Finite Group Databasebeta

← #14909272

Subgroups — #14909272

Order 2816.

482 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079129C211yesmaximal, characteristic
2#13079127C211yesmaximal, characteristic
3#13070903C211yesmaximal, characteristic, complemented
4#13070902C211yesmaximal, characteristic, complemented
5#13070901C212yesmaximal, complemented
6#13070900C212yesmaximal, complemented
7#13070899C211yesmaximal, characteristic, complemented
8#13070399C212yesmaximal
9#13070397C212yesmaximal
10D11×#346C211yesmaximal, characteristic
11C11×#2255C211yesmaximal, characteristic, complemented
12#10623259—21no—
13#10623219—21no—
14C11×#500C2211yescharacteristic
15C11×#499C2211yescharacteristic
16#10622692—21no—
17#10622677—21no—
18C2×C16×D11C2212yes—
19#10622493—21no—
20#10622493C2211yescharacteristic
21#10622493C2212yes—
22#10622493C2211yescharacteristic
23#10622491—21no—
24#10622491C2212yes—
25#10622487C2211yescharacteristic
26#10622487C2211yescharacteristic
27#10622473—21no—
28#10622468—21no—
29C4×C8×D11C2211yescharacteristic
30#10622296C2211yescharacteristic
31#10622295C2211yescharacteristic
32C11×#367C2212yes—
33C11×#366C2212yes—
34C11×#346C2211yescharacteristic
35#10622143C2212yes—
36#10622142C2212yes—
37#10622140C2212yes—
38#10622128C2212yes—
39#10622128C2212yes—
40#10622127C2212yes—
41#10622127C2212yes—
42#10622099C2211yescharacteristic
43C11×C4⋊Q8—21no—
44C11×#125—21no—
45#66999—41no—
46Q8×Dic11—41no—
47C2×C8×D11D411yescharacteristic
48C2×C8×D11C2311yescharacteristic
49#66950—41no—
50#66949—41no—
51#66949—41no—
52#66945—21no—
53#66945—21no—
54#66945—22no—
55#66943—22no—
56#66941—21no—
57#66941—21no—
58#66940—41no—
59#66940—41no—
60#66940—41no—
61C42×D11D411yescharacteristic
62#66923—21no—
63#66922—21no—
64C2×C11×C16C2312yes—
65C11×#107—21no—
66C11×#107C2311yescharacteristic
67C11×#107C2311yescharacteristic
68C11×#107C2312yes—
69C11×#106—21no—
70C4×C8×C11C2311yescharacteristic
71#66882—21no—
72#66882C2311yescharacteristic
73#66882C2311yescharacteristic
74#66882C2312yes—
75#66881—21no—
76C8×Dic11D411yescharacteristic
77C8×Dic11C2311yescharacteristic
78C2×C11⋊C16C2312yes—
79#66872—21no—
80#66872—21no—
81#66872—22no—
82#66872—22no—
83#66871—21no—
84#66871—21no—
85C4×C11⋊C8D411yescharacteristic
86C16×D11Q818yescomplemented
87#33728—111nomaximal, Sylow
88C2×Q8×C11—41no—
89C2×C4×D11D811yescharacteristic
90C2×C4×D11D811yescharacteristic
91C2×C4×D11C2×D411yescharacteristic
92C2×Dic22—41no—
93C2×Dic22—41no—
94C2×Dic22—41no—
95C2×C8×C11C2×D411yescharacteristic
96C2×C8×C11C2411yescharacteristic
97C11×C4⋊C4—21no—
98C11×C4⋊C4—21no—
99C11×C4⋊C4—22no—
100C11×C4⋊C4—41no—
101C11×C4⋊C4—41no—
102C11×C4⋊C4—41no—
103C42×C11C2×D411yescharacteristic
104(C2×D11)⋊C4—41no—
105(C2×D11)⋊C4—41no—
106(C2×D11)⋊C4—42no—
107C4⋊Dic11—21no—
108C4⋊Dic11—21no—
109C4⋊Dic11—22no—
110C4⋊Dic11—42no—
111C4⋊Dic11—41no—
112Dic11⋊C4—41no—
113Dic11⋊C4—41no—
114Dic11⋊C4—42no—
115Dic11⋊C4—41no—
116Dic11⋊C4—41no—
117C4×Dic11—41no—
118C4×Dic11—41no—
119C4×Dic11—42no—
120C4×Dic11D811yescharacteristic
121C4×Dic11D811yescharacteristic
122C4×Dic11C2×D411yescharacteristic
123C2×C11⋊C8C2×D411yescharacteristic
124C2×C11⋊C8C2×D411yescharacteristic
125C8×D11Q1614yes—
126C8×D11C2×Q814yes—
127C11×C16C2×Q814yes—
128C11⋊C16C2×Q814yes—
129#3160—111no—
130#3160—111no—
131#2255—111no—
132#2255—111no—
133#2255—112no—
134#2255—112no—
135#2255—111no—
136#2255D1111yescharacteristic, complemented
137#2158—112no—
138#2158—112no—
139C2×#346—111no—
140C22×D11C2×D811yescharacteristic
141Q8×C11—82no—
142C2×C4×C11—42no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11C2×D811yescharacteristic
146C2×C4×C11C2×D811yescharacteristic
147C2×C4×C11C22×D411yescharacteristic
148C2×Dic11—41no—
149C2×Dic11—41no—
150C2×Dic11—42no—
151C2×Dic11C2×D811yescharacteristic
152C2×Dic11C2×D811yescharacteristic
153C2×Dic11C2×D811yescharacteristic
154C4×D11—41no—
155C4×D11—41no—
156C4×D11C4⋊Q812yes—
157C4×D11C2×Q1612yes—
158Dic22—82no—
159Dic22—82no—
160Dic22—82no—
161C8×C11C2×Q1612yes—
162C8×C11C22×Q812yes—
163C11⋊C8C4⋊Q812yes—
164C11⋊C8C2×Q1612yes—
165#533—221no—
166#533—221no—
167C22×C16—112no—
168#500—111no—
169#500—111no—
170#500—111no—
171#500C2×D1111yescharacteristic
172#499—112no—
173#499—111no—
174#499—221no—
175#499—221no—
176#499C2×D1111yescharacteristic
177#498—221no—
178#498—221no—
179#427—111no—
180#427—112no—
181#427—111no—
182#427—221no—
183#427—221no—
184C2×C4×C8—111no—
185#367—112no—
186#367—112no—
187#367—112no—
188#367C2×D1112yes—
189#366—112no—
190#366—112no—
191#366—112no—
192#366C2×D1112yes—
193#346—112no—
194#346—111no—
195#346C2×D1111yescharacteristic
196C22×C11C22×D811yescharacteristic
197C2×D11—21no—
198C2×D11—21no—
199C2×D11#50012yes—
200C4×C11—21no—
201C4×C11—21no—
202C4×C11—82no—
203C4×C11—81no—
204C4×C11—81no—
205C4×C11C2×C4⋊Q811yescharacteristic
206C4×C11C22×Q1611yescharacteristic
207Dic11—21no—
208Dic11—21no—
209Dic11—81no—
210Dic11—81no—
211Dic11—82no—
212Dic11#50012yes—
213C22×C8—111no—
214C22×C8—111no—
215C4⋊Q8—21no—
216C4⋊Q8—221no—
217C4⋊Q8—221no—
218C4⋊Q8—221no—
219#125—21no—
220#125—222no—
221#125—221no—
222C22⋊Q8—441no—
223C22⋊Q8—441no—
224C22⋊Q8—441no—
225C22⋊Q8—441no—
226C4×Q8—441no—
227C4×Q8—441no—
228C4×Q8—441no—
229C4×Q8—441no—
230#117—221no—
231#117—221no—
232#117—222no—
233C2×C42—111no—
234C2×C16—112no—
235C2×C16—118no—
236C2×C16C22×D1112yes—
237#107—21no—
238#107—111no—
239#107—111no—
240#107—112no—
241#107—221no—
242#107—221no—
243#107—221no—
244#107C22×D1111yescharacteristic
245#107C22×D1112yes—
246#107C22×D1111yescharacteristic
247#106—21no—
248#106—221no—
249#106—221no—
250#106—222no—
251#106—222no—
252#106—221no—
253C4×C8—111no—
254C4×C8—111no—
255C4×C8—111no—
256C4×C8C22×D1111yescharacteristic
257C2×C11C2×#50011yescharacteristic
258C2×C11#341411yescharacteristic
259C2×C11#341411yescharacteristic
260D11—22no—
261C2×Q8—41no—
262C2×Q8—441no—
263C2×Q8—441no—
264C2×Q8—441no—
265C22×C4—111no—
266C22×C4—111no—
267C22×C4—111no—
268C2×C8—111no—
269C2×C8—111no—
270C2×C8—114no—
271C2×C8—114no—
272C2×C8D4×D1111yescharacteristic
273C2×C8C23×D1111yescharacteristic
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—22no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—222no—
281C4⋊C4—221no—
282C4⋊C4—221no—
283C4⋊C4—442no—
284C4⋊C4—442no—
285C4⋊C4—441no—
286C4⋊C4—441no—
287C4⋊C4—441no—
288C4⋊C4—441no—
289C4⋊C4—441no—
290C22⋊C4—441no—
291C22⋊C4—441no—
292C22⋊C4—442no—
293C42—111no—
294C42—111no—
295C42—111no—
296C42—441no—
297C42—441no—
298C42—442no—
299C42D4×D1111yescharacteristic
300C16—114no—
301C16Q8×D1114yes—
302C11#3372811yescharacteristic, complemented, Sylow
303C23—111no—
304Q8—82no—
305Q8—882no—
306Q8—882no—
307Q8—882no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—42no—
311C2×C4—111no—
312C2×C4—112no—
313C2×C4—112no—
314C2×C4—111no—
315C2×C4—111no—
316C2×C4—441no—
317C2×C4—441no—
318C2×C4—441no—
319C2×C4—442no—
320C2×C4—441no—
321C2×C4D8×D1111yescharacteristic
322C2×C4D8×D1111yescharacteristic
323C2×C4C2×D4×D1111yescharacteristic
324C8—112no—
325C8—112no—
326C8Q16×D1112yes—
327C8C2×Q8×D1112yes—
328C22—112no—
329C22—221no—
330C22—221no—
331C22C2×D8×D1111yescharacteristic
332C4—21no—
333C4—21no—
334C4—82no—
335C4—81no—
336C4—81no—
337C4—112no—
338C4—221no—
339C4—221no—
340C4—881no—
341C4—882no—
342C4—881no—
343C4D11×C4⋊Q811yescharacteristic
344C4C2×Q16×D1111yescharacteristic
345C2—222no—
346C2D11×#50011yescharacteristic
347C2#1308174811yescharacteristic
348C2#1308175111yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2255C2
socleC22×C11C22×D8
prime radicalC22×D11C2×D8
hypercenter#2255D11
hypocenterC11#33728
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2255

Complements

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

NH ≅ G/Ntype
3. #13070903C2semidirect
4. #13070902C2semidirect
5. #13070901C2semidirect
6. #13070900C2semidirect
7. #13070899C2semidirect
11. C11×#2255C2semidirect
86. C16×D11Q8semidirect
136. #2255D11semidirect
302. C11#33728semidirect

Maximal subgroups

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

subgroupindex
#130791292
#130791272
#130709032
#130709022
#130709012
#130709002
#130708992
#130703992
#130703972
D11×#3462
C11×#22552
#3372811