Finite Group Databasebeta

← #49094330

Subgroups — #49094330

Order 35968.

236 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 53 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#31824089C211yesmaximal, characteristic
2#31823799C212yesmaximal, complemented
3#31823399C211yesmaximal, characteristic
4#31823201C212yesmaximal, complemented
5#323×C281C211yesmaximal, characteristic
6#22582858—21no—
7#22582858C2212yes—
8#22582856—22no—
9#22582856—22no—
10C2×C4⋊Dic281C2211yescharacteristic
11C2×#17985117—21no—
12C2×C22⋊Dic281—21no—
13C2×C22⋊Dic281—21no—
14#22582813—22no—
15#22582804—22no—
16#22582786C2211yescharacteristic
17C2×C22⋊C4×C281C2211yescharacteristic
18C22⋊C8×C281C2212yes—
19C2×Dic562—21no—
20C2×Dic562D412yes—
21C22×Dic281—21no—
22C22×Dic281—21no—
23C22×Dic281—21no—
24C22×Dic281—21no—
25C4⋊Dic281—21no—
26C4⋊Dic281—22no—
27C4⋊Dic281D412yes—
28#17985117—22no—
29#17985117—22no—
30#17985117—42no—
31C22⋊Dic281—22no—
32C22⋊Dic281—22no—
33C22⋊Dic281—42no—
34C24×C281D411yescharacteristic
35C22×C4×C281D411yescharacteristic
36C22×C4×C281C2311yescharacteristic
37C2×C8×C281—22no—
38C22⋊C4×C281—22no—
39Dic562—42no—
40Dic562—81no—
41C2×Dic281—22no—
42C2×Dic281—22no—
43C2×Dic281—22no—
44C2×Dic281—41no—
45C2×Dic281—41no—
46C2×Dic281—41no—
47C2×Dic281—41no—
48C2×Dic281—41no—
49C2×Dic281—81no—
50C2×Dic281—81no—
51C23×C281—21no—
52C23×C281—21no—
53C23×C281—41no—
54C23×C281—41no—
55C23×C281Q1612yes—
56C23×C281C2×D411yescharacteristic
57C2×C4×C281—21no—
58C2×C4×C281—41no—
59C2×C4×C281—41no—
60C2×C4×C281C2×D412yes—
61C8×C281—42no—
62C22×C281—21no—
63C22×C281—21no—
64C22×C281—22no—
65C22×C281—42no—
66C22×C281—41no—
67C22×C281—41no—
68C22×C281—81no—
69C22×C281#12011yescharacteristic
70C22×C281C2×Q1611yescharacteristic
71C22×C281#13711yescharacteristic
72C4×C281—22no—
73C4×C281—41no—
74Dic281—42no—
75Dic281—42no—
76Dic281—42no—
77Dic281—81no—
78C2×C281—21no—
79C2×C281—21no—
80C2×C281—42no—
81C2×C281#45111yescharacteristic
82C2×C281#45311yescharacteristic
83C2×C281#45811yescharacteristic
84C281#161411yescharacteristic, complemented, Sylow
85#1614—2811nomaximal, Sylow
86#543—2811no—
87#484—2812no—
88#399—2811no—
89#328—2812no—
90#323D28111yescharacteristic
91C22⋊Q8—2812no—
92C22⋊Q8—5622no—
93C22⋊Q8—5622no—
94C22⋊Q8—5621no—
95C2×C4⋊C4—2811no—
96C2×C4⋊C4—5621no—
97C2×C22⋊C4—5621no—
98C2×C22⋊C4—5621no—
99C2×C22⋊C4C2×D28111yescharacteristic
100#107—5622no—
101#103—5622no—
102C22⋊C8C2×D28112yes—
103#95—2811no—
104C24D112411yescharacteristic
105C2×Q8—2812no—
106C2×Q8—5621no—
107C22×C4—5621no—
108C22×C4—5621no—
109C22×C4—5621no—
110C22×C4—5621no—
111C22×C4D112411yescharacteristic
112C22×C4C22×D28111yescharacteristic
113C2×C8—22no—
114C4⋊C4—2812no—
115C4⋊C4—5622no—
116C4⋊C4—5621no—
117C4⋊C4—5622no—
118C4⋊C4—5622no—
119C4⋊C4—11242no—
120C22⋊C4—22no—
121C22⋊C4—5622no—
122C22⋊C4—5622no—
123C22⋊C4—11242no—
124C23—21no—
125C23—21no—
126C23—41no—
127C23—41no—
128C23Dic112412yes—
129C23C2×D112411yescharacteristic
130Q8—11242no—
131Q8—22481no—
132C2×C4—21no—
133C2×C4—41no—
134C2×C4—41no—
135C2×C4—5622no—
136C2×C4—5622no—
137C2×C4—5622no—
138C2×C4—11241no—
139C2×C4—11241no—
140C2×C4—11241no—
141C2×C4—11241no—
142C2×C4—11241no—
143C2×C4—22481no—
144C2×C4—22481no—
145C2×C4D4×D28112yes—
146C8—42no—
147C22—21no—
148C22—21no—
149C22—22no—
150C22—42no—
151C22—41no—
152C22—41no—
153C22—81no—
154C22#2258284911yescharacteristic
155C22C2×Dic112411yescharacteristic
156C22#2258291211yescharacteristic
157C4—22no—
158C4—41no—
159C4—11242no—
160C4—11242no—
161C4—11242no—
162C4—22481no—
163C2—21no—
164C2—21no—
165C2—42no—
166C2#3182362111yescharacteristic
167C2#3182363311yescharacteristic
168C2#3182365411yescharacteristic
subgroupG/H
centerC22#22582849
commutator, cosocleC22×C4×C281C23
FrattiniC22×C4C22×D281
Fitting#323×C281C2
socleC22×C281#120
prime radicalC24×C281D4
hypercenter#323D281
hypocenterC281#1614
LCSG ▷ C22×C4×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
2. #31823799C2semidirect
4. #31823201C2semidirect
84. C281#1614semidirect

Maximal subgroups

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

subgroupindex
#318240892
#318237992
#318233992
#318232012
#323×C2812
#1614281