Finite Group Databasebeta

← #49174297

Subgroups — #49174297

Order 37504.

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

normal subgroups only

This group has 260 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
1#34037132C211yesmaximal, characteristic, complemented
2C2×#22627691C211yesmaximal, characteristic, complemented
3#34036988C212yesmaximal, complemented
4#34036987C212yesmaximal, complemented
5#34036674C211yesmaximal, characteristic
6C2×#17989811—21no—
7C22×#14556880—21no—
8#22627691—21no—
9#22627691C2212yes—
10#22627691C2212yes—
11C4⋊#14556880—21no—
12C2×#17989801—21no—
13#22627623C2211yescharacteristic
14#22627620C2211yescharacteristic
15#22627610—21no—
16#22627598C411yescharacteristic
17#22627596—21no—
18D4×Dic293C411yescharacteristic
19#22627586C411yescharacteristic
20#22627584—21no—
21C2×C4×Dic293C2211yescharacteristic
22#121×C293C411yescharacteristic
23#17989811—42no—
24C2×#14556880—22no—
25C2×#14556880—22no—
26C2×#14556880—42no—
27#17989801—42no—
28#17989801—42no—
29C2×Dic586—21no—
30C2×D1172C2×C411yescharacteristic
31C2×C22⋊D293—21no—
32C2×C22⋊D293—21no—
33C2×C22⋊D293—21no—
34C22×Dic293—21no—
35C22×Dic293D411yescharacteristic
36C22×Dic293D411yescharacteristic
37C2×C4×D293—21no—
38C4⋊Dic293C2×C411yescharacteristic
39#17989781—21no—
40C22⋊Dic293—21no—
41#17989779—21no—
42#17989779—21no—
43C4×Dic293C2×C411yescharacteristic
44C4×Dic293D411yescharacteristic
45C4×Dic293D411yescharacteristic
46C4×Dic293C2311yescharacteristic
47C2×D4×C293—21no—
48C2×D4×C293C2×C411yescharacteristic
49C22×C4×C293C2×C411yescharacteristic
50C4⋊C4×C293C2×C411yescharacteristic
51C22⋊C4×C293—21no—
52#14556880—42no—
53#14556880—42no—
54C22×D293—21no—
55Dic586—41no—
56Dic586—41no—
57D1172—41no—
58C22⋊D293—42no—
59C22⋊D293—41no—
60C22⋊D293—41no—
61C22⋊D293—41no—
62C22⋊D293—41no—
63C2×Dic293—21no—
64C2×Dic293—21no—
65C2×Dic293—21no—
66C2×Dic293—42no—
67C2×Dic293C22⋊C411yescharacteristic
68C2×Dic293C22⋊C411yescharacteristic
69C2×Dic293D812yes—
70C2×Dic293SD1612yes—
71C2×Dic293C2×D411yescharacteristic
72C2×Dic293C2×D411yescharacteristic
73C4×D293—42no—
74C23×C293—21no—
75C23×C293C22⋊C411yescharacteristic
76D4×C293—41no—
77D4×C293—42no—
78C2×C4×C293—21no—
79C2×C4×C293—41no—
80C2×C4×C293C22⋊C411yescharacteristic
81C2×C4×C293C22×C411yescharacteristic
82C22×C293—21no—
83C22×C293—21no—
84C22×C293—41no—
85C22×C293—41no—
86C22×C293—41no—
87C22×C293#10212yes—
88C22×C293C2×C22⋊C411yescharacteristic
89C2×D293—41no—
90C2×D293—41no—
91C2×D293—41no—
92C4×C293—21no—
93C4×C293—21no—
94C4×C293—41no—
95Dic293—21no—
96Dic293—41no—
97Dic293#10212yes—
98Dic293C2×D811yescharacteristic
99Dic293C2×SD1611yescharacteristic
100Dic293AGL(1,ℤ/8)11yescharacteristic
101Dic293#13711yescharacteristic
102C2×C293—22no—
103C2×C293—81no—
104C2×C293#41311yescharacteristic
105C2×C293C2×#10211yescharacteristic
106C2×C293#41711yescharacteristic
107D293—81no—
108C293#154711yescharacteristic, complemented, Sylow
109#1547—2931nomaximal, Sylow
110#532—2931no—
111#423—2931no—
112C2×C4⋊C8—2931no—
113#332—2932no—
114#331—2932no—
115C2×#41—5861no—
116C2×M16—5861no—
117C22×C8—5861no—
118C4⋊Q8—2931no—
119#127—2931no—
120#124—5861no—
121#121—2931no—
122#121—5861no—
123#121#1192407811yescharacteristic
124C4×D4—2931no—
125C4×D4—2931no—
126C4×D4—5861no—
127C2×C42—2931no—
128C4⋊C8—2932no—
129C4⋊C8—2932no—
130C4⋊C8—5861no—
131C4⋊C8—5861no—
132#41—11722no—
133#41—11722no—
134C2×Q8—5861no—
135C2×D4—21no—
136C2×D4—2931no—
137C2×D4—5861no—
138C2×D4—5861no—
139C2×D4—5861no—
140C2×D4C2×#1192407811yescharacteristic
141C22×C4—2931no—
142C22×C4—2931no—
143C22×C4—5861no—
144C22×C4—5861no—
145C22×C4C2×#1192407811yescharacteristic
146M16—11722no—
147C2×C8—5862no—
148C2×C8—5862no—
149C2×C8—11722no—
150C4⋊C4—2931no—
151C4⋊C4—5861no—
152C4⋊C4C2×#1192407811yescharacteristic
153C22⋊C4—21no—
154C22⋊C4—5861no—
155C22⋊C4—5861no—
156C22⋊C4—5861no—
157C42—2931no—
158C42—2931no—
159C42—2931no—
160C42—2931no—
161C23—21no—
162C23—5861no—
163C23C22⋊#1192407811yescharacteristic
164Q8—11721no—
165Q8—11721no—
166D4—41no—
167D4—42no—
168D4—11721no—
169D4—11721no—
170D4—11721no—
171D4—11721no—
172D4—11721no—
173D4—11722no—
174C2×C4—21no—
175C2×C4—41no—
176C2×C4—2932no—
177C2×C4—2932no—
178C2×C4—2931no—
179C2×C4—2931no—
180C2×C4—2931no—
181C2×C4—2931no—
182C2×C4—5861no—
183C2×C4—5861no—
184C2×C4—5861no—
185C2×C4—11722no—
186C2×C4—11722no—
187C2×C4C22⋊#1192407811yescharacteristic
188C2×C4C22×#1192407811yescharacteristic
189C8—11722no—
190C8—11722no—
191C22—21no—
192C22—21no—
193C22—41no—
194C22—41no—
195C22—41no—
196C22—11721no—
197C22—11721no—
198C22—11721no—
199C22#2262768612yes—
200C22C2×C22⋊#1192407811yescharacteristic
201C4—21no—
202C4—21no—
203C4—41no—
204C4—2931no—
205C4—2932no—
206C4—2931no—
207C4—2931no—
208C4—2931no—
209C4—5861no—
210C4—11721no—
211C2—22no—
212C2—81no—
213C2—23441no—
214C2#3403711611yescharacteristic
215C2C2×#2262768611yescharacteristic
216C2#3403712011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#11924078
commutatorC2×C4×C293C22×C4
FrattiniC2×C4C22×#11924078
Fitting#121×C293C4
socleC22×C293C2×C22⋊C4
prime radical#34036674C2
cosocleC4×Dic293C23
hypercenter#121#11924078
hypocenterC293#1547
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. #34037132C2semidirect
2. C2×#22627691C2semidirect
3. #34036988C2semidirect
4. #34036987C2semidirect
108. C293#1547semidirect

Maximal subgroups

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

subgroupindex
#340371322
C2×#226276912
#340369882
#340369872
#340366742
#1547293