Finite Group Databasebeta

← #15751174

Subgroups — #15751174

Order 3328.

556 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 556 conjugacy classes of subgroups — too many to draw. Only its 103 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#13117374C211yesmaximal, characteristic
2#13114597C211yesmaximal, characteristic
3#13114528C211yesmaximal, characteristic
4#13112662C211yesmaximal, characteristic, complemented
5#13112660C211yesmaximal, characteristic, complemented
6#13112658C211yesmaximal, characteristic, complemented
7C13×#1272C211yesmaximal, characteristic, complemented
8C2×#88200C411yescharacteristic
9C2×Q8×Dic13C411yescharacteristic
10C22×#6094—21no—
11C2×C42×D13C2211yescharacteristic
12C13×#391C2211yescharacteristic
13C2×#88060—21no—
14C2×#88055—21no—
15#11718648C411yescharacteristic
16C4⋊C4×Dic13C411yescharacteristic
17#11718589C2211yescharacteristic
18#11718329—21no—
19#11718327—21no—
20#11718316—21no—
21#11718310—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×C8×C13—21no—
32C22×C8×C13—21no—
33C2×C13×C4⋊C4C2×C411yescharacteristic
34C2×C42×C13C2311yescharacteristic
35#88200—22no—
36#88200—22no—
37Q8×Dic13—42no—
38C2×#6103—21no—
39C2×#6103—21no—
40C2×C4⋊Dic13—21no—
41C2×C4⋊Dic13C2×C411yescharacteristic
42C2×C4⋊Dic13C2×C411yescharacteristic
43C2×#6101—21no—
44C2×#6101—21no—
45C2×C4×Dic13—21no—
46C2×C4×Dic13—21no—
47C2×C4×Dic13C2×C411yescharacteristic
48C2×C4×Dic13D411yescharacteristic
49C2×C4×Dic13D411yescharacteristic
50C22×#1055—21no—
51C22×#1055—21no—
52C2×#6094—24no—
53C2×#6094—42no—
54C2×#6094—42no—
55C42×D13—42no—
56C13×#95—21no—
57C13×#95—21no—
58#88071—21no—
59#88071—21no—
60#88071—21no—
61#88060—24no—
62#88055—42no—
63#7634—131nomaximal, Sylow
64C23×D13C22⋊C411yescharacteristic
65C2×Q8×C13—21no—
66C2×Q8×C13—41no—
67C2×Q8×C13—41no—
68C2×Q8×C13M1612yescomplemented
69C22×C4×C13—21no—
70C22×C4×C13—21no—
71C22×C4×C13C22×C411yescharacteristic
72C22×C4×C13C2×D411yescharacteristic
73C22×C4×C13C2×D411yescharacteristic
74C22×Dic13—21no—
75C22×Dic13—21no—
76C22×Dic13C22⋊C411yescharacteristic
77C22×Dic13C22⋊C411yescharacteristic
78C22×Dic13C22⋊C411yescharacteristic
79C2×C4×D13—22no—
80C2×C4×D13—21no—
81C2×C4×D13—21no—
82C2×C4×D13—22no—
83C2×C4×D13—21no—
84C2×C4×D13—21no—
85C2×C4×D13—21no—
86C2×C4×D13—21no—
87C2×C4×D13—22no—
88C2×C4×D13—41no—
89C2×C4×D13—41no—
90C2×C4×D13—41no—
91C2×C8×C13—22no—
92C2×C8×C13—22no—
93C2×C8×C13—41no—
94C2×C8×C13—41no—
95C2×C8×C13—41no—
96C2×C8×C13—41no—
97C13×C4⋊C4—41no—
98C42×C13—41no—
99#6103—24no—
100#6103—42no—
101C4⋊Dic13—21no—
102C4⋊Dic13—42no—
103C4⋊Dic13—41no—
104C4⋊Dic13M1612yescomplemented
105#6101—24no—
106#6101—41no—
107#6101—41no—
108C4×Dic13—22no—
109C4×Dic13—22no—
110C4×Dic13—41no—
111C4×Dic13—42no—
112C4×Dic13—42no—
113C2×#1055—22no—
114C2×#1055—22no—
115C2×#1055—41no—
116C2×#1055—41no—
117C2×#1055—41no—
118C2×#1055—41no—
119#6094—48no—
120C4×C22⋊Q8—131no—
121#1749—131no—
122#1728—131no—
123#1272—131no—
124#1272D1311yescharacteristic, complemented
125#1271—131no—
126#1271—131no—
127C23×C13C2×C22⋊C411yescharacteristic
128C22×D13—21no—
129C22×D13—21no—
130C22×D13—21no—
131C22×D13—21no—
132C22×D13—21no—
133C22×D13—21no—
134C22×D13#10412yes—
135Q8×C13—42no—
136Q8×C13—42no—
137C2×C4×C13—21no—
138C2×C4×C13—21no—
139C2×C4×C13—21no—
140C2×C4×C13—21no—
141C2×C4×C13—21no—
142C2×C4×C13—21no—
143C2×C4×C13—22no—
144C2×C4×C13—41no—
145C2×C4×C13—41no—
146C2×C4×C13—41no—
147C2×C4×C13—41no—
148C2×C4×C13—41no—
149C2×C4×C13C2×M1611yescharacteristic
150C2×C4×C13C2×M1611yescharacteristic
151C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
152C2×C4×C13#13711yescharacteristic
153C2×C4×C13#13711yescharacteristic
154C2×C4×C13#13711yescharacteristic
155C2×Dic13—21no—
156C2×Dic13—21no—
157C2×Dic13—21no—
158C2×Dic13—21no—
159C2×Dic13—21no—
160C2×Dic13—22no—
161C2×Dic13—21no—
162C2×Dic13—21no—
163C2×Dic13—41no—
164C2×Dic13—41no—
165C2×Dic13—41no—
166C2×Dic13—41no—
167C2×Dic13—41no—
168C2×Dic13#9912yes—
169C2×Dic13#10412yes—
170C4×D13—24no—
171C4×D13—24no—
172C4×D13—42no—
173C4×D13—42no—
174C4×D13—42no—
175C4×D13—42no—
176C8×C13—42no—
177C8×C13—42no—
178#1055—42no—
179#1055—42no—
180C22×M16—261no—
181C2×C22⋊Q8—131no—
182C2×C4×Q8—131no—
183C22×C42—131no—
184C2×C22⋊C8—261no—
185C2×#97—261no—
186#391C2×D1311yescharacteristic
187#389—131no—
188#387—261no—
189#385—261no—
190#380—131no—
191C4×C4⋊C4—131no—
192C4×C4⋊C4—261no—
193C4×C22⋊C4—261no—
194#336—131no—
195#336—131no—
196#336—261no—
197#336C2×D1311yescharacteristic
198#336C2×D1311yescharacteristic
199C22×C13#40711yescharacteristic
200C22×C13C2×#9911yescharacteristic
201C22×C13#41311yescharacteristic
202C22×C13#41711yescharacteristic
203C22×C13#41911yescharacteristic
204C22×C13C2×#10411yescharacteristic
205C22×C13C2×#10411yescharacteristic
206C2×D13—22no—
207C2×D13—22no—
208C2×D13—22no—
209C2×D13—41no—
210C2×D13—41no—
211C2×D13—41no—
212C2×D13—41no—
213C4×C13—21no—
214C4×C13—21no—
215C4×C13—21no—
216C4×C13—21no—
217C4×C13—21no—
218C4×C13—21no—
219C4×C13—42no—
220C4×C13—81no—
221Dic13—22no—
222Dic13—22no—
223Dic13—41no—
224Dic13—42no—
225Dic13—81no—
226C22×Q8C4×D1311yescharacteristic
227C23×C4—131no—
228C23×C4—131no—
229C23×C4—131no—
230C2×M16—264no—
231C2×M16—522no—
232C2×M16—522no—
233C22×C8—21no—
234C22×C8—21no—
235C22×C8—261no—
236C22×C8—261no—
237C22⋊Q8—262no—
238C22⋊Q8—262no—
239C4×Q8—522no—
240C2×C4⋊C4—131no—
241C2×C4⋊C4—131no—
242C2×C4⋊C4—261no—
243C2×C4⋊C4—261no—
244C2×C4⋊C4—261no—
245C2×C4⋊C4C4×D1311yescharacteristic
246C2×C22⋊C4—261no—
247C2×C22⋊C4—261no—
248C2×C42—131no—
249C2×C42—131no—
250C2×C42—131no—
251C2×C42—261no—
252C2×C42—261no—
253C2×C42—522no—
254C2×C42C22×D1311yescharacteristic
255C22⋊C8—264no—
256#97—522no—
257#95—21no—
258#95—21no—
259#95—261no—
260#95—261no—
261#95—261no—
262C2×C13#146511yescharacteristic
263C2×C13#148911yescharacteristic
264C2×C13#149111yescharacteristic
265C2×C13#150411yescharacteristic
266C2×C13#150811yescharacteristic
267C2×C13#152411yescharacteristic
268C2×C13#155911yescharacteristic
269D13—42no—
270C24—131no—
271C2×Q8—21no—
272C2×Q8—41no—
273C2×Q8—41no—
274C2×Q8#609412yescomplemented
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—131no—
278C22×C4—131no—
279C22×C4—131no—
280C22×C4—262no—
281C22×C4—262no—
282C22×C4—262no—
283C22×C4—261no—
284C22×C4—261no—
285C22×C4—261no—
286C22×C4—261no—
287C22×C4—261no—
288C22×C4—261no—
289C22×C4—261no—
290C22×C4—261no—
291C22×C4—521no—
292C22×C4—521no—
293C22×C4—521no—
294C22×C4C2×C4×D1311yescharacteristic
295C22×C4D4×D1311yescharacteristic
296C22×C4D4×D1311yescharacteristic
297M16—528no—
298C2×C8—22no—
299C2×C8—22no—
300C2×C8—41no—
301C2×C8—41no—
302C2×C8—41no—
303C2×C8—41no—
304C2×C8—262no—
305C2×C8—262no—
306C2×C8—521no—
307C2×C8—521no—
308C2×C8—521no—
309C2×C8—521no—
310C4⋊C4—41no—
311C4⋊C4—132no—
312C4⋊C4—264no—
313C4⋊C4—261no—
314C4⋊C4—521no—
315C4⋊C4—522no—
316C4⋊C4—521no—
317C4⋊C4—521no—
318C22⋊C4—264no—
319C22⋊C4—522no—
320C42—41no—
321C42—262no—
322C42—262no—
323C42—521no—
324C42—522no—
325C42—522no—
326C13#763411yescharacteristic, complemented, Sylow
327C23—132no—
328C23—261no—
329C23—261no—
330C23—261no—
331C23—261no—
332C23—261no—
333C23—261no—
334C23C22⋊C4×D1311yescharacteristic
335Q8—42no—
336Q8—42no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—22no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—132no—
350C2×C4—132no—
351C2×C4—264no—
352C2×C4—264no—
353C2×C4—261no—
354C2×C4—261no—
355C2×C4—261no—
356C2×C4—261no—
357C2×C4—261no—
358C2×C4—261no—
359C2×C4—262no—
360C2×C4—261no—
361C2×C4—522no—
362C2×C4—522no—
363C2×C4—522no—
364C2×C4—522no—
365C2×C4—521no—
366C2×C4—521no—
367C2×C4—521no—
368C2×C4—521no—
369C2×C4—521no—
370C2×C4C2×#609411yescharacteristic
371C2×C4M16×D1311yescharacteristic
372C2×C4#8816811yescharacteristic
373C2×C4#8816911yescharacteristic
374C2×C4#8817211yescharacteristic
375C2×C4#8817211yescharacteristic
376C8—42no—
377C8—42no—
378C8—522no—
379C8—522no—
380C22—262no—
381C22—262no—
382C22—262no—
383C22—521no—
384C22—521no—
385C22—521no—
386C22—521no—
387C22#1171838711yescharacteristic
388C22D13×#9911yescharacteristic
389C22#1171840611yescharacteristic
390C22#1171846311yescharacteristic
391C22#1171846411yescharacteristic
392C22D13×#10411yescharacteristic
393C22D13×#10411yescharacteristic
394C4—21no—
395C4—21no—
396C4—21no—
397C4—21no—
398C4—21no—
399C4—21no—
400C4—42no—
401C4—81no—
402C4—262no—
403C4—262no—
404C4—521no—
405C4—522no—
406C4—1041no—
407C2—522no—
408C2#1311317111yescharacteristic
409C2#1311327411yescharacteristic
410C2#1311328111yescharacteristic
411C2#1311333911yescharacteristic
412C2#1311335411yescharacteristic
413C2#1311342111yescharacteristic
414C2#1311356311yescharacteristic
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#7634
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. #13112660C2semidirect
6. #13112658C2semidirect
7. C13×#1272C2semidirect
68. C2×Q8×C13M16semidirect
104. C4⋊Dic13M16semidirect
124. #1272D13semidirect
274. C2×Q8#6094semidirect
326. C13#7634semidirect

Maximal subgroups

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

subgroupindex
#131173742
#131145972
#131145282
#131126622
#131126602
#131126582
C13×#12722
#763413