Finite Group Databasebeta

← #14672448

Subgroups — #14672448

Order 2816.

500 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 111 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#13068604C211yesmaximal, characteristic
2C4×#66898C211yesmaximal, characteristic
3#13066741C214yesmaximal
4C11×#2563C211yesmaximal, characteristic
5C2×C11×C4⋊Q8C411yescharacteristic, complemented
6C2×C4×D4×C11C2211yescharacteristic
7C11×#393—21no—
8C11×#393—21no—
9C11×#390C2212yes—
10C11×#382C412yescomplemented
11C11×#380—21no—
12C11×#380—21no—
13C4×C11×C4⋊C4C411yescharacteristic, complemented
14C2×#66898C2212yes—
15C2×#66898C2212yes—
16#10622825—21no—
17C4×C22⋊Dic11—21no—
18#10622164—21no—
19#10622164—21no—
20C22×Q8×C11—21no—
21C22×D4×C11C2311yescharacteristic
22C23×C4×C11D411yescharacteristic
23C23×C4×C11D411yescharacteristic
24C11×C4⋊Q8—41no—
25C11×C4⋊Q8—41no—
26C4×D4×C11—41no—
27C4×D4×C11—41no—
28C2×C11×C4⋊C4—21no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4C2×C412yes—
31C2×C11×C4⋊C4C2×C411yescharacteristic
32C2×C11×C22⋊C4—22no—
33C2×C11×C22⋊C4—22no—
34C2×C11×C22⋊C4D411yescharacteristic
35C2×C11×C22⋊C4D411yescharacteristic
36C2×C42×C11C2×C411yescharacteristic
37C2×C42×C11C2×C412yes—
38C2×C22⋊Dic11—22no—
39C2×C22⋊Dic11—22no—
40C2×C4⋊Dic11—41no—
41C2×C4×Dic11—41no—
42C11×#95—21no—
43C11×#95—22no—
44C11×#95—22no—
45#66898—22no—
46#66898—24no—
47#66898Q814yescomplemented
48C11⋊#95—41no—
49C11⋊#95—41no—
50#13299—111nomaximal, Sylow
51C24×C11C2×D411yescharacteristic
52C24×C11C2×D411yescharacteristic
53C2×Q8×C11—42no—
54C2×Q8×C11—82no—
55C2×D4×C11—41no—
56C2×D4×C11—41no—
57C2×D4×C11C2×Q812yes—
58C2×D4×C11#4112yes—
59C22×C4×C11—21no—
60C22×C4×C11—21no—
61C22×C4×C11—21no—
62C22×C4×C11—21no—
63C22×C4×C11—22no—
64C22×C4×C11—22no—
65C22×C4×C11—42no—
66C22×C4×C11—42no—
67C22×C4×C11C22⋊C411yescharacteristic
68C22×C4×C11C22⋊C411yescharacteristic
69C22×C4×C11C22⋊C411yescharacteristic
70C22×C4×C11C22⋊C411yescharacteristic
71C22×C4×C11C22×C411yescharacteristic
72C22×Dic11—42no—
73C22×Dic11—42no—
74C11×C4⋊C4—41no—
75C11×C4⋊C4—42no—
76C11×C4⋊C4—42no—
77C11×C4⋊C4—41no—
78C11×C4⋊C4—41no—
79C11×C22⋊C4—41no—
80C11×C22⋊C4—41no—
81C11×C22⋊C4—82no—
82C11×C22⋊C4—82no—
83C42×C11—21no—
84C42×C11—21no—
85C42×C11—42no—
86C22⋊Dic11—24no—
87C22⋊Dic11—42no—
88C22⋊Dic11—42no—
89C22⋊Dic11—42no—
90C4⋊Dic11—82no—
91C4×Dic11—82no—
92#2563D1111yescharacteristic
93#1799—111no—
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
108Q8×C11—84no—
109D4×C11—42no—
110D4×C11—42no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—22no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—42no—
118C2×C4×C11—42no—
119C2×C4×C11—41no—
120C2×C4×C11—41no—
121C2×C4×C11—41no—
122C2×C4×C11—42no—
123C2×C4×C11—42no—
124C2×C4×C11—42no—
125C2×C4×C11—42no—
126C2×C4×C11—42no—
127C2×C4×C11—42no—
128C2×C4×C11—81no—
129C2×C4×C11—81no—
130C2×C4×C11#9911yescharacteristic
131C2×C4×C11#9911yescharacteristic
132C2×C4×C11C4×Q812yes—
133C2×Dic11—44no—
134C2×Dic11—82no—
135C2×Dic11—82no—
136C2×Dic11—82no—
137C2×Dic11—82no—
138C2×Dic11—82no—
139C2×C4⋊Q8Dic1111yescharacteristic, complemented
140C2×C4×D4C2×D1111yescharacteristic
141C2×#99—112no—
142C2×#99—112no—
143#393—21no—
144#393—21no—
145#390C2×D1112yes—
146#382Dic1112yescomplemented
147#380—21no—
148#380—21no—
149#380—221no—
150C4×C4⋊C4Dic1111yescharacteristic, complemented
151C4×C22⋊C4—221no—
152#342—221no—
153#342—221no—
154C22×C11—21no—
155C22×C11—21no—
156C22×C11—22no—
157C22×C11—21no—
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—82no—
177C4×C11—82no—
178C4×C11#35412yes—
179Dic11—84no—
180Dic11—162no—
181C22×Q8—21no—
182C22×D4C22×D1111yescharacteristic
183C23×C4C22⋊D1111yescharacteristic
184C23×C4C22⋊D1111yescharacteristic
185C4⋊Q8—41no—
186C4⋊Q8—41no—
187C4×D4—41no—
188C4×D4—41no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4—441no—
192C2×C4⋊C4C2×Dic1112yes—
193C2×C4⋊C4C2×Dic1111yescharacteristic
194C2×C22⋊C4—22no—
195C2×C22⋊C4—22no—
196C2×C22⋊C4—222no—
197C2×C22⋊C4—222no—
198C2×C22⋊C4C22⋊D1111yescharacteristic
199C2×C22⋊C4C22⋊D1111yescharacteristic
200C2×C42—441no—
201C2×C42C2×Dic1111yescharacteristic
202C2×C42C2×Dic1112yes—
203#99—114no—
204#99—222no—
205#99—224no—
206#95—21no—
207#95—22no—
208#95—22no—
209#95—441no—
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×C22⋊D1111yescharacteristic
220C24C2×C22⋊D1111yescharacteristic
221C2×Q8—42no—
222C2×Q8—82no—
223C2×D4—41no—
224C2×D4—41no—
225C2×D4Q8×D1112yes—
226C2×D4#434312yes—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—22no—
232C22×C4—22no—
233C22×C4—42no—
234C22×C4—42no—
235C22×C4—442no—
236C22×C4—442no—
237C22×C4C22⋊Dic1111yescharacteristic
238C22×C4C22⋊Dic1111yescharacteristic
239C22×C4C22⋊Dic1111yescharacteristic
240C22×C4C22⋊Dic1111yescharacteristic
241C22×C4C22×Dic1111yescharacteristic
242C4⋊C4—41no—
243C4⋊C4—42no—
244C4⋊C4—42no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C4⋊C4—882no—
248C22⋊C4—41no—
249C22⋊C4—41no—
250C22⋊C4—82no—
251C22⋊C4—82no—
252C22⋊C4—224no—
253C22⋊C4—442no—
254C22⋊C4—442no—
255C22⋊C4—442no—
256C42—21no—
257C42—21no—
258C42—42no—
259C42—882no—
260C11#1329911yescharacteristic, complemented, Sylow
261C23—21no—
262C23—21no—
263C23—21no—
264C23—21no—
265C23—41no—
266C23—41no—
267C23—41no—
268C23—41no—
269C23#6699711yescharacteristic
270C23#6699912yes—
271C23#6700011yescharacteristic
272C23C2×C22⋊Dic1111yescharacteristic
273Q8—84no—
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—42no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—81no—
294C2×C4—81no—
295C2×C4—444no—
296C2×C4—882no—
297C2×C4—882no—
298C2×C4—882no—
299C2×C4—882no—
300C2×C4—882no—
301C2×C4#6689811yescharacteristic
302C2×C4#6689811yescharacteristic
303C2×C4Q8×Dic1112yes—
304C22—21no—
305C22—21no—
306C22—22no—
307C22—21no—
308C22—21no—
309C22—41no—
310C22—42no—
311C22—41no—
312C22—41no—
313C22—41no—
314C22—41no—
315C22—41no—
316C22—81no—
317C22—81no—
318C22C2×#6689811yescharacteristic
319C22#1062284311yescharacteristic
320C22#1062285311yescharacteristic
321C4—22no—
322C4—21no—
323C4—41no—
324C4—41no—
325C4—41no—
326C4—82no—
327C4—82no—
328C4—884no—
329C4—1762no—
330C4#1062217912yes—
331C2—21no—
332C2—21no—
333C2—42no—
334C2—41no—
335C2—41no—
336C2#1306960211yescharacteristic
337C2C2×#1062217911yescharacteristic
338C2#1307028811yescharacteristic
subgroupG/H
centerC22C2×#66898
commutatorC22×C4×C11C22×C4
FrattiniC22×D4C22×D11
FittingC11×#2563C2
socleC22×C11C2×#99
prime radical, cosocleC22×D4×C11C23
hypercenter#2563D11
hypocenterC11#13299
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2563

Complements

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

NH ≅ G/Ntype
5. C2×C11×C4⋊Q8C4semidirect
10. C11×#382C4semidirect
13. C4×C11×C4⋊C4C4semidirect
47. #66898Q8semidirect
139. C2×C4⋊Q8Dic11semidirect
146. #382Dic11semidirect
150. C4×C4⋊C4Dic11semidirect
260. C11#13299semidirect

Maximal subgroups

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

subgroupindex
#130686042
C4×#668982
#130667412
C11×#25632
#1329911