Finite Group Databasebeta

← #31808087

Subgroups — #31808087

Order 17792.

250 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 65 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#22581499C211yesmaximal, characteristic
2#22580937C211yesmaximal, characteristic, complemented
3#22580751C212yesmaximal, complemented
4#22580749C212yesmaximal, complemented
5#413×C139C211yesmaximal, characteristic, complemented
6C2×#14555785C411yescharacteristic
7C2×#14555769—21no—
8#17984840C2211yescharacteristic
9#17984838C411yescharacteristic
10#17984831C2211yescharacteristic
11#17984829C411yescharacteristic
12#17984814—21no—
13#17984814—21no—
14C4×C22⋊D139—21no—
15C4×C22⋊D139—21no—
16C2×C4×Dic139C411yescharacteristic
17#17984761C2212yes—
18#17984759—21no—
19C2×#41×C139C2211yescharacteristic
20C2×M16×C139—21no—
21#101×C139C2212yes—
22#100×C139—21no—
23#14555785—41no—
24#14555785—41no—
25C2×Dic278C2×C411yescharacteristic
26C2×D556C2×C411yescharacteristic
27C2×C22⋊D139—21no—
28C2×C22⋊D139—21no—
29C2×C22⋊D139—21no—
30C22×Dic139—21no—
31C2×C4×D139—21no—
32#14555769—22no—
33#14555769—41no—
34C2×C139⋊C8—41no—
35Dic139⋊C4—21no—
36Dic139⋊C4—21no—
37C22⋊Dic139—21no—
38C22⋊Dic139—21no—
39(C2×D139)⋊C4—21no—
40(C2×D139)⋊C4—21no—
41C4×Dic139—21no—
42C4×Dic139C2×C411yescharacteristic
43C4×Dic139C2×C411yescharacteristic
44#41×C139—41no—
45#41×C139—41no—
46C2×Q8×C139C2311yescharacteristic
47C2×D4×C139C2×C411yescharacteristic
48C2×D4×C139D411yescharacteristic
49C2×D4×C139D411yescharacteristic
50C22×C4×C139C2×C411yescharacteristic
51C22×C4×C139D411yescharacteristic
52C22×C4×C139D411yescharacteristic
53M16×C139—22no—
54M16×C139—41no—
55C2×C8×C139—41no—
56C22×D139—21no—
57Dic278—41no—
58D556—41no—
59C22⋊D139—42no—
60C22⋊D139—42no—
61C22⋊D139—42no—
62C2×Dic139—21no—
63C2×Dic139—21no—
64C2×Dic139—21no—
65C2×Dic139—42no—
66C4×D139—41no—
67C4×D139—41no—
68C139⋊C8—42no—
69C23×C139C22⋊C411yescharacteristic
70C23×C139C22⋊C411yescharacteristic
71C23×C139C22⋊C411yescharacteristic
72Q8×C139—41no—
73D4×C139—41no—
74D4×C139—41no—
75D4×C139—41no—
76C2×C4×C139—21no—
77C2×C4×C139—21no—
78C2×C4×C139—21no—
79C2×C4×C139—21no—
80C2×C4×C139—21no—
81C2×C4×C139—21no—
82C2×C4×C139C22⋊C411yescharacteristic
83C2×C4×C139C22×C411yescharacteristic
84C2×C4×C139C2×D411yescharacteristic
85C2×C4×C139C2×D411yescharacteristic
86C8×C139—42no—
87C22×C139—21no—
88C22×C139—21no—
89C22×C139—21no—
90C22×C139—41no—
91C22×C139—41no—
92C22×C139—41no—
93C22×C139C2×C22⋊C411yescharacteristic
94C2×D139—41no—
95C2×D139—41no—
96C2×D139—41no—
97C4×C139—21no—
98C4×C139—21no—
99C4×C139—21no—
100C4×C139#9911yescharacteristic
101C4×C139#9911yescharacteristic
102Dic139—22no—
103Dic139—41no—
104Dic139—41no—
105C2×C139—21no—
106C2×C139—41no—
107C2×C139—41no—
108C2×C139—41no—
109C2×C139C2×#9911yescharacteristic
110D139—81no—
111C139#213211yescharacteristic, complemented, Sylow
112#2132—1391nomaximal, Sylow
113#532—1391no—
114#413—1391no—
115#413D13911yescharacteristic, complemented
116#356—1392no—
117#355—1392no—
118C2×#41—1391no—
119C2×#41C2×D13911yescharacteristic
120C2×M16—21no—
121C2×M16—2781no—
122C4⋊Q8—1391no—
123#127—1391no—
124#124—1391no—
125#124—1391no—
126#121—2781no—
127#121—2781no—
128C4×D4—2781no—
129C4×D4—2781no—
130C2×C42—1391no—
131#101—1392no—
132#101C2×D13912yes—
133#100—21no—
134#100—2781no—
135#41—41no—
136#41—41no—
137#41—5561no—
138#41—5561no—
139C2×Q8—1391no—
140C2×Q8C22×D13911yescharacteristic
141C2×D4—2781no—
142C2×D4—2781no—
143C2×D4—2781no—
144C2×D4—1391no—
145C2×D4C4×D13911yescharacteristic
146C2×D4C22⋊D13911yescharacteristic
147C2×D4D55611yescharacteristic
148C22×C4—2781no—
149C22×C4—2781no—
150C22×C4C4×D13911yescharacteristic
151C22×C4C22⋊D13911yescharacteristic
152C22×C4D55611yescharacteristic
153M16—22no—
154M16—41no—
155M16—2782no—
156M16—5561no—
157C2×C8—41no—
158C2×C8—5561no—
159C4⋊C4—2781no—
160C4⋊C4—2781no—
161C22⋊C4—2781no—
162C22⋊C4—2781no—
163C22⋊C4—2781no—
164C22⋊C4—2781no—
165C42—2781no—
166C42—1391no—
167C42—1391no—
168C23—2781no—
169C23(C2×D139)⋊C411yescharacteristic
170C23(C2×D139)⋊C411yescharacteristic
171C23(C2×D139)⋊C411yescharacteristic
172Q8—41no—
173Q8—5561no—
174D4—41no—
175D4—41no—
176D4—41no—
177D4—5561no—
178D4—5562no—
179D4—5562no—
180D4—5562no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—2781no—
188C2×C4—2781no—
189C2×C4—2781no—
190C2×C4—5562no—
191C2×C4—5561no—
192C2×C4—5561no—
193C2×C4(C2×D139)⋊C411yescharacteristic
194C2×C4C2×C4×D13911yescharacteristic
195C2×C4C2×C22⋊D13911yescharacteristic
196C2×C4C2×D55611yescharacteristic
197C8—42no—
198C8—5562no—
199C22—21no—
200C22—21no—
201C22—21no—
202C22—41no—
203C22—41no—
204C22—41no—
205C22—5561no—
206C22—5561no—
207C22—5561no—
208C22C2×(C2×D139)⋊C411yescharacteristic
209C4—21no—
210C4—21no—
211C4—21no—
212C4—2782no—
213C4—5561no—
214C4—5561no—
215C4#1798475611yescharacteristic
216C4#1798475611yescharacteristic
217C2—21no—
218C2—41no—
219C2—41no—
220C2—41no—
221C2—11121no—
222C2C2×#1798475611yescharacteristic
subgroupG/H
centerC4#17984756
commutatorC2×C4×C139C22×C4
FrattiniC2×Q8C22×D139
Fitting#413×C139C2
socleC2×C139C2×#99
prime radical#22581499C2
cosocleC2×Q8×C139C23
hypercenter#413D139
hypocenterC139#2132
LCSG ▷ C2×C4×C139 ▷ C22×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #413

Complements

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

NH ≅ G/Ntype
2. #22580937C2semidirect
3. #22580751C2semidirect
4. #22580749C2semidirect
5. #413×C139C2semidirect
111. C139#2132semidirect
115. #413D139semidirect

Maximal subgroups

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

subgroupindex
#225814992
#225809372
#225807512
#225807492
#413×C1392
#2132139