Finite Group Databasebeta

← #22601065

Subgroups — #22601065

Order 9088.

382 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 123 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#17986727C211yesmaximal, characteristic, complemented
2#17986363C212yesmaximal, complemented
3#17986345C211yesmaximal, characteristic, complemented
4#17986299C212yesmaximal, complemented
5#17986279C211yesmaximal, characteristic, complemented
6#17986196C211yesmaximal, characteristic, complemented
7#17986196C212yesmaximal, complemented
8#17986130C211yesmaximal, characteristic, complemented
9#17986099C212yesmaximal, complemented
10C4×#11765853C211yesmaximal, characteristic, complemented
11#550×C71C211yesmaximal, characteristic
12C2×#11765853C2211yescharacteristic
13C2×#11765853C2212yes—
14#14556128C2211yescharacteristic
15#14556126—21no—
16#14556120C2212yes—
17#14556118—22no—
18C4×Dic142C2211yescharacteristic
19C4×Dic142C2212yes—
20#14556093—21no—
21#14556061C2212yes—
22#14556059C2211yescharacteristic
23C4⋊(C71⋊C8)C2211yescharacteristic
24C4⋊(C71⋊C8)C2212yes—
25#14556051C2211yescharacteristic
26#14556049C2211yescharacteristic
27#14556049C2212yes—
28#14556049C2212yes—
29#14556049C2212yes—
30#14556049C2212yes—
31#14556039C2212yes—
32C4×C71⋊C8C2211yescharacteristic
33C2×#41×C71—21no—
34#127×C71C2211yescharacteristic
35#127×C71C2212yes—
36#121×C71—21no—
37#121×C71—22no—
38C4×Q8×C71C2211yescharacteristic
39C4×D4×C71C2211yescharacteristic
40C4×D4×C71C2212yes—
41C2×Dic142—21no—
42C2×Dic142C2311yescharacteristic
43#11765853—22no—
44#11765853—24no—
45C2×C71⋊C8C2311yescharacteristic
46C2×C71⋊C8C2311yescharacteristic
47C2×C71⋊C8C2312yes—
48C4⋊Dic71—21no—
49C4⋊Dic71C2311yescharacteristic
50C4⋊Dic71C2312yes—
51Dic71⋊C4—22no—
52Dic71⋊C4—21no—
53Dic71⋊C4—22no—
54Dic71⋊C4—22no—
55C4×Dic71—22no—
56C4×Dic71—21no—
57#41×C71—44no—
58C2×Q8×C71D411yescharacteristic
59C2×D4×C71—22no—
60C2×D4×C71—21no—
61C2×D4×C71—22no—
62C2×D4×C71—21no—
63C2×D4×C71C2311yescharacteristic
64C2×D4×C71C2312yes—
65C22×C4×C71—22no—
66C22×C4×C71—21no—
67C4⋊C4×C71D411yescharacteristic
68C4⋊C4×C71D412yes—
69C4⋊C4×C71C2311yescharacteristic
70C22⋊C4×C71—22no—
71C22⋊C4×C71—21no—
72C42×C71C2311yescharacteristic
73C42×C71C2312yes—
74C23×C71—22no—
75C23×C71—21no—
76Q8×C71—22no—
77D4×C71—21no—
78D4×C71—22no—
79D4×C71—21no—
80D4×C71—22no—
81D4×C71—44no—
82D4×C71—42no—
83D4×C71—82no—
84D4×C71—81no—
85C2×C4×C71—21no—
86C2×C4×C71—44no—
87C2×C4×C71—42no—
88C2×C4×C71C2×D412yes—
89C2×C4×C71C2×D411yescharacteristic
90C2×C4×C71C2×D412yes—
91C2×C4×C71C2×D411yescharacteristic
92C2×C4×C71C2411yescharacteristic
93C2×Dic71—21no—
94C2×Dic71—21no—
95C2×Dic71—22no—
96Dic142—21no—
97Dic142—42no—
98Dic142#4112yescomplemented
99C71⋊C8—21no—
100C71⋊C8—22no—
101C71⋊C8—21no—
102C22×C71—42no—
103C22×C71—41no—
104C22×C71—42no—
105C22×C71—41no—
106C22×C71—42no—
107C22×C71—41no—
108C22×C71C22×D411yescharacteristic
109C4×C71—22no—
110C4×C71—22no—
111C4×C71—21no—
112C4×C71—41no—
113C4×C71AGL(1,ℤ/8)12yes—
114C4×C71C2×#4111yescharacteristic
115C4×C712−1+411yescharacteristic
116Dic71—22no—
117Dic71—42no—
118Dic71—41no—
119C2×C71—82no—
120C2×C71—81no—
121C2×C71#54811yescharacteristic
122C2×C71C2×AGL(1,ℤ/8)11yescharacteristic
123C2×C71#57711yescharacteristic
124#3368—711nomaximal, Sylow
125C71#336811yescharacteristic, complemented, Sylow
126#557—711no—
127#550D7111yescharacteristic
128#490—712no—
129#486—711no—
130#478—712no—
131#474—711no—
132#460—712no—
133#460—711no—
134#446—711no—
135#440—712no—
136C4×SD16—711no—
137C2×#41—21no—
138C2×SD16—711no—
139C2×SD16—712no—
140C4⋊Q8—711no—
141C4⋊Q8—1421no—
142#127C2×D7111yescharacteristic
143#127C2×D7112yes—
144#125—712no—
145#125—1422no—
146#121—21no—
147#121—22no—
148C4×Q8—711no—
149C4×Q8—712no—
150C4×Q8—1421no—
151C4×Q8C2×D7111yescharacteristic
152C4×D4C2×D7111yescharacteristic
153C4×D4C2×D7112yes—
154#107—712no—
155#106—711no—
156C4⋊C8—711no—
157C4⋊C8—712no—
158#103—711no—
159#102—711no—
160#102—712no—
161#102—712no—
162#102—712no—
163#102—712no—
164#97—712no—
165C4×C8—711no—
166#41—44no—
167C2×Q8—711no—
168C2×Q8—1421no—
169C2×Q8C22⋊D7111yescharacteristic
170C2×D4—22no—
171C2×D4—21no—
172C2×D4—22no—
173C2×D4—21no—
174C2×D4C22×D7111yescharacteristic
175C2×D4C22×D7112yes—
176C22×C4—22no—
177C22×C4—21no—
178SD16—1422no—
179SD16—1424no—
180C2×C8—711no—
181C2×C8—711no—
182C2×C8—712no—
183C4⋊C4—711no—
184C4⋊C4—712no—
185C4⋊C4—1421no—
186C4⋊C4—1422no—
187C4⋊C4—1422no—
188C4⋊C4—1422no—
189C4⋊C4—1421no—
190C4⋊C4C22⋊D7111yescharacteristic
191C4⋊C4C22⋊D7112yes—
192C4⋊C4C22×D7111yescharacteristic
193C22⋊C4—22no—
194C22⋊C4—21no—
195C42—1422no—
196C42—1421no—
197C42C22×D7111yescharacteristic
198C42C22×D7112yes—
199C23—22no—
200C23—21no—
201Q8—22no—
202Q8—2842no—
203Q8—712no—
204Q8—1421no—
205D4—21no—
206D4—22no—
207D4—21no—
208D4—22no—
209D4—44no—
210D4—42no—
211D4—82no—
212D4—81no—
213C2×C4—21no—
214C2×C4—44no—
215C2×C4—42no—
216C2×C4—1421no—
217C2×C4—1422no—
218C2×C4—1421no—
219C2×C4C2×C22⋊D7112yes—
220C2×C4C2×C22⋊D7111yescharacteristic
221C2×C4C2×C22⋊D7112yes—
222C2×C4C2×C22⋊D7111yescharacteristic
223C2×C4C23×D7111yescharacteristic
224C8—1421no—
225C8—1422no—
226C8—1421no—
227C22—42no—
228C22—41no—
229C22—42no—
230C22—41no—
231C22—42no—
232C22—41no—
233C22C22×C22⋊D7111yescharacteristic
234C4—22no—
235C4—22no—
236C4—21no—
237C4—41no—
238C4—2842no—
239C4—2841no—
240C4—1422no—
241C4#1455615412yes—
242C4#41×D7111yescharacteristic
243C4#1455617511yescharacteristic
244C2—82no—
245C2—81no—
246C2#1798665611yescharacteristic
247C2C2×#1455615411yescharacteristic
248C2#1798681011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D71
commutatorC2×C4×C71C24
FrattiniC2×C4C23×D71
Fitting#550×C71C2
socleC22×C71C22×D4
hypercenter#550D71
hypocenterC71#3368
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #550

Complements

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

NH ≅ G/Ntype
1. #17986727C2semidirect
2. #17986363C2semidirect
3. #17986345C2semidirect
4. #17986299C2semidirect
5. #17986279C2semidirect
6. #17986196C2semidirect
7. #17986196C2semidirect
8. #17986130C2semidirect
9. #17986099C2semidirect
10. C4×#11765853C2semidirect
98. Dic142#41semidirect
125. C71#3368semidirect