Finite Group Databasebeta

← #14664366

Subgroups — #14664366

Order 2816.

414 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 73 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073600C211yesmaximal, characteristic
2#13068411C211yesmaximal, characteristic
3#13066958C211yesmaximal, characteristic
4#13066623C211yesmaximal, characteristic
5#13066622C211yesmaximal, characteristic
6#13066621C211yesmaximal, characteristic
7C11×#1346C211yesmaximal, characteristic
8C2×#66941—21no—
9C2×#66941C411yescharacteristic
10C2×#66940C2211yescharacteristic
11C11×#398C2211yescharacteristic
12C2×#66888—21no—
13M16×Dic11—21no—
14#10622596C2211yescharacteristic
15#10622593C411yescharacteristic
16#10622585—21no—
17#10622332—21no—
18#10622274C411yescharacteristic
19#10622262C411yescharacteristic
20#10622260—21no—
21#10622259—21no—
22C11×#343C2211yescharacteristic
23C11×#324C2211yescharacteristic
24#10622168C2211yescharacteristic
25#10622166C2211yescharacteristic
26#10622107—21no—
27C22×Dic22—21no—
28C22×Dic22D411yescharacteristic
29C2×C11×M16—21no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4C2×C411yescharacteristic
32C2×C11×C4⋊C4C2311yescharacteristic
33C2×C4⋊Dic11—21no—
34C2×C4⋊Dic11C2×C411yescharacteristic
35C2×Dic11⋊C4—21no—
36C2×Dic11⋊C4—21no—
37C2×Dic11⋊C4—21no—
38C2×Dic11⋊C4—21no—
39C2×Dic11⋊C4C2×C411yescharacteristic
40C2×Dic11⋊C4D411yescharacteristic
41C2×C4×Dic11—21no—
42C2×C4×Dic11C2×C411yescharacteristic
43C2×C4×Dic11D411yescharacteristic
44C2×C4×Dic11D411yescharacteristic
45C2×#4318—21no—
46#66941—41no—
47#66941—41no—
48#66941—42no—
49#66941—42no—
50#66940—41no—
51#66940—41no—
52C11×C22⋊C8—21no—
53C11×#95—21no—
54C11×#95C2×C411yescharacteristic
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58C11⋊#95C2×C411yescharacteristic
59C22⋊(C11⋊C8)—21no—
60#66888—24no—
61#66879—41no—
62#66879—41no—
63Dic11⋊C8—41no—
64C8×Dic11—41no—
65#11782—111nomaximal, Sylow
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11C22×C411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C22×Dic11—21no—
72C22×Dic11—21no—
73C22×Dic11C22⋊C411yescharacteristic
74C22×Dic11C22⋊C411yescharacteristic
75C22×Dic11C22⋊C411yescharacteristic
76C22×Dic11C22⋊C411yescharacteristic
77C2×Dic22—22no—
78C2×Dic22—21no—
79C2×Dic22—21no—
80C2×Dic22—41no—
81C2×Dic22—42no—
82C2×Dic22—42no—
83C2×Dic22—42no—
84C11×M16—22no—
85C11×M16—41no—
86C2×C8×C11—41no—
87C2×C8×C11—41no—
88C11×C4⋊C4—41no—
89C11×C4⋊C4—41no—
90C11×C4⋊C4—41no—
91C11×C4⋊C4—41no—
92C4⋊Dic11—41no—
93C4⋊Dic11—42no—
94Dic11⋊C4—24no—
95Dic11⋊C4—41no—
96Dic11⋊C4—41no—
97Dic11⋊C4—42no—
98Dic11⋊C4—41no—
99Dic11⋊C4—41no—
100Dic11⋊C4—41no—
101Dic11⋊C4—41no—
102C4×Dic11—21no—
103C4×Dic11—21no—
104C4×Dic11—21no—
105C4×Dic11—21no—
106C4×Dic11—21no—
107C4×Dic11—21no—
108C4×Dic11—42no—
109#4318—22no—
110#4318—41no—
111C2×C11⋊C8—41no—
112C2×C11⋊C8—41no—
113#2546—111no—
114C4×#101—111no—
115#1467—111no—
116#1346—111no—
117#1346—111no—
118#1346—111no—
119#1346D1111yescharacteristic
120C23×C11C2×C22⋊C411yescharacteristic
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—22no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
134C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
135C2×Dic11—21no—
136C2×Dic11—21no—
137C2×Dic11—22no—
138C2×Dic11—22no—
139C2×Dic11—21no—
140C2×Dic11—21no—
141C2×Dic11—21no—
142C2×Dic11—21no—
143C2×Dic11—41no—
144C2×Dic11—41no—
145C2×Dic11—41no—
146C2×Dic11—41no—
147C2×Dic11—41no—
148C2×Dic11—41no—
149C2×Dic11#9911yescharacteristic
150C2×Dic11#9911yescharacteristic
151C2×Dic11#10412yes—
152Dic22—42no—
153Dic22—42no—
154Dic22—84no—
155C8×C11—42no—
156C8×C11—81no—
157C11⋊C8—42no—
158C11⋊C8—81no—
159C2×C4⋊Q8—111no—
160C2×C4⋊Q8—221no—
161C2×C4×Q8—111no—
162#432—221no—
163C2×#101—221no—
164C4×M16—221no—
165#398—111no—
166#398—111no—
167#398—111no—
168#398C2×D1111yescharacteristic
169#391—221no—
170#389—221no—
171#389—221no—
172C4×C4⋊C4—111no—
173#343—111no—
174#343C2×D1111yescharacteristic
175#324—111no—
176#324—221no—
177#324C2×D1111yescharacteristic
178C22×C11—21no—
179C22×C11—21no—
180C22×C11C2×#9911yescharacteristic
181C22×C11#41811yescharacteristic
182C22×C11C2×#10411yescharacteristic
183C4×C11—21no—
184C4×C11—21no—
185C4×C11—42no—
186C4×C11—41no—
187C4×C11—41no—
188C4×C11—81no—
189Dic11—21no—
190Dic11—22no—
191Dic11—42no—
192Dic11—41no—
193Dic11—41no—
194Dic11—81no—
195Dic11#35612yes—
196C22×Q8—111no—
197C22×Q8—221no—
198C2×M16—21no—
199C2×M16—221no—
200C4⋊Q8—441no—
201C4⋊Q8—441no—
202C4⋊Q8—442no—
203C4⋊Q8—442no—
204C4×Q8—441no—
205C4×Q8—441no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—111no—
208C2×C4⋊C4—111no—
209C2×C4⋊C4—111no—
210C2×C4⋊C4—221no—
211C2×C4⋊C4—221no—
212C2×C4⋊C4—221no—
213C2×C4⋊C4—221no—
214C2×C4⋊C4—221no—
215C2×C4⋊C4C4×D1111yescharacteristic
216C2×C4⋊C4C22×D1111yescharacteristic
217C2×C42—111no—
218C2×C42—111no—
219C2×C42—111no—
220C2×C42—221no—
221C4⋊C8—441no—
222#101—224no—
223C22⋊C8—21no—
224C22⋊C8—221no—
225#97—441no—
226#97—441no—
227C4×C8—441no—
228#95—21no—
229#95—111no—
230#95—221no—
231#95—221no—
232#95—221no—
233#95C4×D1111yescharacteristic
234C2×C11—21no—
235C2×C11—21no—
236C2×C11#150711yescharacteristic
237C2×C11#212311yescharacteristic
238C2×C11C2×#35611yescharacteristic
239C2×Q8—222no—
240C2×Q8—221no—
241C2×Q8—221no—
242C2×Q8—441no—
243C2×Q8—442no—
244C2×Q8—442no—
245C2×Q8—442no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—111no—
249C22×C4—111no—
250C22×C4—111no—
251C22×C4—111no—
252C22×C4—221no—
253C22×C4—221no—
254C22×C4C2×C4×D1111yescharacteristic
255C22×C4D4×D1111yescharacteristic
256C22×C4D4×D1111yescharacteristic
257M16—22no—
258M16—41no—
259M16—222no—
260M16—441no—
261C2×C8—41no—
262C2×C8—41no—
263C2×C8—441no—
264C2×C8—441no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—224no—
270C4⋊C4—441no—
271C4⋊C4—441no—
272C4⋊C4—441no—
273C4⋊C4—441no—
274C4⋊C4—441no—
275C4⋊C4—442no—
276C4⋊C4—442no—
277C4⋊C4—441no—
278C4⋊C4—441no—
279C42—221no—
280C42—221no—
281C42—221no—
282C42—221no—
283C42—221no—
284C42—221no—
285C42—442no—
286C11#1178211yescharacteristic, complemented, Sylow
287C23C22⋊C4×D1111yescharacteristic
288Q8—442no—
289Q8—442no—
290Q8—884no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—22no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—111no—
304C2×C4—111no—
305C2×C4—112no—
306C2×C4—222no—
307C2×C4—221no—
308C2×C4—221no—
309C2×C4—222no—
310C2×C4—221no—
311C2×C4—221no—
312C2×C4—221no—
313C2×C4—221no—
314C2×C4—441no—
315C2×C4—441no—
316C2×C4—441no—
317C2×C4—441no—
318C2×C4—441no—
319C2×C4—441no—
320C2×C4#6696411yescharacteristic
321C2×C4#6696711yescharacteristic
322C8—42no—
323C8—81no—
324C8—442no—
325C8—881no—
326C22—21no—
327C22—21no—
328C22D11×#9911yescharacteristic
329C22#1062238311yescharacteristic
330C22D11×#10411yescharacteristic
331C4—21no—
332C4—21no—
333C4—42no—
334C4—41no—
335C4—41no—
336C4—81no—
337C4—112no—
338C4—222no—
339C4—221no—
340C4—442no—
341C4—441no—
342C4—441no—
343C4—881no—
344C2—21no—
345C2—21no—
346C2#1306713011yescharacteristic
347C2#1307026811yescharacteristic
348C2D11×#35611yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1346C2
socleC22×C11C2×#99
prime radicalC23×C11C2×C22⋊C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1346D11
hypocenterC11#11782
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1346

Complements

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

NH ≅ G/Ntype
286. C11#11782semidirect

Maximal subgroups

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

subgroupindex
#130736002
#130684112
#130669582
#130666232
#130666222
#130666212
C11×#13462
#1178211