Finite Group Databasebeta

← #14655529

Subgroups — #14655529

Order 2816.

604 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 604 conjugacy classes of subgroups — too many to draw. Only its 103 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#13079564C211yesmaximal, characteristic, complemented
2C2×#10622698C211yesmaximal, characteristic
3#13078991C211yesmaximal, characteristic
4#13067285C211yesmaximal, characteristic
5#13067070C211yesmaximal, characteristic, complemented
6#13066454C211yesmaximal, characteristic, complemented
7C11×#1997C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C22×#4325—22no—
10C2×#66927C2211yescharacteristic
11#10623001C2211yescharacteristic
12C11×#423C2211yescharacteristic
13C4×C11×M16C2211yescharacteristic
14#10622841—22no—
15#10622744—22no—
16#10622705—21no—
17#10622703—22no—
18#10622698—22no—
19#10622698—22no—
20#10622694—21no—
21#10622538C2211yescharacteristic
22C2×C4×C11⋊C8C2211yescharacteristic
23#10622326—22no—
24#10622307—21no—
25#10622307—21no—
26C11×#343—22no—
27#10622123—22no—
28#10622122—22no—
29C22×Q8×C11D412yes—
30C22×D44—21no—
31C22×D44—21no—
32C22×D44—21no—
33C2×C11×M16—21no—
34C2×C11×M16D412yes—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8—21no—
39C2×C11×C4⋊C4—21no—
40C2×C11×C4⋊C4—21no—
41C2×C42×C11C2311yescharacteristic
42C2×#4326—24no—
43C2×#4325—28no—
44C2×#4325—48no—
45#66979—21no—
46#66977—21no—
47#66977—21no—
48C22×C11⋊C8—21no—
49#66927—21no—
50#66927—21no—
51#66927—21no—
52#66927D412yes—
53#66923—21no—
54#66922D411yescharacteristic
55#66922D411yescharacteristic
56C4×Dic22—21no—
57C4×Dic22—21no—
58C11×C4⋊C8—21no—
59C11×C4⋊C8—21no—
60C11×#97—21no—
61C4×C8×C11—21no—
62#66899—24no—
63C22⋊(C11⋊C8)—21no—
64#66885—24no—
65#66885—24no—
66C4⋊(C11⋊C8)D412yes—
67C4×C11⋊C8—21no—
68C4×C11⋊C8—21no—
69C4×C11⋊C8D412yes—
70#10147—111nomaximal, Sylow
71C23×D11—41no—
72C2×Q8×C11—22no—
73C2×Q8×C11—22no—
74C2×Q8×C11—44no—
75C22×C4×C11—22no—
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11#4111yescharacteristic
79C2×D44—22no—
80C2×D44—22no—
81C2×D44—22no—
82C2×D44—44no—
83C2×D44—41no—
84C2×D44—41no—
85C2×D44—41no—
86C2×D44—42no—
87C2×D44—42no—
88C2×D44—82no—
89C2×Dic22—21no—
90C2×Dic22—21no—
91C11×M16—22no—
92C11×M16—22no—
93C11×M16—42no—
94C2×C8×C11—22no—
95C2×C8×C11—41no—
96C11×C4⋊C4—41no—
97C11×C4⋊C4—41no—
98C11×C4⋊C4—41no—
99C11×C4⋊C4—41no—
100C42×C11C2×D411yescharacteristic
101C42×C11C2×D411yescharacteristic
102C42×C11C2×D411yescharacteristic
103C42×C11C2×D411yescharacteristic
104C22⋊Dic11—41no—
105#4326—84no—
106#4325—416no—
107C4⋊Dic11—21no—
108C4⋊Dic11—21no—
109C4⋊Dic11—21no—
110C4⋊Dic11—21no—
111Dic11⋊C4—41no—
112Dic11⋊C4—41no—
113C4×Dic11—41no—
114C2×C11⋊C8—24no—
115C2×C11⋊C8—22no—
116C2×C11⋊C8—22no—
117#3209—111no—
118C2×#492—111no—
119#3138—111no—
120#1997D1111yescharacteristic, complemented
121#1545—111no—
122#1493—111no—
123#1278—111no—
124C23×C11#12111yescharacteristic
125C22×D11—42no—
126C22×D11—82no—
127C22×D11—82no—
128C22×D11—82no—
129Q8×C11—44no—
130Q8×C11—44no—
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×C11#13512yes—
142C2×C4×C11#13712yes—
143C2×Dic11—41no—
144C2×Dic11—41no—
145D44—44no—
146D44—44no—
147D44—82no—
148D44—82no—
149D44—82no—
150D44—81no—
151D44—81no—
152Dic22—42no—
153Dic22—42no—
154C8×C11—42no—
155C8×C11—81no—
156C11⋊C8—24no—
157C11⋊C8—42no—
158C22×SD16—222no—
159#533—111no—
160C2×C4⋊Q8C2×D1111yescharacteristic
161C2×#127—111no—
162#494—221no—
163#492—222no—
164#492—222no—
165#490—222no—
166#487—221no—
167#486—221no—
168#486—221no—
169#462—222no—
170#451—222no—
171#431—111no—
172#423C2×D1111yescharacteristic
173#418—222no—
174C4×M16C2×D1111yescharacteristic
175C2×C4×C8—111no—
176#343—22no—
177#331—222no—
178Q8⋊C8—222no—
179C22×C11—21no—
180C22×C11—21no—
181C22×C11#39211yescharacteristic
182C22×C11#46412yes—
183C2×D11—82no—
184C2×D11—82no—
185C2×D11—82no—
186C2×D11—164no—
187C4×C11—21no—
188C4×C11—21no—
189C4×C11—82no—
190C4×C11#45212yes—
191C4×C11#45312yes—
192C4×C11#47112yes—
193C4×C11#49511yescharacteristic
194C4×C11#49711yescharacteristic
195Dic11—81no—
196Dic11—81no—
197C22×Q8D4412yes—
198C22×D4—221no—
199C22×D4—221no—
200C22×D4—221no—
201C2×Q16—224no—
202C2×SD16—228no—
203C2×SD16—448no—
204C2×M16—21no—
205C2×M16C22⋊D1112yes—
206C22×C8—221no—
207C4⋊Q8—21no—
208C4⋊Q8—21no—
209C4⋊Q8—21no—
210C4⋊Q8—21no—
211C4⋊Q8—111no—
212C4⋊Q8—111no—
213#127—112no—
214#127—221no—
215#127—221no—
216#127—221no—
217#125—221no—
218C22⋊Q8—221no—
219C22⋊Q8—221no—
220C4×Q8—221no—
221C4×Q8—221no—
222#117—221no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C42C22×D1111yescharacteristic
226C4⋊C8—21no—
227C4⋊C8—21no—
228C4⋊C8—112no—
229#103—224no—
230#102—224no—
231#102—224no—
232C22⋊C8—221no—
233#97—21no—
234C4×C8—21no—
235C4×C8—112no—
236C4×C8—221no—
237C4×C8—221no—
238C2×C11—22no—
239C2×C11#200211yescharacteristic
240C2×C11#201511yescharacteristic
241C2×C11#201911yescharacteristic
242D11—162no—
243C24—441no—
244C2×Q8—22no—
245C2×Q8—22no—
246C2×Q8—44no—
247C2×Q8—221no—
248C2×Q8—221no—
249C2×D4—222no—
250C2×D4—222no—
251C2×D4—222no—
252C2×D4—444no—
253C2×D4—441no—
254C2×D4—441no—
255C2×D4—441no—
256C2×D4—442no—
257C2×D4—442no—
258C2×D4—882no—
259C22×C4—22no—
260C22×C4C2×D4411yescharacteristic
261C22×C4#433911yescharacteristic
262C22×C4C2×C22⋊D1111yescharacteristic
263Q16—884no—
264SD16—4416no—
265M16—22no—
266M16—22no—
267M16—42no—
268C2×C8—22no—
269C2×C8—41no—
270C2×C8—224no—
271C2×C8—222no—
272C2×C8—222no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—221no—
278C4⋊C4—221no—
279C4⋊C4—221no—
280C4⋊C4—221no—
281C4⋊C4—441no—
282C4⋊C4—441no—
283C22⋊C4—441no—
284C42—441no—
285C42D4×D1111yescharacteristic
286C42D4×D1111yescharacteristic
287C42D4×D1111yescharacteristic
288C42D4×D1111yescharacteristic
289C11#1014711yescharacteristic, complemented, Sylow
290C23—442no—
291C23—882no—
292C23—882no—
293C23—882no—
294C23#6698311yescharacteristic
295Q8—44no—
296Q8—44no—
297Q8—442no—
298Q8—442no—
299D4—444no—
300D4—444no—
301D4—882no—
302D4—882no—
303D4—882no—
304D4—881no—
305D4—881no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—42no—
309C2×C4—82no—
310C2×C4—441no—
311C2×C4—441no—
312C2×C4#6693511yescharacteristic
313C2×C4#6693511yescharacteristic
314C2×C4#6693711yescharacteristic
315C2×C4#6693711yescharacteristic
316C2×C4#6699011yescharacteristic
317C2×C4#6699311yescharacteristic
318C2×C4#6699512yes—
319C2×C4#6700312yes—
320C8—42no—
321C8—81no—
322C8—224no—
323C8—442no—
324C22—21no—
325C22—21no—
326C22—882no—
327C22—882no—
328C22—882no—
329C22—1764no—
330C22#1062257311yescharacteristic
331C22#1062264112yes—
332C4—21no—
333C4—21no—
334C4—82no—
335C4—881no—
336C4—881no—
337C4#1062236012yes—
338C4#1062236712yes—
339C4#1062266012yes—
340C4#1062267211yescharacteristic
341C4#1062269911yescharacteristic
342C2—22no—
343C2—1762no—
344C2#1306963311yescharacteristic
345C2#1306970911yescharacteristic
346C2#1306972911yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1997C2
socleC22×C11#392
prime radicalC2×#66927C22
hypercenter#1997D11
hypocenterC11#10147
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1997

Complements

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

NH ≅ G/Ntype
1. #13079564C2semidirect
5. #13067070C2semidirect
6. #13066454C2semidirect
7. C11×#1997C2semidirect
120. #1997D11semidirect
289. C11#10147semidirect

Maximal subgroups

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

subgroupindex
#130795642
C2×#106226982
#130789912
#130672852
#130670702
#130664542
C11×#19972
#1014711