Finite Group Databasebeta

← #22598962

Subgroups — #22598962

Order 9088.

362 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 121 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#17986611C211yesmaximal, characteristic, complemented
2#17986398C211yesmaximal, characteristic, complemented
3#17986371C211yesmaximal, characteristic, complemented
4#17986369C211yesmaximal, characteristic, complemented
5#17986363C211yesmaximal, characteristic, complemented
6#17986243C212yesmaximal, complemented
7#17986226C212yesmaximal, complemented
8#17986099C212yesmaximal, complemented
9C4×#11765853C212yesmaximal, complemented
10#17985955C211yesmaximal, characteristic, complemented
11#540×C71C211yesmaximal, characteristic
12C2×#11765853C2212yes—
13C2×#11765853C2212yes—
14C2×#11765849C2211yescharacteristic
15C22×C71⋊C8C2211yescharacteristic
16#14556128C2211yescharacteristic
17#14556121—22no—
18#14556120C2211yescharacteristic
19#14556118—22no—
20#14556107C2212yes—
21C4×Dic142C2212yes—
22#14556061C2212yes—
23#14556059C2212yes—
24#14556051C2212yes—
25#14556051C2212yes—
26#14556049C2212yes—
27#14556049C2212yes—
28#14556039C2211yescharacteristic
29#14556039C2211yescharacteristic
30C4×C71⋊C8C2211yescharacteristic
31C4×C71⋊C8C2211yescharacteristic
32#127×C71C2211yescharacteristic
33#125×C71C2211yescharacteristic
34#123×C71—22no—
35#121×C71—22no—
36#121×C71C2212yes—
37C4×D4×C71C2212yes—
38#117×C71C2211yescharacteristic
39C2×Dic142C2312yes—
40#11765853—24no—
41#11765853—24no—
42#11765849—22no—
43C2×C71⋊C8—22no—
44C2×C71⋊C8C2311yescharacteristic
45C2×C71⋊C8C2311yescharacteristic
46C2×C71⋊C8C2311yescharacteristic
47C2×C71⋊C8C2311yescharacteristic
48C4⋊Dic71—22no—
49C4⋊Dic71C2312yes—
50Dic71⋊C4—22no—
51Dic71⋊C4—22no—
52Dic71⋊C4—22no—
53C22⋊Dic71—22no—
54C4×Dic71—22no—
55C2×D4×C71—22no—
56C2×D4×C71—22no—
57C2×D4×C71C2312yes—
58C22×C4×C71—22no—
59C22×C4×C71C2311yescharacteristic
60C4⋊C4×C71—22no—
61C4⋊C4×C71D412yes—
62C4⋊C4×C71C2312yes—
63C22⋊C4×C71—22no—
64C22⋊C4×C71—22no—
65C22⋊C4×C71D412yes—
66C42×C71C2311yescharacteristic
67C42×C71C2311yescharacteristic
68C23×C71—22no—
69C23×C71C2×D411yescharacteristic
70D4×C71—22no—
71D4×C71—22no—
72D4×C71—82no—
73D4×C71—82no—
74C2×C4×C71—21no—
75C2×C4×C71—21no—
76C2×C4×C71—22no—
77C2×C4×C71—82no—
78C2×C4×C71C2×D412yes—
79C2×C4×C71C2×D412yes—
80C2×C4×C71C2×D411yescharacteristic
81C2×C4×C71C2411yescharacteristic
82C2×Dic71—22no—
83C2×Dic71—22no—
84Dic142—22no—
85Dic142—22no—
86C71⋊C8—21no—
87C71⋊C8—21no—
88C71⋊C8#4112yes—
89C71⋊C8#4112yes—
90C22×C71—21no—
91C22×C71—22no—
92C22×C71—42no—
93C22×C71—42no—
94C22×C71—42no—
95C22×C71C22×D411yescharacteristic
96C4×C71—21no—
97C4×C71—22no—
98C4×C71—22no—
99C4×C71—42no—
100C4×C71C2×#4111yescharacteristic
101C4×C71C2×#4111yescharacteristic
102Dic71—42no—
103Dic71—42no—
104C2×C71—41no—
105C2×C71—82no—
106C2×C71#53211yescharacteristic
107C2×C71#57712yes—
108#3174—711nomaximal, Sylow
109C71#317411yescharacteristic, complemented, Sylow
110#541—711no—
111#540D7111yescharacteristic
112#499—711no—
113#492—711no—
114#491—711no—
115#490—711no—
116#468—712no—
117#465—712no—
118#440—712no—
119C4×SD16—712no—
120#405—711no—
121C2×SD16—712no—
122C2×SD16—712no—
123C2×M16—711no—
124C22×C8—711no—
125C4⋊Q8—711no—
126#127C2×D7111yescharacteristic
127#126—1422no—
128#125—711no—
129#125—1422no—
130#125C2×D7111yescharacteristic
131#123—22no—
132C22⋊Q8—712no—
133#121—22no—
134#121C2×D7112yes—
135C4×Q8—712no—
136C4×D4C2×D7112yes—
137#117C2×D7111yescharacteristic
138#107—712no—
139#106—712no—
140#103—712no—
141#103—712no—
142#102—712no—
143#102—712no—
144#97—711no—
145#97—711no—
146C4×C8—711no—
147C4×C8—711no—
148C2×Q8—712no—
149C2×D4—22no—
150C2×D4—22no—
151C2×D4C22×D7112yes—
152C22×C4—22no—
153C22×C4C22×D7111yescharacteristic
154SD16—1424no—
155SD16—1424no—
156M16—1422no—
157C2×C8—711no—
158C2×C8—711no—
159C2×C8—711no—
160C2×C8—711no—
161C2×C8—1422no—
162C4⋊C4—22no—
163C4⋊C4—712no—
164C4⋊C4—1422no—
165C4⋊C4—1422no—
166C4⋊C4—1422no—
167C4⋊C4—1422no—
168C4⋊C4C22⋊D7112yes—
169C4⋊C4C22×D7112yes—
170C22⋊C4—22no—
171C22⋊C4—22no—
172C22⋊C4—1422no—
173C22⋊C4C22⋊D7112yes—
174C42—1422no—
175C42C22×D7111yescharacteristic
176C42C22×D7111yescharacteristic
177C23—22no—
178C23C2×C22⋊D7111yescharacteristic
179Q8—1422no—
180Q8—1422no—
181D4—22no—
182D4—22no—
183D4—82no—
184D4—82no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—82no—
189C2×C4—1422no—
190C2×C4—1422no—
191C2×C4C2×C22⋊D7112yes—
192C2×C4C2×C22⋊D7112yes—
193C2×C4C2×C22⋊D7111yescharacteristic
194C2×C4C23×D7111yescharacteristic
195C8—712no—
196C8—712no—
197C8—1421no—
198C8—1421no—
199C22—21no—
200C22—22no—
201C22—42no—
202C22—42no—
203C22—42no—
204C22C22×C22⋊D7111yescharacteristic
205C4—21no—
206C4—22no—
207C4—22no—
208C4—42no—
209C4—2842no—
210C4—2842no—
211C4#41×D7111yescharacteristic
212C4#41×D7111yescharacteristic
213C2—41no—
214C2—82no—
215C2#1798654511yescharacteristic
216C2#1798681012yes—
subgroupG/H
centerC22C22×C22⋊D71
commutatorC2×C4×C71C24
FrattiniC2×C4C23×D71
Fitting#540×C71C2
socleC22×C71C22×D4
hypercenter#540D71
hypocenterC71#3174
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ #117 ◁ #540

Complements

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

NH ≅ G/Ntype
1. #17986611C2semidirect
2. #17986398C2semidirect
3. #17986371C2semidirect
4. #17986369C2semidirect
5. #17986363C2semidirect
6. #17986243C2semidirect
7. #17986226C2semidirect
8. #17986099C2semidirect
9. C4×#11765853C2semidirect
10. #17985955C2semidirect
109. C71#3174semidirect