Finite Group Databasebeta

← #22625944

Subgroups — #22625944

Order 9344.

380 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 88 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
1C22×#11924036C211yesmaximal, characteristic
2C2×#14556654C212yesmaximal, complemented
3#17989529C211yesmaximal, characteristic
4#17989460C212yesmaximal, complemented
5C22⋊Q8×D73C211yesmaximal, characteristic
6C2×#11924036—24no—
7C2×#11924036—21no—
8C2×#11924036C2212yes—
9C22×#10596833—21no—
10C2×C4⋊#64408C2212yes—
11C2×C22⋊#64408—21no—
12#14556654—24no—
13(C2×#64408)⋊C4—21no—
14C2×Q8×D73C2211yescharacteristic
15C22×C4×D73C2211yescharacteristic
16#14556571C411yescharacteristic, complemented
17#14556570C411yescharacteristic, complemented
18#14556569—21no—
19#14556568—21no—
20#14556567C411yescharacteristic, complemented
21C4⋊C4×D73—21no—
22C4⋊C4×D73C2211yescharacteristic
23C22⋊C4×D73—21no—
24C22⋊Q8×C73C411yescharacteristic, complemented
25C22×#64408—22no—
26#11924036—24no—
27#11924036—22no—
28#11924036D414yes—
29C2×#10596833—24no—
30C2×#10596833—22no—
31C4⋊#64408—22no—
32C4⋊#64408—22no—
33C22⋊#64408—42no—
34C23×D73D411yescharacteristic
35C2×Dic146—21no—
36C2×Dic146C2×C411yescharacteristic
37Q8×D73—22no—
38Q8×D73—22no—
39C22×Dic73D411yescharacteristic
40C2×C4×D73—22no—
41C2×C4×D73—22no—
42C2×C4×D73—21no—
43C2×C4×D73—21no—
44C2×C4×D73C2×C411yescharacteristic
45C2×C4×D73D411yescharacteristic
46C2×C4×D73D411yescharacteristic
47C2×C4×D73C2311yescharacteristic
48C4⋊Dic73—21no—
49C4⋊Dic73C2×C411yescharacteristic
50#11924007—21no—
51#11924007—21no—
52#11924007—21no—
53C22⋊Dic73—21no—
54#11924005—21no—
55#11924005—21no—
56C2×Q8×C73C2×C411yescharacteristic
57C22×C4×C73C2×C411yescharacteristic
58C4⋊C4×C73—21no—
59C4⋊C4×C73C2×C411yescharacteristic
60C22⋊C4×C73—21no—
61C23×C73C22⋊C411yescharacteristic
62C22×D73—22no—
63C22×D73—22no—
64C22×D73C22⋊C411yescharacteristic
65C22×D73SD1612yes—
66C22×D73Q1612yes—
67C22×D73C2×D411yescharacteristic
68C2×#64408—42no—
69C2×#64408—42no—
70C2×#64408—42no—
71Q8×C73—22no—
72C2×C4×C73—22no—
73C2×C4×C73—21no—
74C2×C4×C73—21no—
75C2×C4×C73C22⋊C411yescharacteristic
76C2×C4×C73C22×C411yescharacteristic
77C2×Dic73—21no—
78C2×Dic73—21no—
79C2×Dic73—21no—
80C2×Dic73—21no—
81C2×Dic73C22⋊C411yescharacteristic
82C2×Dic73C2×D411yescharacteristic
83C4×D73—22no—
84C4×D73—22no—
85C4×D73—21no—
86C4×D73—21no—
87C4×D73—42no—
88C4×D73—42no—
89C4×D73C2×D412yes—
90C4×D73#4112yes—
91Dic146—22no—
92Dic146—41no—
93Dic146—41no—
94#10596833—24no—
95C22×C73—21no—
96C22×C73—21no—
97C22×C73#10312yescomplemented
98C22×C73C2×C22⋊C411yescharacteristic
99C2×D73—21no—
100C2×D73—21no—
101C2×D73—24no—
102C2×D73—24no—
103C2×D73#10312yescomplemented
104C2×D73#12112yes—
105C2×D73C2×SD1611yescharacteristic
106C2×D73C2×Q1611yescharacteristic
107C2×D73#13512yes—
108#64408—82no—
109C4×C73—21no—
110C4×C73—41no—
111C4×C73—41no—
112C4×C73C4×D412yes—
113Dic73—21no—
114Dic73—41no—
115Dic73—41no—
116Dic73#12011yescharacteristic
117Dic73#12311yescharacteristic
118C2×C73—22no—
119C2×C73#38611yescharacteristic
120C2×C73C2×#10311yescharacteristic
121C2×C73#41611yescharacteristic
122D73—22no—
123D73#46512yes—
124D73#46712yes—
125#1892—731nomaximal, Sylow
126C73#189211yescharacteristic, complemented, Sylow
127C23×C8—731no—
128C2×C22⋊Q8—731no—
129C2×#103—732no—
130#380—731no—
131#340—732no—
132C22×Q8—731no—
133C23×C4—731no—
134C22×C8—732no—
135C22×C8—1464no—
136C22×C8—1461no—
137C22×C8—1461no—
138C22⋊Q8—731no—
139C22⋊Q8—731no—
140C22⋊Q8—731no—
141C22⋊Q8—1461no—
142C22⋊Q8—1461no—
143C22⋊Q8#6440811yescharacteristic, complemented
144C2×C4⋊C4—731no—
145C2×C4⋊C4—732no—
146C2×C4⋊C4—1461no—
147C2×C22⋊C4—1461no—
148C2×C22⋊C4—1461no—
149#103—1464no—
150#95—1461no—
151C24—731no—
152C2×Q8—731no—
153C2×Q8—1461no—
154C2×Q8—1462no—
155C2×Q8—1462no—
156C2×Q8C2×#6440811yescharacteristic
157C22×C4—731no—
158C22×C4—731no—
159C22×C4—731no—
160C22×C4—731no—
161C22×C4—731no—
162C22×C4—1461no—
163C22×C4—1461no—
164C22×C4—1462no—
165C22×C4—1462no—
166C22×C4—1462no—
167C22×C4C2×#6440811yescharacteristic
168C2×C8—734no—
169C2×C8—1462no—
170C2×C8—1462no—
171C2×C8—1464no—
172C2×C8—1464no—
173C4⋊C4—21no—
174C4⋊C4—731no—
175C4⋊C4—1461no—
176C4⋊C4—1461no—
177C4⋊C4—1461no—
178C4⋊C4—1462no—
179C4⋊C4—1462no—
180C4⋊C4—1461no—
181C4⋊C4C2×#6440811yescharacteristic
182C22⋊C4—21no—
183C22⋊C4—2922no—
184C22⋊C4—1461no—
185C22⋊C4—1461no—
186C22⋊C4—1461no—
187C23—731no—
188C23—732no—
189C23—732no—
190C23—731no—
191C23—1462no—
192C23—1462no—
193C23C22⋊#6440811yescharacteristic
194Q8—22no—
195Q8—2921no—
196Q8—2921no—
197Q8—1462no—
198C2×C4—22no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—2922no—
202C2×C4—2922no—
203C2×C4—2922no—
204C2×C4—2922no—
205C2×C4—2922no—
206C2×C4—731no—
207C2×C4—732no—
208C2×C4—732no—
209C2×C4—731no—
210C2×C4—1461no—
211C2×C4—1461no—
212C2×C4—1462no—
213C2×C4—1461no—
214C2×C4—1461no—
215C2×C4—1461no—
216C2×C4—1461no—
217C2×C4—1462no—
218C2×C4C22⋊#6440811yescharacteristic
219C2×C4C22×#6440811yescharacteristic
220C8—1464no—
221C22—21no—
222C22—21no—
223C22—732no—
224C22—731no—
225C22—731no—
226C22—732no—
227C22—732no—
228C22—1464no—
229C22—1464no—
230C22—1461no—
231C22—1461no—
232C22#1455665412yescomplemented
233C22C2×C22⋊#6440811yescharacteristic
234C4—21no—
235C4—41no—
236C4—41no—
237C4—2921no—
238C4—2921no—
239C4—5842no—
240C4—731no—
241C4—731no—
242C4—1461no—
243C4D4×#6440812yes—
244C2—22no—
245C2—732no—
246C2—732no—
247C2—1462no—
248C2#1798953511yescharacteristic
249C2C2×#1455665411yescharacteristic
250C2#1798957711yescharacteristic
subgroupG/H
centerC22C2×C22⋊#64408
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
FittingC22⋊Q8×C73C4
socleC22×C73C2×C22⋊C4
hypercenterC22⋊Q8#64408
hypocenterC73#1892
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. C2×#14556654C2semidirect
4. #17989460C2semidirect
16. #14556571C4semidirect
17. #14556570C4semidirect
20. #14556567C4semidirect
24. C22⋊Q8×C73C4semidirect
97. C22×C73#103semidirect
103. C2×D73#103semidirect
126. C73#1892semidirect
143. C22⋊Q8#64408semidirect
232. C22#14556654semidirect