Finite Group Databasebeta

← #14653328

Subgroups — #14653328

Order 2816.

392 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13067379C211yesmaximal, characteristic, complemented
2#13067218C211yesmaximal, characteristic, complemented
3#13067214C211yesmaximal, characteristic
4#13066972C211yesmaximal, characteristic, complemented
5#13066968C211yesmaximal, characteristic
6C8×#4318C211yesmaximal, characteristic, complemented
7C2×C11×#488C211yesmaximal, characteristic
8C2×C11×#125C2211yescharacteristic
9C2×C11×#124C2211yescharacteristic
10C11×#488—21no—
11C11×#488—21no—
12C11×#488—21no—
13C11×#488—21no—
14C2×C11×#103C411yescharacteristic
15C2×C11×#103C411yescharacteristic
16C2×C11×#102C411yescharacteristic
17C2×C11×#102C411yescharacteristic
18C2×C4×C8×C11C2211yescharacteristic
19#10622539C2211yescharacteristic
20#10622539C2211yescharacteristic
21#10622538C2211yescharacteristic
22C4×#4318C2211yescharacteristic
23#10622181—22no—
24#10622178—22no—
25#10622166—22no—
26#10622163—22no—
27#10622096—21no—
28#10622095—21no—
29#10622092—21no—
30C8×C11⋊C8—21no—
31C22×Q8×C11C2×C411yescharacteristic
32C22×D4×C11C2×C411yescharacteristic
33C22×C8×C11C2×C411yescharacteristic
34C22×C8×C11C2×C411yescharacteristic
35C11×#125—21no—
36C11×#125—21no—
37C11×#125—21no—
38C11×#125—21no—
39C11×#124—21no—
40C11×#124—21no—
41C11×#124—21no—
42C11×#124—21no—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4—21no—
45C2×C11×C4⋊C4C2×C411yescharacteristic
46C2×C11×C4⋊C4C2×C411yescharacteristic
47C2×C11×C22⋊C4—21no—
48C2×C11×C22⋊C4—21no—
49C2×C42×C11C2311yescharacteristic
50C2×#4318—21no—
51C11×#103—21no—
52C11×#103—21no—
53C11×#103—21no—
54C11×#103—21no—
55C11×#102—21no—
56C11×#102—21no—
57C11×#102—21no—
58C11×#102—21no—
59C4×C8×C11D411yescharacteristic
60C4×C8×C11D411yescharacteristic
61C4×C8×C11D411yescharacteristic
62C4×C8×C11D411yescharacteristic
63C22⋊(C11⋊C8)—21no—
64C22⋊(C11⋊C8)—21no—
65C22⋊(C11⋊C8)D412yes—
66C4⋊(C11⋊C8)—21no—
67C4⋊(C11⋊C8)—21no—
68C4⋊(C11⋊C8)—21no—
69#66867—21no—
70#66867—21no—
71#66867D412yes—
72C4×C11⋊C8—21no—
73C4×C11⋊C8—21no—
74#9789—111nomaximal, Sylow
75C24×C11—21no—
76C2×Q8×C11—21no—
77C2×Q8×C11—21no—
78C2×Q8×C11—41no—
79C2×Q8×C11—41no—
80C2×D4×C11—21no—
81C2×D4×C11—21no—
82C2×D4×C11—41no—
83C2×D4×C11—41no—
84C22×C4×C11—21no—
85C22×C4×C11—21no—
86C22×C4×C11—21no—
87C22×C4×C11C22×C411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11#4111yescharacteristic
90C2×C8×C11—41no—
91C2×C8×C11—41no—
92C2×C8×C11C22⋊C411yescharacteristic
93C2×C8×C11C22⋊C411yescharacteristic
94C2×C8×C11C22⋊C411yescharacteristic
95C2×C8×C11C22⋊C411yescharacteristic
96C11×C4⋊C4—21no—
97C11×C4⋊C4—21no—
98C11×C4⋊C4—21no—
99C11×C4⋊C4—21no—
100C11×C4⋊C4—41no—
101C11×C4⋊C4—41no—
102C11×C4⋊C4—41no—
103C11×C4⋊C4—41no—
104C11×C22⋊C4—41no—
105C11×C22⋊C4—41no—
106C11×C22⋊C4—41no—
107C11×C22⋊C4—41no—
108C42×C11C2×D411yescharacteristic
109C42×C11C2×D411yescharacteristic
110C42×C11C2×D411yescharacteristic
111C42×C11#4111yescharacteristic
112#4318—24no—
113C2×C11⋊C8—22no—
114C2×C11⋊C8—22no—
115C2×C11⋊C8—41no—
116C2×C11⋊C8—41no—
117C2×#488D1111yescharacteristic
118#1568—111no—
119#1528—111no—
120#1527—111no—
121#1470—111no—
122#1469—111no—
123C8×M16—111no—
124C23×C11—41no—
125C23×C11—42no—
126C23×C11—81no—
127C23×C11—81no—
128C23×C11C4×D411yescharacteristic
129Q8×C11—41no—
130Q8×C11—41no—
131Q8×C11—81no—
132D4×C11—41no—
133D4×C11—41no—
134D4×C11—81no—
135C2×C4×C11—22no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—42no—
143C2×C4×C11—81no—
144C2×C4×C11—81no—
145C2×C4×C11C2×C22⋊C411yescharacteristic
146C2×C4×C11C4×D411yescharacteristic
147C2×C4×C11#12111yescharacteristic
148C2×C4×C11#12111yescharacteristic
149C2×C4×C11#12411yescharacteristic
150C2×C4×C11#12711yescharacteristic
151C8×C11—21no—
152C8×C11—21no—
153C8×C11—21no—
154C8×C11—21no—
155C11⋊C8—24no—
156C11⋊C8—42no—
157C11⋊C8—81no—
158C11⋊C8—81no—
159C2×#125C2×D1111yescharacteristic
160C2×#124C2×D1111yescharacteristic
161#488—21no—
162#488—21no—
163#488—21no—
164#488—21no—
165#432—111no—
166#432—111no—
167#431—111no—
168C2×#103Dic1111yescharacteristic
169C2×#103Dic1111yescharacteristic
170C2×#102Dic1111yescharacteristic
171C2×#102Dic1111yescharacteristic
172C4×M16—111no—
173C2×C4×C8C2×D1111yescharacteristic
174#335—221no—
175#334—221no—
176#330—222no—
177#329—222no—
178#324—222no—
179#323—222no—
180#322—221no—
181C82—221no—
182C22×C11—21no—
183C22×C11—21no—
184C22×C11—81no—
185C22×C11—81no—
186C22×C11—81no—
187C22×C11—162no—
188C22×C11#39011yescharacteristic
189C22×C11#44312yes—
190C4×C11—21no—
191C4×C11—21no—
192C4×C11—21no—
193C4×C11—21no—
194C4×C11—21no—
195C4×C11—81no—
196C4×C11—81no—
197C4×C11—81no—
198C4×C11#41311yescharacteristic
199C4×C11#41311yescharacteristic
200C22×Q8C2×Dic1111yescharacteristic
201C22×D4C2×Dic1111yescharacteristic
202C2×M16—221no—
203C22×C8C2×Dic1111yescharacteristic
204C22×C8C2×Dic1111yescharacteristic
205#125—21no—
206#125—21no—
207#125—21no—
208#125—21no—
209#124—21no—
210#124—21no—
211#124—21no—
212#124—21no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4C2×Dic1111yescharacteristic
216C2×C4⋊C4C2×Dic1111yescharacteristic
217C2×C22⋊C4—21no—
218C2×C22⋊C4—21no—
219C2×C42C22×D1111yescharacteristic
220C4⋊C8—221no—
221C4⋊C8—221no—
222C4⋊C8—221no—
223#103—21no—
224#103—21no—
225#103—21no—
226#103—21no—
227#102—21no—
228#102—21no—
229#102—21no—
230#102—21no—
231C22⋊C8—112no—
232C22⋊C8—221no—
233C22⋊C8—221no—
234#97—112no—
235#97—221no—
236#97—221no—
237C4×C8—221no—
238C4×C8—221no—
239C4×C8C22⋊D1111yescharacteristic
240C4×C8C22⋊D1111yescharacteristic
241C4×C8C22⋊D1111yescharacteristic
242C4×C8C22⋊D1111yescharacteristic
243C2×C11—22no—
244C2×C11—161no—
245C2×C11#196711yescharacteristic
246C2×C11#197411yescharacteristic
247C2×C11#197611yescharacteristic
248C24—21no—
249C2×Q8—21no—
250C2×Q8—21no—
251C2×Q8—41no—
252C2×Q8—41no—
253C2×D4—21no—
254C2×D4—21no—
255C2×D4—41no—
256C2×D4—41no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4D4×D1111yescharacteristic
261C22×C4#434111yescharacteristic
262C22×C4C22×Dic1111yescharacteristic
263M16—224no—
264C2×C8—41no—
265C2×C8—41no—
266C2×C8—222no—
267C2×C8—222no—
268C2×C8—441no—
269C2×C8—441no—
270C2×C8C22⋊Dic1111yescharacteristic
271C2×C8C22⋊Dic1111yescharacteristic
272C2×C8C22⋊Dic1111yescharacteristic
273C2×C8C22⋊Dic1111yescharacteristic
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C22⋊C4—41no—
283C22⋊C4—41no—
284C22⋊C4—41no—
285C22⋊C4—41no—
286C42D4×D1111yescharacteristic
287C42#434111yescharacteristic
288C42C2×C22⋊D1111yescharacteristic
289C42C2×C22⋊D1111yescharacteristic
290C11#978911yescharacteristic, complemented, Sylow
291C23—41no—
292C23—42no—
293C23—81no—
294C23—81no—
295C23D4×Dic1111yescharacteristic
296Q8—41no—
297Q8—41no—
298Q8—81no—
299D4—41no—
300D4—41no—
301D4—81no—
302C2×C4—22no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—41no—
306C2×C4—42no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4D4×Dic1111yescharacteristic
313C2×C4#6698911yescharacteristic
314C2×C4#6699111yescharacteristic
315C2×C4#6699111yescharacteristic
316C2×C4#6699311yescharacteristic
317C2×C4C2×C22⋊Dic1111yescharacteristic
318C8—21no—
319C8—21no—
320C8—21no—
321C8—21no—
322C8—224no—
323C8—442no—
324C8—881no—
325C8—881no—
326C22—21no—
327C22—21no—
328C22—81no—
329C22—81no—
330C22—81no—
331C22—162no—
332C22#1062280912yes—
333C22#1062283411yescharacteristic
334C4—21no—
335C4—21no—
336C4—21no—
337C4—21no—
338C4—21no—
339C4—81no—
340C4—81no—
341C4—81no—
342C4#1062285011yescharacteristic
343C4#1062285011yescharacteristic
344C2—22no—
345C2—161no—
346C2#1306946611yescharacteristic
347C2#1306950511yescharacteristic
348C2#1306951511yescharacteristic
subgroupG/H
centerC22#10622834
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC2×C11×#488C2
socleC22×C11#390
prime radicalC22×D4×C11C2×C4
cosocleC2×C42×C11C23
hypercenterC2×#488D11
hypocenterC11#9789
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#488

Complements

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

NH ≅ G/Ntype
1. #13067379C2semidirect
2. #13067218C2semidirect
4. #13066972C2semidirect
6. C8×#4318C2semidirect
290. C11#9789semidirect

Maximal subgroups

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

subgroupindex
#130673792
#130672182
#130672142
#130669722
#130669682
C8×#43182
C2×C11×#4882
#978911