Finite Group Databasebeta

← #14655633

Subgroups — #14655633

Order 2816.

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

normal subgroups only

This group has 510 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#13079009C211yesmaximal, characteristic
2C2×#10622694C211yesmaximal, characteristic, complemented
3#13069606C211yesmaximal, characteristic, complemented
4#13067296C211yesmaximal, characteristic, complemented
5#13067067C211yesmaximal, characteristic
6#13066452C211yesmaximal, characteristic, complemented
7C11×#3206C211yesmaximal, characteristic
8C11×#532C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×#66922C2211yescharacteristic
11C11×#492—21no—
12C11×#487—21no—
13C11×#461—22no—
14C11×#448—22no—
15C11×#431C2211yescharacteristic
16#10622845—22no—
17C2×#66899—22no—
18#10622694—21no—
19#10622694—22no—
20#10622694—22no—
21#10622683—21no—
22#10622668—22no—
23#10622537C2211yescharacteristic
24C4×#4318C2211yescharacteristic
25C2×C4×C11⋊C8C2211yescharacteristic
26D4⋊(C11⋊C8)—22no—
27#10622168—22no—
28#10622119—22no—
29C2×C11×#41—21no—
30C22×Q8×C11D412yes—
31C22×Dic22—21no—
32C2×C11×SD16—24no—
33C11×C4⋊Q8—21no—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8D411yescharacteristic
38C11×#127D411yescharacteristic
39C11×#124—21no—
40C11×#121—21no—
41C11×#121—21no—
42C4×D4×C11—21no—
43C4×D4×C11—21no—
44C2×C11×C4⋊C4—21no—
45C2×C11×C4⋊C4—21no—
46C2×C42×C11C2311yescharacteristic
47C2×C4⋊Dic11—21no—
48C2×C4⋊Dic11—21no—
49C2×#4318—21no—
50C2×#4318D412yes—
51C22×C11⋊C8—21no—
52#66922—21no—
53#66922—21no—
54#66922—21no—
55#66922D412yes—
56C11×C4⋊C8D412yes—
57C11×#103—24no—
58C11×C22⋊C8—21no—
59C4×C8×C11—21no—
60#66899—28no—
61#66899—24no—
62#66896—24no—
63C4⋊(C11⋊C8)—21no—
64C4⋊(C11⋊C8)—21no—
65#66867—21no—
66C4×C11⋊C8—21no—
67C4×C11⋊C8—21no—
68C4×C11⋊C8D412yes—
69#10162—111nomaximal, Sylow
70C11×#41—42no—
71C11×#41—42no—
72C2×Q8×C11—21no—
73C2×Q8×C11—22no—
74C2×Q8×C11—22no—
75C2×Q8×C11—44no—
76C2×D4×C11—21no—
77C2×D4×C11—21no—
78C2×D4×C11—21no—
79C2×D4×C11—41no—
80C22×C4×C11—22no—
81C22×C4×C11—41no—
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11#4111yescharacteristic
85C22×Dic11—41no—
86C2×Dic22—22no—
87C2×Dic22—41no—
88C2×Dic22—82no—
89C11×SD16—84no—
90C2×C8×C11—22no—
91C11×C4⋊C4—21no—
92C11×C4⋊C4—21no—
93C11×C4⋊C4—41no—
94C11×C4⋊C4—41no—
95C11×C4⋊C4—41no—
96C11×C4⋊C4—41no—
97C11×C22⋊C4—41no—
98C11×C22⋊C4—41no—
99C42×C11C2×D411yescharacteristic
100C42×C11C2×D411yescharacteristic
101C42×C11C2×D411yescharacteristic
102C42×C11C2×D411yescharacteristic
103C4⋊Dic11—22no—
104C4⋊Dic11—22no—
105C4⋊Dic11—41no—
106C4⋊Dic11—41no—
107#4318—22no—
108#4318—22no—
109#4318—42no—
110C2×C11⋊C8—22no—
111C2×C11⋊C8—22no—
112C2×C11⋊C8—42no—
113C2×C11⋊C8—41no—
114#3206D1111yescharacteristic
115#3141—111no—
116C2×#487—111no—
117#1997—111no—
118#1548—111no—
119#1492—111no—
120#1278—111no—
121C23×C11—41no—
122C23×C11#12111yescharacteristic
123Q8×C11—44no—
124Q8×C11—42no—
125Q8×C11—44no—
126D4×C11—42no—
127D4×C11—42no—
128D4×C11—42no—
129D4×C11—82no—
130C2×C4×C11—22no—
131C2×C4×C11—22no—
132C2×C4×C11—41no—
133C2×C4×C11—42no—
134C2×C4×C11—81no—
135C2×C4×C11—81no—
136C2×C4×C11—82no—
137C2×C4×C11#12011yescharacteristic
138C2×C4×C11#12011yescharacteristic
139C2×C4×C11#12011yescharacteristic
140C2×C4×C11#12111yescharacteristic
141C2×C4×C11#12111yescharacteristic
142C2×C4×C11#12711yescharacteristic
143C2×C4×C11#13512yes—
144C2×C4×C11#13712yes—
145C2×Dic11—42no—
146C2×Dic11—82no—
147Dic22—82no—
148Dic22—82no—
149C8×C11—42no—
150C11⋊C8—42no—
151C11⋊C8—42no—
152C11⋊C8—81no—
153#532C2×D1111yescharacteristic
154C2×C4⋊Q8—111no—
155C2×C4⋊Q8C2×D1111yescharacteristic
156#492—21no—
157#489—222no—
158#487—21no—
159#487—222no—
160#487—222no—
161#487—221no—
162#486—221no—
163#461—22no—
164#448—22no—
165#431C2×D1111yescharacteristic
166#423—111no—
167#417—222no—
168C2×#103—222no—
169C4×M16—111no—
170C2×C4×C8—111no—
171#343—222no—
172#333—222no—
173D4⋊C8—222no—
174C22×C11—21no—
175C22×C11—21no—
176C22×C11—81no—
177C22×C11—81no—
178C22×C11—81no—
179C22×C11#39211yescharacteristic
180C22×C11#46412yes—
181C4×C11—21no—
182C4×C11—21no—
183C4×C11—82no—
184C4×C11—81no—
185C4×C11#45212yes—
186C4×C11#45512yes—
187C4×C11#47112yes—
188C4×C11#49511yescharacteristic
189C4×C11#49711yescharacteristic
190Dic11—82no—
191C2×#41—21no—
192C22×Q8—221no—
193C22×Q8C22⋊D1112yes—
194C2×SD16—24no—
195C2×M16—112no—
196C2×M16—221no—
197C22×C8—221no—
198C4⋊Q8—21no—
199C4⋊Q8—21no—
200C4⋊Q8—21no—
201C4⋊Q8—21no—
202C4⋊Q8—112no—
203C4⋊Q8—221no—
204C4⋊Q8—221no—
205C4⋊Q8—221no—
206C4⋊Q8C22⋊D1111yescharacteristic
207#127C22⋊D1111yescharacteristic
208#124—21no—
209#121—21no—
210#121—21no—
211C4×D4—21no—
212C4×D4—21no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—221no—
216C2×C4⋊C4—221no—
217C2×C42C22×D1111yescharacteristic
218C4⋊C8—221no—
219C4⋊C8—221no—
220C4⋊C8C22⋊D1112yes—
221#103—24no—
222#103—228no—
223#103—224no—
224#102—224no—
225C22⋊C8—21no—
226#97—221no—
227C4×C8—21no—
228C4×C8—112no—
229C4×C8—221no—
230C4×C8—221no—
231C2×C11—22no—
232C2×C11—161no—
233C2×C11#200411yescharacteristic
234C2×C11#201511yescharacteristic
235C2×C11#201911yescharacteristic
236#41—42no—
237#41—42no—
238C2×Q8—21no—
239C2×Q8—22no—
240C2×Q8—22no—
241C2×Q8—44no—
242C2×Q8—222no—
243C2×Q8—441no—
244C2×Q8—882no—
245C2×D4—21no—
246C2×D4—21no—
247C2×D4—21no—
248C2×D4—41no—
249C22×C4—22no—
250C22×C4—41no—
251C22×C4—441no—
252C22×C4D4×D1111yescharacteristic
253C22×C4#434111yescharacteristic
254C22×C4C2×C22⋊D1111yescharacteristic
255SD16—84no—
256M16—222no—
257M16—222no—
258M16—442no—
259C2×C8—22no—
260C2×C8—222no—
261C2×C8—222no—
262C2×C8—442no—
263C2×C8—441no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—222no—
271C4⋊C4—222no—
272C4⋊C4—441no—
273C4⋊C4—441no—
274C22⋊C4—41no—
275C22⋊C4—41no—
276C42D4×D1111yescharacteristic
277C42D4×D1111yescharacteristic
278C42C2×C22⋊D1111yescharacteristic
279C42C2×C22⋊D1111yescharacteristic
280C11#1016211yescharacteristic, complemented, Sylow
281C23—41no—
282C23#6699211yescharacteristic
283Q8—44no—
284Q8—42no—
285Q8—44no—
286Q8—882no—
287Q8—882no—
288D4—42no—
289D4—42no—
290D4—42no—
291D4—82no—
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—41no—
295C2×C4—42no—
296C2×C4—81no—
297C2×C4—81no—
298C2×C4—82no—
299C2×C4—442no—
300C2×C4—882no—
301C2×C4#6696812yes—
302C2×C4#6696912yes—
303C2×C4#6699011yescharacteristic
304C2×C4#6699011yescharacteristic
305C2×C4#6699111yescharacteristic
306C2×C4#6699211yescharacteristic
307C2×C4#6699311yescharacteristic
308C2×C4#6700611yescharacteristic
309C8—42no—
310C8—442no—
311C8—442no—
312C8—881no—
313C22—21no—
314C22—21no—
315C22—81no—
316C22—81no—
317C22—81no—
318C22#1062277912yes—
319C22#1062283611yescharacteristic
320C4—21no—
321C4—21no—
322C4—82no—
323C4—81no—
324C4—882no—
325C4#1062278011yescharacteristic
326C4#1062278111yescharacteristic
327C4#1062278612yes—
328C4#1062281612yes—
329C4#1062285512yes—
330C2—22no—
331C2—161no—
332C2#1306964311yescharacteristic
333C2#1306970811yescharacteristic
334C2#1306972711yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3206C2
socleC22×C11#392
prime radicalC11×#532C22
hypercenter#3206D11
hypocenterC11#10162
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3206

Complements

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

NH ≅ G/Ntype
2. C2×#10622694C2semidirect
3. #13069606C2semidirect
4. #13067296C2semidirect
6. #13066452C2semidirect
280. C11#10162semidirect

Maximal subgroups

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

subgroupindex
#130790092
C2×#106226942
#130696062
#130672962
#130670672
#130664522
C11×#32062
#1016211