Finite Group Databasebeta

← #49157147

Subgroups — #49157147

Order 37504.

270 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 65 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×#22627602C211yesmaximal, characteristic
2#34036091C211yesmaximal, characteristic
3C22⋊C8×D293C211yesmaximal, characteristic
4#34035855C211yesmaximal, characteristic, complemented
5#34035854C211yesmaximal, characteristic, complemented
6#34035854C211yesmaximal, characteristic, complemented
7#324×C293C211yesmaximal, characteristic, complemented
8C22×Dic586C411yescharacteristic
9C22×C4×D293C2211yescharacteristic
10C2×#17989785—21no—
11C2×C8×D293—21no—
12#22627602—21no—
13#22627602—21no—
14#22627602—21no—
15#22627602—21no—
16C2×#17989781C411yescharacteristic
17C2×#17989781C2211yescharacteristic
18C2×#17989779C411yescharacteristic
19C2×#17989779C411yescharacteristic
20C22⋊#14556873C2211yescharacteristic
21C22⋊#14556873C2211yescharacteristic
22#22627536—21no—
23#22627536—21no—
24C2×C4⋊C4×C293C2211yescharacteristic
25C22⋊C8×C293C2211yescharacteristic
26C22⋊C8×C293C2211yescharacteristic
27C23×D293C2×C411yescharacteristic
28C2×Dic586—21no—
29C2×Dic586—21no—
30C2×Dic586—42no—
31C22×Dic293C2×C411yescharacteristic
32C22×Dic293C2×C411yescharacteristic
33C22×Dic293C2×C411yescharacteristic
34C2×C4×D293—42no—
35C2×C4×D293D411yescharacteristic
36C2×C4×D293D411yescharacteristic
37C2×C4×D293D411yescharacteristic
38C2×C4×D293D411yescharacteristic
39#17989785—42no—
40C2×#14556873—21no—
41C2×#14556873—21no—
42C8×D293—42no—
43#17989781—21no—
44#17989781—21no—
45#17989781—21no—
46#17989781—21no—
47#17989779—21no—
48#17989779—21no—
49#17989779—21no—
50#17989779—21no—
51C22×C4×C293C2×C411yescharacteristic
52C22×C4×C293C2×C411yescharacteristic
53C22×C4×C293C2311yescharacteristic
54C2×C8×C293—21no—
55C2×C8×C293—21no—
56C4⋊C4×C293—21no—
57C4⋊C4×C293—21no—
58C22×D293—21no—
59C22×D293—21no—
60C22×D293—22no—
61C22×D293—41no—
62C22×D293C22⋊C411yescharacteristic
63C22×D293C22⋊C411yescharacteristic
64Dic586—42no—
65Dic586—42no—
66C2×Dic293—22no—
67C2×Dic293—21no—
68C2×Dic293—21no—
69C2×Dic293—21no—
70C2×Dic293—21no—
71C2×Dic293—41no—
72C2×Dic293C22⋊C411yescharacteristic
73C2×Dic293C22⋊C411yescharacteristic
74C4×D293—22no—
75C4×D293—22no—
76C4×D293—41no—
77C4×D293—41no—
78#14556873—41no—
79#14556873—41no—
80C23×C293C22×C411yescharacteristic
81C2×C4×C293—21no—
82C2×C4×C293—21no—
83C2×C4×C293—21no—
84C2×C4×C293—21no—
85C2×C4×C293—41no—
86C2×C4×C293—41no—
87C2×C4×C293C2×D411yescharacteristic
88C2×C4×C293C2×D411yescharacteristic
89C8×C293—41no—
90C8×C293—41no—
91C22×C293—21no—
92C22×C293—21no—
93C22×C293C2×C22⋊C411yescharacteristic
94C22×C293#13111yescharacteristic
95C22×C293#13111yescharacteristic
96C2×D293—21no—
97C2×D293—21no—
98C2×D293—21no—
99C2×D293—21no—
100C2×D293—21no—
101C2×D293—42no—
102C2×D293—42no—
103C2×D293#10112yes—
104C4×C293—21no—
105C4×C293—21no—
106C4×C293—41no—
107C4×C293—41no—
108Dic293—21no—
109Dic293—41no—
110Dic293—41no—
111Dic293#9912yes—
112C2×C293—21no—
113C2×C293—21no—
114C2×C293#40811yescharacteristic
115C2×C293C2×#9911yescharacteristic
116C2×C293C2×#10111yescharacteristic
117D293—22no—
118D293—41no—
119C293#147211yescharacteristic, complemented, Sylow
120#1472—2931nomaximal, Sylow
121C2×C22⋊Q8—2931no—
122#407—2931no—
123C2×C22⋊C8—2931no—
124#324—2931no—
125#324—2931no—
126#324—2931no—
127#324D29311yescharacteristic, complemented
128C22×Q8—2931no—
129C23×C4—2931no—
130C2×M16—5861no—
131C22×C8—5861no—
132C22⋊Q8—5861no—
133C22⋊Q8—5861no—
134C22⋊Q8—5861no—
135C22⋊Q8—5861no—
136C2×C4⋊C4—2931no—
137C2×C4⋊C4—2931no—
138C2×C4⋊C4C2×D29311yescharacteristic
139C2×C22⋊C4—2931no—
140C2×C22⋊C4—2931no—
141C22⋊C8—2931no—
142C22⋊C8—2931no—
143C22⋊C8—5861no—
144C22⋊C8—5861no—
145C22⋊C8C2×D29311yescharacteristic
146C22⋊C8C2×D29311yescharacteristic
147C24—2931no—
148C2×Q8—5861no—
149C2×Q8—5861no—
150C2×Q8—11722no—
151C22×C4—2931no—
152C22×C4—2931no—
153C22×C4—2931no—
154C22×C4—2931no—
155C22×C4—2931no—
156C22×C4—2931no—
157C22×C4—2931no—
158C22×C4—11722no—
159C22×C4C4×D29311yescharacteristic
160C22×C4C4×D29311yescharacteristic
161C22×C4C22×D29311yescharacteristic
162M16—11722no—
163C2×C8—21no—
164C2×C8—21no—
165C2×C8—5861no—
166C2×C8—5861no—
167C2×C8—11722no—
168C4⋊C4—21no—
169C4⋊C4—21no—
170C4⋊C4—5861no—
171C4⋊C4—5861no—
172C4⋊C4—5861no—
173C4⋊C4—5861no—
174C22⋊C4—5861no—
175C22⋊C4—5861no—
176C22⋊C4—5861no—
177C22⋊C4—5861no—
178C23—2931no—
179C23—2931no—
180C23—5862no—
181C23—5861no—
182C23—5861no—
183C23—11721no—
184C23C2×C4×D29311yescharacteristic
185Q8—11722no—
186Q8—11722no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—2931no—
194C2×C4—2931no—
195C2×C4—5862no—
196C2×C4—5862no—
197C2×C4—5862no—
198C2×C4—5861no—
199C2×C4—5861no—
200C2×C4—5861no—
201C2×C4—5861no—
202C2×C4—11721no—
203C2×C4—11721no—
204C2×C4—11721no—
205C2×C4D4×D29311yescharacteristic
206C2×C4D4×D29311yescharacteristic
207C8—41no—
208C8—41no—
209C8—11721no—
210C8—11721no—
211C22—21no—
212C22—21no—
213C22—2932no—
214C22—5861no—
215C22—5861no—
216C22—5861no—
217C22—5861no—
218C22—5861no—
219C22—11722no—
220C22—11722no—
221C22C22⋊C4×D29311yescharacteristic
222C22#2262763011yescharacteristic
223C22#2262763211yescharacteristic
224C4—21no—
225C4—21no—
226C4—41no—
227C4—41no—
228C4—2932no—
229C4—5861no—
230C4—11721no—
231C4—11721no—
232C2—21no—
233C2—21no—
234C2—5862no—
235C2—11721no—
236C2#3403609411yescharacteristic
237C2#99×D29311yescharacteristic
238C2#101×D29311yescharacteristic
subgroupG/H
centerC22C22⋊C4×D293
commutatorC23×C293C22×C4
FrattiniC22×C4C22×D293
Fitting#324×C293C2
socleC22×C293C2×C22⋊C4
prime radicalC23×D293C2×C4
cosocleC22×C4×C293C23
hypercenter#324D293
hypocenterC293#1472
LCSG ▷ C23×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
4. #34035855C2semidirect
5. #34035854C2semidirect
6. #34035854C2semidirect
7. #324×C293C2semidirect
119. C293#1472semidirect
127. #324D293semidirect

Maximal subgroups

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

subgroupindex
C2×#226276022
#340360912
C22⋊C8×D2932
#340358552
#340358542
#324×C2932
#1472293