Finite Group Databasebeta

← #31805729

Subgroups — #31805729

Order 17792.

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

normal subgroups only

This group has 196 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#22581697C211yesmaximal, characteristic
2#22581322C211yesmaximal, characteristic, complemented
3#22581313C211yesmaximal, characteristic, complemented
4#22581312C211yesmaximal, characteristic, complemented
5#22580694C211yesmaximal, characteristic, complemented
6#22580692C211yesmaximal, characteristic, complemented
7#329×C139C211yesmaximal, characteristic, complemented
8#17984842C2211yescharacteristic
9#17984834C2211yescharacteristic
10#17984830C2211yescharacteristic
11#17984826—21no—
12#17984824—21no—
13#17984819—21no—
14#17984818—21no—
15#17984815—21no—
16#17984814—21no—
17#17984767—21no—
18#17984767—21no—
19#17984767—21no—
20#17984766—21no—
21#17984764—21no—
22#17984763—21no—
23#17984753C2211yescharacteristic
24#124×C139C2211yescharacteristic
25#97×C139C2211yescharacteristic
26#97×C139C2211yescharacteristic
27C2×Dic278—21no—
28C2×Dic278D411yescharacteristic
29C2×D556D411yescharacteristic
30C2×C22⋊D139—21no—
31C2×C22⋊D139—21no—
32C22×Dic139—21no—
33C2×C4×D139—21no—
34C2×C139⋊C8—21no—
35C4⋊Dic139—21no—
36C4⋊Dic139—21no—
37C4⋊Dic139—21no—
38C4⋊Dic139D411yescharacteristic
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—
47C2×Q8×C139D411yescharacteristic
48C2×D4×C139D411yescharacteristic
49C2×C8×C139—21no—
50C2×C8×C139—21no—
51C22⋊C4×C139—21no—
52C22⋊C4×C139—21no—
53C42×C139C2311yescharacteristic
54C22×D139—21no—
55Dic278—41no—
56Dic278—42no—
57D556—41no—
58C22⋊D139—81no—
59C22⋊D139—81no—
60C2×Dic139—21no—
61C2×Dic139—21no—
62C2×Dic139—21no—
63C2×Dic139—41no—
64C2×Dic139—81no—
65C4×D139—81no—
66C139⋊C8—41no—
67C23×C139—21no—
68Q8×C139—41no—
69D4×C139—41no—
70C2×C4×C139—21no—
71C2×C4×C139C2×D411yescharacteristic
72C2×C4×C139C2×D411yescharacteristic
73C2×C4×C139C2×D411yescharacteristic
74C8×C139—41no—
75C8×C139—41no—
76C22×C139—41no—
77C22×C139—41no—
78C22×C139—41no—
79C22×C139#12011yescharacteristic
80C2×D139—41no—
81C2×D139—41no—
82C2×D139—41no—
83C4×C139—21no—
84C4×C139—21no—
85C4×C139—21no—
86C4×C139—41no—
87Dic139—41no—
88Dic139—41no—
89Dic139—41no—
90Dic139—81no—
91C2×C139—81no—
92C2×C139#45411yescharacteristic
93C2×C139#45511yescharacteristic
94C2×C139#45511yescharacteristic
95D139—81no—
96C139#166211yescharacteristic, complemented, Sylow
97#1662—1391nomaximal, Sylow
98#562—1391no—
99#491—1391no—
100#489—1391no—
101#489—1391no—
102#330—1391no—
103#329—1391no—
104#329D13911yescharacteristic, complemented
105C4⋊Q8—1391no—
106#125—1391no—
107#124—1391no—
108#124C2×D13911yescharacteristic
109#123—2781no—
110#123—2781no—
111C22⋊Q8—2781no—
112C22⋊Q8—2781no—
113#121—2781no—
114#121—2781no—
115#103—2781no—
116#103—2781no—
117#103—2781no—
118#103—2781no—
119#102—2781no—
120#102—2781no—
121#97—1391no—
122#97C2×D13911yescharacteristic
123#97C2×D13911yescharacteristic
124C2×Q8—2781no—
125C2×Q8—1391no—
126C2×Q8D55611yescharacteristic
127C2×D4—2781no—
128C2×D4—2781no—
129C2×D4—1391no—
130C2×D4D55611yescharacteristic
131C22×C4—2781no—
132C22×C4—2781no—
133C2×C8—21no—
134C2×C8—21no—
135C2×C8—2781no—
136C4⋊C4—2781no—
137C4⋊C4—2781no—
138C4⋊C4—2781no—
139C4⋊C4—2781no—
140C4⋊C4—2781no—
141C4⋊C4—2781no—
142C4⋊C4—1391no—
143C4⋊C4—1391no—
144C22⋊C4—21no—
145C22⋊C4—21no—
146C22⋊C4—2781no—
147C22⋊C4—2781no—
148C22⋊C4—2781no—
149C22⋊C4—2781no—
150C42C22×D13911yescharacteristic
151C23—21no—
152C23—2781no—
153Q8—41no—
154Q8—5561no—
155Q8—5562no—
156D4—41no—
157D4—5561no—
158D4—11121no—
159D4—11121no—
160C2×C4—21no—
161C2×C4—2781no—
162C2×C4—2781no—
163C2×C4—2781no—
164C2×C4—5561no—
165C2×C4—11121no—
166C2×C4—11121no—
167C2×C4D4×D13911yescharacteristic
168C2×C4D4×D13911yescharacteristic
169C2×C4C2×D55611yescharacteristic
170C8—41no—
171C8—41no—
172C8—5561no—
173C22—41no—
174C22—41no—
175C22—41no—
176C22—5561no—
177C22—5561no—
178C22—5561no—
179C22#1798481211yescharacteristic
180C4—21no—
181C4—21no—
182C4—21no—
183C4—41no—
184C4—5561no—
185C4—5561no—
186C4—5561no—
187C4—11121no—
188C2—81no—
189C2—11121no—
190C2#2258112711yescharacteristic
191C2#2258113211yescharacteristic
192C2#2258113311yescharacteristic
subgroupG/H
centerC22#17984812
commutator, cosocleC42×C139C23
FrattiniC42C22×D139
Fitting#329×C139C2
socleC22×C139#120
prime radical#22581697C2
hypercenter#329D139
hypocenterC139#1662
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. #22581322C2semidirect
3. #22581313C2semidirect
4. #22581312C2semidirect
5. #22580694C2semidirect
6. #22580692C2semidirect
7. #329×C139C2semidirect
96. C139#1662semidirect
104. #329D139semidirect

Maximal subgroups

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

subgroupindex
#225816972
#225813222
#225813132
#225813122
#225806942
#225806922
#329×C1392
#1662139