Finite Group Databasebeta

← #49174296

Subgroups — #49174296

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#34037134C211yesmaximal, characteristic, complemented
2D293⋊(C4⋊C8)C211yesmaximal, characteristic, complemented
3#34036988C212yesmaximal, complemented
4#34036987C212yesmaximal, complemented
5#34036676C211yesmaximal, characteristic
6C2×#17989812—21no—
7C2×D293⋊C8—21no—
8#22627691—21no—
9#22627691C2212yes—
10#22627691C2212yes—
11C4⋊#14556880—21no—
12C2×#17989802—21no—
13#22627623C2211yescharacteristic
14#22627620C2211yescharacteristic
15#22627610—21no—
16#22627599C411yescharacteristic
17#22627597—21no—
18#22627595C411yescharacteristic
19C4×D1172C411yescharacteristic
20C4×C22⋊D293—21no—
21C42×D293C2211yescharacteristic
22C4×D4×C293C411yescharacteristic
23#17989812—42no—
24D293⋊C8—42no—
25C2×#14556880—22no—
26C2×#14556880—22no—
27#17989802—42no—
28#17989802—42no—
29C2×Dic586—21no—
30C2×D1172—21no—
31C2×D1172C2×C411yescharacteristic
32C2×C22⋊D293—21no—
33C2×C22⋊D293—21no—
34C2×C22⋊D293—21no—
35C2×C4×D293—21no—
36C2×C4×D293C2×C411yescharacteristic
37C2×C4×D293D411yescharacteristic
38C2×C4×D293D411yescharacteristic
39C4⋊Dic293C2×C411yescharacteristic
40#17989781—21no—
41C22⋊Dic293—21no—
42#17989779—21no—
43#17989779—21no—
44C4×Dic293D411yescharacteristic
45C4×Dic293D411yescharacteristic
46C4×Dic293C2311yescharacteristic
47C2×D4×C293C2×C411yescharacteristic
48C22×C4×C293—21no—
49C4⋊C4×C293C2×C411yescharacteristic
50C22⋊C4×C293—21no—
51C42×C293C2×C411yescharacteristic
52#14556880—42no—
53#14556880—42no—
54C22×D293—21no—
55C22×D293C22⋊C411yescharacteristic
56Dic586—41no—
57Dic586—41no—
58D1172—41no—
59D1172—42no—
60C22⋊D293—42no—
61C22⋊D293—41no—
62C22⋊D293—41no—
63C22⋊D293—41no—
64C22⋊D293—41no—
65C2×Dic293—21no—
66C2×Dic293C22⋊C411yescharacteristic
67C2×Dic293C2×D411yescharacteristic
68C2×Dic293C2×D411yescharacteristic
69C4×D293—21no—
70C4×D293—21no—
71C4×D293—41no—
72C4×D293—42no—
73C4×D293D812yes—
74C4×D293SD1612yes—
75C23×C293—21no—
76D4×C293—41no—
77C2×C4×C293—21no—
78C2×C4×C293—42no—
79C2×C4×C293C22⋊C411yescharacteristic
80C2×C4×C293C22⋊C411yescharacteristic
81C2×C4×C293C22×C411yescharacteristic
82C22×C293—41no—
83C22×C293—41no—
84C22×C293—41no—
85C22×C293C2×C22⋊C411yescharacteristic
86C2×D293—21no—
87C2×D293—21no—
88C2×D293—41no—
89C2×D293—41no—
90C2×D293—41no—
91C2×D293#10212yes—
92C4×C293—21no—
93C4×C293—21no—
94C4×C293—41no—
95C4×C293#10212yes—
96Dic293—21no—
97Dic293—41no—
98Dic293C2×D811yescharacteristic
99Dic293C2×SD1611yescharacteristic
100Dic293AGL(1,ℤ/8)11yescharacteristic
101Dic293#13711yescharacteristic
102C2×C293—81no—
103C2×C293#41311yescharacteristic
104C2×C293C2×#10211yescharacteristic
105C2×C293#41711yescharacteristic
106D293—22no—
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—2931no—
123#121—5861no—
124C4×D4—2931no—
125C4×D4—5861no—
126C4×D4#1192407811yescharacteristic
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—2931no—
136C2×D4—5861no—
137C2×D4—5861no—
138C2×D4—5861no—
139C2×D4—5861no—
140C2×D4C2×#1192407811yescharacteristic
141C22×C4—21no—
142C22×C4—2931no—
143C22×C4—2931no—
144C22×C4—2931no—
145C22×C4—5861no—
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—
160C42C2×#1192407811yescharacteristic
161C23—21no—
162C23—2931no—
163C23—5861no—
164Q8—11721no—
165Q8—11721no—
166D4—41no—
167D4—11721no—
168D4—11722no—
169D4—11721no—
170D4—11721no—
171D4—11721no—
172D4—11721no—
173D4—11722no—
174C2×C4—21no—
175C2×C4—42no—
176C2×C4—2931no—
177C2×C4—2931no—
178C2×C4—2932no—
179C2×C4—2932no—
180C2×C4—2931no—
181C2×C4—5861no—
182C2×C4—5861no—
183C2×C4—5861no—
184C2×C4—11721no—
185C2×C4—11722no—
186C2×C4C22⋊#1192407811yescharacteristic
187C2×C4C22⋊#1192407811yescharacteristic
188C2×C4C22×#1192407811yescharacteristic
189C8—11722no—
190C8—11722no—
191C22—41no—
192C22—41no—
193C22—41no—
194C22—2932no—
195C22—5861no—
196C22—5861no—
197C22—11721no—
198C22—11721no—
199C22—11721no—
200C22C2×C22⋊#1192407811yescharacteristic
201C4—21no—
202C4—21no—
203C4—41no—
204C4—2931no—
205C4—2931no—
206C4—2931no—
207C4—2931no—
208C4—5861no—
209C4—11721no—
210C4#2262768612yes—
211C2—81no—
212C2—23441no—
213C2—5862no—
214C2#3403711511yescharacteristic
215C2C2×#2262768611yescharacteristic
216C2#3403712011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#11924078
commutatorC2×C4×C293C22×C4
FrattiniC2×C4C22×#11924078
FittingC4×D4×C293C4
socleC22×C293C2×C22⋊C4
prime radical#34036676C2
cosocleC4×Dic293C23
hypercenterC4×D4#11924078
hypocenterC293#1547
LCSG ▷ C2×C4×C293 ▷ C22×C293 ▷ C293
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #34037134C2semidirect
2. D293⋊(C4⋊C8)C2semidirect
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
#340371342
D293⋊(C4⋊C8)2
#340369882
#340369872
#340366762
#1547293