Finite Group Databasebeta

← #49095695

Subgroups — #49095695

Order 35968.

324 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 83 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
1C2×#22582879C211yesmaximal, characteristic
2#31823940C211yesmaximal, characteristic
3#31823473C211yesmaximal, characteristic
4#31823471C211yesmaximal, characteristic
5C2×#22582797C211yesmaximal, characteristic
6#31823223C211yesmaximal, characteristic
7#339×C281C211yesmaximal, characteristic
8C22×Dic562C2211yescharacteristic
9C22×Dic562C2211yescharacteristic
10C2×#17985122C2211yescharacteristic
11#22582879—22no—
12#22582879C414yescomplemented
13C4×Dic562—22no—
14#22582844—22no—
15#22582838C2211yescharacteristic
16#22582835—22no—
17C2×C4⋊Dic281—22no—
18#22582804—22no—
19#22582802—22no—
20#22582797—22no—
21C2×M16×C281C2211yescharacteristic
22#117×C281C2211yescharacteristic
23C2×C42×C281C2211yescharacteristic
24C2×Dic562—21no—
25C2×Dic562—21no—
26C2×Dic562—21no—
27C2×Dic562—21no—
28C2×Dic562—21no—
29C2×Dic562—21no—
30C2×Dic562—21no—
31C2×Dic562—21no—
32C2×Dic562—21no—
33C2×Dic562C2×C412yes—
34C2×Dic562C2×C412yes—
35C2×Dic562D412yes—
36C22×Dic281—21no—
37C22×Dic281D412yes—
38#17985122—21no—
39#17985122—21no—
40C2×#14555886—21no—
41C4⋊Dic281—28no—
42C4⋊Dic281D412yes—
43#17985117—24no—
44C22⋊Dic281—21no—
45C4×Dic281—24no—
46C4×Dic281—21no—
47C22×C4×C281—21no—
48C22×C4×C281C2311yescharacteristic
49M16×C281—21no—
50M16×C281—21no—
51C2×C8×C281—21no—
52C4⋊C4×C281D412yes—
53C22⋊C4×C281—21no—
54C42×C281—21no—
55C42×C281—21no—
56C42×C281C2×C412yes—
57Dic562—22no—
58Dic562—22no—
59Dic562—22no—
60Dic562—22no—
61Dic562—22no—
62Dic562—22no—
63Dic562—41no—
64Dic562—41no—
65C2×Dic281—22no—
66C2×Dic281—22no—
67C2×Dic281—22no—
68C2×Dic281—22no—
69C2×Dic281—41no—
70C2×Dic281—41no—
71C2×Dic281C22⋊C414yes—
72#14555886—41no—
73C23×C281C2×D411yescharacteristic
74C2×C4×C281—24no—
75C2×C4×C281—22no—
76C2×C4×C281—22no—
77C2×C4×C281C22×C411yescharacteristic
78C2×C4×C281C2×D411yescharacteristic
79C2×C4×C281C2×D411yescharacteristic
80C2×C4×C281C2×D411yescharacteristic
81C2×C4×C281#4111yescharacteristic
82C2×C4×C281#4111yescharacteristic
83C8×C281—41no—
84C22×C281—22no—
85C22×C281C2×C22⋊C411yescharacteristic
86C22×C281#12011yescharacteristic
87C22×C281#12311yescharacteristic
88C4×C281—24no—
89C4×C281—42no—
90C4×C281C4×D411yescharacteristic
91C4×C281C4×D411yescharacteristic
92C4×C281#12111yescharacteristic
93C4×C281#12111yescharacteristic
94Dic281—24no—
95Dic281—42no—
96Dic281—42no—
97C2×C281—21no—
98C2×C281—21no—
99C2×C281#38611yescharacteristic
100C2×C281#45612yes—
101C281#188611yescharacteristic, complemented, Sylow
102#1886—2811nomaximal, Sylow
103C2×C4⋊Q8—2811no—
104#519—2811no—
105#419—2811no—
106#419—2811no—
107C2×#101—2811no—
108#339—2811no—
109#339D28111yescharacteristic
110C22×Q8—2811no—
111C22×Q8—2811no—
112C2×M16—2811no—
113C2×M16C2×D28111yescharacteristic
114C4⋊Q8—2814no—
115C4⋊Q8—5622no—
116C4×Q8—5622no—
117C4×Q8—5622no—
118#117—2811no—
119#117—5622no—
120#117C2×D28111yescharacteristic
121C2×C4⋊C4—5622no—
122C2×C42C2×D28111yescharacteristic
123#103—5622no—
124#103—5622no—
125#101—5622no—
126C2×Q8—2812no—
127C2×Q8—2812no—
128C2×Q8—2812no—
129C2×Q8—5621no—
130C2×Q8—5621no—
131C2×Q8—5621no—
132C2×Q8—5621no—
133C2×Q8—5621no—
134C2×Q8—5621no—
135C2×Q8—5621no—
136C2×Q8—5621no—
137C2×Q8—5621no—
138C22×C4—21no—
139C22×C4—2812no—
140C22×C4—5621no—
141C22×C4C22×D28111yescharacteristic
142M16—21no—
143M16—21no—
144M16—5621no—
145M16—5621no—
146C2×C8—21no—
147C2×C8—5621no—
148C4⋊C4—2812no—
149C4⋊C4—5628no—
150C4⋊C4—5624no—
151C4⋊C4D112412yes—
152C22⋊C4—21no—
153C22⋊C4—5621no—
154C42—21no—
155C42—21no—
156C42—5624no—
157C42—5621no—
158C42C4×D28112yes—
159C23D4×D28111yescharacteristic
160Q8—5622no—
161Q8—5622no—
162Q8—5622no—
163Q8—5622no—
164Q8—5622no—
165Q8—5622no—
166Q8—11241no—
167Q8—11241no—
168C2×C4—24no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—2814no—
172C2×C4—5622no—
173C2×C4—5622no—
174C2×C4—5622no—
175C2×C4—5622no—
176C2×C4—11241no—
177C2×C4—11241no—
178C2×C4C2×C4×D28111yescharacteristic
179C2×C4D4×D28111yescharacteristic
180C2×C4D4×D28111yescharacteristic
181C2×C4C2×D112411yescharacteristic
182C2×C4#1798513811yescharacteristic
183C2×C4#1798513911yescharacteristic
184C8—41no—
185C8—11241no—
186C22—22no—
187C22C22⋊C4×D28111yescharacteristic
188C22#2258284911yescharacteristic
189C22#2258286411yescharacteristic
190C4—24no—
191C4—42no—
192C4—5624no—
193C4—11242no—
194C4—11242no—
195C4#2258284111yescharacteristic
196C4C4×D112411yescharacteristic
197C4#2258285211yescharacteristic
198C4#2258285411yescharacteristic
199C2—21no—
200C2—21no—
201C2#3182334111yescharacteristic
202C2#3182364712yes—
subgroupG/H
centerC22#22582849
commutatorC2×C4×C281C22×C4
FrattiniC22×C4C22×D281
Fitting#339×C281C2
socleC22×C281#120
prime radicalC23×C281C2×D4
cosocleC22×C4×C281C23
hypercenter#339D281
hypocenterC281#1886
LCSG ▷ C2×C4×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
12. #22582879C4semidirect
101. C281#1886semidirect

Maximal subgroups

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

subgroupindex
C2×#225828792
#318239402
#318234732
#318234712
C2×#225827972
#318232232
#339×C2812
#1886281