Finite Group Databasebeta

← #14650705

Subgroups — #14650705

Order 2816.

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

normal subgroups only

This group has 444 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#13071267C211yesmaximal, characteristic
2#13069561C211yesmaximal, characteristic
3#13067128C211yesmaximal, characteristic
4#13067063C211yesmaximal, characteristic
5#13066508C211yesmaximal, characteristic
6#13066473C211yesmaximal, characteristic
7C11×#3113C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C2×C4×Q8×C11C2211yescharacteristic
10C11×#483—21no—
11C11×#475C412yescomplemented
12C11×#462C412yescomplemented
13C11×#451—21no—
14C11×#441—22no—
15C11×#432C2211yescharacteristic
16#10622843—21no—
17#10622598—21no—
18#10622594—22no—
19#10622550—21no—
20#10622549—21no—
21C4×C4⋊Dic11C2211yescharacteristic
22#10622545C2211yescharacteristic
23#10622539C2211yescharacteristic
24C4×#4318C2211yescharacteristic
25#10622176—21no—
26#10622176—21no—
27Q8⋊(C11⋊C8)—22no—
28#10622170—22no—
29C22×Q8×C11D411yescharacteristic
30C2×C11×Q16—22no—
31C11×C4⋊Q8C2×C411yescharacteristic
32C11×C4⋊Q8C2×C411yescharacteristic
33C11×#125—21no—
34C11×C22⋊Q8—21no—
35C11×C22⋊Q8—21no—
36C4×Q8×C11—21no—
37C4×Q8×C11—21no—
38C4×Q8×C11—21no—
39C4×Q8×C11—21no—
40C4×Q8×C11C2×C412yes—
41C4×Q8×C11D412yes—
42C11×#117—21no—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4D411yescharacteristic
45C2×C42×C11—21no—
46C2×C42×C11C2311yescharacteristic
47C2×C4⋊Dic11—21no—
48C2×C4⋊Dic11—22no—
49C2×C4×Dic11—21no—
50C2×C4×Dic11D412yes—
51C2×#4318—21no—
52C11×#106—22no—
53C11×C4⋊C8C2×C412yes—
54C11×#103—22no—
55C11×#103—22no—
56C11×C22⋊C8—21no—
57C11×#97—21no—
58C11⋊#95—22no—
59C11⋊#95—22no—
60C11⋊#95—22no—
61C11⋊#95—21no—
62C11⋊#95—21no—
63C11⋊#95D411yescharacteristic
64C11⋊#95D411yescharacteristic
65C22⋊(C11⋊C8)—21no—
66C4⋊(C11⋊C8)—21no—
67#66867—21no—
68#66867—21no—
69C4×C11⋊C8—21no—
70#9328—111nomaximal, Sylow
71C2×Q8×C11—21no—
72C2×Q8×C11—21no—
73C2×Q8×C11—21no—
74C2×Q8×C11—42no—
75C2×Q8×C11C22⋊C412yes—
76C22×C4×C11—21no—
77C22×C4×C11—21no—
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×Dic11—21no—
82C22×Dic11—22no—
83C22×Dic11—21no—
84C11×Q16—44no—
85C2×C8×C11—22no—
86C11×C4⋊C4—22no—
87C11×C4⋊C4—22no—
88C11×C4⋊C4—21no—
89C11×C4⋊C4—21no—
90C11×C4⋊C4—21no—
91C11×C4⋊C4—21no—
92C11×C4⋊C4—21no—
93C11×C4⋊C4—41no—
94C11×C4⋊C4—41no—
95C11×C4⋊C4C22⋊C412yes—
96C11×C22⋊C4—41no—
97C42×C11—22no—
98C42×C11—22no—
99C42×C11—41no—
100C42×C11C22×C411yescharacteristic
101C42×C11C2×D411yescharacteristic
102C42×C11#4111yescharacteristic
103C42×C11#4111yescharacteristic
104C4⋊Dic11—42no—
105C4⋊Dic11—82no—
106C4×Dic11—42no—
107C4×Dic11—42no—
108#4318—22no—
109#4318—41no—
110C2×C11⋊C8—41no—
111C2×C11⋊C8—41no—
112#3113D1111yescharacteristic
113#2320—111no—
114#1986—111no—
115#1506—111no—
116#1491—111no—
117#1300—111no—
118#1285—111no—
119C23×C11#12011yescharacteristic
120Q8×C11—22no—
121Q8×C11—22no—
122Q8×C11—42no—
123Q8×C11—42no—
124Q8×C11—81no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—22no—
128C2×C4×C11—22no—
129C2×C4×C11—22no—
130C2×C4×C11—41no—
131C2×C4×C11—42no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11C2×C22⋊C411yescharacteristic
137C2×C4×C11C4×D411yescharacteristic
138C2×C4×C11C4×D411yescharacteristic
139C2×C4×C11#12111yescharacteristic
140C2×C4×C11#12111yescharacteristic
141C2×C4×C11#12311yescharacteristic
142C2×Dic11—41no—
143C2×Dic11—41no—
144C2×Dic11—42no—
145C2×Dic11—41no—
146C2×Dic11—42no—
147C2×Dic11—41no—
148C2×Dic11—42no—
149C2×Dic11—41no—
150C2×Dic11—41no—
151C8×C11—42no—
152C11⋊C8—42no—
153C11⋊C8—81no—
154#533C2×D1111yescharacteristic
155C2×C4×Q8C2×D1111yescharacteristic
156#483—21no—
157#475Dic1112yescomplemented
158#462Dic1112yescomplemented
159#451—21no—
160#441—22no—
161#432—111no—
162#432C2×D1111yescharacteristic
163C4×M16—111no—
164#391—221no—
165#389—221no—
166#387—222no—
167#383—221no—
168#382—221no—
169C4×C4⋊C4—111no—
170#376—111no—
171#339—222no—
172#328—221no—
173#328—221no—
174Q8⋊C8—222no—
175C22×C11—21no—
176C22×C11—21no—
177C22×C11#38611yescharacteristic
178C22×C11#45511yescharacteristic
179C22×C11#45611yescharacteristic
180C4×C11—21no—
181C4×C11—21no—
182C4×C11—21no—
183C4×C11—21no—
184C4×C11—21no—
185C4×C11—42no—
186C4×C11—42no—
187C4×C11—81no—
188C4×C11—81no—
189C4×C11#42112yes—
190Dic11—81no—
191Dic11—82no—
192Dic11—81no—
193C22×Q8C22⋊D1111yescharacteristic
194C2×Q16—22no—
195C2×M16—221no—
196C4⋊Q8C2×Dic1111yescharacteristic
197C4⋊Q8C2×Dic1111yescharacteristic
198#125—21no—
199C22⋊Q8—21no—
200C22⋊Q8—21no—
201C4×Q8—21no—
202C4×Q8—21no—
203C4×Q8—21no—
204C4×Q8—21no—
205C4×Q8C2×Dic1112yes—
206C4×Q8C22⋊D1112yes—
207#117—21no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—221no—
210C2×C4⋊C4—222no—
211C2×C4⋊C4C22⋊D1111yescharacteristic
212C2×C42—21no—
213C2×C42—112no—
214C2×C42—221no—
215C2×C42C22×D1111yescharacteristic
216#106—22no—
217C4⋊C8—221no—
218C4⋊C8C2×Dic1112yes—
219#103—22no—
220#103—22no—
221C22⋊C8—21no—
222C22⋊C8—221no—
223#97—21no—
224#97—221no—
225#97—221no—
226C4×C8—221no—
227#95—111no—
228#95—111no—
229#95—222no—
230#95—222no—
231#95—222no—
232#95—221no—
233#95—221no—
234C2×C11—21no—
235C2×C11—21no—
236C2×C11#188211yescharacteristic
237C2×C11#189711yescharacteristic
238C2×C11#190511yescharacteristic
239C2×Q8—21no—
240C2×Q8—21no—
241C2×Q8—21no—
242C2×Q8—42no—
243C2×Q8C22⋊Dic1112yes—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—221no—
247C22×C4—221no—
248C22×C4—222no—
249C22×C4D4×D1111yescharacteristic
250C22×C4D4×D1111yescharacteristic
251C22×C4C2×C22⋊D1111yescharacteristic
252Q16—44no—
253M16—222no—
254M16—441no—
255C2×C8—22no—
256C2×C8—441no—
257C2×C8—441no—
258C4⋊C4—22no—
259C4⋊C4—21no—
260C4⋊C4—22no—
261C4⋊C4—21no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—442no—
268C4⋊C4—882no—
269C4⋊C4C22⋊Dic1112yes—
270C22⋊C4—41no—
271C42—22no—
272C42—22no—
273C42—41no—
274C42—442no—
275C42—442no—
276C42#434111yescharacteristic
277C42#434111yescharacteristic
278C42C22×Dic1111yescharacteristic
279C42C2×C22⋊D1111yescharacteristic
280C11#932811yescharacteristic, complemented, Sylow
281C23#6699011yescharacteristic
282Q8—22no—
283Q8—22no—
284Q8—42no—
285Q8—42no—
286Q8—81no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—22no—
290C2×C4—22no—
291C2×C4—22no—
292C2×C4—41no—
293C2×C4—42no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—441no—
299C2×C4—441no—
300C2×C4—442no—
301C2×C4—441no—
302C2×C4—441no—
303C2×C4—442no—
304C2×C4—442no—
305C2×C4—441no—
306C2×C4—441no—
307C2×C4D4×Dic1111yescharacteristic
308C2×C4D4×Dic1111yescharacteristic
309C2×C4#6698811yescharacteristic
310C2×C4#6699211yescharacteristic
311C2×C4#6699211yescharacteristic
312C2×C4C2×C22⋊Dic1111yescharacteristic
313C8—42no—
314C8—442no—
315C8—881no—
316C22—21no—
317C22—21no—
318C22#1062281511yescharacteristic
319C22#1062281811yescharacteristic
320C22#1062283311yescharacteristic
321C4—21no—
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—42no—
327C4—42no—
328C4—81no—
329C4—81no—
330C4—881no—
331C4—882no—
332C4—881no—
333C4#1062284912yes—
334C2—21no—
335C2—21no—
336C2#1306898711yescharacteristic
337C2#1306906511yescharacteristic
338C2#1306911211yescharacteristic
subgroupG/H
centerC22#10622833
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#3113C2
socleC22×C11#386
prime radicalC23×C11#120
cosocleC2×C42×C11C23
hypercenter#3113D11
hypocenterC11#9328
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3113

Complements

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

NH ≅ G/Ntype
11. C11×#475C4semidirect
12. C11×#462C4semidirect
157. #475Dic11semidirect
158. #462Dic11semidirect
280. C11#9328semidirect

Maximal subgroups

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

subgroupindex
#130712672
#130695612
#130671282
#130670632
#130665082
#130664732
C11×#31132
#932811