Finite Group Databasebeta

← #44486221

Subgroups — #44486221

Order 30592.

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#29505342C211yesmaximal, characteristic
2#29504744C212yesmaximal
3#29504567C211yesmaximal, characteristic, complemented
4#29504566C212yesmaximal, complemented
5#354×C239C211yesmaximal, characteristic, complemented
6C2×#16838547C2211yescharacteristic
7C2×Q8×D239C411yescharacteristic, complemented
8#21439960C411yescharacteristic, complemented
9#21439958C411yescharacteristic, complemented
10#21439947C2211yescharacteristic
11#21439942—22no—
12#21439937—22no—
13#21439917C411yescharacteristic, complemented
14#21439916—22no—
15#21439875C2212yes—
16#21439874—22no—
17#124×C239C2211yescharacteristic
18#99×C239C2212yes—
19#16838547—42no—
20C2×Dic478—21no—
21C2×Dic478C2×C411yescharacteristic
22C2×Dic478C2×C411yescharacteristic
23Q8×D239—42no—
24C2×C22⋊D239D412yes—
25C22×Dic239D412yes—
26C2×C4×D239—21no—
27C2×C4×D239C2×C411yescharacteristic
28C4⋊Dic239—22no—
29Dic239⋊C4—21no—
30Dic239⋊C4—22no—
31Dic239⋊C4—42no—
32C22⋊Dic239—22no—
33C22⋊Dic239—22no—
34(C2×D239)⋊C4—21no—
35C4×Dic239—42no—
36C4×Dic239C2×C411yescharacteristic
37C2×Q8×C239C2×C411yescharacteristic
38C2×D4×C239C2311yescharacteristic
39C22⋊C4×C239—22no—
40C22⋊C4×C239—22no—
41C42×C239C2×C411yescharacteristic
42C22×D239C22⋊C411yescharacteristic
43Dic478—41no—
44Dic478—42no—
45Dic478—41no—
46C22⋊D239—42no—
47C2×Dic239—22no—
48C2×Dic239—22no—
49C2×Dic239—21no—
50C2×Dic239—21no—
51C2×Dic239—42no—
52C2×Dic239C22⋊C412yes—
53C2×Dic239C22⋊C411yescharacteristic
54C4×D239—22no—
55C4×D239—42no—
56C23×C239C2×D412yes—
57Q8×C239—41no—
58D4×C239—41no—
59C2×C4×C239—21no—
60C2×C4×C239—21no—
61C2×C4×C239—42no—
62C2×C4×C239C22×C411yescharacteristic
63C22×C239—22no—
64C22×C239—42no—
65C22×C239C2×C22⋊C411yescharacteristic
66C2×D239—21no—
67C2×D239—41no—
68C4×C239—21no—
69C4×C239—41no—
70C4×C239—41no—
71C4×C239—82no—
72Dic239—22no—
73Dic239—41no—
74Dic239—41no—
75Dic239—82no—
76Dic239#9912yes—
77C2×C239—21no—
78C2×C239—42no—
79C2×C239C2×#9911yescharacteristic
80D239—41no—
81C239#212911yescharacteristic, complemented, Sylow
82#2129—2391nomaximal, Sylow
83#536—2391no—
84#410—2392no—
85#354—2391no—
86#354—2392no—
87#354D23911yescharacteristic, complemented
88C2×#41—2391no—
89C22×Q8—2391no—
90C4⋊Q8—2391no—
91C4⋊Q8—2391no—
92#124—2391no—
93#124C2×D23911yescharacteristic
94#123—4782no—
95C22⋊Q8—4782no—
96#117—4782no—
97#117—2391no—
98#99—4782no—
99#99—2392no—
100#99C2×D23912yes—
101#41—9562no—
102C2×Q8—9562no—
103C2×Q8—4781no—
104C2×Q8—2391no—
105C2×Q8—2391no—
106C2×Q8C4×D23911yescharacteristic
107C2×D4—2392no—
108C2×D4C22×D23911yescharacteristic
109C22×C4—4781no—
110C22×C4—2392no—
111C22×C4—2391no—
112C4⋊C4—9562no—
113C4⋊C4—4781no—
114C4⋊C4—4782no—
115C4⋊C4—4782no—
116C22⋊C4—22no—
117C22⋊C4—22no—
118C22⋊C4—4781no—
119C22⋊C4—4782no—
120C22⋊C4—4782no—
121C42—9562no—
122C42—2391no—
123C42C4×D23911yescharacteristic
124C23—2391no—
125C23D4×D23912yes—
126Q8—41no—
127Q8—9561no—
128Q8—9561no—
129Q8—9562no—
130D4—41no—
131D4—9562no—
132C2×C4—21no—
133C2×C4—21no—
134C2×C4—42no—
135C2×C4—9562no—
136C2×C4—9562no—
137C2×C4—4782no—
138C2×C4—4781no—
139C2×C4—4781no—
140C2×C4—4782no—
141C2×C4—4782no—
142C2×C4—2392no—
143C2×C4—2391no—
144C2×C4C2×C4×D23911yescharacteristic
145C22—22no—
146C22—42no—
147C22—9561no—
148C22—4781no—
149C22C22⋊C4×D23911yescharacteristic
150C4—21no—
151C4—41no—
152C4—41no—
153C4—82no—
154C4—19122no—
155C4—9561no—
156C4—9561no—
157C4—4782no—
158C4—2392no—
159C2—21no—
160C2—42no—
161C2—9561no—
162C2#99×D23911yescharacteristic
subgroupG/H
centerC2#99×D239
commutatorC2×C4×C239C22×C4
FrattiniC2×D4C22×D239
Fitting#354×C239C2
socleC2×C239C2×#99
prime radicalC2×#16838547C22
cosocleC2×D4×C239C23
hypercenter#354D239
hypocenterC239#2129
LCSG ▷ C2×C4×C239 ▷ C22×C239 ▷ C2×C239 ▷ C239
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #354

Complements

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

NH ≅ G/Ntype
3. #29504567C2semidirect
4. #29504566C2semidirect
5. #354×C239C2semidirect
7. C2×Q8×D239C4semidirect
8. #21439960C4semidirect
9. #21439958C4semidirect
13. #21439917C4semidirect
81. C239#2129semidirect
87. #354D239semidirect

Maximal subgroups

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

subgroupindex
#295053422
#295047442
#295045672
#295045662
#354×C2392
#2129239