Finite Group Databasebeta

← #22626122

Subgroups — #22626122

Order 9344.

324 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 72 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#17989529C211yesmaximal, characteristic
2C4×C22⋊#64408C211yesmaximal, characteristic
3#17989465C212yesmaximal
4#17989465C212yesmaximal
5C2×#14556569C211yesmaximal, characteristic
6C2×C4⋊#64408—21no—
7C2×C22⋊#64408C2212yes—
8C2×C22⋊#64408C2212yes—
9C2×C4×#64408—21no—
10(C2×#64408)⋊C4—21no—
11(C2×#64408)⋊C4—21no—
12C22×Dic146C411yescharacteristic, complemented
13C22×C4×D73C2211yescharacteristic
14#14556569—21no—
15#14556569—21no—
16#14556569—21no—
17#14556569—21no—
18C2×#11924007C411yescharacteristic, complemented
19C2×#11924007C411yescharacteristic, complemented
20C2×#11924005C2211yescharacteristic
21C2×#11924005C2211yescharacteristic
22C2×C4⋊C4×C73C411yescharacteristic, complemented
23C22×#64408—22no—
24C22×#64408—22no—
25C4⋊#64408—42no—
26C22⋊#64408—22no—
27C22⋊#64408—24no—
28C22⋊#64408Q814yescomplemented
29C4×#64408—42no—
30C23×D73C2311yescharacteristic
31C2×Dic146—21no—
32C2×Dic146—21no—
33C2×Dic146—42no—
34C22×Dic73C2×C411yescharacteristic
35C22×Dic73C2×C411yescharacteristic
36C22×Dic73C2×C411yescharacteristic
37C2×C4×D73—42no—
38C2×C4×D73D411yescharacteristic
39C2×C4×D73D411yescharacteristic
40C2×C4×D73D411yescharacteristic
41C2×C4×D73D411yescharacteristic
42#11924007—21no—
43#11924007—21no—
44#11924007—21no—
45#11924007—21no—
46#11924005—21no—
47#11924005—21no—
48#11924005—21no—
49#11924005—21no—
50C22×C4×C73C2×C411yescharacteristic
51C22×C4×C73C2×C411yescharacteristic
52C22×C4×C73C2×C411yescharacteristic
53C4⋊C4×C73—21no—
54C4⋊C4×C73—21no—
55C23×C73C22×C411yescharacteristic
56C22×D73—41no—
57C22×D73—41no—
58C22×D73C2×D411yescharacteristic
59C22×D73C2×D411yescharacteristic
60C22×D73C2×Q812yes—
61C22×D73#4112yes—
62C2×#64408—24no—
63C2×#64408—42no—
64C2×#64408—42no—
65C2×#64408—42no—
66C2×#64408—42no—
67C2×#64408—42no—
68C2×C4×C73—21no—
69C2×C4×C73—21no—
70C2×C4×C73—41no—
71C2×C4×C73—41no—
72C2×C4×C73—41no—
73C2×C4×C73C22⋊C411yescharacteristic
74C2×C4×C73C22⋊C411yescharacteristic
75C2×Dic73—22no—
76C2×Dic73—21no—
77C2×Dic73—21no—
78C2×Dic73—41no—
79C2×Dic73—41no—
80C2×Dic73C22⋊C411yescharacteristic
81C2×Dic73C22⋊C411yescharacteristic
82C4×D73—22no—
83C4×D73—22no—
84C4×D73—41no—
85C4×D73—41no—
86Dic146—42no—
87Dic146—42no—
88C22×C73—21no—
89C22×C73—21no—
90C22×C73C2×C22⋊C411yescharacteristic
91C22×C73C4×Q812yes—
92C2×D73—21no—
93C2×D73—21no—
94C2×D73—21no—
95C2×D73—21no—
96C2×D73—42no—
97C2×D73—42no—
98C2×D73C22⋊Q812yes—
99C2×D73#12411yescharacteristic
100C2×D73C4⋊Q811yescharacteristic
101#64408—44no—
102#64408—82no—
103C4×C73—21no—
104C4×C73—21no—
105C4×C73—41no—
106C4×C73—41no—
107Dic73—21no—
108Dic73—41no—
109Dic73—41no—
110Dic73#9912yes—
111C2×C73—22no—
112C2×C73#39111yescharacteristic
113C2×C73C2×#9911yescharacteristic
114C2×C73#41011yescharacteristic
115D73—22no—
116D73—21no—
117D73—21no—
118#1996—731nomaximal, Sylow
119C73#199611yescharacteristic, complemented, Sylow
120C2×C22⋊Q8—731no—
121#380—731no—
122C4×C22⋊C4—731no—
123#342—732no—
124#342—732no—
125C22×Q8—731no—
126C23×C4—731no—
127C22⋊Q8—1461no—
128C22⋊Q8—1461no—
129C22⋊Q8—1461no—
130C22⋊Q8—1461no—
131C2×C4⋊C4—731no—
132C2×C4⋊C4—731no—
133C2×C4⋊C4—1461no—
134C2×C4⋊C4#6440811yescharacteristic, complemented
135C2×C22⋊C4—732no—
136C2×C22⋊C4—731no—
137C2×C22⋊C4—731no—
138C2×C22⋊C4—732no—
139C2×C42—1461no—
140#95—1461no—
141#95—1461no—
142C24—731no—
143C2×Q8—2922no—
144C2×Q8—1461no—
145C2×Q8—1461no—
146C22×C4—2922no—
147C22×C4—731no—
148C22×C4—731no—
149C22×C4—731no—
150C22×C4—731no—
151C22×C4—731no—
152C22×C4—731no—
153C22×C4—731no—
154C22×C4—1462no—
155C22×C4—1462no—
156C22×C4C2×#6440811yescharacteristic
157C22×C4C2×#6440811yescharacteristic
158C22×C4C2×#6440811yescharacteristic
159C4⋊C4—21no—
160C4⋊C4—21no—
161C4⋊C4—2922no—
162C4⋊C4—1461no—
163C4⋊C4—1461no—
164C4⋊C4—1461no—
165C4⋊C4—1461no—
166C22⋊C4—734no—
167C22⋊C4—1461no—
168C22⋊C4—1461no—
169C22⋊C4—1461no—
170C22⋊C4—1461no—
171C22⋊C4—1464no—
172C22⋊C4—1462no—
173C42—2922no—
174C23—2921no—
175C23—2921no—
176C23—732no—
177C23—732no—
178C23—731no—
179C23—731no—
180C23C22×#6440811yescharacteristic
181Q8—2922no—
182Q8—2922no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—2921no—
189C2×C4—2921no—
190C2×C4—2922no—
191C2×C4—2922no—
192C2×C4—2921no—
193C2×C4—2921no—
194C2×C4—2922no—
195C2×C4—2922no—
196C2×C4—2922no—
197C2×C4—731no—
198C2×C4—731no—
199C2×C4—1462no—
200C2×C4—1462no—
201C2×C4—1464no—
202C2×C4—1461no—
203C2×C4—1461no—
204C2×C4—1462no—
205C2×C4C22⋊#6440811yescharacteristic
206C2×C4C22⋊#6440811yescharacteristic
207C22—21no—
208C22—21no—
209C22—2922no—
210C22—2922no—
211C22—731no—
212C22—732no—
213C22—731no—
214C22—1461no—
215C22—1461no—
216C22—1461no—
217C22—1461no—
218C22C2×C22⋊#6440811yescharacteristic
219C22Q8×#6440812yes—
220C4—21no—
221C4—21no—
222C4—41no—
223C4—41no—
224C4—2924no—
225C4—2921no—
226C4—2921no—
227C4—5842no—
228C4—732no—
229C4—1461no—
230C2—22no—
231C2—1462no—
232C2—1461no—
233C2—1461no—
234C2(C2×#64408)⋊Q811yescharacteristic
235C2D73⋊#9911yescharacteristic
236C2#1798956611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#64408
commutatorC23×C73C22×C4
FrattiniC23C22×#64408
FittingC2×C4⋊C4×C73C4
socleC22×C73C2×C22⋊C4
hypercenterC2×C4⋊C4#64408
hypocenterC73#1996
LCSG ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
12. C22×Dic146C4semidirect
18. C2×#11924007C4semidirect
19. C2×#11924007C4semidirect
22. C2×C4⋊C4×C73C4semidirect
28. C22⋊#64408Q8semidirect
119. C73#1996semidirect
134. C2×C4⋊C4#64408semidirect