Finite Group Databasebeta

← #14649759

Subgroups — #14649759

Order 2816.

478 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 99 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#13077701C211yesmaximal, characteristic, complemented
2#13074476C211yesmaximal, characteristic
3#13067213C212yesmaximal
4#13066481C212yesmaximal, complemented
5C4×C11×#101C211yesmaximal, characteristic, complemented
6C2×C4×Q8×C11C2211yescharacteristic
7C2×#66928C2211yescharacteristic
8C2×C11×#101—21no—
9C4×C11×M16C2212yes—
10#10622844—21no—
11#10622637—24no—
12#10622605—21no—
13#10622604C411yescharacteristic
14#10622604C411yescharacteristic
15#10622592C411yescharacteristic
16#10622592C411yescharacteristic
17#10622553—21no—
18#10622553—21no—
19#10622550C2211yescharacteristic
20#10622539—21no—
21#10622539C2212yes—
22#10622538—21no—
23C11×#343—21no—
24#10622102—24no—
25C22×Q8×C11D411yescharacteristic
26C22×D44C2×C411yescharacteristic
27C22×Dic22C2×C411yescharacteristic
28C2×C11×M16—22no—
29C4×Q8×C11—22no—
30C4×Q8×C11—22no—
31C2×C11×C4⋊C4C2×C411yescharacteristic
32C2×C11×C4⋊C4C2×C411yescharacteristic
33C2×C11×C4⋊C4D411yescharacteristic
34C2×C42×C11D411yescharacteristic
35C2×C42×C11D411yescharacteristic
36C2×C42×C11C2311yescharacteristic
37C2×(C2×D11)⋊C4—21no—
38C2×(C2×D11)⋊C4—21no—
39C2×(C2×D11)⋊C4—21no—
40C2×(C2×D11)⋊C4—21no—
41C2×(C2×D11)⋊C4—21no—
42C2×(C2×D11)⋊C4—21no—
43C2×Dic11⋊C4—21no—
44C2×Dic11⋊C4—21no—
45#66928—22no—
46#66928—22no—
47C11×#101—24no—
48C11×#97—22no—
49C4×C8×C11—22no—
50C11⋊#95—21no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95C2×C411yescharacteristic
55C11⋊#95C2×C411yescharacteristic
56C22⋊(C11⋊C8)—22no—
57C4⋊(C11⋊C8)—22no—
58C4⋊(C11⋊C8)—22no—
59C4⋊(C11⋊C8)—22no—
60#66867—22no—
61#66867D414yes—
62C4×C11⋊C8—22no—
63#9188—111nomaximal, Sylow
64C23×D11—21no—
65C2×Q8×C11—22no—
66C2×Q8×C11—22no—
67C2×Q8×C11—41no—
68C22×C4×C11C22⋊C411yescharacteristic
69C22×C4×C11C22⋊C411yescharacteristic
70C22×C4×C11C22⋊C411yescharacteristic
71C22×C4×C11C22⋊C411yescharacteristic
72C22×C4×C11C22×C411yescharacteristic
73C22×C4×C11C2×D411yescharacteristic
74C22×C4×C11C2×D411yescharacteristic
75C22×Dic11—21no—
76C22×Dic11—21no—
77C22×Dic11—21no—
78C2×D44—22no—
79C2×D44—81no—
80C2×Dic22—22no—
81C2×Dic22—81no—
82C11×M16—24no—
83C11×M16—42no—
84C2×C8×C11—42no—
85C11×C4⋊C4—22no—
86C11×C4⋊C4—22no—
87C11×C4⋊C4—22no—
88C42×C11—21no—
89C42×C11—21no—
90C42×C11—21no—
91C42×C11—21no—
92C42×C11C2×D412yes—
93C42×C11#4112yes—
94(C2×D11)⋊C4—42no—
95(C2×D11)⋊C4—42no—
96(C2×D11)⋊C4—41no—
97(C2×D11)⋊C4—42no—
98(C2×D11)⋊C4—41no—
99(C2×D11)⋊C4—81no—
100(C2×D11)⋊C4—81no—
101Dic11⋊C4—81no—
102Dic11⋊C4—81no—
103C2×C11⋊C8—24no—
104#2983—111no—
105#2632—111no—
106C4×#101D1111yescharacteristic, complemented
107#1527—112no—
108#1288—112no—
109C23×C11C2×C22⋊C411yescharacteristic
110C22×D11—41no—
111C22×D11—41no—
112C22×D11—41no—
113C22×D11—41no—
114C22×D11—41no—
115C22×D11—41no—
116C22×D11—41no—
117Q8×C11—44no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11#10412yes—
132C2×C4×C11C4×D412yes—
133C2×C4×C11#12011yescharacteristic
134C2×C4×C11#12112yes—
135C2×C4×C11#12311yescharacteristic
136C2×Dic11—41no—
137C2×Dic11—41no—
138C2×Dic11—41no—
139C2×Dic11—41no—
140C2×Dic11—41no—
141C2×Dic11—41no—
142C2×Dic11—41no—
143C2×Dic11—41no—
144C2×Dic11—41no—
145D44—82no—
146Dic22—82no—
147C8×C11—44no—
148C11⋊C8—44no—
149C2×#124—111no—
150C2×C4×Q8C2×D1111yescharacteristic
151#446—224no—
152#432—112no—
153#432—221no—
154#431—221no—
155C2×#101—21no—
156C4×M16C2×D1112yes—
157#399—221no—
158#395—111no—
159#395—111no—
160#394—111no—
161#394—111no—
162#393—221no—
163#388—221no—
164#388—221no—
165#383—111no—
166#343—21no—
167#329—224no—
168C22×C11—21no—
169C22×C11—21no—
170C22×C11#38611yescharacteristic
171C22×C11C2×#10411yescharacteristic
172C22×C11#42111yescharacteristic
173C2×D11—81no—
174C2×D11—81no—
175C2×D11—81no—
176C2×D11—81no—
177C2×D11—81no—
178C2×D11—81no—
179C2×D11—81no—
180C4×C11—22no—
181C4×C11—22no—
182C4×C11—21no—
183C4×C11—21no—
184C4×C11—22no—
185C4×C11—41no—
186C4×C11—41no—
187C4×C11—41no—
188Dic11—81no—
189Dic11—81no—
190Dic11—81no—
191C22×Q8—111no—
192C22×Q8C22⋊D1111yescharacteristic
193C22×D4—111no—
194C2×M16—22no—
195#124—222no—
196#124—222no—
197C4×Q8—22no—
198C4×Q8—22no—
199C2×C4⋊C4—221no—
200C2×C4⋊C4—221no—
201C2×C4⋊C4C4×D1111yescharacteristic
202C2×C4⋊C4C4×D1111yescharacteristic
203C2×C4⋊C4C22⋊D1111yescharacteristic
204C2×C22⋊C4—221no—
205C2×C22⋊C4—221no—
206C2×C22⋊C4—221no—
207C2×C22⋊C4—221no—
208C2×C22⋊C4—221no—
209C2×C22⋊C4—221no—
210C2×C42D4411yescharacteristic
211C2×C42D4411yescharacteristic
212C2×C42C22×D1111yescharacteristic
213C4⋊C8—222no—
214C4⋊C8—222no—
215C4⋊C8—222no—
216#101—24no—
217C22⋊C8—222no—
218#97—22no—
219#97—114no—
220#97—222no—
221C4×C8—22no—
222C4×C8—222no—
223#95—111no—
224#95—111no—
225#95—221no—
226#95—221no—
227#95—221no—
228#95—221no—
229C2×C11—21no—
230C2×C11—21no—
231C2×C11#187111yescharacteristic
232C2×C11#191211yescharacteristic
233C2×C11#191411yescharacteristic
234D11—161no—
235C24—221no—
236C2×Q8—22no—
237C2×Q8—22no—
238C2×Q8—41no—
239C2×Q8—222no—
240C2×Q8—881no—
241C2×D4—222no—
242C2×D4—881no—
243C22×C4—221no—
244C22×C4—221no—
245C22×C4—221no—
246C22×C4(C2×D11)⋊C411yescharacteristic
247C22×C4(C2×D11)⋊C411yescharacteristic
248C22×C4(C2×D11)⋊C411yescharacteristic
249C22×C4(C2×D11)⋊C411yescharacteristic
250C22×C4C2×C4×D1111yescharacteristic
251C22×C4C2×D4411yescharacteristic
252C22×C4C2×C22⋊D1111yescharacteristic
253M16—24no—
254M16—42no—
255C2×C8—42no—
256C2×C8—224no—
257C4⋊C4—22no—
258C4⋊C4—22no—
259C4⋊C4—22no—
260C4⋊C4—881no—
261C4⋊C4—881no—
262C22⋊C4—442no—
263C22⋊C4—442no—
264C22⋊C4—441no—
265C22⋊C4—441no—
266C22⋊C4—442no—
267C22⋊C4—881no—
268C22⋊C4—881no—
269C42—21no—
270C42—21no—
271C42—21no—
272C42—21no—
273C42D4×D1112yes—
274C42#434112yes—
275C11#918811yescharacteristic, complemented, Sylow
276C23—441no—
277C23—441no—
278C23—441no—
279C23—441no—
280C23—441no—
281C23—441no—
282C23—441no—
283C23C2×(C2×D11)⋊C411yescharacteristic
284Q8—44no—
285Q8—882no—
286D4—882no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—441no—
301C2×C4—441no—
302C2×C4—441no—
303C2×C4—441no—
304C2×C4—441no—
305C2×C4—441no—
306C2×C4—441no—
307C2×C4—441no—
308C2×C4—441no—
309C2×C4#6686912yes—
310C2×C4(C22⋊D11)⋊C412yes—
311C2×C4#6693511yescharacteristic
312C2×C4#6693911yescharacteristic
313C2×C4#6699212yes—
314C8—44no—
315C8—444no—
316C22—21no—
317C22—21no—
318C22—881no—
319C22—881no—
320C22—881no—
321C22—881no—
322C22—881no—
323C22—881no—
324C22—881no—
325C22C2×#6686911yescharacteristic
326C22#1062257111yescharacteristic
327C22#1062261811yescharacteristic
328C4—21no—
329C4—21no—
330C4—22no—
331C4—22no—
332C4—22no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—881no—
337C4—881no—
338C4—881no—
339C2—21no—
340C2—21no—
341C2—1761no—
342C2#1306891611yescharacteristic
343C2#1306915111yescharacteristic
344C2#1306916111yescharacteristic
subgroupG/H
centerC22#10622571
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC4×C11×#101C2
socleC22×C11#386
prime radicalC22×D44C2×C4
cosocleC2×C42×C11C23
hypercenterC4×#101D11
hypocenterC11#9188
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×#101

Complements

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

NH ≅ G/Ntype
1. #13077701C2semidirect
4. #13066481C2semidirect
5. C4×C11×#101C2semidirect
106. C4×#101D11semidirect
275. C11#9188semidirect

Maximal subgroups

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

subgroupindex
#130777012
#130744762
#130672132
#130664812
C4×C11×#1012
#918811