Finite Group Databasebeta

← #15779758

Subgroups — #15779758

Order 3328.

460 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 99 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
1C2×#11718140C211yesmaximal, characteristic
2#13115230C211yesmaximal, characteristic
3#13115050C212yesmaximal
4#13112963C212yesmaximal
5C13×#2369C211yesmaximal, characteristic
6C2×C13×C4⋊Q8C2211yescharacteristic
7#11719517C2211yescharacteristic
8C13×#391—21no—
9C13×#391C2212yes—
10C13×#389—22no—
11C4×C13×C4⋊C4—22no—
12C4×C13×C4⋊C4—21no—
13C2×#88076C2211yescharacteristic
14C2×#88076C2212yes—
15#11718886—21no—
16#11718625—22no—
17#11718140C414yescomplemented
18#11718115—21no—
19#11718115—22no—
20C22×Q8×C13D411yescharacteristic
21C22×Q8×C13C2311yescharacteristic
22C13×C4⋊Q8—22no—
23C13×C4⋊Q8C2×C412yes—
24C13×C4⋊Q8Q812yes—
25C2×C13×C4⋊C4—21no—
26C2×C13×C4⋊C4—22no—
27C2×C13×C4⋊C4—21no—
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4D412yes—
30C2×C42×C13—22no—
31C2×C42×C13—21no—
32C2×C42×C13D411yescharacteristic
33C2×C42×C13D412yes—
34Q8×Dic13—41no—
35Q8×Dic13—41no—
36#88180—22no—
37#88180—21no—
38C2×#6099—22no—
39C2×#6099—21no—
40C13×#95—22no—
41C13×#95—22no—
42C13×#95—22no—
43#88076—22no—
44#88076—22no—
45#88076C2×C414yes—
46#88075—41no—
47#88075—41no—
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—22no—
62C22×C4×C13—21no—
63C22×C4×C13—22no—
64C22×C4×C13C2×D411yescharacteristic
65C22×C4×C13C2×D412yes—
66C13×C4⋊C4—24no—
67C13×C4⋊C4—24no—
68C13×C4⋊C4—24no—
69C13×C4⋊C4—42no—
70C13×C4⋊C4—42no—
71C13×C4⋊C4—81no—
72C42×C13—21no—
73C42×C13—42no—
74C42×C13—44no—
75C42×C13—81no—
76C42×C13C4⋊C412yes—
77C22⋊Dic13—41no—
78C4⋊Dic13—21no—
79C4⋊Dic13—21no—
80C4⋊Dic13—22no—
81C4⋊Dic13—22no—
82C4×Dic13—42no—
83C4×Dic13—41no—
84#6099—24no—
85#6099—42no—
86#6099—41no—
87#6099—41no—
88C2×#1055—42no—
89C2×#1055—41no—
90#2369D1311yescharacteristic
91C2×#356—131no—
92#1886—131no—
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—24no—
109C2×C4×C13—22no—
110C2×C4×C13—42no—
111C2×C4×C13—41no—
112C2×C4×C13—42no—
113C2×C4×C13—41no—
114C2×C4×C13—42no—
115C2×C4×C13—42no—
116C2×C4×C13—42no—
117C2×C4×C13C2×C4⋊C411yescharacteristic
118C2×C4×C13C4×D412yes—
119C2×C4×C13C22⋊Q812yes—
120C2×C4×C13#12311yescharacteristic
121C2×Dic13—41no—
122C2×Dic13—41no—
123#1055—44no—
124#1055—81no—
125C2×C4⋊Q8C2×D1311yescharacteristic
126#519—131no—
127#428—262no—
128#419—261no—
129C2×#101—132no—
130C2×#101—131no—
131#391—21no—
132#391C2×D1312yes—
133#389—22no—
134C4×C4⋊C4—22no—
135C4×C4⋊C4—21no—
136#356—134no—
137#339—262no—
138#339—261no—
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—44no—
150C4×C13—42no—
151C4×C13—82no—
152Dic13—81no—
153Dic13—81no—
154C22×Q8C22⋊D1311yescharacteristic
155C22×Q8C22×D1311yescharacteristic
156C2×M16—262no—
157C2×M16—261no—
158C4⋊Q8—22no—
159C4⋊Q8Dic2612yes—
160C4⋊Q8C4×D1312yes—
161C4×Q8—521no—
162C4×Q8—521no—
163#117—261no—
164#117—262no—
165C2×C4⋊C4—21no—
166C2×C4⋊C4—22no—
167C2×C4⋊C4—21no—
168C2×C4⋊C4—21no—
169C2×C4⋊C4C22⋊D1312yes—
170C2×C42—22no—
171C2×C42—21no—
172C2×C42C22⋊D1311yescharacteristic
173C2×C42C22⋊D1312yes—
174#107—522no—
175#106—522no—
176#103—521no—
177#103—521no—
178#101—134no—
179#101—262no—
180#101—262no—
181#95—22no—
182#95—22no—
183#95—22no—
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#612712yes—
198C22×C4—21no—
199C22×C4—22no—
200C22×C4—21no—
201C22×C4—22no—
202C22×C4C2×C22⋊D1311yescharacteristic
203C22×C4C2×C22⋊D1312yes—
204M16—264no—
205M16—522no—
206M16—521no—
207M16—521no—
208C2×C8—522no—
209C2×C8—521no—
210C4⋊C4—24no—
211C4⋊C4—24no—
212C4⋊C4—24no—
213C4⋊C4—42no—
214C4⋊C4—42no—
215C4⋊C4—81no—
216C4⋊C4—261no—
217C4⋊C4—261no—
218C4⋊C4—262no—
219C4⋊C4—262no—
220C22⋊C4—521no—
221C42—21no—
222C42—42no—
223C42—44no—
224C42—81no—
225C42—522no—
226C42—521no—
227C42#610112yes—
228C13#1297311yescharacteristic, complemented, Sylow
229C23#8820711yescharacteristic
230Q8—41no—
231Q8—41no—
232Q8—42no—
233Q8—42no—
234Q8—81no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—21no—
240C2×C4—22no—
241C2×C4—21no—
242C2×C4—24no—
243C2×C4—22no—
244C2×C4—42no—
245C2×C4—42no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4—42no—
251C2×C4—521no—
252C2×C4—521no—
253C2×C4C2×#610111yescharacteristic
254C2×C4#8817812yes—
255C2×C4C4×C22⋊D1312yes—
256C2×C4#8818311yescharacteristic
257C8—524no—
258C8—1041no—
259C22—21no—
260C22—21no—
261C22#1171887111yescharacteristic
262C22#1171890411yescharacteristic
263C22#1171890511yescharacteristic
264C4—24no—
265C4—22no—
266C4—21no—
267C4—21no—
268C4—22no—
269C4—44no—
270C4—42no—
271C4—82no—
272C4—1041no—
273C4—1041no—
274C2—21no—
275C2—21no—
276C2#1311511711yescharacteristic
277C2#1311686211yescharacteristic
278C2#1311686611yescharacteristic
subgroupG/H
centerC22#11718905
commutatorC2×Q8×C13C22×C4
FrattiniC22×Q8C22×D13
FittingC13×#2369C2
socleC22×C13B(4,𝔽2)
prime radicalC23×C13#120
cosocleC22×Q8×C13C23
hypercenter#2369D13
hypocenterC13#12973
LCSG ▷ C2×Q8×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ #2369

Complements

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

NH ≅ G/Ntype
17. #11718140C4semidirect
228. C13#12973semidirect

Maximal subgroups

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

subgroupindex
C2×#117181402
#131152302
#131150502
#131129632
C13×#23692
#1297313