Finite Group Databasebeta

← #22619417

Subgroups — #22619417

Order 9344.

480 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 137 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×#14556624C211yesmaximal, characteristic
2C2×#14556622C211yesmaximal, characteristic
3C2×#14556589C211yesmaximal, characteristic, complemented
4#17989055C211yesmaximal, characteristic
5#17988796C214yesmaximal, complemented
6#17988791C214yesmaximal, complemented
7#17988610C211yesmaximal, characteristic, complemented
8#17988595C211yesmaximal, characteristic, complemented
9#419×C73C211yesmaximal, characteristic, complemented
10C2×#11924028C2211yescharacteristic
11C22×Dic146C2211yescharacteristic
12#14556624—24no—
13#14556622—24no—
14C2×Dic292C2212yes—
15C2×#11924018C2212yes—
16C2×#11924017C2212yes—
17C2×#11924015C2212yes—
18C2×#11924012C2211yescharacteristic
19#14556589—21no—
20#14556589—21no—
21#14556589C2214yes—
22#14556556C2212yes—
23#14556553C2212yes—
24#14556551—22no—
25#14556548—21no—
26C2×#11924007—22no—
27C2×C4×Dic73C2211yescharacteristic
28C42×D73—21no—
29#14556520C2214yes—
30#14556514C2214yes—
31C22×Q8×C73C2211yescharacteristic
32C2×M16×C73C2211yescharacteristic
33#117×C73C2211yescharacteristic
34#103×C73C2214yes—
35#11924028—22no—
36#11924028D414yes—
37C2×Dic146—22no—
38C2×Dic146—22no—
39C2×Dic146—21no—
40C2×Dic146C2312yes—
41C2×Dic146C2311yescharacteristic
42C2×D292C2311yescharacteristic
43C2×C22⋊D73—21no—
44C22×Dic73—21no—
45C22×Dic73D412yes—
46C2×C4×D73—21no—
47C2×C4×D73—22no—
48Dic292—24no—
49#11924018—24no—
50#11924017—24no—
51#11924015—24no—
52#11924012—22no—
53C2×#10596831C2312yes—
54#11924007—24no—
55#11924007—24no—
56#11924007—22no—
57#11924005—22no—
58C4×Dic73—22no—
59C4×Dic73D411yescharacteristic
60C4×Dic73D411yescharacteristic
61C4×Dic73C2312yes—
62C2×Q8×C73—21no—
63C2×Q8×C73—22no—
64C2×Q8×C73—22no—
65C2×Q8×C73C2312yes—
66C22×C4×C73—21no—
67C22×C4×C73C2311yescharacteristic
68M16×C73—22no—
69C2×C8×C73C2312yes—
70C4⋊C4×C73C2312yes—
71C22⋊C4×C73—21no—
72C42×C73—21no—
73C23×C73C2×D411yescharacteristic
74C22×D73—21no—
75Q8×C73—22no—
76Q8×C73—22no—
77Q8×C73—42no—
78C2×C4×C73—22no—
79C2×C4×C73—22no—
80C2×C4×C73—42no—
81C2×C4×C73C2×D411yescharacteristic
82C2×C4×C73C2×D412yes—
83C2×C4×C73#4112yes—
84C2×C4×C73C2411yescharacteristic
85C22⋊D73—24no—
86C2×Dic73—21no—
87C2×Dic73—24no—
88C2×Dic73—22no—
89C2×Dic73—42no—
90C2×Dic73C2×D412yes—
91C2×Dic73C2×D412yes—
92D292—21no—
93D292C2×D412yes—
94C4×D73—24no—
95C4×D73—44no—
96Dic146—21no—
97Dic146—22no—
98Dic146—22no—
99Dic146—42no—
100Dic146C2×D412yes—
101C8×C73—22no—
102#10596831—22no—
103C22×C73—22no—
104C22×C73#12112yes—
105C22×C73C22×D411yescharacteristic
106C2×D73—22no—
107C2×D73—42no—
108C4×C73—42no—
109C4×C73—42no—
110C4×C73#12112yes—
111C4×C73C22×D411yescharacteristic
112C4×C73C2×#4111yescharacteristic
113Dic73—22no—
114Dic73—22no—
115Dic73—42no—
116Dic73#13714yescomplemented
117C2×C73—22no—
118C2×C73C2×#12111yescharacteristic
119C2×C73C2×#13712yes—
120D73—42no—
121#3039—731nomaximal, Sylow
122C73#303911yescharacteristic, complemented, Sylow
123C2×#137—731no—
124C2×#137—731no—
125C2×C4⋊Q8—731no—
126C4×#41—731no—
127#462—734no—
128#461—734no—
129#423—731no—
130#419—731no—
131#419D7311yescharacteristic, complemented
132C2×#41—731no—
133C22×Q8—731no—
134C22×Q8C2×D7311yescharacteristic
135#137—1464no—
136#137—1464no—
137C2×Q16—732no—
138C2×Q16—732no—
139C2×SD16—732no—
140C2×SD16—732no—
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—1461no—
150#117C2×D7311yescharacteristic
151C2×C4⋊C4—1462no—
152C2×C42—731no—
153C2×C42—1461no—
154C4⋊C8—734no—
155#103—734no—
156#103C2×D7314yes—
157#41—734no—
158#41—1462no—
159C2×Q8—21no—
160C2×Q8—22no—
161C2×Q8—22no—
162C2×Q8—731no—
163C2×Q8—732no—
164C2×Q8—1462no—
165C2×Q8—1462no—
166C2×Q8—1461no—
167C2×Q8C22×D7312yes—
168C2×D4—731no—
169C2×D4—1461no—
170C22×C4—21no—
171C22×C4—732no—
172C22×C4—1462no—
173C22×C4—1461no—
174C22×C4—1461no—
175C22×C4C22×D7311yescharacteristic
176Q16—1464no—
177Q16—1464no—
178SD16—1464no—
179SD16—1464no—
180M16—22no—
181M16—1462no—
182C2×C8—732no—
183C2×C8C22×D7312yes—
184C4⋊C4—1464no—
185C4⋊C4—1464no—
186C4⋊C4—1462no—
187C4⋊C4C22×D7312yes—
188C22⋊C4—21no—
189C22⋊C4—1462no—
190C42—21no—
191C42—731no—
192C42—731no—
193C42—732no—
194C42—1462no—
195C23—1461no—
196C23D4×D7311yescharacteristic
197Q8—22no—
198Q8—22no—
199Q8—42no—
200Q8—2922no—
201Q8—732no—
202Q8—1462no—
203Q8—1462no—
204Q8—1461no—
205D4—732no—
206D4—1464no—
207D4—1461no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—42no—
211C2×C4—2924no—
212C2×C4—2922no—
213C2×C4—732no—
214C2×C4—732no—
215C2×C4—1462no—
216C2×C4—1464no—
217C2×C4—1461no—
218C2×C4—1464no—
219C2×C4D4×D7311yescharacteristic
220C2×C4D4×D7312yes—
221C2×C4#1192402812yes—
222C2×C4C23×D7311yescharacteristic
223C8—22no—
224C8—1462no—
225C22—22no—
226C22—2922no—
227C22—1462no—
228C22#1455656412yes—
229C22C2×D4×D7311yescharacteristic
230C4—42no—
231C4—42no—
232C4—2922no—
233C4—734no—
234C4—1462no—
235C4—1462no—
236C4#1455656412yes—
237C4C2×D4×D7311yescharacteristic
238C4C2×#1192402811yescharacteristic
239C2—22no—
240C2—2922no—
241C2C2×#1455656411yescharacteristic
242C2#137×D7312yes—
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#419×C73C2
socleC22×C73C22×D4
hypercenter#419D73
hypocenterC73#3039
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
3. C2×#14556589C2semidirect
5. #17988796C2semidirect
6. #17988791C2semidirect
7. #17988610C2semidirect
8. #17988595C2semidirect
9. #419×C73C2semidirect
116. Dic73#137semidirect
122. C73#3039semidirect
131. #419D73semidirect