Finite Group Databasebeta

← #22589683

Subgroups — #22589683

Order 9088.

246 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 73 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#17986627C211yesmaximal, characteristic
2#17986039C211yesmaximal, characteristic
3#17985868C211yesmaximal, characteristic
4#17985767C211yesmaximal, characteristic
5#17985760C211yesmaximal, characteristic
6#17985758C211yesmaximal, characteristic
7#428×C71C211yesmaximal, characteristic
8C2×#11765849C2211yescharacteristic
9#14556128—21no—
10#14556127—21no—
11#14556120—21no—
12#14556119—21no—
13#14556105—22no—
14#14556087C2211yescharacteristic
15C2×C4⋊Dic71C2211yescharacteristic
16C2×Dic71⋊C4—22no—
17C2×C4×Dic71C2211yescharacteristic
18#14556061—21no—
19#14556059—21no—
20C2×M16×C71C2211yescharacteristic
21#117×C71C2211yescharacteristic
22C2×C4⋊C4×C71C2211yescharacteristic
23#107×C71—21no—
24#106×C71—21no—
25C2×Dic142—22no—
26C22×Dic71—21no—
27C22×Dic71D412yes—
28#11765849—21no—
29#11765849Q812yescomplemented
30C2×C71⋊C8—21no—
31C4⋊Dic71—22no—
32C4⋊Dic71—21no—
33C4⋊Dic71—21no—
34C4⋊Dic71D411yescharacteristic
35C4⋊Dic71D411yescharacteristic
36Dic71⋊C4—22no—
37Dic71⋊C4—22no—
38Dic71⋊C4—44no—
39C22⋊Dic71—21no—
40C4×Dic71—21no—
41C4×Dic71—21no—
42C4×Dic71Q812yescomplemented
43C22×C4×C71—21no—
44C22×C4×C71C2311yescharacteristic
45M16×C71—21no—
46M16×C71Q812yescomplemented
47C2×C8×C71—21no—
48C4⋊C4×C71—21no—
49C4⋊C4×C71—21no—
50C4⋊C4×C71D411yescharacteristic
51C4⋊C4×C71D411yescharacteristic
52C22⋊C4×C71—21no—
53C42×C71—21no—
54C23×C71C2×D411yescharacteristic
55C2×C4×C71—21no—
56C2×C4×C71—21no—
57C2×C4×C71—42no—
58C2×C4×C71—41no—
59C2×C4×C71C2×D411yescharacteristic
60C2×C4×C71C2×D411yescharacteristic
61C2×C4×C71C2×Q811yescharacteristic
62C2×C4×C71C2×Q811yescharacteristic
63C2×C4×C71C2×Q811yescharacteristic
64C2×C4×C71#4111yescharacteristic
65C2×Dic71—22no—
66C2×Dic71—22no—
67C2×Dic71—22no—
68C2×Dic71—21no—
69C2×Dic71—21no—
70C2×Dic71—22no—
71C2×Dic71—42no—
72Dic142—82no—
73C8×C71—22no—
74C71⋊C8—22no—
75C22×C71—21no—
76C22×C71—21no—
77C22×C71#12011yescharacteristic
78C22×C71C22⋊Q811yescharacteristic
79C22×C71C4⋊Q811yescharacteristic
80C4×C71—41no—
81C4×C71—41no—
82C4×C71—81no—
83C4×C71C22⋊Q811yescharacteristic
84C4×C71C22⋊Q811yescharacteristic
85C4×C71C4⋊Q811yescharacteristic
86C4×C71C4⋊Q811yescharacteristic
87Dic71—24no—
88Dic71—41no—
89Dic71—42no—
90Dic71—41no—
91C2×C71—21no—
92C2×C71—21no—
93C2×C71#39511yescharacteristic
94C2×C71#45311yescharacteristic
95C2×C71#45611yescharacteristic
96#2060—711nomaximal, Sylow
97C71#206011yescharacteristic, complemented, Sylow
98#544—711no—
99#428—711no—
100#428D7111yescharacteristic
101#384—711no—
102#343—711no—
103#339—711no—
104#339—711no—
105C2×M16—711no—
106C2×M16C2×D7111yescharacteristic
107C4⋊Q8—1421no—
108C4⋊Q8—1421no—
109#125—1421no—
110#125—1421no—
111C22⋊Q8—1422no—
112#117—711no—
113#117C2×D7111yescharacteristic
114C2×C4⋊C4—711no—
115C2×C4⋊C4—1422no—
116C2×C4⋊C4C2×D7111yescharacteristic
117C2×C42—711no—
118#107—21no—
119#107—1421no—
120#106—21no—
121#106—1421no—
122C2×Q8—1422no—
123C22×C4—21no—
124C22×C4—712no—
125C22×C4—1421no—
126C22×C4C22×D7111yescharacteristic
127M16—21no—
128M16—712no—
129M16—1421no—
130M16Dic14212yescomplemented
131C2×C8—21no—
132C2×C8—1421no—
133C4⋊C4—21no—
134C4⋊C4—21no—
135C4⋊C4—2844no—
136C4⋊C4—711no—
137C4⋊C4—711no—
138C4⋊C4—1422no—
139C4⋊C4—1422no—
140C4⋊C4—1422no—
141C4⋊C4—1421no—
142C4⋊C4—1421no—
143C4⋊C4C22⋊D7111yescharacteristic
144C4⋊C4C22⋊D7111yescharacteristic
145C22⋊C4—21no—
146C22⋊C4—1421no—
147C42—21no—
148C42—712no—
149C42—1421no—
150C42—1421no—
151C23D4×D7111yescharacteristic
152Q8—5682no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—42no—
156C2×C4—41no—
157C2×C4—2842no—
158C2×C4—1421no—
159C2×C4—1421no—
160C2×C4—1422no—
161C2×C4—1422no—
162C2×C4—1422no—
163C2×C4—1422no—
164C2×C4D4×D7111yescharacteristic
165C2×C4C2×C22⋊D7111yescharacteristic
166C2×C4Q8×D7111yescharacteristic
167C2×C4Q8×D7111yescharacteristic
168C2×C4C2×Dic14211yescharacteristic
169C2×C4#1176586511yescharacteristic
170C8—22no—
171C8—1422no—
172C22—21no—
173C22—21no—
174C22#1455609611yescharacteristic
175C22#1455610611yescharacteristic
176C22#1455612711yescharacteristic
177C4—41no—
178C4—41no—
179C4—81no—
180C4—2842no—
181C4—2841no—
182C4—2841no—
183C4—1424no—
184C4#1455610611yescharacteristic
185C4#1455610711yescharacteristic
186C4#1455612611yescharacteristic
187C4#1455612711yescharacteristic
188C2—21no—
189C2—21no—
190C2#1798591911yescharacteristic
191C2#1798616511yescharacteristic
192C2#1798618011yescharacteristic
subgroupG/H
centerC22#14556096
commutatorC22×C4×C71C23
FrattiniC22×C4C22×D71
Fitting#428×C71C2
socleC22×C71#120
hypercenter#428D71
hypocenterC71#2060
LCSG ▷ C22×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
29. #11765849Q8semidirect
42. C4×Dic71Q8semidirect
46. M16×C71Q8semidirect
97. C71#2060semidirect
130. M16Dic142semidirect