Finite Group Databasebeta

← #15936155

Subgroups — #15936155

Order 3328.

734 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13119433C211yesmaximal, characteristic
2#13116384C211yesmaximal, characteristic, complemented
3#13116151C211yesmaximal, characteristic
4#13116079C211yesmaximal, characteristic, complemented
5#13115919C211yesmaximal, characteristic
6#13115693C211yesmaximal, characteristic
7#13115474C211yesmaximal, characteristic, complemented
8#13115456C211yesmaximal, characteristic
9#13115421C211yesmaximal, characteristic, complemented
10#13115395C211yesmaximal, characteristic, complemented
11#13115191C211yesmaximal, characteristic
12#13115191C211yesmaximal, characteristic
13#13114851C211yesmaximal, characteristic, complemented
14C4×#88075C211yesmaximal, characteristic, complemented
15C13×#2365C211yesmaximal, characteristic, complemented
16C2×C13×C4⋊Q8C2211yescharacteristic
17C2×C4×Q8×C13C2211yescharacteristic
18C2×C4×Q8×C13C2211yescharacteristic
19C22×#6106C2211yescharacteristic
20C22×#6106C2211yescharacteristic
21C13×#391C2211yescharacteristic
22C13×#391C2211yescharacteristic
23C13×#389—21no—
24C13×#387—21no—
25C13×#387—21no—
26C4×C13×C4⋊C4—21no—
27C4×C13×C4⋊C4C2211yescharacteristic
28C4×C13×C4⋊C4C2211yescharacteristic
29C2×#88075C2211yescharacteristic
30C2×#88075C2211yescharacteristic
31C2×#88075C2211yescharacteristic
32C2×#88075C2211yescharacteristic
33C2×#88075C2211yescharacteristic
34C2×#88075C2211yescharacteristic
35#11718654—21no—
36#11718651—21no—
37C2×#88049C2211yescharacteristic
38C2×#88049C2211yescharacteristic
39C2×#88048C2211yescharacteristic
40C2×#88047C2211yescharacteristic
41#11718600C2211yescharacteristic
42#11718600C2211yescharacteristic
43#11718600C2211yescharacteristic
44#11718597C2211yescharacteristic
45C4×C4⋊Dic13C2211yescharacteristic
46#11718589C2211yescharacteristic
47C2×C4⋊#1055C2211yescharacteristic
48C2×C4×#1055C2211yescharacteristic
49#11718336—21no—
50#11718330—21no—
51#11718121C2211yescharacteristic
52#11718121C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718116C2211yescharacteristic
56#11718116C2211yescharacteristic
57#11718116C2211yescharacteristic
58#11718116C2211yescharacteristic
59C22×Q8×C13C2311yescharacteristic
60C22×Q8×C13C2311yescharacteristic
61C22×D52C2311yescharacteristic
62C13×C4⋊Q8—22no—
63C13×C4⋊Q8—22no—
64C4×Q8×C13—22no—
65C4×Q8×C13—22no—
66C4×Q8×C13—41no—
67C4×Q8×C13—41no—
68C2×C13×C4⋊C4—21no—
69C2×C13×C4⋊C4—21no—
70C2×C13×C4⋊C4—21no—
71C2×C13×C4⋊C4—21no—
72C2×C13×C4⋊C4D411yescharacteristic
73C2×C13×C4⋊C4D411yescharacteristic
74C2×C13×C4⋊C4C2311yescharacteristic
75C2×C13×C4⋊C4C2311yescharacteristic
76C2×C42×C13—21no—
77C2×C42×C13—21no—
78C2×C42×C13—21no—
79C2×C42×C13C2311yescharacteristic
80C2×C42×C13C2311yescharacteristic
81C2×C42×C13C2311yescharacteristic
82C2×#6106—22no—
83C2×#6106—22no—
84C2×#6106—22no—
85C2×#6106—41no—
86C2×#6106—41no—
87C2×#6106—41no—
88C2×#6103—21no—
89C2×#6103—21no—
90C2×#6103—21no—
91C2×#6103—21no—
92C2×#6103—21no—
93C2×#6103—21no—
94C2×C4⋊Dic13C2311yescharacteristic
95C2×C4⋊Dic13C2311yescharacteristic
96C2×C4⋊Dic13C2311yescharacteristic
97C2×#6101—21no—
98C2×C4×Dic13—21no—
99C22×#1055C2311yescharacteristic
100C22×#1055C2311yescharacteristic
101C22×#1055C2311yescharacteristic
102C22×#1055C2311yescharacteristic
103C13×#95—21no—
104C13×#95—21no—
105C13×#95—21no—
106C13×#95—21no—
107C13×#95—21no—
108C13×#95D411yescharacteristic
109C13×#95D411yescharacteristic
110#88075—22no—
111#88075—22no—
112#88075—22no—
113#88075—41no—
114#88075—41no—
115#88075—41no—
116#88071—21no—
117#88071—21no—
118#88071—21no—
119#88071—21no—
120#88049—22no—
121#88049—41no—
122#88048—22no—
123#88047—41no—
124C4⋊#1055—41no—
125C4×#1055—41no—
126#27069—131nomaximal, Sylow
127C23×D13—21no—
128C2×Q8×C13—21no—
129C2×Q8×C13—21no—
130C2×Q8×C13—21no—
131C2×Q8×C13—21no—
132C2×Q8×C13—21no—
133C2×Q8×C13—21no—
134C2×Q8×C13—21no—
135C2×Q8×C13—21no—
136C2×Q8×C13—21no—
137C2×Q8×C13—21no—
138C2×Q8×C13#4112yes—
139C2×Q8×C13#4112yes—
140C22×C4×C13—21no—
141C22×C4×C13—21no—
142C22×C4×C13—21no—
143C22×C4×C13—21no—
144C22×C4×C13C2×D411yescharacteristic
145C22×C4×C13C2×D411yescharacteristic
146C22×C4×C13C2×D411yescharacteristic
147C22×C4×C13C2×D411yescharacteristic
148C22×C4×C13C2×D411yescharacteristic
149C22×C4×C13C2×D411yescharacteristic
150C22×C4×C13C2411yescharacteristic
151C22×Dic13—21no—
152C22×Dic13—21no—
153C22×Dic13—21no—
154C2×D52—21no—
155C2×D52—21no—
156C2×D52—21no—
157C2×D52—21no—
158C2×D52—21no—
159C2×D52—21no—
160C13×C4⋊C4—24no—
161C13×C4⋊C4—24no—
162C13×C4⋊C4—22no—
163C13×C4⋊C4—22no—
164C13×C4⋊C4—21no—
165C13×C4⋊C4—21no—
166C13×C4⋊C4—21no—
167C13×C4⋊C4—42no—
168C13×C4⋊C4—42no—
169C13×C4⋊C4#4112yes—
170C42×C13—21no—
171C42×C13—21no—
172C42×C13—21no—
173C42×C13—21no—
174C42×C13—21no—
175C42×C13—21no—
176C42×C13—42no—
177C42×C13—42no—
178C42×C13—42no—
179#6106—44no—
180#6106—44no—
181#6103—42no—
182#6103—42no—
183#6103—81no—
184#6103—81no—
185#6103—81no—
186#6103—81no—
187C4⋊Dic13—21no—
188C4⋊Dic13—21no—
189C4⋊Dic13—21no—
190C4⋊Dic13—21no—
191C4⋊Dic13—21no—
192C4⋊Dic13—21no—
193#6101—81no—
194C4×Dic13—81no—
195C2×#1055—21no—
196C2×#1055—21no—
197C2×#1055—21no—
198C2×#1055—21no—
199C2×#1055—21no—
200C2×#1055—21no—
201C2×#1055—21no—
202C2×#1055—21no—
203C2×#1055—21no—
204C2×#1055—21no—
205C2×#1055—21no—
206C2×#1055#4112yes—
207#2513—131no—
208#2365D1311yescharacteristic, complemented
209#2097—131no—
210#2055—131no—
211#2043—131no—
212#2013—131no—
213#1968—131no—
214#1928—131no—
215#1925—131no—
216#1920—131no—
217#1916—131no—
218#1880—131no—
219#1880—131no—
220#1805—131no—
221C4×#103—131no—
222C23×C13C22×D411yescharacteristic
223C22×D13—41no—
224C22×D13—41no—
225C22×D13—41no—
226C22×D13—41no—
227C22×D13—41no—
228C22×D13—41no—
229C22×D13—41no—
230Q8×C13—22no—
231Q8×C13—22no—
232Q8×C13—22no—
233Q8×C13—22no—
234Q8×C13—41no—
235Q8×C13—41no—
236Q8×C13—41no—
237Q8×C13—41no—
238C2×C4×C13—21no—
239C2×C4×C13—21no—
240C2×C4×C13—21no—
241C2×C4×C13—21no—
242C2×C4×C13—21no—
243C2×C4×C13—22no—
244C2×C4×C13—22no—
245C2×C4×C13—21no—
246C2×C4×C13—21no—
247C2×C4×C13—21no—
248C2×C4×C13—22no—
249C2×C4×C13—21no—
250C2×C4×C13—21no—
251C2×C4×C13—21no—
252C2×C4×C13—21no—
253C2×C4×C13—21no—
254C2×C4×C13—21no—
255C2×C4×C13—21no—
256C2×C4×C13—21no—
257C2×C4×C13—41no—
258C2×C4×C13—41no—
259C2×C4×C13—41no—
260C2×C4×C13—41no—
261C2×C4×C13—41no—
262C2×C4×C13—41no—
263C2×C4×C13—41no—
264C2×C4×C13—41no—
265C2×C4×C13—41no—
266C2×C4×C13#13512yes—
267C2×C4×C13#13712yes—
268C2×C4×C13C2×#4111yescharacteristic
269C2×C4×C13C2×#4111yescharacteristic
270C2×C4×C13C2×#4111yescharacteristic
271C2×C4×C13C2×#4111yescharacteristic
272C2×C4×C13H(5,𝔽2)11yescharacteristic
273C2×C4×C13H(5,𝔽2)11yescharacteristic
274C2×Dic13—41no—
275C2×Dic13—41no—
276C2×Dic13—41no—
277C2×Dic13—41no—
278C2×Dic13—41no—
279C2×Dic13—41no—
280C2×Dic13—41no—
281C2×Dic13—41no—
282C2×Dic13—41no—
283D52—41no—
284D52—41no—
285D52—41no—
286D52—41no—
287#1055—22no—
288#1055—41no—
289#1055—41no—
290#1055—41no—
291C22×SD16—131no—
292C22×SD16—131no—
293C2×C4⋊Q8C2×D1311yescharacteristic
294C2×C4×Q8C2×D1311yescharacteristic
295C2×C4×Q8C2×D1311yescharacteristic
296C2×#107—131no—
297C2×#106—131no—
298C2×C4⋊C8—131no—
299C2×#103—131no—
300C2×#103—131no—
301C2×#103—131no—
302C2×#103—131no—
303C2×#103—131no—
304C2×#103—131no—
305C2×#102—131no—
306C2×#102—131no—
307C2×C4×C8—131no—
308#397—261no—
309#397—261no—
310#391C2×D1311yescharacteristic
311#391C2×D1311yescharacteristic
312#390—131no—
313#390—131no—
314#390—131no—
315#389—21no—
316#389—131no—
317#388—261no—
318#388—261no—
319#387—21no—
320#387—21no—
321#382—131no—
322C4×C4⋊C4—21no—
323C4×C4⋊C4—131no—
324C4×C4⋊C4C2×D1311yescharacteristic
325C4×C4⋊C4C2×D1311yescharacteristic
326#340—131no—
327#340—131no—
328#340—131no—
329#340—131no—
330#336—131no—
331#336—131no—
332#336—131no—
333#336—131no—
334C22×C13#52511yescharacteristic
335C22×C13#54611yescharacteristic
336C22×C13#55011yescharacteristic
337C22×C13C2×#13511yescharacteristic
338C22×C13C2×#13711yescharacteristic
339C22×C13#57711yescharacteristic
340C22×C13#57711yescharacteristic
341C2×D13—81no—
342C2×D13—81no—
343C2×D13—81no—
344C2×D13—81no—
345C2×D13—81no—
346C2×D13—81no—
347C2×D13—81no—
348C4×C13—22no—
349C4×C13—22no—
350C4×C13—41no—
351C4×C13—42no—
352C4×C13—42no—
353C4×C13—41no—
354C4×C13—41no—
355C4×C13—42no—
356C4×C13—41no—
357C4×C13—81no—
358C4×C13#52911yescharacteristic
359C4×C13#53811yescharacteristic
360C4×C13#55111yescharacteristic
361C4×C13#55311yescharacteristic
362Dic13—81no—
363Dic13—81no—
364Dic13—81no—
365C22×Q8C22×D1311yescharacteristic
366C22×Q8C22×D1311yescharacteristic
367C22×D4—131no—
368C2×SD16—262no—
369C2×SD16—262no—
370C2×SD16—262no—
371C2×SD16—521no—
372C2×SD16—521no—
373C2×SD16—521no—
374C22×C8—131no—
375C22×C8—131no—
376C22×C8—131no—
377C22×C8—131no—
378C4⋊Q8—22no—
379C4⋊Q8—22no—
380C4×Q8—22no—
381C4×Q8—22no—
382C4×Q8—41no—
383C4×Q8—41no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—131no—
389C2×C4⋊C4—131no—
390C2×C4⋊C4—131no—
391C2×C4⋊C4—261no—
392C2×C4⋊C4C22⋊D1311yescharacteristic
393C2×C4⋊C4C22⋊D1311yescharacteristic
394C2×C4⋊C4C22×D1311yescharacteristic
395C2×C4⋊C4C22×D1311yescharacteristic
396C2×C22⋊C4—261no—
397C2×C22⋊C4—261no—
398C2×C22⋊C4—261no—
399C2×C22⋊C4—261no—
400C2×C22⋊C4—261no—
401C2×C22⋊C4—261no—
402C2×C42—21no—
403C2×C42—21no—
404C2×C42—21no—
405C2×C42—261no—
406C2×C42C22×D1311yescharacteristic
407C2×C42C22×D1311yescharacteristic
408C2×C42C22×D1311yescharacteristic
409#107—521no—
410#106—262no—
411C4⋊C8—521no—
412#103—262no—
413#103—262no—
414#103—262no—
415#103—521no—
416#103—521no—
417#103—521no—
418#102—262no—
419#102—521no—
420C4×C8—521no—
421#95—21no—
422#95—21no—
423#95—21no—
424#95—21no—
425#95—21no—
426#95—261no—
427#95—261no—
428#95—261no—
429#95—261no—
430#95C22⋊D1311yescharacteristic
431#95C22⋊D1311yescharacteristic
432C2×C13#246711yescharacteristic
433C2×C13#310811yescharacteristic
434C2×C13#312611yescharacteristic
435C2×C13#330311yescharacteristic
436C2×C13#332011yescharacteristic
437C2×C13#339411yescharacteristic
438C2×C13#340011yescharacteristic
439D13—161no—
440C24—261no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8#612712yes—
452C2×Q8#612712yes—
453C2×D4—261no—
454C2×D4—261no—
455C2×D4—261no—
456C2×D4—261no—
457C2×D4—261no—
458C2×D4—261no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—261no—
464C22×C4—261no—
465C22×C4—261no—
466C22×C4C2×C22⋊D1311yescharacteristic
467C22×C4C2×C22⋊D1311yescharacteristic
468C22×C4C2×C22⋊D1311yescharacteristic
469C22×C4C2×C22⋊D1311yescharacteristic
470C22×C4C2×C22⋊D1311yescharacteristic
471C22×C4C2×C22⋊D1311yescharacteristic
472C22×C4C23×D1311yescharacteristic
473SD16—524no—
474SD16—524no—
475C2×C8—132no—
476C2×C8—261no—
477C2×C8—261no—
478C2×C8—261no—
479C2×C8—261no—
480C2×C8—261no—
481C2×C8—261no—
482C2×C8—261no—
483C2×C8—261no—
484C2×C8—261no—
485C2×C8—261no—
486C2×C8—261no—
487C4⋊C4—24no—
488C4⋊C4—24no—
489C4⋊C4—22no—
490C4⋊C4—22no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—42no—
495C4⋊C4—42no—
496C4⋊C4—261no—
497C4⋊C4—261no—
498C4⋊C4—261no—
499C4⋊C4—261no—
500C4⋊C4—261no—
501C4⋊C4—261no—
502C4⋊C4—1041no—
503C4⋊C4#612912yes—
504C22⋊C4—522no—
505C22⋊C4—522no—
506C22⋊C4—1041no—
507C22⋊C4—1041no—
508C22⋊C4—1041no—
509C22⋊C4—1041no—
510C42—21no—
511C42—21no—
512C42—21no—
513C42—21no—
514C42—21no—
515C42—21no—
516C42—42no—
517C42—42no—
518C42—42no—
519C42—1041no—
520C13#2706911yescharacteristic, complemented, Sylow
521C23—521no—
522C23—521no—
523C23—521no—
524C23—521no—
525C23—521no—
526C23—521no—
527C23—521no—
528C23C22×C22⋊D1311yescharacteristic
529Q8—22no—
530Q8—22no—
531Q8—22no—
532Q8—22no—
533Q8—41no—
534Q8—41no—
535Q8—41no—
536Q8—41no—
537D4—521no—
538D4—521no—
539D4—521no—
540D4—521no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—22no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—521no—
570C2×C4—521no—
571C2×C4—521no—
572C2×C4—521no—
573C2×C4—521no—
574C2×C4—521no—
575C2×C4—521no—
576C2×C4—521no—
577C2×C4—521no—
578C2×C4#8819612yes—
579C2×C4#8820412yes—
580C2×C4C2×#612711yescharacteristic
581C2×C4C2×#612711yescharacteristic
582C2×C4C2×#612911yescharacteristic
583C2×C4#8825111yescharacteristic
584C2×C4#41×D1311yescharacteristic
585C2×C4#8825611yescharacteristic
586C8—262no—
587C8—521no—
588C8—521no—
589C8—521no—
590C22—1041no—
591C22—1041no—
592C22—1041no—
593C22—1041no—
594C22—1041no—
595C22—1041no—
596C22—1041no—
597C22#1171949611yescharacteristic
598C22#1171951111yescharacteristic
599C22C2×#8819611yescharacteristic
600C22C2×#8820411yescharacteristic
601C22#1171953911yescharacteristic
602C22#1171954211yescharacteristic
603C22#1171954211yescharacteristic
604C4—22no—
605C4—22no—
606C4—41no—
607C4—41no—
608C4—41no—
609C4—41no—
610C4—42no—
611C4—42no—
612C4—42no—
613C4—81no—
614C4—1041no—
615C4—1041no—
616C4—1041no—
617C4#1171924311yescharacteristic
618C4#1171926111yescharacteristic
619C4#1171926511yescharacteristic
620C4#1171927011yescharacteristic
621C2—2081no—
622C2#1311888111yescharacteristic
623C2#1312491611yescharacteristic
624C2#1312512711yescharacteristic
625C2#1312676411yescharacteristic
626C2#1312700711yescharacteristic
627C2#1312783211yescharacteristic
628C2#1312788511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2365C2
socleC23×C13C22×D4
prime radicalC22×D52C23
hypercenter#2365D13
hypocenterC13#27069
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2365

Complements

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

NH ≅ G/Ntype
2. #13116384C2semidirect
4. #13116079C2semidirect
7. #13115474C2semidirect
9. #13115421C2semidirect
10. #13115395C2semidirect
13. #13114851C2semidirect
14. C4×#88075C2semidirect
15. C13×#2365C2semidirect
208. #2365D13semidirect
520. C13#27069semidirect

Maximal subgroups

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

subgroupindex
#131194332
#131163842
#131161512
#131160792
#131159192
#131156932
#131154742
#131154562
#131154212
#131153952
#131151912
#131148512
C4×#880752
C13×#23652
#2706913