Finite Group Databasebeta

← #22611230

Subgroups — #22611230

Order 9344.

262 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 67 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
2C2×#14556526C211yesmaximal, characteristic, complemented
3#17988589C211yesmaximal, characteristic
4C2×#14556515C211yesmaximal, characteristic, complemented
5#17988555C211yesmaximal, characteristic
6#17988355C211yesmaximal, characteristic, complemented
7C2×#101×C73C211yesmaximal, characteristic, complemented
8C2×#11924028C2211yescharacteristic
9#14556622—22no—
10#14556622—22no—
11C2×#11924018—21no—
12C2×#11924015—21no—
13C2×#11924012C2211yescharacteristic
14C22×#10596831C2211yescharacteristic
15C2×C4⋊Dic73C2211yescharacteristic
16#14556526—22no—
17#14556516—21no—
18#14556515—22no—
19#14556513—21no—
20#14556503—22no—
21C22×Q8×C73C2211yescharacteristic
22C2×M16×C73C2211yescharacteristic
23C2×M16×C73C2211yescharacteristic
24#101×C73—22no—
25#11924028—21no—
26#11924028—21no—
27#11924028—21no—
28#11924028—21no—
29C2×Dic146D411yescharacteristic
30C2×D292D411yescharacteristic
31C2×C22⋊D73—21no—
32C22×Dic73—21no—
33C2×C4×D73—21no—
34#11924018—24no—
35#11924015—24no—
36#11924012—21no—
37#11924012D412yes—
38C2×#10596831—21no—
39C2×#10596831—21no—
40C2×#10596831—21no—
41C2×#10596831D412yes—
42C4⋊Dic73—21no—
43C4⋊Dic73—21no—
44C2×Q8×C73—21no—
45C2×Q8×C73—21no—
46C2×Q8×C73—21no—
47C2×Q8×C73—21no—
48C2×Q8×C73—21no—
49C2×Q8×C73D412yes—
50C22×C4×C73—21no—
51C22×C4×C73C2311yescharacteristic
52M16×C73—21no—
53M16×C73—21no—
54M16×C73—21no—
55M16×C73—21no—
56C2×C8×C73—21no—
57C2×C8×C73—21no—
58C23×C73#4111yescharacteristic
59C22×D73—21no—
60Q8×C73—22no—
61Q8×C73—22no—
62Q8×C73—41no—
63Q8×C73—41no—
64C2×C4×C73—22no—
65C2×C4×C73—41no—
66C2×C4×C73—41no—
67C2×C4×C73C2×D411yescharacteristic
68C2×C4×C73C2×D411yescharacteristic
69C2×C4×C73C2×D411yescharacteristic
70C2×C4×C73C2×D411yescharacteristic
71C2×C4×C73#4111yescharacteristic
72C2×C4×C73#4111yescharacteristic
73C22⋊D73—41no—
74C22⋊D73—41no—
75C2×Dic73—21no—
76C2×Dic73—41no—
77C2×Dic73—81no—
78D292—21no—
79D292—21no—
80C4×D73—41no—
81C4×D73—41no—
82Dic146—21no—
83Dic146—21no—
84C8×C73—41no—
85C8×C73—41no—
86#10596831—22no—
87#10596831—22no—
88C22×C73—21no—
89C22×C73—21no—
90C22×C73#12111yescharacteristic
91C22×C73#12311yescharacteristic
92C22×C73#12411yescharacteristic
93C2×D73—41no—
94C2×D73—41no—
95C2×D73—41no—
96C4×C73—42no—
97C4×C73#12011yescharacteristic
98C4×C73#12111yescharacteristic
99C4×C73#12111yescharacteristic
100C4×C73#12311yescharacteristic
101Dic73—41no—
102Dic73—81no—
103C2×C73—21no—
104C2×C73—21no—
105C2×C73#39411yescharacteristic
106C2×C73#47111yescharacteristic
107C2×C73#47311yescharacteristic
108D73—81no—
109#2052—731nomaximal, Sylow
110C73#205211yescharacteristic, complemented, Sylow
111C2×#137—731no—
112C2×#108—731no—
113#417—731no—
114C2×#103—731no—
115C2×#101D7311yescharacteristic, complemented
116#408—731no—
117#343—731no—
118C2×#41—731no—
119C22×Q8C2×D7311yescharacteristic
120#137—1462no—
121#137—1462no—
122C2×Q16—1461no—
123C2×SD16—1461no—
124C2×M16—731no—
125C2×M16C2×D7311yescharacteristic
126C2×M16C2×D7311yescharacteristic
127C22×C8—731no—
128C2×C4⋊C4—731no—
129#108—1462no—
130#103—1461no—
131#103—1462no—
132#102—1461no—
133#101—22no—
134C22⋊C8—1462no—
135#41—1461no—
136#41—1461no—
137#41—1461no—
138#41—1461no—
139C2×Q8—21no—
140C2×Q8—21no—
141C2×Q8—21no—
142C2×Q8—21no—
143C2×Q8—21no—
144C2×Q8—731no—
145C2×Q8C22⋊D7312yes—
146C2×D4—731no—
147C2×D4—1461no—
148C22×C4—21no—
149C22×C4—1461no—
150C22×C4—1461no—
151C22×C4C22×D7311yescharacteristic
152Q16—1464no—
153SD16—1464no—
154M16—21no—
155M16—21no—
156M16—21no—
157M16—21no—
158M16—732no—
159M16—1461no—
160C2×C8—21no—
161C2×C8—21no—
162C2×C8—732no—
163C2×C8—1461no—
164C2×C8—1461no—
165C2×C8—1461no—
166C4⋊C4—1461no—
167C4⋊C4—1461no—
168C23—1461no—
169C23#1192402811yescharacteristic
170Q8—22no—
171Q8—22no—
172Q8—41no—
173Q8—41no—
174Q8—1461no—
175Q8—1461no—
176D4—2921no—
177D4—2921no—
178D4—1461no—
179D4—1461no—
180C2×C4—22no—
181C2×C4—41no—
182C2×C4—41no—
183C2×C4—2921no—
184C2×C4—2921no—
185C2×C4—2921no—
186C2×C4—5841no—
187C2×C4—1461no—
188C2×C4D4×D7311yescharacteristic
189C2×C4D4×D7311yescharacteristic
190C2×C4D4×D7311yescharacteristic
191C2×C4C2×C22⋊D7311yescharacteristic
192C2×C4#1192402711yescharacteristic
193C2×C4#1192402811yescharacteristic
194C8—41no—
195C8—41no—
196C8—1462no—
197C8—1462no—
198C22—21no—
199C22—21no—
200C22—2921no—
201C22—2921no—
202C22—2921no—
203C22#1455656411yescharacteristic
204C22#1455657411yescharacteristic
205C22#1455657711yescharacteristic
206C4—42no—
207C4—2921no—
208C4—5841no—
209C4#1455655911yescharacteristic
210C4#1455656311yescharacteristic
211C4#1455656411yescharacteristic
212C4#1455657311yescharacteristic
213C2—21no—
214C2—21no—
215C2—5841no—
216C2#1798850211yescharacteristic
217C2#1798885311yescharacteristic
218C2#1798886111yescharacteristic
subgroupG/H
centerC22#14556564
commutatorC22×C4×C73C23
FrattiniC22×C4C22×D73
FittingC2×#101×C73C2
socleC22×C73#121
hypercenterC2×#101D73
hypocenterC73#2052
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
2. C2×#14556526C2semidirect
4. C2×#14556515C2semidirect
6. #17988355C2semidirect
7. C2×#101×C73C2semidirect
110. C73#2052semidirect
115. C2×#101D73semidirect