Finite Group Databasebeta

← #14655379

Subgroups — #14655379

Order 2816.

454 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 81 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#13079802C211yesmaximal, characteristic
2#13079169C211yesmaximal, characteristic, complemented
3#13067089C211yesmaximal, characteristic, complemented
4#13067033C211yesmaximal, characteristic
5#13066973C211yesmaximal, characteristic, complemented
6#13066489C211yesmaximal, characteristic, complemented
7C11×#3216C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C11×#532C2211yescharacteristic
10C2×#66923C2211yescharacteristic
11C11×#497—21no—
12C11×#489—21no—
13C11×#462—21no—
14C11×#460—21no—
15C11×#452—22no—
16C11×#432C2211yescharacteristic
17#10622693—21no—
18#10622693—21no—
19#10622693—21no—
20#10622684—21no—
21#10622677—22no—
22#10622647—21no—
23#10622646—21no—
24#10622622—22no—
25#10622608—21no—
26#10622608—21no—
27#10622539C2211yescharacteristic
28#10622538C2211yescharacteristic
29C4×#4318C2211yescharacteristic
30Q8⋊(C11⋊C8)—22no—
31D4⋊(C11⋊C8)—22no—
32#10622107—22no—
33C2×C11×#41—21no—
34C2×C11×Q16—22no—
35C2×C11×SD16—22no—
36C11×C4⋊Q8D411yescharacteristic
37C11×C4⋊Q8D411yescharacteristic
38C11×C4⋊Q8D411yescharacteristic
39C11×#127D411yescharacteristic
40C11×#125—21no—
41C11×#124—21no—
42C11×C22⋊Q8—21no—
43C11×C22⋊Q8—21no—
44C11×#121—21no—
45C11×#121—21no—
46C4×Q8×C11—21no—
47C4×Q8×C11—21no—
48C4×D4×C11—21no—
49C4×D4×C11—21no—
50C11×#117—21no—
51C2×C42×C11C2311yescharacteristic
52C2×C4⋊Dic11D411yescharacteristic
53C2×C4⋊Dic11D411yescharacteristic
54C2×Dic11⋊C4—21no—
55C2×Dic11⋊C4—21no—
56C2×#4318—21no—
57#66923—21no—
58#66923—21no—
59#66923—21no—
60#66923—21no—
61C11×C4⋊C8—21no—
62C11×#103—22no—
63C11×#102—22no—
64C11×C22⋊C8D412yes—
65C11×#97—21no—
66#66896—22no—
67#66896—22no—
68C22⋊(C11⋊C8)—21no—
69C22⋊(C11⋊C8)—21no—
70#66872—22no—
71#66872—22no—
72#66872—22no—
73#66871—22no—
74#66871—22no—
75#66871—22no—
76C4⋊(C11⋊C8)—21no—
77C4⋊(C11⋊C8)D412yes—
78#66867—21no—
79#66867—21no—
80C4×C11⋊C8—21no—
81C4×C11⋊C8D412yes—
82#10126—111nomaximal, Sylow
83C11×#41—82no—
84C2×Q8×C11—21no—
85C2×Q8×C11—21no—
86C2×Q8×C11—21no—
87C2×D4×C11—21no—
88C2×D4×C11—21no—
89C2×D4×C11—21no—
90C2×D4×C11—41no—
91C22×C4×C11—41no—
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11#4111yescharacteristic
95C22×Dic11—21no—
96C22×Dic11—21no—
97C11×Q16—82no—
98C11×SD16—82no—
99C2×C8×C11—22no—
100C11×C4⋊C4—21no—
101C11×C4⋊C4—21no—
102C11×C4⋊C4—21no—
103C11×C4⋊C4—21no—
104C11×C4⋊C4—21no—
105C11×C4⋊C4—21no—
106C11×C4⋊C4—41no—
107C11×C4⋊C4—41no—
108C11×C22⋊C4—41no—
109C11×C22⋊C4—41no—
110C11×C22⋊C4—41no—
111C42×C11—41no—
112C42×C11C2×D411yescharacteristic
113C42×C11C2×D411yescharacteristic
114C42×C11C2×D411yescharacteristic
115C42×C11C2×D411yescharacteristic
116C4⋊Dic11—21no—
117C4⋊Dic11—21no—
118C4⋊Dic11—21no—
119C4⋊Dic11—21no—
120Dic11⋊C4—41no—
121Dic11⋊C4—41no—
122Dic11⋊C4—41no—
123Dic11⋊C4—41no—
124#4318—24no—
125C2×C11⋊C8—22no—
126C2×C11⋊C8—22no—
127C2×C11⋊C8—41no—
128#3234—111no—
129#3216D1111yescharacteristic
130#3166—111no—
131#1497—111no—
132#1484—111no—
133#1470—111no—
134#1291—111no—
135C23×C11—41no—
136C23×C11#12111yescharacteristic
137Q8×C11—41no—
138Q8×C11—41no—
139Q8×C11—42no—
140Q8×C11—42no—
141D4×C11—42no—
142D4×C11—42no—
143D4×C11—42no—
144D4×C11—82no—
145C2×C4×C11—22no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—82no—
152C2×C4×C11#12011yescharacteristic
153C2×C4×C11#12011yescharacteristic
154C2×C4×C11#12011yescharacteristic
155C2×C4×C11#12111yescharacteristic
156C2×C4×C11#12111yescharacteristic
157C2×C4×C11#12711yescharacteristic
158C2×Dic11—42no—
159C2×Dic11—41no—
160C2×Dic11—41no—
161C2×Dic11—81no—
162C8×C11—42no—
163C11⋊C8—24no—
164C11⋊C8—42no—
165C11⋊C8—81no—
166#533C2×D1111yescharacteristic
167#532C2×D1111yescharacteristic
168C2×#125—111no—
169#501—221no—
170#501—221no—
171#501—221no—
172#499—222no—
173#497—21no—
174#490—221no—
175#489—21no—
176#481—221no—
177#480—221no—
178#478—222no—
179#462—21no—
180#460—21no—
181#452—22no—
182#432—111no—
183#432C2×D1111yescharacteristic
184#431—111no—
185#428—221no—
186#428—221no—
187C4×M16—111no—
188Q8⋊C8—222no—
189D4⋊C8—222no—
190#324—222no—
191C22×C11—21no—
192C22×C11—21no—
193C22×C11—21no—
194C22×C11—81no—
195C22×C11—81no—
196C22×C11—81no—
197C22×C11#39211yescharacteristic
198C4×C11—21no—
199C4×C11—21no—
200C4×C11—21no—
201C4×C11—21no—
202C4×C11—21no—
203C4×C11—81no—
204C4×C11—81no—
205C4×C11—81no—
206C4×C11#45612yes—
207Dic11—81no—
208Dic11—81no—
209C2×#41—21no—
210C2×Q16—22no—
211C2×SD16—22no—
212C2×M16—221no—
213C4⋊Q8C22⋊D1111yescharacteristic
214C4⋊Q8C22⋊D1111yescharacteristic
215C4⋊Q8C22⋊D1111yescharacteristic
216#127C22⋊D1111yescharacteristic
217#125—21no—
218#125—221no—
219#125—221no—
220#125—221no—
221#125—221no—
222#124—21no—
223C22⋊Q8—21no—
224C22⋊Q8—21no—
225#121—21no—
226#121—21no—
227C4×Q8—21no—
228C4×Q8—21no—
229C4×D4—21no—
230C4×D4—21no—
231#117—21no—
232C2×C4⋊C4—111no—
233C2×C4⋊C4—111no—
234C2×C4⋊C4—221no—
235C2×C4⋊C4—221no—
236C2×C42C22×D1111yescharacteristic
237#107—222no—
238#107—222no—
239#107—222no—
240#106—222no—
241#106—222no—
242#106—222no—
243C4⋊C8—21no—
244C4⋊C8—112no—
245C4⋊C8—221no—
246#103—22no—
247#102—22no—
248#102—222no—
249#102—222no—
250C22⋊C8—221no—
251C22⋊C8—221no—
252C22⋊C8C22⋊D1112yes—
253#97—21no—
254#97—221no—
255#97—221no—
256C4×C8—112no—
257C4×C8—221no—
258C2×C11—41no—
259C2×C11—161no—
260C2×C11#200511yescharacteristic
261C2×C11#200811yescharacteristic
262C2×C11#201711yescharacteristic
263#41—82no—
264C2×Q8—21no—
265C2×Q8—21no—
266C2×Q8—21no—
267C2×D4—21no—
268C2×D4—21no—
269C2×D4—21no—
270C2×D4—41no—
271C22×C4—41no—
272C22×C4—221no—
273C22×C4—221no—
274C22×C4D4×D1111yescharacteristic
275C22×C4#434111yescharacteristic
276C22×C4C2×C22⋊D1111yescharacteristic
277Q16—82no—
278SD16—82no—
279M16—224no—
280C2×C8—22no—
281C2×C8—222no—
282C2×C8—222no—
283C2×C8—441no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—21no—
288C4⋊C4—21no—
289C4⋊C4—21no—
290C4⋊C4—41no—
291C4⋊C4—41no—
292C4⋊C4—221no—
293C4⋊C4—221no—
294C4⋊C4—221no—
295C4⋊C4—221no—
296C4⋊C4—441no—
297C4⋊C4—441no—
298C4⋊C4—441no—
299C4⋊C4—441no—
300C22⋊C4—41no—
301C22⋊C4—41no—
302C22⋊C4—41no—
303C42—41no—
304C42D4×D1111yescharacteristic
305C42D4×D1111yescharacteristic
306C42C2×C22⋊D1111yescharacteristic
307C42C2×C22⋊D1111yescharacteristic
308C11#1012611yescharacteristic, complemented, Sylow
309C23—41no—
310C23#6699111yescharacteristic
311Q8—41no—
312Q8—41no—
313Q8—42no—
314Q8—42no—
315D4—42no—
316D4—42no—
317D4—42no—
318D4—82no—
319C2×C4—22no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—82no—
326C2×C4—442no—
327C2×C4—441no—
328C2×C4—441no—
329C2×C4—881no—
330C2×C4#6699011yescharacteristic
331C2×C4#6699011yescharacteristic
332C2×C4#6699211yescharacteristic
333C2×C4#6699211yescharacteristic
334C2×C4#6699311yescharacteristic
335C2×C4#6700611yescharacteristic
336C8—42no—
337C8—224no—
338C8—442no—
339C8—881no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—81no—
344C22—81no—
345C22—81no—
346C22#1062283611yescharacteristic
347C4—21no—
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—81no—
353C4—81no—
354C4—81no—
355C4—881no—
356C4—881no—
357C4#1062281812yes—
358C2—41no—
359C2—161no—
360C2#1306964911yescharacteristic
361C2#1306966911yescharacteristic
362C2#1306971911yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3216C2
socleC22×C11#392
prime radicalC11×#532C22
hypercenter#3216D11
hypocenterC11#10126
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3216

Complements

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

NH ≅ G/Ntype
2. #13079169C2semidirect
3. #13067089C2semidirect
5. #13066973C2semidirect
6. #13066489C2semidirect
308. C11#10126semidirect

Maximal subgroups

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

subgroupindex
#130798022
#130791692
#130670892
#130670332
#130669732
#130664892
C11×#32162
#1012611