Finite Group Databasebeta

← #22589708

Subgroups — #22589708

Order 9088.

208 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 65 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
1C2×#14556063C211yesmaximal, characteristic
2#17986039C211yesmaximal, characteristic
3#17986027C211yesmaximal, characteristic
4#17986009C211yesmaximal, characteristic
5C2×#14556051C211yesmaximal, characteristic
6C2×#14556046C211yesmaximal, characteristic
7#343×C71C211yesmaximal, characteristic
8C22×Dic142C2211yescharacteristic
9C2×#11765849C2211yescharacteristic
10C22×C71⋊C8C2211yescharacteristic
11#14556087C2211yescharacteristic
12#14556063—22no—
13#14556061—21no—
14#14556059—21no—
15Dic71⋊C8—22no—
16#14556053—21no—
17#14556053—21no—
18#14556051—22no—
19#14556046—22no—
20C2×M16×C71C2211yescharacteristic
21C2×M16×C71C2211yescharacteristic
22C2×C4⋊C4×C71C2211yescharacteristic
23C2×Dic142—21no—
24C2×Dic142—21no—
25C2×Dic142—21no—
26C2×Dic142—21no—
27C2×Dic142—21no—
28C2×Dic142Q812yes—
29C22×Dic71—21no—
30#11765849—21no—
31#11765849D412yes—
32C2×C71⋊C8—21no—
33C2×C71⋊C8—21no—
34C2×C71⋊C8—21no—
35C2×C71⋊C8D412yes—
36C4⋊Dic71D411yescharacteristic
37C4⋊Dic71D411yescharacteristic
38C22⋊Dic71—21no—
39C4×Dic71—21no—
40C22×C4×C71—21no—
41C22×C4×C71C2311yescharacteristic
42M16×C71—21no—
43M16×C71—21no—
44M16×C71—21no—
45M16×C71—21no—
46C2×C8×C71—21no—
47C2×C8×C71—21no—
48C4⋊C4×C71—21no—
49C4⋊C4×C71—21no—
50C23×C71#4111yescharacteristic
51C2×C4×C71—41no—
52C2×C4×C71—81no—
53C2×C4×C71C2×D411yescharacteristic
54C2×C4×C71C2×D411yescharacteristic
55C2×C4×C71C2×D411yescharacteristic
56C2×C4×C71C2×Q811yescharacteristic
57C2×C4×C71#4111yescharacteristic
58C2×C4×C71#4111yescharacteristic
59C2×Dic71—21no—
60C2×Dic71—21no—
61C2×Dic71—22no—
62C2×Dic71—41no—
63C2×Dic71—41no—
64Dic142—22no—
65Dic142—22no—
66Dic142—41no—
67Dic142—41no—
68C8×C71—41no—
69C8×C71—41no—
70C71⋊C8—22no—
71C71⋊C8—22no—
72C22×C71—21no—
73C22×C71—21no—
74C22×C71#12111yescharacteristic
75C22×C71C22⋊Q811yescharacteristic
76C22×C71#12611yescharacteristic
77C4×C71—81no—
78C4×C71#12111yescharacteristic
79C4×C71#12111yescharacteristic
80C4×C71C22⋊Q811yescharacteristic
81C4×C71C22⋊Q811yescharacteristic
82Dic71—42no—
83Dic71—41no—
84Dic71—41no—
85C2×C71—21no—
86C2×C71—21no—
87C2×C71#39611yescharacteristic
88C2×C71#47111yescharacteristic
89C2×C71#47311yescharacteristic
90#2064—711nomaximal, Sylow
91C71#206411yescharacteristic, complemented, Sylow
92C2×#108—711no—
93#428—711no—
94#424—711no—
95#419—711no—
96C2×#103—711no—
97C2×#101—711no—
98#343D7111yescharacteristic
99C22×Q8—711no—
100C2×M16—711no—
101C2×M16C2×D7111yescharacteristic
102C2×M16C2×D7111yescharacteristic
103C22×C8—711no—
104#117—711no—
105C2×C4⋊C4C2×D7111yescharacteristic
106#108—1422no—
107#107—1421no—
108#106—1421no—
109C4⋊C8—1422no—
110#103—1422no—
111#103—1421no—
112#103—1421no—
113#101—1422no—
114C2×Q8—712no—
115C2×Q8—1421no—
116C2×Q8—1421no—
117C2×Q8—1421no—
118C2×Q8—1421no—
119C2×Q8—1421no—
120C22×C4—21no—
121C22×C4—1421no—
122C22×C4C22×D7111yescharacteristic
123M16—21no—
124M16—21no—
125M16—21no—
126M16—21no—
127M16—712no—
128M16—1421no—
129C2×C8—21no—
130C2×C8—21no—
131C2×C8—712no—
132C2×C8—1421no—
133C2×C8—1421no—
134C2×C8—1421no—
135C4⋊C4—21no—
136C4⋊C4—21no—
137C4⋊C4—711no—
138C4⋊C4—711no—
139C22⋊C4—1421no—
140C42—1421no—
141C23#1176586511yescharacteristic
142Q8—2841no—
143Q8—2841no—
144Q8—1422no—
145Q8—1422no—
146C2×C4—41no—
147C2×C4—81no—
148C2×C4—2841no—
149C2×C4—2841no—
150C2×C4—1421no—
151C2×C4—1421no—
152C2×C4—1422no—
153C2×C4D4×D7111yescharacteristic
154C2×C4D4×D7111yescharacteristic
155C2×C4D4×D7111yescharacteristic
156C2×C4Q8×D7111yescharacteristic
157C2×C4#1176586511yescharacteristic
158C2×C4#1176586511yescharacteristic
159C8—41no—
160C8—41no—
161C8—1422no—
162C8—1422no—
163C22—21no—
164C22—21no—
165C22#1455610111yescharacteristic
166C22#1455610611yescharacteristic
167C22#1455612211yescharacteristic
168C4—81no—
169C4—2842no—
170C4—2841no—
171C4—2841no—
172C4#1455610111yescharacteristic
173C4#1455610111yescharacteristic
174C4#1455610611yescharacteristic
175C4#1455610611yescharacteristic
176C2—21no—
177C2—21no—
178C2#1798592311yescharacteristic
179C2#1798626111yescharacteristic
180C2#1798627311yescharacteristic
subgroupG/H
centerC22#14556101
commutatorC22×C4×C71C23
FrattiniC22×C4C22×D71
Fitting#343×C71C2
socleC22×C71#121
hypercenter#343D71
hypocenterC71#2064
LCSG ▷ C22×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
91. C71#2064semidirect