Finite Group Databasebeta

← #22622571

Subgroups — #22622571

Order 9344.

370 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 125 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#17989315C211yesmaximal, characteristic, complemented
2D4×Dic146C211yesmaximal, characteristic
3#17988938C211yesmaximal, characteristic, complemented
4#17988936C212yesmaximal, complemented
5#17988872C211yesmaximal, characteristic, complemented
6#17988871C212yesmaximal, complemented
7#17988792C211yesmaximal, characteristic
8#17988790C212yesmaximal
9C8×Dic146C211yesmaximal, characteristic, complemented
10#17988678C212yesmaximal
11C4×SD16×C73C211yesmaximal, characteristic
12C22×Dic146—21no—
13C2×#11924016C2212yes—
14#14556591C2211yescharacteristic
15#14556591C2211yescharacteristic
16#14556590C2212yes—
17#14556589C2212yes—
18#14556583—21no—
19#14556581—22no—
20#14556570—21no—
21#14556568—22no—
22C4×Dic146—21no—
23C4×Dic146C2211yescharacteristic
24#14556556C2212yes—
25D4×Dic73C2212yes—
26#14556522C2212yes—
27C4⋊#10596831C2211yescharacteristic
28#14556520C2212yes—
29#14556516C2212yes—
30#14556516C2212yes—
31#14556515C2212yes—
32#14556514C2212yes—
33C8×Dic73C2212yes—
34C2×SD16×C73C2211yescharacteristic
35C4×Q8×C73C2211yescharacteristic
36C4×D4×C73C2211yescharacteristic
37#106×C73C2211yescharacteristic
38#103×C73C2211yescharacteristic
39#102×C73C2211yescharacteristic
40C4×C8×C73C2211yescharacteristic
41C2×Dic146—21no—
42C2×Dic146—22no—
43C2×Dic146—44no—
44C2×Dic146D411yescharacteristic
45C2×Dic146C2312yes—
46C22×Dic73—22no—
47#11924016—24no—
48C2×#10596831C2312yes—
49C4⋊Dic73—21no—
50C4⋊Dic73—21no—
51C4⋊Dic73—21no—
52C4⋊Dic73D411yescharacteristic
53C4⋊Dic73C2312yes—
54#11924007—22no—
55#11924007—22no—
56#11924007—22no—
57#11924007—22no—
58#11924007D412yes—
59C22⋊Dic73—22no—
60C4×Dic73—22no—
61C4×Dic73C2312yes—
62C2×Q8×C73C2311yescharacteristic
63C2×D4×C73C2311yescharacteristic
64C22×C4×C73—21no—
65SD16×C73—22no—
66C2×C8×C73C2311yescharacteristic
67C2×C8×C73C2311yescharacteristic
68C4⋊C4×C73—21no—
69C4⋊C4×C73C2311yescharacteristic
70C4⋊C4×C73C2311yescharacteristic
71C22⋊C4×C73—21no—
72C42×C73—21no—
73C42×C73C2311yescharacteristic
74C23×C73—21no—
75Q8×C73—21no—
76Q8×C73—21no—
77D4×C73—21no—
78D4×C73#4112yes—
79C2×C4×C73—21no—
80C2×C4×C73—21no—
81C2×C4×C73—21no—
82C2×C4×C73—42no—
83C2×C4×C73C2×D411yescharacteristic
84C2×C4×C73C2×D411yescharacteristic
85C2×C4×C73C2411yescharacteristic
86C2×Dic73—22no—
87C2×Dic73—22no—
88C2×Dic73—44no—
89C2×Dic73C2×D412yes—
90C2×Dic73C2×D412yes—
91Dic146—22no—
92Dic146—22no—
93Dic146—42no—
94Dic146—44no—
95Dic146SD1614yescomplemented
96C8×C73—21no—
97C8×C73—21no—
98#10596831—22no—
99C22×C73—22no—
100C22×C73—41no—
101C22×C73—41no—
102C22×C73C22×D411yescharacteristic
103C4×C73—21no—
104C4×C73—41no—
105C4×C73—41no—
106C4×C73—41no—
107C4×C73C2×SD1612yes—
108C4×C73C2×#4111yescharacteristic
109C4×C732−1+411yescharacteristic
110Dic73—22no—
111Dic73—42no—
112Dic73—42no—
113Dic73C2×SD1614yes—
114C2×C73—42no—
115C2×C73#54811yescharacteristic
116C2×C73C22×SD1611yescharacteristic
117C2×C73#57811yescharacteristic
118#3359—731nomaximal, Sylow
119C73#335911yescharacteristic, complemented, Sylow
120#557—731no—
121D4×Q8—731no—
122#487—732no—
123#487—731no—
124#475—731no—
125#475—732no—
126#461—732no—
127#461—731no—
128C8×Q8—731no—
129C4×SD16—732no—
130C4×SD16D7311yescharacteristic
131C22×Q8—1461no—
132C2×SD16—732no—
133C2×SD16C2×D7311yescharacteristic
134C4⋊Q8—732no—
135C4⋊Q8—732no—
136C4⋊Q8—731no—
137C4⋊Q8—731no—
138#125—1461no—
139#125—1462no—
140C22⋊Q8—1462no—
141C22⋊Q8—1461no—
142C4×Q8—731no—
143C4×Q8—732no—
144C4×Q8—1461no—
145C4×Q8C2×D7311yescharacteristic
146C4×D4—732no—
147C4×D4C2×D7311yescharacteristic
148#106—732no—
149#106C2×D7311yescharacteristic
150C4⋊C8—732no—
151C4⋊C8—731no—
152#103—732no—
153#103—732no—
154#103—732no—
155#103—732no—
156#103C2×D7311yescharacteristic
157#102C2×D7311yescharacteristic
158C4×C8—732no—
159C4×C8C2×D7311yescharacteristic
160C2×Q8—2924no—
161C2×Q8—731no—
162C2×Q8—732no—
163C2×Q8—1462no—
164C2×Q8—1461no—
165C2×Q8C22×D7311yescharacteristic
166C2×D4C22×D7311yescharacteristic
167C22×C4—21no—
168C22×C4—1462no—
169SD16—22no—
170SD16—1464no—
171C2×C8—732no—
172C2×C8C22×D7311yescharacteristic
173C2×C8C22×D7311yescharacteristic
174C4⋊C4—21no—
175C4⋊C4—732no—
176C4⋊C4—731no—
177C4⋊C4—732no—
178C4⋊C4—1462no—
179C4⋊C4—1462no—
180C4⋊C4—1462no—
181C4⋊C4—1462no—
182C4⋊C4—1461no—
183C4⋊C4—1461no—
184C4⋊C4—1461no—
185C4⋊C4C22×D7311yescharacteristic
186C4⋊C4C22×D7311yescharacteristic
187C22⋊C4—21no—
188C22⋊C4—1462no—
189C42—21no—
190C42—732no—
191C42—1462no—
192C42C22×D7311yescharacteristic
193C23—21no—
194Q8—21no—
195Q8—21no—
196Q8—2924no—
197Q8—2922no—
198Q8—734no—
199Q8—1462no—
200Q8—1462no—
201D4—21no—
202D4#1192402812yes—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—42no—
207C2×C4—2924no—
208C2×C4—732no—
209C2×C4—732no—
210C2×C4—1462no—
211C2×C4—1462no—
212C2×C4D4×D7311yescharacteristic
213C2×C4D4×D7311yescharacteristic
214C2×C4C23×D7311yescharacteristic
215C8—21no—
216C8—21no—
217C8—1462no—
218C22—22no—
219C22—41no—
220C22—41no—
221C22C2×D4×D7311yescharacteristic
222C4—21no—
223C4—41no—
224C4—41no—
225C4—41no—
226C4—2922no—
227C4—2922no—
228C4—734no—
229C4—1462no—
230C4SD16×D7312yes—
231C4C2×#1192402811yescharacteristic
232C4#1455663811yescharacteristic
233C2—42no—
234C2#1798924611yescharacteristic
235C2C2×SD16×D7311yescharacteristic
236C2#1798940111yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
FittingC4×SD16×C73C2
socleC22×C73C22×D4
hypercenterC4×SD16D73
hypocenterC73#3359
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. #17989315C2semidirect
3. #17988938C2semidirect
4. #17988936C2semidirect
5. #17988872C2semidirect
6. #17988871C2semidirect
9. C8×Dic146C2semidirect
95. Dic146SD16semidirect
119. C73#3359semidirect