Finite Group Databasebeta

← #31807488

Subgroups — #31807488

Order 17792.

406 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 93 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
1C22×#14555774C211yesmaximal, characteristic
2C22×#14555772C211yesmaximal, characteristic
3C2×#17984840C211yesmaximal, characteristic, complemented
4C2×#17984765C211yesmaximal, characteristic, complemented
5#22580854C211yesmaximal, characteristic
6#22580707C211yesmaximal, characteristic, complemented
7C2×#103×C139C211yesmaximal, characteristic, complemented
8C22×Dic278C2211yescharacteristic
9C22×D556C2211yescharacteristic
10C2×#14555774—22no—
11C2×#14555774—22no—
12C2×#14555774—22no—
13C2×#14555772—22no—
14C2×#14555772—22no—
15C2×#14555772—22no—
16C22×C139⋊C8C2211yescharacteristic
17#17984840—22no—
18#17984840—22no—
19C2×Dic139⋊C4—22no—
20C2×(C2×D139)⋊C4—22no—
21C2×C4×Dic139C2211yescharacteristic
22#17984765—22no—
23C22×Q8×C139C2211yescharacteristic
24C22×C8×C139C2211yescharacteristic
25C2×C4⋊C4×C139C2211yescharacteristic
26#103×C139—22no—
27C23×D139—21no—
28C2×Dic278—21no—
29C2×Dic278—21no—
30C2×Dic278—21no—
31C2×Dic278—21no—
32C2×Dic278—21no—
33C2×Dic278D412yes—
34C2×D556—21no—
35C2×D556—21no—
36C2×D556—21no—
37C2×D556—21no—
38C2×D556—21no—
39C2×D556D412yes—
40C22×Dic139—21no—
41C22×Dic139D412yes—
42#14555774—28no—
43#14555772—28no—
44C2×C139⋊C8—21no—
45C2×C139⋊C8—21no—
46C2×C139⋊C8D412yes—
47Dic139⋊C4—28no—
48(C2×D139)⋊C4—44no—
49C4×Dic139—21no—
50C4×Dic139—21no—
51C2×Q8×C139—21no—
52C2×Q8×C139—21no—
53C2×Q8×C139—21no—
54C2×Q8×C139—21no—
55C2×Q8×C139—21no—
56C2×Q8×C139D412yes—
57C22×C4×C139—21no—
58C22×C4×C139—21no—
59C22×C4×C139C2311yescharacteristic
60C2×C8×C139—21no—
61C2×C8×C139—21no—
62C2×C8×C139D412yes—
63C4⋊C4×C139—21no—
64C4⋊C4×C139—21no—
65C22×D139—22no—
66C22×D139—41no—
67C22×D139—41no—
68C22×D139—42no—
69C22×D139—42no—
70Dic278—22no—
71Dic278—22no—
72Dic278—41no—
73Dic278—41no—
74D556—22no—
75D556—22no—
76D556—41no—
77D556—41no—
78C2×Dic139—22no—
79C2×Dic139—22no—
80C2×Dic139—22no—
81C2×Dic139—41no—
82C2×Dic139—41no—
83C2×Dic139SD1614yescomplemented
84C139⋊C8—22no—
85C23×C139C2×D411yescharacteristic
86Q8×C139—22no—
87Q8×C139—22no—
88Q8×C139—41no—
89Q8×C139—41no—
90C2×C4×C139—22no—
91C2×C4×C139—41no—
92C2×C4×C139—41no—
93C2×C4×C139—41no—
94C2×C4×C139—42no—
95C2×C4×C139C2×D411yescharacteristic
96C2×C4×C139C2×D411yescharacteristic
97C2×C4×C139C2×D411yescharacteristic
98C2×C4×C139C2×D411yescharacteristic
99C2×C4×C139C2×D411yescharacteristic
100C2×C4×C139#4111yescharacteristic
101C8×C139—22no—
102C22×C139#12011yescharacteristic
103C22×C139#12111yescharacteristic
104C22×C139#12711yescharacteristic
105C22×C139C2×SD1612yes—
106C22×C139#13712yes—
107C2×D139—42no—
108C2×D139—44no—
109C2×D139—82no—
110C2×D139—81no—
111C2×D139—81no—
112C4×C139—42no—
113C4×C139—81no—
114C4×C139#12011yescharacteristic
115C4×C139#12011yescharacteristic
116C4×C139#12111yescharacteristic
117C4×C139#12111yescharacteristic
118Dic139—24no—
119Dic139—42no—
120C2×C139#39211yescharacteristic
121C2×C139#44812yes—
122C2×C139#46112yes—
123C2×C139#49211yescharacteristic
124C2×C139#49711yescharacteristic
125D139—82no—
126C139#201311yescharacteristic, complemented, Sylow
127#2013—1391nomaximal, Sylow
128C22×SD16—1391no—
129C22×SD16—1391no—
130C2×C4⋊Q8—1391no—
131C2×#103—1391no—
132C2×#103D13911yescharacteristic, complemented
133#390—1391no—
134#336—1391no—
135C22×Q8—1391no—
136C22×Q8C2×D13911yescharacteristic
137C22×D4—1391no—
138C2×SD16—2782no—
139C2×SD16—2782no—
140C2×SD16—2782no—
141C2×SD16—2782no—
142C2×SD16—2782no—
143C2×SD16—2782no—
144C22×C8—1391no—
145C22×C8C2×D13911yescharacteristic
146C4⋊Q8—2782no—
147C4⋊Q8—2782no—
148C2×C4⋊C4—2782no—
149C2×C4⋊C4C2×D13911yescharacteristic
150C2×C22⋊C4—2782no—
151C2×C42—1391no—
152#103—22no—
153#103—2782no—
154C24—2781no—
155C2×Q8—21no—
156C2×Q8—21no—
157C2×Q8—21no—
158C2×Q8—21no—
159C2×Q8—21no—
160C2×Q8—2781no—
161C2×Q8—2781no—
162C2×Q8—2781no—
163C2×Q8—2781no—
164C2×Q8—2781no—
165C2×Q8—1392no—
166C2×Q8D55612yes—
167C2×D4—2781no—
168C2×D4—2781no—
169C2×D4—2781no—
170C2×D4—2781no—
171C2×D4—2781no—
172C2×D4—1392no—
173C22×C4—21no—
174C22×C4—21no—
175C22×C4—2781no—
176C22×C4—1392no—
177C22×C4C22×D13911yescharacteristic
178SD16—2788no—
179SD16—2788no—
180C2×C8—21no—
181C2×C8—21no—
182C2×C8—2781no—
183C2×C8—2781no—
184C2×C8—1392no—
185C2×C8C22⋊D13912yes—
186C4⋊C4—21no—
187C4⋊C4—21no—
188C4⋊C4—2788no—
189C22⋊C4—5564no—
190C42—2781no—
191C42—2781no—
192C23—2782no—
193C23—5561no—
194C23—5561no—
195C23—5562no—
196C23—5562no—
197C23D4×D13911yescharacteristic
198Q8—22no—
199Q8—22no—
200Q8—41no—
201Q8—41no—
202Q8—2782no—
203Q8—2782no—
204Q8—5561no—
205Q8—5561no—
206D4—2782no—
207D4—2782no—
208D4—5561no—
209D4—5561no—
210C2×C4—22no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—42no—
215C2×C4—2782no—
216C2×C4—2782no—
217C2×C4—2782no—
218C2×C4—5561no—
219C2×C4—5561no—
220C2×C4—1394no—
221C2×C4D4×D13911yescharacteristic
222C2×C4D4×D13911yescharacteristic
223C2×C4D4×D13911yescharacteristic
224C2×C4C2×C22⋊D13911yescharacteristic
225C2×C4C2×D55611yescharacteristic
226C2×C4#1455578511yescharacteristic
227C8—22no—
228C8—2782no—
229C22—5562no—
230C22—5564no—
231C22—11121no—
232C22—11121no—
233C22—11122no—
234C22#1798481211yescharacteristic
235C22#1798481511yescharacteristic
236C22#1798483811yescharacteristic
237C22SD16×D13912yes—
238C22#1798487412yes—
239C4—42no—
240C4—81no—
241C4—2784no—
242C4—5562no—
243C4#1798481011yescharacteristic
244C4#1798481211yescharacteristic
245C4#1798481511yescharacteristic
246C4#1798481611yescharacteristic
247C2—11122no—
248C2#2258086211yescharacteristic
249C2#2258109312yes—
250C2#2258115712yes—
251C2#2258132411yescharacteristic
252C2#2258134611yescharacteristic
subgroupG/H
centerC23D4×D139
commutator, cosocleC22×C4×C139C23
FrattiniC22×C4C22×D139
FittingC2×#103×C139C2
socleC23×C139C2×D4
prime radicalC22×D556C22
hypercenterC2×#103D139
hypocenterC139#2013
LCSG ▷ C22×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
3. C2×#17984840C2semidirect
4. C2×#17984765C2semidirect
6. #22580707C2semidirect
7. C2×#103×C139C2semidirect
83. C2×Dic139SD16semidirect
126. C139#2013semidirect
132. C2×#103D139semidirect

Maximal subgroups

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

subgroupindex
C22×#145557742
C22×#145557722
C2×#179848402
C2×#179847652
#225808542
#225807072
C2×#103×C1392
#2013139