Finite Group Databasebeta

← #22610550

Subgroups — #22610550

Order 9344.

290 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 93 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×#14556513C211yesmaximal, characteristic
2C2×#14556511C211yesmaximal, characteristic
3#17988488C211yesmaximal, characteristic
4C4⋊C4×Dic73C211yesmaximal, characteristic, complemented
5#17988349C211yesmaximal, characteristic, complemented
6#17988341C211yesmaximal, characteristic, complemented
7C2×#107×C73C211yesmaximal, characteristic, complemented
8C22×D292C2211yescharacteristic
9C22×#10596831C2211yescharacteristic
10C2×C4⋊Dic73C2211yescharacteristic
11C2×#11924005—21no—
12C2×#11924005—21no—
13C2×C4×Dic73—21no—
14C2×C4×Dic73C2211yescharacteristic
15#14556513C414yescomplemented
16#14556511—22no—
17#14556498—21no—
18C22×C8×C73C2211yescharacteristic
19C2×C4⋊C4×C73C2211yescharacteristic
20C2×C4⋊C4×C73C2211yescharacteristic
21#107×C73—22no—
22C23×D73—21no—
23C2×D292—21no—
24C2×D292—21no—
25C2×D292—21no—
26C2×D292—21no—
27C2×D292—21no—
28C2×D292C2×C412yes—
29C22×Dic73—21no—
30C22×Dic73D411yescharacteristic
31C22×Dic73D411yescharacteristic
32C2×#10596831—21no—
33C2×#10596831—21no—
34C2×#10596831—21no—
35C4⋊Dic73—21no—
36C4⋊Dic73C2×C412yes—
37#11924005—42no—
38#11924005—42no—
39C4×Dic73—21no—
40C4×Dic73—21no—
41C4×Dic73—42no—
42C22×C4×C73—21no—
43C22×C4×C73—21no—
44C22×C4×C73C2311yescharacteristic
45C2×C8×C73—21no—
46C2×C8×C73—21no—
47C2×C8×C73C2×C412yes—
48C4⋊C4×C73—21no—
49C4⋊C4×C73—21no—
50C4⋊C4×C73—21no—
51C4⋊C4×C73D412yes—
52C23×C73C2×D411yescharacteristic
53C22×D73—22no—
54C22×D73—41no—
55C22×D73—41no—
56C22×D73—41no—
57C22×D73—41no—
58C22×D73—41no—
59C22×D73—41no—
60C2×C4×C73—22no—
61C2×C4×C73—41no—
62C2×C4×C73—41no—
63C2×C4×C73—41no—
64C2×C4×C73—41no—
65C2×C4×C73—41no—
66C2×C4×C73C22×C411yescharacteristic
67C2×C4×C73C2×D411yescharacteristic
68C2×C4×C73#4111yescharacteristic
69C2×C4×C73#4111yescharacteristic
70C2×C4×C73#4111yescharacteristic
71C2×C4×C73#4111yescharacteristic
72C2×Dic73—21no—
73C2×Dic73—21no—
74C2×Dic73—22no—
75C2×Dic73—21no—
76C2×Dic73—21no—
77C2×Dic73—21no—
78C2×Dic73—41no—
79C2×Dic73—41no—
80C2×Dic73D812yes—
81D292—22no—
82D292—22no—
83D292—41no—
84D292—41no—
85C8×C73—22no—
86#10596831—41no—
87C22×C73C4×D411yescharacteristic
88C22×C73#12111yescharacteristic
89C22×C73#12311yescharacteristic
90C22×C73C2×D811yescharacteristic
91C22×C73#13511yescharacteristic
92C22×C73AGL(1,ℤ/8)11yescharacteristic
93C22×C73#13711yescharacteristic
94C2×D73—42no—
95C2×D73—42no—
96C2×D73—42no—
97C2×D73—81no—
98C2×D73—81no—
99C2×D73—81no—
100C2×D73—81no—
101C4×C73—42no—
102C4×C73—81no—
103C4×C73#11711yescharacteristic
104C4×C73C4×D411yescharacteristic
105C4×C73#12411yescharacteristic
106C4×C73#12611yescharacteristic
107Dic73—22no—
108Dic73—42no—
109Dic73—41no—
110C2×C73#38811yescharacteristic
111C2×C73C4×D811yescharacteristic
112C2×C73#44011yescharacteristic
113C2×C73#45911yescharacteristic
114C2×C73#46411yescharacteristic
115C2×C73#48011yescharacteristic
116C2×C73#48211yescharacteristic
117D73—82no—
118#1925—731nomaximal, Sylow
119C73#192511yescharacteristic, complemented, Sylow
120C2×#107D7311yescharacteristic, complemented
121C2×#102—731no—
122C2×#102—731no—
123#390—731no—
124C4×C4⋊C4—731no—
125#340—731no—
126#336—731no—
127C22×D4—731no—
128C22×C8—731no—
129C22×C8C2×D7311yescharacteristic
130C2×C4⋊C4—731no—
131C2×C4⋊C4C2×D7311yescharacteristic
132C2×C4⋊C4C2×D7311yescharacteristic
133C2×C22⋊C4—1461no—
134C2×C22⋊C4—1461no—
135C2×C42—731no—
136C2×C42—1461no—
137#107—22no—
138#102—734no—
139#102—1462no—
140#95—1461no—
141C24—1461no—
142C2×D4—732no—
143C2×D4—1461no—
144C2×D4—1461no—
145C2×D4—1461no—
146C2×D4—1461no—
147C2×D4—1461no—
148C22×C4—21no—
149C22×C4—21no—
150C22×C4—731no—
151C22×C4—731no—
152C22×C4—1461no—
153C22×C4C22×D7311yescharacteristic
154C2×C8—21no—
155C2×C8—21no—
156C2×C8—1461no—
157C2×C8—1461no—
158C2×C8—1461no—
159C2×C8C4×D7312yes—
160C4⋊C4—21no—
161C4⋊C4—21no—
162C4⋊C4—21no—
163C4⋊C4—732no—
164C4⋊C4—1461no—
165C4⋊C4C22⋊D7312yes—
166C22⋊C4—2922no—
167C22⋊C4—2922no—
168C42—2922no—
169C42—1461no—
170C42—1461no—
171C23—2921no—
172C23—2921no—
173C23—2921no—
174C23—2921no—
175C23—2921no—
176C23—2921no—
177C23—1462no—
178C23D4×D7311yescharacteristic
179D4—2921no—
180D4—2921no—
181D4—1462no—
182D4—1462no—
183C2×C4—22no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—2921no—
190C2×C4—2921no—
191C2×C4—732no—
192C2×C4—1462no—
193C2×C4—1461no—
194C2×C4—1461no—
195C2×C4—1461no—
196C2×C4—1461no—
197C2×C4—1461no—
198C2×C4C2×C4×D7311yescharacteristic
199C2×C4C2×C22⋊D7311yescharacteristic
200C2×C4#1192402711yescharacteristic
201C2×C4#1192402811yescharacteristic
202C2×C4#1192402911yescharacteristic
203C2×C4#1192402911yescharacteristic
204C8—22no—
205C8—2921no—
206C22—2922no—
207C22—2922no—
208C22—2922no—
209C22—5841no—
210C22—5841no—
211C22—5841no—
212C22—5841no—
213C22#1455655311yescharacteristic
214C22#1455656311yescharacteristic
215C22#1455657611yescharacteristic
216C22D8×D7311yescharacteristic
217C22#1455661411yescharacteristic
218C22#1455661511yescharacteristic
219C22#1455662311yescharacteristic
220C4—42no—
221C4—81no—
222C4—2921no—
223C4—2922no—
224C4—1462no—
225C4#1455654911yescharacteristic
226C4C4×C22⋊D7311yescharacteristic
227C4#1455658011yescharacteristic
228C4#1455658611yescharacteristic
229C2—5842no—
230C2#1798847711yescharacteristic
231C2#1798866911yescharacteristic
232C2#1798868611yescharacteristic
233C2#1798878011yescharacteristic
234C2#1798881111yescharacteristic
235C2#1798890211yescharacteristic
236C2#1798891411yescharacteristic
subgroupG/H
centerC23D4×D73
commutatorC2×C4×C73C22×C4
FrattiniC22×C4C22×D73
FittingC2×#107×C73C2
socleC23×C73C2×D4
hypercenterC2×#107D73
hypocenterC73#1925
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
4. C4⋊C4×Dic73C2semidirect
5. #17988349C2semidirect
6. #17988341C2semidirect
7. C2×#107×C73C2semidirect
15. #14556513C4semidirect
119. C73#1925semidirect
120. C2×#107D73semidirect