Finite Group Databasebeta

← #22610424

Subgroups — #22610424

Order 9344.

310 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 79 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×#14556624C211yesmaximal, characteristic
2#17989064C211yesmaximal, characteristic, complemented
3#17988603C211yesmaximal, characteristic
4#17988597C211yesmaximal, characteristic, complemented
5#17988560C211yesmaximal, characteristic
6#17988344C211yesmaximal, characteristic, complemented
7#344×C73C211yesmaximal, characteristic, complemented
8C2×#11924028C2211yescharacteristic
9C22×Dic146C2211yescharacteristic
10#14556624—22no—
11#14556624—22no—
12C2×Dic292C412yescomplemented
13C2×#11924017C412yescomplemented
14C4×Dic146—22no—
15#14556556—22no—
16#14556550C2211yescharacteristic
17#14556550C2211yescharacteristic
18#14556547—22no—
19#14556517—22no—
20#14556516—22no—
21#14556505—22no—
22C2×M16×C73C2211yescharacteristic
23C2×M16×C73C2211yescharacteristic
24#117×C73C2211yescharacteristic
25#11924028—21no—
26#11924028—21no—
27#11924028—21no—
28#11924028—21no—
29C2×Dic146—21no—
30C2×Dic146—21no—
31C2×Dic146—21no—
32C2×Dic146C2×C411yescharacteristic
33C2×Dic146C2×C412yes—
34C2×Dic146D412yes—
35C2×Dic146D412yes—
36C2×D292C2×C411yescharacteristic
37C2×C22⋊D73—21no—
38C22×Dic73—21no—
39C2×C4×D73—21no—
40Dic292—24no—
41#11924017—24no—
42C4⋊Dic73—21no—
43C4⋊Dic73—21no—
44#11924007—24no—
45C22⋊Dic73—21no—
46C22⋊Dic73—21no—
47C4×Dic73—24no—
48C4×Dic73—21no—
49C4×Dic73D412yes—
50C22×C4×C73C2311yescharacteristic
51M16×C73—21no—
52M16×C73—21no—
53M16×C73—21no—
54M16×C73—21no—
55C2×C8×C73—21no—
56C2×C8×C73C2×C412yes—
57C4⋊C4×C73—21no—
58C22⋊C4×C73D412yes—
59C42×C73—21no—
60C23×C73C2×D411yescharacteristic
61C22×D73—21no—
62C2×C4×C73—22no—
63C2×C4×C73C22×C411yescharacteristic
64C2×C4×C73C2×D411yescharacteristic
65C2×C4×C73C2×D411yescharacteristic
66C2×C4×C73C2×D411yescharacteristic
67C2×C4×C73#4111yescharacteristic
68C2×C4×C73#4111yescharacteristic
69C22⋊D73—41no—
70C22⋊D73—41no—
71C2×Dic73—22no—
72C2×Dic73—22no—
73C2×Dic73—22no—
74C2×Dic73—21no—
75C2×Dic73—22no—
76C2×Dic73—41no—
77D292—21no—
78D292—21no—
79C4×D73—41no—
80C4×D73—41no—
81Dic146—22no—
82Dic146—22no—
83Dic146—22no—
84Dic146—21no—
85Dic146—21no—
86Dic146C22⋊C414yes—
87C8×C73—22no—
88C8×C73—41no—
89C22×C73—41no—
90C22×C73C4×D411yescharacteristic
91C22×C73#12011yescharacteristic
92C22×C73#12111yescharacteristic
93C2×D73—41no—
94C2×D73—81no—
95C4×C73—42no—
96C4×C73C2×C22⋊C411yescharacteristic
97C4×C73C4×D411yescharacteristic
98C4×C73#12111yescharacteristic
99C4×C73#12311yescharacteristic
100Dic73—24no—
101Dic73—42no—
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#519—731no—
113#421—731no—
114#419—731no—
115#410—731no—
116#344D7311yescharacteristic, complemented
117H(3,ℤ/4)—731no—
118C2×#41—731no—
119C22×Q8—731no—
120#137—1462no—
121#137—1462no—
122C2×Q16—732no—
123C2×SD16—732no—
124C2×M16C2×D7311yescharacteristic
125C2×M16C2×D7311yescharacteristic
126C4×Q8—1462no—
127C4×Q8—1462no—
128#117—731no—
129#117—731no—
130#117—1462no—
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—732no—
140C2×Q8—731no—
141C2×Q8—732no—
142C2×Q8—732no—
143C2×Q8—1461no—
144C2×Q8—1461no—
145C2×Q8—1461no—
146C2×D4—731no—
147C2×D4—1461no—
148C22×C4—1461no—
149C22×C4—1461no—
150C22×C4C22×D7311yescharacteristic
151Q16—1464no—
152SD16—1464no—
153M16—21no—
154M16—21no—
155M16—21no—
156M16—21no—
157C2×C8—21no—
158C2×C8C4×D7312yes—
159C4⋊C4—21no—
160C4⋊C4—1464no—
161C4⋊C4—1461no—
162C4⋊C4—1461no—
163C22⋊C4—1461no—
164C22⋊C4—1461no—
165C22⋊C4D29212yes—
166C42—21no—
167C42—732no—
168C42—1464no—
169C42—1461no—
170C23—1461no—
171C23C2×D29211yescharacteristic
172Q8—734no—
173Q8—1461no—
174Q8—1461no—
175Q8—1462no—
176Q8—1462no—
177Q8—1462no—
178D4—2921no—
179D4—2921no—
180D4—1461no—
181D4—1461no—
182C2×C4—22no—
183C2×C4—2921no—
184C2×C4—2921no—
185C2×C4—2921no—
186C2×C4—1461no—
187C2×C4—1462no—
188C2×C4—1462no—
189C2×C4—1462no—
190C2×C4—1462no—
191C2×C4C2×C4×D7311yescharacteristic
192C2×C4D4×D7311yescharacteristic
193C2×C4D4×D7311yescharacteristic
194C2×C4D4×D7311yescharacteristic
195C2×C4#1192402811yescharacteristic
196C2×C4#1192402911yescharacteristic
197C8—22no—
198C8—41no—
199C22—41no—
200C22—2921no—
201C22—5841no—
202C22C4×D29211yescharacteristic
203C22#1455656111yescharacteristic
204C22#1455656611yescharacteristic
205C4—42no—
206C4—2922no—
207C4—2921no—
208C4—5841no—
209C4—1464no—
210C4C22⋊C4×D7311yescharacteristic
211C4#1455655311yescharacteristic
212C4#1455656411yescharacteristic
213C4#1455657611yescharacteristic
214C2—21no—
215C2—21no—
216C2—21no—
217C2—5841no—
218C2#1798846511yescharacteristic
subgroupG/H
centerC2#17988465
commutatorC2×C4×C73C22×C4
FrattiniC22×C4C22×D73
Fitting#344×C73C2
socleC2×C73#386
hypercenter#344D73
hypocenterC73#1905
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C22×C4 ◁ #344

Complements

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

NH ≅ G/Ntype
2. #17989064C2semidirect
4. #17988597C2semidirect
6. #17988344C2semidirect
7. #344×C73C2semidirect
12. C2×Dic292C4semidirect
13. C2×#11924017C4semidirect
110. C73#1905semidirect
116. #344D73semidirect