Finite Group Databasebeta

← #46834997

Subgroups — #46834997

Order 34688.

238 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 59 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#31774446C211yesmaximal, characteristic
2#31773952C212yesmaximal, complemented
3#31773637C211yesmaximal, characteristic, complemented
4#31773636C212yesmaximal, complemented
5#329×C271C211yesmaximal, characteristic, complemented
6C2×#16864655C411yescharacteristic
7C2×#16864653C411yescharacteristic
8#22576158C411yescharacteristic
9#22576156C411yescharacteristic
10#22576148C2211yescharacteristic
11#22576133—22no—
12(C22⋊D271)⋊C4—22no—
13C42×D271C2211yescharacteristic
14Dic271⋊C8—22no—
15(C2×D271)⋊C8—22no—
16#22576071C2212yes—
17#124×C271C2211yescharacteristic
18#97×C271C2212yes—
19#16864655—42no—
20#16864653—42no—
21C2×Dic542C2×C411yescharacteristic
22C2×D1084—21no—
23C2×D1084C2×C411yescharacteristic
24C2×C22⋊D271—21no—
25C2×C22⋊D271—22no—
26C22×Dic271—21no—
27C2×C4×D271—21no—
28C2×C4×D271C2×C411yescharacteristic
29C2×C4×D271D412yes—
30C2×C271⋊C8—22no—
31Dic271⋊C4—22no—
32(C2×D271)⋊C4—22no—
33C4×Dic271C2×C411yescharacteristic
34C4×Dic271D412yes—
35C2×Q8×C271C2×C411yescharacteristic
36C2×D4×C271C2×C411yescharacteristic
37C2×C8×C271—22no—
38C22⋊C4×C271—22no—
39C42×C271C2311yescharacteristic
40C22×D271—21no—
41C22×D271C22⋊C411yescharacteristic
42Dic542—41no—
43D1084—41no—
44D1084—42no—
45C22⋊D271—44no—
46C22⋊D271—42no—
47C2×Dic271—21no—
48C2×Dic271—42no—
49C2×Dic271C22⋊C412yes—
50C2×Dic271C22⋊C411yescharacteristic
51C4×D271—22no—
52C4×D271—42no—
53C4×D271—42no—
54C271⋊C8—42no—
55C23×C271—21no—
56Q8×C271—41no—
57D4×C271—41no—
58C2×C4×C271—21no—
59C2×C4×C271C22×C411yescharacteristic
60C2×C4×C271C2×D412yes—
61C8×C271—42no—
62C22×C271—41no—
63C22×C271—42no—
64C22×C271C2×C22⋊C411yescharacteristic
65C2×D271—21no—
66C2×D271—22no—
67C2×D271—41no—
68C2×D271—42no—
69C4×C271—21no—
70C4×C271—22no—
71C4×C271—41no—
72Dic271—22no—
73Dic271—41no—
74Dic271#10012yes—
75C2×C271—81no—
76C2×C271C2×#10011yescharacteristic
77C2×C271#42112yes—
78D271—41no—
79D271—81no—
80C271#153611yescharacteristic, complemented, Sylow
81#1536—2711nomaximal, Sylow
82#532—2711no—
83#432—2712no—
84#329—2711no—
85#329—2712no—
86#329D27111yescharacteristic, complemented
87C2×#41—2711no—
88C2×#41—2711no—
89C4⋊Q8—2711no—
90#127—2711no—
91#124—2711no—
92#124C2×D27111yescharacteristic
93#121—5422no—
94C4×D4—5422no—
95C2×C42—2711no—
96C4⋊C8—5422no—
97C22⋊C8—5422no—
98#97—2712no—
99#97C2×D27112yes—
100#41—10842no—
101#41—10842no—
102C2×Q8—2711no—
103C2×Q8C4×D27111yescharacteristic
104C2×D4—2711no—
105C2×D4—5421no—
106C2×D4—5422no—
107C2×D4—5421no—
108C2×D4C4×D27111yescharacteristic
109C22×C4—2711no—
110C22×C4—2712no—
111C22×C4—5421no—
112C22×C4—5421no—
113C2×C8—22no—
114C2×C8—5422no—
115C4⋊C4—5422no—
116C22⋊C4—22no—
117C22⋊C4—5422no—
118C42—2711no—
119C42—2712no—
120C42C22×D27111yescharacteristic
121C23—21no—
122C23—2711no—
123C23—5421no—
124Q8—41no—
125Q8—10841no—
126D4—41no—
127D4—10841no—
128D4—10842no—
129D4—10844no—
130D4—10842no—
131C2×C4—21no—
132C2×C4—2711no—
133C2×C4—2712no—
134C2×C4—5422no—
135C2×C4—5421no—
136C2×C4—10842no—
137C2×C4—10842no—
138C2×C4—10842no—
139C2×C4C2×C4×D27111yescharacteristic
140C2×C4D4×D27112yes—
141C8—42no—
142C8—10842no—
143C22—41no—
144C22—42no—
145C22—5421no—
146C22—5422no—
147C22—10841no—
148C22—10842no—
149C22C22⋊C4×D27111yescharacteristic
150C4—21no—
151C4—22no—
152C4—41no—
153C4—2712no—
154C4—5422no—
155C4—10841no—
156C2—81no—
157C2—10841no—
158C2—21681no—
159C2#100×D27111yescharacteristic
160C2#3177391212yes—
subgroupG/H
centerC22C22⋊C4×D271
commutatorC2×C4×C271C22×C4
FrattiniC42C22×D271
Fitting#329×C271C2
socleC22×C271C2×C22⋊C4
prime radical#31774446C2
cosocleC42×C271C23
hypercenter#329D271
hypocenterC271#1536
LCSG ▷ C2×C4×C271 ▷ C22×C271 ▷ C271
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #31773952C2semidirect
3. #31773637C2semidirect
4. #31773636C2semidirect
5. #329×C271C2semidirect
80. C271#1536semidirect
86. #329D271semidirect

Maximal subgroups

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

subgroupindex
#317744462
#317739522
#317736372
#317736362
#329×C2712
#1536271