Finite Group Databasebeta

← #15834895

Subgroups — #15834895

Order 3328.

612 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125396C211yesmaximal, characteristic
2#13123938C211yesmaximal, characteristic, complemented
3#13123902C211yesmaximal, characteristic
4#13113723C212yesmaximal, complemented
5#13113711C212yesmaximal, complemented
6#13113696C212yesmaximal, complemented
7#13113633C212yesmaximal, complemented
8#13113582C211yesmaximal, characteristic, complemented
9#13113254C211yesmaximal, characteristic
10M16×#1055C211yesmaximal, characteristic, complemented
11C13×#1485C211yesmaximal, characteristic, complemented
12C13×#533C2211yescharacteristic
13#11719182C2211yescharacteristic
14C13×#431C2211yescharacteristic
15C4×C13×M16C2211yescharacteristic
16#11718749C411yescharacteristic
17#11718746C411yescharacteristic
18#11718742C411yescharacteristic
19#11718740C411yescharacteristic
20#11718709C412yes—
21#11718709C412yes—
22C4×#6106C2212yes—
23C4×#6106C2212yes—
24#11718685—21no—
25#11718685C2212yes—
26Q8×#1055—21no—
27Q8×#1055C2212yes—
28#11718661—22no—
29#11718586C2211yescharacteristic
30#11718586C2211yescharacteristic
31C2×C4×#1055C2211yescharacteristic
32#11718499C2212yes—
33#11718495C2212yes—
34#11718388—22no—
35#11718349—21no—
36C8×D52—21no—
37C13×Q8⋊C8C2212yes—
38C13×Q8⋊C8C2212yes—
39#11718072C2211yescharacteristic
40#11718072C2211yescharacteristic
41#11718071C2211yescharacteristic
42#11718071C2211yescharacteristic
43#11718051C2212yes—
44#11718051C2212yes—
45#11718047C2212yes—
46C8×#1055C2212yes—
47C2×#6127—21no—
48C2×C13×M16—21no—
49C13×C4⋊Q8C2×C411yescharacteristic
50C13×C4⋊Q8C2×C411yescharacteristic
51C13×#125—21no—
52C13×C22⋊Q8—21no—
53C13×C22⋊Q8C2×C412yes—
54C4×Q8×C13—21no—
55C4×Q8×C13C2312yes—
56C13×#117—21no—
57C2×C42×C13C2311yescharacteristic
58C2×#6106C2×C412yes—
59C2×#6106C2×C412yes—
60#88184—21no—
61#88184C2×C412yes—
62C22×#1055C2×C411yescharacteristic
63C22×#1055C2×C411yescharacteristic
64C2×#6094—22no—
65C2×C8×D13—22no—
66#88129—21no—
67#88128C2×C411yescharacteristic
68C4×D52—21no—
69C4×D52C2312yes—
70#88123C2×C411yescharacteristic
71C13×C4⋊C8C2311yescharacteristic
72C13×C4⋊C8C2311yescharacteristic
73C13×C22⋊C8—21no—
74C13×#97—21no—
75C4×C8×C13—21no—
76C4×C8×C13C2312yes—
77#88075C2×C412yes—
78#88075C2×C412yes—
79C22⋊#1055—21no—
80C22⋊#1055D412yes—
81#88060—22no—
82#88060—22no—
83#88049C2×C412yes—
84#88049C2×C412yes—
85#88048C2×C412yes—
86#88048C2×C412yes—
87C4⋊#1055—22no—
88C4⋊#1055—22no—
89C4⋊#1055D411yescharacteristic
90C4⋊#1055D411yescharacteristic
91C4⋊#1055C2311yescharacteristic
92C4⋊#1055C2311yescharacteristic
93#88043—22no—
94C4×#1055—21no—
95C4×#1055—22no—
96C4×#1055C2×C411yescharacteristic
97C4×#1055C2×C411yescharacteristic
98C4×#1055C2311yescharacteristic
99C4×#1055C2311yescharacteristic
100C4×#1055C2312yes—
101#18085—131nomaximal, Sylow
102C2×Q8×C13—21no—
103C2×Q8×C13C22×C412yes—
104C22×C4×C13C22×C411yescharacteristic
105C22×C4×C13C2×D411yescharacteristic
106C22×C4×C13#4111yescharacteristic
107C2×C22⋊D13—22no—
108#6127—81no—
109#6127—81no—
110C2×D52—21no—
111C2×D52—21no—
112C2×D52C22×C412yes—
113C2×C4×D13—22no—
114C2×Dic26—21no—
115C13×M16—24no—
116C2×C8×C13—22no—
117C2×C8×C13—21no—
118C2×C8×C13—21no—
119C13×C4⋊C4—21no—
120C13×C4⋊C4—21no—
121C13×C4⋊C4—21no—
122C13×C4⋊C4—22no—
123C13×C4⋊C4—22no—
124C13×C4⋊C4C22×C412yes—
125C13×C22⋊C4—22no—
126C42×C13—22no—
127C42×C13C22×C411yescharacteristic
128C42×C13C2×D411yescharacteristic
129C42×C13#4111yescharacteristic
130C42×C13C2411yescharacteristic
131#6106—24no—
132#6106—42no—
133#6103—22no—
134#6103—22no—
135C4⋊Dic13—21no—
136C4⋊Dic13C22×C412yes—
137C2×#1055—22no—
138C2×#1055—21no—
139C2×#1055—21no—
140C2×#1055—41no—
141C2×#1055C22×C411yescharacteristic
142C2×#1055C22×C411yescharacteristic
143C2×#1055C22×C411yescharacteristic
144C2×#1055C22×C411yescharacteristic
145C2×#1055C2×D412yes—
146C2×#1055C2×D412yes—
147#6094—82no—
148C8×D13—82no—
149#3167—131no—
150#2986—131no—
151#2979—131no—
152#1590—132no—
153#1588—132no—
154#1585—132no—
155C8×SD16—132no—
156#1564—131no—
157#1485D1311yescharacteristic, complemented
158#1484—131no—
159C8×M16—131no—
160C23×C13C4×D411yescharacteristic
161C22×D13—22no—
162Q8×C13—22no—
163Q8×C13—22no—
164Q8×C13—42no—
165C2×C4×C13—21no—
166C2×C4×C13—21no—
167C2×C4×C13—21no—
168C2×C4×C13—21no—
169C2×C4×C13—22no—
170C2×C4×C13—22no—
171C2×C4×C13—22no—
172C2×C4×C13C4×D411yescharacteristic
173C2×C4×C13C4×D411yescharacteristic
174C2×C4×C13C4×D411yescharacteristic
175C2×C4×C13C23×C411yescharacteristic
176C2×C4×C13C22×D411yescharacteristic
177C2×C4×C13C2×#4111yescharacteristic
178C22⋊D13—82no—
179C2×Dic13—22no—
180D52—22no—
181D52—22no—
182D52—42no—
183D52—81no—
184C4×D13—42no—
185C4×D13—42no—
186Dic26—81no—
187C8×C13—24no—
188C8×C13—41no—
189C8×C13—41no—
190#1055—21no—
191#1055—21no—
192#1055—21no—
193#1055—22no—
194#1055—22no—
195#1055—41no—
196#1055—41no—
197#1055#13112yes—
198#533C2×D1311yescharacteristic
199#532—131no—
200#498—131no—
201#492—131no—
202#487—131no—
203#486—131no—
204#465—132no—
205#465—132no—
206#446—132no—
207#446—261no—
208C8×Q8—132no—
209C8×Q8—261no—
210C4×SD16—132no—
211C4×SD16—132no—
212#436—132no—
213#436—261no—
214C8×D4—132no—
215C8×D4—261no—
216#433—262no—
217#431—131no—
218#431—131no—
219#431C2×D1311yescharacteristic
220#408—262no—
221C4×M16C2×D1311yescharacteristic
222C2×C4×C8—131no—
223#335—131no—
224#335—131no—
225#334—131no—
226#334—131no—
227Q8⋊C8C2×D1312yes—
228Q8⋊C8C2×D1312yes—
229D4⋊C8—132no—
230D4⋊C8—132no—
231#322—132no—
232C82—132no—
233C22×C13—21no—
234C22×C13—21no—
235C22×C13—21no—
236C22×C13C2×C4×D411yescharacteristic
237C2×D13—42no—
238C2×D13—42no—
239C2×D13—42no—
240C4×C13—21no—
241C4×C13—21no—
242C4×C13—21no—
243C4×C13—42no—
244C4×C13—42no—
245C4×C13#44312yes—
246C4×C13C2×#13111yescharacteristic
247C4×C13#56811yescharacteristic
248C4×C13#57711yescharacteristic
249C4×C13#57711yescharacteristic
250Dic13—42no—
251C2×#41—261no—
252C2×SD16—132no—
253C2×SD16—132no—
254C2×M16—21no—
255C2×M16—262no—
256C22×C8—131no—
257C22×C8—131no—
258C22×C8—262no—
259C4⋊Q8—131no—
260C4⋊Q8C4×D1311yescharacteristic
261C4⋊Q8C4×D1311yescharacteristic
262#127—131no—
263#125—21no—
264#124—261no—
265C22⋊Q8—21no—
266C22⋊Q8C4×D1312yes—
267#121—132no—
268#121—261no—
269C4×Q8—21no—
270C4×Q8C22×D1312yes—
271C4×D4—132no—
272C4×D4—261no—
273#117—21no—
274C2×C42C22×D1311yescharacteristic
275#106—132no—
276#106—132no—
277C4⋊C8—131no—
278C4⋊C8—131no—
279C4⋊C8—131no—
280C4⋊C8—131no—
281C4⋊C8—262no—
282C4⋊C8—262no—
283C4⋊C8C22×D1311yescharacteristic
284C4⋊C8C22×D1311yescharacteristic
285#103—132no—
286#103—132no—
287#102—132no—
288#102—132no—
289C22⋊C8—21no—
290C22⋊C8—132no—
291C22⋊C8—262no—
292C22⋊C8—262no—
293C22⋊C8—261no—
294#97—21no—
295#97—262no—
296C4×C8—21no—
297C4×C8—131no—
298C4×C8—131no—
299C4×C8—131no—
300C4×C8—132no—
301C4×C8—131no—
302C4×C8—262no—
303C4×C8—261no—
304C4×C8C22×D1312yes—
305C2×C13—41no—
306C2×C13#293511yescharacteristic
307C2×C13#294911yescharacteristic
308C2×C13C2×#44311yescharacteristic
309D13—82no—
310#41—1041no—
311#41—1041no—
312C2×Q8—21no—
313C2×Q8—261no—
314C2×Q8C2×C4×D1312yes—
315C2×D4—132no—
316C2×D4—262no—
317C2×D4—261no—
318C2×D4—261no—
319C22×C4—262no—
320C22×C4C2×C4×D1311yescharacteristic
321C22×C4D4×D1311yescharacteristic
322C22×C4#612911yescharacteristic
323SD16—264no—
324SD16—522no—
325M16—24no—
326M16—1042no—
327C2×C8—22no—
328C2×C8—21no—
329C2×C8—21no—
330C2×C8—131no—
331C2×C8—131no—
332C2×C8—131no—
333C2×C8—131no—
334C2×C8—132no—
335C2×C8—132no—
336C2×C8—262no—
337C2×C8—261no—
338C2×C8—261no—
339C2×C8—521no—
340C2×C8—1042no—
341C4⋊C4—21no—
342C4⋊C4—21no—
343C4⋊C4—21no—
344C4⋊C4—22no—
345C4⋊C4—22no—
346C4⋊C4—132no—
347C4⋊C4—261no—
348C4⋊C4C2×C4×D1312yes—
349C22⋊C4—22no—
350C22⋊C4—262no—
351C22⋊C4—262no—
352C42—22no—
353C42C2×C4×D1311yescharacteristic
354C42D4×D1311yescharacteristic
355C42#612911yescharacteristic
356C42C23×D1311yescharacteristic
357C13#1808511yescharacteristic, complemented, Sylow
358C23—262no—
359C23#8813511yescharacteristic
360Q8—22no—
361Q8—22no—
362Q8—42no—
363Q8—1041no—
364D4—262no—
365D4—262no—
366D4—522no—
367D4—1041no—
368D4—1042no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—22no—
374C2×C4—22no—
375C2×C4—22no—
376C2×C4—262no—
377C2×C4—522no—
378C2×C4—522no—
379C2×C4#8813511yescharacteristic
380C2×C4#8813511yescharacteristic
381C2×C4#8813511yescharacteristic
382C2×C4C22×C4×D1311yescharacteristic
383C2×C4C2×D4×D1311yescharacteristic
384C2×C4C2×#612911yescharacteristic
385C8—24no—
386C8—41no—
387C8—41no—
388C8—132no—
389C8—261no—
390C8—261no—
391C8—261no—
392C8—262no—
393C8—262no—
394C8—521no—
395C8—521no—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—522no—
400C22—522no—
401C22—522no—
402C22C2×#8813511yescharacteristic
403C4—21no—
404C4—21no—
405C4—21no—
406C4—42no—
407C4—42no—
408C4—522no—
409C4#1171848512yes—
410C4D13×#13111yescharacteristic
411C4#1171945511yescharacteristic
412C4#1171948311yescharacteristic
413C4#1171948311yescharacteristic
414C2—41no—
415C2—1042no—
416C2#1312357611yescharacteristic
417C2#1312369111yescharacteristic
418C2C2×#1171848511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1485C2
socleC22×C13C2×C4×D4
prime radical#11719182C22
cosocleC42×C13C24
hypercenter#1485D13
hypocenterC13#18085
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1485

Complements

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

NH ≅ G/Ntype
2. #13123938C2semidirect
4. #13113723C2semidirect
5. #13113711C2semidirect
6. #13113696C2semidirect
7. #13113633C2semidirect
8. #13113582C2semidirect
10. M16×#1055C2semidirect
11. C13×#1485C2semidirect
157. #1485D13semidirect
357. C13#18085semidirect

Maximal subgroups

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

subgroupindex
#131253962
#131239382
#131239022
#131137232
#131137112
#131136962
#131136332
#131135822
#131132542
M16×#10552
C13×#14852
#1808513