Finite Group Databasebeta

← #22619224

Subgroups — #22619224

Order 9344.

700 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 700 conjugacy classes of subgroups — too many to draw. Only its 149 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×#14556638C211yesmaximal, characteristic
2C2×#14556622C211yesmaximal, characteristic, complemented
3C22×#11924018C211yesmaximal, characteristic, complemented
4#17988747C214yesmaximal, complemented
5#17988742C214yesmaximal, complemented
6#17988595C211yesmaximal, characteristic, complemented
7#17988581C211yesmaximal, characteristic, complemented
8#17988554C211yesmaximal, characteristic, complemented
9#536×C73C211yesmaximal, characteristic, complemented
10#14556638—24no—
11#14556638—24no—
12C2×#11924028C2212yes—
13C2×#11924028C2211yescharacteristic
14C2×#11924027—22no—
15C2×#11924027—21no—
16C22×Dic146C2212yes—
17C22×Dic146C2211yescharacteristic
18C2×Q8×D73—21no—
19#14556622—24no—
20C2×#11924018—24no—
21C2×#11924018C2212yes—
22C2×#11924018C2214yes—
23C2×#11924015C2212yes—
24C2×#11924012C2211yescharacteristic
25C22×#10596831C2211yescharacteristic
26#14556514C2212yes—
27#14556514C2214yes—
28#14556511C2212yes—
29C22⋊#10596831C2214yes—
30C2×#41×C73C2211yescharacteristic
31C22×Q8×C73C2211yescharacteristic
32C4⋊Q8×C73—21no—
33#124×C73—21no—
34#123×C73—22no—
35C22⋊Q8×C73C2214yes—
36#117×C73C2211yescharacteristic
37#11924028—22no—
38#11924028—24no—
39#11924028—24no—
40#11924028D414yes—
41#11924027—216no—
42#11924027—28no—
43C2×Dic146—22no—
44C2×Dic146—21no—
45C2×Dic146—22no—
46C2×Dic146—24no—
47C2×Dic146—24no—
48C2×Dic146D414yes—
49C2×Dic146C2311yescharacteristic
50C2×Dic146C2312yes—
51Q8×D73—28no—
52C2×D292C2311yescharacteristic
53C2×C22⋊D73—22no—
54C2×C22⋊D73—21no—
55C22×Dic73—22no—
56C22×Dic73—21no—
57C2×C4×D73—22no—
58C2×C4×D73—21no—
59#11924018—28no—
60#11924018—24no—
61#11924015—24no—
62#11924012—22no—
63C2×#10596831—22no—
64C2×#10596831C2312yes—
65C2×#10596831C2312yes—
66#41×C73—22no—
67#41×C73—22no—
68C2×Q8×C73—21no—
69C2×Q8×C73—22no—
70C2×Q8×C73—22no—
71C2×Q8×C73D411yescharacteristic
72C2×Q8×C73C2312yes—
73C2×D4×C73D412yes—
74C2×D4×C73D411yescharacteristic
75C22×C4×C73—21no—
76C22×C4×C73C2312yes—
77C22×C4×C73C2311yescharacteristic
78C4⋊C4×C73—24no—
79C4⋊C4×C73C2312yes—
80C22⋊C4×C73—21no—
81C22⋊C4×C73—24no—
82C42×C73—21no—
83C23×C73C2×D412yes—
84C23×C73C2×D411yescharacteristic
85C22×D73—21no—
86Q8×C73—22no—
87Q8×C73—22no—
88Q8×C73—22no—
89Q8×C73—42no—
90D4×C73—24no—
91D4×C73—22no—
92C2×C4×C73—22no—
93C2×C4×C73—22no—
94C2×C4×C73—22no—
95C2×C4×C73—22no—
96C2×C4×C73—42no—
97C2×C4×C73C2×D412yes—
98C2×C4×C73C2×D412yes—
99C2×C4×C73C2×D412yes—
100C2×C4×C73C2×D411yescharacteristic
101C2×C4×C73C2411yescharacteristic
102C22⋊D73—28no—
103C22⋊D73—24no—
104C2×Dic73—28no—
105C2×Dic73—24no—
106C2×Dic73—21no—
107C2×Dic73—22no—
108D292—21no—
109D292C2×D412yes—
110C4×D73—28no—
111C4×D73—24no—
112Dic146—28no—
113Dic146—24no—
114Dic146—22no—
115Dic146—21no—
116Dic146C2×D412yes—
117Dic146C2×D414yes—
118#10596831—22no—
119#10596831—22no—
120C22×C73—22no—
121C22×C73—22no—
122C22×C73—24no—
123C22×C73#12012yes—
124C22×C73C22×D411yescharacteristic
125C2×D73—22no—
126C2×D73—42no—
127C4×C73—22no—
128C4×C73—42no—
129C4×C73—42no—
130C4×C73#12012yes—
131C4×C73C22×D411yescharacteristic
132C4×C73C22×D411yescharacteristic
133Dic73—22no—
134Dic73—24no—
135C2×C73—22no—
136C2×C73—42no—
137C2×C73C2×#12011yescharacteristic
138C2×C73#57812yes—
139D73—42no—
140#3011—731nomaximal, Sylow
141C73#301111yescharacteristic, complemented, Sylow
142C2×2−1+4—731no—
143C2×#137—731no—
144C22×Q16—731no—
145#536D7311yescharacteristic, complemented
146#452—734no—
147#451—734no—
148#419—731no—
149#416—731no—
150#408—731no—
1512−1+4—1464no—
1522−1+4—1464no—
153C2×#41—731no—
154C2×#41—732no—
155C2×#41—1462no—
156C2×#41—1461no—
157C2×#41C2×D7311yescharacteristic
158C22×Q8—731no—
159C22×Q8—732no—
160C22×Q8—1461no—
161C22×Q8C2×D7311yescharacteristic
162#137—1464no—
163C2×Q16—734no—
164C2×Q16—732no—
165C2×Q16—1464no—
166C2×SD16—732no—
167C2×M16—731no—
168C22×C8—731no—
169C4⋊Q8—21no—
170#124—21no—
171#123—22no—
172C22⋊Q8C2×D7314yes—
173#117C2×D7311yescharacteristic
174#103—732no—
175#103—734no—
176#102—732no—
177C22⋊C8—734no—
178#41—22no—
179#41—22no—
180#41—734no—
181#41—1464no—
182#41—1464no—
183#41—14616no—
184#41—1468no—
185#41—1462no—
186C2×Q8—21no—
187C2×Q8—22no—
188C2×Q8—22no—
189C2×Q8—734no—
190C2×Q8—732no—
191C2×Q8—731no—
192C2×Q8—1464no—
193C2×Q8—1464no—
194C2×Q8—1468no—
195C2×Q8—1462no—
196C2×Q8—1462no—
197C2×Q8—1461no—
198C2×Q8C22⋊D7311yescharacteristic
199C2×Q8C22×D7312yes—
200C2×D4—731no—
201C2×D4—1462no—
202C2×D4—1461no—
203C2×D4C22⋊D7312yes—
204C2×D4C22⋊D7311yescharacteristic
205C22×C4—21no—
206C22×C4—1462no—
207C22×C4—1461no—
208C22×C4—1462no—
209C22×C4—1461no—
210C22×C4C22×D7312yes—
211C22×C4C22×D7311yescharacteristic
212Q16—1468no—
213Q16—1464no—
214SD16—1464no—
215M16—1462no—
216C2×C8—732no—
217C2×C8—732no—
218C2×C8—1462no—
219C4⋊C4—24no—
220C4⋊C4C22×D7312yes—
221C22⋊C4—21no—
222C22⋊C4—24no—
223C42—21no—
224C23—1461no—
225C23C2×C22⋊D7312yes—
226C23C2×C22⋊D7311yescharacteristic
227Q8—22no—
228Q8—22no—
229Q8—22no—
230Q8—42no—
231Q8—734no—
232Q8—732no—
233Q8—1468no—
234Q8—1464no—
235Q8—1462no—
236Q8—1461no—
237D4—24no—
238D4—22no—
239D4—732no—
240D4—1468no—
241D4—1464no—
242D4—1461no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—42no—
248C2×C4—1468no—
249C2×C4—1468no—
250C2×C4—1464no—
251C2×C4—1462no—
252C2×C4—1461no—
253C2×C4—1464no—
254C2×C4D4×D7312yes—
255C2×C4D4×D7312yes—
256C2×C4C2×C22⋊D7312yes—
257C2×C4C2×C22⋊D7311yescharacteristic
258C2×C4C23×D7311yescharacteristic
259C8—1462no—
260C8—1462no—
261C22—22no—
262C22—24no—
263C22—22no—
264C22—2922no—
265C22—1462no—
266C22#1455655912yes—
267C22C22×C22⋊D7311yescharacteristic
268C4—22no—
269C4—42no—
270C4—42no—
271C4—1464no—
272C4—1462no—
273C4#1455655912yes—
274C4C2×D4×D7311yescharacteristic
275C4C2×D4×D7311yescharacteristic
276C2—22no—
277C2—42no—
278C2—2922no—
279C2C2×#1455655911yescharacteristic
280C2#1798940212yes—
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#536×C73C2
socleC22×C73C22×D4
hypercenter#536D73
hypocenterC73#3011
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×#41 ◁ #536

Complements

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

NH ≅ G/Ntype
2. C2×#14556622C2semidirect
3. C22×#11924018C2semidirect
4. #17988747C2semidirect
5. #17988742C2semidirect
6. #17988595C2semidirect
7. #17988581C2semidirect
8. #17988554C2semidirect
9. #536×C73C2semidirect
141. C73#3011semidirect
145. #536D73semidirect