Finite Group Databasebeta

← #22598955

Subgroups — #22598955

Order 9088.

362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 115 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#17986614C212yesmaximal, complemented
2#17986396C211yesmaximal, characteristic, complemented
3#17986382C211yesmaximal, characteristic, complemented
4#17986357C212yesmaximal, complemented
5#17986258C211yesmaximal, characteristic, complemented
6#17986249C211yesmaximal, characteristic
7#17986227C212yesmaximal, complemented
8#17986107C211yesmaximal, characteristic, complemented
9C4×#11765853C212yesmaximal, complemented
10#17985956C211yesmaximal, characteristic, complemented
11#442×C71C211yesmaximal, characteristic, complemented
12C2×Dic284C2211yescharacteristic
13C2×#11765853C2212yes—
14C2×#11765848C2211yescharacteristic
15C2×C8×D71C2211yescharacteristic
16#14556127C2212yes—
17#14556121—22no—
18#14556115C2212yes—
19#14556114—22no—
20#14556111—22no—
21#14556108C2212yes—
22#14556107—22no—
23#14556099C2212yes—
24C4×Dic142C2212yes—
25#14556085C2211yescharacteristic
26#14556060C2211yescharacteristic
27#14556059C2212yes—
28#14556053C2212yes—
29#14556051C2212yes—
30#14556049C2212yes—
31#14556038C2211yescharacteristic
32C4×C71⋊C8C2211yescharacteristic
33C8×Dic71C2211yescharacteristic
34C2×D8×C71C2211yescharacteristic
35C4×D4×C71C2212yes—
36#106×C71C2211yescharacteristic
37#102×C71C2212yes—
38#97×C71C2211yescharacteristic
39C2×Dic142—22no—
40C2×Dic142C2312yes—
41C2×C22⋊D71—22no—
42C2×C4×D71C2311yescharacteristic
43Dic284—22no—
44#11765853—24no—
45#11765848—22no—
46C2×C71⋊C8C2311yescharacteristic
47C2×C71⋊C8C2311yescharacteristic
48C8×D71—22no—
49C4⋊Dic71—22no—
50C4⋊Dic71C2312yes—
51Dic71⋊C4—22no—
52Dic71⋊C4—22no—
53Dic71⋊C4D412yes—
54C22⋊Dic71—22no—
55C22⋊Dic71—22no—
56C22⋊Dic71—22no—
57(C2×D71)⋊C4—22no—
58(C2×D71)⋊C4D412yes—
59C4×Dic71—22no—
60C4×Dic71C2311yescharacteristic
61C2×D4×C71C2312yes—
62C22×C4×C71—22no—
63D8×C71—22no—
64C2×C8×C71C2311yescharacteristic
65C2×C8×C71C2311yescharacteristic
66C4⋊C4×C71C2312yes—
67C22⋊C4×C71—22no—
68C42×C71C2311yescharacteristic
69C23×C71—22no—
70C22×D71C2×D411yescharacteristic
71D4×C71—22no—
72D4×C71—22no—
73C2×C4×C71—22no—
74C2×C4×C71—82no—
75C2×C4×C71C2×D412yes—
76C2×C4×C71C2411yescharacteristic
77C22⋊D71—82no—
78C2×Dic71—22no—
79C2×Dic71—22no—
80C2×Dic71C2×D412yes—
81C2×Dic71C2×D411yescharacteristic
82C4×D71—21no—
83C4×D71—21no—
84Dic142—22no—
85Dic142—22no—
86Dic142—82no—
87C8×C71—21no—
88C8×C71#4112yes—
89C71⋊C8—21no—
90C71⋊C8#4112yes—
91C22×C71—42no—
92C22×C71—42no—
93C22×C71—42no—
94C22×C71C22×D411yescharacteristic
95C2×D71—21no—
96C2×D71—22no—
97C4×C71—22no—
98C4×C71—42no—
99C4×C71C2×#4111yescharacteristic
100C4×C71C2×#4111yescharacteristic
101Dic71—21no—
102Dic71—22no—
103Dic71—42no—
104Dic71—42no—
105C2×C71—82no—
106C2×C71#53211yescharacteristic
107C2×C71#57712yes—
108D71—41no—
109#3173—711nomaximal, Sylow
110C71#317311yescharacteristic, complemented, Sylow
111#542—712no—
112#498—711no—
113#495—711no—
114#489—712no—
115#470—711no—
116#469—711no—
117#465—712no—
118#442D7111yescharacteristic, complemented
119#441—711no—
120C4×SD16—712no—
121#405—711no—
122C2×Q16—711no—
123C2×SD16—712no—
124C2×D8C2×D7111yescharacteristic
125C2×M16—711no—
126C22×C8—711no—
127C4⋊Q8—712no—
128#126—1422no—
129#124—712no—
130#124—1422no—
131#123—1422no—
132C22⋊Q8—712no—
133C22⋊Q8—1422no—
134#121—712no—
135C4×Q8—712no—
136C4×D4C2×D7112yes—
137#117—711no—
138#106—711no—
139#106—712no—
140#106C2×D7111yescharacteristic
141#103—712no—
142#103—712no—
143#102—712no—
144#102C2×D7112yes—
145#97—711no—
146#97C2×D7111yescharacteristic
147C4×C8—711no—
148C4×C8—711no—
149C2×Q8—712no—
150C2×Q8—1422no—
151C2×D4—1422no—
152C2×D4C22×D7112yes—
153C22×C4—22no—
154C22×C4—711no—
155Q16—1422no—
156SD16—1424no—
157D8—22no—
158M16—1422no—
159C2×C8—711no—
160C2×C8—711no—
161C2×C8—1422no—
162C2×C8C22×D7111yescharacteristic
163C2×C8C22×D7111yescharacteristic
164C4⋊C4—712no—
165C4⋊C4—712no—
166C4⋊C4—1422no—
167C4⋊C4—1422no—
168C4⋊C4—1422no—
169C4⋊C4C22×D7112yes—
170C22⋊C4—22no—
171C22⋊C4—712no—
172C22⋊C4—1422no—
173C22⋊C4—1422no—
174C22⋊C4—1422no—
175C22⋊C4—1422no—
176C42—711no—
177C42—1422no—
178C42C22×D7111yescharacteristic
179C23—22no—
180C23—711no—
181Q8—5682no—
182Q8—1422no—
183Q8—1422no—
184D4—22no—
185D4—22no—
186D4—5682no—
187C2×C4—22no—
188C2×C4—82no—
189C2×C4—712no—
190C2×C4—711no—
191C2×C4—1422no—
192C2×C4—1422no—
193C2×C4—1421no—
194C2×C4—1421no—
195C2×C4D4×D7112yes—
196C2×C4C23×D7111yescharacteristic
197C8—21no—
198C8—712no—
199C8—1421no—
200C8#1176586512yes—
201C22—42no—
202C22—42no—
203C22—42no—
204C22—1421no—
205C22—1422no—
206C22C2×D4×D7111yescharacteristic
207C4—22no—
208C4—42no—
209C4—2842no—
210C4—2842no—
211C4—1421no—
212C4—1422no—
213C4#41×D7111yescharacteristic
214C4C2×#1176586511yescharacteristic
215C2—82no—
216C2—2841no—
217C2#1798654611yescharacteristic
218C2#1798680912yes—
subgroupG/H
centerC22C2×D4×D71
commutatorC2×C4×C71C24
FrattiniC2×C4C23×D71
Fitting#442×C71C2
socleC22×C71C22×D4
hypercenter#442D71
hypocenterC71#3173
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #17986614C2semidirect
2. #17986396C2semidirect
3. #17986382C2semidirect
4. #17986357C2semidirect
5. #17986258C2semidirect
7. #17986227C2semidirect
8. #17986107C2semidirect
9. C4×#11765853C2semidirect
10. #17985956C2semidirect
11. #442×C71C2semidirect
110. C71#3173semidirect
118. #442D71semidirect