Finite Group Databasebeta

← #49174161

Subgroups — #49174161

Order 37504.

304 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 62 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×#22627681C211yesmaximal, characteristic, complemented
2C4×C22⋊#11924078C211yesmaximal, characteristic, complemented
3#34036982C212yesmaximal, complemented
4#34036980C212yesmaximal, complemented
5#34036639C211yesmaximal, characteristic
6C22×#14556880—21no—
7C2×C22⋊#11924078—21no—
8C2×C4×#11924078—21no—
9#22627681—21no—
10#22627681C2212yes—
11(C2×#11924078)⋊C4C2212yes—
12C2×#17989801C411yescharacteristic, complemented
13C22×C4×D293C2211yescharacteristic
14#22627606—21no—
15#22627604C2211yescharacteristic
16#22627603C411yescharacteristic, complemented
17#22627595C2211yescharacteristic
18#22627592—21no—
19D4×Dic293—21no—
20#22627584—21no—
21#22627582C411yescharacteristic, complemented
22#121×C293C411yescharacteristic, complemented
23C22×#11924078—22no—
24C2×#14556880—22no—
25C2×#14556880—42no—
26C22⋊#11924078—24no—
27C4×#11924078—42no—
28C23×D293D411yescharacteristic
29#17989801—42no—
30C2×Dic586C2×C411yescharacteristic
31C2×C22⋊D293—21no—
32C2×C22⋊D293—21no—
33C22×Dic293—21no—
34C22×Dic293D411yescharacteristic
35C2×C4×D293—42no—
36C2×C4×D293C2×C411yescharacteristic
37C2×C4×D293D411yescharacteristic
38C2×C4×D293D411yescharacteristic
39C2×C4×D293C2311yescharacteristic
40C4⋊Dic293—21no—
41C4⋊Dic293C2×C411yescharacteristic
42#17989781—21no—
43C22⋊Dic293—21no—
44C22⋊Dic293—21no—
45#17989779—21no—
46#17989779—21no—
47C4×Dic293—21no—
48C2×D4×C293—21no—
49C2×D4×C293C2×C411yescharacteristic
50C22×C4×C293C2×C411yescharacteristic
51C4⋊C4×C293C2×C411yescharacteristic
52C22⋊C4×C293—21no—
53C2×#11924078—24no—
54C2×#11924078—42no—
55C2×#11924078—42no—
56#14556880—42no—
57C22×D293—22no—
58C22×D293—22no—
59C22×D293—41no—
60C22×D293C22⋊C411yescharacteristic
61C22×D293C2×D411yescharacteristic
62Dic586—41no—
63C22⋊D293—42no—
64C22⋊D293—42no—
65C2×Dic293—22no—
66C2×Dic293—21no—
67C2×Dic293—21no—
68C2×Dic293—42no—
69C2×Dic293C22⋊C411yescharacteristic
70C2×Dic293C2×D411yescharacteristic
71C4×D293—22no—
72C4×D293—22no—
73C4×D293—41no—
74C4×D293—41no—
75C23×C293—21no—
76C23×C293C22⋊C411yescharacteristic
77D4×C293—41no—
78D4×C293—42no—
79C2×C4×C293—21no—
80C2×C4×C293—41no—
81C2×C4×C293C22⋊C411yescharacteristic
82C2×C4×C293C22×C411yescharacteristic
83C22×C293—21no—
84C22×C293—21no—
85C22×C293—41no—
86C22×C293—41no—
87C22×C293—41no—
88C22×C293#10412yes—
89C22×C293C2×C22⋊C411yescharacteristic
90C2×D293—21no—
91C2×D293—21no—
92C2×D293—21no—
93C2×D293—21no—
94C2×D293—21no—
95C2×D293—44no—
96C2×D293#13512yes—
97#11924078—44no—
98C4×C293—21no—
99C4×C293—21no—
100C4×C293—41no—
101Dic293—21no—
102Dic293—41no—
103Dic293—41no—
104Dic293#9912yes—
105C2×C293—22no—
106C2×C293—81no—
107C2×C293C2×#9911yescharacteristic
108C2×C293#41611yescharacteristic
109C2×C293C2×#10411yescharacteristic
110D293—22no—
111D293—41no—
112C293#150111yescharacteristic, complemented, Sylow
113#1501—2931nomaximal, Sylow
114#525—2931no—
115C2×C22⋊C8—2931no—
116C4×C22⋊C4—2931no—
117#328—2932no—
118#327—2932no—
119C2×#41—2931no—
120C23×C4—2931no—
121C22×C8—5861no—
122#123—5861no—
123C22⋊Q8—2931no—
124C22⋊Q8—2931no—
125#121—2931no—
126#121#1192407811yescharacteristic, complemented
127#120—5861no—
128C4×D4—5861no—
129C4×D4—5861no—
130#117—2931no—
131C2×C22⋊C4—5861no—
132C2×C42—5861no—
133C22⋊C8—2932no—
134C22⋊C8—5861no—
135#95—2932no—
136C24—2931no—
137#41—11722no—
138C2×Q8—2931no—
139C2×D4—21no—
140C2×D4—5861no—
141C2×D4—5861no—
142C2×D4C2×#1192407811yescharacteristic
143C22×C4—2931no—
144C22×C4—2931no—
145C22×C4—2931no—
146C22×C4—2931no—
147C22×C4—2931no—
148C22×C4—5861no—
149C22×C4—5862no—
150C22×C4—11722no—
151C22×C4C2×#1192407811yescharacteristic
152C2×C8—5862no—
153C2×C8—11722no—
154C4⋊C4—2931no—
155C4⋊C4—5861no—
156C4⋊C4—5861no—
157C4⋊C4C2×#1192407811yescharacteristic
158C22⋊C4—21no—
159C22⋊C4—5861no—
160C22⋊C4—5861no—
161C22⋊C4—5861no—
162C22⋊C4—5864no—
163C22⋊C4—5861no—
164C42—5861no—
165C42—11722no—
166C23—21no—
167C23—2931no—
168C23—2931no—
169C23—5862no—
170C23—5862no—
171C23—11721no—
172C23C22⋊#1192407811yescharacteristic
173Q8—11721no—
174D4—41no—
175D4—42no—
176D4—11722no—
177D4—11722no—
178C2×C4—21no—
179C2×C4—41no—
180C2×C4—2931no—
181C2×C4—2931no—
182C2×C4—5862no—
183C2×C4—5862no—
184C2×C4—5862no—
185C2×C4—5864no—
186C2×C4—5861no—
187C2×C4—5861no—
188C2×C4—11721no—
189C2×C4—11721no—
190C2×C4—11722no—
191C2×C4—11722no—
192C2×C4—11722no—
193C2×C4C22⋊#1192407811yescharacteristic
194C2×C4C22×#1192407811yescharacteristic
195C8—11722no—
196C22—21no—
197C22—21no—
198C22—41no—
199C22—41no—
200C22—41no—
201C22—2932no—
202C22—5861no—
203C22—5861no—
204C22—5861no—
205C22—5861no—
206C22—5861no—
207C22—11724no—
208C22#2262768812yes—
209C22C2×C22⋊#1192407811yescharacteristic
210C4—21no—
211C4—21no—
212C4—41no—
213C4—2932no—
214C4—5861no—
215C4—11724no—
216C4—11721no—
217C4—11721no—
218C2—22no—
219C2—81no—
220C2—5862no—
221C2—11721no—
222C2D293⋊#9911yescharacteristic
223C2#3403711911yescharacteristic
224C2C2×#2262768811yescharacteristic
subgroupG/H
centerC22C2×C22⋊#11924078
commutatorC2×C4×C293C22×C4
FrattiniC2×C4C22×#11924078
Fitting#121×C293C4
socleC22×C293C2×C22⋊C4
prime radical#34036639C2
cosocleC2×C4×D293C23
hypercenter#121#11924078
hypocenterC293#1501
LCSG ▷ C2×C4×C293 ▷ C22×C293 ▷ C293
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C2×#22627681C2semidirect
2. C4×C22⋊#11924078C2semidirect
3. #34036982C2semidirect
4. #34036980C2semidirect
12. C2×#17989801C4semidirect
16. #22627603C4semidirect
21. #22627582C4semidirect
22. #121×C293C4semidirect
112. C293#1501semidirect
126. #121#11924078semidirect

Maximal subgroups

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

subgroupindex
C2×#226276812
C4×C22⋊#119240782
#340369822
#340369802
#340366392
#1501293