Finite Group Databasebeta

← #14655358

Subgroups — #14655358

Order 2816.

442 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 81 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#13079818C211yesmaximal, characteristic, complemented
2#13079016C211yesmaximal, characteristic
3#13067085C211yesmaximal, characteristic
4#13067037C211yesmaximal, characteristic, complemented
5#13066973C211yesmaximal, characteristic, complemented
6#13066489C211yesmaximal, characteristic, complemented
7C11×#3235C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C11×#532C2211yescharacteristic
10C2×#66923C2211yescharacteristic
11C11×#501—21no—
12C11×#490—21no—
13C11×#482—22no—
14C11×#476—21no—
15C11×#474—21no—
16C11×#432C2211yescharacteristic
17#10622845—21no—
18#10622845—21no—
19#10622695—21no—
20#10622695—21no—
21#10622693—21no—
22#10622684—21no—
23#10622669—22no—
24#10622657—21no—
25#10622656—21no—
26#10622635—22no—
27#10622539C2211yescharacteristic
28#10622538C2211yescharacteristic
29C4×#4318C2211yescharacteristic
30Q8⋊(C11⋊C8)—22no—
31D4⋊(C11⋊C8)—22no—
32#10622107—22no—
33C2×C11×#41—21no—
34C11×C4⋊Q8D411yescharacteristic
35C11×C4⋊Q8D411yescharacteristic
36C11×C4⋊Q8D411yescharacteristic
37C11×#127D411yescharacteristic
38C11×#125—21no—
39C11×#124—21no—
40C11×C22⋊Q8—21no—
41C11×C22⋊Q8—21no—
42C11×#121—21no—
43C11×#121—21no—
44C4×Q8×C11—21no—
45C4×Q8×C11—21no—
46C4×D4×C11—21no—
47C4×D4×C11—21no—
48C11×#117—21no—
49C2×C42×C11C2311yescharacteristic
50C2×C4⋊Dic11D411yescharacteristic
51C2×C4⋊Dic11D411yescharacteristic
52C2×Dic11⋊C4—21no—
53C2×Dic11⋊C4—21no—
54C2×#4318—21no—
55#66923—21no—
56#66923—21no—
57#66923—21no—
58#66923—21no—
59C11×#107—22no—
60C11×#106—22no—
61C11×C4⋊C8—21no—
62C11×#102—22no—
63C11×#102—22no—
64C11×C22⋊C8D412yes—
65C11×#97—21no—
66#66899—22no—
67#66899—22no—
68#66899—22no—
69#66899—22no—
70#66896—22no—
71#66896—22no—
72C22⋊(C11⋊C8)—21no—
73C22⋊(C11⋊C8)—21no—
74#66872—22no—
75#66871—22no—
76C4⋊(C11⋊C8)—21no—
77C4⋊(C11⋊C8)D412yes—
78#66867—21no—
79#66867—21no—
80C4×C11⋊C8—21no—
81C4×C11⋊C8D412yes—
82#10123—111nomaximal, Sylow
83C11×#41—44no—
84C2×Q8×C11—21no—
85C2×Q8×C11—21no—
86C2×Q8×C11—21no—
87C2×D4×C11—21no—
88C2×D4×C11—21no—
89C2×D4×C11—21no—
90C2×D4×C11—41no—
91C22×C4×C11—41no—
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11#4111yescharacteristic
95C22×Dic11—21no—
96C22×Dic11—21no—
97C2×C8×C11—22no—
98C11×C4⋊C4—21no—
99C11×C4⋊C4—21no—
100C11×C4⋊C4—21no—
101C11×C4⋊C4—21no—
102C11×C4⋊C4—21no—
103C11×C4⋊C4—21no—
104C11×C4⋊C4—41no—
105C11×C4⋊C4—41no—
106C11×C22⋊C4—41no—
107C11×C22⋊C4—41no—
108C11×C22⋊C4—41no—
109C42×C11—41no—
110C42×C11C2×D411yescharacteristic
111C42×C11C2×D411yescharacteristic
112C42×C11C2×D411yescharacteristic
113C42×C11C2×D411yescharacteristic
114C4⋊Dic11—21no—
115C4⋊Dic11—21no—
116C4⋊Dic11—21no—
117C4⋊Dic11—21no—
118Dic11⋊C4—41no—
119Dic11⋊C4—41no—
120Dic11⋊C4—41no—
121Dic11⋊C4—41no—
122#4318—42no—
123C2×C11⋊C8—22no—
124C2×C11⋊C8—22no—
125C2×C11⋊C8—41no—
126#3236—111no—
127#3235D1111yescharacteristic
128#3142—111no—
129#1496—111no—
130#1485—111no—
131#1470—111no—
132#1291—111no—
133C23×C11—41no—
134C23×C11#12111yescharacteristic
135Q8×C11—42no—
136Q8×C11—42no—
137Q8×C11—42no—
138D4×C11—42no—
139D4×C11—42no—
140D4×C11—42no—
141D4×C11—82no—
142C2×C4×C11—22no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—82no—
149C2×C4×C11#12011yescharacteristic
150C2×C4×C11#12011yescharacteristic
151C2×C4×C11#12011yescharacteristic
152C2×C4×C11#12111yescharacteristic
153C2×C4×C11#12111yescharacteristic
154C2×C4×C11#12711yescharacteristic
155C2×Dic11—42no—
156C2×Dic11—41no—
157C2×Dic11—41no—
158C2×Dic11—81no—
159C8×C11—42no—
160C11⋊C8—42no—
161C11⋊C8—42no—
162C11⋊C8—81no—
163#533C2×D1111yescharacteristic
164#532C2×D1111yescharacteristic
165C2×#125—111no—
166#501—21no—
167#501—221no—
168#491—221no—
169#491—221no—
170#490—21no—
171#490—221no—
172#488—222no—
173#484—221no—
174#483—221no—
175#482—22no—
176#479—222no—
177#476—21no—
178#474—21no—
179#432—111no—
180#432C2×D1111yescharacteristic
181#431—111no—
182#417—221no—
183#417—221no—
184C4×M16—111no—
185Q8⋊C8—222no—
186D4⋊C8—222no—
187#324—222no—
188C22×C11—21no—
189C22×C11—21no—
190C22×C11—21no—
191C22×C11—81no—
192C22×C11—81no—
193C22×C11—81no—
194C22×C11#39211yescharacteristic
195C4×C11—21no—
196C4×C11—21no—
197C4×C11—21no—
198C4×C11—21no—
199C4×C11—21no—
200C4×C11—81no—
201C4×C11—81no—
202C4×C11—81no—
203C4×C11#45412yes—
204Dic11—81no—
205Dic11—81no—
206C2×#41—21no—
207C2×M16—221no—
208C4⋊Q8C22⋊D1111yescharacteristic
209C4⋊Q8C22⋊D1111yescharacteristic
210C4⋊Q8C22⋊D1111yescharacteristic
211#127C22⋊D1111yescharacteristic
212#125—21no—
213#125—221no—
214#125—221no—
215#125—221no—
216#125—221no—
217#124—21no—
218C22⋊Q8—21no—
219C22⋊Q8—21no—
220#121—21no—
221#121—21no—
222C4×Q8—21no—
223C4×Q8—21no—
224C4×D4—21no—
225C4×D4—21no—
226#117—21no—
227C2×C4⋊C4—111no—
228C2×C4⋊C4—111no—
229C2×C4⋊C4—221no—
230C2×C4⋊C4—221no—
231C2×C42C22×D1111yescharacteristic
232#107—22no—
233#107—222no—
234#106—22no—
235#106—222no—
236C4⋊C8—21no—
237C4⋊C8—112no—
238C4⋊C8—221no—
239#103—222no—
240#103—222no—
241#103—222no—
242#103—222no—
243#102—22no—
244#102—22no—
245#102—222no—
246#102—222no—
247C22⋊C8—221no—
248C22⋊C8—221no—
249C22⋊C8C22⋊D1112yes—
250#97—21no—
251#97—221no—
252#97—221no—
253C4×C8—112no—
254C4×C8—221no—
255C2×C11—41no—
256C2×C11—161no—
257C2×C11#200311yescharacteristic
258C2×C11#200911yescharacteristic
259C2×C11#201711yescharacteristic
260#41—44no—
261C2×Q8—21no—
262C2×Q8—21no—
263C2×Q8—21no—
264C2×D4—21no—
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—41no—
268C22×C4—41no—
269C22×C4—221no—
270C22×C4—221no—
271C22×C4D4×D1111yescharacteristic
272C22×C4#434111yescharacteristic
273C22×C4C2×C22⋊D1111yescharacteristic
274M16—442no—
275C2×C8—22no—
276C2×C8—222no—
277C2×C8—222no—
278C2×C8—441no—
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—21no—
284C4⋊C4—21no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4—221no—
288C4⋊C4—221no—
289C4⋊C4—221no—
290C4⋊C4—221no—
291C4⋊C4—441no—
292C4⋊C4—441no—
293C4⋊C4—441no—
294C4⋊C4—441no—
295C22⋊C4—41no—
296C22⋊C4—41no—
297C22⋊C4—41no—
298C42—41no—
299C42D4×D1111yescharacteristic
300C42D4×D1111yescharacteristic
301C42C2×C22⋊D1111yescharacteristic
302C42C2×C22⋊D1111yescharacteristic
303C11#1012311yescharacteristic, complemented, Sylow
304C23—41no—
305C23#6699111yescharacteristic
306Q8—42no—
307Q8—42no—
308Q8—42no—
309D4—42no—
310D4—42no—
311D4—42no—
312D4—82no—
313C2×C4—22no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—82no—
320C2×C4—442no—
321C2×C4—441no—
322C2×C4—441no—
323C2×C4—881no—
324C2×C4#6699011yescharacteristic
325C2×C4#6699011yescharacteristic
326C2×C4#6699211yescharacteristic
327C2×C4#6699211yescharacteristic
328C2×C4#6699311yescharacteristic
329C2×C4#6700611yescharacteristic
330C8—42no—
331C8—442no—
332C8—442no—
333C8—881no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—81no—
338C22—81no—
339C22—81no—
340C22#1062283611yescharacteristic
341C4—21no—
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—81no—
347C4—81no—
348C4—81no—
349C4—881no—
350C4—881no—
351C4#1062281412yes—
352C2—41no—
353C2—161no—
354C2#1306963511yescharacteristic
355C2#1306967611yescharacteristic
356C2#1306971911yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3235C2
socleC22×C11#392
prime radicalC11×#532C22
hypercenter#3235D11
hypocenterC11#10123
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3235

Complements

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

NH ≅ G/Ntype
1. #13079818C2semidirect
4. #13067037C2semidirect
5. #13066973C2semidirect
6. #13066489C2semidirect
303. C11#10123semidirect

Maximal subgroups

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

subgroupindex
#130798182
#130790162
#130670852
#130670372
#130669732
#130664892
C11×#32352
#1012311