Finite Group Databasebeta

← #13081103

Subgroups — #13081103

Order 1408.

356 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623096C211yesmaximal, characteristic
2#10623074C211yesmaximal, characteristic, complemented
3C11×#435C211yesmaximal, characteristic, complemented
4#10622747C211yesmaximal, characteristic, complemented
5#10622734C211yesmaximal, characteristic, complemented
6#10622727C211yesmaximal, characteristic, complemented
7C2×#66882C211yesmaximal, characteristic, complemented
8#10622459C211yesmaximal, characteristic, complemented
9#10622442C211yesmaximal, characteristic, complemented
10#10622349C211yesmaximal, characteristic, complemented
11#10622348C211yesmaximal, characteristic, complemented
12#10622336C211yesmaximal, characteristic, complemented
13#10622335C211yesmaximal, characteristic, complemented
14#10622323C211yesmaximal, characteristic, complemented
15#10622315C211yesmaximal, characteristic, complemented
16C2×C11×M16C2211yescharacteristic
17C22×C8×C11C2211yescharacteristic
18C4×D4×C11C2211yescharacteristic
19#66992—21no—
20D4×Dic11—21no—
21#66983C2211yescharacteristic
22#66983C2211yescharacteristic
23#66979C2211yescharacteristic
24C2×C4⋊Dic11C2211yescharacteristic
25C2×C4⋊Dic11C2211yescharacteristic
26C2×C4⋊Dic11C2211yescharacteristic
27#66977C2211yescharacteristic
28#66977C2211yescharacteristic
29C2×#4314C2211yescharacteristic
30#66951—21no—
31#66943—21no—
32#66936—21no—
33(C22⋊D11)⋊C4—21no—
34#66931—21no—
35#66931—21no—
36C4×D44C2211yescharacteristic
37#66923C2211yescharacteristic
38#66922C2211yescharacteristic
39C4×Dic22C2211yescharacteristic
40C11×C4⋊C8C2211yescharacteristic
41C11×C22⋊C8C2211yescharacteristic
42C11×C22⋊C8C2211yescharacteristic
43C11×#97C2211yescharacteristic
44#66885C2211yescharacteristic
45#66885C2211yescharacteristic
46#66885C2211yescharacteristic
47#66882C2211yescharacteristic
48#66882C2211yescharacteristic
49#66882C2211yescharacteristic
50#66882C2211yescharacteristic
51#66882C2211yescharacteristic
52#66882C2211yescharacteristic
53#66881C2211yescharacteristic
54#66881C2211yescharacteristic
55#66881C2211yescharacteristic
56#66880C2211yescharacteristic
57#66880C2211yescharacteristic
58#66880C2211yescharacteristic
59C2×D4×C11D411yescharacteristic
60C22×C4×C11C2311yescharacteristic
61C22×C4×C11C2311yescharacteristic
62C2×C22⋊D11—21no—
63C2×C22⋊D11—21no—
64C22×Dic11—21no—
65C22×Dic11—21no—
66C22×Dic11—21no—
67C2×D44C2311yescharacteristic
68C2×C4×D11—21no—
69C2×Dic22—21no—
70C2×Dic22C2311yescharacteristic
71C11×M16—22no—
72C2×C8×C11—22no—
73C2×C8×C11C2311yescharacteristic
74C2×C8×C11C2311yescharacteristic
75C2×C8×C11C2311yescharacteristic
76C2×C8×C11C2311yescharacteristic
77C11×C4⋊C4D411yescharacteristic
78C11×C22⋊C4D411yescharacteristic
79C11×C22⋊C4D411yescharacteristic
80C42×C11C2311yescharacteristic
81C22⋊Dic11—21no—
82C22⋊Dic11—21no—
83C22⋊Dic11—21no—
84(C2×D11)⋊C4—21no—
85(C2×D11)⋊C4—21no—
86(C2×D11)⋊C4—21no—
87C4⋊Dic11—21no—
88C4⋊Dic11—21no—
89C4⋊Dic11—21no—
90C4⋊Dic11—21no—
91C4⋊Dic11C2311yescharacteristic
92C4⋊Dic11C2311yescharacteristic
93C4⋊Dic11C2311yescharacteristic
94C4⋊Dic11C2311yescharacteristic
95C4⋊Dic11C2311yescharacteristic
96C4⋊Dic11C2311yescharacteristic
97Dic11⋊C4—21no—
98Dic11⋊C4—21no—
99Dic11⋊C4—21no—
100Dic11⋊C4—21no—
101Dic11⋊C4—21no—
102C4×Dic11—21no—
103C4×Dic11—21no—
104#4314—22no—
105#3346—111nomaximal, Sylow
106C23×C11C2×D411yescharacteristic
107C23×C11C2×D411yescharacteristic
108C22×D11—21no—
109D4×C11—22no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11C2×D411yescharacteristic
115C2×C4×C11C2×D411yescharacteristic
116C2×C4×C11C2×D411yescharacteristic
117C2×C4×C11C2×D411yescharacteristic
118C2×C4×C11C2411yescharacteristic
119C22⋊D11—42no—
120C22⋊D11—81no—
121C2×Dic11—21no—
122C2×Dic11—21no—
123C2×Dic11—21no—
124C2×Dic11—21no—
125C2×Dic11—21no—
126C2×Dic11—21no—
127C2×Dic11—21no—
128C2×Dic11—81no—
129C2×Dic11—81no—
130C2×Dic11—81no—
131D44—21no—
132D44—21no—
133C4×D11—81no—
134Dic22—21no—
135Dic22—21no—
136Dic22—81no—
137C8×C11—21no—
138C8×C11—21no—
139C8×C11—21no—
140C8×C11#4112yes—
141#554—111no—
142#553—111no—
143#501—111no—
144#485—111no—
145#484—111no—
146#481—111no—
147#480—111no—
148#479—111no—
149#474—111no—
150#468—111no—
151#465—111no—
152#440—111no—
153#435D1111yescharacteristic, complemented
154#428—111no—
155C2×#107—111no—
156C22×C11—21no—
157C22×C11—21no—
158C22×C11—21no—
159C22×C11—21no—
160C22×C11—21no—
161C22×C11#13712yes—
162C22×C11C22×D411yescharacteristic
163C2×D11—41no—
164C2×D11—41no—
165C2×D11—41no—
166C4×C11—21no—
167C4×C11—21no—
168C4×C11—21no—
169C4×C11—21no—
170C4×C11C2×#4111yescharacteristic
171C4×C112−1+411yescharacteristic
172Dic11—41no—
173Dic11—41no—
174Dic11—41no—
175Dic11—41no—
176Dic11—41no—
177Dic11—41no—
178Dic11—41no—
179C2×SD16—111no—
180C2×M16C2×D1111yescharacteristic
181C22×C8C2×D1111yescharacteristic
182C4⋊Q8—111no—
183#126—221no—
184#125—111no—
185#125—221no—
186#123—221no—
187C22⋊Q8—111no—
188C22⋊Q8—111no—
189C22⋊Q8—221no—
190C22⋊Q8—221no—
191#121—111no—
192#121—111no—
193#121—221no—
194C4×Q8—111no—
195C4×D4—111no—
196C4×D4—221no—
197C4×D4—221no—
198C4×D4C2×D1111yescharacteristic
199#117—111no—
200C2×C4⋊C4—111no—
201C2×C4⋊C4—111no—
202C2×C4⋊C4—111no—
203#107—111no—
204#107—111no—
205#107—111no—
206#107—111no—
207#107—111no—
208#107—111no—
209#106—111no—
210#106—111no—
211#106—111no—
212C4⋊C8C2×D1111yescharacteristic
213#103—111no—
214#103—111no—
215#103—111no—
216#102—111no—
217#102—111no—
218#102—111no—
219C22⋊C8C2×D1111yescharacteristic
220C22⋊C8C2×D1111yescharacteristic
221#97C2×D1111yescharacteristic
222C2×C11—22no—
223C2×C11—41no—
224C2×C11#54711yescharacteristic
225C2×C11C2×#13711yescharacteristic
226C2×C11#57611yescharacteristic
227D11—81no—
228C2×Q8—111no—
229C2×Q8—221no—
230C2×D4—111no—
231C2×D4—221no—
232C2×D4—221no—
233C2×D4D4411yescharacteristic
234C22×C4—221no—
235C22×C4—221no—
236C22×C4—221no—
237C22×C4—221no—
238C22×C4C22×D1111yescharacteristic
239C22×C4C22×D1111yescharacteristic
240SD16—222no—
241M16—22no—
242C2×C8—22no—
243C2×C8C22×D1111yescharacteristic
244C2×C8C22×D1111yescharacteristic
245C2×C8C22×D1111yescharacteristic
246C2×C8C22×D1111yescharacteristic
247C4⋊C4—111no—
248C4⋊C4—111no—
249C4⋊C4—111no—
250C4⋊C4—111no—
251C4⋊C4—111no—
252C4⋊C4—111no—
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⋊C4—221no—
262C4⋊C4D4411yescharacteristic
263C22⋊C4—221no—
264C22⋊C4—221no—
265C22⋊C4—221no—
266C22⋊C4—221no—
267C22⋊C4—221no—
268C22⋊C4—221no—
269C22⋊C4D4411yescharacteristic
270C22⋊C4D4411yescharacteristic
271C42—221no—
272C42—221no—
273C42C22×D1111yescharacteristic
274C11#334611yescharacteristic, complemented, Sylow
275C23—221no—
276C23C2×D4411yescharacteristic
277C23C2×D4411yescharacteristic
278Q8—221no—
279Q8—221no—
280Q8—881no—
281D4—22no—
282D4—221no—
283D4—221no—
284D4—442no—
285D4—881no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—221no—
291C2×C4—221no—
292C2×C4—221no—
293C2×C4—221no—
294C2×C4—221no—
295C2×C4—221no—
296C2×C4—221no—
297C2×C4—881no—
298C2×C4—881no—
299C2×C4—881no—
300C2×C4—881no—
301C2×C4C2×D4411yescharacteristic
302C2×C4C2×D4411yescharacteristic
303C2×C4C2×D4411yescharacteristic
304C2×C4C2×D4411yescharacteristic
305C2×C4C23×D1111yescharacteristic
306C8—21no—
307C8—21no—
308C8—21no—
309C8#434112yes—
310C22—21no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—21no—
315C22—441no—
316C22—441no—
317C22—441no—
318C22#6696212yes—
319C22C22×D4411yescharacteristic
320C4—21no—
321C4—21no—
322C4—21no—
323C4—21no—
324C4—441no—
325C4—441no—
326C4—441no—
327C4—441no—
328C4—441no—
329C4—441no—
330C4—441no—
331C4C2×#434111yescharacteristic
332C4#6704311yescharacteristic
333C2—22no—
334C2—41no—
335C2—881no—
336C2#1062308611yescharacteristic
337C2C2×#6696211yescharacteristic
338C2#1062328311yescharacteristic
subgroupG/H
centerC22C22×D44
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#435C2
socleC22×C11C22×D4
prime radical#10623096C2
hypercenter#435D11
hypocenterC11#3346
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
2. #10623074C2semidirect
3. C11×#435C2semidirect
4. #10622747C2semidirect
5. #10622734C2semidirect
6. #10622727C2semidirect
7. C2×#66882C2semidirect
8. #10622459C2semidirect
9. #10622442C2semidirect
10. #10622349C2semidirect
11. #10622348C2semidirect
12. #10622336C2semidirect
13. #10622335C2semidirect
14. #10622323C2semidirect
15. #10622315C2semidirect
153. #435D11semidirect
274. C11#3346semidirect

Maximal subgroups

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

subgroupindex
#106230962
#106230742
C11×#4352
#106227472
#106227342
#106227272
C2×#668822
#106224592
#106224422
#106223492
#106223482
#106223362
#106223352
#106223232
#106223152
#334611