Finite Group Databasebeta

← #14649618

Subgroups — #14649618

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#13078747C211yesmaximal, characteristic
2#13077706C211yesmaximal, characteristic
3#13068449C211yesmaximal, characteristic
4#13067232C211yesmaximal, characteristic
5#13067114C211yesmaximal, characteristic
6#13066514C211yesmaximal, characteristic
7C11×#1285C211yesmaximal, characteristic
8#10623001C2211yescharacteristic
9C2×C4×Dic22C2211yescharacteristic
10C11×#432C2211yescharacteristic
11C11×#432C2211yescharacteristic
12C4×C11×C4⋊C4C2211yescharacteristic
13C2×#66874—21no—
14#10622538C2211yescharacteristic
15C2×#66867C2211yescharacteristic
16#10622464C411yescharacteristic, complemented
17#10622464C411yescharacteristic, complemented
18#10622462C411yescharacteristic, complemented
19#10622462C411yescharacteristic, complemented
20#10622444—21no—
21#10622443—21no—
22#10622352—21no—
23#10622334—21no—
24#10622332—21no—
25#10622331—21no—
26#10622329—21no—
27#10622329—21no—
28#10622314—22no—
29#10622167—21no—
30#10622103—22no—
31#10622090—21no—
32#10622090—21no—
33C22×Dic22D411yescharacteristic
34C2×C11×C4⋊C4—21no—
35C2×C42×C11—21no—
36C2×C42×C11C2311yescharacteristic
37#66979—21no—
38C2×C4⋊Dic11D411yescharacteristic
39#66977—21no—
40#66977—21no—
41C2×Dic11⋊C4—21no—
42C2×C4×Dic11—21no—
43C22×C11⋊C8—21no—
44C2×Dic44—21no—
45C2×Dic44—21no—
46#66923—21no—
47#66922C2×C411yescharacteristic
48#66922C2×C411yescharacteristic
49C4×Dic22—21no—
50C4×Dic22—21no—
51C4×Dic22—21no—
52C4×Dic22—21no—
53C4×Dic22C2×C411yescharacteristic
54C4×Dic22C2×C411yescharacteristic
55C4×Dic22D411yescharacteristic
56C4×Dic22D411yescharacteristic
57C11×C4⋊C8—21no—
58C11×C4⋊C8C2×C411yescharacteristic
59C11×C4⋊C8C2×C411yescharacteristic
60C11×C22⋊C8—21no—
61C11×C22⋊C8—21no—
62C11×#97—21no—
63C11×#97D412yes—
64C11×#95—21no—
65C22⋊(C11⋊C8)D411yescharacteristic
66C22⋊(C11⋊C8)D411yescharacteristic
67#66881—21no—
68#66881—21no—
69#66880—21no—
70#66880—21no—
71#66880—21no—
72#66880—21no—
73#66879—22no—
74Dic11⋊C8—22no—
75Dic11⋊C8—22no—
76C8×Dic11—22no—
77#66874—24no—
78C4⋊(C11⋊C8)—21no—
79#66867—21no—
80#66867—21no—
81C4×C11⋊C8—21no—
82#9166—111nomaximal, Sylow
83C22×C4×C11—41no—
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11#4111yescharacteristic
87C22×Dic11—21no—
88C22×Dic11—21no—
89C2×Dic22—22no—
90C2×Dic22—21no—
91C2×Dic22—21no—
92C2×Dic22—21no—
93C2×Dic22—41no—
94C2×Dic22C22⋊C411yescharacteristic
95C2×Dic22C22⋊C411yescharacteristic
96C2×C8×C11—21no—
97C2×C8×C11—21no—
98C2×C8×C11—22no—
99C11×C4⋊C4—22no—
100C11×C4⋊C4—41no—
101C42×C11—81no—
102C42×C11C22×C411yescharacteristic
103C42×C11C2×D411yescharacteristic
104C42×C11C2×D411yescharacteristic
105C42×C11#4111yescharacteristic
106C22⋊Dic11—41no—
107C4⋊Dic11—21no—
108C4⋊Dic11—21no—
109C4⋊Dic11—21no—
110C4⋊Dic11—21no—
111C4⋊Dic11—21no—
112C4⋊Dic11C22⋊C411yescharacteristic
113C4⋊Dic11C22⋊C411yescharacteristic
114Dic11⋊C4—21no—
115Dic11⋊C4—21no—
116Dic11⋊C4—21no—
117Dic11⋊C4—21no—
118Dic11⋊C4—41no—
119Dic11⋊C4—41no—
120C4×Dic11—21no—
121C4×Dic11—21no—
122C4×Dic11—21no—
123C4×Dic11—21no—
124C4×Dic11—41no—
125C2×C11⋊C8—22no—
126C2×C11⋊C8—21no—
127C2×C11⋊C8—21no—
128C2×C11⋊C8—41no—
129C2×C11⋊C8—41no—
130Dic44—42no—
131Dic44—42no—
132#3113—111no—
133#2984—111no—
134#1763—111no—
135#1531—111no—
136#1503—111no—
137#1302—111no—
138#1285D1111yescharacteristic
139C23×C11#12111yescharacteristic
140C2×C4×C11—21no—
141C2×C4×C11—21no—
142C2×C4×C11—21no—
143C2×C4×C11—21no—
144C2×C4×C11—41no—
145C2×C4×C11—42no—
146C2×C4×C11—81no—
147C2×C4×C11—81no—
148C2×C4×C11C2×C22⋊C411yescharacteristic
149C2×C4×C11C4×D411yescharacteristic
150C2×C4×C11C4×D411yescharacteristic
151C2×C4×C11#12011yescharacteristic
152C2×C4×C11#12111yescharacteristic
153C2×C4×C11#12311yescharacteristic
154C2×Dic11—21no—
155C2×Dic11—21no—
156C2×Dic11—21no—
157C2×Dic11—21no—
158C2×Dic11—42no—
159C2×Dic11—41no—
160C2×Dic11—41no—
161C2×Dic11—41no—
162C2×Dic11—41no—
163Dic22—21no—
164Dic22—21no—
165Dic22—21no—
166Dic22—42no—
167Dic22—41no—
168Dic22—41no—
169Dic22—81no—
170Dic22#10412yes—
171C8×C11—42no—
172C8×C11—41no—
173C8×C11—41no—
174C11⋊C8—41no—
175C11⋊C8—41no—
176C11⋊C8—42no—
177#533—111no—
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—221no—
191#432C2×D1111yescharacteristic
192#432C2×D1111yescharacteristic
193#431—111no—
194#431—221no—
195C2×#103—221no—
196C2×#97—111no—
197C4×C4⋊C4C2×D1111yescharacteristic
198#340—221no—
199#330—222no—
200#328—221no—
201#328—221no—
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×C11C2×#10411yescharacteristic
214C4×C11#42111yescharacteristic
215Dic11—22no—
216Dic11—41no—
217Dic11—41no—
218Dic11—41no—
219Dic11—81no—
220Dic11—81no—
221C22×Q8—111no—
222C2×Q16—221no—
223C2×Q16—221no—
224C22×C8—221no—
225C4⋊Q8—111no—
226C4⋊Q8—111no—
227#125—221no—
228C22⋊Q8—221no—
229C22⋊Q8—221no—
230C4×Q8—111no—
231C4×Q8—111no—
232C4×Q8—111no—
233C4×Q8—111no—
234C4×Q8—221no—
235C4×Q8—221no—
236C4×Q8—221no—
237C4×Q8—221no—
238#117—221no—
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—222no—
249C4⋊C8—222no—
250C4⋊C8—221no—
251C4⋊C8C4×D1111yescharacteristic
252C4⋊C8C4×D1111yescharacteristic
253#103—224no—
254#103—221no—
255#103—221no—
256#103—221no—
257#103—221no—
258C22⋊C8—21no—
259C22⋊C8—21no—
260C22⋊C8—111no—
261C22⋊C8—111no—
262#97—21no—
263#97—222no—
264#97—221no—
265#97—221no—
266#97D4412yes—
267C4×C8—222no—
268C4×C8—221no—
269#95—21no—
270C2×C11—21no—
271C2×C11—21no—
272C2×C11#187111yescharacteristic
273C2×C11#190511yescharacteristic
274C2×C11#190811yescharacteristic
275C2×Q8—111no—
276C2×Q8—111no—
277C2×Q8—222no—
278C2×Q8—221no—
279C2×Q8—221no—
280C2×Q8—221no—
281C2×Q8—441no—
282C22×C4—41no—
283C22×C4—221no—
284C22×C4—221no—
285C22×C4#433911yescharacteristic
286C22×C4D4×D1111yescharacteristic
287C22×C4D4×D1111yescharacteristic
288Q16—442no—
289Q16—442no—
290C2×C8—21no—
291C2×C8—21no—
292C2×C8—22no—
293C2×C8—222no—
294C2×C8—221no—
295C2×C8—221no—
296C2×C8—441no—
297C2×C8—441no—
298C4⋊C4—22no—
299C4⋊C4—41no—
300C4⋊C4—111no—
301C4⋊C4—111no—
302C4⋊C4—221no—
303C4⋊C4—221no—
304C4⋊C4—221no—
305C4⋊C4—221no—
306C4⋊C4—221no—
307C4⋊C4—221no—
308C4⋊C4—221no—
309C4⋊C4—221no—
310C4⋊C4—221no—
311C4⋊C4—441no—
312C4⋊C4—441no—
313C22⋊C4—441no—
314C42—81no—
315C42—221no—
316C42—221no—
317C42—221no—
318C42—221no—
319C42—441no—
320C42C2×C4×D1111yescharacteristic
321C42C2×D4411yescharacteristic
322C42D4×D1111yescharacteristic
323C42#434311yescharacteristic
324C11#916611yescharacteristic, complemented, Sylow
325C23#6693711yescharacteristic
326Q8—112no—
327Q8—221no—
328Q8—221no—
329Q8—221no—
330Q8—442no—
331Q8—441no—
332Q8—441no—
333Q8—881no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—41no—
339C2×C4—42no—
340C2×C4—81no—
341C2×C4—81no—
342C2×C4—221no—
343C2×C4—221no—
344C2×C4—221no—
345C2×C4—221no—
346C2×C4—442no—
347C2×C4—441no—
348C2×C4—441no—
349C2×C4—441no—
350C2×C4—441no—
351C2×C4C4×D4411yescharacteristic
352C2×C4C22⋊C4×D1111yescharacteristic
353C2×C4#6693511yescharacteristic
354C2×C4#6694611yescharacteristic
355C2×C4#6694711yescharacteristic
356C2×C4#6694811yescharacteristic
357C8—42no—
358C8—41no—
359C8—41no—
360C8—442no—
361C8—441no—
362C8—441no—
363C22—21no—
364C22—21no—
365C22#1062227811yescharacteristic
366C22#1062236111yescharacteristic
367C22#1062236811yescharacteristic
368C4—21no—
369C4—21no—
370C4—21no—
371C4—21no—
372C4—21no—
373C4—82no—
374C4—222no—
375C4—441no—
376C4—441no—
377C4—441no—
378C4—881no—
379C4—881no—
380C4D11×#10411yescharacteristic
381C4#1062243411yescharacteristic
382C2—21no—
383C2—21no—
384C2#1306891711yescharacteristic
385C2#1306911111yescharacteristic
386C2#1306913211yescharacteristic
subgroupG/H
centerC22#10622278
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1285C2
socleC22×C11#386
prime radicalC23×C11#121
cosocleC2×C42×C11C23
hypercenter#1285D11
hypocenterC11#9166
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1285

Complements

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

NH ≅ G/Ntype
16. #10622464C4semidirect
17. #10622464C4semidirect
18. #10622462C4semidirect
19. #10622462C4semidirect
324. C11#9166semidirect

Maximal subgroups

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

subgroupindex
#130787472
#130777062
#130684492
#130672322
#130671142
#130665142
C11×#12852
#916611