Finite Group Databasebeta

← #15756467

Subgroups — #15756467

Order 3328.

530 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 530 conjugacy classes of subgroups — too many to draw. Only its 123 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#13117746C211yesmaximal, characteristic
2#13113154C211yesmaximal, characteristic
3#13112714C212yesmaximal, complemented
4#13112703C212yesmaximal, complemented
5C13×#1799C211yesmaximal, characteristic
6C2×C4×D4×C13C2211yescharacteristic
7C2×D4×Dic13—21no—
8C2×C13×#99—21no—
9C13×#380C2212yes—
10#11718873C411yescharacteristic, complemented
11#11718873C2211yescharacteristic
12C2×#88071C411yescharacteristic, complemented
13C2×#88071C2211yescharacteristic
14C2×C22⋊#1055C2212yes—
15#11718646—21no—
16#11718611—21no—
17#11718611—21no—
18#11718597C411yescharacteristic, complemented
19C4×C4⋊Dic13C411yescharacteristic, complemented
20C13×#342—21no—
21#11718120—21no—
22#11718117—21no—
23C22×D4×C13D411yescharacteristic
24C23×C4×C13C2×C411yescharacteristic
25C23×C4×C13C2311yescharacteristic
26C23×Dic13—21no—
27C23×Dic13—21no—
28C4×D4×C13—22no—
29C4×D4×C13—22no—
30C2×C13×C4⋊C4—22no—
31C2×C13×C4⋊C4D411yescharacteristic
32C2×C13×C22⋊C4—22no—
33C2×C13×C22⋊C4D411yescharacteristic
34C2×C13×C22⋊C4D411yescharacteristic
35C2×C42×C13C2×C411yescharacteristic
36C2×C22⋊Dic13—21no—
37C2×C22⋊Dic13—21no—
38D4×Dic13—44no—
39C2×C4⋊Dic13—21no—
40C2×C4⋊Dic13—21no—
41C2×C4⋊Dic13—21no—
42C2×C4⋊Dic13—21no—
43C2×C4×Dic13—21no—
44C22×#1055—22no—
45C13×#99—42no—
46C13×#95—22no—
47#88071—21no—
48#88071—21no—
49#88071—21no—
50#88071C2×C411yescharacteristic
51#88071C2×C411yescharacteristic
52#88071C2×C411yescharacteristic
53#88071C2×C411yescharacteristic
54C22⋊#1055—22no—
55C22⋊#1055—22no—
56#8761—131nomaximal, Sylow
57C24×C13C22⋊C411yescharacteristic
58C24×C13C2×D411yescharacteristic
59C2×D4×C13—22no—
60C2×D4×C13—22no—
61C2×D4×C13SD1612yes—
62C2×D4×C13Q1612yes—
63C22×C4×C13—21no—
64C22×C4×C13—21no—
65C22×C4×C13—42no—
66C22×C4×C13—81no—
67C22×C4×C13—81no—
68C22×C4×C13C22⋊C411yescharacteristic
69C22×C4×C13C22⋊C411yescharacteristic
70C22×C4×C13C22⋊C411yescharacteristic
71C22×C4×C13C22×C411yescharacteristic
72C22×C4×C13C2×D411yescharacteristic
73C22×C4×C13#4112yes—
74C22×C4×C13#4112yes—
75C22×Dic13—21no—
76C22×Dic13—21no—
77C22×Dic13—21no—
78C22×Dic13—21no—
79C22×Dic13—42no—
80C22×Dic13—42no—
81C22×Dic13—42no—
82C22×Dic13—42no—
83C22×Dic13—81no—
84C22×Dic13—81no—
85C13×C4⋊C4—22no—
86C13×C4⋊C4—82no—
87C13×C22⋊C4—22no—
88C13×C22⋊C4—22no—
89C13×C22⋊C4—42no—
90C13×C22⋊C4—42no—
91C42×C13—21no—
92C42×C13—21no—
93C22⋊Dic13—42no—
94C22⋊Dic13—42no—
95C4⋊Dic13—42no—
96C4⋊Dic13—42no—
97C4⋊Dic13—81no—
98C4⋊Dic13—81no—
99C4×Dic13—42no—
100C2×#1055—42no—
101C2×#1055—82no—
102#2349—131no—
103#1799D1311yescharacteristic
104#1459—131no—
105#1294—132no—
106#1289—132no—
107C23×C13—21no—
108C23×C13—21no—
109C23×C13—41no—
110C23×C13—41no—
111C23×C13—41no—
112C23×C13—41no—
113C23×C13#10312yes—
114C23×C13C2×C22⋊C411yescharacteristic
115C23×C13#12312yes—
116C23×C13C2×SD1611yescharacteristic
117C23×C13C2×Q1611yescharacteristic
118C23×C13AGL(1,ℤ/8)12yes—
119D4×C13—24no—
120D4×C13—24no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—42no—
126C2×C4×C13—41no—
127C2×C4×C13—42no—
128C2×C4×C13—41no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
131C2×C4×C13—81no—
132C2×C4×C13—81no—
133C2×C4×C13—82no—
134C2×C4×C13—82no—
135C2×C4×C13—82no—
136C2×C4×C13#10312yes—
137C2×C4×C13#11711yescharacteristic
138C2×C4×C13#11711yescharacteristic
139C2×C4×C13#12312yes—
140C2×Dic13—22no—
141C2×Dic13—41no—
142C2×Dic13—41no—
143C2×Dic13—41no—
144C2×Dic13—41no—
145C2×Dic13—41no—
146C2×Dic13—41no—
147C2×Dic13—41no—
148C2×Dic13—41no—
149C2×Dic13—41no—
150C2×Dic13—41no—
151C2×Dic13—41no—
152C2×Dic13—84no—
153C2×Dic13—84no—
154#1055—82no—
155C2×C4×D4—261no—
156C2×C4×D4C2×D1311yescharacteristic
157C2×#99—21no—
158C2×C22⋊C8—132no—
159#389—261no—
160#385—261no—
161#385—261no—
162#382—131no—
163#380—131no—
164#380—131no—
165#380C2×D1312yes—
166C4×C4⋊C4—131no—
167C2×#95—131no—
168C2×#95—131no—
169#342—21no—
170#324—261no—
171#323—261no—
172C22×C13—21no—
173C22×C13—22no—
174C22×C13—21no—
175C22×C13—22no—
176C22×C13—22no—
177C22×C13—42no—
178C22×C13—41no—
179C22×C13—41no—
180C22×C13—42no—
181C22×C13—42no—
182C22×C13—41no—
183C22×C13—41no—
184C22×C13#38111yescharacteristic
185C22×C13C2×#10311yescharacteristic
186C22×C13#41811yescharacteristic
187C22×C13#48112yes—
188C22×C13#48412yes—
189C4×C13—22no—
190C4×C13—22no—
191C4×C13—21no—
192C4×C13—21no—
193C4×C13—41no—
194C4×C13—41no—
195C4×C13—162no—
196Dic13—42no—
197Dic13—81no—
198Dic13—81no—
199Dic13—81no—
200C22×D4C22⋊D1311yescharacteristic
201C23×C4—261no—
202C23×C4—261no—
203C23×C4C4×D1311yescharacteristic
204C23×C4C22×D1311yescharacteristic
205C22×C8—262no—
206C4×D4—22no—
207C4×D4—22no—
208C4×D4—524no—
209C2×C4⋊C4—22no—
210C2×C4⋊C4—261no—
211C2×C4⋊C4—261no—
212C2×C4⋊C4—261no—
213C2×C4⋊C4—261no—
214C2×C4⋊C4D5211yescharacteristic
215C2×C22⋊C4—22no—
216C2×C22⋊C4—261no—
217C2×C22⋊C4—261no—
218C2×C22⋊C4D5211yescharacteristic
219C2×C22⋊C4C22⋊D1311yescharacteristic
220C2×C42—261no—
221C2×C42C4×D1311yescharacteristic
222#99—42no—
223C22⋊C8—262no—
224C22⋊C8—262no—
225#95—22no—
226#95—131no—
227#95—131no—
228#95—131no—
229#95—131no—
230#95—261no—
231#95—261no—
232#95—261no—
233C2×C13—21no—
234C2×C13—22no—
235C2×C13—21no—
236C2×C13—22no—
237C2×C13—42no—
238C2×C13#182411yescharacteristic
239C2×C13#182711yescharacteristic
240C2×C13#182811yescharacteristic
241C24#610311yescharacteristic
242C24C2×C22⋊D1311yescharacteristic
243C2×D4—22no—
244C2×D4—22no—
245C2×D4#610512yes—
246C2×D4#610712yes—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—42no—
250C22×C4—81no—
251C22×C4—81no—
252C22×C4—261no—
253C22×C4—261no—
254C22×C4—261no—
255C22×C4—261no—
256C22×C4—522no—
257C22×C4—522no—
258C22×C4—522no—
259C22×C4—522no—
260C22×C4—1041no—
261C22×C4—1041no—
262C22×C4#610311yescharacteristic
263C22×C4#610311yescharacteristic
264C22×C4#610311yescharacteristic
265C22×C4C2×C4×D1311yescharacteristic
266C22×C4C2×D5211yescharacteristic
267C22×C4#612912yes—
268C22×C4#612912yes—
269C2×C8—522no—
270C2×C8—1042no—
271C4⋊C4—22no—
272C4⋊C4—82no—
273C4⋊C4—522no—
274C4⋊C4—522no—
275C4⋊C4—1041no—
276C4⋊C4—1041no—
277C22⋊C4—22no—
278C22⋊C4—22no—
279C22⋊C4—42no—
280C22⋊C4—42no—
281C22⋊C4—522no—
282C22⋊C4—522no—
283C42—21no—
284C42—21no—
285C42—522no—
286C13#876111yescharacteristic, complemented, Sylow
287C23—21no—
288C23—21no—
289C23—41no—
290C23—41no—
291C23—41no—
292C23—41no—
293C23#8805012yes—
294C23C2×#610311yescharacteristic
295C23C2×#610511yescharacteristic
296C23#8818912yes—
297C23C2×#610711yescharacteristic
298C23#8820312yes—
299D4—24no—
300D4—24no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—42no—
306C2×C4—41no—
307C2×C4—42no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—81no—
312C2×C4—81no—
313C2×C4—82no—
314C2×C4—82no—
315C2×C4—82no—
316C2×C4—262no—
317C2×C4—521no—
318C2×C4—521no—
319C2×C4—521no—
320C2×C4—521no—
321C2×C4—521no—
322C2×C4—521no—
323C2×C4—521no—
324C2×C4—521no—
325C2×C4—521no—
326C2×C4—521no—
327C2×C4—521no—
328C2×C4—1044no—
329C2×C4—1044no—
330C2×C4#8805012yes—
331C2×C4#8813111yescharacteristic
332C2×C4#8813111yescharacteristic
333C2×C4#8814012yes—
334C8—1042no—
335C22—21no—
336C22—22no—
337C22—21no—
338C22—22no—
339C22—22no—
340C22—42no—
341C22—41no—
342C22—41no—
343C22—42no—
344C22—42no—
345C22—41no—
346C22—41no—
347C22#1171860411yescharacteristic
348C22C2×#8805011yescharacteristic
349C22#1171866211yescharacteristic
350C22#1171869512yes—
351C22#1171870512yes—
352C4—22no—
353C4—22no—
354C4—21no—
355C4—21no—
356C4—41no—
357C4—41no—
358C4—162no—
359C4—522no—
360C4—1041no—
361C4—1041no—
362C4—1041no—
363C2—22no—
364C2—21no—
365C2—21no—
366C2—22no—
367C2—42no—
368C2#1311492411yescharacteristic
369C2#1311493711yescharacteristic
370C2#1311494211yescharacteristic
subgroupG/H
centerC22#11718604
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#1799C2
socleC22×C13#381
prime radicalC22×D4×C13D4
cosocleC23×C4×C13C23
hypercenter#1799D13
hypocenterC13#8761
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1799

Complements

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

NH ≅ G/Ntype
3. #13112714C2semidirect
4. #13112703C2semidirect
10. #11718873C4semidirect
12. C2×#88071C4semidirect
18. #11718597C4semidirect
19. C4×C4⋊Dic13C4semidirect
286. C13#8761semidirect

Maximal subgroups

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

subgroupindex
#131177462
#131131542
#131127142
#131127032
C13×#17992
#876113