Finite Group Databasebeta

← #49168884

Subgroups — #49168884

Order 37504.

444 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 133 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#34036686C211yesmaximal, characteristic, complemented
2#34036464C212yesmaximal, complemented
3#34036409C212yesmaximal, complemented
4#34036334C212yesmaximal, complemented
5#34036280C212yesmaximal
6#34036229C214yesmaximal, complemented
7#34036186C211yesmaximal, characteristic, complemented
8C2×C4×D4×C293C211yesmaximal, characteristic
9C2×#17989790C2214yes—
10#22627624C2211yescharacteristic, complemented
11#22627624C2211yescharacteristic, complemented
12#22627616—21no—
13#22627603—21no—
14#22627603C2212yes—
15C4×Dic586—21no—
16C4×Dic586C2212yescomplemented
17#22627583—21no—
18#22627557C2214yescomplemented
19C4⋊#14556873C2212yescomplemented
20#22627547C2214yescomplemented
21#22627545C2214yes—
22C22⋊#14556873C2212yes—
23#22627535C2212yescomplemented
24C22×D4×C293C2211yescharacteristic
25C23×C4×C293—21no—
26C4×D4×C293—21no—
27C4×D4×C293—21no—
28C4×D4×C293C2212yes—
29C4×D4×C293C2212yes—
30C2×C4⋊C4×C293C2211yescharacteristic
31C2×C22⋊C4×C293—21no—
32C2×C42×C293C2211yescharacteristic
33C2×Dic586—21no—
34C2×Dic586C2312yes—
35#17989790—28no—
36C2×#14556873C2314yes—
37C4⋊Dic293—21no—
38C4⋊Dic293—21no—
39C4⋊Dic293—21no—
40C4⋊Dic293C2312yes—
41#17989781—22no—
42#17989781—22no—
43C22⋊Dic293—22no—
44C4×Dic293—22no—
45C24×C293—21no—
46C2×D4×C293—24no—
47C2×D4×C293—21no—
48C2×D4×C293C2312yes—
49C22×C4×C293—21no—
50C22×C4×C293—22no—
51C22×C4×C293—22no—
52C22×C4×C293—44no—
53C22×C4×C293D411yescharacteristic
54C22×C4×C293D411yescharacteristic
55C22×C4×C293C2311yescharacteristic
56C4⋊C4×C293—21no—
57C4⋊C4×C293C2312yes—
58C22⋊C4×C293—22no—
59C22⋊C4×C293—22no—
60C42×C293D411yescharacteristic
61C42×C293D411yescharacteristic
62C42×C293C2311yescharacteristic
63C42×C293C2311yescharacteristic
64Dic586—24no—
65Dic586—42no—
66C2×Dic293—22no—
67C2×Dic293—22no—
68#14556873—24no—
69C23×C293—24no—
70C23×C293—22no—
71C23×C293—42no—
72C23×C293—42no—
73C23×C293C2×D411yescharacteristic
74D4×C293—24no—
75D4×C293—22no—
76D4×C293#4114yes—
77C2×C4×C293—22no—
78C2×C4×C293—22no—
79C2×C4×C293—22no—
80C2×C4×C293—22no—
81C2×C4×C293—44no—
82C2×C4×C293—42no—
83C2×C4×C293—44no—
84C2×C4×C293C2×D411yescharacteristic
85C2×C4×C293C2×D411yescharacteristic
86C2×C4×C293C2×D411yescharacteristic
87C2×C4×C293C2×D411yescharacteristic
88C2×C4×C293C2×D411yescharacteristic
89C2×C4×C293C2411yescharacteristic
90C22×C293—21no—
91C22×C293—21no—
92C22×C293—24no—
93C22×C293—48no—
94C22×C293—42no—
95C22×C293—42no—
96C22×C293#13712yes—
97C22×C293C22×D411yescharacteristic
98C4×C293—21no—
99C4×C293—21no—
100C4×C293—21no—
101C4×C293—21no—
102C4×C293—42no—
103C4×C293AGL(1,ℤ/8)12yes—
104C4×C293C2×#4112yes—
105Dic293—42no—
106Dic293—42no—
107C2×C293—22no—
108C2×C293—44no—
109C2×C293#52511yescharacteristic
110C2×C293C2×AGL(1,ℤ/8)11yescharacteristic
111C2×C293C2×#13711yescharacteristic
112C293#311011yescharacteristic, complemented, Sylow
113#3110—2931nomaximal, Sylow
114#533—2931no—
115C2×C4×D4D29311yescharacteristic
116#484—2932no—
117#474—2932no—
118#461—2932no—
119#450—2932no—
120#440—2934no—
121#432—2931no—
122C22×D4C2×D29311yescharacteristic
123C23×C4—21no—
124C2×SD16—2934no—
125C4⋊Q8—2931no—
126C4⋊Q8—2931no—
127#125—5861no—
128C22⋊Q8—2932no—
129C22⋊Q8—5861no—
130C4×Q8—2932no—
131C4×Q8—5861no—
132C4×D4—21no—
133C4×D4—21no—
134C4×D4C2×D29312yes—
135C4×D4C2×D29312yes—
136#117—5861no—
137C2×C4⋊C4C2×D29311yescharacteristic
138C2×C22⋊C4—21no—
139C2×C42C2×D29311yescharacteristic
140#107—2934no—
141C4⋊C8—2932no—
142#103—2934no—
143#102—2934no—
144C22⋊C8—2932no—
145#97—2932no—
146C24—21no—
147C2×Q8—2932no—
148C2×Q8—5861no—
149C2×D4—24no—
150C2×D4—21no—
151C2×D4C22×D29312yes—
152C22×C4—21no—
153C22×C4—22no—
154C22×C4—22no—
155C22×C4—44no—
156C22×C4C22⋊D29311yescharacteristic
157C22×C4C22⋊D29311yescharacteristic
158C22×C4C22×D29311yescharacteristic
159SD16—5868no—
160C2×C8—2934no—
161C4⋊C4—21no—
162C4⋊C4—2932no—
163C4⋊C4—5861no—
164C4⋊C4—5861no—
165C4⋊C4—5862no—
166C4⋊C4—5862no—
167C4⋊C4—5861no—
168C4⋊C4C22×D29312yes—
169C22⋊C4—22no—
170C22⋊C4—22no—
171C22⋊C4—5862no—
172C42—5862no—
173C42C22⋊D29311yescharacteristic
174C42C22⋊D29311yescharacteristic
175C42C22×D29311yescharacteristic
176C42C22×D29311yescharacteristic
177C23—24no—
178C23—22no—
179C23—42no—
180C23—42no—
181C23C2×C22⋊D29311yescharacteristic
182Q8—5864no—
183Q8—11722no—
184D4—24no—
185D4—22no—
186D4#1798980214yes—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—44no—
192C2×C4—42no—
193C2×C4—44no—
194C2×C4—5862no—
195C2×C4—5862no—
196C2×C4C2×C22⋊D29311yescharacteristic
197C2×C4C2×C22⋊D29311yescharacteristic
198C2×C4C2×C22⋊D29311yescharacteristic
199C2×C4C2×C22⋊D29311yescharacteristic
200C2×C4C2×C22⋊D29311yescharacteristic
201C2×C4C23×D29311yescharacteristic
202C8—5864no—
203C22—21no—
204C22—21no—
205C22—24no—
206C22—48no—
207C22—42no—
208C22—42no—
209C22#2262765412yes—
210C22C22×C22⋊D29311yescharacteristic
211C4—21no—
212C4—21no—
213C4—21no—
214C4—21no—
215C4—42no—
216C4—11722no—
217C4—11722no—
218C4#2262765012yes—
219C4C2×#1798980212yes—
220C2—22no—
221C2—44no—
222C2#3403664011yescharacteristic
223C2C2×#2262765011yescharacteristic
224C2C2×#2262765411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
FittingC2×C4×D4×C293C2
socleC22×C293C22×D4
prime radicalC22×D4×C293C22
hypercenterC2×C4×D4D293
hypocenterC293#3110
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. #34036686C2semidirect
2. #34036464C2semidirect
3. #34036409C2semidirect
4. #34036334C2semidirect
6. #34036229C2semidirect
7. #34036186C2semidirect
10. #22627624C22semidirect
11. #22627624C22semidirect
16. C4×Dic586C22semidirect
18. #22627557C22semidirect
19. C4⋊#14556873C22semidirect
20. #22627547C22semidirect
23. #22627535C22semidirect
112. C293#3110semidirect

Maximal subgroups

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

subgroupindex
#340366862
#340364642
#340364092
#340363342
#340362802
#340362292
#340361862
C2×C4×D4×C2932
#3110293