Finite Group Databasebeta

← #14656210

Subgroups — #14656210

Order 2816.

536 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 105 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#13079767C211yesmaximal, characteristic, complemented
2#13078413C211yesmaximal, characteristic
3#13067301C211yesmaximal, characteristic, complemented
4#13067114C211yesmaximal, characteristic, complemented
5#13067007C211yesmaximal, characteristic
6#13066519C211yesmaximal, characteristic, complemented
7C11×#2563C211yesmaximal, characteristic
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C4×D4×C11C2211yescharacteristic
10#10623001C2211yescharacteristic
11C11×#393—22no—
12C11×#390—21no—
13C11×#382—21no—
14C11×#380—22no—
15C4×C11×C4⋊C4C2211yescharacteristic
16#10622828—21no—
17#10622706—21no—
18#10622704—22no—
19#10622691—21no—
20#10622622—22no—
21#10622621—21no—
22#10622620—21no—
23#10622583—22no—
24#10622577—21no—
25#10622538C2211yescharacteristic
26#10622538C2211yescharacteristic
27#10622537C2211yescharacteristic
28#10622185—22no—
29D4⋊(C11⋊C8)—22no—
30#10622090—22no—
31C22×Q8×C11—21no—
32C22×D4×C11D411yescharacteristic
33C23×C4×C11—21no—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C4×D4×C11—21no—
39C4×D4×C11—21no—
40C4×D4×C11—21no—
41C4×D4×C11—21no—
42C2×C11×C4⋊C4—21no—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4D411yescharacteristic
45C2×C11×C4⋊C4D412yes—
46C2×C11×C22⋊C4—21no—
47C2×C11×C22⋊C4—24no—
48C2×C42×C11—21no—
49C2×C42×C11C2311yescharacteristic
50#66979—21no—
51#66977—21no—
52#66977—21no—
53C2×#4318—21no—
54#66923—21no—
55#66922D411yescharacteristic
56#66922D411yescharacteristic
57C4×Dic22—21no—
58C4×Dic22—21no—
59C11×#95—24no—
60C11×#95D412yes—
61#66896—22no—
62#66896—22no—
63C22⋊(C11⋊C8)—21no—
64C22⋊(C11⋊C8)—21no—
65#66874—24no—
66#66872—22no—
67#66871—22no—
68#66871—24no—
69C4⋊(C11⋊C8)—21no—
70C4⋊(C11⋊C8)—21no—
71C4⋊(C11⋊C8)D412yes—
72C4⋊(C11⋊C8)D412yes—
73C4×C11⋊C8—21no—
74C4×C11⋊C8—21no—
75#10249—111nomaximal, Sylow
76C24×C11—21no—
77C2×Q8×C11—41no—
78C2×Q8×C11—41no—
79C2×Q8×C11—82no—
80C2×D4×C11—21no—
81C2×D4×C11—21no—
82C2×D4×C11—21no—
83C2×D4×C11—21no—
84C2×D4×C11—21no—
85C2×D4×C11Q1612yes—
86C22×C4×C11—21no—
87C22×C4×C11—22no—
88C22×C4×C11—22no—
89C22×C4×C11—44no—
90C22×C4×C11—41no—
91C22×C4×C11—41no—
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11C2×D411yescharacteristic
95C2×Dic22—21no—
96C2×Dic22—21no—
97C11×C4⋊C4—21no—
98C11×C4⋊C4—22no—
99C11×C4⋊C4—21no—
100C11×C4⋊C4—22no—
101C11×C4⋊C4—42no—
102C11×C4⋊C4—41no—
103C11×C4⋊C4—41no—
104C11×C22⋊C4—41no—
105C11×C22⋊C4—41no—
106C11×C22⋊C4—84no—
107C42×C11—41no—
108C42×C11—41no—
109C42×C11C2×D411yescharacteristic
110C42×C11C2×D411yescharacteristic
111C42×C11C2×D411yescharacteristic
112C42×C11#4111yescharacteristic
113C22⋊Dic11—41no—
114C4⋊Dic11—21no—
115C4⋊Dic11—21no—
116C4⋊Dic11—21no—
117C4⋊Dic11—21no—
118Dic11⋊C4—41no—
119Dic11⋊C4—41no—
120C4×Dic11—41no—
121#4318—41no—
122#4318—41no—
123C2×C11⋊C8—22no—
124C2×C11⋊C8—22no—
125C2×C11⋊C8—41no—
126#3230—111no—
127#3077—111no—
128#2563D1111yescharacteristic
129#1549—111no—
130#1503—111no—
131#1478—111no—
132#1303—111no—
133C23×C11—22no—
134C23×C11—42no—
135C23×C11—42no—
136C23×C11—41no—
137C23×C11—41no—
138C23×C11#12011yescharacteristic
139Q8×C11—82no—
140Q8×C11—82no—
141D4×C11—22no—
142D4×C11—22no—
143D4×C11—41no—
144D4×C11—41no—
145C2×C4×C11—22no—
146C2×C4×C11—41no—
147C2×C4×C11—42no—
148C2×C4×C11—44no—
149C2×C4×C11—42no—
150C2×C4×C11—42no—
151C2×C4×C11—41no—
152C2×C4×C11—42no—
153C2×C4×C11—42no—
154C2×C4×C11—82no—
155C2×C4×C11—82no—
156C2×C4×C11#12011yescharacteristic
157C2×C4×C11#12011yescharacteristic
158C2×C4×C11#12111yescharacteristic
159C2×C4×C11#12111yescharacteristic
160C2×C4×C11#12111yescharacteristic
161C2×C4×C11#12711yescharacteristic
162C2×C4×C11C2×Q1611yescharacteristic
163C2×C4×C11#13511yescharacteristic
164C2×C4×C11#13711yescharacteristic
165C2×C4×C11#13711yescharacteristic
166C2×Dic11—41no—
167C2×Dic11—41no—
168Dic22—42no—
169Dic22—81no—
170C11⋊C8—42no—
171C11⋊C8—42no—
172C11⋊C8—81no—
173#533—111no—
174C2×C4⋊Q8C2×D1111yescharacteristic
175C2×C4×D4C2×D1111yescharacteristic
176#500—221no—
177#487—221no—
178#484—222no—
179#478—222no—
180#477—222no—
181#476—221no—
182#474—221no—
183#431—111no—
184#431—111no—
185#428—221no—
186#423—111no—
187#418—221no—
188#393—22no—
189#390—21no—
190#382—21no—
191#380—22no—
192C4×C4⋊C4C2×D1111yescharacteristic
193#332—222no—
194#328—222no—
195D4⋊C8—222no—
196C22×C11—21no—
197C22×C11—21no—
198C22×C11—44no—
199C22×C11—42no—
200C22×C11—82no—
201C22×C11—81no—
202C22×C11—81no—
203C22×C11#39211yescharacteristic
204C22×C11#45111yescharacteristic
205C22×C11#45211yescharacteristic
206C4×C11—21no—
207C4×C11—21no—
208C4×C11—21no—
209C4×C11—82no—
210C4×C11—81no—
211C4×C11—82no—
212C4×C11#45111yescharacteristic
213C4×C11#45211yescharacteristic
214C4×C11#45412yes—
215C4×C11#46711yescharacteristic
216C4×C11#47011yescharacteristic
217Dic11—81no—
218Dic11—81no—
219C22×Q8—21no—
220C22×D4C22⋊D1111yescharacteristic
221C23×C4—21no—
222C2×M16—221no—
223C4⋊Q8—21no—
224C4⋊Q8—21no—
225C4⋊Q8—21no—
226C4⋊Q8—21no—
227C4⋊Q8—111no—
228C4⋊Q8—111no—
229#125—221no—
230C22⋊Q8—221no—
231C22⋊Q8—221no—
232C4×Q8—221no—
233C4×Q8—221no—
234C4×D4—21no—
235C4×D4—21no—
236C4×D4—21no—
237C4×D4—21no—
238#117—221no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4C22⋊D1111yescharacteristic
242C2×C4⋊C4C22⋊D1112yes—
243C2×C22⋊C4—21no—
244C2×C22⋊C4—24no—
245C2×C42—21no—
246C2×C42C22×D1111yescharacteristic
247#107—222no—
248#107—224no—
249#106—222no—
250C4⋊C8—112no—
251C4⋊C8—112no—
252C4⋊C8—221no—
253C4⋊C8—221no—
254#103—224no—
255#102—222no—
256#102—222no—
257C22⋊C8—221no—
258C22⋊C8—221no—
259C4×C8—221no—
260C4×C8—221no—
261#95—24no—
262#95C22⋊D1112yes—
263C2×C11—21no—
264C2×C11—21no—
265C2×C11—82no—
266C2×C11#200111yescharacteristic
267C2×C11#200311yescharacteristic
268C2×C11#200811yescharacteristic
269C24—21no—
270C2×Q8—41no—
271C2×Q8—41no—
272C2×Q8—82no—
273C2×Q8—221no—
274C2×Q8—221no—
275C2×D4—21no—
276C2×D4—21no—
277C2×D4—21no—
278C2×D4—21no—
279C2×D4—21no—
280C2×D4#432612yes—
281C22×C4—21no—
282C22×C4—22no—
283C22×C4—22no—
284C22×C4—44no—
285C22×C4—41no—
286C22×C4—41no—
287C22×C4C2×C22⋊D1111yescharacteristic
288C22×C4C2×C22⋊D1111yescharacteristic
289C22×C4C2×C22⋊D1111yescharacteristic
290M16—441no—
291M16—441no—
292C2×C8—222no—
293C2×C8—222no—
294C2×C8—441no—
295C4⋊C4—22no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—22no—
299C4⋊C4—42no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—221no—
303C4⋊C4—221no—
304C4⋊C4—221no—
305C4⋊C4—221no—
306C4⋊C4—441no—
307C4⋊C4—441no—
308C22⋊C4—41no—
309C22⋊C4—41no—
310C22⋊C4—84no—
311C22⋊C4—441no—
312C42—41no—
313C42—41no—
314C42—441no—
315C42D4×D1111yescharacteristic
316C42D4×D1111yescharacteristic
317C42D4×D1111yescharacteristic
318C42#434111yescharacteristic
319C11#1024911yescharacteristic, complemented, Sylow
320C23—22no—
321C23—42no—
322C23—42no—
323C23—41no—
324C23—41no—
325C23#6700611yescharacteristic
326Q8—82no—
327Q8—82no—
328Q8—442no—
329Q8—881no—
330D4—22no—
331D4—22no—
332D4—41no—
333D4—41no—
334C2×C4—22no—
335C2×C4—41no—
336C2×C4—42no—
337C2×C4—44no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—41no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—82no—
344C2×C4—82no—
345C2×C4—441no—
346C2×C4—441no—
347C2×C4#6699011yescharacteristic
348C2×C4#6699011yescharacteristic
349C2×C4#6699111yescharacteristic
350C2×C4#6699211yescharacteristic
351C2×C4#6699211yescharacteristic
352C2×C4#6699311yescharacteristic
353C2×C4#6699511yescharacteristic
354C2×C4C2×#432611yescharacteristic
355C2×C4#6700311yescharacteristic
356C2×C4#6700411yescharacteristic
357C8—442no—
358C8—442no—
359C8—881no—
360C22—21no—
361C22—21no—
362C22—44no—
363C22—42no—
364C22—82no—
365C22—81no—
366C22—81no—
367C22#1062283611yescharacteristic
368C22#1062284111yescharacteristic
369C22#1062285211yescharacteristic
370C4—21no—
371C4—21no—
372C4—21no—
373C4—82no—
374C4—81no—
375C4—82no—
376C4—881no—
377C4—881no—
378C4#1062266011yescharacteristic
379C4#1062266311yescharacteristic
380C4#1062266411yescharacteristic
381C4#1062266511yescharacteristic
382C4#1062267512yes—
383C2—21no—
384C2—21no—
385C2—82no—
386C2#1306962411yescharacteristic
387C2#1306963811yescharacteristic
388C2#1306966911yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#2563C2
socleC22×C11#392
prime radicalC22×D4×C11D4
hypercenter#2563D11
hypocenterC11#10249
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2563

Complements

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

NH ≅ G/Ntype
1. #13079767C2semidirect
3. #13067301C2semidirect
4. #13067114C2semidirect
6. #13066519C2semidirect
319. C11#10249semidirect

Maximal subgroups

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

subgroupindex
#130797672
#130784132
#130673012
#130671142
#130670072
#130665192
C11×#25632
#1024911