Finite Group Databasebeta

← #15781606

Subgroups — #15781606

Order 3328.

420 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 107 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#13120041C211yesmaximal, characteristic
2#13114832C211yesmaximal, characteristic
3#13112962C214yesmaximal
4C4×C13×#101C211yesmaximal, characteristic
5C2×C4×Q8×C13C2211yescharacteristic
6C2×#88123C411yescharacteristic
7C2×C13×#101C2212yes—
8C4×C13×M16—21no—
9#11718891C2212yes—
10C2×#88076C2212yes—
11#11718640—21no—
12#11718640—21no—
13#11718637C412yes—
14C4×C4⋊Dic13C411yescharacteristic
15#11718589—21no—
16#11718589—21no—
17#11718585—21no—
18C13×#343—21no—
19#11718122—21no—
20C22×Q8×C13C2311yescharacteristic
21C22×Dic26—21no—
22C2×C13×M16—22no—
23C4×Q8×C13—41no—
24C4×Q8×C13—41no—
25C2×C13×C4⋊C4C2×C411yescharacteristic
26C2×C13×C4⋊C4D411yescharacteristic
27C2×C13×C4⋊C4D411yescharacteristic
28C2×C42×C13C2×C411yescharacteristic
29C2×C42×C13D411yescharacteristic
30C2×C42×C13D411yescharacteristic
31C2×C4⋊Dic13—21no—
32C2×C4⋊Dic13—21no—
33C2×C4⋊Dic13C2×C412yes—
34C2×#6101—22no—
35C2×#6101—22no—
36C2×C4×Dic13C2×C412yes—
37C2×#6099—22no—
38#88123—41no—
39#88123—41no—
40C13×#101—22no—
41C13×#101Q814yescomplemented
42C13×#97—41no—
43C4×C8×C13—41no—
44#88076—24no—
45#88071—21no—
46#88071—22no—
47#88071—22no—
48C4⋊#1055—41no—
49C4⋊#1055—41no—
50#13302—131nomaximal, Sylow
51C2×Q8×C13—41no—
52C2×Q8×C13—41no—
53C2×Q8×C13C2×Q812yes—
54C2×Q8×C13#4112yes—
55C22×C4×C13C22⋊C411yescharacteristic
56C22×C4×C13C22⋊C411yescharacteristic
57C22×C4×C13C22⋊C411yescharacteristic
58C22×C4×C13C22⋊C411yescharacteristic
59C22×C4×C13C22×C411yescharacteristic
60C22×C4×C13C2×D411yescharacteristic
61C22×C4×C13C2×D411yescharacteristic
62C22×Dic13—22no—
63C22×Dic13—22no—
64C2×Dic26—42no—
65C2×Dic26—82no—
66C13×M16—24no—
67C13×M16—42no—
68C2×C8×C13—42no—
69C13×C4⋊C4—41no—
70C13×C4⋊C4—41no—
71C13×C4⋊C4—41no—
72C42×C13—21no—
73C42×C13—21no—
74C42×C13—21no—
75C42×C13—21no—
76C42×C13—21no—
77C42×C13—21no—
78C4⋊Dic13—24no—
79C4⋊Dic13—41no—
80C4⋊Dic13—41no—
81C4⋊Dic13—42no—
82#6101—82no—
83#6101—82no—
84C4×Dic13—42no—
85#6099—42no—
86#6099—42no—
87C2×#1055—42no—
88#2567—131no—
89#1801—131no—
90C4×#101D1311yescharacteristic
91#1394—134no—
92C23×C13C2×C22⋊C411yescharacteristic
93Q8×C13—42no—
94Q8×C13—42no—
95C2×C4×C13—21no—
96C2×C4×C13—21no—
97C2×C4×C13—21no—
98C2×C4×C13—21no—
99C2×C4×C13—21no—
100C2×C4×C13—21no—
101C2×C4×C13—22no—
102C2×C4×C13—21no—
103C2×C4×C13—21no—
104C2×C4×C13—21no—
105C2×C4×C13—41no—
106C2×C4×C13—41no—
107C2×C4×C13—41no—
108C2×C4×C13#9911yescharacteristic
109C2×C4×C13#9911yescharacteristic
110C2×C4×C13C4×Q812yes—
111C2×C4×C13C22⋊Q812yes—
112C2×C4×C13#12411yescharacteristic
113C2×C4×C13C4⋊Q811yescharacteristic
114C2×Dic13—24no—
115C2×Dic13—42no—
116C2×Dic13—42no—
117C2×Dic13—42no—
118C2×Dic13—42no—
119C2×Dic13—42no—
120Dic26—84no—
121C8×C13—44no—
122#1055—82no—
123C2×C4⋊Q8—131no—
124C2×C4×Q8C2×D1311yescharacteristic
125#423—261no—
126C2×#101—132no—
127C2×#101C2×D1312yes—
128C4×M16—21no—
129#395—261no—
130#395—261no—
131#391—132no—
132#389—261no—
133#389—261no—
134#384—132no—
135C4×C4⋊C4—131no—
136#343—21no—
137#343—261no—
138C22×C13—21no—
139C22×C13—21no—
140C22×C13#39111yescharacteristic
141C22×C13C2×#9911yescharacteristic
142C22×C13#41011yescharacteristic
143C4×C13—21no—
144C4×C13—21no—
145C4×C13—22no—
146C4×C13—22no—
147C4×C13—21no—
148C4×C13—41no—
149C4×C13—41no—
150C4×C13—41no—
151C4×C13#35612yes—
152Dic13—44no—
153Dic13—82no—
154C22×Q8—261no—
155C22×Q8C22×D1311yescharacteristic
156C2×M16—22no—
157C2×M16—262no—
158C4⋊Q8—521no—
159C4⋊Q8—521no—
160C4×Q8—41no—
161C4×Q8—41no—
162C2×C4⋊C4—132no—
163C2×C4⋊C4—261no—
164C2×C4⋊C4—261no—
165C2×C4⋊C4—262no—
166C2×C4⋊C4—262no—
167C2×C4⋊C4C4×D1311yescharacteristic
168C2×C4⋊C4D5211yescharacteristic
169C2×C4⋊C4C22⋊D1311yescharacteristic
170C2×C42—132no—
171C2×C42C4×D1311yescharacteristic
172C2×C42D5211yescharacteristic
173C2×C42C22⋊D1311yescharacteristic
174C4⋊C8—521no—
175C4⋊C8—521no—
176#101—22no—
177#101—264no—
178#101Dic2614yescomplemented
179#97—41no—
180C4×C8—41no—
181#95—261no—
182#95—262no—
183#95—262no—
184C2×C13—21no—
185C2×C13—21no—
186C2×C13#199611yescharacteristic
187C2×C13C2×#35611yescharacteristic
188C2×C13#213411yescharacteristic
189C2×Q8—41no—
190C2×Q8—41no—
191C2×Q8—522no—
192C2×Q8—1042no—
193C2×Q8C2×Dic2612yes—
194C2×Q8#612712yes—
195C22×C4—262no—
196C22×C4—262no—
197C22×C4#610311yescharacteristic
198C22×C4#610311yescharacteristic
199C22×C4#610311yescharacteristic
200C22×C4#610311yescharacteristic
201C22×C4C2×C4×D1311yescharacteristic
202C22×C4C2×D5211yescharacteristic
203C22×C4C2×C22⋊D1311yescharacteristic
204M16—24no—
205M16—42no—
206M16—522no—
207M16—522no—
208C2×C8—42no—
209C2×C8—522no—
210C4⋊C4—41no—
211C4⋊C4—41no—
212C4⋊C4—41no—
213C4⋊C4—264no—
214C4⋊C4—522no—
215C4⋊C4—521no—
216C4⋊C4—521no—
217C4⋊C4—1042no—
218C4⋊C4—1042no—
219C42—21no—
220C42—21no—
221C42—21no—
222C42—21no—
223C42—21no—
224C42—21no—
225C42—522no—
226C13#1330211yescharacteristic, complemented, Sylow
227C23C2×#610311yescharacteristic
228Q8—42no—
229Q8—42no—
230Q8—1044no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—264no—
245C2×C4—522no—
246C2×C4—522no—
247C2×C4—522no—
248C2×C4—522no—
249C2×C4—522no—
250C2×C4#8804611yescharacteristic
251C2×C4#8804611yescharacteristic
252C2×C4C4×Dic2612yes—
253C2×C4#8812311yescharacteristic
254C2×C4#8812911yescharacteristic
255C2×C4#8817812yes—
256C8—44no—
257C8—1042no—
258C22—21no—
259C22—21no—
260C22#1171859011yescharacteristic
261C22C2×#8804611yescharacteristic
262C22#1171866711yescharacteristic
263C4—21no—
264C4—22no—
265C4—21no—
266C4—22no—
267C4—21no—
268C4—41no—
269C4—41no—
270C4—41no—
271C4—524no—
272C4—1042no—
273C4#1171807012yes—
274C2—21no—
275C2—21no—
276C2#1311582111yescharacteristic
277C2C2×#1171807011yescharacteristic
278C2#1311652711yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC22×C4×C13C22×C4
FrattiniC22×Q8C22×D13
FittingC4×C13×#101C2
socleC22×C13C2×#99
prime radicalC23×C13C2×C22⋊C4
cosocleC22×Q8×C13C23
hypercenterC4×#101D13
hypocenterC13#13302
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ C4×#101

Complements

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

NH ≅ G/Ntype
41. C13×#101Q8semidirect
178. #101Dic26semidirect
226. C13#13302semidirect

Maximal subgroups

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

subgroupindex
#131200412
#131148322
#131129622
C4×C13×#1012
#1330213