Finite Group Databasebeta

← #31816859

Subgroups — #31816859

Order 17792.

552 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 153 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×#17984875C211yesmaximal, characteristic, complemented
2C2×#17984873C211yesmaximal, characteristic, complemented
3C2×#17984872C211yesmaximal, characteristic, complemented
4#22581499C211yesmaximal, characteristic
5C2×#17984840C211yesmaximal, characteristic, complemented
6#22581346C212yesmaximal, complemented
7#22581344C212yesmaximal, complemented
8#22581331C212yesmaximal, complemented
9#22581324C212yesmaximal, complemented
10M16×Dic139C211yesmaximal, characteristic, complemented
11C2×#137×C139C211yesmaximal, characteristic, complemented
12C2×#14555785C2211yescharacteristic
13C22×Dic278C2211yescharacteristic
14#17984875—24no—
15#17984873—24no—
16#17984872—24no—
17C2×Dic556C2212yes—
18C2×#14555775C2212yes—
19C2×#14555775C2212yes—
20C2×#14555774C2212yes—
21C2×#14555773C2212yes—
22C2×#14555772C2212yes—
23C2×#14555769C2211yescharacteristic
24#17984840—22no—
25#17984840C2212yes—
26#17984840C2211yescharacteristic
27#17984840C2212yes—
28#17984838C2211yescharacteristic
29#17984831C2211yescharacteristic
30#17984829C2211yescharacteristic
31#17984814—22no—
32C4×C22⋊D139—22no—
33C2×Dic139⋊C4—22no—
34C2×C4×Dic139C2211yescharacteristic
35#17984752C2212yes—
36C8×Dic139C2212yes—
37C2×#41×C139C2211yescharacteristic
38C22×Q8×C139C2211yescharacteristic
39#137×C139—24no—
40C2×Q16×C139C2212yes—
41C2×SD16×C139C2212yes—
42C2×M16×C139C2211yescharacteristic
43#14555785—22no—
44#14555785—22no—
45C2×Dic278—21no—
46C2×Dic278—22no—
47C2×Dic278—22no—
48C2×Dic278C2311yescharacteristic
49C2×Dic278C2312yes—
50C2×D556C2311yescharacteristic
51C2×C22⋊D139—22no—
52C2×C22⋊D139—21no—
53C22×Dic139—21no—
54C22×Dic139D412yes—
55C2×C4×D139—21no—
56Dic556—24no—
57#14555775—24no—
58#14555775—24no—
59#14555774—24no—
60#14555773—24no—
61#14555772—24no—
62#14555769D414yescomplemented
63C2×C139⋊C8C2312yes—
64Dic139⋊C4—24no—
65Dic139⋊C4—24no—
66Dic139⋊C4—22no—
67C22⋊Dic139—22no—
68(C2×D139)⋊C4—22no—
69C4×Dic139D412yes—
70C4×Dic139C2311yescharacteristic
71C4×Dic139C2311yescharacteristic
72#41×C139—22no—
73#41×C139—22no—
74C2×Q8×C139—21no—
75C2×Q8×C139—22no—
76C2×Q8×C139—22no—
77C2×Q8×C139C2311yescharacteristic
78C2×Q8×C139C2312yes—
79C2×D4×C139—21no—
80C2×D4×C139C2311yescharacteristic
81C22×C4×C139—21no—
82C22×C4×C139—21no—
83C22×C4×C139C2311yescharacteristic
84Q16×C139—24no—
85SD16×C139—24no—
86M16×C139D414yescomplemented
87C2×C8×C139C2312yes—
88C22×D139—21no—
89Dic278—22no—
90Dic278—22no—
91Dic278—21no—
92Dic278—21no—
93Dic278—42no—
94D556—21no—
95D556—21no—
96C22⋊D139—42no—
97C22⋊D139—44no—
98C2×Dic139—24no—
99C2×Dic139—21no—
100C2×Dic139—22no—
101C2×Dic139—42no—
102C2×Dic139C2×D412yes—
103C2×Dic139C2×D412yes—
104C4×D139—42no—
105C139⋊C8C2×D414yes—
106C23×C139—21no—
107C23×C139C2×D411yescharacteristic
108Q8×C139—22no—
109Q8×C139—21no—
110Q8×C139—22no—
111Q8×C139—21no—
112Q8×C139—42no—
113D4×C139—21no—
114D4×C139—21no—
115D4×C139—42no—
116C2×C4×C139—21no—
117C2×C4×C139—22no—
118C2×C4×C139—42no—
119C2×C4×C139—42no—
120C2×C4×C139C2×D411yescharacteristic
121C2×C4×C139C2×D412yes—
122C2×C4×C139C2×D412yes—
123C2×C4×C139C2411yescharacteristic
124C8×C139C2×D414yes—
125C22×C139—22no—
126C22×C139—41no—
127C22×C139—42no—
128C22×C139#12712yes—
129C22×C139C22×D411yescharacteristic
130C2×D139—41no—
131C2×D139—42no—
132C4×C139—41no—
133C4×C139—42no—
134C4×C139#12712yes—
135C4×C139C22×D411yescharacteristic
136C4×C139C22×D411yescharacteristic
137Dic139—22no—
138Dic139—41no—
139Dic139—42no—
140Dic139#13714yescomplemented
141C2×C139—22no—
142C2×C139—81no—
143C2×C139C2×#12711yescharacteristic
144C2×C139C2×#13712yes—
145D139—81no—
146C139#315211yescharacteristic, complemented, Sylow
147#3152—1391nomaximal, Sylow
148C2×#137—1391no—
149C2×#137—1391no—
150C2×#137—1391no—
151C2×#137D13911yescharacteristic, complemented
152#532—1391no—
153C2×C4⋊Q8—1391no—
154#497—1392no—
155#497—1392no—
156#494—1392no—
157#492—1392no—
158C4×M16—1391no—
159C2×#41—1391no—
160C2×#41C2×D13911yescharacteristic
161C22×Q8—1391no—
162C22×Q8C2×D13911yescharacteristic
163#137—24no—
164#137—2784no—
165#137—2784no—
166#137—2784no—
167C2×Q16—1392no—
168C2×Q16—1392no—
169C2×Q16—1392no—
170C2×Q16C2×D13912yes—
171C2×SD16—1392no—
172C2×SD16—1392no—
173C2×SD16—1392no—
174C2×SD16C2×D13912yes—
175C2×M16—1391no—
176C2×M16C2×D13911yescharacteristic
177C4⋊Q8—2782no—
178C4⋊Q8—1392no—
179C4⋊Q8—1392no—
180C4⋊Q8—1391no—
181#127—1391no—
182#124—1391no—
183#124—1391no—
184#121—2782no—
185C4×D4—2782no—
186C2×C4⋊C4—2782no—
187C2×C42—1391no—
188#97—1392no—
189C4×C8—1392no—
190#41—22no—
191#41—22no—
192#41—2782no—
193#41—2782no—
194C2×Q8—21no—
195C2×Q8—22no—
196C2×Q8—22no—
197C2×Q8—2781no—
198C2×Q8—2782no—
199C2×Q8—2782no—
200C2×Q8—1391no—
201C2×Q8—1392no—
202C2×Q8C22×D13911yescharacteristic
203C2×Q8C22×D13912yes—
204C2×D4—21no—
205C2×D4—2781no—
206C2×D4—2782no—
207C2×D4—1391no—
208C2×D4C22×D13911yescharacteristic
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—2781no—
212C22×C4—2781no—
213C22×C4—1392no—
214C22×C4C22×D13911yescharacteristic
215Q16—24no—
216Q16—2784no—
217Q16—2784no—
218Q16—2784no—
219SD16—24no—
220SD16—2784no—
221SD16—2784no—
222SD16—2784no—
223M16—1394no—
224M16C22⋊D13914yescomplemented
225C2×C8—1392no—
226C2×C8C22×D13912yes—
227C4⋊C4—2784no—
228C4⋊C4—2784no—
229C4⋊C4—2782no—
230C22⋊C4—2782no—
231C22⋊C4—2782no—
232C42—1392no—
233C42—1391no—
234C42—1391no—
235C23—21no—
236C23—2781no—
237C23D4×D13911yescharacteristic
238Q8—22no—
239Q8—21no—
240Q8—22no—
241Q8—21no—
242Q8—42no—
243Q8—2782no—
244Q8—2781no—
245Q8—2782no—
246Q8—2781no—
247Q8—5562no—
248D4—21no—
249D4—21no—
250D4—42no—
251D4—2781no—
252D4—2781no—
253D4—5562no—
254D4—5564no—
255C2×C4—21no—
256C2×C4—22no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—2784no—
260C2×C4—2781no—
261C2×C4—2782no—
262C2×C4—5562no—
263C2×C4—5562no—
264C2×C4—1392no—
265C2×C4—1392no—
266C2×C4D4×D13911yescharacteristic
267C2×C4D4×D13912yes—
268C2×C4C2×C22⋊D13912yes—
269C2×C4C23×D13911yescharacteristic
270C8—1394no—
271C8C2×C22⋊D13914yes—
272C22—22no—
273C22—42no—
274C22—41no—
275C22—5562no—
276C22—5561no—
277C22#1798483812yes—
278C22C2×D4×D13911yescharacteristic
279C4—41no—
280C4—42no—
281C4—2782no—
282C4—5561no—
283C4—5562no—
284C4—1394no—
285C4#1798483812yes—
286C4C2×D4×D13911yescharacteristic
287C4C22×C22⋊D13911yescharacteristic
288C2—22no—
289C2—81no—
290C2—11121no—
291C2C2×#1798483811yescharacteristic
292C2#137×D13912yes—
subgroupG/H
centerC22C2×D4×D139
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
FittingC2×#137×C139C2
socleC22×C139C22×D4
prime radical#22581499C2
hypercenterC2×#137D139
hypocenterC139#3152
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C2×#17984875C2semidirect
2. C2×#17984873C2semidirect
3. C2×#17984872C2semidirect
5. C2×#17984840C2semidirect
6. #22581346C2semidirect
7. #22581344C2semidirect
8. #22581331C2semidirect
9. #22581324C2semidirect
10. M16×Dic139C2semidirect
11. C2×#137×C139C2semidirect
62. #14555769D4semidirect
86. M16×C139D4semidirect
140. Dic139#137semidirect
146. C139#3152semidirect
151. C2×#137D139semidirect
224. M16C22⋊D139semidirect

Maximal subgroups

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

subgroupindex
C2×#179848752
C2×#179848732
C2×#179848722
#225814992
C2×#179848402
#225813462
#225813442
#225813312
#225813242
M16×Dic1392
C2×#137×C1392
#3152139