Finite Group Databasebeta

← #22610422

Subgroups — #22610422

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×#14556621C211yesmaximal, characteristic
2#17989064C211yesmaximal, characteristic, complemented
3#17988597C211yesmaximal, characteristic, complemented
4#17988561C211yesmaximal, characteristic
5#17988359C211yesmaximal, characteristic, complemented
6#17988343C211yesmaximal, characteristic, complemented
7#421×C73C211yesmaximal, characteristic
8C22×Dic146C2211yescharacteristic
9#14556621—22no—
10#14556621—22no—
11C2×#11924018C412yescomplemented
12C2×#11924016C412yescomplemented
13C2×#11924012C2211yescharacteristic
14C4×Dic146—22no—
15#14556556—22no—
16#14556550C2211yescharacteristic
17#14556550C2211yescharacteristic
18#14556547—22no—
19#14556516—22no—
20#14556506—22no—
21C2×#41×C73C2211yescharacteristic
22C2×M16×C73C2211yescharacteristic
23#117×C73C2211yescharacteristic
24#104×C73—22no—
25C2×Dic146—21no—
26C2×Dic146—21no—
27C2×Dic146—21no—
28C2×Dic146C2×C412yes—
29C2×Dic146D412yes—
30C2×Dic146D412yes—
31C22×Dic73—21no—
32#11924018—24no—
33#11924016—24no—
34#11924012—21no—
35#11924012—21no—
36C2×#10596831C2×C412yes—
37C4⋊Dic73—21no—
38C4⋊Dic73—21no—
39#11924007—24no—
40C22⋊Dic73—21no—
41C22⋊Dic73D412yes—
42C4×Dic73—24no—
43C4×Dic73—21no—
44C4×Dic73—21no—
45#41×C73—21no—
46#41×C73—21no—
47#41×C73—21no—
48#41×C73—21no—
49C2×Q8×C73C2×C411yescharacteristic
50C2×D4×C73—21no—
51C2×D4×C73C2×C411yescharacteristic
52C22×C4×C73—21no—
53C22×C4×C73C2311yescharacteristic
54M16×C73—21no—
55M16×C73—21no—
56C2×C8×C73—21no—
57C4⋊C4×C73—21no—
58C22⋊C4×C73—21no—
59C42×C73D412yes—
60C23×C73—21no—
61C23×C73C2×D411yescharacteristic
62Q8×C73—21no—
63Q8×C73—21no—
64D4×C73—21no—
65D4×C73—21no—
66D4×C73—41no—
67D4×C73—41no—
68C2×C4×C73—21no—
69C2×C4×C73—22no—
70C2×C4×C73—41no—
71C2×C4×C73—41no—
72C2×C4×C73C22×C411yescharacteristic
73C2×C4×C73C2×D411yescharacteristic
74C2×C4×C73C2×D411yescharacteristic
75C2×C4×C73C2×D411yescharacteristic
76C2×C4×C73#4111yescharacteristic
77C2×C4×C73#4111yescharacteristic
78C2×Dic73—22no—
79C2×Dic73—22no—
80C2×Dic73—22no—
81C2×Dic73—22no—
82C2×Dic73—41no—
83Dic146—22no—
84Dic146—22no—
85Dic146—22no—
86Dic146C22⋊C414yes—
87C8×C73—41no—
88#10596831—22no—
89C22×C73—41no—
90C22×C73—41no—
91C22×C73—81no—
92C22×C73C4×D411yescharacteristic
93C22×C73#12011yescharacteristic
94C22×C73#12111yescharacteristic
95C4×C73—42no—
96C4×C73—41no—
97C4×C73C2×C22⋊C411yescharacteristic
98C4×C73C4×D411yescharacteristic
99C4×C73#12111yescharacteristic
100C4×C73#12311yescharacteristic
101Dic73—24no—
102Dic73—42no—
103Dic73—81no—
104C2×C73—21no—
105C2×C73—21no—
106C2×C73—21no—
107C2×C73—81no—
108C2×C73#38611yescharacteristic
109#1905—731nomaximal, Sylow
110C73#190511yescharacteristic, complemented, Sylow
111C2×#137—731no—
112#519—731no—
113#421D7311yescharacteristic
114#419—731no—
115#410—731no—
116#344—731no—
117H(3,ℤ/4)—731no—
118C2×#41C2×D7311yescharacteristic
119C22×Q8—731no—
120#137—1462no—
121#137—1462no—
122C2×Q16—732no—
123C2×SD16—732no—
124C2×M16—731no—
125C2×M16C2×D7311yescharacteristic
126C4×Q8—1462no—
127C4×Q8—1462no—
128#117—731no—
129#117—731no—
130#117—1462no—
131#117C2×D7311yescharacteristic
132#104—22no—
133#103—1462no—
134#99—1462no—
135#41—21no—
136#41—21no—
137#41—21no—
138#41—21no—
139C2×Q8—732no—
140C2×Q8—732no—
141C2×Q8—732no—
142C2×Q8—1461no—
143C2×Q8—1461no—
144C2×Q8—1461no—
145C2×Q8C4×D7311yescharacteristic
146C2×D4—21no—
147C2×D4C4×D7311yescharacteristic
148C22×C4—21no—
149C22×C4—1461no—
150C22×C4C22×D7311yescharacteristic
151Q16—1464no—
152SD16—1464no—
153M16—21no—
154M16—21no—
155M16—1461no—
156M16—1461no—
157C2×C8—21no—
158C2×C8—732no—
159C4⋊C4—21no—
160C4⋊C4—1464no—
161C4⋊C4—1461no—
162C4⋊C4—1461no—
163C22⋊C4—21no—
164C22⋊C4—732no—
165C22⋊C4—1461no—
166C42—1464no—
167C42—1461no—
168C42—1461no—
169C42C22⋊D7312yes—
170C23—21no—
171C23D4×D7311yescharacteristic
172Q8—21no—
173Q8—21no—
174Q8—734no—
175Q8—1462no—
176Q8—1462no—
177Q8—1462no—
178D4—21no—
179D4—21no—
180D4—41no—
181D4—41no—
182C2×C4—21no—
183C2×C4—22no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—2921no—
187C2×C4—1462no—
188C2×C4—1462no—
189C2×C4—1462no—
190C2×C4—1462no—
191C2×C4C2×C4×D7311yescharacteristic
192C2×C4D4×D7311yescharacteristic
193C2×C4D4×D7311yescharacteristic
194C2×C4C2×C22⋊D7311yescharacteristic
195C2×C4#1192402711yescharacteristic
196C2×C4#1192402811yescharacteristic
197C8—41no—
198C8—1462no—
199C22—41no—
200C22—41no—
201C22—81no—
202C22#1455655111yescharacteristic
203C22#1455655911yescharacteristic
204C22#1455656411yescharacteristic
205C4—42no—
206C4—41no—
207C4—2922no—
208C4—5841no—
209C4—1464no—
210C4C22⋊C4×D7311yescharacteristic
211C4C4×C22⋊D7311yescharacteristic
212C4#1455656211yescharacteristic
213C4#1455657311yescharacteristic
214C2—21no—
215C2—21no—
216C2—21no—
217C2—81no—
218C2#1798846311yescharacteristic
subgroupG/H
centerC2#17988463
commutatorC2×C4×C73C22×C4
FrattiniC22×C4C22×D73
Fitting#421×C73C2
socleC2×C73#386
hypercenter#421D73
hypocenterC73#1905
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C22×C4 ◁ #421

Complements

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

NH ≅ G/Ntype
2. #17989064C2semidirect
3. #17988597C2semidirect
5. #17988359C2semidirect
6. #17988343C2semidirect
11. C2×#11924018C4semidirect
12. C2×#11924016C4semidirect
110. C73#1905semidirect