Finite Group Databasebeta

← #22620632

Subgroups — #22620632

Order 9344.

410 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 115 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#17989138C211yesmaximal, characteristic, complemented
2#17989116C211yesmaximal, characteristic, complemented
3#17988993C211yesmaximal, characteristic, complemented
4#17988977C211yesmaximal, characteristic, complemented
5#17988952C211yesmaximal, characteristic, complemented
6#17988822C212yesmaximal, complemented
7#17988819C212yesmaximal, complemented
8#17988696C212yesmaximal, complemented
9#17988690C212yesmaximal, complemented
10#97×D73C211yesmaximal, characteristic, complemented
11#489×C73C211yesmaximal, characteristic, complemented
12C2×#11924029—21no—
13C2×#11924015C2212yes—
14C2×#11924013C2212yes—
15C2×C8×D73C2212yes—
16#14556588C2211yescharacteristic
17#14556584—21no—
18#14556583C2211yescharacteristic
19#14556580—21no—
20#14556573—21no—
21#14556567C2211yescharacteristic
22#14556566—21no—
23#14556566C2212yes—
24#14556562C2211yescharacteristic
25Q8×Dic73C2211yescharacteristic
26D4×Dic73C2211yescharacteristic
27#14556553—21no—
28#14556553C2212yes—
29#14556551—21no—
30#14556547—21no—
31C42×D73C2211yescharacteristic
32#14556524C2212yes—
33#14556522C2212yes—
34#14556513C2212yes—
35#14556513C2212yes—
36#14556502C2211yescharacteristic
37#14556501C2212yes—
38C4⋊Q8×C73C2211yescharacteristic
39#124×C73C2211yescharacteristic
40#103×C73C2212yes—
41#102×C73C2212yes—
42#97×C73C2211yescharacteristic
43#11924029—44no—
44C2×D292—22no—
45C2×D292—21no—
46C2×D292—21no—
47C2×D292C2312yes—
48C2×C22⋊D73—21no—
49C22×Dic73—21no—
50C2×C4×D73—22no—
51C2×C4×D73D411yescharacteristic
52C2×C4×D73D411yescharacteristic
53C2×C4×D73C2311yescharacteristic
54#11924015—24no—
55#11924013—24no—
56C2×#10596831C2312yes—
57C8×D73—24no—
58C4⋊Dic73—21no—
59C4⋊Dic73C2311yescharacteristic
60C4⋊Dic73C2311yescharacteristic
61#11924007—21no—
62#11924007—21no—
63#11924007—21no—
64C22⋊Dic73—21no—
65C22⋊Dic73—21no—
66#11924005—21no—
67#11924005—22no—
68#11924005—22no—
69C4×Dic73—21no—
70C4×Dic73D411yescharacteristic
71C4×Dic73D411yescharacteristic
72C4×Dic73C2311yescharacteristic
73C2×Q8×C73—21no—
74C2×Q8×C73C2311yescharacteristic
75C2×D4×C73C2311yescharacteristic
76C2×C8×C73C2312yes—
77C4⋊C4×C73—21no—
78C4⋊C4×C73C2312yes—
79C22⋊C4×C73—21no—
80C22⋊C4×C73—21no—
81C42×C73C2311yescharacteristic
82C23×C73—21no—
83C22×D73—22no—
84C22×D73C2×D411yescharacteristic
85Q8×C73—22no—
86Q8×C73—42no—
87D4×C73—22no—
88C2×C4×C73—21no—
89C2×C4×C73—22no—
90C2×C4×C73C2×D411yescharacteristic
91C2×C4×C73C2×D411yescharacteristic
92C2×C4×C73C2411yescharacteristic
93C22⋊D73—42no—
94C2×Dic73—21no—
95C2×Dic73—21no—
96C2×Dic73—42no—
97C2×Dic73C2×D411yescharacteristic
98C2×Dic73C2×D411yescharacteristic
99C2×Dic73C2×D411yescharacteristic
100D292—22no—
101D292—22no—
102D292—42no—
103D292—42no—
104D292—44no—
105C4×D73—22no—
106C4×D73—22no—
107C4×D73—41no—
108C4×D73—44no—
109C8×C73—22no—
110#10596831#4114yescomplemented
111C22×C73—41no—
112C22×C73—41no—
113C22×C73—41no—
114C22×C73C22×D411yescharacteristic
115C2×D73—21no—
116C2×D73—21no—
117C2×D73—42no—
118C2×D73—42no—
119C2×D73—42no—
120C2×D73AGL(1,ℤ/8)12yes—
121C4×C73—21no—
122C4×C73—21no—
123C4×C73—41no—
124C4×C73—42no—
125C4×C73C2×#4112yes—
126Dic73—21no—
127Dic73—21no—
128Dic73—21no—
129Dic73—41no—
130Dic73—41no—
131C2×C73—81no—
132C2×C73#53211yescharacteristic
133C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
134C2×C73#57511yescharacteristic
135D73—22no—
136D73—82no—
137#3180—731nomaximal, Sylow
138C73#318011yescharacteristic, complemented, Sylow
139#532—731no—
140#529—731no—
141#501—731no—
142#496—731no—
143#490—731no—
144#489D7311yescharacteristic, complemented
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⋊Q8C2×D7311yescharacteristic
155#127—731no—
156#126—1461no—
157#125—731no—
158#124—1461no—
159#124C2×D7311yescharacteristic
160#123—1461no—
161C22⋊Q8—731no—
162#121—731no—
163#121—732no—
164#121—1461no—
165C4×Q8—731no—
166C4×D4—731no—
167C4×D4—732no—
168C4×D4—1461no—
169C4×D4—1461no—
170#117—1461no—
171C2×C42—731no—
172#107—732no—
173#106—732no—
174#103C2×D7312yes—
175#102—732no—
176#102—732no—
177#102C2×D7312yes—
178#97—732no—
179#97—731no—
180#97C2×D7311yescharacteristic
181#41—2924no—
182C2×Q8—21no—
183C2×Q8C22×D7311yescharacteristic
184C2×D4—732no—
185C2×D4—1462no—
186C2×D4—1461no—
187C2×D4—1461no—
188C2×D4—1461no—
189C2×D4C22×D7311yescharacteristic
190C22×C4—731no—
191C22×C4—731no—
192C22×C4—731no—
193C22×C4—1462no—
194C22×C4—1461no—
195SD16—1464no—
196D8—1464no—
197C2×C8—732no—
198C2×C8—1464no—
199C2×C8C22×D7312yes—
200C4⋊C4—21no—
201C4⋊C4—731no—
202C4⋊C4—731no—
203C4⋊C4—1461no—
204C4⋊C4—1461no—
205C4⋊C4—1461no—
206C4⋊C4—1461no—
207C4⋊C4C22×D7312yes—
208C22⋊C4—21no—
209C22⋊C4—21no—
210C22⋊C4—1462no—
211C22⋊C4—1462no—
212C22⋊C4—1461no—
213C22⋊C4—1461no—
214C22⋊C4—1461no—
215C42—731no—
216C42—731no—
217C42—731no—
218C42—1461no—
219C42C22×D7311yescharacteristic
220C23—21no—
221C23—731no—
222C23—1462no—
223Q8—22no—
224Q8—42no—
225D4—22no—
226D4—2922no—
227D4—2922no—
228D4—2924no—
229D4—2922no—
230D4—1462no—
231D4—1462no—
232C2×C4—21no—
233C2×C4—22no—
234C2×C4—2921no—
235C2×C4—2924no—
236C2×C4—2922no—
237C2×C4—731no—
238C2×C4—731no—
239C2×C4—731no—
240C2×C4—1462no—
241C2×C4—1461no—
242C2×C4—1461no—
243C2×C4—1462no—
244C2×C4D4×D7311yescharacteristic
245C2×C4D4×D7311yescharacteristic
246C2×C4C23×D7311yescharacteristic
247C8—22no—
248C8—734no—
249C22—41no—
250C22—41no—
251C22—41no—
252C22—2922no—
253C22—2922no—
254C22—2922no—
255C22—732no—
256C22—1461no—
257C22—1461no—
258C22C2×D4×D7311yescharacteristic
259C4—21no—
260C4—21no—
261C4—41no—
262C4—42no—
263C4—2921no—
264C4—2921no—
265C4—1461no—
266C4—1461no—
267C4—1461no—
268C4#41×D7312yes—
269C2—81no—
270C2—5842no—
271C2—1462no—
272C2#1798913611yescharacteristic
273C2AGL(1,ℤ/8)×D7311yescharacteristic
274C2#1798938611yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#489×C73C2
socleC22×C73C22×D4
hypercenter#489D73
hypocenterC73#3180
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. #17989138C2semidirect
2. #17989116C2semidirect
3. #17988993C2semidirect
4. #17988977C2semidirect
5. #17988952C2semidirect
6. #17988822C2semidirect
7. #17988819C2semidirect
8. #17988696C2semidirect
9. #17988690C2semidirect
10. #97×D73C2semidirect
11. #489×C73C2semidirect
110. #10596831#41semidirect
138. C73#3180semidirect
144. #489D73semidirect