Finite Group Databasebeta

← #14657492

Subgroups — #14657492

Order 2816.

374 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 97 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#13078417C211yesmaximal, characteristic
2#13068609C211yesmaximal, characteristic
3#13067372C211yesmaximal, characteristic
4#13067306C211yesmaximal, characteristic
5C2×#10622094C211yesmaximal, characteristic
6#13066490C211yesmaximal, characteristic
7C11×#1493C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C2×C4×Dic22C2211yescharacteristic
10C11×#423C2211yescharacteristic
11C2×C4×C8×C11C2211yescharacteristic
12C2×#66888—21no—
13#10622707—21no—
14#10622704—21no—
15#10622676—22no—
16#10622617—21no—
17#10622608—21no—
18#10622537C2211yescharacteristic
19#10622537C2211yescharacteristic
20C2×C4⋊(C11⋊C8)C2211yescharacteristic
21C11×Q8⋊C8—21no—
22C11×Q8⋊C8—21no—
23#10622192—21no—
24#10622185—21no—
25#10622184—21no—
26#10622095—22no—
27#10622094—21no—
28#10622094—21no—
29C22×Dic22D411yescharacteristic
30C2×C11×M16—21no—
31C22×C8×C11—21no—
32C11×C4⋊Q8D411yescharacteristic
33C11×C4⋊Q8D411yescharacteristic
34C11×#125—21no—
35C11×C22⋊Q8—21no—
36C11×C22⋊Q8—21no—
37C4×Q8×C11—21no—
38C4×Q8×C11—21no—
39C11×#117—21no—
40C2×C42×C11C2311yescharacteristic
41C2×C4⋊Dic11D411yescharacteristic
42C2×Dic11⋊C4—21no—
43C2×C4×Dic11—21no—
44C2×#4318—21no—
45C2×#4318—21no—
46C22×C11⋊C8—21no—
47C4×Dic22—21no—
48C4×Dic22—21no—
49C4×Dic22—21no—
50C4×Dic22—21no—
51C11×C4⋊C8—21no—
52C11×C4⋊C8—21no—
53C4×C8×C11—21no—
54C4×C8×C11D411yescharacteristic
55C4×C8×C11D411yescharacteristic
56#66888—42no—
57#66874—22no—
58#66874—22no—
59#66872—22no—
60#66871—22no—
61C4⋊(C11⋊C8)—21no—
62C4⋊(C11⋊C8)—21no—
63C4⋊(C11⋊C8)—21no—
64C4⋊(C11⋊C8)—21no—
65C4⋊(C11⋊C8)—21no—
66C4⋊(C11⋊C8)D412yes—
67#10462—111nomaximal, Sylow
68C2×Q8×C11—21no—
69C2×Q8×C11—21no—
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11#4111yescharacteristic
72C22×C4×C11#4111yescharacteristic
73C22×Dic11—21no—
74C22×Dic11—21no—
75C2×Dic22—21no—
76C2×Dic22—21no—
77C2×Dic22—21no—
78C2×Dic22—21no—
79C2×Dic22—21no—
80C2×Dic22SD1612yes—
81C11×M16—41no—
82C11×M16—41no—
83C2×C8×C11—21no—
84C2×C8×C11—21no—
85C2×C8×C11—42no—
86C2×C8×C11—41no—
87C11×C4⋊C4—21no—
88C11×C4⋊C4—21no—
89C11×C4⋊C4—21no—
90C11×C4⋊C4—21no—
91C11×C4⋊C4—41no—
92C11×C4⋊C4—41no—
93C11×C22⋊C4—41no—
94C42×C11—41no—
95C42×C11C2×D411yescharacteristic
96C42×C11C2×D411yescharacteristic
97C42×C11C2×D411yescharacteristic
98C42×C11#4111yescharacteristic
99C4⋊Dic11—21no—
100C4⋊Dic11—21no—
101Dic11⋊C4—41no—
102Dic11⋊C4—41no—
103C4×Dic11—41no—
104C4×Dic11—41no—
105#4318—41no—
106#4318—41no—
107#4318—41no—
108#4318—41no—
109C2×C11⋊C8—22no—
110C2×C11⋊C8—41no—
111C2×C11⋊C8—41no—
112C2×C11⋊C8—81no—
113#3078—111no—
114#1801—111no—
115#1566—111no—
116#1550—111no—
117#1493D1111yescharacteristic
118C2×Q8⋊C8—111no—
119#1292—111no—
120C23×C11#12311yescharacteristic
121Q8×C11—41no—
122Q8×C11—41no—
123Q8×C11—81no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11#12011yescharacteristic
130C2×C4×C11#12111yescharacteristic
131C2×C4×C11#12111yescharacteristic
132C2×C4×C11#12111yescharacteristic
133C2×C4×C11#12311yescharacteristic
134C2×C4×C11#12411yescharacteristic
135C2×C4×C11C2×SD1611yescharacteristic
136C2×C4×C11#13511yescharacteristic
137C2×C4×C11#13711yescharacteristic
138C2×C4×C11#13711yescharacteristic
139C2×Dic11—22no—
140C2×Dic11—41no—
141C2×Dic11—41no—
142C2×Dic11—41no—
143C2×Dic11—81no—
144Dic22—22no—
145Dic22—22no—
146Dic22—41no—
147Dic22—41no—
148C8×C11—22no—
149C8×C11—41no—
150C8×C11—81no—
151C11⋊C8—42no—
152C11⋊C8—81no—
153C11⋊C8—81no—
154#533C2×D1111yescharacteristic
155C2×C4×Q8—111no—
156#479—222no—
157#477—221no—
158#475—221no—
159#428—221no—
160#423—111no—
161#423—111no—
162#423C2×D1111yescharacteristic
163C2×C4⋊C8—111no—
164#419—221no—
165C2×#101—221no—
166C2×C4×C8C2×D1111yescharacteristic
167#343—221no—
168#334—222no—
169#333—221no—
170#332—221no—
171Q8⋊C8—21no—
172Q8⋊C8—21no—
173Q8⋊C8—221no—
174Q8⋊C8—221no—
175C22×C11—21no—
176C22×C11—21no—
177C22×C11#39411yescharacteristic
178C22×C11#48311yescharacteristic
179C22×C11#48511yescharacteristic
180C4×C11—21no—
181C4×C11—21no—
182C4×C11—21no—
183C4×C11—81no—
184C4×C11—81no—
185C4×C11#44811yescharacteristic
186C4×C11#45211yescharacteristic
187C4×C11#46511yescharacteristic
188C4×C11#47011yescharacteristic
189C4×C11#47111yescharacteristic
190C4×C11#47311yescharacteristic
191Dic11—42no—
192Dic11—81no—
193C22×Q8—111no—
194C2×M16—21no—
195C2×M16—221no—
196C2×M16—221no—
197C22×C8—21no—
198C22×C8—221no—
199C4⋊Q8D4411yescharacteristic
200C4⋊Q8D4411yescharacteristic
201#125—21no—
202C22⋊Q8—21no—
203C22⋊Q8—21no—
204C4×Q8—21no—
205C4×Q8—21no—
206C4×Q8—221no—
207C4×Q8—221no—
208C4×Q8—221no—
209C4×Q8—221no—
210#117—21no—
211C2×C4⋊C4—111no—
212C2×C4⋊C4—221no—
213C2×C42—221no—
214C2×C42C22×D1111yescharacteristic
215#107—222no—
216#106—222no—
217C4⋊C8—21no—
218C4⋊C8—21no—
219C4⋊C8—112no—
220C4⋊C8—221no—
221C4⋊C8—221no—
222C4⋊C8—221no—
223C4⋊C8—221no—
224C4⋊C8—221no—
225#103—222no—
226#103—222no—
227#101—442no—
228C4×C8—21no—
229C4×C8C22⋊D1111yescharacteristic
230C4×C8C22⋊D1111yescharacteristic
231C2×C11—21no—
232C2×C11—21no—
233C2×C11#203511yescharacteristic
234C2×C11#205011yescharacteristic
235C2×C11#205211yescharacteristic
236C2×Q8—21no—
237C2×Q8—21no—
238C2×Q8—112no—
239C2×Q8—221no—
240C2×Q8—221no—
241C2×Q8—221no—
242C2×Q8—221no—
243C2×Q8—221no—
244C22×C4—221no—
245C22×C4—221no—
246C22×C4#433911yescharacteristic
247C22×C4D4×D1111yescharacteristic
248C22×C4#434111yescharacteristic
249M16—41no—
250M16—41no—
251M16—441no—
252M16—441no—
253M16—441no—
254M16—441no—
255C2×C8—21no—
256C2×C8—21no—
257C2×C8—42no—
258C2×C8—41no—
259C2×C8—222no—
260C2×C8—441no—
261C2×C8—441no—
262C2×C8—881no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—221no—
270C4⋊C4—221no—
271C4⋊C4—441no—
272C4⋊C4—441no—
273C22⋊C4—41no—
274C42—41no—
275C42—441no—
276C42—441no—
277C42C2×D4411yescharacteristic
278C42D4×D1111yescharacteristic
279C42#434111yescharacteristic
280C42C2×C22⋊D1111yescharacteristic
281C11#1046211yescharacteristic, complemented, Sylow
282C23#6693611yescharacteristic
283Q8—41no—
284Q8—41no—
285Q8—81no—
286Q8—222no—
287Q8—222no—
288Q8—441no—
289Q8—441no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—222no—
296C2×C4—441no—
297C2×C4—441no—
298C2×C4—441no—
299C2×C4—881no—
300C2×C4#6693511yescharacteristic
301C2×C4#6693811yescharacteristic
302C2×C4#6693911yescharacteristic
303C2×C4SD16×D1111yescharacteristic
304C2×C4#6696911yescharacteristic
305C2×C4#6697111yescharacteristic
306C2×C4#6697111yescharacteristic
307C2×C4#6698311yescharacteristic
308C2×C4#6699111yescharacteristic
309C2×C4#6699211yescharacteristic
310C8—22no—
311C8—41no—
312C8—81no—
313C8—442no—
314C8—881no—
315C8—881no—
316C22—21no—
317C22—21no—
318C22#1062241811yescharacteristic
319C22#1062242811yescharacteristic
320C22#1062257411yescharacteristic
321C4—21no—
322C4—21no—
323C4—21no—
324C4—81no—
325C4—81no—
326C4—442no—
327C4—881no—
328C4#1062241911yescharacteristic
329C4#1062242311yescharacteristic
330C4#1062275411yescharacteristic
331C4#1062275611yescharacteristic
332C4#1062278411yescharacteristic
333C4#1062280211yescharacteristic
334C2—21no—
335C2—21no—
336C2#1306981111yescharacteristic
337C2#1306990211yescharacteristic
338C2#1306991411yescharacteristic
subgroupG/H
centerC22#10622574
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1493C2
socleC22×C11#394
prime radicalC23×C11#123
hypercenter#1493D11
hypocenterC11#10462
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
281. C11#10462semidirect

Maximal subgroups

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

subgroupindex
#130784172
#130686092
#130673722
#130673062
C2×#106220942
#130664902
C11×#14932
#1046211