Finite Group Databasebeta

← #49157249

Subgroups — #49157249

Order 37504.

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

normal subgroups only

This group has 216 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#34036666C211yesmaximal, characteristic
2#34036180C211yesmaximal, characteristic, complemented
3#34036151C211yesmaximal, characteristic, complemented
4Q8⋊#14556873C211yesmaximal, characteristic, complemented
5#34035858C211yesmaximal, characteristic, complemented
6#34035856C211yesmaximal, characteristic, complemented
7Q8⋊C8×C293C211yesmaximal, characteristic, complemented
8C2×#17989785—21no—
9#22627619—21no—
10#22627615C411yescharacteristic
11#22627613C411yescharacteristic
12#22627609—21no—
13#22627600C411yescharacteristic
14#22627599C411yescharacteristic
15C4×D1172—21no—
16C4×D1172C2211yescharacteristic
17#22627581—21no—
18C42×D293C2211yescharacteristic
19C4⋊#14556873C2211yescharacteristic
20#22627553—21no—
21#22627553—21no—
22#22627536—21no—
23C4×#14556873C2211yescharacteristic
24C4×Q8×C293C2211yescharacteristic
25C4⋊C8×C293C2211yescharacteristic
26C4×C8×C293C2211yescharacteristic
27C2×D1172—21no—
28C2×D1172C2×C411yescharacteristic
29C2×C4×D293—21no—
30C2×C4×D293C2×C411yescharacteristic
31C2×C4×D293D411yescharacteristic
32C2×C4×D293D411yescharacteristic
33#17989785—42no—
34C2×#14556873—21no—
35C2×#14556873—21no—
36C4⋊Dic293—21no—
37C4⋊Dic293C2×C411yescharacteristic
38#17989781—21no—
39#17989781—21no—
40#17989779—21no—
41#17989779—21no—
42#17989779—21no—
43#17989779—21no—
44#17989779—21no—
45C4×Dic293C2×C411yescharacteristic
46C4×Dic293D411yescharacteristic
47C4×Dic293D411yescharacteristic
48C2×Q8×C293C2×C411yescharacteristic
49C2×C8×C293—21no—
50C2×C8×C293—21no—
51C4⋊C4×C293—21no—
52C4⋊C4×C293C2×C411yescharacteristic
53C42×C293—21no—
54C42×C293C2311yescharacteristic
55C22×D293—21no—
56C22×D293C22⋊C411yescharacteristic
57D1172—21no—
58D1172—21no—
59D1172—42no—
60C2×Dic293—21no—
61C2×Dic293C22⋊C411yescharacteristic
62C2×Dic293C22⋊C411yescharacteristic
63C2×Dic293C22⋊C411yescharacteristic
64C4×D293—21no—
65C4×D293—21no—
66C4×D293—21no—
67C4×D293—21no—
68C4×D293—41no—
69C4×D293—41no—
70C4×D293—41no—
71#14556873—41no—
72#14556873—41no—
73Q8×C293—21no—
74Q8×C293—21no—
75C2×C4×C293—21no—
76C2×C4×C293—21no—
77C2×C4×C293C22×C411yescharacteristic
78C2×C4×C293C2×D411yescharacteristic
79C2×C4×C293C2×D411yescharacteristic
80C8×C293—41no—
81C8×C293—41no—
82C22×C293C2×C22⋊C411yescharacteristic
83C2×D293—21no—
84C2×D293—21no—
85C2×D293—21no—
86C2×D293—41no—
87C2×D293—41no—
88C2×D293—41no—
89C4×C293—21no—
90C4×C293—41no—
91C4×C293—41no—
92C4×C293#13111yescharacteristic
93C4×C293#13111yescharacteristic
94C4×C293AGL(1,ℤ/8)11yescharacteristic
95C4×C293#13711yescharacteristic
96Dic293—21no—
97Dic293—21no—
98Dic293—21no—
99Dic293—41no—
100C2×C293#40811yescharacteristic
101C2×C293#41711yescharacteristic
102C2×C293#42111yescharacteristic
103D293—41no—
104D293—81no—
105C293#149511yescharacteristic, complemented, Sylow
106#1495—2931nomaximal, Sylow
107#529—2931no—
108#431—2931no—
109#423—2931no—
110Q8⋊C8—2931no—
111Q8⋊C8D29311yescharacteristic, complemented
112D4⋊C8—2931no—
113D4⋊C8—2931no—
114C2×M16—5861no—
115#126—5861no—
116#125—2931no—
117#124—2931no—
118#123—5861no—
119C22⋊Q8—2931no—
120#121—2931no—
121C4×Q8C2×D29311yescharacteristic
122C4×D4—2931no—
123C4×D4—5861no—
124#117—5861no—
125C2×C42—2931no—
126C4⋊C8—2931no—
127C4⋊C8—5861no—
128C4⋊C8—5861no—
129C4⋊C8C2×D29311yescharacteristic
130C22⋊C8—5861no—
131C4×C8—2931no—
132C4×C8C2×D29311yescharacteristic
133C2×Q8C4×D29311yescharacteristic
134C2×D4—2931no—
135C2×D4—5861no—
136C22×C4—2931no—
137C22×C4—2931no—
138C22×C4—2931no—
139C22×C4—5861no—
140M16—11722no—
141C2×C8—21no—
142C2×C8—21no—
143C2×C8—5861no—
144C2×C8—5861no—
145C4⋊C4—21no—
146C4⋊C4—2931no—
147C4⋊C4—5861no—
148C4⋊C4—5861no—
149C4⋊C4—5861no—
150C4⋊C4C4×D29311yescharacteristic
151C22⋊C4—5861no—
152C22⋊C4—5861no—
153C22⋊C4—5861no—
154C22⋊C4—5861no—
155C22⋊C4—5861no—
156C42—21no—
157C42—2931no—
158C42—2931no—
159C42—2931no—
160C42C22×D29311yescharacteristic
161C23—2931no—
162C23—5861no—
163Q8—21no—
164Q8—21no—
165D4—5861no—
166D4—5861no—
167D4—11722no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—2931no—
171C2×C4—2931no—
172C2×C4—2931no—
173C2×C4—5861no—
174C2×C4—5861no—
175C2×C4—5861no—
176C2×C4—5861no—
177C2×C4—5861no—
178C2×C4—11721no—
179C2×C4—11721no—
180C2×C4—11721no—
181C2×C4C2×C4×D29311yescharacteristic
182C2×C4D4×D29311yescharacteristic
183C2×C4D4×D29311yescharacteristic
184C8—41no—
185C8—41no—
186C8—11721no—
187C8—11721no—
188C22—5861no—
189C22—5861no—
190C22—5861no—
191C22—11721no—
192C22—11721no—
193C22—11721no—
194C22C22⋊C4×D29311yescharacteristic
195C4—21no—
196C4—41no—
197C4—41no—
198C4—5861no—
199C4—5861no—
200C4—5861no—
201C4—11721no—
202C4#2262763011yescharacteristic
203C4#2262763211yescharacteristic
204C4#2262765111yescharacteristic
205C4#2262765611yescharacteristic
206C2—23441no—
207C2—11721no—
208C2#3403609411yescharacteristic
209C2#3403612911yescharacteristic
210C2#3403614411yescharacteristic
subgroupG/H
centerC2×C4D4×D293
commutatorC2×C4×C293C22×C4
FrattiniC42C22×D293
FittingQ8⋊C8×C293C2
socleC22×C293C2×C22⋊C4
prime radical#22627599C4
cosocleC42×C293C23
hypercenterQ8⋊C8D293
hypocenterC293#1495
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C2×C4 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
2. #34036180C2semidirect
3. #34036151C2semidirect
4. Q8⋊#14556873C2semidirect
5. #34035858C2semidirect
6. #34035856C2semidirect
7. Q8⋊C8×C293C2semidirect
105. C293#1495semidirect
111. Q8⋊C8D293semidirect

Maximal subgroups

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

subgroupindex
#340366662
#340361802
#340361512
Q8⋊#145568732
#340358582
#340358562
Q8⋊C8×C2932
#1495293