Finite Group Databasebeta

← #31805430

Subgroups — #31805430

Order 17792.

236 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 51 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
1#22581578C211yesmaximal, characteristic
2#22581289C211yesmaximal, characteristic, complemented
3#22581286C211yesmaximal, characteristic, complemented
4#22580890C211yesmaximal, characteristic
5#22580689C211yesmaximal, characteristic, complemented
6#22580676C211yesmaximal, characteristic
7#328×C139C211yesmaximal, characteristic, complemented
8#17984822—21no—
9#17984821C2211yescharacteristic
10#17984820—21no—
11#17984820—21no—
12#17984819—21no—
13#17984818—21no—
14C2×C4⋊Dic139—21no—
15C2×C4⋊Dic139C2211yescharacteristic
16C2×(C2×D139)⋊C4—21no—
17C2×(C2×D139)⋊C4C2211yescharacteristic
18C22⋊C4×D139—21no—
19#17984776—21no—
20#17984775—21no—
21#17984767—21no—
22#17984766—21no—
23C22⋊(C139⋊C8)C2211yescharacteristic
24C22⋊Q8×C139C2211yescharacteristic
25C22⋊C8×C139C2211yescharacteristic
26#95×C139C2211yescharacteristic
27C23×D139D411yescharacteristic
28C2×Dic278—21no—
29C2×Dic278D411yescharacteristic
30C22×Dic139—21no—
31C22×Dic139D411yescharacteristic
32C2×C4×D139—21no—
33C2×C4×D139—21no—
34C2×C139⋊C8—21no—
35C4⋊Dic139—21no—
36C4⋊Dic139—21no—
37C4⋊Dic139—21no—
38C4⋊Dic139—42no—
39C4⋊Dic139D411yescharacteristic
40Dic139⋊C4—21no—
41Dic139⋊C4—21no—
42Dic139⋊C4—21no—
43C22⋊Dic139—21no—
44(C2×D139)⋊C4—21no—
45(C2×D139)⋊C4—21no—
46(C2×D139)⋊C4—21no—
47(C2×D139)⋊C4—21no—
48(C2×D139)⋊C4—42no—
49C2×Q8×C139D411yescharacteristic
50C22×C4×C139—21no—
51C22×C4×C139C2311yescharacteristic
52C2×C8×C139—21no—
53C4⋊C4×C139—21no—
54C4⋊C4×C139D411yescharacteristic
55C22⋊C4×C139—21no—
56C22×D139—21no—
57C22×D139—21no—
58C22×D139—41no—
59C22×D139—41no—
60C22×D139Q1612yes—
61Dic278—41no—
62Dic278—81no—
63C2×Dic139—21no—
64C2×Dic139—21no—
65C2×Dic139—21no—
66C2×Dic139—41no—
67C2×Dic139—41no—
68C2×Dic139—41no—
69C2×Dic139—41no—
70C4×D139—81no—
71C4×D139—81no—
72C139⋊C8—41no—
73C23×C139C2×D411yescharacteristic
74Q8×C139—41no—
75C2×C4×C139—22no—
76C2×C4×C139—21no—
77C2×C4×C139—21no—
78C2×C4×C139—41no—
79C2×C4×C139—41no—
80C2×C4×C139—41no—
81C2×C4×C139C2×D411yescharacteristic
82C2×C4×C139C2×D411yescharacteristic
83C8×C139—41no—
84C22×C139—21no—
85C22×C139—21no—
86C22×C139#12011yescharacteristic
87C22×C139C2×Q1611yescharacteristic
88C22×C139#13711yescharacteristic
89C2×D139—22no—
90C2×D139—41no—
91C2×D139—41no—
92C2×D139—42no—
93C2×D139—81no—
94C4×C139—21no—
95C4×C139—21no—
96C4×C139—42no—
97C4×C139—41no—
98C4×C139—41no—
99Dic139—41no—
100Dic139—41no—
101Dic139—41no—
102Dic139—81no—
103C2×C139—21no—
104C2×C139—21no—
105C2×C139#45111yescharacteristic
106C2×C139#45311yescharacteristic
107C2×C139#45811yescharacteristic
108D139—42no—
109C139#161411yescharacteristic, complemented, Sylow
110#1614—1391nomaximal, Sylow
111#543—1391no—
112#484—1391no—
113#484—1391no—
114#399—1391no—
115#328—1391no—
116#328D13911yescharacteristic, complemented
117#323—1391no—
118C22⋊Q8—2781no—
119C22⋊Q8—2781no—
120C22⋊Q8—2781no—
121C22⋊Q8—2781no—
122C22⋊Q8—2781no—
123C22⋊Q8—1391no—
124C22⋊Q8C2×D13911yescharacteristic
125C2×C4⋊C4—2781no—
126C2×C4⋊C4—1391no—
127C2×C22⋊C4—2781no—
128C2×C22⋊C4—2781no—
129C2×C22⋊C4—1391no—
130#107—2781no—
131#107—2781no—
132#103—2781no—
133#103—2781no—
134C22⋊C8—1391no—
135C22⋊C8C2×D13911yescharacteristic
136#95C2×D13911yescharacteristic
137C24—1391no—
138C2×Q8—2781no—
139C2×Q8—1391no—
140C2×Q8D55611yescharacteristic
141C22×C4—21no—
142C22×C4—2781no—
143C22×C4—2781no—
144C22×C4—2781no—
145C22×C4—1391no—
146C22×C4C22×D13911yescharacteristic
147C2×C8—21no—
148C2×C8—2781no—
149C4⋊C4—21no—
150C4⋊C4—2781no—
151C4⋊C4—2781no—
152C4⋊C4—2781no—
153C4⋊C4—2781no—
154C4⋊C4—2781no—
155C4⋊C4—2781no—
156C4⋊C4—5562no—
157C4⋊C4—1391no—
158C4⋊C4D55611yescharacteristic
159C22⋊C4—21no—
160C22⋊C4—2781no—
161C22⋊C4—2781no—
162C22⋊C4—2781no—
163C22⋊C4—2781no—
164C22⋊C4—2781no—
165C22⋊C4—5562no—
166C23—2781no—
167C23—2781no—
168C23—5561no—
169C23—5561no—
170C23—1392no—
171C23D4×D13911yescharacteristic
172Q8—41no—
173Q8—5561no—
174Q8—11121no—
175C2×C4—22no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—41no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—2781no—
182C2×C4—2781no—
183C2×C4—2781no—
184C2×C4—5561no—
185C2×C4—5561no—
186C2×C4—5561no—
187C2×C4—5561no—
188C2×C4—11121no—
189C2×C4—11121no—
190C2×C4D4×D13911yescharacteristic
191C2×C4C2×D55611yescharacteristic
192C8—41no—
193C8—5561no—
194C22—21no—
195C22—21no—
196C22—2782no—
197C22—5562no—
198C22—5561no—
199C22—5561no—
200C22—11121no—
201C22#1798481211yescharacteristic
202C22Q16×D13911yescharacteristic
203C22#1798487111yescharacteristic
204C4—21no—
205C4—21no—
206C4—42no—
207C4—41no—
208C4—41no—
209C4—5561no—
210C4—5561no—
211C4—5561no—
212C4—11121no—
213C2—21no—
214C2—21no—
215C2—5562no—
216C2#2258111011yescharacteristic
217C2#2258112211yescharacteristic
218C2#2258114411yescharacteristic
subgroupG/H
centerC22#17984812
commutator, cosocleC22×C4×C139C23
FrattiniC22×C4C22×D139
Fitting#328×C139C2
socleC22×C139#120
prime radicalC23×D139D4
hypercenter#328D139
hypocenterC139#1614
LCSG ▷ C22×C4×C139 ▷ C22×C139 ▷ C139
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
2. #22581289C2semidirect
3. #22581286C2semidirect
5. #22580689C2semidirect
7. #328×C139C2semidirect
109. C139#1614semidirect
116. #328D139semidirect

Maximal subgroups

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

subgroupindex
#225815782
#225812892
#225812862
#225808902
#225806892
#225806762
#328×C1392
#1614139