Finite Group Databasebeta

← #22622966

Subgroups — #22622966

Order 9344.

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

normal subgroups only

This group has 350 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#17989312C211yesmaximal, characteristic, complemented
2#17989307C211yesmaximal, characteristic
3#17988978C212yesmaximal
4#17988966C211yesmaximal, characteristic, complemented
5#17988807C212yesmaximal
6#17988798C211yesmaximal, characteristic, complemented
7#17988796C212yesmaximal, complemented
8#17988714C211yesmaximal, characteristic, complemented
9#17988691C212yesmaximal, complemented
10C4×#11924016C211yesmaximal, characteristic
11#461×C73C211yesmaximal, characteristic
12C2×Dic292C2212yes—
13C2×#11924018C2212yes—
14C2×#11924018C2212yes—
15C2×#11924016C2211yescharacteristic
16#14556591C2211yescharacteristic
17#14556589C2212yes—
18#14556584—22no—
19#14556582—21no—
20#14556581—22no—
21#14556578C2212yes—
22#14556570—21no—
23Q8×Dic73C2212yes—
24C4×Dic146C2211yescharacteristic
25C4×Dic146C2211yescharacteristic
26#14556556—21no—
27#14556556C2212yes—
28#14556550—21no—
29#14556522C2211yescharacteristic
30#14556520C2212yes—
31#14556516C2212yes—
32#14556514C2211yescharacteristic
33#14556512C2211yescharacteristic
34#14556501C2212yes—
35C4×#10596831C2211yescharacteristic
36C2×SD16×C73C2212yes—
37C4⋊Q8×C73C2211yescharacteristic
38C4×D4×C73C2211yescharacteristic
39C4⋊C8×C73C2211yescharacteristic
40#103×C73C2212yes—
41C2×Dic146D411yescharacteristic
42C2×Dic146C2311yescharacteristic
43C2×Dic146C2312yes—
44Dic292—42no—
45#11924018—24no—
46#11924018—42no—
47#11924016—22no—
48C2×#10596831C2311yescharacteristic
49C2×#10596831C2311yescharacteristic
50C4⋊Dic73—21no—
51C4⋊Dic73—21no—
52C4⋊Dic73—22no—
53C4⋊Dic73D411yescharacteristic
54C4⋊Dic73C2311yescharacteristic
55#11924007—21no—
56#11924007—22no—
57#11924007—22no—
58#11924007—22no—
59#11924007D412yes—
60C22⋊Dic73—22no—
61C22⋊Dic73—22no—
62C4×Dic73—21no—
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—
77Q8×C73—22no—
78Q8×C73—22no—
79D4×C73—21no—
80D4×C73—21no—
81C2×C4×C73—21no—
82C2×C4×C73—22no—
83C2×C4×C73—42no—
84C2×C4×C73C2×D411yescharacteristic
85C2×C4×C73C2×D411yescharacteristic
86C2×C4×C73C2411yescharacteristic
87C2×Dic73—21no—
88C2×Dic73—22no—
89C2×Dic73—21no—
90C2×Dic73C2×D412yes—
91C2×Dic73C2×D412yes—
92Dic146—22no—
93Dic146—21no—
94Dic146—22no—
95Dic146—22no—
96Dic146—21no—
97C8×C73—22no—
98#10596831—21no—
99#10596831#4112yes—
100C22×C73—41no—
101C22×C73—41no—
102C22×C73—41no—
103C22×C73C22×D411yescharacteristic
104C4×C73—21no—
105C4×C73—42no—
106C4×C73—41no—
107C4×C73#13712yes—
108C4×C73C2×#4111yescharacteristic
109C4×C73H(5,𝔽2)11yescharacteristic
110Dic73—22no—
111Dic73—22no—
112Dic73—41no—
113Dic73—42no—
114Dic73—41no—
115C2×C73—81no—
116C2×C73#55011yescharacteristic
117C2×C73C2×#13711yescharacteristic
118C2×C73#57811yescharacteristic
119#3398—731nomaximal, Sylow
120C73#339811yescharacteristic, complemented, Sylow
121#557—731no—
122#556—731no—
123#497—732no—
124#494—731no—
125#464—732no—
126#462—731no—
127#462—732no—
128#461D7311yescharacteristic
129#446—731no—
130#441—732no—
131C4×SD16—731no—
132C2×Q16—732no—
133C2×Q16—732no—
134C2×Q16—732no—
135C2×SD16—731no—
136C2×SD16C2×D7312yes—
137C4⋊Q8—732no—
138C4⋊Q8—731no—
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×D4C2×D7311yescharacteristic
151#117—1461no—
152#106—731no—
153C4⋊C8—732no—
154C4⋊C8C2×D7311yescharacteristic
155#103—732no—
156#103—731no—
157#103C2×D7312yes—
158#102—731no—
159#97—732no—
160C4×C8—731no—
161C2×Q8—731no—
162C2×Q8—732no—
163C2×Q8—731no—
164C2×Q8C22×D7312yes—
165C2×D4C22×D7311yescharacteristic
166C22×C4—21no—
167Q16—2922no—
168Q16—2922no—
169Q16—1464no—
170SD16—42no—
171SD16—1462no—
172C2×C8—731no—
173C2×C8—731no—
174C2×C8C22×D7312yes—
175C4⋊C4—21no—
176C4⋊C4—21no—
177C4⋊C4—732no—
178C4⋊C4—731no—
179C4⋊C4—731no—
180C4⋊C4—1462no—
181C4⋊C4—1462no—
182C4⋊C4—1462no—
183C4⋊C4—1462no—
184C4⋊C4—1461no—
185C4⋊C4—1461no—
186C4⋊C4—1461no—
187C4⋊C4C22×D7311yescharacteristic
188C22⋊C4—21no—
189C22⋊C4—1462no—
190C22⋊C4—1462no—
191C42—732no—
192C42—1462no—
193C42—1462no—
194C42—1461no—
195C42C22×D7311yescharacteristic
196C23—21no—
197Q8—22no—
198Q8—22no—
199Q8—1461no—
200Q8—1462no—
201Q8—1461no—
202Q8—1462no—
203Q8—1462no—
204D4—21no—
205D4—21no—
206C2×C4—21no—
207C2×C4—22no—
208C2×C4—42no—
209C2×C4—732no—
210C2×C4—732no—
211C2×C4—1461no—
212C2×C4—1462no—
213C2×C4—1461no—
214C2×C4D4×D7311yescharacteristic
215C2×C4D4×D7311yescharacteristic
216C2×C4C23×D7311yescharacteristic
217C8—22no—
218C8—732no—
219C8—1461no—
220C22—41no—
221C22—41no—
222C22—41no—
223C22C2×D4×D7311yescharacteristic
224C4—21no—
225C4—41no—
226C4—42no—
227C4—2921no—
228C4—2922no—
229C4—2921no—
230C4—1462no—
231C4—1462no—
232C4#1455662012yes—
233C4#41×D7311yescharacteristic
234C4#1455663611yescharacteristic
235C2—81no—
236C2#1798925511yescharacteristic
237C2C2×#1455662011yescharacteristic
238C2#1798940311yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#461×C73C2
socleC22×C73C22×D4
hypercenter#461D73
hypocenterC73#3398
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. #17989312C2semidirect
4. #17988966C2semidirect
6. #17988798C2semidirect
7. #17988796C2semidirect
8. #17988714C2semidirect
9. #17988691C2semidirect
120. C73#3398semidirect