Finite Group Databasebeta

← #101×#157 #11783809

Subgroups — #101×#157 #11783809

Order 1152.

442 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 90 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×Q8×#157C211yesmaximal, characteristic
2#10593836C211yesmaximal, characteristic
3M16×#157C212yesmaximal
4C3⋊D3×#101C211yesmaximal, characteristic
5#10590188C212yesmaximal
6C2×Q8×C3⋊D3C2211yescharacteristic
7Q8×#157—22no—
8Q8×#157—22no—
9C2×C4⋊#157C412yes—
10C2×C4⋊#157C2211yescharacteristic
11C2×C4×#157C412yes—
12C2×C4×#157C2211yescharacteristic
13#64283C2212yes—
14M16×C3⋊D3C2212yes—
15#63780C414yescomplemented
16#63767—22no—
17C8×#157—22no—
18C32×#101C411yescharacteristic, complemented
19#63663C411yescharacteristic, complemented
20#63651C412yescomplemented
21D3×#101—62no—
22C22×#157C2×C411yescharacteristic
23C22×#157C2×C412yes—
24C22×#157C2×C411yescharacteristic
25C2×C32×Q8C2×C411yescharacteristic
26Q8×C3⋊D3—22no—
27Q8×C3⋊D3—22no—
28C2×C4×C3⋊D3C2×C412yes—
29C2×C4×C3⋊D3C2311yescharacteristic
30C2×#634C2×C411yescharacteristic
31C2×#634C2×C412yes—
32#3792C2×C414yes—
33C4⋊#157—24no—
34C4⋊#157—22no—
35C4×#157—22no—
36C4×#157—22no—
37C4×#157D412yes—
38C4×#157D412yes—
39#3788—22no—
40#3787—22no—
41C32×M16C2×C412yes—
42#3748C2×C412yes—
43#3743—22no—
44C8×C3⋊D3—22no—
45C4×#101—91nomaximal, Sylow
46C2×D3×Q8—62no—
47D3×M16—64no—
48C3×#101—22no—
49#836—62no—
50#824—64no—
51C22×C3⋊D3C22×C411yescharacteristic
52C2×#157—22no—
53C2×#157—22no—
54C2×#157—41no—
55C2×#157—42no—
56C2×#157C22⋊C411yescharacteristic
57C2×#157C22⋊C412yes—
58C2×#157C22⋊C411yescharacteristic
59C32×Q8—22no—
60C2×C32×C4C4212yes—
61C2×C32×C4C22×C411yescharacteristic
62C2×C3⋊Dic3C4212yes—
63C2×C3⋊Dic3C22×C411yescharacteristic
64C4×C3⋊D3—22no—
65C4×C3⋊D3—22no—
66C4×C3⋊D3C2×D412yes—
67C4×C3⋊D3#4112yes—
68#634—22no—
69#634—24no—
70#622—24no—
71C32×C8—22no—
72C3⋊(C3⋊C8)—22no—
73C2×C4×Q8—91no—
74C2×#101—91no—
75C2×#101—91no—
76C4×M16—92no—
77#343—92no—
78C2×C3×Q8—22no—
79D3×Q8—124no—
80D3×Q8—124no—
81C2×C4×D3—62no—
82C2×C4×D3—64no—
83C2×Dic6—62no—
84C2×Dic6—64no—
85C3×M16—24no—
86#208—64no—
87ΓL(1,𝔽25)—124no—
88D3×C8—124no—
89C22×C32C2×C4211yescharacteristic
90C2×C3⋊D3—21no—
91C2×C3⋊D3—21no—
92C2×C3⋊D3C2×C22⋊C411yescharacteristic
93C2×C3⋊D3#11711yescharacteristic
94#157—21no—
95#157—22no—
96#157—42no—
97#157#10112yesdirect product factor
98C32×C4—22no—
99C32×C4C4×D412yes—
100C3⋊Dic3—22no—
101C3⋊Dic3C4×D412yes—
102C22×Q8—91no—
103C2×M16—92no—
104C2×M16—92no—
105C4×Q8—182no—
106C4×Q8—182no—
107C2×C4⋊C4—92no—
108C2×C4⋊C4—91no—
109C2×C42—91no—
110C2×C42—92no—
111#101—94no—
112#101—91no—
113#101—92no—
114#101#15711yescharacteristic, direct product factor
115#97—182no—
116C4×C8—182no—
117C22×D3—62no—
118C3×Q8—44no—
119C2×C3×C4—22no—
120C2×C3×C4—24no—
121C2×Dic3—62no—
122C2×Dic3—64no—
123C4×D3—64no—
124C4×D3—64no—
125C4×D3—124no—
126C4×D3—124no—
127Dic6—128no—
128Dic6—124no—
129C3×C8—44no—
130C3⋊C8—124no—
131C2×C32—21no—
132C2×C32C4×C22⋊C411yescharacteristic
133C3⋊D3—21no—
134C3⋊D3C2×#10111yescharacteristic
135C3⋊D3#41311yescharacteristic
136C2×Q8—91no—
137C2×Q8—92no—
138C2×Q8—182no—
139C2×Q8—182no—
140C2×Q8C2×#15711yescharacteristic
141C22×C4—91no—
142C22×C4—91no—
143C22×C4—91no—
144C22×C4—92no—
145C22×C4—92no—
146M16—94no—
147M16—92no—
148M16—182no—
149M16—182no—
150M16C2×#15712yes—
151C2×C8—182no—
152C2×C8—182no—
153C4⋊C4—182no—
154C4⋊C4—184no—
155C42—92no—
156C42—92no—
157C42—182no—
158C42—182no—
159C22×C3—22no—
160C2×D3—62no—
161C2×D3—62no—
162C2×D3—122no—
163C2×D3—122no—
164C3×C4—24no—
165C3×C4—44no—
166Dic3—64no—
167Dic3—124no—
168C32C4×#10111yescharacteristic, complemented, Sylow
169C23—91no—
170Q8—22no—
171Q8—184no—
172Q8—182no—
173C2×C4—91no—
174C2×C4—91no—
175C2×C4—92no—
176C2×C4—92no—
177C2×C4—91no—
178C2×C4—92no—
179C2×C4—92no—
180C2×C4—182no—
181C2×C4—182no—
182C2×C4—182no—
183C2×C4—182no—
184C2×C4—361no—
185C2×C4—362no—
186C2×C4C4×#15712yes—
187C2×C4C22×#15711yescharacteristic
188C8—22no—
189C8—184no—
190C8—182no—
191C2×C3—22no—
192C2×C3—42no—
193D3—62no—
194D3—62no—
195D3—122no—
196C22—91no—
197C22—91no—
198C22—181no—
199C22—181no—
200C22C2×C4×#15711yescharacteristic
201C4—22no—
202C4—92no—
203C4—92no—
204C4—181no—
205C4—182no—
206C4—182no—
207C4—362no—
208C4D4×#15712yes—
209C3—22no—
210C2—21no—
211C2—91no—
212C2—91no—
213C2—181no—
214C2C22⋊C4×#15711yescharacteristic
subgroupG/H
centerC2C22⋊C4×#157
commutatorC22×C32C2×C42
FrattiniC2×C4C22×#157
FittingC32×#101C4
socleC2×C32C4×C22⋊C4
prime radicalC22×C3⋊D3C22×C4
cosocleC2×C4×C3⋊D3C23
hypercenter#101#157
hypocenterC32C4×#101
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ #101

Complements

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

NH ≅ G/Ntype
15. #63780C4semidirect
18. C32×#101C4semidirect
19. #63663C4semidirect
20. #63651C4semidirect
97. #157#101direct (N × H)
114. #101#157direct (N × H)
168. C32C4×#101semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×#1572
#105938362
M16×#1572
C3⋊D3×#1012
#105901882
C4×#1019