Finite Group Databasebeta

← #15881290

Subgroups — #15881290

Order 3328.

982 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718418C211yesmaximal, characteristic
2C2×#11718418C211yesmaximal, characteristic
3C2×C4×#6105C211yesmaximal, characteristic
4#13117750C211yesmaximal, characteristic, complemented
5#13117741C211yesmaximal, characteristic
6#13115573C211yesmaximal, characteristic, complemented
7#13115566C211yesmaximal, characteristic, complemented
8#13115101C211yesmaximal, characteristic, complemented
9#13115093C211yesmaximal, characteristic, complemented
10#13115085C211yesmaximal, characteristic
11#13115001C211yesmaximal, characteristic, complemented
12#13114850C211yesmaximal, characteristic, complemented
13#13114834C211yesmaximal, characteristic
14#13114707C211yesmaximal, characteristic, complemented
15C13×#1864C211yesmaximal, characteristic
16C2×C4×D4×C13C2211yescharacteristic
17C2×D4×Dic13C2211yescharacteristic
18C2×D4×Dic13C2211yescharacteristic
19C22×#6105C2211yescharacteristic
20C2×#88141C2211yescharacteristic
21C2×#88141C2211yescharacteristic
22C2×C4×Dic26C2211yescharacteristic
23C2×C13×#106C2211yescharacteristic
24C2×C13×#102C2211yescharacteristic
25C2×C13×#102C2211yescharacteristic
26C13×#389C2211yescharacteristic
27C2×#88072C2211yescharacteristic
28#11718871—21no—
29C2×#88071—21no—
30C2×#88058C2211yescharacteristic
31C2×#88056C2211yescharacteristic
32C2×#88056C2211yescharacteristic
33C2×#88055C2211yescharacteristic
34C2×#88055C2211yescharacteristic
35C2×#88054C2211yescharacteristic
36C4×#6105—24no—
37#11718646C2211yescharacteristic
38#11718638C2211yescharacteristic
39#11718637—21no—
40#11718637C2211yescharacteristic
41#11718634C2211yescharacteristic
42#11718633—21no—
43C2×#88050C2211yescharacteristic
44C2×#88048C2211yescharacteristic
45C2×#88047C2211yescharacteristic
46C2×#88047C2211yescharacteristic
47#11718607—21no—
48#11718603—21no—
49C4×#6101C2211yescharacteristic
50#11718589C2211yescharacteristic
51C2×C4×#1055C2211yescharacteristic
52#11718418—24no—
53#11718418C418yescomplemented
54#11718310—21no—
55#11718308—21no—
56C13×#340C2211yescharacteristic
57C13×#336C2211yescharacteristic
58#11718143C2211yescharacteristic
59#11718142C2211yescharacteristic
60#11718121C2211yescharacteristic
61#11718121C2211yescharacteristic
62C22×D4×C13C2311yescharacteristic
63C23×C4×C13—21no—
64C23×Dic13—21no—
65C23×Dic13—21no—
66C22×Dic26C2311yescharacteristic
67C22×C8×C13C2311yescharacteristic
68C22×C8×C13C2311yescharacteristic
69C4×D4×C13—22no—
70C4×D4×C13—41no—
71C2×C13×C4⋊C4—21no—
72C2×C13×C4⋊C4C2311yescharacteristic
73C2×C13×C4⋊C4C2311yescharacteristic
74C2×C13×C4⋊C4C2311yescharacteristic
75C2×C13×C22⋊C4—21no—
76C2×C42×C13C2311yescharacteristic
77C2×C22⋊Dic13—21no—
78C2×C22⋊Dic13—21no—
79D4×Dic13—22no—
80D4×Dic13—22no—
81D4×Dic13—41no—
82D4×Dic13C2×C414yes—
83C2×#6105C2×C414yes—
84C2×#6105D414yes—
85C2×#6105Q814yes—
86C2×C4⋊Dic13—21no—
87C2×C4⋊Dic13C2311yescharacteristic
88C2×C4⋊Dic13C2311yescharacteristic
89C2×C4⋊Dic13C2311yescharacteristic
90C2×#6101—21no—
91C2×#6101—21no—
92C2×#6101—21no—
93C2×#6101—21no—
94C2×#6101—21no—
95C2×#6101—21no—
96C2×#6101—21no—
97C2×#6101D411yescharacteristic
98C2×#6101D411yescharacteristic
99C2×C4×Dic13—21no—
100C2×C4×Dic13—21no—
101C2×C4×Dic13—21no—
102C2×C4×Dic13C2311yescharacteristic
103C2×C4×Dic13C2311yescharacteristic
104C22×#1055C2311yescharacteristic
105C22×#1055C2311yescharacteristic
106#88141—22no—
107#88141—22no—
108#88141—41no—
109#88141C2×C414yescomplemented
110C4×Dic26—22no—
111C4×Dic26—41no—
112C13×#106—41no—
113C13×#102—22no—
114C13×#102C2×C414yes—
115C13×#95—21no—
116#88072—22no—
117#88071—21no—
118#88071—21no—
119#88071—21no—
120#88071—21no—
121#88071—21no—
122#88071D411yescharacteristic
123#88071D411yescharacteristic
124#88058—41no—
125#88056—22no—
126#88056C2×C414yescomplemented
127#88055—22no—
128#88055C2×C414yescomplemented
129#88054—22no—
130#88050—22no—
131#88048—22no—
132#88047—22no—
133#88047C2×C414yescomplemented
134C4×#1055—22no—
135#22678—131nomaximal, Sylow
136C24×C13—21no—
137C2×D4×C13—21no—
138C2×D4×C13—21no—
139C2×D4×C13—21no—
140C2×D4×C13C22×C412yes—
141C2×D4×C13C2×D412yes—
142C2×D4×C13C2×Q812yes—
143C22×C4×C13—21no—
144C22×C4×C13—21no—
145C22×C4×C13—21no—
146C22×C4×C13—42no—
147C22×C4×C13—42no—
148C22×C4×C13—81no—
149C22×C4×C13C2×D411yescharacteristic
150C22×C4×C13C2×D411yescharacteristic
151C22×C4×C13C2411yescharacteristic
152C22×Dic13—21no—
153C22×Dic13—21no—
154C22×Dic13—24no—
155C22×Dic13—21no—
156C22×Dic13—21no—
157C22×Dic13—42no—
158C22×Dic13—42no—
159C22×Dic13—81no—
160C22×Dic13—81no—
161C22×Dic13—81no—
162C22×Dic13C2×D411yescharacteristic
163C22×Dic13C2×D411yescharacteristic
164C22×Dic13C2×D411yescharacteristic
165C22×Dic13C2×D411yescharacteristic
166C2×Dic26—21no—
167C2×Dic26—21no—
168C2×Dic26—21no—
169C2×Dic26C22×C412yes—
170C2×Dic26C2×D412yes—
171C2×Dic26C2×Q812yes—
172C2×C8×C13—21no—
173C2×C8×C13—21no—
174C2×C8×C13—21no—
175C2×C8×C13—21no—
176C2×C8×C13—21no—
177C2×C8×C13C22×C412yes—
178C13×C4⋊C4—21no—
179C13×C4⋊C4—21no—
180C13×C4⋊C4—21no—
181C13×C4⋊C4—21no—
182C13×C4⋊C4—21no—
183C13×C4⋊C4—81no—
184C13×C4⋊C4C22×C412yes—
185C13×C22⋊C4—42no—
186C42×C13—21no—
187C42×C13—21no—
188C22⋊Dic13—24no—
189C22⋊Dic13—42no—
190#6105C4⋊C4116yescomplemented
191C4⋊Dic13—21no—
192C4⋊Dic13—21no—
193C4⋊Dic13—21no—
194C4⋊Dic13—21no—
195C4⋊Dic13—21no—
196C4⋊Dic13—81no—
197C4⋊Dic13C22×C412yes—
198#6101—22no—
199#6101—24no—
200#6101—41no—
201#6101—42no—
202#6101—42no—
203#6101—42no—
204#6101—81no—
205#6101—81no—
206#6101—81no—
207C4×Dic13—21no—
208C4×Dic13—21no—
209C4×Dic13—24no—
210C4×Dic13—42no—
211C4×Dic13—42no—
212C4×Dic13C22×C412yes—
213C4×Dic13#4112yes—
214C2×#1055—21no—
215C2×#1055—21no—
216C2×#1055—21no—
217C2×#1055C22×C412yes—
218C2×#1055C2×D412yes—
219C2×#1055C2×Q812yes—
220C2×#440—131no—
221C2×#440—131no—
222C2×C4×SD16—131no—
223Q8×C4⋊C4—131no—
224#2349—131no—
225#1943—131no—
226#1942—131no—
227#1865—131no—
228#1864D1311yescharacteristic
229#1863—131no—
230#1862—131no—
231#1847—131no—
232#1805—131no—
233#1802—131no—
234#1771—131no—
235C23×C13—22no—
236C23×C13—22no—
237C23×C13—22no—
238C23×C13—41no—
239C23×C13—41no—
240C23×C13—41no—
241C23×C13—41no—
242C23×C13C22×D411yescharacteristic
243D4×C13—22no—
244D4×C13—22no—
245D4×C13—22no—
246D4×C13C2×C4⋊C414yes—
247C2×C4×C13—21no—
248C2×C4×C13—21no—
249C2×C4×C13—22no—
250C2×C4×C13—21no—
251C2×C4×C13—21no—
252C2×C4×C13—21no—
253C2×C4×C13—41no—
254C2×C4×C13—41no—
255C2×C4×C13—41no—
256C2×C4×C13—41no—
257C2×C4×C13—41no—
258C2×C4×C13—41no—
259C2×C4×C13—41no—
260C2×C4×C13—41no—
261C2×C4×C13—84no—
262C2×C4×C13#13712yes—
263C2×C4×C13C23×C411yescharacteristic
264C2×C4×C13C22×D411yescharacteristic
265C2×C4×C13C22×Q811yescharacteristic
266C2×C4×C13C2×#4111yescharacteristic
267C2×C4×C13H(5,𝔽2)11yescharacteristic
268C2×C4×C132−1+411yescharacteristic
269C2×Dic13—22no—
270C2×Dic13—22no—
271C2×Dic13—22no—
272C2×Dic13—21no—
273C2×Dic13—21no—
274C2×Dic13—21no—
275C2×Dic13—21no—
276C2×Dic13—22no—
277C2×Dic13—21no—
278C2×Dic13—21no—
279C2×Dic13—21no—
280C2×Dic13—21no—
281C2×Dic13—21no—
282C2×Dic13—21no—
283C2×Dic13—41no—
284C2×Dic13—41no—
285C2×Dic13—41no—
286C2×Dic13—41no—
287C2×Dic13—41no—
288C2×Dic13—41no—
289C2×Dic13—41no—
290C2×Dic13—41no—
291C2×Dic13—84no—
292C2×Dic13—84no—
293C2×Dic13C4×D412yes—
294C2×Dic13C4×D412yes—
295Dic26—22no—
296Dic26—22no—
297Dic26—22no—
298Dic26C2×C4⋊C414yes—
299C8×C13—22no—
300C8×C13—41no—
301#1055—41no—
302#1055C2×C4⋊C414yes—
303C22×SD16—131no—
304C2×C4×Q8—131no—
305C2×C4×Q8—131no—
306C2×C4×Q8—131no—
307C2×C4×D4—131no—
308C2×C4×D4—131no—
309C2×C4×D4C2×D1311yescharacteristic
310#440—138no—
311#440—264no—
312C4×SD16—264no—
313C2×#107—131no—
314C2×#107—131no—
315C2×#107—131no—
316C2×#106—131no—
317C2×#106C2×D1311yescharacteristic
318C2×C4⋊C8—131no—
319C2×#103—131no—
320C2×#103—131no—
321C2×#103—131no—
322C2×#102—131no—
323C2×#102C2×D1311yescharacteristic
324C2×#102C2×D1311yescharacteristic
325C2×#97—131no—
326C2×#97—131no—
327C2×C4×C8—131no—
328#389—131no—
329#389—131no—
330#389—131no—
331#389—261no—
332#389—261no—
333#389C2×D1311yescharacteristic
334#385—261no—
335#385—261no—
336#384—131no—
337#384—261no—
338#382—131no—
339#380—261no—
340C4×C4⋊C4—131no—
341C4×C4⋊C4—261no—
342C2×#95—261no—
343#340—131no—
344#340—131no—
345#340—131no—
346#340C2×D1311yescharacteristic
347#336—131no—
348#336C2×D1311yescharacteristic
349C22×C13—24no—
350C22×C13—42no—
351C22×C13—42no—
352C22×C13—42no—
353C22×C13—42no—
354C22×C13—42no—
355C22×C13—42no—
356C22×C13C2×C4×D411yescharacteristic
357C22×C13D4211yescharacteristic
358C22×C13D4×Q811yescharacteristic
359C22×C13C2×#13711yescharacteristic
360C22×C13#57511yescharacteristic
361C22×C13#57611yescharacteristic
362C22×C13#57711yescharacteristic
363C4×C13—22no—
364C4×C13—42no—
365C4×C13—41no—
366C4×C13—81no—
367C4×C13—81no—
368C4×C13C22×C4⋊C411yescharacteristic
369C4×C13#52011yescharacteristic
370C4×C13#54711yescharacteristic
371C4×C13#55411yescharacteristic
372Dic13—24no—
373Dic13—22no—
374Dic13—22no—
375Dic13—42no—
376Dic13—41no—
377Dic13—41no—
378Dic13—81no—
379Dic13—81no—
380C22×Q8—131no—
381C22×D4C22×D1311yescharacteristic
382C23×C4—21no—
383C23×C4—261no—
384C23×C4—261no—
385C2×SD16—134no—
386C2×SD16—134no—
387C2×SD16—134no—
388C22×C8—131no—
389C22×C8—131no—
390C22×C8C22×D1311yescharacteristic
391C22×C8C22×D1311yescharacteristic
392C4×Q8—134no—
393C4×Q8—262no—
394C4×Q8—262no—
395C4×Q8—262no—
396C4×Q8—521no—
397C4×Q8—521no—
398C4×D4—22no—
399C4×D4—41no—
400C4×D4—134no—
401C4×D4—262no—
402C4×D4—262no—
403C4×D4—521no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—131no—
406C2×C4⋊C4—131no—
407C2×C4⋊C4—131no—
408C2×C4⋊C4—131no—
409C2×C4⋊C4—131no—
410C2×C4⋊C4—261no—
411C2×C4⋊C4—261no—
412C2×C4⋊C4—261no—
413C2×C4⋊C4—261no—
414C2×C4⋊C4—261no—
415C2×C4⋊C4—261no—
416C2×C4⋊C4—261no—
417C2×C4⋊C4—261no—
418C2×C4⋊C4C22×D1311yescharacteristic
419C2×C4⋊C4C22×D1311yescharacteristic
420C2×C4⋊C4C22×D1311yescharacteristic
421C2×C22⋊C4—21no—
422C2×C22⋊C4—261no—
423C2×C22⋊C4—261no—
424C2×C42—131no—
425C2×C42—131no—
426C2×C42—261no—
427C2×C42—261no—
428C2×C42—261no—
429C2×C42C22×D1311yescharacteristic
430#107—134no—
431#107—262no—
432#107—521no—
433#106—41no—
434#106—262no—
435C4⋊C8—262no—
436#103—134no—
437#103—262no—
438#103—262no—
439#102—22no—
440#102—262no—
441#102C4×D1314yes—
442#97—134no—
443#97—262no—
444C4×C8—262no—
445#95—21no—
446#95—131no—
447#95—131no—
448#95—261no—
449#95—261no—
450#95—261no—
451#95—261no—
452#95—261no—
453C2×C13—44no—
454C2×C13D4×C4⋊C411yescharacteristic
455C2×C13C4×#13711yescharacteristic
456C2×C13#294611yescharacteristic
457C2×C13#326611yescharacteristic
458C2×C13#326811yescharacteristic
459C2×C13#338511yescharacteristic
460C2×C13#338811yescharacteristic
461C24—21no—
462C2×Q8—132no—
463C2×Q8—132no—
464C2×Q8—132no—
465C2×Q8—261no—
466C2×Q8—261no—
467C2×Q8—261no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4C2×C4×D1312yes—
472C2×D4D4×D1312yes—
473C2×D4Q8×D1312yes—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—42no—
478C22×C4—42no—
479C22×C4—81no—
480C22×C4—131no—
481C22×C4—131no—
482C22×C4—131no—
483C22×C4—131no—
484C22×C4—264no—
485C22×C4—261no—
486C22×C4—261no—
487C22×C4—261no—
488C22×C4—261no—
489C22×C4—522no—
490C22×C4—522no—
491C22×C4—1041no—
492C22×C4—1041no—
493C22×C4—1041no—
494C22×C4D4×D1311yescharacteristic
495C22×C4D4×D1311yescharacteristic
496C22×C4C23×D1311yescharacteristic
497SD16—1316no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—132no—
504C2×C8—132no—
505C2×C8—132no—
506C2×C8—261no—
507C2×C8—261no—
508C2×C8—261no—
509C2×C8C2×C4×D1312yes—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—81no—
516C4⋊C4—132no—
517C4⋊C4—264no—
518C4⋊C4—262no—
519C4⋊C4—261no—
520C4⋊C4—261no—
521C4⋊C4—261no—
522C4⋊C4—261no—
523C4⋊C4—261no—
524C4⋊C4—521no—
525C4⋊C4—522no—
526C4⋊C4—522no—
527C4⋊C4—522no—
528C4⋊C4—1041no—
529C4⋊C4—1041no—
530C4⋊C4—1041no—
531C4⋊C4—1041no—
532C4⋊C4C2×C4×D1312yes—
533C22⋊C4—42no—
534C22⋊C4—264no—
535C22⋊C4—522no—
536C42—21no—
537C42—21no—
538C42—132no—
539C42—132no—
540C42—264no—
541C42—261no—
542C42—261no—
543C42—522no—
544C42—522no—
545C13#2267811yescharacteristic, complemented, Sylow
546C23—22no—
547C23—22no—
548C23—22no—
549C23—41no—
550C23—41no—
551C23—41no—
552C23—41no—
553C23C2×D4×D1311yescharacteristic
554Q8—134no—
555Q8—262no—
556Q8—262no—
557Q8—262no—
558D4—22no—
559D4—22no—
560D4—22no—
561D4C4⋊C4×D1314yes—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—22no—
567C2×C4—21no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—84no—
577C2×C4—132no—
578C2×C4—132no—
579C2×C4—261no—
580C2×C4—261no—
581C2×C4—261no—
582C2×C4—261no—
583C2×C4—262no—
584C2×C4—262no—
585C2×C4—262no—
586C2×C4—261no—
587C2×C4—261no—
588C2×C4—261no—
589C2×C4—261no—
590C2×C4—262no—
591C2×C4—261no—
592C2×C4—261no—
593C2×C4—521no—
594C2×C4—521no—
595C2×C4—521no—
596C2×C4—521no—
597C2×C4—521no—
598C2×C4—521no—
599C2×C4—521no—
600C2×C4—521no—
601C2×C4—1044no—
602C2×C4—1044no—
603C2×C4#8816912yes—
604C2×C4C22×C4×D1311yescharacteristic
605C2×C4C2×D4×D1311yescharacteristic
606C2×C4#8825111yescharacteristic
607C2×C4C2×Q8×D1311yescharacteristic
608C2×C4#41×D1311yescharacteristic
609C2×C4#8825711yescharacteristic
610C8—22no—
611C8—41no—
612C8—134no—
613C8—521no—
614C22—24no—
615C22—42no—
616C22—42no—
617C22—42no—
618C22—42no—
619C22—42no—
620C22—42no—
621C22C4×D4×D1311yescharacteristic
622C22#1171929511yescharacteristic
623C22#1171933711yescharacteristic
624C22C2×#8816911yescharacteristic
625C22#1171947311yescharacteristic
626C22#1171947911yescharacteristic
627C22#1171948011yescharacteristic
628C4—22no—
629C4—42no—
630C4—41no—
631C4—81no—
632C4—81no—
633C4—264no—
634C4—262no—
635C4—262no—
636C4—522no—
637C4—521no—
638C4—521no—
639C4—1041no—
640C4—1041no—
641C4C2×C4⋊C4×D1311yescharacteristic
642C4#1171925111yescharacteristic
643C4#1171934111yescharacteristic
644C4#1171936011yescharacteristic
645C2—44no—
646C2#1311773411yescharacteristic
647C2C4×#8816911yescharacteristic
648C2#1312366511yescharacteristic
649C2#1312635011yescharacteristic
650C2#1312638011yescharacteristic
651C2#1312775011yescharacteristic
652C2#1312778511yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1864C2
socleC23×C13C22×D4
prime radicalC22×D4×C13C23
cosocleC22×C4×C13C24
hypercenter#1864D13
hypocenterC13#22678
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1864

Complements

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

NH ≅ G/Ntype
4. #13117750C2semidirect
6. #13115573C2semidirect
7. #13115566C2semidirect
8. #13115101C2semidirect
9. #13115093C2semidirect
11. #13115001C2semidirect
12. #13114850C2semidirect
14. #13114707C2semidirect
53. #11718418C4semidirect
109. #88141C2×C4semidirect
126. #88056C2×C4semidirect
128. #88055C2×C4semidirect
133. #88047C2×C4semidirect
190. #6105C4⋊C4semidirect
545. C13#22678semidirect

Maximal subgroups

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

subgroupindex
C2×#117184182
C2×C4×#61052
#131177502
#131177412
#131155732
#131155662
#131151012
#131150932
#131150852
#131150012
#131148502
#131148342
#131147072
C13×#18642
#2267813