Finite Group Databasebeta

← #14649770

Subgroups — #14649770

Order 2816.

436 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 91 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#13077700C211yesmaximal, characteristic
2#13074495C211yesmaximal, characteristic
3C4×#66888C211yesmaximal, characteristic
4#13067219C211yesmaximal, characteristic
5#13067217C211yesmaximal, characteristic
6#13066480C211yesmaximal, characteristic
7C11×#1288C211yesmaximal, characteristic
8C2×#66923C2211yescharacteristic
9C2×C4×Dic22C2211yescharacteristic
10C11×#432C2211yescharacteristic
11C4×C11×M16C2211yescharacteristic
12C11×#383C2211yescharacteristic
13C2×#66888—21no—
14#10622539C2211yescharacteristic
15C4×#4318C2211yescharacteristic
16#10622441—22no—
17#10622332—21no—
18#10622331—21no—
19#10622314—22no—
20#10622274C411yescharacteristic
21#10622274C411yescharacteristic
22#10622272—21no—
23#10622272C411yescharacteristic
24#10622272C411yescharacteristic
25#10622269—21no—
26#10622266—21no—
27#10622266—21no—
28#10622192—21no—
29#10622103—22no—
30#10622103—22no—
31C22×Dic22D411yescharacteristic
32C2×C11×M16—21no—
33C2×C42×C11C2311yescharacteristic
34C2×C4⋊Dic11—21no—
35C2×C4⋊Dic11—21no—
36C2×C4⋊Dic11C2×C411yescharacteristic
37C2×C4⋊Dic11C2×C411yescharacteristic
38C2×C4⋊Dic11D411yescharacteristic
39C2×Dic11⋊C4—21no—
40C2×Dic11⋊C4—21no—
41C2×Dic11⋊C4C2×C411yescharacteristic
42C2×Dic11⋊C4C2×C411yescharacteristic
43C2×C4×Dic11D411yescharacteristic
44C2×C4×Dic11D411yescharacteristic
45C2×#4318—21no—
46#66923—21no—
47#66923—21no—
48#66923—21no—
49#66923—21no—
50C4×Dic22—21no—
51C4×Dic22—21no—
52C4×Dic22—21no—
53C4×Dic22—21no—
54C11×C4⋊C8—21no—
55C11×C22⋊C8—21no—
56C11×#97—21no—
57C11×#97D412yes—
58C4×C8×C11—21no—
59C11×#95—21no—
60C11×#95—21no—
61C11×#95C2×C411yescharacteristic
62C11×#95C2×C411yescharacteristic
63C11⋊#95—21no—
64C11⋊#95—21no—
65C11⋊#95—21no—
66C11⋊#95—21no—
67C11⋊#95—21no—
68C11⋊#95—21no—
69C22⋊(C11⋊C8)—21no—
70#66888—24no—
71#66879—22no—
72Dic11⋊C8—22no—
73Dic11⋊C8—22no—
74C8×Dic11—22no—
75C4⋊(C11⋊C8)—21no—
76#66867—21no—
77#66867D412yes—
78C4×C11⋊C8—21no—
79#9190—111nomaximal, Sylow
80C22×C4×C11—21no—
81C22×C4×C11—21no—
82C22×C4×C11C22×C411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C22×Dic11—21no—
86C22×Dic11—21no—
87C22×Dic11C22⋊C411yescharacteristic
88C22×Dic11C22⋊C411yescharacteristic
89C22×Dic11C22⋊C411yescharacteristic
90C22×Dic11C22⋊C411yescharacteristic
91C2×Dic22—22no—
92C2×Dic22—21no—
93C2×Dic22—21no—
94C2×Dic22—41no—
95C11×M16—22no—
96C11×M16—41no—
97C2×C8×C11—22no—
98C2×C8×C11—41no—
99C42×C11C2×D411yescharacteristic
100C42×C11C2×D411yescharacteristic
101C42×C11#4111yescharacteristic
102C42×C11#4111yescharacteristic
103C4⋊Dic11—21no—
104C4⋊Dic11—21no—
105C4⋊Dic11—21no—
106C4⋊Dic11—21no—
107C4⋊Dic11—21no—
108C4⋊Dic11—21no—
109C4⋊Dic11—42no—
110C4⋊Dic11—42no—
111Dic11⋊C4—21no—
112Dic11⋊C4—21no—
113Dic11⋊C4—21no—
114Dic11⋊C4—21no—
115Dic11⋊C4—41no—
116Dic11⋊C4—41no—
117Dic11⋊C4—41no—
118Dic11⋊C4—41no—
119C4×Dic11—21no—
120C4×Dic11—21no—
121C4×Dic11—21no—
122C4×Dic11—21no—
123#4318—22no—
124#4318—41no—
125C2×C11⋊C8—22no—
126C2×C11⋊C8—41no—
127#2983—111no—
128#2634—111no—
129C4×#101—111no—
130#1528—111no—
131#1528—111no—
132#1288—111no—
133#1288D1111yescharacteristic
134C23×C11C2×C22⋊C411yescharacteristic
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—41no—
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×C11C4×D411yescharacteristic
146C2×C4×C11C4×D411yescharacteristic
147C2×C4×C11#12011yescharacteristic
148C2×C4×C11#12111yescharacteristic
149C2×C4×C11#12111yescharacteristic
150C2×C4×C11#12311yescharacteristic
151C2×Dic11—21no—
152C2×Dic11—21no—
153C2×Dic11—21no—
154C2×Dic11—21no—
155C2×Dic11—21no—
156C2×Dic11—21no—
157C2×Dic11—21no—
158C2×Dic11—41no—
159C2×Dic11—41no—
160C2×Dic11—42no—
161C2×Dic11—41no—
162C2×Dic11—41no—
163C2×Dic11—41no—
164C2×Dic11—41no—
165C2×Dic11#10412yes—
166Dic22—42no—
167Dic22—42no—
168C8×C11—42no—
169C8×C11—42no—
170C11⋊C8—42no—
171C11⋊C8—42no—
172C2×#125—111no—
173C2×C4×Q8—111no—
174#446—222no—
175#446—222no—
176#432—111no—
177#432—221no—
178#432C2×D1111yescharacteristic
179#431—221no—
180C2×#101—221no—
181C4×M16—111no—
182C4×M16C2×D1111yescharacteristic
183#400—111no—
184#400—111no—
185#400—221no—
186#398—111no—
187#398—111no—
188#395—221no—
189#387—221no—
190#387—221no—
191#383C2×D1111yescharacteristic
192#343—221no—
193#330—222no—
194#330—222no—
195C22×C11—21no—
196C22×C11—21no—
197C22×C11#38611yescharacteristic
198C22×C11C2×#10411yescharacteristic
199C22×C11#42111yescharacteristic
200C4×C11—21no—
201C4×C11—21no—
202C4×C11—21no—
203C4×C11—21no—
204C4×C11—21no—
205C4×C11—21no—
206C4×C11—81no—
207C4×C11—81no—
208Dic11—22no—
209Dic11—41no—
210Dic11—41no—
211Dic11—41no—
212Dic11—81no—
213Dic11—81no—
214C22×Q8—111no—
215C2×M16—21no—
216C2×M16—221no—
217#125—221no—
218#125—221no—
219#125—221no—
220#125—221no—
221C4×Q8—221no—
222C4×Q8—221no—
223C4×Q8—221no—
224C4×Q8—221no—
225C2×C4⋊C4—111no—
226C2×C4⋊C4—111no—
227C2×C4⋊C4—111no—
228C2×C4⋊C4—111no—
229C2×C4⋊C4—111no—
230C2×C4⋊C4—221no—
231C2×C4⋊C4—221no—
232C2×C4⋊C4—221no—
233C2×C4⋊C4—221no—
234C2×C42—111no—
235C2×C42—111no—
236C2×C42C22×D1111yescharacteristic
237C4⋊C8—21no—
238C4⋊C8—222no—
239C4⋊C8—222no—
240C4⋊C8—221no—
241#101—224no—
242C22⋊C8—21no—
243C22⋊C8—221no—
244#97—21no—
245#97—112no—
246#97—222no—
247#97—221no—
248#97D4412yes—
249C4×C8—21no—
250C4×C8—222no—
251C4×C8—221no—
252#95—21no—
253#95—21no—
254#95—221no—
255#95—221no—
256#95—221no—
257#95—221no—
258#95—221no—
259#95—221no—
260#95C4×D1111yescharacteristic
261#95C4×D1111yescharacteristic
262C2×C11—21no—
263C2×C11—21no—
264C2×C11#187111yescharacteristic
265C2×C11#191211yescharacteristic
266C2×C11#191511yescharacteristic
267C2×Q8—222no—
268C2×Q8—221no—
269C2×Q8—221no—
270C2×Q8—441no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—111no—
274C22×C4—111no—
275C22×C4—111no—
276C22×C4—111no—
277C22×C4—221no—
278C22×C4—221no—
279C22×C4C2×C4×D1111yescharacteristic
280C22×C4D4×D1111yescharacteristic
281C22×C4D4×D1111yescharacteristic
282M16—22no—
283M16—41no—
284M16—222no—
285M16—441no—
286C2×C8—22no—
287C2×C8—41no—
288C2×C8—222no—
289C2×C8—441no—
290C4⋊C4—221no—
291C4⋊C4—221no—
292C4⋊C4—221no—
293C4⋊C4—221no—
294C4⋊C4—221no—
295C4⋊C4—221no—
296C4⋊C4—221no—
297C4⋊C4—221no—
298C4⋊C4—221no—
299C4⋊C4—221no—
300C4⋊C4—442no—
301C4⋊C4—442no—
302C4⋊C4—441no—
303C4⋊C4—441no—
304C4⋊C4—441no—
305C4⋊C4—441no—
306C42—221no—
307C42—221no—
308C42—221no—
309C42—221no—
310C42C2×D4411yescharacteristic
311C42#433911yescharacteristic
312C42D4×D1111yescharacteristic
313C42#434311yescharacteristic
314C11#919011yescharacteristic, complemented, Sylow
315C23C22⋊C4×D1111yescharacteristic
316Q8—442no—
317Q8—442no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—112no—
329C2×C4—221no—
330C2×C4—221no—
331C2×C4—221no—
332C2×C4—221no—
333C2×C4—221no—
334C2×C4—221no—
335C2×C4—221no—
336C2×C4—441no—
337C2×C4—441no—
338C2×C4—442no—
339C2×C4—441no—
340C2×C4—441no—
341C2×C4—441no—
342C2×C4—441no—
343C2×C4C4×D4411yescharacteristic
344C2×C4#6693511yescharacteristic
345C2×C4#6693711yescharacteristic
346C2×C4#6694611yescharacteristic
347C2×C4#6694711yescharacteristic
348C2×C4#6694811yescharacteristic
349C8—42no—
350C8—42no—
351C8—442no—
352C8—442no—
353C22—21no—
354C22—21no—
355C22#1062227811yescharacteristic
356C22D11×#10411yescharacteristic
357C22#1062243411yescharacteristic
358C4—21no—
359C4—21no—
360C4—21no—
361C4—21no—
362C4—21no—
363C4—21no—
364C4—81no—
365C4—81no—
366C4—222no—
367C4—441no—
368C4—441no—
369C4—441no—
370C4—881no—
371C4—881no—
372C2—21no—
373C2—21no—
374C2#1306891711yescharacteristic
375C2#1306915211yescharacteristic
376C2#1306916711yescharacteristic
subgroupG/H
centerC22#10622278
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1288C2
socleC22×C11#386
prime radicalC23×C11C2×C22⋊C4
cosocleC2×C42×C11C23
hypercenter#1288D11
hypocenterC11#9190
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1288

Complements

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

NH ≅ G/Ntype
314. C11#9190semidirect

Maximal subgroups

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

subgroupindex
#130777002
#130744952
C4×#668882
#130672192
#130672172
#130664802
C11×#12882
#919011