Finite Group Databasebeta

← #14656211

Subgroups — #14656211

Order 2816.

536 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 103 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#13079769C211yesmaximal, characteristic, complemented
2#13078413C211yesmaximal, characteristic
3#13073789C211yesmaximal, characteristic
4#13067300C211yesmaximal, characteristic, complemented
5#13067116C211yesmaximal, characteristic, complemented
6#13066518C211yesmaximal, characteristic, complemented
7C11×#1478C211yesmaximal, characteristic
8C2×C4×D4×C11C2211yescharacteristic
9#10623001C2211yescharacteristic
10C2×#66922C2211yescharacteristic
11C11×#431C2211yescharacteristic
12C11×#431C2211yescharacteristic
13#10622834—21no—
14#10622828—21no—
15#10622825—22no—
16#10622622—22no—
17#10622621—21no—
18#10622620—21no—
19#10622590—21no—
20#10622577—21no—
21#10622560—22no—
22C4×C4⋊Dic11C2211yescharacteristic
23#10622537C2211yescharacteristic
24#10622463—22no—
25#10622335—22no—
26#10622295—21no—
27#10622294—21no—
28C11×D4⋊C8—22no—
29#10622120—22no—
30#10622105—22no—
31C22×D4×C11D411yescharacteristic
32C23×C4×C11—21no—
33C22×Dic22—21no—
34C4×D4×C11—21no—
35C4×D4×C11—21no—
36C4×D4×C11—21no—
37C4×D4×C11—21no—
38C2×C11×C4⋊C4D411yescharacteristic
39C2×C11×C22⋊C4—21no—
40C2×C42×C11C2311yescharacteristic
41C2×C22⋊Dic11—24no—
42#66979—21no—
43C2×C4⋊Dic11—21no—
44C2×C4⋊Dic11—21no—
45C2×C4⋊Dic11D412yes—
46#66977—21no—
47#66977—21no—
48C2×C4×Dic11—21no—
49C2×#4318—21no—
50#66923—21no—
51#66922—21no—
52#66922—21no—
53#66922—21no—
54#66922—21no—
55#66922D411yescharacteristic
56#66922D411yescharacteristic
57C4×Dic22—21no—
58C4×Dic22—21no—
59C11×C4⋊C8—21no—
60C11×C4⋊C8D412yes—
61C11×C22⋊C8—21no—
62C11×C22⋊C8—21no—
63C4×C8×C11—21no—
64C4×C8×C11—21no—
65#66896—22no—
66#66896—22no—
67C11⋊#95—24no—
68C11⋊#95D412yes—
69#66882—24no—
70#66880—24no—
71#66872—22no—
72#66871—22no—
73C4⋊(C11⋊C8)—21no—
74C4⋊(C11⋊C8)D412yes—
75#10249—111nomaximal, Sylow
76C24×C11—21no—
77C2×D4×C11—21no—
78C2×D4×C11—21no—
79C2×D4×C11—21no—
80C2×D4×C11—21no—
81C2×D4×C11—21no—
82C2×D4×C11Q1612yes—
83C22×C4×C11—21no—
84C22×C4×C11—44no—
85C22×C4×C11—41no—
86C22×C4×C11—41no—
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11C2×D411yescharacteristic
90C22×Dic11—22no—
91C22×Dic11—22no—
92C2×Dic22—21no—
93C2×Dic22—21no—
94C2×Dic22—41no—
95C2×Dic22—41no—
96C2×Dic22—82no—
97C2×C8×C11—22no—
98C2×C8×C11—41no—
99C11×C4⋊C4—21no—
100C11×C4⋊C4—21no—
101C11×C22⋊C4—41no—
102C11×C22⋊C4—41no—
103C42×C11C2×D411yescharacteristic
104C42×C11C2×D411yescharacteristic
105C42×C11C2×D411yescharacteristic
106C42×C11#4111yescharacteristic
107C22⋊Dic11—41no—
108C22⋊Dic11—84no—
109C4⋊Dic11—21no—
110C4⋊Dic11—21no—
111C4⋊Dic11—22no—
112C4⋊Dic11—21no—
113C4⋊Dic11—21no—
114C4⋊Dic11—22no—
115C4⋊Dic11—42no—
116C4⋊Dic11—41no—
117C4⋊Dic11—41no—
118Dic11⋊C4—41no—
119Dic11⋊C4—41no—
120C4×Dic11—41no—
121C4×Dic11—41no—
122C4×Dic11—41no—
123#4318—41no—
124#4318—41no—
125C2×C11⋊C8—22no—
126#3230—111no—
127#3077—111no—
128#2563—111no—
129#1549—111no—
130#1503—111no—
131#1478D1111yescharacteristic
132#1303—111no—
133C23×C11—22no—
134C23×C11—42no—
135C23×C11—42no—
136C23×C11—41no—
137C23×C11—41no—
138C23×C11#12011yescharacteristic
139D4×C11—22no—
140D4×C11—22no—
141D4×C11—41no—
142D4×C11—41no—
143C2×C4×C11—22no—
144C2×C4×C11—41no—
145C2×C4×C11—42no—
146C2×C4×C11—41no—
147C2×C4×C11—82no—
148C2×C4×C11—82no—
149C2×C4×C11#12011yescharacteristic
150C2×C4×C11#12011yescharacteristic
151C2×C4×C11#12111yescharacteristic
152C2×C4×C11#12111yescharacteristic
153C2×C4×C11#12111yescharacteristic
154C2×C4×C11#12711yescharacteristic
155C2×C4×C11C2×Q1611yescharacteristic
156C2×C4×C11#13511yescharacteristic
157C2×C4×C11#13711yescharacteristic
158C2×C4×C11#13711yescharacteristic
159C2×Dic11—42no—
160C2×Dic11—42no—
161C2×Dic11—44no—
162C2×Dic11—41no—
163C2×Dic11—41no—
164C2×Dic11—42no—
165C2×Dic11—42no—
166Dic22—42no—
167Dic22—82no—
168Dic22—82no—
169Dic22—81no—
170C8×C11—42no—
171C8×C11—81no—
172C11⋊C8—42no—
173#533—111no—
174C2×C4⋊Q8—111no—
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#431C2×D1111yescharacteristic
184#431C2×D1111yescharacteristic
185#428—221no—
186#423—111no—
187#418—221no—
188#393—222no—
189#390—221no—
190#382—221no—
191#380—222no—
192C4×C4⋊C4—111no—
193#332—222no—
194#328—222no—
195D4⋊C8—22no—
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—81no—
210C4×C11#45111yescharacteristic
211C4×C11#45211yescharacteristic
212C4×C11#45412yes—
213C4×C11#46711yescharacteristic
214C4×C11#47011yescharacteristic
215Dic11—82no—
216Dic11—81no—
217Dic11—82no—
218Dic11—81no—
219C22×Q8—221no—
220C22×D4D4411yescharacteristic
221C23×C4—21no—
222C2×M16—221no—
223C4⋊Q8—111no—
224C4⋊Q8—111no—
225C4⋊Q8—221no—
226C4⋊Q8—221no—
227C4⋊Q8—221no—
228C4⋊Q8—221no—
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—112no—
240C2×C4⋊C4—221no—
241C2×C4⋊C4—221no—
242C2×C4⋊C4D4411yescharacteristic
243C2×C22⋊C4—21no—
244C2×C22⋊C4—224no—
245C2×C42—221no—
246C2×C42C22×D1111yescharacteristic
247#107—222no—
248#107—224no—
249#106—222no—
250C4⋊C8—21no—
251C4⋊C8—112no—
252C4⋊C8—221no—
253C4⋊C8C22⋊D1112yes—
254#103—224no—
255#102—222no—
256#102—222no—
257C22⋊C8—21no—
258C22⋊C8—21no—
259C4×C8—21no—
260C4×C8—21no—
261#95—112no—
262#95—224no—
263C2×C11—21no—
264C2×C11—21no—
265C2×C11—82no—
266C2×C11#200111yescharacteristic
267C2×C11#200311yescharacteristic
268C2×C11#200811yescharacteristic
269C24—21no—
270C2×Q8—221no—
271C2×Q8—221no—
272C2×Q8—441no—
273C2×Q8—441no—
274C2×Q8—882no—
275C2×D4—21no—
276C2×D4—21no—
277C2×D4—21no—
278C2×D4—21no—
279C2×D4—21no—
280C2×D4Dic4412yes—
281C22×C4—21no—
282C22×C4—44no—
283C22×C4—41no—
284C22×C4—41no—
285C22×C4—222no—
286C22×C4—222no—
287C22×C4C2×D4411yescharacteristic
288C22×C4D4×D1111yescharacteristic
289C22×C4D4×D1111yescharacteristic
290M16—441no—
291M16—441no—
292C2×C8—22no—
293C2×C8—41no—
294C2×C8—222no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—221no—
298C4⋊C4—221no—
299C4⋊C4—222no—
300C4⋊C4—221no—
301C4⋊C4—222no—
302C4⋊C4—221no—
303C4⋊C4—442no—
304C4⋊C4—441no—
305C4⋊C4—441no—
306C4⋊C4—441no—
307C4⋊C4—441no—
308C22⋊C4—41no—
309C22⋊C4—41no—
310C22⋊C4—441no—
311C22⋊C4—884no—
312C42—441no—
313C42—441no—
314C42—441no—
315C42#433911yescharacteristic
316C42D4×D1111yescharacteristic
317C42D4×D1111yescharacteristic
318C42C2×C22⋊D1111yescharacteristic
319C11#1024911yescharacteristic, complemented, Sylow
320C23—22no—
321C23—42no—
322C23—42no—
323C23—41no—
324C23—41no—
325C23#6693511yescharacteristic
326Q8—442no—
327Q8—881no—
328Q8—882no—
329Q8—882no—
330D4—22no—
331D4—22no—
332D4—41no—
333D4—41no—
334C2×C4—22no—
335C2×C4—41no—
336C2×C4—42no—
337C2×C4—41no—
338C2×C4—82no—
339C2×C4—82no—
340C2×C4—442no—
341C2×C4—444no—
342C2×C4—442no—
343C2×C4—441no—
344C2×C4—441no—
345C2×C4—442no—
346C2×C4—442no—
347C2×C4#6693511yescharacteristic
348C2×C4#6693711yescharacteristic
349C2×C4#6693711yescharacteristic
350C2×C4#6695711yescharacteristic
351C2×C4C2×Dic4411yescharacteristic
352C2×C4#6696211yescharacteristic
353C2×C4#6696211yescharacteristic
354C2×C4#6698311yescharacteristic
355C2×C4#6699011yescharacteristic
356C2×C4#6699311yescharacteristic
357C8—42no—
358C8—81no—
359C8—442no—
360C22—21no—
361C22—21no—
362C22—44no—
363C22—42no—
364C22—82no—
365C22—81no—
366C22—81no—
367C22#1062234611yescharacteristic
368C22#1062235211yescharacteristic
369C22#1062257311yescharacteristic
370C4—21no—
371C4—21no—
372C4—21no—
373C4—81no—
374C4—882no—
375C4—881no—
376C4—882no—
377C4—881no—
378C4#1062234611yescharacteristic
379C4#1062235211yescharacteristic
380C4#1062272911yescharacteristic
381C4#1062275011yescharacteristic
382C4#1062281412yes—
383C2—21no—
384C2—21no—
385C2—82no—
386C2#1306962611yescharacteristic
387C2#1306963911yescharacteristic
388C2#1306967011yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1478C2
socleC22×C11#392
prime radicalC22×D4×C11D4
hypercenter#1478D11
hypocenterC11#10249
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1478

Complements

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

NH ≅ G/Ntype
1. #13079769C2semidirect
4. #13067300C2semidirect
5. #13067116C2semidirect
6. #13066518C2semidirect
319. C11#10249semidirect

Maximal subgroups

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

subgroupindex
#130797692
#130784132
#130737892
#130673002
#130671162
#130665182
C11×#14782
#1024911