Finite Group Databasebeta

← #14655692

Subgroups — #14655692

Order 2816.

574 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 574 conjugacy classes of subgroups — too many to draw. Only its 113 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#13079075C211yesmaximal, characteristic
3C2×#10622294C211yesmaximal, characteristic, complemented
4#13069605C211yesmaximal, characteristic, complemented
5#13067287C211yesmaximal, characteristic, complemented
6#13067068C211yesmaximal, characteristic
7C11×#1278C211yesmaximal, characteristic, complemented
8C2×#66962—22no—
9#10623008C2211yescharacteristic
10C2×#66922C2211yescharacteristic
11C2×#66922C2211yescharacteristic
12C11×#431C2211yescharacteristic
13C4×C11×M16C2211yescharacteristic
14C2×C4×C8×C11C2211yescharacteristic
15C2×#66880—22no—
16#10622537C2211yescharacteristic
17#10622454—22no—
18#10622351—22no—
19#10622328—22no—
20#10622312—21no—
21#10622306—21no—
22#10622306—21no—
23#10622294—22no—
24#10622294—21no—
25#10622294—22no—
26#10622192—22no—
27#10622124—22no—
28#10622097—22no—
29C2×#4339—21no—
30C22×Dic22—21no—
31C22×Dic22D412yes—
32C2×C11×M16D412yes—
33C22×C8×C11—21no—
34C2×C42×C11C2311yescharacteristic
35#66983—21no—
36#66983—21no—
37C2×C4⋊Dic11—21no—
38C2×C4⋊Dic11—21no—
39C2×C4⋊Dic11—21no—
40C2×C4⋊Dic11—21no—
41C2×#4318—21no—
42#66962—44no—
43#66962—44no—
44C2×Dic44—24no—
45C2×#4314—24no—
46C2×#4314—24no—
47#66928—21no—
48#66927D411yescharacteristic
49C4×D44—21no—
50C4×D44—21no—
51#66922—21no—
52#66922—21no—
53#66922—21no—
54#66922—21no—
55#66922—21no—
56#66922—21no—
57#66922—21no—
58#66922D412yes—
59#66922D411yescharacteristic
60C11×C4⋊C8D412yes—
61C11×C22⋊C8—21no—
62C11×#97—21no—
63C4×C8×C11—21no—
64C4×C8×C11—21no—
65C4×C8×C11—21no—
66C4×C8×C11D412yes—
67#66880—28no—
68#66880—24no—
69C4⋊(C11⋊C8)—21no—
70C4⋊(C11⋊C8)—21no—
71#10170—111nomaximal, Sylow
72C22×C4×C11C2×D411yescharacteristic
73C22×C4×C11C2×D411yescharacteristic
74C22×C4×C11#4111yescharacteristic
75C2×C22⋊D11—41no—
76C22×Dic11—22no—
77C22×Dic11—41no—
78#4339—42no—
79#4339—42no—
80C2×D44—21no—
81C2×D44—21no—
82C2×D44—21no—
83C2×C4×D11—41no—
84C2×Dic22—22no—
85C2×Dic22—22no—
86C2×Dic22—22no—
87C2×Dic22—21no—
88C2×Dic22—44no—
89C2×Dic22—41no—
90C2×Dic22—42no—
91C2×Dic22—42no—
92C11×M16—22no—
93C11×M16SD1614yescomplemented
94C2×C8×C11—22no—
95C2×C8×C11—22no—
96C2×C8×C11—22no—
97C2×C8×C11—42no—
98C42×C11C2×D411yescharacteristic
99C42×C11C2×D411yescharacteristic
100C42×C11C2×D411yescharacteristic
101C42×C11C2×D411yescharacteristic
102(C2×D11)⋊C4—41no—
103(C2×D11)⋊C4—41no—
104C4⋊Dic11—22no—
105C4⋊Dic11—21no—
106C4⋊Dic11—22no—
107C4⋊Dic11—21no—
108C4⋊Dic11—41no—
109C4⋊Dic11—41no—
110C4⋊Dic11—41no—
111C4⋊Dic11—41no—
112C4⋊Dic11—41no—
113C4⋊Dic11—41no—
114#4318—42no—
115C2×C11⋊C8—41no—
116Dic44—48no—
117#4314—48no—
118#4314—84no—
119#3206—111no—
120#3152—111no—
121C2×#487—111no—
122#1997—111no—
123#1546—111no—
124#1492—111no—
125#1278D1111yescharacteristic, complemented
126C23×C11#12111yescharacteristic
127C22×D11—41no—
128C2×C4×C11—22no—
129C2×C4×C11—22no—
130C2×C4×C11#12011yescharacteristic
131C2×C4×C11#12011yescharacteristic
132C2×C4×C11#12011yescharacteristic
133C2×C4×C11#12111yescharacteristic
134C2×C4×C11#12111yescharacteristic
135C2×C4×C11#12711yescharacteristic
136C2×C4×C11C2×SD1612yes—
137C2×C4×C11AGL(1,ℤ/8)12yes—
138C22⋊D11—82no—
139C2×Dic11—42no—
140C2×Dic11—41no—
141C2×Dic11—42no—
142C2×Dic11—82no—
143C2×Dic11—82no—
144D44—42no—
145D44—42no—
146D44—42no—
147C4×D11—81no—
148C4×D11—81no—
149Dic22—44no—
150Dic22—44no—
151Dic22—42no—
152Dic22—44no—
153Dic22—81no—
154Dic22—81no—
155C8×C11—24no—
156C8×C11—42no—
157C8×C11—42no—
158C11⋊C8—81no—
159C2×#137—222no—
160#532—111no—
161C2×C4⋊Q8—111no—
162C2×C4⋊Q8—111no—
163#497—222no—
164#494—221no—
165#492—221no—
166#492—221no—
167#487—222no—
168#487—221no—
169#487—222no—
170#461—222no—
171#448—222no—
172#431C2×D1111yescharacteristic
173#423—111no—
174C2×#103—222no—
175C4×M16C2×D1111yescharacteristic
176C2×C4×C8C2×D1111yescharacteristic
177#343—222no—
178#332—222no—
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#45012yes—
190C4×C11#45512yes—
191C4×C11#47312yes—
192C4×C11#49211yescharacteristic
193C4×C11#49611yescharacteristic
194Dic11—82no—
195Dic11—82no—
196Dic11—81no—
197C2×#41—221no—
198C22×Q8—112no—
199C22×Q8—221no—
200#137—444no—
201#137—444no—
202C2×Q16—224no—
203C2×SD16—224no—
204C2×SD16—224no—
205C2×M16—221no—
206C2×M16D4412yes—
207C22×C8—21no—
208C4⋊Q8—112no—
209C4⋊Q8—111no—
210C4⋊Q8—221no—
211C4⋊Q8—221no—
212C4⋊Q8—221no—
213C4⋊Q8—221no—
214C4⋊Q8—221no—
215C4⋊Q8—221no—
216C4⋊Q8—221no—
217#127—111no—
218#124—221no—
219#121—221no—
220#121—221no—
221C4×D4—221no—
222C4×D4—221no—
223C2×C4⋊C4—221no—
224C2×C4⋊C4—221no—
225C2×C4⋊C4—221no—
226C2×C4⋊C4—221no—
227C2×C42C22×D1111yescharacteristic
228C4⋊C8—221no—
229C4⋊C8—221no—
230C4⋊C8D4412yes—
231#103—228no—
232#103—224no—
233C22⋊C8—21no—
234#97—21no—
235C4×C8—21no—
236C4×C8—21no—
237C4×C8—21no—
238C4×C8D4412yes—
239C2×C11—22no—
240C2×C11#200411yescharacteristic
241C2×C11#201411yescharacteristic
242C2×C11#202011yescharacteristic
243D11—161no—
244#41—442no—
245#41—442no—
246C2×Q8—222no—
247C2×Q8—222no—
248C2×Q8—221no—
249C2×Q8—222no—
250C2×Q8—444no—
251C2×Q8—441no—
252C2×Q8—442no—
253C2×Q8—442no—
254C2×D4—221no—
255C2×D4—221no—
256C2×D4—221no—
257C2×D4—441no—
258C22×C4—222no—
259C22×C4—441no—
260C22×C4—441no—
261C22×C4C2×D4411yescharacteristic
262C22×C4D4×D1111yescharacteristic
263C22×C4#434311yescharacteristic
264Q16—448no—
265SD16—448no—
266SD16—884no—
267M16—22no—
268M16—442no—
269M16#431414yescomplemented
270C2×C8—22no—
271C2×C8—22no—
272C2×C8—22no—
273C2×C8—42no—
274C2×C8—441no—
275C4⋊C4—222no—
276C4⋊C4—221no—
277C4⋊C4—222no—
278C4⋊C4—221no—
279C4⋊C4—441no—
280C4⋊C4—441no—
281C4⋊C4—441no—
282C4⋊C4—441no—
283C4⋊C4—441no—
284C4⋊C4—441no—
285C22⋊C4—441no—
286C22⋊C4—441no—
287C42C2×D4411yescharacteristic
288C42C2×D4411yescharacteristic
289C42D4×D1111yescharacteristic
290C42D4×D1111yescharacteristic
291C11#1017011yescharacteristic, complemented, Sylow
292C23—441no—
293C23#6694811yescharacteristic
294Q8—444no—
295Q8—444no—
296Q8—442no—
297Q8—444no—
298Q8—881no—
299Q8—881no—
300D4—442no—
301D4—442no—
302D4—442no—
303D4—882no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—441no—
307C2×C4—442no—
308C2×C4—442no—
309C2×C4—882no—
310C2×C4—881no—
311C2×C4—881no—
312C2×C4—882no—
313C2×C4#6692711yescharacteristic
314C2×C4#6693511yescharacteristic
315C2×C4#6693511yescharacteristic
316C2×C4#6693511yescharacteristic
317C2×C4#6694811yescharacteristic
318C2×C4#6694811yescharacteristic
319C2×C4C2×#431412yes—
320C2×C4#6696112yes—
321C8—24no—
322C8—42no—
323C8—42no—
324C8—881no—
325C22—21no—
326C22—21no—
327C22—881no—
328C22—881no—
329C22—881no—
330C22#1062228411yescharacteristic
331C22#1062246112yes—
332C4—21no—
333C4—21no—
334C4—882no—
335C4—881no—
336C4—882no—
337C4#1062230611yescharacteristic
338C4#1062232511yescharacteristic
339C4#1062234412yes—
340C4#1062243812yes—
341C4#1062250912yes—
342C2—22no—
343C2—1761no—
344C2#1306964811yescharacteristic
345C2#1306970611yescharacteristic
346C2#1306973811yescharacteristic
subgroupG/H
centerC22#10622284
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1278C2
socleC22×C11#392
prime radical#10623008C22
hypercenter#1278D11
hypocenterC11#10170
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1278

Complements

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

NH ≅ G/Ntype
3. C2×#10622294C2semidirect
4. #13069605C2semidirect
5. #13067287C2semidirect
7. C11×#1278C2semidirect
93. C11×M16SD16semidirect
125. #1278D11semidirect
269. M16#4314semidirect
291. C11#10170semidirect

Maximal subgroups

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

subgroupindex
#130795432
#130790752
C2×#106222942
#130696052
#130672872
#130670682
C11×#12782
#1017011