Finite Group Databasebeta

← #49157898

Subgroups — #49157898

Order 37504.

216 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 53 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#34036852C211yesmaximal, characteristic, complemented
2#34036476C211yesmaximal, characteristic, complemented
3#34036329C211yesmaximal, characteristic, complemented
4#34036325C211yesmaximal, characteristic
5#34035876C211yesmaximal, characteristic, complemented
6#34035858C211yesmaximal, characteristic, complemented
7Q8⋊C8×C293C211yesmaximal, characteristic, complemented
8C2×#17989789—21no—
9C2×D2344—21no—
10#22627624C2211yescharacteristic
11#22627621C2211yescharacteristic
12#22627619—22no—
13#22627612—21no—
14#22627600—21no—
15C4×Dic586—21no—
16C4×D1172C2211yescharacteristic
17#22627582—21no—
18C4⋊#14556873C2211yescharacteristic
19#22627546—21no—
20#22627546—22no—
21#22627544—21no—
22C4×Q8×C293C2211yescharacteristic
23C4⋊C8×C293C2211yescharacteristic
24C4×C8×C293C2211yescharacteristic
25C2×Dic586—21no—
26C2×D1172—21no—
27C2×D1172—21no—
28C2×D1172—21no—
29C2×D1172D411yescharacteristic
30C2×C4×D293—21no—
31#17989789—42no—
32D2344—42no—
33C2×#14556873—21no—
34C4⋊Dic293—21no—
35C4⋊Dic293D411yescharacteristic
36C4⋊Dic293D412yes—
37#17989781—22no—
38#17989779—22no—
39#17989779—22no—
40#17989779—21no—
41C4×Dic293—22no—
42C2×Q8×C293D411yescharacteristic
43C2×C8×C293—21no—
44C2×C8×C293—21no—
45C4⋊C4×C293—21no—
46C4⋊C4×C293D411yescharacteristic
47C42×C293—21no—
48C42×C293C2311yescharacteristic
49C22×D293—21no—
50C22×D293—41no—
51Dic586—41no—
52Dic586—41no—
53D1172—21no—
54D1172—21no—
55D1172—42no—
56D1172—41no—
57D1172—41no—
58D1172—41no—
59D1172—41no—
60C2×Dic293—21no—
61C2×Dic293—22no—
62C4×D293—41no—
63C4×D293—41no—
64#14556873—41no—
65Q8×C293—21no—
66Q8×C293—21no—
67C2×C4×C293—21no—
68C2×C4×C293—21no—
69C2×C4×C293C2×D411yescharacteristic
70C2×C4×C293C2×D411yescharacteristic
71C2×C4×C293C2×D411yescharacteristic
72C8×C293—41no—
73C8×C293—41no—
74C22×C293#12011yescharacteristic
75C2×D293—41no—
76C2×D293—41no—
77C2×D293—41no—
78C2×D293—81no—
79C2×D293—81no—
80C2×D293—81no—
81C4×C293—21no—
82C4×C293—41no—
83C4×C293—41no—
84C4×C293#13511yescharacteristic
85C4×C293#13511yescharacteristic
86C4×C293AGL(1,ℤ/8)11yescharacteristic
87C4×C293AGL(1,ℤ/8)11yescharacteristic
88Dic293—41no—
89Dic293—42no—
90C2×C293#44911yescharacteristic
91C2×C293#44911yescharacteristic
92C2×C293#45411yescharacteristic
93D293—81no—
94D293—161no—
95C293#162811yescharacteristic, complemented, Sylow
96#1628—2931nomaximal, Sylow
97#556—2931no—
98#486—2931no—
99#460—2931no—
100#459—2931no—
101#332—2931no—
102Q8⋊C8D29311yescharacteristic, complemented
103D4⋊C8—2931no—
104C2×SD16—5861no—
105C2×D8—5861no—
106C4⋊Q8—2931no—
107#127—2931no—
108#126—5862no—
109#124—5861no—
110C22⋊Q8—5861no—
111C4×Q8—5861no—
112C4×Q8C2×D29311yescharacteristic
113C4×D4—2931no—
114#117—5861no—
115C4⋊C8—2931no—
116C4⋊C8C2×D29311yescharacteristic
117#102—5861no—
118#102—5862no—
119#102—5861no—
120C4×C8C2×D29311yescharacteristic
121C2×Q8—5861no—
122C2×Q8D117211yescharacteristic
123C2×D4—2931no—
124C2×D4—5861no—
125C2×D4—5861no—
126C2×D4—5861no—
127C22×C4—5861no—
128SD16—11722no—
129D8—11722no—
130C2×C8—21no—
131C2×C8—21no—
132C2×C8—5861no—
133C4⋊C4—21no—
134C4⋊C4—2931no—
135C4⋊C4—2932no—
136C4⋊C4—5862no—
137C4⋊C4—5861no—
138C4⋊C4D117211yescharacteristic
139C22⋊C4—5862no—
140C22⋊C4—5862no—
141C22⋊C4—5861no—
142C42—21no—
143C42—5862no—
144C42C22×D29311yescharacteristic
145C23—5861no—
146C23—11721no—
147Q8—21no—
148Q8—21no—
149Q8—11721no—
150Q8—11721no—
151D4—5861no—
152D4—5861no—
153D4—11722no—
154D4—11721no—
155D4—11721no—
156D4—11721no—
157D4—11721no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—5861no—
161C2×C4—5862no—
162C2×C4—11721no—
163C2×C4—11721no—
164C2×C4D4×D29311yescharacteristic
165C2×C4D4×D29311yescharacteristic
166C2×C4C2×D117211yescharacteristic
167C8—41no—
168C8—41no—
169C8—11721no—
170C22—23441no—
171C22—23441no—
172C22—23441no—
173C22—11721no—
174C22—11721no—
175C22—11721no—
176C22#2262759411yescharacteristic
177C4—21no—
178C4—41no—
179C4—41no—
180C4—11721no—
181C4—11722no—
182C4#2262764611yescharacteristic
183C4#2262764711yescharacteristic
184C4#2262765111yescharacteristic
185C4#2262765211yescharacteristic
186C2—23441no—
187C2—46881no—
188C2#3403627611yescharacteristic
189C2#3403627711yescharacteristic
190C2#3403630311yescharacteristic
subgroupG/H
centerC22#22627594
commutator, cosocleC42×C293C23
FrattiniC42C22×D293
FittingQ8⋊C8×C293C2
socleC22×C293#120
prime radical#34036325C2
hypercenterQ8⋊C8D293
hypocenterC293#1628
LCSG ▷ C42×C293 ▷ C22×C293 ▷ C293
UCSC1 ◁ C22 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
1. #34036852C2semidirect
2. #34036476C2semidirect
3. #34036329C2semidirect
5. #34035876C2semidirect
6. #34035858C2semidirect
7. Q8⋊C8×C293C2semidirect
95. C293#1628semidirect
102. Q8⋊C8D293semidirect

Maximal subgroups

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

subgroupindex
#340368522
#340364762
#340363292
#340363252
#340358762
#340358582
Q8⋊C8×C2932
#1628293