Finite Group Databasebeta

← #14726838

Subgroups — #14726838

Order 2816.

974 conjugacy classes of subgroups; only the 203 normal subgroups are shown.

normal subgroups only

This group has 974 conjugacy classes of subgroups — too many to draw. Only its 203 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#13078651C212yesmaximal, complemented
2#13073970C211yesmaximal, characteristic
3#13067641C214yesmaximal, complemented
4#13067573C214yesmaximal, complemented
5#13067180C212yesmaximal, complemented
6#13066937C211yesmaximal, characteristic
7C11×#3501C211yesmaximal, characteristic
8C11×#554—22no—
9C11×#554—24no—
10D4×Q8×C11—22no—
11C11×#544—21no—
12C11×#543C2214yes—
13C11×#533C2212yes—
14C2×C11×C22⋊Q8—22no—
15C11×#518—21no—
16C2×C4×D4×C11C2211yescharacteristic
17C2×C4×Dic22C2211yescharacteristic
18#10622834—21no—
19#10622823—22no—
20#10622704—22no—
21#10622703—22no—
22#10622663C2214yes—
23#10622657C2214yes—
24C4×#4326—24no—
25#10622586—21no—
26#10622562C2212yes—
27#10622560C2212yes—
28#10622549C2211yescharacteristic
29#10622538C2212yes—
30#10622176C2218yes—
31#10622163C2214yes—
32C22×Q8×C11—22no—
33C22×D4×C11D411yescharacteristic
34C23×C4×C11D412yes—
35C22×Dic22C2311yescharacteristic
36C11×C4⋊Q8—24no—
37C11×C4⋊Q8D412yes—
38C11×C4⋊Q8D412yes—
39C11×#125—24no—
40C11×#125—22no—
41C11×C22⋊Q8—24no—
42C11×C22⋊Q8—24no—
43C11×C22⋊Q8—28no—
44C11×C22⋊Q8—22no—
45C11×C22⋊Q8—24no—
46C11×C22⋊Q8—28no—
47C11×C22⋊Q8C2314yes—
48C4×Q8×C11—22no—
49C4×Q8×C11D414yes—
50C4×D4×C11—24no—
51C4×D4×C11—24no—
52C4×D4×C11—22no—
53C4×D4×C11—22no—
54C11×#117—22no—
55C2×C11×C4⋊C4—22no—
56C2×C11×C4⋊C4—24no—
57C2×C11×C4⋊C4D411yescharacteristic
58C2×C11×C22⋊C4—24no—
59C2×C11×C22⋊C4C2312yes—
60C2×C42×C11C2311yescharacteristic
61C2×C22⋊Dic11—22no—
62C2×C22⋊Dic11—22no—
63C2×#4326—24no—
64C2×C4⋊Dic11—21no—
65C2×C4⋊Dic11C2311yescharacteristic
66C2×Dic11⋊C4—21no—
67C2×Dic11⋊C4—22no—
68C2×C4×Dic11—21no—
69C4×Dic22—22no—
70C4×Dic22—22no—
71#66899—24no—
72C11⋊#95—21no—
73C11⋊#95—22no—
74C11⋊#95C2312yes—
75C22⋊(C11⋊C8)C2314yes—
76#66874—24no—
77#66871—24no—
78C4⋊(C11⋊C8)—22no—
79C4×C11⋊C8—22no—
80#18213—111nomaximal, Sylow
81C24×C11C2×D412yes—
82C2×Q8×C11—24no—
83C2×Q8×C11—22no—
84C2×Q8×C11—84no—
85C2×Q8×C11C2×D414yes—
86C2×D4×C11—22no—
87C2×D4×C11—22no—
88C2×D4×C11Q1614yescomplemented
89C22×C4×C11—24no—
90C22×C4×C11—24no—
91C22×C4×C11—22no—
92C22×C4×C11—22no—
93C22×C4×C11—82no—
94C22×C4×C11C2×D412yes—
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2411yescharacteristic
98C22×Dic11—21no—
99C22×Dic11—22no—
100C22×Dic11—21no—
101C2×Dic22—22no—
102C2×Dic22—42no—
103C11×C4⋊C4—24no—
104C11×C4⋊C4—28no—
105C11×C4⋊C4—22no—
106C11×C4⋊C4—24no—
107C11×C4⋊C4—22no—
108C11×C4⋊C4—22no—
109C11×C4⋊C4—22no—
110C11×C4⋊C4—24no—
111C11×C4⋊C4C2×D414yes—
112C11×C22⋊C4—28no—
113C11×C22⋊C4—24no—
114C11×C22⋊C4—24no—
115C42×C11—24no—
116C42×C11C2×D412yes—
117C42×C11C2×D412yes—
118C22⋊Dic11—44no—
119C22⋊Dic11—82no—
120#4326—48no—
121C4⋊Dic11—22no—
122C4⋊Dic11—42no—
123Dic11⋊C4—41no—
124Dic11⋊C4—41no—
125Dic11⋊C4—82no—
126C4×Dic11—42no—
127C2×C11⋊C8—24no—
128#3501D1111yescharacteristic
129#3104—112no—
130#2580—111no—
131#1614—114no—
132#1602—114no—
133#1518—112no—
134#1460—111no—
135C23×C11—22no—
136C23×C11—22no—
137C23×C11—42no—
138C23×C11—42no—
139C23×C11C2×Q1614yes—
140C23×C11C22×D411yescharacteristic
141Q8×C11—44no—
142Q8×C11—44no—
143Q8×C11—84no—
144D4×C11—28no—
145C2×C4×C11—24no—
146C2×C4×C11—24no—
147C2×C4×C11—22no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—44no—
151C2×C4×C11—42no—
152C2×C4×C11—82no—
153C2×C4×C11—84no—
154C2×C4×C11—84no—
155C2×C4×C11#12011yescharacteristic
156C2×C4×C11#12011yescharacteristic
157C2×C4×C11#12012yes—
158C2×C4×C11C2×Q1612yes—
159C2×C4×C11#13712yes—
160C2×C4×C11C22×D412yes—
161C2×Dic11—22no—
162C2×Dic11—41no—
163C2×Dic11—41no—
164C2×Dic11—41no—
165C2×Dic11—42no—
166C2×Dic11—42no—
167C2×Dic11—41no—
168C2×Dic11—41no—
169C2×Dic11—42no—
170Dic22—24no—
171Dic22—42no—
172C11⋊C8—44no—
173#554—22no—
174#554—24no—
175D4×Q8—22no—
176#544—21no—
177#543C2×D1114yes—
178#533C2×D1112yes—
179C2×C22⋊Q8—22no—
180#518—21no—
181C2×C4×Q8—111no—
182C2×C4×D4C2×D1111yescharacteristic
183#484—114no—
184#477—222no—
185#462—222no—
186#451—114no—
187C4×Q16—224no—
188#431—112no—
189#399—112no—
190#393—112no—
191#390—221no—
192#389—221no—
193#385—222no—
194#382—111no—
195#328—118no—
196#323—114no—
197C22×C11—21no—
198C22×C11—21no—
199C22×C11—24no—
200C22×C11—44no—
201C22×C11—42no—
202C22×C11—42no—
203C22×C11—82no—
204C22×C11C2×#12011yescharacteristic
205C22×C11C22×Q1611yescharacteristic
206C22×C11C2×#13711yescharacteristic
207C4×C11—21no—
208C4×C11—21no—
209C4×C11—22no—
210C4×C11—42no—
211C4×C11—44no—
212C4×C11—44no—
213C4×C11#45114yes—
214Dic11—42no—
215Dic11—82no—
216Dic11—81no—
217C22×Q8—22no—
218C22×Q8—111no—
219C22×D4C22⋊D1111yescharacteristic
220C23×C4C22⋊D1112yes—
221C2×Q16—224no—
222C4⋊Q8—24no—
223C4⋊Q8C22⋊D1112yes—
224C4⋊Q8C22⋊D1112yes—
225#125—24no—
226#125—22no—
227C22⋊Q8—24no—
228C22⋊Q8—24no—
229C22⋊Q8—28no—
230C22⋊Q8—22no—
231C22⋊Q8—24no—
232C22⋊Q8—28no—
233C22⋊Q8C22×D1114yes—
234C4×Q8—22no—
235C4×Q8—222no—
236C4×Q8—222no—
237C4×Q8C22⋊D1114yes—
238C4×D4—24no—
239C4×D4—24no—
240C4×D4—22no—
241C4×D4—22no—
242#117—22no—
243C2×C4⋊C4—22no—
244C2×C4⋊C4—24no—
245C2×C4⋊C4—111no—
246C2×C4⋊C4—221no—
247C2×C4⋊C4—221no—
248C2×C4⋊C4—222no—
249C2×C4⋊C4C22⋊D1111yescharacteristic
250C2×C22⋊C4—24no—
251C2×C22⋊C4—222no—
252C2×C22⋊C4—222no—
253C2×C22⋊C4C22×D1112yes—
254C2×C42—221no—
255C2×C42C22×D1111yescharacteristic
256#107—224no—
257C4⋊C8—222no—
258#103—224no—
259#103—224no—
260C22⋊C8—114no—
261C4×C8—222no—
262#95—112no—
263#95—221no—
264#95—222no—
265C2×C11—21no—
266C2×C11—21no—
267C2×C11—44no—
268C2×C11C2×#45111yescharacteristic
269C2×C11#301911yescharacteristic
270C2×C11#302511yescharacteristic
271C24C2×C22⋊D1112yes—
272C2×Q8—24no—
273C2×Q8—22no—
274C2×Q8—84no—
275C2×Q8—222no—
276C2×Q8—442no—
277C2×Q8C2×C22⋊D1114yes—
278C2×D4—22no—
279C2×D4—22no—
280C2×D4#432614yescomplemented
281C22×C4—24no—
282C22×C4—24no—
283C22×C4—22no—
284C22×C4—22no—
285C22×C4—82no—
286C22×C4—221no—
287C22×C4—222no—
288C22×C4—221no—
289C22×C4C2×C22⋊D1112yes—
290C22×C4C2×C22⋊D1111yescharacteristic
291C22×C4C2×C22⋊D1111yescharacteristic
292C22×C4C23×D1111yescharacteristic
293Q16—448no—
294C2×C8—224no—
295C4⋊C4—24no—
296C4⋊C4—28no—
297C4⋊C4—22no—
298C4⋊C4—24no—
299C4⋊C4—22no—
300C4⋊C4—22no—
301C4⋊C4—22no—
302C4⋊C4—24no—
303C4⋊C4—222no—
304C4⋊C4—442no—
305C4⋊C4—441no—
306C4⋊C4—441no—
307C4⋊C4—882no—
308C4⋊C4C2×C22⋊D1114yes—
309C22⋊C4—28no—
310C22⋊C4—24no—
311C22⋊C4—24no—
312C22⋊C4—444no—
313C22⋊C4—882no—
314C42—24no—
315C42—442no—
316C42C2×C22⋊D1112yes—
317C42C2×C22⋊D1112yes—
318C11#1821311yescharacteristic, complemented, Sylow
319C23—22no—
320C23—22no—
321C23—42no—
322C23—42no—
323C23C2×#432614yes—
324C23C22×C22⋊D1111yescharacteristic
325Q8—44no—
326Q8—44no—
327Q8—84no—
328Q8—224no—
329Q8—442no—
330D4—28no—
331C2×C4—24no—
332C2×C4—24no—
333C2×C4—22no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—44no—
337C2×C4—42no—
338C2×C4—82no—
339C2×C4—84no—
340C2×C4—84no—
341C2×C4—222no—
342C2×C4—441no—
343C2×C4—441no—
344C2×C4—442no—
345C2×C4—441no—
346C2×C4—442no—
347C2×C4—441no—
348C2×C4—442no—
349C2×C4—441no—
350C2×C4#6699512yes—
351C2×C4C2×#432612yes—
352C2×C4#6700611yescharacteristic
353C2×C4#6700611yescharacteristic
354C2×C4#6700612yes—
355C2×C4C22×C22⋊D1112yes—
356C8—444no—
357C22—21no—
358C22—21no—
359C22—24no—
360C22—44no—
361C22—42no—
362C22—42no—
363C22—82no—
364C22C2×#6699511yescharacteristic
365C22C22×#432611yescharacteristic
366C22C2×#6700611yescharacteristic
367C4—21no—
368C4—21no—
369C4—22no—
370C4—42no—
371C4—44no—
372C4—44no—
373C4—442no—
374C4—882no—
375C4—881no—
376C4#1062284114yes—
377C2—21no—
378C2—21no—
379C2—44no—
380C2C2×#1062284111yescharacteristic
381C2#1307797311yescharacteristic
382C2#1307800811yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#3501C2
socleC22×C11C2×#120
prime radicalC22×D4×C11D4
hypercenter#3501D11
hypocenterC11#18213
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3501

Complements

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

NH ≅ G/Ntype
1. #13078651C2semidirect
3. #13067641C2semidirect
4. #13067573C2semidirect
5. #13067180C2semidirect
88. C2×D4×C11Q16semidirect
280. C2×D4#4326semidirect
318. C11#18213semidirect

Maximal subgroups

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

subgroupindex
#130786512
#130739702
#130676412
#130675732
#130671802
#130669372
C11×#35012
#1821311