Finite Group Databasebeta

← #22609897

Subgroups — #22609897

Order 9344.

548 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 548 conjugacy classes of subgroups — too many to draw. Only its 97 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#17989423C211yesmaximal, characteristic
2#17988605C212yesmaximal, complemented
3#17988581C212yesmaximal, complemented
4#17988554C211yesmaximal, characteristic, complemented
5#410×C73C211yesmaximal, characteristic, complemented
6#14556639C412yescomplemented
7#14556638—22no—
8#14556637—22no—
9#14556636—22no—
10#14556636C412yescomplemented
11C2×#11924028—22no—
12C2×#11924028C2212yes—
13#41×D73—24no—
14C2×#11924012C2211yescharacteristic, complemented
15C22×#10596831C2211yescharacteristic, complemented
16#14556519—24no—
17#14556514—22no—
18#14556511—22no—
19C22⋊#10596831—22no—
20C2×#41×C73C2211yescharacteristic
21#117×C73C2212yescomplemented
22#99×C73—22no—
23#11924029—24no—
24#11924028—24no—
25#11924028—24no—
26#11924028—24no—
27#11924028—22no—
28#11924028—22no—
29#11924028C2×C414yes—
30#11924028D414yes—
31#11924027—28no—
32#11924027—24no—
33C2×Dic146—22no—
34C2×Dic146D412yes—
35Q8×D73—24no—
36C2×D292—22no—
37C2×D292D412yes—
38C2×C22⋊D73—24no—
39C2×C22⋊D73—22no—
40D4×D73—28no—
41D4×D73—24no—
42C2×C4×D73—24no—
43C2×C4×D73—22no—
44#11924012—22no—
45C2×#10596831—21no—
46C2×#10596831—21no—
47C2×#10596831—22no—
48#41×C73—22no—
49#41×C73—22no—
50C2×Q8×C73C2×C411yescharacteristic
51C2×D4×C73C2×C411yescharacteristic
52C2×D4×C73D412yes—
53C22×C4×C73D412yes—
54C22×C4×C73C2311yescharacteristic
55C4⋊C4×C73—22no—
56C22⋊C4×C73—22no—
57C42×C73—22no—
58C23×C73C22⋊C412yes—
59C23×C73C2×D411yescharacteristic
60C22×D73—24no—
61C22×D73—22no—
62Q8×C73—22no—
63D4×C73—24no—
64D4×C73—22no—
65C2×C4×C73—22no—
66C2×C4×C73—22no—
67C2×C4×C73—42no—
68C2×C4×C73C22⋊C412yes—
69C2×C4×C73C22×C411yescharacteristic
70C2×C4×C73C2×D412yes—
71C2×C4×C73C2×D412yes—
72C2×C4×C73C2×D411yescharacteristic
73C22⋊D73—28no—
74C22⋊D73—24no—
75C22⋊D73—24no—
76C2×Dic73—24no—
77C2×Dic73—22no—
78D292—24no—
79D292—22no—
80D292C22⋊C414yes—
81C4×D73—28no—
82C4×D73—24no—
83C4×D73—24no—
84Dic146—24no—
85Dic146—22no—
86Dic146C22⋊C414yes—
87#10596831—41no—
88#10596831—41no—
89C22×C73—22no—
90C22×C73—41no—
91C22×C73—42no—
92C22×C73C2×C22⋊C411yescharacteristic
93C22×C73#12012yes—
94C2×D73—24no—
95C2×D73—82no—
96C2×D73—84no—
97C4×C73—22no—
98C4×C73—82no—
99C4×C73C2×C22⋊C412yes—
100C4×C73#12011yescharacteristic
101C4×C73#12011yescharacteristic
102Dic73—24no—
103C2×C73—22no—
104C2×C73—21no—
105C2×C73—42no—
106C2×C73#37911yescharacteristic
107D73—44no—
108#1794—731nomaximal, Sylow
109C73#179411yescharacteristic, complemented, Sylow
110#585—731no—
111#421—732no—
112#416—732no—
113#410D7311yescharacteristic, complemented
114#408—731no—
1152−1+4—732no—
1162−1+4—1462no—
117H(5,𝔽2)—732no—
118H(5,𝔽2)—1462no—
119H(5,𝔽2)—1462no—
120C2×#41—732no—
121C2×#41—1464no—
122C2×#41—1462no—
123C2×#41C2×D7311yescharacteristic
124C2×M16—731no—
125C22×C8—731no—
126#117C2×D7312yescomplemented
127#104—1464no—
128#103—1462no—
129#102—1462no—
130#99—22no—
131C22⋊C8—1462no—
132#41—22no—
133#41—22no—
134#41—734no—
135#41—734no—
136#41—1464no—
137#41—1464no—
138#41—1464no—
139#41—1468no—
140#41—1464no—
141#41—1464no—
142#41—1462no—
143#41—1462no—
144C2×Q8—732no—
145C2×Q8—1462no—
146C2×Q8—1464no—
147C2×Q8C4×D7311yescharacteristic
148C2×D4—732no—
149C2×D4—1462no—
150C2×D4—1464no—
151C2×D4—1468no—
152C2×D4—1464no—
153C2×D4—1462no—
154C2×D4C4×D7311yescharacteristic
155C2×D4C22⋊D7312yes—
156C22×C4—1464no—
157C22×C4—1462no—
158C22×C4D29212yes—
159C22×C4C22×D7311yescharacteristic
160M16—1462no—
161C2×C8—1462no—
162C2×C8—1461no—
163C2×C8—1461no—
164C4⋊C4—22no—
165C22⋊C4—22no—
166C42—22no—
167C23—1464no—
168C23—1462no—
169C23#1192400512yes—
170C23C2×C22⋊D7311yescharacteristic
171Q8—22no—
172Q8—734no—
173Q8—1464no—
174Q8—1462no—
175D4—24no—
176D4—22no—
177D4—734no—
178D4—1464no—
179D4—1468no—
180D4—1464no—
181D4—1464no—
182D4—1462no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—42no—
186C2×C4—1468no—
187C2×C4—1464no—
188C2×C4—1462no—
189C2×C4—1464no—
190C2×C4—1464no—
191C2×C4#1192400512yes—
192C2×C4C2×C4×D7311yescharacteristic
193C2×C4D4×D7312yes—
194C2×C4D4×D7312yes—
195C2×C4C2×D29211yescharacteristic
196C8—2921no—
197C8—2921no—
198C22—22no—
199C22—41no—
200C22—42no—
201C22—5842no—
202C22—5844no—
203C22—1464no—
204C22C2×#1192400511yescharacteristic
205C22#1455655912yes—
206C4—22no—
207C4—82no—
208C4—1464no—
209C4C22⋊C4×D7312yes—
210C4#1455656111yescharacteristic
211C4#1455656111yescharacteristic
212C2—22no—
213C2—21no—
214C2—42no—
215C2—2924no—
216C2#1798844211yescharacteristic
subgroupG/H
centerC4#14556561
commutatorC2×C4×C73C22×C4
FrattiniC22×C4C22×D73
Fitting#410×C73C2
socleC2×C73#379
hypercenter#410D73
hypocenterC73#1794
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C4 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
2. #17988605C2semidirect
3. #17988581C2semidirect
4. #17988554C2semidirect
5. #410×C73C2semidirect
6. #14556639C4semidirect
10. #14556636C4semidirect
14. C2×#11924012C22semidirect
15. C22×#10596831C22semidirect
21. #117×C73C22semidirect
109. C73#1794semidirect
113. #410D73semidirect
126. #117C2×D73semidirect