Finite Group Databasebeta

← #31804980

Subgroups — #31804980

Order 17792.

218 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 61 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#22581489C211yesmaximal, characteristic
2#22581003C211yesmaximal, characteristic, complemented
3#22580820C211yesmaximal, characteristic, complemented
4#22580690C211yesmaximal, characteristic, complemented
5#22580688C211yesmaximal, characteristic
6#22580686C211yesmaximal, characteristic
7#328×C139C211yesmaximal, characteristic, complemented
8#17984837—21no—
9#17984833C411yescharacteristic, complemented
10#17984831C411yescharacteristic, complemented
11#17984826—21no—
12#17984816C2211yescharacteristic
13Q8×Dic139C411yescharacteristic, complemented
14#17984804C411yescharacteristic, complemented
15(C22⋊D139)⋊C4—21no—
16#17984800—21no—
17C2×C4×Dic139C2211yescharacteristic
18Dic139⋊C8—21no—
19C22⋊(C139⋊C8)C2211yescharacteristic
20C8×Dic139—21no—
21C139⋊#95—21no—
22C139⋊#95—21no—
23C139⋊#95C2211yescharacteristic
24C22⋊Q8×C139C2211yescharacteristic
25C22⋊C8×C139C2211yescharacteristic
26#95×C139C2211yescharacteristic
27C2×D556C2×C411yescharacteristic
28C2×C22⋊D139—21no—
29C22×Dic139—21no—
30C22×Dic139D411yescharacteristic
31C22×Dic139D411yescharacteristic
32C2×C4×D139—21no—
33C2×C139⋊C8—21no—
34C4⋊Dic139—21no—
35C4⋊Dic139—21no—
36C4⋊Dic139C2×C411yescharacteristic
37Dic139⋊C4—21no—
38(C2×D139)⋊C4—21no—
39(C2×D139)⋊C4—21no—
40(C2×D139)⋊C4—21no—
41(C2×D139)⋊C4—21no—
42C4×Dic139—21no—
43C4×Dic139C2×C411yescharacteristic
44C4×Dic139C2×C411yescharacteristic
45C4×Dic139D411yescharacteristic
46C4×Dic139D411yescharacteristic
47C2×Q8×C139C2×C411yescharacteristic
48C22×C4×C139—21no—
49C22×C4×C139C2311yescharacteristic
50C2×C8×C139—21no—
51C4⋊C4×C139—21no—
52C4⋊C4×C139C2×C411yescharacteristic
53C22⋊C4×C139—21no—
54C22×D139—21no—
55D556—41no—
56C22⋊D139—41no—
57C22⋊D139—41no—
58C2×Dic139—21no—
59C2×Dic139—21no—
60C2×Dic139—21no—
61C2×Dic139—41no—
62C2×Dic139—41no—
63C2×Dic139—41no—
64C2×Dic139—41no—
65C2×Dic139C22⋊C411yescharacteristic
66C2×Dic139C22⋊C411yescharacteristic
67C2×Dic139C22⋊C411yescharacteristic
68C2×Dic139C22⋊C411yescharacteristic
69C4×D139—42no—
70C139⋊C8—41no—
71C23×C139C2×D411yescharacteristic
72Q8×C139—41no—
73C2×C4×C139—21no—
74C2×C4×C139—21no—
75C2×C4×C139—41no—
76C2×C4×C139—41no—
77C2×C4×C139—41no—
78C2×C4×C139—41no—
79C2×C4×C139C22×C411yescharacteristic
80C2×C4×C139C2×D411yescharacteristic
81C8×C139—41no—
82C22×C139—21no—
83C22×C139—21no—
84C22×C139C2×C22⋊C411yescharacteristic
85C22×C139#13511yescharacteristic
86C22×C139#13511yescharacteristic
87C2×D139—41no—
88C2×D139—41no—
89C2×D139—41no—
90C4×C139—21no—
91C4×C139—21no—
92C4×C139—41no—
93C4×C139—41no—
94C4×C139—81no—
95Dic139—21no—
96Dic139—21no—
97Dic139—21no—
98Dic139—21no—
99Dic139—41no—
100Dic139—81no—
101C2×C139—21no—
102C2×C139—21no—
103C2×C139#41011yescharacteristic
104C2×C139#41611yescharacteristic
105C2×C139#42111yescharacteristic
106D139—81no—
107C139#152111yescharacteristic, complemented, Sylow
108#1521—1391nomaximal, Sylow
109#529—1391no—
110#431—1391no—
111#383—1391no—
112#328—1391no—
113#328D13911yescharacteristic, complemented
114#327—1391no—
115#327—1391no—
116#126—2781no—
117#125—1391no—
118#124—1391no—
119#123—2781no—
120C22⋊Q8C2×D13911yescharacteristic
121#121—1391no—
122C4×Q8—1391no—
123C4×D4—2781no—
124C4×D4—1391no—
125#117—2781no—
126C2×C42—1391no—
127C4⋊C8—2781no—
128C22⋊C8—1391no—
129C22⋊C8C2×D13911yescharacteristic
130C4×C8—2781no—
131#95—2781no—
132#95—2781no—
133#95—1391no—
134#95C2×D13911yescharacteristic
135C2×Q8C4×D13911yescharacteristic
136C2×D4—2781no—
137C2×D4—1391no—
138C22×C4—21no—
139C22×C4—2781no—
140C22×C4—2781no—
141C22×C4—1391no—
142C22×C4—1391no—
143C22×C4C22×D13911yescharacteristic
144C2×C8—21no—
145C2×C8—2781no—
146C4⋊C4—21no—
147C4⋊C4—2781no—
148C4⋊C4—2781no—
149C4⋊C4—2781no—
150C4⋊C4—1391no—
151C4⋊C4C4×D13911yescharacteristic
152C22⋊C4—21no—
153C22⋊C4—2781no—
154C22⋊C4—2781no—
155C22⋊C4—2781no—
156C22⋊C4—2781no—
157C42—2781no—
158C42—1391no—
159C42—1391no—
160C42—1391no—
161C42—1391no—
162C23—2781no—
163C23D4×D13911yescharacteristic
164Q8—41no—
165D4—5561no—
166D4—5561no—
167D4—5561no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—2781no—
175C2×C4—2781no—
176C2×C4—2781no—
177C2×C4—5562no—
178C2×C4—5561no—
179C2×C4—5561no—
180C2×C4—5561no—
181C2×C4—5561no—
182C2×C4—1391no—
183C2×C4—1391no—
184C2×C4—1391no—
185C2×C4—1391no—
186C2×C4C2×C4×D13911yescharacteristic
187C2×C4D4×D13911yescharacteristic
188C8—41no—
189C8—5561no—
190C22—21no—
191C22—21no—
192C22—5561no—
193C22—5561no—
194C22—5561no—
195C22C22⋊C4×D13911yescharacteristic
196C22#1798486311yescharacteristic
197C22#1798486511yescharacteristic
198C4—21no—
199C4—21no—
200C4—41no—
201C4—41no—
202C4—81no—
203C4—2781no—
204C4—2781no—
205C4—2781no—
206C4—2781no—
207C4—5561no—
208C4—11121no—
209C2—21no—
210C2—21no—
211C2—11121no—
212C2#2258092511yescharacteristic
213C2#2258094811yescharacteristic
214C2#2258096811yescharacteristic
subgroupG/H
centerC22C22⋊C4×D139
commutatorC2×C4×C139C22×C4
FrattiniC22×C4C22×D139
Fitting#328×C139C2
socleC22×C139C2×C22⋊C4
prime radical#17984816C22
cosocleC22×C4×C139C23
hypercenter#328D139
hypocenterC139#1521
LCSG ▷ C2×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. #22581003C2semidirect
3. #22580820C2semidirect
4. #22580690C2semidirect
7. #328×C139C2semidirect
9. #17984833C4semidirect
10. #17984831C4semidirect
13. Q8×Dic139C4semidirect
14. #17984804C4semidirect
107. C139#1521semidirect
113. #328D139semidirect

Maximal subgroups

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

subgroupindex
#225814892
#225810032
#225808202
#225806902
#225806882
#225806862
#328×C1392
#1521139