Finite Group Databasebeta

← #15926466

Subgroups — #15926466

Order 3328.

902 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13117850C211yesmaximal, characteristic
2#13116393C211yesmaximal, characteristic, complemented
3#13116327C211yesmaximal, characteristic, complemented
4#13116221C211yesmaximal, characteristic, complemented
5#13115969C211yesmaximal, characteristic, complemented
6#13115789C211yesmaximal, characteristic, complemented
7#13115404C211yesmaximal, characteristic, complemented
8#13115262C211yesmaximal, characteristic
9#13115153C211yesmaximal, characteristic
10#13115082C211yesmaximal, characteristic, complemented
11#13115023C211yesmaximal, characteristic, complemented
12#13115016C211yesmaximal, characteristic, complemented
13#13114833C211yesmaximal, characteristic, complemented
14C2×#11718121C211yesmaximal, characteristic, complemented
15C13×#2440C211yesmaximal, characteristic, complemented
16C2×C13×C4⋊Q8C2211yescharacteristic
17C2×C13×C22⋊Q8—21no—
18C22×C13×C4⋊C4C2211yescharacteristic
19C2×#88184C2211yescharacteristic
20C22×C4⋊Dic13C2211yescharacteristic
21C23×#1055C2211yescharacteristic
22C2×#88135—21no—
23C2×C4×D52C2211yescharacteristic
24C13×#398—21no—
25C13×#395—21no—
26C13×#389C2211yescharacteristic
27C13×#389C2211yescharacteristic
28C13×#385—21no—
29C13×#384C2211yescharacteristic
30C13×#380C2211yescharacteristic
31C4×C13×C22⋊C4C2211yescharacteristic
32C2×C22⋊#1055C2211yescharacteristic
33C2×#88049C2211yescharacteristic
34C2×#88049C2211yescharacteristic
35C2×#88049C2211yescharacteristic
36C2×#88049C2211yescharacteristic
37C2×#88047C2211yescharacteristic
38C2×#88047C2211yescharacteristic
39#11718619—21no—
40#11718600C2211yescharacteristic
41C4×C4⋊Dic13C2211yescharacteristic
42#11718589C2211yescharacteristic
43C2×C4⋊#1055C2211yescharacteristic
44C2×C4⋊#1055C2211yescharacteristic
45#11718331—21no—
46#11718329—21no—
47#11718121C2211yescharacteristic
48#11718121C2211yescharacteristic
49#11718121C2211yescharacteristic
50#11718121C2211yescharacteristic
51#11718121C2211yescharacteristic
52#11718121C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718116C2211yescharacteristic
58#11718116C2211yescharacteristic
59C22×Q8×C13—21no—
60C23×C4×C13—21no—
61C23×C4×C13C2311yescharacteristic
62C22×C22⋊D13—21no—
63C23×Dic13—21no—
64C22×D52C2311yescharacteristic
65C22×C4×D13—21no—
66C13×C4⋊Q8—22no—
67C13×C4⋊Q8—41no—
68C13×C22⋊Q8—44no—
69C2×C13×C4⋊C4—22no—
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—41no—
77C2×C13×C4⋊C4C2311yescharacteristic
78C2×C13×C4⋊C4C2311yescharacteristic
79C2×C13×C4⋊C4C2311yescharacteristic
80C2×C13×C4⋊C4C2311yescharacteristic
81C2×C13×C22⋊C4—21no—
82C2×C13×C22⋊C4D411yescharacteristic
83C2×C13×C22⋊C4D411yescharacteristic
84C2×C42×C13C2311yescharacteristic
85C2×C42×C13C2311yescharacteristic
86#88184—22no—
87#88184Q814yescomplemented
88C2×#6103—21no—
89C2×#6103—21no—
90C2×#6103—21no—
91C2×#6103—21no—
92C2×C4⋊Dic13—22no—
93C2×C4⋊Dic13—21no—
94C2×C4⋊Dic13—41no—
95C2×C4⋊Dic13C2311yescharacteristic
96C2×C4⋊Dic13C2311yescharacteristic
97C2×C4⋊Dic13C2311yescharacteristic
98C2×#6101—21no—
99C2×C4×Dic13—21no—
100C22×#1055—22no—
101C22×#1055—41no—
102C22×#1055—41no—
103C22×#1055C2311yescharacteristic
104C22×#1055C2311yescharacteristic
105C22×#1055C2311yescharacteristic
106C22×#1055C2311yescharacteristic
107#88135—44no—
108C4×D52—22no—
109C4×D52—41no—
110C13×#95—21no—
111C13×#95—21no—
112C13×#95—21no—
113C13×#95D411yescharacteristic
114C13×#95D411yescharacteristic
115#88071—21no—
116#88071—21no—
117C22⋊#1055—22no—
118#88049—22no—
119#88049—41no—
120#88049—41no—
121#88049—41no—
122#88047—22no—
123#88047—41no—
124C4⋊#1055—41no—
125C4⋊#1055—41no—
126#26408—131nomaximal, Sylow
127C24×C13C2×D411yescharacteristic
128C23×D13—21no—
129C2×Q8×C13—42no—
130C2×Q8×C13—42no—
131C2×Q8×C13—81no—
132C22×C4×C13—21no—
133C22×C4×C13—21no—
134C22×C4×C13—21no—
135C22×C4×C13—21no—
136C22×C4×C13—21no—
137C22×C4×C13—21no—
138C22×C4×C13—21no—
139C22×C4×C13—21no—
140C22×C4×C13—42no—
141C22×C4×C13—42no—
142C22×C4×C13—81no—
143C22×C4×C13C2×D411yescharacteristic
144C22×C4×C13C2×D411yescharacteristic
145C22×C4×C13C2×D411yescharacteristic
146C22×C4×C13C2×D411yescharacteristic
147C22×C4×C13C2×D411yescharacteristic
148C22×C4×C13C2×Q812yes—
149C22×C4×C13#4112yes—
150C22×C4×C13C2411yescharacteristic
151C2×C22⋊D13—24no—
152C2×C22⋊D13—42no—
153C2×C22⋊D13—42no—
154C22×Dic13—21no—
155C22×Dic13—21no—
156C22×Dic13—21no—
157C22×Dic13—42no—
158C22×Dic13—42no—
159C22×Dic13—81no—
160C2×D52—21no—
161C2×D52—21no—
162C2×D52—21no—
163C2×D52—21no—
164C2×D52—21no—
165C2×D52C2×Q812yes—
166C2×C4×D13—42no—
167C2×C4×D13—42no—
168C2×C4×D13—81no—
169C13×C4⋊C4—21no—
170C13×C4⋊C4—21no—
171C13×C4⋊C4—21no—
172C13×C4⋊C4—21no—
173C13×C4⋊C4—21no—
174C13×C4⋊C4—21no—
175C13×C4⋊C4—21no—
176C13×C4⋊C4—42no—
177C13×C4⋊C4—42no—
178C13×C4⋊C4—42no—
179C13×C4⋊C4—42no—
180C13×C4⋊C4—42no—
181C13×C4⋊C4—81no—
182C13×C4⋊C4#4112yes—
183C13×C22⋊C4—22no—
184C13×C22⋊C4—42no—
185C13×C22⋊C4D814yes—
186C42×C13—21no—
187C42×C13—21no—
188C42×C13—21no—
189C42×C13—21no—
190#6103—24no—
191#6103—42no—
192#6103—42no—
193#6103—81no—
194C4⋊Dic13—21no—
195C4⋊Dic13—21no—
196C4⋊Dic13—21no—
197C4⋊Dic13—21no—
198C4⋊Dic13—42no—
199C4⋊Dic13C2×Q812yes—
200C4⋊Dic13#4112yes—
201#6101—42no—
202C4×Dic13—42no—
203C2×#1055—21no—
204C2×#1055—21no—
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—44no—
216#2440D1311yescharacteristic, complemented
217#2361—131no—
218#2099—131no—
219#2086—131no—
220#2067—131no—
221#2023—131no—
222#1988—131no—
223#1918—131no—
224#1893—131no—
225#1874—131no—
226#1862—131no—
227#1852—131no—
228#1850—131no—
229#1802—131no—
230C2×#340—131no—
231C23×C13—21no—
232C23×C13—21no—
233C23×C13—21no—
234C23×C13—21no—
235C23×C13C22⋊Q812yes—
236C23×C13C2×D812yes—
237C23×C13#13712yes—
238C23×C13C22×D411yescharacteristic
239C22×D13—22no—
240C22×D13—41no—
241C22×D13—41no—
242C22×D13—41no—
243C22×D13—41no—
244C22×D13—41no—
245C22×D13—41no—
246Q8×C13—84no—
247C2×C4×C13—21no—
248C2×C4×C13—21no—
249C2×C4×C13—21no—
250C2×C4×C13—21no—
251C2×C4×C13—21no—
252C2×C4×C13—21no—
253C2×C4×C13—22no—
254C2×C4×C13—22no—
255C2×C4×C13—22no—
256C2×C4×C13—22no—
257C2×C4×C13—21no—
258C2×C4×C13—21no—
259C2×C4×C13—22no—
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—41no—
273C2×C4×C13—41no—
274C2×C4×C13—41no—
275C2×C4×C13—84no—
276C2×C4×C13C22⋊Q812yes—
277C2×C4×C13C2×D812yes—
278C2×C4×C13C2×D812yes—
279C2×C4×C13C22×Q811yescharacteristic
280C2×C4×C13C2×#4111yescharacteristic
281C2×C4×C13C2×#4111yescharacteristic
282C2×C4×C13C2×#4111yescharacteristic
283C2×C4×C13H(5,𝔽2)11yescharacteristic
284C2×C4×C13H(5,𝔽2)11yescharacteristic
285C22⋊D13—48no—
286C2×Dic13—22no—
287C2×Dic13—22no—
288C2×Dic13—41no—
289C2×Dic13—41no—
290C2×Dic13—41no—
291C2×Dic13—41no—
292C2×Dic13—41no—
293C2×Dic13—41no—
294C2×Dic13—41no—
295C2×Dic13—84no—
296D52—22no—
297D52—22no—
298D52—41no—
299D52—41no—
300C4×D13—84no—
301#1055—41no—
302#1055—41no—
303#1055—41no—
304#1055—41no—
305C23×C8—131no—
306C2×C4⋊Q8C2×D1311yescharacteristic
307C2×C22⋊Q8—21no—
308C2×#121—131no—
309C2×C4×D4—131no—
310C2×C4×D4—261no—
311C22×C4⋊C4—131no—
312C22×C4⋊C4C2×D1311yescharacteristic
313C2×#107—131no—
314C2×#107—131no—
315C2×C4⋊C8—131no—
316C2×C4⋊C8—131no—
317C2×#102—131no—
318C2×#102—131no—
319C2×#102—131no—
320C2×#102—131no—
321C2×C22⋊C8—131no—
322#398—21no—
323#395—21no—
324#390—131no—
325#389—131no—
326#389C2×D1311yescharacteristic
327#389C2×D1311yescharacteristic
328#388—261no—
329#386—261no—
330#385—21no—
331#385—261no—
332#384C2×D1311yescharacteristic
333#380C2×D1311yescharacteristic
334C4×C4⋊C4—131no—
335C4×C22⋊C4C2×D1311yescharacteristic
336#340—131no—
337#340—131no—
338#340—131no—
339#340—131no—
340#340—131no—
341#340—131no—
342#340—131no—
343#340—131no—
344#340—131no—
345#340—131no—
346#336—131no—
347#336—131no—
348C22×C13—22no—
349C22×C13—22no—
350C22×C13—22no—
351C22×C13—22no—
352C22×C13—22no—
353C22×C13—22no—
354C22×C13#47414yes—
355C22×C13C2×C22⋊Q811yescharacteristic
356C22×C13#54611yescharacteristic
357C22×C13#54611yescharacteristic
358C22×C13C22×D811yescharacteristic
359C22×C13C2×#13711yescharacteristic
360C22×C13#57711yescharacteristic
361C22×C13#57711yescharacteristic
362C2×D13—42no—
363C2×D13—42no—
364C2×D13—42no—
365C2×D13—81no—
366C2×D13—81no—
367C2×D13—81no—
368C2×D13—81no—
369C4×C13—22no—
370C4×C13—22no—
371C4×C13—22no—
372C4×C13—42no—
373C4×C13—41no—
374C4×C13—41no—
375C4×C13—81no—
376C4×C13—81no—
377C4×C13—81no—
378C4×C13#52911yescharacteristic
379C4×C13#53811yescharacteristic
380C4×C13#55411yescharacteristic
381C4×C13#55411yescharacteristic
382Dic13—42no—
383Dic13—42no—
384Dic13—81no—
385C22×Q8—21no—
386C22×D4—131no—
387C22×D4—261no—
388C23×C4—21no—
389C23×C4—261no—
390C23×C4—261no—
391C23×C4C22×D1311yescharacteristic
392C22×C8—131no—
393C22×C8—131no—
394C22×C8—131no—
395C22×C8—131no—
396C22×C8—262no—
397C22×C8—521no—
398C22×C8—521no—
399C4⋊Q8—22no—
400C4⋊Q8—41no—
401C22⋊Q8—44no—
402#121—134no—
403#121—262no—
404C4×D4—262no—
405C4×D4—521no—
406C4×D4—524no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—41no—
415C2×C4⋊C4—131no—
416C2×C4⋊C4—131no—
417C2×C4⋊C4—131no—
418C2×C4⋊C4—262no—
419C2×C4⋊C4—261no—
420C2×C4⋊C4—261no—
421C2×C4⋊C4—521no—
422C2×C4⋊C4C22×D1311yescharacteristic
423C2×C4⋊C4C22×D1311yescharacteristic
424C2×C4⋊C4C22×D1311yescharacteristic
425C2×C4⋊C4C22×D1311yescharacteristic
426C2×C22⋊C4—21no—
427C2×C22⋊C4—261no—
428C2×C22⋊C4—261no—
429C2×C22⋊C4—261no—
430C2×C22⋊C4—261no—
431C2×C22⋊C4C22⋊D1311yescharacteristic
432C2×C22⋊C4C22⋊D1311yescharacteristic
433C2×C42—261no—
434C2×C42C22×D1311yescharacteristic
435C2×C42C22×D1311yescharacteristic
436#107—262no—
437#107—521no—
438C4⋊C8—521no—
439C4⋊C8—521no—
440#102—262no—
441#102—521no—
442#102—521no—
443#102—521no—
444C22⋊C8—262no—
445#95—21no—
446#95—21no—
447#95—21no—
448#95—261no—
449#95—261no—
450#95C22⋊D1311yescharacteristic
451#95C22⋊D1311yescharacteristic
452C2×C13—24no—
453C2×C13#245011yescharacteristic
454C2×C13C2×#47411yescharacteristic
455C2×C13#308411yescharacteristic
456C2×C13#329411yescharacteristic
457C2×C13#329411yescharacteristic
458C2×C13#331611yescharacteristic
459C2×C13#332011yescharacteristic
460D13—82no—
461C24—261no—
462C24C2×C22⋊D1311yescharacteristic
463C2×Q8—42no—
464C2×Q8—42no—
465C2×Q8—81no—
466C2×D4—132no—
467C2×D4—264no—
468C2×D4—261no—
469C2×D4—261no—
470C2×D4—261no—
471C2×D4—261no—
472C2×D4—261no—
473C2×D4—522no—
474C2×D4—522no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—42no—
484C22×C4—42no—
485C22×C4—81no—
486C22×C4—261no—
487C22×C4—261no—
488C22×C4—261no—
489C22×C4—522no—
490C22×C4—522no—
491C22×C4—522no—
492C22×C4—522no—
493C22×C4—1041no—
494C22×C4—1041no—
495C22×C4Q8×D1312yes—
496C22×C4#613112yes—
497C22×C4C2×C22⋊D1311yescharacteristic
498C22×C4C2×C22⋊D1311yescharacteristic
499C22×C4C2×C22⋊D1311yescharacteristic
500C22×C4C2×C22⋊D1311yescharacteristic
501C22×C4C2×C22⋊D1311yescharacteristic
502C22×C4C23×D1311yescharacteristic
503C2×C8—261no—
504C2×C8—261no—
505C2×C8—261no—
506C2×C8—261no—
507C2×C8—261no—
508C2×C8—261no—
509C2×C8—261no—
510C2×C8—261no—
511C2×C8—261no—
512C2×C8—261no—
513C2×C8—261no—
514C2×C8—261no—
515C2×C8—524no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—42no—
524C4⋊C4—42no—
525C4⋊C4—42no—
526C4⋊C4—42no—
527C4⋊C4—42no—
528C4⋊C4—81no—
529C4⋊C4—132no—
530C4⋊C4—132no—
531C4⋊C4—261no—
532C4⋊C4—261no—
533C4⋊C4—261no—
534C4⋊C4—261no—
535C4⋊C4—522no—
536C4⋊C4—522no—
537C4⋊C4#612912yes—
538C22⋊C4—22no—
539C22⋊C4—42no—
540C22⋊C4—264no—
541C22⋊C4—522no—
542C22⋊C4—522no—
543C22⋊C4—1041no—
544C22⋊C4#610414yes—
545C42—21no—
546C42—21no—
547C42—21no—
548C42—21no—
549C42—522no—
550C13#2640811yescharacteristic, complemented, Sylow
551C23—21no—
552C23—21no—
553C23—21no—
554C23—21no—
555C23—262no—
556C23—521no—
557C23—521no—
558C23—521no—
559C23—521no—
560C23—521no—
561C23—521no—
562C23C2×#610412yes—
563C23#8819612yes—
564C23#8820012yes—
565C23C22×C22⋊D1311yescharacteristic
566Q8—84no—
567D4—262no—
568D4—262no—
569D4—528no—
570D4—521no—
571D4—521no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—21no—
583C2×C4—22no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—84no—
601C2×C4—262no—
602C2×C4—262no—
603C2×C4—521no—
604C2×C4—521no—
605C2×C4—521no—
606C2×C4—521no—
607C2×C4—521no—
608C2×C4—521no—
609C2×C4—521no—
610C2×C4—1044no—
611C2×C4—1044no—
612C2×C4C2×#610412yes—
613C2×C4C2×#610412yes—
614C2×C4#8820012yes—
615C2×C4C2×#612911yescharacteristic
616C2×C4#8825111yescharacteristic
617C2×C4C2×Q8×D1311yescharacteristic
618C2×C4C2×#613111yescharacteristic
619C2×C4#41×D1311yescharacteristic
620C2×C4#8825611yescharacteristic
621C8—521no—
622C8—521no—
623C8—521no—
624C8—521no—
625C22—22no—
626C22—22no—
627C22—22no—
628C22—22no—
629C22—22no—
630C22—22no—
631C22—522no—
632C22—522no—
633C22—522no—
634C22—1041no—
635C22—1041no—
636C22—1041no—
637C22—1041no—
638C22#1171874814yes—
639C22C22×#610411yescharacteristic
640C22#1171951111yescharacteristic
641C22C2×#8819611yescharacteristic
642C22C2×#8820011yescharacteristic
643C22#1171953411yescharacteristic
644C22#1171954111yescharacteristic
645C22#1171954211yescharacteristic
646C4—22no—
647C4—22no—
648C4—22no—
649C4—41no—
650C4—41no—
651C4—42no—
652C4—81no—
653C4—81no—
654C4—81no—
655C4—522no—
656C4—522no—
657C4—1041no—
658C4#1171932911yescharacteristic
659C4#1171934011yescharacteristic
660C4#1171934111yescharacteristic
661C4#1171934911yescharacteristic
662C2—24no—
663C2—1042no—
664C2#1311865611yescharacteristic
665C2C2×#1171874811yescharacteristic
666C2#1312469411yescharacteristic
667C2#1312664311yescharacteristic
668C2#1312664911yescharacteristic
669C2#1312694111yescharacteristic
670C2#1312700711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2440C2
socleC23×C13C22×D4
prime radicalC2×#88184C22
hypercenter#2440D13
hypocenterC13#26408
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2440

Complements

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

NH ≅ G/Ntype
2. #13116393C2semidirect
3. #13116327C2semidirect
4. #13116221C2semidirect
5. #13115969C2semidirect
6. #13115789C2semidirect
7. #13115404C2semidirect
10. #13115082C2semidirect
11. #13115023C2semidirect
12. #13115016C2semidirect
13. #13114833C2semidirect
14. C2×#11718121C2semidirect
15. C13×#2440C2semidirect
87. #88184Q8semidirect
216. #2440D13semidirect
550. C13#26408semidirect

Maximal subgroups

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

subgroupindex
#131178502
#131163932
#131163272
#131162212
#131159692
#131157892
#131154042
#131152622
#131151532
#131150822
#131150232
#131150162
#131148332
C2×#117181212
C13×#24402
#2640813