Finite Group Databasebeta

← #14655427

Subgroups — #14655427

Order 2816.

536 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 85 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#13079767C211yesmaximal, characteristic, complemented
2#13079619C211yesmaximal, characteristic
3#13067333C211yesmaximal, characteristic, complemented
4#13067230C211yesmaximal, characteristic, complemented
5#13066968C211yesmaximal, characteristic
6#13066515C211yesmaximal, characteristic, complemented
7C2×C11×#497C211yesmaximal, characteristic
8C22×C11×Q16—21no—
9C22×C11×SD16—21no—
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×C11×#124C2211yescharacteristic
12#10623001C2211yescharacteristic
13C11×#497—22no—
14C11×#497—22no—
15C2×C11×#97C2211yescharacteristic
16#10622841—21no—
17#10622831—21no—
18#10622706—21no—
19#10622704—22no—
20#10622691—21no—
21#10622673—21no—
22#10622668—21no—
23#10622667—22no—
24#10622583—22no—
25#10622539C2211yescharacteristic
26#10622539C2211yescharacteristic
27#10622538C2211yescharacteristic
28#10622185—22no—
29#10622163—22no—
30#10622103—22no—
31C22×Q8×C11—21no—
32C22×Q8×C11D411yescharacteristic
33C22×D4×C11D411yescharacteristic
34C2×C11×Q16—24no—
35C2×C11×Q16—44no—
36C2×C11×SD16—24no—
37C2×C11×SD16—44no—
38C22×C8×C11—21no—
39C11×C4⋊Q8—21no—
40C11×C4⋊Q8—21no—
41C11×C4⋊Q8—21no—
42C11×C4⋊Q8D412yes—
43C11×#124—21no—
44C11×#124—21no—
45C11×#124—21no—
46C11×#124—21no—
47C2×C11×C4⋊C4—21no—
48C2×C11×C4⋊C4—21no—
49C2×C11×C22⋊C4—21no—
50C2×C11×C22⋊C4—21no—
51C2×C42×C11C2311yescharacteristic
52C2×#4326—22no—
53C2×#4324—22no—
54#66979—21no—
55#66977—21no—
56#66977—21no—
57#66923—21no—
58#66922D411yescharacteristic
59#66922D411yescharacteristic
60C4×Dic22—21no—
61C4×Dic22—21no—
62C11×#97—21no—
63C11×#97D412yes—
64#66899—22no—
65#66896—22no—
66C22⋊(C11⋊C8)—21no—
67C22⋊(C11⋊C8)—21no—
68C22⋊(C11⋊C8)D412yes—
69#66874—24no—
70#66871—24no—
71C4⋊(C11⋊C8)—21no—
72C4⋊(C11⋊C8)—21no—
73C4⋊(C11⋊C8)D412yes—
74#66867—21no—
75#66867—21no—
76C4×C11⋊C8—21no—
77#10133—111nomaximal, Sylow
78C24×C11—21no—
79C2×Q8×C11—21no—
80C2×Q8×C11—21no—
81C2×Q8×C11—22no—
82C2×Q8×C11—42no—
83C2×Q8×C11—42no—
84C2×Q8×C11—42no—
85C2×Q8×C11—41no—
86C2×D4×C11—21no—
87C2×D4×C11—21no—
88C2×D4×C11—42no—
89C22×C4×C11—21no—
90C22×C4×C11—41no—
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11#4111yescharacteristic
94C2×Dic22—21no—
95C2×Dic22—21no—
96C11×Q16—48no—
97C11×SD16—48no—
98C2×C8×C11—24no—
99C2×C8×C11—22no—
100C11×C4⋊C4—22no—
101C11×C4⋊C4—22no—
102C11×C4⋊C4—41no—
103C11×C4⋊C4—41no—
104C11×C22⋊C4—41no—
105C11×C22⋊C4—41no—
106C11×C22⋊C4—41no—
107C11×C22⋊C4—41no—
108C42×C11C2×D411yescharacteristic
109C42×C11C2×D411yescharacteristic
110C42×C11C2×D411yescharacteristic
111C42×C11C2×D411yescharacteristic
112C22⋊Dic11—41no—
113#4326—82no—
114#4324—82no—
115C4⋊Dic11—21no—
116C4⋊Dic11—21no—
117C4⋊Dic11—21no—
118C4⋊Dic11—21no—
119Dic11⋊C4—41no—
120Dic11⋊C4—41no—
121C4×Dic11—41no—
122C2×C11⋊C8—22no—
123C2×C11⋊C8—22no—
124C2×C11⋊C8—41no—
125#3230—111no—
126#3215—111no—
127C2×#497D1111yescharacteristic
128#1556—111no—
129#1531—111no—
130#1469—111no—
131#1302—111no—
132C23×C11—41no—
133C23×C11—42no—
134C23×C11—81no—
135C23×C11—81no—
136C23×C11#12111yescharacteristic
137Q8×C11—42no—
138Q8×C11—42no—
139Q8×C11—42no—
140Q8×C11—42no—
141Q8×C11—82no—
142D4×C11—42no—
143D4×C11—42no—
144C2×C4×C11—22no—
145C2×C4×C11—22no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—42no—
149C2×C4×C11—82no—
150C2×C4×C11—81no—
151C2×C4×C11#12011yescharacteristic
152C2×C4×C11#12011yescharacteristic
153C2×C4×C11#12011yescharacteristic
154C2×C4×C11#12111yescharacteristic
155C2×C4×C11#12111yescharacteristic
156C2×C4×C11#12711yescharacteristic
157C2×Dic11—41no—
158C2×Dic11—41no—
159Dic22—42no—
160Dic22—42no—
161C8×C11—24no—
162C11⋊C8—42no—
163C11⋊C8—42no—
164C11⋊C8—81no—
165C22×Q16—21no—
166C22×SD16—21no—
167#533—111no—
168C2×C4⋊Q8C2×D1111yescharacteristic
169C2×#124C2×D1111yescharacteristic
170#500—221no—
171#497—22no—
172#497—22no—
173#497—221no—
174#489—221no—
175#487—221no—
176#484—222no—
177#477—222no—
178#464—222no—
179#451—221no—
180#450—221no—
181#432—111no—
182#432—111no—
183#431—111no—
184C2×#97C2×D1111yescharacteristic
185#332—222no—
186#330—222no—
187#323—222no—
188C22×C11—21no—
189C22×C11—21no—
190C22×C11—81no—
191C22×C11—81no—
192C22×C11—81no—
193C22×C11—162no—
194C22×C11#39211yescharacteristic
195C22×C11#47312yes—
196C4×C11—21no—
197C4×C11—21no—
198C4×C11—21no—
199C4×C11—21no—
200C4×C11—21no—
201C4×C11—82no—
202C4×C11—81no—
203C4×C11#45312yes—
204Dic11—81no—
205Dic11—81no—
206C22×Q8—21no—
207C22×Q8C22⋊D1111yescharacteristic
208C22×D4C22⋊D1111yescharacteristic
209C2×Q16—24no—
210C2×Q16—44no—
211C2×Q16—222no—
212C2×SD16—24no—
213C2×SD16—44no—
214C2×SD16—222no—
215C22×C8—21no—
216C4⋊Q8—21no—
217C4⋊Q8—21no—
218C4⋊Q8—21no—
219C4⋊Q8—111no—
220C4⋊Q8—111no—
221C4⋊Q8C22⋊D1112yes—
222#125—221no—
223#124—21no—
224#124—21no—
225#124—21no—
226#124—21no—
227C22⋊Q8—221no—
228C22⋊Q8—221no—
229C4×Q8—221no—
230C4×Q8—221no—
231#117—221no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C22⋊C4—21no—
235C2×C22⋊C4—21no—
236C2×C42C22×D1111yescharacteristic
237#107—224no—
238C4⋊C8—112no—
239C4⋊C8—221no—
240C4⋊C8—221no—
241#103—224no—
242#103—222no—
243#102—222no—
244C22⋊C8—112no—
245C22⋊C8—221no—
246C22⋊C8—221no—
247#97—21no—
248#97—221no—
249#97—221no—
250#97C22⋊D1112yes—
251C4×C8—221no—
252C2×C11—22no—
253C2×C11—161no—
254C2×C11#200211yescharacteristic
255C2×C11#200911yescharacteristic
256C2×C11#202011yescharacteristic
257C24—21no—
258C2×Q8—21no—
259C2×Q8—21no—
260C2×Q8—22no—
261C2×Q8—42no—
262C2×Q8—42no—
263C2×Q8—42no—
264C2×Q8—41no—
265C2×Q8—221no—
266C2×Q8—221no—
267C2×D4—21no—
268C2×D4—21no—
269C2×D4—42no—
270C22×C4—21no—
271C22×C4—41no—
272C22×C4D4×D1111yescharacteristic
273C22×C4#434111yescharacteristic
274C22×C4C2×C22⋊D1111yescharacteristic
275Q16—48no—
276Q16—882no—
277SD16—48no—
278SD16—882no—
279C2×C8—24no—
280C2×C8—22no—
281C2×C8—222no—
282C2×C8—222no—
283C2×C8—441no—
284C4⋊C4—22no—
285C4⋊C4—22no—
286C4⋊C4—41no—
287C4⋊C4—41no—
288C4⋊C4—221no—
289C4⋊C4—221no—
290C4⋊C4—221no—
291C4⋊C4—221no—
292C4⋊C4—441no—
293C4⋊C4—441no—
294C22⋊C4—41no—
295C22⋊C4—41no—
296C22⋊C4—41no—
297C22⋊C4—41no—
298C22⋊C4—441no—
299C42—441no—
300C42D4×D1111yescharacteristic
301C42D4×D1111yescharacteristic
302C42C2×C22⋊D1111yescharacteristic
303C42C2×C22⋊D1111yescharacteristic
304C11#1013311yescharacteristic, complemented, Sylow
305C23—41no—
306C23—42no—
307C23—81no—
308C23—81no—
309C23#6699211yescharacteristic
310Q8—42no—
311Q8—42no—
312Q8—42no—
313Q8—42no—
314Q8—82no—
315Q8—442no—
316Q8—442no—
317D4—42no—
318D4—42no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—42no—
324C2×C4—82no—
325C2×C4—81no—
326C2×C4—441no—
327C2×C4—441no—
328C2×C4#6699011yescharacteristic
329C2×C4#6699011yescharacteristic
330C2×C4#6699111yescharacteristic
331C2×C4#6699211yescharacteristic
332C2×C4#6699311yescharacteristic
333C2×C4#6700611yescharacteristic
334C8—24no—
335C8—442no—
336C8—442no—
337C8—881no—
338C22—21no—
339C22—21no—
340C22—81no—
341C22—81no—
342C22—81no—
343C22—162no—
344C22#1062281712yes—
345C22#1062283611yescharacteristic
346C4—21no—
347C4—21no—
348C4—21no—
349C4—21no—
350C4—21no—
351C4—82no—
352C4—81no—
353C4—881no—
354C4—881no—
355C4#1062269012yes—
356C2—22no—
357C2—161no—
358C2#1306963111yescharacteristic
359C2#1306967411yescharacteristic
360C2#1306973411yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC2×C11×#497C2
socleC22×C11#392
prime radicalC22×D4×C11D4
hypercenterC2×#497D11
hypocenterC11#10133
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#497

Complements

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

NH ≅ G/Ntype
1. #13079767C2semidirect
3. #13067333C2semidirect
4. #13067230C2semidirect
6. #13066515C2semidirect
304. C11#10133semidirect

Maximal subgroups

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

subgroupindex
#130797672
#130796192
#130673332
#130672302
#130669682
#130665152
C2×C11×#4972
#1013311