Finite Group Databasebeta

← #49174908

Subgroups — #49174908

Order 37504.

396 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 104 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
1C2×#22627691C211yesmaximal, characteristic, complemented
2C2×#22627681C212yesmaximal, complemented
3C2×C22⋊#14556880C212yesmaximal, complemented
4C2×C4×#14556880C211yesmaximal, characteristic, complemented
5C2×#22627584C211yesmaximal, characteristic
6C22×#14556880C2212yes—
7C22×#14556880C2212yes—
8#22627691—22no—
9#22627681—24no—
10C22⋊#14556880—24no—
11C4×#14556880—22no—
12C22×C22⋊D293C411yescharacteristic
13C23×Dic293C2211yescharacteristic
14C22×C4×D293C2211yescharacteristic
15#22627584—22no—
16#22627584—22no—
17C2×#17989781C411yescharacteristic
18C2×#17989779C411yescharacteristic
19C2×C4×Dic293C2211yescharacteristic
20C2×C22⋊C4×C293C411yescharacteristic
21C2×#14556880—22no—
22C2×#14556880—22no—
23C2×#14556880—22no—
24C2×#14556880—22no—
25C2×#14556880—22no—
26C2×#14556880D414yescomplemented
27C23×D293C2×C411yescharacteristic
28C2×C22⋊D293—22no—
29C2×C22⋊D293—22no—
30C2×C22⋊D293C814yescomplemented
31C22×Dic293—21no—
32C22×Dic293—21no—
33C22×Dic293—22no—
34C22×Dic293—22no—
35C22×Dic293C2×C411yescharacteristic
36C22×Dic293C2×C411yescharacteristic
37C22×Dic293C2311yescharacteristic
38C2×C4×D293—21no—
39C2×C4×D293—21no—
40C2×C4×D293—22no—
41C2×C4×D293—22no—
42#17989781—22no—
43#17989779—22no—
44C4×Dic293D412yes—
45C4×Dic293D412yes—
46C24×C293C2×C411yescharacteristic
47C22×C4×C293C2×C411yescharacteristic
48C22×C4×C293C2×C411yescharacteristic
49C22⋊C4×C293—22no—
50#14556880—24no—
51#14556880—42no—
52C22×D293—21no—
53C22×D293—22no—
54C22×D293—21no—
55C22×D293—22no—
56C22×D293C2×C812yes—
57C22⋊D293—28no—
58C2×Dic293—21no—
59C2×Dic293—22no—
60C2×Dic293—42no—
61C2×Dic293—41no—
62C2×Dic293—41no—
63C2×Dic293C22⋊C412yes—
64C2×Dic293C2×C812yes—
65C2×Dic293M1612yes—
66C2×Dic293C2×D411yescharacteristic
67C2×Dic293C2×D412yes—
68C2×Dic293C2×D411yescharacteristic
69C2×Dic293#4112yes—
70C4×D293—42no—
71C4×D293—41no—
72C4×D293—41no—
73C23×C293—21no—
74C23×C293—22no—
75C23×C293—21no—
76C23×C293—22no—
77C23×C293C2×C812yes—
78C23×C293C22×C411yescharacteristic
79C2×C4×C293—22no—
80C2×C4×C293—21no—
81C2×C4×C293—22no—
82C2×C4×C293C22⋊C412yes—
83C22×C293—22no—
84C22×C293—24no—
85C22×C293—41no—
86C22×C293—41no—
87C22×C293—42no—
88C22×C293C2×C22⋊C411yescharacteristic
89C22×C293C4×D412yes—
90C22×C293C22×C811yescharacteristic
91C22×C293C2×M1611yescharacteristic
92C22×C293#13112yes—
93C2×D293—22no—
94C2×D293—24no—
95C2×D293—41no—
96C2×D293—41no—
97C2×D293—42no—
98C4×C293—22no—
99C4×C293—41no—
100Dic293—41no—
101Dic293C22⋊C814yescomplemented
102Dic293#12112yes—
103Dic293#12411yescharacteristic
104Dic293#12711yescharacteristic
105C2×C293—42no—
106C2×C293#39011yescharacteristic
107C2×C293C2×C22⋊C811yescharacteristic
108C2×C293#40811yescharacteristic
109C2×C293C8×D412yes—
110C2×C293#43612yes—
111D293—42no—
112C293#195411yescharacteristic, complemented, Sylow
113#1954—2931nomaximal, Sylow
114C2×C4×D4—2931no—
115C2×C4⋊C8—2931no—
116C2×C22⋊C8—2932no—
117C2×C22⋊C8—2932no—
118C2×C4×C8—2931no—
119C22×D4—2931no—
120C23×C4—2931no—
121C23×C4—2931no—
122C22×C8—2932no—
123C22×C8—2932no—
124C4×D4—5862no—
125C4×D4—5862no—
126C2×C4⋊C4—2931no—
127C2×C22⋊C4—2931no—
128C2×C22⋊C4#1192407811yescharacteristic
129C2×C42—2931no—
130C4⋊C8—5862no—
131C22⋊C8—5864no—
132C22⋊C8—5864no—
133C4×C8—5862no—
134C24—2931no—
135C24C2×#1192407811yescharacteristic
136C2×D4—2934no—
137C2×D4—5862no—
138C2×D4—5862no—
139C22×C4—2931no—
140C22×C4—2931no—
141C22×C4—2931no—
142C22×C4—5862no—
143C22×C4—5861no—
144C22×C4—5861no—
145C22×C4—5862no—
146C22×C4—5862no—
147C22×C4—5861no—
148C22×C4—5861no—
149C22×C4—5862no—
150C22×C4C2×#1192407811yescharacteristic
151C22×C4C2×#1192407811yescharacteristic
152C2×C8—2934no—
153C2×C8—5862no—
154C2×C8—5862no—
155C2×C8—5862no—
156C2×C8—5862no—
157C2×C8—5862no—
158C4⋊C4—5862no—
159C22⋊C4—22no—
160C22⋊C4—5862no—
161C42—2932no—
162C42—2932no—
163C23—21no—
164C23—22no—
165C23—21no—
166C23—22no—
167C23—2932no—
168C23—5861no—
169C23—5862no—
170C23—5861no—
171C23—5862no—
172C23D293⋊C812yes—
173C23C22×#1192407811yescharacteristic
174D4—5868no—
175C2×C4—22no—
176C2×C4—21no—
177C2×C4—22no—
178C2×C4—2932no—
179C2×C4—2931no—
180C2×C4—2931no—
181C2×C4—2932no—
182C2×C4—2932no—
183C2×C4—2932no—
184C2×C4—2932no—
185C2×C4—5861no—
186C2×C4—5862no—
187C2×C4—11722no—
188C2×C4—11721no—
189C2×C4—11721no—
190C2×C4—11722no—
191C2×C4—11721no—
192C2×C4—11721no—
193C2×C4C22⋊#1192407812yes—
194C8—5864no—
195C8—11722no—
196C22—22no—
197C22—24no—
198C22—41no—
199C22—41no—
200C22—42no—
201C22—5862no—
202C22—5864no—
203C22—11721no—
204C22—11721no—
205C22—11722no—
206C22C2×C22⋊#1192407811yescharacteristic
207C22D4×#1192407812yes—
208C22C2×D293⋊C811yescharacteristic
209C22D293⋊M1611yescharacteristic
210C22#2262771112yes—
211C4—22no—
212C4—41no—
213C4—2932no—
214C4—2931no—
215C4—2931no—
216C4—2934no—
217C4—11721no—
218C2—42no—
219C2—11722no—
220C2#3403708111yescharacteristic
221C2D293⋊(C22⋊C8)11yescharacteristic
222C2#3403710211yescharacteristic
223C2#3403715612yes—
224C2#3403716212yes—
subgroupG/H
center, FrattiniC23C22×#11924078
commutatorC22×C293C22×C8
FittingC2×C22⋊C4×C293C4
socleC23×C293C22×C4
prime radicalC22×C22⋊D293C4
cosocleC22×Dic293C23
hypercenterC2×C22⋊C4#11924078
hypocenterC293#1954
LCSG ▷ C22×C293 ▷ C293
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#22627691C2semidirect
2. C2×#22627681C2semidirect
3. C2×C22⋊#14556880C2semidirect
4. C2×C4×#14556880C2semidirect
26. C2×#14556880D4semidirect
30. C2×C22⋊D293C8semidirect
101. Dic293C22⋊C8semidirect
112. C293#1954semidirect

Maximal subgroups

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

subgroupindex
C2×#226276912
C2×#226276812
C2×C22⋊#145568802
C2×C4×#145568802
C2×#226275842
#1954293