Finite Group Databasebeta

← #14653327

Subgroups — #14653327

Order 2816.

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

normal subgroups only

This group has 392 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×#10622681C211yesmaximal, characteristic
2#13067377C211yesmaximal, characteristic, complemented
3#13067213C211yesmaximal, characteristic
4#13066972C211yesmaximal, characteristic, complemented
5#13066969C211yesmaximal, characteristic
6M16×C11⋊C8C211yesmaximal, characteristic, complemented
7C11×#1528C211yesmaximal, characteristic, complemented
8C2×C11×#125C2211yescharacteristic
9C2×#66928C2211yescharacteristic
10C11×#432C2211yescharacteristic
11C4×C11×M16C2211yescharacteristic
12#10622681—21no—
13#10622681—21no—
14#10622681—21no—
15#10622681—21no—
16C2×#66874C411yescharacteristic
17C2×#66874C411yescharacteristic
18C2×#66873C411yescharacteristic
19C2×#66873C411yescharacteristic
20#10622539C2211yescharacteristic
21#10622538C2211yescharacteristic
22C2×C4×C11⋊C8C2211yescharacteristic
23C11×#330—22no—
24#10622166—22no—
25#10622118—21no—
26#10622117—21no—
27#10622106—22no—
28#10622102—22no—
29#10622093—21no—
30C8×C11⋊C8—21no—
31C22×D44C2×C411yescharacteristic
32C22×Dic22C2×C411yescharacteristic
33C2×C11×M16—21no—
34C11×#125—21no—
35C11×#125—21no—
36C11×#125—21no—
37C11×#125—21no—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4—21no—
40C2×C11×C4⋊C4C2×C411yescharacteristic
41C2×C11×C4⋊C4C2×C411yescharacteristic
42C2×C42×C11C2311yescharacteristic
43C2×(C2×D11)⋊C4—21no—
44C2×(C2×D11)⋊C4—21no—
45C22×C11⋊C8C2×C411yescharacteristic
46C22×C11⋊C8C2×C411yescharacteristic
47#66928—21no—
48#66928—21no—
49#66928—21no—
50#66928—21no—
51C11×C4⋊C8—21no—
52C11×C22⋊C8—21no—
53C11×#97—21no—
54C11×#97D412yes—
55C4×C8×C11—21no—
56C22⋊(C11⋊C8)—21no—
57C22⋊(C11⋊C8)D412yes—
58#66874—21no—
59#66874—21no—
60#66874—21no—
61#66874—21no—
62#66873—21no—
63#66873—21no—
64#66873—21no—
65#66873—21no—
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#9789—111nomaximal, Sylow
75C23×D11—21no—
76C22×C4×C11—21no—
77C22×C4×C11—21no—
78C22×C4×C11C22×C411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11#4111yescharacteristic
81C22×Dic11—21no—
82C2×D44—21no—
83C2×D44—21no—
84C2×D44—41no—
85C2×D44—41no—
86C2×Dic22—21no—
87C2×Dic22—21no—
88C2×Dic22—41no—
89C2×Dic22—41no—
90C11×M16—24no—
91C2×C8×C11—22no—
92C2×C8×C11—41no—
93C11×C4⋊C4—21no—
94C11×C4⋊C4—21no—
95C11×C4⋊C4—21no—
96C11×C4⋊C4—21no—
97C11×C4⋊C4—41no—
98C11×C4⋊C4—41no—
99C11×C4⋊C4—41no—
100C11×C4⋊C4—41no—
101C42×C11C2×D411yescharacteristic
102C42×C11C2×D411yescharacteristic
103C42×C11C2×D411yescharacteristic
104C42×C11#4111yescharacteristic
105(C2×D11)⋊C4—41no—
106(C2×D11)⋊C4—41no—
107(C2×D11)⋊C4—41no—
108(C2×D11)⋊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#1528D1111yescharacteristic, complemented
120#1527—111no—
121#1470—111no—
122#1469—111no—
123C8×M16—111no—
124C23×C11C4×D411yescharacteristic
125C22×D11—41no—
126C22×D11—42no—
127C22×D11—81no—
128C22×D11—81no—
129C2×C4×C11—22no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—42no—
136C2×C4×C11—81no—
137C2×C4×C11C2×C22⋊C411yescharacteristic
138C2×C4×C11C4×D411yescharacteristic
139C2×C4×C11#12111yescharacteristic
140C2×C4×C11#12111yescharacteristic
141C2×C4×C11#12411yescharacteristic
142C2×C4×C11#12711yescharacteristic
143C2×Dic11—41no—
144C2×Dic11—81no—
145D44—41no—
146D44—41no—
147D44—81no—
148Dic22—41no—
149Dic22—41no—
150Dic22—81no—
151C8×C11—24no—
152C8×C11—81no—
153C11⋊C8—21no—
154C11⋊C8—21no—
155C11⋊C8—21no—
156C11⋊C8—21no—
157C11⋊C8—42no—
158C11⋊C8—81no—
159C2×#125C2×D1111yescharacteristic
160C2×#124—111no—
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—22no—
177#329—222no—
178#324—222no—
179#323—222no—
180#322—221no—
181C82—221no—
182C22×C11—21no—
183C22×C11—21no—
184C22×C11#39011yescharacteristic
185C22×C11#44312yes—
186C2×D11—81no—
187C2×D11—81no—
188C2×D11—81no—
189C2×D11—162no—
190C4×C11—21no—
191C4×C11—21no—
192C4×C11—21no—
193C4×C11—21no—
194C4×C11—21no—
195C4×C11—81no—
196C4×C11—81no—
197C4×C11#41311yescharacteristic
198C4×C11#41311yescharacteristic
199Dic11—81no—
200C22×Q8—111no—
201C22×D4—111no—
202C2×M16—21no—
203C22×C8—111no—
204C22×C8—111no—
205#125—21no—
206#125—21no—
207#125—21no—
208#125—21no—
209#124—221no—
210#124—221no—
211#124—221no—
212#124—221no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4C4×D1111yescharacteristic
216C2×C4⋊C4C4×D1111yescharacteristic
217C2×C22⋊C4—221no—
218C2×C22⋊C4—221no—
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#196711yescharacteristic
245C2×C11#197411yescharacteristic
246C2×C11#197611yescharacteristic
247D11—161no—
248C24—221no—
249C2×Q8—221no—
250C2×Q8—221no—
251C2×Q8—441no—
252C2×Q8—441no—
253C2×D4—221no—
254C2×D4—221no—
255C2×D4—441no—
256C2×D4—441no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—221no—
260C22×C4C2×C4×D1111yescharacteristic
261C22×C4D4×D1111yescharacteristic
262C22×C4#434111yescharacteristic
263M16—24no—
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—21no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C22⋊C4—441no—
283C22⋊C4—441no—
284C22⋊C4—441no—
285C22⋊C4—441no—
286C42#433911yescharacteristic
287C42D4×D1111yescharacteristic
288C42D4×D1111yescharacteristic
289C42C2×C22⋊D1111yescharacteristic
290C11#978911yescharacteristic, complemented, Sylow
291C23—441no—
292C23—442no—
293C23—881no—
294C23—881no—
295C23(C22⋊D11)⋊C411yescharacteristic
296Q8—441no—
297Q8—441no—
298Q8—881no—
299D4—441no—
300D4—441no—
301D4—881no—
302C2×C4—22no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—42no—
309C2×C4—81no—
310C2×C4—441no—
311C2×C4—881no—
312C2×C4C22⋊C4×D1111yescharacteristic
313C2×C4#6693711yescharacteristic
314C2×C4#6693811yescharacteristic
315C2×C4C4×C22⋊D1111yescharacteristic
316C2×C4#6699211yescharacteristic
317C2×C4#6699311yescharacteristic
318C8—24no—
319C8—81no—
320C8—221no—
321C8—221no—
322C8—221no—
323C8—221no—
324C8—442no—
325C8—881no—
326C22—21no—
327C22—21no—
328C22—881no—
329C22—881no—
330C22—881no—
331C22—1762no—
332C22#1062243712yes—
333C22#1062257011yescharacteristic
334C4—21no—
335C4—21no—
336C4—21no—
337C4—21no—
338C4—21no—
339C4—81no—
340C4—81no—
341C4—881no—
342C4#1062236411yescharacteristic
343C4#1062236411yescharacteristic
344C2—22no—
345C2—1761no—
346C2#1306946411yescharacteristic
347C2#1306950111yescharacteristic
348C2#1306951311yescharacteristic
subgroupG/H
centerC22#10622570
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1528C2
socleC22×C11#390
prime radicalC22×D44C2×C4
cosocleC2×C42×C11C23
hypercenter#1528D11
hypocenterC11#9789
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1528

Complements

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

NH ≅ G/Ntype
2. #13067377C2semidirect
4. #13066972C2semidirect
6. M16×C11⋊C8C2semidirect
7. C11×#1528C2semidirect
119. #1528D11semidirect
290. C11#9789semidirect

Maximal subgroups

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

subgroupindex
C2×#106226812
#130673772
#130672132
#130669722
#130669692
M16×C11⋊C82
C11×#15282
#978911