Finite Group Databasebeta

← #22610413

Subgroups — #22610413

Order 9344.

324 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 93 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#17989354C211yesmaximal, characteristic, complemented
2#17988604C211yesmaximal, characteristic, complemented
3#17988592C211yesmaximal, characteristic, complemented
4C2×#14556508C211yesmaximal, characteristic, complemented
5#17988358C211yesmaximal, characteristic, complemented
6#17988345C211yesmaximal, characteristic, complemented
7C2×AGL(1,ℤ/8)×C73C211yesmaximal, characteristic
8#14556598—22no—
9#14556598—22no—
10C2×#11924012—22no—
11C2×#11924012C2211yescharacteristic
12C2×#11924012C2211yescharacteristic
13C2×#11924012C2211yescharacteristic
14#14556550C2211yescharacteristic
15#14556518—22no—
16#14556512—22no—
17#14556508—22no—
18C2×#41×C73C2211yescharacteristic
19C22×D4×C73C2211yescharacteristic
20AGL(1,ℤ/8)×C73—22no—
21AGL(1,ℤ/8)×C73—22no—
22C2×SD16×C73C412yescomplemented
23C2×D8×C73C412yescomplemented
24C2×M16×C73C2211yescharacteristic
25#11924012—24no—
26#11924012—21no—
27#11924012—21no—
28#11924012—21no—
29#11924012—21no—
30#11924012—21no—
31#11924012D412yes—
32C2×#10596831—24no—
33C2×#10596831—21no—
34C2×#10596831—21no—
35C2×#10596831D412yes—
36C4⋊Dic73—21no—
37C22⋊Dic73—21no—
38C4×Dic73—21no—
39C24×C73—21no—
40#41×C73—21no—
41#41×C73—21no—
42#41×C73D412yes—
43#41×C73D412yes—
44C2×Q8×C73C2×C411yescharacteristic
45C2×D4×C73—21no—
46C2×D4×C73—21no—
47C2×D4×C73—21no—
48C2×D4×C73—21no—
49C2×D4×C73—21no—
50C2×D4×C73—21no—
51C2×D4×C73C2×C412yes—
52C2×D4×C73C2×C411yescharacteristic
53C22×C4×C73—21no—
54C22×C4×C73C2311yescharacteristic
55SD16×C73—24no—
56D8×C73—24no—
57M16×C73—21no—
58M16×C73—21no—
59C2×C8×C73C2×C412yes—
60C23×C73—21no—
61C23×C73—22no—
62C23×C73—41no—
63C23×C73—41no—
64C23×C73—82no—
65C23×C73#4111yescharacteristic
66Q8×C73—21no—
67Q8×C73C22⋊C412yes—
68D4×C73—22no—
69D4×C73—22no—
70D4×C73—22no—
71D4×C73—21no—
72D4×C73—22no—
73D4×C73—41no—
74D4×C73—41no—
75D4×C73C22⋊C412yes—
76C2×C4×C73—21no—
77C2×C4×C73—22no—
78C2×C4×C73—22no—
79C2×C4×C73C22×C411yescharacteristic
80C2×C4×C73C2×D411yescharacteristic
81C2×C4×C73C2×D411yescharacteristic
82C2×C4×C73C2×D411yescharacteristic
83C2×C4×C73C2×D411yescharacteristic
84C2×C4×C73#4111yescharacteristic
85C2×Dic73—41no—
86C8×C73—22no—
87#10596831—22no—
88#10596831—22no—
89#10596831—41no—
90C22×C73—22no—
91C22×C73—41no—
92C22×C73—42no—
93C22×C73—81no—
94C22×C73—82no—
95C22×C73—82no—
96C22×C73—82no—
97C22×C73C4×D411yescharacteristic
98C22×C73#12111yescharacteristic
99C22×C73#12311yescharacteristic
100C4×C73—22no—
101C4×C73C2×C22⋊C411yescharacteristic
102C4×C73C4×D411yescharacteristic
103C4×C73#12011yescharacteristic
104C4×C73#12111yescharacteristic
105Dic73—81no—
106C2×C73—21no—
107C2×C73—21no—
108C2×C73—21no—
109C2×C73—42no—
110C2×C73—82no—
111C2×C73#38611yescharacteristic
112#1903—731nomaximal, Sylow
113C73#190311yescharacteristic, complemented, Sylow
114C2×AGL(1,ℤ/8)D7311yescharacteristic
115#568—731no—
116#421—731no—
117#418—731no—
118C2×#100—731no—
119#344—731no—
120#338—731no—
121C2×#41C2×D7311yescharacteristic
122C22×D4C2×D7311yescharacteristic
123AGL(1,ℤ/8)—22no—
124AGL(1,ℤ/8)—22no—
125C2×SD16Dic7312yescomplemented
126C2×D8Dic7312yescomplemented
127#131—1462no—
128#131—1462no—
129C2×M16—731no—
130C2×M16—731no—
131C2×M16—731no—
132C2×M16—1462no—
133C2×M16C2×D7311yescharacteristic
134#117—731no—
135#104—1462no—
136#102—1462no—
137#100—1462no—
138C24—21no—
139#41—21no—
140#41—21no—
141#41C22⋊D7312yes—
142#41C22⋊D7312yes—
143C2×Q8C2×Dic7311yescharacteristic
144C2×D4—21no—
145C2×D4—21no—
146C2×D4—21no—
147C2×D4—21no—
148C2×D4—21no—
149C2×D4—21no—
150C2×D4C2×Dic7312yes—
151C2×D4C2×Dic7311yescharacteristic
152C22×C4—21no—
153C22×C4C22×D7311yescharacteristic
154SD16—24no—
155D8—24no—
156M16—21no—
157M16—21no—
158M16—732no—
159M16—1461no—
160M16—1461no—
161M16—1464no—
162M16—1461no—
163M16—1461no—
164M16—1461no—
165C2×C8—732no—
166C2×C8—1461no—
167C2×C8—1464no—
168C2×C8—1461no—
169C2×C8C2×Dic7312yes—
170C4⋊C4—1461no—
171C22⋊C4—1461no—
172C42—1461no—
173C23—21no—
174C23—22no—
175C23—41no—
176C23—41no—
177C23—82no—
178C23#1192402711yescharacteristic
179Q8—21no—
180Q8C22⋊Dic7312yes—
181D4—22no—
182D4—22no—
183D4—22no—
184D4—21no—
185D4—22no—
186D4—41no—
187D4—41no—
188D4C22⋊Dic7312yes—
189C2×C4—21no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—2921no—
193C2×C4C22×Dic7311yescharacteristic
194C2×C4D4×D7311yescharacteristic
195C2×C4D4×D7311yescharacteristic
196C2×C4C2×C22⋊D7311yescharacteristic
197C2×C4C2×C22⋊D7311yescharacteristic
198C2×C4#1192402711yescharacteristic
199C8—22no—
200C8—2921no—
201C8—1462no—
202C8—1462no—
203C22—22no—
204C22—41no—
205C22—42no—
206C22—81no—
207C22—82no—
208C22—82no—
209C22—82no—
210C22D4×Dic7311yescharacteristic
211C22#1455656311yescharacteristic
212C22#1455657211yescharacteristic
213C4—22no—
214C4—5841no—
215C4C2×C22⋊Dic7311yescharacteristic
216C4D4×Dic7311yescharacteristic
217C4#1455655911yescharacteristic
218C4#1455656311yescharacteristic
219C2—21no—
220C2—21no—
221C2—21no—
222C2—42no—
223C2—82no—
224C2#1798846711yescharacteristic
subgroupG/H
centerC2#17988467
commutatorC2×C4×C73C22×C4
FrattiniC22×C4C22×D73
FittingC2×AGL(1,ℤ/8)×C73C2
socleC2×C73#386
hypercenterC2×AGL(1,ℤ/8)D73
hypocenterC73#1903
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #17989354C2semidirect
2. #17988604C2semidirect
3. #17988592C2semidirect
4. C2×#14556508C2semidirect
5. #17988358C2semidirect
6. #17988345C2semidirect
22. C2×SD16×C73C4semidirect
23. C2×D8×C73C4semidirect
113. C73#1903semidirect
125. C2×SD16Dic73semidirect
126. C2×D8Dic73semidirect