Finite Group Databasebeta

← #22610417

Subgroups — #22610417

Order 9344.

346 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 79 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×#14556619C211yesmaximal, characteristic
2#17989061C211yesmaximal, characteristic, complemented
3#17988603C211yesmaximal, characteristic, complemented
4#17988593C211yesmaximal, characteristic, complemented
5#17988560C211yesmaximal, characteristic, complemented
6#17988344C211yesmaximal, characteristic, complemented
7#344×C73C211yesmaximal, characteristic, complemented
8C2×#11924028C2211yescharacteristic
9C22×D292C2211yescharacteristic
10#14556619—22no—
11#14556619—22no—
12C2×#11924017C412yescomplemented
13C2×D584C412yescomplemented
14C4×D292—22no—
15#14556553—22no—
16#14556550C2211yescharacteristic
17#14556550C2211yescharacteristic
18C22⋊C4×D73—22no—
19#14556517—22no—
20#14556513—22no—
21#14556505—22no—
22C2×M16×C73C2211yescharacteristic
23C2×M16×C73C2211yescharacteristic
24#117×C73C2211yescharacteristic
25C23×D73—21no—
26#11924028—21no—
27#11924028—21no—
28#11924028—21no—
29#11924028—21no—
30C2×Dic146C2×C411yescharacteristic, complemented
31C2×D292—21no—
32C2×D292—21no—
33C2×D292—21no—
34C2×D292C2×C412yes—
35C2×D292C2×C411yescharacteristic, complemented
36C2×D292D412yes—
37C2×D292D412yes—
38C2×C22⋊D73—21no—
39C2×C4×D73—21no—
40C2×C4×D73—24no—
41#11924017—24no—
42D584—24no—
43C4⋊Dic73—21no—
44C4⋊Dic73—21no—
45C22⋊Dic73—21no—
46C22⋊Dic73—21no—
47#11924005—24no—
48C4×Dic73—21no—
49C4×Dic73D412yes—
50C22×C4×C73C2311yescharacteristic
51M16×C73—21no—
52M16×C73—21no—
53M16×C73—21no—
54M16×C73—21no—
55C2×C8×C73—21no—
56C2×C8×C73C2×C412yescomplemented
57C4⋊C4×C73—21no—
58C22⋊C4×C73D412yes—
59C42×C73—21no—
60C23×C73C2×D411yescharacteristic
61C22×D73—22no—
62C22×D73—22no—
63C22×D73—22no—
64C22×D73—21no—
65C22×D73—82no—
66C2×C4×C73—22no—
67C2×C4×C73C22×C411yescharacteristic
68C2×C4×C73C2×D411yescharacteristic
69C2×C4×C73C2×D411yescharacteristic
70C2×C4×C73C2×D411yescharacteristic
71C2×C4×C73#4111yescharacteristic
72C2×C4×C73#4111yescharacteristic
73C22⋊D73—41no—
74C22⋊D73—41no—
75C2×Dic73—21no—
76C2×Dic73—22no—
77C2×Dic73—41no—
78D292—21no—
79D292—22no—
80D292—21no—
81D292—22no—
82D292—22no—
83D292C22⋊C414yes—
84C4×D73—41no—
85C4×D73—41no—
86C4×D73—84no—
87Dic146—21no—
88Dic146—21no—
89C8×C73—22no—
90C8×C73—41no—
91C22×C73—41no—
92C22×C73C4×D411yescharacteristic
93C22×C73#12011yescharacteristic
94C22×C73#12111yescharacteristic
95C2×D73—24no—
96C2×D73—44no—
97C2×D73—41no—
98C2×D73—82no—
99C2×D73—82no—
100C2×D73—81no—
101C4×C73—42no—
102C4×C73C2×C22⋊C411yescharacteristic
103C4×C73C4×D411yescharacteristic
104C4×C73#12111yescharacteristic
105C4×C73#12311yescharacteristic
106Dic73—42no—
107Dic73—41no—
108Dic73—81no—
109C2×C73—21no—
110C2×C73—21no—
111C2×C73—21no—
112C2×C73#38611yescharacteristic
113D73—44no—
114D73—81no—
115#1904—731nomaximal, Sylow
116C73#190411yescharacteristic, complemented, Sylow
117C2×AGL(1,ℤ/8)—731no—
118#518—731no—
119#421—731no—
120#418—731no—
121#410—731no—
122#344D7311yescharacteristic, complemented
123H(3,ℤ/4)—731no—
124C2×#41—731no—
125C22×D4—731no—
126AGL(1,ℤ/8)—1462no—
127AGL(1,ℤ/8)—1462no—
128C2×SD16—732no—
129C2×D8—732no—
130C2×M16C2×D7311yescharacteristic
131C2×M16C2×D7311yescharacteristic
132C4×D4—1462no—
133C4×D4—1462no—
134#117—731no—
135#117—731no—
136#117C2×D7311yescharacteristic
137C2×C22⋊C4—1462no—
138#104—1462no—
139#102—1462no—
140#99—1462no—
141C24—1461no—
142#41—1461no—
143#41—1461no—
144#41—1461no—
145#41—1461no—
146C2×Q8—731no—
147C2×D4—732no—
148C2×D4—731no—
149C2×D4—732no—
150C2×D4—732no—
151C2×D4—1461no—
152C2×D4—1461no—
153C2×D4—1461no—
154C2×D4—1461no—
155C22×C4—1464no—
156C22×C4—1461no—
157C22×C4C22×D7311yescharacteristic
158SD16—1464no—
159D8—1464no—
160M16—21no—
161M16—21no—
162M16—21no—
163M16—21no—
164C2×C8—21no—
165C2×C8C4×D7312yescomplemented
166C4⋊C4—21no—
167C4⋊C4—1461no—
168C4⋊C4—1461no—
169C22⋊C4—1464no—
170C22⋊C4—1461no—
171C22⋊C4—1461no—
172C22⋊C4D29212yes—
173C42—21no—
174C42—732no—
175C42—1461no—
176C23—5842no—
177C23—1462no—
178C23—1461no—
179C23—1462no—
180C23—1462no—
181C23C2×D29211yescharacteristic
182Q8—1461no—
183Q8—1461no—
184D4—2921no—
185D4—2921no—
186D4—734no—
187D4—1461no—
188D4—1461no—
189D4—1462no—
190D4—1462no—
191D4—1462no—
192C2×C4—22no—
193C2×C4—2921no—
194C2×C4—2921no—
195C2×C4—2921no—
196C2×C4—5844no—
197C2×C4—1461no—
198C2×C4—1462no—
199C2×C4C2×C4×D7311yescharacteristic
200C2×C4D4×D7311yescharacteristic
201C2×C4D4×D7311yescharacteristic
202C2×C4D4×D7311yescharacteristic
203C2×C4#1192402811yescharacteristic
204C2×C4#1192402911yescharacteristic
205C8—22no—
206C8—41no—
207C22—41no—
208C22—2924no—
209C22—2921no—
210C22—5842no—
211C22—5842no—
212C22—5841no—
213C22—1464no—
214C22C4×D29211yescharacteristic
215C22#1455656111yescharacteristic
216C22#1455656611yescharacteristic
217C4—42no—
218C4—2922no—
219C4—2921no—
220C4—5841no—
221C4C22⋊C4×D7311yescharacteristic
222C4#1455655311yescharacteristic
223C4#1455656411yescharacteristic
224C4#1455657611yescharacteristic
225C2—21no—
226C2—21no—
227C2—21no—
228C2—2924no—
229C2—5841no—
230C2#1798846511yescharacteristic
subgroupG/H
centerC2#17988465
commutatorC2×C4×C73C22×C4
FrattiniC22×C4C22×D73
Fitting#344×C73C2
socleC2×C73#386
hypercenter#344D73
hypocenterC73#1904
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C22×C4 ◁ #344

Complements

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

NH ≅ G/Ntype
2. #17989061C2semidirect
3. #17988603C2semidirect
4. #17988593C2semidirect
5. #17988560C2semidirect
6. #17988344C2semidirect
7. #344×C73C2semidirect
12. C2×#11924017C4semidirect
13. C2×D584C4semidirect
30. C2×Dic146C2×C4semidirect
35. C2×D292C2×C4semidirect
56. C2×C8×C73C2×C4semidirect
116. C73#1904semidirect
122. #344D73semidirect
165. C2×C8C4×D73semidirect