Finite Group Databasebeta

← #14649620

Subgroups — #14649620

Order 2816.

436 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 95 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#13078742C211yesmaximal, characteristic
2#13077703C211yesmaximal, characteristic
3#13068449C211yesmaximal, characteristic
4#13067231C211yesmaximal, characteristic
5#13066516C211yesmaximal, characteristic
6#13066472C211yesmaximal, characteristic
7C11×#1503C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C2×C4×Dic22C2211yescharacteristic
10C11×#431C2211yescharacteristic
11C4×C11×C4⋊C4C2211yescharacteristic
12#10622707C411yescharacteristic, complemented
13#10622707C411yescharacteristic, complemented
14#10622703C411yescharacteristic, complemented
15#10622703C411yescharacteristic, complemented
16#10622663—21no—
17#10622656—21no—
18#10622643—21no—
19#10622643—21no—
20C2×#66874—21no—
21#10622539C2211yescharacteristic
22#10622539C2211yescharacteristic
23C2×#66867C2211yescharacteristic
24#10622441—22no—
25#10622332—21no—
26#10622331—21no—
27#10622292—21no—
28C8×Dic22—21no—
29C11×#328—21no—
30C11×#328—21no—
31#10622181—22no—
32#10622167—21no—
33C22×Dic22D411yescharacteristic
34C11×C4⋊Q8C2×C411yescharacteristic
35C11×C4⋊Q8C2×C411yescharacteristic
36C11×#125—21no—
37C11×C22⋊Q8—21no—
38C11×C22⋊Q8—21no—
39C4×Q8×C11—21no—
40C4×Q8×C11—21no—
41C11×#117—21no—
42C2×C11×C4⋊C4—21no—
43C2×C42×C11—21no—
44C2×C42×C11C2311yescharacteristic
45C2×#4326—21no—
46C2×#4326—21no—
47C2×C4⋊Dic11D411yescharacteristic
48C2×Dic11⋊C4—21no—
49C2×C4×Dic11—21no—
50C22×C11⋊C8—21no—
51C4×Dic22—21no—
52C4×Dic22—21no—
53C4×Dic22C2×C411yescharacteristic
54C4×Dic22C2×C411yescharacteristic
55C4×Dic22D411yescharacteristic
56C4×Dic22D411yescharacteristic
57C11×C4⋊C8—21no—
58C11×C22⋊C8D411yescharacteristic
59C11×C22⋊C8D411yescharacteristic
60C4×C8×C11—21no—
61C11×#95—21no—
62#66899—21no—
63#66899—21no—
64C22⋊(C11⋊C8)—21no—
65C22⋊(C11⋊C8)—21no—
66#66879—22no—
67Dic11⋊C8—22no—
68Dic11⋊C8—22no—
69C8×Dic11—22no—
70#66874—24no—
71#66874—21no—
72#66874—21no—
73#66872—21no—
74#66872—21no—
75C4⋊(C11⋊C8)—21no—
76C4⋊(C11⋊C8)C2×C411yescharacteristic
77C4⋊(C11⋊C8)C2×C411yescharacteristic
78#66867—21no—
79#66867—21no—
80#66867—21no—
81#66867D412yes—
82#9166—111nomaximal, Sylow
83C2×Q8×C11—21no—
84C2×Q8×C11—21no—
85C22×C4×C11—41no—
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11#4111yescharacteristic
89C22×Dic11—21no—
90C22×Dic11—21no—
91C2×Dic22—22no—
92C2×Dic22—21no—
93C2×Dic22—41no—
94C2×Dic22C22⋊C411yescharacteristic
95C2×Dic22C22⋊C411yescharacteristic
96C2×C8×C11—21no—
97C2×C8×C11—21no—
98C11×C4⋊C4—22no—
99C11×C4⋊C4—21no—
100C11×C4⋊C4—21no—
101C11×C4⋊C4—21no—
102C11×C4⋊C4—21no—
103C11×C4⋊C4—41no—
104C11×C4⋊C4—41no—
105C11×C4⋊C4—41no—
106C11×C22⋊C4—41no—
107C42×C11—41no—
108C42×C11—81no—
109C42×C11C22×C411yescharacteristic
110C42×C11C2×D411yescharacteristic
111C42×C11C2×D411yescharacteristic
112C42×C11#4111yescharacteristic
113#4326—42no—
114#4326—42no—
115C4⋊Dic11—21no—
116C4⋊Dic11C22⋊C411yescharacteristic
117C4⋊Dic11C22⋊C411yescharacteristic
118Dic11⋊C4—21no—
119Dic11⋊C4—21no—
120Dic11⋊C4—21no—
121Dic11⋊C4—21no—
122C4×Dic11—21no—
123C4×Dic11—21no—
124C4×Dic11—21no—
125C4×Dic11—21no—
126C2×C11⋊C8—22no—
127C2×C11⋊C8—21no—
128C2×C11⋊C8—21no—
129C2×C11⋊C8—22no—
130C2×C11⋊C8—41no—
131C2×C11⋊C8—41no—
132#3113—111no—
133#2984—111no—
134#1763—111no—
135#1531—111no—
136#1503D1111yescharacteristic
137#1302—111no—
138#1285—111no—
139C23×C11#12111yescharacteristic
140Q8×C11—41no—
141Q8×C11—41no—
142Q8×C11—81no—
143C2×C4×C11—21no—
144C2×C4×C11—21no—
145C2×C4×C11—21no—
146C2×C4×C11—21no—
147C2×C4×C11—41no—
148C2×C4×C11—42no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—81no—
152C2×C4×C11—81no—
153C2×C4×C11C2×C22⋊C411yescharacteristic
154C2×C4×C11C4×D411yescharacteristic
155C2×C4×C11C4×D411yescharacteristic
156C2×C4×C11#12011yescharacteristic
157C2×C4×C11#12111yescharacteristic
158C2×C4×C11#12311yescharacteristic
159C2×Dic11—21no—
160C2×Dic11—21no—
161C2×Dic11—21no—
162C2×Dic11—21no—
163C2×Dic11—42no—
164C2×Dic11—41no—
165C2×Dic11—41no—
166Dic22—21no—
167Dic22—21no—
168Dic22—21no—
169Dic22—42no—
170Dic22#10412yes—
171C8×C11—41no—
172C8×C11—41no—
173C11⋊C8—42no—
174C11⋊C8—42no—
175C11⋊C8—41no—
176C11⋊C8—41no—
177#533C2×D1111yescharacteristic
178C2×C4×Q8—111no—
179#483—221no—
180#475—111no—
181#475—111no—
182#462—111no—
183#462—111no—
184#451—221no—
185#446—221no—
186#446—222no—
187C8×Q8—221no—
188#441—221no—
189#441—221no—
190#432—111no—
191#432—111no—
192#432—221no—
193#431—221no—
194#431C2×D1111yescharacteristic
195C2×#103—221no—
196C2×#97—111no—
197C4×C4⋊C4C2×D1111yescharacteristic
198#340—221no—
199#330—222no—
200#328—21no—
201#328—21no—
202C22×C11—21no—
203C22×C11—21no—
204C22×C11#38611yescharacteristic
205C22×C11#47111yescharacteristic
206C22×C11#47311yescharacteristic
207C4×C11—21no—
208C4×C11—21no—
209C4×C11—21no—
210C4×C11—21no—
211C4×C11—21no—
212C4×C11—82no—
213C4×C11—81no—
214C4×C11—81no—
215C4×C11C2×#10411yescharacteristic
216C4×C11#42111yescharacteristic
217Dic11—22no—
218Dic11—41no—
219Dic11—41no—
220Dic11—41no—
221C22×Q8—111no—
222C2×Q16—221no—
223C2×Q16—221no—
224C22×C8—221no—
225C4⋊Q8C4×D1111yescharacteristic
226C4⋊Q8C4×D1111yescharacteristic
227#125—21no—
228C22⋊Q8—21no—
229C22⋊Q8—21no—
230C4×Q8—21no—
231C4×Q8—21no—
232C4×Q8—111no—
233C4×Q8—111no—
234C4×Q8—111no—
235C4×Q8—111no—
236C4×Q8—221no—
237C4×Q8—221no—
238#117—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—111no—
241C2×C4⋊C4—221no—
242C2×C42—21no—
243C2×C42—221no—
244C2×C42C22×D1111yescharacteristic
245#106—221no—
246#106—221no—
247C4⋊C8—21no—
248C4⋊C8—111no—
249C4⋊C8—111no—
250C4⋊C8—222no—
251C4⋊C8—222no—
252C4⋊C8—221no—
253#103—221no—
254#103—221no—
255#103—224no—
256#103—221no—
257#103—221no—
258C22⋊C8—221no—
259C22⋊C8—221no—
260C22⋊C8C22⋊D1111yescharacteristic
261C22⋊C8C22⋊D1111yescharacteristic
262#97—112no—
263#97—222no—
264#97—221no—
265#97—221no—
266#97—221no—
267C4×C8—21no—
268C4×C8—222no—
269#95—21no—
270C2×C11—21no—
271C2×C11—21no—
272C2×C11#187111yescharacteristic
273C2×C11#190511yescharacteristic
274C2×C11#190811yescharacteristic
275C2×Q8—21no—
276C2×Q8—21no—
277C2×Q8—111no—
278C2×Q8—111no—
279C2×Q8—222no—
280C2×Q8—221no—
281C2×Q8—441no—
282C22×C4—41no—
283C22×C4—221no—
284C22×C4—221no—
285C22×C4D4×D1111yescharacteristic
286C22×C4#434111yescharacteristic
287C22×C4C2×C22⋊D1111yescharacteristic
288Q16—442no—
289Q16—442no—
290C2×C8—21no—
291C2×C8—21no—
292C2×C8—222no—
293C2×C8—221no—
294C2×C8—221no—
295C2×C8—222no—
296C2×C8—441no—
297C2×C8—441no—
298C4⋊C4—22no—
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—21no—
302C4⋊C4—21no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4—111no—
307C4⋊C4—111no—
308C4⋊C4—221no—
309C4⋊C4—221no—
310C4⋊C4—221no—
311C4⋊C4—221no—
312C4⋊C4—221no—
313C22⋊C4—41no—
314C42—41no—
315C42—81no—
316C42—221no—
317C42—221no—
318C42—221no—
319C42—221no—
320C42C2×C4×D1111yescharacteristic
321C42#433911yescharacteristic
322C42D4×D1111yescharacteristic
323C42D4×D1111yescharacteristic
324C11#916611yescharacteristic, complemented, Sylow
325C23#6699111yescharacteristic
326Q8—41no—
327Q8—41no—
328Q8—81no—
329Q8—112no—
330Q8—221no—
331Q8—221no—
332Q8—221no—
333Q8—442no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—41no—
339C2×C4—42no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—81no—
343C2×C4—81no—
344C2×C4—221no—
345C2×C4—221no—
346C2×C4—221no—
347C2×C4—221no—
348C2×C4—442no—
349C2×C4—441no—
350C2×C4—441no—
351C2×C4C22⋊C4×D1111yescharacteristic
352C2×C4(C22⋊D11)⋊C411yescharacteristic
353C2×C4#6693611yescharacteristic
354C2×C4#6693711yescharacteristic
355C2×C4C4×C22⋊D1111yescharacteristic
356C2×C4#6699011yescharacteristic
357C8—41no—
358C8—41no—
359C8—442no—
360C8—442no—
361C8—441no—
362C8—441no—
363C22—21no—
364C22—21no—
365C22#1062256911yescharacteristic
366C22#1062279011yescharacteristic
367C22#1062280511yescharacteristic
368C4—21no—
369C4—21no—
370C4—21no—
371C4—21no—
372C4—21no—
373C4—82no—
374C4—81no—
375C4—81no—
376C4—222no—
377C4—441no—
378C4—441no—
379C4—441no—
380C4D11×#10411yescharacteristic
381C4#1062243411yescharacteristic
382C2—21no—
383C2—21no—
384C2#1306891511yescharacteristic
385C2#1306911311yescharacteristic
386C2#1306913411yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1503C2
socleC22×C11#386
prime radicalC23×C11#121
cosocleC2×C42×C11C23
hypercenter#1503D11
hypocenterC11#9166
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1503

Complements

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

NH ≅ G/Ntype
12. #10622707C4semidirect
13. #10622707C4semidirect
14. #10622703C4semidirect
15. #10622703C4semidirect
324. C11#9166semidirect

Maximal subgroups

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

subgroupindex
#130787422
#130777032
#130684492
#130672312
#130665162
#130664722
C11×#15032
#916611