Finite Group Databasebeta

← #14655438

Subgroups — #14655438

Order 2816.

456 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 83 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#13079806C211yesmaximal, characteristic
2#13079746C211yesmaximal, characteristic
3C2×#10622682C211yesmaximal, characteristic, complemented
4#13067332C211yesmaximal, characteristic, complemented
5#13067228C211yesmaximal, characteristic
6#13066516C211yesmaximal, characteristic, complemented
7C11×#1470C211yesmaximal, characteristic, complemented
8C2×C11×#125C2211yescharacteristic
9#10623008C2211yescharacteristic
10C2×#66922C2211yescharacteristic
11C11×#432C2211yescharacteristic
12C11×#431C2211yescharacteristic
13#10622682—22no—
14#10622682—22no—
15#10622680—21no—
16#10622679—22no—
17#10622678—21no—
18C2×#66874—21no—
19C2×#66874—21no—
20#10622581—21no—
21#10622580—21no—
22#10622539C2211yescharacteristic
23C2×#66867C2211yescharacteristic
24#10622455—22no—
25#10622348—22no—
26#10622307—21no—
27#10622293—21no—
28C11×#324—22no—
29#10622124—22no—
30#10622102—22no—
31C2×#4339—21no—
32C22×Dic22—21no—
33C11×#125—21no—
34C11×#125—21no—
35C11×#125—21no—
36C11×#125—21no—
37C2×C11×C4⋊C4—21no—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4D411yescharacteristic
40C2×C11×C4⋊C4D411yescharacteristic
41C2×C42×C11C2311yescharacteristic
42#66983—21no—
43#66983—21no—
44C2×C4⋊Dic11—21no—
45C2×C4⋊Dic11—21no—
46C22×C11⋊C8—21no—
47#66928—21no—
48#66927D411yescharacteristic
49C4×D44—21no—
50C4×D44—21no—
51#66922—21no—
52#66922—21no—
53#66922—21no—
54#66922D412yes—
55#66922D411yescharacteristic
56C11×C4⋊C8—21no—
57C11×C4⋊C8—21no—
58C11×C22⋊C8—21no—
59C11×C22⋊C8D412yes—
60C11×#97—21no—
61C4×C8×C11—21no—
62C22⋊(C11⋊C8)—21no—
63#66885—24no—
64#66881—24no—
65#66874—24no—
66#66874—24no—
67#66873—22no—
68#66873—22no—
69#66872—22no—
70#66871—22no—
71C4⋊(C11⋊C8)D412yes—
72#66867—21no—
73#66867—21no—
74#66867D412yes—
75#10134—111nomaximal, Sylow
76C22×C4×C11—21no—
77C22×C4×C11—21no—
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11#4111yescharacteristic
81C2×C22⋊D11—41no—
82C22×Dic11—41no—
83#4339—82no—
84C2×D44—21no—
85C2×D44—21no—
86C2×D44—21no—
87C2×C4×D11—41no—
88C2×Dic22—22no—
89C2×Dic22—21no—
90C2×Dic22—44no—
91C2×Dic22—41no—
92C2×C8×C11—22no—
93C2×C8×C11—41no—
94C11×C4⋊C4—21no—
95C11×C4⋊C4—21no—
96C11×C4⋊C4—21no—
97C11×C4⋊C4—21no—
98C11×C4⋊C4—41no—
99C11×C4⋊C4—41no—
100C11×C4⋊C4—41no—
101C11×C4⋊C4—41no—
102C42×C11C2×D411yescharacteristic
103C42×C11C2×D411yescharacteristic
104C42×C11C2×D411yescharacteristic
105C42×C11C2×D411yescharacteristic
106(C2×D11)⋊C4—41no—
107(C2×D11)⋊C4—41no—
108C4⋊Dic11—21no—
109C4⋊Dic11—21no—
110C4⋊Dic11—22no—
111C4⋊Dic11—22no—
112C4⋊Dic11—41no—
113C4⋊Dic11—41no—
114C2×C11⋊C8—22no—
115C2×C11⋊C8—22no—
116C2×C11⋊C8—42no—
117#3234—111no—
118#3227—111no—
119C2×#491—111no—
120#1556—111no—
121#1530—111no—
122#1470D1111yescharacteristic, complemented
123#1302—111no—
124C23×C11#12111yescharacteristic
125C22×D11—41no—
126C2×C4×C11—22no—
127C2×C4×C11—22no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11—42no—
132C2×C4×C11—81no—
133C2×C4×C11#12011yescharacteristic
134C2×C4×C11#12011yescharacteristic
135C2×C4×C11#12011yescharacteristic
136C2×C4×C11#12111yescharacteristic
137C2×C4×C11#12111yescharacteristic
138C2×C4×C11#12711yescharacteristic
139C22⋊D11—82no—
140C2×Dic11—42no—
141C2×Dic11—41no—
142C2×Dic11—82no—
143D44—42no—
144D44—42no—
145D44—81no—
146C4×D11—82no—
147Dic22—44no—
148Dic22—82no—
149Dic22—81no—
150C8×C11—42no—
151C8×C11—81no—
152C11⋊C8—42no—
153C11⋊C8—42no—
154#532—111no—
155C2×C4⋊Q8—111no—
156C2×#125C2×D1111yescharacteristic
157#501—221no—
158#498—221no—
159#491—222no—
160#491—222no—
161#490—221no—
162#486—221no—
163#481—221no—
164#481—222no—
165#480—221no—
166#478—222no—
167#476—222no—
168#432—111no—
169#432C2×D1111yescharacteristic
170#431C2×D1111yescharacteristic
171C2×#103—221no—
172C2×#103—221no—
173C2×#97—111no—
174#332—222no—
175#329—222no—
176#324—22no—
177C22×C11—21no—
178C22×C11—21no—
179C22×C11#39211yescharacteristic
180C22×C11#47112yes—
181C2×D11—81no—
182C2×D11—81no—
183C2×D11—81no—
184C4×C11—21no—
185C4×C11—21no—
186C4×C11—21no—
187C4×C11—21no—
188C4×C11—21no—
189C4×C11—81no—
190C4×C11—81no—
191C4×C11#45412yes—
192Dic11—82no—
193Dic11—81no—
194C2×#41—221no—
195C22×Q8—221no—
196C22×C8—221no—
197C4⋊Q8—112no—
198C4⋊Q8—111no—
199C4⋊Q8—221no—
200C4⋊Q8—221no—
201C4⋊Q8—221no—
202#127—111no—
203#125—21no—
204#125—21no—
205#125—21no—
206#125—21no—
207#124—221no—
208#121—221no—
209#121—221no—
210C4×D4—221no—
211C4×D4—221no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—221no—
215C2×C4⋊C4—221no—
216C2×C4⋊C4D4411yescharacteristic
217C2×C4⋊C4D4411yescharacteristic
218C2×C42C22×D1111yescharacteristic
219#107—222no—
220#106—222no—
221#106—224no—
222C4⋊C8—21no—
223C4⋊C8—21no—
224C4⋊C8—112no—
225#103—224no—
226#103—224no—
227#102—222no—
228#102—222no—
229#102—224no—
230C22⋊C8—21no—
231C22⋊C8—221no—
232C22⋊C8C22⋊D1112yes—
233#97—21no—
234#97—112no—
235#97—221no—
236#97—221no—
237C4×C8—21no—
238C2×C11—22no—
239C2×C11#200311yescharacteristic
240C2×C11#200911yescharacteristic
241C2×C11#201911yescharacteristic
242D11—161no—
243#41—882no—
244C2×Q8—222no—
245C2×Q8—221no—
246C2×Q8—444no—
247C2×Q8—441no—
248C2×D4—221no—
249C2×D4—221no—
250C2×D4—221no—
251C2×D4—441no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—441no—
255C22×C4—441no—
256C22×C4C2×D4411yescharacteristic
257C22×C4#433911yescharacteristic
258C22×C4C2×C22⋊D1111yescharacteristic
259C2×C8—22no—
260C2×C8—41no—
261C2×C8—222no—
262C2×C8—222no—
263C2×C8—442no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—221no—
273C4⋊C4—222no—
274C4⋊C4—222no—
275C4⋊C4—221no—
276C4⋊C4—441no—
277C4⋊C4—441no—
278C22⋊C4—441no—
279C22⋊C4—441no—
280C42D4×D1111yescharacteristic
281C42D4×D1111yescharacteristic
282C42D4×D1111yescharacteristic
283C42D4×D1111yescharacteristic
284C11#1013411yescharacteristic, complemented, Sylow
285C23—441no—
286C23#6698311yescharacteristic
287Q8—444no—
288Q8—881no—
289Q8—882no—
290D4—442no—
291D4—442no—
292D4—881no—
293D4—882no—
294C2×C4—22no—
295C2×C4—22no—
296C2×C4—41no—
297C2×C4—42no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—81no—
301C2×C4—441no—
302C2×C4—442no—
303C2×C4—882no—
304C2×C4—882no—
305C2×C4#6693511yescharacteristic
306C2×C4#6693511yescharacteristic
307C2×C4#6693711yescharacteristic
308C2×C4#6693711yescharacteristic
309C2×C4#6699011yescharacteristic
310C2×C4#6699311yescharacteristic
311C8—42no—
312C8—81no—
313C8—442no—
314C8—442no—
315C22—21no—
316C22—21no—
317C22—881no—
318C22—881no—
319C22—881no—
320C22#1062257311yescharacteristic
321C22#1062275412yes—
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—21no—
327C4—81no—
328C4—81no—
329C4—882no—
330C4—881no—
331C4#1062236612yes—
332C2—22no—
333C2—1761no—
334C2#1306964011yescharacteristic
335C2#1306967511yescharacteristic
336C2#1306973111yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1470C2
socleC22×C11#392
prime radical#10623008C22
hypercenter#1470D11
hypocenterC11#10134
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1470

Complements

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

NH ≅ G/Ntype
3. C2×#10622682C2semidirect
4. #13067332C2semidirect
6. #13066516C2semidirect
7. C11×#1470C2semidirect
122. #1470D11semidirect
284. C11#10134semidirect

Maximal subgroups

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

subgroupindex
#130798062
#130797462
C2×#106226822
#130673322
#130672282
#130665162
C11×#14702
#1013411