Finite Group Databasebeta

← #49174183

Subgroups — #49174183

Order 37504.

294 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 294 conjugacy classes of subgroups — too many to draw. Only its 60 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#34037101C211yesmaximal, characteristic
2C4×C22⋊#11924078C211yesmaximal, characteristic
3#34036983C212yesmaximal, complemented
4#34036982C212yesmaximal, complemented
5C22⋊Q8×D293C211yesmaximal, characteristic
6C2×#17989811—21no—
7C2×C22⋊#11924078—21no—
8C2×C4×#11924078—21no—
9#22627681—21no—
10#22627681C2212yes—
11(C2×#11924078)⋊C4C2212yes—
12C2×Q8×D293C411yescharacteristic, complemented
13C22×C4×D293C2211yescharacteristic
14#22627604C2211yescharacteristic
15#22627603C411yescharacteristic, complemented
16#22627602—21no—
17#22627601—21no—
18#22627600C2211yescharacteristic
19C4⋊C4×D293—21no—
20C4⋊C4×D293C411yescharacteristic, complemented
21C22⋊C4×D293—21no—
22C22⋊Q8×C293C411yescharacteristic, complemented
23C22×#11924078—22no—
24#17989811—42no—
25C2×#14556880—22no—
26C22⋊#11924078—24no—
27C4×#11924078—42no—
28C23×D293D411yescharacteristic
29C2×Dic586—21no—
30C2×Dic586C2×C411yescharacteristic
31Q8×D293—42no—
32C22×Dic293D411yescharacteristic
33C2×C4×D293—21no—
34C2×C4×D293—21no—
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—
43#17989781—21no—
44#17989781—21no—
45C22⋊Dic293—21no—
46#17989779—21no—
47#17989779—21no—
48C2×Q8×C293C2×C411yescharacteristic
49C22×C4×C293C2×C411yescharacteristic
50C4⋊C4×C293—21no—
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—42no—
63Dic586—41no—
64C2×Dic293—22no—
65C2×Dic293—21no—
66C2×Dic293—21no—
67C2×Dic293C22⋊C411yescharacteristic
68C2×Dic293C2×D411yescharacteristic
69C4×D293—22no—
70C4×D293—22no—
71C4×D293—41no—
72C4×D293—41no—
73C4×D293—42no—
74C4×D293—42no—
75C23×C293C22⋊C411yescharacteristic
76Q8×C293—41no—
77C2×C4×C293—21no—
78C2×C4×C293—21no—
79C2×C4×C293—41no—
80C2×C4×C293C22⋊C411yescharacteristic
81C2×C4×C293C22×C411yescharacteristic
82C22×C293—21no—
83C22×C293—21no—
84C22×C293—21no—
85C22×C293C2×C22⋊C411yescharacteristic
86C2×D293—21no—
87C2×D293—21no—
88C2×D293—21no—
89C2×D293—21no—
90C2×D293—44no—
91C2×D293#10412yes—
92C2×D293#13712yes—
93#11924078—44no—
94C4×C293—21no—
95C4×C293—21no—
96C4×C293—41no—
97C4×C293—41no—
98Dic293—21no—
99Dic293—41no—
100Dic293—41no—
101Dic293#9912yes—
102C2×C293—41no—
103C2×C293C2×#9911yescharacteristic
104C2×C293#41911yescharacteristic
105C2×C293C2×#10411yescharacteristic
106D293—22no—
107D293—22no—
108C293#150811yescharacteristic, complemented, Sylow
109#1508—2931nomaximal, Sylow
110C2×C22⋊Q8—2931no—
111#407—2931no—
112C4×C22⋊C4—2931no—
113#328—2932no—
114#328—2932no—
115C22×Q8—2931no—
116C23×C4—2931no—
117C2×M16—5861no—
118C22⋊Q8—2931no—
119C22⋊Q8—2931no—
120C22⋊Q8—2931no—
121C22⋊Q8—5861no—
122C22⋊Q8—5861no—
123C22⋊Q8#1192407811yescharacteristic, complemented
124C2×C4⋊C4—2931no—
125C2×C4⋊C4—5861no—
126C2×C22⋊C4—5861no—
127C2×C22⋊C4—5861no—
128C2×C42—5861no—
129C22⋊C8—2932no—
130C22⋊C8—5861no—
131#95—2932no—
132C24—2931no—
133C2×Q8—2931no—
134C2×Q8—5861no—
135C2×Q8—11722no—
136C2×Q8C2×#1192407811yescharacteristic
137C22×C4—2931no—
138C22×C4—2931no—
139C22×C4—2931no—
140C22×C4—2931no—
141C22×C4—2931no—
142C22×C4—5861no—
143C22×C4—5861no—
144C22×C4—5862no—
145C22×C4—11722no—
146C22×C4C2×#1192407811yescharacteristic
147M16—11722no—
148C2×C8—5862no—
149C4⋊C4—21no—
150C4⋊C4—2931no—
151C4⋊C4—5861no—
152C4⋊C4—5861no—
153C4⋊C4—5861no—
154C4⋊C4—5861no—
155C4⋊C4C2×#1192407811yescharacteristic
156C22⋊C4—21no—
157C22⋊C4—5861no—
158C22⋊C4—5861no—
159C22⋊C4—5864no—
160C22⋊C4—5861no—
161C42—11722no—
162C23—2931no—
163C23—2931no—
164C23—5862no—
165C23—5862no—
166C23—11721no—
167C23C22⋊#1192407811yescharacteristic
168Q8—41no—
169Q8—11721no—
170Q8—11722no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—41no—
174C2×C4—2931no—
175C2×C4—2931no—
176C2×C4—5862no—
177C2×C4—5862no—
178C2×C4—5862no—
179C2×C4—5864no—
180C2×C4—5861no—
181C2×C4—5861no—
182C2×C4—11721no—
183C2×C4—11721no—
184C2×C4—11722no—
185C2×C4—11722no—
186C2×C4—11722no—
187C2×C4—11722no—
188C2×C4C22⋊#1192407811yescharacteristic
189C2×C4C22×#1192407811yescharacteristic
190C8—11722no—
191C22—21no—
192C22—21no—
193C22—21no—
194C22—2932no—
195C22—2932no—
196C22—5861no—
197C22—5861no—
198C22—5861no—
199C22—5861no—
200C22—11724no—
201C22C2×C22⋊#1192407811yescharacteristic
202C4—21no—
203C4—21no—
204C4—41no—
205C4—41no—
206C4—2932no—
207C4—5861no—
208C4—11724no—
209C4—11721no—
210C4—11721no—
211C2—41no—
212C2—5862no—
213C2—5862no—
214C2D293⋊#9911yescharacteristic
215C2#3403712211yescharacteristic
216C2D293⋊#10411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#11924078
commutatorC2×C4×C293C22×C4
FrattiniC2×C4C22×#11924078
FittingC22⋊Q8×C293C4
socleC22×C293C2×C22⋊C4
prime radicalC23×D293D4
cosocleC2×C4×D293C23
hypercenterC22⋊Q8#11924078
hypocenterC293#1508
LCSG ▷ C2×C4×C293 ▷ C22×C293 ▷ C293
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. #34036983C2semidirect
4. #34036982C2semidirect
12. C2×Q8×D293C4semidirect
15. #22627603C4semidirect
20. C4⋊C4×D293C4semidirect
22. C22⋊Q8×C293C4semidirect
108. C293#1508semidirect
123. C22⋊Q8#11924078semidirect

Maximal subgroups

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

subgroupindex
#340371012
C4×C22⋊#119240782
#340369832
#340369822
C22⋊Q8×D2932
#1508293