Finite Group Databasebeta

← #15774280

Subgroups — #15774280

Order 3328.

306 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 103 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#13125422C211yesmaximal, characteristic
2#13116639C211yesmaximal, characteristic
3#13112892C212yesmaximal, complemented
4#13112884C212yesmaximal, complemented
5C2×C13×#335C211yesmaximal, characteristic
6#11719175—21no—
7C2×C13×C4⋊C8—21no—
8C2×C4×C8×C13C2211yescharacteristic
9#11718777—21no—
10#11718777C412yes—
11#11718360C2211yescharacteristic
12C4×Dic52—21no—
13C4×Dic52C412yes—
14#11718343C2211yescharacteristic
15#11718342—21no—
16C13×#335—21no—
17C13×#335C2212yes—
18C22⋊#6090—21no—
19C4⋊#6090C2212yes—
20#11718053—21no—
21C22×C8×C13—41no—
22C22×C8×C13C2×C411yescharacteristic
23C22×C8×C13D411yescharacteristic
24C2×C42×C13D411yescharacteristic
25#88180—41no—
26#88178—22no—
27#88178—41no—
28C2×Dic52—21no—
29C2×Dic52C2×C412yes—
30#88124—41no—
31#88123—21no—
32#88123—21no—
33C4×Dic26—22no—
34C4×Dic26—41no—
35C13×C4⋊C8—22no—
36C13×C4⋊C8—41no—
37C4×C8×C13C2×C411yescharacteristic
38C4×C8×C13D411yescharacteristic
39C4×C8×C13D411yescharacteristic
40C4×C8×C13C2311yescharacteristic
41#88058—21no—
42#88058C2×C412yes—
43#88056—22no—
44#88056—22no—
45C2×#6090—22no—
46#11954—131nomaximal, Sylow
47C22×C4×C13C22⋊C411yescharacteristic
48C22×C4×C13D811yescharacteristic
49C22×C4×C13SD1611yescharacteristic
50C2×Dic26—22no—
51C2×Dic26—41no—
52C2×C8×C13—22no—
53C2×C8×C13—41no—
54C2×C8×C13—42no—
55C2×C8×C13—82no—
56C2×C8×C13C22⋊C411yescharacteristic
57C2×C8×C13C22⋊C411yescharacteristic
58C2×C8×C13C22×C411yescharacteristic
59C2×C8×C13C2×D411yescharacteristic
60C42×C13C22⋊C411yescharacteristic
61C42×C13D811yescharacteristic
62C42×C13SD1611yescharacteristic
63C42×C13C2×D411yescharacteristic
64C22⋊Dic13—42no—
65C4⋊Dic13—22no—
66C4⋊Dic13—41no—
67C4⋊Dic13—41no—
68C4⋊Dic13—41no—
69#6101—42no—
70#6101—42no—
71C4×Dic13—42no—
72Dic52—42no—
73Dic52—42no—
74#6090—42no—
75#3170—131no—
76#2163—131no—
77C2×#335D1311yescharacteristic
78#1364—132no—
79#1362—132no—
80C23×C13#10211yescharacteristic
81C2×C4×C13—22no—
82C2×C4×C13—21no—
83C2×C4×C13—21no—
84C2×C4×C13—21no—
85C2×C4×C13—21no—
86C2×C4×C13#10211yescharacteristic
87C2×C4×C13#10211yescharacteristic
88C2×C4×C13#10211yescharacteristic
89C2×C4×C13C2×C22⋊C411yescharacteristic
90C2×C4×C13C2×D811yescharacteristic
91C2×C4×C13C2×SD1611yescharacteristic
92C2×Dic13—42no—
93C2×Dic13—42no—
94Dic26—42no—
95Dic26—42no—
96Dic26—81no—
97Dic26—81no—
98C8×C13—21no—
99C8×C13—21no—
100C8×C13—21no—
101C8×C13—82no—
102C8×C13#13512yes—
103#533—261no—
104#500—131no—
105#494—131no—
106#487—261no—
107#467—132no—
108#467—261no—
109C4×Q16—132no—
110C4×Q16—261no—
111C2×C4⋊C8—21no—
112C2×C4×C8C2×D1311yescharacteristic
113C4⋊C16—132no—
114C22⋊C16—261no—
115#346—261no—
116#335—21no—
117#335C2×D1312yes—
118C22×C13—21no—
119C22×C13—21no—
120C22×C13#36212yes—
121C22×C13C2×#10211yescharacteristic
122C4×C13—21no—
123C4×C13—21no—
124C4×C13—21no—
125C4×C13—21no—
126C4×C13#41311yescharacteristic
127C4×C13#41611yescharacteristic
128C4×C13#50911yescharacteristic
129C4×C13#51011yescharacteristic
130Dic13—82no—
131Dic13—82no—
132C2×Q16—132no—
133C2×Q16—261no—
134C22×C8—41no—
135C22×C8C4×D1311yescharacteristic
136C22×C8D5211yescharacteristic
137C4⋊Q8—261no—
138C4⋊Q8—261no—
139#125—521no—
140C22⋊Q8—262no—
141C22⋊Q8—521no—
142C4×Q8—262no—
143C4×Q8—521no—
144#117—521no—
145C2×C42C22⋊D1311yescharacteristic
146C2×C16—262no—
147#107—132no—
148#107—261no—
149C4⋊C8—22no—
150C4⋊C8—41no—
151#103—262no—
152#103—262no—
153C4×C8C4×D1311yescharacteristic
154C4×C8D5211yescharacteristic
155C4×C8C22⋊D1311yescharacteristic
156C4×C8C22×D1311yescharacteristic
157C2×C13—22no—
158C2×C13#154011yescharacteristic
159C2×C13#213911yescharacteristic
160C2×C13C2×#36211yescharacteristic
161C2×Q8—262no—
162C2×Q8—521no—
163C22×C4#610311yescharacteristic
164C22×C4#610411yescharacteristic
165C22×C4#610611yescharacteristic
166Q16—522no—
167Q16—522no—
168C2×C8—22no—
169C2×C8—41no—
170C2×C8—42no—
171C2×C8—82no—
172C2×C8#610311yescharacteristic
173C2×C8#610311yescharacteristic
174C2×C8C2×C4×D1311yescharacteristic
175C2×C8C2×D5211yescharacteristic
176C4⋊C4—262no—
177C4⋊C4—521no—
178C4⋊C4—521no—
179C4⋊C4—521no—
180C4⋊C4—522no—
181C4⋊C4—522no—
182C22⋊C4—522no—
183C42—522no—
184C42#610311yescharacteristic
185C42#610411yescharacteristic
186C42#610611yescharacteristic
187C42C2×C22⋊D1311yescharacteristic
188C16—522no—
189C13#1195411yescharacteristic, complemented, Sylow
190C23#8804911yescharacteristic
191Q8—522no—
192Q8—522no—
193Q8—1041no—
194Q8—1041no—
195C2×C4—22no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—522no—
201C2×C4—522no—
202C2×C4#8804911yescharacteristic
203C2×C4#8804911yescharacteristic
204C2×C4#8804911yescharacteristic
205C2×C4C2×#610311yescharacteristic
206C2×C4C2×#610411yescharacteristic
207C2×C4C2×#610611yescharacteristic
208C8—21no—
209C8—21no—
210C8—21no—
211C8—82no—
212C8#8815812yes—
213C22—21no—
214C22—21no—
215C22#1171808812yes—
216C22C2×#8804911yescharacteristic
217C4—21no—
218C4—21no—
219C4—21no—
220C4—21no—
221C4—1042no—
222C4—1042no—
223C4#1171877411yescharacteristic
224C4#1171879311yescharacteristic
225C4#1171880811yescharacteristic
226C4#1171884011yescharacteristic
227C2—22no—
228C2#1311348611yescharacteristic
229C2#1311654611yescharacteristic
230C2C2×#1171808811yescharacteristic
subgroupG/H
centerC22C2×#88049
commutatorC2×C8×C13C22×C4
FrattiniC4×C8C22×D13
FittingC2×C13×#335C2
socleC22×C13C2×#102
prime radicalC23×C13#102
cosocleC4×C8×C13C23
hypercenterC2×#335D13
hypocenterC13#11954
LCSG ▷ C2×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×C8 ◁ C2×#335

Complements

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

NH ≅ G/Ntype
3. #13112892C2semidirect
4. #13112884C2semidirect
189. C13#11954semidirect

Maximal subgroups

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

subgroupindex
#131254222
#131166392
#131128922
#131128842
C2×C13×#3352
#1195413