Finite Group Databasebeta

← #15841694

Subgroups — #15841694

Order 3328.

1192 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125957C211yesmaximal, characteristic, complemented
2#13124836C211yesmaximal, characteristic
3#13124308C211yesmaximal, characteristic, complemented
4#13114085C214yesmaximal, complemented
5#13113939C214yesmaximal, complemented
6#13113508C211yesmaximal, characteristic, complemented
7#13113261C211yesmaximal, characteristic, complemented
8#13113231C211yesmaximal, characteristic, complemented
9C2×D4×Q8×C13C211yesmaximal, characteristic, complemented
10C23×Q8×C13—21no—
11D4×Q8×C13—22no—
12D4×Q8×C13—22no—
13D4×Q8×C13—22no—
14D4×Q8×C13C2214yes—
15C2×C13×C4⋊Q8—21no—
16C2×C13×C4⋊Q8C2211yescharacteristic
17C2×C13×C22⋊Q8—21no—
18C2×C13×C22⋊Q8—22no—
19C2×C4×Q8×C13C2211yescharacteristic
20C2×C4×D4×C13—21no—
21C2×C4×D4×C13C2211yescharacteristic
22C2×#88196—21no—
23#11719182C2211yescharacteristic
24#11718878—21no—
25#11718749C2212yescomplemented
26#11718748—22no—
27#11718739C2212yescomplemented
28#11718692C2212yescomplemented
29#11718689—22no—
30#11718688C2212yescomplemented
31#11718676C2212yes—
32C4×#6104—22no—
33#11718668C2212yes—
34#11718628—22no—
35#11718628—21no—
36#11718627—21no—
37#11718586C2211yescharacteristic
38#11718586C2211yescharacteristic
39#11718585C2211yescharacteristic
40#11718139C2214yescomplemented
41Q8⋊#1055C2214yescomplemented
42D4⋊#1055C2214yes—
43C22×Q8×C13—22no—
44C22×Q8×C13—24no—
45C22×Q8×C13—24no—
46C22×Q8×C13—21no—
47C22×Q8×C13—44no—
48C22×Q8×C13—44no—
49C22×Q8×C13D411yescharacteristic
50C22×D4×C13D411yescharacteristic
51C23×C4×C13—22no—
52C23×C4×C13—21no—
53C2×#6127—21no—
54C13×C4⋊Q8—24no—
55C13×C4⋊Q8—24no—
56C13×C4⋊Q8—21no—
57C13×C4⋊Q8—21no—
58C13×C4⋊Q8D412yes—
59C13×C4⋊Q8C2312yes—
60C13×C22⋊Q8—24no—
61C13×C22⋊Q8—28no—
62C13×C22⋊Q8—24no—
63C13×C22⋊Q8—28no—
64C4×Q8×C13—21no—
65C4×Q8×C13—21no—
66C4×Q8×C13D412yes—
67C4×Q8×C13C2312yes—
68C4×D4×C13—24no—
69C4×D4×C13—24no—
70C4×D4×C13—21no—
71C4×D4×C13—21no—
72C4×D4×C13D412yes—
73C4×D4×C13C2312yes—
74C2×C13×C4⋊C4—22no—
75C2×C13×C4⋊C4—21no—
76C2×C13×C4⋊C4—21no—
77C2×C13×C4⋊C4D411yescharacteristic
78C2×C13×C4⋊C4D411yescharacteristic
79C2×C13×C4⋊C4D412yes—
80C2×C13×C22⋊C4—22no—
81C2×C13×C22⋊C4—21no—
82C2×C42×C13—21no—
83C2×C42×C13C2311yescharacteristic
84C2×#6107—22no—
85#88196—44no—
86C2×#6106—22no—
87C2×#6104—22no—
88#88184—21no—
89#88184—21no—
90C2×#6099—21no—
91#88129—21no—
92#88128C2311yescharacteristic
93C4×D52—21no—
94C4×D52—21no—
95#88123C2311yescharacteristic
96#88072—22no—
97C22⋊#1055—21no—
98C22⋊#1055—21no—
99#88050—22no—
100#88049—22no—
101#88049—22no—
102#88049—24no—
103#88047—22no—
104#88047—24no—
105C4⋊#1055—21no—
106C4⋊#1055—21no—
107C4⋊#1055C2312yes—
108C4⋊#1055C2312yes—
109C4×#1055—21no—
110C4×#1055C2312yes—
111#18776—131nomaximal, Sylow
112C24×C13—21no—
113C2×Q8×C13—28no—
114C2×Q8×C13—21no—
115C2×Q8×C13—22no—
116C2×Q8×C13—22no—
117C2×Q8×C13—22no—
118C2×Q8×C13—48no—
119C2×Q8×C13—48no—
120C2×Q8×C13—416no—
121C2×Q8×C13—48no—
122C2×Q8×C13—42no—
123C2×Q8×C13—42no—
124C2×Q8×C13D814yescomplemented
125C2×Q8×C13C2×D412yes—
126C2×D4×C13—24no—
127C2×D4×C13—21no—
128C2×D4×C13C2×D412yes—
129C22×C4×C13—21no—
130C22×C4×C13—28no—
131C22×C4×C13—21no—
132C22×C4×C13—22no—
133C22×C4×C13—21no—
134C22×C4×C13—22no—
135C22×C4×C13—22no—
136C22×C4×C13—48no—
137C22×C4×C13—42no—
138C22×C4×C13—42no—
139C22×C4×C13C2×D411yescharacteristic
140C22×C4×C13C2×D411yescharacteristic
141C22×C4×C13C2×D411yescharacteristic
142C2×C22⋊D13—41no—
143#6127—42no—
144#6127—42no—
145C2×D52—21no—
146C2×D52—21no—
147C2×D52—21no—
148C2×C4×D13—41no—
149C2×Dic26—21no—
150C13×C4⋊C4—28no—
151C13×C4⋊C4—22no—
152C13×C4⋊C4—22no—
153C13×C4⋊C4—21no—
154C13×C4⋊C4—21no—
155C13×C4⋊C4—22no—
156C13×C4⋊C4—22no—
157C13×C4⋊C4—22no—
158C13×C4⋊C4C2×D412yes—
159C13×C4⋊C4C2×D412yes—
160C13×C4⋊C4C2×D414yes—
161C13×C22⋊C4—28no—
162C13×C22⋊C4—22no—
163C13×C22⋊C4—22no—
164C42×C13—22no—
165C42×C13—22no—
166C42×C13C2×D411yescharacteristic
167C42×C13C2×D411yescharacteristic
168C42×C13C2×D411yescharacteristic
169C42×C13C2411yescharacteristic
170#6107—44no—
171#6106—44no—
172#6104—44no—
173#6103—41no—
174#6103—41no—
175C4⋊Dic13—21no—
176C4⋊Dic13—21no—
177#6099—42no—
178C2×#1055—22no—
179C2×#1055—22no—
180C2×#1055—22no—
181C2×D4×Q8D1311yescharacteristic, complemented
182#3226—131no—
183#3100—131no—
184#3037—131no—
185#1649—134no—
186#1627—134no—
187#1546—131no—
188#1486—131no—
189#1479—131no—
190C23×C13—24no—
191C23×C13—22no—
192C23×C13—42no—
193C23×C13—42no—
194C23×C13#12011yescharacteristic
195C22×D13—41no—
196Q8×C13—22no—
197Q8×C13—24no—
198Q8×C13—416no—
199Q8×C13—42no—
200Q8×C13—42no—
201Q8×C13—44no—
202Q8×C13C2×D814yes—
203D4×C13—24no—
204D4×C13—22no—
205D4×C13#13714yescomplemented
206C2×C4×C13—22no—
207C2×C4×C13—24no—
208C2×C4×C13—22no—
209C2×C4×C13—22no—
210C2×C4×C13—24no—
211C2×C4×C13—22no—
212C2×C4×C13—41no—
213C2×C4×C13—416no—
214C2×C4×C13—42no—
215C2×C4×C13—44no—
216C2×C4×C13—42no—
217C2×C4×C13—42no—
218C2×C4×C13—42no—
219C2×C4×C13—44no—
220C2×C4×C13#12011yescharacteristic
221C2×C4×C13#12011yescharacteristic
222C2×C4×C13#12011yescharacteristic
223C2×C4×C13C2×D812yes—
224C2×C4×C13AGL(1,ℤ/8)12yes—
225C2×C4×C13C22×D411yescharacteristic
226C2×C4×C13C22×D411yescharacteristic
227C2×C4×C13C22×D411yescharacteristic
228C22⋊D13—82no—
229C2×Dic13—41no—
230D52—42no—
231D52—41no—
232D52—41no—
233D52—42no—
234C4×D13—82no—
235Dic26—41no—
236Dic26—41no—
237#1055—42no—
238#1055—42no—
239#1055—42no—
240C23×Q8—21no—
241C2×#137—261no—
242D4×Q8—22no—
243D4×Q8—22no—
244D4×Q8—22no—
245D4×Q8C2×D1314yes—
246#532—131no—
247C2×C4⋊Q8—21no—
248C2×C4⋊Q8C2×D1311yescharacteristic
249C2×C22⋊Q8—21no—
250C2×C22⋊Q8—22no—
251C2×C4×Q8C2×D1311yescharacteristic
252C2×C4×D4—21no—
253C2×C4×D4C2×D1311yescharacteristic
254#500—132no—
255#486—132no—
256#480—261no—
257#480—262no—
258#474—132no—
259#474—262no—
260#464—262no—
261#462—132no—
262#460—132no—
263#459—132no—
264#447—261no—
265C4×D8—262no—
266#431—131no—
267#431—131no—
268#423—131no—
269#417—261no—
270#332—134no—
271Q8⋊C8—134no—
272D4⋊C8—134no—
273C22×C13—21no—
274C22×C13—21no—
275C22×C13—24no—
276C22×C13—48no—
277C22×C13—42no—
278C22×C13—42no—
279C22×C13#44712yes—
280C22×C13C2×#12011yescharacteristic
281C2×D13—81no—
282C2×D13—81no—
283C2×D13—81no—
284C4×C13—24no—
285C4×C13—21no—
286C4×C13—21no—
287C4×C13—21no—
288C4×C13—44no—
289C4×C13—42no—
290C4×C13—42no—
291C4×C13#44712yes—
292C4×C13C22×D811yescharacteristic
293C4×C13C2×AGL(1,ℤ/8)11yescharacteristic
294C4×C13C2×#13712yes—
295Dic13—81no—
296C2×#41—261no—
297C22×Q8—22no—
298C22×Q8—24no—
299C22×Q8—24no—
300C22×Q8—21no—
301C22×Q8—44no—
302C22×Q8—44no—
303C22×Q8C22⋊D1311yescharacteristic
304C22×D4C22⋊D1311yescharacteristic
305C23×C4—22no—
306C23×C4—21no—
307#137—524no—
308C2×Q16—262no—
309C2×SD16—262no—
310C2×D8—262no—
311C2×M16—261no—
312C4⋊Q8—24no—
313C4⋊Q8—24no—
314C4⋊Q8—21no—
315C4⋊Q8—21no—
316C4⋊Q8—131no—
317C4⋊Q8C22⋊D1312yes—
318C4⋊Q8C22×D1312yes—
319#127—131no—
320#124—261no—
321C22⋊Q8—24no—
322C22⋊Q8—28no—
323C22⋊Q8—24no—
324C22⋊Q8—28no—
325#121—261no—
326#121—261no—
327C4×Q8—21no—
328C4×Q8—21no—
329C4×Q8C22⋊D1312yes—
330C4×Q8C22×D1312yes—
331C4×D4—24no—
332C4×D4—24no—
333C4×D4—21no—
334C4×D4—21no—
335C4×D4—261no—
336C4×D4—261no—
337C4×D4C22⋊D1312yes—
338C4×D4C22×D1312yes—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4C22⋊D1311yescharacteristic
343C2×C4⋊C4C22⋊D1311yescharacteristic
344C2×C4⋊C4C22⋊D1312yes—
345C2×C22⋊C4—22no—
346C2×C22⋊C4—21no—
347C2×C42—21no—
348C2×C42C22×D1311yescharacteristic
349#107—262no—
350#107—264no—
351C4⋊C8—132no—
352C4⋊C8—132no—
353C4⋊C8—261no—
354C4⋊C8—261no—
355#103—262no—
356#102—262no—
357#102—262no—
358#102—262no—
359#102—264no—
360C22⋊C8—261no—
361C22⋊C8—261no—
362C4×C8—132no—
363C4×C8—261no—
364C2×C13—22no—
365C2×C13—44no—
366C2×C13C2×#44711yescharacteristic
367C2×C13#300411yescharacteristic
368C2×C13#302011yescharacteristic
369D13—161no—
370C24—21no—
371#41—522no—
372#41—522no—
373C2×Q8—28no—
374C2×Q8—22no—
375C2×Q8—21no—
376C2×Q8—22no—
377C2×Q8—22no—
378C2×Q8—48no—
379C2×Q8—48no—
380C2×Q8—416no—
381C2×Q8—48no—
382C2×Q8—42no—
383C2×Q8—42no—
384C2×Q8—261no—
385C2×Q8#610414yescomplemented
386C2×Q8C2×C22⋊D1312yes—
387C2×D4—24no—
388C2×D4—21no—
389C2×D4—261no—
390C2×D4—261no—
391C2×D4—261no—
392C2×D4—521no—
393C2×D4C2×C22⋊D1312yes—
394C22×C4—21no—
395C22×C4—28no—
396C22×C4—21no—
397C22×C4—22no—
398C22×C4—21no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—48no—
402C22×C4—42no—
403C22×C4—42no—
404C22×C4—521no—
405C22×C4C2×C22⋊D1311yescharacteristic
406C22×C4C2×C22⋊D1311yescharacteristic
407C22×C4C2×C22⋊D1311yescharacteristic
408Q16—524no—
409SD16—524no—
410D8—524no—
411M16—522no—
412C2×C8—262no—
413C2×C8—262no—
414C2×C8—262no—
415C4⋊C4—28no—
416C4⋊C4—22no—
417C4⋊C4—22no—
418C4⋊C4—21no—
419C4⋊C4—21no—
420C4⋊C4—22no—
421C4⋊C4—22no—
422C4⋊C4—22no—
423C4⋊C4—261no—
424C4⋊C4—261no—
425C4⋊C4C2×C22⋊D1312yes—
426C4⋊C4C2×C22⋊D1312yes—
427C4⋊C4C2×C22⋊D1314yes—
428C22⋊C4—28no—
429C22⋊C4—22no—
430C22⋊C4—22no—
431C22⋊C4—521no—
432C22⋊C4—521no—
433C42—22no—
434C42—22no—
435C42C2×C22⋊D1311yescharacteristic
436C42C2×C22⋊D1311yescharacteristic
437C42C2×C22⋊D1311yescharacteristic
438C42C23×D1311yescharacteristic
439C13#1877611yescharacteristic, complemented, Sylow
440C23—24no—
441C23—22no—
442C23—42no—
443C23—42no—
444C23—521no—
445C23#8820711yescharacteristic
446Q8—22no—
447Q8—24no—
448Q8—416no—
449Q8—42no—
450Q8—42no—
451Q8—44no—
452Q8—521no—
453Q8—521no—
454Q8C2×#610414yes—
455D4—24no—
456D4—22no—
457D4—522no—
458D4—521no—
459D4—521no—
460D4—522no—
461D4—1042no—
462D4#8819614yescomplemented
463C2×C4—22no—
464C2×C4—24no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—24no—
468C2×C4—22no—
469C2×C4—41no—
470C2×C4—416no—
471C2×C4—42no—
472C2×C4—44no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—44no—
477C2×C4—521no—
478C2×C4—1042no—
479C2×C4C2×#610412yes—
480C2×C4#8818612yes—
481C2×C4#8820711yescharacteristic
482C2×C4#8820711yescharacteristic
483C2×C4#8820711yescharacteristic
484C2×C4C22×C22⋊D1311yescharacteristic
485C2×C4C22×C22⋊D1311yescharacteristic
486C2×C4C22×C22⋊D1311yescharacteristic
487C8—522no—
488C8—522no—
489C8—522no—
490C22—21no—
491C22—21no—
492C22—24no—
493C22—48no—
494C22—42no—
495C22—42no—
496C22—1041no—
497C22—1041no—
498C22—1041no—
499C22#1171887812yes—
500C22C2×#8820711yescharacteristic
501C4—21no—
502C4—21no—
503C4—24no—
504C4—21no—
505C4—42no—
506C4—44no—
507C4—42no—
508C4—1041no—
509C4#1171887812yes—
510C4C22×#610411yescharacteristic
511C4C2×#8818611yescharacteristic
512C4C2×#8819612yes—
513C2—22no—
514C2—44no—
515C2—2081no—
516C2C2×#1171887811yescharacteristic
517C2#1312407011yescharacteristic
518C2#1312420011yescharacteristic
subgroupG/H
centerC22C2×#88207
commutator, cosocleC42×C13C24
FrattiniC42C23×D13
FittingC2×D4×Q8×C13C2
socleC22×C13C2×#120
prime radical#13124836C2
hypercenterC2×D4×Q8D13
hypocenterC13#18776
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
1. #13125957C2semidirect
3. #13124308C2semidirect
4. #13114085C2semidirect
5. #13113939C2semidirect
6. #13113508C2semidirect
7. #13113261C2semidirect
8. #13113231C2semidirect
9. C2×D4×Q8×C13C2semidirect
25. #11718749C22semidirect
27. #11718739C22semidirect
28. #11718692C22semidirect
30. #11718688C22semidirect
40. #11718139C22semidirect
41. Q8⋊#1055C22semidirect
124. C2×Q8×C13D8semidirect
181. C2×D4×Q8D13semidirect
205. D4×C13#137semidirect
385. C2×Q8#6104semidirect
439. C13#18776semidirect
462. D4#88196semidirect

Maximal subgroups

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

subgroupindex
#131259572
#131248362
#131243082
#131140852
#131139392
#131135082
#131132612
#131132312
C2×D4×Q8×C132
#1877613