Finite Group Databasebeta

← #14655684

Subgroups — #14655684

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#13079554C211yesmaximal, characteristic
2#13078998C211yesmaximal, characteristic, complemented
3C2×#10622307C211yesmaximal, characteristic
4#13069455C211yesmaximal, characteristic
5#13067289C211yesmaximal, characteristic, complemented
6#13066453C211yesmaximal, characteristic, complemented
7C11×#1493C211yesmaximal, characteristic, complemented
8C11×#533C2211yescharacteristic
9C2×#66927C2211yescharacteristic
10C2×#66922C2211yescharacteristic
11C11×#423C2211yescharacteristic
12C2×C4×C8×C11C2211yescharacteristic
13C2×#66887—22no—
14C2×#66885—22no—
15#10622706—21no—
16#10622706—21no—
17#10622701—21no—
18#10622698—21no—
19#10622682—22no—
20#10622659—22no—
21#10622640—22no—
22#10622617—22no—
23#10622538C2211yescharacteristic
24C4×#4318C2211yescharacteristic
25#10622307—22no—
26#10622307—22no—
27C11×Q8⋊C8—22no—
28#10622120—22no—
29C22×D44—21no—
30C22×D44—21no—
31C22×D44D412yes—
32C22×Dic22—21no—
33C2×C11×M16—21no—
34C22×C8×C11—21no—
35C11×C4⋊Q8D411yescharacteristic
36C11×C4⋊Q8D411yescharacteristic
37C11×#125—21no—
38C11×C22⋊Q8—21no—
39C11×C22⋊Q8—21no—
40C4×Q8×C11—21no—
41C4×Q8×C11—21no—
42C11×#117—21no—
43C2×C42×C11C2311yescharacteristic
44C2×#4325—24no—
45C2×C4⋊Dic11—21no—
46C2×C4⋊Dic11—21no—
47C2×#4318D412yes—
48#66927—21no—
49#66927—21no—
50#66927—21no—
51#66927—21no—
52#66922—21no—
53#66922—21no—
54#66922—21no—
55#66922D412yes—
56C11×C4⋊C8—21no—
57C11×C4⋊C8—21no—
58C4×C8×C11—21no—
59C4×C8×C11D412yes—
60C22⋊(C11⋊C8)—21no—
61#66887—44no—
62#66885—28no—
63#66874—24no—
64#66874—24no—
65#66873—24no—
66C4⋊(C11⋊C8)D412yes—
67#66867—21no—
68C4×C11⋊C8—21no—
69C4×C11⋊C8—21no—
70#10169—111nomaximal, Sylow
71C23×D11—22no—
72C2×Q8×C11—21no—
73C2×Q8×C11—21no—
74C22×C4×C11C2×D411yescharacteristic
75C22×C4×C11C2×D411yescharacteristic
76C22×C4×C11#4111yescharacteristic
77C22×Dic11—41no—
78C2×D44—22no—
79C2×D44—22no—
80C2×D44—44no—
81C2×D44—41no—
82C2×D44—41no—
83C2×D44—41no—
84C2×D44—41no—
85C2×D44—42no—
86C2×D44—42no—
87C2×D44—82no—
88C2×Dic22—22no—
89C2×Dic22—41no—
90C2×Dic22—42no—
91C2×Dic22—42no—
92C11×M16—42no—
93C2×C8×C11—22no—
94C2×C8×C11—42no—
95C2×C8×C11—41no—
96C11×C4⋊C4—21no—
97C11×C4⋊C4—21no—
98C11×C4⋊C4—21no—
99C11×C4⋊C4—21no—
100C11×C4⋊C4—41no—
101C11×C4⋊C4—41no—
102C11×C22⋊C4—41no—
103C42×C11—41no—
104C42×C11C2×D411yescharacteristic
105C42×C11C2×D411yescharacteristic
106C42×C11C2×D411yescharacteristic
107C42×C11C2×D411yescharacteristic
108#4325—84no—
109C4⋊Dic11—22no—
110C4⋊Dic11—22no—
111C4⋊Dic11—41no—
112C4⋊Dic11—41no—
113#4318—22no—
114#4318—22no—
115C2×C11⋊C8—22no—
116C2×C11⋊C8—22no—
117#3208—111no—
118#3139—111no—
119C2×#486—111no—
120#1965—111no—
121#1546—111no—
122#1493D1111yescharacteristic, complemented
123#1278—111no—
124C23×C11#12111yescharacteristic
125C22×D11—42no—
126C22×D11—44no—
127C22×D11—82no—
128C22×D11—82no—
129Q8×C11—42no—
130Q8×C11—42no—
131C2×C4×C11—22no—
132C2×C4×C11—22no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
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×C11AGL(1,ℤ/8)12yes—
143C2×Dic11—42no—
144C2×Dic11—82no—
145D44—44no—
146D44—44no—
147D44—82no—
148D44—82no—
149D44—82no—
150D44—81no—
151D44—81no—
152Dic22—44no—
153Dic22—81no—
154Dic22—81no—
155C8×C11—42no—
156C8×C11—81no—
157C11⋊C8—42no—
158C11⋊C8—42no—
159#533C2×D1111yescharacteristic
160C2×C4⋊Q8—111no—
161C2×#127—111no—
162#492—221no—
163#491—222no—
164#487—221no—
165#487—221no—
166#486—222no—
167#486—221no—
168#486—222no—
169#460—222no—
170#450—222no—
171#431—111no—
172#423C2×D1111yescharacteristic
173#419—222no—
174C2×#102—222no—
175C2×#100—222no—
176C4×M16—111no—
177C2×C4×C8C2×D1111yescharacteristic
178#332—222no—
179Q8⋊C8—22no—
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—81no—
191C4×C11—81no—
192C4×C11#44912yes—
193C4×C11#45512yes—
194C4×C11#47112yes—
195C4×C11#49511yescharacteristic
196C4×C11#49611yescharacteristic
197Dic11—82no—
198C22×Q8—221no—
199C22×D4—112no—
200C22×D4—221no—
201C22×D4—221no—
202C2×SD16—224no—
203C2×M16—21no—
204C2×M16—112no—
205C22×C8—21no—
206C4⋊Q8—112no—
207C4⋊Q8—221no—
208C4⋊Q8—221no—
209C4⋊Q8—221no—
210C4⋊Q8D4411yescharacteristic
211C4⋊Q8D4411yescharacteristic
212#127—221no—
213#127—221no—
214#127—221no—
215#127—221no—
216#125—21no—
217C22⋊Q8—21no—
218C22⋊Q8—21no—
219C4×Q8—21no—
220C4×Q8—21no—
221#117—21no—
222C2×C4⋊C4—221no—
223C2×C4⋊C4—221no—
224C2×C42C22×D1111yescharacteristic
225C4⋊C8—21no—
226C4⋊C8—21no—
227C4⋊C8—112no—
228#103—224no—
229#103—224no—
230#102—224no—
231#102—228no—
232#100—444no—
233C22⋊C8—221no—
234#97—221no—
235C4×C8—21no—
236C4×C8—221no—
237C4×C8—221no—
238C4×C8C22⋊D1112yes—
239C2×C11—22no—
240C2×C11#200411yescharacteristic
241C2×C11#201211yescharacteristic
242C2×C11#201911yescharacteristic
243D11—162no—
244C24—222no—
245C2×Q8—21no—
246C2×Q8—21no—
247C2×Q8—222no—
248C2×Q8—441no—
249C2×Q8—442no—
250C2×Q8—442no—
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—441no—
262C22×C4#433911yescharacteristic
263C22×C4D4×D1111yescharacteristic
264C22×C4D4×D1111yescharacteristic
265SD16—884no—
266M16—42no—
267M16—222no—
268M16—222no—
269C2×C8—22no—
270C2×C8—42no—
271C2×C8—41no—
272C2×C8—222no—
273C2×C8—222no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—222no—
281C4⋊C4—222no—
282C4⋊C4—441no—
283C4⋊C4—441no—
284C22⋊C4—41no—
285C42—41no—
286C42C2×D4411yescharacteristic
287C42D4×D1111yescharacteristic
288C42D4×D1111yescharacteristic
289C42C2×C22⋊D1111yescharacteristic
290C11#1016911yescharacteristic, complemented, Sylow
291C23—442no—
292C23—444no—
293C23—882no—
294C23—882no—
295C23#6693711yescharacteristic
296Q8—42no—
297Q8—42no—
298Q8—444no—
299Q8—881no—
300Q8—881no—
301D4—444no—
302D4—444no—
303D4—882no—
304D4—882no—
305D4—881no—
306D4—881no—
307D4—882no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—442no—
313C2×C4—882no—
314C2×C4#6693511yescharacteristic
315C2×C4#6693511yescharacteristic
316C2×C4#6693711yescharacteristic
317C2×C4#6696712yes—
318C2×C4#6697212yes—
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#1062243212yes—
333C22#1062257311yescharacteristic
334C4—21no—
335C4—21no—
336C4—81no—
337C4—81no—
338C4—882no—
339C4#1062242412yes—
340C4#1062243812yes—
341C4#1062275412yes—
342C4#1062278911yescharacteristic
343C4#1062280411yescharacteristic
344C2—22no—
345C2—1762no—
346C2#1306964411yescharacteristic
347C2#1306969411yescharacteristic
348C2#1306973111yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1493C2
socleC22×C11#392
prime radicalC2×#66927C22
hypercenter#1493D11
hypocenterC11#10169
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1493

Complements

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

NH ≅ G/Ntype
2. #13078998C2semidirect
5. #13067289C2semidirect
6. #13066453C2semidirect
7. C11×#1493C2semidirect
122. #1493D11semidirect
290. C11#10169semidirect

Maximal subgroups

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

subgroupindex
#130795542
#130789982
C2×#106223072
#130694552
#130672892
#130664532
C11×#14932
#1016911