Finite Group Databasebeta

← #31807433

Subgroups — #31807433

Order 17792.

394 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 75 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×#17984873C211yesmaximal, characteristic, complemented
2#22581520C211yesmaximal, characteristic
3C2×#17984770C211yesmaximal, characteristic, complemented
4#22580962C211yesmaximal, characteristic, complemented
5C2×#17984759C211yesmaximal, characteristic, complemented
6#22580713C211yesmaximal, characteristic, complemented
7C2×#124×C139C211yesmaximal, characteristic, complemented
8C2×#14555785C2211yescharacteristic
9#17984873—22no—
10#17984873—22no—
11C2×#14555775—21no—
12C2×#14555772—21no—
13C2×#14555769C2211yescharacteristic
14C2×#14555769C2211yescharacteristic
15#17984838—21no—
16#17984829—21no—
17#17984813—22no—
18#17984811—22no—
19#17984801C2211yescharacteristic
20#17984770—22no—
21#17984766—22no—
22#17984759—22no—
23C22×Q8×C139C2211yescharacteristic
24C22×D4×C139C2211yescharacteristic
25#124×C139—22no—
26#124×C139—22no—
27C2×C22⋊C4×C139—22no—
28C2×C42×C139C2211yescharacteristic
29#14555785—21no—
30#14555785—21no—
31#14555785—21no—
32#14555785—21no—
33C2×Dic278D411yescharacteristic
34C2×D556D411yescharacteristic
35C2×C22⋊D139—24no—
36C2×C22⋊D139—21no—
37C2×C4×D139—21no—
38#14555775—24no—
39#14555772—24no—
40#14555769—21no—
41#14555769—21no—
42#14555769—21no—
43#14555769D412yescomplemented
44C2×C139⋊C8—21no—
45C2×C139⋊C8—21no—
46C4⋊Dic139D412yes—
47C22⋊Dic139—24no—
48C22⋊Dic139—21no—
49C4×Dic139—21no—
50C24×C139D412yes—
51C2×Q8×C139—21no—
52C2×Q8×C139—21no—
53C2×Q8×C139—21no—
54C2×Q8×C139—21no—
55C2×Q8×C139—21no—
56C2×Q8×C139D412yescomplemented
57C2×D4×C139—21no—
58C2×D4×C139—21no—
59C2×D4×C139—21no—
60C2×D4×C139—21no—
61C2×D4×C139—21no—
62C2×D4×C139—21no—
63C22×C4×C139—21no—
64C22×C4×C139—21no—
65C22×C4×C139C2311yescharacteristic
66C22⋊C4×C139—28no—
67C42×C139—21no—
68C42×C139D412yescomplemented
69C22×D139—21no—
70Dic278—21no—
71Dic278—21no—
72D556—21no—
73D556—21no—
74C22⋊D139—41no—
75C22⋊D139—41no—
76C22⋊D139—84no—
77C2×Dic139—22no—
78C2×Dic139—21no—
79C4×D139—41no—
80C4×D139—41no—
81C139⋊C8—22no—
82C139⋊C8—41no—
83C23×C139—22no—
84C23×C139—22no—
85C23×C139—22no—
86C23×C139—44no—
87C23×C139C2×D411yescharacteristic
88Q8×C139—22no—
89Q8×C139—22no—
90Q8×C139—41no—
91Q8×C139—41no—
92D4×C139—41no—
93D4×C139—41no—
94D4×C139—41no—
95D4×C139—41no—
96C2×C4×C139—22no—
97C2×C4×C139—22no—
98C2×C4×C139—42no—
99C2×C4×C139—41no—
100C2×C4×C139—41no—
101C2×C4×C139C2×D411yescharacteristic
102C2×C4×C139C2×D411yescharacteristic
103C2×C4×C139C2×D411yescharacteristic
104C2×C4×C139C2×D411yescharacteristic
105C2×C4×C139C2×D411yescharacteristic
106C2×C4×C139#4111yescharacteristic
107C22×C139—22no—
108C22×C139—44no—
109C22×C139—42no—
110C22×C139—44no—
111C22×C139—82no—
112C22×C139#12011yescharacteristic
113C22×C139#12011yescharacteristic
114C22×C139#12111yescharacteristic
115C2×D139—41no—
116C2×D139—42no—
117C4×C139—42no—
118C4×C139—42no—
119C4×C139#12011yescharacteristic
120C4×C139#12111yescharacteristic
121C4×C139#12111yescharacteristic
122C4×C139#12711yescharacteristic
123Dic139—41no—
124Dic139—42no—
125C2×C139—21no—
126C2×C139—21no—
127C2×C139—82no—
128C2×C139#39211yescharacteristic
129C2×C139#45512yes—
130D139—81no—
131C139#200411yescharacteristic, complemented, Sylow
132#2004—1391nomaximal, Sylow
133C2×#137—1391no—
134#535—1391no—
135C2×#124D13911yescharacteristic, complemented
136C2×#104—1391no—
137#419—1391no—
138C2×#100—1391no—
139#339—1391no—
140C2×#41—1391no—
141C22×Q8C2×D13911yescharacteristic
142C22×D4C2×D13911yescharacteristic
143#137—2782no—
144#137—2782no—
145C2×Q16—2781no—
146C2×SD16—2781no—
147C2×M16—1391no—
148C2×M16—1391no—
149#127—2781no—
150#124—22no—
151#124—22no—
152#124—2781no—
153#121—2782no—
154#120—2782no—
155#117—1391no—
156C2×C22⋊C4—22no—
157C2×C42C2×D13911yescharacteristic
158#104—2782no—
159#103—2782no—
160#100—2782no—
161C24C22⋊D13912yes—
162#41—2781no—
163#41—2781no—
164#41—2781no—
165#41—2781no—
166C2×Q8—21no—
167C2×Q8—21no—
168C2×Q8—21no—
169C2×Q8—21no—
170C2×Q8—21no—
171C2×Q8—1391no—
172C2×Q8C22⋊D13912yescomplemented
173C2×D4—21no—
174C2×D4—21no—
175C2×D4—21no—
176C2×D4—21no—
177C2×D4—21no—
178C2×D4—21no—
179C2×D4—2781no—
180C2×D4—2784no—
181C2×D4—1391no—
182C22×C4—21no—
183C22×C4—21no—
184C22×C4—2781no—
185C22×C4C22×D13911yescharacteristic
186Q16—2784no—
187SD16—2784no—
188M16—2781no—
189M16—2781no—
190M16—2781no—
191M16—1392no—
192C2×C8—2781no—
193C2×C8—2781no—
194C4⋊C4—1392no—
195C22⋊C4—28no—
196C22⋊C4—2784no—
197C22⋊C4—2781no—
198C42—21no—
199C42—2781no—
200C42C22⋊D13912yescomplemented
201C23—22no—
202C23—22no—
203C23—22no—
204C23—44no—
205C23—2781no—
206C23C2×C22⋊D13911yescharacteristic
207Q8—22no—
208Q8—22no—
209Q8—41no—
210Q8—41no—
211Q8—2781no—
212Q8—2781no—
213D4—41no—
214D4—41no—
215D4—41no—
216D4—41no—
217D4—2781no—
218D4—2781no—
219D4—5561no—
220D4—5561no—
221D4—11124no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—42no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—2782no—
228C2×C4—2781no—
229C2×C4—5561no—
230C2×C4—5561no—
231C2×C4D4×D13911yescharacteristic
232C2×C4D4×D13911yescharacteristic
233C2×C4D4×D13911yescharacteristic
234C2×C4C2×C22⋊D13911yescharacteristic
235C2×C4C2×C22⋊D13911yescharacteristic
236C2×C4#1455578411yescharacteristic
237C8—2782no—
238C8—5561no—
239C22—22no—
240C22—44no—
241C22—42no—
242C22—44no—
243C22—82no—
244C22—5561no—
245C22—5562no—
246C22#1798481011yescharacteristic
247C22#1798481111yescharacteristic
248C22#1798481411yescharacteristic
249C4—42no—
250C4—42no—
251C4—5561no—
252C4—5562no—
253C4#1798481011yescharacteristic
254C4#1798481311yescharacteristic
255C4#1798481411yescharacteristic
256C4#1798483811yescharacteristic
257C2—21no—
258C2—21no—
259C2—82no—
260C2—11121no—
261C2#2258086111yescharacteristic
262C2#2258113012yes—
subgroupG/H
centerC22#17984810
commutator, cosocleC22×C4×C139C23
FrattiniC22×C4C22×D139
FittingC2×#124×C139C2
socleC22×C139#120
prime radical#22581520C2
hypercenterC2×#124D139
hypocenterC139#2004
LCSG ▷ C22×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. C2×#17984873C2semidirect
3. C2×#17984770C2semidirect
4. #22580962C2semidirect
5. C2×#17984759C2semidirect
6. #22580713C2semidirect
7. C2×#124×C139C2semidirect
43. #14555769D4semidirect
56. C2×Q8×C139D4semidirect
68. C42×C139D4semidirect
131. C139#2004semidirect
135. C2×#124D139semidirect
172. C2×Q8C22⋊D139semidirect
200. C42C22⋊D139semidirect

Maximal subgroups

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

subgroupindex
C2×#179848732
#225815202
C2×#179847702
#225809622
C2×#179847592
#225807132
C2×#124×C1392
#2004139