Finite Group Databasebeta

← #14653330

Subgroups — #14653330

Order 2816.

384 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 93 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
1C2×#10622669C211yesmaximal, characteristic
2#13067377C211yesmaximal, characteristic, complemented
3#13067217C211yesmaximal, characteristic, complemented
4#13066973C211yesmaximal, characteristic, complemented
5#13066968C211yesmaximal, characteristic
6#13066903C211yesmaximal, characteristic, complemented
7C11×#1527C211yesmaximal, characteristic
8C2×C11×#124C2211yescharacteristic
9C2×#66923C2211yescharacteristic
10C11×#432C2211yescharacteristic
11C4×C11×M16C2211yescharacteristic
12C2×#66899C411yescharacteristic
13C2×#66899C411yescharacteristic
14C2×#66896C411yescharacteristic
15C2×#66896C411yescharacteristic
16#10622669—21no—
17#10622669—21no—
18#10622669—21no—
19#10622669—21no—
20#10622539C2211yescharacteristic
21#10622538C2211yescharacteristic
22C2×C4×C11⋊C8C2211yescharacteristic
23C11×#329—22no—
24#10622163—22no—
25#10622118—21no—
26#10622117—21no—
27#10622107—22no—
28#10622103—22no—
29#10622092—21no—
30#10622092—21no—
31C22×Q8×C11C2×C411yescharacteristic
32C22×D4×C11C2×C411yescharacteristic
33C2×C11×M16—21no—
34C11×#124—21no—
35C11×#124—21no—
36C11×#124—21no—
37C11×#124—21no—
38C2×C11×C22⋊C4—21no—
39C2×C11×C22⋊C4—21no—
40C2×C42×C11C2311yescharacteristic
41C2×C4⋊Dic11C2×C411yescharacteristic
42C2×C4⋊Dic11C2×C411yescharacteristic
43C2×Dic11⋊C4—21no—
44C2×Dic11⋊C4—21no—
45C22×C11⋊C8C2×C411yescharacteristic
46C22×C11⋊C8C2×C411yescharacteristic
47#66923—21no—
48#66923—21no—
49#66923—21no—
50#66923—21no—
51C11×C4⋊C8—21no—
52C11×C22⋊C8—21no—
53C11×#97—21no—
54C11×#97D412yes—
55C4×C8×C11—21no—
56#66899—21no—
57#66899—21no—
58#66899—21no—
59#66899—21no—
60#66896—21no—
61#66896—21no—
62#66896—21no—
63#66896—21no—
64C22⋊(C11⋊C8)—21no—
65C22⋊(C11⋊C8)D412yes—
66C4⋊(C11⋊C8)—21no—
67C4⋊(C11⋊C8)—21no—
68#66867—21no—
69C4×C11⋊C8—21no—
70C4×C11⋊C8D411yescharacteristic
71C4×C11⋊C8D411yescharacteristic
72C4×C11⋊C8D411yescharacteristic
73C4×C11⋊C8D411yescharacteristic
74#9790—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×C11C22×C411yescharacteristic
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11#4111yescharacteristic
88C22×Dic11—21no—
89C22×Dic11—21no—
90C11×M16—42no—
91C2×C8×C11—22no—
92C2×C8×C11—41no—
93C11×C22⋊C4—41no—
94C11×C22⋊C4—41no—
95C11×C22⋊C4—41no—
96C11×C22⋊C4—41no—
97C42×C11C2×D411yescharacteristic
98C42×C11C2×D411yescharacteristic
99C42×C11C2×D411yescharacteristic
100C42×C11#4111yescharacteristic
101C4⋊Dic11—21no—
102C4⋊Dic11—21no—
103C4⋊Dic11—21no—
104C4⋊Dic11—21no—
105Dic11⋊C4—41no—
106Dic11⋊C4—41no—
107Dic11⋊C4—41no—
108Dic11⋊C4—41no—
109C2×C11⋊C8—22no—
110C2×C11⋊C8—41no—
111C2×C11⋊C8—41no—
112C2×C11⋊C8—41no—
113C2×C11⋊C8C22⋊C411yescharacteristic
114C2×C11⋊C8C22⋊C411yescharacteristic
115C2×C11⋊C8C22⋊C411yescharacteristic
116C2×C11⋊C8C22⋊C411yescharacteristic
117C2×#488—111no—
118#1568—111no—
119#1528—111no—
120#1527D1111yescharacteristic
121#1470—111no—
122#1469—111no—
123#1451—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—81no—
141C2×C4×C11C2×C22⋊C411yescharacteristic
142C2×C4×C11C4×D411yescharacteristic
143C2×C4×C11#12111yescharacteristic
144C2×C4×C11#12111yescharacteristic
145C2×C4×C11#12411yescharacteristic
146C2×C4×C11#12711yescharacteristic
147C2×Dic11—41no—
148C2×Dic11—41no—
149C2×Dic11—42no—
150C2×Dic11—81no—
151C8×C11—42no—
152C8×C11—81no—
153C11⋊C8—21no—
154C11⋊C8—21no—
155C11⋊C8—21no—
156C11⋊C8—21no—
157C11⋊C8—42no—
158C11⋊C8—81no—
159C2×#125—111no—
160C2×#124C2×D1111yescharacteristic
161#488—221no—
162#488—221no—
163#488—221no—
164#488—221no—
165#432—111no—
166#432C2×D1111yescharacteristic
167#431—111no—
168C2×#103—111no—
169C2×#103—111no—
170C2×#102—111no—
171C2×#102—111no—
172C4×M16C2×D1111yescharacteristic
173C2×C4×C8—111no—
174#335—221no—
175#334—221no—
176#330—222no—
177#329—22no—
178#324—222no—
179#323—222no—
180#322—221no—
181#322—221no—
182C22×C11—21no—
183C22×C11—21no—
184C22×C11—81no—
185C22×C11—81no—
186C22×C11—81no—
187C22×C11—162no—
188C22×C11#39011yescharacteristic
189C22×C11#44412yes—
190C4×C11—21no—
191C4×C11—21no—
192C4×C11—21no—
193C4×C11—21no—
194C4×C11—21no—
195C4×C11—81no—
196C4×C11#41311yescharacteristic
197C4×C11#41311yescharacteristic
198Dic11—81no—
199Dic11—81no—
200C22×Q8C4×D1111yescharacteristic
201C22×D4C4×D1111yescharacteristic
202C2×M16—21no—
203C22×C8—111no—
204C22×C8—111no—
205#125—221no—
206#125—221no—
207#125—221no—
208#125—221no—
209#124—21no—
210#124—21no—
211#124—21no—
212#124—21no—
213C2×C4⋊C4—111no—
214C2×C4⋊C4—111no—
215C2×C4⋊C4—221no—
216C2×C4⋊C4—221no—
217C2×C22⋊C4—21no—
218C2×C22⋊C4—21no—
219C2×C42C22×D1111yescharacteristic
220C4⋊C8—21no—
221C4⋊C8—221no—
222C4⋊C8—221no—
223#103—221no—
224#103—221no—
225#103—221no—
226#103—221no—
227#102—221no—
228#102—221no—
229#102—221no—
230#102—221no—
231C22⋊C8—21no—
232C22⋊C8—112no—
233C22⋊C8—221no—
234#97—21no—
235#97—221no—
236#97C22⋊D1112yes—
237C4×C8—21no—
238C4×C8—111no—
239C4×C8—111no—
240C4×C8—111no—
241C4×C8—111no—
242C4×C8—221no—
243C2×C11—22no—
244C2×C11—161no—
245C2×C11#196711yescharacteristic
246C2×C11#197511yescharacteristic
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—221no—
259C22×C4—221no—
260C22×C4C2×C4×D1111yescharacteristic
261C22×C4D4×D1111yescharacteristic
262C22×C4#434111yescharacteristic
263M16—42no—
264C2×C8—22no—
265C2×C8—41no—
266C2×C8—111no—
267C2×C8—111no—
268C2×C8—111no—
269C2×C8—111no—
270C2×C8—222no—
271C2×C8—441no—
272C2×C8—441no—
273C2×C8—441no—
274C4⋊C4—221no—
275C4⋊C4—221no—
276C4⋊C4—221no—
277C4⋊C4—221no—
278C4⋊C4—441no—
279C4⋊C4—441no—
280C4⋊C4—441no—
281C4⋊C4—441no—
282C22⋊C4—41no—
283C22⋊C4—41no—
284C22⋊C4—41no—
285C22⋊C4—41no—
286C42#433911yescharacteristic
287C42D4×D1111yescharacteristic
288C42D4×D1111yescharacteristic
289C42C2×C22⋊D1111yescharacteristic
290C11#979011yescharacteristic, complemented, Sylow
291C23—41no—
292C23—42no—
293C23—81no—
294C23—81no—
295C23(C22⋊D11)⋊C411yescharacteristic
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—41no—
307C2×C4—81no—
308C2×C4—441no—
309C2×C4—441no—
310C2×C4—442no—
311C2×C4—881no—
312C2×C4C22⋊C4×D1111yescharacteristic
313C2×C4#6693711yescharacteristic
314C2×C4#6693811yescharacteristic
315C2×C4C4×C22⋊D1111yescharacteristic
316C2×C4#6699211yescharacteristic
317C2×C4#6699311yescharacteristic
318C8—42no—
319C8—81no—
320C8—221no—
321C8—221no—
322C8—221no—
323C8—221no—
324C8—442no—
325C8—881no—
326C22—21no—
327C22—21no—
328C22—81no—
329C22—81no—
330C22—81no—
331C22—162no—
332C22#1062243612yes—
333C22#1062257011yescharacteristic
334C4—21no—
335C4—21no—
336C4—21no—
337C4—21no—
338C4—21no—
339C4—81no—
340C4—881no—
341C4—881no—
342C4#1062235811yescharacteristic
343C4#1062235811yescharacteristic
344C2—22no—
345C2—161no—
346C2#1306946211yescharacteristic
347C2#1306950611yescharacteristic
348C2#1306951311yescharacteristic
subgroupG/H
centerC22#10622570
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1527C2
socleC22×C11#390
prime radicalC22×D4×C11C2×C4
cosocleC2×C42×C11C23
hypercenter#1527D11
hypocenterC11#9790
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1527

Complements

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

NH ≅ G/Ntype
2. #13067377C2semidirect
3. #13067217C2semidirect
4. #13066973C2semidirect
6. #13066903C2semidirect
290. C11#9790semidirect

Maximal subgroups

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

subgroupindex
C2×#106226692
#130673772
#130672172
#130669732
#130669682
#130669032
C11×#15272
#979011