Finite Group Databasebeta

← #13078835

Subgroups — #13078835

Order 1408.

372 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623228C211yesmaximal, characteristic, complemented
2#10623077C211yesmaximal, characteristic
3C11×#478C211yesmaximal, characteristic, complemented
4#10622676C211yesmaximal, characteristic, complemented
5#10622632C211yesmaximal, characteristic, complemented
6#10622497C211yesmaximal, characteristic, complemented
7#10622486C211yesmaximal, characteristic, complemented
8#10622475C211yesmaximal, characteristic, complemented
9#10622466C211yesmaximal, characteristic, complemented
10#10622462C211yesmaximal, characteristic, complemented
11#10622453C211yesmaximal, characteristic, complemented
12#10622396C211yesmaximal, characteristic
13#10622396C211yesmaximal, characteristic
14#10622371C211yesmaximal, characteristic, complemented
15#10622370C211yesmaximal, characteristic, complemented
16C2×#4341C2211yescharacteristic
17C11×#125C2211yescharacteristic
18C4×D4×C11C2211yescharacteristic
19D4×Dic11C2211yescharacteristic
20C2×#4324C2211yescharacteristic
21C2×#4324C2211yescharacteristic
22C4×C22⋊D11—21no—
23C2×Dic11⋊C4—21no—
24C2×Dic44C2211yescharacteristic
25C2×Dic44C2211yescharacteristic
26#66951—21no—
27#66951—21no—
28#66950C2211yescharacteristic
29#66950C2211yescharacteristic
30C4⋊C4×D11C2211yescharacteristic
31#66943—21no—
32#66943—21no—
33#66940C2211yescharacteristic
34#66940C2211yescharacteristic
35#66940C2211yescharacteristic
36(C22⋊D11)⋊C4—21no—
37#66930—21no—
38#66925C2211yescharacteristic
39#66922C2211yescharacteristic
40C4×Dic22C2211yescharacteristic
41C11×#107C2211yescharacteristic
42C11×#106C2211yescharacteristic
43C11×C4⋊C8C2211yescharacteristic
44C11×#102C2211yescharacteristic
45C11×#102C2211yescharacteristic
46(C2×D11)⋊C8C2211yescharacteristic
47(C2×D11)⋊C8C2211yescharacteristic
48#66880C2211yescharacteristic
49#66880C2211yescharacteristic
50#66879C2211yescharacteristic
51C8×Dic11C2211yescharacteristic
52#66874C2211yescharacteristic
53#66874C2211yescharacteristic
54#66874C2211yescharacteristic
55#66874C2211yescharacteristic
56#66872C2211yescharacteristic
57#66871C2211yescharacteristic
58C4⋊(C11⋊C8)C2211yescharacteristic
59C2×D4×C11C2311yescharacteristic
60C22×C4×C11—21no—
61C2×C22⋊D11—21no—
62C22×Dic11—21no—
63C22×Dic11—21no—
64#4341—22no—
65#4341—22no—
66C2×C4×D11—21no—
67C2×C4×D11C2311yescharacteristic
68C2×Dic22C2311yescharacteristic
69C2×Dic22C2311yescharacteristic
70C2×Dic22C2311yescharacteristic
71C2×C8×C11C2311yescharacteristic
72C2×C8×C11C2311yescharacteristic
73C11×C4⋊C4—21no—
74C11×C4⋊C4—21no—
75C11×C4⋊C4C2311yescharacteristic
76C11×C4⋊C4C2311yescharacteristic
77C11×C4⋊C4C2311yescharacteristic
78C11×C22⋊C4—21no—
79C42×C11C2311yescharacteristic
80C22⋊Dic11—21no—
81#4324—22no—
82#4324—22no—
83(C2×D11)⋊C4—21no—
84(C2×D11)⋊C4—21no—
85(C2×D11)⋊C4D411yescharacteristic
86(C2×D11)⋊C4D411yescharacteristic
87C4⋊Dic11—21no—
88C4⋊Dic11—21no—
89C4⋊Dic11—21no—
90C4⋊Dic11—21no—
91C4⋊Dic11C2311yescharacteristic
92Dic11⋊C4—21no—
93Dic11⋊C4—21no—
94Dic11⋊C4—21no—
95Dic11⋊C4—21no—
96Dic11⋊C4—21no—
97Dic11⋊C4D411yescharacteristic
98Dic11⋊C4D411yescharacteristic
99C4×Dic11—21no—
100C4×Dic11—21no—
101C4×Dic11—21no—
102C4×Dic11—21no—
103C4×Dic11C2311yescharacteristic
104C2×C11⋊C8C2311yescharacteristic
105C2×C11⋊C8C2311yescharacteristic
106Dic44—22no—
107Dic44—22no—
108#3120—111nomaximal, Sylow
109C23×C11—21no—
110C22×D11C2×D411yescharacteristic
111D4×C11—21no—
112D4×C11#4112yes—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—81no—
117C2×C4×C11C2×D411yescharacteristic
118C2×C4×C11C2×D411yescharacteristic
119C2×C4×C11C2411yescharacteristic
120C22⋊D11—24no—
121C2×Dic11—24no—
122C2×Dic11—21no—
123C2×Dic11—21no—
124C2×Dic11—21no—
125C2×Dic11—21no—
126C2×Dic11—81no—
127C2×Dic11C2×D411yescharacteristic
128C2×Dic11C2×D411yescharacteristic
129C2×Dic11C2×D411yescharacteristic
130C4×D11—21no—
131C4×D11—21no—
132C4×D11—81no—
133Dic22—21no—
134Dic22—21no—
135Dic22—21no—
136Dic22—21no—
137Dic22—21no—
138Dic22#4112yes—
139C8×C11—21no—
140C8×C11—21no—
141C11⋊C8—21no—
142C11⋊C8—21no—
143#541—111no—
144#520—111no—
145#484—111no—
146#483—111no—
147#479—111no—
148#478D1111yescharacteristic, complemented
149#462—111no—
150#461—111no—
151#452—111no—
152#452—111no—
153#441—111no—
154#440—111no—
155C4×Q16—111no—
156C4×SD16—111no—
157#433—111no—
158C22×C11—22no—
159C22×C11—41no—
160C22×C11—41no—
161C22×C11C22×D411yescharacteristic
162C2×D11—21no—
163C2×D11—21no—
164C2×D11—21no—
165C4×C11—21no—
166C4×C11—21no—
167C4×C11—41no—
168C4×C11—41no—
169C4×C11—41no—
170C4×C11C2×#4111yescharacteristic
171C4×C11C2×#4111yescharacteristic
172Dic11—22no—
173Dic11—21no—
174Dic11—21no—
175Dic11—21no—
176Dic11—41no—
177Dic11—41no—
178Dic11—41no—
179C2×#41—111no—
180C2×Q16—111no—
181C2×Q16—111no—
182C2×SD16—111no—
183C2×SD16—111no—
184C4⋊Q8—111no—
185#126—221no—
186#126—221no—
187#125—221no—
188#125—221no—
189#125C2×D1111yescharacteristic
190C22⋊Q8—111no—
191C22⋊Q8—111no—
192C4×Q8—111no—
193C4×Q8—111no—
194C4×Q8—111no—
195C4×Q8—111no—
196C4×D4—111no—
197C4×D4—221no—
198C4×D4—221no—
199C4×D4C2×D1111yescharacteristic
200#117—111no—
201#117—221no—
202C2×C4⋊C4—111no—
203C2×C4⋊C4—221no—
204#107—111no—
205#107C2×D1111yescharacteristic
206#106—111no—
207#106C2×D1111yescharacteristic
208C4⋊C8—111no—
209C4⋊C8C2×D1111yescharacteristic
210#103—111no—
211#103—111no—
212#103—111no—
213#103—111no—
214#103—111no—
215#103—111no—
216#102C2×D1111yescharacteristic
217#102C2×D1111yescharacteristic
218C22⋊C8—111no—
219C22⋊C8—111no—
220#97—111no—
221C4×C8—111no—
222C2×C11—42no—
223C2×C11#52511yescharacteristic
224C2×C11#57711yescharacteristic
225C2×C11#57811yescharacteristic
226D11—41no—
227#41—222no—
228#41—222no—
229C2×Q8—111no—
230C2×Q8—111no—
231C2×Q8—111no—
232C2×D4—221no—
233C2×D4C22×D1111yescharacteristic
234C22×C4—21no—
235C22×C4—111no—
236C22×C4—221no—
237C22×C4—221no—
238C22×C4—221no—
239Q16—222no—
240Q16—222no—
241SD16—222no—
242SD16—222no—
243C2×C8—111no—
244C2×C8—111no—
245C2×C8C22×D1111yescharacteristic
246C2×C8C22×D1111yescharacteristic
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—111no—
250C4⋊C4—111no—
251C4⋊C4—111no—
252C4⋊C4—221no—
253C4⋊C4—221no—
254C4⋊C4—221no—
255C4⋊C4—221no—
256C4⋊C4—221no—
257C4⋊C4—221no—
258C4⋊C4—221no—
259C4⋊C4—221no—
260C4⋊C4—221no—
261C4⋊C4C22×D1111yescharacteristic
262C4⋊C4C22×D1111yescharacteristic
263C4⋊C4C22×D1111yescharacteristic
264C22⋊C4—21no—
265C22⋊C4—111no—
266C22⋊C4—111no—
267C22⋊C4—221no—
268C22⋊C4—221no—
269C22⋊C4—221no—
270C42—111no—
271C42—221no—
272C42—221no—
273C42—221no—
274C42—221no—
275C42C22×D1111yescharacteristic
276C11#312011yescharacteristic, complemented, Sylow
277C23—21no—
278C23—111no—
279Q8—112no—
280Q8—221no—
281Q8—221no—
282Q8—221no—
283Q8—221no—
284Q8—221no—
285D4—21no—
286D4—224no—
287D4#434312yes—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—81no—
292C2×C4—111no—
293C2×C4—111no—
294C2×C4—111no—
295C2×C4—224no—
296C2×C4—221no—
297C2×C4—221no—
298C2×C4—221no—
299C2×C4—221no—
300C2×C4—221no—
301C2×C4—221no—
302C2×C4—881no—
303C2×C4—881no—
304C2×C4D4×D1111yescharacteristic
305C2×C4D4×D1111yescharacteristic
306C2×C4C23×D1111yescharacteristic
307C8—21no—
308C8—21no—
309C8—221no—
310C8—221no—
311C22—22no—
312C22—41no—
313C22—41no—
314C22—221no—
315C22—221no—
316C22—221no—
317C22C2×D4×D1111yescharacteristic
318C4—21no—
319C4—21no—
320C4—41no—
321C4—41no—
322C4—41no—
323C4—221no—
324C4—221no—
325C4—221no—
326C4—222no—
327C4—441no—
328C4—441no—
329C4—441no—
330C4C2×#434311yescharacteristic
331C4#41×D1111yescharacteristic
332C2—42no—
333C2—441no—
334C2#1062315811yescharacteristic
335C2#1062330211yescharacteristic
336C2#1062330611yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#478C2
socleC22×C11C22×D4
prime radicalC2×#4341C22
hypercenter#478D11
hypocenterC11#3120
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #10623228C2semidirect
3. C11×#478C2semidirect
4. #10622676C2semidirect
5. #10622632C2semidirect
6. #10622497C2semidirect
7. #10622486C2semidirect
8. #10622475C2semidirect
9. #10622466C2semidirect
10. #10622462C2semidirect
11. #10622453C2semidirect
14. #10622371C2semidirect
15. #10622370C2semidirect
148. #478D11semidirect
276. C11#3120semidirect

Maximal subgroups

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

subgroupindex
#106232282
#106230772
C11×#4782
#106226762
#106226322
#106224972
#106224862
#106224752
#106224662
#106224622
#106224532
#106223962
#106223712
#106223702
#312011