Finite Group Databasebeta

← #22625800

Subgroups — #22625800

Order 9344.

308 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 308 conjugacy classes of subgroups — too many to draw. Only its 94 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
1#17989588C211yesmaximal, characteristic
2C2×#14556654C212yesmaximal
3#17989533C211yesmaximal, characteristic
4#17989460C212yesmaximal
5C4×Q8×D73C211yesmaximal, characteristic
6C2×#11924036C2212yes—
7C2×C4⋊#64408—21no—
8C2×C4⋊#64408—21no—
9C2×C4⋊#64408C2212yes—
10#14556658—21no—
11C4⋊#10596833—21no—
12#14556654—24no—
13C2×Q8×D73C2211yescharacteristic
14Q8×Dic73C411yescharacteristic, complemented
15C4×Dic146—21no—
16C4×Dic146C411yescharacteristic, complemented
17#14556556—21no—
18#14556556C411yescharacteristic, complemented
19C4⋊C4×D73—21no—
20C4⋊C4×D73C2211yescharacteristic
21C42×D73—21no—
22C42×D73C2211yescharacteristic
23C4×Q8×C73C411yescharacteristic, complemented
24C22×#64408—22no—
25#11924036—22no—
26#11924036—22no—
27C2×#10596833—22no—
28C4⋊#64408—22no—
29C4⋊#64408—22no—
30C4⋊#64408—42no—
31C4⋊#64408—42no—
32C2×Dic146—21no—
33C2×Dic146C2×C411yescharacteristic
34Q8×D73—21no—
35Q8×D73—21no—
36Q8×D73D412yes—
37Q8×D73Q812yes—
38C2×C4×D73—21no—
39C2×C4×D73—21no—
40C2×C4×D73D411yescharacteristic
41C2×C4×D73D411yescharacteristic
42C2×C4×D73C2311yescharacteristic
43C4⋊Dic73—21no—
44C4⋊Dic73C2×C411yescharacteristic
45#11924007—21no—
46#11924007—21no—
47#11924007—21no—
48C4×Dic73—21no—
49C4×Dic73—21no—
50C4×Dic73—21no—
51C4×Dic73C2×C411yescharacteristic
52C4×Dic73D411yescharacteristic
53C4×Dic73D411yescharacteristic
54C2×Q8×C73C2×C411yescharacteristic
55C4⋊C4×C73—21no—
56C4⋊C4×C73C2×C411yescharacteristic
57C42×C73—21no—
58C42×C73C2×C411yescharacteristic
59C22×D73C2×D411yescharacteristic
60C2×#64408—42no—
61C2×#64408—42no—
62C2×#64408—42no—
63Q8×C73—21no—
64Q8×C73C4⋊C412yescomplemented
65C2×C4×C73—21no—
66C2×C4×C73—21no—
67C2×C4×C73C22⋊C411yescharacteristic
68C2×C4×C73C22⋊C411yescharacteristic
69C2×C4×C73C22×C411yescharacteristic
70C2×Dic73—21no—
71C2×Dic73—21no—
72C2×Dic73C22⋊C411yescharacteristic
73C2×Dic73C22⋊C411yescharacteristic
74C2×Dic73C2×D411yescharacteristic
75C4×D73—22no—
76C4×D73—22no—
77C4×D73—21no—
78C4×D73—21no—
79C4×D73—41no—
80C4×D73—41no—
81C4×D73SD1612yes—
82C4×D73Q1612yes—
83C4×D73C2×D411yescharacteristic
84C4×D73C2×Q811yescharacteristic
85C4×D73#4111yescharacteristic
86C4×D73#4111yescharacteristic
87Dic146—21no—
88Dic146—22no—
89Dic146—22no—
90Dic146C4⋊C412yescomplemented
91#10596833—42no—
92C22×C73C2×C22⋊C411yescharacteristic
93C2×D73#12111yescharacteristic
94C2×D73C22⋊Q811yescharacteristic
95C2×D73C2×SD1611yescharacteristic
96C2×D73C2×Q1611yescharacteristic
97C2×D73AGL(1,ℤ/8)11yescharacteristic
98C2×D73#13711yescharacteristic
99#64408—82no—
100C4×C73—22no—
101C4×C73—21no—
102C4×C73—41no—
103C4×C73#10312yescomplemented
104C4×C73C2×C4⋊C411yescharacteristic
105C4×C73#11711yescharacteristic
106Dic73—22no—
107Dic73—21no—
108Dic73—41no—
109Dic73#10312yescomplemented
110Dic73#12111yescharacteristic
111Dic73C22⋊Q811yescharacteristic
112C2×C73#38011yescharacteristic
113C2×C73C2×#10311yescharacteristic
114C2×C73#41711yescharacteristic
115D73#46011yescharacteristic
116D73#46211yescharacteristic
117D73#47511yescharacteristic
118D73#47711yescharacteristic
119#1803—731nomaximal, Sylow
120C73#180311yescharacteristic, complemented, Sylow
121C2×C4×Q8—731no—
122C2×C4⋊C8—731no—
123C2×#103—732no—
124#384—731no—
125#340—732no—
126C22×Q8—731no—
127C22×C8—732no—
128C4×Q8—731no—
129C4×Q8—731no—
130C4×Q8—731no—
131C4×Q8—1461no—
132C4×Q8—1461no—
133C4×Q8#6440811yescharacteristic, complemented
134C2×C4⋊C4—731no—
135C2×C4⋊C4—732no—
136C2×C4⋊C4—1461no—
137C2×C4⋊C4—1461no—
138C2×C4⋊C4—1461no—
139C2×C42—731no—
140C2×C42—1461no—
141C4⋊C8—1461no—
142C4⋊C8—1461no—
143#103—1464no—
144C2×Q8—732no—
145C2×Q8—732no—
146C2×Q8—731no—
147C2×Q8—1461no—
148C2×Q8—1461no—
149C2×Q8—1461no—
150C2×Q8C2×#6440811yescharacteristic
151C22×C4—731no—
152C22×C4—731no—
153C22×C4—731no—
154C22×C4—1461no—
155C22×C4—1461no—
156C22×C4—1462no—
157C2×C8—1462no—
158C2×C8—1462no—
159C2×C8—1462no—
160C4⋊C4—21no—
161C4⋊C4—2922no—
162C4⋊C4—2922no—
163C4⋊C4—731no—
164C4⋊C4—1461no—
165C4⋊C4—1461no—
166C4⋊C4—1461no—
167C4⋊C4—1462no—
168C4⋊C4—1462no—
169C4⋊C4—1461no—
170C4⋊C4C2×#6440811yescharacteristic
171C42—21no—
172C42—731no—
173C42—731no—
174C42—731no—
175C42—1461no—
176C42—1461no—
177C42—1461no—
178C42C2×#6440811yescharacteristic
179C23—731no—
180Q8—21no—
181Q8—732no—
182Q8—1462no—
183Q8—1462no—
184Q8—1461no—
185Q8C4⋊#6440812yescomplemented
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—2921no—
189C2×C4—2921no—
190C2×C4—2922no—
191C2×C4—2922no—
192C2×C4—2922no—
193C2×C4—731no—
194C2×C4—731no—
195C2×C4—732no—
196C2×C4—732no—
197C2×C4—731no—
198C2×C4—731no—
199C2×C4—731no—
200C2×C4—731no—
201C2×C4—731no—
202C2×C4—1461no—
203C2×C4—1461no—
204C2×C4—1462no—
205C2×C4—1462no—
206C2×C4—1461no—
207C2×C4—1461no—
208C2×C4C22⋊#6440811yescharacteristic
209C2×C4C22⋊#6440811yescharacteristic
210C2×C4C22×#6440811yescharacteristic
211C8—2922no—
212C22—731no—
213C22—731no—
214C22—731no—
215C22—731no—
216C22—731no—
217C22—731no—
218C22C2×C22⋊#6440811yescharacteristic
219C4—22no—
220C4—21no—
221C4—41no—
222C4—2921no—
223C4—5842no—
224C4—731no—
225C4—731no—
226C4—732no—
227C4—1462no—
228C4—1461no—
229C4#1455665412yescomplemented
230C4C2×C4⋊#6440811yescharacteristic
231C4#1455667011yescharacteristic
232C2—731no—
233C2—731no—
234C2—731no—
235C2—731no—
236C2#1798952911yescharacteristic
237C2C2×#1455665411yescharacteristic
238C2#1798957811yescharacteristic
subgroupG/H
centerC22C2×C22⋊#64408
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
FittingC4×Q8×C73C4
socleC22×C73C2×C22⋊C4
hypercenterC4×Q8#64408
hypocenterC73#1803
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
14. Q8×Dic73C4semidirect
16. C4×Dic146C4semidirect
18. #14556556C4semidirect
23. C4×Q8×C73C4semidirect
64. Q8×C73C4⋊C4semidirect
90. Dic146C4⋊C4semidirect
103. C4×C73#103semidirect
109. Dic73#103semidirect
120. C73#1803semidirect
133. C4×Q8#64408semidirect
185. Q8C4⋊#64408semidirect
229. C4#14556654semidirect