Finite Group Databasebeta

← #22589554

Subgroups — #22589554

Order 9088.

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

normal subgroups only

This group has 278 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#17986042C211yesmaximal, characteristic, complemented
2C2×#14556055C211yesmaximal, characteristic
3#17986000C211yesmaximal, characteristic
4C2×#14556047C211yesmaximal, characteristic, complemented
5#17985906C211yesmaximal, characteristic, complemented
6#17985758C211yesmaximal, characteristic, complemented
7#536×C71C211yesmaximal, characteristic
8C2×#11765849C2211yescharacteristic
9C2×#11765849C2211yescharacteristic
10C2×C4⋊Dic71C2211yescharacteristic
11C2×C4×Dic71C2211yescharacteristic
12#14556061—21no—
13#14556059—21no—
14#14556055—22no—
15#14556052—21no—
16#14556049—21no—
17#14556047—22no—
18C71⋊#95—22no—
19C2×#41×C71C2211yescharacteristic
20C22×Q8×C71C2211yescharacteristic
21C4⋊Q8×C71—21no—
22#124×C71—21no—
23#123×C71—22no—
24C22⋊Q8×C71—21no—
25C22⋊Q8×C71—21no—
26#117×C71C2211yescharacteristic
27C22×Dic71—21no—
28C22×Dic71—21no—
29#11765849—21no—
30#11765849—21no—
31#11765849—21no—
32#11765849D412yes—
33C2×C71⋊C8—21no—
34C2×C71⋊C8—21no—
35C4⋊Dic71—21no—
36C4⋊Dic71—21no—
37C4×Dic71—21no—
38C4×Dic71—21no—
39#41×C71—21no—
40#41×C71—21no—
41#41×C71—21no—
42#41×C71—21no—
43C2×Q8×C71—21no—
44C2×Q8×C71—21no—
45C2×Q8×C71—21no—
46C2×Q8×C71—21no—
47C2×Q8×C71—21no—
48C2×Q8×C71—21no—
49C2×Q8×C71D411yescharacteristic
50C2×D4×C71—21no—
51C2×D4×C71D411yescharacteristic
52C22×C4×C71—21no—
53C22×C4×C71D412yes—
54C22×C4×C71C2311yescharacteristic
55C4⋊C4×C71—22no—
56C4⋊C4×C71—22no—
57C4⋊C4×C71D411yescharacteristic
58C4⋊C4×C71D411yescharacteristic
59C22⋊C4×C71—22no—
60C22⋊C4×C71—22no—
61C22⋊C4×C71—21no—
62C42×C71—21no—
63C23×C71—21no—
64C23×C71C2×D411yescharacteristic
65Q8×C71—21no—
66Q8×C71—21no—
67Q8×C71—41no—
68Q8×C71—41no—
69Q8×C71—41no—
70Q8×C71—41no—
71D4×C71—21no—
72D4×C71—21no—
73D4×C71—41no—
74D4×C71—41no—
75C2×C4×C71—21no—
76C2×C4×C71—21no—
77C2×C4×C71—22no—
78C2×C4×C71—21no—
79C2×C4×C71—22no—
80C2×C4×C71—22no—
81C2×C4×C71—41no—
82C2×C4×C71—41no—
83C2×C4×C71C2×D411yescharacteristic
84C2×C4×C71C2×D411yescharacteristic
85C2×C4×C71C2×D411yescharacteristic
86C2×C4×C71#4111yescharacteristic
87C2×C4×C71#4111yescharacteristic
88C2×C4×C71#4111yescharacteristic
89C2×Dic71—22no—
90C2×Dic71—41no—
91C2×Dic71—41no—
92C2×Dic71—42no—
93C2×Dic71—41no—
94C71⋊C8—22no—
95C71⋊C8—41no—
96C22×C71—21no—
97C22×C71—21no—
98C22×C71—41no—
99C22×C71—41no—
100C22×C71—41no—
101C22×C71#12011yescharacteristic
102C22×C71#12111yescharacteristic
103C22×C71#12311yescharacteristic
104C4×C71—42no—
105C4×C71—41no—
106C4×C71—41no—
107C4×C71—41no—
108C4×C71#12111yescharacteristic
109C4×C71#12111yescharacteristic
110C4×C71#12311yescharacteristic
111C4×C71#12411yescharacteristic
112Dic71—42no—
113Dic71—81no—
114C2×C71—21no—
115C2×C71—21no—
116C2×C71—81no—
117C2×C71#39411yescharacteristic
118C2×C71#45411yescharacteristic
119C2×C71#45611yescharacteristic
120#2038—711nomaximal, Sylow
121C71#203811yescharacteristic, complemented, Sylow
122#536D7111yescharacteristic
123#428—711no—
124C2×#104—711no—
125#417—711no—
126C2×#101—711no—
127#391—711no—
128#339—711no—
129C2×#41C2×D7111yescharacteristic
130C22×Q8C2×D7111yescharacteristic
131C2×M16—711no—
132C2×M16—711no—
133C4⋊Q8—21no—
134#124—21no—
135#123—22no—
136C22⋊Q8—21no—
137C22⋊Q8—21no—
138#117C2×D7111yescharacteristic
139C2×C4⋊C4—711no—
140C2×C42—711no—
141#107—1421no—
142#106—1421no—
143#104—1422no—
144#103—1421no—
145#102—1421no—
146#101—1422no—
147#95—1422no—
148#41—21no—
149#41—21no—
150#41—21no—
151#41—21no—
152C2×Q8—21no—
153C2×Q8—21no—
154C2×Q8—21no—
155C2×Q8—21no—
156C2×Q8—21no—
157C2×Q8—21no—
158C2×Q8C22⋊D7111yescharacteristic
159C2×D4—21no—
160C2×D4C22⋊D7111yescharacteristic
161C22×C4—21no—
162C22×C4—1421no—
163C22×C4—1421no—
164C22×C4C22⋊D7112yes—
165C22×C4C22×D7111yescharacteristic
166M16—712no—
167M16—1421no—
168M16—1421no—
169M16—1421no—
170C2×C8—1421no—
171C2×C8—1421no—
172C4⋊C4—22no—
173C4⋊C4—22no—
174C4⋊C4—1421no—
175C4⋊C4—1421no—
176C4⋊C4C22⋊D7111yescharacteristic
177C4⋊C4C22⋊D7111yescharacteristic
178C22⋊C4—22no—
179C22⋊C4—22no—
180C22⋊C4—21no—
181C42—21no—
182C42—1421no—
183C42—1421no—
184C23—21no—
185C23C2×C22⋊D7111yescharacteristic
186Q8—21no—
187Q8—21no—
188Q8—41no—
189Q8—41no—
190Q8—41no—
191Q8—41no—
192D4—21no—
193D4—21no—
194D4—41no—
195D4—41no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—22no—
199C2×C4—21no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—2841no—
205C2×C4—2841no—
206C2×C4—2842no—
207C2×C4—2841no—
208C2×C4—1422no—
209C2×C4D4×D7111yescharacteristic
210C2×C4C2×C22⋊D7111yescharacteristic
211C2×C4C2×C22⋊D7111yescharacteristic
212C2×C4#1176586411yescharacteristic
213C2×C4#1176586411yescharacteristic
214C2×C4#1176586411yescharacteristic
215C8—2841no—
216C8—1422no—
217C22—21no—
218C22—21no—
219C22—41no—
220C22—41no—
221C22—41no—
222C22#1455609711yescharacteristic
223C22#1455610011yescharacteristic
224C22#1455610911yescharacteristic
225C4—42no—
226C4—41no—
227C4—41no—
228C4—41no—
229C4—2842no—
230C4—5681no—
231C4#1455609911yescharacteristic
232C4#1455610011yescharacteristic
233C4#1455610911yescharacteristic
234C4#1455611511yescharacteristic
235C2—21no—
236C2—21no—
237C2—81no—
238C2#1798591311yescharacteristic
239C2#1798617211yescharacteristic
240C2#1798618211yescharacteristic
subgroupG/H
centerC22#14556097
commutatorC22×C4×C71C23
FrattiniC22×C4C22×D71
Fitting#536×C71C2
socleC22×C71#120
hypercenter#536D71
hypocenterC71#2038
LCSG ▷ C22×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C22×C4 ◁ #536

Complements

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

NH ≅ G/Ntype
1. #17986042C2semidirect
4. C2×#14556047C2semidirect
5. #17985906C2semidirect
6. #17985758C2semidirect
121. C71#2038semidirect