Finite Group Databasebeta

← #13072299

Subgroups — #13072299

Order 1408.

528 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66949C211yesmaximal, characteristic
2C2×#66925C211yesmaximal, characteristic
3C11×#389C211yesmaximal, characteristic, complemented
4#10622602C211yesmaximal, characteristic
5#10622602C211yesmaximal, characteristic
6#10622600C211yesmaximal, characteristic
7#10622596C211yesmaximal, characteristic, complemented
8#10622595C211yesmaximal, characteristic, complemented
9#10622593C211yesmaximal, characteristic, complemented
10#10622592C211yesmaximal, characteristic, complemented
11#10622546C211yesmaximal, characteristic, complemented
12#10622277C211yesmaximal, characteristic
13D11×#95C211yesmaximal, characteristic
14#10622267C211yesmaximal, characteristic, complemented
15#10622259C211yesmaximal, characteristic, complemented
16C22×C4×D11C2211yescharacteristic
17C22×C4×D11C2211yescharacteristic
18C22×C4×D11C2211yescharacteristic
19C22×Dic22C2211yescharacteristic
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×C4⋊Dic11C2211yescharacteristic
30C2×Dic11⋊C4C2211yescharacteristic
31C2×Dic11⋊C4C2211yescharacteristic
32C2×Dic11⋊C4C2211yescharacteristic
33C2×Dic11⋊C4C2211yescharacteristic
34C2×Dic11⋊C4C2211yescharacteristic
35C2×Dic11⋊C4C2211yescharacteristic
36C2×C4×Dic11C2211yescharacteristic
37#66949—24no—
38#66925—24no—
39C11×#95C2211yescharacteristic
40C11×#95C2211yescharacteristic
41C11⋊#95C2211yescharacteristic
42C11⋊#95C2211yescharacteristic
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—22no—
70C2×C4×D11—22no—
71C2×C4×D11—22no—
72C2×C4×D11—22no—
73C2×C4×D11—22no—
74C2×C4×D11—41no—
75C2×C4×D11—41no—
76C2×C4×D11Q814yescomplemented
77C2×Dic22—22no—
78C2×Dic22—22no—
79C2×Dic22—41no—
80C11×C4⋊C4—22no—
81C11×C4⋊C4—22no—
82C11×C4⋊C4—41no—
83C11×C4⋊C4—41no—
84C42×C11—22no—
85(C2×D11)⋊C4—22no—
86(C2×D11)⋊C4—22no—
87(C2×D11)⋊C4—22no—
88(C2×D11)⋊C4D414yes—
89C4⋊Dic11—22no—
90Dic11⋊C4—22no—
91Dic11⋊C4—22no—
92Dic11⋊C4—22no—
93Dic11⋊C4—22no—
94Dic11⋊C4—22no—
95Dic11⋊C4—41no—
96C4×Dic11—22no—
97#2438—111nomaximal, Sylow
98C23×C11C2411yescharacteristic
99C22×D11—21no—
100C22×D11—21no—
101C22×D11—21no—
102C22×D11—21no—
103C22×D11C2×D412yes—
104C22×D11C2×Q812yes—
105C22×D11#4112yes—
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×Q812yes—
147C2×Dic11#4112yes—
148C4×D11—28no—
149C4×D11—44no—
150C4×D11—44no—
151Dic22—44no—
152C2×C22⋊Q8—111no—
153C2×#117—111no—
154#400—111no—
155#398—111no—
156#398—111no—
157#395—111no—
158#391—111no—
159#389D1111yescharacteristic, complemented
160#387—111no—
161#387—111no—
162#385—111no—
163#385—111no—
164#381—111no—
165#380—111no—
166C2×#95—111no—
167C22×C11C22×D411yescharacteristic
168C22×C11C22×Q811yescharacteristic
169C22×C11C2×#4111yescharacteristic
170C22×C11C2×#4111yescharacteristic
171C22×C11C2×#4111yescharacteristic
172C22×C11H(5,𝔽2)11yescharacteristic
173C22×C112−1+411yescharacteristic
174C2×D11—22no—
175C2×D11—22no—
176C2×D11—22no—
177C2×D11—22no—
178C2×D11—22no—
179C2×D11—22no—
180C2×D11C22⋊Q814yes—
181C4×C11—22no—
182C4×C11—22no—
183C4×C11—22no—
184C4×C11—41no—
185C4×C11—41no—
186C4×C11—41no—
187C4×C11—41no—
188Dic11—22no—
189Dic11—22no—
190Dic11—22no—
191Dic11—41no—
192Dic11—41no—
193Dic11—41no—
194Dic11—41no—
195C22×Q8—111no—
196C23×C4—111no—
197C23×C4—111no—
198C23×C4—111no—
199C22⋊Q8—224no—
200#117—224no—
201C2×C4⋊C4—111no—
202C2×C4⋊C4—111no—
203C2×C4⋊C4—111no—
204C2×C4⋊C4—111no—
205C2×C4⋊C4—111no—
206C2×C4⋊C4—111no—
207C2×C4⋊C4—111no—
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×C42—111no—
217C2×C42C2×D1111yescharacteristic
218#95—111no—
219#95—111no—
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—
230#95C2×D1111yescharacteristic
231#95C2×D1111yescharacteristic
232C2×C11C2×C22⋊Q811yescharacteristic
233C2×C11#53311yescharacteristic
234C2×C11#54411yescharacteristic
235C2×C11#54611yescharacteristic
236C2×C11#54711yescharacteristic
237C2×C11#55111yescharacteristic
238C2×C11#55211yescharacteristic
239D11—24no—
240C24—111no—
241C2×Q8—222no—
242C2×Q8—222no—
243C2×Q8—441no—
244C22×C4—111no—
245C22×C4—111no—
246C22×C4—111no—
247C22×C4—114no—
248C22×C4—111no—
249C22×C4—111no—
250C22×C4—111no—
251C22×C4—111no—
252C22×C4—222no—
253C22×C4—222no—
254C22×C4—222no—
255C22×C4—222no—
256C22×C4—222no—
257C22×C4—222no—
258C22×C4—441no—
259C22×C4—441no—
260C22×C4C22×D1111yescharacteristic
261C22×C4C22×D1111yescharacteristic
262C22×C4C22×D1111yescharacteristic
263C22×C4C22×D1111yescharacteristic
264C22×C4C22×D1111yescharacteristic
265C22×C4C22×D1111yescharacteristic
266C22×C4C22×D1111yescharacteristic
267C4⋊C4—22no—
268C4⋊C4—22no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—222no—
272C4⋊C4—222no—
273C4⋊C4—222no—
274C4⋊C4—222no—
275C4⋊C4—222no—
276C4⋊C4—222no—
277C4⋊C4—441no—
278C22⋊C4—114no—
279C22⋊C4—222no—
280C22⋊C4—222no—
281C22⋊C4—222no—
282C42—22no—
283C42—222no—
284C11#243811yescharacteristic, complemented, Sylow
285C23—112no—
286C23—112no—
287C23—112no—
288C23—221no—
289C23—221no—
290C23—221no—
291C23—221no—
292C23C23×D1111yescharacteristic
293Q8—444no—
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—21no—
311C2×C4—21no—
312C2×C4—112no—
313C2×C4—112no—
314C2×C4—112no—
315C2×C4—228no—
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—221no—
332C2×C4—221no—
333C2×C4—221no—
334C2×C4—444no—
335C2×C4—444no—
336C2×C4#433912yes—
337C2×C4D4×D1112yes—
338C2×C4Q8×D1112yes—
339C22—114no—
340C22—222no—
341C22—222no—
342C22—222no—
343C22—222no—
344C22—222no—
345C22—222no—
346C22C2×#433911yescharacteristic
347C22C2×D4×D1111yescharacteristic
348C22#6703711yescharacteristic
349C22C2×Q8×D1111yescharacteristic
350C22#6704011yescharacteristic
351C22#41×D1111yescharacteristic
352C22#41×D1111yescharacteristic
353C4—22no—
354C4—22no—
355C4—22no—
356C4—41no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—222no—
361C4—222no—
362C4—222no—
363C4—441no—
364C4—441no—
365C4—441no—
366C4—441no—
367C2—224no—
368C2#1062303811yescharacteristic
369C2#1062308711yescharacteristic
370C2#1062310911yescharacteristic
371C2#1062314311yescharacteristic
372C2D11×C22⋊Q811yescharacteristic
373C2#1062322411yescharacteristic
374C2#1062326011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#389C2
prime radicalC23×D11C23
hypercenter#389D11
hypocenterC11#2438
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
3. C11×#389C2semidirect
7. #10622596C2semidirect
8. #10622595C2semidirect
9. #10622593C2semidirect
10. #10622592C2semidirect
11. #10622546C2semidirect
14. #10622267C2semidirect
15. #10622259C2semidirect
76. C2×C4×D11Q8semidirect
159. #389D11semidirect
284. C11#2438semidirect

Maximal subgroups

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

subgroupindex
C2×#669492
C2×#669252
C11×#3892
#106226022
#106226002
#106225962
#106225952
#106225932
#106225922
#106225462
#106222772
D11×#952
#106222672
#106222592
#243811