Finite Group Databasebeta

← #46846650

Subgroups — #46846650

Order 34688.

382 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 121 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#31774374C211yesmaximal, characteristic, complemented
2#31774218C212yesmaximal, complemented
3#31774201C212yesmaximal, complemented
4#31774094C212yesmaximal, complemented
5#31774035C212yesmaximal, complemented
6#31773997C212yesmaximal, complemented
7C4×#16864642C212yesmaximal, complemented
8#31773958C211yesmaximal, characteristic, complemented
9#540×C271C211yesmaximal, characteristic
10C22×Dic542C2211yescharacteristic
11C2×#16864642C2212yes—
12C2×#16864642C2212yes—
13C4×Dic542C2212yes—
14C4×Dic542C2212yes—
15#22576125—22no—
16#22576119C2211yescharacteristic
17#22576116—22no—
18#22576093C2212yes—
19#22576091C2212yes—
20C4⋊(C271⋊C8)C2212yes—
21#22576083C2212yes—
22#22576083C2212yes—
23#22576081C2212yes—
24#22576081C2212yes—
25C22⋊(C271⋊C8)C2212yes—
26#22576071C2211yescharacteristic
27C4×C271⋊C8C2211yescharacteristic
28#127×C271C2211yescharacteristic
29#125×C271C2211yescharacteristic
30#123×C271—22no—
31#121×C271—22no—
32#121×C271C2212yes—
33C4×D4×C271C2212yes—
34#117×C271C2211yescharacteristic
35C2×Dic542—24no—
36C2×Dic542—21no—
37C2×Dic542C2312yes—
38C22×Dic271—21no—
39#16864642—24no—
40#16864642—24no—
41C2×C271⋊C8C2312yes—
42C2×C271⋊C8C2312yes—
43C4⋊Dic271C2312yes—
44Dic271⋊C4—22no—
45Dic271⋊C4—22no—
46C22⋊Dic271—21no—
47C4×Dic271—22no—
48C4×Dic271—22no—
49C4×Dic271—21no—
50C2×D4×C271—22no—
51C2×D4×C271—22no—
52C2×D4×C271C2312yes—
53C22×C4×C271—22no—
54C22×C4×C271C2311yescharacteristic
55C4⋊C4×C271—22no—
56C4⋊C4×C271D412yes—
57C4⋊C4×C271C2312yes—
58C22⋊C4×C271—22no—
59C22⋊C4×C271—22no—
60C22⋊C4×C271D412yes—
61C42×C271C2311yescharacteristic
62C42×C271C2311yescharacteristic
63Dic542—24no—
64Dic542—22no—
65Dic542#4114yes—
66C2×Dic271—24no—
67C2×Dic271—22no—
68C2×Dic271—22no—
69C271⋊C8—22no—
70C271⋊C8—22no—
71C23×C271—22no—
72C23×C271C2×D411yescharacteristic
73D4×C271—22no—
74D4×C271—22no—
75D4×C271—82no—
76D4×C271—82no—
77C2×C4×C271—22no—
78C2×C4×C271—22no—
79C2×C4×C271—82no—
80C2×C4×C271C2×D412yes—
81C2×C4×C271C2×D412yes—
82C2×C4×C271C2×D411yescharacteristic
83C2×C4×C271C2411yescharacteristic
84C22×C271—21no—
85C22×C271—22no—
86C22×C271—42no—
87C22×C271—42no—
88C22×C271—42no—
89C22×C271C22×D411yescharacteristic
90C4×C271—21no—
91C4×C271—22no—
92C4×C271—22no—
93C4×C271—42no—
94C4×C271C2×#4112yes—
95Dic271—24no—
96Dic271—42no—
97C2×C271—41no—
98C2×C271—82no—
99C2×C271#52511yescharacteristic
100C2×C271#57712yes—
101C271#312611yescharacteristic, complemented, Sylow
102#3126—2711nomaximal, Sylow
103#540D27111yescharacteristic
104#519—2711no—
105#482—2712no—
106#479—2712no—
107#460—2712no—
108#448—2712no—
109#440—2712no—
110C4×SD16—2712no—
111#433—2711no—
112C22×Q8—2711no—
113C2×SD16—2712no—
114C2×SD16—2712no—
115#127C2×D27111yescharacteristic
116#125C2×D27111yescharacteristic
117#123—22no—
118#121—22no—
119#121C2×D27112yes—
120C4×Q8—2712no—
121C4×Q8—2712no—
122C4×Q8—5422no—
123C4×D4C2×D27112yes—
124#117—2711no—
125#117—5422no—
126#117C2×D27111yescharacteristic
127#107—2712no—
128#106—2712no—
129C4⋊C8—2712no—
130#103—2712no—
131#103—2712no—
132#102—2712no—
133#102—2712no—
134C22⋊C8—2712no—
135#97—2711no—
136C4×C8—2711no—
137C2×Q8—2712no—
138C2×Q8—5424no—
139C2×Q8—5421no—
140C2×D4—22no—
141C2×D4—22no—
142C2×D4C22×D27112yes—
143C22×C4—22no—
144C22×C4—5421no—
145C22×C4C22×D27111yescharacteristic
146SD16—5424no—
147SD16—5424no—
148C2×C8—2712no—
149C2×C8—2712no—
150C4⋊C4—22no—
151C4⋊C4—2712no—
152C4⋊C4—5422no—
153C4⋊C4—5422no—
154C4⋊C4C22⋊D27112yes—
155C4⋊C4C22×D27112yes—
156C22⋊C4—22no—
157C22⋊C4—22no—
158C22⋊C4—5421no—
159C22⋊C4C22⋊D27112yes—
160C42—5421no—
161C42—5422no—
162C42—5422no—
163C42C22×D27111yescharacteristic
164C42C22×D27111yescharacteristic
165C23—22no—
166C23C2×C22⋊D27111yescharacteristic
167Q8—2714no—
168Q8—5424no—
169Q8—5422no—
170D4—22no—
171D4—22no—
172D4—82no—
173D4—82no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—82no—
177C2×C4—5424no—
178C2×C4—5422no—
179C2×C4—5422no—
180C2×C4C2×C22⋊D27112yes—
181C2×C4C2×C22⋊D27112yes—
182C2×C4C2×C22⋊D27111yescharacteristic
183C2×C4C23×D27111yescharacteristic
184C8—5422no—
185C8—5422no—
186C22—21no—
187C22—22no—
188C22—42no—
189C22—42no—
190C22—42no—
191C22C22×C22⋊D27111yescharacteristic
192C4—21no—
193C4—22no—
194C4—22no—
195C4—42no—
196C4—5424no—
197C4—10842no—
198C4#41×D27112yes—
199C2—41no—
200C2—82no—
201C2#3177440411yescharacteristic
202C2#3177470812yes—
subgroupG/H
centerC22C22×C22⋊D271
commutator, cosocleC2×C4×C271C24
FrattiniC2×C4C23×D271
Fitting, prime radical#540×C271C2
socleC22×C271C22×D4
hypercenter#540D271
hypocenterC271#3126
LCSG ▷ C2×C4×C271 ▷ C2×C271 ▷ C271
UCSC1 ◁ C22 ◁ #117 ◁ #540

Complements

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

NH ≅ G/Ntype
1. #31774374C2semidirect
2. #31774218C2semidirect
3. #31774201C2semidirect
4. #31774094C2semidirect
5. #31774035C2semidirect
6. #31773997C2semidirect
7. C4×#16864642C2semidirect
8. #31773958C2semidirect
101. C271#3126semidirect

Maximal subgroups

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

subgroupindex
#317743742
#317742182
#317742012
#317740942
#317740352
#317739972
C4×#168646422
#317739582
#540×C2712
#3126271