Finite Group Databasebeta

← #44486236

Subgroups — #44486236

Order 30592.

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#29505347C211yesmaximal, characteristic
2#101×D239C212yesmaximal, complemented
3#29504571C211yesmaximal, characteristic, complemented
4#29504568C212yesmaximal, complemented
5#356×C239C211yesmaximal, characteristic, complemented
6C2×#16838549C411yescharacteristic
7C2×Q8×D239C2211yescharacteristic
8M16×D239—22no—
9#21439958C411yescharacteristic
10#21439949C2211yescharacteristic
11#21439948C411yescharacteristic
12#21439945—22no—
13#21439938—22no—
14#21439917C411yescharacteristic
15#21439879C2212yes—
16#21439878—22no—
17C4⋊Q8×C239C2211yescharacteristic
18#101×C239C2212yes—
19#16838549—42no—
20C2×Dic478C2×C411yescharacteristic
21C2×Dic478D412yes—
22Q8×D239—42no—
23C2×D956—21no—
24C2×D956C2×C411yescharacteristic
25C2×C4×D239—21no—
26C2×C4×D239C2×C411yescharacteristic
27C2×C4×D239D412yes—
28#16838532—22no—
29#16838531—42no—
30C8×D239—42no—
31Dic239⋊C4—21no—
32Dic239⋊C4—22no—
33(C2×D239)⋊C4—21no—
34(C2×D239)⋊C4—22no—
35(C2×D239)⋊C4—22no—
36C4×Dic239C2×C411yescharacteristic
37C2×Q8×C239C2×C411yescharacteristic
38C2×Q8×C239C2311yescharacteristic
39M16×C239—22no—
40C4⋊C4×C239—22no—
41C42×C239C2×C411yescharacteristic
42C22×D239—21no—
43C22×D239C22⋊C411yescharacteristic
44Dic478—41no—
45Dic478—42no—
46D956—41no—
47D956—42no—
48C2×Dic239—21no—
49C2×Dic239C22⋊C412yes—
50C2×Dic239C22⋊C411yescharacteristic
51C4×D239—22no—
52C4×D239—22no—
53C4×D239—22no—
54C4×D239—42no—
55C239⋊C8—42no—
56Q8×C239—41no—
57Q8×C239—41no—
58C2×C4×C239—21no—
59C2×C4×C239—21no—
60C2×C4×C239C22×C411yescharacteristic
61C2×C4×C239C2×D412yes—
62C8×C239—42no—
63C22×C239C2×C22⋊C411yescharacteristic
64C2×D239—41no—
65C2×D239—42no—
66C2×D239—41no—
67C2×D239#9912yes—
68C4×C239—22no—
69C4×C239—21no—
70C4×C239—41no—
71C4×C239—41no—
72Dic239—21no—
73Dic239—22no—
74Dic239—41no—
75C2×C239—21no—
76C2×C239C2×#9911yescharacteristic
77D239—22no—
78D239—81no—
79C239#213311yescharacteristic, complemented, Sylow
80#2133—2391nomaximal, Sylow
81#536—2391no—
82C2×#101—2392no—
83#356—2391no—
84#356D23911yescharacteristic, complemented
85#355—2392no—
86C2×#41—2391no—
87C22×Q8—2391no—
88C2×M16—4782no—
89C4⋊Q8—2391no—
90C4⋊Q8C2×D23911yescharacteristic
91#124—2391no—
92#124—2391no—
93#123—4782no—
94C22⋊Q8—4782no—
95#117—2391no—
96#101—4782no—
97#101—2392no—
98#101C2×D23912yes—
99#41—9562no—
100C2×Q8—9562no—
101C2×Q8—2391no—
102C2×Q8—2392no—
103C2×Q8C4×D23911yescharacteristic
104C2×Q8C22×D23911yescharacteristic
105C2×D4—4781no—
106C2×D4—2391no—
107C22×C4—4781no—
108C22×C4—2391no—
109C22×C4—2392no—
110M16—22no—
111M16—9562no—
112M16—4782no—
113C2×C8—9562no—
114C4⋊C4—22no—
115C4⋊C4—4781no—
116C4⋊C4—4782no—
117C22⋊C4—4781no—
118C22⋊C4—4782no—
119C22⋊C4—4782no—
120C42—2391no—
121C42C4×D23911yescharacteristic
122C23—4781no—
123C23—2391no—
124Q8—41no—
125Q8—41no—
126Q8—9562no—
127Q8—9561no—
128D4—9561no—
129D4—9562no—
130C2×C4—21no—
131C2×C4—21no—
132C2×C4—9562no—
133C2×C4—4782no—
134C2×C4—4782no—
135C2×C4—4782no—
136C2×C4—4781no—
137C2×C4—2392no—
138C2×C4—2391no—
139C2×C4C2×C4×D23911yescharacteristic
140C2×C4D4×D23912yes—
141C8—42no—
142C8—9562no—
143C22—9562no—
144C22—9561no—
145C22—9561no—
146C22—2392no—
147C22C22⋊C4×D23911yescharacteristic
148C4—22no—
149C4—21no—
150C4—41no—
151C4—41no—
152C4—9561no—
153C4—4781no—
154C4—4782no—
155C2—21no—
156C2—19121no—
157C2—4782no—
158C2#99×D23911yescharacteristic
subgroupG/H
centerC2#99×D239
commutatorC2×C4×C239C22×C4
FrattiniC2×Q8C22×D239
Fitting#356×C239C2
socleC2×C239C2×#99
prime radicalC2×#16838549C4
cosocleC2×Q8×C239C23
hypercenter#356D239
hypocenterC239#2133
LCSG ▷ C2×C4×C239 ▷ C22×C239 ▷ C2×C239 ▷ C239
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #356

Complements

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

NH ≅ G/Ntype
2. #101×D239C2semidirect
3. #29504571C2semidirect
4. #29504568C2semidirect
5. #356×C239C2semidirect
79. C239#2133semidirect
84. #356D239semidirect

Maximal subgroups

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

subgroupindex
#295053472
#101×D2392
#295045712
#295045682
#356×C2392
#2133239