Finite Group Databasebeta

← #16788261

Subgroups — #16788261

Order 3328.

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

normal subgroups only

This group has 300 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#13130761C211yesmaximal, characteristic
3#13129828C214yesmaximal
4#13125420C211yesmaximal, characteristic
5#11719433—21no—
6#11719053—21no—
7C13×#494C411yescharacteristic
8#11718849—21no—
9#11718849C2212yes—
10Q16×Dic13—21no—
11Q16×Dic13C412yes—
12#11718742—21no—
13C4×C8×D13C2211yescharacteristic
14#11718343C411yescharacteristic
15#11718268—21no—
16#11718268C2212yes—
17#11718260—21no—
18#11718259C2212yes—
19#11718231—21no—
20C2×#6118—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#88112—41no—
35#88112—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#11865—131nomaximal, Sylow
46C2×Q8×C13—22no—
47C2×C4×D13SD1611yescharacteristic
48C2×C4×D13SD1611yescharacteristic
49C2×C4×D13C2×D411yescharacteristic
50C2×Dic26—41no—
51C2×#1057—42no—
52#6118—42no—
53#6118—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×Dic13D811yescharacteristic
69C4×Dic13D811yescharacteristic
70C2×#1055C22⋊C411yescharacteristic
71C2×#1055C2×D411yescharacteristic
72C8×D13—41no—
73C8×D13—41no—
74#6092—42no—
75#3170—131no—
76#2163—131no—
77#1837—131no—
78#1350—134no—
79C22×D13C2×SD1611yescharacteristic
80Q8×C13—42no—
81Q8×C13—42no—
82C2×C4×C13—42no—
83C2×C4×C13#10211yescharacteristic
84C2×C4×C13#10211yescharacteristic
85C2×C4×C13C2×C22⋊C411yescharacteristic
86C2×Dic13—42no—
87C2×Dic13#10211yescharacteristic
88C2×Dic13#10211yescharacteristic
89C2×Dic13C2×D811yescharacteristic
90C4×D13—21no—
91C4×D13—21no—
92C4×D13—22no—
93C4×D13—41no—
94Dic26—82no—
95#1057—82no—
96C8×C13—21no—
97C8×C13—21no—
98#1055—21no—
99#1055—21no—
100#533—261no—
101#500—131no—
102#494#26111yescharacteristic
103#487—261no—
104#467—132no—
105#467—261no—
106C4×Q16—132no—
107C4×Q16—261no—
108#423—261no—
109C2×C4×C8—131no—
110C4⋊C16—261no—
111C22⋊C16—132no—
112#346—261no—
113#341—132no—
114#341—261no—
115C22×C13C2×#10211yescharacteristic
116C2×D13—21no—
117C2×D13—21no—
118C2×D13—21no—
119C4×C13—21no—
120C4×C13—21no—
121C4×C13—82no—
122C4×C13#41011yescharacteristic
123C4×C13#42111yescharacteristic
124Dic13—21no—
125Dic13—21no—
126Dic13—82no—
127Dic13#36212yes—
128C2×Q16—21no—
129C2×Q16C2×#26112yes—
130C2×M16—262no—
131C22×C8—131no—
132C22×C8—131no—
133C4⋊Q8—21no—
134C4⋊Q8—261no—
135#125—521no—
136C22⋊Q8—262no—
137C22⋊Q8—521no—
138C4×Q8—262no—
139C4×Q8—521no—
140#117—521no—
141C2×C42—131no—
142C2×C16—262no—
143#107—132no—
144#107—261no—
145C4⋊C8—521no—
146C4⋊C8—521no—
147#103—262no—
148#103—262no—
149C4×C8—131no—
150C4×C8—131no—
151C4×C8—131no—
152C4×C8C2×#26111yescharacteristic
153C2×C13#151711yescharacteristic
154C2×C13#214311yescharacteristic
155C2×C13C2×#36211yescharacteristic
156D13—41no—
157C2×Q8—22no—
158C2×Q8—521no—
159C22×C4—131no—
160C22×C4—131no—
161C22×C4—131no—
162Q16—42no—
163Q16—42no—
164M16—522no—
165M16—522no—
166C2×C8—131no—
167C2×C8—131no—
168C2×C8—521no—
169C2×C8—521no—
170C2×C8—522no—
171C2×C8C22⋊#26111yescharacteristic
172C2×C8C22×#26111yescharacteristic
173C4⋊C4—41no—
174C4⋊C4—41no—
175C4⋊C4—262no—
176C4⋊C4—522no—
177C4⋊C4—522no—
178C4⋊C4—521no—
179C22⋊C4—522no—
180C42—131no—
181C42—131no—
182C42—131no—
183C42—522no—
184C42C22⋊#26111yescharacteristic
185C16—522no—
186C13#1186511yescharacteristic, complemented, Sylow
187C23—131no—
188Q8—42no—
189Q8—42no—
190Q8—1042no—
191C2×C4—42no—
192C2×C4—131no—
193C2×C4—131no—
194C2×C4—131no—
195C2×C4—262no—
196C2×C4—261no—
197C2×C4—261no—
198C2×C4—521no—
199C2×C4—522no—
200C2×C4#8811511yescharacteristic
201C2×C4#8811511yescharacteristic
202C2×C4C2×C22⋊#26111yescharacteristic
203C8—21no—
204C8—21no—
205C8—261no—
206C8—261no—
207C8—1042no—
208C22—261no—
209C22—261no—
210C22—261no—
211C22C2×#8811511yescharacteristic
212C4—21no—
213C4—21no—
214C4—82no—
215C4—132no—
216C4—261no—
217C4—261no—
218C4—1042no—
219C4#1171914011yescharacteristic
220C4#1171914211yescharacteristic
221C2—521no—
222C2#1313026511yescharacteristic
223C2#1313115211yescharacteristic
224C2D13⋊#36211yescharacteristic
subgroupG/H
centerC22C2×#88115
commutatorC2×C8×C13C22×C4
FrattiniC2×C8C22×#261
FittingC13×#494C4
socleC22×C13C2×#102
prime radicalC22×D13C2×SD16
cosocleC2×C8×D13C23
hypercenter#494#261
hypocenterC13#11865
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
186. C13#11865semidirect

Maximal subgroups

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

subgroupindex
#131311992
#131307612
#131298282
#131254202
#1186513