Finite Group Databasebeta

← #14672435

Subgroups — #14672435

Order 2816.

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

normal subgroups only

This group has 616 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#13068608C211yesmaximal, characteristic
2C4×#66898C211yesmaximal, characteristic
3#13066734C214yesmaximal
4C11×#2409C211yesmaximal, characteristic
5C23×Q8×C11C411yescharacteristic, complemented
6C2×C11×C22⋊Q8—21no—
7C2×C4×D4×C11C2211yescharacteristic
8C11×#395—21no—
9C11×#393—21no—
10C11×#391—21no—
11C11×#386C2212yes—
12C11×#385C412yescomplemented
13C11×#380C411yescharacteristic, complemented
14C2×#66898C2212yes—
15C2×#66897C2212yes—
16C4×C22⋊Dic11—21no—
17#10622537—21no—
18#10622168—21no—
19#10622164—21no—
20C22×Q8×C11—21no—
21C22×Q8×C11—21no—
22C22×Q8×C11—41no—
23C22×Q8×C11—41no—
24C22×Q8×C11—44no—
25C22×D4×C11C2311yescharacteristic
26C23×C4×C11C2×C411yescharacteristic
27C23×C4×C11C2×C412yes—
28C23×C4×C11D411yescharacteristic
29C11×C22⋊Q8—44no—
30C4×D4×C11—41no—
31C4×D4×C11—41no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4—22no—
34C2×C11×C4⋊C4D411yescharacteristic
35C2×C11×C22⋊C4—22no—
36C2×C11×C22⋊C4C2×C412yes—
37C2×C11×C22⋊C4C2×C411yescharacteristic
38C2×C11×C22⋊C4D411yescharacteristic
39C2×C42×C11D411yescharacteristic
40C2×C22⋊Dic11—22no—
41C2×C4×Dic11—41no—
42C2×#4318—22no—
43C11×#95—21no—
44C11×#95—22no—
45C11×#95—22no—
46#66898—22no—
47#66898Q814yescomplemented
48#66897—24no—
49C11⋊#95—41no—
50C4⋊(C11⋊C8)—41no—
51C4⋊(C11⋊C8)—41no—
52#13296—111nomaximal, Sylow
53C24×C11C22×C411yescharacteristic
54C24×C11C2×D411yescharacteristic
55C2×Q8×C11—24no—
56C2×Q8×C11—42no—
57C2×Q8×C11—44no—
58C2×Q8×C11—42no—
59C2×Q8×C11—48no—
60C2×Q8×C11—44no—
61C2×Q8×C11—44no—
62C2×Q8×C11—41no—
63C2×Q8×C11—41no—
64C2×D4×C11—41no—
65C2×D4×C11—41no—
66C2×D4×C11C2×Q812yes—
67C2×D4×C11#4112yes—
68C22×C4×C11—22no—
69C22×C4×C11—21no—
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11—21no—
73C22×C4×C11—22no—
74C22×C4×C11—42no—
75C22×C4×C11—44no—
76C22×C4×C11—42no—
77C22×C4×C11—42no—
78C22×C4×C11C22⋊C411yescharacteristic
79C22×C4×C11C22⋊C411yescharacteristic
80C22×C4×C11C22⋊C411yescharacteristic
81C22×C4×C11C22⋊C411yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C22×Dic11—42no—
84C11×C4⋊C4—41no—
85C11×C4⋊C4—42no—
86C11×C4⋊C4—44no—
87C11×C22⋊C4—41no—
88C11×C22⋊C4—41no—
89C11×C22⋊C4—44no—
90C11×C22⋊C4—42no—
91C42×C11—21no—
92C42×C11—21no—
93C22⋊Dic11—24no—
94C22⋊Dic11—42no—
95C4×Dic11—82no—
96#4318—42no—
97#4318—42no—
98C2×C11⋊C8—42no—
99#2409D1111yescharacteristic
100#1800—111no—
101C4×#99—111no—
102#1390—114no—
103C23×C11—21no—
104C23×C11—21no—
105C23×C11—21no—
106C23×C11—21no—
107C23×C11—41no—
108C23×C11—41no—
109C23×C11—41no—
110C23×C11—41no—
111C23×C11C2×C22⋊C411yescharacteristic
112C23×C11C4×Q812yes—
113C23×C11C22⋊Q812yes—
114Q8×C11—44no—
115Q8×C11—48no—
116Q8×C11—44no—
117D4×C11—42no—
118D4×C11—42no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—22no—
122C2×C4×C11—24no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—42no—
127C2×C4×C11—42no—
128C2×C4×C11—44no—
129C2×C4×C11—42no—
130C2×C4×C11—42no—
131C2×C4×C11—42no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—44no—
136C2×C4×C11—42no—
137C2×C4×C11—42no—
138C2×C4×C11—42no—
139C2×C4×C11—81no—
140C2×C4×C11#9911yescharacteristic
141C2×C4×C11#9911yescharacteristic
142C2×C4×C11#12411yescharacteristic
143C2×C4×C11C4⋊Q811yescharacteristic
144C2×Dic11—44no—
145C2×Dic11—82no—
146C2×Dic11—82no—
147C11⋊C8—82no—
148C23×Q8Dic1111yescharacteristic, complemented
149C2×C22⋊Q8—21no—
150C2×C4×D4C2×D1111yescharacteristic
151#423—221no—
152C2×#100—112no—
153C2×#99—112no—
154#395—21no—
155#393—21no—
156#391—21no—
157#386C2×D1112yes—
158#385Dic1112yescomplemented
159#380Dic1111yescharacteristic, complemented
160C4×C22⋊C4—221no—
161#343—221no—
162#342—221no—
163C22×C11—21no—
164C22×C11—21no—
165C22×C11—22no—
166C22×C11—22no—
167C22×C11—42no—
168C22×C11—42no—
169C22×C11—42no—
170C22×C11—41no—
171C22×C11—41no—
172C22×C11—41no—
173C22×C11—41no—
174C22×C11—81no—
175C22×C11#39111yescharacteristic
176C22×C11C2×#9911yescharacteristic
177C22×C11#41011yescharacteristic
178C4×C11—21no—
179C4×C11—21no—
180C4×C11—21no—
181C4×C11—44no—
182C4×C11—41no—
183C4×C11—41no—
184C4×C11—41no—
185C4×C11—82no—
186C4×C11AΣL(1,𝔽16)12yes—
187Dic11—84no—
188C22×Q8—21no—
189C22×Q8—21no—
190C22×Q8—41no—
191C22×Q8—41no—
192C22×Q8—44no—
193C22×D4C22×D1111yescharacteristic
194C23×C4C2×Dic1111yescharacteristic
195C23×C4C2×Dic1112yes—
196C23×C4C22⋊D1111yescharacteristic
197C2×M16—222no—
198C22⋊Q8—44no—
199C4×D4—41no—
200C4×D4—41no—
201C2×C4⋊C4—22no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4C22⋊D1111yescharacteristic
204C2×C22⋊C4—22no—
205C2×C22⋊C4—222no—
206C2×C22⋊C4C2×Dic1112yes—
207C2×C22⋊C4C2×Dic1111yescharacteristic
208C2×C22⋊C4C22⋊D1111yescharacteristic
209C2×C42—441no—
210C2×C42C22⋊D1111yescharacteristic
211C4⋊C8—441no—
212C4⋊C8—441no—
213#100—224no—
214#99—114no—
215#99—222no—
216#95—21no—
217#95—22no—
218#95—22no—
219#95—441no—
220C2×C11—21no—
221C2×C11—21no—
222C2×C11—42no—
223C2×C11—42no—
224C2×C11#199611yescharacteristic
225C2×C11C2×AΣL(1,𝔽16)11yescharacteristic
226C2×C11#212311yescharacteristic
227C24C22×Dic1111yescharacteristic
228C24C2×C22⋊D1111yescharacteristic
229C2×Q8—24no—
230C2×Q8—42no—
231C2×Q8—44no—
232C2×Q8—42no—
233C2×Q8—44no—
234C2×Q8—48no—
235C2×Q8—44no—
236C2×Q8—41no—
237C2×Q8—41no—
238C2×D4—41no—
239C2×D4—41no—
240C2×D4Q8×D1112yes—
241C2×D4#434312yes—
242C22×C4—22no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—22no—
248C22×C4—42no—
249C22×C4—44no—
250C22×C4—42no—
251C22×C4—42no—
252C22×C4—442no—
253C22×C4C22⋊Dic1111yescharacteristic
254C22×C4C22⋊Dic1111yescharacteristic
255C22×C4C22⋊Dic1111yescharacteristic
256C22×C4C22⋊Dic1111yescharacteristic
257C22×C4C2×C22⋊D1111yescharacteristic
258M16—442no—
259M16—442no—
260C2×C8—442no—
261C4⋊C4—41no—
262C4⋊C4—42no—
263C4⋊C4—44no—
264C22⋊C4—41no—
265C22⋊C4—41no—
266C22⋊C4—44no—
267C22⋊C4—42no—
268C22⋊C4—224no—
269C22⋊C4—442no—
270C42—21no—
271C42—21no—
272C42—882no—
273C11#1329611yescharacteristic, complemented, Sylow
274C23—21no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23—41no—
279C23—41no—
280C23—41no—
281C23—41no—
282C23Q8×Dic1112yes—
283C23#6699912yes—
284C23C2×C22⋊Dic1111yescharacteristic
285Q8—44no—
286Q8—48no—
287Q8—44no—
288D4—42no—
289D4—42no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—22no—
293C2×C4—24no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—42no—
298C2×C4—42no—
299C2×C4—44no—
300C2×C4—42no—
301C2×C4—42no—
302C2×C4—42no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—44no—
307C2×C4—42no—
308C2×C4—42no—
309C2×C4—42no—
310C2×C4—81no—
311C2×C4—444no—
312C2×C4—882no—
313C2×C4—882no—
314C2×C4#6689811yescharacteristic
315C2×C4#6689811yescharacteristic
316C2×C4#6699711yescharacteristic
317C2×C4#6700011yescharacteristic
318C8—882no—
319C22—21no—
320C22—21no—
321C22—22no—
322C22—22no—
323C22—42no—
324C22—42no—
325C22—42no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—81no—
331C22C2×#6689811yescharacteristic
332C22#1062284311yescharacteristic
333C22#1062285311yescharacteristic
334C4—21no—
335C4—21no—
336C4—21no—
337C4—44no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4—82no—
342C4—884no—
343C4#1062217412yes—
344C2—21no—
345C2—21no—
346C2—42no—
347C2—42no—
348C2#1306960211yescharacteristic
349C2C2×#1062217411yescharacteristic
350C2#1307027011yescharacteristic
subgroupG/H
centerC22C2×#66898
commutatorC24×C11C22×C4
FrattiniC22×D4C22×D11
FittingC11×#2409C2
socleC22×C11C2×#99
prime radical, cosocleC22×D4×C11C23
hypercenter#2409D11
hypocenterC11#13296
LCSG ▷ C24×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2409

Complements

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

NH ≅ G/Ntype
5. C23×Q8×C11C4semidirect
12. C11×#385C4semidirect
13. C11×#380C4semidirect
47. #66898Q8semidirect
148. C23×Q8Dic11semidirect
158. #385Dic11semidirect
159. #380Dic11semidirect
273. C11#13296semidirect

Maximal subgroups

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

subgroupindex
#130686082
C4×#668982
#130667342
C11×#24092
#1329611