Finite Group Databasebeta

← #14672434

Subgroups — #14672434

Order 2816.

616 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 616 conjugacy classes of subgroups — too many to draw. Only its 107 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#13071981C211yesmaximal, characteristic
2#13068608C211yesmaximal, characteristic
3#13066733C214yesmaximal
4C4×C11×#99C211yesmaximal, characteristic
5C23×Dic22C411yescharacteristic, complemented
6C2×C4×D4×C11C2211yescharacteristic
7C2×#66977—21no—
8C2×C11×#99C2212yes—
9C4×C11×C22⋊C4—21no—
10#10622833C2212yes—
11C2×#66897C2212yes—
12#10622825C411yescharacteristic, complemented
13#10622592—21no—
14#10622560—21no—
15#10622559C412yescomplemented
16#10622542—21no—
17#10622537—21no—
18C11×#342—21no—
19#10622168—21no—
20C22×D4×C11C2311yescharacteristic
21C23×C4×C11C2×C411yescharacteristic
22C23×C4×C11D411yescharacteristic
23C23×Dic11C2×C412yes—
24C22×Dic22—21no—
25C22×Dic22—21no—
26C22×Dic22—44no—
27C22×Dic22—41no—
28C22×Dic22—41no—
29C4×D4×C11—41no—
30C4×D4×C11—41no—
31C2×C11×C4⋊C4D411yescharacteristic
32C2×C11×C22⋊C4—22no—
33C2×C11×C22⋊C4C2×C411yescharacteristic
34C2×C11×C22⋊C4D411yescharacteristic
35C2×C42×C11—41no—
36C2×C42×C11D411yescharacteristic
37C2×C22⋊Dic11—22no—
38C2×C22⋊Dic11C2×C412yes—
39C2×C4⋊Dic11—21no—
40#66977—44no—
41C2×Dic11⋊C4—22no—
42C2×#4318—22no—
43C11×#99—22no—
44C11×#99Q814yescomplemented
45C11×#95—41no—
46#66897—24no—
47C11⋊#95—22no—
48C11⋊#95—21no—
49C11⋊#95—22no—
50C4⋊(C11⋊C8)—41no—
51C4⋊(C11⋊C8)—41no—
52#13296—111nomaximal, Sylow
53C24×C11C22×C411yescharacteristic
54C24×C11C2×D411yescharacteristic
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—42no—
64C22×C4×C11—42no—
65C22×C4×C11—42no—
66C22×C4×C11C22⋊C411yescharacteristic
67C22×C4×C11C22⋊C411yescharacteristic
68C22×C4×C11C22⋊C411yescharacteristic
69C22×C4×C11C22⋊C411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C22×Dic11—22no—
72C22×Dic11—22no—
73C22×Dic11—42no—
74C22×Dic11—44no—
75C2×Dic22—24no—
76C2×Dic22—42no—
77C2×Dic22—42no—
78C2×Dic22—44no—
79C2×Dic22—48no—
80C2×Dic22—44no—
81C2×Dic22—44no—
82C2×Dic22—41no—
83C2×Dic22—41no—
84C11×C4⋊C4—41no—
85C11×C22⋊C4—24no—
86C11×C22⋊C4—41no—
87C11×C22⋊C4—41no—
88C11×C22⋊C4—42no—
89C42×C11—21no—
90C42×C11—21no—
91C42×C11—82no—
92C22⋊Dic11—42no—
93C22⋊Dic11—44no—
94C4⋊Dic11—42no—
95Dic11⋊C4—44no—
96#4318—42no—
97#4318—42no—
98C2×C11⋊C8—42no—
99#2409—111no—
100#1800—111no—
101C4×#99D1111yescharacteristic
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—
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—42no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11—44no—
129C2×C4×C11—81no—
130C2×C4×C11—82no—
131C2×C4×C11—82no—
132C2×C4×C11#9911yescharacteristic
133C2×C4×C11#9911yescharacteristic
134C2×C4×C11#12411yescharacteristic
135C2×C4×C11C4⋊Q811yescharacteristic
136C2×Dic11—24no—
137C2×Dic11—42no—
138C2×Dic11—44no—
139C2×Dic11—42no—
140C2×Dic11—44no—
141C2×Dic11—42no—
142C2×Dic11—42no—
143C2×Dic11—42no—
144Dic22—44no—
145Dic22—48no—
146Dic22—44no—
147C11⋊C8—82no—
148C23×Q8—111no—
149C2×C22⋊Q8—221no—
150C2×C4×D4C2×D1111yescharacteristic
151#423—221no—
152C2×#100—112no—
153C2×#99C2×D1112yes—
154#395—221no—
155#393—221no—
156#391—221no—
157#386—112no—
158#385—112no—
159#380—111no—
160C4×C22⋊C4—21no—
161#343—221no—
162#342—21no—
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—41no—
182C4×C11—41no—
183C4×C11—41no—
184C4×C11—84no—
185C4×C11AΣL(1,𝔽16)12yes—
186Dic11—44no—
187Dic11—82no—
188C22×Q8—221no—
189C22×Q8—221no—
190C22×Q8—441no—
191C22×Q8—441no—
192C22×Q8—444no—
193C22×D4C22×D1111yescharacteristic
194C23×C4—112no—
195C23×C4C4×D1111yescharacteristic
196C23×C4C22⋊D1111yescharacteristic
197C2×M16—222no—
198C22⋊Q8—444no—
199C4×D4—41no—
200C4×D4—41no—
201C2×C4⋊C4—222no—
202C2×C4⋊C4—221no—
203C2×C4⋊C4D4411yescharacteristic
204C2×C22⋊C4—22no—
205C2×C22⋊C4—112no—
206C2×C22⋊C4—222no—
207C2×C22⋊C4C4×D1111yescharacteristic
208C2×C22⋊C4C22⋊D1111yescharacteristic
209C2×C42—41no—
210C2×C42D4411yescharacteristic
211C4⋊C8—441no—
212C4⋊C8—441no—
213#100—224no—
214#99—22no—
215#99Dic2214yescomplemented
216#95—41no—
217#95—221no—
218#95—222no—
219#95—222no—
220C2×C11—21no—
221C2×C11—21no—
222C2×C11—42no—
223C2×C11—42no—
224C2×C11#199611yescharacteristic
225C2×C11C2×AΣL(1,𝔽16)11yescharacteristic
226C2×C11#212311yescharacteristic
227C24C2×C4×D1111yescharacteristic
228C24C2×C22⋊D1111yescharacteristic
229C2×Q8—224no—
230C2×Q8—442no—
231C2×Q8—442no—
232C2×Q8—444no—
233C2×Q8—444no—
234C2×Q8—448no—
235C2×Q8—444no—
236C2×Q8—441no—
237C2×Q8—441no—
238C2×D4—41no—
239C2×D4—41no—
240C2×D4C2×Dic2212yes—
241C2×D4#433912yes—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—42no—
247C22×C4—42no—
248C22×C4—42no—
249C22×C4—222no—
250C22×C4—222no—
251C22×C4—444no—
252C22×C4—442no—
253C22×C4(C2×D11)⋊C411yescharacteristic
254C22×C4(C2×D11)⋊C411yescharacteristic
255C22×C4(C2×D11)⋊C411yescharacteristic
256C22×C4(C2×D11)⋊C411yescharacteristic
257C22×C4C2×D4411yescharacteristic
258M16—442no—
259M16—442no—
260C2×C8—442no—
261C4⋊C4—41no—
262C4⋊C4—442no—
263C4⋊C4—444no—
264C22⋊C4—24no—
265C22⋊C4—41no—
266C22⋊C4—41no—
267C22⋊C4—42no—
268C22⋊C4—444no—
269C22⋊C4—442no—
270C42—21no—
271C42—21no—
272C42—82no—
273C11#1329611yescharacteristic, complemented, Sylow
274C23—21no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23—41no—
279C23—41no—
280C23—41no—
281C23—41no—
282C23C4×Dic2212yes—
283C23#6697712yes—
284C23C2×(C2×D11)⋊C411yescharacteristic
285Q8—444no—
286Q8—448no—
287Q8—444no—
288D4—42no—
289D4—42no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—22no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—42no—
297C2×C4—42no—
298C2×C4—42no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—44no—
303C2×C4—81no—
304C2×C4—82no—
305C2×C4—82no—
306C2×C4—224no—
307C2×C4—442no—
308C2×C4—444no—
309C2×C4—442no—
310C2×C4—444no—
311C2×C4—442no—
312C2×C4—442no—
313C2×C4—442no—
314C2×C4#6687011yescharacteristic
315C2×C4#6687011yescharacteristic
316C2×C4#6692211yescharacteristic
317C2×C4#6692811yescharacteristic
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—
331C22#1062254211yescharacteristic
332C22C2×#6687011yescharacteristic
333C22#1062261911yescharacteristic
334C4—21no—
335C4—21no—
336C4—21no—
337C4—41no—
338C4—41no—
339C4—41no—
340C4—84no—
341C4—444no—
342C4—882no—
343C4#1062210912yes—
344C2—21no—
345C2—21no—
346C2—42no—
347C2—42no—
348C2#1306960111yescharacteristic
349C2C2×#1062210911yescharacteristic
350C2#1307026911yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC24×C11C22×C4
FrattiniC22×D4C22×D11
FittingC4×C11×#99C2
socleC22×C11C2×#99
prime radical, cosocleC22×D4×C11C23
hypercenterC4×#99D11
hypocenterC11#13296
LCSG ▷ C24×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
5. C23×Dic22C4semidirect
12. #10622825C4semidirect
15. #10622559C4semidirect
44. C11×#99Q8semidirect
215. #99Dic22semidirect
273. C11#13296semidirect

Maximal subgroups

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

subgroupindex
#130719812
#130686082
#130667332
C4×C11×#992
#1329611