Finite Group Databasebeta

← #22598984

Subgroups — #22598984

Order 9088.

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

normal subgroups only

This group has 386 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#17986604C211yesmaximal, characteristic, complemented
2#17986398C211yesmaximal, characteristic, complemented
3#17986375C211yesmaximal, characteristic, complemented
4#17986365C211yesmaximal, characteristic, complemented
5#17986363C211yesmaximal, characteristic, complemented
6#17986250C212yesmaximal, complemented
7#17986233C212yesmaximal, complemented
8#17986109C212yesmaximal, complemented
9C4×#11765850C212yesmaximal, complemented
10#17985955C211yesmaximal, characteristic, complemented
11#540×C71C211yesmaximal, characteristic, complemented
12C2×#11765850C2212yes—
13C2×#11765850C2212yes—
14C2×#11765849C2211yescharacteristic
15C22×C71⋊C8C2211yescharacteristic
16#14556125C2211yescharacteristic
17#14556120C2211yescharacteristic
18#14556113—22no—
19#14556102C2212yes—
20#14556101—22no—
21C4×D284C2212yes—
22#14556061C2212yes—
23#14556059C2212yes—
24#14556049C2212yes—
25#14556049C2212yes—
26#14556048C2212yes—
27#14556048C2212yes—
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×D284—22no—
40C2×D284C2312yes—
41C2×C22⋊D71—22no—
42C2×C4×D71—22no—
43#11765850—24no—
44#11765850—24no—
45#11765849—22no—
46C2×C71⋊C8—22no—
47C2×C71⋊C8C2311yescharacteristic
48C2×C71⋊C8C2311yescharacteristic
49C2×C71⋊C8C2311yescharacteristic
50C2×C71⋊C8C2311yescharacteristic
51C4⋊Dic71C2312yes—
52Dic71⋊C4—22no—
53(C2×D71)⋊C4—22no—
54(C2×D71)⋊C4—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
70C22×D71—22no—
71D4×C71—22no—
72D4×C71—22no—
73D4×C71—82no—
74D4×C71—82no—
75C2×C4×C71—21no—
76C2×C4×C71—21no—
77C2×C4×C71—22no—
78C2×C4×C71—82no—
79C2×C4×C71C2×D412yes—
80C2×C4×C71C2×D412yes—
81C2×C4×C71C2×D411yescharacteristic
82C2×C4×C71C2411yescharacteristic
83C22⋊D71—82no—
84C2×Dic71—22no—
85D284—22no—
86D284—22no—
87D284—82no—
88C4×D71—82no—
89C71⋊C8—21no—
90C71⋊C8—21no—
91C71⋊C8#4112yes—
92C71⋊C8#4112yes—
93C22×C71—21no—
94C22×C71—22no—
95C22×C71—42no—
96C22×C71—42no—
97C22×C71—42no—
98C22×C71C22×D411yescharacteristic
99C2×D71—42no—
100C2×D71—42no—
101C2×D71—42no—
102C4×C71—21no—
103C4×C71—22no—
104C4×C71—22no—
105C4×C71—42no—
106C4×C71C2×#4111yescharacteristic
107C4×C71C2×#4111yescharacteristic
108Dic71—42no—
109C2×C71—41no—
110C2×C71—82no—
111C2×C71#53211yescharacteristic
112C2×C71#57612yes—
113D71—82no—
114#3176—711nomaximal, Sylow
115C71#317611yescharacteristic, complemented, Sylow
116#540—711no—
117#540D7111yescharacteristic, complemented
118#499—711no—
119#493—711no—
120#490—711no—
121#490—711no—
122#469—712no—
123#466—712no—
124#442—712no—
125C4×D8—712no—
126#405—711no—
127C2×D8—712no—
128C2×D8—712no—
129C2×M16—711no—
130C22×C8—711no—
131#127—711no—
132#127C2×D7111yescharacteristic
133#125—711no—
134#125C2×D7111yescharacteristic
135#123—22no—
136#123—1422no—
137#121—22no—
138#121—712no—
139#121—1422no—
140#121C2×D7112yes—
141C4×D4—712no—
142C4×D4C2×D7112yes—
143#117C2×D7111yescharacteristic
144#107—712no—
145#106—712no—
146#102—712no—
147#102—712no—
148#102—712no—
149#102—712no—
150#97—711no—
151#97—711no—
152C4×C8—711no—
153C4×C8—711no—
154C2×D4—22no—
155C2×D4—22no—
156C2×D4—712no—
157C2×D4—1422no—
158C2×D4—1422no—
159C2×D4C22×D7112yes—
160C22×C4—22no—
161C22×C4—1422no—
162C22×C4C22×D7111yescharacteristic
163D8—1424no—
164D8—1424no—
165M16—1422no—
166C2×C8—711no—
167C2×C8—711no—
168C2×C8—711no—
169C2×C8—711no—
170C2×C8—1422no—
171C4⋊C4—22no—
172C4⋊C4—712no—
173C4⋊C4—1422no—
174C4⋊C4C22⋊D7112yes—
175C4⋊C4C22×D7112yes—
176C22⋊C4—22no—
177C22⋊C4—22no—
178C22⋊C4—1422no—
179C22⋊C4—1422no—
180C22⋊C4C22⋊D7112yes—
181C42C22×D7111yescharacteristic
182C42C22×D7111yescharacteristic
183C23—22no—
184C23—1422no—
185C23C2×C22⋊D7111yescharacteristic
186D4—22no—
187D4—22no—
188D4—82no—
189D4—82no—
190D4—5682no—
191D4—5682no—
192D4—1422no—
193D4—1422no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—22no—
197C2×C4—82no—
198C2×C4—5682no—
199C2×C4—1422no—
200C2×C4C2×C22⋊D7112yes—
201C2×C4C2×C22⋊D7112yes—
202C2×C4C2×C22⋊D7111yescharacteristic
203C2×C4C23×D7111yescharacteristic
204C8—712no—
205C8—712no—
206C8—1421no—
207C8—1421no—
208C22—21no—
209C22—22no—
210C22—42no—
211C22—42no—
212C22—42no—
213C22—2842no—
214C22—2842no—
215C22—2842no—
216C22C22×C22⋊D7111yescharacteristic
217C4—21no—
218C4—22no—
219C4—22no—
220C4—42no—
221C4—2842no—
222C4#41×D7111yescharacteristic
223C4#41×D7111yescharacteristic
224C2—41no—
225C2—82no—
226C2—5682no—
227C2#1798654511yescharacteristic
228C2#1798680212yes—
subgroupG/H
centerC22C22×C22⋊D71
commutatorC2×C4×C71C24
FrattiniC2×C4C23×D71
Fitting#540×C71C2
socleC22×C71C22×D4
hypercenter#540D71
hypocenterC71#3176
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. #17986604C2semidirect
2. #17986398C2semidirect
3. #17986375C2semidirect
4. #17986365C2semidirect
5. #17986363C2semidirect
6. #17986250C2semidirect
7. #17986233C2semidirect
8. #17986109C2semidirect
9. C4×#11765850C2semidirect
10. #17985955C2semidirect
11. #540×C71C2semidirect
115. C71#3176semidirect
117. #540D71semidirect