Finite Group Databasebeta

← #22622918

Subgroups — #22622918

Order 9344.

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

normal subgroups only

This group has 360 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#17989311C211yesmaximal, characteristic, complemented
2#17989307C211yesmaximal, characteristic, complemented
3#17988968C212yesmaximal
4#17988966C211yesmaximal, characteristic, complemented
5#17988812C212yesmaximal, complemented
6#17988807C212yesmaximal, complemented
7#17988793C211yesmaximal, characteristic, complemented
8#17988711C211yesmaximal, characteristic, complemented
9#17988679C212yesmaximal, complemented
10C4×#11924013C211yesmaximal, characteristic
11#461×C73C211yesmaximal, characteristic, complemented
12C2×#11924018C2212yes—
13C2×#11924018C2212yes—
14C2×#11924017C2212yes—
15C2×#11924013C2211yescharacteristic
16#14556591C2211yescharacteristic
17#14556586—22no—
18#14556584—22no—
19#14556580C2212yes—
20#14556578C2212yes—
21#14556571—21no—
22#14556570—21no—
23Q8×Dic73C2212yes—
24C4×Dic146C2211yescharacteristic
25#14556556C2212yes—
26C4×D292C2211yescharacteristic
27#14556550—21no—
28#14556549—21no—
29#14556524C2211yescharacteristic
30#14556520C2212yes—
31#14556516C2212yes—
32#14556512C2211yescharacteristic
33#14556511C2211yescharacteristic
34C4×#10596831C2211yescharacteristic
35C8×Dic73C2212yes—
36C2×SD16×C73C2212yes—
37C4⋊Q8×C73C2211yescharacteristic
38C4×D4×C73C2211yescharacteristic
39C4⋊C8×C73C2211yescharacteristic
40#103×C73C2212yes—
41C2×Dic146D411yescharacteristic
42C2×Dic146C2312yes—
43C2×D292C2311yescharacteristic
44C2×C4×D73—21no—
45#11924018—24no—
46#11924018—42no—
47#11924017—42no—
48#11924013—22no—
49C2×#10596831C2311yescharacteristic
50C2×#10596831C2311yescharacteristic
51C4⋊Dic73—21no—
52C4⋊Dic73—21no—
53C4⋊Dic73—22no—
54C4⋊Dic73D411yescharacteristic
55C4⋊Dic73C2311yescharacteristic
56#11924007—22no—
57#11924007D412yes—
58C22⋊Dic73—22no—
59C22⋊Dic73—22no—
60#11924005—21no—
61#11924005—22no—
62#11924005—22no—
63C4×Dic73—22no—
64C4×Dic73—22no—
65C4×Dic73C2312yes—
66C2×Q8×C73C2312yes—
67C2×D4×C73C2311yescharacteristic
68C22×C4×C73—21no—
69SD16×C73—42no—
70C2×C8×C73C2312yes—
71C4⋊C4×C73—21no—
72C4⋊C4×C73—21no—
73C4⋊C4×C73C2311yescharacteristic
74C22⋊C4×C73—21no—
75C42×C73C2311yescharacteristic
76C23×C73—21no—
77C22×D73—21no—
78Q8×C73—22no—
79Q8×C73—22no—
80D4×C73—21no—
81D4×C73—21no—
82C2×C4×C73—21no—
83C2×C4×C73—22no—
84C2×C4×C73—42no—
85C2×C4×C73C2×D411yescharacteristic
86C2×C4×C73C2×D411yescharacteristic
87C2×C4×C73C2411yescharacteristic
88C2×Dic73—21no—
89C2×Dic73—22no—
90C2×Dic73C2×D412yes—
91C2×Dic73C2×D412yes—
92D292—21no—
93D292—21no—
94C4×D73—42no—
95Dic146—22no—
96Dic146—22no—
97Dic146—22no—
98C8×C73—22no—
99#10596831—21no—
100#10596831#4112yes—
101C22×C73—41no—
102C22×C73—41no—
103C22×C73—41no—
104C22×C73C22×D411yescharacteristic
105C2×D73—41no—
106C2×D73—41no—
107C2×D73—41no—
108C4×C73—21no—
109C4×C73—42no—
110C4×C73—41no—
111C4×C73#13512yes—
112C4×C73C2×#4111yescharacteristic
113C4×C73H(5,𝔽2)11yescharacteristic
114Dic73—22no—
115Dic73—22no—
116Dic73—42no—
117Dic73—41no—
118C2×C73—81no—
119C2×C73#55011yescharacteristic
120C2×C73C2×#13511yescharacteristic
121C2×C73#57811yescharacteristic
122D73—81no—
123#3393—731nomaximal, Sylow
124C73#339311yescharacteristic, complemented, Sylow
125#556—731no—
126#556—731no—
127#495—732no—
128#494—731no—
129#464—732no—
130#464—732no—
131#461—731no—
132#461D7311yescharacteristic, complemented
133C8×Q8—731no—
134C4×Q16—732no—
135C4×D8—731no—
136C2×Q16—732no—
137C2×Q16—732no—
138C2×SD16—732no—
139C2×SD16C2×D7312yes—
140C2×D8—731no—
141C4⋊Q8—731no—
142C4⋊Q8C2×D7311yescharacteristic
143#126—1462no—
144#126—1462no—
145#124—732no—
146#124—732no—
147C22⋊Q8—1461no—
148C22⋊Q8—1461no—
149C4×Q8—731no—
150C4×Q8—732no—
151C4×Q8—732no—
152C4×D4—731no—
153C4×D4C2×D7311yescharacteristic
154#117—1461no—
155#117—1461no—
156#107—731no—
157C4⋊C8—732no—
158C4⋊C8C2×D7311yescharacteristic
159#103—732no—
160#103C2×D7312yes—
161#102—731no—
162#102—731no—
163C4×C8—732no—
164C4×C8—731no—
165C2×Q8—731no—
166C2×Q8—732no—
167C2×Q8C22×D7312yes—
168C2×D4—731no—
169C2×D4C22×D7311yescharacteristic
170C22×C4—21no—
171C22×C4—1461no—
172Q16—2922no—
173Q16—1464no—
174SD16—42no—
175SD16—2922no—
176D8—1462no—
177C2×C8—731no—
178C2×C8—731no—
179C2×C8C22×D7312yes—
180C4⋊C4—21no—
181C4⋊C4—21no—
182C4⋊C4—732no—
183C4⋊C4—731no—
184C4⋊C4—731no—
185C4⋊C4—1462no—
186C4⋊C4—1462no—
187C4⋊C4—1461no—
188C4⋊C4—1461no—
189C4⋊C4C22×D7311yescharacteristic
190C22⋊C4—21no—
191C22⋊C4—1462no—
192C22⋊C4—1462no—
193C22⋊C4—1462no—
194C22⋊C4—1462no—
195C22⋊C4—1461no—
196C42—732no—
197C42—1462no—
198C42—1462no—
199C42C22×D7311yescharacteristic
200C23—21no—
201C23—1461no—
202Q8—22no—
203Q8—22no—
204Q8—1462no—
205Q8—1462no—
206Q8—1462no—
207D4—21no—
208D4—21no—
209D4—1461no—
210D4—1461no—
211C2×C4—21no—
212C2×C4—22no—
213C2×C4—42no—
214C2×C4—2922no—
215C2×C4—732no—
216C2×C4—732no—
217C2×C4—1461no—
218C2×C4—1462no—
219C2×C4D4×D7311yescharacteristic
220C2×C4D4×D7311yescharacteristic
221C2×C4C23×D7311yescharacteristic
222C8—22no—
223C8—732no—
224C8—1461no—
225C22—41no—
226C22—41no—
227C22—41no—
228C22—2921no—
229C22—2921no—
230C22—2921no—
231C22C2×D4×D7311yescharacteristic
232C4—21no—
233C4—42no—
234C4—41no—
235C4—2922no—
236C4—2921no—
237C4—1462no—
238C4—1462no—
239C4#1455661212yes—
240C4#41×D7311yescharacteristic
241C4#1455663611yescharacteristic
242C2—81no—
243C2—5841no—
244C2#1798925511yescharacteristic
245C2C2×#1455661211yescharacteristic
246C2#1798940311yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#461×C73C2
socleC22×C73C22×D4
hypercenter#461D73
hypocenterC73#3393
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. #17989311C2semidirect
2. #17989307C2semidirect
4. #17988966C2semidirect
5. #17988812C2semidirect
6. #17988807C2semidirect
7. #17988793C2semidirect
8. #17988711C2semidirect
9. #17988679C2semidirect
11. #461×C73C2semidirect
124. C73#3393semidirect
132. #461D73semidirect