Finite Group Databasebeta

← #22589638

Subgroups — #22589638

Order 9088.

262 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 69 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×#14556158C211yesmaximal, characteristic
2C2×#14556064C211yesmaximal, characteristic, complemented
3#17986000C211yesmaximal, characteristic
4C2×#14556053C211yesmaximal, characteristic, complemented
5C2×#14556046C211yesmaximal, characteristic, complemented
6#17985767C211yesmaximal, characteristic, complemented
7#408×C71C211yesmaximal, characteristic
8C22×Dic142C2211yescharacteristic
9#14556158—22no—
10#14556158—22no—
11C2×#11765855—21no—
12C2×#11765853—21no—
13C2×#11765849C2211yescharacteristic
14C2×#11765849C2211yescharacteristic
15C2×C4⋊Dic71C2211yescharacteristic
16#14556064—22no—
17#14556053—22no—
18#14556052—21no—
19#14556049—21no—
20#14556046—22no—
21C2×#41×C71C2211yescharacteristic
22C2×M16×C71C2211yescharacteristic
23C22×C8×C71C2211yescharacteristic
24C22⋊C8×C71—22no—
25C2×Dic142—21no—
26C2×Dic142—21no—
27C2×Dic142—21no—
28C2×Dic142—21no—
29C2×Dic142—21no—
30C2×Dic142D412yes—
31C22×Dic71—21no—
32C22×Dic71—21no—
33#11765855—24no—
34#11765853—24no—
35#11765849—21no—
36#11765849—21no—
37#11765849—21no—
38#11765849D412yes—
39C2×C71⋊C8—21no—
40C2×C71⋊C8—21no—
41C4⋊Dic71—21no—
42C4⋊Dic71—21no—
43#41×C71—21no—
44#41×C71—21no—
45#41×C71—21no—
46#41×C71—21no—
47C2×Q8×C71D411yescharacteristic
48C2×D4×C71—21no—
49C2×D4×C71D411yescharacteristic
50C22×C4×C71—21no—
51C22×C4×C71C2311yescharacteristic
52M16×C71—21no—
53M16×C71—21no—
54C2×C8×C71—21no—
55C2×C8×C71—21no—
56C2×C8×C71—21no—
57C2×C8×C71D412yes—
58C23×C71—21no—
59C23×C71#4111yescharacteristic
60Q8×C71—21no—
61Q8×C71—21no—
62D4×C71—21no—
63D4×C71—21no—
64D4×C71—41no—
65D4×C71—41no—
66C2×C4×C71—21no—
67C2×C4×C71—41no—
68C2×C4×C71—41no—
69C2×C4×C71C2×D411yescharacteristic
70C2×C4×C71C2×D411yescharacteristic
71C2×C4×C71C2×D411yescharacteristic
72C2×C4×C71C2×D411yescharacteristic
73C2×C4×C71#4111yescharacteristic
74C2×C4×C71#4111yescharacteristic
75C2×Dic71—22no—
76C2×Dic71—41no—
77C2×Dic71—41no—
78C2×Dic71—41no—
79C2×Dic71—81no—
80Dic142—22no—
81Dic142—22no—
82Dic142—41no—
83Dic142—41no—
84C8×C71—22no—
85C8×C71—41no—
86C71⋊C8—22no—
87C71⋊C8—41no—
88C22×C71—21no—
89C22×C71—21no—
90C22×C71—41no—
91C22×C71—41no—
92C22×C71—41no—
93C22×C71#12111yescharacteristic
94C22×C71#12311yescharacteristic
95C22×C71#12411yescharacteristic
96C4×C71—41no—
97C4×C71#12011yescharacteristic
98C4×C71#12111yescharacteristic
99C4×C71#12111yescharacteristic
100C4×C71#12311yescharacteristic
101Dic71—42no—
102Dic71—81no—
103C2×C71—21no—
104C2×C71—21no—
105C2×C71—81no—
106C2×C71#39411yescharacteristic
107C2×C71#47111yescharacteristic
108C2×C71#47311yescharacteristic
109#2052—711nomaximal, Sylow
110C71#205211yescharacteristic, complemented, Sylow
111C2×#137—711no—
112C2×#108—711no—
113#417—711no—
114C2×#103—711no—
115C2×#101—711no—
116#408D7111yescharacteristic
117#343—711no—
118C2×#41C2×D7111yescharacteristic
119C22×Q8—711no—
120#137—1422no—
121#137—1422no—
122C2×Q16—1421no—
123C2×SD16—1421no—
124C2×M16—711no—
125C2×M16—711no—
126C2×M16C2×D7111yescharacteristic
127C22×C8C2×D7111yescharacteristic
128C2×C4⋊C4—711no—
129#108—1422no—
130#103—1421no—
131#103—1422no—
132#102—1421no—
133#101—1422no—
134C22⋊C8—22no—
135#41—21no—
136#41—21no—
137#41—21no—
138#41—21no—
139C2×Q8—712no—
140C2×Q8—1421no—
141C2×Q8—1421no—
142C2×Q8—1421no—
143C2×Q8—1421no—
144C2×Q8—1421no—
145C2×Q8D28411yescharacteristic
146C2×D4—21no—
147C2×D4D28411yescharacteristic
148C22×C4—21no—
149C22×C4—1421no—
150C22×C4—1421no—
151C22×C4C22×D7111yescharacteristic
152Q16—1424no—
153SD16—1424no—
154M16—21no—
155M16—21no—
156M16—712no—
157M16—1421no—
158M16—1421no—
159M16—1421no—
160C2×C8—21no—
161C2×C8—21no—
162C2×C8—21no—
163C2×C8—1421no—
164C2×C8—1421no—
165C2×C8C22⋊D7112yes—
166C4⋊C4—1421no—
167C4⋊C4—1421no—
168C23—21no—
169C23#1176586511yescharacteristic
170Q8—21no—
171Q8—21no—
172Q8—2841no—
173Q8—2841no—
174Q8—1422no—
175Q8—1422no—
176D4—21no—
177D4—21no—
178D4—41no—
179D4—41no—
180C2×C4—21no—
181C2×C4—41no—
182C2×C4—41no—
183C2×C4—2841no—
184C2×C4—2841no—
185C2×C4—2841no—
186C2×C4—5681no—
187C2×C4—1422no—
188C2×C4D4×D7111yescharacteristic
189C2×C4D4×D7111yescharacteristic
190C2×C4C2×C22⋊D7111yescharacteristic
191C2×C4C2×D28411yescharacteristic
192C2×C4#1176586411yescharacteristic
193C2×C4#1176586411yescharacteristic
194C8—22no—
195C8—41no—
196C8—2841no—
197C8—1422no—
198C22—21no—
199C22—21no—
200C22—41no—
201C22—41no—
202C22—41no—
203C22#1455610211yescharacteristic
204C22#1455611011yescharacteristic
205C22#1455611411yescharacteristic
206C4—41no—
207C4—2842no—
208C4—5681no—
209C4#1455609811yescharacteristic
210C4#1455609911yescharacteristic
211C4#1455610011yescharacteristic
212C4#1455611211yescharacteristic
213C2—21no—
214C2—21no—
215C2—81no—
216C2#1798591511yescharacteristic
217C2#1798626211yescharacteristic
218C2#1798627411yescharacteristic
subgroupG/H
centerC22#14556102
commutatorC22×C4×C71C23
FrattiniC22×C4C22×D71
Fitting#408×C71C2
socleC22×C71#121
hypercenter#408D71
hypocenterC71#2052
LCSG ▷ C22×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C22×C4 ◁ #408

Complements

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

NH ≅ G/Ntype
2. C2×#14556064C2semidirect
4. C2×#14556053C2semidirect
5. C2×#14556046C2semidirect
6. #17985767C2semidirect
110. C71#2052semidirect