Finite Group Databasebeta

← #34036642

Subgroups — #34036642

Order 18752.

330 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 109 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
1C2×#17989803C211yesmaximal, characteristic, complemented
2C22×C4×D293C211yesmaximal, characteristic, complemented
3#22627609C212yesmaximal, complemented
4#22627600C211yesmaximal, characteristic, complemented
5#22627599C211yesmaximal, characteristic, complemented
6#22627598C211yesmaximal, characteristic, complemented
7#22627594C212yesmaximal, complemented
8#22627586C212yesmaximal, complemented
9#22627584C212yesmaximal, complemented
10#22627582C211yesmaximal, characteristic, complemented
11C22⋊Q8×C293C211yesmaximal, characteristic, complemented
12C23×D293C2211yescharacteristic
13#17989803—24no—
14C2×D1172C2212yes—
15C2×D1172C2212yes—
16C2×D1172C2211yescharacteristic, complemented
17C2×C22⋊D293C2212yes—
18C22×Dic293C2211yescharacteristic
19C2×C4×D293—24no—
20C2×C4×D293C2211yescharacteristic
21C2×C4×D293C2211yescharacteristic
22C2×C4×D293C2211yescharacteristic
23C2×C4×D293C2211yescharacteristic
24C2×C4×D293C2212yescomplemented
25C4⋊Dic293C2211yescharacteristic, complemented
26#17989781C2212yescomplemented
27#17989779C2212yes—
28#17989779C2212yes—
29#17989779C2212yescomplemented
30#17989779C2212yescomplemented
31C4×Dic293C2212yescomplemented
32C2×Q8×C293C2211yescharacteristic, complemented
33C22×C4×C293C2211yescharacteristic
34C4⋊C4×C293C2212yescomplemented
35C4⋊C4×C293C2211yescharacteristic, complemented
36C22⋊C4×C293C2212yes—
37C22×D293—22no—
38C22×D293—22no—
39C22×D293—22no—
40C22×D293C2312yes—
41C22×D293C2311yescharacteristic
42C22×D293C2311yescharacteristic
43D1172—24no—
44D1172—24no—
45D1172—22no—
46C22⋊D293—24no—
47C2×Dic293—22no—
48C2×Dic293C2312yes—
49C2×Dic293C2311yescharacteristic
50C2×Dic293C2311yescharacteristic
51C4×D293—22no—
52C4×D293—22no—
53C4×D293—22no—
54C4×D293—24no—
55C4×D293D414yescomplemented
56C23×C293C2311yescharacteristic
57Q8×C293—22no—
58C2×C4×C293—22no—
59C2×C4×C293C2312yes—
60C2×C4×C293C2312yes—
61C2×C4×C293C2311yescharacteristic
62C2×C4×C293C2311yescharacteristic
63C22×C293—21no—
64C22×C293—21no—
65C22×C293#4112yescomplemented
66C22×C293C2411yescharacteristic
67C2×D293—28no—
68C2×D293—21no—
69C2×D293—21no—
70C2×D293—21no—
71C2×D293—21no—
72C2×D293—22no—
73C2×D293—22no—
74C2×D293—22no—
75C2×D293C2×D412yes—
76C2×D293#4112yescomplemented
77C4×C293—21no—
78C4×C293—22no—
79C4×C293—22no—
80C4×C293C2×D412yes—
81Dic293—21no—
82Dic293—22no—
83Dic293C2×D412yes—
84C2×C293—22no—
85C2×C293C22×D411yescharacteristic
86C2×C293C2×#4111yescharacteristic
87C2×C293C2×#4111yescharacteristic
88D293—22no—
89D293—22no—
90D293—42no—
91C293#52511yescharacteristic, complemented, Sylow
92#525—2931nomaximal, Sylow
93C2×#41—2931no—
94C23×C4—2931no—
95#123—2932no—
96C22⋊Q8—2931no—
97C22⋊Q8D29311yescharacteristic, complemented
98#121—2931no—
99#121—2931no—
100#120—2932no—
101C4×D4—2932no—
102C4×D4—2932no—
103#117—2931no—
104C24—2931no—
105#41—5864no—
106C2×Q8C2×D29311yescharacteristic, complemented
107C2×D4—2932no—
108C2×D4—2932no—
109C2×D4—2932no—
110C2×D4—2931no—
111C22×C4—2931no—
112C22×C4—2931no—
113C22×C4—2931no—
114C22×C4—2932no—
115C22×C4—2931no—
116C22×C4—2931no—
117C22×C4—5864no—
118C22×C4C2×D29311yescharacteristic
119C4⋊C4—2931no—
120C4⋊C4—2932no—
121C4⋊C4C2×D29311yescharacteristic, complemented
122C4⋊C4C2×D29312yescomplemented
123C22⋊C4—2932no—
124C22⋊C4—2932no—
125C22⋊C4—2932no—
126C22⋊C4—2932no—
127C22⋊C4C2×D29312yes—
128C42—2932no—
129C23—2931no—
130C23—2931no—
131C23—2932no—
132C23—5862no—
133C23—5862no—
134C23—5862no—
135C23C22×D29311yescharacteristic
136Q8—22no—
137D4—5864no—
138D4—5864no—
139D4—5864no—
140D4—5862no—
141C2×C4—22no—
142C2×C4—2931no—
143C2×C4—2934no—
144C2×C4—2932no—
145C2×C4—2931no—
146C2×C4—5862no—
147C2×C4—5864no—
148C2×C4—5862no—
149C2×C4—5862no—
150C2×C4—5862no—
151C2×C4C22×D29312yes—
152C2×C4C22×D29311yescharacteristic
153C2×C4C22×D29312yes—
154C2×C4C22×D29311yescharacteristic
155C22—21no—
156C22—21no—
157C22—2932no—
158C22—2932no—
159C22—5868no—
160C22—5861no—
161C22—5861no—
162C22—5861no—
163C22—5861no—
164C22—5862no—
165C22—5862no—
166C22—5862no—
167C22#1798980312yescomplemented
168C22C23×D29311yescharacteristic
169C4—21no—
170C4—22no—
171C4—22no—
172C4—2932no—
173C4—5861no—
174C4—5862no—
175C4D4×D29312yes—
176C2—22no—
177C2—5862no—
178C2—5862no—
179C2—11722no—
180C2C2×D4×D29311yescharacteristic
181C2#41×D29311yescharacteristic
182C2C2×#1798980311yescharacteristic
subgroupG/H
center, FrattiniC22C23×D293
commutator, socle, cosocleC22×C293C24
FittingC22⋊Q8×C293C2
hypercenterC22⋊Q8D293
hypocenterC293#525
LCSG ▷ C22×C293 ▷ C293
UCSC1 ◁ C22 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×#17989803C2semidirect
2. C22×C4×D293C2semidirect
3. #22627609C2semidirect
4. #22627600C2semidirect
5. #22627599C2semidirect
6. #22627598C2semidirect
7. #22627594C2semidirect
8. #22627586C2semidirect
9. #22627584C2semidirect
10. #22627582C2semidirect
11. C22⋊Q8×C293C2semidirect
16. C2×D1172C22semidirect
24. C2×C4×D293C22semidirect
25. C4⋊Dic293C22semidirect
26. #17989781C22semidirect
29. #17989779C22semidirect
30. #17989779C22semidirect
31. C4×Dic293C22semidirect
32. C2×Q8×C293C22semidirect
34. C4⋊C4×C293C22semidirect
35. C4⋊C4×C293C22semidirect
55. C4×D293D4semidirect
65. C22×C293#41semidirect
76. C2×D293#41semidirect
91. C293#525semidirect
97. C22⋊Q8D293semidirect
106. C2×Q8C2×D293semidirect
121. C4⋊C4C2×D293semidirect
122. C4⋊C4C2×D293semidirect
167. C22#17989803semidirect

Maximal subgroups

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

subgroupindex
C2×#179898032
C22×C4×D2932
#226276092
#226276002
#226275992
#226275982
#226275942
#226275862
#226275842
#226275822
C22⋊Q8×C2932
#525293