Finite Group Databasebeta

← #31819816

Subgroups — #31819816

Order 17792.

1160 conjugacy classes of subgroups; only the 471 normal subgroups are shown.

normal subgroups only

This group has 1160 conjugacy classes of subgroups — too many to draw. Only its 471 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#22581552C216yesmaximal, complemented
2#22581543C216yesmaximal, complemented
3#22581515C213yesmaximal, complemented
4#22581489C216yesmaximal, complemented
5#22581466C216yesmaximal, complemented
6C2×(C22⋊D139)⋊C4C213yesmaximal, complemented
7#543×C139C211yesmaximal, characteristic, complemented
8C2×#14555786C2212yescomplemented
9C22×C22⋊D139C2213yes—
10C23×Dic139C2211yescharacteristic
11C22×C4×D139C2213yescomplemented
12#17984837C22112yescomplemented
13#17984833C2216yescomplemented
14#17984831C2216yescomplemented
15#17984827C22112yescomplemented
16#17984826C22112yescomplemented
17#17984818C2216yescomplemented
18#17984817C2216yescomplemented
19#17984816C2216yes—
20#17984816C2216yes—
21#17984812C22112yescomplemented
22Q8×Dic139C2212yescomplemented
23#17984804C2216yescomplemented
24(C22⋊D139)⋊C4C22112yescomplemented
25(C22⋊D139)⋊C4C22112yescomplemented
26#17984800C2216yescomplemented
27C2×Dic139⋊C4C2213yescomplemented
28C2×(C2×D139)⋊C4C2213yescomplemented
29C2×C4×Dic139C2213yescomplemented
30C22⋊Q8×C139C2216yescomplemented
31C22⋊Q8×C139C2216yescomplemented
32C2×C22⋊C4×C139C2213yes—
33C23×D139C2313yes—
34#14555786—44no—
35C2×D556C2316yes—
36C2×D556C2316yes—
37C2×C22⋊D139—212no—
38C2×C22⋊D139C23112yes—
39C22×Dic139—42no—
40C22×Dic139C2313yes—
41C22×Dic139C2313yes—
42C22×Dic139C2313yes—
43C2×C4×D139—46no—
44C2×C4×D139C2316yes—
45C2×C4×D139C2316yes—
46C4⋊Dic139C2316yes—
47C4⋊Dic139C2316yes—
48Dic139⋊C4C23112yes—
49(C2×D139)⋊C4C23112yes—
50(C2×D139)⋊C4C23112yes—
51(C2×D139)⋊C4C23112yes—
52C4×Dic139C2316yes—
53C4×Dic139C2316yes—
54C24×C139C2311yescharacteristic
55C2×Q8×C139C2312yes—
56C2×Q8×C139C2312yes—
57C22×C4×C139C2313yes—
58C22×C4×C139C2313yes—
59C4⋊C4×C139C2316yes—
60C4⋊C4×C139C2316yes—
61C22⋊C4×C139C23112yes—
62C22×D139—26no—
63C22×D139—43no—
64C22×D139—43no—
65C22×D139C2416yes—
66D556—46no—
67D556—46no—
68C22⋊D139—224no—
69C2×Dic139—26no—
70C2×Dic139—26no—
71C2×Dic139—43no—
72C2×Dic139C2413yes—
73C2×Dic139C2416yes—
74C2×Dic139C2411yescharacteristic
75C4×D139—212no—
76C4×D139—46no—
77C23×C139—41no—
78C23×C139—41no—
79C23×C139#4114yescomplemented
80C23×C139C2413yes—
81Q8×C139—42no—
82Q8×C139—42no—
83C2×C4×C139—43no—
84C2×C4×C139—43no—
85C2×C4×C139C2416yes—
86C2×C4×C139C2416yes—
87C22×C139—23no—
88C22×C139—23no—
89C22×C139—44no—
90C22×C139C2×#4116yes—
91C22×C139C2511yescharacteristic
92C2×D139—26no—
93C2×D139—26no—
94C2×D139—26no—
95C2×D139—412no—
96C4×C139—26no—
97C4×C139—26no—
98Dic139—26no—
99Dic139—23no—
100Dic139H(5,𝔽2)12yes—
101C2×C139—26no—
102C2×C139C22×#4111yescharacteristic
103C2×C139C2×H(5,𝔽2)11yescharacteristic
104C2×C139#58511yescharacteristic
105D139—46no—
106C139#345911yescharacteristic, complemented, Sylow
107#3459—1391nomaximal, Sylow
108#543D13911yescharacteristic, complemented
109#539—1396no—
110#538—1396no—
111#534—1393no—
112#529—1396no—
113#525—1396no—
114C2×C4×D4—1393no—
115C2×#41—1392no—
116C22×D4—1393no—
117C23×C4—1391no—
118C23×C4—1393no—
119#126—13912no—
120#125—1396no—
121#124—1396no—
122#123—13912no—
123#123—13912no—
124C22⋊Q8—1396no—
125C22⋊Q8C2×D13916yescomplemented
126C22⋊Q8C2×D13916yescomplemented
127#121—1396no—
128#121—1396no—
129#121—1396no—
130#120—13912no—
131C4×Q8—1392no—
132C4×D4—1396no—
133C4×D4—13912no—
134C4×D4—13912no—
135#117—1396no—
136C2×C4⋊C4—1393no—
137C2×C22⋊C4—1393no—
138C2×C22⋊C4C2×D13913yes—
139C2×C42—1393no—
140C24—1393no—
141C24C22×D13911yescharacteristic
142#41—5564no—
143C2×Q8C22×D13912yes—
144C2×Q8C22×D13912yes—
145C2×D4—27812no—
146C2×D4—13912no—
147C2×D4—1396no—
148C2×D4—1396no—
149C22×C4—5566no—
150C22×C4—5562no—
151C22×C4—1393no—
152C22×C4—1393no—
153C22×C4—1396no—
154C22×C4—1393no—
155C22×C4—1396no—
156C22×C4C22×D13913yes—
157C22×C4C22×D13913yes—
158C4⋊C4—13912no—
159C4⋊C4—1396no—
160C4⋊C4—1396no—
161C4⋊C4C22×D13916yes—
162C4⋊C4C22×D13916yes—
163C22⋊C4—13912no—
164C22⋊C4—13912no—
165C22⋊C4—13912no—
166C22⋊C4C22×D139112yes—
167C42—1396no—
168C42—1396no—
169C23—41no—
170C23—41no—
171C23—2786no—
172C23—5563no—
173C23—5563no—
174C23—1396no—
175C23#1455578614yescomplemented
176C23C23×D13913yes—
177Q8—42no—
178Q8—42no—
179D4—27824no—
180D4—5566no—
181D4—5566no—
182C2×C4—43no—
183C2×C4—43no—
184C2×C4—27812no—
185C2×C4—2786no—
186C2×C4—2786no—
187C2×C4—5566no—
188C2×C4—5563no—
189C2×C4—1396no—
190C2×C4—1393no—
191C2×C4—1391no—
192C2×C4C23×D13916yes—
193C2×C4C23×D13916yes—
194C22—23no—
195C22—23no—
196C22—44no—
197C22—2786no—
198C22—2786no—
199C22—2786no—
200C22—55612no—
201C22C2×#1455578616yes—
202C22C24×D13911yescharacteristic
203C4—26no—
204C4—26no—
205C4—2786no—
206C4—2783no—
207C4—1392no—
208C2—26no—
209C2—5566no—
210C2C22×#1455578611yescharacteristic
211C2H(5,𝔽2)×D13911yescharacteristic
212C2#2258178811yescharacteristic
subgroupG/H
center, FrattiniC22C24×D139
commutator, socle, cosocleC22×C139C25
Fitting#543×C139C2
hypercenter#543D139
hypocenterC139#3459
LCSG ▷ C22×C139 ▷ C139
UCSC1 ◁ C22 ◁ #543

Complements

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

NH ≅ G/Ntype
1. #22581552C2semidirect
2. #22581543C2semidirect
3. #22581515C2semidirect
4. #22581489C2semidirect
5. #22581466C2semidirect
6. C2×(C22⋊D139)⋊C4C2semidirect
7. #543×C139C2semidirect
8. C2×#14555786C22semidirect
11. C22×C4×D139C22semidirect
12. #17984837C22semidirect
13. #17984833C22semidirect
14. #17984831C22semidirect
15. #17984827C22semidirect
16. #17984826C22semidirect
17. #17984818C22semidirect
18. #17984817C22semidirect
21. #17984812C22semidirect
22. Q8×Dic139C22semidirect
23. #17984804C22semidirect
24. (C22⋊D139)⋊C4C22semidirect
25. (C22⋊D139)⋊C4C22semidirect
26. #17984800C22semidirect
27. C2×Dic139⋊C4C22semidirect
28. C2×(C2×D139)⋊C4C22semidirect
29. C2×C4×Dic139C22semidirect
30. C22⋊Q8×C139C22semidirect
31. C22⋊Q8×C139C22semidirect
79. C23×C139#41semidirect
106. C139#3459semidirect
108. #543D139semidirect
125. C22⋊Q8C2×D139semidirect
126. C22⋊Q8C2×D139semidirect
175. C23#14555786semidirect

Maximal subgroups

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

subgroupindex
#225815522
#225815432
#225815152
#225814892
#225814662
C2×(C22⋊D139)⋊C42
#543×C1392
#3459139