Finite Group Databasebeta

← #31805712

Subgroups — #31805712

Order 17792.

228 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 45 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#22581695C211yesmaximal, characteristic
2#22581347C211yesmaximal, characteristic, complemented
3#22581313C211yesmaximal, characteristic, complemented
4#22581312C211yesmaximal, characteristic, complemented
5#22580692C211yesmaximal, characteristic, complemented
6#22580692C211yesmaximal, characteristic, complemented
7#329×C139C211yesmaximal, characteristic, complemented
8C2×Dic556—21no—
9C2×#14555774—21no—
10#17984842C2211yescharacteristic, complemented
11#17984831—21no—
12#17984830C2211yescharacteristic
13#17984830C2211yescharacteristic
14#17984828—21no—
15#17984828—21no—
16#17984812—21no—
17#17984812—21no—
18#17984810—21no—
19#17984767—21no—
20#17984766—21no—
21#17984764—21no—
22#17984763—21no—
23#17984753C2211yescharacteristic, complemented
24#124×C139C2211yescharacteristic
25#97×C139C2211yescharacteristic, complemented
26#97×C139C2211yescharacteristic, complemented
27C23×D139—21no—
28C2×Dic278—21no—
29C2×Dic278D411yescharacteristic
30C2×Dic278D411yescharacteristic
31C2×D556—21no—
32C2×D556D411yescharacteristic
33C2×D556D411yescharacteristic
34C2×C22⋊D139—21no—
35C2×C22⋊D139—21no—
36Dic556—42no—
37#14555774—42no—
38C2×C139⋊C8—21no—
39C4⋊Dic139—21no—
40C4⋊Dic139—21no—
41C22⋊Dic139—21no—
42(C2×D139)⋊C4—21no—
43(C2×D139)⋊C4—21no—
44(C2×D139)⋊C4—21no—
45(C2×D139)⋊C4—21no—
46(C2×D139)⋊C4—21no—
47(C2×D139)⋊C4—21no—
48C4×Dic139—21no—
49C2×Q8×C139D411yescharacteristic
50C2×D4×C139D411yescharacteristic
51C2×C8×C139—21no—
52C2×C8×C139—21no—
53C22⋊C4×C139—21no—
54C22⋊C4×C139—21no—
55C42×C139C2311yescharacteristic
56C22×D139—21no—
57C22×D139—21no—
58C22×D139—81no—
59C22×D139—81no—
60C22×D139—81no—
61Dic278—41no—
62Dic278—41no—
63Dic278—41no—
64Dic278—41no—
65D556—41no—
66D556—41no—
67D556—81no—
68C22⋊D139—81no—
69C22⋊D139—81no—
70C2×Dic139—21no—
71C2×Dic139—21no—
72C2×Dic139—41no—
73C139⋊C8—41no—
74C23×C139—21no—
75Q8×C139—41no—
76D4×C139—41no—
77C2×C4×C139—21no—
78C2×C4×C139C2×D411yescharacteristic
79C2×C4×C139C2×D411yescharacteristic
80C2×C4×C139C2×D411yescharacteristic
81C8×C139—22no—
82C8×C139—41no—
83C22×C139—41no—
84C22×C139—41no—
85C22×C139—41no—
86C22×C139#12011yescharacteristic
87C2×D139—41no—
88C2×D139—41no—
89C2×D139—41no—
90C2×D139—41no—
91C2×D139—41no—
92C2×D139—41no—
93C2×D139—84no—
94C4×C139—21no—
95C4×C139—21no—
96C4×C139—21no—
97C4×C139—41no—
98Dic139—41no—
99Dic139—41no—
100Dic139—81no—
101C2×C139—81no—
102C2×C139#45311yescharacteristic
103C2×C139#45511yescharacteristic
104C2×C139#45511yescharacteristic
105D139—81no—
106D139—81no—
107C139#165911yescharacteristic, complemented, Sylow
108#1659—1391nomaximal, Sylow
109H(3,𝔽4)—1391no—
110#497—1391no—
111#489—1391no—
112#489—1391no—
113#329—1391no—
114#329—1391no—
115#329D13911yescharacteristic, complemented
116C2×Q16—2781no—
117C2×SD16—2781no—
118C4⋊Q8—1391no—
119#124—2781no—
120#124—2781no—
121#124—2781no—
122#124—1391no—
123#124—1391no—
124#124C2×D13911yescharacteristic
125#120—2781no—
126#120—2781no—
127#120—2781no—
128#103—2781no—
129#103—2781no—
130#102—2781no—
131#102—2781no—
132#97—1391no—
133#97C2×D13911yescharacteristic, complemented
134#97C2×D13911yescharacteristic, complemented
135C24—2781no—
136C2×Q8—2781no—
137C2×Q8—1391no—
138C2×Q8—1391no—
139C2×Q8D55611yescharacteristic
140C2×D4—2781no—
141C2×D4—2781no—
142C2×D4—2781no—
143C2×D4—1391no—
144C2×D4—1391no—
145C2×D4D55611yescharacteristic
146Q16—5562no—
147SD16—5562no—
148C2×C8—21no—
149C2×C8—21no—
150C2×C8—2781no—
151C4⋊C4—2781no—
152C4⋊C4—2781no—
153C22⋊C4—21no—
154C22⋊C4—21no—
155C22⋊C4—2781no—
156C22⋊C4—2781no—
157C22⋊C4—2781no—
158C22⋊C4—2781no—
159C22⋊C4—2781no—
160C22⋊C4—2781no—
161C22⋊C4—2781no—
162C42—2781no—
163C42C22×D13911yescharacteristic
164C23—21no—
165C23—2781no—
166C23—2781no—
167C23—11121no—
168C23—11121no—
169C23—11121no—
170Q8—41no—
171Q8—5561no—
172Q8—5561no—
173Q8—5561no—
174Q8—5561no—
175D4—41no—
176D4—5561no—
177D4—5561no—
178D4—11121no—
179D4—11121no—
180D4—11121no—
181C2×C4—21no—
182C2×C4—2781no—
183C2×C4—2781no—
184C2×C4—5561no—
185C2×C4D4×D13911yescharacteristic
186C2×C4D4×D13911yescharacteristic
187C2×C4C2×D55611yescharacteristic
188C8—22no—
189C8—41no—
190C8—5561no—
191C22—41no—
192C22—41no—
193C22—41no—
194C22—5561no—
195C22—5561no—
196C22—5561no—
197C22—5561no—
198C22—5561no—
199C22—5561no—
200C22—11124no—
201C22#1798481211yescharacteristic
202C4—21no—
203C4—21no—
204C4—21no—
205C4—41no—
206C4—5561no—
207C4—5561no—
208C4—11121no—
209C2—81no—
210C2—11121no—
211C2—11121no—
212C2#2258112211yescharacteristic
213C2#2258113211yescharacteristic
214C2#2258113311yescharacteristic
subgroupG/H
centerC22#17984812
commutator, cosocleC42×C139C23
FrattiniC42C22×D139
Fitting#329×C139C2
socleC22×C139#120
prime radical#22581695C2
hypercenter#329D139
hypocenterC139#1659
LCSG ▷ C42×C139 ▷ C22×C139 ▷ C139
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #22581347C2semidirect
3. #22581313C2semidirect
4. #22581312C2semidirect
5. #22580692C2semidirect
6. #22580692C2semidirect
7. #329×C139C2semidirect
10. #17984842C22semidirect
23. #17984753C22semidirect
25. #97×C139C22semidirect
26. #97×C139C22semidirect
107. C139#1659semidirect
115. #329D139semidirect
133. #97C2×D139semidirect
134. #97C2×D139semidirect

Maximal subgroups

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

subgroupindex
#225816952
#225813472
#225813132
#225813122
#225806922
#329×C1392
#1659139