Finite Group Databasebeta

← #14656239

Subgroups — #14656239

Order 2816.

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

normal subgroups only

This group has 504 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
2#13078421C211yesmaximal, characteristic
3#13073821C211yesmaximal, characteristic
4#13067300C211yesmaximal, characteristic
5#13067116C211yesmaximal, characteristic
6#13066518C211yesmaximal, characteristic
7C11×#1479C211yesmaximal, characteristic
8C2×C4×Q8×C11C2211yescharacteristic
9#10623001C2211yescharacteristic
10C2×#66922C2211yescharacteristic
11C11×#431C2211yescharacteristic
12C11×#431C2211yescharacteristic
13#10622843—21no—
14#10622838—21no—
15#10622635—22no—
16#10622634—21no—
17#10622633—21no—
18#10622592—22no—
19#10622589—21no—
20#10622577—21no—
21C4×C4⋊Dic11C2211yescharacteristic
22#10622541—22no—
23#10622537C2211yescharacteristic
24#10622463—22no—
25#10622335—22no—
26#10622295—21no—
27#10622294—21no—
28C11×Q8⋊C8—22no—
29#10622120—22no—
30#10622105—22no—
31C22×Q8×C11D411yescharacteristic
32C22×Dic22—21no—
33C4×Q8×C11—21no—
34C4×Q8×C11—21no—
35C4×Q8×C11—21no—
36C4×Q8×C11—21no—
37C2×C11×C4⋊C4—21no—
38C2×C11×C4⋊C4D411yescharacteristic
39C2×C42×C11—21no—
40C2×C42×C11C2311yescharacteristic
41#66979—21no—
42C2×C4⋊Dic11—21no—
43C2×C4⋊Dic11—21no—
44C2×C4⋊Dic11D412yes—
45#66977—21no—
46#66977—21no—
47C2×Dic11⋊C4—24no—
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#66899—22no—
66#66899—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#10253—111nomaximal, Sylow
76C2×Q8×C11—21no—
77C2×Q8×C11—21no—
78C2×Q8×C11—21no—
79C2×Q8×C11—21no—
80C2×Q8×C11—21no—
81C2×Q8×C11Q1612yes—
82C22×C4×C11—21no—
83C22×C4×C11—21no—
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11C2×D411yescharacteristic
87C22×Dic11—22no—
88C22×Dic11—22no—
89C2×Dic22—21no—
90C2×Dic22—21no—
91C2×Dic22—41no—
92C2×Dic22—41no—
93C2×Dic22—82no—
94C2×C8×C11—22no—
95C2×C8×C11—41no—
96C11×C4⋊C4—21no—
97C11×C4⋊C4—21no—
98C11×C4⋊C4—41no—
99C11×C4⋊C4—41no—
100C42×C11—41no—
101C42×C11—41no—
102C42×C11C2×D411yescharacteristic
103C42×C11C2×D411yescharacteristic
104C42×C11C2×D411yescharacteristic
105C42×C11#4111yescharacteristic
106C22⋊Dic11—41no—
107C4⋊Dic11—24no—
108C4⋊Dic11—21no—
109C4⋊Dic11—21no—
110C4⋊Dic11—22no—
111C4⋊Dic11—21no—
112C4⋊Dic11—21no—
113C4⋊Dic11—22no—
114C4⋊Dic11—41no—
115C4⋊Dic11—41no—
116Dic11⋊C4—41no—
117Dic11⋊C4—41no—
118Dic11⋊C4—84no—
119C4×Dic11—41no—
120C4×Dic11—41no—
121C4×Dic11—41no—
122#4318—41no—
123#4318—41no—
124C2×C11⋊C8—22no—
125#3230—111no—
126#3078—111no—
127#2567—111no—
128#1549—111no—
129#1503—111no—
130#1479D1111yescharacteristic
131#1303—111no—
132C23×C11#12011yescharacteristic
133Q8×C11—22no—
134Q8×C11—22no—
135Q8×C11—41no—
136Q8×C11—41no—
137C2×C4×C11—22no—
138C2×C4×C11—22no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—42no—
143C2×C4×C11—41no—
144C2×C4×C11#12011yescharacteristic
145C2×C4×C11#12011yescharacteristic
146C2×C4×C11#12111yescharacteristic
147C2×C4×C11#12111yescharacteristic
148C2×C4×C11#12111yescharacteristic
149C2×C4×C11#12711yescharacteristic
150C2×C4×C11C2×Q1611yescharacteristic
151C2×C4×C11#13511yescharacteristic
152C2×C4×C11#13711yescharacteristic
153C2×C4×C11#13711yescharacteristic
154C2×Dic11—24no—
155C2×Dic11—42no—
156C2×Dic11—42no—
157C2×Dic11—44no—
158C2×Dic11—41no—
159C2×Dic11—41no—
160C2×Dic11—42no—
161Dic22—42no—
162Dic22—82no—
163Dic22—82no—
164Dic22—81no—
165C8×C11—42no—
166C8×C11—81no—
167C11⋊C8—42no—
168#533—111no—
169C2×C4⋊Q8—111no—
170C2×C4×Q8C2×D1111yescharacteristic
171#500—221no—
172#487—221no—
173#484—222no—
174#479—222no—
175#477—221no—
176#477—222no—
177#475—221no—
178#431C2×D1111yescharacteristic
179#431C2×D1111yescharacteristic
180#428—221no—
181#423—111no—
182#419—221no—
183#395—222no—
184#391—221no—
185#389—222no—
186#384—221no—
187C4×C4⋊C4—111no—
188#332—222no—
189#328—222no—
190Q8⋊C8—22no—
191C22×C11—21no—
192C22×C11—21no—
193C22×C11#39211yescharacteristic
194C22×C11#45111yescharacteristic
195C22×C11#45211yescharacteristic
196C4×C11—21no—
197C4×C11—21no—
198C4×C11—21no—
199C4×C11—42no—
200C4×C11—81no—
201C4×C11#45111yescharacteristic
202C4×C11#45211yescharacteristic
203C4×C11#45612yes—
204C4×C11#46711yescharacteristic
205C4×C11#47011yescharacteristic
206Dic11—44no—
207Dic11—81no—
208Dic11—82no—
209Dic11—81no—
210C22×Q8—221no—
211C22×Q8D4411yescharacteristic
212C2×M16—221no—
213C4⋊Q8—111no—
214C4⋊Q8—111no—
215C4⋊Q8—221no—
216C4⋊Q8—221no—
217C4⋊Q8—221no—
218C4⋊Q8—221no—
219#125—221no—
220C22⋊Q8—221no—
221C22⋊Q8—221no—
222C4×Q8—21no—
223C4×Q8—21no—
224C4×Q8—21no—
225C4×Q8—21no—
226C4×Q8—221no—
227C4×Q8—221no—
228#117—221no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—112no—
231C2×C4⋊C4—221no—
232C2×C4⋊C4—221no—
233C2×C4⋊C4—224no—
234C2×C4⋊C4D4411yescharacteristic
235C2×C42—21no—
236C2×C42—221no—
237C2×C42C22×D1111yescharacteristic
238#107—222no—
239#107—224no—
240#106—222no—
241C4⋊C8—21no—
242C4⋊C8—112no—
243C4⋊C8—221no—
244C4⋊C8C22⋊D1112yes—
245#103—224no—
246#103—222no—
247#103—222no—
248C22⋊C8—21no—
249C22⋊C8—21no—
250C4×C8—21no—
251C4×C8—21no—
252#95—112no—
253#95—224no—
254C2×C11—21no—
255C2×C11—21no—
256C2×C11#200111yescharacteristic
257C2×C11#200511yescharacteristic
258C2×C11#200811yescharacteristic
259C2×Q8—21no—
260C2×Q8—21no—
261C2×Q8—21no—
262C2×Q8—21no—
263C2×Q8—21no—
264C2×Q8—221no—
265C2×Q8—221no—
266C2×Q8—441no—
267C2×Q8—441no—
268C2×Q8—882no—
269C2×Q8Dic4412yes—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—222no—
273C22×C4—222no—
274C22×C4C2×D4411yescharacteristic
275C22×C4D4×D1111yescharacteristic
276C22×C4D4×D1111yescharacteristic
277M16—441no—
278M16—441no—
279C2×C8—22no—
280C2×C8—41no—
281C2×C8—222no—
282C4⋊C4—21no—
283C4⋊C4—21no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—224no—
287C4⋊C4—221no—
288C4⋊C4—221no—
289C4⋊C4—222no—
290C4⋊C4—221no—
291C4⋊C4—222no—
292C4⋊C4—221no—
293C4⋊C4—441no—
294C4⋊C4—441no—
295C4⋊C4—441no—
296C4⋊C4—441no—
297C4⋊C4—884no—
298C22⋊C4—441no—
299C42—41no—
300C42—41no—
301C42—441no—
302C42—441no—
303C42—441no—
304C42#433911yescharacteristic
305C42D4×D1111yescharacteristic
306C42D4×D1111yescharacteristic
307C42C2×C22⋊D1111yescharacteristic
308C11#1025311yescharacteristic, complemented, Sylow
309C23#6693511yescharacteristic
310Q8—22no—
311Q8—22no—
312Q8—41no—
313Q8—41no—
314Q8—442no—
315Q8—881no—
316Q8—882no—
317Q8—882no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—42no—
324C2×C4—41no—
325C2×C4—224no—
326C2×C4—442no—
327C2×C4—442no—
328C2×C4—444no—
329C2×C4—441no—
330C2×C4—441no—
331C2×C4—442no—
332C2×C4#6693511yescharacteristic
333C2×C4#6693711yescharacteristic
334C2×C4#6693711yescharacteristic
335C2×C4#6695711yescharacteristic
336C2×C4C2×Dic4411yescharacteristic
337C2×C4#6696211yescharacteristic
338C2×C4#6696211yescharacteristic
339C2×C4#6698311yescharacteristic
340C2×C4#6699011yescharacteristic
341C2×C4#6699311yescharacteristic
342C8—42no—
343C8—81no—
344C8—442no—
345C22—21no—
346C22—21no—
347C22#1062234611yescharacteristic
348C22#1062235211yescharacteristic
349C22#1062257311yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—42no—
354C4—81no—
355C4—444no—
356C4—881no—
357C4—882no—
358C4—881no—
359C4#1062234611yescharacteristic
360C4#1062235211yescharacteristic
361C4#1062272911yescharacteristic
362C4#1062275011yescharacteristic
363C4#1062281812yes—
364C2—21no—
365C2—21no—
366C2#1306962611yescharacteristic
367C2#1306965311yescharacteristic
368C2#1306967011yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1479C2
socleC22×C11#392
prime radicalC23×C11#120
hypercenter#1479D11
hypocenterC11#10253
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1479

Complements

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

NH ≅ G/Ntype
308. C11#10253semidirect

Maximal subgroups

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

subgroupindex
#130797692
#130784212
#130738212
#130673002
#130671162
#130665182
C11×#14792
#1025311