Finite Group Databasebeta

← #14672087

Subgroups — #14672087

Order 2816.

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

normal subgroups only

This group has 552 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
1C2×#10622179C214yesmaximal
2#13068604C211yesmaximal, characteristic
3C4×#66898C211yesmaximal, characteristic
4C11×#2547C211yesmaximal, characteristic
5C2×C11×C4⋊Q8C411yescharacteristic, complemented
6C2×C11×#124C2212yes—
7C2×C4×D4×C11C2211yescharacteristic
8C11×#397—21no—
9C11×#397—21no—
10C11×#391C412yescomplemented
11C11×#380—21no—
12C11×#380—21no—
13C4×C11×C4⋊C4C411yescharacteristic, complemented
14C2×#66898C2212yes—
15C2×#66898C2212yes—
16#10622825—21no—
17C4×C22⋊Dic11—21no—
18#10622179—28no—
19#10622164—21no—
20#10622164—21no—
21C22×Q8×C11C2×C412yes—
22C22×D4×C11C2311yescharacteristic
23C23×C4×C11D411yescharacteristic
24C23×C4×C11D411yescharacteristic
25C11×C4⋊Q8—41no—
26C11×C4⋊Q8—41no—
27C11×#124—24no—
28C11×#124—24no—
29C4×D4×C11—41no—
30C4×D4×C11—41no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4C2×C411yescharacteristic
35C2×C11×C22⋊C4—22no—
36C2×C11×C22⋊C4—22no—
37C2×C11×C22⋊C4D411yescharacteristic
38C2×C11×C22⋊C4D411yescharacteristic
39C2×C42×C11C2×C412yes—
40C2×C42×C11C2×C411yescharacteristic
41C2×C22⋊Dic11—22no—
42C2×C22⋊Dic11—22no—
43C2×C4⋊Dic11—41no—
44C2×C4×Dic11—41no—
45C11×#95—21no—
46C11×#95—22no—
47C11×#95—22no—
48#66898—22no—
49#66898—24no—
50#66898D414yes—
51C11⋊#95—41no—
52C11⋊#95—41no—
53#13224—111nomaximal, Sylow
54C24×C11C2×D411yescharacteristic
55C24×C11C2×D411yescharacteristic
56C2×Q8×C11—24no—
57C2×Q8×C11—42no—
58C2×Q8×C11—42no—
59C2×D4×C11—41no—
60C2×D4×C11—41no—
61C2×D4×C11C2×D412yes—
62C2×D4×C11#4112yes—
63C22×C4×C11—21no—
64C22×C4×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11—22no—
68C22×C4×C11—22no—
69C22×C4×C11—42no—
70C22×C4×C11—42no—
71C22×C4×C11C22⋊C411yescharacteristic
72C22×C4×C11C22⋊C411yescharacteristic
73C22×C4×C11C22⋊C411yescharacteristic
74C22×C4×C11C22⋊C411yescharacteristic
75C22×C4×C11C22×C411yescharacteristic
76C22×Dic11—42no—
77C22×Dic11—42no—
78C11×C4⋊C4—41no—
79C11×C4⋊C4—42no—
80C11×C4⋊C4—42no—
81C11×C4⋊C4—41no—
82C11×C4⋊C4—41no—
83C11×C22⋊C4—41no—
84C11×C22⋊C4—41no—
85C11×C22⋊C4—44no—
86C11×C22⋊C4—42no—
87C11×C22⋊C4—42no—
88C42×C11—21no—
89C42×C11—21no—
90C42×C11—24no—
91C22⋊Dic11—24no—
92C22⋊Dic11—42no—
93C22⋊Dic11—42no—
94C22⋊Dic11—42no—
95C4⋊Dic11—82no—
96C4×Dic11—82no—
97#2547D1111yescharacteristic
98C2×#354—114no—
99#1799—111no—
100C4×#99—111no—
101C23×C11—21no—
102C23×C11—21no—
103C23×C11—21no—
104C23×C11—21no—
105C23×C11—41no—
106C23×C11—41no—
107C23×C11—41no—
108C23×C11—41no—
109C23×C11C2×C22⋊C411yescharacteristic
110C23×C11#12112yes—
111C23×C11#12411yescharacteristic
112C23×C11#12711yescharacteristic
113Q8×C11—84no—
114D4×C11—42no—
115D4×C11—42no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—22no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—42no—
123C2×C4×C11—42no—
124C2×C4×C11—41no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11—42no—
128C2×C4×C11—42no—
129C2×C4×C11—42no—
130C2×C4×C11—42no—
131C2×C4×C11—42no—
132C2×C4×C11—42no—
133C2×C4×C11—81no—
134C2×C4×C11—81no—
135C2×C4×C11#9911yescharacteristic
136C2×C4×C11#9911yescharacteristic
137C2×C4×C11C4×D412yes—
138C2×Dic11—44no—
139C2×Dic11—82no—
140C2×Dic11—82no—
141C2×Dic11—82no—
142C2×Dic11—82no—
143C2×Dic11—82no—
144C2×C4⋊Q8Dic1111yescharacteristic, complemented
145C2×#124C2×D1112yes—
146C2×C4×D4C2×D1111yescharacteristic
147C2×#99—112no—
148C2×#99—112no—
149#397—21no—
150#397—21no—
151#391Dic1112yescomplemented
152#380—21no—
153#380—21no—
154#380—221no—
155C4×C4⋊C4Dic1111yescharacteristic, complemented
156C4×C22⋊C4—221no—
157#354—228no—
158#342—221no—
159#342—221no—
160C22×C11—21no—
161C22×C11—21no—
162C22×C11—22no—
163C22×C11—21no—
164C22×C11—21no—
165C22×C11—42no—
166C22×C11—41no—
167C22×C11—41no—
168C22×C11—41no—
169C22×C11—41no—
170C22×C11—41no—
171C22×C11—41no—
172C22×C11—81no—
173C22×C11—81no—
174C22×C11#39011yescharacteristic
175C22×C11C2×#9911yescharacteristic
176C22×C11#41011yescharacteristic
177C4×C11—21no—
178C4×C11—22no—
179C4×C11—41no—
180C4×C11—41no—
181C4×C11—41no—
182C4×C11—82no—
183C4×C11—82no—
184C4×C11#35412yescomplemented
185Dic11—84no—
186Dic11—162no—
187C22×Q8C2×Dic1112yes—
188C22×D4C22×D1111yescharacteristic
189C23×C4C22⋊D1111yescharacteristic
190C23×C4C22⋊D1111yescharacteristic
191C4⋊Q8—41no—
192C4⋊Q8—41no—
193#124—24no—
194#124—24no—
195C4×D4—41no—
196C4×D4—41no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—441no—
201C2×C4⋊C4C2×Dic1111yescharacteristic
202C2×C22⋊C4—22no—
203C2×C22⋊C4—22no—
204C2×C22⋊C4—222no—
205C2×C22⋊C4—222no—
206C2×C22⋊C4C22⋊D1111yescharacteristic
207C2×C22⋊C4C22⋊D1111yescharacteristic
208C2×C42—441no—
209C2×C42C2×Dic1112yes—
210C2×C42C2×Dic1111yescharacteristic
211#99—114no—
212#99—222no—
213#99—224no—
214#95—21no—
215#95—22no—
216#95—22no—
217#95—441no—
218#95—441no—
219C2×C11—21no—
220C2×C11—21no—
221C2×C11—42no—
222C2×C11—41no—
223C2×C11—41no—
224C2×C11#196411yescharacteristic
225C2×C11C2×#35411yescharacteristic
226C2×C11#212911yescharacteristic
227C24C2×C22⋊D1111yescharacteristic
228C24C2×C22⋊D1111yescharacteristic
229C2×Q8—24no—
230C2×Q8—42no—
231C2×Q8—42no—
232C2×D4—41no—
233C2×D4—41no—
234C2×D4D4×D1112yes—
235C2×D4#434112yes—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—22no—
241C22×C4—22no—
242C22×C4—42no—
243C22×C4—42no—
244C22×C4—442no—
245C22×C4—442no—
246C22×C4C22⋊Dic1111yescharacteristic
247C22×C4C22⋊Dic1111yescharacteristic
248C22×C4C22⋊Dic1111yescharacteristic
249C22×C4C22⋊Dic1111yescharacteristic
250C22×C4C22×Dic1111yescharacteristic
251C4⋊C4—41no—
252C4⋊C4—42no—
253C4⋊C4—42no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—882no—
257C22⋊C4—41no—
258C22⋊C4—41no—
259C22⋊C4—42no—
260C22⋊C4—44no—
261C22⋊C4—42no—
262C22⋊C4—224no—
263C22⋊C4—442no—
264C22⋊C4—442no—
265C22⋊C4—442no—
266C42—21no—
267C42—21no—
268C42—24no—
269C42—882no—
270C11#1322411yescharacteristic, complemented, Sylow
271C23—21no—
272C23—21no—
273C23—21no—
274C23—21no—
275C23—41no—
276C23—41no—
277C23—41no—
278C23—41no—
279C23#6698911yescharacteristic
280C23#6699112yes—
281C23#6699311yescharacteristic
282C23C2×C22⋊Dic1111yescharacteristic
283Q8—84no—
284D4—42no—
285D4—42no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—22no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—42no—
293C2×C4—42no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—42no—
298C2×C4—42no—
299C2×C4—42no—
300C2×C4—42no—
301C2×C4—42no—
302C2×C4—42no—
303C2×C4—81no—
304C2×C4—81no—
305C2×C4—444no—
306C2×C4—882no—
307C2×C4—882no—
308C2×C4—882no—
309C2×C4—882no—
310C2×C4—882no—
311C2×C4#6689811yescharacteristic
312C2×C4#6689811yescharacteristic
313C2×C4D4×Dic1112yes—
314C22—21no—
315C22—21no—
316C22—22no—
317C22—21no—
318C22—21no—
319C22—41no—
320C22—42no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—81no—
327C22—81no—
328C22C2×#6689811yescharacteristic
329C22#1062283411yescharacteristic
330C22#1062285311yescharacteristic
331C4—22no—
332C4—21no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—82no—
337C4—82no—
338C4—884no—
339C4—1762no—
340C4#1062217912yescomplemented
341C2—21no—
342C2—21no—
343C2—42no—
344C2—41no—
345C2—41no—
346C2#1306945311yescharacteristic
347C2C2×#1062217911yescharacteristic
348C2#1307029111yescharacteristic
subgroupG/H
centerC22C2×#66898
commutatorC22×C4×C11C22×C4
FrattiniC22×D4C22×D11
FittingC11×#2547C2
socleC22×C11C2×#99
prime radical, cosocleC22×D4×C11C23
hypercenter#2547D11
hypocenterC11#13224
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2547

Complements

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

NH ≅ G/Ntype
5. C2×C11×C4⋊Q8C4semidirect
10. C11×#391C4semidirect
13. C4×C11×C4⋊C4C4semidirect
144. C2×C4⋊Q8Dic11semidirect
151. #391Dic11semidirect
155. C4×C4⋊C4Dic11semidirect
184. C4×C11#354semidirect
270. C11#13224semidirect
340. C4#10622179semidirect

Maximal subgroups

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

subgroupindex
C2×#106221792
#130686042
C4×#668982
C11×#25472
#1322411