Finite Group Databasebeta

← #22610455

Subgroups — #22610455

Order 9344.

344 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 79 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#17989353C211yesmaximal, characteristic, complemented
2#17989154C211yesmaximal, characteristic
3#17988592C211yesmaximal, characteristic, complemented
4#17988560C211yesmaximal, characteristic, complemented
5#17988344C211yesmaximal, characteristic, complemented
6#17988343C211yesmaximal, characteristic, complemented
7#418×C73C211yesmaximal, characteristic, complemented
8C2×#11924028C2211yescharacteristic
9#14556599—22no—
10#14556597—22no—
11C2×#11924012C2211yescharacteristic
12M16×D73—22no—
13#14556587C412yescomplemented
14#14556578C412yescomplemented
15#14556562—22no—
16#14556560—22no—
17#14556550C2211yescharacteristic
18#14556550C2211yescharacteristic
19#14556512—22no—
20#14556505—22no—
21C22×D4×C73C2211yescharacteristic
22C2×M16×C73C2211yescharacteristic
23#117×C73C2211yescharacteristic
24#102×C73—22no—
25#11924028—21no—
26#11924028—21no—
27#11924028—21no—
28#11924028—21no—
29C2×Dic146C2×C411yescharacteristic
30C2×D292C2×C411yescharacteristic
31C2×C22⋊D73—24no—
32C2×C22⋊D73D412yes—
33C2×C4×D73D412yes—
34#11924012—21no—
35#11924012—21no—
36#11924011—24no—
37C2×#10596831D412yescomplemented
38C8×D73—24no—
39C4⋊Dic73—21no—
40C4⋊Dic73—21no—
41C22⋊Dic73—21no—
42C22⋊Dic73—24no—
43C22⋊Dic73—21no—
44C4×Dic73—21no—
45C4×Dic73C2×C412yes—
46C24×C73—21no—
47C2×D4×C73—21no—
48C2×D4×C73—21no—
49C2×D4×C73—21no—
50C2×D4×C73—21no—
51C2×D4×C73—21no—
52C2×D4×C73C2×C412yes—
53C22×C4×C73C2311yescharacteristic
54M16×C73—21no—
55M16×C73—21no—
56C2×C8×C73D412yescomplemented
57C4⋊C4×C73—21no—
58C22⋊C4×C73—21no—
59C42×C73—21no—
60C23×C73—22no—
61C23×C73—41no—
62C23×C73—41no—
63C23×C73—82no—
64C23×C73C2×D411yescharacteristic
65C22×D73C22⋊C412yes—
66D4×C73—22no—
67D4×C73—22no—
68D4×C73—41no—
69D4×C73—41no—
70C2×C4×C73—41no—
71C2×C4×C73C22×C411yescharacteristic
72C2×C4×C73C2×D411yescharacteristic
73C2×C4×C73C2×D411yescharacteristic
74C2×C4×C73C2×D411yescharacteristic
75C2×C4×C73#4111yescharacteristic
76C2×C4×C73#4111yescharacteristic
77C22⋊D73—22no—
78C22⋊D73—22no—
79C22⋊D73—84no—
80C2×Dic73—22no—
81C2×Dic73—41no—
82C2×Dic73C22⋊C412yes—
83D292—21no—
84D292—21no—
85C4×D73—22no—
86C4×D73—22no—
87Dic146—21no—
88Dic146—21no—
89C8×C73—22no—
90#10596831—22no—
91C22×C73—41no—
92C22×C73—44no—
93C22×C73—42no—
94C22×C73—82no—
95C22×C73—82no—
96C22×C73C2×C22⋊C411yescharacteristic
97C22×C73#12111yescharacteristic
98C22×C73#12111yescharacteristic
99C2×D73—22no—
100C2×D73—42no—
101C4×C73—81no—
102C4×C73C4×D411yescharacteristic
103C4×C73C4×D411yescharacteristic
104C4×C73#12011yescharacteristic
105C4×C73#12311yescharacteristic
106Dic73—22no—
107Dic73—42no—
108Dic73—81no—
109C2×C73—21no—
110C2×C73—21no—
111C2×C73—21no—
112C2×C73—82no—
113C2×C73#38611yescharacteristic
114D73—42no—
115#1910—731nomaximal, Sylow
116C73#191011yescharacteristic, complemented, Sylow
117#568—731no—
118#535—731no—
119#418—731no—
120#418D7311yescharacteristic, complemented
121#410—731no—
122H(3,ℤ/4)—731no—
123H(3,ℤ/4)—731no—
124C2×#41—731no—
125C22×D4C2×D7311yescharacteristic
126#131—1462no—
127#131—1462no—
128C2×M16—731no—
129C2×M16—1462no—
130C2×M16C2×D7311yescharacteristic
131#127—732no—
132#124—732no—
133#121—1462no—
134#120—1462no—
135#117—731no—
136#117—731no—
137#117C2×D7311yescharacteristic
138#102—22no—
139#102—1462no—
140#99—1462no—
141C24—21no—
142#41—1461no—
143#41—1461no—
144#41—1461no—
145#41—1461no—
146C2×Q8—731no—
147C2×D4—21no—
148C2×D4—21no—
149C2×D4—21no—
150C2×D4—21no—
151C2×D4—21no—
152C2×D4—732no—
153C2×D4—731no—
154C2×D4—1464no—
155C2×D4C4×D7312yes—
156C22×C4—732no—
157C22×C4C22×D7311yescharacteristic
158M16—21no—
159M16—21no—
160M16—1464no—
161M16—1461no—
162M16—1461no—
163C2×C8—732no—
164C2×C8—1464no—
165C2×C8C22⋊D7312yescomplemented
166C4⋊C4—21no—
167C4⋊C4—1461no—
168C4⋊C4—1461no—
169C22⋊C4—21no—
170C22⋊C4—1461no—
171C22⋊C4—1464no—
172C22⋊C4—1461no—
173C42—21no—
174C42—732no—
175C42—1461no—
176C23—22no—
177C23—41no—
178C23—41no—
179C23—82no—
180C23—732no—
181C23D4×D7311yescharacteristic
182Q8—1461no—
183Q8—1461no—
184D4—22no—
185D4—22no—
186D4—41no—
187D4—41no—
188D4—5844no—
189D4—1462no—
190D4—1462no—
191D4—1461no—
192D4—1461no—
193C2×C4—41no—
194C2×C4—2921no—
195C2×C4—732no—
196C2×C4—1462no—
197C2×C4—1462no—
198C2×C4—1462no—
199C2×C4C2×C4×D7311yescharacteristic
200C2×C4D4×D7311yescharacteristic
201C2×C4D4×D7311yescharacteristic
202C2×C4C2×C22⋊D7311yescharacteristic
203C2×C4#1192402711yescharacteristic
204C2×C4#1192402811yescharacteristic
205C8—22no—
206C8—1462no—
207C22—41no—
208C22—44no—
209C22—42no—
210C22—82no—
211C22—82no—
212C22—2922no—
213C22—1462no—
214C22C22⋊C4×D7311yescharacteristic
215C22#1455656211yescharacteristic
216C22#1455656411yescharacteristic
217C4—81no—
218C4—2922no—
219C4—5841no—
220C4—1462no—
221C4#1455655111yescharacteristic
222C4C4×C22⋊D7311yescharacteristic
223C4#1455655911yescharacteristic
224C4#1455657311yescharacteristic
225C2—21no—
226C2—21no—
227C2—21no—
228C2—82no—
229C2—2922no—
230C2#1798846311yescharacteristic
subgroupG/H
centerC2#17988463
commutatorC2×C4×C73C22×C4
FrattiniC22×C4C22×D73
Fitting#418×C73C2
socleC2×C73#386
hypercenter#418D73
hypocenterC73#1910
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. #17989353C2semidirect
3. #17988592C2semidirect
4. #17988560C2semidirect
5. #17988344C2semidirect
6. #17988343C2semidirect
7. #418×C73C2semidirect
13. #14556587C4semidirect
14. #14556578C4semidirect
37. C2×#10596831D4semidirect
56. C2×C8×C73D4semidirect
116. C73#1910semidirect
120. #418D73semidirect
165. C2×C8C22⋊D73semidirect