Finite Group Databasebeta

← #14655645

Subgroups — #14655645

Order 2816.

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

normal subgroups only

This group has 498 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#13079741C211yesmaximal, characteristic
2C2×#10622691C211yesmaximal, characteristic, complemented
3#13069605C211yesmaximal, characteristic, complemented
4#13067297C211yesmaximal, characteristic, complemented
5#13067067C211yesmaximal, characteristic
6#13066454C211yesmaximal, characteristic, complemented
7C11×#3141C211yesmaximal, characteristic
8C11×#532C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×#66922C2211yescharacteristic
11C11×#489—22no—
12C11×#487—21no—
13C11×#486—21no—
14C11×#417—22no—
15C4×C11×M16C2211yescharacteristic
16#10622692—21no—
17#10622691—22no—
18#10622691—22no—
19#10622683—21no—
20#10622647—22no—
21#10622621—22no—
22C2×#66871—22no—
23#10622538C2211yescharacteristic
24#10622537C2211yescharacteristic
25C2×C4×C11⋊C8C2211yescharacteristic
26#10622192—22no—
27#10622184—22no—
28D4⋊(C11⋊C8)—22no—
29C2×C11×#41—21no—
30C22×Q8×C11—21no—
31C22×Dic22—21no—
32C2×C11×M16D412yes—
33C11×C4⋊Q8—21no—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8D412yes—
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⋊Dic11D412yes—
49C2×#4318—21no—
50C22×C11⋊C8—21no—
51#66922—21no—
52#66922—21no—
53#66922—21no—
54#66922—21no—
55C11×#103—24no—
56C11×#102—24no—
57C11×#97—21no—
58C4×C8×C11—21no—
59#66896—24no—
60C22⋊(C11⋊C8)—21no—
61#66872—24no—
62#66871—28no—
63C4⋊(C11⋊C8)—21no—
64C4⋊(C11⋊C8)—21no—
65C4⋊(C11⋊C8)D412yes—
66C4×C11⋊C8—21no—
67C4×C11⋊C8—21no—
68C4×C11⋊C8D412yes—
69#10164—111nomaximal, Sylow
70C11×#41—42no—
71C11×#41—42no—
72C2×Q8×C11—21no—
73C2×Q8×C11—22no—
74C2×Q8×C11—41no—
75C2×Q8×C11—82no—
76C2×D4×C11—21no—
77C2×D4×C11—21no—
78C2×D4×C11—21no—
79C2×D4×C11—41no—
80C22×C4×C11—41no—
81C22×C4×C11—41no—
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11#4111yescharacteristic
85C22×Dic11—22no—
86C2×Dic22—41no—
87C2×Dic22—41no—
88C2×Dic22—82no—
89C11×M16—22no—
90C11×M16—22no—
91C2×C8×C11—22no—
92C11×C4⋊C4—22no—
93C11×C4⋊C4—21no—
94C11×C4⋊C4—22no—
95C11×C4⋊C4—21no—
96C11×C4⋊C4—41no—
97C11×C4⋊C4—41no—
98C11×C22⋊C4—41no—
99C11×C22⋊C4—41no—
100C42×C11C2×D411yescharacteristic
101C42×C11C2×D411yescharacteristic
102C42×C11C2×D411yescharacteristic
103C42×C11C2×D411yescharacteristic
104C4⋊Dic11—22no—
105C4⋊Dic11—22no—
106C4⋊Dic11—41no—
107C4⋊Dic11—41no—
108#4318—42no—
109C2×C11⋊C8—24no—
110C2×C11⋊C8—22no—
111C2×C11⋊C8—22no—
112C2×C11⋊C8—41no—
113#3227—111no—
114C2×#500—111no—
115#3141D1111yescharacteristic
116#1997—111no—
117#1548—111no—
118#1492—111no—
119#1278—111no—
120C23×C11—41no—
121C23×C11#12111yescharacteristic
122Q8×C11—42no—
123Q8×C11—82no—
124Q8×C11—82no—
125D4×C11—42no—
126D4×C11—42no—
127D4×C11—42no—
128D4×C11—82no—
129C2×C4×C11—22no—
130C2×C4×C11—22no—
131C2×C4×C11—41no—
132C2×C4×C11—42no—
133C2×C4×C11—82no—
134C2×C4×C11—81no—
135C2×C4×C11—81no—
136C2×C4×C11#12011yescharacteristic
137C2×C4×C11#12011yescharacteristic
138C2×C4×C11#12011yescharacteristic
139C2×C4×C11#12111yescharacteristic
140C2×C4×C11#12111yescharacteristic
141C2×C4×C11#12711yescharacteristic
142C2×C4×C11#13512yes—
143C2×C4×C11#13712yes—
144C2×Dic11—42no—
145C2×Dic11—82no—
146Dic22—82no—
147Dic22—82no—
148C8×C11—42no—
149C11⋊C8—24no—
150C11⋊C8—42no—
151C11⋊C8—81no—
152#532C2×D1111yescharacteristic
153C2×C4⋊Q8—111no—
154C2×C4⋊Q8C2×D1111yescharacteristic
155#500—222no—
156#500—222no—
157#498—221no—
158#489—22no—
159#487—21no—
160#486—21no—
161#486—221no—
162#481—222no—
163#476—222no—
164#431—111no—
165C2×#107—222no—
166#423—111no—
167#417—22no—
168C4×M16C2×D1111yescharacteristic
169C2×C4×C8—111no—
170#343—222no—
171#333—222no—
172D4⋊C8—222no—
173C22×C11—21no—
174C22×C11—21no—
175C22×C11—81no—
176C22×C11—81no—
177C22×C11—81no—
178C22×C11#39211yescharacteristic
179C22×C11#46412yes—
180C4×C11—21no—
181C4×C11—21no—
182C4×C11—81no—
183C4×C11—82no—
184C4×C11#45212yes—
185C4×C11#45612yes—
186C4×C11#47212yes—
187C4×C11#49511yescharacteristic
188C4×C11#49711yescharacteristic
189Dic11—82no—
190C2×#41—21no—
191C22×Q8—21no—
192C22×Q8—221no—
193C2×M16—221no—
194C2×M16C22⋊D1112yes—
195C22×C8—221no—
196C4⋊Q8—21no—
197C4⋊Q8—21no—
198C4⋊Q8—21no—
199C4⋊Q8—221no—
200C4⋊Q8—221no—
201C4⋊Q8—221no—
202C4⋊Q8—221no—
203C4⋊Q8C22⋊D1112yes—
204C4⋊Q8C22⋊D1111yescharacteristic
205#127C22⋊D1111yescharacteristic
206#124—21no—
207#121—21no—
208#121—21no—
209C4×D4—21no—
210C4×D4—21no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—112no—
214C2×C4⋊C4—221no—
215C2×C42C22×D1111yescharacteristic
216#107—228no—
217#106—224no—
218C4⋊C8—112no—
219C4⋊C8—221no—
220C4⋊C8—221no—
221#103—24no—
222#102—24no—
223#102—224no—
224C22⋊C8—221no—
225#97—21no—
226C4×C8—21no—
227C4×C8—112no—
228C4×C8—221no—
229C4×C8—221no—
230C2×C11—22no—
231C2×C11—161no—
232C2×C11#200511yescharacteristic
233C2×C11#201511yescharacteristic
234C2×C11#201811yescharacteristic
235#41—42no—
236#41—42no—
237C2×Q8—22no—
238C2×Q8—21no—
239C2×Q8—41no—
240C2×Q8—82no—
241C2×Q8—441no—
242C2×Q8—441no—
243C2×Q8—882no—
244C2×D4—21no—
245C2×D4—21no—
246C2×D4—21no—
247C2×D4—41no—
248C22×C4—41no—
249C22×C4—41no—
250C22×C4—222no—
251C22×C4D4×D1111yescharacteristic
252C22×C4#434111yescharacteristic
253C22×C4C2×C22⋊D1111yescharacteristic
254M16—22no—
255M16—22no—
256M16—442no—
257C2×C8—22no—
258C2×C8—224no—
259C2×C8—222no—
260C2×C8—222no—
261C2×C8—441no—
262C4⋊C4—21no—
263C4⋊C4—22no—
264C4⋊C4—21no—
265C4⋊C4—22no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—222no—
269C4⋊C4—222no—
270C4⋊C4—441no—
271C4⋊C4—441no—
272C22⋊C4—41no—
273C22⋊C4—41no—
274C42D4×D1111yescharacteristic
275C42D4×D1111yescharacteristic
276C42C2×C22⋊D1111yescharacteristic
277C42C2×C22⋊D1111yescharacteristic
278C11#1016411yescharacteristic, complemented, Sylow
279C23—41no—
280C23#6699111yescharacteristic
281Q8—42no—
282Q8—82no—
283Q8—82no—
284Q8—882no—
285Q8—882no—
286D4—42no—
287D4—42no—
288D4—42no—
289D4—82no—
290C2×C4—22no—
291C2×C4—22no—
292C2×C4—41no—
293C2×C4—42no—
294C2×C4—82no—
295C2×C4—81no—
296C2×C4—81no—
297C2×C4—442no—
298C2×C4—882no—
299C2×C4#6699011yescharacteristic
300C2×C4#6699011yescharacteristic
301C2×C4#6699211yescharacteristic
302C2×C4#6699211yescharacteristic
303C2×C4#6699311yescharacteristic
304C2×C4#6700312yes—
305C2×C4#6700412yes—
306C2×C4#6700611yescharacteristic
307C8—42no—
308C8—224no—
309C8—442no—
310C8—881no—
311C22—21no—
312C22—21no—
313C22—81no—
314C22—81no—
315C22—81no—
316C22#1062266712yes—
317C22#1062283611yescharacteristic
318C4—21no—
319C4—21no—
320C4—81no—
321C4—82no—
322C4—882no—
323C4#1062267211yescharacteristic
324C4#1062267311yescharacteristic
325C4#1062281212yes—
326C4#1062281812yes—
327C4#1062285212yes—
328C2—22no—
329C2—161no—
330C2#1306964911yescharacteristic
331C2#1306971011yescharacteristic
332C2#1306972211yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3141C2
socleC22×C11#392
prime radicalC11×#532C22
hypercenter#3141D11
hypocenterC11#10164
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3141

Complements

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

NH ≅ G/Ntype
2. C2×#10622691C2semidirect
3. #13069605C2semidirect
4. #13067297C2semidirect
6. #13066454C2semidirect
278. C11#10164semidirect

Maximal subgroups

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

subgroupindex
#130797412
C2×#106226912
#130696052
#130672972
#130670672
#130664542
C11×#31412
#1016411