Finite Group Databasebeta

← #14655578

Subgroups — #14655578

Order 2816.

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

normal subgroups only

This group has 574 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#13079541C211yesmaximal, characteristic
2C2×#10622705C211yesmaximal, characteristic, complemented
3#13079010C211yesmaximal, characteristic
4#13067302C211yesmaximal, characteristic, complemented
5#13067066C211yesmaximal, characteristic
6#13066454C211yesmaximal, characteristic, complemented
7C11×#1997C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C22×#4326—22no—
10#10623008C2211yescharacteristic
11C2×#66922C2211yescharacteristic
12C11×#423C2211yescharacteristic
13C4×C11×M16C2211yescharacteristic
14#10622840—22no—
15#10622746—22no—
16#10622705—22no—
17#10622705—22no—
18#10622698—21no—
19#10622696—22no—
20#10622694—21no—
21#10622538C2211yescharacteristic
22C2×C4×C11⋊C8C2211yescharacteristic
23#10622327—22no—
24#10622307—21no—
25#10622294—21no—
26C11×#343—22no—
27#10622124—22no—
28#10622121—22no—
29C22×Q8×C11D412yes—
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⋊C4—21no—
40C2×C42×C11C2311yescharacteristic
41C2×#4326—28no—
42C2×#4326—48no—
43C2×#4325—24no—
44#66983—21no—
45#66983—21no—
46C2×C4⋊Dic11—21no—
47C2×C4⋊Dic11—21no—
48C22×C11⋊C8—21no—
49#66928—21no—
50#66927D411yescharacteristic
51C4×D44—21no—
52C4×D44—21no—
53#66922—21no—
54#66922—21no—
55#66922—21no—
56#66922D412yes—
57#66922D411yescharacteristic
58C11×C4⋊C8—21no—
59C11×C4⋊C8—21no—
60C11×#97—21no—
61C4×C8×C11—21no—
62#66899—24no—
63C22⋊(C11⋊C8)—21no—
64#66885—24no—
65#66880—24no—
66C4⋊(C11⋊C8)D412yes—
67C4×C11⋊C8—21no—
68C4×C11⋊C8—21no—
69C4×C11⋊C8D412yes—
70#10154—111nomaximal, Sylow
71C2×Q8×C11—22no—
72C2×Q8×C11—22no—
73C2×Q8×C11—44no—
74C22×C4×C11—22no—
75C22×C4×C11C2×D411yescharacteristic
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11#4111yescharacteristic
78C2×C22⋊D11—41no—
79C22×Dic11—41no—
80#4339—42no—
81#4339—42no—
82C2×D44—21no—
83C2×D44—21no—
84C2×D44—21no—
85C2×C4×D11—41no—
86C2×Dic22—21no—
87C2×Dic22—22no—
88C2×Dic22—44no—
89C2×Dic22—41no—
90C11×M16—22no—
91C11×M16—22no—
92C11×M16—42no—
93C2×C8×C11—22no—
94C2×C8×C11—41no—
95C11×C4⋊C4—41no—
96C11×C4⋊C4—41no—
97C11×C4⋊C4—41no—
98C11×C4⋊C4—41no—
99C42×C11C2×D411yescharacteristic
100C42×C11C2×D411yescharacteristic
101C42×C11C2×D411yescharacteristic
102C42×C11C2×D411yescharacteristic
103#4326—416no—
104#4325—84no—
105(C2×D11)⋊C4—41no—
106(C2×D11)⋊C4—41no—
107C4⋊Dic11—22no—
108C4⋊Dic11—21no—
109C4⋊Dic11—22no—
110C4⋊Dic11—21no—
111C4⋊Dic11—41no—
112C4⋊Dic11—41no—
113C2×C11⋊C8—24no—
114C2×C11⋊C8—22no—
115C2×C11⋊C8—22no—
116#3206—111no—
117C2×#494—111no—
118#3141—111no—
119#1997D1111yescharacteristic, complemented
120#1549—111no—
121#1492—111no—
122#1278—111no—
123C23×C11#12111yescharacteristic
124C22×D11—41no—
125Q8×C11—44no—
126Q8×C11—44no—
127C2×C4×C11—22no—
128C2×C4×C11—22no—
129C2×C4×C11—42no—
130C2×C4×C11—82no—
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×C11#13712yes—
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—24no—
154C11⋊C8—42no—
155C22×Q16—222no—
156#532—111no—
157C2×C4⋊Q8—111no—
158C2×C4⋊Q8C2×D1111yescharacteristic
159#494—222no—
160#494—222no—
161#492—221no—
162#489—222no—
163#487—221no—
164#487—221no—
165#486—221no—
166#461—222no—
167#448—222no—
168#431—111no—
169#423C2×D1111yescharacteristic
170#417—222no—
171C4×M16C2×D1111yescharacteristic
172C2×C4×C8—111no—
173#343—22no—
174#332—222no—
175D4⋊C8—222no—
176C22×C11—21no—
177C22×C11—21no—
178C22×C11#39211yescharacteristic
179C22×C11#46412yes—
180C2×D11—81no—
181C2×D11—81no—
182C2×D11—81no—
183C4×C11—21no—
184C4×C11—21no—
185C4×C11—82no—
186C4×C11#45212yes—
187C4×C11#45312yes—
188C4×C11#47312yes—
189C4×C11#49511yescharacteristic
190C4×C11#49711yescharacteristic
191Dic11—82no—
192Dic11—81no—
193C2×#41—221no—
194C22×Q8—221no—
195C22×Q8D4412yes—
196C2×Q16—228no—
197C2×Q16—448no—
198C2×SD16—224no—
199C2×M16—21no—
200C2×M16C22⋊D1112yes—
201C22×C8—221no—
202C4⋊Q8—21no—
203C4⋊Q8—21no—
204C4⋊Q8—21no—
205C4⋊Q8—21no—
206C4⋊Q8—112no—
207C4⋊Q8—111no—
208C4⋊Q8—221no—
209C4⋊Q8—221no—
210C4⋊Q8—221no—
211#127—111no—
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—221no—
220C2×C4⋊C4—221no—
221C2×C42C22×D1111yescharacteristic
222C4⋊C8—21no—
223C4⋊C8—21no—
224C4⋊C8—112no—
225#103—224no—
226#103—224no—
227#102—224no—
228C22⋊C8—221no—
229#97—21no—
230C4×C8—21no—
231C4×C8—112no—
232C4×C8—221no—
233C4×C8—221no—
234C2×C11—22no—
235C2×C11#200211yescharacteristic
236C2×C11#201511yescharacteristic
237C2×C11#202011yescharacteristic
238D11—161no—
239#41—442no—
240#41—442no—
241C2×Q8—22no—
242C2×Q8—22no—
243C2×Q8—44no—
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—22no—
253C22×C4—441no—
254C22×C4—441no—
255C22×C4C2×D4411yescharacteristic
256C22×C4#433911yescharacteristic
257C22×C4C2×C22⋊D1111yescharacteristic
258Q16—4416no—
259SD16—884no—
260M16—22no—
261M16—22no—
262M16—42no—
263C2×C8—22no—
264C2×C8—41no—
265C2×C8—224no—
266C2×C8—222no—
267C2×C8—222no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—221no—
273C4⋊C4—222no—
274C4⋊C4—221no—
275C4⋊C4—222no—
276C4⋊C4—441no—
277C4⋊C4—441no—
278C22⋊C4—441no—
279C22⋊C4—441no—
280C42D4×D1111yescharacteristic
281C42D4×D1111yescharacteristic
282C42D4×D1111yescharacteristic
283C42D4×D1111yescharacteristic
284C11#1015411yescharacteristic, complemented, Sylow
285C23—441no—
286C23#6698311yescharacteristic
287Q8—44no—
288Q8—44no—
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—82no—
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#6699011yescharacteristic
310C2×C4#6699311yescharacteristic
311C2×C4#6699512yes—
312C2×C4#6700312yes—
313C8—42no—
314C8—81no—
315C8—224no—
316C8—442no—
317C22—21no—
318C22—21no—
319C22—881no—
320C22—881no—
321C22—881no—
322C22#1062257311yescharacteristic
323C22#1062264112yes—
324C4—21no—
325C4—21no—
326C4—82no—
327C4—882no—
328C4—881no—
329C4#1062236012yes—
330C4#1062236812yes—
331C4#1062266012yes—
332C4#1062267211yescharacteristic
333C4#1062269911yescharacteristic
334C2—22no—
335C2—1761no—
336C2#1306963311yescharacteristic
337C2#1306970911yescharacteristic
338C2#1306973611yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1997C2
socleC22×C11#392
prime radical#10623008C22
hypercenter#1997D11
hypocenterC11#10154
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1997

Complements

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

NH ≅ G/Ntype
2. C2×#10622705C2semidirect
4. #13067302C2semidirect
6. #13066454C2semidirect
7. C11×#1997C2semidirect
119. #1997D11semidirect
284. C11#10154semidirect

Maximal subgroups

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

subgroupindex
#130795412
C2×#106227052
#130790102
#130673022
#130670662
#130664542
C11×#19972
#1015411