Finite Group Databasebeta

← #22620998

Subgroups — #22620998

Order 9344.

396 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 109 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#17989198C211yesmaximal, characteristic, complemented
2#17989155C211yesmaximal, characteristic
3#17988961C211yesmaximal, characteristic, complemented
4#17988952C211yesmaximal, characteristic, complemented
5#17988941C211yesmaximal, characteristic, complemented
6#17988811C212yesmaximal, complemented
7#17988785C212yesmaximal, complemented
8#17988748C212yesmaximal, complemented
9#17988736C212yesmaximal, complemented
10#17988649C211yesmaximal, characteristic, complemented
11#497×C73C211yesmaximal, characteristic, complemented
12C2×#11924029C2211yescharacteristic
13C2×D4×D73C2211yescharacteristic
14C2×#11924015C2212yes—
15C2×#11924015C2212yescomplemented
16#14556588C2211yescharacteristic
17#14556587C2211yescharacteristic
18#14556586—22no—
19#14556583C2211yescharacteristic, complemented
20#14556581—22no—
21#14556580C2211yescharacteristic
22#14556567C2212yes—
23#14556564—22no—
24#14556561—22no—
25Q8×Dic73C2212yescomplemented
26#14556548C2211yescharacteristic
27#14556520C2212yescomplemented
28#14556515C2212yescomplemented
29#14556513C2212yes—
30#14556513C2212yescomplemented
31#14556512C2212yes—
32#14556503C2212yes—
33C4×#10596831C2211yescharacteristic, complemented
34C2×Q16×C73C2212yescomplemented
35C2×SD16×C73C2212yes—
36C4⋊Q8×C73C2211yescharacteristic, complemented
37#124×C73C2211yescharacteristic
38#97×C73C2211yescharacteristic, complemented
39C23×D73—21no—
40#11924029—42no—
41C2×D292—21no—
42C2×D292—22no—
43C2×D292C2311yescharacteristic
44C2×D292C2311yescharacteristic
45C2×C22⋊D73—21no—
46C2×C22⋊D73—22no—
47D4×D73—42no—
48C2×C4×D73—21no—
49C2×C4×D73C2311yescharacteristic
50#11924015—42no—
51#11924015—42no—
52C2×#10596831C2312yes—
53C4⋊Dic73—22no—
54C4⋊Dic73C2312yes—
55#11924007—22no—
56#11924007—22no—
57#11924007D412yes—
58#11924005—22no—
59#11924005—22no—
60#11924005D412yes—
61C4×Dic73—22no—
62C4×Dic73C2311yescharacteristic
63C2×Q8×C73C2311yescharacteristic
64C2×Q8×C73C2312yes—
65C2×D4×C73C2311yescharacteristic
66Q16×C73—42no—
67SD16×C73—42no—
68C2×C8×C73C2312yes—
69C4⋊C4×C73—22no—
70C22⋊C4×C73—22no—
71C42×C73C2311yescharacteristic
72C23×C73—21no—
73C22×D73—21no—
74C22×D73—21no—
75C22×D73—42no—
76C22×D73—82no—
77C22×D73C2×D411yescharacteristic
78Q8×C73—22no—
79Q8×C73—22no—
80Q8×C73—22no—
81D4×C73—22no—
82C2×C4×C73—21no—
83C2×C4×C73—22no—
84C2×C4×C73C2×D412yes—
85C2×C4×C73C2411yescharacteristic
86C22⋊D73—42no—
87C22⋊D73—82no—
88C2×Dic73—22no—
89C2×Dic73C2×D412yes—
90C2×Dic73C2×D411yescharacteristic
91D292—22no—
92D292—22no—
93D292—42no—
94D292—82no—
95C4×D73—22no—
96C4×D73—42no—
97C8×C73—22no—
98#10596831—22no—
99C22×C73—41no—
100C22×C73—42no—
101C22×C73C22×D411yescharacteristic
102C2×D73—21no—
103C2×D73—22no—
104C2×D73—41no—
105C2×D73—41no—
106C2×D73—42no—
107C2×D73—42no—
108C2×D73—84no—
109C4×C73—22no—
110C4×C73—41no—
111C4×C73—42no—
112C4×C73H(5,𝔽2)12yes—
113Dic73—21no—
114Dic73—22no—
115Dic73—42no—
116C2×C73—81no—
117C2×C73#53511yescharacteristic
118C2×C73#57712yes—
119D73—41no—
120D73—81no—
121D73—81no—
122#3222—731nomaximal, Sylow
123C73#322211yescharacteristic, complemented, Sylow
124#541—731no—
125#535—731no—
126#497D7311yescharacteristic, complemented
127#492—731no—
128#490—731no—
129#488—731no—
130#464—732no—
131#460—732no—
132#452—732no—
133#450—732no—
134#433—731no—
135C2×#41—731no—
136C22×D4—731no—
137C2×Q16C2×D7312yescomplemented
138C2×SD16—732no—
139C2×SD16—732no—
140C2×SD16C2×D7312yes—
141C4⋊Q8C2×D7311yescharacteristic, complemented
142#127—731no—
143#127—731no—
144#126—1462no—
145#125—731no—
146#125—1462no—
147#124—731no—
148#124C2×D7311yescharacteristic
149C22⋊Q8—732no—
150#121—1462no—
151#120—1462no—
152C4×Q8—732no—
153#117—731no—
154C4⋊C8—732no—
155#103—732no—
156#102—732no—
157#102—732no—
158#102—732no—
159C22⋊C8—732no—
160#97C2×D7311yescharacteristic, complemented
161C4×C8—731no—
162C24—1461no—
163#41—2922no—
164C2×Q8C22×D7311yescharacteristic
165C2×Q8C22×D7312yes—
166C2×D4—2922no—
167C2×D4—731no—
168C2×D4—731no—
169C2×D4—1461no—
170C2×D4—1461no—
171C2×D4—1462no—
172C2×D4—1462no—
173C2×D4C22×D7311yescharacteristic
174C22×C4—731no—
175C22×C4—1461no—
176Q16—42no—
177SD16—42no—
178SD16—2922no—
179SD16—2922no—
180C2×C8—732no—
181C2×C8C22×D7312yes—
182C4⋊C4—22no—
183C4⋊C4—732no—
184C4⋊C4—732no—
185C4⋊C4—1462no—
186C4⋊C4—1462no—
187C4⋊C4—1462no—
188C22⋊C4—22no—
189C22⋊C4—732no—
190C22⋊C4—1462no—
191C22⋊C4—1462no—
192C42—731no—
193C42—1462no—
194C42C22×D7311yescharacteristic
195C23—21no—
196C23—2922no—
197C23—5842no—
198C23—731no—
199C23—1461no—
200C23—1461no—
201Q8—22no—
202Q8—22no—
203Q8—22no—
204D4—22no—
205D4—2922no—
206D4—2922no—
207D4—5842no—
208D4—5842no—
209D4—1462no—
210D4—1462no—
211C2×C4—22no—
212C2×C4—21no—
213C2×C4—2922no—
214C2×C4—732no—
215C2×C4—731no—
216C2×C4—1462no—
217C2×C4—1462no—
218C2×C4D4×D7312yes—
219C2×C4C23×D7311yescharacteristic
220C8—22no—
221C8—1462no—
222C22—42no—
223C22—41no—
224C22—2922no—
225C22—2922no—
226C22—2921no—
227C22—2921no—
228C22—5844no—
229C22—1462no—
230C22—1461no—
231C22C2×D4×D7311yescharacteristic
232C4—22no—
233C4—41no—
234C4—42no—
235C4—2922no—
236C4—1462no—
237C4—1461no—
238C4#1455663612yes—
239C2—81no—
240C2—2921no—
241C2—5841no—
242C2—5841no—
243C2#1798915011yescharacteristic
244C2#1798939612yes—
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#497×C73C2
socleC22×C73C22×D4
hypercenter#497D73
hypocenterC73#3222
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #497

Complements

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

NH ≅ G/Ntype
1. #17989198C2semidirect
3. #17988961C2semidirect
4. #17988952C2semidirect
5. #17988941C2semidirect
6. #17988811C2semidirect
7. #17988785C2semidirect
8. #17988748C2semidirect
9. #17988736C2semidirect
10. #17988649C2semidirect
11. #497×C73C2semidirect
15. C2×#11924015C22semidirect
19. #14556583C22semidirect
25. Q8×Dic73C22semidirect
27. #14556520C22semidirect
28. #14556515C22semidirect
30. #14556513C22semidirect
33. C4×#10596831C22semidirect
34. C2×Q16×C73C22semidirect
36. C4⋊Q8×C73C22semidirect
38. #97×C73C22semidirect
123. C73#3222semidirect
126. #497D73semidirect
137. C2×Q16C2×D73semidirect
141. C4⋊Q8C2×D73semidirect
160. #97C2×D73semidirect