Finite Group Databasebeta

← #15833573

Subgroups — #15833573

Order 3328.

640 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125411C211yesmaximal, characteristic
2#13123914C211yesmaximal, characteristic, complemented
3#13123912C211yesmaximal, characteristic, complemented
4#13113747C212yesmaximal, complemented
5#13113718C212yesmaximal, complemented
6#13113657C212yesmaximal, complemented
7#13113628C212yesmaximal, complemented
8#13113597C211yesmaximal, characteristic, complemented
9#13113306C211yesmaximal, characteristic, complemented
10#13113120C211yesmaximal, characteristic, complemented
11C13×#1496C211yesmaximal, characteristic, complemented
12C13×#532C2211yescharacteristic
13#11719182C2211yescharacteristic
14C13×#432C2211yescharacteristic
15C13×#431C2211yescharacteristic
16#11718895—22no—
17#11718749C411yescharacteristic
18#11718739C411yescharacteristic
19#11718734C411yescharacteristic
20#11718731C411yescharacteristic
21#11718699C412yes—
22#11718699C412yes—
23C4×#6104C2212yes—
24C4×#6104C2212yes—
25#11718673C2212yes—
26#11718672—22no—
27D4×#1055C2212yes—
28#11718587C2211yescharacteristic
29#11718586C2211yescharacteristic
30C2×C4×#1055C2211yescharacteristic
31#11718499C2212yes—
32#11718495C2212yes—
33#11718388—22no—
34#11718367—22no—
35C13×D4⋊C8C2212yes—
36C13×D4⋊C8C2212yes—
37#11718072C2212yes—
38#11718071C2212yes—
39#11718051C2212yes—
40#11718051C2212yes—
41#11718046C2211yescharacteristic
42#11718046C2211yescharacteristic
43C8×#1055C2211yescharacteristic
44C8×#1055C2211yescharacteristic
45C2×C13×#41—21no—
46C2×#6127—21no—
47C13×C4⋊Q8C2×C411yescharacteristic
48C13×#127C2×C411yescharacteristic
49C13×#124—21no—
50C13×#121—21no—
51C13×#121C2×C412yes—
52C4×D4×C13—21no—
53C4×D4×C13C2312yes—
54C2×C42×C13C2311yescharacteristic
55C2×#6104C2×C412yes—
56C2×#6104C2×C412yes—
57#88184—21no—
58#88184C2×C412yes—
59C2×#6099—22no—
60C22×#1055—22no—
61C22×#1055C2×C411yescharacteristic
62C22×#1055C2×C411yescharacteristic
63C2×#6094—22no—
64C2×C8×D13—22no—
65#88129—21no—
66#88128C2×C411yescharacteristic
67C4×D52—21no—
68C4×D52C2312yes—
69#88123C2×C411yescharacteristic
70C13×C4⋊C8—21no—
71C13×C4⋊C8C2312yes—
72C13×C22⋊C8—21no—
73C13×C22⋊C8—21no—
74C13×#97—21no—
75C4×C8×C13C2311yescharacteristic
76C4×C8×C13C2311yescharacteristic
77#88072C2×C412yes—
78#88072C2×C412yes—
79C22⋊#1055—21no—
80C22⋊#1055—22no—
81C22⋊#1055—22no—
82C22⋊#1055D412yes—
83#88060—22no—
84#88060—22no—
85#88049C2×C412yes—
86#88049C2×C412yes—
87#88047C2×C412yes—
88#88047C2×C412yes—
89C4⋊#1055D412yes—
90C4⋊#1055C2312yes—
91#88043—21no—
92C4×#1055C2×C411yescharacteristic
93C4×#1055C2×C411yescharacteristic
94C4×#1055C2311yescharacteristic
95C4×#1055C2311yescharacteristic
96C4×#1055C2311yescharacteristic
97C4×#1055C2311yescharacteristic
98#17970—131nomaximal, Sylow
99C13×#41—82no—
100C2×Q8×C13—21no—
101C2×D4×C13—22no—
102C2×D4×C13—21no—
103C2×D4×C13—21no—
104C2×D4×C13C22×C412yes—
105C22×C4×C13—22no—
106C22×C4×C13C22×C411yescharacteristic
107C22×C4×C13C2×D411yescharacteristic
108C22×C4×C13#4111yescharacteristic
109C2×C22⋊D13—22no—
110#6127—82no—
111C2×D52—21no—
112C2×D52—21no—
113C2×D52C22×C412yes—
114C2×C4×D13—22no—
115C2×Dic26—21no—
116C2×C8×C13—22no—
117C2×C8×C13—21no—
118C2×C8×C13—21no—
119C13×C4⋊C4—21no—
120C13×C4⋊C4C22×C412yes—
121C13×C22⋊C4—22no—
122C13×C22⋊C4—22no—
123C42×C13C22×C411yescharacteristic
124C42×C13C2×D411yescharacteristic
125C42×C13#4111yescharacteristic
126C42×C13C2411yescharacteristic
127#6104—24no—
128#6104—24no—
129#6103—22no—
130#6103—22no—
131C4⋊Dic13—21no—
132C4⋊Dic13C22×C412yes—
133#6099—82no—
134C2×#1055—22no—
135C2×#1055—22no—
136C2×#1055—22no—
137C2×#1055—82no—
138C2×#1055C22×C411yescharacteristic
139C2×#1055C22×C411yescharacteristic
140C2×#1055C22×C411yescharacteristic
141C2×#1055C22×C411yescharacteristic
142C2×#1055C2×D412yes—
143C2×#1055C2×D412yes—
144#6094—82no—
145C8×D13—82no—
146#3169—131no—
147#2981—131no—
148#2981—131no—
149#1594—132no—
150#1589—132no—
151#1580—132no—
152C8×D8—132no—
153#1568—131no—
154#1496—131no—
155#1496D1311yescharacteristic, complemented
156#1450—131no—
157C23×C13—22no—
158C23×C13C4×D411yescharacteristic
159C22×D13—22no—
160Q8×C13—81no—
161D4×C13—22no—
162D4×C13—22no—
163D4×C13—81no—
164D4×C13—81no—
165D4×C13—82no—
166C2×C4×C13—21no—
167C2×C4×C13—21no—
168C2×C4×C13—22no—
169C2×C4×C13—22no—
170C2×C4×C13—41no—
171C2×C4×C13—42no—
172C2×C4×C13—42no—
173C2×C4×C13C4×D411yescharacteristic
174C2×C4×C13C4×D411yescharacteristic
175C2×C4×C13C4×D411yescharacteristic
176C2×C4×C13C23×C411yescharacteristic
177C2×C4×C13C22×D411yescharacteristic
178C2×C4×C13C2×#4111yescharacteristic
179C22⋊D13—82no—
180C2×Dic13—22no—
181D52—22no—
182D52—22no—
183D52—81no—
184D52—81no—
185C4×D13—42no—
186C4×D13—42no—
187Dic26—81no—
188C8×C13—41no—
189C8×C13—41no—
190C8×C13—42no—
191#1055—21no—
192#1055—21no—
193#1055—22no—
194#1055—22no—
195#1055—42no—
196#1055#13112yes—
197#1055#13112yes—
198#532—131no—
199#532C2×D1311yescharacteristic
200#500—131no—
201#493—131no—
202#486—131no—
203#486—131no—
204#466—132no—
205#466—132no—
206C4×D8—132no—
207C4×D8—132no—
208#436—132no—
209#436—132no—
210#435—262no—
211#435—262no—
212C8×D4—132no—
213C8×D4—132no—
214#432—131no—
215#432C2×D1311yescharacteristic
216#431—131no—
217#431C2×D1311yescharacteristic
218#408—262no—
219#408—262no—
220C2×C4×C8—131no—
221#335—132no—
222#334—132no—
223D4⋊C8—132no—
224D4⋊C8—132no—
225D4⋊C8C2×D1312yes—
226D4⋊C8C2×D1312yes—
227#322—131no—
228#322—131no—
229C82—131no—
230C82—131no—
231C22×C13—21no—
232C22×C13—21no—
233C22×C13—21no—
234C22×C13—42no—
235C22×C13—42no—
236C22×C13—42no—
237C22×C13C2×C4×D411yescharacteristic
238C2×D13—42no—
239C2×D13—42no—
240C2×D13—42no—
241C4×C13—21no—
242C4×C13—21no—
243C4×C13—21no—
244C4×C13—21no—
245C4×C13—42no—
246C4×C13C2×#13111yescharacteristic
247C4×C13C2×#13111yescharacteristic
248C4×C13#57612yes—
249Dic13—42no—
250C2×#41—21no—
251C2×#41—261no—
252C2×D8—132no—
253C2×D8—132no—
254C2×M16—262no—
255C2×M16—262no—
256C22×C8—131no—
257C22×C8—131no—
258C22×C8—262no—
259C22×C8—262no—
260C4⋊Q8—131no—
261C4⋊Q8C4×D1311yescharacteristic
262#127—131no—
263#127C4×D1311yescharacteristic
264#124—21no—
265#124—261no—
266#121—21no—
267#121—132no—
268#121—261no—
269#121C4×D1312yes—
270C4×D4—21no—
271C4×D4—132no—
272C4×D4—261no—
273C4×D4C22×D1312yes—
274C2×C42C22×D1311yescharacteristic
275#107—132no—
276#107—132no—
277C4⋊C8—21no—
278C4⋊C8—132no—
279C4⋊C8—132no—
280C4⋊C8C22×D1312yes—
281#102—132no—
282#102—132no—
283#102—132no—
284#102—132no—
285C22⋊C8—21no—
286C22⋊C8—21no—
287C22⋊C8—132no—
288C22⋊C8—262no—
289C22⋊C8—262no—
290C22⋊C8—262no—
291C22⋊C8—262no—
292C22⋊C8—261no—
293#97—21no—
294#97—261no—
295C4×C8—131no—
296C4×C8—131no—
297C4×C8—131no—
298C4×C8—131no—
299C4×C8—131no—
300C4×C8—131no—
301C4×C8C22×D1311yescharacteristic
302C4×C8C22×D1311yescharacteristic
303C2×C13—41no—
304C2×C13—82no—
305C2×C13#293111yescharacteristic
306C2×C13#294811yescharacteristic
307C2×C13#295711yescharacteristic
308D13—82no—
309#41—82no—
310#41—1042no—
311C2×Q8—21no—
312C2×Q8—261no—
313C2×D4—22no—
314C2×D4—21no—
315C2×D4—21no—
316C2×D4—132no—
317C2×D4—262no—
318C2×D4—261no—
319C2×D4—261no—
320C2×D4C2×C4×D1312yes—
321C22×C4—22no—
322C22×C4—262no—
323C22×C4C2×C4×D1311yescharacteristic
324C22×C4D4×D1311yescharacteristic
325C22×C4#612911yescharacteristic
326D8—264no—
327D8—264no—
328M16—1042no—
329M16—1042no—
330C2×C8—22no—
331C2×C8—21no—
332C2×C8—21no—
333C2×C8—131no—
334C2×C8—131no—
335C2×C8—131no—
336C2×C8—131no—
337C2×C8—132no—
338C2×C8—132no—
339C2×C8—262no—
340C2×C8—262no—
341C2×C8—262no—
342C2×C8—1042no—
343C2×C8—1042no—
344C4⋊C4—21no—
345C4⋊C4—132no—
346C4⋊C4—261no—
347C4⋊C4C2×C4×D1312yes—
348C22⋊C4—22no—
349C22⋊C4—22no—
350C22⋊C4—262no—
351C22⋊C4—262no—
352C42C2×C4×D1311yescharacteristic
353C42D4×D1311yescharacteristic
354C42#612911yescharacteristic
355C42C23×D1311yescharacteristic
356C13#1797011yescharacteristic, complemented, Sylow
357C23—22no—
358C23—262no—
359C23#8813511yescharacteristic
360Q8—81no—
361Q8—1041no—
362D4—22no—
363D4—22no—
364D4—81no—
365D4—81no—
366D4—82no—
367D4—262no—
368D4—262no—
369D4—1041no—
370D4—1041no—
371D4—1042no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—22no—
375C2×C4—22no—
376C2×C4—41no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—262no—
380C2×C4—522no—
381C2×C4—522no—
382C2×C4#8813511yescharacteristic
383C2×C4#8813511yescharacteristic
384C2×C4#8813511yescharacteristic
385C2×C4C22×C4×D1311yescharacteristic
386C2×C4C2×D4×D1311yescharacteristic
387C2×C4C2×#612911yescharacteristic
388C8—41no—
389C8—41no—
390C8—42no—
391C8—132no—
392C8—132no—
393C8—261no—
394C8—261no—
395C8—262no—
396C8—262no—
397C8—522no—
398C22—21no—
399C22—21no—
400C22—21no—
401C22—42no—
402C22—42no—
403C22—42no—
404C22—522no—
405C22—522no—
406C22—522no—
407C22C2×#8813511yescharacteristic
408C4—21no—
409C4—21no—
410C4—21no—
411C4—21no—
412C4—42no—
413C4—522no—
414C4D13×#13111yescharacteristic
415C4D13×#13111yescharacteristic
416C4#1171947912yes—
417C2—41no—
418C2—82no—
419C2—1042no—
420C2#1312354411yescharacteristic
421C2#1312368411yescharacteristic
422C2#1312374911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1496C2
socleC22×C13C2×C4×D4
prime radical#13125411C2
cosocleC42×C13C24
hypercenter#1496D13
hypocenterC13#17970
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1496

Complements

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

NH ≅ G/Ntype
2. #13123914C2semidirect
3. #13123912C2semidirect
4. #13113747C2semidirect
5. #13113718C2semidirect
6. #13113657C2semidirect
7. #13113628C2semidirect
8. #13113597C2semidirect
9. #13113306C2semidirect
10. #13113120C2semidirect
11. C13×#1496C2semidirect
155. #1496D13semidirect
356. C13#17970semidirect

Maximal subgroups

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

subgroupindex
#131254112
#131239142
#131239122
#131137472
#131137182
#131136572
#131136282
#131135972
#131133062
#131131202
C13×#14962
#1797013