Finite Group Databasebeta

← #22611046

Subgroups — #22611046

Order 9344.

362 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 73 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
1C2×#14556621C211yesmaximal, characteristic, complemented
2C2×#14556616C211yesmaximal, characteristic
3C22×#11924017C211yesmaximal, characteristic, complemented
4C2×#14556509C211yesmaximal, characteristic, complemented
5C2×#14556507C211yesmaximal, characteristic, complemented
6#17988352C211yesmaximal, characteristic, complemented
7#408×C73C211yesmaximal, characteristic, complemented
8C22×Dic146C2211yescharacteristic
9C22×D292C2211yescharacteristic
10#14556621—22no—
11#14556621—22no—
12#14556616—22no—
13#14556616—22no—
14C2×#11924018—21no—
15C2×#11924017—22no—
16C2×#11924017—22no—
17C2×#11924017—22no—
18C2×#11924016—21no—
19C2×#11924015—21no—
20C2×#11924013—21no—
21C2×#11924012C2211yescharacteristic
22C2×#11924012C2211yescharacteristic
23#14556509—22no—
24#14556507—22no—
25C2×#41×C73C2211yescharacteristic
26C2×M16×C73C2211yescharacteristic
27C22×C8×C73C2211yescharacteristic
28C22⋊C8×C73—22no—
29C23×D73—21no—
30C2×Dic146—21no—
31C2×Dic146—21no—
32C2×Dic146—21no—
33C2×Dic146—21no—
34C2×Dic146—21no—
35C2×Dic146D412yes—
36C2×D292—21no—
37C2×D292—21no—
38C2×D292—21no—
39C2×D292—21no—
40C2×D292—21no—
41C2×D292D412yes—
42C22×Dic73—21no—
43#11924018—24no—
44#11924017—28no—
45#11924016—24no—
46#11924015—24no—
47#11924013—24no—
48#11924012—21no—
49#11924012—21no—
50#11924012D412yes—
51#11924012D412yes—
52C2×#10596831—21no—
53C2×#10596831—21no—
54#41×C73—21no—
55#41×C73—21no—
56#41×C73—21no—
57#41×C73—21no—
58C2×Q8×C73D411yescharacteristic
59C2×D4×C73—21no—
60C2×D4×C73D411yescharacteristic
61C22×C4×C73—21no—
62C22×C4×C73C2311yescharacteristic
63M16×C73—21no—
64M16×C73—21no—
65C2×C8×C73—21no—
66C2×C8×C73—21no—
67C2×C8×C73—21no—
68C2×C8×C73D412yes—
69C23×C73—21no—
70C23×C73#4111yescharacteristic
71C22×D73—22no—
72C22×D73—41no—
73C22×D73—41no—
74C22×D73—82no—
75Q8×C73—21no—
76Q8×C73—21no—
77D4×C73—21no—
78D4×C73—21no—
79D4×C73—41no—
80D4×C73—41no—
81C2×C4×C73—21no—
82C2×C4×C73—41no—
83C2×C4×C73—41no—
84C2×C4×C73C2×D411yescharacteristic
85C2×C4×C73C2×D411yescharacteristic
86C2×C4×C73C2×D411yescharacteristic
87C2×C4×C73C2×D411yescharacteristic
88C2×C4×C73C2×D411yescharacteristic
89C2×C4×C73C2×D411yescharacteristic
90C2×Dic73—22no—
91C2×Dic73—41no—
92C2×Dic73—41no—
93D292—22no—
94D292—22no—
95D292—41no—
96D292—41no—
97Dic146—22no—
98Dic146—22no—
99Dic146—41no—
100Dic146—41no—
101C8×C73—22no—
102C8×C73—41no—
103#10596831—22no—
104#10596831—22no—
105C22×C73—22no—
106C22×C73—41no—
107C22×C73—42no—
108C22×C73#12111yescharacteristic
109C22×C73#12111yescharacteristic
110C22×C73#12111yescharacteristic
111C2×D73—42no—
112C2×D73—82no—
113C2×D73—82no—
114C2×D73—82no—
115C4×C73—41no—
116C4×C73#12011yescharacteristic
117C4×C73#12011yescharacteristic
118C4×C73#12011yescharacteristic
119C4×C73#12711yescharacteristic
120Dic73—42no—
121C2×C73—21no—
122C2×C73—21no—
123C2×C73—81no—
124C2×C73#39211yescharacteristic
125C2×C73#47112yes—
126D73—82no—
127#2019—731nomaximal, Sylow
128C73#201911yescharacteristic, complemented, Sylow
129C2×#137—731no—
130C2×AGL(1,ℤ/8)—731no—
131C22×SD16—731no—
132C2×#101—731no—
133C2×#100—731no—
134#408D7311yescharacteristic, complemented
135#341—731no—
136C2×#41C2×D7311yescharacteristic
137C22×Q8—731no—
138C22×D4—731no—
139#137—1462no—
140#137—1462no—
141AGL(1,ℤ/8)—1462no—
142AGL(1,ℤ/8)—1462no—
143C2×Q16—1461no—
144C2×SD16—1462no—
145C2×SD16—1462no—
146C2×SD16—1461no—
147C2×SD16—1461no—
148C2×SD16—1462no—
149C2×D8—1461no—
150C2×M16—731no—
151C2×M16—731no—
152C2×M16C2×D7311yescharacteristic
153C22×C8C2×D7311yescharacteristic
154#101—1462no—
155#100—1462no—
156C22⋊C8—22no—
157C24—1461no—
158#41—21no—
159#41—21no—
160#41—21no—
161#41—21no—
162C2×Q8—732no—
163C2×Q8—1461no—
164C2×Q8—1461no—
165C2×Q8—1461no—
166C2×Q8—1461no—
167C2×Q8—1461no—
168C2×Q8D29211yescharacteristic
169C2×D4—21no—
170C2×D4—732no—
171C2×D4—1461no—
172C2×D4—1461no—
173C2×D4—1461no—
174C2×D4—1461no—
175C2×D4—1461no—
176C2×D4D29211yescharacteristic
177C22×C4—21no—
178C22×C4—1461no—
179C22×C4C22×D7311yescharacteristic
180Q16—1464no—
181SD16—1468no—
182SD16—1464no—
183SD16—1464no—
184D8—1464no—
185M16—21no—
186M16—21no—
187M16—732no—
188M16—732no—
189M16—1461no—
190M16—1461no—
191C2×C8—21no—
192C2×C8—21no—
193C2×C8—21no—
194C2×C8—1461no—
195C2×C8—1461no—
196C2×C8C22⋊D7312yes—
197C23—21no—
198C23—2921no—
199C23—2921no—
200C23—5842no—
201C23—1462no—
202C23#1192402811yescharacteristic
203Q8—21no—
204Q8—21no—
205Q8—2921no—
206Q8—2921no—
207Q8—1462no—
208Q8—1462no—
209D4—21no—
210D4—21no—
211D4—41no—
212D4—41no—
213D4—2921no—
214D4—2921no—
215D4—1462no—
216D4—1462no—
217C2×C4—21no—
218C2×C4—41no—
219C2×C4—41no—
220C2×C4—2921no—
221C2×C4—2921no—
222C2×C4—1462no—
223C2×C4D4×D7311yescharacteristic
224C2×C4D4×D7311yescharacteristic
225C2×C4D4×D7311yescharacteristic
226C2×C4D4×D7311yescharacteristic
227C2×C4C2×C22⋊D7311yescharacteristic
228C2×C4C2×D29211yescharacteristic
229C8—22no—
230C8—41no—
231C8—1462no—
232C8—1462no—
233C22—22no—
234C22—41no—
235C22—42no—
236C22—2922no—
237C22—5842no—
238C22—5842no—
239C22—5842no—
240C22#1455656411yescharacteristic
241C22#1455656411yescharacteristic
242C22#1455656511yescharacteristic
243C4—41no—
244C4—2922no—
245C4#1455655911yescharacteristic
246C4#1455656111yescharacteristic
247C4#1455656111yescharacteristic
248C4#1455658711yescharacteristic
249C2—21no—
250C2—21no—
251C2—81no—
252C2—5842no—
253C2#1798849611yescharacteristic
254C2#1798885012yes—
subgroupG/H
centerC22#14556565
commutatorC22×C4×C73C23
FrattiniC22×C4C22×D73
Fitting#408×C73C2
socleC22×C73#121
hypercenter#408D73
hypocenterC73#2019
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #408

Complements

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

NH ≅ G/Ntype
1. C2×#14556621C2semidirect
3. C22×#11924017C2semidirect
4. C2×#14556509C2semidirect
5. C2×#14556507C2semidirect
6. #17988352C2semidirect
7. #408×C73C2semidirect
128. C73#2019semidirect
134. #408D73semidirect