Finite Group Databasebeta

← #46835530

Subgroups — #46835530

Order 34688.

228 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 57 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#31774562C211yesmaximal, characteristic
2#31774249C211yesmaximal, characteristic, complemented
3#31774193C211yesmaximal, characteristic, complemented
4#31774188C211yesmaximal, characteristic
5#31773627C211yesmaximal, characteristic, complemented
6#31773624C211yesmaximal, characteristic
7#332×C271C211yesmaximal, characteristic, complemented
8C2×Q8×D271—21no—
9#22576160C2211yescharacteristic
10#22576159—21no—
11#22576138—22no—
12#22576136—21no—
13C4×Dic542C2211yescharacteristic
14C4×D1084C2211yescharacteristic
15#22576122—21no—
16#22576094—21no—
17#22576092—21no—
18#22576085—21no—
19#22576083—22no—
20#22576082—21no—
21C4×C271⋊C8C2211yescharacteristic
22C4⋊Q8×C271C2211yescharacteristic
23C4⋊C8×C271C2211yescharacteristic
24C4⋊C8×C271C2211yescharacteristic
25C2×Dic542—22no—
26C2×Dic542—21no—
27C2×Dic542D411yescharacteristic
28Q8×D271—42no—
29Q8×D271—42no—
30C2×D1084D411yescharacteristic
31C2×C4×D271—22no—
32C2×C4×D271—21no—
33C2×C271⋊C8—21no—
34C4⋊Dic271—21no—
35C4⋊Dic271—21no—
36C4⋊Dic271D411yescharacteristic
37C4⋊Dic271D411yescharacteristic
38Dic271⋊C4—22no—
39Dic271⋊C4—21no—
40(C2×D271)⋊C4—22no—
41(C2×D271)⋊C4—21no—
42C4×Dic271—21no—
43C2×Q8×C271—21no—
44C2×C8×C271—21no—
45C2×C8×C271—21no—
46C4⋊C4×C271—21no—
47C4⋊C4×C271D412yes—
48C42×C271C2311yescharacteristic
49C22×D271—21no—
50Dic542—21no—
51Dic542—44no—
52Dic542—42no—
53Dic542SD1612yes—
54D1084—21no—
55D1084Q1612yes—
56C2×Dic271—21no—
57C2×Dic271—21no—
58C2×Dic271—21no—
59C2×Dic271—41no—
60C4×D271—44no—
61C4×D271—41no—
62C4×D271—41no—
63C271⋊C8—41no—
64Q8×C271—41no—
65Q8×C271—41no—
66C2×C4×C271—22no—
67C2×C4×C271C2×D411yescharacteristic
68C2×C4×C271C2×D411yescharacteristic
69C2×C4×C271C2×D411yescharacteristic
70C8×C271—41no—
71C8×C271—41no—
72C22×C271#12011yescharacteristic
73C2×D271—22no—
74C2×D271—41no—
75C2×D271—41no—
76C4×C271—21no—
77C4×C271—42no—
78C4×C271C2×SD1611yescharacteristic
79C4×C271C2×Q1611yescharacteristic
80C4×C271AGL(1,ℤ/8)11yescharacteristic
81C4×C271#13711yescharacteristic
82Dic271—22no—
83Dic271—41no—
84Dic271—41no—
85Dic271—81no—
86C2×C271#45011yescharacteristic
87C2×C271#45111yescharacteristic
88C2×C271#45411yescharacteristic
89D271—42no—
90C271#163711yescharacteristic, complemented, Sylow
91#1637—2711nomaximal, Sylow
92D4×Q8—2711no—
93#487—2711no—
94#477—2711no—
95#476—2711no—
96#332D27111yescharacteristic, complemented
97Q8⋊C8—2711no—
98D4⋊C8—2711no—
99C22×Q8—5421no—
100C4⋊Q8—2711no—
101C4⋊Q8—5421no—
102C4⋊Q8C2×D27111yescharacteristic
103C22⋊Q8—5421no—
104C22⋊Q8—5422no—
105C4×Q8—2711no—
106C4×D4—2711no—
107C4×D4—5421no—
108#107—5421no—
109#106—5421no—
110C4⋊C8C2×D27111yescharacteristic
111C4⋊C8C2×D27111yescharacteristic
112#103—5421no—
113#103—5422no—
114#102—5421no—
115C4×C8—2711no—
116C2×Q8—21no—
117C2×Q8—2711no—
118C2×Q8—5422no—
119C2×Q8—5421no—
120C2×Q8—10842no—
121C2×Q8—10842no—
122C2×D4—2711no—
123C22×C4—5422no—
124C22×C4—5421no—
125C2×C8—21no—
126C2×C8—21no—
127C2×C8—5421no—
128C4⋊C4—21no—
129C4⋊C4—2711no—
130C4⋊C4—2711no—
131C4⋊C4—5422no—
132C4⋊C4—5421no—
133C4⋊C4—5421no—
134C4⋊C4—5421no—
135C4⋊C4D108412yes—
136C22⋊C4—5422no—
137C22⋊C4—5421no—
138C42—5421no—
139C42C22×D27111yescharacteristic
140C23—5421no—
141Q8—41no—
142Q8—41no—
143Q8—2712no—
144Q8—5421no—
145Q8—10842no—
146Q8—10844no—
147D4—2712no—
148D4—5421no—
149C2×C4—22no—
150C2×C4—5421no—
151C2×C4—5421no—
152C2×C4—5421no—
153C2×C4—10844no—
154C2×C4—10841no—
155C2×C4—10841no—
156C2×C4—10841no—
157C2×C4D4×D27111yescharacteristic
158C2×C4D4×D27111yescharacteristic
159C2×C4C2×D108411yescharacteristic
160C8—41no—
161C8—41no—
162C8—10841no—
163C22—5422no—
164C22—10841no—
165C22—10841no—
166C22#2257613011yescharacteristic
167C4—21no—
168C4—42no—
169C4—5422no—
170C4—10841no—
171C4—10841no—
172C4—21681no—
173C4SD16×D27111yescharacteristic
174C4Q16×D27111yescharacteristic
175C4#2257618411yescharacteristic
176C4#2257618911yescharacteristic
177C2—10842no—
178C2#3177404911yescharacteristic
179C2#3177405411yescharacteristic
180C2#3177407211yescharacteristic
subgroupG/H
centerC22#22576130
commutator, cosocleC42×C271C23
FrattiniC42C22×D271
Fitting#332×C271C2
socleC22×C271#120
prime radicalC2×D1084D4
hypercenter#332D271
hypocenterC271#1637
LCSG ▷ C42×C271 ▷ C22×C271 ▷ C271
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
2. #31774249C2semidirect
3. #31774193C2semidirect
5. #31773627C2semidirect
7. #332×C271C2semidirect
90. C271#1637semidirect
96. #332D271semidirect

Maximal subgroups

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

subgroupindex
#317745622
#317742492
#317741932
#317741882
#317736272
#317736242
#332×C2712
#1637271