Finite Group Databasebeta

← #22610425

Subgroups — #22610425

Order 9344.

310 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 89 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
1C2×#14556622C211yesmaximal, characteristic
2#17988605C211yesmaximal, characteristic
3#17988596C211yesmaximal, characteristic, complemented
4#17988560C211yesmaximal, characteristic
5#17988357C211yesmaximal, characteristic, complemented
6#17988343C211yesmaximal, characteristic, complemented
7#519×C73C211yesmaximal, characteristic, complemented
8C2×#11924028C2211yescharacteristic
9#14556622—22no—
10#14556622—22no—
11C2×#11924018C412yescomplemented
12C2×#11924015C412yescomplemented
13C2×#11924012C2211yescharacteristic
14C2×#11924012C2211yescharacteristic
15#14556550C2211yescharacteristic
16#14556519—22no—
17#14556515—22no—
18#14556505—22no—
19C22×Q8×C73C2211yescharacteristic
20C4×Q8×C73—22no—
21C4×Q8×C73—22no—
22#117×C73—22no—
23#117×C73C2211yescharacteristic
24#117×C73C2211yescharacteristic
25#11924028—21no—
26#11924028—21no—
27#11924028—21no—
28#11924028—21no—
29C2×Dic146C2×C411yescharacteristic
30C2×D292C2×C411yescharacteristic
31C2×C22⋊D73—21no—
32C2×C4×D73—21no—
33#11924018—24no—
34#11924015—24no—
35#11924012—21no—
36#11924012—21no—
37#11924012—21no—
38#11924012—21no—
39C2×#10596831—21no—
40C2×#10596831C2×C412yes—
41C4⋊Dic73—21no—
42C22⋊Dic73—21no—
43C4×Dic73—21no—
44C2×Q8×C73—21no—
45C2×Q8×C73—21no—
46C2×Q8×C73—21no—
47C2×Q8×C73C2×C412yes—
48C2×Q8×C73D412yes—
49C2×Q8×C73D412yes—
50C22×C4×C73—21no—
51C22×C4×C73C2311yescharacteristic
52C4⋊C4×C73—24no—
53C4⋊C4×C73—21no—
54C4⋊C4×C73—21no—
55C22⋊C4×C73—21no—
56C22⋊C4×C73D412yes—
57C42×C73—24no—
58C42×C73—21no—
59C42×C73D412yes—
60C23×C73C2×D411yescharacteristic
61C22×D73—21no—
62Q8×C73—22no—
63Q8×C73—22no—
64Q8×C73—22no—
65Q8×C73C22⋊C414yes—
66C2×C4×C73—22no—
67C2×C4×C73—22no—
68C2×C4×C73—22no—
69C2×C4×C73—22no—
70C2×C4×C73—22no—
71C2×C4×C73C22×C411yescharacteristic
72C2×C4×C73C2×D411yescharacteristic
73C2×C4×C73C2×D411yescharacteristic
74C2×C4×C73C2×D411yescharacteristic
75C2×C4×C73#4111yescharacteristic
76C2×C4×C73#4111yescharacteristic
77C22⋊D73—41no—
78C22⋊D73—41no—
79C2×Dic73—21no—
80C2×Dic73—41no—
81D292—21no—
82D292—21no—
83C4×D73—41no—
84C4×D73—41no—
85Dic146—21no—
86Dic146—21no—
87#10596831—22no—
88#10596831—41no—
89C22×C73—41no—
90C22×C73C4×D411yescharacteristic
91C22×C73#12011yescharacteristic
92C22×C73#12111yescharacteristic
93C2×D73—41no—
94C2×D73—81no—
95C4×C73—24no—
96C4×C73—42no—
97C4×C73—42no—
98C4×C73C2×C22⋊C411yescharacteristic
99C4×C73C4×D411yescharacteristic
100C4×C73#12111yescharacteristic
101C4×C73#12311yescharacteristic
102Dic73—41no—
103Dic73—81no—
104C2×C73—21no—
105C2×C73—21no—
106C2×C73—21no—
107C2×C73#38611yescharacteristic
108D73—81no—
109#1905—731nomaximal, Sylow
110C73#190511yescharacteristic, complemented, Sylow
111C2×#137—731no—
112#519D7311yescharacteristic, complemented
113#421—731no—
114#419—731no—
115#410—731no—
116#344—731no—
117H(3,ℤ/4)—731no—
118C2×#41—731no—
119C22×Q8C2×D7311yescharacteristic
120#137—1462no—
121#137—1462no—
122C2×Q16—732no—
123C2×SD16—732no—
124C2×M16—731no—
125C2×M16—731no—
126C4×Q8—22no—
127C4×Q8—22no—
128#117—22no—
129#117—731no—
130#117C2×D7311yescharacteristic
131#117C2×D7311yescharacteristic
132#104—1462no—
133#103—1462no—
134#99—1462no—
135#41—1461no—
136#41—1461no—
137#41—1461no—
138#41—1461no—
139C2×Q8—21no—
140C2×Q8—21no—
141C2×Q8—21no—
142C2×Q8—731no—
143C2×Q8C4×D7312yes—
144C2×Q8D29212yes—
145C2×Q8C22⋊D7312yes—
146C2×D4—731no—
147C2×D4—1461no—
148C22×C4—21no—
149C22×C4—1461no—
150C22×C4C22×D7311yescharacteristic
151Q16—1464no—
152SD16—1464no—
153M16—1461no—
154M16—1461no—
155M16—1461no—
156M16—1461no—
157C2×C8—732no—
158C2×C8—1461no—
159C4⋊C4—24no—
160C4⋊C4—21no—
161C4⋊C4—21no—
162C4⋊C4—1461no—
163C22⋊C4—21no—
164C22⋊C4—1461no—
165C22⋊C4C22⋊D7312yes—
166C42—24no—
167C42—21no—
168C42—1461no—
169C42C22⋊D7312yes—
170C23—1461no—
171C23C2×C22⋊D7311yescharacteristic
172Q8—22no—
173Q8—22no—
174Q8—22no—
175Q8—1461no—
176Q8—1461no—
177Q8#1192400514yes—
178D4—2921no—
179D4—2921no—
180D4—1461no—
181D4—1461no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—2921no—
188C2×C4—2921no—
189C2×C4—2921no—
190C2×C4—1461no—
191C2×C4C2×C4×D7311yescharacteristic
192C2×C4C2×C22⋊D7311yescharacteristic
193C2×C4C2×C22⋊D7311yescharacteristic
194C2×C4C2×D29211yescharacteristic
195C2×C4#1192402811yescharacteristic
196C2×C4#1192402811yescharacteristic
197C8—2921no—
198C8—1462no—
199C22—41no—
200C22—2921no—
201C22—5841no—
202C22C4×C22⋊D7311yescharacteristic
203C22#1455656011yescharacteristic
204C22#1455656511yescharacteristic
205C4—24no—
206C4—42no—
207C4—42no—
208C4—2921no—
209C4—5841no—
210C4C2×#1192400511yescharacteristic
211C4C4×C22⋊D7311yescharacteristic
212C4#1455656511yescharacteristic
213C4#1455657411yescharacteristic
214C2—21no—
215C2—21no—
216C2—21no—
217C2—5841no—
218C2#1798846611yescharacteristic
subgroupG/H
centerC2#17988466
commutatorC2×C4×C73C22×C4
FrattiniC22×C4C22×D73
Fitting#519×C73C2
socleC2×C73#386
hypercenter#519D73
hypocenterC73#1905
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C22×C4 ◁ #519

Complements

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

NH ≅ G/Ntype
3. #17988596C2semidirect
5. #17988357C2semidirect
6. #17988343C2semidirect
7. #519×C73C2semidirect
11. C2×#11924018C4semidirect
12. C2×#11924015C4semidirect
110. C73#1905semidirect
112. #519D73semidirect