Finite Group Databasebeta

← #14657502

Subgroups — #14657502

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#13078423C211yesmaximal, characteristic
2#13068609C211yesmaximal, characteristic
3#13067307C211yesmaximal, characteristic
4#13067072C211yesmaximal, characteristic
5C2×#10622094C211yesmaximal, characteristic
6#13066490C211yesmaximal, characteristic
7C11×#1567C211yesmaximal, characteristic
8#10623001C2211yescharacteristic
9C2×C4×Dic22C2211yescharacteristic
10C11×#423C2211yescharacteristic
11C11×#423C2211yescharacteristic
12C2×C4×C8×C11C2211yescharacteristic
13C2×#66888—21no—
14#10622734—21no—
15#10622733—21no—
16#10622537C2211yescharacteristic
17C2×C4⋊(C11⋊C8)C2211yescharacteristic
18#10622464—21no—
19#10622463—21no—
20#10622442—22no—
21C11×#335—22no—
22#10622192—21no—
23#10622124—21no—
24#10622119—21no—
25#10622094—21no—
26#10622094—21no—
27#10622094—21no—
28#10622094—21no—
29C22×Dic22D411yescharacteristic
30C2×C11×M16—21no—
31C2×C11×M16—21no—
32C22×C8×C11—21no—
33C2×C42×C11C2311yescharacteristic
34#66979—21no—
35C2×C4⋊Dic11D411yescharacteristic
36#66977—21no—
37#66977—21no—
38C2×Dic11⋊C4—21no—
39C2×C4×Dic11—21no—
40C2×#4318—21no—
41C22×C11⋊C8—21no—
42#66923—21no—
43#66922D411yescharacteristic
44#66922D411yescharacteristic
45C4×Dic22—21no—
46C4×Dic22—21no—
47C4×Dic22—21no—
48C4×Dic22—21no—
49C4×Dic22—21no—
50C4×Dic22—21no—
51C11×C4⋊C8—21no—
52C11×C4⋊C8—21no—
53C11×C4⋊C8—21no—
54C11×C4⋊C8D412yes—
55C4×C8×C11—21no—
56C4×C8×C11D411yescharacteristic
57C4×C8×C11D411yescharacteristic
58#66888—42no—
59#66882—22no—
60#66881—22no—
61#66880—22no—
62#66880—22no—
63C4⋊(C11⋊C8)—21no—
64C4⋊(C11⋊C8)—21no—
65C4⋊(C11⋊C8)—21no—
66C4⋊(C11⋊C8)—21no—
67#10463—111nomaximal, Sylow
68C22×C4×C11C2×D411yescharacteristic
69C22×C4×C11#4111yescharacteristic
70C22×C4×C11#4111yescharacteristic
71C22×Dic11—21no—
72C22×Dic11—21no—
73C2×Dic22—21no—
74C2×Dic22—21no—
75C2×Dic22—21no—
76C2×Dic22—21no—
77C2×Dic22—21no—
78C2×Dic22—21no—
79C2×Dic22—21no—
80C2×Dic22Q1612yes—
81C11×M16—41no—
82C11×M16—41no—
83C11×M16—41no—
84C11×M16—41no—
85C2×C8×C11—22no—
86C2×C8×C11—21no—
87C2×C8×C11—21no—
88C2×C8×C11—42no—
89C2×C8×C11—41no—
90C42×C11C2×D411yescharacteristic
91C42×C11C2×D411yescharacteristic
92C42×C11C2×D411yescharacteristic
93C42×C11#4111yescharacteristic
94C22⋊Dic11—41no—
95C4⋊Dic11—21no—
96C4⋊Dic11—21no—
97C4⋊Dic11—21no—
98C4⋊Dic11—21no—
99C4⋊Dic11—21no—
100C4⋊Dic11—21no—
101Dic11⋊C4—41no—
102Dic11⋊C4—41no—
103Dic11⋊C4—41no—
104Dic11⋊C4—41no—
105C4×Dic11—41no—
106C4×Dic11—41no—
107C4×Dic11—41no—
108#4318—41no—
109#4318—41no—
110C2×C11⋊C8—41no—
111C2×C11⋊C8—41no—
112C2×C11⋊C8—81no—
113#3078—111no—
114#1801—111no—
115#1567D1111yescharacteristic
116#1550—111no—
117#1493—111no—
118C2×Q8⋊C8—111no—
119#1292—111no—
120C23×C11#12311yescharacteristic
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—41no—
124C2×C4×C11#12011yescharacteristic
125C2×C4×C11#12111yescharacteristic
126C2×C4×C11#12111yescharacteristic
127C2×C4×C11#12111yescharacteristic
128C2×C4×C11#12311yescharacteristic
129C2×C4×C11#12411yescharacteristic
130C2×C4×C11C2×Q1611yescharacteristic
131C2×C4×C11#13511yescharacteristic
132C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
133C2×C4×C11#13711yescharacteristic
134C2×Dic11—22no—
135C2×Dic11—41no—
136C2×Dic11—41no—
137C2×Dic11—41no—
138C2×Dic11—41no—
139C2×Dic11—41no—
140C2×Dic11—81no—
141Dic22—22no—
142Dic22—22no—
143Dic22—41no—
144Dic22—41no—
145Dic22—41no—
146Dic22—41no—
147Dic22—81no—
148C8×C11—22no—
149C8×C11—41no—
150C8×C11—42no—
151C8×C11—81no—
152C11⋊C8—81no—
153C11⋊C8—81no—
154#533—111no—
155C2×C4×Q8—111no—
156#479—222no—
157#477—221no—
158#475—221no—
159#428—221no—
160#423—111no—
161#423C2×D1111yescharacteristic
162#423C2×D1111yescharacteristic
163C2×C4⋊C8—111no—
164#419—221no—
165C2×#101—221no—
166C2×C4×C8C2×D1111yescharacteristic
167#343—221no—
168#335—22no—
169#333—221no—
170#332—221no—
171Q8⋊C8—221no—
172Q8⋊C8—221no—
173Q8⋊C8—221no—
174Q8⋊C8—221no—
175C22×C11—21no—
176C22×C11—21no—
177C22×C11#39411yescharacteristic
178C22×C11#48411yescharacteristic
179C22×C11#48511yescharacteristic
180C4×C11—21no—
181C4×C11—21no—
182C4×C11—21no—
183C4×C11#44911yescharacteristic
184C4×C11#45111yescharacteristic
185C4×C11#46711yescharacteristic
186C4×C11#46811yescharacteristic
187C4×C11#47111yescharacteristic
188C4×C11#47311yescharacteristic
189Dic11—42no—
190Dic11—81no—
191Dic11—81no—
192Dic11—81no—
193C22×Q8—111no—
194C2×M16—21no—
195C2×M16—21no—
196C2×M16—221no—
197C22×C8—21no—
198C22×C8—221no—
199C4⋊Q8—111no—
200C4⋊Q8—111no—
201#125—221no—
202C22⋊Q8—221no—
203C22⋊Q8—221no—
204C4×Q8—221no—
205C4×Q8—221no—
206C4×Q8—221no—
207C4×Q8—221no—
208C4×Q8—221no—
209C4×Q8—221no—
210#117—221no—
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—21no—
220C4⋊C8—221no—
221C4⋊C8—221no—
222C4⋊C8—221no—
223C4⋊C8—221no—
224C4⋊C8C22⋊D1112yes—
225#103—222no—
226#103—222no—
227#101—442no—
228C4×C8—21no—
229C4×C8D4411yescharacteristic
230C4×C8D4411yescharacteristic
231C2×C11—21no—
232C2×C11—21no—
233C2×C11#203611yescharacteristic
234C2×C11#205011yescharacteristic
235C2×C11#205211yescharacteristic
236C2×Q8—112no—
237C2×Q8—221no—
238C2×Q8—221no—
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#434311yescharacteristic
249M16—41no—
250M16—41no—
251M16—41no—
252M16—41no—
253M16—441no—
254M16—441no—
255C2×C8—21no—
256C2×C8—21no—
257C2×C8—22no—
258C2×C8—42no—
259C2×C8—41no—
260C2×C8—441no—
261C2×C8—441no—
262C2×C8—881no—
263C4⋊C4—221no—
264C4⋊C4—221no—
265C4⋊C4—221no—
266C4⋊C4—221no—
267C4⋊C4—221no—
268C4⋊C4—221no—
269C4⋊C4—441no—
270C4⋊C4—441no—
271C4⋊C4—441no—
272C4⋊C4—441no—
273C22⋊C4—441no—
274C42—441no—
275C42—441no—
276C42—441no—
277C42C2×D4411yescharacteristic
278C42D4×D1111yescharacteristic
279C42#434311yescharacteristic
280C42C2×C22⋊D1111yescharacteristic
281C11#1046311yescharacteristic, complemented, Sylow
282C23#6694711yescharacteristic
283Q8—222no—
284Q8—222no—
285Q8—441no—
286Q8—441no—
287Q8—441no—
288Q8—441no—
289Q8—881no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—41no—
293C2×C4—222no—
294C2×C4—441no—
295C2×C4—441no—
296C2×C4—441no—
297C2×C4—441no—
298C2×C4—441no—
299C2×C4—881no—
300C2×C4#6694711yescharacteristic
301C2×C4#6694811yescharacteristic
302C2×C4#6694811yescharacteristic
303C2×C4#6696411yescharacteristic
304C2×C4#6696511yescharacteristic
305C2×C4Q16×D1111yescharacteristic
306C2×C4#6697111yescharacteristic
307C2×C4#6698311yescharacteristic
308C2×C4#6699011yescharacteristic
309C2×C4#6700011yescharacteristic
310C8—22no—
311C8—41no—
312C8—42no—
313C8—81no—
314C8—881no—
315C8—881no—
316C22—21no—
317C22—21no—
318C22#1062249711yescharacteristic
319C22#1062250111yescharacteristic
320C22#1062260411yescharacteristic
321C4—21no—
322C4—21no—
323C4—21no—
324C4—442no—
325C4—881no—
326C4—881no—
327C4—881no—
328C4#1062249911yescharacteristic
329C4#1062250011yescharacteristic
330C4#1062250911yescharacteristic
331C4#1062251111yescharacteristic
332C4#1062277111yescharacteristic
333C4#1062279911yescharacteristic
334C2—21no—
335C2—21no—
336C2#1306982111yescharacteristic
337C2#1306990311yescharacteristic
338C2#1306991711yescharacteristic
subgroupG/H
centerC22#10622604
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1567C2
socleC22×C11#394
prime radicalC23×C11#123
hypercenter#1567D11
hypocenterC11#10463
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1567

Complements

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

NH ≅ G/Ntype
281. C11#10463semidirect

Maximal subgroups

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

subgroupindex
#130784232
#130686092
#130673072
#130670722
C2×#106220942
#130664902
C11×#15672
#1046311