Finite Group Databasebeta

← #46838341

Subgroups — #46838341

Order 34688.

206 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 47 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#31774710C211yesmaximal, characteristic
2#31774338C211yesmaximal, characteristic, complemented
3#31774169C211yesmaximal, characteristic, complemented
4#31773713C211yesmaximal, characteristic, complemented
5#31773705C211yesmaximal, characteristic, complemented
6#31773680C211yesmaximal, characteristic, complemented
7C2×Q32×C271C211yesmaximal, characteristic, complemented
8#22576208—21no—
9#22576192—22no—
10#22576191—21no—
11#22576191—21no—
12#22576183—21no—
13#22576182C2211yescharacteristic
14Q16×D271—21no—
15#22576166C2211yescharacteristic
16#22576106—21no—
17#22576103—21no—
18#22576100C2211yescharacteristic
19#22576096C2211yescharacteristic
20#22576079—21no—
21C2×Q16×C271C2211yescharacteristic
22C2×Q16×C271C2211yescharacteristic
23Q32×C271—22no—
24C2×C16×C271C2211yescharacteristic
25#16864655—22no—
26#16864655—41no—
27#16864654—21no—
28#16864654—42no—
29#16864654D411yescharacteristic
30Q8×D271—22no—
31Q8×D271—41no—
32Dic1084D411yescharacteristic
33#16864644—22no—
34#16864644—41no—
35#16864643—21no—
36#16864641—22no—
37#16864641—41no—
38D2168D411yescharacteristic
39#16864638—21no—
40#16864638D411yescharacteristic
41#16864637—21no—
42C8×D271—21no—
43C271⋊C16—21no—
44C2×Q8×C271—21no—
45C2×Q8×C271—21no—
46Q16×C271—21no—
47Q16×C271—21no—
48Q16×C271—21no—
49Q16×C271D412yes—
50C2×C8×C271C2311yescharacteristic
51C16×C271—21no—
52Dic542—21no—
53Dic542—42no—
54Dic542D811yescharacteristic
55D1084—21no—
56D1084—42no—
57D1084D811yescharacteristic
58C22⋊D271—21no—
59C22⋊D271—41no—
60C4×D271—21no—
61C4×D271—42no—
62C4×D271—42no—
63C4×D271—41no—
64C271⋊C8—21no—
65C271⋊C8—41no—
66Q8×C271—22no—
67Q8×C271—41no—
68Q8×C271—41no—
69Q8×C271—41no—
70C2×C4×C271—41no—
71C2×C4×C271—41no—
72C2×C4×C271C2×D411yescharacteristic
73C8×C271C2×D411yescharacteristic
74C8×C271C2×D411yescharacteristic
75C22×C271AGL(1,ℤ/8)11yescharacteristic
76C2×D271—21no—
77C2×D271—41no—
78C4×C271—42no—
79C4×C271—81no—
80C4×C271#12011yescharacteristic
81C4×C271C2×D811yescharacteristic
82Dic271—21no—
83Dic271—41no—
84C2×C271—21no—
85C2×C271#44711yescharacteristic
86D271—41no—
87D271—81no—
88C271#219511yescharacteristic, complemented, Sylow
89#2195—2711nomaximal, Sylow
90#578—2711no—
91#510—2711no—
92C2×Q32D27111yescharacteristic, complemented
93#473—2711no—
94#362—2711no—
95#359—2711no—
96#350—2711no—
972−1+4—5421no—
98#137—5421no—
99#137—5422no—
100#137—5421no—
101#135—2711no—
102#135—5421no—
103C2×Q16—5421no—
104C2×Q16C2×D27111yescharacteristic
105C2×Q16C2×D27111yescharacteristic
106#131—2711no—
107Q32—22no—
108Q32—5421no—
109SD32—5421no—
110M32—2711no—
111C2×C16C2×D27111yescharacteristic
112#108—2711no—
113#101—5421no—
114#41—2711no—
115#41—5422no—
116#41—5421no—
117#41—10842no—
118#41—10841no—
119C2×Q8—21no—
120C2×Q8—21no—
121C2×Q8—5422no—
122C2×Q8—10841no—
123Q16—21no—
124Q16—21no—
125Q16—21no—
126Q16—2711no—
127Q16—5422no—
128Q16—10841no—
129Q16C22⋊D27112yes—
130SD16—5422no—
131SD16—5421no—
132SD16—10841no—
133D8—2711no—
134M16—2711no—
135M16—5421no—
136M16—5421no—
137C2×C8—5421no—
138C2×C8C22×D27111yescharacteristic
139C16—21no—
140C16—5421no—
141Q8—22no—
142Q8—41no—
143Q8—41no—
144Q8—41no—
145Q8—2711no—
146Q8—5421no—
147Q8—10842no—
148D4—2711no—
149D4—5421no—
150D4—5421no—
151D4—10842no—
152D4—10841no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—5421no—
156C2×C4—10842no—
157C2×C4—10842no—
158C2×C4—10841no—
159C2×C4D4×D27111yescharacteristic
160C8—5421no—
161C8—10841no—
162C8D4×D27111yescharacteristic
163C8C2×C22⋊D27111yescharacteristic
164C22—5421no—
165C22—10841no—
166C22#2257618411yescharacteristic
167C4—42no—
168C4—81no—
169C4—5421no—
170C4—10841no—
171C4#2257612811yescharacteristic
172C4D8×D27111yescharacteristic
173C2—21no—
174C2—10841no—
175C2—21681no—
176C2#3177402911yescharacteristic
subgroupG/H
centerC2#31774029
commutator, cosocleC2×C8×C271C23
FrattiniC2×C8C22×D271
FittingC2×Q32×C271C2
socleC2×C271#447
prime radical#31774710C2
hypercenterC2×Q32D271
hypocenterC271#2195
LCSG ▷ C2×C8×C271 ▷ C4×C271 ▷ C2×C271 ▷ C271
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q32

Complements

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

NH ≅ G/Ntype
2. #31774338C2semidirect
3. #31774169C2semidirect
4. #31773713C2semidirect
5. #31773705C2semidirect
6. #31773680C2semidirect
7. C2×Q32×C271C2semidirect
88. C271#2195semidirect
92. C2×Q32D271semidirect

Maximal subgroups

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

subgroupindex
#317747102
#317743382
#317741692
#317737132
#317737052
#317736802
C2×Q32×C2712
#2195271