Finite Group Databasebeta

← #31814778

Subgroups — #31814778

Order 17792.

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

normal subgroups only

This group has 524 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×#17984833C211yesmaximal, characteristic, complemented
2C2×#17984831C211yesmaximal, characteristic
3#22580860C211yesmaximal, characteristic, complemented
4#22580855C211yesmaximal, characteristic
5#22580854C211yesmaximal, characteristic
6#22580845C214yesmaximal, complemented
7#22580842C214yesmaximal, complemented
8C42×Dic139C211yesmaximal, characteristic, complemented
9#391×C139C211yesmaximal, characteristic, complemented
10C22×D556C2211yescharacteristic
11#17984833—24no—
12#17984831—24no—
13C2×C4⋊Dic139C2212yes—
14C2×C4⋊Dic139C2211yescharacteristic
15C2×Dic139⋊C4C2212yes—
16C2×(C2×D139)⋊C4C2212yes—
17C2×(C2×D139)⋊C4C2214yes—
18C2×(C2×D139)⋊C4C2214yes—
19C2×(C2×D139)⋊C4C2212yes—
20C2×C4×Dic139C2212yes—
21C2×C4×Dic139C2212yes—
22C2×C4×Dic139C2211yescharacteristic
23C2×C4×Dic139C2211yescharacteristic
24C139⋊#95C2214yes—
25C22×Q8×C139C2211yescharacteristic
26C2×C4⋊C4×C139C2211yescharacteristic
27C2×C42×C139C2211yescharacteristic
28#95×C139C2214yes—
29C23×D139C2312yes—
30C2×D556—22no—
31C2×D556—22no—
32C2×D556—22no—
33C22×Dic139C2312yes—
34C22×Dic139C2311yescharacteristic
35C22×Dic139C2311yescharacteristic
36C22×Dic139C2312yes—
37C4⋊Dic139—24no—
38C4⋊Dic139—22no—
39Dic139⋊C4—24no—
40(C2×D139)⋊C4—24no—
41(C2×D139)⋊C4—24no—
42(C2×D139)⋊C4—28no—
43(C2×D139)⋊C4—28no—
44C4×Dic139—24no—
45C4×Dic139—22no—
46C4×Dic139—24no—
47C4×Dic139D414yes—
48C2×Q8×C139—22no—
49C2×Q8×C139—22no—
50C2×Q8×C139—22no—
51C22×C4×C139C2312yes—
52C22×C4×C139C2312yes—
53C22×C4×C139C2312yes—
54C22×C4×C139C2311yescharacteristic
55C4⋊C4×C139—22no—
56C42×C139—22no—
57C22×D139—22no—
58C22×D139—24no—
59C22×D139—24no—
60C22×D139—22no—
61C22×D139—22no—
62D556—44no—
63C2×Dic139—22no—
64C2×Dic139—22no—
65C2×Dic139—22no—
66C2×Dic139—22no—
67C2×Dic139—22no—
68C2×Dic139—24no—
69C2×Dic139C2×D412yes—
70C2×Dic139C2×D412yes—
71C2×Dic139#4114yes—
72C23×C139C2411yescharacteristic
73Q8×C139—44no—
74C2×C4×C139—22no—
75C2×C4×C139—22no—
76C2×C4×C139—22no—
77C2×C4×C139—22no—
78C2×C4×C139—22no—
79C2×C4×C139—22no—
80C2×C4×C139—24no—
81C2×C4×C139C2×D412yes—
82C2×C4×C139#4112yes—
83C2×C4×C139#4112yes—
84C2×C4×C139#4114yes—
85C22×C139C22×D411yescharacteristic
86C22×C139C2×#4112yes—
87C22×C139C2×#4111yescharacteristic
88C22×C139C2×#4111yescharacteristic
89C22×C139C2×#4112yes—
90C2×D139—42no—
91C2×D139—44no—
92C2×D139—44no—
93C2×D139—42no—
94C2×D139—42no—
95C4×C139—24no—
96C4×C139—42no—
97C4×C139—42no—
98C4×C139#12414yes—
99Dic139—24no—
100Dic139—22no—
101Dic139—22no—
102Dic139—42no—
103C2×C139C2×#12411yescharacteristic
104C2×C139#52912yes—
105C2×C139#52912yes—
106C2×C139#53211yescharacteristic
107C2×C139#53211yescharacteristic
108D139—82no—
109C139#286111yescharacteristic, complemented, Sylow
110#2861—1391nomaximal, Sylow
111C2×#125—1391no—
112C2×#124—1391no—
113#391—1391no—
114#391D13911yescharacteristic, complemented
115#390—1391no—
116#390—1391no—
117#388—1394no—
118#388—1394no—
119C43—1391no—
120C22×Q8C2×D13911yescharacteristic
121C22×D4—1391no—
122#125—2784no—
123#124—2784no—
124C2×C4⋊C4—1392no—
125C2×C4⋊C4—1392no—
126C2×C4⋊C4—1391no—
127C2×C4⋊C4C2×D13911yescharacteristic
128C2×C22⋊C4—1392no—
129C2×C22⋊C4—1392no—
130C2×C22⋊C4—1394no—
131C2×C22⋊C4—1394no—
132C2×C42—1392no—
133C2×C42—1392no—
134C2×C42—1391no—
135C2×C42—1391no—
136C2×C42C2×D13911yescharacteristic
137#95—1394no—
138#95C2×D13914yes—
139C24—1392no—
140C2×Q8—22no—
141C2×Q8—22no—
142C2×Q8—22no—
143C2×D4—2782no—
144C2×D4—2782no—
145C2×D4—2782no—
146C22×C4—1392no—
147C22×C4—1392no—
148C22×C4—1391no—
149C22×C4—1391no—
150C22×C4C22×D13912yes—
151C22×C4C22×D13912yes—
152C22×C4C22×D13912yes—
153C22×C4C22×D13911yescharacteristic
154C4⋊C4—22no—
155C4⋊C4—2784no—
156C4⋊C4—2784no—
157C4⋊C4—2782no—
158C22⋊C4—2788no—
159C22⋊C4—2784no—
160C22⋊C4—2784no—
161C22⋊C4—2788no—
162C42—22no—
163C42—2784no—
164C42—2782no—
165C42—2784no—
166C42—1394no—
167C23—2782no—
168C23—2784no—
169C23—2782no—
170C23—2782no—
171C23—2784no—
172C23C23×D13911yescharacteristic
173Q8—44no—
174D4—5564no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—24no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—2782no—
183C2×C4—2782no—
184C2×C4—2782no—
185C2×C4—2782no—
186C2×C4—2782no—
187C2×C4—2784no—
188C2×C4—1392no—
189C2×C4—1392no—
190C2×C4—1394no—
191C2×C4D4×D13912yes—
192C2×C4#1455578412yes—
193C2×C4#1455578512yes—
194C2×C4#1455578614yes—
195C22—5562no—
196C22—5562no—
197C22—5564no—
198C22—5564no—
199C22—5562no—
200C22C2×D4×D13911yescharacteristic
201C22#41×D13912yes—
202C22C2×#1455578411yescharacteristic
203C22C2×#1455578511yescharacteristic
204C22C2×#1455578612yes—
205C4—24no—
206C4—42no—
207C4—42no—
208C4—2782no—
209C4—2784no—
210C4—2782no—
211C4—5562no—
212C4#1798482814yes—
213C2—11122no—
214C2C2×#1798482811yescharacteristic
215C2#2258148912yes—
216C2#2258149012yes—
217C2#2258150211yescharacteristic
218C2#2258150411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D139
commutator, socle, cosocleC23×C139C24
Fitting#391×C139C2
prime radicalC22×D556C22
hypercenter#391D139
hypocenterC139#2861
LCSG ▷ C23×C139 ▷ C139
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
1. C2×#17984833C2semidirect
3. #22580860C2semidirect
6. #22580845C2semidirect
7. #22580842C2semidirect
8. C42×Dic139C2semidirect
9. #391×C139C2semidirect
109. C139#2861semidirect
114. #391D139semidirect

Maximal subgroups

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

subgroupindex
C2×#179848332
C2×#179848312
#225808602
#225808552
#225808542
#225808452
#225808422
C42×Dic1392
#391×C1392
#2861139