Finite Group Databasebeta

← #14664634

Subgroups — #14664634

Order 2816.

446 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 79 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#13074182C211yesmaximal, characteristic
2#13066930C211yesmaximal, characteristic, complemented
3#13066639C212yesmaximal, complemented
4#13066612C212yesmaximal
5C11×#1820C211yesmaximal, characteristic, complemented
6C2×C11×#117C2211yescharacteristic
7C2×C4×D44C411yescharacteristic, complemented
8C11×#381—21no—
9#10622826—21no—
10#10622604C411yescharacteristic, complemented
11#10622602—21no—
12#10622599C411yescharacteristic, complemented
13#10622573C2211yescharacteristic
14#10622569—21no—
15#10622562C2211yescharacteristic
16#10622553—21no—
17#10622550C411yescharacteristic, complemented
18#10622538—21no—
19C11×#342—21no—
20C11×#342C2212yes—
21#10622166—21no—
22#10622163C2212yes—
23C23×C4×C11D411yescharacteristic
24C22×C22⋊D11—21no—
25C22×D44C2×C411yescharacteristic
26C22×C4×D11—21no—
27C11×#117—41no—
28C11×#117—41no—
29C2×C11×C4⋊C4C2×C411yescharacteristic
30C2×C11×C4⋊C4D411yescharacteristic
31C2×C11×C22⋊C4—22no—
32C2×C11×C22⋊C4D411yescharacteristic
33C2×C11×C22⋊C4C2311yescharacteristic
34C2×C42×C11C2×C411yescharacteristic
35C2×C42×C11D411yescharacteristic
36C2×C22⋊Dic11—21no—
37C2×(C2×D11)⋊C4—21no—
38C2×(C2×D11)⋊C4—21no—
39C2×(C2×D11)⋊C4—21no—
40C2×(C2×D11)⋊C4—21no—
41C2×C4⋊Dic11C2×C411yescharacteristic
42C2×Dic11⋊C4—21no—
43C4×D44—41no—
44C4×D44—41no—
45C11×#95—41no—
46C11×#95—41no—
47C11⋊#95—21no—
48C11⋊#95—21no—
49C11⋊#95—21no—
50C11⋊#95—21no—
51C11⋊#95C2×C411yescharacteristic
52C11⋊#95C2×C411yescharacteristic
53C22⋊(C11⋊C8)—22no—
54C4⋊(C11⋊C8)—41no—
55C4×C11⋊C8—41no—
56#11840—111nomaximal, Sylow
57C24×C11C2×D411yescharacteristic
58C23×D11—21no—
59C22×C4×C11—22no—
60C22×C4×C11—21no—
61C22×C4×C11—21no—
62C22×C4×C11—41no—
63C22×C4×C11—42no—
64C22×C4×C11C22⋊C411yescharacteristic
65C22×C4×C11C22⋊C411yescharacteristic
66C22×C4×C11C22⋊C411yescharacteristic
67C22×C4×C11C22⋊C411yescharacteristic
68C22×C4×C11C22×C411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C2×C22⋊D11—42no—
71C2×C22⋊D11—42no—
72C2×C22⋊D11—81no—
73C22×Dic11—21no—
74C22×Dic11—21no—
75C22×Dic11—21no—
76C2×D44—41no—
77C2×D44—42no—
78C2×C4×D11—42no—
79C2×C4×D11—81no—
80C2×C4×D11—81no—
81C11×C4⋊C4—41no—
82C11×C4⋊C4—41no—
83C11×C22⋊C4—41no—
84C11×C22⋊C4—41no—
85C11×C22⋊C4—42no—
86C11×C22⋊C4—42no—
87C42×C11—21no—
88C42×C11—21no—
89C42×C11—21no—
90C42×C11—21no—
91C22⋊Dic11—81no—
92(C2×D11)⋊C4—42no—
93(C2×D11)⋊C4—42no—
94(C2×D11)⋊C4—41no—
95(C2×D11)⋊C4—41no—
96(C2×D11)⋊C4—81no—
97C4⋊Dic11—41no—
98Dic11⋊C4—81no—
99C2×C11⋊C8—42no—
100#2598—111no—
101#1820D1111yescharacteristic, complemented
102#1458—111no—
103#1352—112no—
104#1343—112no—
105C23×C11—21no—
106C23×C11—21no—
107C23×C11—41no—
108C23×C11—41no—
109C23×C11C2×C22⋊C411yescharacteristic
110C23×C11#13512yes—
111C22×D11—22no—
112C22×D11—41no—
113C22×D11—41no—
114C22×D11—41no—
115C22×D11—41no—
116C22×D11—41no—
117C22×D11—41no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
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—42no—
128C2×C4×C11—42no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—82no—
134C2×C4×C11—82no—
135C2×C4×C11—82no—
136C2×C4×C11#9911yescharacteristic
137C2×C4×C11#9911yescharacteristic
138C22⋊D11—84no—
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—
151C11⋊C8—82no—
152C2×C4×D4—111no—
153C2×#117C2×D1111yescharacteristic
154#431—221no—
155#400—111no—
156#399—111no—
157#394—111no—
158#392—111no—
159#388—221no—
160#386—221no—
161#386—221no—
162#385—221no—
163#383—111no—
164#381—21no—
165#342—21no—
166#342C2×D1112yes—
167#324—221no—
168#323—112no—
169C22×C11—21no—
170C22×C11—21no—
171C22×C11—22no—
172C22×C11—42no—
173C22×C11—41no—
174C22×C11—41no—
175C22×C11—81no—
176C22×C11C2×#9911yescharacteristic
177C22×C11#41611yescharacteristic
178C22×C11#42111yescharacteristic
179C2×D11—42no—
180C2×D11—42no—
181C2×D11—42no—
182C2×D11—81no—
183C2×D11—81no—
184C2×D11—81no—
185C2×D11—81no—
186C4×C11—21no—
187C4×C11—21no—
188C4×C11—41no—
189C4×C11—41no—
190C4×C11—41no—
191C4×C11—41no—
192C4×C11—41no—
193C4×C11—162no—
194Dic11—81no—
195Dic11—81no—
196Dic11—81no—
197C22×D4—111no—
198C22×D4—221no—
199C23×C4—221no—
200C23×C4C22⋊D1111yescharacteristic
201C4×D4—441no—
202C4×D4—441no—
203#117—41no—
204#117—41no—
205C2×C4⋊C4—111no—
206C2×C4⋊C4—221no—
207C2×C4⋊C4C4×D1111yescharacteristic
208C2×C4⋊C4D4411yescharacteristic
209C2×C22⋊C4—22no—
210C2×C22⋊C4—221no—
211C2×C22⋊C4—221no—
212C2×C22⋊C4—221no—
213C2×C22⋊C4—221no—
214C2×C22⋊C4—221no—
215C2×C22⋊C4C22⋊D1111yescharacteristic
216C2×C22⋊C4C22×D1111yescharacteristic
217C2×C42C4×D1111yescharacteristic
218C2×C42D4411yescharacteristic
219C4⋊C8—441no—
220C22⋊C8—222no—
221C4×C8—441no—
222#95—41no—
223#95—41no—
224#95—111no—
225#95—111no—
226#95—221no—
227#95—221no—
228#95—221no—
229#95—221no—
230C2×C11—21no—
231C2×C11—21no—
232C2×C11—42no—
233C2×C11#151611yescharacteristic
234C2×C11#212011yescharacteristic
235C2×C11#212811yescharacteristic
236D11—82no—
237C24—221no—
238C24C2×C22⋊D1111yescharacteristic
239C2×D4—441no—
240C2×D4—442no—
241C2×D4—442no—
242C2×D4—442no—
243C2×D4—881no—
244C22×C4—22no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—41no—
248C22×C4—42no—
249C22×C4—221no—
250C22×C4—221no—
251C22×C4—221no—
252C22×C4—442no—
253C22×C4—881no—
254C22×C4—881no—
255C22×C4(C2×D11)⋊C411yescharacteristic
256C22×C4(C2×D11)⋊C411yescharacteristic
257C22×C4(C2×D11)⋊C411yescharacteristic
258C22×C4(C2×D11)⋊C411yescharacteristic
259C22×C4C2×C4×D1111yescharacteristic
260C22×C4C2×D4411yescharacteristic
261C2×C8—442no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—441no—
265C4⋊C4—881no—
266C22⋊C4—41no—
267C22⋊C4—41no—
268C22⋊C4—42no—
269C22⋊C4—42no—
270C22⋊C4—442no—
271C22⋊C4—442no—
272C22⋊C4—441no—
273C22⋊C4—441no—
274C22⋊C4—881no—
275C22⋊C4—881no—
276C42—21no—
277C42—21no—
278C42—21no—
279C42—21no—
280C11#1184011yescharacteristic, complemented, Sylow
281C23—21no—
282C23—21no—
283C23—41no—
284C23—41no—
285C23—222no—
286C23—441no—
287C23—441no—
288C23—441no—
289C23—441no—
290C23—441no—
291C23—441no—
292C23C2×(C2×D11)⋊C411yescharacteristic
293C23#6700312yes—
294D4—442no—
295D4—442no—
296D4—884no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—42no—
307C2×C4—42no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—82no—
313C2×C4—82no—
314C2×C4—82no—
315C2×C4—441no—
316C2×C4—441no—
317C2×C4—441no—
318C2×C4—441no—
319C2×C4—441no—
320C2×C4—441no—
321C2×C4—441no—
322C2×C4—441no—
323C2×C4—441no—
324C2×C4—884no—
325C2×C4#6687011yescharacteristic
326C2×C4#6687011yescharacteristic
327C8—882no—
328C22—21no—
329C22—21no—
330C22—22no—
331C22—42no—
332C22—41no—
333C22—41no—
334C22—81no—
335C22—442no—
336C22—442no—
337C22—442no—
338C22—881no—
339C22—881no—
340C22—881no—
341C22—881no—
342C22C2×#6687011yescharacteristic
343C22#1062261511yescharacteristic
344C22#1062261811yescharacteristic
345C4—21no—
346C4—21no—
347C4—41no—
348C4—41no—
349C4—41no—
350C4—41no—
351C4—41no—
352C4—162no—
353C4—881no—
354C4—881no—
355C4—881no—
356C2—21no—
357C2—21no—
358C2—42no—
359C2—882no—
360C2#1306717011yescharacteristic
361C2#1307025511yescharacteristic
362C2#1307028711yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1820C2
socleC22×C11C2×#99
prime radical#10622573C22
cosocleC2×C11×C22⋊C4C23
hypercenter#1820D11
hypocenterC11#11840
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1820

Complements

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

NH ≅ G/Ntype
2. #13066930C2semidirect
3. #13066639C2semidirect
5. C11×#1820C2semidirect
7. C2×C4×D44C4semidirect
10. #10622604C4semidirect
12. #10622599C4semidirect
17. #10622550C4semidirect
101. #1820D11semidirect
280. C11#11840semidirect

Maximal subgroups

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

subgroupindex
#130741822
#130669302
#130666392
#130666122
C11×#18202
#1184011