Finite Group Databasebeta

← #15751491

Subgroups — #15751491

Order 3328.

500 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 97 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#13123185C211yesmaximal, characteristic
2#13114903C211yesmaximal, characteristic
3#13114597C211yesmaximal, characteristic
4#13112662C211yesmaximal, characteristic, complemented
5#13112661C211yesmaximal, characteristic, complemented
6#13112661C211yesmaximal, characteristic, complemented
7C13×#1272C211yesmaximal, characteristic, complemented
8C2×#88200C411yescharacteristic
9C2×#88198C411yescharacteristic
10C2×#88151C411yescharacteristic
11C2×C42×D13C2211yescharacteristic
12C13×#391C2211yescharacteristic
13C2×#88060—21no—
14C2×#88060—21no—
15C2×#88055—21no—
16#11718637C411yescharacteristic
17#11718590C2211yescharacteristic
18#11718328—21no—
19#11718328—21no—
20#11718308—21no—
21#11718308—21no—
22C13×#336C2211yescharacteristic
23C13×#336C2211yescharacteristic
24#11718142—21no—
25#11718116C2211yescharacteristic
26#11718116C2211yescharacteristic
27C22×Q8×C13C2×C411yescharacteristic
28C22×C4×D13C2×C411yescharacteristic
29C22×C4×D13D411yescharacteristic
30C22×C4×D13D411yescharacteristic
31C22×Dic26C2×C411yescharacteristic
32C22×C8×C13—21no—
33C22×C8×C13—21no—
34C2×C13×C4⋊C4C2×C411yescharacteristic
35C2×C42×C13C2311yescharacteristic
36#88200—42no—
37#88198—42no—
38C2×#6103—21no—
39C2×#6103—21no—
40C2×C4⋊Dic13—21no—
41C2×C4⋊Dic13C2×C411yescharacteristic
42C2×#6101—21no—
43C2×#6101—21no—
44C2×#6101—21no—
45C2×#6101—21no—
46C2×#6101—21no—
47C2×C4×Dic13C2×C411yescharacteristic
48C2×C4×Dic13D411yescharacteristic
49C2×C4×Dic13D411yescharacteristic
50C22×#1055—21no—
51C22×#1055—21no—
52#88151—42no—
53C42×D13—42no—
54C13×#95—21no—
55C13×#95—21no—
56#88071—21no—
57#88071—21no—
58#88060—24no—
59#88060—42no—
60#88055—42no—
61#7707—131nomaximal, Sylow
62C23×D13C22⋊C411yescharacteristic
63C2×Q8×C13—21no—
64C2×Q8×C13—21no—
65C2×Q8×C13—41no—
66C2×Q8×C13—41no—
67C22×C4×C13—21no—
68C22×C4×C13—21no—
69C22×C4×C13C22×C411yescharacteristic
70C22×C4×C13C2×D411yescharacteristic
71C22×C4×C13C2×D411yescharacteristic
72C22×Dic13—21no—
73C22×Dic13—21no—
74C22×Dic13C22⋊C411yescharacteristic
75C22×Dic13C22⋊C411yescharacteristic
76C22×Dic13C22⋊C411yescharacteristic
77C2×C4×D13—22no—
78C2×C4×D13—21no—
79C2×C4×D13—21no—
80C2×C4×D13—21no—
81C2×C4×D13—21no—
82C2×C4×D13—21no—
83C2×C4×D13—21no—
84C2×C4×D13—22no—
85C2×C4×D13—22no—
86C2×C4×D13—41no—
87C2×C4×D13—41no—
88C2×C4×D13—41no—
89C2×Dic26—21no—
90C2×Dic26—21no—
91C2×Dic26—41no—
92C2×Dic26—41no—
93C2×C8×C13—22no—
94C2×C8×C13—41no—
95C2×C8×C13—41no—
96C2×C8×C13—41no—
97C2×C8×C13—41no—
98C2×C8×C13—41no—
99C13×C4⋊C4—41no—
100C42×C13—41no—
101#6103—42no—
102#6103—42no—
103C4⋊Dic13—42no—
104C4⋊Dic13—41no—
105#6101—42no—
106#6101—42no—
107#6101—42no—
108#6101—42no—
109#6101—42no—
110C4×Dic13—22no—
111C4×Dic13—22no—
112C4×Dic13—41no—
113C2×#1055—22no—
114C2×#1055—41no—
115C2×#1055—41no—
116C2×#1055—41no—
117C2×#1055—41no—
118C2×#1055—41no—
119#2857—131no—
120#1817—131no—
121#1749—131no—
122#1272—131no—
123#1272—131no—
124#1272—131no—
125#1272D1311yescharacteristic, complemented
126C23×C13C2×C22⋊C411yescharacteristic
127C22×D13—21no—
128C22×D13—21no—
129C22×D13—21no—
130C22×D13—21no—
131C22×D13—21no—
132C22×D13—21no—
133C22×D13#10012yes—
134Q8×C13—81no—
135Q8×C13—81no—
136C2×C4×C13—21no—
137C2×C4×C13—21no—
138C2×C4×C13—21no—
139C2×C4×C13—21no—
140C2×C4×C13—21no—
141C2×C4×C13—21no—
142C2×C4×C13—41no—
143C2×C4×C13—41no—
144C2×C4×C13—41no—
145C2×C4×C13—41no—
146C2×C4×C13—41no—
147C2×C4×C13—41no—
148C2×C4×C13#13111yescharacteristic
149C2×C4×C13#13111yescharacteristic
150C2×C4×C13#13711yescharacteristic
151C2×C4×C13#13711yescharacteristic
152C2×C4×C13#13711yescharacteristic
153C2×C4×C13#13711yescharacteristic
154C2×Dic13—21no—
155C2×Dic13—21no—
156C2×Dic13—21no—
157C2×Dic13—21no—
158C2×Dic13—21no—
159C2×Dic13—21no—
160C2×Dic13—21no—
161C2×Dic13—41no—
162C2×Dic13—41no—
163C2×Dic13—41no—
164C2×Dic13—41no—
165C2×Dic13—41no—
166C2×Dic13—41no—
167C2×Dic13#9912yes—
168C2×Dic13#10412yes—
169C4×D13—42no—
170C4×D13—42no—
171C4×D13—42no—
172C4×D13—42no—
173C4×D13—42no—
174C4×D13—42no—
175Dic26—81no—
176Dic26—81no—
177C8×C13—42no—
178C8×C13—81no—
179#1055—42no—
180#1055—81no—
181C2×C4⋊Q8—131no—
182C2×C22⋊Q8—131no—
183C2×C22⋊Q8—131no—
184C22×C42—131no—
185C2×C22⋊C8—261no—
186C2×C22⋊C8—261no—
187C2×#97—261no—
188#391—131no—
189#391C2×D1311yescharacteristic
190#389—261no—
191#389—261no—
192#384—131no—
193#380—261no—
194#380—261no—
195#336—131no—
196#336—131no—
197#336—261no—
198#336C2×D1311yescharacteristic
199#336C2×D1311yescharacteristic
200C22×C13#40811yescharacteristic
201C22×C13C2×#9911yescharacteristic
202C22×C13C2×#10011yescharacteristic
203C22×C13#41911yescharacteristic
204C22×C13#41911yescharacteristic
205C22×C13C2×#10411yescharacteristic
206C22×C13#42111yescharacteristic
207C2×D13—22no—
208C2×D13—22no—
209C2×D13—22no—
210C2×D13—41no—
211C2×D13—41no—
212C2×D13—41no—
213C2×D13—41no—
214C4×C13—21no—
215C4×C13—21no—
216C4×C13—21no—
217C4×C13—21no—
218C4×C13—21no—
219C4×C13—21no—
220C4×C13—81no—
221C4×C13—81no—
222Dic13—22no—
223Dic13—22no—
224Dic13—41no—
225Dic13—81no—
226Dic13—81no—
227C22×Q8—131no—
228C22×Q8C4×D1311yescharacteristic
229C23×C4—131no—
230C23×C4—131no—
231C23×C4—131no—
232C22×C8—21no—
233C22×C8—21no—
234C22×C8—261no—
235C22×C8—261no—
236C4⋊Q8—522no—
237C22⋊Q8—522no—
238C22⋊Q8—522no—
239C2×C4⋊C4—131no—
240C2×C4⋊C4—261no—
241C2×C4⋊C4—261no—
242C2×C4⋊C4—261no—
243C2×C4⋊C4—261no—
244C2×C4⋊C4—261no—
245C2×C4⋊C4—261no—
246C2×C4⋊C4C4×D1311yescharacteristic
247C2×C22⋊C4—261no—
248C2×C22⋊C4—261no—
249C2×C42—131no—
250C2×C42—131no—
251C2×C42—131no—
252C2×C42—522no—
253C2×C42C22×D1311yescharacteristic
254C22⋊C8—264no—
255C22⋊C8—522no—
256#97—522no—
257#95—21no—
258#95—21no—
259#95—261no—
260#95—261no—
261C2×C13#147111yescharacteristic
262C2×C13#148511yescharacteristic
263C2×C13#149711yescharacteristic
264C2×C13#150811yescharacteristic
265C2×C13#151111yescharacteristic
266C2×C13#153011yescharacteristic
267C2×C13#155811yescharacteristic
268D13—42no—
269C24—131no—
270C2×Q8—21no—
271C2×Q8—21no—
272C2×Q8—41no—
273C2×Q8—41no—
274C2×Q8—261no—
275C2×Q8—261no—
276C2×Q8—521no—
277C2×Q8—521no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—131no—
281C22×C4—131no—
282C22×C4—131no—
283C22×C4—262no—
284C22×C4—262no—
285C22×C4—262no—
286C22×C4—261no—
287C22×C4—261no—
288C22×C4—261no—
289C22×C4—261no—
290C22×C4—261no—
291C22×C4—261no—
292C22×C4—261no—
293C22×C4—261no—
294C22×C4—521no—
295C22×C4—521no—
296C22×C4—521no—
297C22×C4C2×C4×D1311yescharacteristic
298C22×C4D4×D1311yescharacteristic
299C22×C4D4×D1311yescharacteristic
300C2×C8—22no—
301C2×C8—41no—
302C2×C8—41no—
303C2×C8—41no—
304C2×C8—41no—
305C2×C8—41no—
306C2×C8—262no—
307C2×C8—521no—
308C2×C8—521no—
309C2×C8—521no—
310C2×C8—521no—
311C2×C8—521no—
312C4⋊C4—41no—
313C4⋊C4—521no—
314C4⋊C4—522no—
315C4⋊C4—522no—
316C4⋊C4—522no—
317C4⋊C4—522no—
318C4⋊C4—522no—
319C4⋊C4—522no—
320C22⋊C4—522no—
321C22⋊C4—522no—
322C42—41no—
323C42—262no—
324C42—262no—
325C42—521no—
326C13#770711yescharacteristic, complemented, Sylow
327C23—132no—
328C23—261no—
329C23—261no—
330C23—261no—
331C23—261no—
332C23—261no—
333C23—261no—
334C23C22⋊C4×D1311yescharacteristic
335Q8—81no—
336Q8—81no—
337Q8—1041no—
338Q8—1041no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—132no—
352C2×C4—132no—
353C2×C4—261no—
354C2×C4—261no—
355C2×C4—261no—
356C2×C4—261no—
357C2×C4—261no—
358C2×C4—261no—
359C2×C4—261no—
360C2×C4—522no—
361C2×C4—522no—
362C2×C4—522no—
363C2×C4—522no—
364C2×C4—522no—
365C2×C4—522no—
366C2×C4—521no—
367C2×C4—521no—
368C2×C4—521no—
369C2×C4—521no—
370C2×C4—521no—
371C2×C4—521no—
372C2×C4#8815511yescharacteristic
373C2×C4#8816111yescharacteristic
374C2×C4#8816911yescharacteristic
375C2×C4#8816911yescharacteristic
376C2×C4#8817211yescharacteristic
377C2×C4#8817211yescharacteristic
378C8—42no—
379C8—81no—
380C8—522no—
381C8—1041no—
382C22—262no—
383C22—262no—
384C22—262no—
385C22—521no—
386C22—521no—
387C22—521no—
388C22—521no—
389C22#1171838811yescharacteristic
390C22D13×#9911yescharacteristic
391C22D13×#10011yescharacteristic
392C22#1171846311yescharacteristic
393C22#1171846311yescharacteristic
394C22D13×#10411yescharacteristic
395C22#1171848211yescharacteristic
396C4—21no—
397C4—21no—
398C4—21no—
399C4—21no—
400C4—21no—
401C4—21no—
402C4—81no—
403C4—81no—
404C4—262no—
405C4—262no—
406C4—521no—
407C4—1041no—
408C4—1041no—
409C2—522no—
410C2#1311319411yescharacteristic
411C2#1311325511yescharacteristic
412C2#1311330711yescharacteristic
413C2#1311335411yescharacteristic
414C2#1311336711yescharacteristic
415C2#1311344511yescharacteristic
416C2#1311356011yescharacteristic
subgroupG/H
centerC23C22⋊C4×D13
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1272C2
socleC23×C13C2×C22⋊C4
prime radicalC23×D13C22⋊C4
cosocleC2×C42×C13C23
hypercenter#1272D13
hypocenterC13#7707
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
4. #13112662C2semidirect
5. #13112661C2semidirect
6. #13112661C2semidirect
7. C13×#1272C2semidirect
125. #1272D13semidirect
326. C13#7707semidirect

Maximal subgroups

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

subgroupindex
#131231852
#131149032
#131145972
#131126622
#131126612
C13×#12722
#770713