Finite Group Databasebeta

← #14653930

Subgroups — #14653930

Order 2816.

438 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076977C211yesmaximal, characteristic
2#13068767C211yesmaximal, characteristic
3#13068471C211yesmaximal, 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×#66879—21no—
13C2×Dic11⋊C8—21no—
14C2×Dic11⋊C8—21no—
15#10622598—21no—
16#10622598—21no—
17#10622590C412yes—
18#10622586—21no—
19#10622586—21no—
20#10622548C2211yescharacteristic
21C42×Dic11C2211yescharacteristic
22C2×C4⋊(C11⋊C8)C2211yescharacteristic
23C2×C4⋊(C11⋊C8)C2211yescharacteristic
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—
51#66879—42no—
52Dic11⋊C8—42no—
53Dic11⋊C8—42no—
54C4⋊(C11⋊C8)—21no—
55C4⋊(C11⋊C8)—21no—
56C4⋊(C11⋊C8)—21no—
57C4⋊(C11⋊C8)Q812yes—
58#9906—111nomaximal, Sylow
59C22×C4×C11—22no—
60C22×C4×C11C22×C411yescharacteristic
61C22×C4×C11C2×D411yescharacteristic
62C22×C4×C11C2×D411yescharacteristic
63C22×Dic11—22no—
64C22×Dic11C22⋊C411yescharacteristic
65C22×Dic11C22⋊C411yescharacteristic
66C22×Dic11C22⋊C411yescharacteristic
67C22×Dic11C22⋊C411yescharacteristic
68C2×C8×C11—22no—
69C2×C8×C11—41no—
70C2×C8×C11—41no—
71C2×C8×C11—41no—
72C2×C8×C11—41no—
73C2×C8×C11—41no—
74C11×C4⋊C4—42no—
75C11×C4⋊C4—41no—
76C11×C4⋊C4—41no—
77C11×C4⋊C4—41no—
78C11×C4⋊C4—41no—
79C42×C11C2×Q811yescharacteristic
80C42×C11C2×Q811yescharacteristic
81C42×C11#4111yescharacteristic
82C42×C11#4111yescharacteristic
83C4⋊Dic11—42no—
84C4⋊Dic11—44no—
85C4⋊Dic11—41no—
86C4⋊Dic11—41no—
87C4⋊Dic11—41no—
88C4⋊Dic11—41no—
89Dic11⋊C4—44no—
90C4×Dic11—22no—
91C4×Dic11—22no—
92C4×Dic11—21no—
93C4×Dic11—21no—
94C4×Dic11—21no—
95C4×Dic11—21no—
96C4×Dic11—21no—
97C4×Dic11—21no—
98C4×Dic11—21no—
99C4×Dic11—21no—
100C2×C11⋊C8—22no—
101C2×C11⋊C8—41no—
102C2×C11⋊C8—41no—
103C2×C11⋊C8—41no—
104C2×C11⋊C8—41no—
105C2×C11⋊C8—41no—
106#2859—111no—
107#1842—111no—
108#1767—111no—
109#1296—111no—
110#1296—111no—
111#1296—111no—
112#1296D1111yescharacteristic
113C23×C11C2×C22⋊C411yescharacteristic
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—42no—
117C2×C4×C11—42no—
118C2×C4×C11—42no—
119C2×C4×C11C4×Q811yescharacteristic
120C2×C4×C11C4×Q811yescharacteristic
121C2×C4×C11C22⋊Q811yescharacteristic
122C2×C4×C11C22⋊Q811yescharacteristic
123C2×C4×C11#12411yescharacteristic
124C2×C4×C11C4⋊Q811yescharacteristic
125C2×C4×C11#13511yescharacteristic
126C2×C4×C11#13511yescharacteristic
127C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
128C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
129C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
130C2×C4×C11#13711yescharacteristic
131C2×C4×C11#13711yescharacteristic
132C2×C4×C11#13711yescharacteristic
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—42no—
144C2×Dic11—42no—
145C2×Dic11—42no—
146C2×Dic11#10012yes—
147C2×Dic11#10112yes—
148C8×C11—42no—
149C8×C11—81no—
150C11⋊C8—42no—
151C11⋊C8—81no—
152C2×#125—112no—
153C2×C4⋊C8—111no—
154C2×C4⋊C8—111no—
155C2×C4⋊C8—221no—
156C2×C4⋊C8—221no—
157C2×C4⋊C8C2×D1111yescharacteristic
158C2×C4⋊C8C2×D1111yescharacteristic
159C2×#97—221no—
160#389—221no—
161#389—221no—
162#389—221no—
163#389—221no—
164#384—111no—
165#384C2×D1111yescharacteristic
166#382—112no—
167C43—111no—
168#336—221no—
169C22×C11#39111yescharacteristic
170C22×C11C2×#10011yescharacteristic
171C22×C11C2×#10111yescharacteristic
172C22×C11#41611yescharacteristic
173C22×C11#41711yescharacteristic
174C22×C11#41711yescharacteristic
175C22×C11#41711yescharacteristic
176C4×C11—21no—
177C4×C11—21no—
178C4×C11—82no—
179C4×C11#47811yescharacteristic
180C4×C11#47811yescharacteristic
181C4×C11#47911yescharacteristic
182C4×C11#47911yescharacteristic
183C4×C11#49011yescharacteristic
184C4×C11#49111yescharacteristic
185C4×C11#50111yescharacteristic
186C4×C11#50111yescharacteristic
187Dic11—22no—
188Dic11—22no—
189Dic11—41no—
190Dic11—41no—
191Dic11—82no—
192C22×C8—21no—
193C22×C8—21no—
194C22×C8—221no—
195C22×C8—221no—
196#125—444no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—112no—
200C2×C4⋊C4—222no—
201C2×C4⋊C4—222no—
202C2×C4⋊C4—221no—
203C2×C4⋊C4—221no—
204C2×C4⋊C4C4×D1112yes—
205C2×C42—111no—
206C2×C42—111no—
207C2×C42—111no—
208C2×C42—111no—
209C2×C42—111no—
210C2×C42—111no—
211C2×C42C22×D1111yescharacteristic
212C4⋊C8—21no—
213C4⋊C8—21no—
214C4⋊C8—21no—
215C4⋊C8—112no—
216C4⋊C8—221no—
217C4⋊C8—221no—
218C4⋊C8—221no—
219C4⋊C8—442no—
220C4⋊C8—442no—
221C4⋊C8Dic2212yes—
222#97—442no—
223#95—222no—
224#95—222no—
225C2×C11#155111yescharacteristic
226C2×C11#155211yescharacteristic
227C2×C11#156011yescharacteristic
228C2×C11#156111yescharacteristic
229C2×C11#198911yescharacteristic
230C2×C11#199211yescharacteristic
231C2×C11#199711yescharacteristic
232C22×C4—22no—
233C22×C4—111no—
234C22×C4—111no—
235C22×C4—111no—
236C22×C4—111no—
237C22×C4—222no—
238C22×C4C2×C4×D1111yescharacteristic
239C22×C4D4×D1111yescharacteristic
240C22×C4D4×D1111yescharacteristic
241C2×C8—22no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—41no—
245C2×C8—41no—
246C2×C8—41no—
247C2×C8—222no—
248C2×C8—441no—
249C2×C8—441no—
250C2×C8—441no—
251C2×C8—441no—
252C2×C8—441no—
253C4⋊C4—42no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—442no—
259C4⋊C4—444no—
260C4⋊C4—444no—
261C4⋊C4—441no—
262C4⋊C4—441no—
263C4⋊C4—441no—
264C4⋊C4—441no—
265C42—222no—
266C42—222no—
267C42—221no—
268C42—221no—
269C42—221no—
270C42—221no—
271C42—221no—
272C42—221no—
273C42—221no—
274C42—221no—
275C42C2×Dic2211yescharacteristic
276C42#433911yescharacteristic
277C42#434111yescharacteristic
278C42Q8×D1111yescharacteristic
279C11#990611yescharacteristic, complemented, Sylow
280C23C22⋊C4×D1111yescharacteristic
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—112no—
287C2×C4—112no—
288C2×C4—221no—
289C2×C4—221no—
290C2×C4—221no—
291C2×C4—221no—
292C2×C4—221no—
293C2×C4—221no—
294C2×C4—221no—
295C2×C4—221no—
296C2×C4—221no—
297C2×C4—221no—
298C2×C4—442no—
299C2×C4—442no—
300C2×C4—442no—
301C2×C4C4×Dic2211yescharacteristic
302C2×C4#6693111yescharacteristic
303C2×C4#6693811yescharacteristic
304C2×C4#6694011yescharacteristic
305C2×C4#6694111yescharacteristic
306C2×C4#6694911yescharacteristic
307C2×C4#6696411yescharacteristic
308C2×C4#6696411yescharacteristic
309C2×C4#6696711yescharacteristic
310C2×C4#6696811yescharacteristic
311C2×C4#6696811yescharacteristic
312C2×C4#6696911yescharacteristic
313C2×C4#6697111yescharacteristic
314C2×C4#6697211yescharacteristic
315C8—42no—
316C8—81no—
317C8—442no—
318C8—881no—
319C22#1062225911yescharacteristic
320C22D11×#10011yescharacteristic
321C22D11×#10111yescharacteristic
322C22#1062238411yescharacteristic
323C22#1062238411yescharacteristic
324C22#1062241611yescharacteristic
325C22#1062241711yescharacteristic
326C4—21no—
327C4—21no—
328C4—82no—
329C4—222no—
330C4—222no—
331C4—441no—
332C4—441no—
333C4—882no—
334C4#1062237611yescharacteristic
335C4#1062237711yescharacteristic
336C4#1062240911yescharacteristic
337C4#1062241011yescharacteristic
338C4#1062246911yescharacteristic
339C4#1062247011yescharacteristic
340C4#1062248911yescharacteristic
341C4#1062250411yescharacteristic
342C2#1306731011yescharacteristic
343C2#1306731511yescharacteristic
344C2#1306734811yescharacteristic
345C2#1306735211yescharacteristic
346C2#1306957011yescharacteristic
347C2#1306958311yescharacteristic
348C2#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#9906
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
279. C11#9906semidirect

Maximal subgroups

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

subgroupindex
#130769772
#130687672
#130684712
#130665002
#130664992
C11×#12962
#990611