Finite Group Databasebeta

← #22625805

Subgroups — #22625805

Order 9344.

312 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 78 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#17989592C211yesmaximal, characteristic, complemented
2C2×#14556655C212yesmaximal
3C4×C4⋊#64408C211yesmaximal, characteristic, complemented
4#17989457C212yesmaximal, complemented
5C4×#11924027C211yesmaximal, characteristic
6C2×#11924038C2212yes—
7C2×C4⋊#64408—21no—
8C2×C4×#64408C2212yes—
9#14556658—21no—
10#14556658—21no—
11#14556655—24no—
12(C2×#64408)⋊C4—21no—
13C2×#11924027C2211yescharacteristic
14C4×Dic146C411yescharacteristic, complemented
15#14556556C411yescharacteristic, complemented
16D4×Dic73C411yescharacteristic, complemented
17C4×C22⋊D73—21no—
18#14556551—21no—
19#14556549C2211yescharacteristic
20#14556547—21no—
21C2×C4×Dic73—21no—
22C42×D73C2211yescharacteristic
23C4×D4×C73C411yescharacteristic, complemented
24C22×#64408—22no—
25#11924038—22no—
26#11924038—22no—
27C2×#10596833—22no—
28C4⋊#64408—24no—
29C4×#64408—22no—
30C4×#64408—22no—
31#11924027—21no—
32#11924027—21no—
33#11924027D412yes—
34#11924027Q812yes—
35C2×Dic146C2×C411yescharacteristic
36C2×C22⋊D73—21no—
37C22×Dic73—21no—
38C22×Dic73—21no—
39C2×C4×D73D411yescharacteristic
40C2×C4×D73D411yescharacteristic
41C2×C4×D73C2311yescharacteristic
42C4⋊Dic73C2×C411yescharacteristic
43#11924007—21no—
44#11924007—21no—
45C22⋊Dic73—21no—
46#11924005—21no—
47C4×Dic73—21no—
48C4×Dic73—21no—
49C4×Dic73—21no—
50C4×Dic73C2×C411yescharacteristic
51C4×Dic73D411yescharacteristic
52C4×Dic73D411yescharacteristic
53C2×D4×C73C2×C411yescharacteristic
54C22×C4×C73—21no—
55C4⋊C4×C73C2×C411yescharacteristic
56C22⋊C4×C73—21no—
57C42×C73C2×C411yescharacteristic
58C23×C73—21no—
59C22×D73C2×D411yescharacteristic
60C2×#64408—24no—
61C2×#64408—42no—
62C2×#64408—42no—
63D4×C73—21no—
64D4×C73C4⋊C412yescomplemented
65C2×C4×C73—21no—
66C2×C4×C73—42no—
67C2×C4×C73C22⋊C411yescharacteristic
68C2×C4×C73C22⋊C411yescharacteristic
69C2×C4×C73C22×C411yescharacteristic
70C22⋊D73—22no—
71C22⋊D73—22no—
72C2×Dic73—21no—
73C2×Dic73—22no—
74C2×Dic73—22no—
75C2×Dic73—21no—
76C2×Dic73—42no—
77C2×Dic73C22⋊C411yescharacteristic
78C2×Dic73C22⋊C411yescharacteristic
79C2×Dic73C2×D411yescharacteristic
80C4×D73—22no—
81C4×D73—41no—
82C4×D73C2×D411yescharacteristic
83C4×D73C2×Q811yescharacteristic
84C4×D73#4111yescharacteristic
85C4×D73#4111yescharacteristic
86Dic146—21no—
87Dic146C4⋊C412yescomplemented
88#10596833—42no—
89C22×C73—22no—
90C22×C73—41no—
91C22×C73—41no—
92C22×C73C2×C22⋊C411yescharacteristic
93C2×D73—21no—
94C2×D73—21no—
95C2×D73#12111yescharacteristic
96C2×D73C22⋊Q811yescharacteristic
97#64408—44no—
98C4×C73—21no—
99C4×C73—21no—
100C4×C73—41no—
101C4×C73C2×C4⋊C411yescharacteristic
102C4×C73#11711yescharacteristic
103Dic73—22no—
104Dic73—21no—
105Dic73—41no—
106Dic73#10412yescomplemented
107Dic73#12111yescharacteristic
108Dic73C22⋊Q811yescharacteristic
109C2×C73—42no—
110C2×C73#38011yescharacteristic
111C2×C73C2×#10411yescharacteristic
112C2×C73#42111yescharacteristic
113D73—21no—
114D73—21no—
115#1806—731nomaximal, Sylow
116C73#180611yescharacteristic, complemented, Sylow
117C4×#41—731no—
118#423—731no—
119C2×#104—732no—
120C4×C4⋊C4—731no—
121#339—732no—
122C2×#41—731no—
123C2×M16—732no—
124C4×Q8—731no—
125C4×Q8—731no—
126C4×D4—731no—
127C4×D4—1461no—
128C4×D4—1461no—
129C4×D4#6440811yescharacteristic, complemented
130#117—731no—
131#117—1461no—
132C2×C4⋊C4—1461no—
133C2×C42—731no—
134C2×C42—732no—
135C2×C42—1461no—
136C4⋊C8—1461no—
137C4⋊C8—1461no—
138#104—1464no—
139#95—1461no—
140#41—732no—
141#41—732no—
142#41—1461no—
143#41—1461no—
144C2×Q8—731no—
145C2×D4—1461no—
146C2×D4C2×#6440811yescharacteristic
147C22×C4—21no—
148C22×C4—731no—
149C22×C4—731no—
150C22×C4—731no—
151C22×C4—1461no—
152C22×C4—1462no—
153C22×C4—1461no—
154M16—1462no—
155M16—1462no—
156C2×C8—1462no—
157C4⋊C4—731no—
158C4⋊C4—1461no—
159C4⋊C4—1464no—
160C4⋊C4—1461no—
161C4⋊C4C2×#6440811yescharacteristic
162C22⋊C4—21no—
163C22⋊C4—1461no—
164C22⋊C4—1461no—
165C42—731no—
166C42—731no—
167C42—731no—
168C42—1461no—
169C42—1461no—
170C42—1462no—
171C42—1462no—
172C42—1461no—
173C42C2×#6440811yescharacteristic
174C23—21no—
175C23—731no—
176Q8—732no—
177Q8—1461no—
178D4—21no—
179D4—1462no—
180D4—1462no—
181D4C4⋊#6440812yescomplemented
182C2×C4—21no—
183C2×C4—42no—
184C2×C4—2921no—
185C2×C4—2922no—
186C2×C4—2922no—
187C2×C4—2922no—
188C2×C4—731no—
189C2×C4—731no—
190C2×C4—731no—
191C2×C4—731no—
192C2×C4—731no—
193C2×C4—731no—
194C2×C4—731no—
195C2×C4—1462no—
196C2×C4—1464no—
197C2×C4—1461no—
198C2×C4—1462no—
199C2×C4—1462no—
200C2×C4—1461no—
201C2×C4C22⋊#6440811yescharacteristic
202C2×C4C22⋊#6440811yescharacteristic
203C2×C4C22×#6440811yescharacteristic
204C8—2922no—
205C22—22no—
206C22—41no—
207C22—41no—
208C22—731no—
209C22—731no—
210C22—1461no—
211C22—1461no—
212C22C2×C22⋊#6440811yescharacteristic
213C4—21no—
214C4—21no—
215C4—41no—
216C4—2924no—
217C4—2921no—
218C4—731no—
219C4—731no—
220C4—732no—
221C4—1462no—
222C4—1461no—
223C4C2×C4⋊#6440811yescharacteristic
224C4#1455667011yescharacteristic
225C2—42no—
226C2—1461no—
227C2—1461no—
228C2#1798952911yescharacteristic
229C2D73⋊#10411yescharacteristic
230C2#1798958511yescharacteristic
subgroupG/H
centerC22C2×C22⋊#64408
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
FittingC4×D4×C73C4
socleC22×C73C2×C22⋊C4
hypercenterC4×D4#64408
hypocenterC73#1806
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #17989592C2semidirect
3. C4×C4⋊#64408C2semidirect
4. #17989457C2semidirect
14. C4×Dic146C4semidirect
15. #14556556C4semidirect
16. D4×Dic73C4semidirect
23. C4×D4×C73C4semidirect
64. D4×C73C4⋊C4semidirect
87. Dic146C4⋊C4semidirect
106. Dic73#104semidirect
116. C73#1806semidirect
129. C4×D4#64408semidirect
181. D4C4⋊#64408semidirect