Finite Group Databasebeta

← #14651873

Subgroups — #14651873

Order 2816.

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

normal subgroups only

This group has 412 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#13078787C211yesmaximal, characteristic
2#13077601C211yesmaximal, characteristic
3#13067248C211yesmaximal, characteristic
4#13066960C211yesmaximal, characteristic, complemented
5C11⋊#1308C211yesmaximal, characteristic, complemented
6#13066488C211yesmaximal, characteristic, complemented
7C11×#1491C211yesmaximal, characteristic, complemented
8C2×C4×Q8×C11C2211yescharacteristic
9#10623010C2211yescharacteristic
10C11×#432C2211yescharacteristic
11C4×C11×M16C2211yescharacteristic
12#10622841C411yescharacteristic
13#10622840C411yescharacteristic
14#10622741—21no—
15#10622740—21no—
16#10622643—21no—
17#10622641—21no—
18#10622639—21no—
19#10622635—21no—
20#10622583C411yescharacteristic
21#10622581C411yescharacteristic
22#10622539C2211yescharacteristic
23#10622539C2211yescharacteristic
24#10622539C2211yescharacteristic
25#10622319—21no—
26#10622314—21no—
27#10622303—21no—
28#10622302—21no—
29C11×Q8⋊C8—21no—
30C11×Q8⋊C8—21no—
31#10622166—21no—
32#10622166—21no—
33#10622103—21no—
34#10622102—21no—
35C22×Q8×C11C2×C411yescharacteristic
36C2×C11×M16—21no—
37C4×Q8×C11—21no—
38C4×Q8×C11—21no—
39C4×Q8×C11—21no—
40C4×Q8×C11—21no—
41C2×C11×C4⋊C4—21no—
42C2×C11×C4⋊C4C2×C411yescharacteristic
43C2×C42×C11—21no—
44C2×C42×C11C2311yescharacteristic
45C2×#4326—21no—
46C2×#4325—21no—
47#66983C2×C411yescharacteristic
48#66982—21no—
49C4×C22⋊D11—21no—
50#66977C2×C411yescharacteristic
51C2×#4313—21no—
52C2×C8×D11—21no—
53#66929—21no—
54#66928D411yescharacteristic
55C4×D44D411yescharacteristic
56#66925—21no—
57#66923D411yescharacteristic
58C4×Dic22D411yescharacteristic
59C11×C4⋊C8—21no—
60C11×C22⋊C8—21no—
61C11×#97—21no—
62C11×#97—21no—
63C4×C8×C11D411yescharacteristic
64C4×C8×C11D411yescharacteristic
65#66899—21no—
66#66899—21no—
67C22⋊(C11⋊C8)—21no—
68C22⋊(C11⋊C8)C2×C411yescharacteristic
69C22⋊(C11⋊C8)C2×C411yescharacteristic
70C22⋊(C11⋊C8)D411yescharacteristic
71C22⋊(C11⋊C8)D411yescharacteristic
72(C2×D11)⋊C8—21no—
73(C2×D11)⋊C8—21no—
74#66879—21no—
75Dic11⋊C8—21no—
76Dic11⋊C8—21no—
77C8×Dic11—21no—
78#66874—21no—
79#66873—21no—
80#66872—21no—
81#66871—21no—
82C4⋊(C11⋊C8)—21no—
83C4⋊(C11⋊C8)—21no—
84C4⋊(C11⋊C8)—21no—
85#66867—21no—
86#66867—21no—
87#66867—21no—
88#9531—111nomaximal, Sylow
89C2×Q8×C11—21no—
90C2×Q8×C11—21no—
91C2×Q8×C11—42no—
92C22×C4×C11—21no—
93C22×C4×C11—21no—
94C22×C4×C11C22×C411yescharacteristic
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11#4111yescharacteristic
97C2×C22⋊D11—21no—
98C2×D44C22⋊C411yescharacteristic
99C2×C4×D11—21no—
100C2×Dic22C22⋊C411yescharacteristic
101C11×M16—42no—
102C2×C8×C11—21no—
103C2×C8×C11—21no—
104C2×C8×C11—41no—
105C11×C4⋊C4—21no—
106C11×C4⋊C4—21no—
107C11×C4⋊C4—41no—
108C11×C4⋊C4—41no—
109C42×C11—41no—
110C42×C11—41no—
111C42×C11C2×D411yescharacteristic
112C42×C11C2×D411yescharacteristic
113C42×C11C2×D411yescharacteristic
114C42×C11#4111yescharacteristic
115C22⋊Dic11—21no—
116#4326—42no—
117#4325—42no—
118(C2×D11)⋊C4—21no—
119(C2×D11)⋊C4—21no—
120(C2×D11)⋊C4—21no—
121(C2×D11)⋊C4—21no—
122C4⋊Dic11C22⋊C411yescharacteristic
123C4⋊Dic11C22⋊C411yescharacteristic
124Dic11⋊C4—21no—
125Dic11⋊C4—21no—
126Dic11⋊C4—21no—
127Dic11⋊C4—21no—
128C4×Dic11—21no—
129C2×C11⋊C8—21no—
130C2×C11⋊C8—21no—
131C2×C11⋊C8—21no—
132C2×C11⋊C8—21no—
133C2×C11⋊C8—41no—
134#4313—42no—
135C8×D11—42no—
136#3117—111no—
137#2967—111no—
138#1535—111no—
139#1491D1111yescharacteristic, complemented
140#1467—111no—
141#1308—111no—
142#1291—111no—
143C23×C11C4×D411yescharacteristic
144C22×D11—21no—
145Q8×C11—22no—
146Q8×C11—22no—
147Q8×C11—41no—
148Q8×C11—41no—
149C2×C4×C11—22no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—41no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—81no—
157C2×C4×C11C2×C22⋊C411yescharacteristic
158C2×C4×C11C4×D411yescharacteristic
159C2×C4×C11#12011yescharacteristic
160C2×C4×C11#12111yescharacteristic
161C2×C4×C11#12111yescharacteristic
162C2×C4×C11#12311yescharacteristic
163C22⋊D11—81no—
164C2×Dic11—21no—
165C2×Dic11—21no—
166C2×Dic11—21no—
167D44—41no—
168C4×D11—41no—
169C4×D11—41no—
170Dic22—41no—
171C8×C11—22no—
172C8×C11—41no—
173C8×C11—81no—
174C11⋊C8—41no—
175C11⋊C8—41no—
176C11⋊C8—41no—
177C11⋊C8—41no—
178C11⋊C8—81no—
179#529—111no—
180C2×C4×Q8C2×D1111yescharacteristic
181#484—111no—
182#481—111no—
183#479—221no—
184#464—221no—
185#451—111no—
186#448—111no—
187#446—221no—
188#441—221no—
189#440—221no—
190#436—221no—
191#435—221no—
192#435—221no—
193#433—221no—
194#432—111no—
195#432—111no—
196#432—111no—
197#432C2×D1111yescharacteristic
198#405—221no—
199C4×M16C2×D1111yescharacteristic
200#330—221no—
201#329—221no—
202Q8⋊C8—21no—
203Q8⋊C8—21no—
204#324—221no—
205#324—221no—
206C22×C11—21no—
207C22×C11—21no—
208C22×C11—21no—
209C22×C11#38611yescharacteristic
210C2×D11—41no—
211C2×D11—41no—
212C2×D11—41no—
213C4×C11—21no—
214C4×C11—21no—
215C4×C11—21no—
216C4×C11—21no—
217C4×C11—21no—
218C4×C11—21no—
219C4×C11—42no—
220C4×C11—81no—
221Dic11—41no—
222Dic11—41no—
223Dic11—41no—
224C22×Q8C4×D1111yescharacteristic
225C2×Q16—221no—
226C2×SD16—221no—
227C2×M16—21no—
228C2×M16—221no—
229C22×C8—221no—
230#126—221no—
231#125—111no—
232#124—111no—
233#123—221no—
234C22⋊Q8—111no—
235#121—111no—
236C4×Q8—21no—
237C4×Q8—21no—
238C4×Q8—21no—
239C4×Q8—21no—
240C4×Q8—111no—
241C4×D4—111no—
242C4×D4—221no—
243#117—221no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4C4×D1111yescharacteristic
246C2×C42—21no—
247C2×C42C22×D1111yescharacteristic
248#107—221no—
249#106—221no—
250C4⋊C8—21no—
251C4⋊C8—221no—
252C4⋊C8—221no—
253C4⋊C8—221no—
254C4⋊C8—221no—
255C4⋊C8—221no—
256#103—221no—
257#103—221no—
258#103—221no—
259#102—221no—
260C22⋊C8—21no—
261C22⋊C8—111no—
262C22⋊C8—111no—
263C22⋊C8—111no—
264C22⋊C8—111no—
265C22⋊C8—221no—
266C22⋊C8—221no—
267C22⋊C8—221no—
268#97—21no—
269#97—21no—
270#97—221no—
271#97—221no—
272#97—221no—
273#97—221no—
274C4×C8—221no—
275C4×C8C22⋊D1111yescharacteristic
276C4×C8C22⋊D1111yescharacteristic
277C2×C11—41no—
278C2×C11#189111yescharacteristic
279C2×C11#190211yescharacteristic
280C2×C11#190611yescharacteristic
281D11—81no—
282C2×Q8—21no—
283C2×Q8—21no—
284C2×Q8—42no—
285C2×Q8—111no—
286C2×D4—111no—
287C2×D4—221no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—221no—
291C22×C4C2×C4×D1111yescharacteristic
292C22×C4D4×D1111yescharacteristic
293C22×C4#434111yescharacteristic
294Q16—442no—
295SD16—442no—
296M16—42no—
297M16—442no—
298C2×C8—21no—
299C2×C8—21no—
300C2×C8—41no—
301C2×C8—221no—
302C2×C8—221no—
303C2×C8—221no—
304C2×C8—221no—
305C2×C8—442no—
306C2×C8—441no—
307C4⋊C4—21no—
308C4⋊C4—21no—
309C4⋊C4—41no—
310C4⋊C4—41no—
311C4⋊C4—111no—
312C4⋊C4—111no—
313C4⋊C4—221no—
314C4⋊C4—221no—
315C4⋊C4—221no—
316C4⋊C4—221no—
317C22⋊C4—221no—
318C22⋊C4—221no—
319C22⋊C4—221no—
320C22⋊C4—221no—
321C22⋊C4—221no—
322C42—41no—
323C42—41no—
324C42—221no—
325C42#433911yescharacteristic
326C42D4×D1111yescharacteristic
327C42D4×D1111yescharacteristic
328C42C2×C22⋊D1111yescharacteristic
329C11#953111yescharacteristic, complemented, Sylow
330C23—221no—
331C23(C22⋊D11)⋊C411yescharacteristic
332Q8—22no—
333Q8—22no—
334Q8—41no—
335Q8—41no—
336Q8—441no—
337D4—441no—
338D4—881no—
339C2×C4—22no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—81no—
347C2×C4—221no—
348C2×C4—221no—
349C2×C4—221no—
350C2×C4—441no—
351C2×C4—441no—
352C2×C4C22⋊C4×D1111yescharacteristic
353C2×C4#6693611yescharacteristic
354C2×C4#6693711yescharacteristic
355C2×C4C4×C22⋊D1111yescharacteristic
356C2×C4#6699011yescharacteristic
357C2×C4#6699111yescharacteristic
358C8—22no—
359C8—41no—
360C8—81no—
361C8—441no—
362C8—441no—
363C8—441no—
364C8—441no—
365C8—881no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—441no—
370C22—441no—
371C22—441no—
372C22#1062256911yescharacteristic
373C4—21no—
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—21no—
379C4—42no—
380C4—81no—
381C4—441no—
382C4—441no—
383C4—441no—
384C2—41no—
385C2—881no—
386C2#1306903111yescharacteristic
387C2#1306908611yescharacteristic
388C2#1306912011yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1491C2
socleC22×C11#386
prime radical#66983C2×C4
cosocleC2×C42×C11C23
hypercenter#1491D11
hypocenterC11#9531
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1491

Complements

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

NH ≅ G/Ntype
4. #13066960C2semidirect
5. C11⋊#1308C2semidirect
6. #13066488C2semidirect
7. C11×#1491C2semidirect
139. #1491D11semidirect
329. C11#9531semidirect

Maximal subgroups

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

subgroupindex
#130787872
#130776012
#130672482
#130669602
C11⋊#13082
#130664882
C11×#14912
#953111