Finite Group Databasebeta

← #14655649

Subgroups — #14655649

Order 2816.

498 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 498 conjugacy classes of subgroups — too many to draw. Only its 103 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×#10622295C211yesmaximal, characteristic, complemented
3#13079009C211yesmaximal, characteristic
4#13069604C211yesmaximal, characteristic, complemented
5#13067298C211yesmaximal, characteristic, complemented
6#13066453C211yesmaximal, characteristic, complemented
7C11×#1492C211yesmaximal, characteristic
8C11×#532C2211yescharacteristic
9C2×#66922C2211yescharacteristic
10C2×#66922C2211yescharacteristic
11C11×#423C2211yescharacteristic
12C2×C4×C8×C11C2211yescharacteristic
13#10622845—22no—
14C2×#66882—22no—
15#10622694—21no—
16#10622692—21no—
17#10622683—21no—
18#10622683—21no—
19#10622668—22no—
20#10622647—22no—
21#10622621—22no—
22#10622538C2211yescharacteristic
23C4×#4318C2211yescharacteristic
24#10622295—22no—
25#10622295—22no—
26C11×D4⋊C8—22no—
27#10622192—22no—
28#10622119—22no—
29C2×C11×#41—21no—
30C22×Dic22—21no—
31C22×Dic22—21no—
32C2×C11×M16—21no—
33C22×C8×C11—21no—
34C11×C4⋊Q8D411yescharacteristic
35C11×#127D411yescharacteristic
36C11×#124—21no—
37C11×#121—21no—
38C11×#121—21no—
39C4×D4×C11—21no—
40C4×D4×C11—21no—
41C2×C42×C11C2311yescharacteristic
42C2×C4⋊Dic11—21no—
43C2×C4⋊Dic11—21no—
44C2×C4⋊Dic11—21no—
45C2×C4⋊Dic11D412yes—
46C2×#4318D412yes—
47#66922—21no—
48#66922—21no—
49#66922—21no—
50#66922—21no—
51#66922—21no—
52#66922—21no—
53#66922—21no—
54#66922D412yes—
55C11×C4⋊C8—21no—
56C11×C4⋊C8—21no—
57C4×C8×C11—21no—
58C4×C8×C11D412yes—
59#66899—24no—
60#66896—24no—
61#66896—24no—
62C22⋊(C11⋊C8)—21no—
63#66882—28no—
64#66872—24no—
65C4⋊(C11⋊C8)D412yes—
66#66867—21no—
67C4×C11⋊C8—21no—
68C4×C11⋊C8—21no—
69#10164—111nomaximal, Sylow
70C11×#41—42no—
71C11×#41—42no—
72C2×Q8×C11—21no—
73C2×D4×C11—21no—
74C2×D4×C11—21no—
75C2×D4×C11—21no—
76C2×D4×C11—41no—
77C22×C4×C11—41no—
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11#4111yescharacteristic
81C22×Dic11—22no—
82C22×Dic11—41no—
83C2×Dic22—22no—
84C2×Dic22—41no—
85C2×Dic22—41no—
86C2×Dic22—41no—
87C2×Dic22—82no—
88C2×Dic22—82no—
89C11×M16—42no—
90C2×C8×C11—24no—
91C2×C8×C11—22no—
92C2×C8×C11—41no—
93C11×C4⋊C4—21no—
94C11×C4⋊C4—21no—
95C11×C22⋊C4—41no—
96C11×C22⋊C4—41no—
97C42×C11C2×D411yescharacteristic
98C42×C11C2×D411yescharacteristic
99C42×C11C2×D411yescharacteristic
100C42×C11C2×D411yescharacteristic
101C4⋊Dic11—22no—
102C4⋊Dic11—22no—
103C4⋊Dic11—22no—
104C4⋊Dic11—22no—
105C4⋊Dic11—41no—
106C4⋊Dic11—41no—
107C4⋊Dic11—41no—
108C4⋊Dic11—41no—
109#4318—22no—
110#4318—22no—
111C2×C11⋊C8—22no—
112C2×C11⋊C8—22no—
113#3227—111no—
114C2×#500—111no—
115#3141—111no—
116#1997—111no—
117#1548—111no—
118#1492D1111yescharacteristic
119#1278—111no—
120C23×C11—41no—
121C23×C11#12111yescharacteristic
122Q8×C11—42no—
123D4×C11—42no—
124D4×C11—42no—
125D4×C11—42no—
126D4×C11—82no—
127C2×C4×C11—22no—
128C2×C4×C11—22no—
129C2×C4×C11—41no—
130C2×C4×C11—81no—
131C2×C4×C11—81no—
132C2×C4×C11#12011yescharacteristic
133C2×C4×C11#12011yescharacteristic
134C2×C4×C11#12011yescharacteristic
135C2×C4×C11#12111yescharacteristic
136C2×C4×C11#12111yescharacteristic
137C2×C4×C11#12711yescharacteristic
138C2×C4×C11#13512yes—
139C2×C4×C11#13712yes—
140C2×Dic11—42no—
141C2×Dic11—42no—
142C2×Dic11—82no—
143C2×Dic11—82no—
144Dic22—82no—
145Dic22—82no—
146Dic22—82no—
147Dic22—82no—
148C8×C11—24no—
149C8×C11—81no—
150C11⋊C8—42no—
151C11⋊C8—42no—
152#532C2×D1111yescharacteristic
153C2×C4⋊Q8—111no—
154C2×C4⋊Q8—111no—
155#500—222no—
156#500—222no—
157#498—221no—
158#489—222no—
159#487—221no—
160#486—221no—
161#486—221no—
162#481—222no—
163#476—222no—
164#431—111no—
165C2×#107—222no—
166#423C2×D1111yescharacteristic
167#417—222no—
168C4×M16—111no—
169C2×C4×C8C2×D1111yescharacteristic
170#343—222no—
171#333—222no—
172D4⋊C8—22no—
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#45212yes—
184C4×C11#45612yes—
185C4×C11#47212yes—
186C4×C11#49511yescharacteristic
187C4×C11#49711yescharacteristic
188Dic11—82no—
189Dic11—82no—
190C2×#41—21no—
191C22×Q8—221no—
192C22×Q8—221no—
193C2×M16—21no—
194C2×M16—112no—
195C22×C8—21no—
196C4⋊Q8—112no—
197C4⋊Q8—221no—
198C4⋊Q8—221no—
199C4⋊Q8—221no—
200C4⋊Q8—221no—
201C4⋊Q8—221no—
202C4⋊Q8—221no—
203C4⋊Q8—221no—
204C4⋊Q8D4411yescharacteristic
205#127D4411yescharacteristic
206#124—21no—
207#121—21no—
208#121—21no—
209C4×D4—21no—
210C4×D4—21no—
211C2×C4⋊C4—112no—
212C2×C4⋊C4—221no—
213C2×C4⋊C4—221no—
214C2×C4⋊C4—221no—
215C2×C42C22×D1111yescharacteristic
216#107—228no—
217#106—224no—
218C4⋊C8—21no—
219C4⋊C8—21no—
220C4⋊C8—112no—
221#103—224no—
222#102—224no—
223#102—224no—
224C22⋊C8—221no—
225#97—221no—
226C4×C8—21no—
227C4×C8—221no—
228C4×C8—221no—
229C4×C8C22⋊D1112yes—
230C2×C11—22no—
231C2×C11—161no—
232C2×C11#200511yescharacteristic
233C2×C11#201511yescharacteristic
234C2×C11#201811yescharacteristic
235#41—42no—
236#41—42no—
237C2×Q8—21no—
238C2×Q8—222no—
239C2×Q8—441no—
240C2×Q8—441no—
241C2×Q8—441no—
242C2×Q8—882no—
243C2×Q8—882no—
244C2×D4—21no—
245C2×D4—21no—
246C2×D4—21no—
247C2×D4—41no—
248C22×C4—41no—
249C22×C4—222no—
250C22×C4—441no—
251C22×C4#433911yescharacteristic
252C22×C4D4×D1111yescharacteristic
253C22×C4D4×D1111yescharacteristic
254M16—42no—
255M16—222no—
256M16—222no—
257C2×C8—24no—
258C2×C8—22no—
259C2×C8—41no—
260C2×C8—222no—
261C2×C8—222no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—222no—
265C4⋊C4—222no—
266C4⋊C4—222no—
267C4⋊C4—222no—
268C4⋊C4—441no—
269C4⋊C4—441no—
270C4⋊C4—441no—
271C4⋊C4—441no—
272C22⋊C4—41no—
273C22⋊C4—41no—
274C42C2×D4411yescharacteristic
275C42D4×D1111yescharacteristic
276C42D4×D1111yescharacteristic
277C42C2×C22⋊D1111yescharacteristic
278C11#1016411yescharacteristic, complemented, Sylow
279C23—41no—
280C23#6693711yescharacteristic
281Q8—42no—
282Q8—882no—
283Q8—882no—
284Q8—882no—
285Q8—882no—
286D4—42no—
287D4—42no—
288D4—42no—
289D4—82no—
290C2×C4—22no—
291C2×C4—22no—
292C2×C4—41no—
293C2×C4—81no—
294C2×C4—81no—
295C2×C4—442no—
296C2×C4—442no—
297C2×C4—882no—
298C2×C4—882no—
299C2×C4#6693511yescharacteristic
300C2×C4#6693511yescharacteristic
301C2×C4#6693711yescharacteristic
302C2×C4#6696512yes—
303C2×C4#6696812yes—
304C2×C4#6698311yescharacteristic
305C2×C4#6699011yescharacteristic
306C2×C4#6699311yescharacteristic
307C8—24no—
308C8—81no—
309C8—442no—
310C8—442no—
311C22—21no—
312C22—21no—
313C22—81no—
314C22—81no—
315C22—81no—
316C22#1062238012yes—
317C22#1062257311yescharacteristic
318C4—21no—
319C4—21no—
320C4—81no—
321C4—882no—
322C4—882no—
323C4#1062239612yes—
324C4#1062243912yes—
325C4#1062275512yes—
326C4#1062276811yescharacteristic
327C4#1062278011yescharacteristic
328C2—22no—
329C2—161no—
330C2#1306965111yescharacteristic
331C2#1306971211yescharacteristic
332C2#1306972511yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1492C2
socleC22×C11#392
prime radicalC11×#532C22
hypercenter#1492D11
hypocenterC11#10164
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1492

Complements

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

NH ≅ G/Ntype
2. C2×#10622295C2semidirect
4. #13069604C2semidirect
5. #13067298C2semidirect
6. #13066453C2semidirect
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×#106222952
#130790092
#130696042
#130672982
#130664532
C11×#14922
#1016411