Finite Group Databasebeta

← #13080930

Subgroups — #13080930

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#10623162C211yesmaximal, characteristic
2#10623042C211yesmaximal, characteristic, complemented
3C11×#483C211yesmaximal, characteristic, complemented
4#10622665C211yesmaximal, characteristic, complemented
5#10622579C211yesmaximal, characteristic, complemented
6#10622483C211yesmaximal, characteristic, complemented
7#10622481C211yesmaximal, characteristic, complemented
8#10622475C211yesmaximal, characteristic, complemented
9#10622465C211yesmaximal, characteristic, complemented
10#10622423C211yesmaximal, characteristic, complemented
11#10622416C211yesmaximal, characteristic, complemented
12#10622406C211yesmaximal, characteristic, complemented
13#10622405C211yesmaximal, characteristic, complemented
14#10622346C211yesmaximal, characteristic, complemented
15#10622342C211yesmaximal, characteristic, complemented
16C2×#4343C2211yescharacteristic
17C2×#4339C2211yescharacteristic
18C11×C22⋊Q8C2211yescharacteristic
19C2×C11×C4⋊C4C2211yescharacteristic
20#66997C2211yescharacteristic
21C2×#4326C2211yescharacteristic
22C4×C22⋊D11—21no—
23C4×C22⋊D11C2211yescharacteristic
24#66977—21no—
25#66977C2211yescharacteristic
26C2×#4318C2211yescharacteristic
27C2×Dic44C2211yescharacteristic
28C2×#4314C2211yescharacteristic
29C2×#4313C2211yescharacteristic
30#66950C2211yescharacteristic
31#66950C2211yescharacteristic
32#66949—21no—
33#66947—21no—
34#66946C2211yescharacteristic
35C4⋊C4×D11—21no—
36C4⋊C4×D11C2211yescharacteristic
37#66942—21no—
38#66941C2211yescharacteristic
39#66940C2211yescharacteristic
40#66937—21no—
41#66936—21no—
42C11×#106C2211yescharacteristic
43C11×#106C2211yescharacteristic
44C11×#103C2211yescharacteristic
45C11×#103C2211yescharacteristic
46C11×C22⋊C8C2211yescharacteristic
47#66899C2211yescharacteristic
48#66885C2211yescharacteristic
49(C2×D11)⋊C8C2211yescharacteristic
50#66880C2211yescharacteristic
51Dic11⋊C8C2211yescharacteristic
52C8×Dic11C2211yescharacteristic
53#66874C2211yescharacteristic
54#66874C2211yescharacteristic
55#66874C2211yescharacteristic
56#66873C2211yescharacteristic
57#66873C2211yescharacteristic
58#66872C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C22×C4×C11—21no—
61C22×C4×C11C2311yescharacteristic
62C2×C22⋊D11—21no—
63C2×C22⋊D11D411yescharacteristic
64#4343—22no—
65#4343—41no—
66#4339—22no—
67#4339—41no—
68C2×D44—21no—
69C2×D44C2311yescharacteristic
70C2×C4×D11—21no—
71C2×C4×D11—21no—
72C2×C4×D11—21no—
73C2×C4×D11—21no—
74C2×C4×D11C2311yescharacteristic
75C2×Dic22—21no—
76C2×Dic22C2311yescharacteristic
77C2×Dic22C2311yescharacteristic
78C2×C8×C11C2311yescharacteristic
79C2×C8×C11C2311yescharacteristic
80C11×C4⋊C4—21no—
81C11×C4⋊C4—21no—
82C11×C4⋊C4C2311yescharacteristic
83C11×C4⋊C4C2311yescharacteristic
84C11×C4⋊C4C2311yescharacteristic
85C11×C22⋊C4—21no—
86C22⋊Dic11—21no—
87C22⋊Dic11D411yescharacteristic
88#4326—41no—
89(C2×D11)⋊C4—21no—
90(C2×D11)⋊C4—21no—
91(C2×D11)⋊C4—21no—
92(C2×D11)⋊C4D411yescharacteristic
93C4⋊Dic11—21no—
94C4⋊Dic11—21no—
95C4⋊Dic11C2311yescharacteristic
96Dic11⋊C4—21no—
97Dic11⋊C4—21no—
98Dic11⋊C4—21no—
99Dic11⋊C4—21no—
100Dic11⋊C4—21no—
101Dic11⋊C4—21no—
102Dic11⋊C4D411yescharacteristic
103C4×Dic11—21no—
104C4×Dic11C2311yescharacteristic
105#4318—41no—
106C2×C11⋊C8C2311yescharacteristic
107C2×C11⋊C8C2311yescharacteristic
108Dic44—41no—
109#4314—22no—
110#4313—41no—
111#3331—111nomaximal, Sylow
112C23×C11C2×D411yescharacteristic
113C22×D11—21no—
114C22×D11C2×D411yescharacteristic
115Q8×C11—21no—
116Q8×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—81no—
124C2×C4×C11C2×D411yescharacteristic
125C2×C4×C11C2411yescharacteristic
126C22⋊D11—22no—
127C22⋊D11—42no—
128C2×Dic11—21no—
129C2×Dic11—21no—
130C2×Dic11—21no—
131C2×Dic11C2×D411yescharacteristic
132C2×Dic11C2×D411yescharacteristic
133C2×Dic11C2×D411yescharacteristic
134D44—21no—
135D44—42no—
136D44#4112yes—
137C4×D11—21no—
138C4×D11—21no—
139C4×D11—42no—
140C4×D11—42no—
141C4×D11—42no—
142C4×D11—81no—
143Dic22—21no—
144Dic22—21no—
145Dic22—21no—
146Dic22—21no—
147Dic22—81no—
148C8×C11—21no—
149C8×C11—21no—
150C11⋊C8—21no—
151C11⋊C8—21no—
152#554—111no—
153#547—111no—
154#487—111no—
155#483—111no—
156#483D1111yescharacteristic, complemented
157#476—111no—
158#470—111no—
159#470—111no—
160#462—111no—
161#452—111no—
162#452—111no—
163C4×SD16—111no—
164#436—111no—
165#417—111no—
166#417—111no—
167C22×C11—21no—
168C22×C11—21no—
169C22×C11—21no—
170C22×C11C22×D411yescharacteristic
171C2×D11—22no—
172C2×D11—21no—
173C2×D11—21no—
174C2×D11—21no—
175C2×D11—41no—
176C2×D11—41no—
177C4×C11—21no—
178C4×C11—41no—
179C4×C11—41no—
180C4×C11—41no—
181C4×C11—41no—
182C4×C11C2×#4111yescharacteristic
183C4×C11H(5,𝔽2)11yescharacteristic
184Dic11—21no—
185Dic11—21no—
186Dic11—41no—
187Dic11—41no—
188Dic11—41no—
189Dic11#13712yes—
190C2×#41—111no—
191C2×#41—111no—
192C2×Q16—111no—
193C2×Q16—111no—
194C2×SD16—111no—
195C2×M16—111no—
196C2×M16—111no—
197C4⋊Q8—111no—
198C4⋊Q8—111no—
199#125—221no—
200#123—221no—
201#123—221no—
202C22⋊Q8—111no—
203C22⋊Q8—111no—
204C22⋊Q8—111no—
205C22⋊Q8—221no—
206C22⋊Q8—221no—
207C22⋊Q8C2×D1111yescharacteristic
208#121—221no—
209C4×Q8—111no—
210C4×D4—111no—
211C4×D4—111no—
212C4×D4—221no—
213C2×C4⋊C4—111no—
214C2×C4⋊C4—221no—
215C2×C4⋊C4C2×D1111yescharacteristic
216#106—111no—
217#106C2×D1111yescharacteristic
218#106C2×D1111yescharacteristic
219C4⋊C8—111no—
220#103—111no—
221#103—111no—
222#103—111no—
223#103—111no—
224#103—111no—
225#103C2×D1111yescharacteristic
226#103C2×D1111yescharacteristic
227#102—111no—
228#102—111no—
229#102—111no—
230C22⋊C8—111no—
231C22⋊C8C2×D1111yescharacteristic
232C4×C8—111no—
233C2×C11—41no—
234C2×C11#54611yescharacteristic
235C2×C11C2×#13711yescharacteristic
236C2×C11#57711yescharacteristic
237D11—41no—
238D11—42no—
239#41—222no—
240#41—222no—
241#41—441no—
242#41—441no—
243C2×Q8—111no—
244C2×Q8—111no—
245C2×Q8—221no—
246C2×Q8C22×D1111yescharacteristic
247C2×D4—111no—
248C2×D4—111no—
249C2×D4—221no—
250C2×D4—221no—
251C22×C4—21no—
252C22×C4—111no—
253C22×C4—221no—
254C22×C4—221no—
255C22×C4—221no—
256C22×C4—221no—
257C22×C4C22×D1111yescharacteristic
258Q16—441no—
259Q16—441no—
260SD16—222no—
261M16—441no—
262M16—441no—
263C2×C8—111no—
264C2×C8—111no—
265C2×C8C22×D1111yescharacteristic
266C2×C8C22×D1111yescharacteristic
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—111no—
270C4⋊C4—111no—
271C4⋊C4—221no—
272C4⋊C4—221no—
273C4⋊C4—221no—
274C4⋊C4—221no—
275C4⋊C4—221no—
276C4⋊C4—221no—
277C4⋊C4—221no—
278C4⋊C4—221no—
279C4⋊C4C22×D1111yescharacteristic
280C4⋊C4C22×D1111yescharacteristic
281C4⋊C4C22×D1111yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—111no—
284C22⋊C4—111no—
285C22⋊C4—221no—
286C22⋊C4—221no—
287C22⋊C4—221no—
288C22⋊C4—221no—
289C42—111no—
290C42—221no—
291C11#333111yescharacteristic, complemented, Sylow
292C23—111no—
293C23—221no—
294C23D4×D1111yescharacteristic
295Q8—21no—
296Q8—21no—
297Q8—221no—
298Q8—221no—
299Q8—221no—
300Q8—221no—
301Q8—881no—
302D4—112no—
303D4—222no—
304D4—221no—
305D4—442no—
306D4—442no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—81no—
314C2×C4—111no—
315C2×C4—111no—
316C2×C4—111no—
317C2×C4—221no—
318C2×C4—221no—
319C2×C4—221no—
320C2×C4—221no—
321C2×C4—221no—
322C2×C4—442no—
323C2×C4—442no—
324C2×C4—442no—
325C2×C4—881no—
326C2×C4D4×D1111yescharacteristic
327C2×C4C23×D1111yescharacteristic
328C8—21no—
329C8—21no—
330C8—221no—
331C8—221no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—221no—
336C22—221no—
337C22—221no—
338C22—222no—
339C22—441no—
340C22—441no—
341C22C2×D4×D1111yescharacteristic
342C4—21no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4—112no—
348C4—221no—
349C4—221no—
350C4—441no—
351C4—441no—
352C4—441no—
353C4#41×D1111yescharacteristic
354C4#6704211yescharacteristic
355C2—41no—
356C2—441no—
357C2—442no—
358C2#1062318511yescharacteristic
359C2#1062329311yescharacteristic
360C2D11×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#483C2
socleC22×C11C22×D4
prime radical#10623162C2
hypercenter#483D11
hypocenterC11#3331
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
2. #10623042C2semidirect
3. C11×#483C2semidirect
4. #10622665C2semidirect
5. #10622579C2semidirect
6. #10622483C2semidirect
7. #10622481C2semidirect
8. #10622475C2semidirect
9. #10622465C2semidirect
10. #10622423C2semidirect
11. #10622416C2semidirect
12. #10622406C2semidirect
13. #10622405C2semidirect
14. #10622346C2semidirect
15. #10622342C2semidirect
156. #483D11semidirect
291. C11#3331semidirect

Maximal subgroups

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

subgroupindex
#106231622
#106230422
C11×#4832
#106226652
#106225792
#106224832
#106224812
#106224752
#106224652
#106224232
#106224162
#106224062
#106224052
#106223462
#106223422
#333111