Finite Group Databasebeta

← #14653909

Subgroups — #14653909

Order 2816.

430 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076977C211yesmaximal, characteristic
2#13068732C211yesmaximal, characteristic
3C4⋊C8×Dic11C211yesmaximal, characteristic
4#13066500C211yesmaximal, characteristic
5#13066500C211yesmaximal, characteristic
6#13066499C211yesmaximal, characteristic
7C11×#1296C211yesmaximal, characteristic
8C2×#66943C412yes—
9C2×C11×C4⋊C8C2211yescharacteristic
10C2×C11×C4⋊C8C2211yescharacteristic
11C11×#384C2211yescharacteristic
12C2×C8×Dic11—21no—
13#10622598—21no—
14#10622598—21no—
15#10622590C412yes—
16#10622586—21no—
17#10622586—21no—
18#10622548C2211yescharacteristic
19C42×Dic11C2211yescharacteristic
20C2×C4⋊(C11⋊C8)C2211yescharacteristic
21C2×C4⋊(C11⋊C8)C2211yescharacteristic
22#10622188—21no—
23#10622188—21no—
24#10622188—21no—
25C22×C8×C11—21no—
26C22×C8×C11—21no—
27C2×C11×C4⋊C4—21no—
28C2×C11×C4⋊C4—21no—
29C2×C11×C4⋊C4C2×C412yes—
30C2×C42×C11C2311yescharacteristic
31C2×C4⋊Dic11—21no—
32C2×C4⋊Dic11—21no—
33C2×C4⋊Dic11—22no—
34C2×C4⋊Dic11C2×C412yes—
35C2×Dic11⋊C4—22no—
36C2×C4×Dic11C2×C411yescharacteristic
37C2×C4×Dic11C2×C411yescharacteristic
38C2×C4×Dic11D411yescharacteristic
39C2×C4×Dic11D411yescharacteristic
40C2×C4×Dic11D411yescharacteristic
41C2×C4×Dic11D411yescharacteristic
42C22×C11⋊C8—21no—
43C22×C11⋊C8—21no—
44#66943—44no—
45C11×C4⋊C8—21no—
46C11×C4⋊C8—21no—
47C11×C4⋊C8—21no—
48C11×C4⋊C8Q812yes—
49C11⋊#95—22no—
50C11⋊#95—22no—
51C8×Dic11—42no—
52C4⋊(C11⋊C8)—21no—
53C4⋊(C11⋊C8)—21no—
54C4⋊(C11⋊C8)—21no—
55C4⋊(C11⋊C8)Q812yes—
56#9901—111nomaximal, Sylow
57C22×C4×C11—22no—
58C22×C4×C11C22×C411yescharacteristic
59C22×C4×C11C2×D411yescharacteristic
60C22×C4×C11C2×D411yescharacteristic
61C22×Dic11—22no—
62C22×Dic11C22⋊C411yescharacteristic
63C22×Dic11C22⋊C411yescharacteristic
64C22×Dic11C22⋊C411yescharacteristic
65C22×Dic11C22⋊C411yescharacteristic
66C2×C8×C11—22no—
67C2×C8×C11—41no—
68C2×C8×C11—41no—
69C2×C8×C11—41no—
70C2×C8×C11—41no—
71C2×C8×C11—41no—
72C11×C4⋊C4—42no—
73C11×C4⋊C4—41no—
74C11×C4⋊C4—41no—
75C11×C4⋊C4—41no—
76C11×C4⋊C4—41no—
77C42×C11C2×Q811yescharacteristic
78C42×C11C2×Q811yescharacteristic
79C42×C11#4111yescharacteristic
80C42×C11#4111yescharacteristic
81C4⋊Dic11—42no—
82C4⋊Dic11—44no—
83C4⋊Dic11—41no—
84C4⋊Dic11—41no—
85C4⋊Dic11—41no—
86C4⋊Dic11—41no—
87Dic11⋊C4—44no—
88C4×Dic11—22no—
89C4×Dic11—22no—
90C4×Dic11—21no—
91C4×Dic11—21no—
92C4×Dic11—21no—
93C4×Dic11—21no—
94C4×Dic11—21no—
95C4×Dic11—21no—
96C4×Dic11—21no—
97C4×Dic11—21no—
98C2×C11⋊C8—22no—
99C2×C11⋊C8—41no—
100C2×C11⋊C8—41no—
101C2×C11⋊C8—41no—
102C2×C11⋊C8—41no—
103C2×C11⋊C8—41no—
104#2859—111no—
105#1831—111no—
106C4×C4⋊C8—111no—
107#1296—111no—
108#1296—111no—
109#1296—111no—
110#1296D1111yescharacteristic
111C23×C11C2×C22⋊C411yescharacteristic
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—42no—
115C2×C4×C11—42no—
116C2×C4×C11—42no—
117C2×C4×C11C4×Q811yescharacteristic
118C2×C4×C11C4×Q811yescharacteristic
119C2×C4×C11C22⋊Q811yescharacteristic
120C2×C4×C11C22⋊Q811yescharacteristic
121C2×C4×C11#12411yescharacteristic
122C2×C4×C11C4⋊Q811yescharacteristic
123C2×C4×C11#13511yescharacteristic
124C2×C4×C11#13511yescharacteristic
125C2×C4×C11#13511yescharacteristic
126C2×C4×C11#13511yescharacteristic
127C2×C4×C11#13511yescharacteristic
128C2×C4×C11#13511yescharacteristic
129C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
130C2×C4×C11#13711yescharacteristic
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—42no—
142C2×Dic11—42no—
143C2×Dic11—42no—
144C2×Dic11#10012yes—
145C2×Dic11#10112yes—
146C8×C11—42no—
147C8×C11—81no—
148C11⋊C8—42no—
149C11⋊C8—81no—
150C2×#125—112no—
151C2×C4⋊C8—111no—
152C2×C4⋊C8—111no—
153C2×C4⋊C8C2×D1111yescharacteristic
154C2×C4⋊C8C2×D1111yescharacteristic
155C2×C4×C8—221no—
156#389—221no—
157#389—221no—
158#389—221no—
159#389—221no—
160#384—111no—
161#384C2×D1111yescharacteristic
162#382—112no—
163C43—111no—
164#336—221no—
165#336—221no—
166#336—221no—
167C22×C11#39111yescharacteristic
168C22×C11C2×#10011yescharacteristic
169C22×C11C2×#10111yescharacteristic
170C22×C11#41611yescharacteristic
171C22×C11#41611yescharacteristic
172C22×C11#41611yescharacteristic
173C22×C11#41711yescharacteristic
174C4×C11—21no—
175C4×C11—21no—
176C4×C11—82no—
177C4×C11#47811yescharacteristic
178C4×C11#47811yescharacteristic
179C4×C11#47911yescharacteristic
180C4×C11#47911yescharacteristic
181C4×C11#48811yescharacteristic
182C4×C11#48811yescharacteristic
183C4×C11#49911yescharacteristic
184C4×C11#49911yescharacteristic
185Dic11—22no—
186Dic11—22no—
187Dic11—41no—
188Dic11—41no—
189Dic11—82no—
190C22×C8—21no—
191C22×C8—21no—
192C22×C8—221no—
193C22×C8—221no—
194#125—444no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—112no—
198C2×C4⋊C4—222no—
199C2×C4⋊C4—222no—
200C2×C4⋊C4—221no—
201C2×C4⋊C4—221no—
202C2×C4⋊C4C4×D1112yes—
203C2×C42—111no—
204C2×C42—111no—
205C2×C42—111no—
206C2×C42—111no—
207C2×C42—111no—
208C2×C42—111no—
209C2×C42C22×D1111yescharacteristic
210C4⋊C8—21no—
211C4⋊C8—21no—
212C4⋊C8—21no—
213C4⋊C8—112no—
214C4⋊C8—221no—
215C4⋊C8—221no—
216C4⋊C8—221no—
217C4⋊C8Dic2212yes—
218C4×C8—442no—
219#95—222no—
220#95—222no—
221C2×C11#154311yescharacteristic
222C2×C11#154411yescharacteristic
223C2×C11#155111yescharacteristic
224C2×C11#155211yescharacteristic
225C2×C11#198911yescharacteristic
226C2×C11#199111yescharacteristic
227C2×C11#199711yescharacteristic
228C22×C4—22no—
229C22×C4—111no—
230C22×C4—111no—
231C22×C4—111no—
232C22×C4—111no—
233C22×C4—222no—
234C22×C4C2×C4×D1111yescharacteristic
235C22×C4D4×D1111yescharacteristic
236C22×C4D4×D1111yescharacteristic
237C2×C8—22no—
238C2×C8—41no—
239C2×C8—41no—
240C2×C8—41no—
241C2×C8—41no—
242C2×C8—41no—
243C2×C8—222no—
244C2×C8—441no—
245C2×C8—441no—
246C2×C8—441no—
247C2×C8—441no—
248C2×C8—441no—
249C4⋊C4—42no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—442no—
255C4⋊C4—444no—
256C4⋊C4—444no—
257C4⋊C4—441no—
258C4⋊C4—441no—
259C4⋊C4—441no—
260C4⋊C4—441no—
261C42—222no—
262C42—222no—
263C42—221no—
264C42—221no—
265C42—221no—
266C42—221no—
267C42—221no—
268C42—221no—
269C42—221no—
270C42—221no—
271C42C2×Dic2211yescharacteristic
272C42#433911yescharacteristic
273C42#434111yescharacteristic
274C42Q8×D1111yescharacteristic
275C11#990111yescharacteristic, complemented, Sylow
276C23C22⋊C4×D1111yescharacteristic
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—112no—
283C2×C4—112no—
284C2×C4—221no—
285C2×C4—221no—
286C2×C4—221no—
287C2×C4—221no—
288C2×C4—221no—
289C2×C4—221no—
290C2×C4—221no—
291C2×C4—221no—
292C2×C4—221no—
293C2×C4—221no—
294C2×C4—442no—
295C2×C4—442no—
296C2×C4—442no—
297C2×C4C4×Dic2211yescharacteristic
298C2×C4#6693111yescharacteristic
299C2×C4#6693811yescharacteristic
300C2×C4#6694011yescharacteristic
301C2×C4#6694111yescharacteristic
302C2×C4#6694911yescharacteristic
303C2×C4#6696411yescharacteristic
304C2×C4#6696511yescharacteristic
305C2×C4#6696811yescharacteristic
306C2×C4#6696911yescharacteristic
307C2×C4#6696911yescharacteristic
308C2×C4#6696911yescharacteristic
309C2×C4#6697211yescharacteristic
310C2×C4#6697211yescharacteristic
311C8—42no—
312C8—81no—
313C8—442no—
314C8—881no—
315C22#1062225911yescharacteristic
316C22D11×#10011yescharacteristic
317C22D11×#10111yescharacteristic
318C22#1062238411yescharacteristic
319C22#1062238511yescharacteristic
320C22#1062241711yescharacteristic
321C22#1062241711yescharacteristic
322C4—21no—
323C4—21no—
324C4—82no—
325C4—222no—
326C4—222no—
327C4—441no—
328C4—441no—
329C4—882no—
330C4#1062237611yescharacteristic
331C4#1062238111yescharacteristic
332C4#1062240911yescharacteristic
333C4#1062241311yescharacteristic
334C4#1062247011yescharacteristic
335C4#1062247111yescharacteristic
336C4#1062249111yescharacteristic
337C4#1062250411yescharacteristic
338C2#1306727711yescharacteristic
339C2#1306727911yescharacteristic
340C2#1306730811yescharacteristic
341C2#1306731511yescharacteristic
342C2#1306957011yescharacteristic
343C2#1306957911yescharacteristic
344C2#1306960311yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1296C2
socle, prime radicalC23×C11C2×C22⋊C4
cosocleC2×C42×C11C23
hypercenter#1296D11
hypocenterC11#9901
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
275. C11#9901semidirect

Maximal subgroups

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

subgroupindex
#130769772
#130687322
C4⋊C8×Dic112
#130665002
#130664992
C11×#12962
#990111