Finite Group Databasebeta

← #14655544

Subgroups — #14655544

Order 2816.

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

normal subgroups only

This group has 528 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#13079764C211yesmaximal, characteristic, complemented
2#13078992C211yesmaximal, characteristic
3C2×#10622307C211yesmaximal, characteristic
4#13069604C211yesmaximal, characteristic, complemented
5#13067285C211yesmaximal, characteristic
6#13066453C211yesmaximal, characteristic, complemented
7C11×#1493C211yesmaximal, characteristic, complemented
8C11×#533C2211yescharacteristic
9C2×#66927C2211yescharacteristic
10C2×#66922C2211yescharacteristic
11C11×#423C2211yescharacteristic
12C2×C4×C8×C11C2211yescharacteristic
13C2×#66885—22no—
14#10622701—21no—
15#10622701—21no—
16#10622694—21no—
17#10622691—21no—
18#10622680—22no—
19#10622657—22no—
20#10622634—22no—
21#10622614—22no—
22#10622538C2211yescharacteristic
23C4×#4318C2211yescharacteristic
24#10622307—22no—
25#10622307—22no—
26C11×Q8⋊C8—22no—
27#10622192—22no—
28#10622123—22no—
29C22×D44—21no—
30C22×D44—21no—
31C22×D44—21no—
32C22×Dic22—21no—
33C2×C11×M16—21no—
34C22×C8×C11—21no—
35C11×C4⋊Q8D411yescharacteristic
36C11×C4⋊Q8D411yescharacteristic
37C11×#125—21no—
38C11×C22⋊Q8—21no—
39C11×C22⋊Q8—21no—
40C4×Q8×C11—21no—
41C4×Q8×C11—21no—
42C11×#117—21no—
43C2×C42×C11C2311yescharacteristic
44C2×C4⋊Dic11—21no—
45C2×C4⋊Dic11D412yes—
46C2×#4318D412yes—
47#66927—21no—
48#66927—21no—
49#66927—21no—
50#66927D412yes—
51#66922—21no—
52#66922—21no—
53#66922—21no—
54#66922—21no—
55C11×C4⋊C8—21no—
56C11×C4⋊C8—21no—
57C4×C8×C11—21no—
58C4×C8×C11D412yes—
59#66899—24no—
60C22⋊(C11⋊C8)—21no—
61#66885—28no—
62#66873—24no—
63#66873—24no—
64#66871—24no—
65C4⋊(C11⋊C8)D412yes—
66#66867—21no—
67C4×C11⋊C8—21no—
68C4×C11⋊C8—21no—
69#10149—111nomaximal, Sylow
70C23×D11—41no—
71C2×Q8×C11—21no—
72C2×Q8×C11—21no—
73C22×C4×C11C2×D411yescharacteristic
74C22×C4×C11C2×D411yescharacteristic
75C22×C4×C11#4111yescharacteristic
76C22×Dic11—22no—
77C2×D44—22no—
78C2×D44—22no—
79C2×D44—22no—
80C2×D44—44no—
81C2×D44—41no—
82C2×D44—41no—
83C2×D44—41no—
84C2×D44—42no—
85C2×D44—42no—
86C2×D44—82no—
87C2×Dic22—41no—
88C2×Dic22—41no—
89C2×Dic22—82no—
90C11×M16—42no—
91C2×C8×C11—22no—
92C2×C8×C11—42no—
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×C22⋊C4—41no—
101C42×C11—41no—
102C42×C11C2×D411yescharacteristic
103C42×C11C2×D411yescharacteristic
104C42×C11C2×D411yescharacteristic
105C42×C11C2×D411yescharacteristic
106C4⋊Dic11—22no—
107C4⋊Dic11—22no—
108C4⋊Dic11—41no—
109C4⋊Dic11—41no—
110#4318—22no—
111#4318—22no—
112C2×C11⋊C8—22no—
113C2×C11⋊C8—22no—
114#3230—111no—
115#3138—111no—
116C2×#486—111no—
117#1997—111no—
118#1545—111no—
119#1493D1111yescharacteristic, complemented
120#1278—111no—
121C23×C11#12111yescharacteristic
122C22×D11—42no—
123C22×D11—82no—
124C22×D11—82no—
125C22×D11—82no—
126Q8×C11—42no—
127Q8×C11—42no—
128C2×C4×C11—22no—
129C2×C4×C11—22no—
130C2×C4×C11—41no—
131C2×C4×C11—41no—
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—82no—
142D44—44no—
143D44—44no—
144D44—82no—
145D44—82no—
146D44—82no—
147D44—81no—
148D44—81no—
149Dic22—82no—
150Dic22—82no—
151C8×C11—42no—
152C8×C11—81no—
153C11⋊C8—42no—
154C11⋊C8—42no—
155#533C2×D1111yescharacteristic
156C2×C4⋊Q8—111no—
157C2×#127—111no—
158#500—221no—
159#490—222no—
160#487—221no—
161#486—222no—
162#486—221no—
163#486—221no—
164#486—222no—
165#484—222no—
166#477—222no—
167#431—111no—
168#423C2×D1111yescharacteristic
169#418—222no—
170C2×#102—222no—
171C4×M16—111no—
172C2×C4×C8C2×D1111yescharacteristic
173#343—222no—
174#331—222no—
175Q8⋊C8—22no—
176C22×C11—21no—
177C22×C11—21no—
178C22×C11#39211yescharacteristic
179C22×C11#46412yes—
180C2×D11—82no—
181C2×D11—82no—
182C2×D11—82no—
183C2×D11—164no—
184C4×C11—21no—
185C4×C11—21no—
186C4×C11—81no—
187C4×C11—81no—
188C4×C11#45212yes—
189C4×C11#45412yes—
190C4×C11#47212yes—
191C4×C11#49511yescharacteristic
192C4×C11#49711yescharacteristic
193Dic11—82no—
194C22×Q8—221no—
195C22×D4—221no—
196C22×D4—221no—
197C22×D4—221no—
198C2×M16—21no—
199C2×M16—112no—
200C22×C8—21no—
201C4⋊Q8—221no—
202C4⋊Q8—221no—
203C4⋊Q8—221no—
204C4⋊Q8—221no—
205C4⋊Q8D4411yescharacteristic
206C4⋊Q8D4411yescharacteristic
207#127—112no—
208#127—221no—
209#127—221no—
210#127—221no—
211#125—21no—
212C22⋊Q8—21no—
213C22⋊Q8—21no—
214C4×Q8—21no—
215C4×Q8—21no—
216#117—21no—
217C2×C4⋊C4—112no—
218C2×C4⋊C4—221no—
219C2×C42C22×D1111yescharacteristic
220#107—224no—
221C4⋊C8—21no—
222C4⋊C8—21no—
223C4⋊C8—112no—
224#103—224no—
225#102—224no—
226#102—224no—
227#102—228no—
228C22⋊C8—221no—
229#97—221no—
230C4×C8—21no—
231C4×C8—221no—
232C4×C8—221no—
233C4×C8C22⋊D1112yes—
234C2×C11—22no—
235C2×C11#200311yescharacteristic
236C2×C11#201511yescharacteristic
237C2×C11#201811yescharacteristic
238D11—162no—
239C24—441no—
240C2×Q8—21no—
241C2×Q8—21no—
242C2×Q8—441no—
243C2×Q8—441no—
244C2×Q8—882no—
245C2×D4—222no—
246C2×D4—222no—
247C2×D4—222no—
248C2×D4—444no—
249C2×D4—441no—
250C2×D4—442no—
251C2×D4—442no—
252C2×D4—441no—
253C2×D4—441no—
254C2×D4—882no—
255C22×C4—222no—
256C22×C4#433911yescharacteristic
257C22×C4D4×D1111yescharacteristic
258C22×C4D4×D1111yescharacteristic
259M16—42no—
260M16—222no—
261M16—222no—
262C2×C8—22no—
263C2×C8—42no—
264C2×C8—41no—
265C2×C8—222no—
266C2×C8—222no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—222no—
274C4⋊C4—222no—
275C4⋊C4—441no—
276C4⋊C4—441no—
277C22⋊C4—41no—
278C42—41no—
279C42C2×D4411yescharacteristic
280C42D4×D1111yescharacteristic
281C42D4×D1111yescharacteristic
282C42C2×C22⋊D1111yescharacteristic
283C11#1014911yescharacteristic, complemented, Sylow
284C23—442no—
285C23—882no—
286C23—882no—
287C23—882no—
288C23#6693711yescharacteristic
289Q8—42no—
290Q8—42no—
291Q8—882no—
292Q8—882no—
293D4—444no—
294D4—444no—
295D4—882no—
296D4—882no—
297D4—881no—
298D4—881no—
299D4—882no—
300C2×C4—22no—
301C2×C4—22no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—442no—
305C2×C4—882no—
306C2×C4#6693511yescharacteristic
307C2×C4#6693511yescharacteristic
308C2×C4#6693711yescharacteristic
309C2×C4#6696912yes—
310C2×C4#6697112yes—
311C2×C4#6698311yescharacteristic
312C2×C4#6699011yescharacteristic
313C2×C4#6699311yescharacteristic
314C8—42no—
315C8—81no—
316C8—442no—
317C8—442no—
318C22—21no—
319C22—21no—
320C22—882no—
321C22—882no—
322C22—882no—
323C22—1764no—
324C22#1062241112yes—
325C22#1062257311yescharacteristic
326C4—21no—
327C4—21no—
328C4—81no—
329C4—81no—
330C4—882no—
331C4#1062242312yes—
332C4#1062244012yes—
333C4#1062275512yes—
334C4#1062278111yescharacteristic
335C4#1062280311yescharacteristic
336C2—22no—
337C2—1762no—
338C2#1306963711yescharacteristic
339C2#1306971111yescharacteristic
340C2#1306972511yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1493C2
socleC22×C11#392
prime radicalC2×#66927C22
hypercenter#1493D11
hypocenterC11#10149
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1493

Complements

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

NH ≅ G/Ntype
1. #13079764C2semidirect
4. #13069604C2semidirect
6. #13066453C2semidirect
7. C11×#1493C2semidirect
119. #1493D11semidirect
283. C11#10149semidirect

Maximal subgroups

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

subgroupindex
#130797642
#130789922
C2×#106223072
#130696042
#130672852
#130664532
C11×#14932
#1014911