Q8—21no—
299Q8—112no—
300Q8—221no—
301Q8—442no—
302Q8—442no—
303D4—21no—
304D4—21no—
305D4—222no—
306D4—442no—
307D4—881no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—81no—
312C2×C4—111no—
313C2×C4—111no—
314C2×C4—221no—
315C2×C4—221no—
316C2×C4—221no—
317C2×C4—221no—
318C2×C4—221no—
319C2×C4—221no—
320C2×C4—221no—
321C2×C4—221no—
322C2×C4—442no—
323C2×C4—442no—
324C2×C4—881no—
325C2×C4D4×D1111yescharacteristic
326C2×C4D4×D1111yescharacteristic
327C2×C4C23×D1111yescharacteristic
328C8—21no—
329C8—21no—
330C8—221no—
331C8—221no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—112no—
336C22—221no—
337C22—221no—
338C22—221no—
339C22—221no—
340C22—221no—
341C22C2×D4×D1111yescharacteristic
342C4—21no—
343C4—21no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4—221no—
348C4—221no—
349C4—222no—
350C4—441no—
351C4—441no—
352C4—441no—
353C4#6703711yescharacteristic
354C4#41×D1111yescharacteristic
355C2—81no—
356C2—222no—
357C2—441no—
358C2#1062314311yescharacteristic
359C2#1062329311yescharacteristic
360C2D11×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#461C2
socleC22×C11C22×D4
prime radical#10623089C2
hypercenter#461D11
hypocenterC11#3320
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. #10623258C2semidirect
3. C11×#461C2semidirect
4. #10622787C2semidirect
5. #10622784C2semidirect
6. #10622783C2semidirect
7. #10622783C2semidirect
8. #10622695C2semidirect
9. #10622631C2semidirect
10. #10622449C2semidirect
11. #10622442C2semidirect
12. #10622428C2semidirect
13. #10622422C2semidirect
14. #10622415C2semidirect
15. D11×#103C2semidirect
160. #461D11semidirect
291. C11#3320semidirect

Maximal subgroups

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

subgroupindex
#106232582
#106230892
C11×#4612
#106227872
#106227842
#106227832
#106226952
#106226312
#106224492
#106224422
#106224282
#106224222
#106224152
D11×#1032
#332011