Finite Group Databasebeta

← #15766708

Subgroups — #15766708

Order 3328.

574 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718733C211yesmaximal, characteristic
2#13115630C211yesmaximal, characteristic, complemented
3#13114833C211yesmaximal, characteristic, complemented
4C2×#11718050C211yesmaximal, characteristic, complemented
5C2×#11718136C211yesmaximal, characteristic, complemented
6#13112719C211yesmaximal, characteristic, complemented
7C13×#1957C211yesmaximal, characteristic, complemented
8C2×C13×#127C2211yescharacteristic
9C22×#6104—21no—
10C2×C4×D52C2211yescharacteristic
11C2×C13×#102—21no—
12C2×C13×#102—21no—
13C2×C4×C8×C13C2211yescharacteristic
14C13×#384C2211yescharacteristic
15C2×#88072—21no—
16C2×#88060—21no—
17C2×#88060—21no—
18#11718733—22no—
19#11718733—22no—
20C2×#88049—21no—
21C2×C4⋊#1055C2211yescharacteristic
22C2×C4⋊#1055C2211yescharacteristic
23C2×C4⋊#1055C2211yescharacteristic
24#11718136—22no—
25#11718121—21no—
26#11718050—22no—
27C22×D4×C13—21no—
28C22×D4×C13—21no—
29C22×D4×C13—21no—
30C22×D52D411yescharacteristic
31C22×C4×D13—21no—
32C22×C8×C13D411yescharacteristic
33C22×C8×C13D411yescharacteristic
34C13×#127—21no—
35C13×#127—21no—
36C13×#127—21no—
37C13×#127D412yes—
38C2×C13×C4⋊C4—21no—
39C2×C13×C4⋊C4—21no—
40C2×C13×C4⋊C4—21no—
41C2×C42×C13C2311yescharacteristic
42C2×#6104—24no—
43C2×#6104—42no—
44C2×#6104—42no—
45C2×#6103—21no—
46C2×C4⋊Dic13D411yescharacteristic
47C22×#1055—21no—
48C22×#1055—21no—
49C22×#1055—21no—
50C4×D52—21no—
51C4×D52—21no—
52C4×D52—21no—
53C4×D52—21no—
54C13×#102—42no—
55C13×#102—42no—
56C4×C8×C13—21no—
57C4×C8×C13—21no—
58#88072—24no—
59#88060—42no—
60#88060—42no—
61#88049—42no—
62C4⋊#1055—21no—
63C4⋊#1055—21no—
64C4⋊#1055—21no—
65C4⋊#1055—21no—
66C4⋊#1055—21no—
67C4⋊#1055D412yes—
68#10472—131nomaximal, Sylow
69C24×C13—41no—
70C23×D13—21no—
71C2×D4×C13—22no—
72C2×D4×C13—22no—
73C2×D4×C13—22no—
74C2×D4×C13—41no—
75C2×D4×C13—41no—
76C2×D4×C13—41no—
77C2×D4×C13—41no—
78C2×D4×C13—41no—
79C2×D4×C13—41no—
80C2×D4×C13—41no—
81C2×D4×C13—41no—
82C2×D4×C13—41no—
83C2×D4×C13—41no—
84C2×D4×C13—41no—
85C2×D4×C13—81no—
86C2×D4×C13—81no—
87C22×C4×C13—41no—
88C22×C4×C13C2×D411yescharacteristic
89C22×C4×C13C2×D411yescharacteristic
90C22×C4×C13#4111yescharacteristic
91C22×Dic13—21no—
92C2×D52—21no—
93C2×D52—21no—
94C2×D52—21no—
95C2×D52—21no—
96C2×D52—21no—
97C2×D52D812yes—
98C2×C4×D13—41no—
99C2×C4×D13—41no—
100C2×C4×D13—41no—
101C2×C4×D13—41no—
102C2×C4×D13—41no—
103C2×C4×D13—41no—
104C2×C8×C13—21no—
105C2×C8×C13—21no—
106C2×C8×C13—21no—
107C2×C8×C13—21no—
108C2×C8×C13—21no—
109C2×C8×C13D812yescomplemented
110C13×C4⋊C4—41no—
111C13×C4⋊C4—41no—
112C13×C4⋊C4—41no—
113C13×C4⋊C4—41no—
114C13×C4⋊C4—81no—
115C42×C13C2×D411yescharacteristic
116C42×C13C2×D411yescharacteristic
117C42×C13#4111yescharacteristic
118C42×C13#4111yescharacteristic
119#6104—48no—
120#6103—41no—
121#6103—41no—
122C4⋊Dic13—21no—
123C4⋊Dic13—21no—
124C2×#1055—22no—
125C2×#1055—41no—
126C2×#1055—41no—
127C2×#1055—41no—
128C2×#1055—41no—
129C2×#1055—41no—
130C2×#1055—41no—
131C2×#1055—41no—
132C2×#1055—41no—
133C2×#459—131no—
134#1957D1311yescharacteristic, complemented
135#1954—131no—
136#1802—131no—
137C2×#335—131no—
138C2×#331—131no—
139#1296—131no—
140C23×C13—42no—
141C23×C13—81no—
142C23×C13—81no—
143C23×C13—81no—
144C23×C13—81no—
145C23×C13—81no—
146C23×C13—81no—
147C23×C13#12111yescharacteristic
148C22×D13—22no—
149C22×D13—41no—
150C22×D13—41no—
151C22×D13—41no—
152C22×D13—41no—
153C22×D13—41no—
154C22×D13—41no—
155D4×C13—42no—
156D4×C13—42no—
157D4×C13—42no—
158D4×C13—42no—
159D4×C13—82no—
160D4×C13—82no—
161D4×C13—81no—
162D4×C13—81no—
163D4×C13—81no—
164D4×C13—81no—
165C2×C4×C13—21no—
166C2×C4×C13—21no—
167C2×C4×C13—81no—
168C2×C4×C13—81no—
169C2×C4×C13—81no—
170C2×C4×C13#12011yescharacteristic
171C2×C4×C13#12111yescharacteristic
172C2×C4×C13#12111yescharacteristic
173C2×C4×C13#12311yescharacteristic
174C2×C4×C13#12311yescharacteristic
175C2×C4×C13#12411yescharacteristic
176C2×C4×C13C2×D811yescharacteristic
177C2×C4×C13C2×D811yescharacteristic
178C2×C4×C13#13511yescharacteristic
179C2×C4×C13#13511yescharacteristic
180C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
181C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
182C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
183C2×C4×C13#13711yescharacteristic
184C2×Dic13—41no—
185C2×Dic13—41no—
186C2×Dic13—41no—
187D52—22no—
188D52—22no—
189D52—41no—
190D52—41no—
191C4×D13—81no—
192C4×D13—81no—
193C4×D13—81no—
194C4×D13—81no—
195C8×C13—22no—
196C8×C13—41no—
197#1055—42no—
198#1055—81no—
199#1055—81no—
200C22×D8—261no—
201C2×#127C2×D1311yescharacteristic
202C2×C4×D4—131no—
203#459—262no—
204#459—262no—
205C2×C4⋊C8—131no—
206C2×C4⋊C8—131no—
207C2×C4⋊C8—131no—
208C2×#102—21no—
209C2×#102—21no—
210C2×#102—261no—
211C2×#102—261no—
212C2×C22⋊C8—261no—
213C2×C22⋊C8—261no—
214C2×C4×C8C2×D1311yescharacteristic
215#384C2×D1311yescharacteristic
216#340—261no—
217#335—262no—
218#331—262no—
219C22×C13—82no—
220C22×C13—82no—
221C22×C13—82no—
222C22×C13—161no—
223C22×C13—161no—
224C22×C13—161no—
225C22×C13—161no—
226C22×C13#39411yescharacteristic
227C22×C13#45911yescharacteristic
228C22×C13#46311yescharacteristic
229C22×C13#46611yescharacteristic
230C22×C13#46811yescharacteristic
231C22×C13#47111yescharacteristic
232C22×C13#47211yescharacteristic
233C2×D13—42no—
234C2×D13—42no—
235C2×D13—42no—
236C2×D13—81no—
237C2×D13—81no—
238C2×D13—81no—
239C2×D13—81no—
240C4×C13—21no—
241C4×C13—21no—
242C4×C13—161no—
243C4×C13#44711yescharacteristic
244C4×C13#45211yescharacteristic
245C4×C13#45911yescharacteristic
246C4×C13#46311yescharacteristic
247C4×C13#46611yescharacteristic
248C4×C13#46911yescharacteristic
249C4×C13#48011yescharacteristic
250C4×C13#48211yescharacteristic
251Dic13—81no—
252C22×D4—21no—
253C22×D4—21no—
254C22×D4—21no—
255C22×D4—131no—
256C23×C4—261no—
257C2×D8—264no—
258C2×D8—522no—
259C2×D8—522no—
260C22×C8—261no—
261C22×C8—261no—
262C22×C8—261no—
263C22×C8C22⋊D1311yescharacteristic
264C22×C8C22⋊D1311yescharacteristic
265#127—21no—
266#127—21no—
267#127—21no—
268#127D5212yes—
269C4×D4—261no—
270C4×D4—261no—
271C4×D4—261no—
272C4×D4—261no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—131no—
277C2×C22⋊C4—261no—
278C2×C42C22×D1311yescharacteristic
279C4⋊C8—132no—
280C4⋊C8—261no—
281C4⋊C8—261no—
282C4⋊C8—261no—
283C4⋊C8—261no—
284C4⋊C8—261no—
285#102—42no—
286#102—42no—
287#102—264no—
288#102—522no—
289C22⋊C8—522no—
290C22⋊C8—522no—
291C4×C8—21no—
292C4×C8—21no—
293C2×C13—162no—
294C2×C13#166711yescharacteristic
295C2×C13#168111yescharacteristic
296C2×C13#168511yescharacteristic
297C2×C13#169711yescharacteristic
298C2×C13#203311yescharacteristic
299C2×C13#205111yescharacteristic
300C2×C13#205411yescharacteristic
301D13—82no—
302C24—41no—
303C24—261no—
304C2×D4—22no—
305C2×D4—22no—
306C2×D4—22no—
307C2×D4—41no—
308C2×D4—41no—
309C2×D4—41no—
310C2×D4—41no—
311C2×D4—41no—
312C2×D4—41no—
313C2×D4—41no—
314C2×D4—41no—
315C2×D4—41no—
316C2×D4—41no—
317C2×D4—41no—
318C2×D4—81no—
319C2×D4—81no—
320C2×D4—132no—
321C2×D4—261no—
322C2×D4—261no—
323C2×D4—261no—
324C2×D4—261no—
325C2×D4—261no—
326C22×C4—41no—
327C22×C4—261no—
328C22×C4—521no—
329C22×C4—521no—
330C22×C4—521no—
331C22×C4—521no—
332C22×C4—521no—
333C22×C4—521no—
334C22×C4D4×D1311yescharacteristic
335C22×C4#612911yescharacteristic
336C22×C4C2×C22⋊D1311yescharacteristic
337D8—528no—
338C2×C8—21no—
339C2×C8—21no—
340C2×C8—21no—
341C2×C8—21no—
342C2×C8—21no—
343C2×C8—262no—
344C2×C8—521no—
345C2×C8—521no—
346C2×C8—521no—
347C2×C8—521no—
348C2×C8—521no—
349C2×C8—521no—
350C2×C8—521no—
351C2×C8—521no—
352C2×C8#610412yescomplemented
353C4⋊C4—41no—
354C4⋊C4—41no—
355C4⋊C4—41no—
356C4⋊C4—41no—
357C4⋊C4—81no—
358C4⋊C4—261no—
359C4⋊C4—261no—
360C22⋊C4—521no—
361C22⋊C4—521no—
362C42C2×D5211yescharacteristic
363C42#612711yescharacteristic
364C42D4×D1311yescharacteristic
365C42#612911yescharacteristic
366C13#1047211yescharacteristic, complemented, Sylow
367C23—42no—
368C23—81no—
369C23—81no—
370C23—81no—
371C23—81no—
372C23—81no—
373C23—81no—
374C23—262no—
375C23—521no—
376C23—521no—
377C23—521no—
378C23—521no—
379C23—521no—
380C23—521no—
381C23#8819211yescharacteristic
382D4—42no—
383D4—42no—
384D4—42no—
385D4—42no—
386D4—82no—
387D4—82no—
388D4—81no—
389D4—81no—
390D4—81no—
391D4—81no—
392D4—262no—
393D4—262no—
394D4—521no—
395D4—521no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—81no—
399C2×C4—81no—
400C2×C4—81no—
401C2×C4—521no—
402C2×C4—521no—
403C2×C4—521no—
404C2×C4—1041no—
405C2×C4—1041no—
406C2×C4—1041no—
407C2×C4—1041no—
408C2×C4#8813611yescharacteristic
409C2×C4#8813711yescharacteristic
410C2×C4#8813911yescharacteristic
411C2×C4#8814011yescharacteristic
412C2×C4D8×D1311yescharacteristic
413C2×C4#8816611yescharacteristic
414C2×C4#8816811yescharacteristic
415C2×C4#8816911yescharacteristic
416C2×C4#8818411yescharacteristic
417C2×C4C2×#610411yescharacteristic
418C2×C4#8818611yescharacteristic
419C2×C4#8819311yescharacteristic
420C2×C4#8820311yescharacteristic
421C2×C4#8820411yescharacteristic
422C8—22no—
423C8—41no—
424C8—522no—
425C8—1041no—
426C8—1041no—
427C22—82no—
428C22—82no—
429C22—82no—
430C22—161no—
431C22—161no—
432C22—161no—
433C22—161no—
434C22—522no—
435C22—522no—
436C22—522no—
437C22—1041no—
438C22—1041no—
439C22—1041no—
440C22—1041no—
441C22#1171862211yescharacteristic
442C22#1171871811yescharacteristic
443C22#1171873311yescharacteristic
444C22#1171881811yescharacteristic
445C22#1171882111yescharacteristic
446C22#1171883511yescharacteristic
447C22#1171883811yescharacteristic
448C4—21no—
449C4—21no—
450C4—161no—
451C4—1041no—
452C4#1171843411yescharacteristic
453C4#1171843511yescharacteristic
454C4#1171844411yescharacteristic
455C4#1171844511yescharacteristic
456C4#1171867611yescharacteristic
457C4#1171867711yescharacteristic
458C4#1171869911yescharacteristic
459C4#1171870011yescharacteristic
460C2—162no—
461C2—1042no—
462C2#1311418811yescharacteristic
463C2#1311427011yescharacteristic
464C2#1311429811yescharacteristic
465C2#1311436611yescharacteristic
466C2#1311601711yescharacteristic
467C2#1311612911yescharacteristic
468C2#1311614611yescharacteristic
subgroupG/H
centerC23#88192
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1957C2
socleC23×C13#121
prime radicalC2×#11718733C2
hypercenter#1957D13
hypocenterC13#10472
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1957

Complements

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

NH ≅ G/Ntype
2. #13115630C2semidirect
3. #13114833C2semidirect
4. C2×#11718050C2semidirect
5. C2×#11718136C2semidirect
6. #13112719C2semidirect
7. C13×#1957C2semidirect
109. C2×C8×C13D8semidirect
134. #1957D13semidirect
352. C2×C8#6104semidirect
366. C13#10472semidirect

Maximal subgroups

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

subgroupindex
C2×#117187332
#131156302
#131148332
C2×#117180502
C2×#117181362
#131127192
C13×#19572
#1047213