Finite Group Databasebeta

← #14656899

Subgroups — #14656899

Order 2816.

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

normal subgroups only

This group has 454 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#13071910C211yesmaximal, characteristic, complemented
2#13069449C211yesmaximal, characteristic
3#13067111C211yesmaximal, characteristic
4#13066519C211yesmaximal, characteristic, complemented
5#13066518C211yesmaximal, characteristic, complemented
6#13066444C211yesmaximal, characteristic, complemented
7C11×#1502C211yesmaximal, characteristic
8C11×#532C2211yescharacteristic
9C2×C4×Dic22—21no—
10C11×#431C2211yescharacteristic
11C4×C11×C4⋊C4C2211yescharacteristic
12C2×#66901—21no—
13C2×#66901—21no—
14#10622597—21no—
15#10622592—21no—
16C4×C4⋊Dic11C2211yescharacteristic
17#10622545C2211yescharacteristic
18C4×Dic11⋊C4—21no—
19#10622538C2211yescharacteristic
20#10622537C2211yescharacteristic
21#10622270—21no—
22#10622269—21no—
23C11×#327—21no—
24C11×#327—21no—
25#10622175—21no—
26#10622175—21no—
27C2×C11×#41—21no—
28C22×Dic22—21no—
29C11×C4⋊Q8Q811yescharacteristic, complemented
30C11×#127Q811yescharacteristic, complemented
31C11×#124—21no—
32C11×#121—21no—
33C11×#121—21no—
34C4×D4×C11—21no—
35C4×D4×C11—21no—
36C2×C11×C4⋊C4—21no—
37C2×C42×C11—21no—
38C2×C42×C11C2311yescharacteristic
39C2×C4⋊Dic11—21no—
40C2×C4⋊Dic11—21no—
41C2×Dic11⋊C4—21no—
42C2×Dic11⋊C4—21no—
43C2×Dic11⋊C4—21no—
44C2×Dic11⋊C4—21no—
45C2×C4×Dic11—21no—
46C2×C4×Dic11D411yescharacteristic
47C2×C4×Dic11D411yescharacteristic
48C2×#4318—21no—
49C4×Dic22—42no—
50C4×Dic22—42no—
51C11×C4⋊C8—21no—
52C11×C22⋊C8—21no—
53C4×C8×C11—21no—
54C11×#95D411yescharacteristic
55C11×#95D411yescharacteristic
56#66901—42no—
57#66901—42no—
58C11⋊#95—21no—
59C11⋊#95—21no—
60C11⋊#95—21no—
61C11⋊#95—21no—
62C11⋊#95D411yescharacteristic
63C11⋊#95D411yescharacteristic
64C22⋊(C11⋊C8)—21no—
65C4⋊(C11⋊C8)—21no—
66C4⋊(C11⋊C8)—21no—
67C4⋊(C11⋊C8)—21no—
68C4×C11⋊C8—21no—
69#10370—111nomaximal, Sylow
70C11×#41—41no—
71C11×#41—41no—
72C11×#41—41no—
73C11×#41—41no—
74C2×Q8×C11—21no—
75C2×D4×C11—21no—
76C2×D4×C11—21no—
77C2×D4×C11—21no—
78C2×D4×C11—41no—
79C22×C4×C11—21no—
80C22×C4×C11—21no—
81C22×C4×C11—41no—
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C22×Dic11—21no—
86C22×Dic11—21no—
87C22×Dic11—21no—
88C22×Dic11—21no—
89C2×Dic22—42no—
90C2×Dic22—42no—
91C2×Dic22—42no—
92C2×C8×C11—41no—
93C11×C4⋊C4—21no—
94C11×C4⋊C4—21no—
95C11×C4⋊C4—42no—
96C11×C22⋊C4—41no—
97C11×C22⋊C4—41no—
98C42×C11—41no—
99C42×C11—41no—
100C42×C11C2×Q811yescharacteristic
101C42×C11#4111yescharacteristic
102C42×C11#4111yescharacteristic
103C42×C11#4111yescharacteristic
104C4⋊Dic11—42no—
105C4⋊Dic11—42no—
106Dic11⋊C4—42no—
107Dic11⋊C4—42no—
108Dic11⋊C4—42no—
109Dic11⋊C4—42no—
110C4×Dic11—21no—
111C4×Dic11—21no—
112C4×Dic11—41no—
113C4×Dic11—41no—
114C4×Dic11D812yes—
115C4×Dic11SD1612yes—
116#4318—41no—
117#4318—41no—
118C2×C11⋊C8—41no—
119C2×C11⋊C8—41no—
120#2399—111no—
121#1963—111no—
122#1502—111no—
123#1502D1111yescharacteristic
124#1303—111no—
125#1303—111no—
126#1274—111no—
127C23×C11—41no—
128C23×C11#12011yescharacteristic
129Q8×C11—41no—
130Q8×C11—41no—
131D4×C11—41no—
132D4×C11—41no—
133D4×C11—81no—
134D4×C11—81no—
135D4×C11—81no—
136D4×C11—81no—
137C2×C4×C11—22no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
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×C11C22⋊Q811yescharacteristic
149C2×C4×C11C22⋊Q811yescharacteristic
150C2×C4×C11C22⋊Q811yescharacteristic
151C2×C4×C11#12411yescharacteristic
152C2×C4×C11#12411yescharacteristic
153C2×C4×C11#12411yescharacteristic
154C2×C4×C11C2×D811yescharacteristic
155C2×C4×C11C2×SD1611yescharacteristic
156C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
157C2×C4×C11#13711yescharacteristic
158C2×Dic11—22no—
159C2×Dic11—22no—
160C2×Dic11—22no—
161C2×Dic11—41no—
162C2×Dic11—41no—
163C2×Dic11—41no—
164C2×Dic11—41no—
165C2×Dic11—41no—
166C2×Dic11—41no—
167C2×Dic11—41no—
168C2×Dic11—41no—
169C2×Dic11—41no—
170Dic22—48no—
171C8×C11—81no—
172C11⋊C8—81no—
173C11⋊C8—81no—
174#532C2×D1111yescharacteristic
175C2×C4×Q8—221no—
176#431—111no—
177#431C2×D1111yescharacteristic
178#423—111no—
179C2×#104—221no—
180C2×#104—221no—
181#398—221no—
182#398—221no—
183#395—221no—
184#395—221no—
185C4×C4⋊C4—111no—
186C4×C4⋊C4—221no—
187C4×C4⋊C4C2×D1111yescharacteristic
188#376—111no—
189#327—21no—
190#327—21no—
191#327—221no—
192#327—221no—
193C22×C11—21no—
194C22×C11—21no—
195C22×C11—81no—
196C22×C11—81no—
197C22×C11—81no—
198C22×C11#39311yescharacteristic
199C22×C11#44711yescharacteristic
200C22×C11#44811yescharacteristic
201C4×C11—21no—
202C4×C11—21no—
203C4×C11—21no—
204C4×C11—21no—
205C4×C11—42no—
206C4×C11—81no—
207C4×C11—81no—
208C4×C11#47411yescharacteristic
209C4×C11#47611yescharacteristic
210C4×C11#48611yescharacteristic
211C4×C11#48911yescharacteristic
212Dic11—42no—
213Dic11—42no—
214Dic11—42no—
215Dic11—81no—
216C2×#41—21no—
217C22×Q8—221no—
218C2×M16—221no—
219C4⋊Q8Dic2211yescharacteristic, complemented
220#127Dic2211yescharacteristic, complemented
221#124—21no—
222#121—21no—
223#121—21no—
224C4×Q8—442no—
225C4×Q8—442no—
226C4×D4—21no—
227C4×D4—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—221no—
230C2×C4⋊C4—221no—
231C2×C4⋊C4—221no—
232C2×C4⋊C4—221no—
233C2×C4⋊C4—221no—
234C2×C4⋊C4—221no—
235C2×C42—21no—
236C2×C42—111no—
237C2×C42—111no—
238C2×C42—221no—
239C2×C42C22×D1111yescharacteristic
240C4⋊C8—21no—
241C4⋊C8—221no—
242C4⋊C8—221no—
243C4⋊C8—221no—
244#104—442no—
245#104—442no—
246C22⋊C8—21no—
247C22⋊C8—221no—
248C4×C8—21no—
249C4×C8—221no—
250#95—111no—
251#95—111no—
252#95—221no—
253#95—221no—
254#95—221no—
255#95—221no—
256#95C22⋊D1111yescharacteristic
257#95C22⋊D1111yescharacteristic
258C2×C11—21no—
259C2×C11—21no—
260C2×C11—161no—
261C2×C11#202311yescharacteristic
262C2×C11#203111yescharacteristic
263C2×C11#203111yescharacteristic
264#41—41no—
265#41—41no—
266#41—41no—
267#41—41no—
268C2×Q8—21no—
269C2×Q8—442no—
270C2×Q8—442no—
271C2×Q8—442no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—21no—
275C2×D4—41no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—41no—
279C22×C4—221no—
280C22×C4—221no—
281C22×C4—221no—
282C22×C4—221no—
283C22×C4D4×D1111yescharacteristic
284C22×C4D4×D1111yescharacteristic
285C22×C4C2×C22⋊D1111yescharacteristic
286M16—441no—
287M16—441no—
288C2×C8—41no—
289C2×C8—441no—
290C2×C8—441no—
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4—42no—
294C4⋊C4—442no—
295C4⋊C4—442no—
296C4⋊C4—442no—
297C4⋊C4—442no—
298C4⋊C4—442no—
299C4⋊C4—442no—
300C22⋊C4—41no—
301C22⋊C4—41no—
302C42—41no—
303C42—41no—
304C42—112no—
305C42—112no—
306C42—221no—
307C42—221no—
308C42—441no—
309C42—441no—
310C42C2×Dic2211yescharacteristic
311C42#433911yescharacteristic
312C42#434111yescharacteristic
313C42#434111yescharacteristic
314C11#1037011yescharacteristic, complemented, Sylow
315C23—41no—
316C23#6699011yescharacteristic
317Q8—41no—
318Q8—41no—
319Q8—448no—
320D4—41no—
321D4—41no—
322D4—81no—
323D4—81no—
324D4—81no—
325D4—81no—
326C2×C4—22no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4—222no—
338C2×C4—222no—
339C2×C4—222no—
340C2×C4—441no—
341C2×C4—441no—
342C2×C4—441no—
343C2×C4—441no—
344C2×C4—441no—
345C2×C4—441no—
346C2×C4—441no—
347C2×C4—441no—
348C2×C4—441no—
349C2×C4#6693111yescharacteristic
350C2×C4#6693111yescharacteristic
351C2×C4#6693811yescharacteristic
352C2×C4#6693811yescharacteristic
353C2×C4D8×D1111yescharacteristic
354C2×C4#6696411yescharacteristic
355C2×C4SD16×D1111yescharacteristic
356C2×C4#6696811yescharacteristic
357C2×C4#6697711yescharacteristic
358C2×C4#6698911yescharacteristic
359C8—81no—
360C8—881no—
361C8—881no—
362C22—21no—
363C22—21no—
364C22—81no—
365C22—81no—
366C22—81no—
367C22#1062256011yescharacteristic
368C22#1062276911yescharacteristic
369C22#1062278311yescharacteristic
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—42no—
375C4—81no—
376C4—81no—
377C4—442no—
378C4—442no—
379C4—442no—
380C4—881no—
381C4#1062237211yescharacteristic
382C4#1062237311yescharacteristic
383C4#1062237411yescharacteristic
384C4#1062237811yescharacteristic
385C2—21no—
386C2—21no—
387C2—161no—
388C2#1306975011yescharacteristic
389C2#1306978811yescharacteristic
390C2#1306979011yescharacteristic
subgroupG/H
centerC2×C4#66938
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1502C2
socleC22×C11#393
prime radicalC11×#532C22
hypercenter#1502D11
hypocenterC11#10370
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1502

Complements

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

NH ≅ G/Ntype
1. #13071910C2semidirect
4. #13066519C2semidirect
5. #13066518C2semidirect
6. #13066444C2semidirect
29. C11×C4⋊Q8Q8semidirect
30. C11×#127Q8semidirect
219. C4⋊Q8Dic22semidirect
220. #127Dic22semidirect
314. C11#10370semidirect

Maximal subgroups

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

subgroupindex
#130719102
#130694492
#130671112
#130665192
#130665182
#130664442
C11×#15022
#1037011