Finite Group Databasebeta

← #49174828

Subgroups — #49174828

Order 37504.

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

normal subgroups only

This group has 344 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#34037207C211yesmaximal, characteristic, complemented
2#34037121C212yesmaximal, complemented
3#34037109C211yesmaximal, characteristic, complemented
4#34036996C212yesmaximal, complemented
5#34036692C211yesmaximal, characteristic
6#22627711—24no—
7D293⋊M16C2212yes—
8C2×#17989811—22no—
9#22627703C2212yes—
10#22627686—24no—
11#22627682—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
21#17989812—22no—
22#17989811—24no—
23#17989811—22no—
24D293⋊C8D414yescomplemented
25C2×#14556880—24no—
26C4⋊#11924078—22no—
27C22⋊#11924078—22no—
28C4×#11924078—22no—
29C23×D293—21no—
30#17989801—22no—
31#17989801—22no—
32C2×Dic586C2×C411yescharacteristic
33C2×D1172C2×C411yescharacteristic
34C2×C22⋊D293—21no—
35C2×C22⋊D293—22no—
36C2×C22⋊D293D412yes—
37D4×D293—22no—
38D4×D293—22no—
39C22×Dic293D412yes—
40C2×C4×D293C2311yescharacteristic
41#17989781—21no—
42C22⋊Dic293—22no—
43#17989779—21no—
44#17989779—22no—
45C4×Dic293C2×C411yescharacteristic
46C2×D4×C293—22no—
47C2×D4×C293C2×C411yescharacteristic
48C2×D4×C293C2×C411yescharacteristic
49C42×C293C2×C411yescharacteristic
50C2×#11924078—42no—
51#14556880—24no—
52C22×D293—21no—
53C22×D293—42no—
54C22×D293—82no—
55C22×D293C2×D411yescharacteristic
56Dic586—22no—
57D1172—22no—
58C22⋊D293—24no—
59C22⋊D293—41no—
60C22⋊D293—41no—
61C22⋊D293—82no—
62C2×Dic293—22no—
63C2×Dic293—22no—
64C2×Dic293—21no—
65C2×Dic293C22⋊C412yes—
66C2×Dic293C2×D411yescharacteristic
67C4×D293C2×D412yes—
68C4×D293#4112yes—
69C23×C293—21no—
70C23×C293C22⋊C412yes—
71D4×C293—22no—
72D4×C293—22no—
73D4×C293—82no—
74C2×C4×C293—21no—
75C2×C4×C293C22×C411yescharacteristic
76C22×C293—22no—
77C22×C293—42no—
78C22×C293—42no—
79C22×C293—41no—
80C22×C293C2×C22⋊C411yescharacteristic
81C2×D293—41no—
82C2×D293—42no—
83C2×D293—41no—
84C2×D293—84no—
85C2×D293#12112yes—
86#11924078—82no—
87C4×C293—41no—
88C4×C293C4×D412yes—
89Dic293—22no—
90Dic293—41no—
91Dic293#12011yescharacteristic
92Dic293#12311yescharacteristic
93C2×C293—21no—
94C2×C293—42no—
95C2×C293—81no—
96C2×C293#38611yescharacteristic
97D293—22no—
98D293—81no—
99C293#191011yescharacteristic, complemented, Sylow
100#1910—2931nomaximal, Sylow
101#568—2931no—
102#535—2931no—
103#418—2932no—
104#410—2931no—
105H(3,ℤ/4)—2932no—
106C2×#41—2931no—
107C22×D4—2931no—
108#131—5864no—
109C2×M16—2932no—
110C2×M16—5862no—
111#127—2931no—
112#127#1192407811yescharacteristic, complemented
113#124—2931no—
114#124—2931no—
115#121—5862no—
116#120—5862no—
117#117—2931no—
118#117—2932no—
119#102—5864no—
120#99—5862no—
121C24—5861no—
122#41—5862no—
123#41—5862no—
124C2×Q8—2931no—
125C2×D4—22no—
126C2×D4—2932no—
127C2×D4—2931no—
128C2×D4—5862no—
129C2×D4—5862no—
130C2×D4—5861no—
131C2×D4—5862no—
132C2×D4C2×#1192407811yescharacteristic
133C2×D4C2×#1192407811yescharacteristic
134C22×C4—2931no—
135C22×C4—2932no—
136M16—5862no—
137M16—5862no—
138M16—5864no—
139C2×C8—2934no—
140C2×C8—5864no—
141C4⋊C4—5861no—
142C4⋊C4—5862no—
143C22⋊C4—5862no—
144C22⋊C4—5861no—
145C22⋊C4—5862no—
146C22⋊C4—5862no—
147C42—2931no—
148C42—5862no—
149C42C2×#1192407811yescharacteristic
150C23—21no—
151C23—2931no—
152C23—23442no—
153C23—5861no—
154C23—11722no—
155C23C22⋊#1192407812yes—
156Q8—5862no—
157D4—22no—
158D4—22no—
159D4—82no—
160D4—23442no—
161D4—5864no—
162D4—5862no—
163D4—11721no—
164D4—11721no—
165C2×C4—21no—
166C2×C4—2931no—
167C2×C4—2932no—
168C2×C4—2932no—
169C2×C4—2932no—
170C2×C4—5862no—
171C2×C4—5862no—
172C2×C4—5861no—
173C2×C4—11722no—
174C2×C4C22×#1192407811yescharacteristic
175C8—5864no—
176C22—22no—
177C22—42no—
178C22—42no—
179C22—41no—
180C22—2932no—
181C22—23444no—
182C22—11722no—
183C22—11721no—
184C22—11721no—
185C22C2×C22⋊#1192407811yescharacteristic
186C4—41no—
187C4—2931no—
188C4—2931no—
189C4—23442no—
190C4—5862no—
191C4—11721no—
192C4D4×#1192407812yes—
193C2—21no—
194C2—42no—
195C2—81no—
196C2—23441no—
197C2—5862no—
198C2#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#1910
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. #34037207C2semidirect
2. #34037121C2semidirect
3. #34037109C2semidirect
4. #34036996C2semidirect
14. #22627620C4semidirect
15. #22627612C4semidirect
16. #22627611C4semidirect
20. #127×C293C4semidirect
24. D293⋊C8D4semidirect
99. C293#1910semidirect
112. #127#11924078semidirect

Maximal subgroups

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

subgroupindex
#340372072
#340371212
#340371092
#340369962
#340366922
#1910293