Finite Group Databasebeta

← #14656879

Subgroups — #14656879

Order 2816.

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

normal subgroups only

This group has 402 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#13077001C211yesmaximal, characteristic, complemented
2#13069445C211yesmaximal, characteristic
3#13067176C211yesmaximal, characteristic
4#13066475C211yesmaximal, characteristic, complemented
5#13066474C211yesmaximal, characteristic, complemented
6#13066448C211yesmaximal, characteristic, complemented
7C11×#1517C211yesmaximal, characteristic
8C11×#532C2211yescharacteristic
9C11×#431C2211yescharacteristic
10C11×#382C2211yescharacteristic
11C2×#66901—21no—
12C2×#66901—21no—
13#10622598—21no—
14#10622586—21no—
15#10622549C2211yescharacteristic
16C42×Dic11C2211yescharacteristic
17#10622538C2211yescharacteristic
18#10622537C2211yescharacteristic
19#10622268—22no—
20#10622267—22no—
21C11×#327—22no—
22#10622175—22no—
23C2×C11×#41—21no—
24C11×C4⋊Q8Q811yescharacteristic
25C11×#127Q811yescharacteristic
26C11×#124—21no—
27C11×#121—21no—
28C11×#121—21no—
29C4×D4×C11—21no—
30C4×D4×C11—21no—
31C2×C11×C4⋊C4—21no—
32C2×C42×C11C2311yescharacteristic
33C2×C4⋊Dic11—22no—
34C2×C4⋊Dic11—21no—
35C2×Dic11⋊C4—22no—
36C2×C4×Dic11—21no—
37C2×C4×Dic11—21no—
38C2×C4×Dic11D411yescharacteristic
39C2×C4×Dic11D411yescharacteristic
40C2×#4318—21no—
41C11×C4⋊C8—21no—
42C11×C22⋊C8—21no—
43C4×C8×C11—21no—
44C11×#95—21no—
45C11×#95D412yes—
46#66901—42no—
47#66901—42no—
48C11⋊#95—22no—
49C11⋊#95—22no—
50C11⋊#95—21no—
51C11⋊#95D412yes—
52C22⋊(C11⋊C8)—21no—
53C4⋊(C11⋊C8)—21no—
54C4⋊(C11⋊C8)—21no—
55C4⋊(C11⋊C8)—21no—
56C4×C11⋊C8—21no—
57#10366—111nomaximal, Sylow
58C11×#41—41no—
59C11×#41—41no—
60C11×#41—41no—
61C11×#41—41no—
62C2×Q8×C11—21no—
63C2×D4×C11—21no—
64C2×D4×C11—21no—
65C2×D4×C11—21no—
66C2×D4×C11—41no—
67C22×C4×C11—22no—
68C22×C4×C11—41no—
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×Dic11—21no—
73C22×Dic11—21no—
74C22×Dic11—22no—
75C2×C8×C11—41no—
76C11×C4⋊C4—21no—
77C11×C4⋊C4—21no—
78C11×C4⋊C4—41no—
79C11×C4⋊C4—41no—
80C11×C22⋊C4—41no—
81C11×C22⋊C4—41no—
82C42×C11C2×Q811yescharacteristic
83C42×C11#4111yescharacteristic
84C42×C11#4111yescharacteristic
85C42×C11#4111yescharacteristic
86C4⋊Dic11—44no—
87C4⋊Dic11—41no—
88C4⋊Dic11—41no—
89Dic11⋊C4—44no—
90C4×Dic11—21no—
91C4×Dic11—21no—
92C4×Dic11—21no—
93C4×Dic11—21no—
94C4×Dic11—42no—
95C4×Dic11—42no—
96#4318—41no—
97#4318—41no—
98C2×C11⋊C8—41no—
99C2×C11⋊C8—41no—
100#2864—111no—
101#1962—111no—
102#1517—111no—
103#1517D1111yescharacteristic
104#1286—111no—
105#1286—111no—
106#1276—111no—
107C23×C11—41no—
108C23×C11#12011yescharacteristic
109Q8×C11—41no—
110Q8×C11—41no—
111D4×C11—41no—
112D4×C11—41no—
113D4×C11—81no—
114D4×C11—81no—
115D4×C11—81no—
116D4×C11—81no—
117C2×C4×C11—41no—
118C2×C4×C11—41no—
119C2×C4×C11—42no—
120C2×C4×C11—42no—
121C2×C4×C11—41no—
122C2×C4×C11—42no—
123C2×C4×C11—81no—
124C2×C4×C11—81no—
125C2×C4×C11C22⋊Q811yescharacteristic
126C2×C4×C11C22⋊Q811yescharacteristic
127C2×C4×C11C22⋊Q811yescharacteristic
128C2×C4×C11#12411yescharacteristic
129C2×C4×C11#12411yescharacteristic
130C2×C4×C11#12411yescharacteristic
131C2×C4×C11#13511yescharacteristic
132C2×C4×C11#13511yescharacteristic
133C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
134C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
135C2×Dic11—22no—
136C2×Dic11—22no—
137C2×Dic11—41no—
138C2×Dic11—41no—
139C2×Dic11—41no—
140C2×Dic11—41no—
141C2×Dic11—42no—
142C2×Dic11—42no—
143C2×Dic11—42no—
144C8×C11—81no—
145C11⋊C8—81no—
146C11⋊C8—81no—
147#532C2×D1111yescharacteristic
148#431—111no—
149#431C2×D1111yescharacteristic
150#423—111no—
151C2×#104—221no—
152C2×#104—221no—
153#389—221no—
154#389—221no—
155#387—222no—
156#387—222no—
157#382—111no—
158#382C2×D1111yescharacteristic
159C43—111no—
160#327—22no—
161#327—222no—
162C22×C11—21no—
163C22×C11—21no—
164C22×C11—81no—
165C22×C11—81no—
166C22×C11—81no—
167C22×C11#39311yescharacteristic
168C22×C11#44911yescharacteristic
169C22×C11#44911yescharacteristic
170C4×C11—21no—
171C4×C11—21no—
172C4×C11—21no—
173C4×C11—21no—
174C4×C11—82no—
175C4×C11—81no—
176C4×C11#47811yescharacteristic
177C4×C11#47811yescharacteristic
178C4×C11#48811yescharacteristic
179C4×C11#49011yescharacteristic
180Dic11—42no—
181Dic11—42no—
182Dic11—82no—
183C2×#41—21no—
184C2×M16—221no—
185C4⋊Q8Dic2211yescharacteristic
186#127Dic2211yescharacteristic
187#124—21no—
188#121—21no—
189#121—21no—
190C4×D4—21no—
191C4×D4—21no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—222no—
194C2×C4⋊C4—222no—
195C2×C4⋊C4—221no—
196C2×C42—111no—
197C2×C42—111no—
198C2×C42—221no—
199C2×C42—221no—
200C2×C42C22×D1111yescharacteristic
201C4⋊C8—21no—
202C4⋊C8—221no—
203C4⋊C8—221no—
204C4⋊C8—221no—
205#104—442no—
206#104—442no—
207C22⋊C8—21no—
208C22⋊C8—221no—
209C4×C8—21no—
210C4×C8—221no—
211#95—21no—
212#95—112no—
213#95—222no—
214#95—222no—
215#95—221no—
216#95C22⋊D1112yes—
217C2×C11—21no—
218C2×C11—21no—
219C2×C11—161no—
220C2×C11#202511yescharacteristic
221C2×C11#203111yescharacteristic
222C2×C11#203111yescharacteristic
223#41—41no—
224#41—41no—
225#41—41no—
226#41—41no—
227C2×Q8—21no—
228C2×D4—21no—
229C2×D4—21no—
230C2×D4—21no—
231C2×D4—41no—
232C22×C4—22no—
233C22×C4—41no—
234C22×C4—221no—
235C22×C4—221no—
236C22×C4—222no—
237C22×C4D4×D1111yescharacteristic
238C22×C4D4×D1111yescharacteristic
239C22×C4C2×C22⋊D1111yescharacteristic
240M16—441no—
241M16—441no—
242C2×C8—41no—
243C2×C8—441no—
244C2×C8—441no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—444no—
250C4⋊C4—444no—
251C4⋊C4—441no—
252C4⋊C4—441no—
253C22⋊C4—41no—
254C22⋊C4—41no—
255C42—221no—
256C42—221no—
257C42—221no—
258C42—221no—
259C42—442no—
260C42—442no—
261C42C2×Dic2211yescharacteristic
262C42#433911yescharacteristic
263C42#434111yescharacteristic
264C42#434111yescharacteristic
265C11#1036611yescharacteristic, complemented, Sylow
266C23—41no—
267C23#6699011yescharacteristic
268Q8—41no—
269Q8—41no—
270D4—41no—
271D4—41no—
272D4—81no—
273D4—81no—
274D4—81no—
275D4—81no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—41no—
282C2×C4—81no—
283C2×C4—81no—
284C2×C4—222no—
285C2×C4—222no—
286C2×C4—441no—
287C2×C4—441no—
288C2×C4—441no—
289C2×C4—441no—
290C2×C4—442no—
291C2×C4—442no—
292C2×C4—442no—
293C2×C4#6693111yescharacteristic
294C2×C4#6693111yescharacteristic
295C2×C4#6693811yescharacteristic
296C2×C4#6693811yescharacteristic
297C2×C4#6696411yescharacteristic
298C2×C4#6696511yescharacteristic
299C2×C4#6696711yescharacteristic
300C2×C4#6696911yescharacteristic
301C2×C4#6697711yescharacteristic
302C2×C4#6698911yescharacteristic
303C8—81no—
304C8—881no—
305C8—881no—
306C22—21no—
307C22—21no—
308C22—81no—
309C22—81no—
310C22—81no—
311C22#1062256011yescharacteristic
312C22#1062277111yescharacteristic
313C22#1062278511yescharacteristic
314C4—21no—
315C4—21no—
316C4—21no—
317C4—21no—
318C4—82no—
319C4—81no—
320C4—442no—
321C4—442no—
322C4—882no—
323C4#1062237611yescharacteristic
324C4#1062237711yescharacteristic
325C4#1062237911yescharacteristic
326C4#1062238111yescharacteristic
327C2—21no—
328C2—21no—
329C2—161no—
330C2#1306976011yescharacteristic
331C2#1306978611yescharacteristic
332C2#1306979011yescharacteristic
subgroupG/H
centerC22#10622560
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1517C2
socleC22×C11#393
prime radicalC11×#532C22
hypercenter#1517D11
hypocenterC11#10366
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1517

Complements

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

NH ≅ G/Ntype
1. #13077001C2semidirect
4. #13066475C2semidirect
5. #13066474C2semidirect
6. #13066448C2semidirect
265. C11#10366semidirect

Maximal subgroups

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

subgroupindex
#130770012
#130694452
#130671762
#130664752
#130664742
#130664482
C11×#15172
#1036611