Finite Group Databasebeta

← #14655681

Subgroups — #14655681

Order 2816.

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

normal subgroups only

This group has 556 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#13079559C211yesmaximal, characteristic
2#13078996C211yesmaximal, characteristic, complemented
3C2×#10622701C211yesmaximal, characteristic
4#13069455C211yesmaximal, characteristic
5#13067070C211yesmaximal, characteristic, complemented
6#13066452C211yesmaximal, characteristic, complemented
7C11×#1546C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×#66927C2211yescharacteristic
10#10623001C2211yescharacteristic
11C11×#431C2211yescharacteristic
12C11×#423C2211yescharacteristic
13#10622838—22no—
14C2×#66887—22no—
15#10622701—22no—
16#10622701—22no—
17#10622695—22no—
18#10622694—21no—
19#10622694—21no—
20C2×#66873—22no—
21C4×#4318C2211yescharacteristic
22C2×C4×C11⋊C8C2211yescharacteristic
23#10622461—22no—
24#10622344—22no—
25#10622307—21no—
26#10622306—21no—
27C11×#332—22no—
28#10622122—22no—
29C22×Q8×C11—21no—
30C22×D44—21no—
31C22×D44—21no—
32C22×D44D412yes—
33C2×C11×M16—21no—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8D412yes—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4—21no—
40C2×C42×C11C2311yescharacteristic
41#66979—21no—
42#66977—21no—
43#66977—21no—
44C2×#4318D412yes—
45C22×C11⋊C8—21no—
46C2×#4314—24no—
47#66927—21no—
48#66927—21no—
49#66927—21no—
50#66927—21no—
51#66923—21no—
52#66922D411yescharacteristic
53#66922D411yescharacteristic
54C4×Dic22—21no—
55C4×Dic22—21no—
56C11×C4⋊C8—21no—
57C11×C4⋊C8—21no—
58C11×C4⋊C8D412yes—
59C11×C22⋊C8—21no—
60C4×C8×C11—21no—
61#66899—24no—
62#66899—24no—
63#66887—44no—
64#66885—24no—
65#66873—28no—
66#66867—21no—
67C4×C11⋊C8—21no—
68C4×C11⋊C8—21no—
69C4×C11⋊C8D412yes—
70#10169—111nomaximal, Sylow
71C23×D11—22no—
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×D44—22no—
81C2×D44—22no—
82C2×D44—44no—
83C2×D44—41no—
84C2×D44—41no—
85C2×D44—41no—
86C2×D44—41no—
87C2×D44—42no—
88C2×D44—42no—
89C2×D44—82no—
90C2×Dic22—21no—
91C2×Dic22—21no—
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
103C22⋊Dic11—41no—
104C4⋊Dic11—21no—
105C4⋊Dic11—21no—
106C4⋊Dic11—21no—
107C4⋊Dic11—21no—
108Dic11⋊C4—41no—
109Dic11⋊C4—41no—
110C4×Dic11—41no—
111#4318—22no—
112#4318—22no—
113C2×C11⋊C8—22no—
114C2×C11⋊C8—22no—
115C2×C11⋊C8—42no—
116#4314—84no—
117#3208—111no—
118#3139—111no—
119C2×#486—111no—
120#1965—111no—
121#1546D1111yescharacteristic, complemented
122#1493—111no—
123#1278—111no—
124C23×C11#12111yescharacteristic
125C22×D11—42no—
126C22×D11—44no—
127C22×D11—82no—
128C22×D11—82no—
129Q8×C11—44no—
130Q8×C11—81no—
131Q8×C11—81no—
132C2×C4×C11—22no—
133C2×C4×C11—22no—
134C2×C4×C11—42no—
135C2×C4×C11—82no—
136C2×C4×C11#12011yescharacteristic
137C2×C4×C11#12011yescharacteristic
138C2×C4×C11#12011yescharacteristic
139C2×C4×C11#12111yescharacteristic
140C2×C4×C11#12111yescharacteristic
141C2×C4×C11#12711yescharacteristic
142C2×C4×C11#13512yes—
143C2×C4×C11AGL(1,ℤ/8)12yes—
144C2×Dic11—41no—
145C2×Dic11—41no—
146D44—44no—
147D44—44no—
148D44—82no—
149D44—82no—
150D44—82no—
151D44—81no—
152D44—81no—
153Dic22—42no—
154Dic22—42no—
155C8×C11—42no—
156C8×C11—81no—
157C11⋊C8—42no—
158C11⋊C8—42no—
159#533—111no—
160C2×C4⋊Q8C2×D1111yescharacteristic
161C2×#127—111no—
162#492—221no—
163#491—222no—
164#487—221no—
165#487—221no—
166#486—221no—
167#486—222no—
168#486—222no—
169#460—222no—
170#450—222no—
171#431C2×D1111yescharacteristic
172#423C2×D1111yescharacteristic
173#419—222no—
174C2×#102—222no—
175C2×#100—222no—
176C4×M16—111no—
177C2×C4×C8—111no—
178#332—22no—
179Q8⋊C8—222no—
180C22×C11—21no—
181C22×C11—21no—
182C22×C11#39211yescharacteristic
183C22×C11#46312yes—
184C2×D11—82no—
185C2×D11—82no—
186C2×D11—82no—
187C2×D11—164no—
188C4×C11—21no—
189C4×C11—21no—
190C4×C11—82no—
191C4×C11#44912yes—
192C4×C11#45512yes—
193C4×C11#47112yes—
194C4×C11#49511yescharacteristic
195C4×C11#49611yescharacteristic
196Dic11—81no—
197Dic11—81no—
198C22×Q8—21no—
199C22×D4—112no—
200C22×D4—221no—
201C22×D4—221no—
202C2×SD16—224no—
203C2×M16—21no—
204C2×M16—112no—
205C22×C8—221no—
206C4⋊Q8—21no—
207C4⋊Q8—21no—
208C4⋊Q8—21no—
209C4⋊Q8—111no—
210C4⋊Q8—111no—
211C4⋊Q8D4412yes—
212#127—221no—
213#127—221no—
214#127—221no—
215#127—221no—
216#125—221no—
217C22⋊Q8—221no—
218C22⋊Q8—221no—
219C4×Q8—221no—
220C4×Q8—221no—
221#117—221no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—21no—
224C2×C42C22×D1111yescharacteristic
225C4⋊C8—21no—
226C4⋊C8—21no—
227C4⋊C8C22⋊D1112yes—
228#103—224no—
229#103—224no—
230#102—228no—
231#102—224no—
232#100—444no—
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#201211yescharacteristic
242C2×C11#201911yescharacteristic
243D11—162no—
244C24—222no—
245C2×Q8—22no—
246C2×Q8—41no—
247C2×Q8—42no—
248C2×Q8—42no—
249C2×Q8—221no—
250C2×Q8—221no—
251C2×D4—222no—
252C2×D4—222no—
253C2×D4—444no—
254C2×D4—441no—
255C2×D4—441no—
256C2×D4—442no—
257C2×D4—442no—
258C2×D4—441no—
259C2×D4—441no—
260C2×D4—882no—
261C22×C4—41no—
262C22×C4#433911yescharacteristic
263C22×C4D4×D1111yescharacteristic
264C22×C4D4×D1111yescharacteristic
265SD16—884no—
266M16—42no—
267M16—222no—
268M16—222no—
269C2×C8—22no—
270C2×C8—41no—
271C2×C8—222no—
272C2×C8—222no—
273C2×C8—442no—
274C4⋊C4—22no—
275C4⋊C4—22no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—221no—
279C4⋊C4—221no—
280C4⋊C4—221no—
281C4⋊C4—221no—
282C4⋊C4—441no—
283C4⋊C4—441no—
284C22⋊C4—441no—
285C42—441no—
286C42C2×D4411yescharacteristic
287C42D4×D1111yescharacteristic
288C42D4×D1111yescharacteristic
289C42C2×C22⋊D1111yescharacteristic
290C11#1016911yescharacteristic, complemented, Sylow
291C23—442no—
292C23—444no—
293C23—882no—
294C23—882no—
295C23#6693711yescharacteristic
296Q8—44no—
297Q8—81no—
298Q8—81no—
299Q8—442no—
300Q8—442no—
301D4—444no—
302D4—444no—
303D4—882no—
304D4—881no—
305D4—881no—
306D4—882no—
307D4—882no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—42no—
311C2×C4—82no—
312C2×C4—441no—
313C2×C4—441no—
314C2×C4#6693511yescharacteristic
315C2×C4#6693511yescharacteristic
316C2×C4#6693711yescharacteristic
317C2×C4#6696412yes—
318C2×C4#6696912yes—
319C2×C4#6698311yescharacteristic
320C2×C4#6699011yescharacteristic
321C2×C4#6699311yescharacteristic
322C8—42no—
323C8—81no—
324C8—442no—
325C8—442no—
326C22—21no—
327C22—21no—
328C22—882no—
329C22—882no—
330C22—882no—
331C22—1764no—
332C22#1062240012yes—
333C22#1062257311yescharacteristic
334C4—21no—
335C4—21no—
336C4—82no—
337C4—881no—
338C4—881no—
339C4#1062236712yes—
340C4#1062239412yes—
341C4#1062276711yescharacteristic
342C4#1062278111yescharacteristic
343C4#1062281512yes—
344C2—22no—
345C2—1762no—
346C2#1306964611yescharacteristic
347C2#1306969511yescharacteristic
348C2#1306972911yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1546C2
socleC22×C11#392
prime radicalC2×#66927C22
hypercenter#1546D11
hypocenterC11#10169
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
2. #13078996C2semidirect
5. #13067070C2semidirect
6. #13066452C2semidirect
7. C11×#1546C2semidirect
121. #1546D11semidirect
290. C11#10169semidirect

Maximal subgroups

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

subgroupindex
#130795592
#130789962
C2×#106227012
#130694552
#130670702
#130664522
C11×#15462
#1016911