Finite Group Databasebeta

← #11859475

Subgroups — #11859475

Order 1152.

810 conjugacy classes of subgroups; only the 166 normal subgroups are shown.

normal subgroups only

This group has 810 conjugacy classes of subgroups — too many to draw. Only its 166 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×#64289C211yesmaximal, characteristic, complemented
2C2×#64287C211yesmaximal, characteristic, complemented
3#10596139C211yesmaximal, characteristic
4#10593834C211yesmaximal, characteristic, complemented
5#10593823C211yesmaximal, characteristic, complemented
6#10593742C214yesmaximal, complemented
7#10593739C214yesmaximal, complemented
8#10593729C211yesmaximal, characteristic, complemented
9C4×#3787C211yesmaximal, characteristic, complemented
10C2×#3832C2211yescharacteristic
11C2×#3830C2211yescharacteristic
12C2×#3792C2212yes—
13C22×#622C2212yes—
14#64289—24no—
15#64287—24no—
16C2×#3788C2211yescharacteristic
17C2×#3788C2211yescharacteristic
18C2×#3788C2212yes—
19C2×#3787C2211yescharacteristic
20C2×#3787C2212yes—
21C2×#3787C2211yescharacteristic
22C32×#124C411yescharacteristic
23#64153C411yescharacteristic
24#64149C411yescharacteristic
25#64093C414yes—
26#64090C2214yes—
27#64084C411yescharacteristic
28C42×C3⋊D3C2211yescharacteristic
29C22⋊#622C2214yes—
30#63779C2214yes—
31#63778C2214yes—
32C4×#622C2212yes—
33C4×#622C2212yes—
34#5668—62no—
35C2×C32×Q8C2×C411yescharacteristic
36C2×C32×D4C2×C411yescharacteristic
37C2×#638C2×C414yes—
38C2×#638C2×C412yes—
39C22×C3⋊Dic3C2312yes—
40#3832—22no—
41#3832—22no—
42#3830—22no—
43#3830—22no—
44C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
45C2×C4⋊(C3⋊D3)C2×C412yes—
46C2×C4×C3⋊D3C2×C412yes—
47C2×C4×C3⋊D3C2312yes—
48C2×C4×C3⋊D3C2311yescharacteristic
49C2×#634C2×C411yescharacteristic
50#3792—24no—
51C2×#622—24no—
52C2×#622C2312yes—
53C2×#622C2312yes—
54C2×#622C2312yes—
55C2×#622C2311yescharacteristic
56C2×#622C2311yescharacteristic
57#3788—22no—
58#3788—22no—
59#3788—24no—
60#3787—22no—
61#3787—24no—
62#3787D414yescomplemented
63C32×C22⋊C4C2×C414yes—
64C32×C42C2×C411yescharacteristic
65#3752C2×C414yes—
66#3750C2×C414yes—
67C4×C3⋊Dic3C2×C411yescharacteristic
68C4×C3⋊Dic3C2312yes—
69#2931—91nomaximal, Sylow
70C2×#239—62no—
71C2×#237—62no—
72C3×#124—22no—
73#944—62no—
74#940—62no—
75#884—68no—
76#67⋊C4—68no—
77#875—62no—
78C42×D3—62no—
79C23×C32C22×C412yes—
80C22×C3⋊D3C22×C412yes—
81C22×C3⋊D3C22×C411yescharacteristic
82C32×Q8—22no—
83C32×D4—22no—
84C2×C32×C4C22×C412yes—
85C2×C32×C4C22×C412yes—
86C2×C32×C4C22×C411yescharacteristic
87#638—24no—
88#638—28no—
89C2×C3⋊Dic3—22no—
90C2×C3⋊Dic3—22no—
91C2×C3⋊Dic3C22×C412yes—
92C2×C3⋊Dic3C22×C412yes—
93C2×C3⋊Dic3C2411yescharacteristic
94C4⋊(C3⋊D3)—24no—
95C4⋊(C3⋊D3)—22no—
96C4×C3⋊D3—24no—
97C4×C3⋊D3—22no—
98C4×C3⋊D3—22no—
99C4×C3⋊D3C2×D412yes—
100C4×C3⋊D3#4112yes—
101#634—22no—
102#622—22no—
103#622—22no—
104#622—22no—
105#622C2×D412yes—
106#622C2×D412yes—
107C2×#131—91no—
108C2×#131—91no—
109#532—91no—
110#436—94no—
111C8×D4—94no—
112#423—91no—
113#408—91no—
114#408—91no—
115C2×C4×C8—91no—
116C2×C3×Q8—22no—
117C2×C3×D4—22no—
118C2×#67—68no—
119C2×#67—64no—
120C22×Dic3—64no—
121#239—124no—
122#239—124no—
123#237—124no—
124#237—124no—
125C2×D12—62no—
126C2×D12—64no—
127C2×C4×D3—62no—
128C2×C4×D3—64no—
129C2×C4×D3—64no—
130C2×Dic6—62no—
131C3×C22⋊C4—28no—
132C3×C42—22no—
133(C2×D3)⋊C4—68no—
134Dic3⋊C4—68no—
135C4×Dic3—64no—
136C4×Dic3—62no—
137C22×C32—22no—
138C22×C32—24no—
139C22×C32C23×C411yescharacteristic
140C2×C3⋊D3—22no—
141C2×C3⋊D3—22no—
142C2×C3⋊D3—24no—
143C2×C3⋊D3C4×D412yes—
144C32×C4—22no—
145C32×C4—22no—
146C32×C4C4×D412yes—
147C3⋊Dic3—22no—
148C3⋊Dic3#13114yescomplemented
149C3⋊Dic3C22×D411yescharacteristic
150C3⋊Dic3C2×#4111yescharacteristic
151C2×#41—91no—
152C2×#41—91no—
153#131—184no—
154#131—184no—
155C2×M16—91no—
156C2×M16—91no—
157C2×M16—92no—
158C2×M16—92no—
159C22×C8—91no—
160C22×C8—92no—
161C22×C8—91no—
162C22×C8—92no—
163C4⋊Q8—91no—
164#127—91no—
165#124—91no—
166#124#15711yescharacteristic
167#121—94no—
168C4×D4—94no—
169C2×C42—91no—
170C4⋊C8—94no—
171C22⋊C8—94no—
172C22⋊C8—94no—
173C4×C8—92no—
174C4×C8—92no—
175C23×C3—24no—
176C22×D3—62no—
177C22×D3—64no—
178C3×Q8—44no—
179C3×D4—44no—
180C2×C3×C4—22no—
181C2×C3×C4—24no—
182C2×C3×C4—24no—
183#67—1216no—
184#67—128no—
185C2×Dic3—64no—
186C2×Dic3—62no—
187C2×Dic3—64no—
188C2×Dic3—124no—
189C2×Dic3—124no—
190D12—124no—
191D12—128no—
192C4×D3—64no—
193C4×D3—64no—
194C4×D3—128no—
195C4×D3—124no—
196C4×D3—124no—
197Dic6—124no—
198C2×C32—42no—
199C2×C32C2×C4×D411yescharacteristic
200C2×C32C2×#13112yes—
201C3⋊D3—22no—
202C3⋊D3—42no—
203#41—182no—
204#41—182no—
205#41—182no—
206#41—182no—
207C2×Q8—91no—
208C2×Q8C2×#15711yescharacteristic
209C2×D4—94no—
210C2×D4—92no—
211C2×D4—92no—
212C2×D4—91no—
213C2×D4C2×#15711yescharacteristic
214C22×C4—91no—
215C22×C4—92no—
216C22×C4—92no—
217C22×C4—92no—
218M16—184no—
219M16—184no—
220M16—182no—
221M16—182no—
222C2×C8—91no—
223C2×C8—91no—
224C2×C8—94no—
225C2×C8—92no—
226C2×C8—92no—
227C2×C8—92no—
228C2×C8—184no—
229C2×C8—184no—
230C2×C8—182no—
231C4⋊C4—94no—
232C22⋊C4—94no—
233C22⋊C4C2×#15714yes—
234C42—92no—
235C42—91no—
236C42C2×#15711yescharacteristic
237C22×C3—22no—
238C22×C3—44no—
239C22×C3—48no—
240C2×D3—64no—
241C2×D3—124no—
242C2×D3—124no—
243C2×D3—128no—
244C3×C4—24no—
245C3×C4—44no—
246C3×C4—44no—
247Dic3—62no—
248Dic3—62no—
249Dic3—68no—
250Dic3—124no—
251C32#293111yescharacteristic, complemented, Sylow
252C23—91no—
253C23—92no—
254C23C22×#15712yes—
255Q8—22no—
256Q8—182no—
257D4—22no—
258D4—184no—
259D4—188no—
260D4—184no—
261D4—182no—
262C2×C4—92no—
263C2×C4—91no—
264C2×C4—92no—
265C2×C4—92no—
266C2×C4—92no—
267C2×C4—182no—
268C2×C4—182no—
269C2×C4—184no—
270C2×C4—182no—
271C2×C4—182no—
272C2×C4C22×#15712yes—
273C2×C4C22×#15712yes—
274C2×C4C22×#15711yescharacteristic
275C8—92no—
276C8—92no—
277C8—182no—
278C8—182no—
279C8—182no—
280C2×C3—22no—
281C2×C3—24no—
282C2×C3—84no—
283D3—124no—
284D3—244no—
285C22—22no—
286C22—24no—
287C22—92no—
288C22—182no—
289C22—182no—
290C22—184no—
291C22C23×#15711yescharacteristic
292C4—22no—
293C4—22no—
294C4—91no—
295C4—91no—
296C4—94no—
297C4—182no—
298C4D4×#15712yes—
299C3—22no—
300C2—42no—
301C2—182no—
302C2—362no—
303C2C2×D4×#15711yescharacteristic
304C2#1059664712yes—
subgroupG/H
center, FrattiniC22C23×#157
commutator, socleC22×C32C23×C4
FittingC32×#124C4
prime radical#10596139C2
cosocleC2×C3⋊Dic3C24
hypercenter#124#157
hypocenterC32#2931
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #124

Complements

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

NH ≅ G/Ntype
1. C2×#64289C2semidirect
2. C2×#64287C2semidirect
4. #10593834C2semidirect
5. #10593823C2semidirect
6. #10593742C2semidirect
7. #10593739C2semidirect
8. #10593729C2semidirect
9. C4×#3787C2semidirect
62. #3787D4semidirect
148. C3⋊Dic3#131semidirect
251. C32#2931semidirect

Maximal subgroups

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

subgroupindex
C2×#642892
C2×#642872
#105961392
#105938342
#105938232
#105937422
#105937392
#105937292
C4×#37872
#29319