Finite Group Databasebeta

← #22589684

Subgroups — #22589684

Order 9088.

246 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 75 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#17986042C211yesmaximal, characteristic
3#17986041C211yesmaximal, characteristic
4#17985869C211yesmaximal, characteristic
5#17985767C211yesmaximal, characteristic
6#17985759C211yesmaximal, characteristic
7#339×C71C211yesmaximal, characteristic
8C2×#11765849C2211yescharacteristic
9#14556128—21no—
10#14556127—21no—
11#14556120—21no—
12#14556119—21no—
13#14556105—22no—
14#14556087C2211yescharacteristic
15C2×C4⋊Dic71—22no—
16C2×C4⋊Dic71C2211yescharacteristic
17C2×C4⋊Dic71C2211yescharacteristic
18#14556062—21no—
19#14556061—21no—
20#14556060—21no—
21#14556059—21no—
22C2×M16×C71C2211yescharacteristic
23#117×C71C2211yescharacteristic
24C2×C42×C71C2211yescharacteristic
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⋊Dic71—21no—
35C4⋊Dic71—21no—
36C4⋊Dic71—44no—
37C4⋊Dic71D411yescharacteristic
38C4⋊Dic71D411yescharacteristic
39Dic71⋊C4—22no—
40Dic71⋊C4—22no—
41C22⋊Dic71—21no—
42C4×Dic71—21no—
43C22×C4×C71—21no—
44C22×C4×C71C2311yescharacteristic
45M16×C71—21no—
46M16×C71Q812yescomplemented
47C2×C8×C71—21no—
48C4⋊C4×C71D411yescharacteristic
49C4⋊C4×C71D411yescharacteristic
50C22⋊C4×C71—21no—
51C42×C71—21no—
52C42×C71—21no—
53C42×C71Q812yescomplemented
54C23×C71C2×D411yescharacteristic
55C2×C4×C71—22no—
56C2×C4×C71—22no—
57C2×C4×C71—22no—
58C2×C4×C71—21no—
59C2×C4×C71—21no—
60C2×C4×C71C2×D411yescharacteristic
61C2×C4×C71C2×D411yescharacteristic
62C2×C4×C71C2×Q811yescharacteristic
63C2×C4×C71C2×Q811yescharacteristic
64C2×C4×C71C2×Q811yescharacteristic
65C2×C4×C71#4111yescharacteristic
66C2×Dic71—21no—
67C2×Dic71—21no—
68C2×Dic71—22no—
69C2×Dic71—42no—
70C2×Dic71—42no—
71C2×Dic71—41no—
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—24no—
81C4×C71—41no—
82C4×C71—41no—
83C4×C71C22⋊Q811yescharacteristic
84C4×C71C22⋊Q811yescharacteristic
85C4×C71C4⋊Q811yescharacteristic
86C4×C71C4⋊Q811yescharacteristic
87Dic71—41no—
88Dic71—42no—
89Dic71—41no—
90Dic71—81no—
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#428—711no—
101#384—711no—
102#343—711no—
103#339—711no—
104#339D7111yescharacteristic
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—711no—
116C2×C4⋊C4—1422no—
117C2×C42C2×D7111yescharacteristic
118#107—1421no—
119#107—1421no—
120#106—1421no—
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—2844no—
134C4⋊C4—711no—
135C4⋊C4—711no—
136C4⋊C4—1422no—
137C4⋊C4—1422no—
138C4⋊C4—1422no—
139C4⋊C4—1421no—
140C4⋊C4—1421no—
141C4⋊C4—1421no—
142C4⋊C4—1421no—
143C4⋊C4D28411yescharacteristic
144C4⋊C4D28411yescharacteristic
145C22⋊C4—21no—
146C22⋊C4—1421no—
147C42—21no—
148C42—21no—
149C42—1421no—
150C42Dic14212yescomplemented
151C23D4×D7111yescharacteristic
152Q8—5682no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—2842no—
159C2×C4—2842no—
160C2×C4—2841no—
161C2×C4—1421no—
162C2×C4—1421no—
163C2×C4—1422no—
164C2×C4D4×D7111yescharacteristic
165C2×C4C2×D28411yescharacteristic
166C2×C4Q8×D7111yescharacteristic
167C2×C4C2×Dic14211yescharacteristic
168C2×C4C2×Dic14211yescharacteristic
169C2×C4#1176586411yescharacteristic
170C8—22no—
171C8—1422no—
172C22—21no—
173C22—21no—
174C22#1455609811yescharacteristic
175C22#1455610511yescharacteristic
176C22#1455612711yescharacteristic
177C4—24no—
178C4—41no—
179C4—41no—
180C4—2842no—
181C4—2841no—
182C4—2841no—
183C4—5681no—
184C4#1455610511yescharacteristic
185C4#1455610811yescharacteristic
186C4#1455612711yescharacteristic
187C4#1455612811yescharacteristic
188C2—21no—
189C2—21no—
190C2#1798592011yescharacteristic
191C2#1798616811yescharacteristic
192C2#1798618311yescharacteristic
subgroupG/H
centerC22#14556098
commutatorC22×C4×C71C23
FrattiniC22×C4C22×D71
Fitting#339×C71C2
socleC22×C71#120
hypercenter#339D71
hypocenterC71#2060
LCSG ▷ C22×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
29. #11765849Q8semidirect
46. M16×C71Q8semidirect
53. C42×C71Q8semidirect
97. C71#2060semidirect
130. M16Dic142semidirect
150. C42Dic142semidirect