Finite Group Databasebeta

← #49122949

Subgroups — #49122949

Order 36224.

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

normal subgroups only

This group has 230 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#31827040C211yesmaximal, characteristic
2#101×D283C212yesmaximal, complemented
3#31826264C211yesmaximal, characteristic, complemented
4#31826261C212yesmaximal, complemented
5#356×C283C211yesmaximal, characteristic, complemented
6C2×#17985393C411yescharacteristic
7C2×Q8×D283C2211yescharacteristic
8M16×D283—22no—
9#22583608C411yescharacteristic
10#22583599C2211yescharacteristic
11#22583598C411yescharacteristic
12#22583595—22no—
13#22583588—22no—
14#22583567C411yescharacteristic
15#22583529C2212yes—
16#22583528—22no—
17C4⋊Q8×C283C2211yescharacteristic
18#101×C283C2212yes—
19#17985393—42no—
20C2×Dic566C2×C411yescharacteristic
21C2×Dic566D412yes—
22Q8×D283—42no—
23C2×D1132—21no—
24C2×D1132C2×C411yescharacteristic
25C2×C4×D283—21no—
26C2×C4×D283C2×C411yescharacteristic
27C2×C4×D283D412yes—
28#17985376—22no—
29#17985375—42no—
30C8×D283—42no—
31Dic283⋊C4—21no—
32Dic283⋊C4—22no—
33(C2×D283)⋊C4—21no—
34(C2×D283)⋊C4—22no—
35(C2×D283)⋊C4—22no—
36C4×Dic283C2×C411yescharacteristic
37C2×Q8×C283C2×C411yescharacteristic
38C2×Q8×C283C2311yescharacteristic
39M16×C283—22no—
40C4⋊C4×C283—22no—
41C42×C283C2×C411yescharacteristic
42C22×D283—21no—
43C22×D283C22⋊C411yescharacteristic
44Dic566—41no—
45Dic566—42no—
46D1132—41no—
47D1132—42no—
48C2×Dic283—21no—
49C2×Dic283C22⋊C412yes—
50C2×Dic283C22⋊C411yescharacteristic
51C4×D283—22no—
52C4×D283—22no—
53C4×D283—22no—
54C4×D283—42no—
55C283⋊C8—42no—
56Q8×C283—41no—
57Q8×C283—41no—
58C2×C4×C283—21no—
59C2×C4×C283—21no—
60C2×C4×C283C22×C411yescharacteristic
61C2×C4×C283C2×D412yes—
62C8×C283—42no—
63C22×C283C2×C22⋊C411yescharacteristic
64C2×D283—41no—
65C2×D283—42no—
66C2×D283—41no—
67C2×D283#9912yes—
68C4×C283—22no—
69C4×C283—21no—
70C4×C283—41no—
71C4×C283—41no—
72Dic283—21no—
73Dic283—22no—
74Dic283—41no—
75C2×C283—21no—
76C2×C283C2×#9911yescharacteristic
77D283—22no—
78D283—81no—
79C283#213311yescharacteristic, complemented, Sylow
80#2133—2831nomaximal, Sylow
81#536—2831no—
82C2×#101—2832no—
83#356—2831no—
84#356D28311yescharacteristic, complemented
85#355—2832no—
86C2×#41—2831no—
87C22×Q8—2831no—
88C2×M16—5662no—
89C4⋊Q8—2831no—
90C4⋊Q8C2×D28311yescharacteristic
91#124—2831no—
92#124—2831no—
93#123—5662no—
94C22⋊Q8—5662no—
95#117—2831no—
96#101—2832no—
97#101—5662no—
98#101C2×D28312yes—
99#41—11322no—
100C2×Q8—2831no—
101C2×Q8—2832no—
102C2×Q8—11322no—
103C2×Q8C4×D28311yescharacteristic
104C2×Q8C22×D28311yescharacteristic
105C2×D4—2831no—
106C2×D4—5661no—
107C22×C4—2831no—
108C22×C4—2832no—
109C22×C4—5661no—
110M16—22no—
111M16—5662no—
112M16—11322no—
113C2×C8—11322no—
114C4⋊C4—22no—
115C4⋊C4—5661no—
116C4⋊C4—5662no—
117C22⋊C4—5662no—
118C22⋊C4—5661no—
119C22⋊C4—5662no—
120C42—2831no—
121C42C4×D28311yescharacteristic
122C23—2831no—
123C23—5661no—
124Q8—41no—
125Q8—41no—
126Q8—11322no—
127Q8—11321no—
128D4—11321no—
129D4—11322no—
130C2×C4—21no—
131C2×C4—21no—
132C2×C4—2832no—
133C2×C4—2831no—
134C2×C4—5662no—
135C2×C4—5662no—
136C2×C4—5662no—
137C2×C4—5661no—
138C2×C4—11322no—
139C2×C4C2×C4×D28311yescharacteristic
140C2×C4D4×D28312yes—
141C8—42no—
142C8—11322no—
143C22—2832no—
144C22—11321no—
145C22—11322no—
146C22—11321no—
147C22C22⋊C4×D28311yescharacteristic
148C4—22no—
149C4—21no—
150C4—41no—
151C4—41no—
152C4—5661no—
153C4—5662no—
154C4—11321no—
155C2—21no—
156C2—5662no—
157C2—22641no—
158C2#99×D28311yescharacteristic
subgroupG/H
centerC2#99×D283
commutatorC2×C4×C283C22×C4
FrattiniC2×Q8C22×D283
Fitting#356×C283C2
socleC2×C283C2×#99
prime radicalC2×#17985393C4
cosocleC2×Q8×C283C23
hypercenter#356D283
hypocenterC283#2133
LCSG ▷ C2×C4×C283 ▷ C22×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #356

Complements

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

NH ≅ G/Ntype
2. #101×D283C2semidirect
3. #31826264C2semidirect
4. #31826261C2semidirect
5. #356×C283C2semidirect
79. C283#2133semidirect
84. #356D283semidirect

Maximal subgroups

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

subgroupindex
#318270402
#101×D2832
#318262642
#318262612
#356×C2832
#2133283