Finite Group Databasebeta

← #14655528

Subgroups — #14655528

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
1C2×#10622698C211yesmaximal, characteristic
2#13078992C211yesmaximal, characteristic
3#13069606C211yesmaximal, characteristic, complemented
4#13067283C211yesmaximal, characteristic
5#13067071C211yesmaximal, characteristic, complemented
6#13066452C211yesmaximal, characteristic, complemented
7C11×#3209C211yesmaximal, characteristic, complemented
8C11×#533C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C22×#4325—22no—
11C2×#66927C2211yescharacteristic
12C11×#494—21no—
13C11×#487—21no—
14C11×#462—22no—
15C11×#451—22no—
16C11×#431C2211yescharacteristic
17#10622701—21no—
18#10622701—21no—
19#10622698—22no—
20#10622698—22no—
21#10622680—22no—
22#10622614—22no—
23#10622537C2211yescharacteristic
24C4×#4318C2211yescharacteristic
25C2×C4×C11⋊C8C2211yescharacteristic
26Q8⋊(C11⋊C8)—22no—
27#10622168—22no—
28#10622123—22no—
29C22×Q8×C11D412yes—
30C22×D44—21no—
31C22×D44—21no—
32C22×D44—21no—
33C2×C11×Q16—24no—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8D411yescharacteristic
39C11×C4⋊Q8D411yescharacteristic
40C11×#125—21no—
41C11×C22⋊Q8—21no—
42C11×C22⋊Q8—21no—
43C4×Q8×C11—21no—
44C4×Q8×C11—21no—
45C11×#117—21no—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4—21no—
48C2×C42×C11C2311yescharacteristic
49C2×#4325—28no—
50C2×#4325—48no—
51C2×#4318—21no—
52C2×#4318D412yes—
53C22×C11⋊C8—21no—
54#66927—21no—
55#66927—21no—
56#66927—21no—
57#66927D412yes—
58C11×C4⋊C8D412yes—
59C11×#103—24no—
60C11×C22⋊C8—21no—
61C4×C8×C11—21no—
62#66873—24no—
63#66873—24no—
64C4⋊(C11⋊C8)—21no—
65C4⋊(C11⋊C8)—21no—
66#66867—21no—
67C4×C11⋊C8—21no—
68C4×C11⋊C8—21no—
69C4×C11⋊C8D412yes—
70#10147—111nomaximal, Sylow
71C23×D11—41no—
72C2×Q8×C11—22no—
73C2×Q8×C11—22no—
74C2×Q8×C11—21no—
75C2×Q8×C11—21no—
76C2×Q8×C11—44no—
77C22×C4×C11—22no—
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11#4111yescharacteristic
81C2×D44—22no—
82C2×D44—22no—
83C2×D44—22no—
84C2×D44—44no—
85C2×D44—41no—
86C2×D44—41no—
87C2×D44—41no—
88C2×D44—42no—
89C2×D44—42no—
90C2×D44—82no—
91C11×Q16—84no—
92C2×C8×C11—22no—
93C11×C4⋊C4—21no—
94C11×C4⋊C4—21no—
95C11×C4⋊C4—21no—
96C11×C4⋊C4—21no—
97C11×C4⋊C4—41no—
98C11×C4⋊C4—41no—
99C11×C4⋊C4—41no—
100C11×C4⋊C4—41no—
101C11×C4⋊C4—41no—
102C11×C4⋊C4—41no—
103C11×C22⋊C4—41no—
104C42×C11—41no—
105C42×C11C2×D411yescharacteristic
106C42×C11C2×D411yescharacteristic
107C42×C11C2×D411yescharacteristic
108C42×C11C2×D411yescharacteristic
109#4325—416no—
110#4318—22no—
111#4318—22no—
112#4318—42no—
113C2×C11⋊C8—24no—
114C2×C11⋊C8—22no—
115C2×C11⋊C8—22no—
116C2×C11⋊C8—41no—
117#3209D1111yescharacteristic, complemented
118C2×#492—111no—
119#3138—111no—
120#1997—111no—
121#1545—111no—
122#1493—111no—
123#1278—111no—
124C23×C11#12111yescharacteristic
125C22×D11—42no—
126C22×D11—82no—
127C22×D11—82no—
128C22×D11—82no—
129Q8×C11—44no—
130Q8×C11—42no—
131Q8×C11—44no—
132Q8×C11—42no—
133C2×C4×C11—22no—
134C2×C4×C11—22no—
135C2×C4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11—42no—
138C2×C4×C11—82no—
139C2×C4×C11#12011yescharacteristic
140C2×C4×C11#12011yescharacteristic
141C2×C4×C11#12011yescharacteristic
142C2×C4×C11#12111yescharacteristic
143C2×C4×C11#12111yescharacteristic
144C2×C4×C11#12711yescharacteristic
145C2×C4×C11#13512yes—
146C2×C4×C11#13712yes—
147D44—44no—
148D44—44no—
149D44—82no—
150D44—82no—
151D44—82no—
152D44—81no—
153D44—81no—
154C8×C11—42no—
155C11⋊C8—24no—
156C11⋊C8—42no—
157C11⋊C8—81no—
158C22×SD16—222no—
159#533C2×D1111yescharacteristic
160C2×C4⋊Q8C2×D1111yescharacteristic
161C2×#127—111no—
162#494—21no—
163#492—222no—
164#492—222no—
165#490—222no—
166#487—21no—
167#486—221no—
168#486—221no—
169#462—22no—
170#451—22no—
171#431C2×D1111yescharacteristic
172#423—111no—
173#418—222no—
174C4×M16—111no—
175C2×C4×C8—111no—
176#343—222no—
177#331—222no—
178Q8⋊C8—222no—
179C22×C11—21no—
180C22×C11—21no—
181C22×C11#39211yescharacteristic
182C22×C11#46412yes—
183C2×D11—82no—
184C2×D11—82no—
185C2×D11—82no—
186C2×D11—164no—
187C4×C11—21no—
188C4×C11—21no—
189C4×C11—82no—
190C4×C11—81no—
191C4×C11—81no—
192C4×C11#45212yes—
193C4×C11#45312yes—
194C4×C11#47112yes—
195C4×C11#49511yescharacteristic
196C4×C11#49711yescharacteristic
197C22×Q8C22⋊D1112yes—
198C22×D4—221no—
199C22×D4—221no—
200C22×D4—221no—
201C2×Q16—24no—
202C2×SD16—228no—
203C2×SD16—448no—
204C2×M16—112no—
205C2×M16—221no—
206C22×C8—221no—
207C4⋊Q8—21no—
208C4⋊Q8—21no—
209C4⋊Q8—21no—
210C4⋊Q8—21no—
211C4⋊Q8C22⋊D1111yescharacteristic
212C4⋊Q8C22⋊D1111yescharacteristic
213#127—112no—
214#127—221no—
215#127—221no—
216#127—221no—
217#125—21no—
218C22⋊Q8—21no—
219C22⋊Q8—21no—
220C4×Q8—21no—
221C4×Q8—21no—
222#117—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C42C22×D1111yescharacteristic
226C4⋊C8—221no—
227C4⋊C8—221no—
228C4⋊C8C22⋊D1112yes—
229#103—24no—
230#102—224no—
231#102—224no—
232C22⋊C8—21no—
233#97—221no—
234C4×C8—21no—
235C4×C8—112no—
236C4×C8—221no—
237C4×C8—221no—
238C2×C11—22no—
239C2×C11#200211yescharacteristic
240C2×C11#201511yescharacteristic
241C2×C11#201911yescharacteristic
242D11—162no—
243C24—441no—
244C2×Q8—22no—
245C2×Q8—21no—
246C2×Q8—22no—
247C2×Q8—21no—
248C2×Q8—44no—
249C2×D4—222no—
250C2×D4—222no—
251C2×D4—222no—
252C2×D4—444no—
253C2×D4—442no—
254C2×D4—442no—
255C2×D4—441no—
256C2×D4—441no—
257C2×D4—441no—
258C2×D4—882no—
259C22×C4—22no—
260C22×C4D4×D1111yescharacteristic
261C22×C4#434111yescharacteristic
262C22×C4C2×C22⋊D1111yescharacteristic
263Q16—84no—
264SD16—4416no—
265M16—222no—
266M16—222no—
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—41no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C22⋊C4—41no—
284C42—41no—
285C42D4×D1111yescharacteristic
286C42D4×D1111yescharacteristic
287C42C2×C22⋊D1111yescharacteristic
288C42C2×C22⋊D1111yescharacteristic
289C11#1014711yescharacteristic, complemented, Sylow
290C23—442no—
291C23—882no—
292C23—882no—
293C23—882no—
294C23#6699211yescharacteristic
295Q8—44no—
296Q8—42no—
297Q8—42no—
298Q8—44no—
299D4—444no—
300D4—444no—
301D4—882no—
302D4—881no—
303D4—881no—
304D4—882no—
305D4—882no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—42no—
311C2×C4—82no—
312C2×C4#6697112yes—
313C2×C4#6697212yes—
314C2×C4#6699011yescharacteristic
315C2×C4#6699011yescharacteristic
316C2×C4#6699111yescharacteristic
317C2×C4#6699211yescharacteristic
318C2×C4#6699311yescharacteristic
319C2×C4#6700611yescharacteristic
320C8—42no—
321C8—224no—
322C8—442no—
323C8—881no—
324C22—21no—
325C22—21no—
326C22—882no—
327C22—882no—
328C22—882no—
329C22—1764no—
330C22#1062279812yes—
331C22#1062283611yescharacteristic
332C4—21no—
333C4—21no—
334C4—82no—
335C4—81no—
336C4—81no—
337C4#1062280012yes—
338C4#1062280311yescharacteristic
339C4#1062280411yescharacteristic
340C4#1062281612yes—
341C4#1062285412yes—
342C2—22no—
343C2—1762no—
344C2#1306962911yescharacteristic
345C2#1306970711yescharacteristic
346C2#1306972711yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3209C2
socleC22×C11#392
prime radicalC2×#66927C22
hypercenter#3209D11
hypocenterC11#10147
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3209

Complements

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

NH ≅ G/Ntype
3. #13069606C2semidirect
5. #13067071C2semidirect
6. #13066452C2semidirect
7. C11×#3209C2semidirect
117. #3209D11semidirect
289. C11#10147semidirect

Maximal subgroups

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

subgroupindex
C2×#106226982
#130789922
#130696062
#130672832
#130670712
#130664522
C11×#32092
#1014711