Finite Group Databasebeta

← #22589030

Subgroups — #22589030

Order 9088.

248 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 93 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×#14556053C211yesmaximal, characteristic
2C2×#14556053C211yesmaximal, characteristic
3#17985905C211yesmaximal, characteristic
4#17985897C211yesmaximal, characteristic
5#17985762C211yesmaximal, characteristic
6#17985762C211yesmaximal, characteristic
7C2×#97×C71C211yesmaximal, characteristic
8C22×Dic142C2211yescharacteristic
9C2×C4⋊Dic71C2211yescharacteristic
10C2×C4⋊Dic71C2211yescharacteristic
11C2×C4⋊Dic71C2211yescharacteristic
12C2×Dic71⋊C4—21no—
13#14556053—22no—
14#14556053C414yescomplemented
15C71⋊#95—21no—
16C71⋊#95—21no—
17C71⋊#95—21no—
18C22×C8×C71C2211yescharacteristic
19C22×C8×C71C2211yescharacteristic
20C2×C42×C71C2211yescharacteristic
21#97×C71—22no—
22C2×Dic142—21no—
23C2×Dic142—21no—
24C2×Dic142—21no—
25C2×Dic142—21no—
26C2×Dic142—21no—
27C2×Dic142C2×C412yes—
28C22×Dic71—21no—
29C22×Dic71—21no—
30C22×Dic71—21no—
31C22×Dic71—21no—
32C4⋊Dic71—21no—
33C4⋊Dic71—21no—
34C4⋊Dic71—21no—
35C4⋊Dic71—21no—
36C4⋊Dic71—21no—
37C4⋊Dic71C2×C412yes—
38Dic71⋊C4—42no—
39C22×C4×C71D411yescharacteristic
40C22×C4×C71D411yescharacteristic
41C22×C4×C71C2311yescharacteristic
42C2×C8×C71—21no—
43C2×C8×C71—21no—
44C2×C8×C71—21no—
45C2×C8×C71—21no—
46C2×C8×C71C2×C412yes—
47C2×C8×C71D412yes—
48C42×C71—21no—
49C42×C71—21no—
50C23×C71C2×D411yescharacteristic
51C2×C4×C71—21no—
52C2×C4×C71—21no—
53C2×C4×C71—21no—
54C2×C4×C71—21no—
55C2×C4×C71—21no—
56C2×C4×C71—21no—
57C2×C4×C71C22×C411yescharacteristic
58C2×C4×C71C2×D411yescharacteristic
59C2×C4×C71#4111yescharacteristic
60C2×C4×C71#4111yescharacteristic
61C2×C4×C71#4111yescharacteristic
62C2×C4×C71#4111yescharacteristic
63C2×Dic71—22no—
64C2×Dic71—22no—
65C2×Dic71—41no—
66C2×Dic71—41no—
67C2×Dic71—41no—
68C2×Dic71—41no—
69C2×Dic71—41no—
70C2×Dic71—41no—
71C2×Dic71—41no—
72C2×Dic71—41no—
73C2×Dic71—41no—
74C2×Dic71—41no—
75Dic142—22no—
76Dic142—22no—
77Dic142—41no—
78Dic142—41no—
79C8×C71—22no—
80C8×C71—22no—
81C22×C71C4×D411yescharacteristic
82C22×C71#12111yescharacteristic
83C22×C71#12411yescharacteristic
84C22×C71AGL(1,ℤ/8)11yescharacteristic
85C22×C71#13711yescharacteristic
86C22×C71#13711yescharacteristic
87C22×C71#13711yescharacteristic
88C4×C71—41no—
89C4×C71—41no—
90C4×C71#11711yescharacteristic
91C4×C71C4×D411yescharacteristic
92C4×C71#12311yescharacteristic
93C4×C71#12611yescharacteristic
94Dic71—42no—
95Dic71—42no—
96Dic71—81no—
97Dic71—81no—
98C2×C71#38811yescharacteristic
99C2×C71#44011yescharacteristic
100C2×C71#44111yescharacteristic
101C2×C71#46811yescharacteristic
102C2×C71#47011yescharacteristic
103C2×C71#48911yescharacteristic
104C2×C71#49111yescharacteristic
105#1935—711nomaximal, Sylow
106C71#193511yescharacteristic, complemented, Sylow
107C2×#103—711no—
108C2×#103—711no—
109C2×#97D7111yescharacteristic
110#391—711no—
111#389—711no—
112#340—711no—
113#340—711no—
114C22×Q8—711no—
115C22×C8C2×D7111yescharacteristic
116C22×C8C2×D7111yescharacteristic
117C2×C4⋊C4—711no—
118C2×C4⋊C4—711no—
119C2×C4⋊C4—711no—
120C2×C4⋊C4—1421no—
121C2×C42C2×D7111yescharacteristic
122#103—714no—
123#103—1422no—
124#97—22no—
125#95—1421no—
126#95—1421no—
127#95—1421no—
128C2×Q8—712no—
129C2×Q8—1421no—
130C2×Q8—1421no—
131C2×Q8—1421no—
132C2×Q8—1421no—
133C2×Q8—1421no—
134C22×C4—1421no—
135C22×C4—1421no—
136C22×C4—1421no—
137C22×C4—1421no—
138C22×C4D28411yescharacteristic
139C22×C4D28411yescharacteristic
140C22×C4C22×D7111yescharacteristic
141C2×C8—21no—
142C2×C8—21no—
143C2×C8—21no—
144C2×C8—21no—
145C2×C8C4×D7112yes—
146C2×C8C22⋊D7112yes—
147C4⋊C4—2842no—
148C4⋊C4—712no—
149C4⋊C4—1421no—
150C4⋊C4—1421no—
151C4⋊C4—1421no—
152C4⋊C4—1421no—
153C4⋊C4—1421no—
154C42—21no—
155C42—21no—
156C23C2×D28411yescharacteristic
157Q8—2841no—
158Q8—2841no—
159Q8—1422no—
160Q8—1422no—
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—2841no—
168C2×C4—2841no—
169C2×C4—2841no—
170C2×C4—2841no—
171C2×C4—2841no—
172C2×C4—2841no—
173C2×C4—2841no—
174C2×C4—2841no—
175C2×C4—2841no—
176C2×C4—2841no—
177C2×C4—1422no—
178C2×C4—1422no—
179C2×C4C2×C4×D7111yescharacteristic
180C2×C4C2×C22⋊D7111yescharacteristic
181C2×C4#1176586511yescharacteristic
182C2×C4#1176586511yescharacteristic
183C2×C4#1176586511yescharacteristic
184C2×C4#1176586511yescharacteristic
185C8—22no—
186C8—22no—
187C22C4×D28411yescharacteristic
188C22#1455610211yescharacteristic
189C22#1455611611yescharacteristic
190C22#1455615611yescharacteristic
191C22#1455616111yescharacteristic
192C22#1455616111yescharacteristic
193C22#1455616111yescharacteristic
194C4—41no—
195C4—41no—
196C4—2842no—
197C4—2842no—
198C4—5681no—
199C4—5681no—
200C4#1455608511yescharacteristic
201C4C4×C22⋊D7111yescharacteristic
202C4#1455611111yescharacteristic
203C4#1455612211yescharacteristic
204C2#1798589011yescharacteristic
205C2#1798610111yescharacteristic
206C2#1798610711yescharacteristic
207C2#1798624511yescharacteristic
208C2#1798625711yescharacteristic
209C2#1798635911yescharacteristic
210C2#1798636811yescharacteristic
subgroupG/H
centerC23C2×D284
commutatorC2×C4×C71C22×C4
FrattiniC22×C4C22×D71
FittingC2×#97×C71C2
socleC23×C71C2×D4
hypercenterC2×#97D71
hypocenterC71#1935
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#97

Complements

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

NH ≅ G/Ntype
14. #14556053C4semidirect
106. C71#1935semidirect