Finite Group Databasebeta

← #13075804

Subgroups — #13075804

Order 1408.

448 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#386C211yesmaximal, characteristic
2#10622835C211yesmaximal, characteristic
3#10622833C211yesmaximal, characteristic
4#10622825C211yesmaximal, characteristic, complemented
5#10622824C211yesmaximal, characteristic, complemented
6#10622566C211yesmaximal, characteristic, complemented
7#10622563C211yesmaximal, characteristic, complemented
8#10622562C211yesmaximal, characteristic, complemented
9#10622559C211yesmaximal, characteristic, complemented
10#10622558C211yesmaximal, characteristic, complemented
11#10622558C211yesmaximal, characteristic, complemented
12C11⋊#401C211yesmaximal, characteristic, complemented
13#10622273C211yesmaximal, characteristic, complemented
14#10622270C211yesmaximal, characteristic, complemented
15#10622266C211yesmaximal, characteristic, complemented
16C22×D4×C11C2211yescharacteristic
17C23×C4×C11C2211yescharacteristic
18C23×Dic11C2211yescharacteristic
19C2×C11×C22⋊C4C2211yescharacteristic
20C2×C11×C22⋊C4C2211yescharacteristic
21C2×C11×C22⋊C4C2211yescharacteristic
22C2×C22⋊Dic11C2211yescharacteristic
23C2×C22⋊Dic11C2211yescharacteristic
24C2×C22⋊Dic11C2211yescharacteristic
25C2×C22⋊Dic11C2211yescharacteristic
26C2×C22⋊Dic11C2211yescharacteristic
27C2×C22⋊Dic11C2211yescharacteristic
28C2×C22⋊Dic11C2211yescharacteristic
29C2×C4⋊Dic11C2211yescharacteristic
30C2×C4⋊Dic11C2211yescharacteristic
31C2×C4⋊Dic11C2211yescharacteristic
32C2×Dic11⋊C4C2211yescharacteristic
33C2×Dic11⋊C4C2211yescharacteristic
34C2×Dic11⋊C4C2211yescharacteristic
35C2×Dic11⋊C4C2211yescharacteristic
36C2×C4×Dic11C2211yescharacteristic
37C11×#95C2211yescharacteristic
38C11×#95C2211yescharacteristic
39C11⋊#95C2211yescharacteristic
40C11⋊#95C2211yescharacteristic
41C11⋊#95C2211yescharacteristic
42C11⋊#95C2211yescharacteristic
43C11⋊#95C2211yescharacteristic
44C11⋊#95C2211yescharacteristic
45C11⋊#95C2211yescharacteristic
46C11⋊#95C2211yescharacteristic
47C11⋊#95C2211yescharacteristic
48C11⋊#95C2211yescharacteristic
49C11⋊#95C2211yescharacteristic
50C11⋊#95C2211yescharacteristic
51C24×C11C2311yescharacteristic
52C24×C11C2311yescharacteristic
53C2×D4×C11—22no—
54C2×D4×C11—22no—
55C2×D4×C11—41no—
56C22×C4×C11—22no—
57C22×C4×C11—22no—
58C22×C4×C11—41no—
59C22×C4×C11C2311yescharacteristic
60C22×C4×C11C2311yescharacteristic
61C22×C4×C11C2311yescharacteristic
62C22×C4×C11C2311yescharacteristic
63C22×C4×C11C2311yescharacteristic
64C22×Dic11—41no—
65C22×Dic11—41no—
66C22×Dic11—41no—
67C22×Dic11C2311yescharacteristic
68C22×Dic11C2311yescharacteristic
69C22×Dic11C2311yescharacteristic
70C22×Dic11C2311yescharacteristic
71C22×Dic11C2311yescharacteristic
72C22×Dic11C2311yescharacteristic
73C22×Dic11C2311yescharacteristic
74C22×Dic11C2311yescharacteristic
75C11×C22⋊C4—22no—
76C11×C22⋊C4—41no—
77C11×C22⋊C4—41no—
78C22⋊Dic11—22no—
79C22⋊Dic11—22no—
80C22⋊Dic11—22no—
81C22⋊Dic11—41no—
82C22⋊Dic11—41no—
83C22⋊Dic11—41no—
84C22⋊Dic11—41no—
85C4⋊Dic11—22no—
86C4⋊Dic11—41no—
87C4⋊Dic11—41no—
88Dic11⋊C4—41no—
89Dic11⋊C4—41no—
90Dic11⋊C4—41no—
91Dic11⋊C4—41no—
92C4×Dic11—41no—
93#2746—111nomaximal, Sylow
94C23×C11—21no—
95C23×C11—21no—
96C23×C11—21no—
97C23×C11—21no—
98C23×C11—21no—
99C23×C11—21no—
100C23×C11—21no—
101C23×C11—21no—
102C23×C11—21no—
103C23×C11—21no—
104C23×C11—21no—
105C23×C11—21no—
106C23×C11#4112yes—
107C23×C11#4112yes—
108C23×C11C2411yescharacteristic
109D4×C11—44no—
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×C11—44no—
125C2×C4×C11#4112yes—
126C2×Dic11—21no—
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×Dic11—21no—
146C2×Dic11—21no—
147C2×Dic11—21no—
148C2×Dic11—21no—
149C2×Dic11—21no—
150C2×Dic11—44no—
151#401—111no—
152#400—111no—
153#399—111no—
154#398—111no—
155#397—111no—
156#394—111no—
157#388—111no—
158#388—111no—
159#387—111no—
160#386—111no—
161#386D1111yescharacteristic
162#385—111no—
163#385—111no—
164#381—111no—
165#380—111no—
166C22×C11—22no—
167C22×C11—22no—
168C22×C11—22no—
169C22×C11—22no—
170C22×C11—22no—
171C22×C11—22no—
172C22×C11—41no—
173C22×C11—41no—
174C22×C11—41no—
175C22×C11—41no—
176C22×C11—41no—
177C22×C11—41no—
178C22×C11—41no—
179C22×C11—41no—
180C22×C11C2×#4111yescharacteristic
181C22×C11C2×#4111yescharacteristic
182C22×C11C2×#4111yescharacteristic
183C22×C11H(5,𝔽2)11yescharacteristic
184C22×C11H(5,𝔽2)11yescharacteristic
185C22×C11H(5,𝔽2)11yescharacteristic
186C22×C112−1+411yescharacteristic
187C4×C11—22no—
188C4×C11—41no—
189C4×C11—41no—
190C4×C11—41no—
191C4×C11—41no—
192Dic11—41no—
193Dic11—41no—
194Dic11—41no—
195Dic11—41no—
196Dic11—41no—
197Dic11—41no—
198Dic11—41no—
199Dic11—41no—
200C22×D4C2×D1111yescharacteristic
201C23×C4—111no—
202C23×C4C2×D1111yescharacteristic
203C2×C4⋊C4—111no—
204C2×C4⋊C4—111no—
205C2×C4⋊C4—111no—
206C2×C4⋊C4—111no—
207C2×C4⋊C4—111no—
208C2×C4⋊C4—111no—
209C2×C4⋊C4—111no—
210C2×C22⋊C4—111no—
211C2×C22⋊C4—111no—
212C2×C22⋊C4—111no—
213C2×C22⋊C4—111no—
214C2×C22⋊C4—111no—
215C2×C22⋊C4—111no—
216C2×C22⋊C4—111no—
217C2×C22⋊C4C2×D1111yescharacteristic
218C2×C22⋊C4C2×D1111yescharacteristic
219C2×C22⋊C4C2×D1111yescharacteristic
220C2×C42—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#95—111no—
231#95—111no—
232#95—111no—
233#95C2×D1111yescharacteristic
234#95C2×D1111yescharacteristic
235C2×C11—42no—
236C2×C11—42no—
237C2×C11#53911yescharacteristic
238C2×C11#53911yescharacteristic
239C2×C11#54211yescharacteristic
240C2×C11#55111yescharacteristic
241C2×C11#55111yescharacteristic
242C2×C11#55311yescharacteristic
243C2×C11#56011yescharacteristic
244C24C22×D1111yescharacteristic
245C24C22×D1111yescharacteristic
246C2×D4—22no—
247C2×D4—22no—
248C2×D4—41no—
249C22×C4—22no—
250C22×C4—22no—
251C22×C4—41no—
252C22×C4—111no—
253C22×C4—111no—
254C22×C4—111no—
255C22×C4—111no—
256C22×C4—111no—
257C22×C4—111no—
258C22×C4—111no—
259C22×C4—111no—
260C22×C4—441no—
261C22×C4—441no—
262C22×C4—441no—
263C22×C4C22×D1111yescharacteristic
264C22×C4C22×D1111yescharacteristic
265C22×C4C22×D1111yescharacteristic
266C22×C4C22×D1111yescharacteristic
267C22×C4C22×D1111yescharacteristic
268C4⋊C4—222no—
269C4⋊C4—441no—
270C4⋊C4—441no—
271C4⋊C4—441no—
272C4⋊C4—441no—
273C4⋊C4—441no—
274C4⋊C4—441no—
275C22⋊C4—22no—
276C22⋊C4—41no—
277C22⋊C4—41no—
278C22⋊C4—222no—
279C22⋊C4—222no—
280C22⋊C4—222no—
281C22⋊C4—441no—
282C22⋊C4—441no—
283C22⋊C4—441no—
284C22⋊C4—441no—
285C42—441no—
286C11#274611yescharacteristic, complemented, Sylow
287C23—21no—
288C23—21no—
289C23—21no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23—21no—
296C23—21no—
297C23—21no—
298C23—21no—
299C23#433912yes—
300C23#434112yes—
301C23C23×D1111yescharacteristic
302D4—44no—
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—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—44no—
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—221no—
335C2×C4—221no—
336C2×C4—221no—
337C2×C4—221no—
338C2×C4—221no—
339C2×C4—221no—
340C2×C4—221no—
341C2×C4—221no—
342C2×C4—444no—
343C2×C4#434112yes—
344C22—22no—
345C22—22no—
346C22—22no—
347C22—22no—
348C22—22no—
349C22—22no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22C2×#433911yescharacteristic
359C22C2×#434111yescharacteristic
360C22C2×#434111yescharacteristic
361C22#6703711yescharacteristic
362C22#6703711yescharacteristic
363C22#6704211yescharacteristic
364C22#6704311yescharacteristic
365C4—22no—
366C4—41no—
367C4—41no—
368C4—41no—
369C4—41no—
370C4—441no—
371C4—441no—
372C4—441no—
373C4—441no—
374C4—441no—
375C4—441no—
376C4—441no—
377C4—441no—
378C2—42no—
379C2—42no—
380C2#1062302611yescharacteristic
381C2#1062309511yescharacteristic
382C2#1062309611yescharacteristic
383C2#1062311811yescharacteristic
384C2#1062313411yescharacteristic
385C2#1062315111yescharacteristic
386C2#1062319611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#386C2
prime radicalC22×D4×C11C22
hypercenter#386D11
hypocenterC11#2746
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
4. #10622825C2semidirect
5. #10622824C2semidirect
6. #10622566C2semidirect
7. #10622563C2semidirect
8. #10622562C2semidirect
9. #10622559C2semidirect
10. #10622558C2semidirect
11. #10622558C2semidirect
12. C11⋊#401C2semidirect
13. #10622273C2semidirect
14. #10622270C2semidirect
15. #10622266C2semidirect
286. C11#2746semidirect

Maximal subgroups

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

subgroupindex
C11×#3862
#106228352
#106228332
#106228252
#106228242
#106225662
#106225632
#106225622
#106225592
#106225582
C11⋊#4012
#106222732
#106222702
#106222662
#274611