Finite Group Databasebeta

← #22611172

Subgroups — #22611172

Order 9344.

318 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 318 conjugacy classes of subgroups — too many to draw. Only its 85 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×#14556579C211yesmaximal, characteristic
2C2×#14556514C211yesmaximal, characteristic, complemented
3C2×#14556514C211yesmaximal, characteristic, complemented
4C2×#14556511C211yesmaximal, characteristic
5C2×#14556511C211yesmaximal, characteristic
6#17988342C211yesmaximal, characteristic, complemented
7#389×C73C211yesmaximal, characteristic, complemented
8C22×Dic146C2211yescharacteristic
9C22×D292C2211yescharacteristic
10C22×#10596831C2211yescharacteristic
11C22×#10596831C2211yescharacteristic
12#14556579—22no—
13#14556579—22no—
14C2×#11924005—21no—
15C2×#11924005—21no—
16#14556514—22no—
17#14556514—22no—
18#14556511—22no—
19#14556511—22no—
20C2×C4⋊C4×C73—21no—
21C2×C4⋊C4×C73C2211yescharacteristic
22C2×C4⋊C4×C73C2211yescharacteristic
23C2×C42×C73C2211yescharacteristic
24#95×C73—21no—
25C23×D73—21no—
26C2×Dic146—21no—
27C2×Dic146—21no—
28C2×Dic146—21no—
29C2×Dic146—21no—
30C2×Dic146—21no—
31C2×Dic146D412yes—
32C2×D292—21no—
33C2×D292—21no—
34C2×D292—21no—
35C2×D292—21no—
36C2×D292—21no—
37C2×D292D412yes—
38C22×Dic73—21no—
39C2×#10596831—21no—
40C2×#10596831—21no—
41C2×#10596831—21no—
42C2×#10596831—21no—
43C2×#10596831—21no—
44C2×#10596831—21no—
45#11924005—24no—
46#11924005—24no—
47C22×C4×C73—21no—
48C22×C4×C73—21no—
49C22×C4×C73D411yescharacteristic
50C22×C4×C73D411yescharacteristic
51C22×C4×C73C2311yescharacteristic
52C4⋊C4×C73—21no—
53C4⋊C4×C73—21no—
54C4⋊C4×C73—21no—
55C4⋊C4×C73—42no—
56C4⋊C4×C73D412yes—
57C42×C73—21no—
58C42×C73—21no—
59C23×C73C2×D411yescharacteristic
60C22×D73—22no—
61C22×D73—41no—
62C22×D73—41no—
63C22×D73—41no—
64C22×D73—41no—
65C22×D73—41no—
66C22×D73—41no—
67C2×C4×C73—21no—
68C2×C4×C73—21no—
69C2×C4×C73—22no—
70C2×C4×C73—21no—
71C2×C4×C73—21no—
72C2×C4×C73—21no—
73C2×C4×C73—21no—
74C2×C4×C73—41no—
75C2×C4×C73—41no—
76C2×C4×C73—41no—
77C2×C4×C73—41no—
78C2×C4×C73—41no—
79C2×C4×C73C2×D411yescharacteristic
80C2×C4×C73C2×D411yescharacteristic
81C2×C4×C73C2×D411yescharacteristic
82C2×C4×C73#4111yescharacteristic
83C2×C4×C73#4111yescharacteristic
84C2×C4×C73#4111yescharacteristic
85C2×Dic73—22no—
86C2×Dic73—41no—
87C2×Dic73—41no—
88D292—22no—
89D292—22no—
90D292—41no—
91D292—41no—
92Dic146—22no—
93Dic146—22no—
94Dic146—41no—
95Dic146—41no—
96#10596831—41no—
97#10596831—41no—
98C22×C73#12011yescharacteristic
99C22×C73#12111yescharacteristic
100C22×C73#12411yescharacteristic
101C22×C73#13511yescharacteristic
102C22×C73#13511yescharacteristic
103C22×C73AGL(1,ℤ/8)11yescharacteristic
104C22×C73#13711yescharacteristic
105C2×D73—42no—
106C2×D73—42no—
107C2×D73—42no—
108C2×D73—81no—
109C2×D73—81no—
110C2×D73—81no—
111C2×D73—81no—
112C4×C73—41no—
113C4×C73—41no—
114C4×C73—42no—
115C4×C73—81no—
116C4×C73#12111yescharacteristic
117C4×C73#12111yescharacteristic
118C4×C73#12311yescharacteristic
119C4×C73#12311yescharacteristic
120Dic73—42no—
121C2×C73#39411yescharacteristic
122C2×C73#44911yescharacteristic
123C2×C73#45211yescharacteristic
124C2×C73#46311yescharacteristic
125C2×C73#46411yescharacteristic
126C2×C73#48811yescharacteristic
127C2×C73#48911yescharacteristic
128D73—82no—
129#2042—731nomaximal, Sylow
130C73#204211yescharacteristic, complemented, Sylow
131C2×#124—731no—
132C2×#103—731no—
133C2×#103—731no—
134C2×#102—731no—
135C2×#102—731no—
136#389D7311yescharacteristic, complemented
137#336—731no—
138C22×Q8—731no—
139C22×D4—731no—
140C22×C8—731no—
141C22×C8—731no—
142#124—1462no—
143#124—1462no—
144C2×C4⋊C4—21no—
145C2×C4⋊C4C2×D7311yescharacteristic
146C2×C4⋊C4C2×D7311yescharacteristic
147C2×C22⋊C4—1461no—
148C2×C22⋊C4—1461no—
149C2×C42C2×D7311yescharacteristic
150#103—1462no—
151#103—1462no—
152#102—1462no—
153#102—1462no—
154#95—21no—
155C24—1461no—
156C2×Q8—732no—
157C2×Q8—1461no—
158C2×Q8—1461no—
159C2×Q8—1461no—
160C2×Q8—1461no—
161C2×Q8—1461no—
162C2×D4—732no—
163C2×D4—1461no—
164C2×D4—1461no—
165C2×D4—1461no—
166C2×D4—1461no—
167C2×D4—1461no—
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—1461no—
171C22×C4C22⋊D7311yescharacteristic
172C22×C4C22⋊D7311yescharacteristic
173C22×C4C22×D7311yescharacteristic
174C2×C8—1461no—
175C2×C8—1461no—
176C2×C8—1461no—
177C2×C8—1461no—
178C2×C8—1461no—
179C2×C8—1461no—
180C4⋊C4—21no—
181C4⋊C4—21no—
182C4⋊C4—21no—
183C4⋊C4—42no—
184C4⋊C4D29212yes—
185C22⋊C4—1464no—
186C22⋊C4—1464no—
187C42—21no—
188C42—21no—
189C23—2921no—
190C23—2921no—
191C23—2921no—
192C23—2921no—
193C23—2921no—
194C23—2921no—
195C23—1462no—
196C23C2×C22⋊D7311yescharacteristic
197Q8—2921no—
198Q8—2921no—
199Q8—1462no—
200Q8—1462no—
201D4—2921no—
202D4—2921no—
203D4—1462no—
204D4—1462no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—22no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—41no—
215C2×C4—41no—
216C2×C4—41no—
217C2×C4—2921no—
218C2×C4—2921no—
219C2×C4—1462no—
220C2×C4D4×D7311yescharacteristic
221C2×C4D4×D7311yescharacteristic
222C2×C4C2×D29211yescharacteristic
223C2×C4#1192402811yescharacteristic
224C2×C4#1192402911yescharacteristic
225C2×C4#1192402911yescharacteristic
226C8—2921no—
227C8—2921no—
228C22—2922no—
229C22—2922no—
230C22—2922no—
231C22—5841no—
232C22—5841no—
233C22—5841no—
234C22—5841no—
235C22#1455655911yescharacteristic
236C22#1455656511yescharacteristic
237C22#1455658011yescharacteristic
238C22#1455661111yescharacteristic
239C22#1455661111yescharacteristic
240C22#1455661711yescharacteristic
241C22#1455662211yescharacteristic
242C4—41no—
243C4—41no—
244C4—42no—
245C4—81no—
246C4—2922no—
247C4#1455656611yescharacteristic
248C4#1455656611yescharacteristic
249C4#1455657611yescharacteristic
250C4#1455657611yescharacteristic
251C2—5842no—
252C2#1798850411yescharacteristic
253C2#1798873011yescharacteristic
254C2#1798874711yescharacteristic
255C2#1798880211yescharacteristic
256C2#1798880911yescharacteristic
257C2#1798894411yescharacteristic
258C2#1798894911yescharacteristic
subgroupG/H
centerC23C2×C22⋊D73
commutatorC22×C4×C73C23
FrattiniC22×C4C22×D73
Fitting#389×C73C2
socleC23×C73C2×D4
hypercenter#389D73
hypocenterC73#2042
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
2. C2×#14556514C2semidirect
3. C2×#14556514C2semidirect
6. #17988342C2semidirect
7. #389×C73C2semidirect
130. C73#2042semidirect
136. #389D73semidirect