Finite Group Databasebeta

← #14672446

Subgroups — #14672446

Order 2816.

500 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 103 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#13073789C211yesmaximal, characteristic
2C4×#66898C211yesmaximal, characteristic
3#13066740C214yesmaximal
4C11×#1799C211yesmaximal, characteristic
5C2×C4×D4×C11C2211yescharacteristic
6C2×#66922C411yescharacteristic, complemented
7C2×C11×#99C2212yes—
8C11×#380—21no—
9#10622834C2212yes—
10C2×#66898C2212yes—
11#10622825—21no—
12#10622825—21no—
13C4×C22⋊Dic11—21no—
14#10622590C412yescomplemented
15#10622560—21no—
16#10622560—21no—
17C4×C4⋊Dic11C411yescharacteristic, complemented
18C11×#342—21no—
19#10622164—21no—
20C22×D4×C11C2311yescharacteristic
21C23×C4×C11D411yescharacteristic
22C23×C4×C11D411yescharacteristic
23C22×Dic22—21no—
24C4×D4×C11—41no—
25C4×D4×C11—41no—
26C2×C11×C4⋊C4—41no—
27C2×C11×C4⋊C4C2×C411yescharacteristic
28C2×C11×C22⋊C4—22no—
29C2×C11×C22⋊C4D411yescharacteristic
30C2×C11×C22⋊C4D411yescharacteristic
31C2×C42×C11C2×C411yescharacteristic
32C2×C22⋊Dic11—22no—
33C2×C22⋊Dic11—22no—
34C2×C22⋊Dic11—22no—
35C2×C4⋊Dic11—21no—
36C2×C4⋊Dic11—21no—
37C2×C4⋊Dic11C2×C412yes—
38C2×C4×Dic11—41no—
39C2×C4×Dic11C2×C412yes—
40#66922—41no—
41#66922—41no—
42C11×#99—24no—
43C11×#95—41no—
44#66898—22no—
45#66898Q814yescomplemented
46C11⋊#95—21no—
47C11⋊#95—22no—
48C11⋊#95—22no—
49C11⋊#95—41no—
50#13299—111nomaximal, Sylow
51C24×C11C2×D411yescharacteristic
52C24×C11C2×D411yescharacteristic
53C2×D4×C11—41no—
54C2×D4×C11—41no—
55C2×D4×C11C2×Q812yes—
56C2×D4×C11#4112yes—
57C22×C4×C11—21no—
58C22×C4×C11—21no—
59C22×C4×C11—21no—
60C22×C4×C11—21no—
61C22×C4×C11—42no—
62C22×C4×C11—42no—
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×Dic11—22no—
70C22×Dic11—22no—
71C22×Dic11—42no—
72C2×Dic22—42no—
73C2×Dic22—82no—
74C11×C4⋊C4—41no—
75C11×C4⋊C4—82no—
76C11×C22⋊C4—41no—
77C11×C22⋊C4—41no—
78C11×C22⋊C4—42no—
79C11×C22⋊C4—42no—
80C42×C11—21no—
81C42×C11—21no—
82C22⋊Dic11—24no—
83C22⋊Dic11—42no—
84C22⋊Dic11—82no—
85C22⋊Dic11—82no—
86C4⋊Dic11—42no—
87C4⋊Dic11—42no—
88C4⋊Dic11—41no—
89C4⋊Dic11—41no—
90C4×Dic11—42no—
91C4×Dic11—82no—
92#2563—111no—
93#1799D1111yescharacteristic
94C4×#99—111no—
95#1393—114no—
96C23×C11—21no—
97C23×C11—21no—
98C23×C11—21no—
99C23×C11—21no—
100C23×C11—41no—
101C23×C11—41no—
102C23×C11—41no—
103C23×C11—41no—
104C23×C11C2×C22⋊C411yescharacteristic
105C23×C11C22⋊Q812yes—
106C23×C11#12411yescharacteristic
107C23×C11C4⋊Q811yescharacteristic
108D4×C11—42no—
109D4×C11—42no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—22no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—42no—
117C2×C4×C11—42no—
118C2×C4×C11—41no—
119C2×C4×C11—41no—
120C2×C4×C11—41no—
121C2×C4×C11—81no—
122C2×C4×C11—81no—
123C2×C4×C11—82no—
124C2×C4×C11—82no—
125C2×C4×C11—82no—
126C2×C4×C11#9911yescharacteristic
127C2×C4×C11#9911yescharacteristic
128C2×C4×C11C4×Q812yes—
129C2×Dic11—42no—
130C2×Dic11—44no—
131C2×Dic11—42no—
132C2×Dic11—42no—
133C2×Dic11—42no—
134C2×Dic11—42no—
135C2×Dic11—42no—
136C2×Dic11—82no—
137C2×Dic11—82no—
138Dic22—84no—
139C2×C4⋊Q8—111no—
140C2×C4×D4C2×D1111yescharacteristic
141C2×#99—112no—
142C2×#99C2×D1112yes—
143#393—221no—
144#393—221no—
145#390—112no—
146#382—112no—
147#380—21no—
148#380—221no—
149#380—221no—
150C4×C4⋊C4—111no—
151C4×C22⋊C4—221no—
152#342—21no—
153#342—221no—
154C22×C11—21no—
155C22×C11—21no—
156C22×C11—21no—
157C22×C11—22no—
158C22×C11—21no—
159C22×C11—42no—
160C22×C11—41no—
161C22×C11—41no—
162C22×C11—41no—
163C22×C11—41no—
164C22×C11—41no—
165C22×C11—41no—
166C22×C11—81no—
167C22×C11—81no—
168C22×C11#39111yescharacteristic
169C22×C11C2×#9911yescharacteristic
170C22×C11#41011yescharacteristic
171C4×C11—21no—
172C4×C11—22no—
173C4×C11—41no—
174C4×C11—41no—
175C4×C11—41no—
176C4×C11—162no—
177C4×C11#35412yes—
178Dic11—82no—
179Dic11—84no—
180Dic11—82no—
181C22×Q8—221no—
182C22×D4C22×D1111yescharacteristic
183C23×C4D4411yescharacteristic
184C23×C4C22⋊D1111yescharacteristic
185C4⋊Q8—441no—
186C4⋊Q8—441no—
187C4×D4—41no—
188C4×D4—41no—
189C2×C4⋊C4—41no—
190C2×C4⋊C4—112no—
191C2×C4⋊C4—221no—
192C2×C4⋊C4—221no—
193C2×C4⋊C4C4×D1111yescharacteristic
194C2×C22⋊C4—22no—
195C2×C22⋊C4—222no—
196C2×C22⋊C4—222no—
197C2×C22⋊C4—222no—
198C2×C22⋊C4D4411yescharacteristic
199C2×C22⋊C4C22⋊D1111yescharacteristic
200C2×C42—112no—
201C2×C42—441no—
202C2×C42C4×D1111yescharacteristic
203#99—24no—
204#99—114no—
205#99—222no—
206#95—41no—
207#95—221no—
208#95—222no—
209#95—222no—
210#95—441no—
211C2×C11—21no—
212C2×C11—21no—
213C2×C11—42no—
214C2×C11—41no—
215C2×C11—41no—
216C2×C11#199611yescharacteristic
217C2×C11C2×#35411yescharacteristic
218C2×C11#212811yescharacteristic
219C24C2×D4411yescharacteristic
220C24C2×C22⋊D1111yescharacteristic
221C2×Q8—442no—
222C2×Q8—882no—
223C2×D4—41no—
224C2×D4—41no—
225C2×D4#434112yes—
226C2×D4Q8×D1112yes—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—42no—
232C22×C4—42no—
233C22×C4—42no—
234C22×C4—222no—
235C22×C4—222no—
236C22×C4—442no—
237C22×C4(C2×D11)⋊C411yescharacteristic
238C22×C4(C2×D11)⋊C411yescharacteristic
239C22×C4(C2×D11)⋊C411yescharacteristic
240C22×C4(C2×D11)⋊C411yescharacteristic
241C22×C4C2×C4×D1111yescharacteristic
242C4⋊C4—41no—
243C4⋊C4—82no—
244C4⋊C4—442no—
245C4⋊C4—442no—
246C4⋊C4—441no—
247C4⋊C4—441no—
248C22⋊C4—41no—
249C22⋊C4—41no—
250C22⋊C4—42no—
251C22⋊C4—42no—
252C22⋊C4—224no—
253C22⋊C4—442no—
254C22⋊C4—882no—
255C22⋊C4—882no—
256C42—21no—
257C42—21no—
258C42—442no—
259C42—882no—
260C11#1329911yescharacteristic, complemented, Sylow
261C23—21no—
262C23—21no—
263C23—21no—
264C23—21no—
265C23—41no—
266C23—41no—
267C23—41no—
268C23—41no—
269C23#6695012yes—
270C23C2×(C2×D11)⋊C411yescharacteristic
271C23#6698911yescharacteristic
272C23#6699711yescharacteristic
273Q8—884no—
274D4—42no—
275D4—42no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—22no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—81no—
288C2×C4—81no—
289C2×C4—82no—
290C2×C4—82no—
291C2×C4—82no—
292C2×C4—444no—
293C2×C4—442no—
294C2×C4—442no—
295C2×C4—442no—
296C2×C4—442no—
297C2×C4—442no—
298C2×C4—442no—
299C2×C4—882no—
300C2×C4—882no—
301C2×C4#6687011yescharacteristic
302C2×C4#6687011yescharacteristic
303C2×C4#6694012yes—
304C22—21no—
305C22—21no—
306C22—21no—
307C22—22no—
308C22—21no—
309C22—42no—
310C22—41no—
311C22—41no—
312C22—41no—
313C22—41no—
314C22—41no—
315C22—41no—
316C22—81no—
317C22—81no—
318C22C2×#6687011yescharacteristic
319C22#1062258711yescharacteristic
320C22#1062261911yescharacteristic
321C4—22no—
322C4—21no—
323C4—41no—
324C4—41no—
325C4—41no—
326C4—162no—
327C4—882no—
328C4—884no—
329C4—882no—
330C4#1062211112yes—
331C2—21no—
332C2—21no—
333C2—41no—
334C2—42no—
335C2—41no—
336C2#1306960011yescharacteristic
337C2C2×#1062211111yescharacteristic
338C2#1307028711yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC22×D4C22×D11
FittingC11×#1799C2
socleC22×C11C2×#99
prime radical, cosocleC22×D4×C11C23
hypercenter#1799D11
hypocenterC11#13299
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1799

Complements

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

NH ≅ G/Ntype
6. C2×#66922C4semidirect
14. #10622590C4semidirect
17. C4×C4⋊Dic11C4semidirect
45. #66898Q8semidirect
260. C11#13299semidirect

Maximal subgroups

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

subgroupindex
#130737892
C4×#668982
#130667402
C11×#17992
#1329911