Finite Group Databasebeta

← #31806786

Subgroups — #31806786

Order 17792.

332 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 79 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#22581719C211yesmaximal, characteristic, complemented
2#22581503C211yesmaximal, characteristic
3#22580971C211yesmaximal, characteristic, complemented
4#22580969C211yesmaximal, characteristic, complemented
5#22580926C211yesmaximal, characteristic, complemented
6#22580713C211yesmaximal, characteristic, complemented
7#339×C139C211yesmaximal, characteristic, complemented
8C2×#14555785C2211yescharacteristic
9C2×#14555785C2211yescharacteristic
10#17984850—22no—
11#17984848—22no—
12C2×#14555769C2211yescharacteristic
13M16×D139—22no—
14#17984842C411yescharacteristic, complemented
15#17984839C411yescharacteristic, complemented
16#17984830C411yescharacteristic, complemented
17#17984830C411yescharacteristic, complemented
18#17984816—22no—
19C4×D556—22no—
20#17984801C2211yescharacteristic
21#17984770—22no—
22#17984768—22no—
23#17984756—22no—
24C2×M16×C139C2211yescharacteristic
25#117×C139C2211yescharacteristic
26C2×C42×C139C2211yescharacteristic
27#14555785—21no—
28#14555785—21no—
29#14555785—21no—
30#14555785—21no—
31#14555785—21no—
32#14555785—21no—
33#14555785—21no—
34#14555785—21no—
35C2×Dic278C2×C411yescharacteristic
36C2×Dic278C2×C411yescharacteristic
37C2×D556—22no—
38C2×D556C2×C411yescharacteristic
39C2×D556C2×C411yescharacteristic
40C2×C22⋊D139—21no—
41C2×C22⋊D139D412yes—
42C2×C4×D139—21no—
43C2×C4×D139D412yes—
44#14555769—21no—
45#14555769D412yescomplemented
46#14555768—24no—
47C2×C139⋊C8—21no—
48C8×D139—24no—
49C4⋊Dic139—22no—
50C4⋊Dic139—21no—
51C22⋊Dic139—21no—
52(C2×D139)⋊C4—22no—
53(C2×D139)⋊C4—22no—
54C4×Dic139—21no—
55C22×C4×C139—21no—
56C22×C4×C139C2311yescharacteristic
57M16×C139—21no—
58M16×C139D412yescomplemented
59C2×C8×C139—21no—
60C4⋊C4×C139—21no—
61C22⋊C4×C139—21no—
62C42×C139—21no—
63C42×C139—21no—
64C42×C139C2×C411yescharacteristic
65C42×C139C2×C411yescharacteristic
66C22×D139—21no—
67C22×D139C22⋊C412yes—
68Dic278—21no—
69Dic278—21no—
70Dic278—21no—
71Dic278—21no—
72D556—21no—
73D556—21no—
74D556—21no—
75D556—21no—
76D556—44no—
77C22⋊D139—22no—
78C22⋊D139—22no—
79C22⋊D139—41no—
80C22⋊D139—41no—
81C2×Dic139—21no—
82C2×Dic139—41no—
83C2×Dic139C22⋊C412yes—
84C4×D139—22no—
85C4×D139—22no—
86C4×D139—41no—
87C4×D139—41no—
88C139⋊C8—22no—
89C23×C139C2×D411yescharacteristic
90C2×C4×C139—21no—
91C2×C4×C139—21no—
92C2×C4×C139—42no—
93C2×C4×C139—41no—
94C2×C4×C139C22×C411yescharacteristic
95C2×C4×C139C2×D411yescharacteristic
96C2×C4×C139C2×D411yescharacteristic
97C2×C4×C139C2×D411yescharacteristic
98C2×C4×C139#4111yescharacteristic
99C2×C4×C139#4111yescharacteristic
100C8×C139—22no—
101C22×C139—41no—
102C22×C139C2×C22⋊C411yescharacteristic
103C22×C139#12111yescharacteristic
104C22×C139#12111yescharacteristic
105C2×D139—22no—
106C2×D139—42no—
107C2×D139—42no—
108C2×D139—41no—
109C4×C139—22no—
110C4×C139—41no—
111C4×C139—81no—
112C4×C139C4×D411yescharacteristic
113C4×C139C4×D411yescharacteristic
114C4×C139#12011yescharacteristic
115C4×C139#12311yescharacteristic
116Dic139—22no—
117Dic139—41no—
118Dic139—81no—
119C2×C139—21no—
120C2×C139—21no—
121C2×C139—21no—
122C2×C139#38611yescharacteristic
123D139—42no—
124D139—81no—
125C139#188411yescharacteristic, complemented, Sylow
126#1884—1391nomaximal, Sylow
127#568—1391no—
128#532—1391no—
129#421—1391no—
130#421—1391no—
131#410—1391no—
132#339—1391no—
133#339D13911yescharacteristic, complemented
134C2×#41—1391no—
135C2×#41—1391no—
136#131—2782no—
137#131—2782no—
138C2×M16—2782no—
139C2×M16—1391no—
140C2×M16C2×D13911yescharacteristic
141C4⋊Q8—1391no—
142#127—1391no—
143#124—1391no—
144#124—1391no—
145#121—2782no—
146C4×D4—2782no—
147#117—1391no—
148#117C2×D13911yescharacteristic
149C2×C42C2×D13911yescharacteristic
150#104—2782no—
151#104—2782no—
152#99—2782no—
153#41—2781no—
154#41—2781no—
155#41—2781no—
156#41—2781no—
157#41—2781no—
158#41—2781no—
159#41—2781no—
160#41—2781no—
161C2×Q8—1391no—
162C2×Q8—1391no—
163C2×D4—2782no—
164C2×D4—2781no—
165C2×D4—1392no—
166C2×D4—1391no—
167C2×D4—1391no—
168C22×C4—21no—
169C22×C4—2781no—
170C22×C4—1392no—
171C22×C4C22×D13911yescharacteristic
172M16—21no—
173M16—2784no—
174M16—2781no—
175M16—1392no—
176M16D55612yescomplemented
177C2×C8—21no—
178C2×C8—2784no—
179C2×C8—2781no—
180C4⋊C4—21no—
181C4⋊C4—2782no—
182C4⋊C4—2781no—
183C22⋊C4—21no—
184C22⋊C4—2782no—
185C22⋊C4—2782no—
186C22⋊C4—2781no—
187C42—21no—
188C42—21no—
189C42—2781no—
190C42C4×D13911yescharacteristic
191C42C4×D13911yescharacteristic
192C23—2781no—
193C23—1392no—
194C23D4×D13911yescharacteristic
195Q8—2781no—
196Q8—2781no—
197Q8—2781no—
198Q8—2781no—
199D4—2782no—
200D4—2782no—
201D4—2781no—
202D4—2781no—
203D4—2781no—
204D4—2781no—
205D4—5564no—
206D4—5561no—
207D4—5561no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—42no—
211C2×C4—41no—
212C2×C4—2782no—
213C2×C4—2782no—
214C2×C4—2781no—
215C2×C4—5561no—
216C2×C4—5561no—
217C2×C4—5561no—
218C2×C4—1392no—
219C2×C4C2×C4×D13911yescharacteristic
220C2×C4D4×D13911yescharacteristic
221C2×C4D4×D13911yescharacteristic
222C2×C4C2×D55611yescharacteristic
223C2×C4#1455578511yescharacteristic
224C2×C4#1455578611yescharacteristic
225C8—22no—
226C8—2782no—
227C22—41no—
228C22—2782no—
229C22—5562no—
230C22—5562no—
231C22—5561no—
232C22C22⋊C4×D13911yescharacteristic
233C22#1798481511yescharacteristic
234C22#1798481711yescharacteristic
235C4—22no—
236C4—41no—
237C4—81no—
238C4—2782no—
239C4—5561no—
240C4—11121no—
241C4#1798480411yescharacteristic
242C4C4×D55611yescharacteristic
243C4#1798481211yescharacteristic
244C4#1798482711yescharacteristic
245C2—21no—
246C2—21no—
247C2—21no—
248C2—5562no—
249C2—11121no—
250C2#2258083111yescharacteristic
subgroupG/H
centerC4#17984812
commutatorC2×C4×C139C22×C4
FrattiniC22×C4C22×D139
Fitting#339×C139C2
socleC2×C139#386
prime radical#22581503C2
cosocleC22×C4×C139C23
hypercenter#339D139
hypocenterC139#1884
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
1. #22581719C2semidirect
3. #22580971C2semidirect
4. #22580969C2semidirect
5. #22580926C2semidirect
6. #22580713C2semidirect
7. #339×C139C2semidirect
14. #17984842C4semidirect
15. #17984839C4semidirect
16. #17984830C4semidirect
17. #17984830C4semidirect
45. #14555769D4semidirect
58. M16×C139D4semidirect
125. C139#1884semidirect
133. #339D139semidirect
176. M16D556semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#225817192
#225815032
#225809712
#225809692
#225809262
#225807132
#339×C1392
#1884139