Finite Group Databasebeta

← #14655650

Subgroups — #14655650

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#13079746C211yesmaximal, characteristic
2C2×#10622295C211yesmaximal, characteristic, complemented
3#13079010C211yesmaximal, characteristic
4#13069605C211yesmaximal, characteristic, complemented
5#13067296C211yesmaximal, characteristic, complemented
6#13067068C211yesmaximal, characteristic
7C11×#1278C211yesmaximal, characteristic, complemented
8#10623008C2211yescharacteristic
9C2×#66922C2211yescharacteristic
10C2×#66922C2211yescharacteristic
11C11×#431C2211yescharacteristic
12C4×C11×M16C2211yescharacteristic
13C2×C4×C8×C11C2211yescharacteristic
14#10622746—22no—
15C2×#66882—22no—
16#10622537C2211yescharacteristic
17#10622455—22no—
18#10622348—22no—
19#10622327—22no—
20#10622307—21no—
21#10622307—21no—
22#10622295—22no—
23#10622295—22no—
24#10622294—21no—
25#10622293—21no—
26#10622192—22no—
27#10622119—22no—
28#10622097—22no—
29C2×#4339—21no—
30C22×Dic22—21no—
31C22×Dic22—21no—
32C2×C11×M16D412yes—
33C22×C8×C11—21no—
34C2×C42×C11C2311yescharacteristic
35#66983—21no—
36#66983—21no—
37C2×C4⋊Dic11—21no—
38C2×C4⋊Dic11—21no—
39C2×C4⋊Dic11—21no—
40C2×C4⋊Dic11D412yes—
41C2×#4318—21no—
42#66928—21no—
43#66927D411yescharacteristic
44C4×D44—21no—
45C4×D44—21no—
46#66922—21no—
47#66922—21no—
48#66922—21no—
49#66922—21no—
50#66922—21no—
51#66922—21no—
52#66922—21no—
53#66922D412yes—
54#66922D411yescharacteristic
55C11×C4⋊C8D412yes—
56C11×C22⋊C8—21no—
57C11×#97—21no—
58C4×C8×C11—21no—
59C4×C8×C11—21no—
60C4×C8×C11—21no—
61C4×C8×C11D412yes—
62#66885—24no—
63#66885—24no—
64#66882—28no—
65#66881—24no—
66#66880—24no—
67C4⋊(C11⋊C8)—21no—
68C4⋊(C11⋊C8)—21no—
69#10164—111nomaximal, Sylow
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11#4111yescharacteristic
73C2×C22⋊D11—41no—
74C22×Dic11—22no—
75C22×Dic11—41no—
76#4339—42no—
77#4339—42no—
78C2×D44—21no—
79C2×D44—21no—
80C2×D44—21no—
81C2×C4×D11—41no—
82C2×Dic22—21no—
83C2×Dic22—22no—
84C2×Dic22—41no—
85C2×Dic22—41no—
86C2×Dic22—41no—
87C2×Dic22—82no—
88C2×Dic22—82no—
89C11×M16—22no—
90C11×M16—22no—
91C2×C8×C11—24no—
92C2×C8×C11—22no—
93C2×C8×C11—22no—
94C2×C8×C11—22no—
95C42×C11C2×D411yescharacteristic
96C42×C11C2×D411yescharacteristic
97C42×C11C2×D411yescharacteristic
98C42×C11C2×D411yescharacteristic
99(C2×D11)⋊C4—41no—
100(C2×D11)⋊C4—41no—
101C4⋊Dic11—22no—
102C4⋊Dic11—21no—
103C4⋊Dic11—22no—
104C4⋊Dic11—22no—
105C4⋊Dic11—22no—
106C4⋊Dic11—21no—
107C4⋊Dic11—41no—
108C4⋊Dic11—41no—
109C4⋊Dic11—41no—
110C4⋊Dic11—41no—
111#4318—42no—
112C2×C11⋊C8—41no—
113#3227—111no—
114C2×#500—111no—
115#3141—111no—
116#1997—111no—
117#1548—111no—
118#1492—111no—
119#1278D1111yescharacteristic, complemented
120C23×C11#12111yescharacteristic
121C22×D11—41no—
122C2×C4×C11—22no—
123C2×C4×C11—22no—
124C2×C4×C11#12011yescharacteristic
125C2×C4×C11#12011yescharacteristic
126C2×C4×C11#12011yescharacteristic
127C2×C4×C11#12111yescharacteristic
128C2×C4×C11#12111yescharacteristic
129C2×C4×C11#12711yescharacteristic
130C2×C4×C11#13512yes—
131C2×C4×C11#13712yes—
132C22⋊D11—82no—
133C2×Dic11—42no—
134C2×Dic11—42no—
135C2×Dic11—41no—
136C2×Dic11—82no—
137C2×Dic11—82no—
138D44—42no—
139D44—42no—
140D44—42no—
141C4×D11—81no—
142C4×D11—81no—
143Dic22—42no—
144Dic22—82no—
145Dic22—82no—
146Dic22—82no—
147Dic22—82no—
148C8×C11—24no—
149C8×C11—42no—
150C8×C11—42no—
151C11⋊C8—81no—
152#532—111no—
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#431C2×D1111yescharacteristic
165C2×#107—222no—
166#423—111no—
167#417—222no—
168C4×M16C2×D1111yescharacteristic
169C2×C4×C8C2×D1111yescharacteristic
170#343—222no—
171#333—222no—
172D4⋊C8—222no—
173C22×C11—21no—
174C22×C11—21no—
175C22×C11#39211yescharacteristic
176C22×C11#46412yes—
177C2×D11—81no—
178C2×D11—81no—
179C2×D11—81no—
180C4×C11—21no—
181C4×C11—21no—
182C4×C11#45212yes—
183C4×C11#45612yes—
184C4×C11#47212yes—
185C4×C11#49511yescharacteristic
186C4×C11#49711yescharacteristic
187Dic11—81no—
188Dic11—82no—
189Dic11—82no—
190C2×#41—221no—
191C22×Q8—221no—
192C22×Q8—221no—
193C2×M16—221no—
194C2×M16D4412yes—
195C22×C8—21no—
196C4⋊Q8—112no—
197C4⋊Q8—111no—
198C4⋊Q8—221no—
199C4⋊Q8—221no—
200C4⋊Q8—221no—
201C4⋊Q8—221no—
202C4⋊Q8—221no—
203C4⋊Q8—221no—
204C4⋊Q8—221no—
205#127—111no—
206#124—221no—
207#121—221no—
208#121—221no—
209C4×D4—221no—
210C4×D4—221no—
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—221no—
219C4⋊C8—221no—
220C4⋊C8D4412yes—
221#103—224no—
222#102—224no—
223#102—224no—
224C22⋊C8—21no—
225#97—21no—
226C4×C8—21no—
227C4×C8—21no—
228C4×C8—21no—
229C4×C8D4412yes—
230C2×C11—22no—
231C2×C11#200511yescharacteristic
232C2×C11#201511yescharacteristic
233C2×C11#201811yescharacteristic
234D11—161no—
235#41—442no—
236#41—442no—
237C2×Q8—221no—
238C2×Q8—222no—
239C2×Q8—441no—
240C2×Q8—441no—
241C2×Q8—441no—
242C2×Q8—882no—
243C2×Q8—882no—
244C2×D4—221no—
245C2×D4—221no—
246C2×D4—221no—
247C2×D4—441no—
248C22×C4—222no—
249C22×C4—441no—
250C22×C4—441no—
251C22×C4C2×D4411yescharacteristic
252C22×C4D4×D1111yescharacteristic
253C22×C4#434311yescharacteristic
254M16—22no—
255M16—22no—
256M16—442no—
257C2×C8—24no—
258C2×C8—22no—
259C2×C8—22no—
260C2×C8—22no—
261C2×C8—441no—
262C4⋊C4—222no—
263C4⋊C4—222no—
264C4⋊C4—221no—
265C4⋊C4—222no—
266C4⋊C4—222no—
267C4⋊C4—221no—
268C4⋊C4—441no—
269C4⋊C4—441no—
270C4⋊C4—441no—
271C4⋊C4—441no—
272C22⋊C4—441no—
273C22⋊C4—441no—
274C42C2×D4411yescharacteristic
275C42C2×D4411yescharacteristic
276C42D4×D1111yescharacteristic
277C42D4×D1111yescharacteristic
278C11#1016411yescharacteristic, complemented, Sylow
279C23—441no—
280C23#6694811yescharacteristic
281Q8—442no—
282Q8—882no—
283Q8—882no—
284Q8—882no—
285Q8—882no—
286D4—442no—
287D4—442no—
288D4—442no—
289D4—882no—
290C2×C4—22no—
291C2×C4—22no—
292C2×C4—441no—
293C2×C4—442no—
294C2×C4—442no—
295C2×C4—882no—
296C2×C4—881no—
297C2×C4—881no—
298C2×C4—882no—
299C2×C4#6692711yescharacteristic
300C2×C4#6693511yescharacteristic
301C2×C4#6693511yescharacteristic
302C2×C4#6693511yescharacteristic
303C2×C4#6694811yescharacteristic
304C2×C4#6694811yescharacteristic
305C2×C4#6695712yes—
306C2×C4#6696212yes—
307C8—24no—
308C8—42no—
309C8—42no—
310C8—881no—
311C22—21no—
312C22—21no—
313C22—881no—
314C22—881no—
315C22—881no—
316C22#1062228411yescharacteristic
317C22#1062245812yes—
318C4—21no—
319C4—21no—
320C4—881no—
321C4—882no—
322C4—882no—
323C4#1062230911yescharacteristic
324C4#1062232811yescharacteristic
325C4#1062234612yes—
326C4#1062243912yes—
327C4#1062251012yes—
328C2—22no—
329C2—1761no—
330C2#1306965511yescharacteristic
331C2#1306971311yescharacteristic
332C2#1306972611yescharacteristic
subgroupG/H
centerC22#10622284
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1278C2
socleC22×C11#392
prime radical#10623008C22
hypercenter#1278D11
hypocenterC11#10164
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1278

Complements

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

NH ≅ G/Ntype
2. C2×#10622295C2semidirect
4. #13069605C2semidirect
5. #13067296C2semidirect
7. C11×#1278C2semidirect
119. #1278D11semidirect
278. C11#10164semidirect

Maximal subgroups

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

subgroupindex
#130797462
C2×#106222952
#130790102
#130696052
#130672962
#130670682
C11×#12782
#1016411