Finite Group Databasebeta

← #14669404

Subgroups — #14669404

Order 2816.

714 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 714 conjugacy classes of subgroups — too many to draw. Only its 127 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#13070285C212yesmaximal
2C2×#10622179C212yesmaximal, complemented
3#13068724C212yesmaximal, complemented
4C11×#3510C211yesmaximal, characteristic
5C11×#559—22no—
6C11×#556—22no—
7C11×#551—24no—
8C11×#542—22no—
9C11×#536C411yescharacteristic, complemented
10C11×#535C2211yescharacteristic
11C11×#533C411yescharacteristic, complemented
12C11×#529—22no—
13C2×C11×#124C2211yescharacteristic
14C11×#519C411yescharacteristic, complemented
15C11×#518C2211yescharacteristic
16C4×C11×#41C411yescharacteristic, complemented
17C2×#66898C2214yes—
18#10622183—22no—
19#10622179—22no—
20#10622179—22no—
21#10622179—22no—
22#10622165—24no—
23C2×C11×#41C2×C411yescharacteristic
24C22×Q8×C11C2×C411yescharacteristic
25C22×D4×C11C2311yescharacteristic
26C11×C4⋊Q8—21no—
27C11×C4⋊Q8—21no—
28C11×#127D412yes—
29C11×#126—24no—
30C11×#126—24no—
31C11×#125—21no—
32C11×#124—24no—
33C11×#124—21no—
34C11×#124—22no—
35C11×#124D412yes—
36C11×#124D412yes—
37C11×#124D412yes—
38C11×#123—24no—
39C11×#123—24no—
40C11×#123—22no—
41C11×C22⋊Q8—24no—
42C11×C22⋊Q8—22no—
43C11×C22⋊Q8—22no—
44C11×#121—22no—
45C11×#120—22no—
46C4×Q8×C11—21no—
47C4×Q8×C11—22no—
48C4×Q8×C11—22no—
49C4×Q8×C11—22no—
50C4×D4×C11—24no—
51C4×D4×C11—21no—
52C4×D4×C11—22no—
53C4×D4×C11—22no—
54C4×D4×C11—22no—
55C11×#117—24no—
56C11×#117—22no—
57C11×#117—21no—
58C11×#117C2×C411yescharacteristic
59C11×#117C2×C411yescharacteristic
60C11×#117C2×C411yescharacteristic
61C2×C11×C22⋊C4—22no—
62C2×C11×C22⋊C4D414yes—
63C2×C42×C11—21no—
64C2×C42×C11C2×C411yescharacteristic
65C2×C22⋊Dic11—24no—
66#66898—24no—
67#66898—24no—
68#12728—111nomaximal, Sylow
69C24×C11C2×D412yes—
70C11×#41—42no—
71C2×Q8×C11—22no—
72C2×Q8×C11—21no—
73C2×Q8×C11—42no—
74C2×Q8×C11C22⋊C412yes—
75C2×Q8×C11C22⋊C411yescharacteristic
76C2×D4×C11—21no—
77C2×D4×C11—24no—
78C2×D4×C11—42no—
79C2×D4×C11C22⋊C411yescharacteristic
80C2×D4×C11C2×D412yes—
81C2×D4×C11C2×D412yes—
82C22×C4×C11—21no—
83C22×C4×C11—22no—
84C22×C4×C11—21no—
85C22×C4×C11—24no—
86C22×C4×C11—21no—
87C22×C4×C11C22×C411yescharacteristic
88C22×Dic11—44no—
89C11×C4⋊C4—22no—
90C11×C4⋊C4—22no—
91C11×C4⋊C4—24no—
92C11×C4⋊C4—24no—
93C11×C4⋊C4—22no—
94C11×C4⋊C4—22no—
95C11×C4⋊C4—21no—
96C11×C4⋊C4—21no—
97C11×C4⋊C4—21no—
98C11×C22⋊C4—22no—
99C11×C22⋊C4—24no—
100C11×C22⋊C4—21no—
101C11×C22⋊C4—24no—
102C11×C22⋊C4—24no—
103C11×C22⋊C4—24no—
104C11×C22⋊C4—24no—
105C11×C22⋊C4C22⋊C412yes—
106C11×C22⋊C4C22⋊C412yes—
107C42×C11—22no—
108C42×C11—24no—
109C42×C11—21no—
110C42×C11—21no—
111C42×C11—21no—
112C42×C11C22⋊C411yescharacteristic
113C42×C11C22⋊C411yescharacteristic
114C42×C11C22⋊C412yes—
115C22⋊Dic11—44no—
116C22⋊Dic11—44no—
117#3510D1111yescharacteristic
118#2127—112no—
119C2×#354—112no—
120#1828—112no—
121C23×C11—24no—
122C23×C11—21no—
123C23×C11—82no—
124C23×C11C2×C22⋊C411yescharacteristic
125C23×C11#12014yes—
126Q8×C11—42no—
127Q8×C11—41no—
128Q8×C11—42no—
129Q8×C11—82no—
130D4×C11—42no—
131D4×C11—42no—
132D4×C11—41no—
133D4×C11—42no—
134D4×C11—84no—
135C2×C4×C11—22no—
136C2×C4×C11—22no—
137C2×C4×C11—21no—
138C2×C4×C11—22no—
139C2×C4×C11—22no—
140C2×C4×C11—21no—
141C2×C4×C11—21no—
142C2×C4×C11—22no—
143C2×C4×C11—42no—
144C2×C4×C11—42no—
145C2×C4×C11—82no—
146C2×C4×C11—84no—
147C2×C4×C11—81no—
148C2×C4×C11C2×C22⋊C411yescharacteristic
149C2×C4×C11C2×C22⋊C411yescharacteristic
150C2×Dic11—84no—
151C2×Dic11—164no—
152#559—22no—
153#556—22no—
154#551—24no—
155#542—22no—
156#536Dic1111yescharacteristic, complemented
157#535C2×D1111yescharacteristic
158#533Dic1111yescharacteristic, complemented
159#529—22no—
160C2×#124C2×D1111yescharacteristic
161#519Dic1111yescharacteristic, complemented
162#518C2×D1111yescharacteristic
163C4×#41Dic1111yescharacteristic, complemented
164C2×#99—114no—
165#354—222no—
166#354—222no—
167#354—222no—
168#353—222no—
169#342—224no—
170C22×C11—24no—
171C22×C11—41no—
172C22×C11—44no—
173C22×C11—42no—
174C22×C11—41no—
175C22×C11—84no—
176C22×C11#37911yescharacteristic
177C22×C11#41012yes—
178C4×C11—21no—
179C4×C11—21no—
180C4×C11—42no—
181C4×C11—41no—
182C4×C11—42no—
183C4×C11—41no—
184C4×C11—42no—
185C4×C11—41no—
186C4×C11—42no—
187Dic11—164no—
188C2×#41C2×Dic1111yescharacteristic
189C22×Q8C2×Dic1111yescharacteristic
190C22×D4C22×D1111yescharacteristic
191C4⋊Q8—21no—
192C4⋊Q8—21no—
193#127C22⋊D1112yes—
194#126—24no—
195#126—24no—
196#125—21no—
197#124—24no—
198#124—21no—
199#124—22no—
200#124C22⋊D1112yes—
201#124C22⋊D1112yes—
202#124C22⋊D1112yes—
203#123—24no—
204#123—24no—
205#123—22no—
206C22⋊Q8—24no—
207C22⋊Q8—22no—
208C22⋊Q8—22no—
209#121—22no—
210#120—22no—
211C4×Q8—21no—
212C4×Q8—22no—
213C4×Q8—22no—
214C4×Q8—22no—
215C4×D4—24no—
216C4×D4—21no—
217C4×D4—22no—
218C4×D4—22no—
219C4×D4—22no—
220#117—24no—
221#117—22no—
222#117—21no—
223#117C2×Dic1111yescharacteristic
224#117C2×Dic1111yescharacteristic
225#117C2×Dic1111yescharacteristic
226C2×C22⋊C4—22no—
227C2×C22⋊C4—224no—
228C2×C22⋊C4C22⋊D1114yes—
229C2×C42—21no—
230C2×C42C2×Dic1111yescharacteristic
231#99—224no—
232#99—224no—
233C2×C11—21no—
234C2×C11—22no—
235C2×C11—44no—
236C2×C11—81no—
237C2×C11#178211yescharacteristic
238C24C2×C22⋊D1112yes—
239#41—42no—
240C2×Q8—22no—
241C2×Q8—21no—
242C2×Q8—42no—
243C2×Q8C22⋊Dic1112yes—
244C2×Q8C22⋊Dic1111yescharacteristic
245C2×D4—21no—
246C2×D4—24no—
247C2×D4—42no—
248C2×D4C22⋊Dic1111yescharacteristic
249C2×D4C2×C22⋊D1112yes—
250C2×D4C2×C22⋊D1112yes—
251C22×C4—21no—
252C22×C4—22no—
253C22×C4—21no—
254C22×C4—24no—
255C22×C4—21no—
256C22×C4—444no—
257C22×C4C22×Dic1111yescharacteristic
258C4⋊C4—22no—
259C4⋊C4—22no—
260C4⋊C4—24no—
261C4⋊C4—24no—
262C4⋊C4—22no—
263C4⋊C4—22no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C22⋊C4—22no—
268C22⋊C4—24no—
269C22⋊C4—21no—
270C22⋊C4—24no—
271C22⋊C4—24no—
272C22⋊C4—24no—
273C22⋊C4—24no—
274C22⋊C4—444no—
275C22⋊C4—444no—
276C22⋊C4C22⋊Dic1112yes—
277C22⋊C4C22⋊Dic1112yes—
278C42—22no—
279C42—24no—
280C42—21no—
281C42—21no—
282C42—21no—
283C42C22⋊Dic1111yescharacteristic
284C42C22⋊Dic1111yescharacteristic
285C42C22⋊Dic1112yes—
286C11#1272811yescharacteristic, complemented, Sylow
287C23—24no—
288C23—21no—
289C23—82no—
290C23C2×C22⋊Dic1111yescharacteristic
291C23#6700614yes—
292Q8—42no—
293Q8—41no—
294Q8—42no—
295Q8—82no—
296D4—42no—
297D4—42no—
298D4—41no—
299D4—42no—
300D4—84no—
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—21no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—22no—
309C2×C4—42no—
310C2×C4—42no—
311C2×C4—82no—
312C2×C4—84no—
313C2×C4—81no—
314C2×C4—884no—
315C2×C4—1764no—
316C2×C4C2×C22⋊Dic1111yescharacteristic
317C2×C4C2×C22⋊Dic1111yescharacteristic
318C22—24no—
319C22—41no—
320C22—44no—
321C22—42no—
322C22—41no—
323C22—84no—
324C22#1062285312yes—
325C22#1062286011yescharacteristic
326C4—21no—
327C4—21no—
328C4—42no—
329C4—41no—
330C4—42no—
331C4—41no—
332C4—42no—
333C4—41no—
334C4—42no—
335C4—1764no—
336C2—21no—
337C2—22no—
338C2—44no—
339C2—81no—
340C2#1306853411yescharacteristic
subgroupG/H
centerC2#13068534
commutatorC22×C4×C11C22×C4
FrattiniC22×D4C22×D11
FittingC11×#3510C2
socleC2×C11#1782
prime radicalC11×#535C22
cosocleC22×D4×C11C23
hypercenter#3510D11
hypocenterC11#12728
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C23 ◁ #518 ◁ #3510

Complements

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

NH ≅ G/Ntype
2. C2×#10622179C2semidirect
3. #13068724C2semidirect
9. C11×#536C4semidirect
11. C11×#533C4semidirect
14. C11×#519C4semidirect
16. C4×C11×#41C4semidirect
156. #536Dic11semidirect
158. #533Dic11semidirect
161. #519Dic11semidirect
163. C4×#41Dic11semidirect
286. C11#12728semidirect

Maximal subgroups

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

subgroupindex
#130702852
C2×#106221792
#130687242
C11×#35102
#1272811