Finite Group Databasebeta

← #31906963

Subgroups — #31906963

Order 18176.

262 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 71 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#22597279C211yesmaximal, characteristic
2#22590153C212yesmaximal
3#22586293C211yesmaximal, characteristic
4#22586290C212yesmaximal
5C71×#1328C211yesmaximal, characteristic
6#17986552C411yescharacteristic
7#17986128—22no—
8#17986126—22no—
9#17986025C411yescharacteristic
10#17986022C2211yescharacteristic
11#17985957C2211yescharacteristic
12#17985955C411yescharacteristic
13C2×#14556038C411yescharacteristic
14#17985819—22no—
15#17985781C2212yes—
16#17985776—22no—
17#424×C71C2211yescharacteristic
18#349×C71C2212yes—
19C2×#11765849C2×C411yescharacteristic
20C22×C71⋊C8C2×C411yescharacteristic
21#14556127—21no—
22#14556119—21no—
23#14556105—22no—
24C4×Dic142—22no—
25#14556087C2×C411yescharacteristic
26C2×C4×Dic71C2×C411yescharacteristic
27#14556068—22no—
28Dic71⋊C8—22no—
29Dic71⋊C8—22no—
30#14556039—21no—
31#14556038—21no—
32#14556038—21no—
33#14556038D412yes—
34C4×C71⋊C8—21no—
35C8×Dic71D412yes—
36C2×M16×C71C2311yescharacteristic
37C22×C8×C71C2×C411yescharacteristic
38#117×C71C2×C411yescharacteristic
39M32×C71—22no—
40C4⋊C8×C71—22no—
41C2×Dic142—22no—
42C22×Dic71—21no—
43#11765849—41no—
44C2×C71⋊C8—22no—
45C2×C71⋊C8—21no—
46C2×C71⋊C8C22⋊C411yescharacteristic
47C2×C71⋊C8C22⋊C411yescharacteristic
48C4⋊Dic71—22no—
49C4⋊Dic71—21no—
50Dic71⋊C4—22no—
51Dic71⋊C4—22no—
52C22⋊Dic71—21no—
53C4×Dic71—21no—
54C4×Dic71C22⋊C412yes—
55C4×Dic71M1611yescharacteristic
56C4×Dic71M1611yescharacteristic
57C71⋊C16—42no—
58C22×C4×C71C22×C411yescharacteristic
59M16×C71—41no—
60C2×C8×C71—21no—
61C2×C8×C71—41no—
62C2×C8×C71C2×D412yes—
63C4⋊C4×C71—21no—
64C22⋊C4×C71M1612yes—
65C42×C71—21no—
66C16×C71—42no—
67C23×C71C2×M1611yescharacteristic
68C2×C4×C71—21no—
69C2×C4×C71—21no—
70C2×C4×C71—22no—
71C2×C4×C71C2×C22⋊C411yescharacteristic
72C2×C4×C71C2×M1611yescharacteristic
73C2×Dic71—21no—
74C2×Dic71—21no—
75C2×Dic71—22no—
76C2×Dic71—81no—
77Dic142—82no—
78C8×C71—22no—
79C8×C71—41no—
80C71⋊C8—21no—
81C71⋊C8—41no—
82C71⋊C8#10112yes—
83C22×C71—21no—
84C22×C71—41no—
85C22×C71#40711yescharacteristic
86C4×C71—21no—
87C4×C71—42no—
88C4×C71#41011yescharacteristic
89C4×C71C2×#10111yescharacteristic
90Dic71—41no—
91Dic71—42no—
92Dic71—41no—
93#11540—711nomaximal, Sylow
94C2×C71—21no—
95C2×C71—41no—
96C2×C71#146711yescharacteristic
97#2961—711no—
98#2166—712no—
99#1328—711no—
100#1328D7111yescharacteristic
101#1327—712no—
102C71#1154011yescharacteristic, complemented, Sylow
103#533—711no—
104#446—1422no—
105#446—1422no—
106#424—711no—
107#424C2×D7111yescharacteristic
108#423—711no—
109#405—711no—
110#405—711no—
111C2×#97—711no—
112#364—1422no—
113#349—712no—
114#349C2×D7112yes—
115#347—1422no—
116C2×M16—711no—
117C2×M16C22×D7111yescharacteristic
118C22×C8—711no—
119C22×C8C4×D7111yescharacteristic
120C4⋊Q8—1421no—
121#125—1421no—
122C22⋊Q8—1422no—
123C4×Q8—1422no—
124#117—711no—
125#117C4×D7111yescharacteristic
126C2×C42—711no—
127M32—22no—
128M32—1422no—
129C4⋊C8—22no—
130C4⋊C8—1422no—
131C4⋊C8—1422no—
132#97—712no—
133#97—1421no—
134#97—1421no—
135#97—1421no—
136C4×C8—712no—
137C4×C8—1421no—
138C2×Q8—1422no—
139C22×C4—1421no—
140C22×C4C2×C4×D7111yescharacteristic
141M16—41no—
142M16—2841no—
143C2×C8—21no—
144C2×C8—41no—
145C2×C8—711no—
146C2×C8—711no—
147C2×C8—1421no—
148C2×C8—1422no—
149C2×C8D4×D7112yes—
150C4⋊C4—21no—
151C4⋊C4—1422no—
152C4⋊C4—1422no—
153C4⋊C4—1422no—
154C4⋊C4—1421no—
155C22⋊C4—1421no—
156C22⋊C4#1176584812yes—
157C42—21no—
158C42—712no—
159C42—711no—
160C42—711no—
161C42—1421no—
162C16—42no—
163C16—2842no—
164C23C2×#1176584811yescharacteristic
165Q8—5682no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—22no—
169C2×C4—5681no—
170C2×C4—1421no—
171C2×C4—1421no—
172C2×C4—1422no—
173C2×C4C22⋊C4×D7111yescharacteristic
174C2×C4M16×D7111yescharacteristic
175C8—22no—
176C8—41no—
177C8—2841no—
178C8—712no—
179C8—1421no—
180C22—21no—
181C22—41no—
182C22#1798596111yescharacteristic
183C4—21no—
184C4—42no—
185C4—2841no—
186C4—2841no—
187C4—2842no—
188C4#1798597111yescharacteristic
189C4#101×D7111yescharacteristic
190C2—21no—
191C2—41no—
192C2#2258668211yescharacteristic
subgroupG/H
centerC4#17985971
commutatorC22×C4×C71C22×C4
FrattiniC2×M16C22×D71
FittingC71×#1328C2
socleC2×C71#1467
prime radicalC23×C71C2×M16
cosocleC2×M16×C71C23
hypercenter#1328D71
hypocenterC71#11540
LCSG ▷ C22×C4×C71 ▷ C22×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16 ◁ #1328

Complements

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

NH ≅ G/Ntype
102. C71#11540semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#225972792
#225901532
#225862932
#225862902
C71×#13282
#1154071