Finite Group Databasebeta

← #15923061

Subgroups — #15923061

Order 3328.

826 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718689C211yesmaximal, characteristic
2C2×C4×#6107C211yesmaximal, characteristic, complemented
3#13118634C211yesmaximal, characteristic
4#13116365C211yesmaximal, characteristic
5#13116327C211yesmaximal, characteristic, complemented
6#13116245C211yesmaximal, characteristic, complemented
7#13116077C211yesmaximal, characteristic
8#13115518C211yesmaximal, characteristic
9#13115395C211yesmaximal, characteristic, complemented
10#13115191C211yesmaximal, characteristic
11#13115191C211yesmaximal, characteristic
12#13115177C211yesmaximal, characteristic, complemented
13#13115090C211yesmaximal, characteristic, complemented
14#13115089C211yesmaximal, characteristic, complemented
15Q8×C13×C4⋊C4C211yesmaximal, characteristic, complemented
16C2×C4×Q8×C13C2211yescharacteristic
17C2×C4×Q8×C13C2211yescharacteristic
18C2×C4×Q8×C13C2211yescharacteristic
19C22×#6107C2211yescharacteristic
20C22×#6106C2211yescharacteristic
21C2×#88129C2211yescharacteristic
22C2×C4×Dic26C2211yescharacteristic
23C13×#389—21no—
24C13×#389—21no—
25C13×#389C2211yescharacteristic
26C13×#389C2211yescharacteristic
27C13×#384—21no—
28C13×#384C2211yescharacteristic
29C4×C13×C4⋊C4—21no—
30C4×C13×C4⋊C4C2211yescharacteristic
31C2×#88075C2211yescharacteristic
32C2×#88075C2211yescharacteristic
33C4×#6107—24no—
34#11718689—24no—
35#11718653—21no—
36#11718651—21no—
37C2×#88050C2211yescharacteristic
38C2×#88050C2211yescharacteristic
39C2×#88050C2211yescharacteristic
40C2×#88049C2211yescharacteristic
41C2×#88049C2211yescharacteristic
42C2×#88049C2211yescharacteristic
43C2×#88047C2211yescharacteristic
44C2×#88047C2211yescharacteristic
45#11718600C2211yescharacteristic
46#11718600C2211yescharacteristic
47#11718590C2211yescharacteristic
48#11718589C2211yescharacteristic
49C2×C4⋊#1055C2211yescharacteristic
50C2×C4×#1055C2211yescharacteristic
51#11718336—21no—
52#11718330—21no—
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718116C2211yescharacteristic
58#11718116C2211yescharacteristic
59#11718116C2211yescharacteristic
60#11718116C2211yescharacteristic
61C22×Q8×C13C2311yescharacteristic
62C22×D52C2311yescharacteristic
63C22×Dic26C2311yescharacteristic
64C4×Q8×C13—22no—
65C4×Q8×C13—22no—
66C4×Q8×C13—22no—
67C4×Q8×C13—22no—
68C4×Q8×C13—41no—
69C4×Q8×C13—41no—
70C2×C13×C4⋊C4—21no—
71C2×C13×C4⋊C4—21no—
72C2×C13×C4⋊C4—21no—
73C2×C13×C4⋊C4—21no—
74C2×C13×C4⋊C4—21no—
75C2×C13×C4⋊C4—21no—
76C2×C13×C4⋊C4—21no—
77C2×C13×C4⋊C4D411yescharacteristic
78C2×C13×C4⋊C4D411yescharacteristic
79C2×C13×C4⋊C4C2311yescharacteristic
80C2×C13×C4⋊C4C2311yescharacteristic
81C2×C13×C4⋊C4C2311yescharacteristic
82C2×C42×C13—21no—
83C2×C42×C13—21no—
84C2×C42×C13—21no—
85C2×C42×C13C2311yescharacteristic
86C2×C42×C13C2311yescharacteristic
87C2×C42×C13C2311yescharacteristic
88C2×#6107—22no—
89C2×#6107—22no—
90C2×#6107D414yes—
91C2×#6106—22no—
92C2×#6106—22no—
93C2×#6106—22no—
94C2×#6103—21no—
95C2×#6103—21no—
96C2×#6103—21no—
97C2×#6103—21no—
98C2×#6103—21no—
99C2×#6103—21no—
100C2×C4⋊Dic13C2311yescharacteristic
101C2×C4⋊Dic13C2311yescharacteristic
102C2×#6101—21no—
103C2×#6101—21no—
104C2×C4×Dic13—21no—
105C22×#1055C2311yescharacteristic
106C22×#1055C2311yescharacteristic
107C22×#1055C2311yescharacteristic
108C22×#1055C2311yescharacteristic
109#88129—22no—
110#88129—41no—
111C4×Dic26—22no—
112C4×Dic26—41no—
113C13×#95—21no—
114C13×#95—21no—
115C13×#95D411yescharacteristic
116C13×#95D411yescharacteristic
117#88075—22no—
118#88075—22no—
119#88071—21no—
120#88071—21no—
121#88071—21no—
122#88050—22no—
123#88050—22no—
124#88050—22no—
125#88049—22no—
126#88049—22no—
127#88049—41no—
128#88047—22no—
129#88047—41no—
130C4⋊#1055—22no—
131C4×#1055—22no—
132#26169—131nomaximal, Sylow
133C23×D13—21no—
134C2×Q8×C13—21no—
135C2×Q8×C13—21no—
136C2×Q8×C13—21no—
137C2×Q8×C13C2×D412yes—
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—
160C2×Dic26—21no—
161C2×Dic26—21no—
162C2×Dic26—21no—
163C2×Dic26—21no—
164C2×Dic26—21no—
165C2×Dic26C2×D412yes—
166C13×C4⋊C4—24no—
167C13×C4⋊C4—22no—
168C13×C4⋊C4—22no—
169C13×C4⋊C4—21no—
170C13×C4⋊C4—21no—
171C13×C4⋊C4—21no—
172C13×C4⋊C4—21no—
173C13×C4⋊C4—21no—
174C13×C4⋊C4—42no—
175C13×C4⋊C4—42no—
176C13×C4⋊C4—42no—
177C13×C4⋊C4—81no—
178C13×C4⋊C4—81no—
179C13×C4⋊C4—81no—
180C13×C4⋊C4#4112yes—
181C42×C13—24no—
182C42×C13—21no—
183C42×C13—21no—
184C42×C13—21no—
185C42×C13—21no—
186C42×C13—21no—
187C42×C13—21no—
188C42×C13—42no—
189C42×C13—42no—
190#6107—28no—
191#6106—44no—
192#6103—42no—
193#6103—42no—
194#6103—42no—
195#6103—42no—
196#6103—81no—
197#6103—81no—
198C4⋊Dic13—21no—
199C4⋊Dic13—21no—
200C4⋊Dic13—21no—
201C4⋊Dic13—21no—
202#6101—42no—
203#6101—81no—
204C4×Dic13—42no—
205C2×#1055—21no—
206C2×#1055—21no—
207C2×#1055—21no—
208C2×#1055—21no—
209C2×#1055—21no—
210C2×#1055—21no—
211C2×#1055—21no—
212C2×#1055—21no—
213C2×#1055—21no—
214C2×#1055—21no—
215C2×#1055—21no—
216C2×#1055C2×D412yes—
217C2×#464—131no—
218C2×C4×Q16—131no—
219#2448—131no—
220Q8×C4⋊C4D1311yescharacteristic, complemented
221#2093—131no—
222#2086—131no—
223#2072—131no—
224#2042—131no—
225#1934—131no—
226#1916—131no—
227#1880—131no—
228#1880—131no—
229#1878—131no—
230#1863—131no—
231#1863—131no—
232C23×C13C22×D411yescharacteristic
233C22×D13—41no—
234C22×D13—41no—
235C22×D13—41no—
236C22×D13—41no—
237C22×D13—41no—
238C22×D13—41no—
239C22×D13—41no—
240Q8×C13—22no—
241Q8×C13—22no—
242Q8×C13—22no—
243Q8×C13#12314yes—
244C2×C4×C13—21no—
245C2×C4×C13—22no—
246C2×C4×C13—21no—
247C2×C4×C13—22no—
248C2×C4×C13—22no—
249C2×C4×C13—21no—
250C2×C4×C13—21no—
251C2×C4×C13—21no—
252C2×C4×C13—22no—
253C2×C4×C13—21no—
254C2×C4×C13—21no—
255C2×C4×C13—21no—
256C2×C4×C13—21no—
257C2×C4×C13—21no—
258C2×C4×C13—21no—
259C2×C4×C13—21no—
260C2×C4×C13—21no—
261C2×C4×C13—21no—
262C2×C4×C13—21no—
263C2×C4×C13—21no—
264C2×C4×C13—41no—
265C2×C4×C13—41no—
266C2×C4×C13—41no—
267C2×C4×C13—41no—
268C2×C4×C13—41no—
269C2×C4×C13—41no—
270C2×C4×C13—41no—
271C2×C4×C13—41no—
272C2×C4×C13#13512yes—
273C2×C4×C13#13712yes—
274C2×C4×C13C22×D411yescharacteristic
275C2×C4×C13C2×#4111yescharacteristic
276C2×C4×C13C2×#4111yescharacteristic
277C2×C4×C13C2×#4111yescharacteristic
278C2×C4×C13H(5,𝔽2)11yescharacteristic
279C2×C4×C132−1+411yescharacteristic
280C2×Dic13—22no—
281C2×Dic13—41no—
282C2×Dic13—41no—
283C2×Dic13—41no—
284C2×Dic13—41no—
285C2×Dic13—41no—
286C2×Dic13—41no—
287C2×Dic13—41no—
288C2×Dic13—41no—
289D52—41no—
290D52—41no—
291D52—41no—
292D52—41no—
293Dic26—22no—
294Dic26—22no—
295Dic26—41no—
296Dic26—41no—
297#1055—22no—
298#1055—41no—
299#1055—41no—
300#1055—41no—
301C22×Q16—131no—
302C22×SD16—131no—
303C2×#124—131no—
304C2×C4×Q8—131no—
305C2×C4×Q8C2×D1311yescharacteristic
306C2×C4×Q8C2×D1311yescharacteristic
307C2×C4×Q8C2×D1311yescharacteristic
308#464—264no—
309C4×Q16—264no—
310C2×#107—131no—
311C2×#107—131no—
312C2×C4⋊C8—131no—
313C2×#103—131no—
314C2×#103—131no—
315C2×#103—131no—
316C2×#103—131no—
317C2×#103—131no—
318C2×#102—131no—
319C2×#102—131no—
320C2×#102—131no—
321C2×C4×C8—131no—
322#399—261no—
323#397—261no—
324#391—131no—
325#390—131no—
326#390—131no—
327#389—21no—
328#389—21no—
329#389—131no—
330#389C2×D1311yescharacteristic
331#389C2×D1311yescharacteristic
332#388—261no—
333#388—261no—
334#384—21no—
335#384C2×D1311yescharacteristic
336C4×C4⋊C4—21no—
337C4×C4⋊C4C2×D1311yescharacteristic
338#340—131no—
339#340—131no—
340#340—131no—
341#340—131no—
342#336—131no—
343#336—131no—
344#336—131no—
345#336—131no—
346C22×C13#52511yescharacteristic
347C22×C13D4211yescharacteristic
348C22×C13#54811yescharacteristic
349C22×C13C2×#13511yescharacteristic
350C22×C13C2×#13711yescharacteristic
351C22×C13#57611yescharacteristic
352C22×C13#57811yescharacteristic
353C2×D13—81no—
354C2×D13—81no—
355C2×D13—81no—
356C2×D13—81no—
357C2×D13—81no—
358C2×D13—81no—
359C2×D13—81no—
360C4×C13—22no—
361C4×C13—24no—
362C4×C13—22no—
363C4×C13—41no—
364C4×C13—42no—
365C4×C13—41no—
366C4×C13—41no—
367C4×C13—41no—
368C4×C13—81no—
369C4×C13—81no—
370C4×C13C2×#12311yescharacteristic
371C4×C13#53911yescharacteristic
372C4×C13#54711yescharacteristic
373C4×C13#55311yescharacteristic
374Dic13—42no—
375Dic13—81no—
376Dic13—81no—
377C22×Q8—131no—
378C22×Q8C22×D1311yescharacteristic
379C22×D4—131no—
380C2×Q16—134no—
381C2×Q16—262no—
382C2×Q16—262no—
383C2×SD16—262no—
384C2×SD16—262no—
385C2×SD16—262no—
386C22×C8—131no—
387C22×C8—131no—
388C22×C8—131no—
389C22×C8—131no—
390#124—262no—
391#124—521no—
392C4×Q8—22no—
393C4×Q8—22no—
394C4×Q8—22no—
395C4×Q8—22no—
396C4×Q8—41no—
397C4×Q8—41no—
398C4×Q8—262no—
399C4×Q8—521no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—131no—
408C2×C4⋊C4—131no—
409C2×C4⋊C4—261no—
410C2×C4⋊C4—261no—
411C2×C4⋊C4C22⋊D1311yescharacteristic
412C2×C4⋊C4C22⋊D1311yescharacteristic
413C2×C4⋊C4C22×D1311yescharacteristic
414C2×C4⋊C4C22×D1311yescharacteristic
415C2×C4⋊C4C22×D1311yescharacteristic
416C2×C22⋊C4—261no—
417C2×C22⋊C4—261no—
418C2×C22⋊C4—261no—
419C2×C22⋊C4—261no—
420C2×C22⋊C4—261no—
421C2×C22⋊C4—261no—
422C2×C42—21no—
423C2×C42—21no—
424C2×C42—21no—
425C2×C42—261no—
426C2×C42C22×D1311yescharacteristic
427C2×C42C22×D1311yescharacteristic
428C2×C42C22×D1311yescharacteristic
429#107—262no—
430#107—521no—
431C4⋊C8—262no—
432#103—262no—
433#103—262no—
434#103—262no—
435#103—262no—
436#103—262no—
437#102—262no—
438#102—262no—
439#102—521no—
440C4×C8—262no—
441#95—21no—
442#95—21no—
443#95—261no—
444#95—261no—
445#95—261no—
446#95C22⋊D1311yescharacteristic
447#95C22⋊D1311yescharacteristic
448C2×C13#244311yescharacteristic
449C2×C13#310811yescharacteristic
450C2×C13#312411yescharacteristic
451C2×C13#327011yescharacteristic
452C2×C13#328711yescharacteristic
453C2×C13#336411yescharacteristic
454C2×C13#337511yescharacteristic
455D13—161no—
456C24—261no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—132no—
461C2×Q8—261no—
462C2×Q8—261no—
463C2×Q8—261no—
464C2×Q8—261no—
465C2×Q8—261no—
466C2×Q8#612712yes—
467C2×Q8D4×D1312yes—
468C2×Q8#613112yes—
469C2×D4—261no—
470C2×D4—261no—
471C2×D4—261no—
472C2×D4—261no—
473C2×D4—261no—
474C2×D4—261no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—261no—
480C22×C4—261no—
481C22×C4—261no—
482C22×C4C2×C22⋊D1311yescharacteristic
483C22×C4C2×C22⋊D1311yescharacteristic
484C22×C4C2×C22⋊D1311yescharacteristic
485C22×C4C2×C22⋊D1311yescharacteristic
486C22×C4C2×C22⋊D1311yescharacteristic
487C22×C4C2×C22⋊D1311yescharacteristic
488C22×C4C23×D1311yescharacteristic
489Q16—268no—
490SD16—524no—
491C2×C8—132no—
492C2×C8—261no—
493C2×C8—261no—
494C2×C8—261no—
495C2×C8—261no—
496C2×C8—261no—
497C2×C8—261no—
498C2×C8—261no—
499C2×C8—261no—
500C2×C8—261no—
501C2×C8—261no—
502C2×C8—261no—
503C4⋊C4—24no—
504C4⋊C4—22no—
505C4⋊C4—22no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—42no—
512C4⋊C4—42no—
513C4⋊C4—42no—
514C4⋊C4—81no—
515C4⋊C4—81no—
516C4⋊C4—81no—
517C4⋊C4—261no—
518C4⋊C4—261no—
519C4⋊C4—261no—
520C4⋊C4—261no—
521C4⋊C4—522no—
522C4⋊C4—1041no—
523C4⋊C4#612712yes—
524C22⋊C4—522no—
525C22⋊C4—522no—
526C22⋊C4—522no—
527C22⋊C4—522no—
528C22⋊C4—1041no—
529C22⋊C4—1041no—
530C42—24no—
531C42—21no—
532C42—21no—
533C42—21no—
534C42—21no—
535C42—21no—
536C42—21no—
537C42—42no—
538C42—42no—
539C42—522no—
540C13#2616911yescharacteristic, complemented, Sylow
541C23—521no—
542C23—521no—
543C23—521no—
544C23—521no—
545C23—521no—
546C23—521no—
547C23—521no—
548C23C22×C22⋊D1311yescharacteristic
549Q8—22no—
550Q8—22no—
551Q8—22no—
552Q8—262no—
553Q8—262no—
554Q8—521no—
555Q8—521no—
556Q8#8814814yes—
557D4—521no—
558D4—521no—
559D4—521no—
560D4—521no—
561C2×C4—21no—
562C2×C4—22no—
563C2×C4—21no—
564C2×C4—22no—
565C2×C4—21no—
566C2×C4—22no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—22no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—262no—
590C2×C4—521no—
591C2×C4—521no—
592C2×C4—521no—
593C2×C4—521no—
594C2×C4—521no—
595C2×C4—521no—
596C2×C4—521no—
597C2×C4—521no—
598C2×C4#8819612yes—
599C2×C4#8820412yes—
600C2×C4C2×#612711yescharacteristic
601C2×C4C2×#612711yescharacteristic
602C2×C4C2×D4×D1311yescharacteristic
603C2×C4#8825111yescharacteristic
604C2×C4C2×#613111yescharacteristic
605C2×C4#8825411yescharacteristic
606C8—262no—
607C8—521no—
608C8—521no—
609C8—521no—
610C22—1041no—
611C22—1041no—
612C22—1041no—
613C22—1041no—
614C22—1041no—
615C22—1041no—
616C22—1041no—
617C22#1171949611yescharacteristic
618C22D4×C22⋊D1311yescharacteristic
619C22C2×#8819611yescharacteristic
620C22#1171952211yescharacteristic
621C22C2×#8820411yescharacteristic
622C22#1171954011yescharacteristic
623C22#1171954311yescharacteristic
624C4—22no—
625C4—22no—
626C4—24no—
627C4—41no—
628C4—41no—
629C4—41no—
630C4—41no—
631C4—42no—
632C4—81no—
633C4—81no—
634C4—522no—
635C4—1041no—
636C4—1041no—
637C4C2×#8814811yescharacteristic
638C4#1171921211yescharacteristic
639C4#1171921911yescharacteristic
640C4#1171922011yescharacteristic
641C2—2081no—
642C2#1311857111yescharacteristic
643C2#1312491611yescharacteristic
644C2#1312509811yescharacteristic
645C2#1312640711yescharacteristic
646C2#1312659211yescharacteristic
647C2#1312752111yescharacteristic
648C2#1312765011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingQ8×C13×C4⋊C4C2
socleC23×C13C22×D4
prime radicalC22×D52C23
hypercenterQ8×C4⋊C4D13
hypocenterC13#26169
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ Q8×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×#6107C2semidirect
5. #13116327C2semidirect
6. #13116245C2semidirect
9. #13115395C2semidirect
12. #13115177C2semidirect
13. #13115090C2semidirect
14. #13115089C2semidirect
15. Q8×C13×C4⋊C4C2semidirect
220. Q8×C4⋊C4D13semidirect
540. C13#26169semidirect

Maximal subgroups

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

subgroupindex
C2×#117186892
C2×C4×#61072
#131186342
#131163652
#131163272
#131162452
#131160772
#131155182
#131153952
#131151912
#131151772
#131150902
#131150892
Q8×C13×C4⋊C42
#2616913