Finite Group Databasebeta

← #13078595

Subgroups — #13078595

Order 1408.

398 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623160C211yesmaximal, characteristic
2#10623035C211yesmaximal, characteristic, complemented
3C11×#484C211yesmaximal, characteristic, complemented
4#10622658C211yesmaximal, characteristic, complemented
5#10622580C211yesmaximal, characteristic, complemented
6#10622498C211yesmaximal, characteristic, complemented
7#10622495C211yesmaximal, characteristic, complemented
8#10622494C211yesmaximal, characteristic, complemented
9D11×#107C211yesmaximal, characteristic, complemented
10#10622428C211yesmaximal, characteristic, complemented
11#10622422C211yesmaximal, characteristic, complemented
12#10622417C211yesmaximal, characteristic, complemented
13#10622416C211yesmaximal, characteristic, complemented
14#10622350C211yesmaximal, characteristic, complemented
15#10622340C211yesmaximal, characteristic, complemented
16C2×#4343C2211yescharacteristic
17C2×#4339C2211yescharacteristic
18C11×C22⋊Q8C2211yescharacteristic
19C2×C11×C4⋊C4C2211yescharacteristic
20#66999C2211yescharacteristic
21#66983C2211yescharacteristic
22C4×C22⋊D11—21no—
23C4×C22⋊D11—21no—
24#66979C2211yescharacteristic
25C2×#4313C2211yescharacteristic
26C2×C8×D11C2211yescharacteristic
27#66949—21no—
28#66948—21no—
29#66948C2211yescharacteristic
30#66946—21no—
31#66945C2211yescharacteristic
32#66945C2211yescharacteristic
33C4⋊C4×D11C2211yescharacteristic
34C4⋊C4×D11C2211yescharacteristic
35C4⋊C4×D11C2211yescharacteristic
36#66940—21no—
37#66937—21no—
38#66937—21no—
39C11×#107C2211yescharacteristic
40C11×#107C2211yescharacteristic
41C11×#103C2211yescharacteristic
42C11×#103C2211yescharacteristic
43C11×C22⋊C8C2211yescharacteristic
44#66899C2211yescharacteristic
45#66899C2211yescharacteristic
46C22⋊(C11⋊C8)C2211yescharacteristic
47#66885C2211yescharacteristic
48#66885C2211yescharacteristic
49(C2×D11)⋊C8C2211yescharacteristic
50(C2×D11)⋊C8C2211yescharacteristic
51#66882C2211yescharacteristic
52#66881C2211yescharacteristic
53#66873C2211yescharacteristic
54#66873C2211yescharacteristic
55#66872C2211yescharacteristic
56#66871C2211yescharacteristic
57#66871C2211yescharacteristic
58#66871C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C22×C4×C11—21no—
61C22×C4×C11C2311yescharacteristic
62C2×C22⋊D11—21no—
63C2×C22⋊D11D411yescharacteristic
64C2×C22⋊D11D411yescharacteristic
65#4343—22no—
66#4343—22no—
67#4339—22no—
68#4339—22no—
69C2×D44—21no—
70C2×D44—21no—
71C2×D44D411yescharacteristic
72C2×D44C2311yescharacteristic
73C2×C4×D11—21no—
74C2×C4×D11—21no—
75C2×C4×D11—21no—
76C2×C4×D11—21no—
77C2×C4×D11C2311yescharacteristic
78C2×C4×D11C2311yescharacteristic
79C2×Dic22D411yescharacteristic
80C2×C8×C11C2311yescharacteristic
81C2×C8×C11C2311yescharacteristic
82C11×C4⋊C4—21no—
83C11×C4⋊C4—21no—
84C11×C4⋊C4C2311yescharacteristic
85C11×C4⋊C4C2311yescharacteristic
86C11×C4⋊C4C2311yescharacteristic
87C11×C22⋊C4—21no—
88C22⋊Dic11—21no—
89(C2×D11)⋊C4—21no—
90(C2×D11)⋊C4—21no—
91(C2×D11)⋊C4—21no—
92(C2×D11)⋊C4—21no—
93(C2×D11)⋊C4—21no—
94C4⋊Dic11C2311yescharacteristic
95C4⋊Dic11C2311yescharacteristic
96C4⋊Dic11C2311yescharacteristic
97Dic11⋊C4—21no—
98Dic11⋊C4—21no—
99Dic11⋊C4—21no—
100Dic11⋊C4—21no—
101C4×Dic11—21no—
102C4×Dic11—21no—
103C4×Dic11—21no—
104C2×C11⋊C8C2311yescharacteristic
105C2×C11⋊C8C2311yescharacteristic
106#4313—22no—
107C8×D11—22no—
108#3098—111nomaximal, Sylow
109C23×C11C2×D411yescharacteristic
110C22×D11—21no—
111C22×D11C2×D411yescharacteristic
112C22×D11C2×D411yescharacteristic
113Q8×C11—21no—
114Q8×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—81no—
122C2×C4×C11C2×D411yescharacteristic
123C2×C4×C11C2411yescharacteristic
124C22⋊D11—22no—
125C22⋊D11—22no—
126C22⋊D11—81no—
127C2×Dic11—21no—
128C2×Dic11—21no—
129C2×Dic11—21no—
130C2×Dic11C2×D411yescharacteristic
131C2×Dic11C2×D411yescharacteristic
132D44—22no—
133D44—21no—
134D44—21no—
135D44—42no—
136D44—81no—
137C4×D11—21no—
138C4×D11—21no—
139C4×D11—42no—
140C4×D11—81no—
141C4×D11—81no—
142C4×D11—81no—
143C4×D11#4112yes—
144C4×D11#4112yes—
145Dic22—22no—
146C8×C11—21no—
147C8×C11—21no—
148C11⋊C8—21no—
149C11⋊C8—21no—
150#537—111no—
151#520—111no—
152#485—111no—
153#485—111no—
154#484—111no—
155#484D1111yescharacteristic, complemented
156#482—111no—
157#482—111no—
158#480—111no—
159#480—111no—
160#428—111no—
161C2×#107—111no—
162#417—111no—
163#416—111no—
164#408—111no—
165C22×C11—21no—
166C22×C11—21no—
167C22×C11—21no—
168C22×C11C22×D411yescharacteristic
169C2×D11—21no—
170C2×D11—21no—
171C2×D11—21no—
172C2×D11—21no—
173C2×D11—21no—
174C2×D11—41no—
175C2×D11—41no—
176C2×D11—41no—
177C2×D11#12312yes—
178C4×C11—21no—
179C4×C11—41no—
180C4×C11—41no—
181C4×C11—41no—
182C4×C11—41no—
183C4×C11C2×#4111yescharacteristic
184C4×C11C2×#4111yescharacteristic
185Dic11—21no—
186Dic11—41no—
187Dic11—41no—
188Dic11—41no—
189Dic11#12312yes—
190C2×#41—111no—
191C2×#41—111no—
192C2×M16—111no—
193C22×C8—111no—
194C22⋊Q8—111no—
195C22⋊Q8—221no—
196C22⋊Q8C2×D1111yescharacteristic
197#121—111no—
198#121—111no—
199#121—221no—
200#121—221no—
201#121—221no—
202C4×Q8—221no—
203C4×D4—221no—
204C4×D4—221no—
205C4×D4—221no—
206#117—111no—
207#117—111no—
208#117—111no—
209C2×C4⋊C4—111no—
210C2×C4⋊C4—111no—
211C2×C4⋊C4—111no—
212C2×C4⋊C4C2×D1111yescharacteristic
213#107—111no—
214#107—111no—
215#107—111no—
216#107—111no—
217#107C2×D1111yescharacteristic
218#107C2×D1111yescharacteristic
219#106—111no—
220#106—111no—
221#103—111no—
222#103—111no—
223#103C2×D1111yescharacteristic
224#103C2×D1111yescharacteristic
225#102—111no—
226#102—111no—
227#102—111no—
228#102—111no—
229C22⋊C8—111no—
230C22⋊C8—111no—
231C22⋊C8—111no—
232C22⋊C8C2×D1111yescharacteristic
233C2×C11—41no—
234C2×C11C2×#12311yescharacteristic
235C2×C11#57611yescharacteristic
236C2×C11#57811yescharacteristic
237D11—22no—
238D11—41no—
239D11—81no—
240#41—222no—
241#41—222no—
242#41—222no—
243#41—222no—
244C2×Q8—111no—
245C2×Q8C22×D1111yescharacteristic
246C2×D4—111no—
247C2×D4—111no—
248C2×D4—111no—
249C2×D4—111no—
250C2×D4—221no—
251C2×D4—221no—
252C2×D4—221no—
253C22×C4—21no—
254C22×C4—111no—
255C22×C4—111no—
256C22×C4—221no—
257C22×C4—221no—
258C22×C4—221no—
259C22×C4—221no—
260C22×C4C22×D1111yescharacteristic
261M16—222no—
262C2×C8—111no—
263C2×C8—111no—
264C2×C8—222no—
265C2×C8C22×D1111yescharacteristic
266C2×C8C22×D1111yescharacteristic
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—111no—
270C4⋊C4—111no—
271C4⋊C4—111no—
272C4⋊C4—221no—
273C4⋊C4—221no—
274C4⋊C4—221no—
275C4⋊C4—221no—
276C4⋊C4C22×D1111yescharacteristic
277C4⋊C4C22×D1111yescharacteristic
278C4⋊C4C22×D1111yescharacteristic
279C22⋊C4—21no—
280C22⋊C4—221no—
281C22⋊C4—221no—
282C22⋊C4—221no—
283C22⋊C4—221no—
284C22⋊C4—221no—
285C22⋊C4—221no—
286C42—221no—
287C42—221no—
288C42—221no—
289C11#309811yescharacteristic, complemented, Sylow
290C23—111no—
291C23—111no—
292C23—221no—
293C23D4×D1111yescharacteristic
294Q8—21no—
295Q8—21no—
296Q8—222no—
297D4—222no—
298D4—222no—
299D4—222no—
300D4—221no—
301D4—221no—
302D4—442no—
303D4—881no—
304D4—881no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—81no—
312C2×C4—111no—
313C2×C4—112no—
314C2×C4—112no—
315C2×C4—111no—
316C2×C4—221no—
317C2×C4—221no—
318C2×C4—221no—
319C2×C4—221no—
320C2×C4—221no—
321C2×C4—442no—
322C2×C4—881no—
323C2×C4—881no—
324C2×C4—881no—
325C2×C4D4×D1111yescharacteristic
326C2×C4C23×D1111yescharacteristic
327C8—21no—
328C8—21no—
329C8—221no—
330C8—221no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—112no—
335C22—221no—
336C22—221no—
337C22—221no—
338C22—221no—
339C22—221no—
340C22—441no—
341C22—441no—
342C22—441no—
343C22C2×D4×D1111yescharacteristic
344C4—21no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4—112no—
350C4—221no—
351C4—441no—
352C4—441no—
353C4—441no—
354C4#41×D1111yescharacteristic
355C4#41×D1111yescharacteristic
356C2—41no—
357C2—222no—
358C2—441no—
359C2—881no—
360C2D11×#12311yescharacteristic
361C2#1062329711yescharacteristic
362C2#1062330511yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#484C2
socleC22×C11C22×D4
prime radical#10623160C2
hypercenter#484D11
hypocenterC11#3098
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
2. #10623035C2semidirect
3. C11×#484C2semidirect
4. #10622658C2semidirect
5. #10622580C2semidirect
6. #10622498C2semidirect
7. #10622495C2semidirect
8. #10622494C2semidirect
9. D11×#107C2semidirect
10. #10622428C2semidirect
11. #10622422C2semidirect
12. #10622417C2semidirect
13. #10622416C2semidirect
14. #10622350C2semidirect
15. #10622340C2semidirect
155. #484D11semidirect
289. C11#3098semidirect

Maximal subgroups

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

subgroupindex
#106231602
#106230352
C11×#4842
#106226582
#106225802
#106224982
#106224952
#106224942
D11×#1072
#106224282
#106224222
#106224172
#106224162
#106223502
#106223402
#309811