Finite Group Databasebeta

← #11860979

Subgroups — #11860979

Order 1152.

778 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 778 conjugacy classes of subgroups — too many to draw. Only its 151 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
1C2×#64237C211yesmaximal, characteristic
2#10594051C212yesmaximal, complemented
3#10593738C211yesmaximal, characteristic, complemented
4C2×#63742C211yesmaximal, characteristic, complemented
5#10593496C212yesmaximal, complemented
6#10593433C212yesmaximal, complemented
7C4×#3775C212yesmaximal, complemented
8#10593419C212yesmaximal, complemented
9#10593369C212yesmaximal, complemented
10C2×#3805C2212yes—
11C2×#3792C2211yescharacteristic
12C22×#622C2211yescharacteristic
13C2×#3776C2211yescharacteristic
14C2×#3775C2212yes—
15#64237C418yescomplemented
16C2×#3774C2211yescharacteristic
17#64086C2211yescharacteristic
18C3×#67⋊C4—22no—
19Dic3×#67—22no—
20C2×#3724C2212yes—
21C4×#627C2212yes—
22#63902C2212yes—
23C4×#625C2212yes—
24#63877—22no—
25D3×Dic3⋊C4—22no—
26#63838C2212yes—
27#63777C2212yes—
28C4×#622C2212yes—
29#63742C2212yes—
30#63742C2211yescharacteristic
31#63742C2211yescharacteristic
32#63740C2212yes—
33#63740C2212yes—
34#63739C2212yes—
35#63739C2212yes—
36#5546—62no—
37C22×C3⋊Dic3C2311yescharacteristic
38C2×C3×#67—22no—
39C22×C3×Dic3—22no—
40C2×C3×C4×D3—22no—
41C2×#627C2312yes—
42C2×#625C2312yes—
43#3805—24no—
44#3805C2×C418yescomplemented
45C2×D3×Dic3—22no—
46C2×D3×Dic3—22no—
47#3792—22no—
48C2×#622C2×C414yescomplemented
49C2×#622C2312yes—
50C2×#622C2311yescharacteristic
51C2×#622C2311yescharacteristic
52#3776C2×C414yescomplemented
53#3775C2×C418yescomplemented
54#3774C2×C414yescomplemented
55C32×C22⋊C4D411yescharacteristic
56#3757D411yescharacteristic
57#3750D412yes—
58C4×C3⋊Dic3C2312yes—
59C3×(C2×D3)⋊C4—22no—
60C3×Dic3⋊C4—22no—
61C3×C4×Dic3—22no—
62#3724—22no—
63#3724C2312yes—
64#3724C2312yes—
65Dic3⋊Dic3—22no—
66(C2×D3)⋊Dic3—22no—
67Dic32—22no—
68#2952—91nomaximal, Sylow
69C2×#237—62no—
70C3×C4×D4—62no—
71D4×Dic3—62no—
72C4×#67—62no—
73C4×#67—62no—
74C2×Dic3⋊C4—62no—
75C2×Dic3⋊C4—62no—
76D3×C4⋊C4—62no—
77#887—62no—
78#67⋊C4—22no—
79#67⋊C4—62no—
80#877—62no—
81#877—62no—
82#872—62no—
83C4×Dic6—62no—
84C23×C32C2×D411yescharacteristic
85C22×C3×D3—22no—
86C2×C32×C4C2×D412yes—
87C2×C3⋊Dic3C22×C412yes—
88C2×C3⋊Dic3C2×D412yes—
89C2×C3⋊Dic3C2×D411yescharacteristic
90C2×C3⋊Dic3#4112yes—
91C2×C3⋊Dic3C2411yescharacteristic
92C3×#67—28no—
93C2×C3×Dic3—22no—
94C2×C3×Dic3—22no—
95C2×C3×Dic3—22no—
96C2×C3×Dic3—82no—
97C3×C4×D3—82no—
98#627—22no—
99#627C22×C414yes—
100#625—22no—
101#625C22×C414yes—
102D3×Dic3—28no—
103D3×Dic3—82no—
104#622—22no—
105#622C22×C412yes—
106#622C22×C412yes—
107C2×#135—91no—
108#520—92no—
109#442—92no—
110#441—92no—
111C4×SD16—92no—
112C4×SD16—92no—
113C2×#106—91no—
114#417—92no—
115#405—91no—
116C2×C3×D4—62no—
117C22×C3×C4—62no—
118C22×C3×C4—62no—
119C2×#67—22no—
120C2×#67—62no—
121C22×Dic3—22no—
122C22×Dic3—62no—
123C22×Dic3—62no—
124C22×Dic3—62no—
125#237—68no—
126#237—68no—
127C2×C4×D3—22no—
128C2×C4×D3—62no—
129C2×C4×D3—62no—
130C2×Dic6—62no—
131C3×C4⋊C4—62no—
132C3×C22⋊C4—22no—
133C3×C22⋊C4—62no—
134C3×C42—62no—
135#217—62no—
136#217—62no—
137(C2×D3)⋊C4—22no—
138(C2×D3)⋊C4—62no—
139C4⋊Dic3—62no—
140Dic3⋊C4—22no—
141Dic3⋊C4—62no—
142Dic3⋊C4—62no—
143Dic3⋊C4—62no—
144Dic3⋊C4—62no—
145Dic3⋊C4—62no—
146Dic3⋊C4—62no—
147Dic3⋊C4—62no—
148C4×Dic3—22no—
149C4×Dic3—62no—
150C4×Dic3—62no—
151C4×Dic3—62no—
152C4×Dic3—62no—
153C22×C32—22no—
154C22×C32C4×D412yes—
155C22×C32C22×D411yescharacteristic
156C2×C3×D3—24no—
157C2×C3×D3—42no—
158C2×C3×D3—42no—
159C32×C4—22no—
160C3⋊Dic3—22no—
161C3⋊Dic3C4×D412yes—
162C3⋊Dic3C23×C411yescharacteristic
163C3⋊Dic3C2×#4111yescharacteristic
164C3×Dic3—24no—
165C3×Dic3—42no—
166C3×Dic3—42no—
167C2×#41—92no—
168#135—98no—
169C2×Q16—91no—
170C2×SD16—92no—
171C2×D8—91no—
172C2×M16—91no—
173C22×C8—91no—
174C4×Q8—92no—
175C4×Q8—92no—
176C4×D4—62no—
177C4×D4—92no—
178C4×D4—92no—
179C4×D4—182no—
180#117—91no—
181#117—182no—
182C2×C4⋊C4—92no—
183C2×C4⋊C4—182no—
184#106—91no—
185#106—91no—
186#106—92no—
187#103—92no—
188#103—92no—
189#102—92no—
190#102—92no—
191#97—92no—
192C4×C8—92no—
193C23×C3—22no—
194C23×C3—62no—
195C22×D3—22no—
196C3×D4—68no—
197C2×C3×C4—22no—
198C2×C3×C4—22no—
199C2×C3×C4—62no—
200C2×C3×C4—62no—
201C2×C3×C4—62no—
202C2×C3×C4—242no—
203C2×C3×C4—242no—
204#67—28no—
205#67—64no—
206#67—64no—
207C2×Dic3—22no—
208C2×Dic3—22no—
209C2×Dic3—22no—
210C2×Dic3—64no—
211C2×Dic3—62no—
212C2×Dic3—64no—
213C2×Dic3—62no—
214C2×Dic3—62no—
215C2×Dic3—62no—
216C2×Dic3—68no—
217C2×Dic3—82no—
218C2×Dic3—242no—
219C4×D3—68no—
220C4×D3—82no—
221C4×D3—242no—
222Dic6—64no—
223Dic6—64no—
224C2×C32—22no—
225C2×C32C2×C4×D411yescharacteristic
226C2×C32#57712yes—
227C3×D3—44no—
228#41—98no—
229#41—184no—
230C2×Q8—92no—
231C2×D4—62no—
232C2×D4—92no—
233C22×C4—62no—
234C22×C4—62no—
235C22×C4—91no—
236C22×C4—182no—
237C22×C4—182no—
238Q16—94no—
239SD16—98no—
240D8—94no—
241M16—182no—
242C2×C8—91no—
243C2×C8—91no—
244C2×C8—94no—
245C2×C8—92no—
246C4⋊C4—62no—
247C4⋊C4—92no—
248C4⋊C4—92no—
249C4⋊C4—92no—
250C4⋊C4—182no—
251C4⋊C4—182no—
252C22⋊C4—62no—
253C22⋊C4—91no—
254C22⋊C4—182no—
255C22⋊C4GO+(4,𝔽2)11yescharacteristic
256C42—62no—
257C42—92no—
258C42—182no—
259C22×C3—22no—
260C22×C3—24no—
261C22×C3—42no—
262C22×C3—42no—
263C22×C3—64no—
264C22×C3—122no—
265C22×C3—122no—
266C2×D3—24no—
267C2×D3—42no—
268C2×D3—42no—
269C3×C4—42no—
270C3×C4—42no—
271C3×C4—64no—
272C3×C4—122no—
273C3×C4—122no—
274Dic3—24no—
275Dic3—42no—
276Dic3—42no—
277Dic3—62no—
278Dic3—62no—
279Dic3—64no—
280Dic3—122no—
281Dic3—122no—
282C32#295211yescharacteristic, complemented, Sylow
283C23—62no—
284C23C2×GO+(4,𝔽2)11yescharacteristic
285Q8—94no—
286Q8—182no—
287D4—68no—
288D4—94no—
289D4—182no—
290C2×C4—62no—
291C2×C4—62no—
292C2×C4—62no—
293C2×C4—91no—
294C2×C4—91no—
295C2×C4—92no—
296C2×C4—92no—
297C2×C4—92no—
298C2×C4—188no—
299C2×C4—242no—
300C2×C4—242no—
301C2×C4—722no—
302C2×C4C2×GO+(4,𝔽2)12yes—
303C8—92no—
304C8—92no—
305C8—182no—
306C2×C3—22no—
307C2×C3—22no—
308C2×C3—22no—
309C2×C3—44no—
310C2×C3—124no—
311D3—44no—
312C22—22no—
313C22—64no—
314C22—122no—
315C22—122no—
316C22C4×GO+(4,𝔽2)12yes—
317C22C22×GO+(4,𝔽2)11yescharacteristic
318C4—22no—
319C4—64no—
320C4—91no—
321C4—91no—
322C4—92no—
323C4—122no—
324C4—122no—
325C4—182no—
326C3—22no—
327C2—22no—
328C2—124no—
329C2C2×C4×GO+(4,𝔽2)11yescharacteristic
330C2#1059651512yes—
subgroupG/H
center, FrattiniC22C22×GO+(4,𝔽2)
commutatorC3⋊Dic3C23×C4
FittingC32×C22⋊C4D4
socleC22×C32C22×D4
prime radicalC2×#64237C2
cosocleC2×C3⋊Dic3C24
hypercenterC22⋊C4GO+(4,𝔽2)
hypocenterC32#2952
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #10594051C2semidirect
3. #10593738C2semidirect
4. C2×#63742C2semidirect
5. #10593496C2semidirect
6. #10593433C2semidirect
7. C4×#3775C2semidirect
8. #10593419C2semidirect
9. #10593369C2semidirect
15. #64237C4semidirect
44. #3805C2×C4semidirect
48. C2×#622C2×C4semidirect
52. #3776C2×C4semidirect
53. #3775C2×C4semidirect
54. #3774C2×C4semidirect
282. C32#2952semidirect

Maximal subgroups

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

subgroupindex
C2×#642372
#105940512
#105937382
C2×#637422
#105934962
#105934332
C4×#37752
#105934192
#105933692
#29529