Finite Group Databasebeta

← #14739110

Subgroups — #14739110

Order 2816.

622 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079757C211yesmaximal, characteristic
2#13078417C211yesmaximal, characteristic
3C2×#10622462C211yesmaximal, characteristic
4#13077696C211yesmaximal, characteristic
5#13068045C214yesmaximal, complemented
6#13068001C214yesmaximal, complemented
7#13067386C211yesmaximal, characteristic
8#13067287C211yesmaximal, characteristic
9C11×#1542C211yesmaximal, characteristic
10C11×#533C2211yescharacteristic
11C22×Dic44—21no—
12C2×#66922C2211yescharacteristic
13C2×C4×Dic22C2211yescharacteristic
14C11×#431C2211yescharacteristic
15C2×C11×C4⋊C8C2211yescharacteristic
16C2×#66880—21no—
17#10622707C2212yes—
18#10622704C2212yes—
19#10622694C2212yes—
20#10622692C2212yes—
21#10622676—22no—
22#10622656—22no—
23#10622633—22no—
24#10622617—21no—
25#10622608—21no—
26#10622538C2211yescharacteristic
27#10622537C2211yescharacteristic
28#10622462—22no—
29#10622462C2214yes—
30#10622443C2214yes—
31#10622331—22no—
32C8×Dic22—22no—
33C11×#333C2212yes—
34C11×#332C2212yes—
35#10622124C2214yes—
36#10622118C2214yes—
37C22×Dic22—21no—
38C22×Dic22D411yescharacteristic
39C22×C8×C11—21no—
40C11×C4⋊Q8C2311yescharacteristic
41C11×C4⋊Q8C2311yescharacteristic
42C11×#125—21no—
43C11×C22⋊Q8—21no—
44C11×C22⋊Q8—21no—
45C4×Q8×C11—21no—
46C4×Q8×C11—21no—
47C11×#117—21no—
48C2×C42×C11C2311yescharacteristic
49C2×C4⋊Dic11—21no—
50C2×C4⋊Dic11—21no—
51C2×C4⋊Dic11D411yescharacteristic
52C2×Dic11⋊C4—21no—
53C2×C4×Dic11—21no—
54C2×#4318—21no—
55C2×Dic44—24no—
56C2×Dic44—44no—
57#66922—21no—
58#66922—21no—
59#66922—21no—
60#66922C2312yes—
61C4×Dic22—21no—
62C4×Dic22—21no—
63C4×Dic22D412yes—
64C4×Dic22C2312yes—
65C11×C4⋊C8—21no—
66C11×C4⋊C8C2312yes—
67C11×C4⋊C8C2312yes—
68C11×C22⋊C8—21no—
69C4×C8×C11—21no—
70#66899—24no—
71C22⋊(C11⋊C8)D412yes—
72#66880—24no—
73Dic11⋊C8—24no—
74C8×Dic11—24no—
75#66874—22no—
76#66874—22no—
77#66872—22no—
78#66872—24no—
79#66871—22no—
80C4⋊(C11⋊C8)—21no—
81C4⋊(C11⋊C8)D412yes—
82C4⋊(C11⋊C8)C2312yes—
83C4×C11⋊C8C2312yes—
84#19402—111nomaximal, Sylow
85C2×Q8×C11—21no—
86C2×Q8×C11—21no—
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11#4111yescharacteristic
90C22×Dic11—21no—
91C22×Dic11—21no—
92C22×Dic11—41no—
93C2×Dic22—21no—
94C2×Dic22—22no—
95C2×Dic22—22no—
96C2×Dic22—41no—
97C2×Dic22—42no—
98C2×Dic22—42no—
99C2×Dic22SD1614yes—
100C2×Dic22C2×D412yes—
101C2×C8×C11—22no—
102C2×C8×C11—22no—
103C2×C8×C11—42no—
104C11×C4⋊C4—21no—
105C11×C4⋊C4—21no—
106C11×C4⋊C4—21no—
107C11×C4⋊C4—21no—
108C11×C4⋊C4—41no—
109C11×C4⋊C4—41no—
110C11×C22⋊C4—41no—
111C42×C11—41no—
112C42×C11C2×D411yescharacteristic
113C42×C11C2×D411yescharacteristic
114C42×C11#4111yescharacteristic
115C42×C11C2411yescharacteristic
116C4⋊Dic11—21no—
117C4⋊Dic11—22no—
118C4⋊Dic11—22no—
119C4⋊Dic11—41no—
120C4⋊Dic11—41no—
121C4⋊Dic11C2×D412yes—
122Dic11⋊C4—22no—
123Dic11⋊C4—22no—
124C4×Dic11—22no—
125C4×Dic11—22no—
126#4318—42no—
127C2×C11⋊C8—22no—
128C2×C11⋊C8C2×D414yes—
129Dic44—48no—
130#3229—111no—
131#3078—111no—
132C2×#462—111no—
133#2982—111no—
134#1680—114no—
135#1672—114no—
136#1570—111no—
137#1546—111no—
138#1542D1111yescharacteristic
139C23×C11#12111yescharacteristic
140Q8×C11—42no—
141Q8×C11—81no—
142C2×C4×C11—22no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11#12111yescharacteristic
147C2×C4×C11#12111yescharacteristic
148C2×C4×C11#12111yescharacteristic
149C2×C4×C11C2×SD1612yes—
150C2×C4×C11#13512yes—
151C2×C4×C11C22×D411yescharacteristic
152C2×C4×C11C22×D411yescharacteristic
153C2×C4×C11C2×#4111yescharacteristic
154C2×Dic11—22no—
155C2×Dic11—24no—
156C2×Dic11—22no—
157C2×Dic11—42no—
158C2×Dic11—81no—
159C2×Dic11—82no—
160Dic22—22no—
161Dic22—24no—
162Dic22—42no—
163Dic22—42no—
164Dic22—82no—
165Dic22C2×SD1614yes—
166C8×C11—42no—
167C8×C11—42no—
168C11⋊C8—24no—
169C11⋊C8—42no—
170C22×Q16—221no—
171#533C2×D1111yescharacteristic
172C2×C4⋊Q8—111no—
173C2×C4×Q8—111no—
174#498—112no—
175#487—112no—
176#483—222no—
177#479—222no—
178#477—112no—
179#475—112no—
180#475—222no—
181#462—114no—
182#462—222no—
183C8×Q8—114no—
184C8×Q8—222no—
185#431—111no—
186#431—222no—
187#431C2×D1111yescharacteristic
188#428—221no—
189#423—111no—
190C2×C4⋊C8C2×D1111yescharacteristic
191#419—221no—
192C2×#103—221no—
193#334—114no—
194#333C2×D1112yes—
195#332—114no—
196#332C2×D1112yes—
197C22×C11—21no—
198C22×C11—21no—
199C22×C11#46512yes—
200C22×C11C2×#12111yescharacteristic
201C4×C11—21no—
202C4×C11—21no—
203C4×C11—21no—
204C4×C11—81no—
205C4×C11—81no—
206C4×C11#46512yes—
207C4×C11C22×SD1611yescharacteristic
208C4×C11C2×#13511yescharacteristic
209C4×C11#57812yes—
210Dic11—24no—
211Dic11—42no—
212Dic11—82no—
213C22×Q8—111no—
214C22×Q8—221no—
215C2×Q16—224no—
216C2×Q16—444no—
217C2×M16—221no—
218C22×C8—21no—
219C4⋊Q8—112no—
220C4⋊Q8—221no—
221C4⋊Q8—221no—
222C4⋊Q8—221no—
223C4⋊Q8C22×D1111yescharacteristic
224C4⋊Q8C22×D1111yescharacteristic
225#125—21no—
226C22⋊Q8—21no—
227C22⋊Q8—21no—
228C4×Q8—21no—
229C4×Q8—21no—
230C4×Q8—112no—
231C4×Q8—112no—
232C4×Q8—221no—
233C4×Q8—221no—
234#117—21no—
235C2×C4⋊C4—111no—
236C2×C4⋊C4—221no—
237C2×C4⋊C4—221no—
238C2×C4⋊C4—221no—
239C2×C42—221no—
240C2×C42C22×D1111yescharacteristic
241#107—222no—
242#106—222no—
243#106—224no—
244C4⋊C8—21no—
245C4⋊C8—112no—
246C4⋊C8—112no—
247C4⋊C8—224no—
248C4⋊C8—221no—
249C4⋊C8C22×D1112yes—
250C4⋊C8C22×D1112yes—
251#103—222no—
252#103—222no—
253#103—224no—
254#103—224no—
255C22⋊C8—21no—
256C22⋊C8—112no—
257C4×C8—21no—
258C4×C8—112no—
259C4×C8—224no—
260C2×C11—22no—
261C2×C11#304411yescharacteristic
262C2×C11C2×#46511yescharacteristic
263C2×C11#306911yescharacteristic
264C2×Q8—21no—
265C2×Q8—21no—
266C2×Q8—114no—
267C2×Q8—112no—
268C2×Q8—221no—
269C2×Q8—222no—
270C2×Q8—222no—
271C2×Q8—441no—
272C2×Q8—442no—
273C2×Q8—442no—
274C22×C4—221no—
275C22×C4—221no—
276C22×C4—441no—
277C22×C4#433911yescharacteristic
278C22×C4D4×D1111yescharacteristic
279C22×C4D4×D1111yescharacteristic
280Q16—448no—
281M16—442no—
282C2×C8—22no—
283C2×C8—22no—
284C2×C8—42no—
285C2×C8—114no—
286C2×C8—222no—
287C4⋊C4—21no—
288C4⋊C4—21no—
289C4⋊C4—21no—
290C4⋊C4—21no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C4⋊C4—112no—
294C4⋊C4—221no—
295C4⋊C4—222no—
296C4⋊C4—222no—
297C4⋊C4—222no—
298C4⋊C4—222no—
299C4⋊C4—441no—
300C4⋊C4—441no—
301C22⋊C4—41no—
302C42—41no—
303C42—222no—
304C42—222no—
305C42#433911yescharacteristic
306C42D4×D1111yescharacteristic
307C42D4×D1111yescharacteristic
308C42C23×D1111yescharacteristic
309C11#1940211yescharacteristic, complemented, Sylow
310C23#6693711yescharacteristic
311Q8—42no—
312Q8—81no—
313Q8—114no—
314Q8—222no—
315Q8—224no—
316Q8—442no—
317Q8—442no—
318Q8—882no—
319C2×C4—22no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—222no—
324C2×C4—224no—
325C2×C4—222no—
326C2×C4—442no—
327C2×C4—881no—
328C2×C4—882no—
329C2×C4#6693711yescharacteristic
330C2×C4#6693711yescharacteristic
331C2×C4#6693711yescharacteristic
332C2×C4SD16×D1112yes—
333C2×C4#6697212yes—
334C2×C4C2×#433911yescharacteristic
335C2×C4C2×D4×D1111yescharacteristic
336C2×C4C2×D4×D1111yescharacteristic
337C8—42no—
338C8—42no—
339C8—224no—
340C8—442no—
341C22—21no—
342C22—21no—
343C22#1062242012yes—
344C22C2×#6693711yescharacteristic
345C4—21no—
346C4—21no—
347C4—21no—
348C4—81no—
349C4—81no—
350C4—224no—
351C4—442no—
352C4—882no—
353C4#1062242012yes—
354C4C2×SD16×D1111yescharacteristic
355C4C2×#6697211yescharacteristic
356C4#1062330212yes—
357C2—22no—
358C2#1307814911yescharacteristic
359C2C2×#1062242011yescharacteristic
360C2#1307835611yescharacteristic
subgroupG/H
centerC22C2×#66937
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#1542C2
socleC22×C11C2×#121
prime radicalC23×C11#121
hypercenter#1542D11
hypocenterC11#19402
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1542

Complements

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

NH ≅ G/Ntype
5. #13068045C2semidirect
6. #13068001C2semidirect
309. C11#19402semidirect

Maximal subgroups

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

subgroupindex
#130797572
#130784172
C2×#106224622
#130776962
#130680452
#130680012
#130673862
#130672872
C11×#15422
#1940211