Finite Group Databasebeta

← #31806606

Subgroups — #31806606

Order 17792.

316 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 99 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×#17984800C211yesmaximal, characteristic
2C2×#17984776C211yesmaximal, characteristic, complemented
3C2×#17984773C211yesmaximal, characteristic, complemented
4C2×(C2×D139)⋊C8C211yesmaximal, characteristic
5#22580810C211yesmaximal, characteristic
6#22580715C211yesmaximal, characteristic, complemented
7#340×C139C211yesmaximal, characteristic, complemented
8C22×C4×D139C2211yescharacteristic
9C22×C139⋊C8C2211yescharacteristic
10#17984800—22no—
11#17984800—22no—
12C2×C4⋊Dic139C2211yescharacteristic
13C2×C4⋊Dic139C2211yescharacteristic
14C2×(C2×D139)⋊C4—21no—
15C2×(C2×D139)⋊C4—21no—
16C2×C4×Dic139—21no—
17#17984776—22no—
18#17984773—22no—
19(C2×D139)⋊C8C414yescomplemented
20C139⋊#95—21no—
21C22×C8×C139C2211yescharacteristic
22C2×C4⋊C4×C139C2211yescharacteristic
23C2×C4⋊C4×C139C2211yescharacteristic
24C23×D139D411yescharacteristic
25C22×Dic139—21no—
26C22×Dic139—21no—
27C22×Dic139D411yescharacteristic
28C2×C4×D139—21no—
29C2×C4×D139—21no—
30C2×C4×D139—21no—
31C2×C4×D139—21no—
32C2×C4×D139C2×C412yes—
33C2×C4×D139Q812yes—
34C2×C139⋊C8—21no—
35C2×C139⋊C8—21no—
36C2×C139⋊C8C2×C412yes—
37C4⋊Dic139—21no—
38C4⋊Dic139—21no—
39C4⋊Dic139—21no—
40C4⋊Dic139D412yes—
41(C2×D139)⋊C4—24no—
42(C2×D139)⋊C4—42no—
43C4×Dic139—24no—
44C22×C4×C139—21no—
45C22×C4×C139—21no—
46C22×C4×C139C2311yescharacteristic
47C2×C8×C139—21no—
48C2×C8×C139—21no—
49C2×C8×C139C2×C412yes—
50C4⋊C4×C139—21no—
51C4⋊C4×C139—21no—
52C4⋊C4×C139—21no—
53C4⋊C4×C139D412yes—
54C22×D139—21no—
55C22×D139—21no—
56C22×D139—21no—
57C22×D139—21no—
58C22×D139—21no—
59C22×D139—21no—
60C22×D139C4⋊C412yes—
61C2×Dic139—21no—
62C2×Dic139—21no—
63C2×Dic139—22no—
64C2×Dic139—41no—
65C2×Dic139—41no—
66C2×Dic139—41no—
67C2×Dic139—41no—
68C2×Dic139—41no—
69C2×Dic139C4⋊C412yes—
70C4×D139—22no—
71C4×D139—22no—
72C4×D139—22no—
73C4×D139—22no—
74C139⋊C8—22no—
75C23×C139C2×D411yescharacteristic
76C2×C4×C139—22no—
77C2×C4×C139—41no—
78C2×C4×C139—41no—
79C2×C4×C139—41no—
80C2×C4×C139—41no—
81C2×C4×C139—41no—
82C2×C4×C139C22×C411yescharacteristic
83C2×C4×C139C2×D411yescharacteristic
84C2×C4×C139C2×D411yescharacteristic
85C2×C4×C139C2×Q811yescharacteristic
86C2×C4×C139#4111yescharacteristic
87C2×C4×C139#4111yescharacteristic
88C8×C139—22no—
89C22×C139C2×C4⋊C411yescharacteristic
90C22×C139#12011yescharacteristic
91C22×C139#12311yescharacteristic
92C22×C139#13511yescharacteristic
93C22×C139#13511yescharacteristic
94C22×C139AGL(1,ℤ/8)11yescharacteristic
95C22×C139#13711yescharacteristic
96C2×D139—22no—
97C2×D139—22no—
98C2×D139—22no—
99C2×D139—41no—
100C2×D139—41no—
101C2×D139—41no—
102C2×D139—41no—
103C4×C139—42no—
104C4×C139—81no—
105C4×C139C4×D411yescharacteristic
106C4×C139C4×D411yescharacteristic
107C4×C139C22⋊Q811yescharacteristic
108C4×C139C22⋊Q811yescharacteristic
109Dic139—22no—
110Dic139—42no—
111Dic139—81no—
112C2×C139#38511yescharacteristic
113C2×C139#42711yescharacteristic
114C2×C139#42811yescharacteristic
115C2×C139#44911yescharacteristic
116C2×C139#45211yescharacteristic
117C2×C139#48211yescharacteristic
118C2×C139#48511yescharacteristic
119D139—42no—
120C139#185411yescharacteristic, complemented, Sylow
121#1854—1391nomaximal, Sylow
122C2×#117—1391no—
123C2×#107—1391no—
124C2×#106—1391no—
125C2×C22⋊C8—1391no—
126#380—1391no—
127#340—1391no—
128#340D13911yescharacteristic, complemented
129C23×C4—1391no—
130C22×C8—1391no—
131C22×C8C2×D13911yescharacteristic
132#117—2782no—
133#117—2782no—
134C2×C4⋊C4—1391no—
135C2×C4⋊C4—1391no—
136C2×C4⋊C4C2×D13911yescharacteristic
137C2×C4⋊C4C2×D13911yescharacteristic
138C2×C22⋊C4—2781no—
139C2×C22⋊C4—2781no—
140C2×C42—2781no—
141#107—2782no—
142#106—2782no—
143C22⋊C8—1394no—
144#95—2781no—
145C24—1391no—
146C22×C4—21no—
147C22×C4—21no—
148C22×C4—2781no—
149C22×C4—2781no—
150C22×C4—2781no—
151C22×C4—2781no—
152C22×C4—2781no—
153C22×C4—2781no—
154C22×C4—1391no—
155C22×C4—1392no—
156C22×C4—1392no—
157C22×C4C22×D13911yescharacteristic
158C2×C8—21no—
159C2×C8—21no—
160C2×C8—2781no—
161C2×C8—2781no—
162C2×C8—1392no—
163C2×C8C4×D13912yes—
164C4⋊C4—21no—
165C4⋊C4—21no—
166C4⋊C4—21no—
167C4⋊C4—2781no—
168C4⋊C4—2781no—
169C4⋊C4—2781no—
170C4⋊C4—1392no—
171C4⋊C4D55612yes—
172C22⋊C4—2784no—
173C22⋊C4—5562no—
174C42—2784no—
175C23—2781no—
176C23—2781no—
177C23—2781no—
178C23—2781no—
179C23—2781no—
180C23—2781no—
181C23—1392no—
182C23D4×D13911yescharacteristic
183C2×C4—22no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—2781no—
190C2×C4—2781no—
191C2×C4—2782no—
192C2×C4—2782no—
193C2×C4—2782no—
194C2×C4—2782no—
195C2×C4—2782no—
196C2×C4—5561no—
197C2×C4—5561no—
198C2×C4—5561no—
199C2×C4—5561no—
200C2×C4—5561no—
201C2×C4—1392no—
202C2×C4C2×C4×D13911yescharacteristic
203C2×C4D4×D13911yescharacteristic
204C2×C4C2×D55611yescharacteristic
205C2×C4Q8×D13911yescharacteristic
206C2×C4#1455578411yescharacteristic
207C2×C4#1455578511yescharacteristic
208C8—22no—
209C8—2782no—
210C22—2782no—
211C22—2782no—
212C22—2782no—
213C22—5561no—
214C22—5561no—
215C22—5561no—
216C22—5561no—
217C22C4⋊C4×D13911yescharacteristic
218C22#1798481211yescharacteristic
219C22#1798482411yescharacteristic
220C22#1798486111yescharacteristic
221C22#1798486511yescharacteristic
222C22#1798486911yescharacteristic
223C22#1798487111yescharacteristic
224C4—42no—
225C4—81no—
226C4—2782no—
227C4—5562no—
228C4—11121no—
229C4(C22⋊D139)⋊C411yescharacteristic
230C4C4×D55611yescharacteristic
231C4#1798482011yescharacteristic
232C4#1798482211yescharacteristic
233C2—5562no—
234C2#2258082711yescharacteristic
235C2#2258099011yescharacteristic
236C2#2258099211yescharacteristic
237C2#2258110111yescharacteristic
238C2#2258111611yescharacteristic
239C2#2258127511yescharacteristic
240C2#2258129311yescharacteristic
subgroupG/H
centerC23D4×D139
commutatorC2×C4×C139C22×C4
FrattiniC22×C4C22×D139
Fitting#340×C139C2
socleC23×C139C2×D4
prime radicalC23×D139D4
cosocleC22×C4×C139C23
hypercenter#340D139
hypocenterC139#1854
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
2. C2×#17984776C2semidirect
3. C2×#17984773C2semidirect
6. #22580715C2semidirect
7. #340×C139C2semidirect
19. (C2×D139)⋊C8C4semidirect
120. C139#1854semidirect
128. #340D139semidirect

Maximal subgroups

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

subgroupindex
C2×#179848002
C2×#179847762
C2×#179847732
C2×(C2×D139)⋊C82
#225808102
#225807152
#340×C1392
#1854139