Finite Group Databasebeta

← #14655276

Subgroups — #14655276

Order 2816.

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

normal subgroups only

This group has 476 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#13079999C211yesmaximal, characteristic
2#13079012C211yesmaximal, characteristic
3#13069606C211yesmaximal, characteristic, complemented
4#13067211C211yesmaximal, characteristic, complemented
5#13067032C211yesmaximal, characteristic
6#13066507C211yesmaximal, characteristic, complemented
7C11×#3229C211yesmaximal, characteristic, complemented
8C11×#533C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10#10623008C2211yescharacteristic
11C11×#498—21no—
12C11×#487—21no—
13C11×#483—22no—
14C11×#475—22no—
15C11×#431C2211yescharacteristic
16#10622706—21no—
17#10622702—22no—
18#10622701—21no—
19#10622700—21no—
20#10622696—21no—
21#10622662—22no—
22#10622640—21no—
23#10622634—21no—
24#10622579—22no—
25#10622537C2211yescharacteristic
26C4×#4318C2211yescharacteristic
27C4×#4318C2211yescharacteristic
28#10622181—22no—
29#10622168—22no—
30#10622121—22no—
31C22×Q8×C11—21no—
32C2×#4339—21no—
33C11×C4⋊Q8—21no—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8D411yescharacteristic
38C11×C4⋊Q8D411yescharacteristic
39C11×#125—21no—
40C11×C22⋊Q8—21no—
41C11×C22⋊Q8—21no—
42C4×Q8×C11—21no—
43C4×Q8×C11—21no—
44C11×#117—21no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4D412yes—
47C2×C42×C11C2311yescharacteristic
48C2×#4325—22no—
49#66983—21no—
50#66983—21no—
51C2×#4318—21no—
52C2×#4318—21no—
53C2×#4318D412yes—
54#66928—21no—
55#66927D411yescharacteristic
56C4×D44—21no—
57C4×D44—21no—
58#66922D411yescharacteristic
59C11×#106—24no—
60C11×C4⋊C8D412yes—
61C11×#103—24no—
62C11×C22⋊C8—21no—
63C4×C8×C11—21no—
64#66899—22no—
65#66874—24no—
66#66873—24no—
67#66873—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#10111—111nomaximal, Sylow
76C2×Q8×C11—21no—
77C2×Q8×C11—21no—
78C2×Q8×C11—41no—
79C2×Q8×C11—41no—
80C2×Q8×C11—82no—
81C22×C4×C11—22no—
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11#4111yescharacteristic
85C2×C22⋊D11—41no—
86#4339—44no—
87C2×D44—21no—
88C2×D44—21no—
89C2×D44—21no—
90C2×C4×D11—41no—
91C2×Dic22—21no—
92C2×C8×C11—22no—
93C11×C4⋊C4—21no—
94C11×C4⋊C4—22no—
95C11×C4⋊C4—22no—
96C11×C4⋊C4—21no—
97C11×C4⋊C4—21no—
98C11×C4⋊C4—21no—
99C11×C4⋊C4—41no—
100C11×C4⋊C4—41no—
101C11×C4⋊C4—41no—
102C11×C4⋊C4—41no—
103C11×C22⋊C4—41no—
104C42×C11—41no—
105C42×C11C2×D411yescharacteristic
106C42×C11C2×D411yescharacteristic
107C42×C11C2×D411yescharacteristic
108C42×C11C2×D411yescharacteristic
109#4325—82no—
110(C2×D11)⋊C4—41no—
111(C2×D11)⋊C4—41no—
112C4⋊Dic11—21no—
113C4⋊Dic11—21no—
114#4318—22no—
115#4318—42no—
116#4318—42no—
117#4318—41no—
118C2×C11⋊C8—22no—
119C2×C11⋊C8—22no—
120C2×C11⋊C8—41no—
121#3254—111no—
122#3229D1111yescharacteristic, complemented
123#3141—111no—
124#1997—111no—
125#1526—111no—
126#1484—111no—
127#1299—111no—
128C23×C11#12111yescharacteristic
129C22×D11—41no—
130Q8×C11—42no—
131Q8×C11—41no—
132Q8×C11—41no—
133Q8×C11—82no—
134Q8×C11—82no—
135C2×C4×C11—22no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—22no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—42no—
142C2×C4×C11—82no—
143C2×C4×C11#12011yescharacteristic
144C2×C4×C11#12011yescharacteristic
145C2×C4×C11#12011yescharacteristic
146C2×C4×C11#12111yescharacteristic
147C2×C4×C11#12111yescharacteristic
148C2×C4×C11#12711yescharacteristic
149C22⋊D11—82no—
150C2×Dic11—41no—
151D44—42no—
152D44—41no—
153D44—41no—
154D44—42no—
155C4×D11—82no—
156Dic22—42no—
157C8×C11—42no—
158C11⋊C8—42no—
159C11⋊C8—42no—
160C11⋊C8—42no—
161#533C2×D1111yescharacteristic
162#532—111no—
163C2×C4⋊Q8C2×D1111yescharacteristic
164#498—21no—
165#489—222no—
166#487—21no—
167#487—221no—
168#486—221no—
169#483—22no—
170#477—221no—
171#475—22no—
172#474—221no—
173#468—222no—
174#461—221no—
175#460—221no—
176#431C2×D1111yescharacteristic
177#423—111no—
178#417—222no—
179C4×M16—111no—
180C4×M16—111no—
181#343—222no—
182#330—222no—
183D4⋊C8—222no—
184C22×C11—21no—
185C22×C11—21no—
186C22×C11—21no—
187C22×C11#39211yescharacteristic
188C2×D11—81no—
189C2×D11—81no—
190C2×D11—81no—
191C4×C11—21no—
192C4×C11—21no—
193C4×C11—21no—
194C4×C11—81no—
195C4×C11—81no—
196C4×C11—82no—
197C4×C11#45412yes—
198C4×C11#45511yescharacteristic
199C4×C11#45611yescharacteristic
200C4×C11#47112yes—
201Dic11—81no—
202C2×#41—221no—
203C22×Q8—21no—
204C2×SD16—222no—
205C2×M16—112no—
206C2×M16—221no—
207C2×M16—221no—
208C4⋊Q8—21no—
209C4⋊Q8—21no—
210C4⋊Q8—21no—
211C4⋊Q8—21no—
212C4⋊Q8—111no—
213C4⋊Q8C22⋊D1111yescharacteristic
214C4⋊Q8C22⋊D1111yescharacteristic
215#127—111no—
216#125—21no—
217#124—221no—
218C22⋊Q8—21no—
219C22⋊Q8—21no—
220#121—221no—
221#121—221no—
222C4×Q8—21no—
223C4×Q8—21no—
224C4×D4—221no—
225C4×D4—221no—
226#117—21no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4C22⋊D1112yes—
229C2×C42C22×D1111yescharacteristic
230#107—222no—
231#106—24no—
232C4⋊C8—221no—
233C4⋊C8—221no—
234C4⋊C8C22⋊D1112yes—
235#103—24no—
236#103—224no—
237#103—222no—
238#102—224no—
239#102—222no—
240C22⋊C8—21no—
241#97—112no—
242#97—221no—
243C4×C8—21no—
244C4×C8—221no—
245C4×C8—221no—
246C2×C11—41no—
247C2×C11#200311yescharacteristic
248C2×C11#200711yescharacteristic
249C2×C11#201911yescharacteristic
250D11—161no—
251#41—444no—
252C2×Q8—21no—
253C2×Q8—21no—
254C2×Q8—41no—
255C2×Q8—41no—
256C2×Q8—82no—
257C2×Q8—221no—
258C2×D4—221no—
259C2×D4—221no—
260C2×D4—221no—
261C2×D4—441no—
262C22×C4—22no—
263C22×C4—441no—
264C22×C4D4×D1111yescharacteristic
265C22×C4#434111yescharacteristic
266C22×C4C2×C22⋊D1111yescharacteristic
267SD16—882no—
268M16—222no—
269M16—442no—
270M16—441no—
271M16—442no—
272C2×C8—22no—
273C2×C8—222no—
274C2×C8—222no—
275C2×C8—441no—
276C4⋊C4—22no—
277C4⋊C4—21no—
278C4⋊C4—21no—
279C4⋊C4—21no—
280C4⋊C4—22no—
281C4⋊C4—21no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—221no—
287C4⋊C4—221no—
288C22⋊C4—41no—
289C22⋊C4—441no—
290C22⋊C4—441no—
291C42—41no—
292C42D4×D1111yescharacteristic
293C42D4×D1111yescharacteristic
294C42C2×C22⋊D1111yescharacteristic
295C42C2×C22⋊D1111yescharacteristic
296C11#1011111yescharacteristic, complemented, Sylow
297C23—441no—
298C23#6699211yescharacteristic
299Q8—41no—
300Q8—41no—
301Q8—42no—
302Q8—82no—
303Q8—82no—
304Q8—442no—
305D4—442no—
306D4—442no—
307D4—441no—
308D4—441no—
309D4—882no—
310C2×C4—22no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—22no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—42no—
317C2×C4—82no—
318C2×C4—441no—
319C2×C4—882no—
320C2×C4#6699011yescharacteristic
321C2×C4#6699011yescharacteristic
322C2×C4#6699111yescharacteristic
323C2×C4#6699211yescharacteristic
324C2×C4#6699311yescharacteristic
325C2×C4#6700611yescharacteristic
326C8—42no—
327C8—442no—
328C8—442no—
329C8—442no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—881no—
334C22—881no—
335C22—881no—
336C22#1062283611yescharacteristic
337C4—21no—
338C4—21no—
339C4—21no—
340C4—81no—
341C4—81no—
342C4—82no—
343C4—881no—
344C4#1062279012yes—
345C4#1062281511yescharacteristic
346C4#1062281811yescharacteristic
347C4#1062285812yes—
348C2—41no—
349C2—1761no—
350C2#1306963611yescharacteristic
351C2#1306966111yescharacteristic
352C2#1306972811yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3229C2
socleC22×C11#392
prime radical#10623008C22
hypercenter#3229D11
hypocenterC11#10111
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3229

Complements

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

NH ≅ G/Ntype
3. #13069606C2semidirect
4. #13067211C2semidirect
6. #13066507C2semidirect
7. C11×#3229C2semidirect
122. #3229D11semidirect
296. C11#10111semidirect

Maximal subgroups

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

subgroupindex
#130799992
#130790122
#130696062
#130672112
#130670322
#130665072
C11×#32292
#1011111