Finite Group Databasebeta

← #49174180

Subgroups — #49174180

Order 37504.

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

normal subgroups only

This group has 346 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, complemented
2C4×C22⋊#11924078C211yesmaximal, characteristic, complemented
3#34036981C212yesmaximal, complemented
4#34036980C212yesmaximal, complemented
5#121×D293C211yesmaximal, characteristic
6C2×#17989811—21no—
7C2×C22⋊#11924078—21no—
8C2×C4×#11924078—21no—
9#22627681—21no—
10#22627681C2212yescomplemented
11(C2×#11924078)⋊C4C2212yescomplemented
12C2×D4×D293—21no—
13C2×D4×D293C411yescharacteristic, complemented
14C22×C4×D293C2211yescharacteristic
15#22627599C2211yescharacteristic
16#22627598C411yescharacteristic, complemented
17#22627597—21no—
18#22627596—21no—
19#22627595C2211yescharacteristic
20C4⋊C4×D293C411yescharacteristic, complemented
21C22⋊C4×D293—21no—
22#121×C293C411yescharacteristic, complemented
23C22×#11924078—22no—
24#17989811—42no—
25C2×#14556880—22no—
26C22⋊#11924078—24no—
27C4×#11924078—42no—
28C23×D293—21no—
29C23×D293D411yescharacteristic
30C2×D1172—21no—
31C2×D1172C2×C411yescharacteristic
32C2×C22⋊D293—21no—
33C2×C22⋊D293—21no—
34C2×C22⋊D293—21no—
35D4×D293—42no—
36D4×D293—44no—
37C22×Dic293D411yescharacteristic
38C2×C4×D293—21no—
39C2×C4×D293—42no—
40C2×C4×D293C2×C411yescharacteristic
41C2×C4×D293D411yescharacteristic
42C2×C4×D293D411yescharacteristic
43C2×C4×D293C2311yescharacteristic
44C4⋊Dic293C2×C411yescharacteristic
45#17989781—21no—
46C22⋊Dic293—21no—
47#17989779—21no—
48#17989779—21no—
49C2×D4×C293—21no—
50C2×D4×C293C2×C411yescharacteristic
51C22×C4×C293C2×C411yescharacteristic
52C4⋊C4×C293C2×C411yescharacteristic
53C22⋊C4×C293—21no—
54C2×#11924078—24no—
55C2×#11924078—42no—
56C2×#11924078—42no—
57#14556880—42no—
58C22×D293—22no—
59C22×D293—22no—
60C22×D293—21no—
61C22×D293—41no—
62C22×D293—42no—
63C22×D293—42no—
64C22×D293—42no—
65C22×D293C22⋊C411yescharacteristic
66C22×D293C2×D411yescharacteristic
67D1172—41no—
68D1172—42no—
69C22⋊D293—42no—
70C22⋊D293—42no—
71C22⋊D293—42no—
72C2×Dic293—22no—
73C2×Dic293—21no—
74C2×Dic293C22⋊C411yescharacteristic
75C2×Dic293C2×D411yescharacteristic
76C4×D293—22no—
77C4×D293—22no—
78C4×D293—41no—
79C4×D293—41no—
80C4×D293—42no—
81C23×C293—21no—
82C23×C293C22⋊C411yescharacteristic
83D4×C293—41no—
84D4×C293—42no—
85C2×C4×C293—21no—
86C2×C4×C293—41no—
87C2×C4×C293C22⋊C411yescharacteristic
88C2×C4×C293C22×C411yescharacteristic
89C22×C293—21no—
90C22×C293—21no—
91C22×C293—21no—
92C22×C293—41no—
93C22×C293—41no—
94C22×C293—41no—
95C22×C293C2×C22⋊C411yescharacteristic
96C2×D293—21no—
97C2×D293—21no—
98C2×D293—21no—
99C2×D293—21no—
100C2×D293—44no—
101C2×D293—41no—
102C2×D293—41no—
103C2×D293—41no—
104C2×D293—84no—
105C2×D293#10412yes—
106C2×D293AGL(1,ℤ/8)12yes—
107#11924078—44no—
108C4×C293—21no—
109C4×C293—21no—
110C4×C293—41no—
111Dic293—21no—
112Dic293—41no—
113Dic293#9912yes—
114C2×C293—41no—
115C2×C293—81no—
116C2×C293C2×#9911yescharacteristic
117C2×C293#41811yescharacteristic
118C2×C293C2×#10411yescharacteristic
119D293—22no—
120D293—22no—
121D293—81no—
122C293#150711yescharacteristic, complemented, Sylow
123#1507—2931nomaximal, Sylow
124C2×#121—2931no—
125#407—2931no—
126C4×C22⋊C4—2931no—
127#327—2932no—
128#327—2932no—
129C22×D4—2931no—
130C22×D4—5861no—
131C23×C4—2931no—
132C2×M16—5861no—
133#121—2931no—
134#121—2931no—
135#121—2931no—
136#121—5861no—
137#121—5861no—
138#121#1192407811yescharacteristic, complemented
139C2×C4⋊C4—2931no—
140C2×C22⋊C4—5861no—
141C2×C22⋊C4—5861no—
142C2×C42—5861no—
143C22⋊C8—2932no—
144C22⋊C8—5861no—
145#95—2932no—
146C24—2931no—
147C24—5861no—
148C2×D4—21no—
149C2×D4—2931no—
150C2×D4—5861no—
151C2×D4—5861no—
152C2×D4—5861no—
153C2×D4—5861no—
154C2×D4—11722no—
155C2×D4—11724no—
156C2×D4C2×#1192407811yescharacteristic
157C22×C4—2931no—
158C22×C4—2931no—
159C22×C4—2931no—
160C22×C4—2931no—
161C22×C4—2931no—
162C22×C4—5861no—
163C22×C4—5862no—
164C22×C4—11722no—
165C22×C4C2×#1192407811yescharacteristic
166M16—11722no—
167C2×C8—5862no—
168C4⋊C4—2931no—
169C4⋊C4—5861no—
170C4⋊C4C2×#1192407811yescharacteristic
171C22⋊C4—21no—
172C22⋊C4—5861no—
173C22⋊C4—5861no—
174C22⋊C4—5864no—
175C22⋊C4—5861no—
176C42—11722no—
177C23—21no—
178C23—2931no—
179C23—2931no—
180C23—5862no—
181C23—5862no—
182C23—5861no—
183C23—11721no—
184C23—11722no—
185C23—11722no—
186C23—11722no—
187C23C22⋊#1192407811yescharacteristic
188D4—41no—
189D4—42no—
190D4—11721no—
191D4—11722no—
192D4—11722no—
193D4—11722no—
194D4—11722no—
195C2×C4—21no—
196C2×C4—41no—
197C2×C4—2931no—
198C2×C4—2931no—
199C2×C4—5862no—
200C2×C4—5862no—
201C2×C4—5862no—
202C2×C4—5864no—
203C2×C4—5861no—
204C2×C4—11721no—
205C2×C4—11721no—
206C2×C4—11722no—
207C2×C4—11722no—
208C2×C4—11722no—
209C2×C4C22⋊#1192407811yescharacteristic
210C2×C4C22×#1192407811yescharacteristic
211C8—11722no—
212C22—21no—
213C22—21no—
214C22—21no—
215C22—41no—
216C22—41no—
217C22—41no—
218C22—2932no—
219C22—2932no—
220C22—23444no—
221C22—5861no—
222C22—5861no—
223C22—5861no—
224C22—5861no—
225C22—11724no—
226C22—11721no—
227C22—11721no—
228C22—11721no—
229C22C2×C22⋊#1192407811yescharacteristic
230C4—21no—
231C4—21no—
232C4—41no—
233C4—2932no—
234C4—5861no—
235C4—11724no—
236C4—11721no—
237C2—41no—
238C2—81no—
239C2—23441no—
240C2—5862no—
241C2—5862no—
242C2D293⋊#9911yescharacteristic
243C2#3403712111yescharacteristic
244C2D293⋊#10411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#11924078
commutatorC2×C4×C293C22×C4
FrattiniC2×C4C22×#11924078
Fitting#121×C293C4
socleC22×C293C2×C22⋊C4
prime radical#121×D293C2
cosocleC2×C4×D293C23
hypercenter#121#11924078
hypocenterC293#1507
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. #34037101C2semidirect
2. C4×C22⋊#11924078C2semidirect
3. #34036981C2semidirect
4. #34036980C2semidirect
10. #22627681C22semidirect
11. (C2×#11924078)⋊C4C22semidirect
13. C2×D4×D293C4semidirect
16. #22627598C4semidirect
20. C4⋊C4×D293C4semidirect
22. #121×C293C4semidirect
122. C293#1507semidirect
138. #121#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
#340369812
#340369802
#121×D2932
#1507293