Finite Group Databasebeta

← #22619670

Subgroups — #22619670

Order 9344.

446 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 137 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, complemented
2C2×#14556621C211yesmaximal, characteristic, complemented
3#17989354C211yesmaximal, characteristic, complemented
4#17988860C214yesmaximal, complemented
5#17988848C214yesmaximal, complemented
6#17988635C211yesmaximal, characteristic, complemented
7#17988571C211yesmaximal, characteristic, complemented
8C2×#14556509C211yesmaximal, characteristic, complemented
9#575×C73C211yesmaximal, characteristic
10C22×Dic146C2211yescharacteristic
11#14556621—22no—
12#14556621—22no—
13#14556621—22no—
14#14556621C2214yes—
15C2×#11924018—21no—
16C2×#11924018C2212yescomplemented
17C2×#11924016—21no—
18C2×#11924016C2212yescomplemented
19#14556598—22no—
20#14556598C2214yes—
21C2×#11924012—22no—
22C2×#11924012C2211yescharacteristic
23C2×#11924012C2211yescharacteristic
24C2×#11924012C2211yescharacteristic
25#14556526C2214yescomplemented
26#14556510C2212yescomplemented
27#14556509C2214yescomplemented
28#14556508C2212yescomplemented
29C2×#41×C73C2211yescharacteristic
30C2×#41×C73C2211yescharacteristic
31#137×C73—21no—
32#137×C73C2212yes—
33AGL(1,ℤ/8)×C73—21no—
34AGL(1,ℤ/8)×C73C2212yes—
35#135×C73—22no—
36C2×M16×C73C2211yescharacteristic
37C2×Dic146—21no—
38C2×Dic146—21no—
39C2×Dic146—21no—
40C2×Dic146—21no—
41C2×Dic146—21no—
42C2×Dic146C2312yes—
43C22×Dic73—21no—
44#11924018—24no—
45#11924018—24no—
46#11924016—24no—
47#11924016—24no—
48#11924012—21no—
49#11924012—21no—
50#11924012—24no—
51#11924012D412yes—
52#11924012D412yes—
53#11924012C2312yes—
54#11924012C2312yes—
55C2×#10596831—21no—
56C2×#10596831—21no—
57C2×#10596831—24no—
58C2×#10596831C2312yes—
59#41×C73—21no—
60#41×C73—21no—
61#41×C73—21no—
62#41×C73—21no—
63#41×C73—21no—
64#41×C73—21no—
65#41×C73D412yes—
66#41×C73C2312yes—
67C2×Q8×C73D411yescharacteristic
68C2×Q8×C73C2311yescharacteristic
69C2×D4×C73—21no—
70C2×D4×C73—21no—
71C2×D4×C73D411yescharacteristic
72C2×D4×C73C2311yescharacteristic
73C22×C4×C73—21no—
74C22×C4×C73—21no—
75C22×C4×C73C2311yescharacteristic
76Q16×C73—22no—
77SD16×C73—22no—
78SD16×C73—22no—
79D8×C73—22no—
80M16×C73—21no—
81M16×C73C2312yes—
82C2×C8×C73—21no—
83C23×C73—21no—
84C23×C73—21no—
85C23×C73#4111yescharacteristic
86Q8×C73—21no—
87Q8×C73—21no—
88Q8×C73—21no—
89Q8×C73C2×D412yes—
90D4×C73—22no—
91D4×C73—22no—
92D4×C73—21no—
93D4×C73—21no—
94D4×C73—21no—
95D4×C73—41no—
96D4×C73—41no—
97D4×C73C2×D412yes—
98C2×C4×C73—21no—
99C2×C4×C73—22no—
100C2×C4×C73—22no—
101C2×C4×C73—21no—
102C2×C4×C73—41no—
103C2×C4×C73—41no—
104C2×C4×C73C2×D411yescharacteristic
105C2×C4×C73C2×D411yescharacteristic
106C2×C4×C73C2×D411yescharacteristic
107C2×C4×C73C2×D411yescharacteristic
108C2×C4×C73#4111yescharacteristic
109C2×C4×C73C2411yescharacteristic
110C2×Dic73—22no—
111C2×Dic73—41no—
112C2×Dic73—41no—
113Dic146—22no—
114Dic146—22no—
115Dic146—41no—
116Dic146—41no—
117C8×C73—22no—
118#10596831—22no—
119#10596831—22no—
120#10596831C2×D414yes—
121C22×C73—22no—
122C22×C73—41no—
123C22×C73—41no—
124C22×C73—81no—
125C22×C73—81no—
126C22×C73#12111yescharacteristic
127C22×C73#12111yescharacteristic
128C22×C73C2×#4111yescharacteristic
129C4×C73—22no—
130C4×C73—41no—
131C4×C73#12111yescharacteristic
132C4×C73#12111yescharacteristic
133C4×C73C22×D411yescharacteristic
134C4×C73C22×D411yescharacteristic
135Dic73—42no—
136C2×C73—21no—
137C2×C73—21no—
138C2×C73—21no—
139C2×C73—42no—
140C2×C73—81no—
141C2×C73C2×#12111yescharacteristic
142#3069—731nomaximal, Sylow
143C73#306911yescharacteristic, complemented, Sylow
144#575D7311yescharacteristic
145C2×#137—731no—
146C2×#137—731no—
147#568—731no—
148#473—734no—
149#471—734no—
150#430—731no—
151#413—731no—
152C2×#101—731no—
153C2×#41C2×D7311yescharacteristic
154C2×#41C2×D7311yescharacteristic
155C22×Q8—731no—
156#137—21no—
157#137—734no—
158#137—1462no—
159#137—1462no—
160#137—1462no—
161#137C2×D7312yes—
162AGL(1,ℤ/8)—21no—
163AGL(1,ℤ/8)C2×D7312yes—
164#135—22no—
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—731no—
174C2×M16—1462no—
175C2×M16C2×D7311yescharacteristic
176#108—734no—
177#101—732no—
178#101—734no—
179#100—732no—
180#41—21no—
181#41—21no—
182#41—21no—
183#41—21no—
184#41—21no—
185#41—21no—
186#41C22⋊D7312yes—
187#41C22×D7312yes—
188C2×Q8—732no—
189C2×Q8—1461no—
190C2×Q8—1461no—
191C2×Q8—1461no—
192C2×Q8—1461no—
193C2×Q8—1461no—
194C2×Q8C22⋊D7311yescharacteristic
195C2×Q8C22×D7311yescharacteristic
196C2×D4—21no—
197C2×D4—21no—
198C2×D4C22⋊D7311yescharacteristic
199C2×D4C22×D7311yescharacteristic
200C22×C4—21no—
201C22×C4—21no—
202C22×C4—1461no—
203C22×C4C22×D7311yescharacteristic
204Q16—22no—
205Q16—1464no—
206Q16—1464no—
207SD16—22no—
208SD16—22no—
209SD16—1464no—
210SD16—1464no—
211D8—22no—
212M16—21no—
213M16—732no—
214M16—732no—
215M16—732no—
216M16—732no—
217M16—1464no—
218M16—1461no—
219M16—1461no—
220M16C22×D7312yes—
221C2×C8—21no—
222C2×C8—732no—
223C2×C8—1464no—
224C2×C8—1461no—
225C2×C8—1461no—
226C23—21no—
227C23—21no—
228C23#1192402711yescharacteristic
229Q8—21no—
230Q8—21no—
231Q8—21no—
232Q8—2921no—
233Q8—2921no—
234Q8—1462no—
235Q8—1462no—
236Q8C2×C22⋊D7312yes—
237D4—22no—
238D4—22no—
239D4—21no—
240D4—21no—
241D4—21no—
242D4—41no—
243D4—41no—
244D4C2×C22⋊D7312yes—
245C2×C4—21no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—21no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—2921no—
252C2×C4—2921no—
253C2×C4—1462no—
254C2×C4D4×D7311yescharacteristic
255C2×C4D4×D7311yescharacteristic
256C2×C4C2×C22⋊D7311yescharacteristic
257C2×C4C2×C22⋊D7311yescharacteristic
258C2×C4#1192402711yescharacteristic
259C2×C4C23×D7311yescharacteristic
260C8—22no—
261C8—734no—
262C8—1462no—
263C8—1462no—
264C22—22no—
265C22—41no—
266C22—41no—
267C22—81no—
268C22—81no—
269C22#1455656311yescharacteristic
270C22#1455656311yescharacteristic
271C22C2×#1192402711yescharacteristic
272C4—22no—
273C4—41no—
274C4—2922no—
275C4#1455656311yescharacteristic
276C4#1455656311yescharacteristic
277C4C2×D4×D7311yescharacteristic
278C4C22×C22⋊D7311yescharacteristic
279C2—21no—
280C2—21no—
281C2—21no—
282C2—42no—
283C2—81no—
284C2C2×#1455656311yescharacteristic
subgroupG/H
centerC2C2×#14556563
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#575×C73C2
socleC2×C73C2×#121
hypercenter#575D73
hypocenterC73#3069
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C22×C4 ◁ #575

Complements

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

NH ≅ G/Ntype
1. C2×#14556621C2semidirect
2. C2×#14556621C2semidirect
3. #17989354C2semidirect
4. #17988860C2semidirect
5. #17988848C2semidirect
6. #17988635C2semidirect
7. #17988571C2semidirect
8. C2×#14556509C2semidirect
16. C2×#11924018C22semidirect
18. C2×#11924016C22semidirect
25. #14556526C22semidirect
26. #14556510C22semidirect
27. #14556509C22semidirect
28. #14556508C22semidirect
143. C73#3069semidirect