Finite Group Databasebeta

← #22611027

Subgroups — #22611027

Order 9344.

390 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 89 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
1C22×Dic292C211yesmaximal, characteristic, complemented
2C22×#11924016C211yesmaximal, characteristic
3C2×#14556578C211yesmaximal, characteristic
4C2×#14556514C211yesmaximal, characteristic, complemented
5#17988492C211yesmaximal, characteristic, complemented
6#17988341C211yesmaximal, characteristic, complemented
7C2×#102×C73C211yesmaximal, characteristic
8C22×Dic146C2211yescharacteristic
9C22×Dic146C2211yescharacteristic
10C2×Dic292—22no—
11C2×Dic292—22no—
12C2×Dic292—22no—
13C2×#11924016—22no—
14C2×#11924016—22no—
15C2×#11924016—22no—
16C22×#10596831C2211yescharacteristic
17#14556578—22no—
18#14556578—22no—
19C2×C22⋊Dic73—22no—
20C2×C4×Dic73C2211yescharacteristic
21#14556514—22no—
22#14556498—22no—
23C22×D4×C73C2211yescharacteristic
24C22×C8×C73C2211yescharacteristic
25C2×C4⋊C4×C73C2211yescharacteristic
26#102×C73—22no—
27C2×Dic146—21no—
28C2×Dic146—21no—
29C2×Dic146—21no—
30C2×Dic146—21no—
31C2×Dic146—21no—
32C2×Dic146—21no—
33C2×Dic146—21no—
34C2×Dic146—21no—
35C2×Dic146—21no—
36C2×Dic146—21no—
37C2×Dic146D412yes—
38C2×Dic146D412yes—
39C22×Dic73—21no—
40C22×Dic73—21no—
41C22×Dic73D412yes—
42Dic292—28no—
43#11924016—28no—
44C2×#10596831—21no—
45C2×#10596831—21no—
46C2×#10596831D412yes—
47C22⋊Dic73—28no—
48C4×Dic73—21no—
49C4×Dic73—21no—
50C24×C73—21no—
51C2×D4×C73—21no—
52C2×D4×C73—21no—
53C2×D4×C73—21no—
54C2×D4×C73—21no—
55C2×D4×C73—21no—
56C2×D4×C73D412yes—
57C22×C4×C73—21no—
58C22×C4×C73C2311yescharacteristic
59C2×C8×C73—21no—
60C2×C8×C73—21no—
61C2×C8×C73D412yes—
62C4⋊C4×C73—21no—
63C4⋊C4×C73—21no—
64C23×C73—22no—
65C23×C73—41no—
66C23×C73—41no—
67C23×C73—42no—
68C23×C73—42no—
69C23×C73C2×D411yescharacteristic
70D4×C73—22no—
71D4×C73—22no—
72D4×C73—41no—
73D4×C73—41no—
74C2×C4×C73—41no—
75C2×C4×C73—42no—
76C2×C4×C73C2×D411yescharacteristic
77C2×C4×C73C2×D411yescharacteristic
78C2×C4×C73C2×D411yescharacteristic
79C2×C4×C73C2×D411yescharacteristic
80C2×C4×C73C2×D411yescharacteristic
81C2×C4×C73#4111yescharacteristic
82C2×Dic73—22no—
83C2×Dic73—22no—
84C2×Dic73—22no—
85C2×Dic73—22no—
86C2×Dic73—22no—
87C2×Dic73—41no—
88C2×Dic73—41no—
89C2×Dic73—41no—
90C2×Dic73—41no—
91Dic146—22no—
92Dic146—22no—
93Dic146—22no—
94Dic146—22no—
95Dic146—41no—
96Dic146—41no—
97Dic146—41no—
98Dic146—41no—
99C8×C73—22no—
100#10596831—22no—
101C22×C73—42no—
102C22×C73—44no—
103C22×C73—82no—
104C22×C73—81no—
105C22×C73—81no—
106C22×C73#12011yescharacteristic
107C22×C73#12111yescharacteristic
108C22×C73#12711yescharacteristic
109C22×C73#13512yes—
110C22×C73#13712yes—
111C4×C73—81no—
112C4×C73#12011yescharacteristic
113C4×C73#12011yescharacteristic
114C4×C73#12111yescharacteristic
115C4×C73#12111yescharacteristic
116Dic73—42no—
117Dic73—42no—
118Dic73—42no—
119C2×C73—82no—
120C2×C73#39211yescharacteristic
121C2×C73#45212yes—
122C2×C73#46412yes—
123C2×C73#49511yescharacteristic
124C2×C73#49711yescharacteristic
125#2015—731nomaximal, Sylow
126C73#201511yescharacteristic, complemented, Sylow
127C22×Q16—731no—
128C22×SD16—731no—
129C2×#124—731no—
130C2×#103—731no—
131C2×#102D7311yescharacteristic
132#391—731no—
133#336—731no—
134C22×Q8—731no—
135C22×Q8—731no—
136C22×D4C2×D7311yescharacteristic
137C2×Q16—1462no—
138C2×Q16—1462no—
139C2×Q16—1462no—
140C2×SD16—1462no—
141C2×SD16—1462no—
142C2×SD16—1462no—
143C22×C8—731no—
144C22×C8C2×D7311yescharacteristic
145#124—1462no—
146#124—1462no—
147C2×C4⋊C4C2×D7311yescharacteristic
148C2×C22⋊C4—1462no—
149C2×C42—731no—
150#103—1462no—
151#102—22no—
152#95—1462no—
153C24—21no—
154C2×Q8—732no—
155C2×Q8—732no—
156C2×Q8—1461no—
157C2×Q8—1461no—
158C2×Q8—1461no—
159C2×Q8—1461no—
160C2×Q8—1461no—
161C2×Q8—1461no—
162C2×Q8—1461no—
163C2×Q8—1461no—
164C2×Q8—1461no—
165C2×Q8—1461no—
166C2×D4—21no—
167C2×D4—21no—
168C2×D4—21no—
169C2×D4—21no—
170C2×D4—21no—
171C2×D4D29212yes—
172C22×C4—21no—
173C22×C4—732no—
174C22×C4—1461no—
175C22×C4—1461no—
176C22×C4C22×D7311yescharacteristic
177Q16—1468no—
178SD16—1468no—
179C2×C8—21no—
180C2×C8—21no—
181C2×C8—732no—
182C2×C8—1461no—
183C2×C8—1461no—
184C2×C8C22⋊D7312yes—
185C4⋊C4—21no—
186C4⋊C4—21no—
187C22⋊C4—1468no—
188C42—1461no—
189C42—1461no—
190C23—22no—
191C23—41no—
192C23—41no—
193C23—42no—
194C23—42no—
195C23D4×D7311yescharacteristic
196Q8—2921no—
197Q8—2921no—
198Q8—2921no—
199Q8—2921no—
200Q8—1462no—
201Q8—1462no—
202Q8—1462no—
203Q8—1462no—
204D4—22no—
205D4—22no—
206D4—41no—
207D4—41no—
208C2×C4—41no—
209C2×C4—42no—
210C2×C4—2921no—
211C2×C4—2921no—
212C2×C4—2921no—
213C2×C4—2921no—
214C2×C4—1462no—
215C2×C4—1462no—
216C2×C4—1462no—
217C2×C4—1462no—
218C2×C4—1462no—
219C2×C4D4×D7311yescharacteristic
220C2×C4D4×D7311yescharacteristic
221C2×C4D4×D7311yescharacteristic
222C2×C4C2×C22⋊D7311yescharacteristic
223C2×C4C2×D29211yescharacteristic
224C2×C4#1192402811yescharacteristic
225C8—22no—
226C8—1462no—
227C22—44no—
228C22—42no—
229C22—81no—
230C22—81no—
231C22—82no—
232C22#1455656111yescharacteristic
233C22#1455656411yescharacteristic
234C22#1455658711yescharacteristic
235C22#1455661012yes—
236C22#1455662012yes—
237C4—81no—
238C4—2922no—
239C4—2922no—
240C4—2922no—
241C4#1455655911yescharacteristic
242C4#1455656111yescharacteristic
243C4#1455656411yescharacteristic
244C4#1455656511yescharacteristic
245C2—82no—
246C2#1798849611yescharacteristic
247C2#1798875012yes—
248C2#1798880812yes—
249C2#1798897011yescharacteristic
250C2#1798897811yescharacteristic
subgroupG/H
centerC23D4×D73
commutatorC22×C4×C73C23
FrattiniC22×C4C22×D73
FittingC2×#102×C73C2
socleC23×C73C2×D4
hypercenterC2×#102D73
hypocenterC73#2015
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. C22×Dic292C2semidirect
4. C2×#14556514C2semidirect
5. #17988492C2semidirect
6. #17988341C2semidirect
126. C73#2015semidirect