Finite Group Databasebeta

← #14664813

Subgroups — #14664813

Order 2816.

440 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 95 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#13073521C211yesmaximal, characteristic
2#13066940C211yesmaximal, characteristic, complemented
3#13066621C212yesmaximal, complemented
4#13066618C212yesmaximal
5C11×#1801C211yesmaximal, characteristic, complemented
6C2×C4×Q8×C11C2211yescharacteristic
7C2×#66999—21no—
8C2×C4×D44C411yescharacteristic
9C11×#423—21no—
10C2×C11×#101—21no—
11#10622604C411yescharacteristic
12#10622604C2211yescharacteristic
13#10622600—21no—
14#10622596C411yescharacteristic
15#10622596C2211yescharacteristic
16#10622553—21no—
17#10622553—21no—
18#10622549C411yescharacteristic
19#10622538—21no—
20C11×#343C2212yes—
21#10622166—21no—
22#10622166C2212yes—
23C22×Q8×C11D411yescharacteristic
24C22×D44C2×C411yescharacteristic
25C22×C4×D11—21no—
26C2×C11×M16—22no—
27C4×Q8×C11—41no—
28C4×Q8×C11—41no—
29C2×C11×C4⋊C4C2×C411yescharacteristic
30C2×C11×C4⋊C4D411yescharacteristic
31C2×C11×C4⋊C4C2311yescharacteristic
32C2×C42×C11C2×C411yescharacteristic
33C2×C42×C11D411yescharacteristic
34C2×C42×C11D411yescharacteristic
35#66999—42no—
36#66999—42no—
37C2×(C2×D11)⋊C4—21no—
38C2×(C2×D11)⋊C4—21no—
39C2×(C2×D11)⋊C4—21no—
40C2×(C2×D11)⋊C4—21no—
41C2×(C2×D11)⋊C4—21no—
42C2×C4⋊Dic11—21no—
43C2×C4⋊Dic11C2×C411yescharacteristic
44C2×Dic11⋊C4—21no—
45C2×Dic11⋊C4—21no—
46C4×D44—41no—
47C4×D44—41no—
48C11×C4⋊C8—41no—
49C11×C4⋊C8—41no—
50C11×#101—42no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95C2×C411yescharacteristic
55C11⋊#95C2×C411yescharacteristic
56C22⋊(C11⋊C8)—22no—
57C4⋊(C11⋊C8)—41no—
58C4×C11⋊C8—41no—
59#11879—111nomaximal, Sylow
60C23×D11—21no—
61C2×Q8×C11—41no—
62C2×Q8×C11—41no—
63C2×Q8×C11D812yes—
64C2×Q8×C11SD1612yes—
65C22×C4×C11C22⋊C411yescharacteristic
66C22×C4×C11C22⋊C411yescharacteristic
67C22×C4×C11C22⋊C411yescharacteristic
68C22×C4×C11C22⋊C411yescharacteristic
69C22×C4×C11C22×C411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×Dic11—21no—
73C22×Dic11—21no—
74C22×Dic11—21no—
75C2×D44—41no—
76C2×D44—42no—
77C2×C4×D11—42no—
78C2×C4×D11—42no—
79C2×C4×D11—42no—
80C11×M16—42no—
81C11×M16—42no—
82C2×C8×C11—42no—
83C11×C4⋊C4—41no—
84C11×C4⋊C4—41no—
85C11×C4⋊C4—41no—
86C42×C11—21no—
87C42×C11—21no—
88C42×C11—21no—
89C42×C11—21no—
90C42×C11—21no—
91C42×C11—21no—
92(C2×D11)⋊C4—42no—
93(C2×D11)⋊C4—42no—
94(C2×D11)⋊C4—41no—
95(C2×D11)⋊C4—41no—
96(C2×D11)⋊C4—42no—
97(C2×D11)⋊C4—41no—
98(C2×D11)⋊C4—41no—
99C4⋊Dic11—41no—
100C4⋊Dic11—42no—
101Dic11⋊C4—42no—
102Dic11⋊C4—41no—
103Dic11⋊C4—41no—
104C2×C11⋊C8—42no—
105#2536—111no—
106#1801D1111yescharacteristic, complemented
107#1461—111no—
108#1346—112no—
109#1345—112no—
110C23×C11C2×C22⋊C411yescharacteristic
111C22×D11—22no—
112C22×D11—41no—
113C22×D11—41no—
114C22×D11—41no—
115C22×D11—41no—
116C22×D11—41no—
117C22×D11—41no—
118Q8×C11—42no—
119Q8×C11—42no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11#9911yescharacteristic
134C2×C4×C11#9911yescharacteristic
135C2×C4×C11#10212yes—
136C2×C4×C11#10212yes—
137C2×C4×C11C2×D811yescharacteristic
138C2×C4×C11C2×SD1611yescharacteristic
139C2×Dic11—41no—
140C2×Dic11—41no—
141C2×Dic11—41no—
142C2×Dic11—41no—
143C2×Dic11—41no—
144C2×Dic11—41no—
145C2×Dic11—41no—
146C2×Dic11—41no—
147C2×Dic11—41no—
148D44—42no—
149D44—42no—
150C4×D11—84no—
151C8×C11—82no—
152C11⋊C8—82no—
153C2×C22⋊Q8—221no—
154C2×C4×Q8C2×D1111yescharacteristic
155C2×C4×D4—111no—
156#431—221no—
157#423—21no—
158C2×#101—21no—
159#398—111no—
160#398—111no—
161#394—111no—
162#394—111no—
163#388—221no—
164#388—221no—
165#382—111no—
166#380—221no—
167#343C2×D1112yes—
168#324—112no—
169#324—221no—
170C22×C11—21no—
171C22×C11—21no—
172C22×C11C2×#9911yescharacteristic
173C22×C11C2×#10211yescharacteristic
174C22×C11#42111yescharacteristic
175C2×D11—42no—
176C2×D11—42no—
177C2×D11—42no—
178C2×D11—81no—
179C2×D11—81no—
180C2×D11—81no—
181C2×D11—81no—
182C4×C11—21no—
183C4×C11—21no—
184C4×C11—22no—
185C4×C11—22no—
186C4×C11—21no—
187C4×C11—21no—
188C4×C11—41no—
189C4×C11—41no—
190C4×C11—41no—
191Dic11—81no—
192Dic11—81no—
193Dic11—81no—
194C22×Q8C22⋊D1111yescharacteristic
195C22×D4—111no—
196C23×C4—221no—
197C2×M16—22no—
198C22⋊Q8—442no—
199C22⋊Q8—442no—
200C4×Q8—41no—
201C4×Q8—41no—
202C4×D4—441no—
203C4×D4—441no—
204C2×C4⋊C4—111no—
205C2×C4⋊C4—221no—
206C2×C4⋊C4—221no—
207C2×C4⋊C4—221no—
208C2×C4⋊C4C4×D1111yescharacteristic
209C2×C4⋊C4D4411yescharacteristic
210C2×C4⋊C4C22×D1111yescharacteristic
211C2×C22⋊C4—221no—
212C2×C22⋊C4—221no—
213C2×C22⋊C4—221no—
214C2×C22⋊C4—221no—
215C2×C22⋊C4—221no—
216C2×C42C4×D1111yescharacteristic
217C2×C42D4411yescharacteristic
218C2×C42C22⋊D1111yescharacteristic
219C4⋊C8—41no—
220C4⋊C8—41no—
221C4⋊C8—441no—
222#101—42no—
223C22⋊C8—222no—
224C4×C8—441no—
225#95—111no—
226#95—111no—
227#95—221no—
228#95—221no—
229#95—221no—
230C2×C11—21no—
231C2×C11—21no—
232C2×C11#151911yescharacteristic
233C2×C11#212011yescharacteristic
234C2×C11#213311yescharacteristic
235D11—82no—
236C24—221no—
237C2×Q8—41no—
238C2×Q8—41no—
239C2×Q8#432312yes—
240C2×Q8#432512yes—
241C2×D4—441no—
242C2×D4—442no—
243C22×C4—221no—
244C22×C4—221no—
245C22×C4—221no—
246C22×C4—442no—
247C22×C4—442no—
248C22×C4—442no—
249C22×C4(C2×D11)⋊C411yescharacteristic
250C22×C4(C2×D11)⋊C411yescharacteristic
251C22×C4(C2×D11)⋊C411yescharacteristic
252C22×C4(C2×D11)⋊C411yescharacteristic
253C22×C4C2×C4×D1111yescharacteristic
254C22×C4C2×D4411yescharacteristic
255C22×C4C2×C22⋊D1111yescharacteristic
256M16—42no—
257M16—42no—
258C2×C8—42no—
259C2×C8—442no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—441no—
264C4⋊C4—442no—
265C4⋊C4—442no—
266C4⋊C4—441no—
267C4⋊C4—441no—
268C22⋊C4—442no—
269C22⋊C4—442no—
270C22⋊C4—441no—
271C22⋊C4—441no—
272C22⋊C4—442no—
273C22⋊C4—441no—
274C22⋊C4—441no—
275C42—21no—
276C42—21no—
277C42—21no—
278C42—21no—
279C42—21no—
280C42—21no—
281C11#1187911yescharacteristic, complemented, Sylow
282C23—222no—
283C23—441no—
284C23—441no—
285C23—441no—
286C23—441no—
287C23—441no—
288C23—441no—
289C23C2×(C2×D11)⋊C411yescharacteristic
290Q8—42no—
291Q8—42no—
292D4—442no—
293D4—442no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—441no—
308C2×C4—441no—
309C2×C4—441no—
310C2×C4—441no—
311C2×C4—441no—
312C2×C4—441no—
313C2×C4—441no—
314C2×C4—441no—
315C2×C4—441no—
316C2×C4—884no—
317C2×C4#6687011yescharacteristic
318C2×C4#6687011yescharacteristic
319C2×C4#6687312yes—
320C2×C4#6687312yes—
321C2×C4C2×#432311yescharacteristic
322C2×C4C2×#432511yescharacteristic
323C8—82no—
324C8—882no—
325C22—21no—
326C22—21no—
327C22—442no—
328C22—442no—
329C22—442no—
330C22—881no—
331C22—881no—
332C22—881no—
333C22—881no—
334C22C2×#6687011yescharacteristic
335C22C2×#6687311yescharacteristic
336C22#1062261811yescharacteristic
337C4—21no—
338C4—22no—
339C4—22no—
340C4—21no—
341C4—21no—
342C4—21no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—881no—
347C4—881no—
348C4—881no—
349C2—21no—
350C2—21no—
351C2—882no—
352C2#1306718311yescharacteristic
353C2#1307025811yescharacteristic
354C2#1307030311yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1801C2
socleC22×C11C2×#99
prime radicalC22×D44C2×C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1801D11
hypocenterC11#11879
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1801

Complements

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

NH ≅ G/Ntype
2. #13066940C2semidirect
3. #13066621C2semidirect
5. C11×#1801C2semidirect
106. #1801D11semidirect
281. C11#11879semidirect

Maximal subgroups

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

subgroupindex
#130735212
#130669402
#130666212
#130666182
C11×#18012
#1187911