Finite Group Databasebeta

← #14807393

Subgroups — #14807393

Order 2816.

1052 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623049C211yesmaximal, characteristic
2C2×#10622312C211yesmaximal, characteristic, complemented
3C2×#10622316C211yesmaximal, characteristic, complemented
4#13074382C211yesmaximal, characteristic
5#13069626C214yesmaximal
6#13069581C211yesmaximal, characteristic, complemented
7#13069436C211yesmaximal, characteristic, complemented
8#13068956C214yesmaximal, complemented
9C11×#1750C211yesmaximal, characteristic
10C2×C11×#117C2211yescharacteristic
11C2×#66977C2212yes—
12C2×#66977C2212yes—
13C22×Dic44C2214yes—
14#10623049—24no—
15#10623049—24no—
16C2×#66942—22no—
17C2×#66932—22no—
18C2×#66923C2211yescharacteristic
19C2×#66922C2211yescharacteristic
20C2×#66922C2211yescharacteristic
21C2×C4×Dic22C2212yes—
22C2×C11×C22⋊C8C2212yes—
23C2×C11×#97C2211yescharacteristic
24C2×C4×C8×C11C2211yescharacteristic
25C2×#66880C2214yes—
26C2×#66880C2214yes—
27#10622596—22no—
28#10622566—22no—
29#10622549C2211yescharacteristic
30#10622542C2212yes—
31#10622316—24no—
32#10622312—24no—
33C11×#336C2212yes—
34#10622189C2214yes—
35C23×C4×C11C2311yescharacteristic
36C22×Dic22C2312yes—
37C22×Dic22C2312yes—
38C22×C8×C11C2312yes—
39C22×C8×C11C2312yes—
40C11×#117—22no—
41C11×#117—22no—
42C2×C11×C4⋊C4D412yes—
43C2×C11×C22⋊C4D412yes—
44C2×C42×C11C2311yescharacteristic
45C2×C42×C11C2311yescharacteristic
46C2×C22⋊Dic11—22no—
47C2×C22⋊Dic11—22no—
48C2×C4⋊Dic11—22no—
49C2×C4⋊Dic11—22no—
50C2×C4⋊Dic11C2312yes—
51C2×C4⋊Dic11C2312yes—
52#66977—24no—
53#66977—24no—
54#66977—44no—
55C2×Dic11⋊C4—22no—
56C2×Dic11⋊C4—22no—
57C2×Dic11⋊C4—22no—
58C2×Dic11⋊C4—22no—
59C2×C4×Dic11—22no—
60C2×Dic44—28no—
61C2×Dic44—28no—
62C2×Dic44—44no—
63#66942—216no—
64#66932—216no—
65#66923—22no—
66#66923D414yes—
67#66922—22no—
68#66922—22no—
69#66922—22no—
70#66922D414yes—
71C4×Dic22—24no—
72C4×Dic22—24no—
73C11×C22⋊C8—24no—
74C11×#97—22no—
75C4×C8×C11—22no—
76C11⋊#95—24no—
77C11⋊#95—22no—
78#66880—28no—
79#66880—44no—
80#25609—111nomaximal, Sylow
81C24×C11C2×D411yescharacteristic
82C22×C4×C11—21no—
83C22×C4×C11—21no—
84C22×C4×C11—22no—
85C22×C4×C11—22no—
86C22×C4×C11C2×D412yes—
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D412yes—
89C22×C4×C11C2411yescharacteristic
90C22×Dic11—22no—
91C22×Dic11—22no—
92C22×Dic11—22no—
93C22×Dic11—22no—
94C2×Dic22—22no—
95C2×Dic22—22no—
96C2×Dic22—22no—
97C2×Dic22—24no—
98C2×Dic22—24no—
99C2×Dic22—24no—
100C2×Dic22—24no—
101C2×Dic22C2×D414yes—
102C2×C8×C11—22no—
103C2×C8×C11—22no—
104C2×C8×C11—22no—
105C2×C8×C11—22no—
106C2×C8×C11—22no—
107C2×C8×C11#4114yes—
108C11×C4⋊C4—24no—
109C11×C22⋊C4—24no—
110C42×C11—21no—
111C42×C11—21no—
112C42×C11C2×D412yes—
113C42×C11C2×D412yes—
114C22⋊Dic11—28no—
115C22⋊Dic11—44no—
116C4⋊Dic11—28no—
117C4⋊Dic11—22no—
118C4⋊Dic11—24no—
119C4⋊Dic11—44no—
120C4⋊Dic11C2×D414yes—
121Dic11⋊C4—28no—
122Dic11⋊C4—28no—
123Dic11⋊C4—28no—
124Dic11⋊C4—44no—
125C4×Dic11—28no—
126Dic44—416no—
127C2×#541—111no—
128C2×#494—111no—
129C2×#491—111no—
130#2621—111no—
131#2001—114no—
132#1991—111no—
133#1960—111no—
134#1878—114no—
135#1750D1111yescharacteristic
136C23×C11—21no—
137C23×C11—21no—
138C23×C11—21no—
139C23×C11—24no—
140C23×C11C22×D411yescharacteristic
141C2×C4×C11—24no—
142C2×C4×C11—22no—
143C2×C4×C11—21no—
144C2×C4×C11—21no—
145C2×C4×C11—21no—
146C2×C4×C11—24no—
147C2×C4×C11—42no—
148C2×C4×C11—42no—
149C2×C4×C11#12014yes—
150C2×C4×C11C22×D411yescharacteristic
151C2×C4×C11C22×D411yescharacteristic
152C2×C4×C11C2×#4112yes—
153C2×C4×C11H(5,𝔽2)12yes—
154C2×Dic11—24no—
155C2×Dic11—24no—
156C2×Dic11—42no—
157C2×Dic11—42no—
158C2×Dic11—44no—
159C2×Dic11—42no—
160C2×Dic11—42no—
161C2×Dic11—42no—
162C2×Dic11—42no—
163C2×Dic11—44no—
164Dic22—28no—
165Dic22—44no—
166Dic22—44no—
167Dic22—44no—
168C8×C11—24no—
169C8×C11—42no—
170C22×Q16—114no—
171#541—224no—
172#541—224no—
173C2×C4⋊Q8—111no—
174C2×C4⋊Q8—111no—
175C2×#126—222no—
176C2×#125—111no—
177C2×#125—222no—
178C2×C22⋊Q8—112no—
179C2×C22⋊Q8—112no—
180C2×C4×Q8—112no—
181C2×#117C2×D1111yescharacteristic
182#494—224no—
183#491—224no—
184C2×#103—114no—
185C2×#103—114no—
186C2×C22⋊C8C2×D1112yes—
187C2×#97C2×D1111yescharacteristic
188C2×C4×C8C2×D1111yescharacteristic
189#398—222no—
190#397—222no—
191#391—112no—
192#382—111no—
193#340—114no—
194#336C2×D1112yes—
195C22×C11—42no—
196C22×C11—41no—
197C22×C11—42no—
198C22×C11—42no—
199C22×C11C2×#12011yescharacteristic
200C22×C11#53211yescharacteristic
201C22×C11#53511yescharacteristic
202C22×C11#57814yes—
203C4×C11—24no—
204C4×C11—41no—
205C4×C11—42no—
206C4×C11#54612yes—
207C4×C11#55012yes—
208Dic11—44no—
209Dic11—44no—
210Dic11—82no—
211Dic11—82no—
212C22×Q8—112no—
213C22×Q8—112no—
214C23×C4C22×D1111yescharacteristic
215C2×Q16—228no—
216C2×Q16—228no—
217C2×Q16—444no—
218C22×C8C22×D1112yes—
219C22×C8C22×D1112yes—
220C4⋊Q8—114no—
221C4⋊Q8—222no—
222C4⋊Q8—222no—
223C4⋊Q8—222no—
224#126—2216no—
225#125—114no—
226#125—2216no—
227#125—222no—
228C22⋊Q8—224no—
229C22⋊Q8—224no—
230C22⋊Q8—444no—
231C4×Q8—224no—
232C4×Q8—224no—
233#117—22no—
234#117—22no—
235C2×C4⋊C4—112no—
236C2×C4⋊C4—112no—
237C2×C4⋊C4—222no—
238C2×C4⋊C4—222no—
239C2×C4⋊C4—222no—
240C2×C4⋊C4—222no—
241C2×C4⋊C4—222no—
242C2×C4⋊C4—222no—
243C2×C4⋊C4D4412yes—
244C2×C22⋊C4—222no—
245C2×C22⋊C4—222no—
246C2×C22⋊C4D4412yes—
247C2×C42—222no—
248C2×C42C22×D1111yescharacteristic
249C2×C42C22×D1111yescharacteristic
250#103—228no—
251#103—444no—
252C22⋊C8—24no—
253#97—22no—
254C4×C8—22no—
255#95—222no—
256#95—224no—
257C2×C11—81no—
258C2×C11#243111yescharacteristic
259C2×C11#301112yes—
260C2×C11#317712yes—
261C2×C11#322312yes—
262C24C2×D4411yescharacteristic
263C2×Q8—114no—
264C2×Q8—222no—
265C2×Q8—224no—
266C2×Q8—224no—
267C2×Q8—222no—
268C2×Q8—222no—
269C2×Q8—224no—
270C2×Q8—224no—
271C22×C4—22no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—22no—
275C22×C4—222no—
276C22×C4—222no—
277C22×C4—222no—
278C22×C4—222no—
279C22×C4C2×D4412yes—
280C22×C4C2×D4411yescharacteristic
281C22×C4C2×D4412yes—
282C22×C4C23×D1111yescharacteristic
283Q16—4416no—
284C2×C8—22no—
285C2×C8—22no—
286C2×C8—22no—
287C2×C8—22no—
288C2×C8—22no—
289C2×C8#433914yes—
290C4⋊C4—24no—
291C4⋊C4—114no—
292C4⋊C4—228no—
293C4⋊C4—228no—
294C4⋊C4—228no—
295C4⋊C4—228no—
296C4⋊C4—222no—
297C4⋊C4—224no—
298C4⋊C4—444no—
299C4⋊C4—444no—
300C22⋊C4—24no—
301C22⋊C4—228no—
302C22⋊C4—444no—
303C42—21no—
304C42—21no—
305C42—228no—
306C42D4×D1112yes—
307C42D4×D1112yes—
308C11#2560911yescharacteristic, complemented, Sylow
309C23—21no—
310C23—21no—
311C23—24no—
312C23—21no—
313C23C22×D4411yescharacteristic
314Q8—228no—
315Q8—444no—
316Q8—444no—
317Q8—444no—
318C2×C4—24no—
319C2×C4—21no—
320C2×C4—22no—
321C2×C4—21no—
322C2×C4—24no—
323C2×C4—21no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—224no—
327C2×C4—224no—
328C2×C4—442no—
329C2×C4—444no—
330C2×C4—442no—
331C2×C4—442no—
332C2×C4—442no—
333C2×C4—444no—
334C2×C4—442no—
335C2×C4—442no—
336C2×C4#6693514yes—
337C2×C4C2×#433912yes—
338C2×C4C2×D4×D1111yescharacteristic
339C2×C4C2×D4×D1111yescharacteristic
340C2×C4#6704212yes—
341C8—24no—
342C8—42no—
343C22—41no—
344C22—42no—
345C22—42no—
346C22—42no—
347C22#1062300811yescharacteristic
348C22C2×#6693511yescharacteristic
349C22#1062305611yescharacteristic
350C22#1062328414yes—
351C4—24no—
352C4—41no—
353C4—42no—
354C4—444no—
355C4—444no—
356C4—882no—
357C4—882no—
358C4#1062308112yes—
359C4#1062308412yes—
360C2—81no—
361C2#1307223511yescharacteristic
362C2#1307791312yes—
363C2#1307927512yes—
364C2#1307970112yes—
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1750C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenter#1750D11
hypocenterC11#25609
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ #1750

Complements

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

NH ≅ G/Ntype
2. C2×#10622312C2semidirect
3. C2×#10622316C2semidirect
6. #13069581C2semidirect
7. #13069436C2semidirect
8. #13068956C2semidirect
308. C11#25609semidirect

Maximal subgroups

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

subgroupindex
C2×#106230492
C2×#106223122
C2×#106223162
#130743822
#130696262
#130695812
#130694362
#130689562
C11×#17502
#2560911