Finite Group Databasebeta

← #49174164

Subgroups — #49174164

Order 37504.

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

normal subgroups only

This group has 284 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#34037147C211yesmaximal, characteristic, complemented
2C4×C4⋊#11924078C211yesmaximal, characteristic, complemented
3#34036981C212yesmaximal, complemented
4#34036980C212yesmaximal, complemented
5#34036676C211yesmaximal, characteristic
6C2×C4⋊#11924078—21no—
7C2×C4×#11924078—21no—
8#22627691—21no—
9#22627681C2212yes—
10C4×#14556880—21no—
11(C2×#11924078)⋊C4C2212yes—
12C2×#17989802—21no—
13#22627623C411yescharacteristic, complemented
14#22627620C411yescharacteristic, complemented
15#22627610—21no—
16#22627599C2211yescharacteristic
17#22627597—21no—
18#22627595C2211yescharacteristic
19C4×D1172C411yescharacteristic, complemented
20C4×C22⋊D293—21no—
21C42×D293C2211yescharacteristic
22C4×D4×C293C411yescharacteristic, complemented
23C22×#11924078—22no—
24C2×#14556880—22no—
25C4⋊#11924078—24no—
26C4×#11924078—42no—
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×D293D411yescharacteristic
37C2×C4×D293D411yescharacteristic
38C2×C4×D293C2311yescharacteristic
39C4⋊Dic293C2×C411yescharacteristic
40#17989781—21no—
41C22⋊Dic293—21no—
42#17989779—21no—
43#17989779—21no—
44C4×Dic293C2×C411yescharacteristic
45C4×Dic293D411yescharacteristic
46C4×Dic293D411yescharacteristic
47C2×D4×C293C2×C411yescharacteristic
48C22×C4×C293—21no—
49C4⋊C4×C293C2×C411yescharacteristic
50C22⋊C4×C293—21no—
51C42×C293C2×C411yescharacteristic
52C2×#11924078—24no—
53C2×#11924078—42no—
54C2×#11924078—42no—
55#14556880—42no—
56C22×D293—21no—
57C22×D293C2×D411yescharacteristic
58Dic586—42no—
59D1172—41no—
60D1172—41no—
61D1172—41no—
62C22⋊D293—41no—
63C22⋊D293—41no—
64C22⋊D293—42no—
65C22⋊D293—42no—
66C2×Dic293—21no—
67C2×Dic293C22⋊C411yescharacteristic
68C2×Dic293C22⋊C411yescharacteristic
69C2×Dic293C2×D411yescharacteristic
70C4×D293—22no—
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×D293C2×D811yescharacteristic
92C2×D293C2×SD1611yescharacteristic
93#11924078—44no—
94C4×C293—21no—
95C4×C293—21no—
96C4×C293—41no—
97C4×C293#10212yes—
98Dic293—21no—
99Dic293—41no—
100Dic293#10212yes—
101Dic293#10412yes—
102C2×C293—81no—
103C2×C293#41011yescharacteristic
104C2×C293C2×#10211yescharacteristic
105C2×C293C2×#10411yescharacteristic
106D293—21no—
107D293—21no—
108D293—81no—
109C293#150211yescharacteristic, complemented, Sylow
110#1502—2931nomaximal, Sylow
111#532—2931no—
112#431—2931no—
113C4×C4⋊C4—2931no—
114#327—2932no—
115#327—2932no—
116C2×#41—5861no—
117C4⋊Q8—2931no—
118#127—2931no—
119#124—5861no—
120#121—2931no—
121#121—2931no—
122#121—5861no—
123C4×D4—2931no—
124C4×D4—5861no—
125C4×D4#1192407811yescharacteristic, complemented
126C2×C4⋊C4—5861no—
127C2×C42—2931no—
128C2×C42—5861no—
129C4⋊C8—5861no—
130C22⋊C8—2932no—
131C4×C8—5861no—
132#95—2932no—
133#41—11722no—
134#41—11722no—
135C2×Q8—5861no—
136C2×D4—2931no—
137C2×D4—5861no—
138C2×D4—5861no—
139C2×D4—5861no—
140C2×D4—5861no—
141C2×D4C2×#1192407811yescharacteristic
142C22×C4—21no—
143C22×C4—2931no—
144C22×C4—2931no—
145C22×C4—2931no—
146C22×C4—5862no—
147C22×C4—5861no—
148C2×C8—5862no—
149C4⋊C4—2931no—
150C4⋊C4—5861no—
151C4⋊C4—5864no—
152C4⋊C4C2×#1192407811yescharacteristic
153C22⋊C4—21no—
154C22⋊C4—5861no—
155C22⋊C4—5861no—
156C22⋊C4—5861no—
157C42—2931no—
158C42—2931no—
159C42—2931no—
160C42—11722no—
161C42C2×#1192407811yescharacteristic
162C23—21no—
163C23—2931no—
164C23—5861no—
165Q8—11722no—
166D4—41no—
167D4—11721no—
168D4—11721no—
169D4—11721no—
170D4—11722no—
171D4—11722no—
172D4—11721no—
173D4—11721no—
174C2×C4—21no—
175C2×C4—42no—
176C2×C4—2931no—
177C2×C4—2931no—
178C2×C4—2932no—
179C2×C4—2932no—
180C2×C4—2931no—
181C2×C4—5862no—
182C2×C4—5864no—
183C2×C4—5861no—
184C2×C4—11721no—
185C2×C4—11722no—
186C2×C4—11722no—
187C2×C4—11722no—
188C2×C4C22⋊#1192407811yescharacteristic
189C2×C4C22⋊#1192407811yescharacteristic
190C2×C4C22×#1192407811yescharacteristic
191C8—11722no—
192C22—41no—
193C22—41no—
194C22—41no—
195C22—2931no—
196C22—2931no—
197C22—5861no—
198C22—5861no—
199C22—11721no—
200C22—11721no—
201C22—11721no—
202C22C2×C22⋊#1192407811yescharacteristic
203C4—21no—
204C4—21no—
205C4—41no—
206C4—2932no—
207C4—2932no—
208C4—5861no—
209C4—11724no—
210C4—11721no—
211C4#2262768612yes—
212C2—81no—
213C2—23441no—
214C2—5861no—
215C2—5861no—
216C2#3403710811yescharacteristic
217C2C2×#2262768611yescharacteristic
218C2D293⋊#10411yescharacteristic
subgroupG/H
centerC2×C4C22⋊#11924078
commutatorC2×C4×C293C22×C4
FrattiniC2×C4C22×#11924078
FittingC4×D4×C293C4
socleC22×C293C2×C22⋊C4
prime radical#34036676C2
cosocleC2×C4×D293C23
hypercenterC4×D4#11924078
hypocenterC293#1502
LCSG ▷ C2×C4×C293 ▷ C22×C293 ▷ C293
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #34037147C2semidirect
2. C4×C4⋊#11924078C2semidirect
3. #34036981C2semidirect
4. #34036980C2semidirect
13. #22627623C4semidirect
14. #22627620C4semidirect
19. C4×D1172C4semidirect
22. C4×D4×C293C4semidirect
109. C293#1502semidirect
125. C4×D4#11924078semidirect

Maximal subgroups

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

subgroupindex
#340371472
C4×C4⋊#119240782
#340369812
#340369802
#340366762
#1502293