Finite Group Databasebeta

← #14651616

Subgroups — #14651616

Order 2816.

474 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 474 conjugacy classes of subgroups — too many to draw. Only its 113 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#13077696C211yesmaximal, characteristic
2#13073983C211yesmaximal, characteristic
3#13068609C211yesmaximal, characteristic
4#13067046C211yesmaximal, characteristic
5#13067044C211yesmaximal, characteristic
6#13066474C211yesmaximal, characteristic
7C11×#1286C211yesmaximal, characteristic
8C2×C4×Dic22C2211yescharacteristic
9C2×C4×Dic22C2211yescharacteristic
10C11×#431C2211yescharacteristic
11C11×#423C2211yescharacteristic
12C11×#382C2211yescharacteristic
13C2×#66888—21no—
14#10622598—21no—
15#10622587—21no—
16#10622538C2211yescharacteristic
17#10622537C2211yescharacteristic
18#10622443—22no—
19#10622331—22no—
20C8×Dic22—22no—
21#10622272C412yes—
22#10622269C412yes—
23#10622266—22no—
24#10622192—21no—
25#10622122—22no—
26#10622094—22no—
27C22×Dic22C2×C411yescharacteristic
28C22×Dic22D411yescharacteristic
29C2×C11×M16—21no—
30C2×C11×C4⋊C4—21no—
31C2×C42×C11C2311yescharacteristic
32C2×C4⋊Dic11—22no—
33C2×C4⋊Dic11C2×C411yescharacteristic
34C2×C4⋊Dic11D411yescharacteristic
35C2×Dic11⋊C4—21no—
36C2×Dic11⋊C4C2×C412yes—
37C2×C4×Dic11—21no—
38C2×C4×Dic11D412yes—
39C2×#4318—21no—
40C4×Dic22—21no—
41C4×Dic22—21no—
42C4×Dic22—21no—
43C4×Dic22—21no—
44C4×Dic22—21no—
45C4×Dic22—21no—
46C4×Dic22—21no—
47C4×Dic22—21no—
48C11×C4⋊C8—21no—
49C11×C4⋊C8—21no—
50C11×C4⋊C8—21no—
51C11×C22⋊C8—21no—
52C4×C8×C11D412yes—
53C11×#95—21no—
54C11×#95C2×C412yes—
55C11⋊#95—22no—
56C11⋊#95—22no—
57C11⋊#95—22no—
58C22⋊(C11⋊C8)—21no—
59#66888—42no—
60Dic11⋊C8—24no—
61C8×Dic11—24no—
62C4⋊(C11⋊C8)—21no—
63C4⋊(C11⋊C8)—21no—
64C4⋊(C11⋊C8)—21no—
65C4×C11⋊C8D412yes—
66#9484—111nomaximal, Sylow
67C22×C4×C11—22no—
68C22×C4×C11C22×C411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C22×Dic11—21no—
72C22×Dic11—21no—
73C22×Dic11C22⋊C412yes—
74C22×Dic11C22⋊C412yes—
75C2×Dic22—21no—
76C2×Dic22—21no—
77C2×Dic22—21no—
78C2×Dic22—21no—
79C2×Dic22—21no—
80C2×Dic22—21no—
81C2×Dic22—42no—
82C2×Dic22SD1612yes—
83C2×Dic22Q1612yes—
84C11×M16—41no—
85C11×M16—41no—
86C2×C8×C11—22no—
87C2×C8×C11—41no—
88C11×C4⋊C4—41no—
89C11×C4⋊C4—41no—
90C42×C11C2×D411yescharacteristic
91C42×C11C2×D411yescharacteristic
92C42×C11#4111yescharacteristic
93C42×C11#4111yescharacteristic
94C4⋊Dic11—21no—
95C4⋊Dic11—21no—
96C4⋊Dic11—21no—
97C4⋊Dic11—21no—
98C4⋊Dic11—44no—
99Dic11⋊C4—22no—
100Dic11⋊C4—22no—
101Dic11⋊C4—41no—
102Dic11⋊C4—41no—
103C4×Dic11—22no—
104C4×Dic11—22no—
105C4×Dic11—41no—
106C4×Dic11—41no—
107#4318—41no—
108#4318—41no—
109C2×C11⋊C8—22no—
110C2×C11⋊C8—41no—
111#2982—111no—
112#2581—111no—
113#1801—111no—
114#1487—111no—
115#1487—111no—
116#1286—111no—
117#1286D1111yescharacteristic
118C23×C11C2×C22⋊C411yescharacteristic
119C2×C4×C11—41no—
120C2×C4×C11—41no—
121C2×C4×C11—42no—
122C2×C4×C11—42no—
123C2×C4×C11—42no—
124C2×C4×C11C4×D411yescharacteristic
125C2×C4×C11C4×D411yescharacteristic
126C2×C4×C11#12011yescharacteristic
127C2×C4×C11#12111yescharacteristic
128C2×C4×C11#12111yescharacteristic
129C2×C4×C11#12311yescharacteristic
130C2×C4×C11C2×SD1611yescharacteristic
131C2×C4×C11C2×Q1611yescharacteristic
132C2×C4×C11#13511yescharacteristic
133C2×C4×C11#13511yescharacteristic
134C2×Dic11—22no—
135C2×Dic11—22no—
136C2×Dic11—22no—
137C2×Dic11—22no—
138C2×Dic11—41no—
139C2×Dic11—41no—
140C2×Dic11—42no—
141C2×Dic11—42no—
142C2×Dic11—41no—
143C2×Dic11#10314yes—
144Dic22—22no—
145Dic22—22no—
146Dic22—22no—
147Dic22—22no—
148Dic22—22no—
149Dic22—22no—
150Dic22—41no—
151Dic22—41no—
152C8×C11—42no—
153C8×C11—81no—
154C11⋊C8—42no—
155C11⋊C8—81no—
156C2×C4×Q8—111no—
157C2×C4×Q8—111no—
158C8×Q8—222no—
159C8×Q8—222no—
160#431—111no—
161#431—222no—
162#431C2×D1111yescharacteristic
163#423—111no—
164#423C2×D1111yescharacteristic
165C2×#101—221no—
166#400—112no—
167#395—112no—
168#391—221no—
169#389—221no—
170#387—222no—
171#382C2×D1111yescharacteristic
172#343—221no—
173Q8⋊C8—222no—
174Q8⋊C8—222no—
175C22×C11—21no—
176C22×C11—21no—
177C22×C11#38611yescharacteristic
178C22×C11C2×#10311yescharacteristic
179C22×C11#41611yescharacteristic
180C4×C11—21no—
181C4×C11—21no—
182C4×C11—21no—
183C4×C11—21no—
184C4×C11—82no—
185C4×C11#46511yescharacteristic
186C4×C11#46511yescharacteristic
187C4×C11#46711yescharacteristic
188C4×C11#46711yescharacteristic
189Dic11—24no—
190Dic11—42no—
191Dic11—42no—
192Dic11—81no—
193C22×Q8—111no—
194C22×Q8—111no—
195C2×M16—21no—
196C2×M16—221no—
197C4×Q8—221no—
198C4×Q8—221no—
199C4×Q8—221no—
200C4×Q8—221no—
201C4×Q8—221no—
202C4×Q8—221no—
203C4×Q8—221no—
204C4×Q8—221no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—112no—
207C2×C4⋊C4—111no—
208C2×C4⋊C4—111no—
209C2×C4⋊C4—222no—
210C2×C4⋊C4—221no—
211C2×C42—112no—
212C2×C42—221no—
213C2×C42C22×D1111yescharacteristic
214C4⋊C8—21no—
215C4⋊C8—21no—
216C4⋊C8—21no—
217C4⋊C8—224no—
218C4⋊C8—221no—
219C4⋊C8—221no—
220C4⋊C8—221no—
221#101—442no—
222C22⋊C8—21no—
223C22⋊C8—221no—
224C4×C8—112no—
225C4×C8—224no—
226C4×C8D4412yes—
227#95—21no—
228#95—222no—
229#95—222no—
230#95—222no—
231#95C4×D1112yes—
232C2×C11—21no—
233C2×C11—21no—
234C2×C11#189111yescharacteristic
235C2×C11#189211yescharacteristic
236C2×C11#191211yescharacteristic
237C2×Q8—112no—
238C2×Q8—112no—
239C2×Q8—221no—
240C2×Q8—221no—
241C2×Q8—221no—
242C2×Q8—221no—
243C2×Q8—221no—
244C2×Q8—221no—
245C2×Q8—442no—
246C22×C4—22no—
247C22×C4—112no—
248C22×C4—112no—
249C22×C4—221no—
250C22×C4—221no—
251C22×C4C2×C4×D1111yescharacteristic
252C22×C4D4×D1111yescharacteristic
253C22×C4D4×D1111yescharacteristic
254M16—41no—
255M16—41no—
256M16—441no—
257M16—441no—
258C2×C8—22no—
259C2×C8—41no—
260C2×C8—222no—
261C2×C8—441no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—222no—
265C4⋊C4—221no—
266C4⋊C4—222no—
267C4⋊C4—221no—
268C4⋊C4—221no—
269C4⋊C4—221no—
270C4⋊C4—444no—
271C4⋊C4—441no—
272C4⋊C4—441no—
273C42—222no—
274C42—222no—
275C42—441no—
276C42—441no—
277C42C2×D4411yescharacteristic
278C42#433911yescharacteristic
279C42D4×D1111yescharacteristic
280C42#434311yescharacteristic
281C11#948411yescharacteristic, complemented, Sylow
282C23C22⋊C4×D1111yescharacteristic
283Q8—222no—
284Q8—222no—
285Q8—222no—
286Q8—222no—
287Q8—222no—
288Q8—222no—
289Q8—441no—
290Q8—441no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4—114no—
297C2×C4—222no—
298C2×C4—222no—
299C2×C4—222no—
300C2×C4—222no—
301C2×C4—441no—
302C2×C4—441no—
303C2×C4—442no—
304C2×C4—442no—
305C2×C4—441no—
306C2×C4C4×D4411yescharacteristic
307C2×C4#6693511yescharacteristic
308C2×C4#6693711yescharacteristic
309C2×C4#6694611yescharacteristic
310C2×C4#6694711yescharacteristic
311C2×C4#6694811yescharacteristic
312C2×C4#6696511yescharacteristic
313C2×C4SD16×D1111yescharacteristic
314C2×C4#6696911yescharacteristic
315C2×C4Q16×D1111yescharacteristic
316C8—42no—
317C8—81no—
318C8—442no—
319C8—881no—
320C22—21no—
321C22—21no—
322C22#1062227811yescharacteristic
323C22#1062238511yescharacteristic
324C22D11×#10311yescharacteristic
325C4—21no—
326C4—21no—
327C4—21no—
328C4—21no—
329C4—82no—
330C4—224no—
331C4—442no—
332C4—442no—
333C4—881no—
334C4#1062239111yescharacteristic
335C4#1062242611yescharacteristic
336C4#1062247711yescharacteristic
337C4#1062250011yescharacteristic
338C2—21no—
339C2—21no—
340C2#1306903311yescharacteristic
341C2#1306903811yescharacteristic
342C2#1306915211yescharacteristic
subgroupG/H
centerC22#10622278
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1286C2
socleC22×C11#386
prime radicalC23×C11C2×C22⋊C4
cosocleC2×C42×C11C23
hypercenter#1286D11
hypocenterC11#9484
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1286

Complements

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

NH ≅ G/Ntype
281. C11#9484semidirect

Maximal subgroups

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

subgroupindex
#130776962
#130739832
#130686092
#130670462
#130670442
#130664742
C11×#12862
#948411