Finite Group Databasebeta

← #49174831

Subgroups — #49174831

Order 37504.

362 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 66 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#34037196C211yesmaximal, characteristic, complemented
2#34037127C212yesmaximal, complemented
3D293⋊#100C211yesmaximal, characteristic, complemented
4#34036996C212yesmaximal, complemented
5#34036692C211yesmaximal, characteristic
6D293⋊M16C2212yes—
7D4×#11924078—24no—
8#22627703C2212yes—
9C2×C22⋊#11924078—22no—
10#22627688—24no—
11#22627684—22no—
12C2×#17989801C2211yescharacteristic
13C2×D4×D293C2211yescharacteristic
14#22627620C411yescharacteristic, complemented
15#22627612C411yescharacteristic, complemented
16#22627611C411yescharacteristic, complemented
17#22627596—22no—
18#22627592—22no—
19#22627581C2211yescharacteristic
20#127×C293C411yescharacteristic, complemented
21C22×#11924078—24no—
22#17989812—22no—
23#17989811—22no—
24D293⋊C8—22no—
25C4⋊#11924078—22no—
26C22⋊#11924078—24no—
27C22⋊#11924078—22no—
28C4×#11924078D414yescomplemented
29C23×D293D412yes—
30#17989801—22no—
31#17989801—22no—
32C2×Dic586C2×C411yescharacteristic, complemented
33C2×D1172C2×C411yescharacteristic
34C2×C22⋊D293—21no—
35C2×C22⋊D293—22no—
36C2×C22⋊D293D412yes—
37D4×D293—22no—
38D4×D293—22no—
39C22×Dic293—21no—
40C2×C4×D293C2311yescharacteristic
41#17989781—21no—
42C22⋊Dic293—22no—
43#17989779—22no—
44#17989779—21no—
45C4×Dic293C2×C411yescharacteristic, complemented
46C2×D4×C293—22no—
47C2×D4×C293C2×C411yescharacteristic
48C2×D4×C293C2×C411yescharacteristic, complemented
49C42×C293C2×C411yescharacteristic, complemented
50C2×#11924078—24no—
51C2×#11924078—84no—
52#14556880—42no—
53C22×D293—22no—
54C22×D293—22no—
55C22×D293—82no—
56C22×D293C22⋊C412yes—
57C22×D293C2×D411yescharacteristic
58Dic586—22no—
59D1172—22no—
60C22⋊D293—24no—
61C22⋊D293—41no—
62C22⋊D293—41no—
63C22⋊D293—82no—
64C2×Dic293—21no—
65C2×Dic293—21no—
66C2×Dic293—42no—
67C2×Dic293C2×D411yescharacteristic
68C4×D293C2×D412yes—
69C4×D293#4112yes—
70C23×C293—21no—
71C23×C293C22⋊C412yes—
72D4×C293—22no—
73D4×C293—22no—
74D4×C293—82no—
75C2×C4×C293—21no—
76C2×C4×C293C22×C411yescharacteristic
77C22×C293—22no—
78C22×C293—42no—
79C22×C293—42no—
80C22×C293—41no—
81C22×C293C2×C22⋊C411yescharacteristic
82C2×D293—22no—
83C2×D293—41no—
84C2×D293—44no—
85C2×D293—42no—
86C2×D293—82no—
87C2×D293#12011yescharacteristic
88C2×D293#12311yescharacteristic
89#11924078—44no—
90C4×C293—41no—
91C4×C293C4×D412yes—
92Dic293—41no—
93Dic293—41no—
94Dic293#12112yes—
95C2×C293—21no—
96C2×C293—42no—
97C2×C293—81no—
98C2×C293#38611yescharacteristic
99D293—21no—
100D293—21no—
101D293—42no—
102C293#191111yescharacteristic, complemented, Sylow
103#1911—2931nomaximal, Sylow
104#535—2931no—
105#518—2931no—
106#421—2932no—
107C2×#100—2931no—
108H(3,ℤ/4)—2932no—
109C2×#41—2931no—
110C22×D4—2931no—
111C2×M16—2932no—
112#127—2931no—
113#127#1192407811yescharacteristic, complemented
114#124—2931no—
115#124—2931no—
116#121—5862no—
117#120—5862no—
118C4×D4—5864no—
119#117—2932no—
120#117—2931no—
121C2×C22⋊C4—5862no—
122#104—5864no—
123#100—5862no—
124C24—2932no—
125#41—5862no—
126#41—5862no—
127C2×Q8—2931no—
128C2×D4—22no—
129C2×D4—2932no—
130C2×D4—2931no—
131C2×D4—5862no—
132C2×D4—5862no—
133C2×D4—5862no—
134C2×D4—5861no—
135C2×D4C2×#1192407811yescharacteristic
136C2×D4C2×#1192407811yescharacteristic, complemented
137C22×C4—2931no—
138C22×C4—5861no—
139C22×C4—5864no—
140M16—5862no—
141M16—5862no—
142C2×C8—5862no—
143C4⋊C4—5861no—
144C4⋊C4—5862no—
145C22⋊C4—5861no—
146C22⋊C4—5862no—
147C22⋊C4—5862no—
148C22⋊C4—5864no—
149C22⋊C4—5862no—
150C42—2934no—
151C42—2931no—
152C42C2×#1192407811yescharacteristic, complemented
153C23—21no—
154C23—2931no—
155C23—2932no—
156C23—23442no—
157C23—5862no—
158C23—5862no—
159C23C22⋊#1192407812yes—
160Q8—5862no—
161D4—22no—
162D4—22no—
163D4—82no—
164D4—23442no—
165D4—5864no—
166D4—5862no—
167D4—11721no—
168D4—11721no—
169C2×C4—21no—
170C2×C4—2931no—
171C2×C4—2932no—
172C2×C4—2932no—
173C2×C4—23444no—
174C2×C4—5864no—
175C2×C4—5861no—
176C2×C4—5861no—
177C2×C4—11722no—
178C2×C4C22×#1192407811yescharacteristic
179C8—11722no—
180C22—22no—
181C22—42no—
182C22—42no—
183C22—41no—
184C22—2931no—
185C22—2931no—
186C22—23442no—
187C22—5862no—
188C22—11721no—
189C22—11722no—
190C22—11724no—
191C22C2×C22⋊#1192407811yescharacteristic
192C4—41no—
193C4—2932no—
194C4—11721no—
195C4—11724no—
196C4—11721no—
197C4D4×#1192407812yes—
198C2—21no—
199C2—42no—
200C2—81no—
201C2—5861no—
202C2—5861no—
203C2—11722no—
204C2#3403707711yescharacteristic
subgroupG/H
centerC2#34037077
commutatorC2×C4×C293C22×C4
FrattiniC2×C4C22×#11924078
Fitting#127×C293C4
socleC2×C293#386
prime radical#34036692C2
cosocleC2×C4×D293C23
hypercenter#127#11924078
hypocenterC293#1911
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C2 ◁ C2×C4 ◁ #127

Complements

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

NH ≅ G/Ntype
1. #34037196C2semidirect
2. #34037127C2semidirect
3. D293⋊#100C2semidirect
4. #34036996C2semidirect
14. #22627620C4semidirect
15. #22627612C4semidirect
16. #22627611C4semidirect
20. #127×C293C4semidirect
28. C4×#11924078D4semidirect
32. C2×Dic586C2×C4semidirect
45. C4×Dic293C2×C4semidirect
48. C2×D4×C293C2×C4semidirect
49. C42×C293C2×C4semidirect
102. C293#1911semidirect
113. #127#11924078semidirect
136. C2×D4C2×#11924078semidirect
152. C42C2×#11924078semidirect

Maximal subgroups

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

subgroupindex
#340371962
#340371272
D293⋊#1002
#340369962
#340366922
#1911293