Finite Group Databasebeta

← #14739124

Subgroups — #14739124

Order 2816.

676 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079737C211yesmaximal, characteristic
2#13078090C211yesmaximal, characteristic
3C2×#10622703C211yesmaximal, characteristic, complemented
4#13077696C211yesmaximal, characteristic, complemented
5#13068063C214yesmaximal, complemented
6#13068009C214yesmaximal, complemented
7#13067392C211yesmaximal, characteristic, complemented
8#13067263C211yesmaximal, characteristic
9C11×#1546C211yesmaximal, characteristic, complemented
10C2×C11×C4⋊Q8C2211yescharacteristic
11C22×#4326—21no—
12C2×#66962—21no—
13#10623008C2211yescharacteristic
14C2×C4×Dic22C2211yescharacteristic
15C11×#431C2211yescharacteristic
16C11×#423C2211yescharacteristic
17C2×#66899—21no—
18#10622746—21no—
19#10622703—22no—
20#10622703C2214yes—
21#10622701C2212yes—
22#10622700—22no—
23#10622691C2212yes—
24#10622580—22no—
25#10622538C2211yescharacteristic
26C2×C4⋊(C11⋊C8)C2211yescharacteristic
27#10622462C2212yes—
28#10622461C2212yes—
29#10622458—22no—
30#10622443C2214yes—
31#10622331—22no—
32C8×Dic22—22no—
33C11×#332C2214yes—
34#10622124C2212yes—
35#10622123C2212yes—
36#10622117C2214yes—
37C22×Q8×C11—21no—
38C2×#4339—21no—
39C22×Dic22D411yescharacteristic
40C2×C11×M16—21no—
41C11×C4⋊Q8—21no—
42C11×C4⋊Q8—21no—
43C11×C4⋊Q8—21no—
44C11×C4⋊Q8C2312yes—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4—21no—
47C2×C42×C11C2311yescharacteristic
48C2×#4326—24no—
49C2×#4326—44no—
50#66983—21no—
51#66983—21no—
52C2×C4⋊Dic11D411yescharacteristic
53C2×Dic11⋊C4—21no—
54C2×C4×Dic11—21no—
55C22×C11⋊C8—21no—
56#66962—44no—
57C2×Dic44—22no—
58C2×#4314—22no—
59#66928—21no—
60#66927C2311yescharacteristic
61C4×D44—21no—
62C4×D44—21no—
63#66922C2311yescharacteristic
64C4×Dic22—21no—
65C4×Dic22—21no—
66C4×Dic22D412yes—
67C4×Dic22C2312yes—
68C11×C4⋊C8—21no—
69C11×C4⋊C8C2312yes—
70C11×C4⋊C8C2312yes—
71C11×C22⋊C8—21no—
72C4×C8×C11—21no—
73#66899—24no—
74C22⋊(C11⋊C8)D412yes—
75#66885—22no—
76#66880—22no—
77Dic11⋊C8—24no—
78C8×Dic11—24no—
79#66873—24no—
80#66871—24no—
81C4⋊(C11⋊C8)—21no—
82C4⋊(C11⋊C8)D412yes—
83C4⋊(C11⋊C8)C2312yes—
84C4×C11⋊C8C2312yes—
85#19404—111nomaximal, Sylow
86C2×Q8×C11—22no—
87C2×Q8×C11—41no—
88C2×Q8×C11—42no—
89C2×Q8×C11—42no—
90C22×C4×C11—41no—
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11#4111yescharacteristic
94C2×C22⋊D11—41no—
95C22×Dic11—21no—
96C22×Dic11—21no—
97#4339—42no—
98#4339—42no—
99C2×D44—21no—
100C2×D44—21no—
101C2×D44—21no—
102C2×C4×D11—41no—
103C2×Dic22—21no—
104C2×Dic22—22no—
105C2×Dic22—21no—
106C2×Dic22D814yes—
107C2×Dic22C2×D412yes—
108C11×M16—42no—
109C2×C8×C11—22no—
110C2×C8×C11—22no—
111C11×C4⋊C4—22no—
112C11×C4⋊C4—22no—
113C11×C4⋊C4—41no—
114C11×C4⋊C4—41no—
115C42×C11C2×D411yescharacteristic
116C42×C11C2×D411yescharacteristic
117C42×C11#4111yescharacteristic
118C42×C11C2411yescharacteristic
119#4326—48no—
120(C2×D11)⋊C4—41no—
121(C2×D11)⋊C4—41no—
122C4⋊Dic11—21no—
123C4⋊Dic11—21no—
124C4⋊Dic11—21no—
125C4⋊Dic11C2×D412yes—
126Dic11⋊C4—22no—
127Dic11⋊C4—22no—
128C4×Dic11—22no—
129C4×Dic11—22no—
130C2×C11⋊C8—22no—
131C2×C11⋊C8—42no—
132C2×C11⋊C8C2×D414yes—
133Dic44—44no—
134#4314—44no—
135#3226—111no—
136#3037—111no—
137C2×#462—111no—
138#2982—111no—
139#1682—114no—
140#1674—114no—
141#1571—111no—
142#1546D1111yescharacteristic, complemented
143#1540—111no—
144C23×C11#12111yescharacteristic
145C22×D11—41no—
146Q8×C11—42no—
147Q8×C11—42no—
148Q8×C11—82no—
149C2×C4×C11—22no—
150C2×C4×C11—41no—
151C2×C4×C11—42no—
152C2×C4×C11—82no—
153C2×C4×C11#12111yescharacteristic
154C2×C4×C11#12111yescharacteristic
155C2×C4×C11#12111yescharacteristic
156C2×C4×C11C2×D812yes—
157C2×C4×C11#13512yes—
158C2×C4×C11C22×D411yescharacteristic
159C2×C4×C11C22×D411yescharacteristic
160C2×C4×C11C2×#4111yescharacteristic
161C22⋊D11—82no—
162C2×Dic11—22no—
163C2×Dic11—24no—
164C2×Dic11—22no—
165C2×Dic11—41no—
166C2×Dic11—81no—
167D44—41no—
168D44—41no—
169D44—42no—
170D44—81no—
171C4×D11—82no—
172Dic22—22no—
173Dic22—24no—
174Dic22—41no—
175Dic22—41no—
176Dic22C2×D814yes—
177C8×C11—42no—
178C8×C11—42no—
179C11⋊C8—24no—
180C11⋊C8—42no—
181C2×#137—221no—
182C22×Q16—221no—
183#532—111no—
184C2×C4⋊Q8C2×D1111yescharacteristic
185C2×C4×Q8—111no—
186#500—112no—
187#486—112no—
188#480—222no—
189#474—222no—
190#464—222no—
191#462—114no—
192#462—112no—
193#462—222no—
194#460—112no—
195C8×Q8—114no—
196C8×Q8—222no—
197#431—111no—
198#431—222no—
199#431C2×D1111yescharacteristic
200#423C2×D1111yescharacteristic
201C2×C4⋊C8—111no—
202#417—221no—
203C2×#103—221no—
204#335—114no—
205#332—112no—
206#332C2×D1114yes—
207#331—112no—
208C22×C11—21no—
209C22×C11—21no—
210C22×C11#46612yes—
211C22×C11C2×#12111yescharacteristic
212C2×D11—81no—
213C2×D11—81no—
214C2×D11—81no—
215C4×C11—21no—
216C4×C11—21no—
217C4×C11—21no—
218C4×C11—82no—
219C4×C11#46612yes—
220C4×C11C22×D811yescharacteristic
221C4×C11C2×#13511yescharacteristic
222C4×C11#57812yes—
223Dic11—24no—
224Dic11—42no—
225Dic11—81no—
226C2×#41—221no—
227C22×Q8—21no—
228C22×Q8—111no—
229#137—444no—
230C2×Q16—222no—
231C2×Q16—224no—
232C2×Q16—444no—
233C2×SD16—222no—
234C2×M16—21no—
235C22×C8—221no—
236C4⋊Q8—21no—
237C4⋊Q8—21no—
238C4⋊Q8—21no—
239C4⋊Q8—111no—
240C4⋊Q8C22×D1112yes—
241#127—111no—
242#124—221no—
243#121—221no—
244#121—221no—
245C4×Q8—112no—
246C4×Q8—112no—
247C4×Q8—221no—
248C4×Q8—221no—
249C4×D4—221no—
250C4×D4—221no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—111no—
254C2×C4⋊C4—221no—
255C2×C42—221no—
256C2×C42C22×D1111yescharacteristic
257#107—224no—
258C4⋊C8—21no—
259C4⋊C8—112no—
260C4⋊C8—112no—
261C4⋊C8—224no—
262C4⋊C8—221no—
263C4⋊C8C22×D1112yes—
264C4⋊C8C22×D1112yes—
265#103—222no—
266#103—224no—
267#102—224no—
268#102—222no—
269C22⋊C8—21no—
270C22⋊C8—112no—
271C4×C8—21no—
272C4×C8—112no—
273C4×C8—224no—
274C2×C11—22no—
275C2×C11#304411yescharacteristic
276C2×C11C2×#46611yescharacteristic
277C2×C11#306911yescharacteristic
278D11—161no—
279#41—442no—
280#41—442no—
281C2×Q8—22no—
282C2×Q8—41no—
283C2×Q8—42no—
284C2×Q8—42no—
285C2×Q8—114no—
286C2×Q8—112no—
287C2×Q8—221no—
288C2×Q8—222no—
289C2×Q8—221no—
290C2×D4—221no—
291C2×D4—221no—
292C2×D4—221no—
293C2×D4—441no—
294C22×C4—41no—
295C22×C4—221no—
296C22×C4—221no—
297C22×C4—441no—
298C22×C4#433911yescharacteristic
299C22×C4D4×D1111yescharacteristic
300C22×C4D4×D1111yescharacteristic
301Q16—444no—
302Q16—448no—
303SD16—444no—
304M16—42no—
305C2×C8—22no—
306C2×C8—22no—
307C2×C8—114no—
308C2×C8—222no—
309C2×C8—442no—
310C4⋊C4—22no—
311C4⋊C4—22no—
312C4⋊C4—41no—
313C4⋊C4—41no—
314C4⋊C4—112no—
315C4⋊C4—221no—
316C4⋊C4—222no—
317C4⋊C4—222no—
318C4⋊C4—221no—
319C4⋊C4—221no—
320C22⋊C4—441no—
321C22⋊C4—441no—
322C42—222no—
323C42—222no—
324C42#433911yescharacteristic
325C42D4×D1111yescharacteristic
326C42D4×D1111yescharacteristic
327C42C23×D1111yescharacteristic
328C11#1940411yescharacteristic, complemented, Sylow
329C23—441no—
330C23#6693711yescharacteristic
331Q8—42no—
332Q8—42no—
333Q8—82no—
334Q8—114no—
335Q8—222no—
336Q8—224no—
337Q8—441no—
338Q8—441no—
339D4—441no—
340D4—441no—
341D4—442no—
342D4—881no—
343D4—882no—
344C2×C4—22no—
345C2×C4—41no—
346C2×C4—42no—
347C2×C4—82no—
348C2×C4—222no—
349C2×C4—224no—
350C2×C4—222no—
351C2×C4—441no—
352C2×C4—881no—
353C2×C4—882no—
354C2×C4#6693711yescharacteristic
355C2×C4#6693711yescharacteristic
356C2×C4#6693711yescharacteristic
357C2×C4D8×D1112yes—
358C2×C4#6696912yes—
359C2×C4C2×#433911yescharacteristic
360C2×C4C2×D4×D1111yescharacteristic
361C2×C4C2×D4×D1111yescharacteristic
362C8—42no—
363C8—42no—
364C8—224no—
365C8—442no—
366C22—21no—
367C22—21no—
368C22—881no—
369C22—881no—
370C22—881no—
371C22#1062238812yes—
372C22C2×#6693711yescharacteristic
373C4—21no—
374C4—21no—
375C4—21no—
376C4—82no—
377C4—224no—
378C4—442no—
379C4—881no—
380C4#1062238812yes—
381C4C2×D8×D1111yescharacteristic
382C4C2×#6696911yescharacteristic
383C4#1062331012yes—
384C2—22no—
385C2—1761no—
386C2#1307814511yescharacteristic
387C2C2×#1062238811yescharacteristic
388C2#1307835211yescharacteristic
subgroupG/H
centerC22C2×#66937
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#1546C2
socleC22×C11C2×#121
prime radical#10623008C22
hypercenter#1546D11
hypocenterC11#19404
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1546

Complements

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

NH ≅ G/Ntype
3. C2×#10622703C2semidirect
4. #13077696C2semidirect
5. #13068063C2semidirect
6. #13068009C2semidirect
7. #13067392C2semidirect
9. C11×#1546C2semidirect
142. #1546D11semidirect
328. C11#19404semidirect

Maximal subgroups

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

subgroupindex
#130797372
#130780902
C2×#106227032
#130776962
#130680632
#130680092
#130673922
#130672632
C11×#15462
#1940411