Finite Group Databasebeta

← #49096976

Subgroups — #49096976

Order 35968.

238 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 55 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#31824033C211yesmaximal, characteristic
2#31823435C212yesmaximal
3#31823258C211yesmaximal, characteristic, complemented
4#31823257C212yesmaximal, complemented
5#354×C281C211yesmaximal, characteristic, complemented
6C2×#17985137C2211yescharacteristic
7C2×Q8×D281C411yescharacteristic, complemented
8#22582879C411yescharacteristic, complemented
9#22582877C411yescharacteristic, complemented
10#22582866C2211yescharacteristic
11#22582861—22no—
12#22582856—22no—
13#22582836C411yescharacteristic, complemented
14#22582835—22no—
15#22582794C2212yes—
16#22582793—22no—
17#124×C281C2211yescharacteristic
18#99×C281C2212yes—
19#17985137—42no—
20C2×Dic562—21no—
21C2×Dic562C2×C411yescharacteristic
22C2×Dic562C2×C411yescharacteristic
23Q8×D281—42no—
24C2×C22⋊D281D412yes—
25C22×Dic281D412yes—
26C2×C4×D281—21no—
27C2×C4×D281C2×C411yescharacteristic
28C4⋊Dic281—22no—
29#17985117—21no—
30#17985117—22no—
31#17985117—42no—
32C22⋊Dic281—22no—
33C22⋊Dic281—22no—
34#17985115—21no—
35C4×Dic281—42no—
36C4×Dic281C2×C411yescharacteristic
37C2×Q8×C281C2×C411yescharacteristic
38C2×D4×C281C2311yescharacteristic
39C22⋊C4×C281—22no—
40C22⋊C4×C281—22no—
41C42×C281C2×C411yescharacteristic
42C22×D281C22⋊C411yescharacteristic
43Dic562—41no—
44Dic562—42no—
45Dic562—41no—
46C22⋊D281—42no—
47C2×Dic281—22no—
48C2×Dic281—22no—
49C2×Dic281—21no—
50C2×Dic281—21no—
51C2×Dic281—42no—
52C2×Dic281C22⋊C412yes—
53C2×Dic281C22⋊C411yescharacteristic
54C4×D281—22no—
55C4×D281—42no—
56C23×C281C2×D412yes—
57Q8×C281—41no—
58D4×C281—41no—
59C2×C4×C281—21no—
60C2×C4×C281—21no—
61C2×C4×C281—42no—
62C2×C4×C281C22×C411yescharacteristic
63C22×C281—22no—
64C22×C281—42no—
65C22×C281C2×C22⋊C411yescharacteristic
66C2×D281—21no—
67C2×D281—41no—
68C4×C281—21no—
69C4×C281—41no—
70C4×C281—41no—
71C4×C281—82no—
72Dic281—22no—
73Dic281—41no—
74Dic281—41no—
75Dic281—82no—
76Dic281#9912yes—
77C2×C281—21no—
78C2×C281—42no—
79C2×C281C2×#9911yescharacteristic
80D281—41no—
81C281#212911yescharacteristic, complemented, Sylow
82#2129—2811nomaximal, Sylow
83#536—2811no—
84#410—2812no—
85#354—2811no—
86#354—2812no—
87#354D28111yescharacteristic, complemented
88C2×#41—2811no—
89C22×Q8—2811no—
90C4⋊Q8—2811no—
91C4⋊Q8—2811no—
92#124—2811no—
93#124C2×D28111yescharacteristic
94#123—5622no—
95C22⋊Q8—5622no—
96#117—2811no—
97#117—5622no—
98#99—2812no—
99#99—5622no—
100#99C2×D28112yes—
101#41—11242no—
102C2×Q8—2811no—
103C2×Q8—2811no—
104C2×Q8—5621no—
105C2×Q8—11242no—
106C2×Q8C4×D28111yescharacteristic
107C2×D4—2812no—
108C2×D4C22×D28111yescharacteristic
109C22×C4—2812no—
110C22×C4—2811no—
111C22×C4—5621no—
112C4⋊C4—5621no—
113C4⋊C4—5622no—
114C4⋊C4—5622no—
115C4⋊C4—11242no—
116C22⋊C4—22no—
117C22⋊C4—22no—
118C22⋊C4—5621no—
119C22⋊C4—5622no—
120C22⋊C4—5622no—
121C42—2811no—
122C42—11242no—
123C42C4×D28111yescharacteristic
124C23—2811no—
125C23D4×D28112yes—
126Q8—41no—
127Q8—11241no—
128Q8—11241no—
129Q8—11242no—
130D4—41no—
131D4—11242no—
132C2×C4—21no—
133C2×C4—21no—
134C2×C4—42no—
135C2×C4—2811no—
136C2×C4—2812no—
137C2×C4—5622no—
138C2×C4—5622no—
139C2×C4—5622no—
140C2×C4—5621no—
141C2×C4—5621no—
142C2×C4—11242no—
143C2×C4—11242no—
144C2×C4C2×C4×D28111yescharacteristic
145C22—22no—
146C22—42no—
147C22—5621no—
148C22—11241no—
149C22C22⋊C4×D28111yescharacteristic
150C4—21no—
151C4—41no—
152C4—41no—
153C4—82no—
154C4—2812no—
155C4—5622no—
156C4—11241no—
157C4—11241no—
158C4—22482no—
159C2—21no—
160C2—42no—
161C2—11241no—
162C2#99×D28111yescharacteristic
subgroupG/H
centerC2#99×D281
commutatorC2×C4×C281C22×C4
FrattiniC2×D4C22×D281
Fitting#354×C281C2
socleC2×C281C2×#99
prime radicalC2×#17985137C22
cosocleC2×D4×C281C23
hypercenter#354D281
hypocenterC281#2129
LCSG ▷ C2×C4×C281 ▷ C22×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #354

Complements

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

NH ≅ G/Ntype
3. #31823258C2semidirect
4. #31823257C2semidirect
5. #354×C281C2semidirect
7. C2×Q8×D281C4semidirect
8. #22582879C4semidirect
9. #22582877C4semidirect
13. #22582836C4semidirect
81. C281#2129semidirect
87. #354D281semidirect

Maximal subgroups

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

subgroupindex
#318240332
#318234352
#318232582
#318232572
#354×C2812
#2129281