Finite Group Databasebeta

← #14656229

Subgroups — #14656229

Order 2816.

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

normal subgroups only

This group has 500 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#13078417C211yesmaximal, characteristic
2#13073832C211yesmaximal, characteristic
3#13067297C211yesmaximal, characteristic
4#13067115C211yesmaximal, characteristic
5#13067010C211yesmaximal, characteristic
6#13066518C211yesmaximal, characteristic
7C11×#3209C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C4×Dic22C2211yescharacteristic
11C11×#494—21no—
12C11×#487—21no—
13C11×#462—22no—
14C11×#451—22no—
15C11×#431C2211yescharacteristic
16#10622843—22no—
17#10622707—21no—
18#10622704—21no—
19#10622676—22no—
20#10622617—21no—
21#10622608—21no—
22#10622595—22no—
23#10622590—21no—
24#10622587—21no—
25C4×C4⋊Dic11C2211yescharacteristic
26#10622538C2211yescharacteristic
27#10622537C2211yescharacteristic
28#10622184—22no—
29#10622176—22no—
30#10622122—22no—
31C22×Q8×C11D412yes—
32C22×Dic22D411yescharacteristic
33C2×C11×Q16—24no—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8D411yescharacteristic
39C11×C4⋊Q8D411yescharacteristic
40C11×#125—21no—
41C11×C22⋊Q8—21no—
42C11×C22⋊Q8—21no—
43C4×Q8×C11—21no—
44C4×Q8×C11—21no—
45C11×#117—21no—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4—21no—
48C2×C42×C11C2311yescharacteristic
49C2×C4⋊Dic11—21no—
50C2×C4⋊Dic11D411yescharacteristic
51C2×Dic11⋊C4—21no—
52C2×C4×Dic11—21no—
53C2×C4×Dic11—21no—
54C2×#4318—21no—
55C4×Dic22—21no—
56C4×Dic22—21no—
57C4×Dic22—21no—
58C4×Dic22—21no—
59C11×C4⋊C8D412yes—
60C11×#103—24no—
61C11×C22⋊C8—21no—
62C4×C8×C11—21no—
63C11⋊#95—24no—
64C11⋊#95—24no—
65C11⋊#95D412yes—
66C22⋊(C11⋊C8)—21no—
67#66874—22no—
68#66874—22no—
69#66872—22no—
70#66871—22no—
71C4⋊(C11⋊C8)—21no—
72C4⋊(C11⋊C8)—21no—
73C4⋊(C11⋊C8)D412yes—
74C4×C11⋊C8—21no—
75#10252—111nomaximal, Sylow
76C2×Q8×C11—22no—
77C2×Q8×C11—21no—
78C2×Q8×C11—21no—
79C2×Q8×C11—22no—
80C2×Q8×C11—44no—
81C22×C4×C11—22no—
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C22×Dic11—21no—
86C22×Dic11—22no—
87C22×Dic11—21no—
88C2×Dic22—21no—
89C2×Dic22—21no—
90C2×Dic22—21no—
91C2×Dic22—21no—
92C2×Dic22—21no—
93C2×Dic22Q1612yescomplemented
94C11×Q16—84no—
95C2×C8×C11—22no—
96C11×C4⋊C4—21no—
97C11×C4⋊C4—21no—
98C11×C4⋊C4—21no—
99C11×C4⋊C4—21no—
100C11×C4⋊C4—41no—
101C11×C4⋊C4—41no—
102C11×C4⋊C4—41no—
103C11×C4⋊C4—41no—
104C11×C4⋊C4—41no—
105C11×C4⋊C4—41no—
106C11×C22⋊C4—41no—
107C42×C11—41no—
108C42×C11C2×D411yescharacteristic
109C42×C11C2×D411yescharacteristic
110C42×C11C2×D411yescharacteristic
111C42×C11#4111yescharacteristic
112C4⋊Dic11—21no—
113C4⋊Dic11—21no—
114C4⋊Dic11—42no—
115Dic11⋊C4—41no—
116Dic11⋊C4—41no—
117C4×Dic11—41no—
118C4×Dic11—41no—
119C4×Dic11—41no—
120C4×Dic11—41no—
121#4318—41no—
122#4318—41no—
123C2×C11⋊C8—22no—
124C2×C11⋊C8—41no—
125#3209D1111yescharacteristic
126#3078—111no—
127#2568—111no—
128#1548—111no—
129#1503—111no—
130#1479—111no—
131#1303—111no—
132C23×C11#12011yescharacteristic
133Q8×C11—42no—
134Q8×C11—44no—
135Q8×C11—81no—
136Q8×C11—82no—
137C2×C4×C11—22no—
138C2×C4×C11—41no—
139C2×C4×C11—44no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—42no—
143C2×C4×C11#12011yescharacteristic
144C2×C4×C11#12011yescharacteristic
145C2×C4×C11#12111yescharacteristic
146C2×C4×C11#12111yescharacteristic
147C2×C4×C11#12111yescharacteristic
148C2×C4×C11#12711yescharacteristic
149C2×C4×C11C2×Q1611yescharacteristic
150C2×C4×C11#13511yescharacteristic
151C2×C4×C11#13711yescharacteristic
152C2×C4×C11#13711yescharacteristic
153C2×Dic11—22no—
154C2×Dic11—41no—
155C2×Dic11—41no—
156C2×Dic11—42no—
157C2×Dic11—42no—
158C2×Dic11—42no—
159C2×Dic11—41no—
160C2×Dic11—42no—
161Dic22—22no—
162Dic22—22no—
163Dic22—41no—
164Dic22—41no—
165C8×C11—42no—
166C11⋊C8—42no—
167C11⋊C8—81no—
168#533C2×D1111yescharacteristic
169C2×C4⋊Q8C2×D1111yescharacteristic
170C2×C4×Q8—111no—
171#494—21no—
172#487—21no—
173#479—222no—
174#477—221no—
175#475—221no—
176#462—22no—
177#451—22no—
178#431—111no—
179#431C2×D1111yescharacteristic
180#428—221no—
181#423—111no—
182#419—221no—
183#400—222no—
184#391—221no—
185#391—222no—
186#382—221no—
187C4×C4⋊C4—111no—
188#333—222no—
189#328—222no—
190Q8⋊C8—222no—
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—82no—
200C4×C11—81no—
201C4×C11—81no—
202C4×C11#45111yescharacteristic
203C4×C11#45211yescharacteristic
204C4×C11#45512yes—
205C4×C11#46711yescharacteristic
206C4×C11#47011yescharacteristic
207Dic11—42no—
208Dic11—82no—
209Dic11—81no—
210C22×Q8—111no—
211C22×Q8C22⋊D1112yes—
212C2×Q16—24no—
213C2×M16—221no—
214C4⋊Q8—21no—
215C4⋊Q8—21no—
216C4⋊Q8—21no—
217C4⋊Q8—21no—
218C4⋊Q8C22⋊D1111yescharacteristic
219C4⋊Q8C22⋊D1111yescharacteristic
220#125—21no—
221C22⋊Q8—21no—
222C22⋊Q8—21no—
223C4×Q8—21no—
224C4×Q8—21no—
225C4×Q8—221no—
226C4×Q8—221no—
227C4×Q8—221no—
228C4×Q8—221no—
229#117—21no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—111no—
233C2×C4⋊C4—221no—
234C2×C4⋊C4—221no—
235C2×C42—221no—
236C2×C42—221no—
237C2×C42C22×D1111yescharacteristic
238#107—222no—
239#106—222no—
240C4⋊C8—112no—
241C4⋊C8—221no—
242C4⋊C8—221no—
243C4⋊C8C22⋊D1112yes—
244#103—24no—
245#103—222no—
246#103—222no—
247C22⋊C8—21no—
248C22⋊C8—221no—
249C4×C8—21no—
250C4×C8—221no—
251#95—112no—
252#95—224no—
253#95—224no—
254C2×C11—21no—
255C2×C11—21no—
256C2×C11#200111yescharacteristic
257C2×C11#200411yescharacteristic
258C2×C11#200911yescharacteristic
259C2×Q8—21no—
260C2×Q8—22no—
261C2×Q8—22no—
262C2×Q8—21no—
263C2×Q8—44no—
264C2×Q8—112no—
265C2×Q8—221no—
266C2×Q8—221no—
267C2×Q8—221no—
268C2×Q8—221no—
269C2×Q8—221no—
270C22×C4—22no—
271C22×C4—221no—
272C22×C4—222no—
273C22×C4—221no—
274C22×C4D4×D1111yescharacteristic
275C22×C4D4×D1111yescharacteristic
276C22×C4C2×C22⋊D1111yescharacteristic
277Q16—84no—
278M16—441no—
279M16—441no—
280C2×C8—22no—
281C2×C8—222no—
282C2×C8—441no—
283C4⋊C4—21no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C4⋊C4—41no—
290C4⋊C4—41no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C4⋊C4—221no—
294C4⋊C4—221no—
295C4⋊C4—442no—
296C4⋊C4—441no—
297C4⋊C4—441no—
298C22⋊C4—41no—
299C42—41no—
300C42—441no—
301C42—441no—
302C42—441no—
303C42—441no—
304C42D4×D1111yescharacteristic
305C42#434111yescharacteristic
306C42C2×C22⋊D1111yescharacteristic
307C42C2×C22⋊D1111yescharacteristic
308C11#1025211yescharacteristic, complemented, Sylow
309C23#6699011yescharacteristic
310Q8—42no—
311Q8—44no—
312Q8—81no—
313Q8—82no—
314Q8—222no—
315Q8—222no—
316Q8—441no—
317Q8—441no—
318C2×C4—22no—
319C2×C4—41no—
320C2×C4—44no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—42no—
324C2×C4—222no—
325C2×C4—441no—
326C2×C4—441no—
327C2×C4—442no—
328C2×C4—442no—
329C2×C4—442no—
330C2×C4—442no—
331C2×C4—441no—
332C2×C4Q16×D1111yescharacteristic
333C2×C4#6697111yescharacteristic
334C2×C4#6697111yescharacteristic
335C2×C4#6697211yescharacteristic
336C2×C4#6699011yescharacteristic
337C2×C4#6699111yescharacteristic
338C2×C4#6699211yescharacteristic
339C2×C4#6699211yescharacteristic
340C2×C4#6699311yescharacteristic
341C2×C4#6700611yescharacteristic
342C8—42no—
343C8—442no—
344C8—881no—
345C22—21no—
346C22—21no—
347C22#1062279911yescharacteristic
348C22#1062280011yescharacteristic
349C22#1062283611yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—82no—
354C4—81no—
355C4—81no—
356C4—442no—
357C4—882no—
358C4—881no—
359C4#1062279911yescharacteristic
360C4#1062280011yescharacteristic
361C4#1062280111yescharacteristic
362C4#1062280211yescharacteristic
363C4#1062285512yes—
364C2—21no—
365C2—21no—
366C2#1306962311yescharacteristic
367C2#1306964311yescharacteristic
368C2#1306967411yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3209C2
socleC22×C11#392
prime radicalC23×C11#120
hypercenter#3209D11
hypocenterC11#10252
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3209

Complements

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

NH ≅ G/Ntype
93. C2×Dic22Q16semidirect
308. C11#10252semidirect

Maximal subgroups

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

subgroupindex
#130784172
#130738322
#130672972
#130671152
#130670102
#130665182
C11×#32092
#1025211