Finite Group Databasebeta

← #11772615

Subgroups — #11772615

Order 1152.

318 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 318 conjugacy classes of subgroups — too many to draw. Only its 40 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#10593837C211yesmaximal, characteristic
2#10593836C211yesmaximal, characteristic
3C3⋊D3×#101C211yesmaximal, characteristic
4C2×Q8×C3⋊D3C2211yescharacteristic
5C2×C4⋊#157C411yescharacteristic
6C2×C4×#157C411yescharacteristic
7#64283—21no—
8M16×C3⋊D3—21no—
9#63781—21no—
10#63781—21no—
11#63780—21no—
12#63780C412yescomplemented
13C32×#101C411yescharacteristic, complemented
14#63663C411yescharacteristic, complemented
15#63651—21no—
16D3×#101—62no—
17C22×#157—21no—
18C22×#157—21no—
19C2×C32×Q8C2×C411yescharacteristic
20Q8×C3⋊D3—41no—
21Q8×C3⋊D3—41no—
22C2×C4×C3⋊D3C2×C411yescharacteristic
23C2×C4×C3⋊D3D411yescharacteristic
24C2×C4×C3⋊D3D411yescharacteristic
25C2×#634C2×C411yescharacteristic
26C2×#634D411yescharacteristic
27C2×#634Q811yescharacteristic
28#3792—22no—
29C4⋊#157—41no—
30C4×#157—41no—
31#3788—41no—
32#3787—41no—
33C32×M16—21no—
34#3748—21no—
35#3743—41no—
36C8×C3⋊D3—41no—
37#1394—91nomaximal, Sylow
38C2×D3×Q8—62no—
39D3×M16—64no—
40C3×#101—22no—
41#836—62no—
42#824—64no—
43C22×C3⋊D3C22⋊C411yescharacteristic
44C2×#157—22no—
45C2×#157—41no—
46C2×#157—41no—
47C2×#157—42no—
48C2×#157—41no—
49C32×Q8—41no—
50C2×C32×C4C4211yescharacteristic
51C2×C32×C4C22⋊C411yescharacteristic
52C2×C32×C4C4⋊C411yescharacteristic
53C2×C3⋊Dic3C22⋊C411yescharacteristic
54C2×C3⋊Dic3C4⋊C411yescharacteristic
55C2×C3⋊Dic3C4⋊C411yescharacteristic
56C4×C3⋊D3—21no—
57C4×C3⋊D3—21no—
58C4×C3⋊D3—21no—
59C4×C3⋊D3—21no—
60C4×C3⋊D3—21no—
61C4×C3⋊D3—21no—
62#634—41no—
63#634—41no—
64#634—41no—
65#622—42no—
66C32×C8—41no—
67C3⋊(C3⋊C8)—41no—
68C2×#101—91no—
69C2×#101—91no—
70#391—91no—
71C2×C3×Q8—22no—
72D3×Q8—124no—
73D3×Q8—124no—
74C2×C4×D3—62no—
75C2×C4×D3—62no—
76C2×C4×D3—62no—
77C2×Dic6—62no—
78C2×Dic6—62no—
79C2×Dic6—62no—
80C3×M16—24no—
81#208—64no—
82ΓL(1,𝔽25)—124no—
83D3×C8—124no—
84C22×C32#9511yescharacteristic
85C2×C3⋊D3—21no—
86C2×C3⋊D3—21no—
87C2×C3⋊D3#9911yescharacteristic
88C2×C3⋊D3#9911yescharacteristic
89#157—42no—
90#157—81no—
91C32×C4—21no—
92C32×C4—21no—
93C32×C4—21no—
94C3⋊Dic3—21no—
95C3⋊Dic3—21no—
96C3⋊Dic3—21no—
97C22×Q8—91no—
98C2×M16—181no—
99C2×M16—181no—
100C2×C4⋊C4—91no—
101C2×C42—91no—
102#101—92no—
103#101—91no—
104#101—181no—
105#101—181no—
106#101#15711yescharacteristic, complemented
107#95—181no—
108#95—181no—
109C22×D3—62no—
110C3×Q8—44no—
111C2×C3×C4—22no—
112C2×C3×C4—22no—
113C2×C3×C4—22no—
114C2×Dic3—62no—
115C2×Dic3—62no—
116C2×Dic3—62no—
117C4×D3—64no—
118C4×D3—64no—
119C4×D3—122no—
120C4×D3—122no—
121C4×D3—122no—
122C4×D3—122no—
123Dic6—124no—
124Dic6—124no—
125Dic6—124no—
126C3×C8—44no—
127C3⋊C8—124no—
128C2×C32—21no—
129C2×C32#34211yescharacteristic
130C3⋊D3—21no—
131C3⋊D3#35511yescharacteristic
132C3⋊D3#35611yescharacteristic
133C2×Q8—91no—
134C2×Q8—91no—
135C2×Q8—91no—
136C2×Q8—361no—
137C2×Q8—361no—
138C2×Q8C2×#15711yescharacteristic
139C22×C4—91no—
140C22×C4—91no—
141C22×C4—91no—
142C22×C4—181no—
143C22×C4—181no—
144M16—21no—
145M16—182no—
146M16—181no—
147M16—361no—
148M16—361no—
149C2×C8—361no—
150C2×C8—361no—
151C4⋊C4—361no—
152C42—361no—
153C22×C3—22no—
154C2×D3—62no—
155C2×D3—62no—
156C2×D3—122no—
157C2×D3—122no—
158C3×C4—24no—
159C3×C4—42no—
160C3×C4—42no—
161Dic3—64no—
162Dic3—122no—
163Dic3—122no—
164C32#139411yescharacteristic, complemented, Sylow
165C23—91no—
166Q8—41no—
167Q8—361no—
168Q8—361no—
169Q8—361no—
170C2×C4—91no—
171C2×C4—91no—
172C2×C4—91no—
173C2×C4—181no—
174C2×C4—181no—
175C2×C4—181no—
176C2×C4—181no—
177C2×C4—181no—
178C2×C4—181no—
179C2×C4—182no—
180C2×C4—361no—
181C2×C4—361no—
182C2×C4—361no—
183C2×C4—362no—
184C2×C4C4×#15711yescharacteristic
185C2×C4C4⋊#15711yescharacteristic
186C2×C4C22⋊#15711yescharacteristic
187C8—41no—
188C8—361no—
189C8—362no—
190C2×C3—22no—
191C2×C3—42no—
192D3—62no—
193D3—62no—
194D3—122no—
195C22—91no—
196C22—91no—
197C22—181no—
198C22—181no—
199C22#6378111yescharacteristic
200C4—21no—
201C4—21no—
202C4—21no—
203C4—181no—
204C4—181no—
205C4—181no—
206C4—362no—
207C4—721no—
208C3—22no—
209C2—21no—
210C2—91no—
211C2—91no—
212C2—181no—
213C2#1059015511yescharacteristic
subgroupG/H
centerC2#10590155
commutatorC2×C32×C4C42
FrattiniC2×Q8C2×#157
FittingC32×#101C4
socleC2×C32#342
prime radicalC22×C3⋊D3C22⋊C4
cosocleC2×Q8×C3⋊D3C22
hypercenter#101#157
hypocenterC32#1394
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #101

Complements

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

NH ≅ G/Ntype
12. #63780C4semidirect
13. C32×#101C4semidirect
14. #63663C4semidirect
106. #101#157semidirect
164. C32#1394semidirect

Maximal subgroups

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

subgroupindex
#105938372
#105938362
C3⋊D3×#1012
#13949