Finite Group Databasebeta

← #22611225

Subgroups — #22611225

Order 9344.

282 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 69 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×#14556619C211yesmaximal, characteristic
2#17988589C211yesmaximal, characteristic, complemented
3C2×#14556513C211yesmaximal, characteristic, complemented
4C2×#14556507C211yesmaximal, characteristic, complemented
5#17988553C211yesmaximal, characteristic, complemented
6#17988355C211yesmaximal, characteristic, complemented
7C2×#108×C73C211yesmaximal, characteristic, complemented
8C2×#11924028C2211yescharacteristic
9C22×D292C2211yescharacteristic
10#14556619—22no—
11#14556619—22no—
12C2×#11924017—21no—
13C2×D584—21no—
14C2×#11924012C2211yescharacteristic
15C2×C4⋊Dic73C2211yescharacteristic
16#14556516—21no—
17#14556513—21no—
18#14556513—22no—
19#14556507—22no—
20#14556503—22no—
21C2×M16×C73C2211yescharacteristic
22C2×M16×C73C2211yescharacteristic
23C22×C8×C73C2211yescharacteristic
24#108×C73—22no—
25C23×D73—21no—
26#11924028—21no—
27#11924028—21no—
28#11924028—21no—
29#11924028—21no—
30C2×Dic146D411yescharacteristic
31C2×D292—21no—
32C2×D292—21no—
33C2×D292—21no—
34C2×D292—21no—
35C2×D292—21no—
36C2×D292D412yes—
37C2×D292D411yescharacteristic
38C2×C22⋊D73—21no—
39C22×Dic73—21no—
40C2×C4×D73—21no—
41#11924017—24no—
42D584—24no—
43#11924012—21no—
44#11924012—21no—
45C2×#10596831—21no—
46C4⋊Dic73—21no—
47C4⋊Dic73—21no—
48C22×C4×C73C2311yescharacteristic
49M16×C73—21no—
50M16×C73—21no—
51M16×C73—21no—
52M16×C73D412yes—
53C2×C8×C73—21no—
54C2×C8×C73—21no—
55C2×C8×C73—21no—
56C2×C8×C73—21no—
57C2×C8×C73D412yes—
58C23×C73#4111yescharacteristic
59C22×D73—21no—
60C22×D73—22no—
61C22×D73—41no—
62C22×D73—41no—
63C22×D73—81no—
64C22×D73—81no—
65C2×C4×C73C2×D411yescharacteristic
66C2×C4×C73C2×D411yescharacteristic
67C2×C4×C73C2×D411yescharacteristic
68C2×C4×C73C2×D411yescharacteristic
69C2×C4×C73#4111yescharacteristic
70C2×C4×C73#4111yescharacteristic
71C22⋊D73—41no—
72C22⋊D73—41no—
73C2×Dic73—21no—
74C2×Dic73—41no—
75C2×Dic73—81no—
76D292—21no—
77D292—22no—
78D292—22no—
79D292—21no—
80D292—41no—
81D292—41no—
82C4×D73—41no—
83C4×D73—41no—
84Dic146—21no—
85Dic146—21no—
86C8×C73—22no—
87C8×C73—22no—
88C8×C73—41no—
89#10596831—41no—
90C22×C73—21no—
91C22×C73—21no—
92C22×C73#12111yescharacteristic
93C22×C73#12311yescharacteristic
94C22×C73#12411yescharacteristic
95C2×D73—41no—
96C2×D73—42no—
97C2×D73—41no—
98C2×D73—41no—
99C2×D73—82no—
100C2×D73—81no—
101C2×D73—81no—
102C2×D73—82no—
103C4×C73#12011yescharacteristic
104C4×C73#12111yescharacteristic
105C4×C73#12111yescharacteristic
106C4×C73#12311yescharacteristic
107Dic73—41no—
108Dic73—81no—
109C2×C73—21no—
110C2×C73—21no—
111C2×C73#39411yescharacteristic
112C2×C73#47111yescharacteristic
113C2×C73#47211yescharacteristic
114D73—81no—
115D73—82no—
116#2051—731nomaximal, Sylow
117C73#205111yescharacteristic, complemented, Sylow
118C2×AGL(1,ℤ/8)—731no—
119C2×#108D7311yescharacteristic, complemented
120#417—731no—
121C2×#102—731no—
122C2×#100—731no—
123#408—731no—
124#343—731no—
125C2×#41—731no—
126C22×D4—731no—
127AGL(1,ℤ/8)—1462no—
128AGL(1,ℤ/8)—1462no—
129C2×SD16—1461no—
130C2×D8—1461no—
131C2×M16—731no—
132C2×M16C2×D7311yescharacteristic
133C2×M16C2×D7311yescharacteristic
134C22×C8C2×D7311yescharacteristic
135C2×C4⋊C4—731no—
136#108—22no—
137#103—1461no—
138#102—1461no—
139#102—1462no—
140#100—1462no—
141C22⋊C8—1462no—
142C24—1461no—
143#41—1461no—
144#41—1461no—
145#41—1461no—
146#41—1461no—
147C2×Q8—731no—
148C2×D4—732no—
149C2×D4—731no—
150C2×D4—1461no—
151C2×D4—1461no—
152C2×D4—1461no—
153C2×D4—1461no—
154C2×D4—1461no—
155C2×D4—1461no—
156C22×C4—1461no—
157C22×C4—1461no—
158C22×C4C22×D7311yescharacteristic
159SD16—1464no—
160D8—1464no—
161M16—21no—
162M16—21no—
163M16—21no—
164M16—1461no—
165M16—1461no—
166M16C22⋊D7312yes—
167C2×C8—21no—
168C2×C8—21no—
169C2×C8—21no—
170C2×C8—21no—
171C2×C8—1461no—
172C2×C8D29212yes—
173C4⋊C4—1461no—
174C4⋊C4—1461no—
175C23—2921no—
176C23—2921no—
177C23—5841no—
178C23—5841no—
179C23—1461no—
180C23—1462no—
181C23#1192402911yescharacteristic
182Q8—1461no—
183Q8—1461no—
184D4—2921no—
185D4—2921no—
186D4—2921no—
187D4—2921no—
188D4—1461no—
189D4—1462no—
190D4—1462no—
191D4—1461no—
192C2×C4—2921no—
193C2×C4—2921no—
194C2×C4—2921no—
195C2×C4—5841no—
196C2×C4—1461no—
197C2×C4D4×D7311yescharacteristic
198C2×C4D4×D7311yescharacteristic
199C2×C4C2×C22⋊D7311yescharacteristic
200C2×C4C2×D29211yescharacteristic
201C2×C4#1192402811yescharacteristic
202C2×C4#1192402911yescharacteristic
203C8—22no—
204C8—22no—
205C8—41no—
206C8—2921no—
207C22—21no—
208C22—21no—
209C22—2921no—
210C22—2922no—
211C22—2921no—
212C22—2921no—
213C22—5842no—
214C22—5842no—
215C22—5841no—
216C22—5841no—
217C22#1455656611yescharacteristic
218C22#1455657611yescharacteristic
219C22#1455658011yescharacteristic
220C4—2921no—
221C4—5841no—
222C4#1455655911yescharacteristic
223C4#1455656511yescharacteristic
224C4#1455656611yescharacteristic
225C4#1455657611yescharacteristic
226C2—21no—
227C2—21no—
228C2—5841no—
229C2—5842no—
230C2#1798850411yescharacteristic
231C2#1798885111yescharacteristic
232C2#1798885811yescharacteristic
subgroupG/H
centerC22#14556566
commutatorC22×C4×C73C23
FrattiniC22×C4C22×D73
FittingC2×#108×C73C2
socleC22×C73#121
hypercenterC2×#108D73
hypocenterC73#2051
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#108

Complements

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

NH ≅ G/Ntype
2. #17988589C2semidirect
3. C2×#14556513C2semidirect
4. C2×#14556507C2semidirect
5. #17988553C2semidirect
6. #17988355C2semidirect
7. C2×#108×C73C2semidirect
117. C73#2051semidirect
119. C2×#108D73semidirect