Finite Group Databasebeta

← #14655606

Subgroups — #14655606

Order 2816.

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

normal subgroups only

This group has 514 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#13079737C211yesmaximal, characteristic
2#13079010C211yesmaximal, characteristic
3C2×#10622706C211yesmaximal, characteristic, complemented
4#13067302C211yesmaximal, characteristic, complemented
5#13067066C211yesmaximal, characteristic
6#13066454C211yesmaximal, characteristic, complemented
7C11×#1966C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9#10623008C2211yescharacteristic
10C2×#66922C2211yescharacteristic
11C11×#423C2211yescharacteristic
12C2×C11×#101—22no—
13C4×C11×M16C2211yescharacteristic
14#10622746—22no—
15#10622706—22no—
16#10622706—22no—
17#10622701—21no—
18#10622700—22no—
19#10622691—21no—
20C2×#66874—22no—
21#10622580—22no—
22#10622538C2211yescharacteristic
23C2×C4×C11⋊C8C2211yescharacteristic
24#10622327—22no—
25#10622307—21no—
26#10622294—21no—
27#10622124—22no—
28#10622121—22no—
29C22×Q8×C11—21no—
30C2×#4339—21no—
31C22×Dic22—21no—
32C2×C11×M16—21no—
33C2×C11×M16D412yes—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4D412yes—
40C2×C42×C11C2311yescharacteristic
41#66983—21no—
42#66983—21no—
43C2×C4⋊Dic11—21no—
44C2×C4⋊Dic11—21no—
45C22×C11⋊C8—21no—
46#66928—21no—
47#66927D411yescharacteristic
48C4×D44—21no—
49C4×D44—21no—
50#66922—21no—
51#66922—21no—
52#66922—21no—
53#66922D412yes—
54#66922D411yescharacteristic
55C11×C4⋊C8—21no—
56C11×C4⋊C8—21no—
57C11×#101—44no—
58C11×#97—21no—
59C4×C8×C11—21no—
60C22⋊(C11⋊C8)—21no—
61#66885—24no—
62#66880—24no—
63#66874—28no—
64#66873—24no—
65#66871—24no—
66C4⋊(C11⋊C8)D412yes—
67C4×C11⋊C8—21no—
68C4×C11⋊C8—21no—
69C4×C11⋊C8D412yes—
70#10158—111nomaximal, Sylow
71C2×Q8×C11—41no—
72C2×Q8×C11—41no—
73C2×Q8×C11—42no—
74C2×Q8×C11—42no—
75C22×C4×C11—22no—
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11#4111yescharacteristic
79C2×C22⋊D11—41no—
80C22×Dic11—41no—
81#4339—42no—
82#4339—42no—
83C2×D44—21no—
84C2×D44—21no—
85C2×D44—21no—
86C2×C4×D11—41no—
87C2×Dic22—22no—
88C2×Dic22—21no—
89C2×Dic22—44no—
90C2×Dic22—41no—
91C11×M16—22no—
92C11×M16—22no—
93C11×M16—42no—
94C2×C8×C11—22no—
95C2×C8×C11—41no—
96C11×C4⋊C4—22no—
97C11×C4⋊C4—22no—
98C11×C4⋊C4—41no—
99C11×C4⋊C4—41no—
100C42×C11C2×D411yescharacteristic
101C42×C11C2×D411yescharacteristic
102C42×C11C2×D411yescharacteristic
103C42×C11C2×D411yescharacteristic
104(C2×D11)⋊C4—41no—
105(C2×D11)⋊C4—41no—
106C4⋊Dic11—21no—
107C4⋊Dic11—22no—
108C4⋊Dic11—22no—
109C4⋊Dic11—21no—
110C4⋊Dic11—41no—
111C4⋊Dic11—41no—
112C2×C11⋊C8—22no—
113C2×C11⋊C8—22no—
114C2×C11⋊C8—42no—
115#3226—111no—
116#3141—111no—
117C2×#487—111no—
118#1966D1111yescharacteristic, complemented
119#1549—111no—
120#1492—111no—
121#1278—111no—
122C23×C11#12111yescharacteristic
123C22×D11—41no—
124Q8×C11—82no—
125Q8×C11—81no—
126Q8×C11—81no—
127C2×C4×C11—22no—
128C2×C4×C11—22no—
129C2×C4×C11—42no—
130C2×C4×C11—44no—
131C2×C4×C11#12011yescharacteristic
132C2×C4×C11#12011yescharacteristic
133C2×C4×C11#12011yescharacteristic
134C2×C4×C11#12111yescharacteristic
135C2×C4×C11#12111yescharacteristic
136C2×C4×C11#12711yescharacteristic
137C2×C4×C11#13512yes—
138C2×C4×C11AGL(1,ℤ/8)12yes—
139C22⋊D11—82no—
140C2×Dic11—42no—
141C2×Dic11—41no—
142C2×Dic11—82no—
143D44—42no—
144D44—42no—
145D44—42no—
146C4×D11—81no—
147C4×D11—81no—
148Dic22—44no—
149Dic22—42no—
150Dic22—82no—
151C8×C11—42no—
152C8×C11—81no—
153C11⋊C8—42no—
154C11⋊C8—42no—
155#532—111no—
156C2×C4⋊Q8—111no—
157C2×C4⋊Q8C2×D1111yescharacteristic
158#500—221no—
159#489—222no—
160#487—221no—
161#487—222no—
162#487—222no—
163#486—221no—
164#486—221no—
165#480—222no—
166#474—222no—
167#431—111no—
168#423C2×D1111yescharacteristic
169#417—222no—
170C2×#103—222no—
171C2×#101—22no—
172C4×M16C2×D1111yescharacteristic
173C2×C4×C8—111no—
174#332—222no—
175D4⋊C8—222no—
176C22×C11—21no—
177C22×C11—21no—
178C22×C11#39211yescharacteristic
179C22×C11#46312yes—
180C2×D11—81no—
181C2×D11—81no—
182C2×D11—81no—
183C4×C11—21no—
184C4×C11—21no—
185C4×C11—82no—
186C4×C11#44912yes—
187C4×C11#45412yes—
188C4×C11#47312yes—
189C4×C11#49511yescharacteristic
190C4×C11#49611yescharacteristic
191Dic11—82no—
192Dic11—81no—
193C2×#41—221no—
194C22×Q8—21no—
195C22×Q8—221no—
196C2×M16—21no—
197C2×M16C22⋊D1112yes—
198C22×C8—221no—
199C4⋊Q8—21no—
200C4⋊Q8—21no—
201C4⋊Q8—21no—
202C4⋊Q8—21no—
203C4⋊Q8—112no—
204C4⋊Q8—111no—
205C4⋊Q8—221no—
206C4⋊Q8—221no—
207C4⋊Q8—221no—
208#127—111no—
209#124—221no—
210#121—221no—
211#121—221no—
212C4×D4—221no—
213C4×D4—221no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—221no—
216C2×C4⋊C4—221no—
217C2×C4⋊C4D4412yes—
218C2×C42C22×D1111yescharacteristic
219#107—224no—
220C4⋊C8—21no—
221C4⋊C8—21no—
222C4⋊C8—112no—
223#103—228no—
224#103—224no—
225#102—224no—
226#102—224no—
227#101—44no—
228C22⋊C8—221no—
229#97—21no—
230C4×C8—21no—
231C4×C8—112no—
232C4×C8—221no—
233C4×C8—221no—
234C2×C11—22no—
235C2×C11#200311yescharacteristic
236C2×C11#201211yescharacteristic
237C2×C11#202011yescharacteristic
238D11—161no—
239#41—442no—
240#41—442no—
241C2×Q8—42no—
242C2×Q8—41no—
243C2×Q8—41no—
244C2×Q8—42no—
245C2×Q8—222no—
246C2×Q8—221no—
247C2×Q8—444no—
248C2×Q8—441no—
249C2×D4—221no—
250C2×D4—221no—
251C2×D4—221no—
252C2×D4—441no—
253C22×C4—22no—
254C22×C4—441no—
255C22×C4—441no—
256C22×C4C2×D4411yescharacteristic
257C22×C4#433911yescharacteristic
258C22×C4C2×C22⋊D1111yescharacteristic
259M16—22no—
260M16—22no—
261M16—42no—
262C2×C8—22no—
263C2×C8—41no—
264C2×C8—222no—
265C2×C8—222no—
266C2×C8—442no—
267C4⋊C4—22no—
268C4⋊C4—22no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—221no—
272C4⋊C4—222no—
273C4⋊C4—221no—
274C4⋊C4—222no—
275C4⋊C4—441no—
276C4⋊C4—441no—
277C22⋊C4—441no—
278C22⋊C4—441no—
279C42D4×D1111yescharacteristic
280C42D4×D1111yescharacteristic
281C42D4×D1111yescharacteristic
282C42D4×D1111yescharacteristic
283C11#1015811yescharacteristic, complemented, Sylow
284C23—441no—
285C23#6698311yescharacteristic
286Q8—82no—
287Q8—81no—
288Q8—81no—
289Q8—444no—
290Q8—442no—
291Q8—882no—
292D4—442no—
293D4—442no—
294D4—442no—
295D4—882no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—42no—
299C2×C4—44no—
300C2×C4—441no—
301C2×C4—442no—
302C2×C4—882no—
303C2×C4—881no—
304C2×C4—881no—
305C2×C4#6693511yescharacteristic
306C2×C4#6693511yescharacteristic
307C2×C4#6693711yescharacteristic
308C2×C4#6693711yescharacteristic
309C2×C4#6698512yes—
310C2×C4#6699011yescharacteristic
311C2×C4#6699311yescharacteristic
312C2×C4#6700312yes—
313C8—42no—
314C8—81no—
315C8—442no—
316C8—442no—
317C22—21no—
318C22—21no—
319C22—881no—
320C22—881no—
321C22—881no—
322C22#1062257311yescharacteristic
323C22#1062262912yes—
324C4—21no—
325C4—21no—
326C4—82no—
327C4—882no—
328C4—881no—
329C4#1062236612yes—
330C4#1062236812yes—
331C4#1062265012yes—
332C4#1062267211yescharacteristic
333C4#1062268711yescharacteristic
334C2—22no—
335C2—1761no—
336C2#1306964011yescharacteristic
337C2#1306969211yescharacteristic
338C2#1306973611yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1966C2
socleC22×C11#392
prime radical#10623008C22
hypercenter#1966D11
hypocenterC11#10158
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1966

Complements

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

NH ≅ G/Ntype
3. C2×#10622706C2semidirect
4. #13067302C2semidirect
6. #13066454C2semidirect
7. C11×#1966C2semidirect
118. #1966D11semidirect
283. C11#10158semidirect

Maximal subgroups

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

subgroupindex
#130797372
#130790102
C2×#106227062
#130673022
#130670662
#130664542
C11×#19662
#1015811