Finite Group Databasebeta

← #11861207

Subgroups — #11861207

Order 1152.

718 conjugacy classes of subgroups; only the 158 normal subgroups are shown.

normal subgroups only

This group has 718 conjugacy classes of subgroups — too many to draw. Only its 158 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
1#10596644C212yesmaximal, complemented
2C2×#64128C211yesmaximal, characteristic
3#10593831C212yesmaximal, complemented
4#10593788C214yesmaximal, complemented
5#10593787C214yesmaximal, complemented
6#10593771C211yesmaximal, characteristic, complemented
7#10593765C211yesmaximal, characteristic, complemented
8C2×#3832C2212yes—
9#64289—24no—
10#64289C2218yescomplemented
11#64286C2211yescharacteristic
12#64283—24no—
13#64283C2212yes—
14#64283C2211yescharacteristic
15C2×C32×Q16C411yescharacteristic, complemented
16C2×#3755C412yescomplemented
17#64128C412yescomplemented
18#64128C412yescomplemented
19#64128C2212yes—
20#64128C2212yes—
21C2×#3745C411yescharacteristic, complemented
22C2×C8×C3⋊D3C2211yescharacteristic
23#63785C2218yescomplemented
24#63771C2212yescomplemented
25#63770C2212yescomplemented
26#63767C2212yescomplemented
27C8×#157C2212yescomplemented
28C2×#919—62no—
29C2×C32×Q8C2×C412yes—
30#3832—22no—
31#3832—22no—
32#3832C2×C414yes—
33#3832C2314yes—
34C2×C4⋊(C3⋊D3)—22no—
35C2×C4⋊(C3⋊D3)C2×C412yes—
36C2×C4×C3⋊D3—22no—
37C2×C4×C3⋊D3C2311yescharacteristic
38C22⋊#157—21no—
39#3792—22no—
40#3792D412yes—
41C4⋊#157—21no—
42C4×#157C2312yes—
43#3788—28no—
44#3788D412yes—
45#3788C2314yes—
46#3787—22no—
47#3787—28no—
48#3787C2312yes—
49C32×Q16C2×C412yes—
50C32×Q16C2×C412yes—
51C2×C32×C8C2×C411yescharacteristic
52#3755C2×C414yes—
53#3755C2×C414yes—
54C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
55#3745C2×C412yes—
56#3745C2×C412yes—
57C8×C3⋊D3C2×C411yescharacteristic
58C8×C3⋊D3C2×C411yescharacteristic
59C8×C3⋊D3C2311yescharacteristic
60C8×C3⋊D3C2311yescharacteristic
61#2957—91nomaximal, Sylow
62C2×#239—64no—
63C2×C3×Q16—22no—
64C2×#215—64no—
65#919—64no—
66#919—64no—
67#919—64no—
68#919—64no—
69C2×D24—62no—
70C2×D3×C8—62no—
71C22×C3⋊D3—22no—
72C22×C3⋊D3#4111yescharacteristic
73C2×#157—22no—
74C32×Q8—22no—
75C32×Q8C22×C414yes—
76C2×C32×C4—22no—
77C2×C32×C4C22×C411yescharacteristic
78C2×C3⋊Dic3C2×D411yescharacteristic
79C4⋊(C3⋊D3)—24no—
80C4⋊(C3⋊D3)—24no—
81C4⋊(C3⋊D3)—22no—
82C4⋊(C3⋊D3)C22×C414yes—
83C4×C3⋊D3—24no—
84C4×C3⋊D3—24no—
85C4×C3⋊D3C22×C411yescharacteristic
86C4×C3⋊D3C2×D411yescharacteristic
87C4×C3⋊D3#4111yescharacteristic
88C4×C3⋊D3C2411yescharacteristic
89#622—24no—
90#622C2×D414yes—
91C32×C8C22×C411yescharacteristic
92C32×C8C22×C411yescharacteristic
93C3⋊(C3⋊C8)C22×C411yescharacteristic
94C3⋊(C3⋊C8)C22×C411yescharacteristic
95C2×#135—91no—
96#568—92no—
97#444—94no—
98#443—94no—
99C2×#108—91no—
100#421—92no—
101#405—91no—
102C2×C3×Q8—24no—
103#239—68no—
104#239—68no—
105#239—124no—
106#239—124no—
107C2×D12—64no—
108C2×D12—124no—
109C2×C4×D3—62no—
110C2×C4×D3—124no—
111C3×Q16—24no—
112C3×Q16—24no—
113C2×C3×C8—22no—
114#215—68no—
115#215—68no—
116C2×C3⋊C8—62no—
117D24—64no—
118D24—64no—
119D3×C8—62no—
120D3×C8—62no—
121D3×C8—62no—
122D3×C8—62no—
123C22×C32C4×D411yescharacteristic
124C2×C3⋊D3—24no—
125C2×C3⋊D3—41no—
126C2×C3⋊D3—82no—
127C2×C3⋊D3C4×D411yescharacteristic
128C2×C3⋊D3C2×#4111yescharacteristic
129#157—42no—
130C32×C4—24no—
131C32×C4C4×D411yescharacteristic
132C32×C4C23×C411yescharacteristic
133C3⋊Dic3C4×D411yescharacteristic
134C3⋊Dic3C22×D411yescharacteristic
135C2×#41—92no—
136#135—92no—
137#135—92no—
138#135—92no—
139#135—92no—
140C2×Q16#15711yescharacteristic, complemented
141C2×SD16—92no—
142C2×D8—91no—
143#131—98no—
144#131—184no—
145C2×M16—91no—
146C2×M16—92no—
147C2×M16—184no—
148C22×C8—91no—
149#117—91no—
150#108—92no—
151#108—92no—
152#104—98no—
153#97—92no—
154C4×C8—92no—
155C22×D3—62no—
156C22×D3—124no—
157C3×Q8—28no—
158C3×Q8—44no—
159C2×C3×C4—22no—
160C2×C3×C4—44no—
161C2×Dic3—62no—
162D12—68no—
163D12—124no—
164D12—128no—
165D12—128no—
166C4×D3—62no—
167C4×D3—62no—
168C4×D3—62no—
169C4×D3—62no—
170C4×D3—128no—
171C4×D3—128no—
172C3×C8—22no—
173C3×C8—22no—
174C3⋊C8—62no—
175C3⋊C8—62no—
176C2×C32—21no—
177C2×C32C2×C4×D411yescharacteristic
178C3⋊D3—21no—
179C3⋊D3—21no—
180C3⋊D3—44no—
181#41—94no—
182#41—94no—
183#41—182no—
184#41—182no—
185C2×Q8C2×#15712yes—
186C2×D4—92no—
187C2×D4—182no—
188C22×C4—91no—
189C22×C4—182no—
190Q16C2×#15712yes—
191Q16C2×#15712yes—
192SD16—94no—
193SD16—94no—
194D8—92no—
195D8—92no—
196M16—92no—
197M16—92no—
198M16—94no—
199M16—188no—
200M16—182no—
201C2×C8—92no—
202C2×C8—91no—
203C2×C8—91no—
204C2×C8—91no—
205C2×C8—91no—
206C2×C8—91no—
207C2×C8—188no—
208C2×C8—182no—
209C2×C8C2×#15711yescharacteristic
210C4⋊C4—181no—
211C22⋊C4—181no—
212C42—92no—
213C22×C3—22no—
214C2×D3—62no—
215C2×D3—62no—
216C2×D3—128no—
217C2×D3—124no—
218C2×D3—248no—
219C3×C4—22no—
220C3×C4—22no—
221C3×C4—48no—
222Dic3—62no—
223Dic3—62no—
224C32#295711yescharacteristic, complemented, Sylow
225C23—91no—
226C23—182no—
227Q8—22no—
228Q8C22×#15714yes—
229D4—94no—
230D4—184no—
231D4—184no—
232D4—182no—
233C2×C4—22no—
234C2×C4—91no—
235C2×C4—91no—
236C2×C4—91no—
237C2×C4—91no—
238C2×C4—91no—
239C2×C4—184no—
240C2×C4—184no—
241C2×C4—182no—
242C2×C4C22×#15711yescharacteristic
243C8—94no—
244C8—91no—
245C8—91no—
246C8—184no—
247C8C22×#15711yescharacteristic
248C8C22×#15711yescharacteristic
249C2×C3—24no—
250C2×C3—22no—
251D3—122no—
252D3—122no—
253D3—248no—
254C22—91no—
255C22—91no—
256C22—184no—
257C22—361no—
258C22—722no—
259C22D4×#15711yescharacteristic
260C4—24no—
261C4—91no—
262C4—91no—
263C4—362no—
264C4D4×#15711yescharacteristic
265C4C23×#15711yescharacteristic
266C3—22no—
267C2—21no—
268C2—181no—
269C2—181no—
270C2—364no—
271C2C2×D4×#15711yescharacteristic
subgroupG/H
centerC2C2×D4×#157
commutatorC32×C4C23×C4
FrattiniC4C23×#157
FittingC2×C32×Q16C4
socleC2×C32C2×C4×D4
prime radicalC2×#64128C2
cosocleC4×C3⋊D3C24
hypercenterC2×Q16#157
hypocenterC32#2957
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
1. #10596644C2semidirect
3. #10593831C2semidirect
4. #10593788C2semidirect
5. #10593787C2semidirect
6. #10593771C2semidirect
7. #10593765C2semidirect
10. #64289C22semidirect
15. C2×C32×Q16C4semidirect
16. C2×#3755C4semidirect
17. #64128C4semidirect
18. #64128C4semidirect
21. C2×#3745C4semidirect
23. #63785C22semidirect
24. #63771C22semidirect
25. #63770C22semidirect
26. #63767C22semidirect
27. C8×#157C22semidirect
140. C2×Q16#157semidirect
224. C32#2957semidirect

Maximal subgroups

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

subgroupindex
#105966442
C2×#641282
#105938312
#105937882
#105937872
#105937712
#105937652
#29579