Finite Group Databasebeta

← #16779848

Subgroups — #16779848

Order 3328.

954 conjugacy classes of subgroups; only the 156 normal subgroups are shown.

normal subgroups only

This group has 954 conjugacy classes of subgroups — too many to draw. Only its 156 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#13131280C212yesmaximal
2#13129716C214yesmaximal, complemented
3C2×#11718787C211yesmaximal, characteristic
4C23×C4×D13C2211yescharacteristic
5C2×#88237—22no—
6C22×C13×M16C411yescharacteristic, complemented
7C22×#6099C411yescharacteristic, complemented
8#11719171—22no—
9#11719136—22no—
10#11719136C414yescomplemented
11#11719135C414yescomplemented
12C4×C22⋊#261—22no—
13C4×C22⋊#261C2214yes—
14#11718787—22no—
15#11718787C412yescomplemented
16#11718787C2212yes—
17C2×#88060—22no—
18C24×D13D411yescharacteristic
19C23×C4×C13C2×C411yescharacteristic
20C23×Dic13Q811yescharacteristic
21C22×C4×D13—42no—
22C22×C4×D13—42no—
23C22×C4×D13C2×C411yescharacteristic
24C22×C4×D13C2×C412yes—
25C22×C4×D13C2×C412yes—
26C22×C4×D13D412yes—
27C22×C4×D13D411yescharacteristic
28C22×C4×D13D412yes—
29C22×C4×D13Q811yescharacteristic
30C22×C4×D13C2311yescharacteristic
31C2×C22⋊#261—24no—
32C2×C22⋊#261—24no—
33C2×C22⋊#261—24no—
34#88237—44no—
35#88237—44no—
36C2×C4⋊#261—24no—
37C2×C4×#261—24no—
38C2×C13×M16—21no—
39C2×C13×M16—42no—
40C2×C13×M16C2×C412yes—
41C22×C8×C13—21no—
42C2×#6099—21no—
43C2×#6099—42no—
44C2×#6099C2×C412yes—
45C22×#1055—21no—
46(C2×#261)⋊C4—24no—
47(C2×#261)⋊C4C2×C418yes—
48#88060—24no—
49#88060—24no—
50#8049—131nomaximal, Sylow
51C24×C13C4⋊C411yescharacteristic
52C23×D13—44no—
53C23×D13—42no—
54C23×D13C22⋊C412yes—
55C23×D13C22⋊C412yes—
56C23×D13C4⋊C411yescharacteristic
57C23×D13C2×D411yescharacteristic
58C22×#261—28no—
59C22×C4×C13—22no—
60C22×C4×C13—22no—
61C22×C4×C13C4211yescharacteristic
62C22×C4×C13C4211yescharacteristic
63C22×C4×C13C22⋊C411yescharacteristic
64C22×C4×C13C22⋊C411yescharacteristic
65C22×C4×C13C4⋊C411yescharacteristic
66C22×C4×C13C22×C411yescharacteristic
67C22×Dic13—42no—
68C22×Dic13C4⋊C412yes—
69C22×Dic13C4⋊C411yescharacteristic
70C22×Dic13C4⋊C412yes—
71C22×Dic13C2×Q811yescharacteristic
72C2×C4×D13—24no—
73C2×C4×D13—24no—
74C2×C4×D13—44no—
75C2×C4×D13—41no—
76C2×C4×D13—41no—
77C2×C4×D13—42no—
78C2×C4×D13—42no—
79C2×C4×D13—42no—
80C2×C4×D13—42no—
81C2×C4×D13—41no—
82C2×C4×D13—41no—
83C2×C4×D13—44no—
84C2×C4×D13C4212yes—
85C2×C4×D13C22⋊C412yes—
86C2×C4×D13C22⋊C412yes—
87C2×C4×D13C22⋊C412yes—
88C2×C4×D13C4⋊C412yes—
89C2×C4×D13C4⋊C412yes—
90C2×C4×D13C22×C412yes—
91C2×C4×D13C2×D412yes—
92C22⋊#261—48no—
93C22⋊#261—48no—
94C22⋊#261—48no—
95C4⋊#261—48no—
96C4×#261—44no—
97C4×#261—44no—
98C13×M16—42no—
99C13×M16—42no—
100C2×C8×C13—22no—
101C2×C8×C13—42no—
102#6099—42no—
103#6099—42no—
104C2×#1055—22no—
105C2×#1055—42no—
106C2×#407—131no—
107#2280—132no—
108#1297—134no—
109C23×C13—22no—
110C23×C13—42no—
111C23×C13#9511yescharacteristic
112C23×C13#9511yescharacteristic
113C23×C13C2×C4⋊C411yescharacteristic
114C22×D13—24no—
115C22×D13—24no—
116C22×D13—24no—
117C22×D13—24no—
118C22×D13—42no—
119C22×D13—41no—
120C22×D13—41no—
121C22×D13—42no—
122C22×D13—42no—
123C22×D13—42no—
124C22×D13—416no—
125C22×D13#9512yes—
126C22×D13C2×C22⋊C412yes—
127C2×#261—48no—
128C2×#261—48no—
129C2×#261—48no—
130C2×C4×C13—22no—
131C2×C4×C13—22no—
132C2×C4×C13—22no—
133C2×C4×C13—21no—
134C2×C4×C13—21no—
135C2×C4×C13—21no—
136C2×C4×C13—21no—
137C2×C4×C13#9511yescharacteristic
138C2×C4×C13#9511yescharacteristic
139C2×C4×C13#9912yes—
140C2×C4×C13#9912yes—
141C2×C4×C13C2×C4211yescharacteristic
142C2×C4×C13C2×C22⋊C411yescharacteristic
143C2×Dic13—24no—
144C2×Dic13—41no—
145C2×Dic13—42no—
146C2×Dic13—41no—
147C2×Dic13#9512yes—
148C2×Dic13C2×C4⋊C412yes—
149C4×D13—24no—
150C4×D13—24no—
151C4×D13—22no—
152C4×D13—22no—
153C4×D13—22no—
154C4×D13—22no—
155C4×D13—42no—
156C4×D13—42no—
157C4×D13—42no—
158C4×D13—42no—
159C8×C13—42no—
160#1055—42no—
161C24×C4—131no—
162C22×M16—131no—
163C22×M16#26111yescharacteristic, complemented
164C2×#117—262no—
165#407—132no—
166#407—132no—
167#407—262no—
168C2×C22⋊C8—262no—
169#381—134no—
170#380—134no—
171#380—262no—
172#379—262no—
173C4×C22⋊C4—134no—
174C4×C22⋊C4—262no—
175C22×C13—22no—
176C22×C13—22no—
177C22×C13—22no—
178C22×C13—21no—
179C22×C13—21no—
180C22×C13—44no—
181C22×C13#34212yes—
182C22×C13C2×#9511yescharacteristic
183C2×D13—22no—
184C2×D13—22no—
185C2×D13—22no—
186C2×D13—22no—
187C2×D13—22no—
188C2×D13—44no—
189C2×D13—48no—
190C2×D13—48no—
191C2×D13—44no—
192C2×D13#42114yes—
193#261—88no—
194C4×C13—21no—
195C4×C13—21no—
196C4×C13#34212yes—
197C4×C13C2×#9911yescharacteristic
198C4×C13C2×#9911yescharacteristic
199Dic13—22no—
200Dic13—22no—
201C25—131no—
202C23×C4—131no—
203C23×C4—132no—
204C23×C4—132no—
205C23×C4—132no—
206C23×C4—131no—
207C23×C4—131no—
208C23×C4—132no—
209C23×C4—131no—
210C23×C4—131no—
211C23×C4—522no—
212C23×C4—522no—
213C23×C4C2×#26111yescharacteristic
214C2×M16—21no—
215C2×M16—42no—
216C2×M16—132no—
217C2×M16—261no—
218C2×M16—522no—
219C2×M16C2×#26112yes—
220C22×C8—21no—
221C22×C8—261no—
222#117—524no—
223#117—524no—
224C2×C4⋊C4—264no—
225C2×C22⋊C4—264no—
226C2×C22⋊C4—264no—
227C2×C22⋊C4—264no—
228C2×C42—264no—
229C22⋊C8—264no—
230C22⋊C8—264no—
231#95—138no—
232#95—264no—
233C2×C13—22no—
234C2×C13—41no—
235C2×C13—41no—
236C2×C13#173312yes—
237C2×C13C2×#34211yescharacteristic
238D13—24no—
239D13—42no—
240C24—132no—
241C24—131no—
242C24—132no—
243C24—131no—
244C24—522no—
245C24—524no—
246C24C4⋊#26111yescharacteristic
247C22×C4—22no—
248C22×C4—22no—
249C22×C4—132no—
250C22×C4—132no—
251C22×C4—131no—
252C22×C4—131no—
253C22×C4—132no—
254C22×C4—132no—
255C22×C4—132no—
256C22×C4—132no—
257C22×C4—132no—
258C22×C4—132no—
259C22×C4—132no—
260C22×C4—132no—
261C22×C4—264no—
262C22×C4—264no—
263C22×C4—268no—
264C22×C4—524no—
265C22×C4—522no—
266C22×C4—522no—
267C22×C4—522no—
268C22×C4—521no—
269C22×C4—521no—
270C22×C4—522no—
271C22×C4—521no—
272C22×C4—521no—
273C22×C4—524no—
274C22×C4—522no—
275C22×C4C4×#26111yescharacteristic
276C22×C4C4×#26111yescharacteristic
277C22×C4C4⋊#26111yescharacteristic
278C22×C4C22⋊#26111yescharacteristic
279C22×C4C22⋊#26111yescharacteristic
280C22×C4C22×#26111yescharacteristic
281M16—42no—
282M16—42no—
283M16—522no—
284M16—522no—
285C2×C8—22no—
286C2×C8—42no—
287C2×C8—262no—
288C2×C8—522no—
289C4⋊C4—528no—
290C22⋊C4—528no—
291C22⋊C4—528no—
292C22⋊C4—528no—
293C42—524no—
294C42—524no—
295C13#804911yescharacteristic, complemented, Sylow
296C23—22no—
297C23—42no—
298C23—132no—
299C23—132no—
300C23—264no—
301C23—264no—
302C23—264no—
303C23—264no—
304C23—522no—
305C23—521no—
306C23—521no—
307C23—522no—
308C23—522no—
309C23—522no—
310C23—5216no—
311C23(C2×#261)⋊C411yescharacteristic
312C23(C2×#261)⋊C411yescharacteristic
313C23C2×C4⋊#26111yescharacteristic
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—132no—
322C2×C4—132no—
323C2×C4—264no—
324C2×C4—264no—
325C2×C4—264no—
326C2×C4—262no—
327C2×C4—262no—
328C2×C4—262no—
329C2×C4—262no—
330C2×C4—522no—
331C2×C4—522no—
332C2×C4—522no—
333C2×C4—522no—
334C2×C4—522no—
335C2×C4—521no—
336C2×C4—521no—
337C2×C4—528no—
338C2×C4—528no—
339C2×C4—528no—
340C2×C4#8810712yes—
341C2×C4(C2×#261)⋊C411yescharacteristic
342C2×C4(C2×#261)⋊C411yescharacteristic
343C2×C4#8811912yes—
344C2×C4C2×C4×#26111yescharacteristic
345C2×C4C2×C22⋊#26111yescharacteristic
346C8—42no—
347C8—522no—
348C22—22no—
349C22—22no—
350C22—22no—
351C22—21no—
352C22—21no—
353C22—44no—
354C22—134no—
355C22—262no—
356C22—262no—
357C22—262no—
358C22—262no—
359C22—262no—
360C22—528no—
361C22—524no—
362C22—528no—
363C22—524no—
364C22#1171828912yes—
365C22C2×(C2×#261)⋊C411yescharacteristic
366C4—21no—
367C4—21no—
368C4—262no—
369C4—262no—
370C4—1048no—
371C4#1171828912yes—
372C4C2×#8810711yescharacteristic
373C4C2×#8811911yescharacteristic
374C2—22no—
375C2—41no—
376C2—41no—
377C2—264no—
378C2—522no—
379C2#1313051812yes—
380C2C2×#1171828911yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#261
commutatorC2×C4×C13C2×C42
FrattiniC22×C4C22×#261
FittingC22×C13×M16C4
socleC22×C13C2×#95
prime radicalC24×D13D4
cosocleC22×C4×D13C23
hypercenterC22×M16#261
hypocenterC13#8049
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×M16

Complements

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

NH ≅ G/Ntype
2. #13129716C2semidirect
6. C22×C13×M16C4semidirect
7. C22×#6099C4semidirect
10. #11719136C4semidirect
11. #11719135C4semidirect
15. #11718787C4semidirect
163. C22×M16#261semidirect
295. C13#8049semidirect

Maximal subgroups

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

subgroupindex
#131312802
#131297162
C2×#117187872
#804913