Finite Group Databasebeta

← #22610418

Subgroups — #22610418

Order 9344.

346 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 89 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×#14556617C211yesmaximal, characteristic
2#17988605C211yesmaximal, characteristic, complemented
3#17988592C211yesmaximal, characteristic, complemented
4#17988560C211yesmaximal, characteristic, complemented
5#17988357C211yesmaximal, characteristic, complemented
6#17988343C211yesmaximal, characteristic, complemented
7#518×C73C211yesmaximal, characteristic, complemented
8C2×#11924028C2211yescharacteristic
9#14556617—22no—
10#14556617—22no—
11C2×#11924016C412yescomplemented
12C2×#11924013C412yescomplemented
13C2×#11924012C2211yescharacteristic
14C2×#11924012C2211yescharacteristic
15#14556550C2211yescharacteristic
16#14556519—22no—
17#14556512—22no—
18#14556505—22no—
19C22×D4×C73C2211yescharacteristic
20C4×D4×C73—22no—
21C4×D4×C73—22no—
22#117×C73C2211yescharacteristic
23#117×C73C2211yescharacteristic
24C2×C22⋊C4×C73—22no—
25#11924028—21no—
26#11924028—21no—
27#11924028—21no—
28#11924028—21no—
29C2×Dic146C2×C411yescharacteristic, complemented
30C2×D292C2×C411yescharacteristic, complemented
31C2×C22⋊D73—21no—
32C2×C4×D73—21no—
33#11924016—24no—
34#11924013—24no—
35#11924012—21no—
36#11924012—21no—
37#11924012—21no—
38#11924012—21no—
39C2×#10596831—21no—
40C2×#10596831C2×C412yescomplemented
41C4⋊Dic73—21no—
42C22⋊Dic73—21no—
43C4×Dic73—21no—
44C24×C73—21no—
45C2×D4×C73—21no—
46C2×D4×C73—21no—
47C2×D4×C73—21no—
48C2×D4×C73C2×C412yes—
49C2×D4×C73D412yes—
50C2×D4×C73D412yes—
51C22×C4×C73—24no—
52C22×C4×C73C2311yescharacteristic
53C4⋊C4×C73—21no—
54C4⋊C4×C73—21no—
55C22⋊C4×C73—24no—
56C22⋊C4×C73—21no—
57C22⋊C4×C73D412yes—
58C42×C73—21no—
59C42×C73D412yes—
60C23×C73—22no—
61C23×C73—22no—
62C23×C73—22no—
63C23×C73—82no—
64C23×C73C2×D411yescharacteristic
65C22×D73—21no—
66D4×C73—22no—
67D4×C73—22no—
68D4×C73—22no—
69D4×C73C22⋊C414yes—
70C2×C4×C73—22no—
71C2×C4×C73—22no—
72C2×C4×C73—84no—
73C2×C4×C73C22×C411yescharacteristic
74C2×C4×C73C2×D411yescharacteristic
75C2×C4×C73C2×D411yescharacteristic
76C2×C4×C73C2×D411yescharacteristic
77C2×C4×C73#4111yescharacteristic
78C2×C4×C73#4111yescharacteristic
79C22⋊D73—41no—
80C22⋊D73—41no—
81C2×Dic73—21no—
82C2×Dic73—41no—
83D292—21no—
84D292—21no—
85C4×D73—41no—
86C4×D73—41no—
87Dic146—21no—
88Dic146—21no—
89#10596831—22no—
90#10596831—41no—
91C22×C73—24no—
92C22×C73—41no—
93C22×C73—44no—
94C22×C73—82no—
95C22×C73—82no—
96C22×C73C4×D411yescharacteristic
97C22×C73#12011yescharacteristic
98C22×C73#12111yescharacteristic
99C2×D73—41no—
100C2×D73—81no—
101C4×C73—42no—
102C4×C73—42no—
103C4×C73C2×C22⋊C411yescharacteristic
104C4×C73C4×D411yescharacteristic
105C4×C73#12111yescharacteristic
106C4×C73#12311yescharacteristic
107Dic73—41no—
108Dic73—81no—
109C2×C73—21no—
110C2×C73—21no—
111C2×C73—21no—
112C2×C73—44no—
113C2×C73#38611yescharacteristic
114D73—81no—
115#1904—731nomaximal, Sylow
116C73#190411yescharacteristic, complemented, Sylow
117C2×AGL(1,ℤ/8)—731no—
118#518D7311yescharacteristic, complemented
119#421—731no—
120#418—731no—
121#410—731no—
122#344—731no—
123H(3,ℤ/4)—731no—
124C2×#41—731no—
125C22×D4C2×D7311yescharacteristic
126AGL(1,ℤ/8)—1462no—
127AGL(1,ℤ/8)—1462no—
128C2×SD16—732no—
129C2×D8—732no—
130C2×M16—731no—
131C2×M16—731no—
132C4×D4—22no—
133C4×D4—22no—
134#117—731no—
135#117C2×D7311yescharacteristic
136#117C2×D7311yescharacteristic
137C2×C22⋊C4—22no—
138#104—1462no—
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—731no—
151C2×D4—1461no—
152C2×D4C4×D7312yes—
153C2×D4D29212yes—
154C2×D4C22⋊D7312yes—
155C22×C4—24no—
156C22×C4—1461no—
157C22×C4C22×D7311yescharacteristic
158SD16—1464no—
159D8—1464no—
160M16—1461no—
161M16—1461no—
162M16—1461no—
163M16—1461no—
164C2×C8—732no—
165C2×C8—1461no—
166C4⋊C4—21no—
167C4⋊C4—21no—
168C4⋊C4—1461no—
169C22⋊C4—24no—
170C22⋊C4—21no—
171C22⋊C4—1461no—
172C22⋊C4C22⋊D7312yes—
173C42—21no—
174C42—1461no—
175C42C22⋊D7312yes—
176C23—22no—
177C23—22no—
178C23—22no—
179C23—82no—
180C23—1461no—
181C23C2×C22⋊D7311yescharacteristic
182Q8—1461no—
183Q8—1461no—
184D4—22no—
185D4—22no—
186D4—22no—
187D4—2921no—
188D4—2921no—
189D4—1461no—
190D4—1461no—
191D4#1192400514yes—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—84no—
195C2×C4—2921no—
196C2×C4—2921no—
197C2×C4—2921no—
198C2×C4—1461no—
199C2×C4C2×C4×D7311yescharacteristic
200C2×C4C2×C22⋊D7311yescharacteristic
201C2×C4C2×C22⋊D7311yescharacteristic
202C2×C4C2×D29211yescharacteristic
203C2×C4#1192402811yescharacteristic
204C2×C4#1192402811yescharacteristic
205C8—2921no—
206C8—1462no—
207C22—24no—
208C22—41no—
209C22—44no—
210C22—82no—
211C22—82no—
212C22—2921no—
213C22—5841no—
214C22C4×C22⋊D7311yescharacteristic
215C22#1455656011yescharacteristic
216C22#1455656511yescharacteristic
217C4—42no—
218C4—42no—
219C4—2921no—
220C4—5841no—
221C4C2×#1192400511yescharacteristic
222C4C4×C22⋊D7311yescharacteristic
223C4#1455656511yescharacteristic
224C4#1455657411yescharacteristic
225C2—21no—
226C2—21no—
227C2—21no—
228C2—44no—
229C2—5841no—
230C2#1798846611yescharacteristic
subgroupG/H
centerC2#17988466
commutatorC2×C4×C73C22×C4
FrattiniC22×C4C22×D73
Fitting#518×C73C2
socleC2×C73#386
hypercenter#518D73
hypocenterC73#1904
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C22×C4 ◁ #518

Complements

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

NH ≅ G/Ntype
2. #17988605C2semidirect
3. #17988592C2semidirect
4. #17988560C2semidirect
5. #17988357C2semidirect
6. #17988343C2semidirect
7. #518×C73C2semidirect
11. C2×#11924016C4semidirect
12. C2×#11924013C4semidirect
29. C2×Dic146C2×C4semidirect
30. C2×D292C2×C4semidirect
40. C2×#10596831C2×C4semidirect
116. C73#1904semidirect
118. #518D73semidirect