Finite Group Databasebeta

← #49169173

Subgroups — #49169173

Order 37504.

400 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 125 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#34036682C211yesmaximal, characteristic, complemented
2C2×#22627613C211yesmaximal, characteristic
3#34036490C214yesmaximal, complemented
4#34036485C214yesmaximal, complemented
5#34036138C211yesmaximal, characteristic, complemented
6#34036135C211yesmaximal, characteristic
7#34036133C211yesmaximal, characteristic
8M16×Dic293C211yesmaximal, characteristic, complemented
9#419×C293C211yesmaximal, characteristic, complemented
10C22×D1172C2211yescharacteristic
11C2×#17989786C2211yescharacteristic
12#22627623C2212yescomplemented
13#22627615C2212yescomplemented
14#22627613—22no—
15#22627613C2212yes—
16#22627613C2212yes—
17#22627601—22no—
18C4×Dic586—22no—
19#22627583C2211yescharacteristic
20C2×#17989779—22no—
21C2×C4×Dic293C2211yescharacteristic
22#22627548C2214yescomplemented
23#22627546C2214yes—
24#22627544C2214yes—
25#22627534C2212yescomplemented
26C8×Dic293C2212yescomplemented
27C22×Q8×C293C2211yescharacteristic
28C2×M16×C293C2211yescharacteristic
29#117×C293C2211yescharacteristic
30#103×C293C2214yescomplemented
31C23×D293—21no—
32C2×Dic586—22no—
33C2×D1172—21no—
34C2×D1172—22no—
35C2×D1172—22no—
36C2×D1172C2312yes—
37C22×Dic293D412yes—
38#17989786—22no—
39C2×#14556873C2312yes—
40C4⋊Dic293—22no—
41C4⋊Dic293C2312yes—
42#17989781—22no—
43#17989781—22no—
44C22⋊Dic293—21no—
45#17989779—24no—
46#17989779—24no—
47C4×Dic293—21no—
48C4×Dic293D412yes—
49C4×Dic293C2311yescharacteristic
50C4×Dic293C2311yescharacteristic
51C2×Q8×C293—21no—
52C2×Q8×C293—22no—
53C2×Q8×C293—22no—
54C2×Q8×C293C2312yes—
55C22×C4×C293—21no—
56C22×C4×C293C2311yescharacteristic
57M16×C293—22no—
58C2×C8×C293C2312yes—
59C4⋊C4×C293C2312yes—
60C22⋊C4×C293—21no—
61C42×C293—21no—
62C22×D293—22no—
63C22×D293—44no—
64C22×D293—42no—
65Dic586—44no—
66D1172—22no—
67D1172—22no—
68D1172—42no—
69C2×Dic293—22no—
70C2×Dic293—42no—
71C2×Dic293C2×D412yes—
72C2×Dic293C2×D412yes—
73#14556873—22no—
74C23×C293C2×D411yescharacteristic
75Q8×C293—22no—
76Q8×C293—22no—
77Q8×C293—42no—
78C2×C4×C293—22no—
79C2×C4×C293—22no—
80C2×C4×C293—42no—
81C2×C4×C293C2×D411yescharacteristic
82C2×C4×C293#4112yes—
83C2×C4×C293#4112yes—
84C2×C4×C293C2411yescharacteristic
85C8×C293—22no—
86C22×C293—22no—
87C22×C293#12412yes—
88C22×C293C22×D411yescharacteristic
89C2×D293—42no—
90C2×D293—44no—
91C2×D293—84no—
92C4×C293—42no—
93C4×C293—42no—
94C4×C293#12412yes—
95C4×C293C2×#4111yescharacteristic
96C4×C293C2×#4111yescharacteristic
97Dic293—22no—
98Dic293—22no—
99Dic293—42no—
100C2×C293—22no—
101C2×C293C2×#12411yescharacteristic
102C2×C293#57512yes—
103D293—82no—
104C293#314011yescharacteristic, complemented, Sylow
105#3140—2931nomaximal, Sylow
106#533—2931no—
107C2×#124—2931no—
108#489—2934no—
109#488—2934no—
110#419—2931no—
111#419D29311yescharacteristic, complemented
112#418—2931no—
113#418—2931no—
114C4×M16—2931no—
115C22×Q8C2×D29311yescharacteristic
116C22×D4—2931no—
117C2×M16—2931no—
118C2×M16C2×D29311yescharacteristic
119C4⋊Q8—2932no—
120#125—2932no—
121#124—2932no—
122#124—2932no—
123#124—5862no—
124C22⋊Q8—5862no—
125C4×Q8—5862no—
126#117—2931no—
127#117C2×D29311yescharacteristic
128C2×C22⋊C4—5862no—
129C2×C42—2931no—
130#103—2934no—
131#103C2×D29314yescomplemented
132#102—2934no—
133#102—2934no—
134#97—2932no—
135C4×C8—2932no—
136C24—5861no—
137C2×Q8—21no—
138C2×Q8—22no—
139C2×Q8—22no—
140C2×Q8—5862no—
141C2×Q8C22×D29312yes—
142C2×D4—2932no—
143C2×D4—5861no—
144C2×D4—5862no—
145C2×D4—5862no—
146C22×C4—21no—
147C22×C4—2932no—
148C22×C4C22×D29311yescharacteristic
149M16—22no—
150M16—5862no—
151C2×C8—2932no—
152C2×C8C22×D29312yes—
153C4⋊C4—2932no—
154C4⋊C4—5862no—
155C4⋊C4—5862no—
156C4⋊C4—5862no—
157C4⋊C4C22×D29312yes—
158C22⋊C4—21no—
159C22⋊C4—5864no—
160C22⋊C4—5864no—
161C22⋊C4—5861no—
162C42—21no—
163C42—2932no—
164C42—2931no—
165C42—2931no—
166C42—5861no—
167C23—5862no—
168C23—11724no—
169C23—11722no—
170C23D4×D29311yescharacteristic
171Q8—22no—
172Q8—22no—
173Q8—42no—
174Q8—11724no—
175D4—5862no—
176D4—5862no—
177D4—11722no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—42no—
181C2×C4—2932no—
182C2×C4—2932no—
183C2×C4—5862no—
184C2×C4—11722no—
185C2×C4D4×D29311yescharacteristic
186C2×C4#1798980112yes—
187C2×C4#1798980212yes—
188C2×C4C23×D29311yescharacteristic
189C8—22no—
190C8—5862no—
191C22—22no—
192C22—23444no—
193C22—11722no—
194C22—11724no—
195C22#2262761012yes—
196C22C2×D4×D29311yescharacteristic
197C4—42no—
198C4—42no—
199C4—5862no—
200C4—5862no—
201C4—11722no—
202C4#2262761012yes—
203C4C2×#1798980111yescharacteristic
204C4C2×#1798980211yescharacteristic
205C2—22no—
206C2—23442no—
207C2C2×#2262761011yescharacteristic
208C2#3403692812yes—
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#419×C293C2
socleC22×C293C22×D4
prime radicalC22×D1172C22
hypercenter#419D293
hypocenterC293#3140
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
1. #34036682C2semidirect
3. #34036490C2semidirect
4. #34036485C2semidirect
5. #34036138C2semidirect
8. M16×Dic293C2semidirect
9. #419×C293C2semidirect
12. #22627623C22semidirect
13. #22627615C22semidirect
22. #22627548C22semidirect
25. #22627534C22semidirect
26. C8×Dic293C22semidirect
30. #103×C293C22semidirect
104. C293#3140semidirect
111. #419D293semidirect
131. #103C2×D293semidirect

Maximal subgroups

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

subgroupindex
#340366822
C2×#226276132
#340364902
#340364852
#340361382
#340361352
#340361332
M16×Dic2932
#419×C2932
#3140293