Finite Group Databasebeta

← #22611896

Subgroups — #22611896

Order 9344.

210 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 47 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#17989401C211yesmaximal, characteristic, complemented
2#17989022C211yesmaximal, characteristic, complemented
3C2×#14556536C211yesmaximal, characteristic, complemented
4#17988858C211yesmaximal, characteristic, complemented
5#17988402C211yesmaximal, characteristic, complemented
6#17988370C211yesmaximal, characteristic, complemented
7#359×C73C211yesmaximal, characteristic, complemented
8#14556638—21no—
9#14556621—21no—
10#14556620—22no—
11#14556619—21no—
12#14556610—21no—
13C2×Dic292C2211yescharacteristic
14Q16×D73—21no—
15C2×D584C2211yescharacteristic
16#14556597C2211yescharacteristic
17#14556536—22no—
18#14556534—21no—
19#14556532—21no—
20#14556531C2211yescharacteristic
21#14556507—21no—
22#135×C73C2211yescharacteristic
23C2×C16×C73C2211yescharacteristic
24#108×C73C2211yescharacteristic
25#11924028—41no—
26#11924028D411yescharacteristic
27#11924027—22no—
28#11924027—42no—
29C2×Dic146—21no—
30C2×Dic146—41no—
31Q8×D73—22no—
32C2×D292—21no—
33Dic292—21no—
34Dic292D412yes—
35#11924018—22no—
36#11924017—41no—
37#11924016—22no—
38D584—21no—
39D584—21no—
40D584—41no—
41#11924012D411yescharacteristic
42#11924011—21no—
43C8×D73—21no—
44#11924003—21no—
45#41×C73—21no—
46Q16×C73D411yescharacteristic
47SD16×C73—21no—
48D8×C73D411yescharacteristic
49M16×C73—21no—
50C2×C8×C73C2311yescharacteristic
51C16×C73—21no—
52C22×D73—41no—
53Q8×C73—21no—
54D4×C73—21no—
55D4×C73—41no—
56C2×C4×C73—41no—
57C2×C4×C73C2×D411yescharacteristic
58C22⋊D73—21no—
59C22⋊D73—42no—
60C2×Dic73—42no—
61C2×Dic73—41no—
62D292—41no—
63D292—41no—
64D292D811yescharacteristic
65C4×D73—21no—
66C4×D73—42no—
67Dic146—22no—
68Dic146—42no—
69Dic146—41no—
70Dic146D811yescharacteristic
71C8×C73—41no—
72C8×C73C2×D411yescharacteristic
73C8×C73C2×D411yescharacteristic
74#10596831—21no—
75C22×C73—41no—
76C22×C73AGL(1,ℤ/8)11yescharacteristic
77C2×D73—21no—
78C2×D73—81no—
79C2×D73—161no—
80C4×C73—41no—
81C4×C73#12011yescharacteristic
82C4×C73C2×D811yescharacteristic
83Dic73—21no—
84Dic73—42no—
85C2×C73—21no—
86C2×C73—81no—
87C2×C73#44711yescharacteristic
88D73—41no—
89D73—161no—
90#2193—731nomaximal, Sylow
91C73#219311yescharacteristic, complemented, Sylow
92#578—731no—
93#509—731no—
94C2×SD32—731no—
95#472—731no—
96#362—731no—
97#359D7311yescharacteristic, complemented
98#350—731no—
992−1+4—1461no—
100#137—1461no—
101#137—1462no—
102AGL(1,ℤ/8)—1461no—
103#135—1461no—
104#135C2×D7311yescharacteristic
105C2×Q16—731no—
106C2×Q16—1461no—
107C2×D8—731no—
108#131—731no—
109SD32—1462no—
110SD32—1461no—
111D16—1461no—
112M32—731no—
113C2×C16C2×D7311yescharacteristic
114#108C2×D7311yescharacteristic
115#100—1461no—
116#41—21no—
117#41—2921no—
118#41—2922no—
119#41—731no—
120#41—1462no—
121C2×Q8—2921no—
122C2×Q8—1462no—
123C2×Q8—1461no—
124C2×D4—1461no—
125Q16—732no—
126Q16—1462no—
127Q16—1461no—
128Q16D29211yescharacteristic
129SD16—21no—
130SD16—2921no—
131SD16—1462no—
132D8—2921no—
133D8—1461no—
134D8—1461no—
135D8D29211yescharacteristic
136M16—21no—
137M16—731no—
138M16—1461no—
139C2×C8—1461no—
140C2×C8C22×D7311yescharacteristic
141C16—21no—
142C16—1461no—
143C23—2921no—
144Q8—21no—
145Q8—2922no—
146Q8—2921no—
147Q8—731no—
148Q8—1462no—
149D4—21no—
150D4—41no—
151D4—2922no—
152D4—2921no—
153D4—2921no—
154D4—731no—
155D4—1461no—
156C2×C4—41no—
157C2×C4—2922no—
158C2×C4—2921no—
159C2×C4—2922no—
160C2×C4—1461no—
161C2×C4D4×D7311yescharacteristic
162C8—41no—
163C8—1461no—
164C8D4×D7311yescharacteristic
165C8C2×D29211yescharacteristic
166C22—41no—
167C22—5841no—
168C22—11681no—
169C22—1461no—
170C22#1455661811yescharacteristic
171C4—41no—
172C4—2922no—
173C4—1461no—
174C4#1455656111yescharacteristic
175C4D8×D7311yescharacteristic
176C2—21no—
177C2—81no—
178C2—2921no—
179C2—11681no—
180C2#1798872211yescharacteristic
subgroupG/H
centerC2#17988722
commutatorC2×C8×C73C23
FrattiniC2×C8C22×D73
Fitting#359×C73C2
socleC2×C73#447
hypercenter#359D73
hypocenterC73#2193
LCSG ▷ C2×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #359

Complements

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

NH ≅ G/Ntype
1. #17989401C2semidirect
2. #17989022C2semidirect
3. C2×#14556536C2semidirect
4. #17988858C2semidirect
5. #17988402C2semidirect
6. #17988370C2semidirect
7. #359×C73C2semidirect
91. C73#2193semidirect
97. #359D73semidirect