Finite Group Databasebeta

← #15779757

Subgroups — #15779757

Order 3328.

460 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 95 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#13117926C211yesmaximal, characteristic
2C2×#11718140C211yesmaximal, characteristic
3#13115051C212yesmaximal
4#13112962C212yesmaximal
5C13×#1886C211yesmaximal, characteristic
6C2×C13×C4⋊Q8C2211yescharacteristic
7C13×#519C2211yescharacteristic
8C13×#419—21no—
9C2×C13×#101C2211yescharacteristic
10#11718891—21no—
11#11718891C2212yes—
12C2×#88076C2212yes—
13#11718656—22no—
14#11718646—22no—
15C4⋊C4×Dic13—22no—
16C4×C4⋊Dic13—21no—
17C13×#339—21no—
18#11718140C414yescomplemented
19#11718124—22no—
20C22×Q8×C13D411yescharacteristic
21C22×Q8×C13C2311yescharacteristic
22C2×C13×M16—21no—
23C13×C4⋊Q8—22no—
24C13×C4⋊Q8C2×C412yes—
25C13×C4⋊Q8Q812yes—
26C4×Q8×C13—41no—
27C4×Q8×C13—41no—
28C13×#117—22no—
29C13×#117—21no—
30C2×C13×C4⋊C4—22no—
31C2×C42×C13D411yescharacteristic
32C2×C4⋊Dic13—21no—
33C2×C4⋊Dic13—21no—
34C2×C4⋊Dic13—21no—
35C2×C4⋊Dic13D412yes—
36C2×C4×Dic13—22no—
37C2×C4×Dic13—21no—
38C2×C4×Dic13D412yes—
39C2×#6099—22no—
40C13×#103—41no—
41C13×#103—41no—
42C13×#101—22no—
43#88076—22no—
44#88076C2×C414yes—
45#88071—22no—
46#88071—22no—
47#88071—22no—
48#88048—42no—
49#88047—42no—
50#12973—131nomaximal, Sylow
51C2×Q8×C13—21no—
52C2×Q8×C13—41no—
53C2×Q8×C13—41no—
54C2×Q8×C13—41no—
55C2×Q8×C13—41no—
56C2×Q8×C13C4⋊C412yes—
57C2×Q8×C13C22×C411yescharacteristic
58C2×Q8×C13C2×Q811yescharacteristic
59C2×Q8×C13#4112yes—
60C22×C4×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13C2×D412yes—
63C22×C4×C13C2×D411yescharacteristic
64C22×Dic13—22no—
65C22×Dic13—22no—
66C13×M16—41no—
67C13×M16—41no—
68C2×C8×C13—41no—
69C13×C4⋊C4—24no—
70C13×C4⋊C4—24no—
71C13×C4⋊C4—21no—
72C13×C4⋊C4—21no—
73C13×C4⋊C4—22no—
74C13×C4⋊C4—22no—
75C13×C22⋊C4—41no—
76C42×C13—21no—
77C42×C13—42no—
78C42×C13—41no—
79C42×C13C4⋊C412yes—
80C4⋊Dic13—24no—
81C4⋊Dic13—42no—
82C4⋊Dic13—42no—
83C4⋊Dic13—81no—
84C4×Dic13—44no—
85C4×Dic13—42no—
86C4×Dic13—81no—
87#6099—24no—
88#6099—42no—
89C2×#1055—42no—
90#2369—131no—
91C2×#356—131no—
92#1886D1311yescharacteristic
93#1857—132no—
94#1394—132no—
95C23×C13#12011yescharacteristic
96Q8×C13—41no—
97Q8×C13—41no—
98Q8×C13—42no—
99Q8×C13—42no—
100Q8×C13—81no—
101C2×C4×C13—22no—
102C2×C4×C13—22no—
103C2×C4×C13—22no—
104C2×C4×C13—22no—
105C2×C4×C13—21no—
106C2×C4×C13—22no—
107C2×C4×C13—21no—
108C2×C4×C13—22no—
109C2×C4×C13—41no—
110C2×C4×C13—41no—
111C2×C4×C13—41no—
112C2×C4×C13—41no—
113C2×C4×C13C2×C4⋊C411yescharacteristic
114C2×C4×C13C4×D412yes—
115C2×C4×C13C22⋊Q812yes—
116C2×C4×C13#12311yescharacteristic
117C2×Dic13—24no—
118C2×Dic13—42no—
119C2×Dic13—42no—
120C2×Dic13—42no—
121C2×Dic13—42no—
122C2×Dic13—42no—
123C8×C13—81no—
124#1055—44no—
125C2×C4⋊Q8C2×D1311yescharacteristic
126#519C2×D1311yescharacteristic
127#428—262no—
128#419—21no—
129C2×#101—132no—
130C2×#101C2×D1311yescharacteristic
131#391—132no—
132#391—261no—
133#389—262no—
134C4×C4⋊C4—262no—
135C4×C4⋊C4—261no—
136#356—134no—
137#339—21no—
138#339—262no—
139C22×C13—21no—
140C22×C13—21no—
141C22×C13#38511yescharacteristic
142C22×C13B(4,𝔽2)11yescharacteristic
143C22×C13#45811yescharacteristic
144C4×C13—24no—
145C4×C13—22no—
146C4×C13—21no—
147C4×C13—21no—
148C4×C13—22no—
149C4×C13—42no—
150C4×C13—81no—
151C4×C13—81no—
152Dic13—44no—
153Dic13—82no—
154C22×Q8C22⋊D1311yescharacteristic
155C22×Q8C22×D1311yescharacteristic
156C2×M16—21no—
157C2×M16—262no—
158C4⋊Q8—22no—
159C4⋊Q8Dic2612yes—
160C4⋊Q8C4×D1312yes—
161C4×Q8—41no—
162C4×Q8—41no—
163#117—22no—
164#117—21no—
165C2×C4⋊C4—22no—
166C2×C4⋊C4—132no—
167C2×C4⋊C4—261no—
168C2×C4⋊C4—261no—
169C2×C4⋊C4—261no—
170C2×C42—132no—
171C2×C42—262no—
172C2×C42—261no—
173C2×C42C22⋊D1311yescharacteristic
174#107—522no—
175#106—522no—
176#103—41no—
177#103—41no—
178#101—22no—
179#101—134no—
180#101—262no—
181#95—262no—
182#95—262no—
183#95—262no—
184C2×C13—21no—
185C2×C13—21no—
186C2×C13#186711yescharacteristic
187C2×C13#220411yescharacteristic
188C2×C13#220511yescharacteristic
189C2×Q8—21no—
190C2×Q8—41no—
191C2×Q8—41no—
192C2×Q8—41no—
193C2×Q8—41no—
194C2×Q8#610112yes—
195C2×Q8C2×Dic2611yescharacteristic
196C2×Q8C2×C4×D1311yescharacteristic
197C2×Q8#612912yes—
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—262no—
201C22×C4—262no—
202C22×C4D4×D1312yes—
203C22×C4C2×C22⋊D1311yescharacteristic
204M16—41no—
205M16—41no—
206M16—264no—
207M16—522no—
208C2×C8—41no—
209C2×C8—522no—
210C4⋊C4—24no—
211C4⋊C4—24no—
212C4⋊C4—21no—
213C4⋊C4—21no—
214C4⋊C4—22no—
215C4⋊C4—22no—
216C4⋊C4—264no—
217C4⋊C4—522no—
218C4⋊C4—522no—
219C4⋊C4—1041no—
220C22⋊C4—41no—
221C42—21no—
222C42—42no—
223C42—41no—
224C42—522no—
225C42—524no—
226C42—1041no—
227C42#610112yes—
228C13#1297311yescharacteristic, complemented, Sylow
229C23#8819111yescharacteristic
230Q8—41no—
231Q8—41no—
232Q8—42no—
233Q8—42no—
234Q8—81no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—21no—
239C2×C4—22no—
240C2×C4—21no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—264no—
248C2×C4—522no—
249C2×C4—522no—
250C2×C4—522no—
251C2×C4—522no—
252C2×C4—522no—
253C2×C4#8813212yes—
254C2×C4#8813512yes—
255C2×C4C2×#610111yescharacteristic
256C2×C4#8818911yescharacteristic
257C8—81no—
258C8—524no—
259C22—21no—
260C22—21no—
261C22#1171860711yescharacteristic
262C22#1171869311yescharacteristic
263C22#1171871411yescharacteristic
264C4—24no—
265C4—21no—
266C4—22no—
267C4—22no—
268C4—21no—
269C4—42no—
270C4—81no—
271C4—81no—
272C4—524no—
273C4—1042no—
274C2—21no—
275C2—21no—
276C2#1311511611yescharacteristic
277C2#1311686111yescharacteristic
278C2#1311686511yescharacteristic
subgroupG/H
centerC22#11718693
commutatorC2×Q8×C13C22×C4
FrattiniC22×Q8C22×D13
FittingC13×#1886C2
socleC22×C13B(4,𝔽2)
prime radicalC23×C13#120
cosocleC22×Q8×C13C23
hypercenter#1886D13
hypocenterC13#12973
LCSG ▷ C2×Q8×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ #1886

Complements

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

NH ≅ G/Ntype
18. #11718140C4semidirect
228. C13#12973semidirect

Maximal subgroups

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

subgroupindex
#131179262
C2×#117181402
#131150512
#131129622
C13×#18862
#1297313