Finite Group Databasebeta

← #14655526

Subgroups — #14655526

Order 2816.

604 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 604 conjugacy classes of subgroups — too many to draw. Only its 105 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#13079561C211yesmaximal, characteristic, complemented
2C2×#10622689C211yesmaximal, characteristic
3#13069605C211yesmaximal, characteristic, complemented
4#13067284C211yesmaximal, characteristic
5#13067071C211yesmaximal, characteristic, complemented
6#13066454C211yesmaximal, characteristic, complemented
7C11×#3138C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C2×C11×#127C2211yescharacteristic
10C22×#4324—22no—
11C2×#66922C2211yescharacteristic
12C11×#490—22no—
13C11×#486—21no—
14C11×#486—21no—
15C11×#418—22no—
16C4×C11×M16C2211yescharacteristic
17#10622706—21no—
18#10622705—21no—
19#10622689—22no—
20#10622689—22no—
21#10622663—22no—
22#10622644—22no—
23#10622538C2211yescharacteristic
24#10622537C2211yescharacteristic
25C2×C4×C11⋊C8C2211yescharacteristic
26#10622192—22no—
27#10622182—22no—
28Q8⋊(C11⋊C8)—22no—
29C22×D4×C11—21no—
30C22×D4×C11—21no—
31C22×D4×C11—21no—
32C22×Dic22D412yes—
33C2×C11×M16D412yes—
34C11×C4⋊Q8D411yescharacteristic
35C11×C4⋊Q8D411yescharacteristic
36C11×#127—21no—
37C11×#127—21no—
38C11×#127—21no—
39C11×#127D412yes—
40C11×#125—21no—
41C11×C22⋊Q8—21no—
42C11×C22⋊Q8—21no—
43C4×Q8×C11—21no—
44C4×Q8×C11—21no—
45C11×#117—21no—
46C2×C42×C11C2311yescharacteristic
47C2×#4326—24no—
48C2×#4324—28no—
49C2×#4324—48no—
50C2×C4⋊Dic11—21no—
51C2×C4⋊Dic11—21no—
52C2×#4318—21no—
53C22×C11⋊C8—21no—
54#66922—21no—
55#66922—21no—
56#66922—21no—
57#66922—21no—
58C11×#102—24no—
59C11×#102—24no—
60C11×#97—21no—
61C4×C8×C11—21no—
62C22⋊(C11⋊C8)—21no—
63#66874—24no—
64C4⋊(C11⋊C8)—21no—
65C4⋊(C11⋊C8)—21no—
66C4⋊(C11⋊C8)D412yes—
67C4×C11⋊C8—21no—
68C4×C11⋊C8—21no—
69C4×C11⋊C8D412yes—
70#10147—111nomaximal, Sylow
71C24×C11—41no—
72C2×Q8×C11—21no—
73C2×Q8×C11—21no—
74C2×D4×C11—22no—
75C2×D4×C11—22no—
76C2×D4×C11—22no—
77C2×D4×C11—44no—
78C2×D4×C11—41no—
79C2×D4×C11—41no—
80C2×D4×C11—41no—
81C2×D4×C11—42no—
82C2×D4×C11—42no—
83C2×D4×C11—82no—
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11#4111yescharacteristic
87C22×Dic11—22no—
88C2×Dic22—22no—
89C2×Dic22—22no—
90C2×Dic22—44no—
91C11×M16—22no—
92C11×M16—22no—
93C2×C8×C11—22no—
94C11×C4⋊C4—21no—
95C11×C4⋊C4—21no—
96C11×C4⋊C4—21no—
97C11×C4⋊C4—21no—
98C11×C4⋊C4—41no—
99C11×C4⋊C4—41no—
100C11×C22⋊C4—41no—
101C42×C11—41no—
102C42×C11C2×D411yescharacteristic
103C42×C11C2×D411yescharacteristic
104C42×C11C2×D411yescharacteristic
105C42×C11C2×D411yescharacteristic
106#4326—84no—
107#4324—416no—
108C4⋊Dic11—41no—
109C4⋊Dic11—41no—
110C4⋊Dic11—41no—
111C4⋊Dic11—41no—
112#4318—42no—
113C2×C11⋊C8—24no—
114C2×C11⋊C8—22no—
115C2×C11⋊C8—22no—
116C2×C11⋊C8—41no—
117#3209—111no—
118C2×#492—111no—
119#3138D1111yescharacteristic
120#1997—111no—
121#1545—111no—
122#1493—111no—
123#1278—111no—
124C23×C11—42no—
125C23×C11—82no—
126C23×C11—82no—
127C23×C11—82no—
128C23×C11#12111yescharacteristic
129Q8×C11—42no—
130Q8×C11—42no—
131D4×C11—44no—
132D4×C11—44no—
133D4×C11—82no—
134D4×C11—82no—
135D4×C11—82no—
136D4×C11—81no—
137D4×C11—81no—
138C2×C4×C11—22no—
139C2×C4×C11—22no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11#12011yescharacteristic
143C2×C4×C11#12011yescharacteristic
144C2×C4×C11#12011yescharacteristic
145C2×C4×C11#12111yescharacteristic
146C2×C4×C11#12111yescharacteristic
147C2×C4×C11#12711yescharacteristic
148C2×C4×C11#13512yes—
149C2×C4×C11#13712yes—
150C2×Dic11—42no—
151C2×Dic11—82no—
152Dic22—44no—
153Dic22—44no—
154C8×C11—42no—
155C11⋊C8—24no—
156C11⋊C8—42no—
157C11⋊C8—81no—
158C22×SD16—222no—
159#533C2×D1111yescharacteristic
160C2×C4⋊Q8—111no—
161C2×#127C2×D1111yescharacteristic
162#494—221no—
163#492—222no—
164#492—222no—
165#490—22no—
166#487—221no—
167#486—21no—
168#486—21no—
169#462—222no—
170#451—222no—
171#431—111no—
172#423—111no—
173#418—22no—
174C4×M16C2×D1111yescharacteristic
175C2×C4×C8—111no—
176#343—222no—
177#331—222no—
178Q8⋊C8—222no—
179C22×C11—21no—
180C22×C11—21no—
181C22×C11—82no—
182C22×C11—82no—
183C22×C11—82no—
184C22×C11—164no—
185C22×C11#39211yescharacteristic
186C22×C11#46412yes—
187C4×C11—21no—
188C4×C11—21no—
189C4×C11—81no—
190C4×C11—81no—
191C4×C11#45212yes—
192C4×C11#45312yes—
193C4×C11#47112yes—
194C4×C11#49511yescharacteristic
195C4×C11#49711yescharacteristic
196Dic11—82no—
197C22×Q8—112no—
198C22×D4—21no—
199C22×D4—21no—
200C22×D4—21no—
201C2×Q16—224no—
202C2×SD16—228no—
203C2×SD16—448no—
204C2×M16—221no—
205C2×M16C22⋊D1112yes—
206C22×C8—221no—
207C4⋊Q8—221no—
208C4⋊Q8—221no—
209C4⋊Q8—221no—
210C4⋊Q8—221no—
211C4⋊Q8C22⋊D1111yescharacteristic
212C4⋊Q8C22⋊D1111yescharacteristic
213#127—21no—
214#127—21no—
215#127—21no—
216#127C22⋊D1112yes—
217#125—21no—
218C22⋊Q8—21no—
219C22⋊Q8—21no—
220C4×Q8—21no—
221C4×Q8—21no—
222#117—21no—
223C2×C4⋊C4—221no—
224C2×C4⋊C4—221no—
225C2×C42C22×D1111yescharacteristic
226C4⋊C8—112no—
227C4⋊C8—221no—
228C4⋊C8—221no—
229#103—224no—
230#102—24no—
231#102—24no—
232C22⋊C8—221no—
233#97—21no—
234C4×C8—21no—
235C4×C8—112no—
236C4×C8—221no—
237C4×C8—221no—
238C2×C11—22no—
239C2×C11—162no—
240C2×C11#200211yescharacteristic
241C2×C11#201511yescharacteristic
242C2×C11#201911yescharacteristic
243C24—41no—
244C2×Q8—21no—
245C2×Q8—21no—
246C2×Q8—222no—
247C2×Q8—222no—
248C2×Q8—444no—
249C2×D4—22no—
250C2×D4—22no—
251C2×D4—22no—
252C2×D4—44no—
253C2×D4—41no—
254C2×D4—41no—
255C2×D4—41no—
256C2×D4—42no—
257C2×D4—42no—
258C2×D4—82no—
259C22×C4—222no—
260C22×C4D4×D1111yescharacteristic
261C22×C4#434111yescharacteristic
262C22×C4C2×C22⋊D1111yescharacteristic
263Q16—884no—
264SD16—4416no—
265M16—22no—
266M16—22no—
267M16—442no—
268C2×C8—22no—
269C2×C8—224no—
270C2×C8—222no—
271C2×C8—222no—
272C2×C8—441no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—441no—
280C4⋊C4—441no—
281C4⋊C4—441no—
282C4⋊C4—441no—
283C22⋊C4—41no—
284C42—41no—
285C42D4×D1111yescharacteristic
286C42D4×D1111yescharacteristic
287C42C2×C22⋊D1111yescharacteristic
288C42C2×C22⋊D1111yescharacteristic
289C11#1014711yescharacteristic, complemented, Sylow
290C23—42no—
291C23—82no—
292C23—82no—
293C23—82no—
294C23#6699111yescharacteristic
295Q8—42no—
296Q8—42no—
297Q8—444no—
298Q8—444no—
299D4—44no—
300D4—44no—
301D4—82no—
302D4—82no—
303D4—82no—
304D4—81no—
305D4—81no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—442no—
311C2×C4—882no—
312C2×C4#6699011yescharacteristic
313C2×C4#6699011yescharacteristic
314C2×C4#6699211yescharacteristic
315C2×C4#6699211yescharacteristic
316C2×C4#6699311yescharacteristic
317C2×C4#6700312yes—
318C2×C4#6700412yes—
319C2×C4#6700611yescharacteristic
320C8—42no—
321C8—224no—
322C8—442no—
323C8—881no—
324C22—21no—
325C22—21no—
326C22—82no—
327C22—82no—
328C22—82no—
329C22—164no—
330C22#1062266712yes—
331C22#1062283611yescharacteristic
332C4—21no—
333C4—21no—
334C4—81no—
335C4—81no—
336C4—882no—
337C4#1062267211yescharacteristic
338C4#1062267311yescharacteristic
339C4#1062281112yes—
340C4#1062281312yes—
341C4#1062285212yes—
342C2—22no—
343C2—162no—
344C2#1306962811yescharacteristic
345C2#1306971011yescharacteristic
346C2#1306973011yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3138C2
socleC22×C11#392
prime radicalC2×C11×#127C22
hypercenter#3138D11
hypocenterC11#10147
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3138

Complements

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

NH ≅ G/Ntype
1. #13079561C2semidirect
3. #13069605C2semidirect
5. #13067071C2semidirect
6. #13066454C2semidirect
289. C11#10147semidirect

Maximal subgroups

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

subgroupindex
#130795612
C2×#106226892
#130696052
#130672842
#130670712
#130664542
C11×#31382
#1014711