Finite Group Databasebeta

← #46846656

Subgroups — #46846656

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#31774502C211yesmaximal, characteristic
2#31774374C211yesmaximal, characteristic, complemented
3#31774222C212yesmaximal, complemented
4#31774205C212yesmaximal, complemented
5#31774098C212yesmaximal, complemented
6#31774038C212yesmaximal, complemented
7#31773999C212yesmaximal, complemented
8C4×#16864643C212yesmaximal, complemented
9#433×C271C211yesmaximal, characteristic, complemented
10C22×Dic542C2211yescharacteristic
11C2×#16864643C2212yes—
12C2×#16864643C2212yes—
13#22576157C2211yescharacteristic
14#22576152C2211yescharacteristic
15#22576145—22no—
16#22576134C2212yes—
17#22576133—22no—
18C4×Dic542C2212yes—
19C4×Dic542C2212yes—
20#22576125—22no—
21C4×D1084C2212yes—
22#22576119C2211yescharacteristic
23#22576116—22no—
24#22576094C2212yes—
25#22576092C2212yes—
26#22576085C2212yes—
27#22576085C2212yes—
28#22576082C2212yes—
29#22576082C2212yes—
30#117×C271C2211yescharacteristic
31C4⋊C8×C271C2212yes—
32C22⋊C8×C271C2212yes—
33#97×C271C2211yescharacteristic
34C4×C8×C271C2211yescharacteristic
35C2×Dic542—24no—
36C2×Dic542—21no—
37C2×Dic542C2312yes—
38C2×D1084—22no—
39C2×D1084C2312yes—
40C2×C22⋊D271—22no—
41C22×Dic271—21no—
42C2×C4×D271—22no—
43#16864643—24no—
44#16864643—24no—
45C4⋊Dic271C2312yes—
46C4⋊Dic271C2312yes—
47Dic271⋊C4—22no—
48Dic271⋊C4—22no—
49Dic271⋊C4—22no—
50C22⋊Dic271—21no—
51(C2×D271)⋊C4—22no—
52(C2×D271)⋊C4—22no—
53C4×Dic271—22no—
54C4×Dic271—22no—
55C4×Dic271—21no—
56C22×C4×C271C2311yescharacteristic
57C2×C8×C271C2312yes—
58C2×C8×C271C2312yes—
59C4⋊C4×C271D412yes—
60C22⋊C4×C271D412yes—
61C42×C271C2311yescharacteristic
62C42×C271C2311yescharacteristic
63C22×D271—22no—
64Dic542—24no—
65Dic542—22no—
66Dic542#4114yes—
67D1084—22no—
68D1084—22no—
69D1084—82no—
70C22⋊D271—82no—
71C2×Dic271—24no—
72C2×Dic271—22no—
73C2×Dic271—22no—
74C2×Dic271—22no—
75C4×D271—82no—
76C23×C271C2×D411yescharacteristic
77C2×C4×C271—22no—
78C2×C4×C271C2×D412yes—
79C2×C4×C271C2×D412yes—
80C2×C4×C271C2×D411yescharacteristic
81C2×C4×C271C2411yescharacteristic
82C8×C271—22no—
83C8×C271—22no—
84C22×C271—21no—
85C22×C271—22no—
86C22×C271C22×D411yescharacteristic
87C2×D271—42no—
88C2×D271—42no—
89C2×D271—42no—
90C4×C271—21no—
91C4×C271—22no—
92C4×C271—22no—
93C4×C271C2×#4112yes—
94Dic271—24no—
95Dic271—42no—
96Dic271—42no—
97C2×C271—41no—
98C2×C271#52511yescharacteristic
99C2×C271#57712yes—
100D271—82no—
101C271#312611yescharacteristic, complemented, Sylow
102#3126—2711nomaximal, Sylow
103#540—2711no—
104#519—2711no—
105#482—2712no—
106#479—2712no—
107#460—2712no—
108#448—2712no—
109#440—2712no—
110C4×SD16—2712no—
111#433D27111yescharacteristic, complemented
112C22×Q8—2711no—
113C2×SD16—2712no—
114C2×SD16—2712no—
115#127—2711no—
116#125—2711no—
117#123—5422no—
118#121—2712no—
119#121—5422no—
120C4×Q8—2712no—
121C4×Q8—2712no—
122C4×Q8—5422no—
123C4×D4—2712no—
124#117—2711no—
125#117—5422no—
126#117C2×D27111yescharacteristic
127#107—2712no—
128#106—2712no—
129C4⋊C8C2×D27112yes—
130#103—2712no—
131#103—2712no—
132#102—2712no—
133#102—2712no—
134C22⋊C8C2×D27112yes—
135#97C2×D27111yescharacteristic
136C4×C8C2×D27111yescharacteristic
137C2×Q8—2712no—
138C2×Q8—5424no—
139C2×Q8—5421no—
140C2×D4—2712no—
141C2×D4—5422no—
142C2×D4—5422no—
143C22×C4—5421no—
144C22×C4—5422no—
145C22×C4C22×D27111yescharacteristic
146SD16—5424no—
147SD16—5424no—
148C2×C8C22×D27112yes—
149C2×C8C22×D27112yes—
150C4⋊C4—2712no—
151C4⋊C4—2712no—
152C4⋊C4—5422no—
153C4⋊C4—5422no—
154C4⋊C4—5422no—
155C4⋊C4D108412yes—
156C22⋊C4—5421no—
157C22⋊C4—5422no—
158C22⋊C4—5422no—
159C22⋊C4D108412yes—
160C42—5421no—
161C42—5422no—
162C42—5422no—
163C42C22×D27111yescharacteristic
164C42C22×D27111yescharacteristic
165C23—5422no—
166C23C2×D108411yescharacteristic
167Q8—2714no—
168Q8—5424no—
169Q8—5422no—
170D4—5422no—
171D4—5422no—
172D4—21682no—
173D4—21682no—
174C2×C4—22no—
175C2×C4—5424no—
176C2×C4—5422no—
177C2×C4—5422no—
178C2×C4—5422no—
179C2×C4—21682no—
180C2×C4C2×D108412yes—
181C2×C4C2×D108412yes—
182C2×C4C2×D108411yescharacteristic
183C2×C4C23×D27111yescharacteristic
184C8—22no—
185C8—22no—
186C22—21no—
187C22—22no—
188C22—10842no—
189C22—10842no—
190C22—10842no—
191C22C22×D108411yescharacteristic
192C4—21no—
193C4—22no—
194C4—22no—
195C4—5424no—
196C4—10842no—
197C4—10842no—
198C4#41×D27112yes—
199C2—41no—
200C2—21682no—
201C2#3177440911yescharacteristic
202C2#3177470912yes—
subgroupG/H
centerC22C22×D1084
commutator, cosocleC2×C4×C271C24
FrattiniC2×C4C23×D271
Fitting#433×C271C2
socleC22×C271C22×D4
prime radical#31774502C2
hypercenter#433D271
hypocenterC271#3126
LCSG ▷ C2×C4×C271 ▷ C2×C271 ▷ C271
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
2. #31774374C2semidirect
3. #31774222C2semidirect
4. #31774205C2semidirect
5. #31774098C2semidirect
6. #31774038C2semidirect
7. #31773999C2semidirect
8. C4×#16864643C2semidirect
9. #433×C271C2semidirect
101. C271#3126semidirect
111. #433D271semidirect

Maximal subgroups

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

subgroupindex
#317745022
#317743742
#317742222
#317742052
#317740982
#317740382
#317739992
C4×#168646432
#433×C2712
#3126271