Finite Group Databasebeta

← #49095687

Subgroups — #49095687

Order 35968.

332 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 93 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#31824230C211yesmaximal, characteristic, complemented
2#31823480C212yesmaximal, complemented
3#31823437C211yesmaximal, characteristic, complemented
4#31823223C212yesmaximal, complemented
5#532×C281C211yesmaximal, characteristic
6#22582886—24no—
7C2×#17985122—22no—
8C2×#17985122C2212yes—
9#22582838C2212yes—
10#22582806—24no—
11#22582794—22no—
12C2×#41×C281C2211yescharacteristic
13C2×#41×C281C2211yescharacteristic
14C4⋊Q8×C281C411yescharacteristic, complemented
15#127×C281C411yescharacteristic, complemented
16#124×C281C411yescharacteristic, complemented
17#124×C281C411yescharacteristic, complemented
18#121×C281—22no—
19C4×D4×C281—22no—
20C2×C42×C281C2211yescharacteristic
21#17985122—24no—
22#17985122—22no—
23#17985122D414yescomplemented
24C2×#14555886—24no—
25C2×#14555886—22no—
26C4⋊Dic281—22no—
27C22⋊Dic281—22no—
28C4×Dic281—22no—
29#41×C281—22no—
30#41×C281—22no—
31#41×C281—22no—
32#41×C281—22no—
33C2×Q8×C281C2×C411yescharacteristic
34C2×Q8×C281C2×C411yescharacteristic
35C2×D4×C281—22no—
36C2×D4×C281—21no—
37C2×D4×C281C2×C411yescharacteristic
38C2×D4×C281C2×C411yescharacteristic
39C2×D4×C281D412yes—
40C22×C4×C281—21no—
41C22×C4×C281—21no—
42C22×C4×C281D412yes—
43C22×C4×C281C2311yescharacteristic
44C4⋊C4×C281—22no—
45C22⋊C4×C281—22no—
46C22⋊C4×C281—22no—
47C42×C281—21no—
48C42×C281C2×C411yescharacteristic
49C42×C281C2×C411yescharacteristic
50C2×Dic281—42no—
51#14555886—24no—
52C23×C281—21no—
53C23×C281C22⋊C412yes—
54C23×C281C2×D411yescharacteristic
55Q8×C281—22no—
56Q8×C281—22no—
57D4×C281—24no—
58D4×C281—22no—
59D4×C281—22no—
60D4×C281—44no—
61D4×C281—42no—
62C2×C4×C281—21no—
63C2×C4×C281—22no—
64C2×C4×C281—22no—
65C2×C4×C281—21no—
66C2×C4×C281—21no—
67C2×C4×C281—42no—
68C2×C4×C281—41no—
69C2×C4×C281—41no—
70C2×C4×C281C22⋊C412yes—
71C2×C4×C281C22×C411yescharacteristic
72C2×C4×C281C2×D412yes—
73C2×C4×C281C2×D411yescharacteristic
74C2×C4×C281#4112yes—
75C22×C281—22no—
76C22×C281—41no—
77C22×C281—42no—
78C22×C281—42no—
79C22×C281—41no—
80C22×C281C2×C22⋊C411yescharacteristic
81C22×C281#12112yes—
82C4×C281—22no—
83C4×C281—22no—
84C4×C281—41no—
85C4×C281—41no—
86C4×C281C4×D412yes—
87C4×C281#12011yescharacteristic
88C4×C281#12311yescharacteristic
89Dic281—82no—
90C2×C281—22no—
91C2×C281—21no—
92C2×C281—42no—
93C2×C281—81no—
94C2×C281#38611yescharacteristic
95C281#188411yescharacteristic, complemented, Sylow
96#1884—2811nomaximal, Sylow
97#568—2811no—
98#532D28111yescharacteristic
99#421—2812no—
100#410—2811no—
101#339—2812no—
102C2×#41C2×D28111yescharacteristic
103C2×#41C2×D28111yescharacteristic
104#131—5624no—
105C2×M16—2812no—
106C2×M16—5622no—
107C4⋊Q8Dic28111yescharacteristic, complemented
108#127Dic28111yescharacteristic, complemented
109#124Dic28111yescharacteristic, complemented
110#124Dic28111yescharacteristic, complemented
111#121—22no—
112C4×D4—22no—
113#117—2812no—
114C2×C42C2×D28111yescharacteristic
115#104—5624no—
116#99—5622no—
117#41—22no—
118#41—22no—
119#41—22no—
120#41—22no—
121C2×Q8C2×Dic28111yescharacteristic
122C2×Q8C2×Dic28111yescharacteristic
123C2×D4—22no—
124C2×D4—21no—
125C2×D4C2×Dic28111yescharacteristic
126C2×D4C2×Dic28111yescharacteristic
127C2×D4C22⋊D28112yes—
128C22×C4—21no—
129C22×C4—21no—
130C22×C4C22⋊D28112yes—
131C22×C4C22×D28111yescharacteristic
132M16—2814no—
133M16—5624no—
134M16—5622no—
135C2×C8—5624no—
136C2×C8—5622no—
137C4⋊C4—22no—
138C4⋊C4—5622no—
139C22⋊C4—22no—
140C22⋊C4—22no—
141C22⋊C4—5622no—
142C42—21no—
143C42—5622no—
144C42C2×Dic28111yescharacteristic
145C42C2×Dic28111yescharacteristic
146C23—21no—
147C23C22⋊Dic28112yes—
148C23C2×C22⋊D28111yescharacteristic
149Q8—22no—
150Q8—22no—
151D4—24no—
152D4—22no—
153D4—22no—
154D4—44no—
155D4—42no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—42no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—11242no—
165C2×C4C22⋊Dic28112yes—
166C2×C4C22×Dic28111yescharacteristic
167C2×C4D4×D28112yes—
168C2×C4C2×C22⋊D28111yescharacteristic
169C2×C4#1798513712yes—
170C8—5624no—
171C22—22no—
172C22—41no—
173C22—42no—
174C22—42no—
175C22—41no—
176C22C2×C22⋊Dic28111yescharacteristic
177C22#2258285112yes—
178C4—22no—
179C4—22no—
180C4—41no—
181C4—41no—
182C4—22482no—
183C4D4×Dic28112yes—
184C4#2258284711yescharacteristic
185C4#2258286011yescharacteristic
186C2—21no—
187C2—22no—
188C2—42no—
189C2—81no—
190C2#3182334311yescharacteristic
subgroupG/H
centerC4#22582847
commutatorC2×C4×C281C22×C4
FrattiniC22×C4C22×D281
Fitting, prime radical#532×C281C2
socleC2×C281#386
cosocleC22×C4×C281C23
hypercenter#532D281
hypocenterC281#1884
LCSG ▷ C2×C4×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C4 ◁ C22×C4 ◁ #532

Complements

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

NH ≅ G/Ntype
1. #31824230C2semidirect
2. #31823480C2semidirect
3. #31823437C2semidirect
4. #31823223C2semidirect
14. C4⋊Q8×C281C4semidirect
15. #127×C281C4semidirect
16. #124×C281C4semidirect
17. #124×C281C4semidirect
23. #17985122D4semidirect
95. C281#1884semidirect
107. C4⋊Q8Dic281semidirect
108. #127Dic281semidirect
109. #124Dic281semidirect
110. #124Dic281semidirect

Maximal subgroups

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

subgroupindex
#318242302
#318234802
#318234372
#318232232
#532×C2812
#1884281