Finite Group Databasebeta

← #22598145

Subgroups — #22598145

Order 9088.

376 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 153 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#17986556C211yesmaximal, characteristic
2#17986306C214yesmaximal, complemented
3#17986294C212yesmaximal, complemented
4#17986284C212yesmaximal, complemented
5#17986039C212yesmaximal
6#17986023C211yesmaximal, characteristic
7#17986008C212yesmaximal
8C2×C4×Q8×C71C211yesmaximal, characteristic
9C2×#11765849C2212yes—
10#14556128C2211yescharacteristic
11#14556128C2211yescharacteristic
12#14556120C2212yes—
13#14556107—21no—
14#14556107—21no—
15C4×Dic142—21no—
16C4×Dic142—21no—
17#14556087C2212yes—
18#14556061C2214yes—
19#14556059C2214yes—
20C4⋊(C71⋊C8)C2212yes—
21C4⋊(C71⋊C8)C2212yes—
22#14556052C2214yes—
23#14556052C2214yes—
24C22×Q8×C71C2211yescharacteristic
25C4×Q8×C71—21no—
26C4×Q8×C71—21no—
27C4×Q8×C71C2212yes—
28C4×Q8×C71C2212yes—
29C2×C4⋊C4×C71—21no—
30C2×C4⋊C4×C71C2211yescharacteristic
31C2×C42×C71—21no—
32C2×C42×C71C2211yescharacteristic
33C2×Dic142—21no—
34C2×Dic142—21no—
35#11765849—24no—
36C2×C71⋊C8C2314yes—
37C4⋊Dic71—21no—
38C4⋊Dic71—21no—
39C4⋊Dic71C2312yes—
40C4⋊Dic71C2312yes—
41Dic71⋊C4—22no—
42Dic71⋊C4—22no—
43C22⋊Dic71—22no—
44C4×Dic71—22no—
45C2×Q8×C71—21no—
46C2×Q8×C71—22no—
47C2×Q8×C71Q814yescomplemented
48C2×Q8×C71C2312yes—
49C22×C4×C71—21no—
50C22×C4×C71—21no—
51C22×C4×C71D411yescharacteristic
52C22×C4×C71D411yescharacteristic
53C22×C4×C71C2311yescharacteristic
54C4⋊C4×C71—22no—
55C4⋊C4×C71—22no—
56C4⋊C4×C71—21no—
57C4⋊C4×C71C2312yes—
58C42×C71—22no—
59C42×C71—22no—
60C42×C71D411yescharacteristic
61C42×C71D411yescharacteristic
62C42×C71C2311yescharacteristic
63C42×C71C2311yescharacteristic
64C23×C71C2×D411yescharacteristic
65Q8×C71—24no—
66Q8×C71—22no—
67Q8×C71C2×Q814yes—
68C2×C4×C71—24no—
69C2×C4×C71—22no—
70C2×C4×C71—22no—
71C2×C4×C71—22no—
72C2×C4×C71—41no—
73C2×C4×C71—42no—
74C2×C4×C71C2×D411yescharacteristic
75C2×C4×C71C2×D411yescharacteristic
76C2×C4×C71C2×D411yescharacteristic
77C2×C4×C71C2×D411yescharacteristic
78C2×C4×C71C2×D411yescharacteristic
79C2×C4×C71C2×Q812yes—
80C2×C4×C71#4112yes—
81C2×C4×C71C2411yescharacteristic
82C2×Dic71—22no—
83C2×Dic71—22no—
84Dic142—42no—
85Dic142—42no—
86C71⋊C8—24no—
87C22×C71—21no—
88C22×C71—21no—
89C22×C71C22⋊Q812yes—
90C22×C71C22×D411yescharacteristic
91C4×C71—24no—
92C4×C71—21no—
93C4×C71—21no—
94C4×C71—21no—
95C4×C71—42no—
96C4×C71C22⋊Q812yes—
97C4×C71#13712yes—
98C4×C71C22×Q811yescharacteristic
99C4×C71C2×#4111yescharacteristic
100Dic71—42no—
101Dic71—42no—
102C2×C71—22no—
103C2×C71C2×C22⋊Q811yescharacteristic
104C2×C71C2×#13711yescharacteristic
105C2×C71#57511yescharacteristic
106#3078—711nomaximal, Sylow
107C71#307811yescharacteristic, complemented, Sylow
108#533—711no—
109C2×C4×Q8D7111yescharacteristic
110#479—714no—
111#477—712no—
112#475—712no—
113#428—712no—
114#423—711no—
115#419—712no—
116C22×Q8C2×D7111yescharacteristic
117C2×M16—712no—
118C4⋊Q8—711no—
119C4⋊Q8—711no—
120#125—712no—
121C22⋊Q8—1421no—
122C22⋊Q8—1421no—
123C4×Q8—21no—
124C4×Q8—21no—
125C4×Q8—1421no—
126C4×Q8—1421no—
127C4×Q8C2×D7112yes—
128C4×Q8C2×D7112yes—
129#117—712no—
130C2×C4⋊C4—21no—
131C2×C4⋊C4C2×D7111yescharacteristic
132C2×C42—21no—
133C2×C42C2×D7111yescharacteristic
134#107—714no—
135#106—714no—
136C4⋊C8—712no—
137C4⋊C8—712no—
138#103—714no—
139#103—714no—
140C2×Q8—21no—
141C2×Q8—22no—
142C2×Q8—1421no—
143C2×Q8—1421no—
144C2×Q8Dic14214yescomplemented
145C2×Q8C22×D7112yes—
146C22×C4—21no—
147C22×C4—21no—
148C22×C4C22⋊D7111yescharacteristic
149C22×C4C22⋊D7111yescharacteristic
150C22×C4C22×D7111yescharacteristic
151M16—1424no—
152C2×C8—714no—
153C4⋊C4—22no—
154C4⋊C4—22no—
155C4⋊C4—21no—
156C4⋊C4—712no—
157C4⋊C4—712no—
158C4⋊C4—1422no—
159C4⋊C4—1422no—
160C4⋊C4—1421no—
161C4⋊C4—1421no—
162C4⋊C4C22×D7112yes—
163C22⋊C4—1422no—
164C42—22no—
165C42—22no—
166C42—1422no—
167C42C22⋊D7111yescharacteristic
168C42C22⋊D7111yescharacteristic
169C42C22×D7111yescharacteristic
170C42C22×D7111yescharacteristic
171C23C2×C22⋊D7111yescharacteristic
172Q8—22no—
173Q8—24no—
174Q8—2842no—
175Q8—2842no—
176Q8C2×Dic14214yes—
177C2×C4—22no—
178C2×C4—24no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—41no—
182C2×C4—42no—
183C2×C4—1422no—
184C2×C4—1422no—
185C2×C4C2×C22⋊D7111yescharacteristic
186C2×C4C2×C22⋊D7111yescharacteristic
187C2×C4C2×C22⋊D7111yescharacteristic
188C2×C4C2×C22⋊D7111yescharacteristic
189C2×C4C2×C22⋊D7111yescharacteristic
190C2×C4C2×Dic14212yes—
191C2×C4#1176586512yes—
192C2×C4C23×D7111yescharacteristic
193C8—1424no—
194C22—21no—
195C22—21no—
196C22#1455610712yes—
197C22C22×C22⋊D7111yescharacteristic
198C4—24no—
199C4—21no—
200C4—21no—
201C4—21no—
202C4—42no—
203C4—2842no—
204C4—2842no—
205C4#1455610712yes—
206C4#1455615912yes—
207C4C22×Dic14211yescharacteristic
208C4C2×#1176586511yescharacteristic
209C2—22no—
210C2C2×#1455610711yescharacteristic
211C2C2×#1455615911yescharacteristic
212C2#1798679711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D71
commutatorC2×C4×C71C24
FrattiniC2×C4C23×D71
FittingC2×C4×Q8×C71C2
socleC22×C71C22×D4
hypercenterC2×C4×Q8D71
hypocenterC71#3078
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
2. #17986306C2semidirect
3. #17986294C2semidirect
4. #17986284C2semidirect
47. C2×Q8×C71Q8semidirect
107. C71#3078semidirect
144. C2×Q8Dic142semidirect