Finite Group Databasebeta

← #14739106

Subgroups — #14739106

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#13079760C211yesmaximal, characteristic
2#13078423C211yesmaximal, characteristic
3C2×#10622703C211yesmaximal, characteristic
4#13077696C211yesmaximal, characteristic
5#13068049C214yesmaximal, complemented
6#13067997C214yesmaximal, complemented
7#13067388C211yesmaximal, characteristic
8#13067271C211yesmaximal, characteristic
9C11×#1546C211yesmaximal, characteristic
10C2×C11×C4⋊Q8C2211yescharacteristic
11C22×#4326—21no—
12#10623001C2211yescharacteristic
13C2×C4×Dic22C2211yescharacteristic
14C11×#431C2211yescharacteristic
15C11×#423C2211yescharacteristic
16C2×#66899—21no—
17#10622734—21no—
18#10622733—21no—
19#10622707—22no—
20#10622706C2212yes—
21#10622703—22no—
22#10622703C2214yes—
23#10622692C2212yes—
24#10622584—22no—
25#10622538C2211yescharacteristic
26C2×C4⋊(C11⋊C8)C2211yescharacteristic
27#10622464C2212yes—
28#10622463C2212yes—
29#10622443C2214yes—
30#10622442—22no—
31#10622331—22no—
32C8×Dic22—22no—
33C11×#332C2214yes—
34#10622120C2212yes—
35#10622119C2212yes—
36#10622118C2214yes—
37C22×Q8×C11—21no—
38C22×Dic22D411yescharacteristic
39C2×C11×M16—21no—
40C11×C4⋊Q8—21no—
41C11×C4⋊Q8—21no—
42C11×C4⋊Q8—21no—
43C11×C4⋊Q8C2312yes—
44C2×C11×C4⋊C4—21no—
45C2×C11×C4⋊C4—21no—
46C2×C42×C11C2311yescharacteristic
47C2×#4326—24no—
48C2×#4326—44no—
49#66979—21no—
50C2×C4⋊Dic11D411yescharacteristic
51#66977—21no—
52#66977—21no—
53C2×Dic11⋊C4—21no—
54C2×C4×Dic11—21no—
55C22×C11⋊C8—21no—
56#66923—21no—
57#66922C2311yescharacteristic
58#66922C2311yescharacteristic
59C4×Dic22—21no—
60C4×Dic22—21no—
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#66882—22no—
73#66881—22no—
74#66880—22no—
75#66880—22no—
76Dic11⋊C8—24no—
77C8×Dic11—24no—
78#66874—24no—
79#66872—24no—
80C4⋊(C11⋊C8)—21no—
81C4⋊(C11⋊C8)D412yes—
82C4⋊(C11⋊C8)C2312yes—
83C4×C11⋊C8C2312yes—
84#19402—111nomaximal, Sylow
85C2×Q8×C11—22no—
86C2×Q8×C11—41no—
87C2×Q8×C11—42no—
88C2×Q8×C11—42no—
89C22×C4×C11—41no—
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11#4111yescharacteristic
93C22×Dic11—21no—
94C22×Dic11—21no—
95C2×Dic22—21no—
96C2×Dic22—22no—
97C2×Dic22—21no—
98C2×Dic22—21no—
99C2×Dic22SD1614yes—
100C2×Dic22C2×D412yes—
101C11×M16—42no—
102C2×C8×C11—22no—
103C2×C8×C11—22no—
104C11×C4⋊C4—22no—
105C11×C4⋊C4—22no—
106C11×C4⋊C4—41no—
107C11×C4⋊C4—41no—
108C42×C11C2×D411yescharacteristic
109C42×C11C2×D411yescharacteristic
110C42×C11#4111yescharacteristic
111C42×C11C2411yescharacteristic
112C22⋊Dic11—41no—
113#4326—48no—
114C4⋊Dic11—21no—
115C4⋊Dic11—21no—
116C4⋊Dic11—21no—
117C4⋊Dic11—21no—
118C4⋊Dic11—21no—
119C4⋊Dic11C2×D412yes—
120Dic11⋊C4—22no—
121Dic11⋊C4—22no—
122Dic11⋊C4—41no—
123Dic11⋊C4—41no—
124C4×Dic11—22no—
125C4×Dic11—22no—
126C4×Dic11—41no—
127C2×C11⋊C8—22no—
128C2×C11⋊C8—42no—
129C2×C11⋊C8C2×D414yes—
130#3229—111no—
131#3078—111no—
132C2×#462—111no—
133#2982—111no—
134#1680—114no—
135#1672—114no—
136#1570—111no—
137#1546D1111yescharacteristic
138#1542—111no—
139C23×C11#12111yescharacteristic
140Q8×C11—42no—
141Q8×C11—42no—
142Q8×C11—82no—
143C2×C4×C11—22no—
144C2×C4×C11—41no—
145C2×C4×C11—42no—
146C2×C4×C11—82no—
147C2×C4×C11#12111yescharacteristic
148C2×C4×C11#12111yescharacteristic
149C2×C4×C11#12111yescharacteristic
150C2×C4×C11C2×SD1612yes—
151C2×C4×C11#13512yes—
152C2×C4×C11C22×D411yescharacteristic
153C2×C4×C11C22×D411yescharacteristic
154C2×C4×C11C2×#4111yescharacteristic
155C2×Dic11—22no—
156C2×Dic11—24no—
157C2×Dic11—22no—
158C2×Dic11—41no—
159C2×Dic11—41no—
160C2×Dic11—81no—
161Dic22—22no—
162Dic22—24no—
163Dic22—42no—
164Dic22—81no—
165Dic22C2×SD1614yes—
166C8×C11—42no—
167C8×C11—42no—
168C11⋊C8—24no—
169C11⋊C8—42no—
170C22×Q16—221no—
171#533—111no—
172C2×C4⋊Q8C2×D1111yescharacteristic
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#423C2×D1111yescharacteristic
190C2×C4⋊C8—111no—
191#419—221no—
192C2×#103—221no—
193#334—114no—
194#333—112no—
195#332—112no—
196#332C2×D1114yes—
197C22×C11—21no—
198C22×C11—21no—
199C22×C11#46512yes—
200C22×C11C2×#12111yescharacteristic
201C4×C11—21no—
202C4×C11—21no—
203C4×C11—21no—
204C4×C11—82no—
205C4×C11#46512yes—
206C4×C11C22×SD1611yescharacteristic
207C4×C11C2×#13511yescharacteristic
208C4×C11#57812yes—
209Dic11—24no—
210Dic11—42no—
211Dic11—81no—
212Dic11—81no—
213C22×Q8—21no—
214C22×Q8—111no—
215C2×Q16—224no—
216C2×Q16—444no—
217C2×M16—21no—
218C22×C8—221no—
219C4⋊Q8—21no—
220C4⋊Q8—21no—
221C4⋊Q8—21no—
222C4⋊Q8—111no—
223C4⋊Q8—111no—
224C4⋊Q8C22×D1112yes—
225#125—221no—
226C22⋊Q8—221no—
227C22⋊Q8—221no—
228C4×Q8—112no—
229C4×Q8—112no—
230C4×Q8—221no—
231C4×Q8—221no—
232C4×Q8—221no—
233C4×Q8—221no—
234#117—221no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—111no—
238C2×C4⋊C4—221no—
239C2×C42—221no—
240C2×C42C22×D1111yescharacteristic
241#107—222no—
242#106—224no—
243#106—222no—
244C4⋊C8—21no—
245C4⋊C8—112no—
246C4⋊C8—112no—
247C4⋊C8—224no—
248C4⋊C8—221no—
249C4⋊C8C22×D1112yes—
250C4⋊C8C22×D1112yes—
251#103—224no—
252#103—224no—
253#103—222no—
254#103—222no—
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—22no—
265C2×Q8—41no—
266C2×Q8—42no—
267C2×Q8—42no—
268C2×Q8—114no—
269C2×Q8—112no—
270C2×Q8—221no—
271C2×Q8—222no—
272C2×Q8—221no—
273C2×Q8—221no—
274C22×C4—41no—
275C22×C4—221no—
276C22×C4—221no—
277C22×C4#433911yescharacteristic
278C22×C4D4×D1111yescharacteristic
279C22×C4D4×D1111yescharacteristic
280Q16—448no—
281M16—42no—
282C2×C8—22no—
283C2×C8—22no—
284C2×C8—114no—
285C2×C8—222no—
286C2×C8—442no—
287C4⋊C4—22no—
288C4⋊C4—22no—
289C4⋊C4—41no—
290C4⋊C4—41no—
291C4⋊C4—112no—
292C4⋊C4—221no—
293C4⋊C4—222no—
294C4⋊C4—222no—
295C4⋊C4—221no—
296C4⋊C4—221no—
297C4⋊C4—221no—
298C4⋊C4—221no—
299C4⋊C4—441no—
300C4⋊C4—441no—
301C22⋊C4—441no—
302C42—222no—
303C42—222no—
304C42—441no—
305C42#433911yescharacteristic
306C42D4×D1111yescharacteristic
307C42D4×D1111yescharacteristic
308C42C23×D1111yescharacteristic
309C11#1940211yescharacteristic, complemented, Sylow
310C23#6693711yescharacteristic
311Q8—42no—
312Q8—42no—
313Q8—82no—
314Q8—114no—
315Q8—222no—
316Q8—224no—
317Q8—442no—
318Q8—881no—
319C2×C4—22no—
320C2×C4—41no—
321C2×C4—42no—
322C2×C4—82no—
323C2×C4—222no—
324C2×C4—224no—
325C2×C4—222no—
326C2×C4—441no—
327C2×C4—441no—
328C2×C4—881no—
329C2×C4#6693711yescharacteristic
330C2×C4#6693711yescharacteristic
331C2×C4#6693711yescharacteristic
332C2×C4#6696512yes—
333C2×C4SD16×D1112yes—
334C2×C4C2×#433911yescharacteristic
335C2×C4C2×D4×D1111yescharacteristic
336C2×C4C2×D4×D1111yescharacteristic
337C8—42no—
338C8—42no—
339C8—224no—
340C8—442no—
341C22—21no—
342C22—21no—
343C22#1062239112yes—
344C22C2×#6693711yescharacteristic
345C4—21no—
346C4—21no—
347C4—21no—
348C4—82no—
349C4—224no—
350C4—442no—
351C4—881no—
352C4—881no—
353C4#1062239112yes—
354C4C2×#6696511yescharacteristic
355C4C2×SD16×D1111yescharacteristic
356C4#1062331012yes—
357C2—22no—
358C2#1307814511yescharacteristic
359C2C2×#1062239111yescharacteristic
360C2#1307835211yescharacteristic
subgroupG/H
centerC22C2×#66937
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#1546C2
socleC22×C11C2×#121
prime radicalC23×C11#121
hypercenter#1546D11
hypocenterC11#19402
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
5. #13068049C2semidirect
6. #13067997C2semidirect
309. C11#19402semidirect

Maximal subgroups

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

subgroupindex
#130797602
#130784232
C2×#106227032
#130776962
#130680492
#130679972
#130673882
#130672712
C11×#15462
#1940211