Finite Group Databasebeta

← #22622958

Subgroups — #22622958

Order 9344.

350 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 123 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#17989310C211yesmaximal, characteristic
2#17988979C212yesmaximal
3#17988966C211yesmaximal, characteristic, complemented
4#17988809C212yesmaximal
5#17988797C211yesmaximal, characteristic, complemented
6#17988794C212yesmaximal, complemented
7#17988789C211yesmaximal, characteristic
8#17988718C211yesmaximal, characteristic, complemented
9#17988692C212yesmaximal, complemented
10C4×#11924015C211yesmaximal, characteristic
11#557×C73C211yesmaximal, characteristic, complemented
12C2×#11924018C2212yes—
13C2×#11924018C2212yes—
14C2×#11924018C2212yes—
15C2×#11924015C2211yescharacteristic
16C2×#11924015C2212yes—
17#14556591C2211yescharacteristic
18#14556586—22no—
19#14556579C2212yes—
20#14556567—21no—
21C4×Dic146C2212yes—
22C4×D292C2211yescharacteristic
23#14556549—21no—
24#14556522C2211yescharacteristic
25C4⋊#10596831C2211yescharacteristic
26C4⋊#10596831C2212yes—
27#14556515C2211yescharacteristic
28#14556515C2212yes—
29#14556514C2212yes—
30#14556511C2211yescharacteristic
31#14556502C2212yes—
32C4×#10596831C2211yescharacteristic
33C4⋊Q8×C73C2211yescharacteristic
34C4⋊Q8×C73C2212yes—
35#125×C73—21no—
36#125×C73—22no—
37C4×Q8×C73—21no—
38C4×Q8×C73C2211yescharacteristic
39C4×Q8×C73C2212yes—
40C4×Q8×C73C2211yescharacteristic
41C2×Dic146C2312yes—
42C2×D292C2311yescharacteristic
43C2×C4×D73—21no—
44#11924018—24no—
45#11924018—42no—
46#11924018—42no—
47#11924015—22no—
48#11924015—42no—
49C2×#10596831C2311yescharacteristic
50C2×#10596831C2312yes—
51C2×#10596831C2311yescharacteristic
52C4⋊Dic73—21no—
53C4⋊Dic73—21no—
54C4⋊Dic73C2311yescharacteristic
55#11924007—22no—
56#11924005—22no—
57#11924005—21no—
58#11924005—22no—
59C4×Dic73—22no—
60C2×Q8×C73D411yescharacteristic
61C2×Q8×C73C2311yescharacteristic
62C2×Q8×C73C2312yes—
63C4⋊C4×C73—22no—
64C4⋊C4×C73—21no—
65C4⋊C4×C73—22no—
66C4⋊C4×C73—21no—
67C4⋊C4×C73—22no—
68C4⋊C4×C73—21no—
69C4⋊C4×C73D411yescharacteristic
70C4⋊C4×C73D412yes—
71C4⋊C4×C73C2311yescharacteristic
72C42×C73—22no—
73C42×C73—21no—
74C42×C73C2311yescharacteristic
75C42×C73C2312yes—
76C22×D73—21no—
77Q8×C73—22no—
78Q8×C73—21no—
79Q8×C73—22no—
80Q8×C73—22no—
81Q8×C73—21no—
82C2×C4×C73—21no—
83C2×C4×C73—21no—
84C2×C4×C73—22no—
85C2×C4×C73C2×D412yes—
86C2×C4×C73C2×D412yes—
87C2×C4×C73C2×D411yescharacteristic
88C2×C4×C73C2×D411yescharacteristic
89C2×C4×C73C2411yescharacteristic
90C2×Dic73—21no—
91C2×Dic73—22no—
92D292—21no—
93D292—21no—
94C4×D73—42no—
95Dic146—22no—
96Dic146—22no—
97#10596831—22no—
98#10596831—21no—
99#10596831#4112yes—
100C22×C73C22×D411yescharacteristic
101C2×D73—41no—
102C2×D73—41no—
103C2×D73—41no—
104C4×C73—22no—
105C4×C73—22no—
106C4×C73—21no—
107C4×C73—41no—
108C4×C73—42no—
109C4×C73—41no—
110C4×C73#13712yes—
111C4×C73C2×#4111yescharacteristic
112C4×C73H(5,𝔽2)11yescharacteristic
113Dic73—42no—
114Dic73—41no—
115C2×C73#55011yescharacteristic
116C2×C73C2×#13711yescharacteristic
117C2×C73#57811yescharacteristic
118D73—81no—
119#3398—731nomaximal, Sylow
120C73#339811yescharacteristic, complemented, Sylow
121#557D7311yescharacteristic, complemented
122#556—731no—
123#497—732no—
124#494—731no—
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×Q16—732no—
134C2×Q16—732no—
135C2×SD16—732no—
136C2×SD16—731no—
137C4⋊Q8—731no—
138C4⋊Q8C2×D7311yescharacteristic
139C4⋊Q8C2×D7312yes—
140#126—1462no—
141#125—21no—
142#125—22no—
143#124—732no—
144C22⋊Q8—1461no—
145C4×Q8—21no—
146C4×Q8—732no—
147C4×Q8C2×D7311yescharacteristic
148C4×Q8C2×D7312yes—
149C4×Q8C2×D7311yescharacteristic
150C4×D4—731no—
151#117—1461no—
152#106—731no—
153C4⋊C8—731no—
154C4⋊C8—732no—
155#103—731no—
156#103—732no—
157#103—732no—
158#102—731no—
159#97—732no—
160C4×C8—731no—
161C2×Q8—732no—
162C2×Q8C22⋊D7311yescharacteristic
163C2×Q8C22×D7311yescharacteristic
164C2×Q8C22×D7312yes—
165C2×D4—731no—
166C22×C4—1461no—
167Q16—2922no—
168Q16—2922no—
169Q16—1464no—
170SD16—2922no—
171SD16—1462no—
172C2×C8—731no—
173C2×C8—731no—
174C2×C8—732no—
175C4⋊C4—22no—
176C4⋊C4—21no—
177C4⋊C4—22no—
178C4⋊C4—21no—
179C4⋊C4—22no—
180C4⋊C4—21no—
181C4⋊C4—731no—
182C4⋊C4—1462no—
183C4⋊C4—1461no—
184C4⋊C4—1461no—
185C4⋊C4C22⋊D7311yescharacteristic
186C4⋊C4C22⋊D7312yes—
187C4⋊C4C22×D7311yescharacteristic
188C22⋊C4—1462no—
189C22⋊C4—1461no—
190C22⋊C4—1462no—
191C42—22no—
192C42—21no—
193C42—1462no—
194C42C22×D7311yescharacteristic
195C42C22×D7312yes—
196C23—1461no—
197Q8—22no—
198Q8—21no—
199Q8—22no—
200Q8—22no—
201Q8—21no—
202Q8—1462no—
203Q8—1462no—
204D4—1461no—
205D4—1461no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—22no—
209C2×C4—2922no—
210C2×C4—1461no—
211C2×C4—1462no—
212C2×C4C2×C22⋊D7312yes—
213C2×C4C2×C22⋊D7312yes—
214C2×C4C2×C22⋊D7311yescharacteristic
215C2×C4C2×C22⋊D7311yescharacteristic
216C2×C4C23×D7311yescharacteristic
217C8—732no—
218C8—1462no—
219C8—1461no—
220C22—2921no—
221C22—2921no—
222C22—2921no—
223C22C22×C22⋊D7311yescharacteristic
224C4—22no—
225C4—22no—
226C4—21no—
227C4—41no—
228C4—41no—
229C4—42no—
230C4—2921no—
231C4—2922no—
232C4#1455662212yes—
233C4#41×D7311yescharacteristic
234C4#1455663711yescharacteristic
235C2—5841no—
236C2#1798925611yescharacteristic
237C2C2×#1455662211yescharacteristic
238C2#1798940211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#557×C73C2
socleC22×C73C22×D4
hypercenter#557D73
hypocenterC73#3398
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #557

Complements

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

NH ≅ G/Ntype
3. #17988966C2semidirect
5. #17988797C2semidirect
6. #17988794C2semidirect
8. #17988718C2semidirect
9. #17988692C2semidirect
11. #557×C73C2semidirect
120. C73#3398semidirect
121. #557D73semidirect