Finite Group Databasebeta

← #49174191

Subgroups — #49174191

Order 37504.

326 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 58 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#34037100C211yesmaximal, characteristic, complemented
2#34037072C211yesmaximal, characteristic, complemented
3#34036981C212yesmaximal, complemented
4#34036980C212yesmaximal, complemented
5#121×D293C211yesmaximal, characteristic
6C2×#17989812—21no—
7C2×C22⋊#11924078—21no—
8#22627681C2212yescomplemented
9C22⋊#14556880—21no—
10(C2×#11924078)⋊C4—21no—
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#17989812—42no—
25C2×#14556880—22no—
26C22⋊#11924078—42no—
27C23×D293—21no—
28C23×D293D411yescharacteristic
29C2×D1172—21no—
30C2×D1172C2×C411yescharacteristic
31C2×C22⋊D293—21no—
32C2×C22⋊D293—21no—
33C2×C22⋊D293—21no—
34D4×D293—42no—
35D4×D293—44no—
36C22×Dic293D411yescharacteristic
37C2×C4×D293—21no—
38C2×C4×D293—42no—
39C2×C4×D293C2×C411yescharacteristic
40C2×C4×D293D411yescharacteristic
41C2×C4×D293D411yescharacteristic
42C2×C4×D293C2311yescharacteristic
43C4⋊Dic293C2×C411yescharacteristic
44#17989781—21no—
45C22⋊Dic293—21no—
46#17989779—21no—
47#17989779—21no—
48C2×D4×C293—21no—
49C2×D4×C293C2×C411yescharacteristic
50C22×C4×C293C2×C411yescharacteristic
51C4⋊C4×C293C2×C411yescharacteristic
52C22⋊C4×C293—21no—
53C2×#11924078—42no—
54C2×#11924078—42no—
55C2×#11924078—42no—
56#14556880—42no—
57C22×D293—22no—
58C22×D293—22no—
59C22×D293—21no—
60C22×D293—41no—
61C22×D293—42no—
62C22×D293—42no—
63C22×D293—42no—
64C22×D293C22⋊C411yescharacteristic
65C22×D293C2×D411yescharacteristic
66D1172—41no—
67D1172—42no—
68C22⋊D293—42no—
69C22⋊D293—42no—
70C22⋊D293—42no—
71C2×Dic293—21no—
72C2×Dic293—41no—
73C2×Dic293C22⋊C411yescharacteristic
74C2×Dic293C2×D411yescharacteristic
75C4×D293—22no—
76C4×D293—22no—
77C4×D293—41no—
78C4×D293—41no—
79C4×D293—42no—
80C23×C293—21no—
81C23×C293C22⋊C411yescharacteristic
82D4×C293—41no—
83D4×C293—42no—
84C2×C4×C293—21no—
85C2×C4×C293—41no—
86C2×C4×C293C22⋊C411yescharacteristic
87C2×C4×C293C22×C411yescharacteristic
88C22×C293—21no—
89C22×C293—21no—
90C22×C293—21no—
91C22×C293—41no—
92C22×C293—41no—
93C22×C293—41no—
94C22×C293C2×C22⋊C411yescharacteristic
95C2×D293—21no—
96C2×D293—21no—
97C2×D293—21no—
98C2×D293—21no—
99C2×D293—44no—
100C2×D293—41no—
101C2×D293—41no—
102C2×D293—41no—
103C2×D293—84no—
104C2×D293#9912yes—
105C2×D293AGL(1,ℤ/8)12yes—
106#11924078—82no—
107C4×C293—21no—
108C4×C293—21no—
109C4×C293—41no—
110Dic293—21no—
111Dic293—21no—
112Dic293—41no—
113C2×C293—41no—
114C2×C293—81no—
115C2×C293C2×#9911yescharacteristic
116C2×C293#41811yescharacteristic
117C2×C293#42111yescharacteristic
118D293—22no—
119D293—22no—
120D293—81no—
121C293#151011yescharacteristic, complemented, Sylow
122#1510—2931nomaximal, Sylow
123C2×#121—2931no—
124#407—2931no—
125#381—2931no—
126#327—2932no—
127#327—2932no—
128C22×D4—2931no—
129C22×D4—5861no—
130C23×C4—2931no—
131C2×M16—5861no—
132#121—2931no—
133#121—2931no—
134#121—2931no—
135#121—5861no—
136#121—5861no—
137#121#1192407811yescharacteristic, complemented
138C2×C4⋊C4—2931no—
139C2×C22⋊C4—5861no—
140C2×C22⋊C4—5861no—
141C22⋊C8—2932no—
142C22⋊C8—5861no—
143#95—2932no—
144#95—5861no—
145C24—2931no—
146C24—5861no—
147C2×D4—21no—
148C2×D4—2931no—
149C2×D4—5861no—
150C2×D4—5861no—
151C2×D4—5861no—
152C2×D4—5861no—
153C2×D4—11722no—
154C2×D4—11724no—
155C2×D4C2×#1192407811yescharacteristic
156C22×C4—2931no—
157C22×C4—2931no—
158C22×C4—2931no—
159C22×C4—2931no—
160C22×C4—2931no—
161C22×C4—5861no—
162C22×C4—5862no—
163C22×C4—11722no—
164C22×C4C2×#1192407811yescharacteristic
165M16—11722no—
166C2×C8—5862no—
167C4⋊C4—2931no—
168C4⋊C4—5861no—
169C4⋊C4C2×#1192407811yescharacteristic
170C22⋊C4—21no—
171C22⋊C4—5861no—
172C22⋊C4—5861no—
173C22⋊C4—5861no—
174C22⋊C4—11722no—
175C23—21no—
176C23—2931no—
177C23—2931no—
178C23—5862no—
179C23—5862no—
180C23—5861no—
181C23—11721no—
182C23—11722no—
183C23—11722no—
184C23—11722no—
185C23C22⋊#1192407811yescharacteristic
186D4—41no—
187D4—42no—
188D4—11721no—
189D4—11722no—
190D4—11722no—
191D4—11722no—
192D4—11722no—
193C2×C4—21no—
194C2×C4—41no—
195C2×C4—2931no—
196C2×C4—2931no—
197C2×C4—5862no—
198C2×C4—5862no—
199C2×C4—5861no—
200C2×C4—11721no—
201C2×C4—11721no—
202C2×C4—11722no—
203C2×C4—11722no—
204C2×C4—11722no—
205C2×C4—11722no—
206C2×C4—11721no—
207C2×C4C22⋊#1192407811yescharacteristic
208C2×C4C22×#1192407811yescharacteristic
209C8—11722no—
210C22—21no—
211C22—21no—
212C22—21no—
213C22—41no—
214C22—41no—
215C22—41no—
216C22—2932no—
217C22—2932no—
218C22—23444no—
219C22—5861no—
220C22—5861no—
221C22—5861no—
222C22—5861no—
223C22—11724no—
224C22—11721no—
225C22—11721no—
226C22—11721no—
227C22C2×C22⋊#1192407811yescharacteristic
228C4—21no—
229C4—21no—
230C4—41no—
231C4—23442no—
232C4—5861no—
233C4—5861no—
234C4—11721no—
235C2—41no—
236C2—81no—
237C2—23441no—
238C2—5862no—
239C2—5862no—
240C2D293⋊#9911yescharacteristic
241C2#3403712111yescharacteristic
242C2#3403712611yescharacteristic
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#1510
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. #34037100C2semidirect
2. #34037072C2semidirect
3. #34036981C2semidirect
4. #34036980C2semidirect
8. #22627681C22semidirect
11. (C2×#11924078)⋊C4C22semidirect
13. C2×D4×D293C4semidirect
16. #22627598C4semidirect
20. C4⋊C4×D293C4semidirect
22. #121×C293C4semidirect
121. C293#1510semidirect
137. #121#11924078semidirect

Maximal subgroups

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

subgroupindex
#340371002
#340370722
#340369812
#340369802
#121×D2932
#1510293