Finite Group Databasebeta

← #22622967

Subgroups — #22622967

Order 9344.

350 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 117 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#17989312C211yesmaximal, characteristic, complemented
2#17989311C211yesmaximal, characteristic
3#17988980C212yesmaximal
4#17988811C212yesmaximal
5#17988795C212yesmaximal, complemented
6#17988794C211yesmaximal, characteristic, complemented
7#17988789C211yesmaximal, characteristic
8#17988717C211yesmaximal, characteristic, complemented
9#17988694C212yesmaximal, complemented
10C4×#11924017C211yesmaximal, characteristic
11#494×C73C211yesmaximal, characteristic, complemented
12C2×#11924018C2212yes—
13C2×#11924017C2211yescharacteristic
14C2×#11924015C2212yes—
15#14556589C2212yes—
16#14556586—22no—
17#14556582—21no—
18#14556581—22no—
19#14556580C2212yes—
20#14556571—21no—
21Q8×Dic73C2212yes—
22Q8×Dic73C2212yes—
23C4×Dic146C2211yescharacteristic
24C4×Dic146C2211yescharacteristic
25#14556556—21no—
26C4×D292C2211yescharacteristic
27#14556549—21no—
28#14556523C2211yescharacteristic
29C4⋊#10596831C2211yescharacteristic
30#14556520C2212yes—
31#14556516C2211yescharacteristic
32#14556515C2212yes—
33#14556515C2212yes—
34#14556513C2211yescharacteristic
35#14556501C2212yes—
36C2×Q16×C73C2212yes—
37C2×Q16×C73C2212yes—
38C4⋊Q8×C73C2211yescharacteristic
39C4⋊Q8×C73C2211yescharacteristic
40C4×C8×C73C2211yescharacteristic
41C2×Dic146D411yescharacteristic
42C2×Dic146C2311yescharacteristic
43C2×D292C2311yescharacteristic
44C2×C4×D73—21no—
45#11924018—42no—
46#11924017—22no—
47#11924015—42no—
48C2×#10596831C2312yes—
49C4⋊Dic73—22no—
50C4⋊Dic73—22no—
51C4⋊Dic73D411yescharacteristic
52C4⋊Dic73C2311yescharacteristic
53C4⋊Dic73C2311yescharacteristic
54#11924007—21no—
55#11924007—22no—
56#11924007—22no—
57#11924007D412yes—
58#11924005—21no—
59#11924005—22no—
60#11924005—22no—
61C4×Dic73—21no—
62C4×Dic73—22no—
63C4×Dic73—22no—
64C4×Dic73C2312yes—
65C2×Q8×C73C2312yes—
66C2×Q8×C73C2312yes—
67Q16×C73—24no—
68Q16×C73—42no—
69C2×C8×C73C2311yescharacteristic
70C2×C8×C73C2311yescharacteristic
71C4⋊C4×C73—21no—
72C4⋊C4×C73—21no—
73C4⋊C4×C73—21no—
74C4⋊C4×C73—21no—
75C42×C73C2311yescharacteristic
76C22×D73—21no—
77Q8×C73—22no—
78Q8×C73—22no—
79Q8×C73—22no—
80Q8×C73—22no—
81C2×C4×C73—22no—
82C2×C4×C73—22no—
83C2×C4×C73C2×D411yescharacteristic
84C2×C4×C73C2×D411yescharacteristic
85C2×C4×C73C2411yescharacteristic
86C2×Dic73—21no—
87C2×Dic73—21no—
88C2×Dic73—21no—
89C2×Dic73C2×D412yes—
90C2×Dic73C2×D412yes—
91D292—21no—
92D292—21no—
93C4×D73—42no—
94Dic146—22no—
95Dic146—21no—
96Dic146—21no—
97C8×C73—21no—
98C8×C73#4112yes—
99#10596831—22no—
100C22×C73C22×D411yescharacteristic
101C2×D73—41no—
102C2×D73—41no—
103C2×D73—41no—
104C4×C73—21no—
105C4×C73—42no—
106C4×C73—42no—
107C4×C73#13712yes—
108C4×C73C2×#4111yescharacteristic
109C4×C73H(5,𝔽2)11yescharacteristic
110Dic73—22no—
111Dic73—22no—
112Dic73—41no—
113Dic73—41no—
114Dic73—41no—
115C2×C73#55011yescharacteristic
116C2×C73C2×#13711yescharacteristic
117C2×C73#57811yescharacteristic
118D73—81no—
119#3398—731nomaximal, Sylow
120C73#339811yescharacteristic, complemented, Sylow
121#557—731no—
122#556—731no—
123#497—732no—
124#494D7311yescharacteristic, complemented
125#464—732no—
126#462—732no—
127#462—731no—
128#461—731no—
129#446—731no—
130#441—732no—
131C4×SD16—731no—
132C2×Q16—732no—
133C2×Q16C2×D7312yes—
134C2×Q16C2×D7312yes—
135C2×SD16—732no—
136C2×SD16—731no—
137C4⋊Q8—732no—
138C4⋊Q8C2×D7311yescharacteristic
139C4⋊Q8C2×D7311yescharacteristic
140#126—1462no—
141#125—1462no—
142#125—1461no—
143#124—732no—
144C22⋊Q8—1461no—
145C4×Q8—731no—
146C4×Q8—732no—
147C4×Q8—732no—
148C4×Q8—731no—
149C4×Q8—1461no—
150C4×D4—731no—
151#117—1461no—
152#106—731no—
153C4⋊C8—732no—
154C4⋊C8—731no—
155#103—732no—
156#103—732no—
157#103—731no—
158#102—731no—
159#97—732no—
160C4×C8C2×D7311yescharacteristic
161C2×Q8—731no—
162C2×Q8—731no—
163C2×Q8C22×D7312yes—
164C2×Q8C22×D7312yes—
165C2×D4—731no—
166C22×C4—1461no—
167Q16—24no—
168Q16—42no—
169Q16—2922no—
170SD16—2922no—
171SD16—1462no—
172C2×C8—732no—
173C2×C8C22×D7311yescharacteristic
174C2×C8C22×D7311yescharacteristic
175C4⋊C4—21no—
176C4⋊C4—21no—
177C4⋊C4—21no—
178C4⋊C4—21no—
179C4⋊C4—732no—
180C4⋊C4—731no—
181C4⋊C4—731no—
182C4⋊C4—731no—
183C4⋊C4—1462no—
184C4⋊C4—1462no—
185C4⋊C4—1462no—
186C4⋊C4—1462no—
187C4⋊C4—1461no—
188C22⋊C4—1462no—
189C22⋊C4—1462no—
190C22⋊C4—1461no—
191C42—732no—
192C42—1462no—
193C42—1462no—
194C42—1461no—
195C42C22×D7311yescharacteristic
196C23—1461no—
197Q8—22no—
198Q8—22no—
199Q8—22no—
200Q8—22no—
201Q8—1461no—
202Q8—1461no—
203Q8—1462no—
204D4—1461no—
205D4—1461no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—2922no—
209C2×C4—732no—
210C2×C4—732no—
211C2×C4—1461no—
212C2×C4—1461no—
213C2×C4—1461no—
214C2×C4D4×D7311yescharacteristic
215C2×C4D4×D7311yescharacteristic
216C2×C4C23×D7311yescharacteristic
217C8—21no—
218C8—1462no—
219C8#1192402712yes—
220C22—2921no—
221C22—2921no—
222C22—2921no—
223C22C2×D4×D7311yescharacteristic
224C4—21no—
225C4—42no—
226C4—42no—
227C4—2921no—
228C4—2921no—
229C4—2921no—
230C4—1462no—
231C4—1462no—
232C4#1455662312yes—
233C4C2×#1192402711yescharacteristic
234C4#1455663611yescharacteristic
235C2—5841no—
236C2#1798925711yescharacteristic
237C2C2×#1455662311yescharacteristic
238C2#1798940011yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#494×C73C2
socleC22×C73C22×D4
hypercenter#494D73
hypocenterC73#3398
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #494

Complements

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

NH ≅ G/Ntype
1. #17989312C2semidirect
5. #17988795C2semidirect
6. #17988794C2semidirect
8. #17988717C2semidirect
9. #17988694C2semidirect
11. #494×C73C2semidirect
120. C73#3398semidirect
124. #494D73semidirect