Finite Group Databasebeta

← #13074929

Subgroups — #13074929

Order 1408.

544 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
1C2×#66950C211yesmaximal, characteristic
2C2×#66949C211yesmaximal, characteristic
3C2×#66941C211yesmaximal, characteristic, complemented
4C2×#66922C211yesmaximal, characteristic, complemented
5C11×#387C211yesmaximal, characteristic, complemented
6#10622596C211yesmaximal, characteristic, complemented
7#10622553C211yesmaximal, characteristic
8#10622290C211yesmaximal, characteristic
9#10622286C211yesmaximal, characteristic
10#10622283C211yesmaximal, characteristic
11#10622281C211yesmaximal, characteristic
12#10622274C211yesmaximal, characteristic, complemented
13#10622269C211yesmaximal, characteristic, complemented
14#10622269C211yesmaximal, characteristic, complemented
15#10622266C211yesmaximal, characteristic, complemented
16C22×C4×D11C2211yescharacteristic
17C22×Dic22C2211yescharacteristic
18C22×Dic22C2211yescharacteristic
19C22×Dic22C2211yescharacteristic
20C2×C11×C4⋊C4C2211yescharacteristic
21C2×C11×C4⋊C4C2211yescharacteristic
22C2×C42×C11C2211yescharacteristic
23C2×(C2×D11)⋊C4C2211yescharacteristic
24C2×(C2×D11)⋊C4C2211yescharacteristic
25C2×(C2×D11)⋊C4C2211yescharacteristic
26C2×(C2×D11)⋊C4C2211yescharacteristic
27C2×(C2×D11)⋊C4C2211yescharacteristic
28C2×(C2×D11)⋊C4C2211yescharacteristic
29C2×C4⋊Dic11C2211yescharacteristic
30C2×C4⋊Dic11C2211yescharacteristic
31C2×C4⋊Dic11C2211yescharacteristic
32C2×C4⋊Dic11C2211yescharacteristic
33C2×C4⋊Dic11C2211yescharacteristic
34C2×C4⋊Dic11C2211yescharacteristic
35C2×C4⋊Dic11C2211yescharacteristic
36C2×Dic11⋊C4C2211yescharacteristic
37C2×Dic11⋊C4C2211yescharacteristic
38C2×Dic11⋊C4C2211yescharacteristic
39C2×Dic11⋊C4C2211yescharacteristic
40C2×C4×Dic11C2211yescharacteristic
41#66950—24no—
42#66949—24no—
43#66941—24no—
44#66922—24no—
45C11×#95C2211yescharacteristic
46C11×#95C2211yescharacteristic
47C11×#95C2211yescharacteristic
48C11×#95C2211yescharacteristic
49C11⋊#95C2211yescharacteristic
50C11⋊#95C2211yescharacteristic
51C11⋊#95C2211yescharacteristic
52C11⋊#95C2211yescharacteristic
53C11⋊#95C2211yescharacteristic
54C11⋊#95C2211yescharacteristic
55C23×D11C2311yescharacteristic
56C22×C4×C11C2311yescharacteristic
57C22×C4×C11C2311yescharacteristic
58C22×C4×C11C2311yescharacteristic
59C22×C4×C11C2311yescharacteristic
60C22×C4×C11C2311yescharacteristic
61C22×C4×C11C2311yescharacteristic
62C22×C4×C11C2311yescharacteristic
63C22×Dic11C2311yescharacteristic
64C22×Dic11C2311yescharacteristic
65C22×Dic11C2311yescharacteristic
66C22×Dic11C2311yescharacteristic
67C22×Dic11C2311yescharacteristic
68C22×Dic11C2311yescharacteristic
69C22×Dic11C2311yescharacteristic
70C2×C4×D11—22no—
71C2×C4×D11—22no—
72C2×C4×D11—41no—
73C2×Dic22—22no—
74C2×Dic22—22no—
75C2×Dic22—22no—
76C2×Dic22—22no—
77C2×Dic22—22no—
78C2×Dic22—22no—
79C2×Dic22—41no—
80C2×Dic22—41no—
81C2×Dic22—41no—
82C11×C4⋊C4—22no—
83C11×C4⋊C4D414yes—
84C42×C11—22no—
85(C2×D11)⋊C4—22no—
86(C2×D11)⋊C4—22no—
87(C2×D11)⋊C4—22no—
88(C2×D11)⋊C4—22no—
89(C2×D11)⋊C4—41no—
90(C2×D11)⋊C4Q814yescomplemented
91C4⋊Dic11—22no—
92C4⋊Dic11—22no—
93C4⋊Dic11—22no—
94C4⋊Dic11—22no—
95C4⋊Dic11—22no—
96C4⋊Dic11—41no—
97C4⋊Dic11D414yes—
98Dic11⋊C4—22no—
99Dic11⋊C4—22no—
100Dic11⋊C4—22no—
101Dic11⋊C4—22no—
102C4×Dic11—22no—
103#2677—111nomaximal, Sylow
104C23×C11C2411yescharacteristic
105C22×D11—21no—
106C22×D11—21no—
107C22×D11—21no—
108C22×D11—21no—
109C22×D11—21no—
110C22×D11—21no—
111C22×D11C2×Q812yes—
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—21no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11C2×D412yes—
129C2×C4×C11C2×D412yes—
130C2×C4×C11C2×D412yes—
131C2×C4×C11C2×D412yes—
132C2×C4×C11C2×Q812yes—
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—21no—
151C2×Dic11C2×D412yes—
152C2×Dic11C2×D412yes—
153C2×Dic11C2×Q812yes—
154C4×D11—44no—
155Dic22—44no—
156Dic22—44no—
157Dic22—44no—
158C2×C4⋊Q8—111no—
159C2×C4⋊Q8—111no—
160C2×C22⋊Q8—111no—
161C2×C22⋊Q8—111no—
162#399—111no—
163#398—111no—
164#398—111no—
165#395—111no—
166#395—111no—
167#393—111no—
168#388—111no—
169#388—111no—
170#387—111no—
171#387D1111yescharacteristic, complemented
172#385—111no—
173C22×C11C22×D411yescharacteristic
174C22×C11C22×D411yescharacteristic
175C22×C11C22×Q811yescharacteristic
176C22×C11H(5,𝔽2)11yescharacteristic
177C22×C112−1+411yescharacteristic
178C22×C112−1+411yescharacteristic
179C22×C112−1+411yescharacteristic
180C2×D11—22no—
181C2×D11—22no—
182C2×D11—22no—
183C2×D11—41no—
184C2×D11—41no—
185C2×D11—41no—
186C2×D11—41no—
187C4×C11—22no—
188C4×C11—22no—
189C4×C11—22no—
190C4×C11—22no—
191C4×C11—22no—
192C4×C11—41no—
193C4×C11—41no—
194Dic11—22no—
195Dic11—22no—
196Dic11—22no—
197Dic11—41no—
198Dic11—41no—
199Dic11—41no—
200Dic11—41no—
201C22×Q8—111no—
202C22×Q8—111no—
203C22×Q8—111no—
204C23×C4—111no—
205C4⋊Q8—224no—
206C4⋊Q8—224no—
207C22⋊Q8—224no—
208C22⋊Q8—224no—
209C2×C4⋊C4—111no—
210C2×C4⋊C4—111no—
211C2×C4⋊C4—111no—
212C2×C4⋊C4—111no—
213C2×C4⋊C4—111no—
214C2×C4⋊C4—111no—
215C2×C4⋊C4—111no—
216C2×C4⋊C4—111no—
217C2×C4⋊C4—111no—
218C2×C4⋊C4—111no—
219C2×C4⋊C4—111no—
220C2×C4⋊C4C2×D1111yescharacteristic
221C2×C4⋊C4C2×D1111yescharacteristic
222C2×C22⋊C4—111no—
223C2×C22⋊C4—111no—
224C2×C22⋊C4—111no—
225C2×C22⋊C4—111no—
226C2×C22⋊C4—111no—
227C2×C22⋊C4—111no—
228C2×C42—111no—
229C2×C42C2×D1111yescharacteristic
230#95—111no—
231#95—111no—
232#95—111no—
233#95—111no—
234#95—111no—
235#95—111no—
236#95C2×D1111yescharacteristic
237#95C2×D1111yescharacteristic
238#95C2×D1111yescharacteristic
239#95C2×D1111yescharacteristic
240C2×C11#53611yescharacteristic
241C2×C11#53611yescharacteristic
242C2×C11#54411yescharacteristic
243C2×C11D4211yescharacteristic
244C2×C11D4×Q811yescharacteristic
245C2×C11D4×Q811yescharacteristic
246C2×C11#56311yescharacteristic
247D11—42no—
248C24—111no—
249C2×Q8—222no—
250C2×Q8—222no—
251C2×Q8—222no—
252C2×Q8—222no—
253C2×Q8—222no—
254C2×Q8—222no—
255C2×Q8—441no—
256C2×Q8—441no—
257C2×Q8—441no—
258C22×C4—111no—
259C22×C4—111no—
260C22×C4—111no—
261C22×C4—111no—
262C22×C4—111no—
263C22×C4—111no—
264C22×C4—111no—
265C22×C4—222no—
266C22×C4—222no—
267C22×C4—441no—
268C22×C4C22×D1111yescharacteristic
269C22×C4C22×D1111yescharacteristic
270C22×C4C22×D1111yescharacteristic
271C22×C4C22×D1111yescharacteristic
272C22×C4C22×D1111yescharacteristic
273C22×C4C22×D1111yescharacteristic
274C22×C4C22×D1111yescharacteristic
275C4⋊C4—22no—
276C4⋊C4—114no—
277C4⋊C4—222no—
278C4⋊C4—222no—
279C4⋊C4—222no—
280C4⋊C4—222no—
281C4⋊C4—222no—
282C4⋊C4—222no—
283C4⋊C4—222no—
284C4⋊C4—222no—
285C4⋊C4—222no—
286C4⋊C4—441no—
287C4⋊C4D4414yes—
288C22⋊C4—114no—
289C22⋊C4—222no—
290C22⋊C4—222no—
291C22⋊C4—222no—
292C22⋊C4—222no—
293C22⋊C4—441no—
294C42—22no—
295C42—222no—
296C11#267711yescharacteristic, complemented, Sylow
297C23—112no—
298C23—221no—
299C23—221no—
300C23—221no—
301C23—221no—
302C23—221no—
303C23—221no—
304C23C23×D1111yescharacteristic
305Q8—444no—
306Q8—444no—
307Q8—444no—
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—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—112no—
325C2×C4—112no—
326C2×C4—112no—
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—221no—
343C2×C4—221no—
344C2×C4—221no—
345C2×C4—444no—
346C2×C4C2×D4412yes—
347C2×C4C2×D4412yes—
348C2×C4C2×D4412yes—
349C2×C4D4×D1112yes—
350C2×C4Q8×D1112yes—
351C22—222no—
352C22—222no—
353C22—222no—
354C22—441no—
355C22—441no—
356C22—441no—
357C22—441no—
358C22C22×D4411yescharacteristic
359C22C2×D4×D1111yescharacteristic
360C22C2×Q8×D1111yescharacteristic
361C22#6704211yescharacteristic
362C22#6704311yescharacteristic
363C22#6704311yescharacteristic
364C22#6704311yescharacteristic
365C4—22no—
366C4—22no—
367C4—22no—
368C4—22no—
369C4—22no—
370C4—41no—
371C4—41no—
372C4—222no—
373C4—222no—
374C4—222no—
375C4—441no—
376C4—441no—
377C4—441no—
378C4—441no—
379C2—442no—
380C2#1062305711yescharacteristic
381C2D4×D4411yescharacteristic
382C2Q8×D4411yescharacteristic
383C2#1062316311yescharacteristic
384C2#1062317911yescharacteristic
385C2#1062322011yescharacteristic
386C2#1062324311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#387C2
prime radicalC23×D11C23
hypercenter#387D11
hypocenterC11#2677
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
3. C2×#66941C2semidirect
4. C2×#66922C2semidirect
5. C11×#387C2semidirect
6. #10622596C2semidirect
12. #10622274C2semidirect
13. #10622269C2semidirect
14. #10622269C2semidirect
15. #10622266C2semidirect
90. (C2×D11)⋊C4Q8semidirect
171. #387D11semidirect
296. C11#2677semidirect

Maximal subgroups

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

subgroupindex
C2×#669502
C2×#669492
C2×#669412
C2×#669222
C11×#3872
#106225962
#106225532
#106222902
#106222862
#106222832
#106222812
#106222742
#106222692
#106222662
#267711