Finite Group Databasebeta

← #22625979

Subgroups — #22625979

Order 9344.

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

normal subgroups only

This group has 314 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#17989655C211yesmaximal, characteristic, complemented
2#17989585C212yesmaximal
3D73⋊#101C211yesmaximal, characteristic, complemented
4#17989454C212yesmaximal, complemented
5#17989157C211yesmaximal, characteristic
6D73⋊M16C2212yes—
7Q8×#64408—24no—
8#14556670—22no—
9#14556670C2212yes—
10#14556655—24no—
11#14556652—22no—
12C2×#11924027C2211yescharacteristic
13C2×Q8×D73C2211yescharacteristic
14#14556591C411yescharacteristic, complemented
15#14556589C411yescharacteristic, complemented
16#14556578C411yescharacteristic, complemented
17#14556573—22no—
18#14556568—22no—
19#14556548C2211yescharacteristic
20#124×C73C411yescharacteristic, complemented
21#11924038—22no—
22#11924037—22no—
23#11924036—22no—
24C4⋊#64408—24no—
25C4⋊#64408—22no—
26C22⋊#64408—22no—
27C4×#64408—24no—
28C4×#64408D414yes—
29#11924027—22no—
30#11924027—22no—
31C2×Dic146C2×C411yescharacteristic
32C2×Dic146C2×C411yescharacteristic
33C2×Dic146D412yes—
34Q8×D73—22no—
35Q8×D73—22no—
36C2×C22⋊D73—21no—
37C22×Dic73—21no—
38C2×C4×D73D412yes—
39C2×C4×D73C2311yescharacteristic
40C4⋊Dic73—22no—
41#11924007—22no—
42#11924007—21no—
43C22⋊Dic73—22no—
44#11924005—21no—
45C4×Dic73C2×C411yescharacteristic
46C2×Q8×C73C2×C411yescharacteristic
47C2×D4×C73C2×C411yescharacteristic
48C22⋊C4×C73—22no—
49C42×C73C2×C411yescharacteristic
50C23×C73—21no—
51C22×D73C2×D411yescharacteristic
52C2×#64408—24no—
53Q8×C73—22no—
54D4×C73—22no—
55C2×C4×C73—21no—
56C2×C4×C73C22⋊C412yes—
57C2×C4×C73C22×C411yescharacteristic
58C22⋊D73—41no—
59C22⋊D73—41no—
60C2×Dic73—21no—
61C2×Dic73—21no—
62C2×Dic73—42no—
63C2×Dic73C22⋊C412yes—
64C2×Dic73C2×D411yescharacteristic
65C4×D73—22no—
66C4×D73—22no—
67C4×D73C2×D412yes—
68C4×D73#4112yes—
69Dic146—22no—
70Dic146—24no—
71Dic146—22no—
72#10596833—42no—
73C22×C73—42no—
74C22×C73—41no—
75C22×C73C2×C22⋊C411yescharacteristic
76C2×D73—41no—
77C2×D73#12011yescharacteristic
78C2×D73#12311yescharacteristic
79#64408—44no—
80C4×C73—22no—
81C4×C73—41no—
82C4×C73C4×D412yes—
83Dic73—22no—
84Dic73—41no—
85Dic73—41no—
86Dic73#12112yes—
87C2×C73—21no—
88C2×C73—81no—
89C2×C73#38611yescharacteristic
90D73—21no—
91D73—21no—
92#1912—731nomaximal, Sylow
93C73#191211yescharacteristic, complemented, Sylow
94#536—731no—
95#519—731no—
96#421—732no—
97C2×#101—731no—
98H(3,ℤ/4)—732no—
99C2×#41—731no—
100C22×Q8—731no—
101C2×M16—732no—
102C4⋊Q8—731no—
103C4⋊Q8—731no—
104#124—731no—
105#124#6440811yescharacteristic, complemented
106#123—1462no—
107C22⋊Q8—1462no—
108C4×Q8—1464no—
109#117—732no—
110#117—731no—
111#117—1462no—
112#104—1464no—
113#101—1462no—
114#41—1462no—
115#41—1462no—
116C2×Q8—732no—
117C2×Q8—731no—
118C2×Q8—731no—
119C2×Q8—1462no—
120C2×Q8—1462no—
121C2×Q8C2×#6440811yescharacteristic
122C2×D4—1461no—
123C2×D4C2×#6440811yescharacteristic
124C22×C4—731no—
125C22×C4—732no—
126C22×C4—1461no—
127M16—1462no—
128M16—1462no—
129C2×C8—1462no—
130C4⋊C4—1461no—
131C4⋊C4—1462no—
132C4⋊C4—1462no—
133C4⋊C4—1464no—
134C4⋊C4—1462no—
135C22⋊C4—22no—
136C22⋊C4—1461no—
137C22⋊C4—1462no—
138C22⋊C4—1462no—
139C42—734no—
140C42—731no—
141C42—1464no—
142C42C2×#6440811yescharacteristic
143C23—21no—
144C23—731no—
145Q8—22no—
146Q8—1464no—
147Q8—1462no—
148Q8—1462no—
149D4—22no—
150D4—2921no—
151D4—2921no—
152C2×C4—21no—
153C2×C4—2922no—
154C2×C4—731no—
155C2×C4—732no—
156C2×C4—732no—
157C2×C4—732no—
158C2×C4—1462no—
159C2×C4—1462no—
160C2×C4—1464no—
161C2×C4—1461no—
162C2×C4—1461no—
163C2×C4C22⋊#6440812yes—
164C2×C4C22×#6440811yescharacteristic
165C8—2922no—
166C22—42no—
167C22—41no—
168C22—2921no—
169C22—731no—
170C22—731no—
171C22C2×C22⋊#6440811yescharacteristic
172C4—22no—
173C4—41no—
174C4—2921no—
175C4—2924no—
176C4—2921no—
177C4—732no—
178C4—1462no—
179C4D4×#6440812yes—
180C2—21no—
181C2—81no—
182C2—1461no—
183C2—1461no—
184C2#1798953511yescharacteristic
subgroupG/H
centerC2#17989535
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
Fitting#124×C73C4
socleC2×C73#386
hypercenter#124#64408
hypocenterC73#1912
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C2×C4 ◁ #124

Complements

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

NH ≅ G/Ntype
1. #17989655C2semidirect
3. D73⋊#101C2semidirect
4. #17989454C2semidirect
14. #14556591C4semidirect
15. #14556589C4semidirect
16. #14556578C4semidirect
20. #124×C73C4semidirect
93. C73#1912semidirect
105. #124#64408semidirect