Finite Group Databasebeta

← #13079901

Subgroups — #13079901

Order 1408.

320 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623065C211yesmaximal, characteristic
2#10623050C211yesmaximal, characteristic, complemented
3C11×#433C211yesmaximal, characteristic, complemented
4#10622463C211yesmaximal, characteristic, complemented
5#10622460C211yesmaximal, characteristic, complemented
6#10622459C211yesmaximal, characteristic, complemented
7#10622442C211yesmaximal, characteristic, complemented
8#10622350C211yesmaximal, characteristic
9#10622349C211yesmaximal, characteristic
10#10622336C211yesmaximal, characteristic, complemented
11#10622335C211yesmaximal, characteristic, complemented
12#10622327C211yesmaximal, characteristic, complemented
13#10622315C211yesmaximal, characteristic, complemented
14#10622310C211yesmaximal, characteristic, complemented
15#10622295C211yesmaximal, characteristic, complemented
16C11×#117C2211yescharacteristic
17#66983C2211yescharacteristic
18#66979C2211yescharacteristic
19C2×C4⋊Dic11C2211yescharacteristic
20#66977C2211yescharacteristic
21#66951—21no—
22#66949—21no—
23#66943—21no—
24#66941—21no—
25#66938—21no—
26#66936—21no—
27#66931—21no—
28#66931—21no—
29#66928C2211yescharacteristic
30C4×D44C2211yescharacteristic
31#66923C2211yescharacteristic
32#66923C2211yescharacteristic
33#66922C2211yescharacteristic
34#66922C2211yescharacteristic
35#66922C2211yescharacteristic
36C4×Dic22C2211yescharacteristic
37C11×C4⋊C8C2211yescharacteristic
38C11×C4⋊C8C2211yescharacteristic
39C11×C22⋊C8C2211yescharacteristic
40C11×C22⋊C8C2211yescharacteristic
41C11×#97C2211yescharacteristic
42C4×C8×C11C2211yescharacteristic
43#66885C2211yescharacteristic
44#66885C2211yescharacteristic
45#66885C2211yescharacteristic
46#66885C2211yescharacteristic
47#66882C2211yescharacteristic
48#66882C2211yescharacteristic
49#66882C2211yescharacteristic
50#66882C2211yescharacteristic
51#66882C2211yescharacteristic
52#66882C2211yescharacteristic
53#66881C2211yescharacteristic
54#66881C2211yescharacteristic
55#66880C2211yescharacteristic
56#66880C2211yescharacteristic
57#66880C2211yescharacteristic
58#66880C2211yescharacteristic
59C22×C4×C11C2311yescharacteristic
60C2×C22⋊D11—21no—
61C22×Dic11—21no—
62C2×D44C2311yescharacteristic
63C2×C4×D11—21no—
64C2×Dic22—21no—
65C2×Dic22—21no—
66C2×Dic22—21no—
67C2×Dic22C2311yescharacteristic
68C2×C8×C11C2311yescharacteristic
69C2×C8×C11C2311yescharacteristic
70C2×C8×C11C2311yescharacteristic
71C2×C8×C11C2311yescharacteristic
72C11×C4⋊C4D411yescharacteristic
73C11×C4⋊C4D411yescharacteristic
74C11×C22⋊C4D411yescharacteristic
75C11×C22⋊C4D411yescharacteristic
76C42×C11C2311yescharacteristic
77C42×C11C2311yescharacteristic
78C22⋊Dic11—21no—
79C22⋊Dic11—21no—
80(C2×D11)⋊C4—21no—
81(C2×D11)⋊C4—21no—
82(C2×D11)⋊C4—21no—
83(C2×D11)⋊C4—21no—
84C4⋊Dic11—21no—
85C4⋊Dic11—21no—
86C4⋊Dic11—21no—
87C4⋊Dic11—21no—
88C4⋊Dic11C2311yescharacteristic
89C4⋊Dic11C2311yescharacteristic
90C4⋊Dic11C2311yescharacteristic
91C4⋊Dic11C2311yescharacteristic
92C4⋊Dic11C2311yescharacteristic
93C4⋊Dic11C2311yescharacteristic
94Dic11⋊C4—21no—
95Dic11⋊C4—21no—
96Dic11⋊C4—21no—
97Dic11⋊C4—21no—
98Dic11⋊C4—21no—
99Dic11⋊C4—21no—
100C4×Dic11—21no—
101C4×Dic11—21no—
102#3243—111nomaximal, Sylow
103C23×C11C2×D411yescharacteristic
104C22×D11—21no—
105C2×C4×C11—21no—
106C2×C4×C11—21no—
107C2×C4×C11C2×D411yescharacteristic
108C2×C4×C11C2×D411yescharacteristic
109C2×C4×C11C2×D411yescharacteristic
110C2×C4×C11C2×D411yescharacteristic
111C2×C4×C11C2×D411yescharacteristic
112C2×C4×C11C2411yescharacteristic
113C22⋊D11—81no—
114C2×Dic11—21no—
115C2×Dic11—21no—
116C2×Dic11—21no—
117C2×Dic11—21no—
118C2×Dic11—21no—
119C2×Dic11—21no—
120C2×Dic11—21no—
121C2×Dic11—81no—
122D44—21no—
123D44—21no—
124C4×D11—81no—
125Dic22—21no—
126Dic22—21no—
127Dic22—81no—
128Dic22—81no—
129Dic22—81no—
130C8×C11—21no—
131C8×C11—21no—
132C8×C11—21no—
133C8×C11—21no—
134#544—111no—
135#542—111no—
136#501—111no—
137#500—111no—
138#489—111no—
139#488—111no—
140#485—111no—
141#484—111no—
142#482—111no—
143#480—111no—
144#479—111no—
145#478—111no—
146#477—111no—
147#474—111no—
148#433D1111yescharacteristic, complemented
149C22×C11—21no—
150C22×C11—21no—
151C22×C11—21no—
152C22×C11C22×D411yescharacteristic
153C2×D11—41no—
154C2×D11—41no—
155C2×D11—41no—
156C4×C11—21no—
157C4×C11—21no—
158C4×C11—21no—
159C4×C11—21no—
160C4×C11—21no—
161C4×C112−1+411yescharacteristic
162C4×C112−1+411yescharacteristic
163Dic11—41no—
164Dic11—41no—
165Dic11—41no—
166Dic11—41no—
167Dic11—41no—
168Dic11—41no—
169Dic11—41no—
170C4⋊Q8—111no—
171C4⋊Q8—111no—
172C4⋊Q8—111no—
173C4⋊Q8—221no—
174#126—221no—
175#125—111no—
176#125—111no—
177#125—221no—
178#124—111no—
179#124—221no—
180#123—221no—
181C22⋊Q8—111no—
182C22⋊Q8—221no—
183C22⋊Q8—221no—
184C22⋊Q8—221no—
185#121—111no—
186C4×Q8—111no—
187C4×D4—111no—
188#117—111no—
189#117C2×D1111yescharacteristic
190C2×C4⋊C4—111no—
191#107—111no—
192#107—111no—
193#107—111no—
194#107—111no—
195#107—111no—
196#107—111no—
197#106—111no—
198#106—111no—
199C4⋊C8C2×D1111yescharacteristic
200C4⋊C8C2×D1111yescharacteristic
201#103—111no—
202#103—111no—
203#103—111no—
204#103—111no—
205#102—111no—
206#102—111no—
207#102—111no—
208#102—111no—
209C22⋊C8C2×D1111yescharacteristic
210C22⋊C8C2×D1111yescharacteristic
211#97C2×D1111yescharacteristic
212C4×C8C2×D1111yescharacteristic
213C2×C11—41no—
214C2×C11#53611yescharacteristic
215C2×C11#57611yescharacteristic
216C2×C11#57811yescharacteristic
217D11—81no—
218C2×Q8—111no—
219C2×Q8—221no—
220C2×Q8—221no—
221C2×Q8—221no—
222C2×D4—111no—
223C2×D4—221no—
224C22×C4—221no—
225C22×C4—221no—
226C22×C4C22×D1111yescharacteristic
227C2×C8C22×D1111yescharacteristic
228C2×C8C22×D1111yescharacteristic
229C2×C8C22×D1111yescharacteristic
230C2×C8C22×D1111yescharacteristic
231C4⋊C4—111no—
232C4⋊C4—111no—
233C4⋊C4—111no—
234C4⋊C4—111no—
235C4⋊C4—111no—
236C4⋊C4—111no—
237C4⋊C4—221no—
238C4⋊C4—221no—
239C4⋊C4—221no—
240C4⋊C4—221no—
241C4⋊C4—221no—
242C4⋊C4—221no—
243C4⋊C4—221no—
244C4⋊C4—221no—
245C4⋊C4—221no—
246C4⋊C4—221no—
247C4⋊C4D4411yescharacteristic
248C4⋊C4D4411yescharacteristic
249C22⋊C4—221no—
250C22⋊C4—221no—
251C22⋊C4—221no—
252C22⋊C4—221no—
253C22⋊C4—221no—
254C22⋊C4—221no—
255C22⋊C4D4411yescharacteristic
256C22⋊C4D4411yescharacteristic
257C42—221no—
258C42—221no—
259C42C22×D1111yescharacteristic
260C42C22×D1111yescharacteristic
261C11#324311yescharacteristic, complemented, Sylow
262C23—221no—
263C23C2×D4411yescharacteristic
264Q8—221no—
265Q8—221no—
266Q8—881no—
267Q8—881no—
268Q8—881no—
269D4—221no—
270D4—221no—
271D4—881no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—221no—
275C2×C4—221no—
276C2×C4—221no—
277C2×C4—221no—
278C2×C4—221no—
279C2×C4—221no—
280C2×C4—221no—
281C2×C4—881no—
282C2×C4—881no—
283C2×C4C2×D4411yescharacteristic
284C2×C4C2×D4411yescharacteristic
285C2×C4C2×D4411yescharacteristic
286C2×C4C2×D4411yescharacteristic
287C2×C4C2×D4411yescharacteristic
288C2×C4C23×D1111yescharacteristic
289C8—21no—
290C8—21no—
291C8—21no—
292C8—21no—
293C22—21no—
294C22—21no—
295C22—21no—
296C22—441no—
297C22—441no—
298C22—441no—
299C22C22×D4411yescharacteristic
300C4—21no—
301C4—21no—
302C4—21no—
303C4—21no—
304C4—21no—
305C4—441no—
306C4—441no—
307C4—441no—
308C4—441no—
309C4—441no—
310C4—441no—
311C4—441no—
312C4#6704311yescharacteristic
313C4#6704311yescharacteristic
314C2—41no—
315C2—881no—
316C2#1062305711yescharacteristic
317C2#1062328311yescharacteristic
318C2#1062328411yescharacteristic
subgroupG/H
centerC22C22×D44
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#433C2
socleC22×C11C22×D4
prime radical#66983C22
hypercenter#433D11
hypocenterC11#3243
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
2. #10623050C2semidirect
3. C11×#433C2semidirect
4. #10622463C2semidirect
5. #10622460C2semidirect
6. #10622459C2semidirect
7. #10622442C2semidirect
10. #10622336C2semidirect
11. #10622335C2semidirect
12. #10622327C2semidirect
13. #10622315C2semidirect
14. #10622310C2semidirect
15. #10622295C2semidirect
148. #433D11semidirect
261. C11#3243semidirect

Maximal subgroups

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

subgroupindex
#106230652
#106230502
C11×#4332
#106224632
#106224602
#106224592
#106224422
#106223502
#106223492
#106223362
#106223352
#106223272
#106223152
#106223102
#106222952
#324311