Finite Group Databasebeta

← #22619667

Subgroups — #22619667

Order 9344.

446 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 129 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#17989387C211yesmaximal, characteristic
2C2×#14556622C211yesmaximal, characteristic, complemented
3C2×#14556622C211yesmaximal, characteristic, complemented
4#17989353C211yesmaximal, characteristic, complemented
5#17988861C214yesmaximal, complemented
6#17988853C214yesmaximal, complemented
7#17988635C211yesmaximal, characteristic, complemented
8#17988569C211yesmaximal, characteristic, complemented
9C2×#101×C73C211yesmaximal, characteristic, complemented
10C2×#11924028C2211yescharacteristic
11C2×#11924028C2211yescharacteristic
12#14556624—21no—
13#14556624C2212yes—
14#14556622—22no—
15#14556622—22no—
16#14556622—22no—
17#14556622C2214yes—
18#14556619—21no—
19#14556619C2212yes—
20#14556613—22no—
21C2×#11924018—21no—
22C2×#11924018C2212yescomplemented
23C2×#11924015—21no—
24C2×#11924015C2212yescomplemented
25#14556599C2214yes—
26#14556597—22no—
27C2×#11924012C2211yescharacteristic
28C2×#11924012C2211yescharacteristic
29M16×D73—22no—
30#14556526C2214yescomplemented
31#14556509C2212yescomplemented
32#14556507C2212yescomplemented
33C22×Q8×C73C2211yescharacteristic
34C2×M16×C73C2211yescharacteristic
35C2×M16×C73C2211yescharacteristic
36#101×C73C2214yescomplemented
37#11924028—21no—
38#11924028—21no—
39#11924028—21no—
40#11924028—21no—
41#11924028—21no—
42#11924028—21no—
43#11924028D412yes—
44#11924028C2312yes—
45C2×Dic146D411yescharacteristic
46C2×Dic146C2311yescharacteristic
47C2×D292D411yescharacteristic
48C2×D292C2311yescharacteristic
49C2×C22⋊D73—21no—
50C2×C22⋊D73—21no—
51C2×C4×D73—21no—
52C2×C4×D73—21no—
53Dic292—22no—
54#11924018—24no—
55#11924018—24no—
56#11924017—22no—
57#11924017—22no—
58#11924015—24no—
59#11924015—24no—
60D584—22no—
61#11924012—21no—
62#11924012D412yes—
63#11924012D412yes—
64#11924012C2312yes—
65#11924011—24no—
66C2×#10596831—21no—
67C2×#10596831C2312yes—
68C8×D73—24no—
69C2×Q8×C73—21no—
70C2×Q8×C73—21no—
71C2×Q8×C73—21no—
72C2×Q8×C73—21no—
73C2×Q8×C73—21no—
74C2×Q8×C73C2312yes—
75C22×C4×C73—21no—
76C22×C4×C73C2311yescharacteristic
77M16×C73—21no—
78M16×C73—21no—
79M16×C73C2312yes—
80M16×C73C2312yes—
81C2×C8×C73—21no—
82C2×C8×C73—21no—
83C23×C73#4111yescharacteristic
84C22×D73—21no—
85C22×D73—21no—
86Q8×C73—22no—
87Q8×C73—22no—
88Q8×C73—41no—
89Q8×C73—41no—
90C2×C4×C73—22no—
91C2×C4×C73—41no—
92C2×C4×C73—41no—
93C2×C4×C73C2×D411yescharacteristic
94C2×C4×C73C2×D411yescharacteristic
95C2×C4×C73C2×D411yescharacteristic
96C2×C4×C73C2×D411yescharacteristic
97C2×C4×C73#4111yescharacteristic
98C2×C4×C73C2411yescharacteristic
99C22⋊D73—22no—
100C22⋊D73—22no—
101C22⋊D73—41no—
102C22⋊D73—41no—
103C2×Dic73—21no—
104C2×Dic73—21no—
105D292—21no—
106D292—21no—
107D292—21no—
108D292C2×D412yes—
109C4×D73—22no—
110C4×D73—22no—
111C4×D73—41no—
112C4×D73—41no—
113Dic146—21no—
114Dic146—21no—
115Dic146—21no—
116Dic146C2×D412yes—
117C8×C73—22no—
118C8×C73—22no—
119#10596831—22no—
120#10596831C2×D414yes—
121C22×C73—41no—
122C22×C73#12111yescharacteristic
123C22×C73#12111yescharacteristic
124C22×C73C2×#4111yescharacteristic
125C2×D73—22no—
126C2×D73—41no—
127C2×D73—81no—
128C2×D73—81no—
129C4×C73—42no—
130C4×C73#12111yescharacteristic
131C4×C73#12111yescharacteristic
132C4×C73C22×D411yescharacteristic
133C4×C73C22×D411yescharacteristic
134Dic73—22no—
135Dic73—41no—
136C2×C73—21no—
137C2×C73—21no—
138C2×C73—21no—
139C2×C73C2×#12111yescharacteristic
140D73—42no—
141D73—81no—
142#3069—731nomaximal, Sylow
143C73#306911yescharacteristic, complemented, Sylow
144#575—731no—
145C2×#137—731no—
146C2×#137—731no—
147#568—731no—
148#473—734no—
149#471—734no—
150#430—731no—
151#413—731no—
152C2×#101D7311yescharacteristic, complemented
153C2×#41—731no—
154C2×#41—731no—
155C22×Q8C2×D7311yescharacteristic
156#137—734no—
157#137—732no—
158#137—1461no—
159#137—1462no—
160#137—1462no—
161#137—1462no—
162AGL(1,ℤ/8)—732no—
163AGL(1,ℤ/8)—1461no—
164#135—1462no—
165C2×Q16—732no—
166C2×Q16—1461no—
167C2×SD16—732no—
168C2×SD16—1461no—
169#131—734no—
170#131—1462no—
171C2×M16—731no—
172C2×M16—731no—
173C2×M16—1462no—
174C2×M16C2×D7311yescharacteristic
175C2×M16C2×D7311yescharacteristic
176#108—734no—
177#101—732no—
178#101C2×D7314yescomplemented
179#100—732no—
180#41—732no—
181#41—732no—
182#41—1461no—
183#41—1461no—
184#41—1461no—
185#41—1461no—
186#41—1461no—
187#41—1461no—
188C2×Q8—21no—
189C2×Q8—21no—
190C2×Q8—21no—
191C2×Q8—21no—
192C2×Q8—21no—
193C2×Q8—731no—
194C2×Q8—731no—
195C2×Q8C22×D7312yes—
196C2×D4—731no—
197C2×D4—731no—
198C2×D4—1461no—
199C2×D4—1461no—
200C22×C4—21no—
201C22×C4—1461no—
202C22×C4—1461no—
203C22×C4C22×D7311yescharacteristic
204Q16—1462no—
205Q16—1464no—
206Q16—1464no—
207SD16—1462no—
208SD16—1462no—
209SD16—1464no—
210SD16—1464no—
211D8—1462no—
212M16—21no—
213M16—21no—
214M16—732no—
215M16—732no—
216M16—732no—
217M16—1464no—
218M16—1461no—
219M16C22×D7312yes—
220M16C22×D7312yes—
221C2×C8—21no—
222C2×C8—21no—
223C2×C8—732no—
224C2×C8—1464no—
225C2×C8—1461no—
226C23—1461no—
227C23—1461no—
228C23#1192402811yescharacteristic
229Q8—22no—
230Q8—22no—
231Q8—41no—
232Q8—41no—
233Q8—732no—
234Q8—1461no—
235Q8—1461no—
236Q8—1461no—
237D4—2921no—
238D4—2921no—
239D4—732no—
240D4—1462no—
241D4—1462no—
242D4—1461no—
243D4—1461no—
244D4—1461no—
245C2×C4—22no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—2921no—
249C2×C4—2921no—
250C2×C4—1461no—
251C2×C4—1461no—
252C2×C4—1462no—
253C2×C4—1462no—
254C2×C4D4×D7311yescharacteristic
255C2×C4D4×D7311yescharacteristic
256C2×C4D4×D7311yescharacteristic
257C2×C4D4×D7311yescharacteristic
258C2×C4#1192402811yescharacteristic
259C2×C4C23×D7311yescharacteristic
260C8—22no—
261C8—22no—
262C8—734no—
263C8—1462no—
264C22—41no—
265C22—2921no—
266C22—5841no—
267C22—5841no—
268C22—1462no—
269C22#1455656411yescharacteristic
270C22#1455656411yescharacteristic
271C22C2×#1192402811yescharacteristic
272C4—42no—
273C4—2921no—
274C4—1462no—
275C4#1455656411yescharacteristic
276C4#1455656411yescharacteristic
277C4C2×D4×D7311yescharacteristic
278C4C2×D4×D7311yescharacteristic
279C2—21no—
280C2—21no—
281C2—21no—
282C2—2922no—
283C2—5841no—
284C2C2×#1455656411yescharacteristic
subgroupG/H
centerC2C2×#14556564
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
FittingC2×#101×C73C2
socleC2×C73C2×#121
hypercenterC2×#101D73
hypocenterC73#3069
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
2. C2×#14556622C2semidirect
3. C2×#14556622C2semidirect
4. #17989353C2semidirect
5. #17988861C2semidirect
6. #17988853C2semidirect
7. #17988635C2semidirect
8. #17988569C2semidirect
9. C2×#101×C73C2semidirect
22. C2×#11924018C22semidirect
24. C2×#11924015C22semidirect
30. #14556526C22semidirect
31. #14556509C22semidirect
32. #14556507C22semidirect
36. #101×C73C22semidirect
143. C73#3069semidirect
152. C2×#101D73semidirect
178. #101C2×D73semidirect