Finite Group Databasebeta

← #13075491

Subgroups — #13075491

Order 1408.

472 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66949C211yesmaximal, characteristic
2C2×#66942C211yesmaximal, characteristic, complemented
3C11×#384C211yesmaximal, characteristic, complemented
4#10622607C211yesmaximal, characteristic
5#10622605C211yesmaximal, characteristic
6#10622603C211yesmaximal, characteristic
7#10622602C211yesmaximal, characteristic
8#10622602C211yesmaximal, characteristic
9#10622597C211yesmaximal, characteristic, complemented
10#10622595C211yesmaximal, characteristic, complemented
11#10622592C211yesmaximal, characteristic, complemented
12#10622592C211yesmaximal, characteristic, complemented
13#10622585C211yesmaximal, characteristic, complemented
14#10622553C211yesmaximal, characteristic
15#10622546C211yesmaximal, characteristic, complemented
16C22×C4×D11C2211yescharacteristic
17C22×Dic22C2211yescharacteristic
18C2×C11×C4⋊C4C2211yescharacteristic
19C2×C11×C4⋊C4C2211yescharacteristic
20C2×C11×C4⋊C4C2211yescharacteristic
21C2×C11×C4⋊C4C2211yescharacteristic
22C2×C11×C4⋊C4C2211yescharacteristic
23C2×C11×C4⋊C4C2211yescharacteristic
24C2×C42×C11C2211yescharacteristic
25C2×(C2×D11)⋊C4C2211yescharacteristic
26C2×(C2×D11)⋊C4C2211yescharacteristic
27C2×(C2×D11)⋊C4C2211yescharacteristic
28C2×(C2×D11)⋊C4C2211yescharacteristic
29C2×(C2×D11)⋊C4C2211yescharacteristic
30C2×(C2×D11)⋊C4C2211yescharacteristic
31C2×C4⋊Dic11C2211yescharacteristic
32C2×Dic11⋊C4C2211yescharacteristic
33C2×Dic11⋊C4C2211yescharacteristic
34C2×Dic11⋊C4C2211yescharacteristic
35C2×Dic11⋊C4C2211yescharacteristic
36C2×Dic11⋊C4C2211yescharacteristic
37C2×Dic11⋊C4C2211yescharacteristic
38C2×Dic11⋊C4C2211yescharacteristic
39C2×Dic11⋊C4C2211yescharacteristic
40C2×C4×Dic11C2211yescharacteristic
41#66949—24no—
42#66942—24no—
43C11⋊#95C2211yescharacteristic
44C11⋊#95C2211yescharacteristic
45C11⋊#95C2211yescharacteristic
46C11⋊#95C2211yescharacteristic
47C11⋊#95C2211yescharacteristic
48C11⋊#95C2211yescharacteristic
49C11⋊#95C2211yescharacteristic
50C11⋊#95C2211yescharacteristic
51C11⋊#95C2211yescharacteristic
52C11⋊#95C2211yescharacteristic
53C23×D11C2311yescharacteristic
54C22×C4×C11C2311yescharacteristic
55C22×C4×C11C2311yescharacteristic
56C22×C4×C11C2311yescharacteristic
57C22×C4×C11C2311yescharacteristic
58C22×C4×C11C2311yescharacteristic
59C22×C4×C11C2311yescharacteristic
60C22×C4×C11C2311yescharacteristic
61C22×Dic11C2311yescharacteristic
62C22×Dic11C2311yescharacteristic
63C22×Dic11C2311yescharacteristic
64C22×Dic11C2311yescharacteristic
65C22×Dic11C2311yescharacteristic
66C22×Dic11C2311yescharacteristic
67C22×Dic11C2311yescharacteristic
68C2×C4×D11—22no—
69C2×C4×D11—41no—
70C2×C4×D11—41no—
71C2×Dic22—22no—
72C2×Dic22—41no—
73C2×Dic22—41no—
74C11×C4⋊C4—22no—
75C11×C4⋊C4—22no—
76C11×C4⋊C4—41no—
77C11×C4⋊C4—41no—
78C11×C4⋊C4—41no—
79C11×C4⋊C4—41no—
80C42×C11—22no—
81(C2×D11)⋊C4—22no—
82(C2×D11)⋊C4—22no—
83(C2×D11)⋊C4—22no—
84(C2×D11)⋊C4—41no—
85(C2×D11)⋊C4—41no—
86(C2×D11)⋊C4Q814yescomplemented
87C4⋊Dic11—22no—
88Dic11⋊C4—22no—
89Dic11⋊C4—22no—
90Dic11⋊C4—22no—
91Dic11⋊C4—22no—
92Dic11⋊C4—22no—
93Dic11⋊C4—41no—
94Dic11⋊C4—41no—
95Dic11⋊C4D414yes—
96C4×Dic11—22no—
97#2720—111nomaximal, Sylow
98C23×C11C2411yescharacteristic
99C22×D11—21no—
100C22×D11—21no—
101C22×D11—21no—
102C22×D11—21no—
103C22×D11—21no—
104C22×D11—21no—
105C22×D11C2×Q812yes—
106C2×C4×C11—21no—
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×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—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11C2×D412yes—
125C2×C4×C11C2×Q812yes—
126C2×C4×C11#4112yes—
127C2×Dic11—21no—
128C2×Dic11—21no—
129C2×Dic11—21no—
130C2×Dic11—21no—
131C2×Dic11—21no—
132C2×Dic11—21no—
133C2×Dic11—21no—
134C2×Dic11—21no—
135C2×Dic11—21no—
136C2×Dic11—21no—
137C2×Dic11—21no—
138C2×Dic11—21no—
139C2×Dic11—21no—
140C2×Dic11—21no—
141C2×Dic11—21no—
142C2×Dic11—21no—
143C2×Dic11—21no—
144C2×Dic11—21no—
145C2×Dic11C2×D412yes—
146C2×Dic11C2×D412yes—
147C2×Dic11C2×Q812yes—
148C4×D11—44no—
149Dic22—44no—
150C2×#125—111no—
151C2×C22⋊Q8—111no—
152#400—111no—
153#399—111no—
154#398—111no—
155#396—111no—
156#395—111no—
157#395—111no—
158#389—111no—
159#388—111no—
160#388—111no—
161#387—111no—
162#385—111no—
163#385—111no—
164#384D1111yescharacteristic, complemented
165C22×C11C22×D411yescharacteristic
166C22×C11C22×Q811yescharacteristic
167C22×C11C2×#4111yescharacteristic
168C22×C11H(5,𝔽2)11yescharacteristic
169C22×C11H(5,𝔽2)11yescharacteristic
170C22×C112−1+411yescharacteristic
171C22×C112−1+411yescharacteristic
172C2×D11—22no—
173C2×D11—22no—
174C2×D11—22no—
175C2×D11—41no—
176C2×D11—41no—
177C2×D11—41no—
178C2×D11—41no—
179C4×C11—22no—
180C4×C11—22no—
181C4×C11—22no—
182C4×C11—41no—
183C4×C11—41no—
184C4×C11—41no—
185C4×C11—41no—
186Dic11—22no—
187Dic11—22no—
188Dic11—22no—
189Dic11—41no—
190Dic11—41no—
191Dic11—41no—
192Dic11—41no—
193C22×Q8—111no—
194C23×C4—111no—
195#125—224no—
196C22⋊Q8—224no—
197C2×C4⋊C4—111no—
198C2×C4⋊C4—111no—
199C2×C4⋊C4—111no—
200C2×C4⋊C4—111no—
201C2×C4⋊C4—111no—
202C2×C4⋊C4—111no—
203C2×C4⋊C4—111no—
204C2×C4⋊C4—111no—
205C2×C4⋊C4—111no—
206C2×C4⋊C4C2×D1111yescharacteristic
207C2×C4⋊C4C2×D1111yescharacteristic
208C2×C4⋊C4C2×D1111yescharacteristic
209C2×C4⋊C4C2×D1111yescharacteristic
210C2×C4⋊C4C2×D1111yescharacteristic
211C2×C4⋊C4C2×D1111yescharacteristic
212C2×C22⋊C4—111no—
213C2×C22⋊C4—111no—
214C2×C22⋊C4—111no—
215C2×C22⋊C4—111no—
216C2×C22⋊C4—111no—
217C2×C22⋊C4—111no—
218C2×C42—111no—
219C2×C42C2×D1111yescharacteristic
220#95—111no—
221#95—111no—
222#95—111no—
223#95—111no—
224#95—111no—
225#95—111no—
226#95—111no—
227#95—111no—
228#95—111no—
229#95—111no—
230C2×C11#53511yescharacteristic
231C2×C11#53911yescharacteristic
232C2×C11#54411yescharacteristic
233C2×C11#54711yescharacteristic
234C2×C11D4×Q811yescharacteristic
235C2×C11#55411yescharacteristic
236C2×C11#56311yescharacteristic
237D11—42no—
238C24—111no—
239C2×Q8—222no—
240C2×Q8—441no—
241C2×Q8—441no—
242C22×C4—111no—
243C22×C4—111no—
244C22×C4—111no—
245C22×C4—111no—
246C22×C4—111no—
247C22×C4—111no—
248C22×C4—111no—
249C22×C4—222no—
250C22×C4—441no—
251C22×C4—441no—
252C22×C4C22×D1111yescharacteristic
253C22×C4C22×D1111yescharacteristic
254C22×C4C22×D1111yescharacteristic
255C22×C4C22×D1111yescharacteristic
256C22×C4C22×D1111yescharacteristic
257C22×C4C22×D1111yescharacteristic
258C22×C4C22×D1111yescharacteristic
259C4⋊C4—22no—
260C4⋊C4—22no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—114no—
266C4⋊C4—222no—
267C4⋊C4—222no—
268C4⋊C4—222no—
269C4⋊C4—222no—
270C4⋊C4—222no—
271C4⋊C4—222no—
272C4⋊C4—441no—
273C4⋊C4—441no—
274C22⋊C4—114no—
275C22⋊C4—222no—
276C22⋊C4—222no—
277C22⋊C4—222no—
278C22⋊C4—441no—
279C22⋊C4—441no—
280C42—22no—
281C42—222no—
282C11#272011yescharacteristic, complemented, Sylow
283C23—112no—
284C23—221no—
285C23—221no—
286C23—221no—
287C23—221no—
288C23—221no—
289C23—221no—
290C23C23×D1111yescharacteristic
291Q8—444no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—112no—
311C2×C4—112no—
312C2×C4—112no—
313C2×C4—221no—
314C2×C4—221no—
315C2×C4—221no—
316C2×C4—221no—
317C2×C4—221no—
318C2×C4—221no—
319C2×C4—221no—
320C2×C4—221no—
321C2×C4—221no—
322C2×C4—221no—
323C2×C4—221no—
324C2×C4—221no—
325C2×C4—221no—
326C2×C4—221no—
327C2×C4—221no—
328C2×C4—221no—
329C2×C4—221no—
330C2×C4—221no—
331C2×C4—444no—
332C2×C4#433912yes—
333C2×C4D4×D1112yes—
334C2×C4Q8×D1112yes—
335C22—222no—
336C22—222no—
337C22—222no—
338C22—441no—
339C22—441no—
340C22—441no—
341C22—441no—
342C22C2×#433911yescharacteristic
343C22C2×D4×D1111yescharacteristic
344C22#6703711yescharacteristic
345C22#6703711yescharacteristic
346C22C2×Q8×D1111yescharacteristic
347C22#6704011yescharacteristic
348C22#6704011yescharacteristic
349C4—22no—
350C4—22no—
351C4—22no—
352C4—41no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—222no—
357C4—222no—
358C4—222no—
359C4—441no—
360C4—441no—
361C4—441no—
362C4—441no—
363C2—442no—
364C2#1062303811yescharacteristic
365C2#1062304211yescharacteristic
366C2#1062304611yescharacteristic
367C2#1062324611yescharacteristic
368C2#1062325811yescharacteristic
369C2#1062326011yescharacteristic
370C2#1062326611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#384C2
prime radicalC23×D11C23
hypercenter#384D11
hypocenterC11#2720
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #384

Complements

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

NH ≅ G/Ntype
2. C2×#66942C2semidirect
3. C11×#384C2semidirect
9. #10622597C2semidirect
10. #10622595C2semidirect
11. #10622592C2semidirect
12. #10622592C2semidirect
13. #10622585C2semidirect
15. #10622546C2semidirect
86. (C2×D11)⋊C4Q8semidirect
164. #384D11semidirect
282. C11#2720semidirect

Maximal subgroups

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

subgroupindex
C2×#669492
C2×#669422
C11×#3842
#106226072
#106226052
#106226032
#106226022
#106225972
#106225952
#106225922
#106225852
#106225532
#106225462
#272011