Finite Group Databasebeta

← #22625806

Subgroups — #22625806

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×#14556656C212yesmaximal
3C4×C4⋊#64408C211yesmaximal, characteristic, complemented
4#17989457C212yesmaximal, complemented
5C4×#11924029C211yesmaximal, characteristic
6C2×#11924038C2212yes—
7C2×C4⋊#64408—21no—
8C2×C4×#64408C2212yes—
9#14556658—21no—
10#14556658—21no—
11#14556656—24no—
12(C2×#64408)⋊C4—21no—
13C2×#11924029C2211yescharacteristic
14Q8×Dic73C411yescharacteristic, complemented
15C4×D292—21no—
16C4×D292C411yescharacteristic, complemented
17#14556553—21no—
18#14556553C411yescharacteristic, complemented
19#14556549—21no—
20#14556549C2211yescharacteristic
21C42×D73—21no—
22C42×D73C2211yescharacteristic
23C4×Q8×C73C411yescharacteristic, complemented
24C22×#64408—22no—
25#11924038—22no—
26#11924038—22no—
27C2×#10596833—22no—
28C4⋊#64408—24no—
29C4×#64408—22no—
30C4×#64408—22no—
31#11924029—21no—
32#11924029—21no—
33#11924029D412yes—
34#11924029Q812yes—
35C2×D292—21no—
36C2×D292C2×C411yescharacteristic
37C2×C4×D73—21no—
38C2×C4×D73—21no—
39C2×C4×D73—21no—
40C2×C4×D73D411yescharacteristic
41C2×C4×D73D411yescharacteristic
42C2×C4×D73C2311yescharacteristic
43C4⋊Dic73—21no—
44C4⋊Dic73C2×C411yescharacteristic
45#11924005—21no—
46#11924005—21no—
47#11924005—21no—
48C4×Dic73—21no—
49C4×Dic73—21no—
50C4×Dic73C2×C411yescharacteristic
51C4×Dic73D411yescharacteristic
52C4×Dic73D411yescharacteristic
53C2×Q8×C73C2×C411yescharacteristic
54C4⋊C4×C73—21no—
55C4⋊C4×C73C2×C411yescharacteristic
56C42×C73—21no—
57C42×C73C2×C411yescharacteristic
58C22×D73—21no—
59C22×D73C2×D411yescharacteristic
60C2×#64408—24no—
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×Dic73C22⋊C411yescharacteristic
72C2×Dic73C22⋊C411yescharacteristic
73C2×Dic73C2×D411yescharacteristic
74D292—22no—
75D292—22no—
76D292—21no—
77D292C4⋊C412yescomplemented
78C4×D73—22no—
79C4×D73—22no—
80C4×D73—22no—
81C4×D73—41no—
82C4×D73—42no—
83C4×D73—42no—
84C4×D73C2×D411yescharacteristic
85C4×D73C2×Q811yescharacteristic
86C4×D73#4111yescharacteristic
87C4×D73#4111yescharacteristic
88#10596833—42no—
89C22×C73C2×C22⋊C411yescharacteristic
90C2×D73—21no—
91C2×D73—21no—
92C2×D73—22no—
93C2×D73—41no—
94C2×D73—41no—
95C2×D73#12111yescharacteristic
96C2×D73C22⋊Q811yescharacteristic
97#64408—44no—
98C4×C73—22no—
99C4×C73—21no—
100C4×C73—21no—
101C4×C73—41no—
102C4×C73C2×C4⋊C411yescharacteristic
103C4×C73#11711yescharacteristic
104Dic73—21no—
105Dic73—41no—
106Dic73#10412yescomplemented
107Dic73#12111yescharacteristic
108Dic73C22⋊Q811yescharacteristic
109C2×C73#38011yescharacteristic
110C2×C73C2×#10411yescharacteristic
111C2×C73#42111yescharacteristic
112D73—21no—
113D73—21no—
114D73—42no—
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#6440811yescharacteristic, complemented
126C4×D4—731no—
127C4×D4—731no—
128C4×D4—1461no—
129C4×D4—1461no—
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×Q8C2×#6440811yescharacteristic
145C2×D4—731no—
146C2×D4—1461no—
147C22×C4—731no—
148C22×C4—731no—
149C22×C4—731no—
150C22×C4—1461no—
151C22×C4—1461no—
152C22×C4—1462no—
153C22×C4—1461no—
154M16—1462no—
155M16—1462no—
156C2×C8—1462no—
157C4⋊C4—21no—
158C4⋊C4—731no—
159C4⋊C4—1461no—
160C4⋊C4—1464no—
161C4⋊C4C2×#6440811yescharacteristic
162C22⋊C4—1461no—
163C22⋊C4—1461no—
164C22⋊C4—1461no—
165C42—21no—
166C42—731no—
167C42—731no—
168C42—731no—
169C42—1461no—
170C42—1461no—
171C42—1462no—
172C42—1462no—
173C42C2×#6440811yescharacteristic
174C23—731no—
175C23—1461no—
176Q8—21no—
177Q8C4⋊#6440812yescomplemented
178D4—732no—
179D4—1462no—
180D4—1462no—
181D4—1461no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—2922no—
185C2×C4—2921no—
186C2×C4—2922no—
187C2×C4—2922no—
188C2×C4—2922no—
189C2×C4—731no—
190C2×C4—731no—
191C2×C4—731no—
192C2×C4—731no—
193C2×C4—731no—
194C2×C4—731no—
195C2×C4—731no—
196C2×C4—1462no—
197C2×C4—1462no—
198C2×C4—1462no—
199C2×C4—1464no—
200C2×C4—1461no—
201C2×C4C22⋊#6440811yescharacteristic
202C2×C4C22⋊#6440811yescharacteristic
203C2×C4C22×#6440811yescharacteristic
204C8—2922no—
205C22—2921no—
206C22—2921no—
207C22—731no—
208C22—731no—
209C22—1462no—
210C22—1461no—
211C22—1461no—
212C22C2×C22⋊#6440811yescharacteristic
213C4—22no—
214C4—21no—
215C4—21no—
216C4—41no—
217C4—2924no—
218C4—2921no—
219C4—731no—
220C4—731no—
221C4—732no—
222C4—1461no—
223C4C2×C4⋊#6440811yescharacteristic
224C4#1455667011yescharacteristic
225C2—2922no—
226C2—1461no—
227C2—1461no—
228C2#1798952911yescharacteristic
229C2D73⋊#10411yescharacteristic
230C2#1798958611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#64408
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
FittingC4×Q8×C73C4
socleC22×C73C2×C22⋊C4
hypercenterC4×Q8#64408
hypocenterC73#1806
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
1. #17989592C2semidirect
3. C4×C4⋊#64408C2semidirect
4. #17989457C2semidirect
14. Q8×Dic73C4semidirect
16. C4×D292C4semidirect
18. #14556553C4semidirect
23. C4×Q8×C73C4semidirect
64. Q8×C73C4⋊C4semidirect
77. D292C4⋊C4semidirect
106. Dic73#104semidirect
116. C73#1806semidirect
125. C4×Q8#64408semidirect
177. Q8C4⋊#64408semidirect