Finite Group Databasebeta

← #49174220

Subgroups — #49174220

Order 37504.

340 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 68 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
2#34037071C211yesmaximal, characteristic, complemented
3#34036981C212yesmaximal, complemented
4#34036980C212yesmaximal, complemented
5#121×D293C211yesmaximal, characteristic
6C22×#14556880—21no—
7C2×C4⋊#11924078—21no—
8C2×C22⋊#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—
24C2×#14556880—22no—
25C2×#14556880—42no—
26C4⋊#11924078—42no—
27C22⋊#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—42no—
37D4×D293—42no—
38C22×Dic293D411yescharacteristic
39C2×C4×D293—21no—
40C2×C4×D293—42no—
41C2×C4×D293C2×C411yescharacteristic
42C2×C4×D293D411yescharacteristic
43C2×C4×D293D411yescharacteristic
44C2×C4×D293C2311yescharacteristic
45C4⋊Dic293C2×C411yescharacteristic
46#17989781—21no—
47C22⋊Dic293—21no—
48#17989779—21no—
49#17989779—21no—
50C2×D4×C293—21no—
51C2×D4×C293C2×C411yescharacteristic
52C22×C4×C293C2×C411yescharacteristic
53C4⋊C4×C293C2×C411yescharacteristic
54C22⋊C4×C293—21no—
55C2×#11924078—42no—
56C2×#11924078—42no—
57C2×#11924078—42no—
58#14556880—42no—
59C22×D293—21no—
60C22×D293—41no—
61C22×D293—41no—
62C22×D293—42no—
63C22×D293—42no—
64C22×D293—42no—
65C22×D293C22⋊C411yescharacteristic
66C22×D293D812yes—
67C22×D293SD1612yes—
68C22×D293C2×D411yescharacteristic
69D1172—41no—
70D1172—41no—
71D1172—41no—
72C22⋊D293—42no—
73C22⋊D293—41no—
74C22⋊D293—41no—
75C22⋊D293—42no—
76C2×Dic293—22no—
77C2×Dic293—21no—
78C2×Dic293C22⋊C411yescharacteristic
79C2×Dic293C2×D411yescharacteristic
80C4×D293—22no—
81C4×D293—22no—
82C4×D293—41no—
83C4×D293—41no—
84C4×D293—42no—
85C23×C293—21no—
86C23×C293C22⋊C411yescharacteristic
87D4×C293—41no—
88D4×C293—42no—
89C2×C4×C293—21no—
90C2×C4×C293—41no—
91C2×C4×C293C22⋊C411yescharacteristic
92C2×C4×C293C22×C411yescharacteristic
93C22×C293—21no—
94C22×C293—21no—
95C22×C293—41no—
96C22×C293—41no—
97C22×C293—41no—
98C22×C293#10212yes—
99C22×C293C2×C22⋊C411yescharacteristic
100C2×D293—21no—
101C2×D293—21no—
102C2×D293—21no—
103C2×D293—21no—
104C2×D293—42no—
105C2×D293—42no—
106C2×D293—41no—
107C2×D293—41no—
108C2×D293—41no—
109C2×D293—84no—
110C2×D293#10212yes—
111C2×D293C2×D811yescharacteristic
112C2×D293C2×SD1611yescharacteristic
113#11924078—82no—
114C4×C293—21no—
115C4×C293—21no—
116C4×C293—41no—
117Dic293—21no—
118Dic293—41no—
119Dic293#9912yes—
120C2×C293—22no—
121C2×C293—81no—
122C2×C293C2×#9911yescharacteristic
123C2×C293C2×#10211yescharacteristic
124C2×C293#42111yescharacteristic
125D293—21no—
126D293—22no—
127D293—21no—
128D293—81no—
129C293#151911yescharacteristic, complemented, Sylow
130#1519—2931nomaximal, Sylow
131C2×#121—2931no—
132C2×C22⋊C8—2931no—
133#380—2931no—
134#327—2932no—
135#327—2932no—
136C22×D4—2931no—
137C22×D4—5861no—
138C23×C4—2931no—
139C22×C8—5861no—
140#121—2931no—
141#121—2931no—
142#121—2931no—
143#121—5861no—
144#121—5861no—
145#121#1192407811yescharacteristic, complemented
146C2×C4⋊C4—2931no—
147C2×C4⋊C4—5861no—
148C2×C22⋊C4—5861no—
149C2×C22⋊C4—5861no—
150C22⋊C8—2932no—
151C22⋊C8—5861no—
152#95—2932no—
153C24—2931no—
154C24—5861no—
155C2×D4—21no—
156C2×D4—2931no—
157C2×D4—5861no—
158C2×D4—5861no—
159C2×D4—5861no—
160C2×D4—5861no—
161C2×D4—11722no—
162C2×D4—11722no—
163C2×D4—11722no—
164C2×D4C2×#1192407811yescharacteristic
165C22×C4—2931no—
166C22×C4—2931no—
167C22×C4—2931no—
168C22×C4—2931no—
169C22×C4—2931no—
170C22×C4—5861no—
171C22×C4—5862no—
172C22×C4—11722no—
173C22×C4C2×#1192407811yescharacteristic
174C2×C8—5862no—
175C2×C8—11722no—
176C4⋊C4—2931no—
177C4⋊C4—5861no—
178C4⋊C4—11722no—
179C4⋊C4C2×#1192407811yescharacteristic
180C22⋊C4—21no—
181C22⋊C4—5861no—
182C22⋊C4—5861no—
183C22⋊C4—5861no—
184C22⋊C4—11722no—
185C23—21no—
186C23—2931no—
187C23—2931no—
188C23—2932no—
189C23—2932no—
190C23—5861no—
191C23—11721no—
192C23—11721no—
193C23—11722no—
194C23—11722no—
195C23—11722no—
196C23C22⋊#1192407811yescharacteristic
197D4—41no—
198D4—42no—
199D4—11721no—
200D4—11721no—
201D4—11721no—
202D4—11722no—
203D4—11721no—
204D4—11721no—
205D4—11722no—
206C2×C4—21no—
207C2×C4—41no—
208C2×C4—2931no—
209C2×C4—2931no—
210C2×C4—5862no—
211C2×C4—5862no—
212C2×C4—5862no—
213C2×C4—5861no—
214C2×C4—11721no—
215C2×C4—11721no—
216C2×C4—11722no—
217C2×C4—11722no—
218C2×C4—11722no—
219C2×C4—11722no—
220C2×C4C22⋊#1192407811yescharacteristic
221C2×C4C22×#1192407811yescharacteristic
222C8—11722no—
223C22—21no—
224C22—21no—
225C22—41no—
226C22—41no—
227C22—41no—
228C22—2931no—
229C22—2932no—
230C22—2931no—
231C22—23444no—
232C22—5861no—
233C22—5861no—
234C22—5861no—
235C22—5861no—
236C22—11722no—
237C22—11722no—
238C22—11721no—
239C22—11721no—
240C22—11721no—
241C22#2262768612yes—
242C22C2×C22⋊#1192407811yescharacteristic
243C4—21no—
244C4—21no—
245C4—41no—
246C4—2932no—
247C4—23442no—
248C4—5861no—
249C4—11721no—
250C2—22no—
251C2—81no—
252C2—23441no—
253C2—5861no—
254C2—5862no—
255C2—5861no—
256C2D293⋊#9911yescharacteristic
257C2C2×#2262768611yescharacteristic
258C2#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#1519
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. #34037071C2semidirect
3. #34036981C2semidirect
4. #34036980C2semidirect
10. #22627681C22semidirect
11. (C2×#11924078)⋊C4C22semidirect
13. C2×D4×D293C4semidirect
16. #22627598C4semidirect
20. C4⋊C4×D293C4semidirect
22. #121×C293C4semidirect
129. C293#1519semidirect
145. #121#11924078semidirect

Maximal subgroups

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

subgroupindex
C2×#226276812
#340370712
#340369812
#340369802
#121×D2932
#1519293