Finite Group Databasebeta

← #22620315

Subgroups — #22620315

Order 9344.

400 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 125 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#17989140C211yesmaximal, characteristic, complemented
2C2×#14556578C211yesmaximal, characteristic
3#17988945C214yesmaximal, complemented
4#17988940C214yesmaximal, complemented
5#17988597C211yesmaximal, characteristic, complemented
6#17988595C211yesmaximal, characteristic, complemented
7#17988592C211yesmaximal, characteristic
8M16×Dic73C211yesmaximal, characteristic, complemented
9#418×C73C211yesmaximal, characteristic
10C22×Dic146C2211yescharacteristic
11C2×#11924012C2211yescharacteristic
12#14556590C2212yescomplemented
13#14556582C2212yescomplemented
14#14556578—22no—
15#14556578C2212yes—
16#14556578C2212yes—
17#14556568—22no—
18C4×Dic146—22no—
19#14556550C2211yescharacteristic
20C2×C22⋊Dic73—22no—
21C2×C4×Dic73C2211yescharacteristic
22#14556516C2214yescomplemented
23#14556514C2214yescomplemented
24#14556512C2214yes—
25#14556501C2212yescomplemented
26C8×Dic73C2212yescomplemented
27C22×D4×C73C2211yescharacteristic
28C2×M16×C73C2211yescharacteristic
29#117×C73C2211yescharacteristic
30#102×C73C2214yes—
31C2×Dic146—22no—
32C2×Dic146—22no—
33C2×Dic146—21no—
34C2×Dic146—22no—
35C2×Dic146C2312yes—
36C22×Dic73—21no—
37C22×Dic73D412yes—
38#11924012—22no—
39C2×#10596831C2312yes—
40C4⋊Dic73—22no—
41C4⋊Dic73C2312yes—
42#11924007—22no—
43#11924007—22no—
44C22⋊Dic73—21no—
45C22⋊Dic73—24no—
46C22⋊Dic73—24no—
47C4×Dic73—21no—
48C4×Dic73D412yes—
49C4×Dic73C2311yescharacteristic
50C4×Dic73C2311yescharacteristic
51C24×C73—21no—
52C2×D4×C73—21no—
53C2×D4×C73—22no—
54C2×D4×C73—22no—
55C2×D4×C73C2312yes—
56C22×C4×C73C2311yescharacteristic
57M16×C73—22no—
58C2×C8×C73C2312yes—
59C4⋊C4×C73C2312yes—
60C22⋊C4×C73—21no—
61C42×C73—21no—
62C23×C73—22no—
63C23×C73—44no—
64C23×C73—42no—
65C23×C73C2×D411yescharacteristic
66D4×C73—22no—
67D4×C73—22no—
68D4×C73—42no—
69C2×C4×C73—22no—
70C2×C4×C73C2×D411yescharacteristic
71C2×C4×C73#4112yes—
72C2×C4×C73#4112yes—
73C2×C4×C73C2411yescharacteristic
74C2×Dic73—22no—
75C2×Dic73—22no—
76C2×Dic73—42no—
77C2×Dic73—42no—
78C2×Dic73C2×D412yes—
79C2×Dic73C2×D412yes—
80Dic146—22no—
81Dic146—22no—
82Dic146—44no—
83Dic146—42no—
84C8×C73—22no—
85#10596831—22no—
86C22×C73—22no—
87C22×C73—42no—
88C22×C73—44no—
89C22×C73—84no—
90C22×C73#12412yes—
91C22×C73C22×D411yescharacteristic
92C4×C73—42no—
93C4×C73#12412yes—
94C4×C73C2×#4111yescharacteristic
95C4×C73C2×#4111yescharacteristic
96Dic73—22no—
97Dic73—22no—
98Dic73—42no—
99Dic73—42no—
100C2×C73—22no—
101C2×C73—82no—
102C2×C73C2×#12411yescharacteristic
103C2×C73#57512yes—
104#3140—731nomaximal, Sylow
105C73#314011yescharacteristic, complemented, Sylow
106#533—731no—
107C2×#124—731no—
108#489—734no—
109#488—734no—
110#419—731no—
111#419—731no—
112#418—731no—
113#418D7311yescharacteristic
114C4×M16—731no—
115C22×Q8—731no—
116C22×D4C2×D7311yescharacteristic
117C2×M16—731no—
118C2×M16C2×D7311yescharacteristic
119C4⋊Q8—732no—
120#125—732no—
121#124—732no—
122#124—732no—
123#124—1462no—
124C22⋊Q8—1462no—
125C4×Q8—1462no—
126#117—731no—
127#117C2×D7311yescharacteristic
128C2×C22⋊C4—1462no—
129C2×C42—731no—
130#103—734no—
131#103—734no—
132#102—734no—
133#102C2×D7314yes—
134#97—732no—
135C4×C8—732no—
136C24—21no—
137C2×Q8—732no—
138C2×Q8—1462no—
139C2×Q8—1462no—
140C2×Q8—1462no—
141C2×Q8—1461no—
142C2×D4—21no—
143C2×D4—22no—
144C2×D4—22no—
145C2×D4C22×D7312yes—
146C22×C4—732no—
147C22×C4—1461no—
148C22×C4C22×D7311yescharacteristic
149M16—22no—
150M16—1462no—
151C2×C8—732no—
152C2×C8C22×D7312yes—
153C4⋊C4—732no—
154C4⋊C4—1462no—
155C4⋊C4—1462no—
156C4⋊C4—1462no—
157C4⋊C4C22×D7312yes—
158C22⋊C4—21no—
159C22⋊C4—1464no—
160C22⋊C4—1464no—
161C22⋊C4—1461no—
162C42—21no—
163C42—732no—
164C42—731no—
165C42—731no—
166C42—1461no—
167C23—22no—
168C23—44no—
169C23—42no—
170C23D4×D7311yescharacteristic
171Q8—2924no—
172Q8—2922no—
173Q8—1462no—
174Q8—1462no—
175D4—22no—
176D4—22no—
177D4—42no—
178C2×C4—22no—
179C2×C4—2922no—
180C2×C4—2922no—
181C2×C4—732no—
182C2×C4—732no—
183C2×C4—1462no—
184C2×C4—1462no—
185C2×C4D4×D7311yescharacteristic
186C2×C4#1192402712yes—
187C2×C4#1192402812yes—
188C2×C4C23×D7311yescharacteristic
189C8—22no—
190C8—1462no—
191C22—22no—
192C22—44no—
193C22—42no—
194C22—84no—
195C22#1455657712yes—
196C22C2×D4×D7311yescharacteristic
197C4—42no—
198C4—2922no—
199C4—2922no—
200C4—1462no—
201C4—1462no—
202C4#1455657712yes—
203C4C2×#1192402711yescharacteristic
204C4C2×#1192402811yescharacteristic
205C2—22no—
206C2—82no—
207C2C2×#1455657711yescharacteristic
208C2#1798938312yes—
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#418×C73C2
socleC22×C73C22×D4
hypercenter#418D73
hypocenterC73#3140
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. #17989140C2semidirect
3. #17988945C2semidirect
4. #17988940C2semidirect
5. #17988597C2semidirect
6. #17988595C2semidirect
8. M16×Dic73C2semidirect
12. #14556590C22semidirect
13. #14556582C22semidirect
22. #14556516C22semidirect
23. #14556514C22semidirect
25. #14556501C22semidirect
26. C8×Dic73C22semidirect
105. C73#3140semidirect