Finite Group Databasebeta

← #22609113

Subgroups — #22609113

Order 9344.

308 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 308 conjugacy classes of subgroups — too many to draw. Only its 59 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
1D4×D292C211yesmaximal, characteristic
2#17988934C211yesmaximal, characteristic, complemented
3#17988867C211yesmaximal, characteristic, complemented
4#17988793C211yesmaximal, characteristic, complemented
5#17988330C211yesmaximal, characteristic, complemented
6#17988316C211yesmaximal, characteristic, complemented
7D4⋊C8×C73C211yesmaximal, characteristic, complemented
8C22×D292—21no—
9C2×D4×D73—21no—
10C2×#11924017—21no—
11#14556591C2211yescharacteristic, complemented
12#14556588C2211yescharacteristic
13#14556566—21no—
14#14556565—21no—
15#14556561—22no—
16C4×D292C2211yescharacteristic
17#14556524—21no—
18C4⋊#10596831C2211yescharacteristic, complemented
19#14556516—21no—
20#14556513—22no—
21#14556512—21no—
22C4×D4×C73C2211yescharacteristic
23C4⋊C8×C73C2211yescharacteristic, complemented
24C4×C8×C73C2211yescharacteristic, complemented
25C23×D73—22no—
26C2×Dic146—21no—
27C2×D292—22no—
28C2×D292—21no—
29C2×D292—21no—
30C2×D292—42no—
31C2×D292—42no—
32C2×D292D411yescharacteristic
33C2×D292D412yes—
34C2×C22⋊D73—22no—
35D4×D73—42no—
36D4×D73—42no—
37C2×C4×D73—21no—
38#11924017—42no—
39C2×#10596831—21no—
40C4⋊Dic73—21no—
41C4⋊Dic73—21no—
42C4⋊Dic73D411yescharacteristic
43#11924005—22no—
44#11924005—21no—
45C2×D4×C73D411yescharacteristic
46C22×C4×C73—21no—
47C2×C8×C73—21no—
48C2×C8×C73—21no—
49C4⋊C4×C73D411yescharacteristic
50C22⋊C4×C73—21no—
51C42×C73C2311yescharacteristic
52C23×C73—21no—
53C22×D73—21no—
54C22×D73—22no—
55C22×D73—44no—
56C22×D73—44no—
57C22×D73—82no—
58D4×C73—21no—
59D4×C73SD1612yescomplemented
60C2×C4×C73—21no—
61C2×C4×C73—41no—
62C2×C4×C73—41no—
63C2×C4×C73C2×D411yescharacteristic
64C2×C4×C73C2×D411yescharacteristic
65C2×C4×C73C2×D411yescharacteristic
66C22⋊D73—44no—
67C2×Dic73—21no—
68C2×Dic73—41no—
69D292—21no—
70D292—42no—
71D292—44no—
72D292—41no—
73D292—41no—
74D292—41no—
75D292—41no—
76D292D812yes—
77C4×D73—41no—
78C4×D73—41no—
79Dic146—41no—
80Dic146—41no—
81C8×C73—41no—
82C8×C73—41no—
83#10596831—41no—
84C22×C73—22no—
85C22×C73—41no—
86C22×C73—41no—
87C22×C73#12011yescharacteristic
88C2×D73—22no—
89C2×D73—41no—
90C2×D73—41no—
91C2×D73—42no—
92C2×D73—42no—
93C2×D73—42no—
94C2×D73—88no—
95C4×C73—21no—
96C4×C73—41no—
97C4×C73C2×D811yescharacteristic
98C4×C73C2×SD1611yescharacteristic
99C4×C73AGL(1,ℤ/8)11yescharacteristic
100C4×C73AGL(1,ℤ/8)11yescharacteristic
101Dic73—41no—
102Dic73—81no—
103C2×C73—42no—
104C2×C73#44711yescharacteristic
105C2×C73#45011yescharacteristic
106C2×C73#45511yescharacteristic
107D73—42no—
108D73—82no—
109#1639—731nomaximal, Sylow
110C73#163911yescharacteristic, complemented, Sylow
111D42—731no—
112#486—731no—
113#474—731no—
114#461—731no—
115#331—731no—
116D4⋊C8—731no—
117D4⋊C8D7311yescharacteristic, complemented
118C22×D4—1461no—
119C22×D4—1461no—
120C2×SD16—1461no—
121C4⋊Q8—731no—
122#127—731no—
123#121—1461no—
124#121—1461no—
125#120—1462no—
126C4×D4—731no—
127C4×D4C2×D7311yescharacteristic
128#107—1461no—
129C4⋊C8—731no—
130C4⋊C8C2×D7311yescharacteristic, complemented
131#103—1461no—
132#102—1462no—
133#102—1461no—
134C4×C8C2×D7311yescharacteristic, complemented
135C24—1462no—
136C2×Q8—1461no—
137C2×D4—2922no—
138C2×D4—2922no—
139C2×D4—2922no—
140C2×D4—2922no—
141C2×D4—732no—
142C2×D4—731no—
143C2×D4—1462no—
144C2×D4—1462no—
145C2×D4—1461no—
146C2×D4—1461no—
147C2×D4D29211yescharacteristic
148C22×C4—21no—
149C22×C4—1461no—
150SD16—2922no—
151C2×C8—21no—
152C2×C8—21no—
153C2×C8—1461no—
154C4⋊C4—731no—
155C4⋊C4—1461no—
156C4⋊C4—1461no—
157C4⋊C4D29211yescharacteristic
158C22⋊C4—21no—
159C22⋊C4—1462no—
160C22⋊C4—1461no—
161C42C22×D7311yescharacteristic
162C23—21no—
163C23—2924no—
164C23—2924no—
165C23—5842no—
166C23—1462no—
167C23—1461no—
168Q8—2921no—
169Q8—2921no—
170D4—21no—
171D4—2922no—
172D4—2924no—
173D4—2924no—
174D4—2921no—
175D4—2921no—
176D4—2921no—
177D4—2921no—
178D4—732no—
179D4—1461no—
180D4#1192401712yescomplemented
181C2×C4—21no—
182C2×C4—41no—
183C2×C4—41no—
184C2×C4—2921no—
185C2×C4—2921no—
186C2×C4—2921no—
187C2×C4—1461no—
188C2×C4D4×D7311yescharacteristic
189C2×C4D4×D7311yescharacteristic
190C2×C4C2×D29211yescharacteristic
191C8—41no—
192C8—41no—
193C8—2921no—
194C22—22no—
195C22—41no—
196C22—41no—
197C22—2921no—
198C22—2921no—
199C22—2922no—
200C22—2922no—
201C22—2922no—
202C22—5848no—
203C22—1462no—
204C22#1455656111yescharacteristic
205C4—21no—
206C4—41no—
207C4—2921no—
208C4—5841no—
209C4D8×D7311yescharacteristic
210C4C2×#1192401711yescharacteristic
211C4#1455661811yescharacteristic
212C4#1455661911yescharacteristic
213C2—42no—
214C2—2922no—
215C2—5842no—
216C2#1798872211yescharacteristic
217C2#1798874011yescharacteristic
218C2#1798876611yescharacteristic
subgroupG/H
centerC22#14556561
commutatorC42×C73C23
FrattiniC42C22×D73
FittingD4⋊C8×C73C2
socleC22×C73#120
hypercenterD4⋊C8D73
hypocenterC73#1639
LCSG ▷ C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #17988934C2semidirect
3. #17988867C2semidirect
4. #17988793C2semidirect
5. #17988330C2semidirect
6. #17988316C2semidirect
7. D4⋊C8×C73C2semidirect
11. #14556591C22semidirect
18. C4⋊#10596831C22semidirect
23. C4⋊C8×C73C22semidirect
24. C4×C8×C73C22semidirect
59. D4×C73SD16semidirect
110. C73#1639semidirect
117. D4⋊C8D73semidirect
130. C4⋊C8C2×D73semidirect
134. C4×C8C2×D73semidirect
180. D4#11924017semidirect