Finite Group Databasebeta

← #14650950

Subgroups — #14650950

Order 2816.

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

normal subgroups only

This group has 500 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#13071501C211yesmaximal, characteristic
2#13069602C211yesmaximal, characteristic
3#13068715C211yesmaximal, characteristic
4#13067136C211yesmaximal, characteristic
5#13066521C211yesmaximal, characteristic
6#13066501C211yesmaximal, characteristic
7C11×#3095C211yesmaximal, characteristic
8C2×C11×C22⋊Q8C2211yescharacteristic
9C2×C11×#117C2211yescharacteristic
10C11×#485—22no—
11C11×#484—21no—
12C11×#483—21no—
13C11×#428C412yescomplemented
14C11×#419C412yescomplemented
15C11×#407C2211yescharacteristic
16#10622825C2211yescharacteristic
17C4×C22⋊Dic11C2211yescharacteristic
18C4×C22⋊Dic11C2211yescharacteristic
19#10622820C2211yescharacteristic
20#10622598—21no—
21C4⋊C4×Dic11—21no—
22#10622564—22no—
23#10622549—21no—
24#10622545—21no—
25#10622176—21no—
26#10622176—21no—
27#10622170—22no—
28#10622164—22no—
29C22×Q8×C11C2×C411yescharacteristic
30C23×C4×C11C2311yescharacteristic
31C2×C11×M16C2×C412yes—
32C11×C22⋊Q8—21no—
33C11×C22⋊Q8—21no—
34C11×C22⋊Q8—21no—
35C11×C22⋊Q8—21no—
36C11×#117—21no—
37C11×#117—21no—
38C11×#117C2×C412yes—
39C11×#117D412yes—
40C2×C11×C4⋊C4—21no—
41C2×C11×C4⋊C4C2×C411yescharacteristic
42C2×C11×C4⋊C4D411yescharacteristic
43C2×C11×C4⋊C4D411yescharacteristic
44C2×C11×C22⋊C4—21no—
45C2×C11×C22⋊C4—21no—
46C2×C42×C11—21no—
47C2×C22⋊Dic11—21no—
48C2×C22⋊Dic11—21no—
49C2×C22⋊Dic11D412yes—
50C2×C4⋊Dic11—21no—
51C2×C4⋊Dic11—22no—
52C2×C4×Dic11—22no—
53C2×C4×Dic11—21no—
54C2×C4×Dic11—21no—
55C2×#4318—21no—
56C11×#107—22no—
57C11×#106—22no—
58C11×#103—22no—
59C11×#103—22no—
60C11×C22⋊C8—21no—
61C11×C22⋊C8—21no—
62C11⋊#95—22no—
63C11⋊#95—22no—
64C11⋊#95—21no—
65C11⋊#95—21no—
66C11⋊#95D411yescharacteristic
67C11⋊#95D411yescharacteristic
68C22⋊(C11⋊C8)—21no—
69C22⋊(C11⋊C8)—21no—
70#9363—111nomaximal, Sylow
71C24×C11C2×D411yescharacteristic
72C2×Q8×C11—21no—
73C2×Q8×C11—21no—
74C2×Q8×C11—42no—
75C22×C4×C11—21no—
76C22×C4×C11—21no—
77C22×C4×C11—21no—
78C22×C4×C11—21no—
79C22×C4×C11—42no—
80C22×C4×C11C22×C411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11#4111yescharacteristic
85C22×C4×C11#4111yescharacteristic
86C22×Dic11—21no—
87C22×Dic11—22no—
88C22×Dic11—21no—
89C22×Dic11—41no—
90C11×M16—42no—
91C2×C8×C11—22no—
92C11×C4⋊C4—21no—
93C11×C4⋊C4—21no—
94C11×C4⋊C4—21no—
95C11×C4⋊C4—21no—
96C11×C4⋊C4—41no—
97C11×C4⋊C4—41no—
98C11×C4⋊C4C22⋊C412yes—
99C11×C4⋊C4C22⋊C412yes—
100C11×C22⋊C4—22no—
101C11×C22⋊C4—22no—
102C11×C22⋊C4—41no—
103C11×C22⋊C4—41no—
104C42×C11—22no—
105C42×C11—22no—
106C22⋊Dic11—22no—
107C22⋊Dic11—42no—
108C22⋊Dic11—41no—
109C22⋊Dic11—42no—
110C4⋊Dic11—42no—
111C4⋊Dic11—82no—
112C4×Dic11—42no—
113C4×Dic11—42no—
114C4×Dic11—44no—
115#4318—42no—
116C2×C11⋊C8—41no—
117#3095D1111yescharacteristic
118#2346—111no—
119#1996—111no—
120#1826—111no—
121#1508—111no—
122#1305—111no—
123#1297—111no—
124C23×C11—21no—
125C23×C11—21no—
126C23×C11—41no—
127C23×C11—41no—
128C23×C11C4×D411yescharacteristic
129C23×C11#12011yescharacteristic
130C23×C11#12111yescharacteristic
131Q8×C11—42no—
132Q8×C11—81no—
133C2×C4×C11—22no—
134C2×C4×C11—22no—
135C2×C4×C11—22no—
136C2×C4×C11—22no—
137C2×C4×C11—22no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—42no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—81no—
147C2×C4×C11—81no—
148C2×C4×C11C2×C22⋊C411yescharacteristic
149C2×C4×C11C4×D411yescharacteristic
150C2×C4×C11#12111yescharacteristic
151C2×C4×C11#12311yescharacteristic
152C2×Dic11—22no—
153C2×Dic11—41no—
154C2×Dic11—41no—
155C2×Dic11—41no—
156C2×Dic11—42no—
157C2×Dic11—42no—
158C2×Dic11—42no—
159C2×Dic11—41no—
160C2×Dic11—41no—
161C2×Dic11—42no—
162C2×Dic11—81no—
163C2×Dic11—81no—
164C8×C11—42no—
165C11⋊C8—81no—
166C2×C22⋊Q8C2×D1111yescharacteristic
167C2×#117C2×D1111yescharacteristic
168#485—22no—
169#484—21no—
170#483—21no—
171#428Dic1112yescomplemented
172#419Dic1112yescomplemented
173#407—111no—
174#407C2×D1111yescharacteristic
175#389—221no—
176#388—222no—
177#382—221no—
178#380—111no—
179C4×C4⋊C4—221no—
180C4×C22⋊C4—111no—
181C4×C22⋊C4—111no—
182#376—221no—
183#342—222no—
184#339—222no—
185#328—221no—
186#328—221no—
187C22×C11—21no—
188C22×C11—21no—
189C22×C11—21no—
190C22×C11—21no—
191C22×C11—21no—
192C22×C11—21no—
193C22×C11—21no—
194C22×C11—21no—
195C22×C11—81no—
196C22×C11—81no—
197C22×C11#38611yescharacteristic
198C22×C11#45511yescharacteristic
199C22×C11#45611yescharacteristic
200C4×C11—21no—
201C4×C11—21no—
202C4×C11—21no—
203C4×C11—42no—
204C4×C11—42no—
205C4×C11—81no—
206C4×C11—81no—
207C4×C11#41012yes—
208Dic11—42no—
209Dic11—82no—
210Dic11—81no—
211Dic11—82no—
212C22×Q8C2×Dic1111yescharacteristic
213C23×C4C22×D1111yescharacteristic
214C2×M16—221no—
215C2×M16C2×Dic1112yes—
216C22⋊Q8—21no—
217C22⋊Q8—21no—
218C22⋊Q8—21no—
219C22⋊Q8—21no—
220#117—21no—
221#117—21no—
222#117C2×Dic1112yes—
223#117C22⋊D1112yes—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—221no—
226C2×C4⋊C4—222no—
227C2×C4⋊C4C2×Dic1111yescharacteristic
228C2×C4⋊C4C22⋊D1111yescharacteristic
229C2×C4⋊C4C22⋊D1111yescharacteristic
230C2×C22⋊C4—21no—
231C2×C22⋊C4—21no—
232C2×C22⋊C4—112no—
233C2×C22⋊C4—221no—
234C2×C22⋊C4—221no—
235C2×C42—21no—
236C2×C42—222no—
237C2×C42—221no—
238C2×C42—221no—
239#107—22no—
240#106—22no—
241#103—22no—
242#103—22no—
243C22⋊C8—21no—
244C22⋊C8—21no—
245C22⋊C8—221no—
246C22⋊C8—221no—
247#95—111no—
248#95—111no—
249#95—222no—
250#95—222no—
251#95—221no—
252#95—221no—
253C2×C11—21no—
254C2×C11—21no—
255C2×C11—41no—
256C2×C11—41no—
257C2×C11#188211yescharacteristic
258C2×C11#189911yescharacteristic
259C2×C11#190611yescharacteristic
260C24D4×D1111yescharacteristic
261C2×Q8—21no—
262C2×Q8—21no—
263C2×Q8—42no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—42no—
269C22×C4—221no—
270C22×C4—221no—
271C22×C4—222no—
272C22×C4—441no—
273C22×C4D4×D1111yescharacteristic
274C22×C4#434111yescharacteristic
275C22×C4#434111yescharacteristic
276C22×C4C22×Dic1111yescharacteristic
277C22×C4C2×C22⋊D1111yescharacteristic
278C22×C4C2×C22⋊D1111yescharacteristic
279M16—42no—
280M16—442no—
281C2×C8—22no—
282C2×C8—441no—
283C4⋊C4—21no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C4⋊C4—442no—
290C4⋊C4—882no—
291C4⋊C4C22⋊Dic1112yes—
292C4⋊C4C22⋊Dic1112yes—
293C22⋊C4—22no—
294C22⋊C4—22no—
295C22⋊C4—41no—
296C22⋊C4—41no—
297C22⋊C4—222no—
298C22⋊C4—442no—
299C22⋊C4—441no—
300C22⋊C4—442no—
301C42—22no—
302C42—22no—
303C42—442no—
304C42—442no—
305C42—444no—
306C11#936311yescharacteristic, complemented, Sylow
307C23—21no—
308C23—21no—
309C23—41no—
310C23—41no—
311C23D4×Dic1111yescharacteristic
312C23#6699011yescharacteristic
313C23#6699211yescharacteristic
314Q8—42no—
315Q8—81no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—42no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—81no—
330C2×C4—81no—
331C2×C4—222no—
332C2×C4—441no—
333C2×C4—441no—
334C2×C4—441no—
335C2×C4—442no—
336C2×C4—442no—
337C2×C4—441no—
338C2×C4—442no—
339C2×C4—442no—
340C2×C4—441no—
341C2×C4—881no—
342C2×C4—881no—
343C2×C4D4×Dic1111yescharacteristic
344C2×C4#6698811yescharacteristic
345C2×C4#6699211yescharacteristic
346C2×C4C2×C22⋊Dic1111yescharacteristic
347C8—42no—
348C8—881no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—81no—
358C22—81no—
359C22#1062281511yescharacteristic
360C22#1062281811yescharacteristic
361C22#1062283311yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—42no—
366C4—42no—
367C4—81no—
368C4—81no—
369C4—442no—
370C4—881no—
371C4—882no—
372C4—882no—
373C4#1062285312yes—
374C2—21no—
375C2—21no—
376C2—41no—
377C2—41no—
378C2#1306898711yescharacteristic
379C2#1306907511yescharacteristic
380C2#1306911911yescharacteristic
subgroupG/H
centerC22#10622833
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#3095C2
socleC22×C11#386
prime radicalC24×C11C2×D4
cosocleC23×C4×C11C23
hypercenter#3095D11
hypocenterC11#9363
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3095

Complements

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

NH ≅ G/Ntype
13. C11×#428C4semidirect
14. C11×#419C4semidirect
171. #428Dic11semidirect
172. #419Dic11semidirect
306. C11#9363semidirect

Maximal subgroups

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

subgroupindex
#130715012
#130696022
#130687152
#130671362
#130665212
#130665012
C11×#30952
#936311