Finite Group Databasebeta

← #22609111

Subgroups — #22609111

Order 9344.

308 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 308 conjugacy classes of subgroups — too many to draw. Only its 57 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#17989222C211yesmaximal, characteristic
2#17988933C211yesmaximal, characteristic, complemented
3#17988868C211yesmaximal, characteristic, complemented
4#17988793C211yesmaximal, characteristic, complemented
5#17988314C211yesmaximal, characteristic, complemented
6#17988314C211yesmaximal, characteristic, complemented
7#331×C73C211yesmaximal, characteristic, complemented
8C2×D4×D73—21no—
9C2×D4×D73—21no—
10C2×#11924017—21no—
11#14556591C2211yescharacteristic, complemented
12#14556562—21no—
13#14556562—21no—
14#14556559—22no—
15C4×D292C2211yescharacteristic
16C4×D292C2211yescharacteristic
17#14556525—21no—
18#14556516—21no—
19#14556513—21no—
20#14556512—22no—
21C4×#10596831C2211yescharacteristic, complemented
22#127×C73C2211yescharacteristic
23C4⋊C8×C73C2211yescharacteristic, complemented
24C4⋊C8×C73C2211yescharacteristic, complemented
25C23×D73—22no—
26C2×Dic146—21no—
27C2×D292D411yescharacteristic
28C2×D292D411yescharacteristic
29C2×C22⋊D73—22no—
30C2×C22⋊D73—22no—
31D4×D73—42no—
32D4×D73—42no—
33D4×D73—42no—
34D4×D73—42no—
35C2×C4×D73—21no—
36C2×C4×D73—21no—
37#11924017—42no—
38C2×#10596831—21no—
39C4⋊Dic73—21no—
40C4⋊Dic73—21no—
41C4⋊Dic73D411yescharacteristic
42C4⋊Dic73D411yescharacteristic
43C22⋊Dic73—22no—
44#11924005—21no—
45#11924005—21no—
46C2×D4×C73—21no—
47C2×D4×C73—21no—
48C2×D4×C73D412yes—
49C2×C8×C73—21no—
50C2×C8×C73—21no—
51C42×C73C2311yescharacteristic
52C23×C73—22no—
53C22×D73—21no—
54C22×D73—21no—
55C22×D73—44no—
56C22×D73—44no—
57C22×D73—82no—
58D4×C73—42no—
59D4×C73—41no—
60D4×C73—41no—
61D4×C73—41no—
62D4×C73—41no—
63C2×C4×C73C2×D411yescharacteristic
64C2×C4×C73C2×D411yescharacteristic
65C2×C4×C73C2×D411yescharacteristic
66C22⋊D73—44no—
67C22⋊D73—44no—
68C2×Dic73—21no—
69C2×Dic73—21no—
70C2×Dic73—41no—
71D292—21no—
72D292—21no—
73D292D812yes—
74D292SD1612yescomplemented
75C4×D73—41no—
76C4×D73—41no—
77C4×D73—41no—
78C4×D73—41no—
79Dic146—41no—
80Dic146—41no—
81C8×C73—41no—
82C8×C73—41no—
83#10596831—41no—
84C22×C73—42no—
85C22×C73—42no—
86C22×C73—42no—
87C22×C73#12011yescharacteristic
88C2×D73—22no—
89C2×D73—22no—
90C2×D73—41no—
91C2×D73—41no—
92C2×D73—41no—
93C2×D73—41no—
94C2×D73—88no—
95C4×C73—21no—
96C4×C73C2×D811yescharacteristic
97C4×C73C2×SD1611yescharacteristic
98C4×C73AGL(1,ℤ/8)11yescharacteristic
99C4×C73AGL(1,ℤ/8)11yescharacteristic
100Dic73—41no—
101Dic73—41no—
102Dic73—81no—
103C2×C73—82no—
104C2×C73#44711yescharacteristic
105C2×C73#45011yescharacteristic
106C2×C73#45511yescharacteristic
107D73—42no—
108D73—42no—
109#1639—731nomaximal, Sylow
110C73#163911yescharacteristic, complemented, Sylow
111D42—731no—
112#486—731no—
113#474—731no—
114#461—731no—
115#331D7311yescharacteristic, complemented
116D4⋊C8—731no—
117D4⋊C8—731no—
118C22×D4—1461no—
119C22×D4—1461no—
120C2×SD16—1461no—
121C4⋊Q8—731no—
122#127C2×D7311yescharacteristic
123#121—1461no—
124#121—1461no—
125#120—1462no—
126C4×D4—731no—
127C4×D4—731no—
128#107—1461no—
129C4⋊C8C2×D7311yescharacteristic, complemented
130C4⋊C8C2×D7311yescharacteristic, complemented
131#103—1461no—
132#102—1461no—
133#102—1462no—
134C4×C8—731no—
135C24—1462no—
136C2×Q8—1461no—
137C2×D4—21no—
138C2×D4—21no—
139C2×D4—2922no—
140C2×D4—2922no—
141C2×D4—2922no—
142C2×D4—2922no—
143C2×D4—731no—
144C2×D4—731no—
145C2×D4—1462no—
146C2×D4—1462no—
147C2×D4D29212yes—
148C22×C4—1461no—
149C22×C4—1461no—
150SD16—2922no—
151C2×C8—21no—
152C2×C8—21no—
153C2×C8—1461no—
154C4⋊C4—731no—
155C4⋊C4—731no—
156C4⋊C4—1461no—
157C4⋊C4—1461no—
158C22⋊C4—1462no—
159C22⋊C4—1461no—
160C22⋊C4—1461no—
161C42C22×D7311yescharacteristic
162C23—22no—
163C23—2924no—
164C23—2924no—
165C23—5842no—
166C23—1461no—
167C23—1461no—
168Q8—2921no—
169Q8—2921no—
170D4—42no—
171D4—41no—
172D4—41no—
173D4—41no—
174D4—41no—
175D4—2924no—
176D4—2924no—
177D4—732no—
178D4—732no—
179D4—1461no—
180D4—1461no—
181C2×C4—2921no—
182C2×C4—2921no—
183C2×C4—2921no—
184C2×C4—2921no—
185C2×C4—2921no—
186C2×C4—1461no—
187C2×C4—1461no—
188C2×C4D4×D7311yescharacteristic
189C2×C4D4×D7311yescharacteristic
190C2×C4C2×D29211yescharacteristic
191C8—41no—
192C8—41no—
193C8—2921no—
194C22—42no—
195C22—42no—
196C22—42no—
197C22—2921no—
198C22—2921no—
199C22—2921no—
200C22—2921no—
201C22—5848no—
202C22—1462no—
203C22—1462no—
204C22#1455656111yescharacteristic
205C4—21no—
206C4—2921no—
207C4—2921no—
208C4—5841no—
209C4D8×D7311yescharacteristic
210C4SD16×D7311yescharacteristic
211C4#1455661511yescharacteristic
212C4#1455661811yescharacteristic
213C2—82no—
214C2—2922no—
215C2—2922no—
216C2#1798872211yescharacteristic
217C2#1798873911yescharacteristic
218C2#1798876711yescharacteristic
subgroupG/H
centerC22#14556561
commutatorC42×C73C23
FrattiniC42C22×D73
Fitting#331×C73C2
socleC22×C73#120
hypercenter#331D73
hypocenterC73#1639
LCSG ▷ C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
2. #17988933C2semidirect
3. #17988868C2semidirect
4. #17988793C2semidirect
5. #17988314C2semidirect
6. #17988314C2semidirect
7. #331×C73C2semidirect
11. #14556591C22semidirect
21. C4×#10596831C22semidirect
23. C4⋊C8×C73C22semidirect
24. C4⋊C8×C73C22semidirect
74. D292SD16semidirect
110. C73#1639semidirect
115. #331D73semidirect
129. C4⋊C8C2×D73semidirect
130. C4⋊C8C2×D73semidirect