Finite Group Databasebeta

← #46838050

Subgroups — #46838050

Order 34688.

230 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 55 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#31774467C211yesmaximal, characteristic
2#101×D271C212yesmaximal, complemented
3#31773695C212yesmaximal, complemented
4#31773694C211yesmaximal, characteristic, complemented
5#355×C271C211yesmaximal, characteristic, complemented
6C2×#16864653C411yescharacteristic
7C2×Q8×D271C2211yescharacteristic
8M16×D271—22no—
9#22576160C411yescharacteristic
10#22576158C2211yescharacteristic
11#22576147C411yescharacteristic
12#22576142—22no—
13#22576137—22no—
14#22576117C411yescharacteristic
15#22576079C2212yes—
16#22576078—22no—
17#124×C271C2211yescharacteristic
18#101×C271C2212yes—
19#16864653—42no—
20C2×Dic542C2×C411yescharacteristic
21C2×Dic542C2×C411yescharacteristic
22C2×Dic542D412yes—
23Q8×D271—42no—
24C2×C22⋊D271—21no—
25C22×Dic271—21no—
26C2×C4×D271C2×C411yescharacteristic
27C2×C4×D271D412yes—
28#16864638—22no—
29#16864637—42no—
30C8×D271—42no—
31C4⋊Dic271—22no—
32Dic271⋊C4—21no—
33Dic271⋊C4—22no—
34C22⋊Dic271—22no—
35(C2×D271)⋊C4—21no—
36C4×Dic271C2×C411yescharacteristic
37C2×Q8×C271C2311yescharacteristic
38C2×D4×C271C2×C411yescharacteristic
39M16×C271—22no—
40C22⋊C4×C271—22no—
41C42×C271C2×C411yescharacteristic
42C22×D271C22⋊C411yescharacteristic
43Dic542—41no—
44Dic542—42no—
45Dic542—41no—
46C22⋊D271—42no—
47C2×Dic271—21no—
48C2×Dic271—21no—
49C2×Dic271—42no—
50C2×Dic271C22⋊C412yes—
51C2×Dic271C22⋊C411yescharacteristic
52C4×D271—22no—
53C4×D271—22no—
54C4×D271—22no—
55C271⋊C8—42no—
56C23×C271—21no—
57Q8×C271—41no—
58D4×C271—41no—
59C2×C4×C271—21no—
60C2×C4×C271C22×C411yescharacteristic
61C2×C4×C271C2×D412yes—
62C8×C271—42no—
63C22×C271—42no—
64C22×C271—41no—
65C22×C271C2×C22⋊C411yescharacteristic
66C2×D271—41no—
67C2×D271#9912yes—
68C4×C271—22no—
69C4×C271—21no—
70C4×C271—41no—
71Dic271—21no—
72Dic271—22no—
73Dic271—41no—
74Dic271—41no—
75C2×C271—21no—
76C2×C271—81no—
77C2×C271C2×#9911yescharacteristic
78D271—22no—
79C271#213311yescharacteristic, complemented, Sylow
80#2133—2711nomaximal, Sylow
81#536—2711no—
82C2×#101—2712no—
83#356—2712no—
84#355—2711no—
85#355D27111yescharacteristic, complemented
86C2×#41—2711no—
87C22×Q8—2711no—
88C2×M16—5422no—
89C4⋊Q8—2711no—
90C4⋊Q8—2711no—
91#124—2711no—
92#124C2×D27111yescharacteristic
93#123—5422no—
94C22⋊Q8—5422no—
95#117—2711no—
96#101—2712no—
97#101—5422no—
98#101C2×D27112yes—
99#41—10842no—
100C2×Q8—2711no—
101C2×Q8—2712no—
102C2×Q8—2711no—
103C2×Q8—10842no—
104C2×Q8C22×D27111yescharacteristic
105C2×D4—5421no—
106C2×D4C4×D27111yescharacteristic
107C22×C4—2711no—
108C22×C4—2712no—
109C22×C4—5421no—
110M16—22no—
111M16—5422no—
112M16—10842no—
113C2×C8—10842no—
114C4⋊C4—5421no—
115C4⋊C4—5422no—
116C4⋊C4—5422no—
117C22⋊C4—22no—
118C22⋊C4—5421no—
119C22⋊C4—5422no—
120C42—2711no—
121C42C4×D27111yescharacteristic
122C23—21no—
123C23—2711no—
124Q8—41no—
125Q8—10842no—
126Q8—10841no—
127Q8—10841no—
128D4—41no—
129D4—10842no—
130C2×C4—21no—
131C2×C4—2712no—
132C2×C4—2711no—
133C2×C4—5422no—
134C2×C4—5422no—
135C2×C4—5422no—
136C2×C4—5421no—
137C2×C4—5421no—
138C2×C4—10842no—
139C2×C4C2×C4×D27111yescharacteristic
140C2×C4D4×D27112yes—
141C8—42no—
142C8—10842no—
143C22—42no—
144C22—41no—
145C22—2712no—
146C22—10841no—
147C22C22⋊C4×D27111yescharacteristic
148C4—22no—
149C4—21no—
150C4—41no—
151C4—5421no—
152C4—5422no—
153C4—10841no—
154C4—10841no—
155C2—21no—
156C2—81no—
157C2—5422no—
158C2#99×D27111yescharacteristic
subgroupG/H
centerC2#99×D271
commutatorC2×C4×C271C22×C4
FrattiniC2×Q8C22×D271
Fitting#355×C271C2
socleC2×C271C2×#99
prime radicalC2×#16864653C4
cosocleC2×Q8×C271C23
hypercenter#355D271
hypocenterC271#2133
LCSG ▷ C2×C4×C271 ▷ C22×C271 ▷ C2×C271 ▷ C271
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #355

Complements

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

NH ≅ G/Ntype
2. #101×D271C2semidirect
3. #31773695C2semidirect
4. #31773694C2semidirect
5. #355×C271C2semidirect
79. C271#2133semidirect
85. #355D271semidirect

Maximal subgroups

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

subgroupindex
#317744672
#101×D2712
#317736952
#317736942
#355×C2712
#2133271