Finite Group Databasebeta

← #22609963

Subgroups — #22609963

Order 9344.

316 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 101 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
1C22×#11924011C211yesmaximal, characteristic
2C2×#14556524C211yesmaximal, characteristic, complemented
3C2×#14556522C211yesmaximal, characteristic, complemented
4#17988444C211yesmaximal, characteristic
5#17988444C211yesmaximal, characteristic
6#17988350C211yesmaximal, characteristic, complemented
7#340×C73C211yesmaximal, characteristic, complemented
8C22×C4×D73C2211yescharacteristic
9C2×#11924011—22no—
10C2×#11924011—22no—
11C2×#11924011C414yescomplemented
12C22×#10596831C2211yescharacteristic
13C2×C4⋊Dic73C2211yescharacteristic
14C2×C4⋊Dic73C2211yescharacteristic
15C2×#11924005—21no—
16C2×#11924005—21no—
17#14556524—22no—
18#14556522—22no—
19#14556498—21no—
20#14556498—21no—
21C22×C8×C73C2211yescharacteristic
22C2×C4⋊C4×C73C2211yescharacteristic
23C2×C4⋊C4×C73C2211yescharacteristic
24C23×D73D411yescharacteristic
25C22×Dic73—21no—
26C22×Dic73—21no—
27C22×Dic73D411yescharacteristic
28C2×C4×D73—21no—
29C2×C4×D73—21no—
30C2×C4×D73—21no—
31C2×C4×D73—21no—
32C2×C4×D73C2×C412yes—
33C2×C4×D73Q812yes—
34#11924011—28no—
35C2×#10596831C2×C412yes—
36C2×#10596831D412yes—
37C2×#10596831D412yes—
38C4⋊Dic73—21no—
39C4⋊Dic73—21no—
40C4⋊Dic73—21no—
41C4⋊Dic73—21no—
42#11924005—42no—
43#11924005—42no—
44C22×C4×C73—21no—
45C22×C4×C73—21no—
46C22×C4×C73C2311yescharacteristic
47C2×C8×C73—21no—
48C2×C8×C73—21no—
49C2×C8×C73C2×C412yes—
50C4⋊C4×C73—21no—
51C4⋊C4×C73—21no—
52C4⋊C4×C73—21no—
53C4⋊C4×C73—21no—
54C23×C73C2×D411yescharacteristic
55C22×D73—21no—
56C22×D73—21no—
57C22×D73—21no—
58C22×D73—21no—
59C22×D73—21no—
60C22×D73—21no—
61C22×D73C4⋊C412yes—
62C2×C4×C73—41no—
63C2×C4×C73—41no—
64C2×C4×C73—41no—
65C2×C4×C73—41no—
66C2×C4×C73—41no—
67C2×C4×C73—41no—
68C2×C4×C73C22×C411yescharacteristic
69C2×C4×C73C2×D411yescharacteristic
70C2×C4×C73C2×D411yescharacteristic
71C2×C4×C73C2×Q811yescharacteristic
72C2×C4×C73#4111yescharacteristic
73C2×C4×C73#4111yescharacteristic
74C2×Dic73—21no—
75C2×Dic73—21no—
76C2×Dic73—41no—
77C2×Dic73—41no—
78C2×Dic73—41no—
79C2×Dic73—41no—
80C2×Dic73—41no—
81C2×Dic73—41no—
82C2×Dic73C4⋊C412yes—
83C4×D73—22no—
84C4×D73—22no—
85C4×D73—22no—
86C4×D73—22no—
87C8×C73—22no—
88#10596831C22⋊C414yescomplemented
89C22×C73C2×C4⋊C411yescharacteristic
90C22×C73#12111yescharacteristic
91C22×C73#12111yescharacteristic
92C22×C73AGL(1,ℤ/8)11yescharacteristic
93C22×C73AGL(1,ℤ/8)11yescharacteristic
94C22×C73#13711yescharacteristic
95C22×C73#13711yescharacteristic
96C2×D73—22no—
97C2×D73—22no—
98C2×D73—22no—
99C2×D73—41no—
100C2×D73—41no—
101C2×D73—41no—
102C2×D73—41no—
103C4×C73—81no—
104C4×C73—81no—
105C4×C73C2×C22⋊C411yescharacteristic
106C4×C73#11711yescharacteristic
107C4×C73C22⋊Q811yescharacteristic
108C4×C73C22⋊Q811yescharacteristic
109Dic73—22no—
110Dic73—81no—
111Dic73—81no—
112C2×C73#38011yescharacteristic
113C2×C73#42811yescharacteristic
114C2×C73#42811yescharacteristic
115C2×C73#46811yescharacteristic
116C2×C73#46811yescharacteristic
117C2×C73#46911yescharacteristic
118C2×C73#47011yescharacteristic
119D73—42no—
120#1809—731nomaximal, Sylow
121C73#180911yescharacteristic, complemented, Sylow
122C22×M16—731no—
123C2×#107—731no—
124C2×#106—731no—
125#380—731no—
126#380—731no—
127#340—731no—
128#340D7311yescharacteristic, complemented
129C23×C4—731no—
130C2×M16—734no—
131C2×M16—1462no—
132C2×M16—1462no—
133C22×C8—731no—
134C22×C8C2×D7311yescharacteristic
135C2×C4⋊C4—731no—
136C2×C4⋊C4—731no—
137C2×C4⋊C4C2×D7311yescharacteristic
138C2×C4⋊C4C2×D7311yescharacteristic
139C2×C22⋊C4—1461no—
140C2×C22⋊C4—1461no—
141#107—1462no—
142#106—1462no—
143#95—1461no—
144#95—1461no—
145C24—731no—
146C22×C4—21no—
147C22×C4—21no—
148C22×C4—731no—
149C22×C4—732no—
150C22×C4—732no—
151C22×C4—1461no—
152C22×C4—1461no—
153C22×C4—1461no—
154C22×C4—1461no—
155C22×C4—1461no—
156C22×C4—1461no—
157C22×C4C22×D7311yescharacteristic
158M16—1468no—
159C2×C8—21no—
160C2×C8—21no—
161C2×C8—732no—
162C2×C8—732no—
163C2×C8—732no—
164C2×C8C4×D7312yes—
165C4⋊C4—21no—
166C4⋊C4—21no—
167C4⋊C4—21no—
168C4⋊C4—21no—
169C4⋊C4—1461no—
170C4⋊C4—1461no—
171C4⋊C4—1461no—
172C4⋊C4—1461no—
173C22⋊C4—2922no—
174C22⋊C4—2922no—
175C23—732no—
176C23—1461no—
177C23—1461no—
178C23—1461no—
179C23—1461no—
180C23—1461no—
181C23—1461no—
182C23D4×D7311yescharacteristic
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—2921no—
190C2×C4—2921no—
191C2×C4—2921no—
192C2×C4—2921no—
193C2×C4—2921no—
194C2×C4—2921no—
195C2×C4—732no—
196C2×C4—1461no—
197C2×C4—1461no—
198C2×C4—1462no—
199C2×C4—1462no—
200C2×C4—1462no—
201C2×C4—1462no—
202C2×C4C2×C4×D7311yescharacteristic
203C2×C4D4×D7311yescharacteristic
204C2×C4D4×D7311yescharacteristic
205C2×C4Q8×D7311yescharacteristic
206C2×C4#1192402811yescharacteristic
207C2×C4#1192402811yescharacteristic
208C8—22no—
209C8—734no—
210C22—2921no—
211C22—2921no—
212C22—2921no—
213C22—2921no—
214C22—1462no—
215C22—1462no—
216C22—1462no—
217C22C4⋊C4×D7311yescharacteristic
218C22#1455656411yescharacteristic
219C22#1455656411yescharacteristic
220C22#1455661511yescharacteristic
221C22#1455661811yescharacteristic
222C22#1455662011yescharacteristic
223C22#1455662311yescharacteristic
224C4—81no—
225C4—81no—
226C4—5841no—
227C4—5841no—
228C4—1462no—
229C4C22⋊C4×D7311yescharacteristic
230C4#1455654811yescharacteristic
231C4#1455656911yescharacteristic
232C4#1455656911yescharacteristic
233C2—2922no—
234C2#1798844611yescharacteristic
235C2#1798862611yescharacteristic
236C2#1798862811yescharacteristic
237C2#1798883211yescharacteristic
238C2#1798883611yescharacteristic
239C2#1798883911yescharacteristic
240C2#1798884411yescharacteristic
subgroupG/H
centerC23D4×D73
commutatorC2×C4×C73C22×C4
FrattiniC22×C4C22×D73
Fitting#340×C73C2
socleC23×C73C2×D4
hypercenter#340D73
hypocenterC73#1809
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
2. C2×#14556524C2semidirect
3. C2×#14556522C2semidirect
6. #17988350C2semidirect
7. #340×C73C2semidirect
11. C2×#11924011C4semidirect
88. #10596831C22⋊C4semidirect
121. C73#1809semidirect
128. #340D73semidirect