Finite Group Databasebeta

← #22620630

Subgroups — #22620630

Order 9344.

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

normal subgroups only

This group has 410 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#17989137C211yesmaximal, characteristic, complemented
2#17988997C211yesmaximal, characteristic, complemented
3#17988977C211yesmaximal, characteristic, complemented
4#17988953C211yesmaximal, characteristic, complemented
5#17988946C211yesmaximal, characteristic, complemented
6#17988821C212yesmaximal, complemented
7#17988818C212yesmaximal, complemented
8#17988697C212yesmaximal, complemented
9#17988685C212yesmaximal, complemented
10C2×#14556502C211yesmaximal, characteristic, complemented
11#529×C73C211yesmaximal, characteristic, complemented
12C2×#11924028—21no—
13C2×#11924015C2212yes—
14C2×#11924013C2212yes—
15C22×#10596831C2212yes—
16#14556591C2211yescharacteristic
17#14556588C2211yescharacteristic
18#14556579—21no—
19#14556565—21no—
20#14556565C2212yes—
21C4×D292—21no—
22C4×D292C2212yes—
23#14556524C2212yes—
24#14556522C2212yes—
25#14556515C2212yes—
26#14556512C2212yes—
27#14556511C2212yes—
28#14556511C2212yes—
29#14556502C2212yes—
30#14556502C2211yescharacteristic
31#14556502C2211yescharacteristic
32#126×C73—21no—
33#125×C73C2211yescharacteristic
34#124×C73C2211yescharacteristic
35#123×C73—21no—
36C22⋊Q8×C73C2211yescharacteristic
37#121×C73C2211yescharacteristic
38C4×Q8×C73C2211yescharacteristic
39C4×D4×C73—21no—
40C4×D4×C73C2211yescharacteristic
41#117×C73—21no—
42C2×C42×C73C2211yescharacteristic
43#11924028—44no—
44C2×Dic146—21no—
45C2×D292—21no—
46C2×D292—21no—
47C2×D292C2312yes—
48C2×C22⋊D73—22no—
49C2×C4×D73—22no—
50#11924015—24no—
51#11924013—24no—
52C2×#10596831—24no—
53C2×#10596831C2312yes—
54C2×#10596831C2312yes—
55C4⋊Dic73—21no—
56C4⋊Dic73C2312yes—
57#11924005—22no—
58#11924005—22no—
59C2×Q8×C73C2311yescharacteristic
60C2×D4×C73—21no—
61C2×D4×C73C2311yescharacteristic
62C22×C4×C73—21no—
63C22×C4×C73D411yescharacteristic
64C22×C4×C73D411yescharacteristic
65C22×C4×C73C2311yescharacteristic
66C4⋊C4×C73—21no—
67C4⋊C4×C73—21no—
68C4⋊C4×C73—21no—
69C4⋊C4×C73—21no—
70C4⋊C4×C73C2311yescharacteristic
71C4⋊C4×C73C2311yescharacteristic
72C22⋊C4×C73—21no—
73C22⋊C4×C73—21no—
74C22⋊C4×C73—21no—
75C22⋊C4×C73—21no—
76C22⋊C4×C73—21no—
77C42×C73—21no—
78C42×C73D411yescharacteristic
79C42×C73D411yescharacteristic
80C42×C73C2311yescharacteristic
81C42×C73C2311yescharacteristic
82C23×C73—21no—
83C23×C73C2×D411yescharacteristic
84C22×D73—22no—
85Q8×C73—22no—
86D4×C73—22no—
87D4×C73—42no—
88C2×C4×C73—22no—
89C2×C4×C73—22no—
90C2×C4×C73—21no—
91C2×C4×C73—21no—
92C2×C4×C73—21no—
93C2×C4×C73—41no—
94C2×C4×C73—42no—
95C2×C4×C73C2×D411yescharacteristic
96C2×C4×C73C2×D411yescharacteristic
97C2×C4×C73C2×D411yescharacteristic
98C2×C4×C73C2×D411yescharacteristic
99C2×C4×C73C2×D411yescharacteristic
100C2×C4×C73C2411yescharacteristic
101C22⋊D73—44no—
102C2×Dic73—22no—
103D292—22no—
104D292—22no—
105D292—42no—
106D292—42no—
107C4×D73—44no—
108Dic146—42no—
109#10596831—22no—
110#10596831#4114yescomplemented
111C22×C73—21no—
112C22×C73—21no—
113C22×C73—41no—
114C22×C73—41no—
115C22×C73—41no—
116C22×C73AGL(1,ℤ/8)12yes—
117C22×C73C22×D411yescharacteristic
118C2×D73—42no—
119C2×D73—42no—
120C2×D73—42no—
121C4×C73—21no—
122C4×C73—21no—
123C4×C73—21no—
124C4×C73—21no—
125C4×C73—21no—
126C4×C73—41no—
127C4×C73—41no—
128C4×C73—41no—
129C4×C73C2×#4112yes—
130Dic73—42no—
131C2×C73—22no—
132C2×C73—81no—
133C2×C73#53211yescharacteristic
134C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
135C2×C73#57511yescharacteristic
136D73—82no—
137#3180—731nomaximal, Sylow
138C73#318011yescharacteristic, complemented, Sylow
139#532—731no—
140#529D7311yescharacteristic, complemented
141#501—731no—
142#496—731no—
143#490—731no—
144#489—731no—
145#466—732no—
146#465—732no—
147#442—732no—
148#440—732no—
149C2×#97—731no—
150C2×#41—1461no—
151C2×SD16—732no—
152C2×D8—732no—
153C22×C8—732no—
154C4⋊Q8—731no—
155#127—731no—
156#126—21no—
157#125C2×D7311yescharacteristic
158#124—1461no—
159#124C2×D7311yescharacteristic
160#123—21no—
161C22⋊Q8C2×D7311yescharacteristic
162#121—732no—
163#121—1461no—
164#121C2×D7311yescharacteristic
165C4×Q8C2×D7311yescharacteristic
166C4×D4—21no—
167C4×D4—732no—
168C4×D4—1461no—
169C4×D4C2×D7311yescharacteristic
170#117—21no—
171C2×C42C2×D7311yescharacteristic
172#107—732no—
173#106—732no—
174#103—732no—
175#102—732no—
176#102—732no—
177#102—732no—
178#97—732no—
179#97—731no—
180#97—731no—
181#41—2924no—
182C2×Q8—1461no—
183C2×Q8C22×D7311yescharacteristic
184C2×D4—21no—
185C2×D4—732no—
186C2×D4—1462no—
187C2×D4—1461no—
188C2×D4—1461no—
189C2×D4C22×D7311yescharacteristic
190C22×C4—21no—
191C22×C4—1462no—
192C22×C4C22⋊D7311yescharacteristic
193C22×C4C22⋊D7311yescharacteristic
194C22×C4C22×D7311yescharacteristic
195SD16—1464no—
196D8—1464no—
197C2×C8—732no—
198C2×C8—732no—
199C2×C8—1464no—
200C4⋊C4—21no—
201C4⋊C4—21no—
202C4⋊C4—21no—
203C4⋊C4—21no—
204C4⋊C4—732no—
205C4⋊C4—1461no—
206C4⋊C4C22×D7311yescharacteristic
207C4⋊C4C22×D7311yescharacteristic
208C22⋊C4—21no—
209C22⋊C4—21no—
210C22⋊C4—21no—
211C22⋊C4—21no—
212C22⋊C4—21no—
213C22⋊C4—1462no—
214C22⋊C4—1462no—
215C42—21no—
216C42C22⋊D7311yescharacteristic
217C42C22⋊D7311yescharacteristic
218C42C22×D7311yescharacteristic
219C42C22×D7311yescharacteristic
220C23—21no—
221C23—1462no—
222C23C2×C22⋊D7311yescharacteristic
223Q8—22no—
224Q8—2922no—
225D4—22no—
226D4—42no—
227D4—2922no—
228D4—2922no—
229D4—2924no—
230D4—1462no—
231D4—1462no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—41no—
238C2×C4—42no—
239C2×C4—2924no—
240C2×C4—1462no—
241C2×C4C2×C22⋊D7311yescharacteristic
242C2×C4C2×C22⋊D7311yescharacteristic
243C2×C4C2×C22⋊D7311yescharacteristic
244C2×C4C2×C22⋊D7311yescharacteristic
245C2×C4C2×C22⋊D7311yescharacteristic
246C2×C4C23×D7311yescharacteristic
247C8—734no—
248C8—1462no—
249C22—21no—
250C22—21no—
251C22—41no—
252C22—41no—
253C22—41no—
254C22—2922no—
255C22—2922no—
256C22—2922no—
257C22#1455661612yes—
258C22C22×C22⋊D7311yescharacteristic
259C4—21no—
260C4—21no—
261C4—21no—
262C4—21no—
263C4—21no—
264C4—41no—
265C4—41no—
266C4—41no—
267C4—2922no—
268C4#41×D7312yes—
269C2—22no—
270C2—81no—
271C2—5842no—
272C2#1798913311yescharacteristic
273C2C2×#1455661611yescharacteristic
274C2#1798938511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#529×C73C2
socleC22×C73C22×D4
hypercenter#529D73
hypocenterC73#3180
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
1. #17989137C2semidirect
2. #17988997C2semidirect
3. #17988977C2semidirect
4. #17988953C2semidirect
5. #17988946C2semidirect
6. #17988821C2semidirect
7. #17988818C2semidirect
8. #17988697C2semidirect
9. #17988685C2semidirect
10. C2×#14556502C2semidirect
11. #529×C73C2semidirect
110. #10596831#41semidirect
138. C73#3180semidirect
140. #529D73semidirect