Finite Group Databasebeta

← #22611893

Subgroups — #22611893

Order 9344.

210 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 49 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#17989404C211yesmaximal, characteristic, complemented
2#17989023C211yesmaximal, characteristic, complemented
3C2×#14556535C211yesmaximal, characteristic, complemented
4#17988402C211yesmaximal, characteristic, complemented
5#17988393C211yesmaximal, characteristic, complemented
6#17988371C211yesmaximal, characteristic, complemented
7#472×C73C211yesmaximal, characteristic, complemented
8#14556638—21no—
9#14556624—22no—
10#14556624—21no—
11#14556613—21no—
12#14556613C2211yescharacteristic
13C2×Dic292—21no—
14C2×Dic292C2211yescharacteristic
15#14556535—22no—
16#14556535—21no—
17#14556532—21no—
18#14556531C2211yescharacteristic
19C2×#11924003C2211yescharacteristic
20AGL(1,ℤ/8)×C73—21no—
21C2×D8×C73C2211yescharacteristic
22#131×C73C2211yescharacteristic
23#108×C73C2211yescharacteristic
24#100×C73—21no—
25#11924028—22no—
26#11924028—21no—
27#11924027—42no—
28#11924027—41no—
29C2×Dic146—22no—
30C2×Dic146—21no—
31Q8×D73—41no—
32Dic292—22no—
33Dic292—21no—
34Dic292D411yescharacteristic
35Dic292D412yes—
36#11924017—22no—
37#11924017—21no—
38D584D411yescharacteristic
39#11924003—21no—
40#11924003—21no—
41#41×C73D411yescharacteristic
42C2×D4×C73—21no—
43SD16×C73—41no—
44D8×C73—21no—
45D8×C73—21no—
46D8×C73—41no—
47M16×C73—21no—
48M16×C73—21no—
49M16×C73D411yescharacteristic
50C2×C8×C73—21no—
51C2×C8×C73C2311yescharacteristic
52C23×C73—41no—
53Q8×C73D811yescharacteristic
54D4×C73—21no—
55D4×C73—41no—
56D4×C73—41no—
57D4×C73D811yescharacteristic
58C2×C4×C73—21no—
59C2×C4×C73C2×D411yescharacteristic
60C22⋊D73—42no—
61C22⋊D73—41no—
62C2×Dic73—42no—
63C2×Dic73—41no—
64D292—21no—
65C4×D73—42no—
66C4×D73—41no—
67Dic146—22no—
68Dic146—21no—
69Dic146—42no—
70Dic146—41no—
71C8×C73—21no—
72C8×C73—41no—
73C8×C73C2×D411yescharacteristic
74C8×C73C2×D411yescharacteristic
75C22×C73—21no—
76C22×C73—81no—
77C22×C73—161no—
78C22×C73AGL(1,ℤ/8)11yescharacteristic
79C2×D73—41no—
80C4×C73—21no—
81C4×C73#12011yescharacteristic
82C4×C73C2×D811yescharacteristic
83Dic73—41no—
84Dic73—42no—
85C2×C73—21no—
86C2×C73—41no—
87C2×C73—161no—
88C2×C73#44711yescharacteristic
89D73—81no—
90#2193—731nomaximal, Sylow
91C73#219311yescharacteristic, complemented, Sylow
92#578—731no—
93#509—731no—
94C2×SD32—731no—
95#472D7311yescharacteristic, complemented
96#362—731no—
97#359—731no—
98#350—731no—
992−1+4—1461no—
100#137—1462no—
101#137—1461no—
102AGL(1,ℤ/8)—21no—
103#135—731no—
104#135—1461no—
105C2×Q16—731no—
106C2×Q16—1461no—
107C2×D8C2×D7311yescharacteristic
108#131C2×D7311yescharacteristic
109SD32—1462no—
110SD32—1461no—
111D16—1461no—
112M32—731no—
113C2×C16—731no—
114#108C2×D7311yescharacteristic
115#100—21no—
116#41—2922no—
117#41—2921no—
118#41—1462no—
119#41—1461no—
120#41C22⋊D7311yescharacteristic
121C2×Q8—2921no—
122C2×Q8—1462no—
123C2×Q8—1461no—
124C2×D4—21no—
125Q16—732no—
126Q16—731no—
127Q16—1462no—
128Q16—1461no—
129SD16—41no—
130SD16—1462no—
131SD16—1461no—
132D8—21no—
133D8—21no—
134D8—41no—
135D8—731no—
136M16—21no—
137M16—21no—
138M16C22⋊D7311yescharacteristic
139C2×C8—21no—
140C2×C8C22×D7311yescharacteristic
141C16—1461no—
142C16—1461no—
143C23—41no—
144Q8—2922no—
145Q8—2921no—
146Q8—1462no—
147Q8—1461no—
148Q8#1192401311yescharacteristic
149D4—21no—
150D4—41no—
151D4—41no—
152D4—2922no—
153D4—2921no—
154D4—1461no—
155D4#1192401311yescharacteristic
156C2×C4—21no—
157C2×C4—2922no—
158C2×C4—2922no—
159C2×C4—2921no—
160C2×C4—2921no—
161C2×C4C2×C22⋊D7311yescharacteristic
162C8—21no—
163C8—41no—
164C8D4×D7311yescharacteristic
165C8D4×D7311yescharacteristic
166C22—21no—
167C22—81no—
168C22—161no—
169C22—2921no—
170C22#1455661611yescharacteristic
171C4—21no—
172C4—2922no—
173C4—2921no—
174C4#1455655911yescharacteristic
175C4C2×#1192401311yescharacteristic
176C2—21no—
177C2—41no—
178C2—161no—
179C2—5841no—
180C2#1798872011yescharacteristic
subgroupG/H
centerC2#17988720
commutatorC2×C8×C73C23
FrattiniC2×C8C22×D73
Fitting#472×C73C2
socleC2×C73#447
hypercenter#472D73
hypocenterC73#2193
LCSG ▷ C2×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C2×C4 ◁ #131 ◁ #472

Complements

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

NH ≅ G/Ntype
1. #17989404C2semidirect
2. #17989023C2semidirect
3. C2×#14556535C2semidirect
4. #17988402C2semidirect
5. #17988393C2semidirect
6. #17988371C2semidirect
7. #472×C73C2semidirect
91. C73#2193semidirect
95. #472D73semidirect