Finite Group Databasebeta

← #16778367

Subgroups — #16778367

Order 3328.

406 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 102 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#13130764C211yesmaximal, characteristic
2#13130752C211yesmaximal, characteristic
3#13129657C212yesmaximal
4#13129654C212yesmaximal
5#13117307C211yesmaximal, characteristic
6C2×#88141C411yescharacteristic
7C2×#88112—21no—
8C13×#389C411yescharacteristic
9#11718646C2211yescharacteristic
10#11718639—21no—
11C4⋊C4×Dic13—21no—
12C4⋊C4×Dic13C411yescharacteristic
13#11718635C2211yescharacteristic
14C42×Dic13C2211yescharacteristic
15#11718590C411yescharacteristic
16#11718316—21no—
17#11718309—21no—
18#11718290—21no—
19#11718290—21no—
20#11718290—21no—
21#11718290C2212yes—
22#11718290C2212yes—
23C22×Dic26C2×C411yescharacteristic
24C22×#1057—22no—
25C22×#1057—22no—
26C2×C13×C4⋊C4—21no—
27C2×C13×C4⋊C4C2×C411yescharacteristic
28C2×C13×C4⋊C4C2×C411yescharacteristic
29C2×C42×C13C2×C411yescharacteristic
30C2×C4⋊Dic13—21no—
31C2×C4⋊Dic13C2×C411yescharacteristic
32C2×#6101—21no—
33C2×C4×Dic13—21no—
34C2×C4×Dic13—21no—
35C2×C4×Dic13C2×C411yescharacteristic
36C2×C4×Dic13D411yescharacteristic
37C2×C4×Dic13D411yescharacteristic
38C2×C4×Dic13D411yescharacteristic
39C2×C4×Dic13D411yescharacteristic
40C2×C4×Dic13C2311yescharacteristic
41#88141—22no—
42#88141C814yescomplemented
43#88112—42no—
44C13×#95—21no—
45#88071—21no—
46#88071—21no—
47#88071—21no—
48#88071—21no—
49#88071—21no—
50#88071—21no—
51#7596—131nomaximal, Sylow
52C22×C4×C13—21no—
53C22×C4×C13—21no—
54C22×C4×C13C22⋊C411yescharacteristic
55C22×C4×C13C22⋊C411yescharacteristic
56C22×C4×C13C22×C411yescharacteristic
57C22×Dic13—21no—
58C22×Dic13—21no—
59C22×Dic13C22⋊C411yescharacteristic
60C22×Dic13C22⋊C411yescharacteristic
61C22×Dic13C2×D411yescharacteristic
62C22×Dic13C2×D411yescharacteristic
63C2×Dic26—21no—
64C2×Dic26—41no—
65C2×Dic26—41no—
66C2×Dic26C2×C812yes—
67C2×#1057—42no—
68C2×#1057—42no—
69C2×#1057—42no—
70C2×#1057—42no—
71C2×#1057—42no—
72C2×#1057—42no—
73C13×C4⋊C4—21no—
74C13×C4⋊C4—41no—
75C13×C4⋊C4—42no—
76C13×C4⋊C4C2×C812yes—
77C42×C13—41no—
78C4⋊Dic13—41no—
79C4⋊Dic13—41no—
80C4⋊Dic13—41no—
81#6101—24no—
82C4×Dic13—24no—
83C4×Dic13—21no—
84C4×Dic13—21no—
85C4×Dic13—22no—
86C4×Dic13—41no—
87C4×Dic13—41no—
88C4×Dic13—41no—
89C4×Dic13—42no—
90C4×Dic13C2×C812yes—
91C4×Dic13M1612yes—
92#2295—131no—
93#1839—131no—
94#1831—131no—
95#1272—132no—
96#1271—132no—
97C23×C13C2×C22⋊C411yescharacteristic
98C2×C4×C13—21no—
99C2×C4×C13—21no—
100C2×C4×C13—22no—
101C2×C4×C13—21no—
102C2×C4×C13—21no—
103C2×C4×C13—21no—
104C2×C4×C13—21no—
105C2×C4×C13—21no—
106C2×C4×C13—21no—
107C2×C4×C13—41no—
108C2×C4×C13—41no—
109C2×C4×C13—41no—
110C2×C4×C13—41no—
111C2×C4×C13—41no—
112C2×C4×C13C22×C811yescharacteristic
113C2×C4×C13C2×M1611yescharacteristic
114C2×Dic13—21no—
115C2×Dic13—21no—
116C2×Dic13—21no—
117C2×Dic13—21no—
118C2×Dic13—21no—
119C2×Dic13—21no—
120C2×Dic13—21no—
121C2×Dic13—21no—
122C2×Dic13—22no—
123C2×Dic13—41no—
124C2×Dic13—41no—
125C2×Dic13—41no—
126C2×Dic13—41no—
127C2×Dic13—41no—
128C2×Dic13C22⋊C812yes—
129C2×Dic13C22⋊C812yes—
130C2×Dic13AGL(1,ℤ/8)11yescharacteristic
131C2×Dic13#13711yescharacteristic
132C2×Dic13#13712yes—
133Dic26—42no—
134Dic26—42no—
135#1057—82no—
136#1057—82no—
137C2×C4×Q8—131no—
138C2×C4⋊C8—261no—
139#391—131no—
140#391—131no—
141#389—131no—
142#389#26111yescharacteristic
143#387—261no—
144#387—261no—
145C4×C4⋊C4—131no—
146C4×C4⋊C4—261no—
147#376—261no—
148C43—131no—
149#336—132no—
150#336—132no—
151#336—261no—
152#336—261no—
153#336—261no—
154C22×C13C2×C22⋊C811yescharacteristic
155C22×C13#41011yescharacteristic
156C22×C13#41311yescharacteristic
157C22×C13#41711yescharacteristic
158C22×C13#41911yescharacteristic
159C22×C13#42111yescharacteristic
160C22×C13#42111yescharacteristic
161C4×C13—21no—
162C4×C13—21no—
163C4×C13—41no—
164C4×C13—42no—
165C4×C13—41no—
166C4×C13—81no—
167Dic13—22no—
168Dic13—22no—
169Dic13—21no—
170Dic13—21no—
171Dic13—22no—
172Dic13—42no—
173Dic13—81no—
174C22×Q8—131no—
175C22×C8—262no—
176C22×C8—262no—
177C4×Q8—134no—
178C4×Q8—262no—
179C2×C4⋊C4—21no—
180C2×C4⋊C4—131no—
181C2×C4⋊C4—261no—
182C2×C4⋊C4—261no—
183C2×C4⋊C4C2×#26111yescharacteristic
184C2×C4⋊C4C2×#26111yescharacteristic
185C2×C42—131no—
186C2×C42—131no—
187C2×C42—131no—
188C2×C42—131no—
189C2×C42—131no—
190C2×C42—131no—
191C2×C42—261no—
192C2×C42—261no—
193C2×C42C2×#26111yescharacteristic
194C4⋊C8—522no—
195#95—21no—
196#95—261no—
197#95—261no—
198#95—261no—
199#95—261no—
200#95—261no—
201#95—261no—
202C2×C13#145811yescharacteristic
203C2×C13#147711yescharacteristic
204C2×C13#147911yescharacteristic
205C2×C13#151211yescharacteristic
206C2×C13#151511yescharacteristic
207C2×C13#153511yescharacteristic
208C2×C13#155911yescharacteristic
209C2×Q8—132no—
210C2×Q8—261no—
211C2×Q8—521no—
212C2×Q8—521no—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—131no—
216C22×C4—131no—
217C22×C4—131no—
218C22×C4—131no—
219C22×C4—261no—
220C22×C4—261no—
221C22×C4C22⋊#26111yescharacteristic
222C22×C4C22⋊#26111yescharacteristic
223C22×C4C22×#26111yescharacteristic
224C2×C8—522no—
225C2×C8—522no—
226C2×C8—522no—
227C2×C8—522no—
228C2×C8—522no—
229C2×C8—522no—
230C4⋊C4—21no—
231C4⋊C4—41no—
232C4⋊C4—42no—
233C4⋊C4—264no—
234C4⋊C4—521no—
235C4⋊C4—521no—
236C4⋊C4—521no—
237C4⋊C4D13⋊C812yes—
238C42—41no—
239C42—132no—
240C42—132no—
241C42—261no—
242C42—262no—
243C42—261no—
244C42—264no—
245C42—521no—
246C42—521no—
247C42—521no—
248C42—522no—
249C13#759611yescharacteristic, complemented, Sylow
250C23C2×C22⋊#26111yescharacteristic
251Q8—522no—
252Q8—522no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—22no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—132no—
268C2×C4—132no—
269C2×C4—132no—
270C2×C4—131no—
271C2×C4—131no—
272C2×C4—261no—
273C2×C4—261no—
274C2×C4—261no—
275C2×C4—261no—
276C2×C4—261no—
277C2×C4—261no—
278C2×C4—261no—
279C2×C4—261no—
280C2×C4—262no—
281C2×C4—521no—
282C2×C4—521no—
283C2×C4—521no—
284C2×C4—521no—
285C2×C4—521no—
286C2×C4C2×D13⋊C811yescharacteristic
287C2×C4D13⋊M1611yescharacteristic
288C8—1042no—
289C8—1042no—
290C22D13⋊(C22⋊C8)11yescharacteristic
291C22#1171914011yescharacteristic
292C22#1171914811yescharacteristic
293C22#1171915311yescharacteristic
294C22#1171915611yescharacteristic
295C22#1171916411yescharacteristic
296C22#1171916611yescharacteristic
297C4—21no—
298C4—21no—
299C4—41no—
300C4—41no—
301C4—42no—
302C4—81no—
303C4—261no—
304C4—261no—
305C4—262no—
306C4—262no—
307C4—262no—
308C4—522no—
309C4—1041no—
310C2#1313007011yescharacteristic
311C2#1313013211yescharacteristic
312C2#1313013911yescharacteristic
313C2#1313025011yescharacteristic
314C2#1313025911yescharacteristic
315C2#1313032111yescharacteristic
316C2#1313037211yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC2×C4×C13C22×C8
FrattiniC22×C4C22×#261
FittingC13×#389C4
socle, prime radicalC23×C13C2×C22⋊C4
cosocleC2×C4×Dic13C23
hypercenter#389#261
hypocenterC13#7596
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
42. #88141C8semidirect
249. C13#7596semidirect

Maximal subgroups

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

subgroupindex
#131307642
#131307522
#131296572
#131296542
#131173072
#759613