Finite Group Databasebeta

← #49157252

Subgroups — #49157252

Order 37504.

246 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 65 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#34036676C211yesmaximal, characteristic
2#34036185C211yesmaximal, characteristic, complemented
3#34036180C211yesmaximal, characteristic, complemented
4#34035858C211yesmaximal, characteristic, complemented
5D4⋊#14556873C211yesmaximal, characteristic, complemented
6#34035856C211yesmaximal, characteristic, complemented
7D4⋊C8×C293C211yesmaximal, characteristic, complemented
8C2×#17989802—21no—
9#22627623C411yescharacteristic
10#22627620C411yescharacteristic
11#22627610—21no—
12#22627599C411yescharacteristic
13#22627597—21no—
14#22627595C411yescharacteristic
15C4×D1172C2211yescharacteristic
16C4×C22⋊D293—21no—
17C42×D293C2211yescharacteristic
18C4⋊#14556873C2211yescharacteristic
19#22627553—21no—
20#22627536—21no—
21#22627536—21no—
22#22627534—21no—
23C4×#14556873C2211yescharacteristic
24C4×D4×C293C2211yescharacteristic
25C4⋊C8×C293C2211yescharacteristic
26C4×C8×C293C2211yescharacteristic
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
39C2×#14556873—21no—
40C2×#14556873—21no—
41C4⋊Dic293C2×C411yescharacteristic
42#17989781—21no—
43C22⋊Dic293—21no—
44#17989779—21no—
45#17989779—21no—
46C4×Dic293C2×C411yescharacteristic
47C4×Dic293D411yescharacteristic
48C4×Dic293D411yescharacteristic
49C2×D4×C293C2×C411yescharacteristic
50C22×C4×C293—21no—
51C2×C8×C293—21no—
52C2×C8×C293—21no—
53C4⋊C4×C293C2×C411yescharacteristic
54C22⋊C4×C293—21no—
55C42×C293C2311yescharacteristic
56C22×D293—21no—
57C22×D293C22⋊C411yescharacteristic
58Dic586—42no—
59D1172—21no—
60D1172—21no—
61D1172—42no—
62C22⋊D293—42no—
63C22⋊D293—42no—
64C22⋊D293—42no—
65C2×Dic293—21no—
66C2×Dic293C22⋊C411yescharacteristic
67C2×Dic293C22⋊C411yescharacteristic
68C2×Dic293C22⋊C411yescharacteristic
69C4×D293—21no—
70C4×D293—21no—
71C4×D293—21no—
72C4×D293—21no—
73C4×D293—41no—
74C4×D293—41no—
75C4×D293—41no—
76#14556873—41no—
77#14556873—41no—
78C23×C293—21no—
79D4×C293—21no—
80D4×C293—21no—
81C2×C4×C293—21no—
82C2×C4×C293—41no—
83C2×C4×C293—41no—
84C2×C4×C293C22×C411yescharacteristic
85C2×C4×C293C2×D411yescharacteristic
86C2×C4×C293C2×D411yescharacteristic
87C8×C293—41no—
88C8×C293—41no—
89C22×C293—41no—
90C22×C293—41no—
91C22×C293—41no—
92C22×C293C2×C22⋊C411yescharacteristic
93C2×D293—21no—
94C2×D293—21no—
95C2×D293—21no—
96C2×D293—41no—
97C2×D293—41no—
98C2×D293—41no—
99C4×C293—21no—
100C4×C293—41no—
101C4×C293#13111yescharacteristic
102C4×C293#13111yescharacteristic
103C4×C293AGL(1,ℤ/8)11yescharacteristic
104C4×C293AGL(1,ℤ/8)11yescharacteristic
105Dic293—21no—
106Dic293—21no—
107Dic293—21no—
108Dic293—41no—
109C2×C293—81no—
110C2×C293#40811yescharacteristic
111C2×C293#41811yescharacteristic
112C2×C293#42111yescharacteristic
113D293—41no—
114D293—81no—
115C293#149611yescharacteristic, complemented, Sylow
116#1496—2931nomaximal, Sylow
117#532—2931no—
118#432—2931no—
119#431—2931no—
120D4⋊C8—2931no—
121D4⋊C8—2931no—
122D4⋊C8—2931no—
123D4⋊C8D29311yescharacteristic, complemented
124C2×#41—5861no—
125C4⋊Q8—2931no—
126#127—2931no—
127#124—5861no—
128#121—2931no—
129#121—2931no—
130#121—5861no—
131C4×D4—2931no—
132C4×D4—5861no—
133C4×D4C2×D29311yescharacteristic
134C2×C42—2931no—
135C4⋊C8—2931no—
136C4⋊C8—5861no—
137C4⋊C8C2×D29311yescharacteristic
138C22⋊C8—5861no—
139C22⋊C8—5861no—
140#97—5861no—
141C4×C8—2931no—
142C4×C8C2×D29311yescharacteristic
143#41—11722no—
144#41—11722no—
145C2×Q8—5861no—
146C2×D4—2931no—
147C2×D4—5861no—
148C2×D4—5861no—
149C2×D4—5861no—
150C2×D4—5861no—
151C2×D4C4×D29311yescharacteristic
152C22×C4—21no—
153C22×C4—2931no—
154C22×C4—2931no—
155C22×C4—2931no—
156C22×C4—5861no—
157C2×C8—21no—
158C2×C8—21no—
159C2×C8—5861no—
160C2×C8—5861no—
161C4⋊C4—2931no—
162C4⋊C4—5861no—
163C4⋊C4C4×D29311yescharacteristic
164C22⋊C4—21no—
165C22⋊C4—5861no—
166C22⋊C4—5861no—
167C22⋊C4—5861no—
168C42—2931no—
169C42—2931no—
170C42—2931no—
171C42C22×D29311yescharacteristic
172C23—21no—
173C23—2931no—
174C23—5861no—
175Q8—11722no—
176D4—21no—
177D4—21no—
178D4—5861no—
179D4—5861no—
180D4—11722no—
181D4—11722no—
182D4—11722no—
183D4—11722no—
184C2×C4—21no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—2931no—
188C2×C4—2931no—
189C2×C4—2931no—
190C2×C4—5861no—
191C2×C4—5861no—
192C2×C4—5861no—
193C2×C4—5861no—
194C2×C4—5861no—
195C2×C4—11721no—
196C2×C4—11721no—
197C2×C4—11721no—
198C2×C4C2×C4×D29311yescharacteristic
199C2×C4D4×D29311yescharacteristic
200C2×C4D4×D29311yescharacteristic
201C8—41no—
202C8—41no—
203C8—11721no—
204C8—11721no—
205C22—41no—
206C22—41no—
207C22—41no—
208C22—5861no—
209C22—5861no—
210C22—5861no—
211C22—11721no—
212C22—11721no—
213C22—11721no—
214C22C22⋊C4×D29311yescharacteristic
215C4—21no—
216C4—41no—
217C4—5861no—
218C4—5861no—
219C4—5861no—
220C4—11721no—
221C4#2262763011yescharacteristic
222C4#2262763211yescharacteristic
223C4#2262764811yescharacteristic
224C4#2262765111yescharacteristic
225C2—81no—
226C2—23441no—
227C2—11721no—
228C2#3403609411yescharacteristic
229C2#3403613211yescharacteristic
230C2#3403614411yescharacteristic
subgroupG/H
centerC2×C4D4×D293
commutatorC2×C4×C293C22×C4
FrattiniC42C22×D293
FittingD4⋊C8×C293C2
socleC22×C293C2×C22⋊C4
prime radical#34036676C2
cosocleC42×C293C23
hypercenterD4⋊C8D293
hypocenterC293#1496
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C2×C4 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #34036185C2semidirect
3. #34036180C2semidirect
4. #34035858C2semidirect
5. D4⋊#14556873C2semidirect
6. #34035856C2semidirect
7. D4⋊C8×C293C2semidirect
115. C293#1496semidirect
123. D4⋊C8D293semidirect

Maximal subgroups

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

subgroupindex
#340366762
#340361852
#340361802
#340358582
D4⋊#145568732
#340358562
D4⋊C8×C2932
#1496293