Finite Group Databasebeta

← #22586936

Subgroups — #22586936

Order 9088.

264 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 61 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#124×D71C211yesmaximal, characteristic
2#17986054C211yesmaximal, characteristic, complemented
3#17985951C211yesmaximal, characteristic, complemented
4#17985739C211yesmaximal, characteristic, complemented
5#17985738C211yesmaximal, characteristic, complemented
6#17985738C211yesmaximal, characteristic, complemented
7#329×C71C211yesmaximal, characteristic, complemented
8C2×Q8×D71C411yescharacteristic
9C2×D4×D71C411yescharacteristic
10C2×#11765848—21no—
11#14556117C411yescharacteristic
12#14556116C2211yescharacteristic
13#14556115C411yescharacteristic
14#14556114—21no—
15#14556114—21no—
16C22⋊C4×D71—21no—
17C22⋊C4×D71—21no—
18C42×D71C2211yescharacteristic
19Dic71⋊C8—21no—
20(C2×D71)⋊C8—21no—
21#14556039C2211yescharacteristic, complemented
22#14556039C2211yescharacteristic, complemented
23C8×Dic71—21no—
24#124×C71C2211yescharacteristic
25#97×C71C2211yescharacteristic, complemented
26#97×C71C2211yescharacteristic, complemented
27C23×D71—21no—
28C2×Dic142—21no—
29C2×Dic142C2×C411yescharacteristic
30Q8×D71—42no—
31C2×D284C2×C411yescharacteristic
32C2×C22⋊D71—21no—
33D4×D71—42no—
34C2×C4×D71—21no—
35C2×C4×D71C2×C411yescharacteristic
36C2×C4×D71D411yescharacteristic
37C2×C4×D71D411yescharacteristic
38#11765848—24no—
39C2×C71⋊C8—21no—
40C2×C71⋊C8—21no—
41C22⋊Dic71—21no—
42C22⋊Dic71—21no—
43(C2×D71)⋊C4—21no—
44(C2×D71)⋊C4—21no—
45(C2×D71)⋊C4—21no—
46(C2×D71)⋊C4—21no—
47C4×Dic71C2×C411yescharacteristic
48C4×Dic71D411yescharacteristic
49C4×Dic71D411yescharacteristic
50C2×Q8×C71C2×C411yescharacteristic
51C2×D4×C71C2×C411yescharacteristic
52C2×C8×C71—21no—
53C2×C8×C71—21no—
54C22⋊C4×C71—21no—
55C22⋊C4×C71—21no—
56C42×C71C2311yescharacteristic
57C23×C71—21no—
58C22×D71—21no—
59C22×D71—42no—
60C22×D71—42no—
61C22×D71—42no—
62C22×D71C22⋊C411yescharacteristic
63Q8×C71—41no—
64D4×C71—41no—
65C2×C4×C71—21no—
66C2×C4×C71C22×C411yescharacteristic
67C2×C4×C71C2×D411yescharacteristic
68C2×C4×C71C2×D411yescharacteristic
69C22⋊D71—42no—
70C2×Dic71—21no—
71C2×Dic71C22⋊C411yescharacteristic
72C2×Dic71C22⋊C411yescharacteristic
73C2×Dic71C22⋊C411yescharacteristic
74D284—41no—
75C4×D71—22no—
76C4×D71—22no—
77C4×D71—41no—
78C4×D71—42no—
79Dic142—42no—
80Dic142—41no—
81C8×C71—22no—
82C8×C71—41no—
83C71⋊C8—22no—
84C71⋊C8—41no—
85C22×C71—41no—
86C22×C71—41no—
87C22×C71—41no—
88C22×C71C2×C22⋊C411yescharacteristic
89C2×D71—21no—
90C2×D71—21no—
91C2×D71—41no—
92C2×D71—41no—
93C2×D71—41no—
94C2×D71—84no—
95C2×D71#10412yes—
96C4×C71—21no—
97C4×C71—21no—
98C4×C71—21no—
99C4×C71—41no—
100Dic71—21no—
101Dic71—21no—
102Dic71—41no—
103Dic71#10012yes—
104C2×C71—81no—
105C2×C71C2×#10011yescharacteristic
106C2×C71C2×#10411yescharacteristic
107C2×C71#42111yescharacteristic
108D71—22no—
109D71—81no—
110#1527—711nomaximal, Sylow
111C71#152711yescharacteristic, complemented, Sylow
112C2×#124—711no—
113#432—711no—
114C4×M16—711no—
115#329—711no—
116#329—711no—
117#329—711no—
118#329D7111yescharacteristic, complemented
119C22×Q8—711no—
120C22×D4—711no—
121C2×M16—1421no—
122#124—711no—
123#124—711no—
124#124—711no—
125#124—1421no—
126#124—1421no—
127#124C2×D7111yescharacteristic
128C2×C22⋊C4—1421no—
129C2×C22⋊C4—1421no—
130C2×C42—711no—
131C4⋊C8—1421no—
132C22⋊C8—1421no—
133#97—711no—
134#97—711no—
135#97C2×D7111yescharacteristic, complemented
136#97C2×D7111yescharacteristic, complemented
137C4×C8—1421no—
138C24—1421no—
139C2×Q8—2842no—
140C2×Q8—711no—
141C2×Q8—1421no—
142C2×Q8C4×D7111yescharacteristic
143C2×D4—2842no—
144C2×D4—711no—
145C2×D4—1421no—
146C2×D4C4×D7111yescharacteristic
147C22×C4—711no—
148C22×C4—711no—
149C22×C4—711no—
150C22×C4—1421no—
151M16—1424no—
152C2×C8—21no—
153C2×C8—21no—
154C2×C8—1421no—
155C2×C8—1421no—
156C22⋊C4—21no—
157C22⋊C4—21no—
158C22⋊C4—1421no—
159C22⋊C4—1421no—
160C22⋊C4—1421no—
161C22⋊C4—1421no—
162C22⋊C4—1421no—
163C22⋊C4—1421no—
164C42—711no—
165C42—711no—
166C42—711no—
167C42C22×D7111yescharacteristic
168C23—21no—
169C23—2842no—
170C23—2842no—
171C23—2842no—
172C23—711no—
173C23—1421no—
174Q8—41no—
175Q8—2841no—
176Q8—2842no—
177D4—41no—
178D4—2841no—
179D4—2842no—
180C2×C4—21no—
181C2×C4—2841no—
182C2×C4—2842no—
183C2×C4—711no—
184C2×C4—711no—
185C2×C4—711no—
186C2×C4—1422no—
187C2×C4—1422no—
188C2×C4—1421no—
189C2×C4C2×C4×D7111yescharacteristic
190C2×C4D4×D7111yescharacteristic
191C2×C4D4×D7111yescharacteristic
192C8—22no—
193C8—41no—
194C8—2841no—
195C8—1422no—
196C22—41no—
197C22—41no—
198C22—41no—
199C22—2841no—
200C22—2841no—
201C22—2841no—
202C22—5684no—
203C22—712no—
204C22—1421no—
205C22—1421no—
206C22C22⋊C4×D7111yescharacteristic
207C4—21no—
208C4—21no—
209C4—21no—
210C4—41no—
211C4—2841no—
212C4—712no—
213C4—1421no—
214C4—1421no—
215C2—81no—
216C2—5681no—
217C2—1422no—
218C2#100×D7111yescharacteristic
219C2#104×D7111yescharacteristic
220C2#1798601411yescharacteristic
subgroupG/H
centerC22C22⋊C4×D71
commutatorC2×C4×C71C22×C4
FrattiniC42C22×D71
Fitting#329×C71C2
socleC22×C71C2×C22⋊C4
hypercenter#329D71
hypocenterC71#1527
LCSG ▷ C2×C4×C71 ▷ C22×C71 ▷ C71
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #17986054C2semidirect
3. #17985951C2semidirect
4. #17985739C2semidirect
5. #17985738C2semidirect
6. #17985738C2semidirect
7. #329×C71C2semidirect
21. #14556039C22semidirect
22. #14556039C22semidirect
25. #97×C71C22semidirect
26. #97×C71C22semidirect
111. C71#1527semidirect
118. #329D71semidirect
135. #97C2×D71semidirect
136. #97C2×D71semidirect