Finite Group Databasebeta

← #14650866

Subgroups — #14650866

Order 2816.

416 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077630C211yesmaximal, characteristic
2#13067218C211yesmaximal, characteristic, complemented
3#13067050C211yesmaximal, characteristic
4#13066972C211yesmaximal, characteristic, complemented
5#13066527C211yesmaximal, characteristic, complemented
6#13066505C211yesmaximal, characteristic, complemented
7C11×#3080C211yesmaximal, characteristic
8C2×C11×#125C2211yescharacteristic
9C4×C11×#41C2211yescharacteristic
10C11×#479—21no—
11C11×#479—21no—
12C11×#478—21no—
13C11×#478—21no—
14C11×#428C411yescharacteristic
15C11×#428C411yescharacteristic
16C11×#423C2211yescharacteristic
17C11×#417C411yescharacteristic
18C11×#417C411yescharacteristic
19#10622637—21no—
20#10622624—22no—
21D4×C11⋊C8—21no—
22#10622539—21no—
23#10622539C2211yescharacteristic
24#10622539C2211yescharacteristic
25#10622538C2211yescharacteristic
26C4×#4318C2211yescharacteristic
27C2×#66867—21no—
28#10622181—21no—
29#10622181—21no—
30Q8⋊(C11⋊C8)—21no—
31D4⋊(C11⋊C8)—21no—
32#10622166—22no—
33C2×C11×#41C2×C411yescharacteristic
34C2×C11×M16C2×C411yescharacteristic
35C2×C11×M16C2×C411yescharacteristic
36C11×#125—21no—
37C11×#125—21no—
38C11×#125—21no—
39C11×#125—21no—
40C4×Q8×C11D411yescharacteristic
41C4×Q8×C11D411yescharacteristic
42C4×D4×C11—21no—
43C4×D4×C11—21no—
44C4×D4×C11D411yescharacteristic
45C4×D4×C11D411yescharacteristic
46C11×#117—21no—
47C11×#117C2×C411yescharacteristic
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4C2×C411yescharacteristic
51C2×C11×C4⋊C4C2×C411yescharacteristic
52C2×C42×C11—21no—
53C2×C42×C11C2311yescharacteristic
54C2×#4318—21no—
55C22×C11⋊C8—22no—
56C11×#107—21no—
57C11×#107—21no—
58C11×#106—21no—
59C11×#106—21no—
60C11×C4⋊C8—21no—
61C11×C4⋊C8—21no—
62C11×#103—21no—
63C11×#103—21no—
64C11×#102—21no—
65C11×#102—21no—
66C22⋊(C11⋊C8)—22no—
67C22⋊(C11⋊C8)—21no—
68C22⋊(C11⋊C8)—21no—
69C22⋊(C11⋊C8)D412yes—
70C4⋊(C11⋊C8)—22no—
71C4⋊(C11⋊C8)—21no—
72C4⋊(C11⋊C8)—21no—
73C4⋊(C11⋊C8)—21no—
74#66867—22no—
75#66867—21no—
76#66867—21no—
77#66867D411yescharacteristic
78#66867D411yescharacteristic
79C4×C11⋊C8—21no—
80C4×C11⋊C8—21no—
81#9351—111nomaximal, Sylow
82C11×#41—22no—
83C11×#41—41no—
84C2×Q8×C11C22⋊C411yescharacteristic
85C2×D4×C11—21no—
86C2×D4×C11C22⋊C411yescharacteristic
87C22×C4×C11—21no—
88C22×C4×C11—21no—
89C22×C4×C11—21no—
90C22×C4×C11—21no—
91C22×C4×C11—21no—
92C22×C4×C11C22×C411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11#4111yescharacteristic
95C11×M16—41no—
96C11×M16—41no—
97C2×C8×C11—21no—
98C2×C8×C11—21no—
99C11×C4⋊C4—21no—
100C11×C4⋊C4—21no—
101C11×C4⋊C4—21no—
102C11×C4⋊C4—21no—
103C11×C4⋊C4—21no—
104C11×C4⋊C4—21no—
105C11×C4⋊C4—41no—
106C11×C4⋊C4—41no—
107C11×C4⋊C4—41no—
108C11×C4⋊C4—41no—
109C11×C4⋊C4C22⋊C411yescharacteristic
110C11×C4⋊C4C22⋊C411yescharacteristic
111C11×C22⋊C4—21no—
112C11×C22⋊C4—21no—
113C11×C22⋊C4—21no—
114C42×C11—21no—
115C42×C11—21no—
116C42×C11—21no—
117C42×C11C2×D411yescharacteristic
118C42×C11C2×D411yescharacteristic
119C42×C11C2×D411yescharacteristic
120C42×C11#4111yescharacteristic
121#4318—42no—
122C2×C11⋊C8—21no—
123C2×C11⋊C8—21no—
124C2×C11⋊C8—22no—
125C2×C11⋊C8—44no—
126C2×C11⋊C8—41no—
127C2×C11⋊C8—41no—
128#3080D1111yescharacteristic
129#2970—111no—
130#1528—111no—
131#1488—111no—
132#1470—111no—
133#1307—111no—
134#1299—111no—
135C23×C11—21no—
136C23×C11C4×D411yescharacteristic
137Q8×C11—21no—
138Q8×C11—21no—
139D4×C11—21no—
140D4×C11—42no—
141D4×C11#10112yes—
142C2×C4×C11—21no—
143C2×C4×C11—21no—
144C2×C4×C11—21no—
145C2×C4×C11—21no—
146C2×C4×C11—21no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—42no—
150C2×C4×C11—42no—
151C2×C4×C11—42no—
152C2×C4×C11—41no—
153C2×C4×C11—41no—
154C2×C4×C11—81no—
155C2×C4×C11—81no—
156C2×C4×C11C2×C22⋊C411yescharacteristic
157C2×C4×C11C4×D411yescharacteristic
158C2×C4×C11#12011yescharacteristic
159C2×C4×C11#12111yescharacteristic
160C2×C4×C11#12111yescharacteristic
161C2×C4×C11#12311yescharacteristic
162C8×C11—41no—
163C8×C11—41no—
164C11⋊C8—22no—
165C11⋊C8—42no—
166C11⋊C8—41no—
167C11⋊C8—81no—
168C11⋊C8—81no—
169C2×#125C2×D1111yescharacteristic
170C4×#41C2×D1111yescharacteristic
171#479—21no—
172#479—21no—
173#478—21no—
174#478—21no—
175#446—221no—
176#435—222no—
177C8×D4—221no—
178#432—111no—
179#432—111no—
180#432—221no—
181#431—111no—
182#428Dic1111yescharacteristic
183#428Dic1111yescharacteristic
184#423C2×D1111yescharacteristic
185#417Dic1111yescharacteristic
186#417Dic1111yescharacteristic
187C4×M16—111no—
188C2×#97—221no—
189#330—221no—
190#330—221no—
191Q8⋊C8—221no—
192D4⋊C8—221no—
193#324—222no—
194C22×C11—21no—
195C22×C11—21no—
196C22×C11—22no—
197C22×C11—21no—
198C22×C11—41no—
199C22×C11—41no—
200C22×C11#38611yescharacteristic
201C4×C11—21no—
202C4×C11—21no—
203C4×C11—21no—
204C4×C11—21no—
205C4×C11—21no—
206C4×C11—41no—
207C4×C11—41no—
208C4×C11—41no—
209C4×C11—81no—
210C4×C11—81no—
211C4×C11C2×#10111yescharacteristic
212C4×C11#41311yescharacteristic
213C2×#41C2×Dic1111yescharacteristic
214C2×M16—221no—
215C2×M16C2×Dic1111yescharacteristic
216C2×M16C2×Dic1111yescharacteristic
217C22×C8—222no—
218#125—21no—
219#125—21no—
220#125—21no—
221#125—21no—
222C4×Q8C22⋊D1111yescharacteristic
223C4×Q8C22⋊D1111yescharacteristic
224C4×D4—21no—
225C4×D4—21no—
226C4×D4C22⋊D1111yescharacteristic
227C4×D4C22⋊D1111yescharacteristic
228#117—21no—
229#117C2×Dic1111yescharacteristic
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4C2×Dic1111yescharacteristic
233C2×C4⋊C4C2×Dic1111yescharacteristic
234C2×C42—21no—
235C2×C42C22×D1111yescharacteristic
236#107—21no—
237#107—21no—
238#106—21no—
239#106—21no—
240C4⋊C8—21no—
241C4⋊C8—21no—
242C4⋊C8—222no—
243C4⋊C8—221no—
244C4⋊C8—221no—
245C4⋊C8—221no—
246#103—21no—
247#103—21no—
248#102—21no—
249#102—21no—
250C22⋊C8—112no—
251C22⋊C8—222no—
252C22⋊C8—221no—
253C22⋊C8—221no—
254#97—111no—
255#97—111no—
256#97—222no—
257#97—221no—
258#97—221no—
259C4×C8—221no—
260C4×C8—221no—
261C2×C11—41no—
262C2×C11—42no—
263C2×C11#188111yescharacteristic
264C2×C11#190111yescharacteristic
265C2×C11#190611yescharacteristic
266#41—22no—
267#41—41no—
268C2×Q8C22⋊Dic1111yescharacteristic
269C2×D4—21no—
270C2×D4C22⋊Dic1111yescharacteristic
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4D4×D1111yescharacteristic
277C22×C4#434111yescharacteristic
278C22×C4C22×Dic1111yescharacteristic
279M16—41no—
280M16—41no—
281M16—442no—
282C2×C8—21no—
283C2×C8—21no—
284C2×C8—221no—
285C2×C8—221no—
286C2×C8—222no—
287C2×C8—444no—
288C2×C8—441no—
289C2×C8—441no—
290C4⋊C4—21no—
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C4⋊C4C22⋊Dic1111yescharacteristic
301C4⋊C4C22⋊Dic1111yescharacteristic
302C22⋊C4—21no—
303C22⋊C4—21no—
304C22⋊C4—21no—
305C42—21no—
306C42—21no—
307C42—21no—
308C42D4×D1111yescharacteristic
309C42#434111yescharacteristic
310C42C2×C22⋊D1111yescharacteristic
311C42C2×C22⋊D1111yescharacteristic
312C11#935111yescharacteristic, complemented, Sylow
313C23—21no—
314C23D4×Dic1111yescharacteristic
315Q8—21no—
316Q8—21no—
317D4—21no—
318D4—42no—
319D4#6690012yes—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—81no—
333C2×C4—81no—
334C2×C4D4×Dic1111yescharacteristic
335C2×C4#6698811yescharacteristic
336C2×C4#6699011yescharacteristic
337C2×C4#6699211yescharacteristic
338C2×C4#6699211yescharacteristic
339C2×C4C2×C22⋊Dic1111yescharacteristic
340C8—41no—
341C8—41no—
342C8—222no—
343C8—442no—
344C8—441no—
345C8—881no—
346C8—881no—
347C22—21no—
348C22—22no—
349C22—21no—
350C22—21no—
351C22—41no—
352C22—41no—
353C22#1062283311yescharacteristic
354C4—21no—
355C4—21no—
356C4—21no—
357C4—21no—
358C4—21no—
359C4—41no—
360C4—41no—
361C4—41no—
362C4—81no—
363C4—81no—
364C4C2×#6690011yescharacteristic
365C4#1062285011yescharacteristic
366C2—41no—
367C2—42no—
368C2#1306898011yescharacteristic
369C2#1306908511yescharacteristic
370C2#1306911911yescharacteristic
subgroupG/H
centerC22#10622833
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#3080C2
socleC22×C11#386
prime radicalC2×C11×#41C2×C4
cosocleC2×C42×C11C23
hypercenter#3080D11
hypocenterC11#9351
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3080

Complements

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

NH ≅ G/Ntype
2. #13067218C2semidirect
4. #13066972C2semidirect
5. #13066527C2semidirect
6. #13066505C2semidirect
312. C11#9351semidirect

Maximal subgroups

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

subgroupindex
#130776302
#130672182
#130670502
#130669722
#130665272
#130665052
C11×#30802
#935111