Finite Group Databasebeta

← #44483181

Subgroups — #44483181

Order 30592.

238 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 59 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#29505321C211yesmaximal, characteristic
2#29504827C212yesmaximal, complemented
3#29504512C211yesmaximal, characteristic, complemented
4#29504511C212yesmaximal, complemented
5#329×C239C211yesmaximal, characteristic, complemented
6C2×#16838549C411yescharacteristic
7C2×#16838547C411yescharacteristic
8#21439958C411yescharacteristic
9#21439956C411yescharacteristic
10#21439948C2211yescharacteristic
11#21439933—22no—
12(C22⋊D239)⋊C4—22no—
13C42×D239C2211yescharacteristic
14Dic239⋊C8—22no—
15(C2×D239)⋊C8—22no—
16#21439871C2212yes—
17#124×C239C2211yescharacteristic
18#97×C239C2212yes—
19#16838549—42no—
20#16838547—42no—
21C2×Dic478C2×C411yescharacteristic
22C2×D956—21no—
23C2×D956C2×C411yescharacteristic
24C2×C22⋊D239—21no—
25C2×C22⋊D239—22no—
26C22×Dic239—21no—
27C2×C4×D239—21no—
28C2×C4×D239C2×C411yescharacteristic
29C2×C4×D239D412yes—
30C2×C239⋊C8—22no—
31Dic239⋊C4—22no—
32(C2×D239)⋊C4—22no—
33C4×Dic239C2×C411yescharacteristic
34C4×Dic239D412yes—
35C2×Q8×C239C2×C411yescharacteristic
36C2×D4×C239C2×C411yescharacteristic
37C2×C8×C239—22no—
38C22⋊C4×C239—22no—
39C42×C239C2311yescharacteristic
40C22×D239—21no—
41C22×D239C22⋊C411yescharacteristic
42Dic478—41no—
43D956—41no—
44D956—42no—
45C22⋊D239—44no—
46C22⋊D239—42no—
47C2×Dic239—21no—
48C2×Dic239—42no—
49C2×Dic239C22⋊C412yes—
50C2×Dic239C22⋊C411yescharacteristic
51C4×D239—22no—
52C4×D239—42no—
53C4×D239—42no—
54C239⋊C8—42no—
55C23×C239—21no—
56Q8×C239—41no—
57D4×C239—41no—
58C2×C4×C239—21no—
59C2×C4×C239C22×C411yescharacteristic
60C2×C4×C239C2×D412yes—
61C8×C239—42no—
62C22×C239—41no—
63C22×C239—42no—
64C22×C239C2×C22⋊C411yescharacteristic
65C2×D239—21no—
66C2×D239—22no—
67C2×D239—41no—
68C2×D239—42no—
69C4×C239—21no—
70C4×C239—22no—
71C4×C239—41no—
72Dic239—22no—
73Dic239—41no—
74Dic239#10012yes—
75C2×C239—81no—
76C2×C239C2×#10011yescharacteristic
77C2×C239#42112yes—
78D239—41no—
79D239—81no—
80C239#153611yescharacteristic, complemented, Sylow
81#1536—2391nomaximal, Sylow
82#532—2391no—
83#432—2392no—
84#329—2391no—
85#329—2392no—
86#329D23911yescharacteristic, complemented
87C2×#41—2391no—
88C2×#41—2391no—
89C4⋊Q8—2391no—
90#127—2391no—
91#124—2391no—
92#124C2×D23911yescharacteristic
93#121—4782no—
94C4×D4—4782no—
95C2×C42—2391no—
96C4⋊C8—4782no—
97C22⋊C8—4782no—
98#97—2392no—
99#97C2×D23912yes—
100#41—9562no—
101#41—9562no—
102C2×Q8—2391no—
103C2×Q8C4×D23911yescharacteristic
104C2×D4—4781no—
105C2×D4—4781no—
106C2×D4—4782no—
107C2×D4—2391no—
108C2×D4C4×D23911yescharacteristic
109C22×C4—4781no—
110C22×C4—4781no—
111C22×C4—2392no—
112C22×C4—2391no—
113C2×C8—22no—
114C2×C8—4782no—
115C4⋊C4—4782no—
116C22⋊C4—22no—
117C22⋊C4—4782no—
118C42—2391no—
119C42—2392no—
120C42C22×D23911yescharacteristic
121C23—21no—
122C23—4781no—
123C23—2391no—
124Q8—41no—
125Q8—9561no—
126D4—41no—
127D4—9561no—
128D4—9562no—
129D4—9562no—
130D4—9564no—
131C2×C4—21no—
132C2×C4—9562no—
133C2×C4—9562no—
134C2×C4—9562no—
135C2×C4—4782no—
136C2×C4—4781no—
137C2×C4—2392no—
138C2×C4—2391no—
139C2×C4C2×C4×D23911yescharacteristic
140C2×C4D4×D23912yes—
141C8—42no—
142C8—9562no—
143C22—42no—
144C22—41no—
145C22—9562no—
146C22—9561no—
147C22—4782no—
148C22—4781no—
149C22C22⋊C4×D23911yescharacteristic
150C4—22no—
151C4—21no—
152C4—41no—
153C4—9561no—
154C4—4782no—
155C4—2392no—
156C2—81no—
157C2—19121no—
158C2—9561no—
159C2#100×D23911yescharacteristic
160C2#2950478712yes—
subgroupG/H
centerC22C22⋊C4×D239
commutatorC2×C4×C239C22×C4
FrattiniC42C22×D239
Fitting#329×C239C2
socleC22×C239C2×C22⋊C4
prime radical#29505321C2
cosocleC42×C239C23
hypercenter#329D239
hypocenterC239#1536
LCSG ▷ C2×C4×C239 ▷ C22×C239 ▷ C239
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #29504827C2semidirect
3. #29504512C2semidirect
4. #29504511C2semidirect
5. #329×C239C2semidirect
80. C239#1536semidirect
86. #329D239semidirect

Maximal subgroups

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

subgroupindex
#295053212
#295048272
#295045122
#295045112
#329×C2392
#1536239