Finite Group Databasebeta

← #13078680

Subgroups — #13078680

Order 1408.

390 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41×Dic11C211yesmaximal, characteristic
2#10623153C211yesmaximal, characteristic, complemented
3C11×#452C211yesmaximal, characteristic
4#10622852C211yesmaximal, characteristic
5Q16×Dic11C211yesmaximal, characteristic, complemented
6#10622795C211yesmaximal, characteristic, complemented
7#10622775C211yesmaximal, characteristic, complemented
8SD16×Dic11C211yesmaximal, characteristic, complemented
9#10622658C211yesmaximal, characteristic, complemented
10#10622404C211yesmaximal, characteristic, complemented
11#10622403C211yesmaximal, characteristic, complemented
12#10622372C211yesmaximal, characteristic, complemented
13#10622371C211yesmaximal, characteristic, complemented
14#10622336C211yesmaximal, characteristic, complemented
15#10622331C211yesmaximal, characteristic, complemented
16C2×C11×#41C2211yescharacteristic
17C2×C11×Q16C2211yescharacteristic
18C2×C11×SD16C2211yescharacteristic
19C11×C22⋊Q8C2211yescharacteristic
20Q8×Dic11C2211yescharacteristic
21Q8×Dic11C2211yescharacteristic
22Q8×Dic11C2211yescharacteristic
23#66997C2211yescharacteristic
24C2×#4326C2211yescharacteristic
25D4×Dic11—21no—
26D4×Dic11—21no—
27D4×Dic11C2211yescharacteristic
28D4×Dic11C2211yescharacteristic
29C2×#4324C2211yescharacteristic
30#66979—21no—
31#66979C2211yescharacteristic
32#66977C2211yescharacteristic
33C2×C4×Dic11—21no—
34C2×C4×Dic11C2211yescharacteristic
35#66942—21no—
36#66941C2211yescharacteristic
37#66940—21no—
38#66940C2211yescharacteristic
39#66931—21no—
40#66930—21no—
41C11×#103C2211yescharacteristic
42C11×#102C2211yescharacteristic
43C11×C22⋊C8C2211yescharacteristic
44#66899C2211yescharacteristic
45#66899C2211yescharacteristic
46#66899C2211yescharacteristic
47#66896C2211yescharacteristic
48C22⋊(C11⋊C8)C2211yescharacteristic
49#66882C2211yescharacteristic
50#66881C2211yescharacteristic
51#66880C2211yescharacteristic
52#66880C2211yescharacteristic
53Dic11⋊C8C2211yescharacteristic
54Dic11⋊C8C2211yescharacteristic
55C8×Dic11C2211yescharacteristic
56C8×Dic11C2211yescharacteristic
57#66872C2211yescharacteristic
58#66871C2211yescharacteristic
59C11×#41—22no—
60C11×#41—22no—
61C2×Q8×C11C2311yescharacteristic
62C2×Q8×C11C2311yescharacteristic
63C2×D4×C11—21no—
64C2×D4×C11C2311yescharacteristic
65C22×C4×C11—21no—
66C22×C4×C11C2311yescharacteristic
67C22×Dic11—21no—
68C22×Dic11—21no—
69C22×Dic11D411yescharacteristic
70C22×Dic11D411yescharacteristic
71C2×Dic22—21no—
72C2×Dic22C2311yescharacteristic
73C11×Q16—22no—
74C11×SD16—22no—
75C2×C8×C11C2311yescharacteristic
76C2×C8×C11C2311yescharacteristic
77C11×C4⋊C4—21no—
78C11×C4⋊C4C2311yescharacteristic
79C11×C22⋊C4—21no—
80C22⋊Dic11—21no—
81C22⋊Dic11—21no—
82C22⋊Dic11—21no—
83C22⋊Dic11—21no—
84#4326—22no—
85#4324—22no—
86C4⋊Dic11—21no—
87C4⋊Dic11—21no—
88C4⋊Dic11—21no—
89C4⋊Dic11C2311yescharacteristic
90C4⋊Dic11C2311yescharacteristic
91C4⋊Dic11C2311yescharacteristic
92Dic11⋊C4—21no—
93Dic11⋊C4—21no—
94Dic11⋊C4—21no—
95Dic11⋊C4—21no—
96Dic11⋊C4—21no—
97C4×Dic11—21no—
98C4×Dic11—21no—
99C4×Dic11—21no—
100C4×Dic11—21no—
101C4×Dic11—21no—
102C4×Dic11D411yescharacteristic
103C4×Dic11D411yescharacteristic
104C4×Dic11C2311yescharacteristic
105C4×Dic11C2311yescharacteristic
106C2×C11⋊C8C2311yescharacteristic
107C2×C11⋊C8C2311yescharacteristic
108#3107—111nomaximal, Sylow
109C23×C11—21no—
110C23×C11C2×D411yescharacteristic
111Q8×C11—21no—
112Q8×C11—21no—
113Q8×C11—21no—
114Q8×C11#4112yes—
115D4×C11—24no—
116D4×C11—21no—
117D4×C11#4112yes—
118C2×C4×C11—24no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11C2×D411yescharacteristic
125C2×C4×C11C2411yescharacteristic
126C2×Dic11—22no—
127C2×Dic11—22no—
128C2×Dic11—21no—
129C2×Dic11—21no—
130C2×Dic11—21no—
131C2×Dic11—21no—
132C2×Dic11—42no—
133C2×Dic11—42no—
134C2×Dic11C2×D411yescharacteristic
135C2×Dic11C2×D411yescharacteristic
136C2×Dic11C2×D411yescharacteristic
137C2×Dic11C2×D411yescharacteristic
138Dic22—21no—
139Dic22—21no—
140Dic22—42no—
141C8×C11—21no—
142C8×C11—21no—
143C11⋊C8—21no—
144C11⋊C8—21no—
145#533—111no—
146C4×#41—111no—
147#485—111no—
148#485—111no—
149#475—111no—
150#474—111no—
151#462—111no—
152#461—111no—
153#452—111no—
154#452D1111yescharacteristic
155C4×Q16—111no—
156C4×Q16—111no—
157C4×SD16—111no—
158C4×SD16—111no—
159#431—111no—
160C22×C11—21no—
161C22×C11—22no—
162C22×C11—21no—
163C22×C11—21no—
164C22×C11—41no—
165C22×C11—41no—
166C22×C11C22×D411yescharacteristic
167C4×C11—21no—
168C4×C11—22no—
169C4×C11—41no—
170C4×C11—41no—
171C4×C11C2×#4111yescharacteristic
172C4×C11C2×#4111yescharacteristic
173Dic11—21no—
174Dic11—21no—
175Dic11—41no—
176Dic11—41no—
177Dic11—41no—
178Dic11—41no—
179Dic11#13512yes—
180Dic11#13712yes—
181C2×#41C2×D1111yescharacteristic
182C2×Q16—111no—
183C2×Q16C2×D1111yescharacteristic
184C2×SD16—111no—
185C2×SD16C2×D1111yescharacteristic
186C4⋊Q8—111no—
187C4⋊Q8—111no—
188#125—221no—
189C22⋊Q8—111no—
190C22⋊Q8—221no—
191C22⋊Q8C2×D1111yescharacteristic
192C4×Q8—111no—
193C4×Q8—111no—
194C4×Q8—111no—
195C4×Q8—111no—
196C4×Q8—221no—
197C4×D4—111no—
198C4×D4—111no—
199C4×D4—221no—
200C4×D4—221no—
201#117—111no—
202#117—221no—
203#117—221no—
204C2×C42—111no—
205C2×C42—221no—
206#107—111no—
207#107—111no—
208#106—111no—
209#106—111no—
210C4⋊C8—111no—
211C4⋊C8—111no—
212#103—111no—
213#103—111no—
214#103—111no—
215#103—111no—
216#103—111no—
217#103C2×D1111yescharacteristic
218#102—111no—
219#102C2×D1111yescharacteristic
220C22⋊C8—111no—
221C22⋊C8C2×D1111yescharacteristic
222C4×C8—111no—
223C4×C8—111no—
224C2×C11—41no—
225C2×C11—42no—
226C2×C11#52511yescharacteristic
227C2×C11C2×#13511yescharacteristic
228C2×C11C2×#13711yescharacteristic
229#41—22no—
230#41—22no—
231C2×Q8—111no—
232C2×Q8—221no—
233C2×Q8C22×D1111yescharacteristic
234C2×Q8C22×D1111yescharacteristic
235C2×D4—21no—
236C2×D4C22×D1111yescharacteristic
237C22×C4—21no—
238C22×C4—111no—
239C22×C4—111no—
240C22×C4—221no—
241C22×C4—221no—
242C22×C4C22×D1111yescharacteristic
243Q16—22no—
244Q16—222no—
245SD16—22no—
246SD16—222no—
247C2×C8—111no—
248C2×C8—111no—
249C2×C8C22×D1111yescharacteristic
250C2×C8C22×D1111yescharacteristic
251C4⋊C4—21no—
252C4⋊C4—111no—
253C4⋊C4—111no—
254C4⋊C4—111no—
255C4⋊C4—221no—
256C4⋊C4—221no—
257C4⋊C4—221no—
258C4⋊C4—221no—
259C4⋊C4—221no—
260C4⋊C4—221no—
261C4⋊C4—221no—
262C4⋊C4—221no—
263C4⋊C4C22×D1111yescharacteristic
264C22⋊C4—21no—
265C22⋊C4—221no—
266C22⋊C4—221no—
267C22⋊C4—221no—
268C22⋊C4—221no—
269C42—111no—
270C42—111no—
271C42—111no—
272C42—111no—
273C42—221no—
274C42—221no—
275C42—221no—
276C42—221no—
277C42—221no—
278C11#310711yescharacteristic, complemented, Sylow
279C23—21no—
280C23D4×D1111yescharacteristic
281Q8—21no—
282Q8—21no—
283Q8—21no—
284Q8—221no—
285Q8—221no—
286Q8—442no—
287Q8#434112yes—
288D4—24no—
289D4—21no—
290D4#434112yes—
291C2×C4—24no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—111no—
298C2×C4—111no—
299C2×C4—111no—
300C2×C4—111no—
301C2×C4—222no—
302C2×C4—222no—
303C2×C4—221no—
304C2×C4—221no—
305C2×C4—221no—
306C2×C4—221no—
307C2×C4—442no—
308C2×C4—442no—
309C2×C4D4×D1111yescharacteristic
310C2×C4C23×D1111yescharacteristic
311C8—21no—
312C8—21no—
313C8—221no—
314C8—221no—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—22no—
319C22—41no—
320C22—41no—
321C22C2×D4×D1111yescharacteristic
322C4—21no—
323C4—22no—
324C4—41no—
325C4—41no—
326C4—112no—
327C4—112no—
328C4—221no—
329C4—221no—
330C4—441no—
331C4—441no—
332C4—441no—
333C4—441no—
334C4C2×#434111yescharacteristic
335C4C2×#434111yescharacteristic
336C2—41no—
337C2—42no—
338C2#1062311711yescharacteristic
339C2D11×#13511yescharacteristic
340C2D11×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#452C2
socleC22×C11C22×D4
prime radicalC2×C11×#41C22
hypercenter#452D11
hypocenterC11#3107
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
2. #10623153C2semidirect
5. Q16×Dic11C2semidirect
6. #10622795C2semidirect
7. #10622775C2semidirect
8. SD16×Dic11C2semidirect
9. #10622658C2semidirect
10. #10622404C2semidirect
11. #10622403C2semidirect
12. #10622372C2semidirect
13. #10622371C2semidirect
14. #10622336C2semidirect
15. #10622331C2semidirect
278. C11#3107semidirect

Maximal subgroups

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

subgroupindex
#41×Dic112
#106231532
C11×#4522
#106228522
Q16×Dic112
#106227952
#106227752
SD16×Dic112
#106226582
#106224042
#106224032
#106223722
#106223712
#106223362
#106223312
#310711