Finite Group Databasebeta

← #14655572

Subgroups — #14655572

Order 2816.

620 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 620 conjugacy classes of subgroups — too many to draw. Only its 107 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#13079163C211yesmaximal, characteristic, complemented
3C2×#10622306C211yesmaximal, characteristic
4#13069455C211yesmaximal, characteristic
5#13067302C211yesmaximal, characteristic, complemented
6#13066453C211yesmaximal, characteristic, complemented
7C11×#1493C211yesmaximal, characteristic, complemented
8C11×#533C2211yescharacteristic
9C22×#4314—22no—
10C2×#66927C2211yescharacteristic
11C2×#66922C2211yescharacteristic
12C11×#423C2211yescharacteristic
13C2×C4×C8×C11C2211yescharacteristic
14C2×#66887—22no—
15#10622701—21no—
16#10622698—21no—
17#10622692—21no—
18#10622691—21no—
19#10622678—22no—
20#10622659—22no—
21#10622640—22no—
22#10622608—22no—
23#10622538C2211yescharacteristic
24C4×#4318C2211yescharacteristic
25#10622306—22no—
26#10622306—22no—
27C11×Q8⋊C8—22no—
28#10622124—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—
48C2×#4314—28no—
49C2×#4314—48no—
50#66927—21no—
51#66927—21no—
52#66927—21no—
53#66927—21no—
54#66922—21no—
55#66922—21no—
56#66922—21no—
57#66922D412yes—
58C11×C4⋊C8—21no—
59C11×C4⋊C8—21no—
60C4×C8×C11—21no—
61C4×C8×C11D412yes—
62C22⋊(C11⋊C8)—21no—
63#66887—44no—
64#66873—24no—
65#66872—24no—
66#66871—24no—
67C4⋊(C11⋊C8)D412yes—
68#66867—21no—
69C4×C11⋊C8—21no—
70C4×C11⋊C8—21no—
71#10153—111nomaximal, Sylow
72C23×D11—22no—
73C2×Q8×C11—21no—
74C2×Q8×C11—21no—
75C22×C4×C11C2×D411yescharacteristic
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11#4111yescharacteristic
78C22×Dic11—41no—
79C2×D44—22no—
80C2×D44—22no—
81C2×D44—44no—
82C2×D44—41no—
83C2×D44—41no—
84C2×D44—41no—
85C2×D44—41no—
86C2×D44—42no—
87C2×D44—42no—
88C2×D44—82no—
89C2×Dic22—22no—
90C2×Dic22—44no—
91C2×Dic22—41no—
92C11×M16—42no—
93C2×C8×C11—24no—
94C2×C8×C11—22no—
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#4318SD1614yescomplemented
115C2×C11⋊C8—22no—
116C2×C11⋊C8—22no—
117#4314—416no—
118#3208—111no—
119#3165—111no—
120C2×#492—111no—
121#1965—111no—
122#1549—111no—
123#1493D1111yescharacteristic, complemented
124#1278—111no—
125C23×C11#12111yescharacteristic
126C22×D11—42no—
127C22×D11—44no—
128C22×D11—82no—
129C22×D11—82no—
130Q8×C11—42no—
131Q8×C11—42no—
132C2×C4×C11—22no—
133C2×C4×C11—22no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
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×C11C2×SD1612yes—
143C2×C4×C11#13712yes—
144C2×Dic11—42no—
145C2×Dic11—82no—
146D44—44no—
147D44—44no—
148D44—82no—
149D44—82no—
150D44—82no—
151D44—81no—
152D44—81no—
153Dic22—44no—
154Dic22—82no—
155C8×C11—24no—
156C8×C11—81no—
157C11⋊C8—24no—
158C11⋊C8—42no—
159C22×SD16—222no—
160#533C2×D1111yescharacteristic
161C2×C4⋊Q8—111no—
162C2×#127—111no—
163#501—222no—
164#500—221no—
165#498—221no—
166#492—222no—
167#492—221no—
168#492—222no—
169#486—221no—
170#460—222no—
171#450—222no—
172#431—111no—
173#428—222no—
174#423C2×D1111yescharacteristic
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#46112yes—
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#44812yes—
193C4×C11#45312yes—
194C4×C11#47112yes—
195C4×C11#49211yescharacteristic
196C4×C11#49711yescharacteristic
197Dic11—82no—
198C22×Q8—221no—
199C22×D4—112no—
200C22×D4—221no—
201C22×D4—221no—
202C2×SD16—228no—
203C2×SD16—224no—
204C2×SD16—448no—
205C2×M16—21no—
206C2×M16—112no—
207C22×C8—21no—
208C4⋊Q8—112no—
209C4⋊Q8—221no—
210C4⋊Q8—221no—
211C4⋊Q8—221no—
212C4⋊Q8D4411yescharacteristic
213C4⋊Q8D4411yescharacteristic
214#127—221no—
215#127—221no—
216#127—221no—
217#127—221no—
218#125—21no—
219C22⋊Q8—21no—
220C22⋊Q8—21no—
221C4×Q8—21no—
222C4×Q8—21no—
223#117—21no—
224C2×C4⋊C4—221no—
225C2×C4⋊C4—221no—
226C2×C42C22×D1111yescharacteristic
227#107—224no—
228#106—224no—
229C4⋊C8—21no—
230C4⋊C8—21no—
231C4⋊C8—112no—
232#102—224no—
233#100—444no—
234C22⋊C8—221no—
235#97—221no—
236C4×C8—21no—
237C4×C8—221no—
238C4×C8—221no—
239C4×C8C22⋊D1112yes—
240C2×C11—22no—
241C2×C11#200211yescharacteristic
242C2×C11#201311yescharacteristic
243C2×C11#201911yescharacteristic
244D11—162no—
245C24—222no—
246C2×Q8—21no—
247C2×Q8—21no—
248C2×Q8—222no—
249C2×Q8—444no—
250C2×Q8—441no—
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—4416no—
266SD16—884no—
267M16—42no—
268M16—114no—
269M16—222no—
270C2×C8—24no—
271C2×C8—22no—
272C2×C8—41no—
273C2×C8—222no—
274C2×C8—222no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—21no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—222no—
282C4⋊C4—222no—
283C4⋊C4—441no—
284C4⋊C4—441no—
285C22⋊C4—41no—
286C42—41no—
287C42C2×D4411yescharacteristic
288C42D4×D1111yescharacteristic
289C42D4×D1111yescharacteristic
290C42C2×C22⋊D1111yescharacteristic
291C11#1015311yescharacteristic, complemented, Sylow
292C23—442no—
293C23—444no—
294C23—882no—
295C23—882no—
296C23#6693711yescharacteristic
297Q8—42no—
298Q8—42no—
299Q8—444no—
300Q8—882no—
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×C4SD16×D1112yes—
318C2×C4#6697112yes—
319C2×C4#6698311yescharacteristic
320C2×C4#6699011yescharacteristic
321C2×C4#6699311yescharacteristic
322C8—24no—
323C8—81no—
324C8—224no—
325C8—442no—
326C22—21no—
327C22—21no—
328C22—882no—
329C22—882no—
330C22—882no—
331C22—1764no—
332C22#1062243112yes—
333C22#1062257311yescharacteristic
334C4—21no—
335C4—21no—
336C4—81no—
337C4—81no—
338C4—882no—
339C4#1062241912yes—
340C4#1062243512yes—
341C4#1062275412yes—
342C4#1062278811yescharacteristic
343C4#1062280311yescharacteristic
344C2—22no—
345C2—1762no—
346C2#1306963011yescharacteristic
347C2#1306970011yescharacteristic
348C2#1306973111yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1493C2
socleC22×C11#392
prime radicalC2×#66927C22
hypercenter#1493D11
hypocenterC11#10153
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. #13079163C2semidirect
5. #13067302C2semidirect
6. #13066453C2semidirect
7. C11×#1493C2semidirect
114. #4318SD16semidirect
123. #1493D11semidirect
291. C11#10153semidirect

Maximal subgroups

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

subgroupindex
#130795542
#130791632
C2×#106223062
#130694552
#130673022
#130664532
C11×#14932
#1015311