Finite Group Databasebeta

← #16788241

Subgroups — #16788241

Order 3328.

314 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 74 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#13131199C211yesmaximal, characteristic
2#13130758C211yesmaximal, characteristic
3#13129824C214yesmaximal
4#13125420C211yesmaximal, characteristic
5#11719433—21no—
6#11719060—21no—
7C13×#494C411yescharacteristic, complemented
8#11718849—21no—
9#11718849C2212yes—
10Q16×Dic13—21no—
11Q16×Dic13C412yescomplemented
12#11718742—21no—
13C4×C8×D13C2211yescharacteristic
14#11718343C411yescharacteristic, complemented
15#11718265—21no—
16#11718265C2212yes—
17#11718260—21no—
18#11718259C2212yes—
19#11718231—21no—
20C2×C4⋊#261—22no—
21C2×C13×Q16—21no—
22C2×C13×Q16C2×C412yes—
23C13×C4⋊Q8—21no—
24#88200—22no—
25Q8×Dic13—22no—
26C2×C8×D13D411yescharacteristic
27C2×C8×D13C2311yescharacteristic
28#88151—41no—
29#88146—41no—
30#88144—41no—
31#88141—41no—
32C42×D13D411yescharacteristic
33#88123—21no—
34(C2×#261)⋊C4—41no—
35(C2×#261)⋊C4—41no—
36C2×#6092—22no—
37C4×C8×C13C2×C411yescharacteristic
38#88075—22no—
39#88075—22no—
40#88058—21no—
41#88058C2×C412yes—
42C8×Dic13C2×C411yescharacteristic
43C8×Dic13D411yescharacteristic
44C4×#1055D411yescharacteristic
45#11859—131nomaximal, Sylow
46C22×#261—42no—
47C2×Q8×C13—22no—
48C2×C4×D13D811yescharacteristic
49C2×C4×D13D811yescharacteristic
50C2×C4×D13C2×D411yescharacteristic
51C2×Dic26—41no—
52C4⋊#261—42no—
53C4⋊#261—42no—
54C13×Q16—42no—
55C13×Q16—42no—
56C2×C8×C13C22⋊C411yescharacteristic
57C2×C8×C13C22×C411yescharacteristic
58C13×C4⋊C4—41no—
59C13×C4⋊C4—41no—
60C42×C13C22⋊C411yescharacteristic
61#6103—42no—
62C4⋊Dic13—22no—
63C4⋊Dic13—41no—
64C4⋊Dic13—42no—
65#6101—42no—
66C4×Dic13—42no—
67C4×Dic13C22⋊C411yescharacteristic
68C4×Dic13SD1611yescharacteristic
69C4×Dic13SD1611yescharacteristic
70C2×#1055C22⋊C411yescharacteristic
71C2×#1055C2×D411yescharacteristic
72C8×D13—41no—
73C8×D13—41no—
74#6092—42no—
75#3170—131no—
76#2163—131no—
77#1835—131no—
78#1348—134no—
79C22×D13C2×D811yescharacteristic
80C2×#261—82no—
81C2×#261—82no—
82C2×#261—82no—
83Q8×C13—42no—
84Q8×C13—42no—
85C2×C4×C13—42no—
86C2×C4×C13#10211yescharacteristic
87C2×C4×C13#10211yescharacteristic
88C2×C4×C13C2×C22⋊C411yescharacteristic
89C2×Dic13—42no—
90C2×Dic13#10211yescharacteristic
91C2×Dic13#10211yescharacteristic
92C2×Dic13C2×SD1611yescharacteristic
93C4×D13—22no—
94C4×D13—21no—
95C4×D13—21no—
96C4×D13—41no—
97Dic26—82no—
98C8×C13—21no—
99C8×C13—21no—
100#1055—21no—
101#1055—21no—
102#533—261no—
103#500—131no—
104#494#26111yescharacteristic, complemented
105#487—261no—
106#467—132no—
107#467—261no—
108C4×Q16—132no—
109C4×Q16—261no—
110C2×C4×C8—131no—
111#382—261no—
112C4⋊C16—261no—
113C22⋊C16—132no—
114#346—261no—
115#340—132no—
116#340—261no—
117C22×C13C2×#10211yescharacteristic
118C2×D13—21no—
119C2×D13—21no—
120C2×D13#51012yes—
121#261—162no—
122C4×C13—21no—
123C4×C13—21no—
124C4×C13—82no—
125C4×C13#41011yescharacteristic
126C4×C13#42111yescharacteristic
127Dic13—21no—
128Dic13—21no—
129Dic13—21no—
130Dic13—82no—
131C2×Q16—21no—
132C2×Q16C2×#26112yes—
133C22×C8—131no—
134C22×C8—131no—
135C4⋊Q8—21no—
136C4⋊Q8—261no—
137#125—521no—
138C22⋊Q8—262no—
139C22⋊Q8—521no—
140C4×Q8—262no—
141C4×Q8—521no—
142#117—521no—
143C2×C4⋊C4—262no—
144C2×C42—131no—
145C2×C16—262no—
146#107—132no—
147#107—261no—
148#103—262no—
149#103—262no—
150C4×C8—131no—
151C4×C8—131no—
152C4×C8—131no—
153C4×C8C2×#26111yescharacteristic
154#95—521no—
155#95—521no—
156C2×C13#151711yescharacteristic
157C2×C13#214111yescharacteristic
158C2×C13#214511yescharacteristic
159D13—22no—
160C2×Q8—22no—
161C2×Q8—521no—
162C22×C4—131no—
163C22×C4—131no—
164C22×C4—131no—
165C22×C4—522no—
166Q16—42no—
167Q16—42no—
168C2×C8—131no—
169C2×C8—131no—
170C2×C8—521no—
171C2×C8—521no—
172C2×C8C22⋊#26111yescharacteristic
173C2×C8C22×#26111yescharacteristic
174C4⋊C4—41no—
175C4⋊C4—41no—
176C4⋊C4—262no—
177C4⋊C4—522no—
178C4⋊C4—522no—
179C4⋊C4—522no—
180C4⋊C4—522no—
181C4⋊C4—521no—
182C22⋊C4—522no—
183C42—131no—
184C42—131no—
185C42—131no—
186C42—522no—
187C42C22⋊#26111yescharacteristic
188C16—522no—
189C13#1185911yescharacteristic, complemented, Sylow
190C23—131no—
191Q8—42no—
192Q8—42no—
193Q8—1042no—
194C2×C4—42no—
195C2×C4—131no—
196C2×C4—131no—
197C2×C4—131no—
198C2×C4—262no—
199C2×C4—261no—
200C2×C4—261no—
201C2×C4—521no—
202C2×C4—522no—
203C2×C4—1042no—
204C2×C4—1042no—
205C2×C4—1042no—
206C2×C4#8811511yescharacteristic
207C2×C4#8811511yescharacteristic
208C2×C4C2×C22⋊#26111yescharacteristic
209C8—21no—
210C8—21no—
211C8—261no—
212C8—261no—
213C22—132no—
214C22—261no—
215C22—261no—
216C22C2×#8811511yescharacteristic
217C4—21no—
218C4—21no—
219C4—82no—
220C4—261no—
221C4—261no—
222C4—261no—
223C4—1042no—
224C4—2082no—
225C4#1171914011yescharacteristic
226C4#1171914211yescharacteristic
227C2—262no—
228C2#1313026511yescharacteristic
229C2#1313114611yescharacteristic
230C2#1313115811yescharacteristic
subgroupG/H
centerC22C2×#88115
commutatorC2×C8×C13C22×C4
FrattiniC2×C8C22×#261
FittingC13×#494C4
socleC22×C13C2×#102
prime radicalC22×D13C2×D8
cosocleC2×C8×D13C23
hypercenter#494#261
hypocenterC13#11859
LCSG ▷ C2×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #494

Complements

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

NH ≅ G/Ntype
7. C13×#494C4semidirect
11. Q16×Dic13C4semidirect
14. #11718343C4semidirect
104. #494#261semidirect
189. C13#11859semidirect

Maximal subgroups

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

subgroupindex
#131311992
#131307582
#131298242
#131254202
#1185913