Finite Group Databasebeta

← #14655297

Subgroups — #14655297

Order 2816.

488 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 89 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#13080003C211yesmaximal, characteristic
2#13078996C211yesmaximal, characteristic, complemented
3#13069606C211yesmaximal, characteristic, complemented
4#13067208C211yesmaximal, characteristic
5#13067036C211yesmaximal, characteristic, complemented
6#13066507C211yesmaximal, characteristic, complemented
7C11×#3206C211yesmaximal, characteristic
8C11×#532C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10#10623001C2211yescharacteristic
11C11×#492—21no—
12C11×#487—21no—
13C11×#461—22no—
14C11×#448—22no—
15C11×#431C2211yescharacteristic
16#10622838—22no—
17#10622704—21no—
18#10622695—22no—
19#10622694—21no—
20#10622694—21no—
21#10622688—21no—
22#10622655—22no—
23#10622632—21no—
24#10622620—21no—
25#10622537C2211yescharacteristic
26C4×#4318C2211yescharacteristic
27C4×#4318C2211yescharacteristic
28#10622178—22no—
29#10622168—22no—
30#10622122—22no—
31C2×C11×#41—21no—
32C22×Q8×C11D412yes—
33C2×C11×SD16—24no—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8D411yescharacteristic
39C11×#127D411yescharacteristic
40C11×#124—21no—
41C11×#121—21no—
42C11×#121—21no—
43C4×D4×C11—21no—
44C4×D4×C11—21no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4—21no—
47C2×C42×C11C2311yescharacteristic
48C2×#4324—22no—
49#66979—21no—
50#66977—21no—
51#66977—21no—
52C2×#4318—21no—
53C2×#4318—21no—
54C2×#4318D412yes—
55#66923—21no—
56#66922D411yescharacteristic
57#66922D411yescharacteristic
58C4×Dic22—21no—
59C4×Dic22—21no—
60C11×C4⋊C8D412yes—
61C11×#103—24no—
62C11×C22⋊C8—21no—
63C4×C8×C11—21no—
64#66899—24no—
65#66899—24no—
66#66896—22no—
67#66874—22no—
68#66871—22no—
69C4⋊(C11⋊C8)—21no—
70C4⋊(C11⋊C8)—21no—
71#66867—21no—
72#66867D412yes—
73C4×C11⋊C8—21no—
74C4×C11⋊C8—21no—
75#10114—111nomaximal, Sylow
76C11×#41—82no—
77C2×Q8×C11—22no—
78C2×Q8×C11—22no—
79C2×Q8×C11—21no—
80C2×Q8×C11—44no—
81C2×D4×C11—21no—
82C2×D4×C11—21no—
83C2×D4×C11—21no—
84C2×D4×C11—41no—
85C22×C4×C11—22no—
86C22×C4×C11—41no—
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11#4111yescharacteristic
90C2×Dic22—21no—
91C2×Dic22—21no—
92C11×SD16—84no—
93C2×C8×C11—22no—
94C11×C4⋊C4—21no—
95C11×C4⋊C4—21no—
96C11×C4⋊C4—41no—
97C11×C4⋊C4—41no—
98C11×C4⋊C4—41no—
99C11×C4⋊C4—41no—
100C11×C22⋊C4—41no—
101C11×C22⋊C4—41no—
102C42×C11C2×D411yescharacteristic
103C42×C11C2×D411yescharacteristic
104C42×C11C2×D411yescharacteristic
105C42×C11C2×D411yescharacteristic
106C22⋊Dic11—41no—
107#4324—82no—
108C4⋊Dic11—21no—
109C4⋊Dic11—21no—
110C4⋊Dic11—21no—
111C4⋊Dic11—21no—
112Dic11⋊C4—41no—
113Dic11⋊C4—41no—
114C4×Dic11—41no—
115#4318—22no—
116#4318—42no—
117#4318—41no—
118#4318—42no—
119C2×C11⋊C8—22no—
120C2×C11⋊C8—22no—
121C2×C11⋊C8—41no—
122#3254—111no—
123#3206D1111yescharacteristic
124#3139—111no—
125#1997—111no—
126#1525—111no—
127#1485—111no—
128#1299—111no—
129C23×C11—41no—
130C23×C11#12111yescharacteristic
131Q8×C11—44no—
132Q8×C11—44no—
133Q8×C11—81no—
134D4×C11—41no—
135D4×C11—42no—
136D4×C11—41no—
137D4×C11—81no—
138D4×C11—82no—
139C2×C4×C11—21no—
140C2×C4×C11—22no—
141C2×C4×C11—21no—
142C2×C4×C11—22no—
143C2×C4×C11—41no—
144C2×C4×C11—42no—
145C2×C4×C11—82no—
146C2×C4×C11—82no—
147C2×C4×C11#12011yescharacteristic
148C2×C4×C11#12011yescharacteristic
149C2×C4×C11#12011yescharacteristic
150C2×C4×C11#12111yescharacteristic
151C2×C4×C11#12111yescharacteristic
152C2×C4×C11#12711yescharacteristic
153C2×Dic11—41no—
154C2×Dic11—41no—
155Dic22—41no—
156Dic22—41no—
157Dic22—42no—
158C8×C11—42no—
159C11⋊C8—42no—
160C11⋊C8—42no—
161C11⋊C8—42no—
162#533—111no—
163#532C2×D1111yescharacteristic
164C2×C4⋊Q8C2×D1111yescharacteristic
165#492—21no—
166#491—222no—
167#487—21no—
168#487—221no—
169#487—221no—
170#477—221no—
171#474—221no—
172#468—222no—
173#461—22no—
174#461—221no—
175#460—221no—
176#448—22no—
177#431C2×D1111yescharacteristic
178#423—111no—
179#419—222no—
180C4×M16—111no—
181C4×M16—111no—
182#343—222no—
183#329—222no—
184Q8⋊C8—222no—
185C22×C11—21no—
186C22×C11—21no—
187C22×C11—21no—
188C22×C11—81no—
189C22×C11—81no—
190C22×C11—81no—
191C22×C11#39211yescharacteristic
192C4×C11—21no—
193C4×C11—21no—
194C4×C11—21no—
195C4×C11—82no—
196C4×C11—81no—
197C4×C11#45511yescharacteristic
198C4×C11#45512yes—
199C4×C11#45611yescharacteristic
200C4×C11#47112yes—
201Dic11—81no—
202Dic11—81no—
203C2×#41—21no—
204C22×Q8C22⋊D1112yes—
205C2×SD16—24no—
206C2×SD16—222no—
207C2×M16—112no—
208C2×M16—221no—
209C2×M16—221no—
210C4⋊Q8—21no—
211C4⋊Q8—21no—
212C4⋊Q8—21no—
213C4⋊Q8—21no—
214C4⋊Q8—111no—
215C4⋊Q8—111no—
216C4⋊Q8C22⋊D1111yescharacteristic
217#127C22⋊D1111yescharacteristic
218#125—221no—
219#124—21no—
220C22⋊Q8—221no—
221C22⋊Q8—221no—
222#121—21no—
223#121—21no—
224C4×Q8—221no—
225C4×Q8—221no—
226C4×D4—21no—
227C4×D4—21no—
228#117—221no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—21no—
231C2×C42C22×D1111yescharacteristic
232#107—222no—
233C4⋊C8—221no—
234C4⋊C8—221no—
235C4⋊C8C22⋊D1112yes—
236#103—24no—
237#103—222no—
238#103—224no—
239#103—224no—
240#102—222no—
241C22⋊C8—21no—
242#97—112no—
243#97—221no—
244C4×C8—21no—
245C4×C8—221no—
246C4×C8—221no—
247C2×C11—41no—
248C2×C11—161no—
249C2×C11#200411yescharacteristic
250C2×C11#200711yescharacteristic
251C2×C11#201911yescharacteristic
252#41—82no—
253C2×Q8—22no—
254C2×Q8—21no—
255C2×Q8—22no—
256C2×Q8—44no—
257C2×Q8—221no—
258C2×Q8—221no—
259C2×D4—21no—
260C2×D4—21no—
261C2×D4—21no—
262C2×D4—41no—
263C22×C4—22no—
264C22×C4—41no—
265C22×C4D4×D1111yescharacteristic
266C22×C4#434111yescharacteristic
267C22×C4C2×C22⋊D1111yescharacteristic
268SD16—84no—
269SD16—882no—
270M16—222no—
271M16—442no—
272M16—441no—
273M16—442no—
274C2×C8—22no—
275C2×C8—222no—
276C2×C8—222no—
277C2×C8—441no—
278C4⋊C4—21no—
279C4⋊C4—21no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—221no—
285C4⋊C4—221no—
286C4⋊C4—221no—
287C4⋊C4—221no—
288C4⋊C4—441no—
289C4⋊C4—441no—
290C22⋊C4—41no—
291C22⋊C4—41no—
292C22⋊C4—441no—
293C42—441no—
294C42D4×D1111yescharacteristic
295C42D4×D1111yescharacteristic
296C42C2×C22⋊D1111yescharacteristic
297C42C2×C22⋊D1111yescharacteristic
298C11#1011411yescharacteristic, complemented, Sylow
299C23—41no—
300C23#6699211yescharacteristic
301Q8—44no—
302Q8—44no—
303Q8—81no—
304Q8—442no—
305Q8—441no—
306Q8—441no—
307D4—41no—
308D4—41no—
309D4—42no—
310D4—81no—
311D4—82no—
312C2×C4—22no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—22no—
316C2×C4—41no—
317C2×C4—42no—
318C2×C4—82no—
319C2×C4—82no—
320C2×C4—441no—
321C2×C4—441no—
322C2×C4#6699011yescharacteristic
323C2×C4#6699011yescharacteristic
324C2×C4#6699111yescharacteristic
325C2×C4#6699211yescharacteristic
326C2×C4#6699311yescharacteristic
327C2×C4#6700611yescharacteristic
328C8—42no—
329C8—442no—
330C8—442no—
331C8—442no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—81no—
336C22—81no—
337C22—81no—
338C22#1062283611yescharacteristic
339C4—21no—
340C4—21no—
341C4—21no—
342C4—82no—
343C4—81no—
344C4—881no—
345C4—881no—
346C4#1062279012yes—
347C4#1062281511yescharacteristic
348C4#1062281811yescharacteristic
349C4#1062285512yes—
350C2—41no—
351C2—161no—
352C2#1306964311yescharacteristic
353C2#1306966111yescharacteristic
354C2#1306972811yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3206C2
socleC22×C11#392
prime radicalC11×#532C22
hypercenter#3206D11
hypocenterC11#10114
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3206

Complements

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

NH ≅ G/Ntype
2. #13078996C2semidirect
3. #13069606C2semidirect
5. #13067036C2semidirect
6. #13066507C2semidirect
298. C11#10114semidirect

Maximal subgroups

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

subgroupindex
#130800032
#130789962
#130696062
#130672082
#130670362
#130665072
C11×#32062
#1011411