Finite Group Databasebeta

← #49159950

Subgroups — #49159950

Order 37504.

466 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 67 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#34036755C211yesmaximal, characteristic, complemented
2#34035984C212yesmaximal
3#34035984C211yesmaximal, characteristic
4#34035895C212yesmaximal, complemented
5#342×C293C211yesmaximal, characteristic, complemented
6C24×D293C2211yescharacteristic
7#22627603—22no—
8#22627601—24no—
9C2×C22⋊Dic293C2211yescharacteristic
10C2×C22⋊Dic293C2212yes—
11C2×#17989779—24no—
12C2×#17989779—22no—
13C2×C22⋊C4×C293C2212yes—
14C2×C22⋊C4×C293C2211yescharacteristic
15C23×D293—22no—
16C23×D293—21no—
17C23×D293—21no—
18C23×D293—22no—
19C23×D293—44no—
20C23×D293Q812yescomplemented
21C2×Dic586—22no—
22C22×Dic293—21no—
23C22×Dic293D414yes—
24C4⋊Dic293—22no—
25#17989781—24no—
26C22⋊Dic293—22no—
27C22⋊Dic293—22no—
28C22⋊Dic293—22no—
29#17989779—44no—
30#17989779—48no—
31C24×C293C2311yescharacteristic
32C22×C4×C293—22no—
33C22×C4×C293D412yes—
34C22⋊C4×C293—22no—
35C22⋊C4×C293—22no—
36C22⋊C4×C293—22no—
37C22×D293—28no—
38C22×D293—24no—
39C22×D293—24no—
40C22×D293—22no—
41C22×D293—44no—
42C22×D293—44no—
43C22×D293—48no—
44C22×D293—44no—
45C22×D293—42no—
46C22×D293—41no—
47C22×D293—42no—
48C22×D293—41no—
49Dic586—82no—
50C2×Dic293—24no—
51C2×Dic293—44no—
52C2×Dic293—42no—
53C2×Dic293—41no—
54C23×C293—42no—
55C23×C293C2×D412yes—
56C23×C293C2×D411yescharacteristic
57C23×C293C2×Q811yescharacteristic
58C23×C293#4111yescharacteristic
59C23×C293#4112yes—
60C2×C4×C293—22no—
61C2×C4×C293—42no—
62C2×C4×C293—44no—
63C2×C4×C293—42no—
64C22×C293—24no—
65C22×C293—22no—
66C22×C293—41no—
67C22×C293—41no—
68C22×C293—42no—
69C22×C293#12011yescharacteristic
70C22×C293C22⋊Q812yes—
71C22×C293C22⋊Q811yescharacteristic
72C22×C293#12412yes—
73C22×C293#12411yescharacteristic
74C2×D293—28no—
75C2×D293—24no—
76C2×D293—44no—
77C2×D293—48no—
78C2×D293—44no—
79C2×D293—42no—
80C2×D293—42no—
81C2×D293—44no—
82C4×C293—42no—
83C4×C293—82no—
84Dic293—44no—
85Dic293—81no—
86C2×C293—21no—
87C2×C293—22no—
88C2×C293—22no—
89C2×C293—21no—
90C2×C293#39311yescharacteristic
91C2×C293B(4,𝔽2)12yes—
92D293—44no—
93C293#202911yescharacteristic, complemented, Sylow
94#2029—2931nomaximal, Sylow
95#543—2931no—
96#379—2932no—
97#379—2931no—
98#342—2932no—
99#342D29311yescharacteristic, complemented
100C25—2931no—
101C22⋊Q8—5864no—
102C22⋊Q8—5862no—
103C2×C22⋊C4—2932no—
104C2×C22⋊C4—2931no—
105C2×C22⋊C4—5864no—
106C2×C22⋊C4—5862no—
107C2×C22⋊C4C2×D29312yes—
108C2×C22⋊C4C2×D29311yescharacteristic
109C24—2932no—
110C24—5862no—
111C24—5861no—
112C24—5861no—
113C24—5862no—
114C24—11724no—
115C24C22×D29311yescharacteristic
116C2×Q8—5862no—
117C22×C4—22no—
118C22×C4—2934no—
119C22×C4—5861no—
120C22×C4D117212yes—
121C4⋊C4—5864no—
122C4⋊C4—5862no—
123C22⋊C4—22no—
124C22⋊C4—22no—
125C22⋊C4—22no—
126C22⋊C4—5862no—
127C22⋊C4—5862no—
128C22⋊C4—5862no—
129C22⋊C4—11724no—
130C22⋊C4—11728no—
131C23—42no—
132C23—5868no—
133C23—5864no—
134C23—5864no—
135C23—5862no—
136C23—11724no—
137C23—11722no—
138C23—11724no—
139C23—11724no—
140C23—11728no—
141C23—11721no—
142C23—11722no—
143C23—11721no—
144C23D4×D29312yes—
145C23C2×D117211yescharacteristic
146C23Q8×D29311yescharacteristic
147C23#1798980111yescharacteristic
148C23#1798980212yes—
149Q8—23442no—
150C2×C4—22no—
151C2×C4—42no—
152C2×C4—44no—
153C2×C4—42no—
154C2×C4—5864no—
155C2×C4—11722no—
156C2×C4—11721no—
157C2×C4—11724no—
158C22—24no—
159C22—22no—
160C22—41no—
161C22—41no—
162C22—42no—
163C22—5868no—
164C22—5864no—
165C22—11728no—
166C22—11724no—
167C22—11724no—
168C22—11722no—
169C22—11722no—
170C22—11724no—
171C22#2262759411yescharacteristic
172C22#2262760212yes—
173C22#2262760411yescharacteristic
174C22#2262761012yes—
175C22#2262761211yescharacteristic
176C4—42no—
177C4—82no—
178C4—23441no—
179C4—11724no—
180C2—22no—
181C2—21no—
182C2—22no—
183C2—21no—
184C2—11724no—
185C2#3403604211yescharacteristic
186C2#3403631712yes—
subgroupG/H
centerC22#22627594
commutator, cosocleC24×C293C23
FrattiniC24C22×D293
Fitting#342×C293C2
socleC22×C293#120
prime radicalC24×D293C22
hypercenter#342D293
hypocenterC293#2029
LCSG ▷ C24×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
1. #34036755C2semidirect
4. #34035895C2semidirect
5. #342×C293C2semidirect
20. C23×D293Q8semidirect
93. C293#2029semidirect
99. #342D293semidirect

Maximal subgroups

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

subgroupindex
#340367552
#340359842
#340358952
#342×C2932
#2029293