Finite Group Databasebeta

← #14655150

Subgroups — #14655150

Order 2816.

496 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 85 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#13079012C211yesmaximal, characteristic
3#13067333C211yesmaximal, characteristic, complemented
4#13067218C211yesmaximal, characteristic, complemented
5#13067123C211yesmaximal, characteristic
6#13066509C211yesmaximal, characteristic, complemented
7C11×#2660C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C11×#125C2211yescharacteristic
10#10623008C2211yescharacteristic
11C11×#398—22no—
12C11×#395—22no—
13C11×#384—21no—
14C11×#382—21no—
15C11×#376C2211yescharacteristic
16#10622706—21no—
17#10622702—22no—
18#10622701—21no—
19#10622680—21no—
20#10622679—22no—
21#10622678—21no—
22#10622581—21no—
23#10622580—21no—
24#10622579—22no—
25#10622539C2211yescharacteristic
26#10622539C2211yescharacteristic
27C4×#4318C2211yescharacteristic
28#10622185—22no—
29#10622181—22no—
30#10622089—22no—
31C22×Q8×C11—21no—
32C2×#4339—21no—
33C11×C4⋊Q8—21no—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×#125—21no—
38C11×#125—21no—
39C11×#125—21no—
40C11×#125—21no—
41C2×C11×C4⋊C4—21no—
42C2×C11×C4⋊C4—21no—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4—24no—
45C2×C11×C4⋊C4D412yes—
46C2×C11×C4⋊C4D411yescharacteristic
47C2×C11×C4⋊C4D411yescharacteristic
48C2×C42×C11—21no—
49C2×C42×C11C2311yescharacteristic
50#66983—21no—
51#66983—21no—
52C2×#4318—21no—
53#66928—21no—
54#66927D411yescharacteristic
55C4×D44—21no—
56C4×D44—21no—
57#66922D411yescharacteristic
58C11×#95—24no—
59C11×#95—21no—
60C11×#95D412yes—
61C22⋊(C11⋊C8)—21no—
62C22⋊(C11⋊C8)—21no—
63#66874—24no—
64#66873—24no—
65#66873—22no—
66#66873—22no—
67#66872—22no—
68#66871—22no—
69C4⋊(C11⋊C8)—21no—
70C4⋊(C11⋊C8)D412yes—
71#66867—21no—
72#66867—21no—
73#66867D412yes—
74C4×C11⋊C8—21no—
75#10093—111nomaximal, Sylow
76C2×Q8×C11—41no—
77C2×Q8×C11—41no—
78C2×Q8×C11—82no—
79C22×C4×C11—22no—
80C22×C4×C11—21no—
81C22×C4×C11—22no—
82C22×C4×C11—21no—
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C2×C22⋊D11—41no—
87#4339—44no—
88C2×D44—21no—
89C2×D44—21no—
90C2×D44—21no—
91C2×C4×D11—41no—
92C2×Dic22—21no—
93C11×C4⋊C4—21no—
94C11×C4⋊C4—21no—
95C11×C4⋊C4—22no—
96C11×C4⋊C4—21no—
97C11×C4⋊C4—21no—
98C11×C4⋊C4—22no—
99C11×C4⋊C4—41no—
100C11×C4⋊C4—41no—
101C11×C4⋊C4—41no—
102C11×C4⋊C4—41no—
103C11×C4⋊C4—41no—
104C11×C4⋊C4—41no—
105C11×C4⋊C4—84no—
106C42×C11—24no—
107C42×C11C2×D411yescharacteristic
108C42×C11C2×D411yescharacteristic
109C42×C11C2×D411yescharacteristic
110C42×C11#4111yescharacteristic
111(C2×D11)⋊C4—41no—
112(C2×D11)⋊C4—41no—
113C4⋊Dic11—21no—
114C4⋊Dic11—21no—
115#4318—42no—
116C2×C11⋊C8—22no—
117C2×C11⋊C8—22no—
118C2×C11⋊C8—41no—
119#3234—111no—
120#3141—111no—
121#2660D1111yescharacteristic, complemented
122#1556—111no—
123#1528—111no—
124#1505—111no—
125#1300—111no—
126C23×C11#12011yescharacteristic
127C22×D11—41no—
128Q8×C11—82no—
129Q8×C11—82no—
130C2×C4×C11—22no—
131C2×C4×C11—22no—
132C2×C4×C11—24no—
133C2×C4×C11—41no—
134C2×C4×C11—42no—
135C2×C4×C11—42no—
136C2×C4×C11—42no—
137C2×C4×C11—44no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—42no—
141C2×C4×C11—42no—
142C2×C4×C11#12011yescharacteristic
143C2×C4×C11#12011yescharacteristic
144C2×C4×C11#12111yescharacteristic
145C2×C4×C11#12111yescharacteristic
146C2×C4×C11#12111yescharacteristic
147C2×C4×C11#12711yescharacteristic
148C22⋊D11—82no—
149C2×Dic11—41no—
150D44—42no—
151D44—42no—
152D44—81no—
153C4×D11—82no—
154Dic22—42no—
155C11⋊C8—42no—
156C11⋊C8—42no—
157C11⋊C8—81no—
158#532—111no—
159C2×C4⋊Q8C2×D1111yescharacteristic
160C2×#125C2×D1111yescharacteristic
161#501—221no—
162#490—221no—
163#489—222no—
164#487—221no—
165#486—221no—
166#481—221no—
167#480—221no—
168#478—222no—
169#432—111no—
170#432—111no—
171#417—222no—
172C4×M16—111no—
173#398—22no—
174#395—22no—
175#384—21no—
176#382—21no—
177#376C2×D1111yescharacteristic
178#332—222no—
179#330—222no—
180#327—222no—
181C22×C11—21no—
182C22×C11—21no—
183C22×C11#39211yescharacteristic
184C22×C11#45412yes—
185C2×D11—81no—
186C2×D11—81no—
187C2×D11—81no—
188C4×C11—21no—
189C4×C11—21no—
190C4×C11—21no—
191C4×C11—21no—
192C4×C11—21no—
193C4×C11—44no—
194C4×C11—81no—
195C4×C11—81no—
196C4×C11—82no—
197C4×C11#45612yes—
198Dic11—81no—
199C2×#41—221no—
200C22×Q8—21no—
201C2×M16—221no—
202C4⋊Q8—21no—
203C4⋊Q8—21no—
204C4⋊Q8—21no—
205C4⋊Q8—21no—
206C4⋊Q8—111no—
207#127—111no—
208#125—21no—
209#125—21no—
210#125—21no—
211#125—21no—
212#124—221no—
213#121—221no—
214#121—221no—
215C4×D4—221no—
216C4×D4—221no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—24no—
221C2×C4⋊C4C22⋊D1111yescharacteristic
222C2×C4⋊C4C22⋊D1111yescharacteristic
223C2×C4⋊C4C22⋊D1112yes—
224C2×C42—21no—
225C2×C42C22×D1111yescharacteristic
226#107—222no—
227#106—222no—
228C4⋊C8—112no—
229C4⋊C8—221no—
230#103—224no—
231#102—224no—
232#102—222no—
233#102—222no—
234C22⋊C8—221no—
235C22⋊C8—221no—
236#97—112no—
237#97—221no—
238#97—221no—
239C4×C8—221no—
240#95—24no—
241#95—21no—
242#95C22⋊D1112yes—
243C2×C11—22no—
244C2×C11#200311yescharacteristic
245C2×C11#200511yescharacteristic
246C2×C11#200811yescharacteristic
247D11—161no—
248#41—444no—
249C2×Q8—41no—
250C2×Q8—41no—
251C2×Q8—82no—
252C2×Q8—221no—
253C2×D4—221no—
254C2×D4—221no—
255C2×D4—221no—
256C2×D4—441no—
257C22×C4—22no—
258C22×C4—21no—
259C22×C4—22no—
260C22×C4—21no—
261C22×C4—441no—
262C22×C4C2×C22⋊D1111yescharacteristic
263C22×C4C2×C22⋊D1111yescharacteristic
264C22×C4C2×C22⋊D1111yescharacteristic
265M16—442no—
266C2×C8—222no—
267C2×C8—222no—
268C2×C8—441no—
269C4⋊C4—22no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—22no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—84no—
282C4⋊C4—221no—
283C4⋊C4—221no—
284C22⋊C4—441no—
285C22⋊C4—441no—
286C42—24no—
287C42D4×D1111yescharacteristic
288C42D4×D1111yescharacteristic
289C42D4×D1111yescharacteristic
290C42#434111yescharacteristic
291C11#1009311yescharacteristic, complemented, Sylow
292C23—441no—
293C23#6700611yescharacteristic
294Q8—82no—
295Q8—82no—
296Q8—442no—
297D4—442no—
298D4—442no—
299D4—881no—
300D4—882no—
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—24no—
304C2×C4—41no—
305C2×C4—42no—
306C2×C4—42no—
307C2×C4—42no—
308C2×C4—44no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—441no—
314C2×C4—882no—
315C2×C4#6699011yescharacteristic
316C2×C4#6699011yescharacteristic
317C2×C4#6699111yescharacteristic
318C2×C4#6699211yescharacteristic
319C2×C4#6699211yescharacteristic
320C2×C4#6699311yescharacteristic
321C8—442no—
322C8—442no—
323C8—881no—
324C22—21no—
325C22—21no—
326C22—881no—
327C22—881no—
328C22—881no—
329C22#1062283611yescharacteristic
330C22#1062285812yes—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—21no—
336C4—44no—
337C4—81no—
338C4—82no—
339C4—81no—
340C4—881no—
341C4#1062270812yes—
342C2—22no—
343C2—1761no—
344C2#1306963611yescharacteristic
345C2#1306965211yescharacteristic
346C2#1306966911yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#2660C2
socleC22×C11#392
prime radical#10623008C22
hypercenter#2660D11
hypocenterC11#10093
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2660

Complements

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

NH ≅ G/Ntype
3. #13067333C2semidirect
4. #13067218C2semidirect
6. #13066509C2semidirect
7. C11×#2660C2semidirect
121. #2660D11semidirect
291. C11#10093semidirect

Maximal subgroups

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

subgroupindex
#130798062
#130790122
#130673332
#130672182
#130671232
#130665092
C11×#26602
#1009311