Finite Group Databasebeta

← #22619416

Subgroups — #22619416

Order 9344.

480 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 145 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×#14556621C211yesmaximal, characteristic
2C2×#14556589C211yesmaximal, characteristic, complemented
3#41×Dic73C211yesmaximal, characteristic
4#17988795C214yesmaximal, complemented
5#17988790C214yesmaximal, complemented
6#17988610C211yesmaximal, characteristic, complemented
7#17988597C211yesmaximal, characteristic, complemented
8#17988596C211yesmaximal, characteristic, complemented
9C2×#137×C73C211yesmaximal, characteristic
10C22×Dic146C2211yescharacteristic
11#14556621—24no—
12C2×#11924018C2212yes—
13C2×#11924016C2212yes—
14C2×#11924012C2211yescharacteristic
15#14556589—21no—
16#14556589—21no—
17#14556589C2214yes—
18Q8×Dic73C2212yes—
19D4×Dic73—22no—
20D4×Dic73C2212yes—
21#14556550—21no—
22#14556550C2211yescharacteristic
23C2×#11924007—22no—
24C2×C4×Dic73—21no—
25C2×C4×Dic73C2211yescharacteristic
26#14556520C2214yes—
27#14556516C2214yes—
28#14556515C2214yes—
29C2×#41×C73C2211yescharacteristic
30C22×Q8×C73C2211yescharacteristic
31#137×C73—24no—
32C2×Q16×C73C2212yes—
33C2×SD16×C73C2212yes—
34C2×M16×C73C2211yescharacteristic
35C2×Dic146—22no—
36C2×Dic146—22no—
37C2×Dic146—21no—
38C2×Dic146C2312yes—
39C22×Dic73—21no—
40C22×Dic73—22no—
41C22×Dic73D412yes—
42#11924018—24no—
43#11924016—24no—
44#11924012—22no—
45C2×#10596831C2312yes—
46C4⋊Dic73—22no—
47C4⋊Dic73C2312yes—
48#11924007—24no—
49#11924007—24no—
50C22⋊Dic73—21no—
51C22⋊Dic73—22no—
52C4×Dic73—21no—
53C4×Dic73—22no—
54C4×Dic73D411yescharacteristic
55C4×Dic73D411yescharacteristic
56C4×Dic73C2312yes—
57#41×C73—22no—
58#41×C73D414yes—
59C2×Q8×C73—21no—
60C2×Q8×C73—22no—
61C2×Q8×C73—22no—
62C2×Q8×C73C2312yes—
63C2×Q8×C73C2311yescharacteristic
64C2×D4×C73—21no—
65C2×D4×C73C2311yescharacteristic
66C22×C4×C73—21no—
67C22×C4×C73—21no—
68C22×C4×C73C2311yescharacteristic
69Q16×C73—24no—
70SD16×C73—24no—
71M16×C73—22no—
72C2×C8×C73C2312yes—
73C23×C73—21no—
74C23×C73C2×D411yescharacteristic
75Q8×C73—21no—
76Q8×C73—22no—
77Q8×C73—22no—
78Q8×C73—42no—
79Q8×C73C2×D412yes—
80D4×C73—24no—
81D4×C73—21no—
82D4×C73C2×D412yes—
83C2×C4×C73—21no—
84C2×C4×C73—24no—
85C2×C4×C73—22no—
86C2×C4×C73—42no—
87C2×C4×C73C2×D411yescharacteristic
88C2×C4×C73C2×D412yes—
89C2×C4×C73#4112yes—
90C2×C4×C73C2411yescharacteristic
91C2×Dic73—24no—
92C2×Dic73—22no—
93C2×Dic73—22no—
94C2×Dic73—42no—
95C2×Dic73—44no—
96C2×Dic73C2×D412yes—
97C2×Dic73C2×D412yes—
98Dic146—22no—
99Dic146—22no—
100Dic146—42no—
101C8×C73—22no—
102#10596831—22no—
103C22×C73—22no—
104C22×C73—22no—
105C22×C73—42no—
106C22×C73#12112yes—
107C22×C73C22×D411yescharacteristic
108C4×C73—22no—
109C4×C73—42no—
110C4×C73#12112yes—
111C4×C73C22×D411yescharacteristic
112C4×C73C2×#4111yescharacteristic
113Dic73—22no—
114Dic73—42no—
115Dic73—42no—
116Dic73#13714yescomplemented
117C2×C73—22no—
118C2×C73—42no—
119C2×C73C2×#12111yescharacteristic
120C2×C73C2×#13712yes—
121#3039—731nomaximal, Sylow
122C73#303911yescharacteristic, complemented, Sylow
123C2×#137—731no—
124C2×#137D7311yescharacteristic
125C2×C4⋊Q8—731no—
126C4×#41—731no—
127#462—734no—
128#461—734no—
129#423—731no—
130#419—731no—
131#419—731no—
132C2×#41C2×D7311yescharacteristic
133C22×Q8—731no—
134C22×Q8C2×D7311yescharacteristic
135#137—24no—
136#137—1464no—
137C2×Q16—732no—
138C2×Q16C2×D7312yes—
139C2×SD16—732no—
140C2×SD16C2×D7312yes—
141C2×M16—731no—
142C2×M16C2×D7311yescharacteristic
143C4⋊Q8—734no—
144C4⋊Q8—1461no—
145C4⋊Q8—1461no—
146C4×Q8—732no—
147C4×D4—732no—
148C4×D4—1462no—
149#117—731no—
150#117—1461no—
151C2×C4⋊C4—1462no—
152C2×C42—731no—
153C2×C42—1461no—
154C4⋊C8—734no—
155#103—734no—
156#103—734no—
157#41—22no—
158#41C22⋊D7314yes—
159C2×Q8—21no—
160C2×Q8—22no—
161C2×Q8—22no—
162C2×Q8—732no—
163C2×Q8—1462no—
164C2×Q8—1462no—
165C2×Q8—1461no—
166C2×Q8C22×D7312yes—
167C2×Q8C22×D7311yescharacteristic
168C2×D4—21no—
169C2×D4C22×D7311yescharacteristic
170C22×C4—21no—
171C22×C4—21no—
172C22×C4—732no—
173C22×C4—1462no—
174C22×C4—1461no—
175C22×C4C22×D7311yescharacteristic
176Q16—24no—
177Q16—1464no—
178SD16—24no—
179SD16—1464no—
180M16—22no—
181M16—1462no—
182C2×C8—732no—
183C2×C8C22×D7312yes—
184C4⋊C4—732no—
185C4⋊C4—1464no—
186C4⋊C4—1464no—
187C4⋊C4—1462no—
188C22⋊C4—1462no—
189C22⋊C4—1461no—
190C42—731no—
191C42—731no—
192C42—732no—
193C42—1462no—
194C42—1461no—
195C23—21no—
196C23D4×D7311yescharacteristic
197Q8—21no—
198Q8—22no—
199Q8—22no—
200Q8—42no—
201Q8—2922no—
202Q8—1462no—
203Q8—1462no—
204Q8C2×C22⋊D7312yes—
205D4—24no—
206D4—21no—
207D4C2×C22⋊D7312yes—
208C2×C4—21no—
209C2×C4—24no—
210C2×C4—22no—
211C2×C4—42no—
212C2×C4—2922no—
213C2×C4—2924no—
214C2×C4—732no—
215C2×C4—732no—
216C2×C4—1462no—
217C2×C4—1462no—
218C2×C4—1464no—
219C2×C4D4×D7311yescharacteristic
220C2×C4C2×C22⋊D7312yes—
221C2×C4#1192402712yes—
222C2×C4C23×D7311yescharacteristic
223C8—22no—
224C8—1462no—
225C22—22no—
226C22—22no—
227C22—42no—
228C22#1455656312yes—
229C22C2×D4×D7311yescharacteristic
230C4—22no—
231C4—42no—
232C4—2922no—
233C4—2922no—
234C4—734no—
235C4—1462no—
236C4#1455656312yes—
237C4C22×C22⋊D7311yescharacteristic
238C4C2×#1192402711yescharacteristic
239C2—22no—
240C2—42no—
241C2C2×#1455656311yescharacteristic
242C2#137×D7312yes—
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
FittingC2×#137×C73C2
socleC22×C73C22×D4
hypercenterC2×#137D73
hypocenterC73#3039
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
2. C2×#14556589C2semidirect
4. #17988795C2semidirect
5. #17988790C2semidirect
6. #17988610C2semidirect
7. #17988597C2semidirect
8. #17988596C2semidirect
116. Dic73#137semidirect
122. C73#3039semidirect