Finite Group Databasebeta

← #49168908

Subgroups — #49168908

Order 37504.

424 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 129 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#34036679C211yesmaximal, characteristic
2C2×C4×Dic586C211yesmaximal, characteristic, complemented
3#34036443C212yesmaximal, complemented
4#34036425C212yesmaximal, complemented
5#34036330C212yesmaximal, complemented
6#34036270C212yesmaximal, complemented
7#34036231C214yesmaximal, complemented
8#432×C293C211yesmaximal, characteristic, complemented
9C2×#17989802—21no—
10C22×Dic586C2211yescharacteristic
11C2×#17989791C2214yes—
12#22627624C2211yescharacteristic
13#22627621C2211yescharacteristic
14#22627612—21no—
15#22627598—21no—
16#22627598C2212yes—
17C4×Dic586—21no—
18C4×Dic586—21no—
19C4×Dic586C2212yes—
20C4×Dic586C2212yes—
21C4×D1172—21no—
22C4×D1172C2212yes—
23C2×C4⋊Dic293C2211yescharacteristic
24C2×#17989781—21no—
25C2×C4×Dic293—21no—
26#22627558C2214yes—
27#22627549C2214yes—
28#22627546C2214yes—
29C2×C42×C293C2211yescharacteristic
30C4⋊C8×C293C2212yes—
31C22⋊C8×C293C2212yes—
32#97×C293C2212yes—
33#17989802—44no—
34C2×Dic586—24no—
35C2×Dic586—21no—
36C2×Dic586—21no—
37C2×Dic586C2312yes—
38C2×D1172—21no—
39C2×D1172—21no—
40C2×D1172C2312yes—
41C2×C22⋊D293—22no—
42C22×Dic293—21no—
43C22×Dic293—21no—
44C2×C4×D293—22no—
45#17989791—28no—
46C4⋊Dic293—21no—
47C4⋊Dic293—21no—
48C4⋊Dic293C2312yes—
49C4⋊Dic293C2312yes—
50#17989781—22no—
51#17989781—22no—
52#17989779—22no—
53#17989779—22no—
54C4×Dic293—22no—
55C4×Dic293—22no—
56C22×C4×C293D411yescharacteristic
57C22×C4×C293D411yescharacteristic
58C22×C4×C293C2311yescharacteristic
59C2×C8×C293C2314yes—
60C42×C293D411yescharacteristic
61C42×C293D411yescharacteristic
62C42×C293C2311yescharacteristic
63C42×C293C2311yescharacteristic
64C22×D293—22no—
65Dic586—24no—
66Dic586—22no—
67Dic586—42no—
68Dic586#4114yescomplemented
69D1172—24no—
70D1172—42no—
71D1172—42no—
72C22⋊D293—44no—
73C2×Dic293—24no—
74C2×Dic293—22no—
75C2×Dic293—22no—
76C2×Dic293—22no—
77C2×Dic293—42no—
78C4×D293—44no—
79C23×C293C2×D411yescharacteristic
80C2×C4×C293—22no—
81C2×C4×C293—22no—
82C2×C4×C293—22no—
83C2×C4×C293C2×D411yescharacteristic
84C2×C4×C293C2×D411yescharacteristic
85C2×C4×C293C2×D411yescharacteristic
86C2×C4×C293C2×D411yescharacteristic
87C2×C4×C293C2×D411yescharacteristic
88C2×C4×C293C2411yescharacteristic
89C8×C293—24no—
90C22×C293—21no—
91C22×C293—21no—
92C22×C293AGL(1,ℤ/8)12yes—
93C22×C293C22×D411yescharacteristic
94C2×D293—42no—
95C2×D293—42no—
96C2×D293—42no—
97C4×C293—21no—
98C4×C293—21no—
99C4×C293—21no—
100C4×C293—21no—
101C4×C293#13712yes—
102C4×C293C2×#4112yes—
103Dic293—24no—
104Dic293—42no—
105Dic293—42no—
106C2×C293—22no—
107C2×C293#52511yescharacteristic
108C2×C293C2×AGL(1,ℤ/8)11yescharacteristic
109C2×C293C2×#13711yescharacteristic
110D293—82no—
111C293#311211yescharacteristic, complemented, Sylow
112#3112—2931nomaximal, Sylow
113#532—2931no—
114C2×C4×Q8—2931no—
115#480—2932no—
116#477—2932no—
117#460—2932no—
118#448—2932no—
119#440—2934no—
120#432D29311yescharacteristic, complemented
121C2×#41—5861no—
122C22×Q8—2931no—
123C2×SD16—2934no—
124C4⋊Q8—2931no—
125#127—2931no—
126#124—5861no—
127#121—2932no—
128#121—5861no—
129C4×Q8—2932no—
130C4×Q8—2932no—
131C4×Q8—5861no—
132C4×Q8—5861no—
133C4×D4—2932no—
134C4×D4—5861no—
135C2×C4⋊C4—2931no—
136C2×C4⋊C4—5861no—
137C2×C42—5861no—
138C2×C42C2×D29311yescharacteristic
139#107—2934no—
140C4⋊C8C2×D29312yes—
141#103—2934no—
142#102—2934no—
143C22⋊C8C2×D29312yes—
144#97C2×D29312yes—
145#41—11724no—
146C2×Q8—2932no—
147C2×Q8—5864no—
148C2×Q8—5861no—
149C2×Q8—5861no—
150C2×D4—2932no—
151C2×D4—5862no—
152C2×D4—5861no—
153C2×D4—5861no—
154C22×C4—5861no—
155C22×C4—5861no—
156C22×C4—5862no—
157C22×C4D117211yescharacteristic
158C22×C4D117211yescharacteristic
159C22×C4C22×D29311yescharacteristic
160SD16—5868no—
161C2×C8C22×D29314yes—
162C4⋊C4—2932no—
163C4⋊C4—2932no—
164C4⋊C4—5861no—
165C4⋊C4—5862no—
166C4⋊C4—5862no—
167C4⋊C4—5861no—
168C22⋊C4—5862no—
169C22⋊C4—5862no—
170C42—5862no—
171C42—5862no—
172C42D117211yescharacteristic
173C42D117211yescharacteristic
174C42C22×D29311yescharacteristic
175C42C22×D29311yescharacteristic
176C23—5862no—
177C23C2×D117211yescharacteristic
178Q8—2934no—
179Q8—5864no—
180Q8—5862no—
181Q8—11722no—
182D4—5864no—
183D4—11722no—
184D4—11724no—
185D4—11722no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—5864no—
190C2×C4—5862no—
191C2×C4—5862no—
192C2×C4—5862no—
193C2×C4—11724no—
194C2×C4—11722no—
195C2×C4C2×D117211yescharacteristic
196C2×C4C2×D117211yescharacteristic
197C2×C4C2×D117211yescharacteristic
198C2×C4C2×D117211yescharacteristic
199C2×C4C2×D117211yescharacteristic
200C2×C4C23×D29311yescharacteristic
201C8—24no—
202C22—21no—
203C22—21no—
204C22—11722no—
205C22—11722no—
206C22—11722no—
207C22#2262765212yes—
208C22C22×D117211yescharacteristic
209C4—21no—
210C4—21no—
211C4—21no—
212C4—21no—
213C4—5864no—
214C4—11722no—
215C4—11722no—
216C4#2262765712yes—
217C4#41×D29312yes—
218C2—22no—
219C2—23442no—
220C2#3403664111yescharacteristic
221C2C2×#2262765211yescharacteristic
222C2C2×#2262765711yescharacteristic
subgroupG/H
centerC22C22×D1172
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#432×C293C2
socleC22×C293C22×D4
prime radical#34036679C2
hypercenter#432D293
hypocenterC293#3112
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. C2×C4×Dic586C2semidirect
3. #34036443C2semidirect
4. #34036425C2semidirect
5. #34036330C2semidirect
6. #34036270C2semidirect
7. #34036231C2semidirect
8. #432×C293C2semidirect
68. Dic586#41semidirect
111. C293#3112semidirect
120. #432D293semidirect

Maximal subgroups

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

subgroupindex
#340366792
C2×C4×Dic5862
#340364432
#340364252
#340363302
#340362702
#340362312
#432×C2932
#3112293