Finite Group Databasebeta

← #14655688

Subgroups — #14655688

Order 2816.

574 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 574 conjugacy classes of subgroups — too many to draw. Only its 107 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#13079543C211yesmaximal, characteristic
2#13079073C211yesmaximal, characteristic
3C2×#10622706C211yesmaximal, characteristic, complemented
4#13069604C211yesmaximal, characteristic, complemented
5#13067066C211yesmaximal, characteristic
6#13066452C211yesmaximal, characteristic, complemented
7C11×#1546C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×#66995—22no—
10#10623008C2211yescharacteristic
11C2×#66922C2211yescharacteristic
12C11×#431C2211yescharacteristic
13C11×#423C2211yescharacteristic
14#10622706—22no—
15#10622706—22no—
16#10622705—21no—
17#10622699—22no—
18#10622698—21no—
19C2×#66874—22no—
20C4×#4318C2211yescharacteristic
21C2×C4×C11⋊C8C2211yescharacteristic
22#10622454—22no—
23#10622351—22no—
24#10622306—21no—
25#10622294—21no—
26C11×#332—22no—
27#10622192—22no—
28#10622121—22no—
29C22×Q8×C11—21no—
30C2×#4339—21no—
31C22×Dic22D412yes—
32C2×C11×M16—21no—
33C11×C4⋊Q8—21no—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8D412yes—
37C2×C11×C4⋊C4—21no—
38C2×C11×C4⋊C4—21no—
39C2×C42×C11C2311yescharacteristic
40C2×#4326—24no—
41#66995—44no—
42#66995—44no—
43C2×#4325—24no—
44#66983—21no—
45#66983—21no—
46C2×C4⋊Dic11—21no—
47C2×C4⋊Dic11—21no—
48C2×#4318D412yes—
49C22×C11⋊C8—21no—
50C2×#4314—24no—
51#66928—21no—
52#66927D411yescharacteristic
53C4×D44—21no—
54C4×D44—21no—
55#66922—21no—
56#66922—21no—
57#66922—21no—
58#66922—21no—
59#66922D411yescharacteristic
60C11×C4⋊C8—21no—
61C11×C4⋊C8—21no—
62C11×C4⋊C8D412yes—
63C11×C22⋊C8—21no—
64C4×C8×C11—21no—
65#66880—24no—
66#66874—28no—
67#66867—21no—
68C4×C11⋊C8—21no—
69C4×C11⋊C8—21no—
70C4×C11⋊C8D412yes—
71#10170—111nomaximal, Sylow
72C2×Q8×C11—22no—
73C2×Q8×C11—41no—
74C2×Q8×C11—42no—
75C2×Q8×C11—42no—
76C22×C4×C11—41no—
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11#4111yescharacteristic
80C2×C22⋊D11—41no—
81C22×Dic11—22no—
82#4339—42no—
83#4339—42no—
84C2×D44—21no—
85C2×D44—21no—
86C2×D44—21no—
87C2×C4×D11—41no—
88C2×Dic22—22no—
89C2×Dic22—22no—
90C2×Dic22—21no—
91C2×Dic22—44no—
92C11×M16—42no—
93C2×C8×C11—22no—
94C2×C8×C11—41no—
95C11×C4⋊C4—22no—
96C11×C4⋊C4—22no—
97C11×C4⋊C4—41no—
98C11×C4⋊C4—41no—
99C42×C11C2×D411yescharacteristic
100C42×C11C2×D411yescharacteristic
101C42×C11C2×D411yescharacteristic
102C42×C11C2×D411yescharacteristic
103#4326—48no—
104#4325—48no—
105(C2×D11)⋊C4—41no—
106(C2×D11)⋊C4—41no—
107C4⋊Dic11—21no—
108C4⋊Dic11—21no—
109C4⋊Dic11—41no—
110C4⋊Dic11—41no—
111C4⋊Dic11—41no—
112C4⋊Dic11—41no—
113#4318—22no—
114#4318SD1614yescomplemented
115C2×C11⋊C8—22no—
116C2×C11⋊C8—22no—
117C2×C11⋊C8—42no—
118#4314—84no—
119#3206—111no—
120#3152—111no—
121C2×#487—111no—
122#1997—111no—
123#1546D1111yescharacteristic, complemented
124#1492—111no—
125#1278—111no—
126C23×C11#12111yescharacteristic
127C22×D11—41no—
128Q8×C11—44no—
129Q8×C11—81no—
130Q8×C11—81no—
131C2×C4×C11—22no—
132C2×C4×C11—22no—
133C2×C4×C11—42no—
134C2×C4×C11—82no—
135C2×C4×C11#12011yescharacteristic
136C2×C4×C11#12011yescharacteristic
137C2×C4×C11#12011yescharacteristic
138C2×C4×C11#12111yescharacteristic
139C2×C4×C11#12111yescharacteristic
140C2×C4×C11#12711yescharacteristic
141C2×C4×C11C2×SD1612yes—
142C2×C4×C11AGL(1,ℤ/8)12yes—
143C22⋊D11—82no—
144C2×Dic11—41no—
145C2×Dic11—42no—
146C2×Dic11—82no—
147D44—42no—
148D44—42no—
149D44—42no—
150C4×D11—81no—
151C4×D11—81no—
152Dic22—44no—
153Dic22—42no—
154Dic22—44no—
155C8×C11—42no—
156C8×C11—81no—
157C11⋊C8—24no—
158C11⋊C8—42no—
159C2×#137—222no—
160#532—111no—
161C2×C4⋊Q8—111no—
162C2×C4⋊Q8C2×D1111yescharacteristic
163#497—222no—
164#494—221no—
165#492—221no—
166#492—221no—
167#487—221no—
168#487—222no—
169#487—222no—
170#461—222no—
171#448—222no—
172#431C2×D1111yescharacteristic
173#423C2×D1111yescharacteristic
174C2×#103—222no—
175C4×M16—111no—
176C2×C4×C8—111no—
177#343—222no—
178#332—22no—
179D4⋊C8—222no—
180C22×C11—21no—
181C22×C11—21no—
182C22×C11#39211yescharacteristic
183C22×C11#46012yes—
184C2×D11—81no—
185C2×D11—81no—
186C2×D11—81no—
187C4×C11—21no—
188C4×C11—21no—
189C4×C11—82no—
190C4×C11#45012yes—
191C4×C11#45512yes—
192C4×C11#47312yes—
193C4×C11#49211yescharacteristic
194C4×C11#49611yescharacteristic
195Dic11—82no—
196Dic11—81no—
197C2×#41—221no—
198C22×Q8—21no—
199C22×Q8—112no—
200#137—444no—
201#137—444no—
202C2×Q16—224no—
203C2×SD16—224no—
204C2×SD16—224no—
205C2×M16—21no—
206C2×M16—112no—
207C22×C8—221no—
208C4⋊Q8—21no—
209C4⋊Q8—21no—
210C4⋊Q8—21no—
211C4⋊Q8—111no—
212C4⋊Q8—221no—
213C4⋊Q8—221no—
214C4⋊Q8—221no—
215C4⋊Q8—221no—
216C4⋊Q8D4412yes—
217#127—111no—
218#124—221no—
219#121—221no—
220#121—221no—
221C4×D4—221no—
222C4×D4—221no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—221no—
226C2×C4⋊C4—221no—
227C2×C42C22×D1111yescharacteristic
228C4⋊C8—21no—
229C4⋊C8—21no—
230C4⋊C8C22⋊D1112yes—
231#103—228no—
232#103—224no—
233C22⋊C8—21no—
234#97—221no—
235C4×C8—21no—
236C4×C8—112no—
237C4×C8—221no—
238C4×C8—221no—
239C2×C11—22no—
240C2×C11#200411yescharacteristic
241C2×C11#201411yescharacteristic
242C2×C11#202011yescharacteristic
243D11—161no—
244#41—442no—
245#41—442no—
246C2×Q8—22no—
247C2×Q8—41no—
248C2×Q8—42no—
249C2×Q8—42no—
250C2×Q8—222no—
251C2×Q8—221no—
252C2×Q8—222no—
253C2×Q8—444no—
254C2×D4—221no—
255C2×D4—221no—
256C2×D4—221no—
257C2×D4—441no—
258C22×C4—41no—
259C22×C4—222no—
260C22×C4—441no—
261C22×C4#433911yescharacteristic
262C22×C4D4×D1111yescharacteristic
263C22×C4D4×D1111yescharacteristic
264Q16—448no—
265SD16—448no—
266SD16—884no—
267M16—42no—
268M16—114no—
269M16—222no—
270C2×C8—22no—
271C2×C8—41no—
272C2×C8—222no—
273C2×C8—222no—
274C2×C8—442no—
275C4⋊C4—22no—
276C4⋊C4—22no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—221no—
280C4⋊C4—221no—
281C4⋊C4—441no—
282C4⋊C4—441no—
283C4⋊C4—441no—
284C4⋊C4—441no—
285C22⋊C4—441no—
286C22⋊C4—441no—
287C42C2×D4411yescharacteristic
288C42D4×D1111yescharacteristic
289C42D4×D1111yescharacteristic
290C42C2×C22⋊D1111yescharacteristic
291C11#1017011yescharacteristic, complemented, Sylow
292C23—441no—
293C23#6693711yescharacteristic
294Q8—44no—
295Q8—81no—
296Q8—81no—
297Q8—444no—
298Q8—444no—
299Q8—442no—
300D4—442no—
301D4—442no—
302D4—442no—
303D4—882no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—42no—
307C2×C4—82no—
308C2×C4—441no—
309C2×C4—442no—
310C2×C4—881no—
311C2×C4—881no—
312C2×C4—882no—
313C2×C4#6693511yescharacteristic
314C2×C4#6693511yescharacteristic
315C2×C4#6693711yescharacteristic
316C2×C4#6696412yes—
317C2×C4SD16×D1112yes—
318C2×C4#6698311yescharacteristic
319C2×C4#6699011yescharacteristic
320C2×C4#6699311yescharacteristic
321C8—42no—
322C8—81no—
323C8—224no—
324C8—442no—
325C22—21no—
326C22—21no—
327C22—881no—
328C22—881no—
329C22—881no—
330C22#1062237512yes—
331C22#1062257311yescharacteristic
332C4—21no—
333C4—21no—
334C4—82no—
335C4—882no—
336C4—881no—
337C4#1062236812yes—
338C4#1062238912yes—
339C4#1062276711yescharacteristic
340C4#1062278811yescharacteristic
341C4#1062281512yes—
342C2—22no—
343C2—1761no—
344C2#1306964611yescharacteristic
345C2#1306970511yescharacteristic
346C2#1306973611yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1546C2
socleC22×C11#392
prime radical#10623008C22
hypercenter#1546D11
hypocenterC11#10170
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1546

Complements

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

NH ≅ G/Ntype
3. C2×#10622706C2semidirect
4. #13069604C2semidirect
6. #13066452C2semidirect
7. C11×#1546C2semidirect
114. #4318SD16semidirect
123. #1546D11semidirect
291. C11#10170semidirect

Maximal subgroups

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

subgroupindex
#130795432
#130790732
C2×#106227062
#130696042
#130670662
#130664522
C11×#15462
#1017011