Finite Group Databasebeta

← #31807554

Subgroups — #31807554

Order 17792.

258 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 83 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×#17984833C211yesmaximal, characteristic
2C2×#17984767C211yesmaximal, characteristic
3C2×#17984765C211yesmaximal, characteristic
4#22580858C211yesmaximal, characteristic
5#22580715C211yesmaximal, characteristic
6#22580707C211yesmaximal, characteristic
7#340×C139C211yesmaximal, characteristic
8C22×Dic278C2211yescharacteristic
9C22×C139⋊C8C2211yescharacteristic
10#17984833—22no—
11#17984833—22no—
12C2×C4⋊Dic139—21no—
13C2×C4⋊Dic139C2211yescharacteristic
14C2×Dic139⋊C4—21no—
15C2×C4×Dic139C2211yescharacteristic
16#17984767—22no—
17#17984765—22no—
18C139⋊#95—21no—
19C139⋊#95—21no—
20C22×C8×C139C2211yescharacteristic
21C2×C4⋊C4×C139C2211yescharacteristic
22C2×C4⋊C4×C139C2211yescharacteristic
23C2×Dic278—21no—
24C2×Dic278—21no—
25C2×Dic278—21no—
26C2×Dic278—21no—
27C2×Dic278—21no—
28C2×Dic278Q812yes—
29C22×Dic139—21no—
30C22×Dic139—21no—
31C22×Dic139D411yescharacteristic
32C22×Dic139D411yescharacteristic
33C2×C139⋊C8—21no—
34C2×C139⋊C8—21no—
35C2×C139⋊C8—21no—
36C4⋊Dic139—24no—
37C4⋊Dic139—21no—
38C4⋊Dic139D412yes—
39Dic139⋊C4—24no—
40C4×Dic139—21no—
41C4×Dic139—21no—
42C22×C4×C139—21no—
43C22×C4×C139—21no—
44C22×C4×C139C2311yescharacteristic
45C2×C8×C139—21no—
46C2×C8×C139—21no—
47C2×C8×C139—21no—
48C4⋊C4×C139—21no—
49C4⋊C4×C139—21no—
50C4⋊C4×C139—21no—
51C4⋊C4×C139D412yes—
52Dic278—22no—
53Dic278—22no—
54Dic278—41no—
55Dic278—41no—
56C2×Dic139—21no—
57C2×Dic139—21no—
58C2×Dic139—22no—
59C2×Dic139—22no—
60C2×Dic139—21no—
61C2×Dic139—21no—
62C2×Dic139—21no—
63C2×Dic139—21no—
64C2×Dic139—41no—
65C2×Dic139—41no—
66C2×Dic139—41no—
67C2×Dic139—41no—
68C139⋊C8—41no—
69C23×C139C2×D411yescharacteristic
70C2×C4×C139—22no—
71C2×C4×C139—41no—
72C2×C4×C139—41no—
73C2×C4×C139—41no—
74C2×C4×C139—41no—
75C2×C4×C139—41no—
76C2×C4×C139C2×D411yescharacteristic
77C2×C4×C139C2×D411yescharacteristic
78C2×C4×C139C2×Q811yescharacteristic
79C2×C4×C139#4111yescharacteristic
80C2×C4×C139#4111yescharacteristic
81C2×C4×C139#4111yescharacteristic
82C8×C139—41no—
83C22×C139#12011yescharacteristic
84C22×C139C22⋊Q811yescharacteristic
85C22×C139#12411yescharacteristic
86C22×C139#13511yescharacteristic
87C22×C139#13511yescharacteristic
88C22×C139#13711yescharacteristic
89C22×C139#13711yescharacteristic
90C4×C139—42no—
91C4×C139—81no—
92C4×C139C22⋊Q811yescharacteristic
93C4×C139C22⋊Q811yescharacteristic
94C4×C139#12411yescharacteristic
95C4×C139#12411yescharacteristic
96Dic139—42no—
97Dic139—41no—
98Dic139—41no—
99Dic139—42no—
100C2×C139#39311yescharacteristic
101C2×C139#45211yescharacteristic
102C2×C139#45211yescharacteristic
103C2×C139#47911yescharacteristic
104C2×C139#47911yescharacteristic
105C2×C139#48811yescharacteristic
106C2×C139#49111yescharacteristic
107C139#202611yescharacteristic, complemented, Sylow
108#2026—1391nomaximal, Sylow
109C2×#125—1391no—
110C2×#103—1391no—
111C2×#103—1391no—
112#391—1391no—
113#340—1391no—
114#340D13911yescharacteristic
115#336—1391no—
116C22×Q8—1391no—
117C22×C8—1391no—
118C22×C8C2×D13911yescharacteristic
119#125—2782no—
120#125—2782no—
121C2×C4⋊C4—2781no—
122C2×C4⋊C4—2781no—
123C2×C4⋊C4—1391no—
124C2×C4⋊C4C2×D13911yescharacteristic
125C2×C4⋊C4C2×D13911yescharacteristic
126C2×C42—1391no—
127#103—2782no—
128#103—2782no—
129#95—2781no—
130#95—2781no—
131C2×Q8—2781no—
132C2×Q8—2781no—
133C2×Q8—2781no—
134C2×Q8—2781no—
135C2×Q8—2781no—
136C2×Q8—1392no—
137C22×C4—21no—
138C22×C4—21no—
139C22×C4—2781no—
140C22×C4—2781no—
141C22×C4—1391no—
142C22×C4—1391no—
143C22×C4C22×D13911yescharacteristic
144C2×C8—21no—
145C2×C8—21no—
146C2×C8—21no—
147C2×C8—2781no—
148C2×C8—2781no—
149C2×C8—2781no—
150C4⋊C4—21no—
151C4⋊C4—21no—
152C4⋊C4—21no—
153C4⋊C4—2784no—
154C4⋊C4—2784no—
155C4⋊C4—2781no—
156C4⋊C4—1392no—
157C4⋊C4D55612yes—
158C42—2781no—
159C42—2781no—
160C23D4×D13911yescharacteristic
161Q8—2782no—
162Q8—2782no—
163Q8—5561no—
164Q8—5561no—
165C2×C4—22no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—2781no—
172C2×C4—2781no—
173C2×C4—2782no—
174C2×C4—2782no—
175C2×C4—2781no—
176C2×C4—2781no—
177C2×C4—2781no—
178C2×C4—2781no—
179C2×C4—5561no—
180C2×C4—5561no—
181C2×C4—5561no—
182C2×C4—5561no—
183C2×C4D4×D13911yescharacteristic
184C2×C4C2×D55611yescharacteristic
185C2×C4Q8×D13911yescharacteristic
186C2×C4#1455578411yescharacteristic
187C2×C4#1455578511yescharacteristic
188C2×C4#1455578511yescharacteristic
189C8—41no—
190C8—5561no—
191C22#1798481211yescharacteristic
192C22#1798482011yescharacteristic
193C22#1798482811yescharacteristic
194C22#1798486111yescharacteristic
195C22#1798486311yescharacteristic
196C22#1798487111yescharacteristic
197C22#1798487411yescharacteristic
198C4—42no—
199C4—81no—
200C4—5561no—
201C4—5561no—
202C4—5562no—
203C4—5562no—
204C4#1798482011yescharacteristic
205C4#1798482211yescharacteristic
206C4#1798482811yescharacteristic
207C4#1798483011yescharacteristic
208C2#2258086611yescharacteristic
209C2#2258111611yescharacteristic
210C2#2258111811yescharacteristic
211C2#2258125911yescharacteristic
212C2#2258126311yescharacteristic
213C2#2258130611yescharacteristic
214C2#2258132011yescharacteristic
subgroupG/H
centerC23D4×D139
commutator, cosocleC22×C4×C139C23
FrattiniC22×C4C22×D139
Fitting#340×C139C2
socle, prime radicalC23×C139C2×D4
hypercenter#340D139
hypocenterC139#2026
LCSG ▷ C22×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
107. C139#2026semidirect

Maximal subgroups

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

subgroupindex
C2×#179848332
C2×#179847672
C2×#179847652
#225808582
#225807152
#225807072
#340×C1392
#2026139