Finite Group Databasebeta

← #15920021

Subgroups — #15920021

Order 3328.

958 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718683C211yesmaximal, characteristic, complemented
2C2×#11718894C211yesmaximal, characteristic
3#13118549C211yesmaximal, characteristic, complemented
4#13116369C211yesmaximal, characteristic, complemented
5#13116224C211yesmaximal, characteristic, complemented
6#13116210C211yesmaximal, characteristic, complemented
7#13115982C211yesmaximal, characteristic, complemented
8#13115104C211yesmaximal, characteristic, complemented
9#13115104C211yesmaximal, characteristic, complemented
10#13115033C211yesmaximal, characteristic, complemented
11#13115016C211yesmaximal, characteristic, complemented
12#13114859C211yesmaximal, characteristic, complemented
13#13114841C211yesmaximal, characteristic, complemented
14#13114776C211yesmaximal, characteristic
15C13×#2341C211yesmaximal, characteristic
16C22×C13×#41C2211yescharacteristic
17C2×C4×Q8×C13C2211yescharacteristic
18C2×C4×Q8×C13C2211yescharacteristic
19C2×#88180C2211yescharacteristic
20C23×#1055C2211yescharacteristic
21C2×#88124C2211yescharacteristic
22C13×#390—21no—
23C13×#390—21no—
24C13×#390C2211yescharacteristic
25C13×#390C2211yescharacteristic
26C13×#380—21no—
27C13×#380C2211yescharacteristic
28C4×C13×C22⋊C4—21no—
29C4×C13×C22⋊C4C2211yescharacteristic
30#11718894—24no—
31C2×#88075C2211yescharacteristic
32C2×#88075C2211yescharacteristic
33C2×#88075C2211yescharacteristic
34C2×#88075C2211yescharacteristic
35C2×#88072C2211yescharacteristic
36C2×#88072C2211yescharacteristic
37C2×#88072C2211yescharacteristic
38C2×#88072C2211yescharacteristic
39#11718873C2211yescharacteristic
40C2×C22⋊#1055C2211yescharacteristic
41#11718683—24no—
42C2×#88048C2211yescharacteristic
43C2×#88048C2211yescharacteristic
44C2×#88048C2211yescharacteristic
45C2×#88047C2211yescharacteristic
46#11718610—21no—
47#11718609—21no—
48#11718596C2211yescharacteristic
49#11718589C2211yescharacteristic
50#11718589C2211yescharacteristic
51C2×C4⋊#1055C2211yescharacteristic
52C2×C4⋊#1055C2211yescharacteristic
53#11718315—21no—
54#11718308—21no—
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718116C2211yescharacteristic
60#11718116C2211yescharacteristic
61C2×C13×#41—22no—
62C2×C13×#41—22no—
63C2×C13×#41—22no—
64C2×C13×#41—41no—
65C2×C13×#41—41no—
66C2×C13×#41Q814yes—
67C22×Q8×C13C2311yescharacteristic
68C22×D4×C13—21no—
69C22×D4×C13C2311yescharacteristic
70C23×C4×C13—21no—
71C23×C4×C13C2311yescharacteristic
72C4×Q8×C13—22no—
73C4×Q8×C13—22no—
74C4×Q8×C13—41no—
75C4×Q8×C13—41no—
76C2×C13×C4⋊C4—21no—
77C2×C13×C4⋊C4—21no—
78C2×C13×C4⋊C4C2311yescharacteristic
79C2×C13×C4⋊C4C2311yescharacteristic
80C2×C13×C22⋊C4—21no—
81C2×C13×C22⋊C4—21no—
82C2×C13×C22⋊C4—21no—
83C2×C13×C22⋊C4—21no—
84C2×C13×C22⋊C4—21no—
85C2×C13×C22⋊C4D411yescharacteristic
86C2×C13×C22⋊C4D411yescharacteristic
87C2×C42×C13—21no—
88C2×C42×C13—21no—
89C2×C42×C13C2311yescharacteristic
90C2×C42×C13C2311yescharacteristic
91C2×C22⋊Dic13—21no—
92C2×C22⋊Dic13—21no—
93#88180—22no—
94#88180—41no—
95C2×C4⋊Dic13—21no—
96C2×C4⋊Dic13—21no—
97C2×C4⋊Dic13C2311yescharacteristic
98C2×C4⋊Dic13C2311yescharacteristic
99C2×C4⋊Dic13C2311yescharacteristic
100C2×C4⋊Dic13C2311yescharacteristic
101C2×#6101—21no—
102C2×#6101—21no—
103C2×#6101—21no—
104C2×#6101—21no—
105C2×C4×Dic13—21no—
106C22×#1055—22no—
107C22×#1055—22no—
108C22×#1055—41no—
109C22×#1055C2311yescharacteristic
110C22×#1055C2311yescharacteristic
111C22×#1055C2311yescharacteristic
112C22×#1055C2311yescharacteristic
113#88124—22no—
114#88124—41no—
115C13×#95—21no—
116C13×#95D411yescharacteristic
117C13×#95D411yescharacteristic
118#88075—22no—
119#88075—22no—
120#88075—22no—
121#88075D414yes—
122#88072—22no—
123#88072—22no—
124#88072—41no—
125#88072—41no—
126#88071—21no—
127#88071—21no—
128#88071—21no—
129C22⋊#1055—22no—
130#88048—22no—
131#88048—41no—
132#88048—41no—
133#88047—22no—
134C4⋊#1055—22no—
135C4⋊#1055—41no—
136#25953—131nomaximal, Sylow
137C24×C13—21no—
138C24×C13C2×D411yescharacteristic
139C13×#41—28no—
140C13×#41—44no—
141C13×#41—44no—
142C13×#41—44no—
143C2×Q8×C13—21no—
144C2×Q8×C13—21no—
145C2×Q8×C13—21no—
146C2×Q8×C13C2×D412yes—
147C2×Q8×C13C2×Q812yes—
148C2×Q8×C13#4112yes—
149C2×D4×C13—24no—
150C2×D4×C13—21no—
151C2×D4×C13—21no—
152C2×D4×C13—21no—
153C2×D4×C13—21no—
154C2×D4×C13—21no—
155C2×D4×C13—42no—
156C2×D4×C13—42no—
157C2×D4×C13C2×Q812yes—
158C22×C4×C13—21no—
159C22×C4×C13—21no—
160C22×C4×C13—21no—
161C22×C4×C13—21no—
162C22×C4×C13—21no—
163C22×C4×C13—24no—
164C22×C4×C13—21no—
165C22×C4×C13—21no—
166C22×C4×C13—42no—
167C22×C4×C13—42no—
168C22×C4×C13C2×D411yescharacteristic
169C22×C4×C13C2×D411yescharacteristic
170C22×C4×C13C2×D411yescharacteristic
171C22×C4×C13C2×D411yescharacteristic
172C22×C4×C13C2×D411yescharacteristic
173C22×C4×C13C2×Q812yes—
174C22×C4×C13#4112yes—
175C22×C4×C13C2411yescharacteristic
176C22×Dic13—21no—
177C22×Dic13—21no—
178C22×Dic13—21no—
179C22×Dic13—21no—
180C13×C4⋊C4—21no—
181C13×C4⋊C4—21no—
182C13×C4⋊C4—21no—
183C13×C4⋊C4—21no—
184C13×C4⋊C4—42no—
185C13×C4⋊C4—42no—
186C13×C22⋊C4—22no—
187C13×C22⋊C4—41no—
188C13×C22⋊C4—42no—
189C13×C22⋊C4—42no—
190C13×C22⋊C4—81no—
191C13×C22⋊C4—81no—
192C13×C22⋊C4—81no—
193C42×C13—21no—
194C42×C13—21no—
195C42×C13—21no—
196C42×C13—21no—
197C42×C13—42no—
198C42×C13—42no—
199C22⋊Dic13—42no—
200C22⋊Dic13—81no—
201C4⋊Dic13—21no—
202C4⋊Dic13—21no—
203C4⋊Dic13—21no—
204C4⋊Dic13—21no—
205C4⋊Dic13—21no—
206C4⋊Dic13—21no—
207C4⋊Dic13—21no—
208C4⋊Dic13—42no—
209C4⋊Dic13—81no—
210C4⋊Dic13C2×D412yes—
211#6101—42no—
212#6101—42no—
213#6101—42no—
214#6101—81no—
215C4×Dic13—42no—
216C2×#1055—21no—
217C2×#1055—21no—
218C2×#1055—21no—
219C2×#1055—21no—
220C2×#1055—21no—
221C2×#1055—21no—
222C2×#1055—21no—
223C2×#1055—21no—
224C2×#1055—21no—
225C2×#1055—21no—
226C2×#1055—21no—
227C2×#1055—44no—
228C2×#1055C2×D412yes—
229C2×#479—131no—
230C2×#416—131no—
231#2441—131no—
232#2341D1311yescharacteristic
233#2094—131no—
234#2067—131no—
235#2065—131no—
236#2025—131no—
237#1865—131no—
238#1865—131no—
239#1854—131no—
240#1850—131no—
241#1807—131no—
242#1803—131no—
243#1788—131no—
244C23×C13—21no—
245C23×C13—21no—
246C23×C13—21no—
247C23×C13—21no—
248C23×C13—21no—
249C23×C13—21no—
250C23×C13—22no—
251C23×C13—41no—
252C23×C13—41no—
253C23×C13—41no—
254C23×C13—41no—
255C23×C13—41no—
256C23×C13—41no—
257C23×C13C22⋊Q812yes—
258C23×C13C22×D411yescharacteristic
259Q8×C13—22no—
260Q8×C13—22no—
261Q8×C13—22no—
262Q8×C13C22⋊Q814yes—
263D4×C13—22no—
264D4×C13—22no—
265D4×C13—48no—
266D4×C13—41no—
267D4×C13—41no—
268C2×C4×C13—22no—
269C2×C4×C13—21no—
270C2×C4×C13—22no—
271C2×C4×C13—21no—
272C2×C4×C13—22no—
273C2×C4×C13—21no—
274C2×C4×C13—21no—
275C2×C4×C13—22no—
276C2×C4×C13—22no—
277C2×C4×C13—22no—
278C2×C4×C13—22no—
279C2×C4×C13—21no—
280C2×C4×C13—21no—
281C2×C4×C13—21no—
282C2×C4×C13—21no—
283C2×C4×C13—21no—
284C2×C4×C13—21no—
285C2×C4×C13—21no—
286C2×C4×C13—21no—
287C2×C4×C13—21no—
288C2×C4×C13—48no—
289C2×C4×C13—41no—
290C2×C4×C13—41no—
291C2×C4×C13—41no—
292C2×C4×C13—41no—
293C2×C4×C13—41no—
294C2×C4×C13—41no—
295C2×C4×C13C22⋊Q812yes—
296C2×C4×C13#13512yes—
297C2×C4×C13C22×D411yescharacteristic
298C2×C4×C13C22×Q811yescharacteristic
299C2×C4×C13C2×#4111yescharacteristic
300C2×C4×C13C2×#4111yescharacteristic
301C2×C4×C13H(5,𝔽2)11yescharacteristic
302C2×C4×C13H(5,𝔽2)11yescharacteristic
303C2×Dic13—22no—
304C2×Dic13—41no—
305C2×Dic13—41no—
306C2×Dic13—41no—
307C2×Dic13—41no—
308C2×Dic13—41no—
309C2×Dic13—41no—
310C2×Dic13—41no—
311C2×Dic13—41no—
312C2×Dic13—41no—
313C2×Dic13—41no—
314C2×Dic13—41no—
315#1055—22no—
316#1055—41no—
317#1055—41no—
318#1055—41no—
319C22×#41C2×D1311yescharacteristic
320C23×C8—131no—
321C2×#125—131no—
322C2×C4×Q8C2×D1311yescharacteristic
323C2×C4×Q8C2×D1311yescharacteristic
324C2×#117—131no—
325#479—264no—
326C2×#107—131no—
327C2×#106—131no—
328C2×#106—131no—
329C2×#106—131no—
330C2×C4⋊C8—131no—
331C2×C4⋊C8—131no—
332#416—264no—
333C2×#103—131no—
334C2×#103—131no—
335C2×#103—131no—
336C2×#103—131no—
337C2×#102—131no—
338C2×#102—131no—
339C2×#102—131no—
340C2×#102—131no—
341C2×C22⋊C8—131no—
342#399—261no—
343#396—261no—
344#390—21no—
345#390—21no—
346#390C2×D1311yescharacteristic
347#390C2×D1311yescharacteristic
348#389—131no—
349#389—131no—
350#389—261no—
351#387—261no—
352#384—131no—
353#380—21no—
354#380—131no—
355#380C2×D1311yescharacteristic
356C4×C22⋊C4—21no—
357C4×C22⋊C4C2×D1311yescharacteristic
358#340—131no—
359#340—131no—
360#340—131no—
361#340—131no—
362#336—131no—
363#336—131no—
364C22×C13—22no—
365C22×C13—22no—
366C22×C13—22no—
367C22×C13—41no—
368C22×C13—41no—
369C22×C13—41no—
370C22×C13—41no—
371C22×C13—42no—
372C22×C13—42no—
373C22×C13—42no—
374C22×C13—81no—
375C22×C13—81no—
376C22×C13—81no—
377C22×C13—81no—
378C22×C13C2×C22⋊Q811yescharacteristic
379C22×C13D4211yescharacteristic
380C22×C13#54611yescharacteristic
381C22×C13C2×#13511yescharacteristic
382C22×C13#57511yescharacteristic
383C22×C13#57711yescharacteristic
384C22×C13#57711yescharacteristic
385C4×C13—22no—
386C4×C13—24no—
387C4×C13—22no—
388C4×C13—41no—
389C4×C13—41no—
390C4×C13—41no—
391C4×C13—81no—
392C4×C13—81no—
393C4×C13C2×C22⋊Q811yescharacteristic
394C4×C13#54311yescharacteristic
395C4×C13#54611yescharacteristic
396C4×C13#55111yescharacteristic
397Dic13—42no—
398Dic13—81no—
399Dic13—81no—
400Dic13—81no—
401C2×#41—22no—
402C2×#41—22no—
403C2×#41—22no—
404C2×#41—41no—
405C2×#41—41no—
406C2×#41Dic2614yes—
407C22×Q8C22×D1311yescharacteristic
408C22×D4—21no—
409C22×D4C22×D1311yescharacteristic
410C23×C4—21no—
411C23×C4C22×D1311yescharacteristic
412C22×C8—131no—
413C22×C8—131no—
414C22×C8—131no—
415C22×C8—131no—
416C22×C8—262no—
417C22×C8—262no—
418C22×C8—521no—
419#125—262no—
420#125—521no—
421C4×Q8—22no—
422C4×Q8—22no—
423C4×Q8—41no—
424C4×Q8—41no—
425#117—262no—
426#117—521no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—131no—
430C2×C4⋊C4—131no—
431C2×C4⋊C4—131no—
432C2×C4⋊C4—131no—
433C2×C4⋊C4—261no—
434C2×C4⋊C4—261no—
435C2×C4⋊C4—261no—
436C2×C4⋊C4—261no—
437C2×C4⋊C4—261no—
438C2×C4⋊C4—261no—
439C2×C4⋊C4C22×D1311yescharacteristic
440C2×C4⋊C4C22×D1311yescharacteristic
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—261no—
447C2×C22⋊C4—261no—
448C2×C22⋊C4C22⋊D1311yescharacteristic
449C2×C22⋊C4C22⋊D1311yescharacteristic
450C2×C42—21no—
451C2×C42—21no—
452C2×C42—261no—
453C2×C42C22×D1311yescharacteristic
454C2×C42C22×D1311yescharacteristic
455#107—262no—
456#106—262no—
457#106—521no—
458#106—521no—
459C4⋊C8—262no—
460C4⋊C8—521no—
461#103—134no—
462#103—262no—
463#103—262no—
464#103—262no—
465#102—262no—
466#102—262no—
467#102—521no—
468#102—521no—
469C22⋊C8—262no—
470#95—21no—
471#95—261no—
472#95—261no—
473#95—261no—
474#95C22⋊D1311yescharacteristic
475#95C22⋊D1311yescharacteristic
476C2×C13—42no—
477C2×C13—82no—
478C2×C13#243711yescharacteristic
479C2×C13#307611yescharacteristic
480C2×C13#308411yescharacteristic
481C2×C13#327111yescharacteristic
482C2×C13#328411yescharacteristic
483C2×C13#330111yescharacteristic
484C2×C13#331711yescharacteristic
485C24—21no—
486C24C2×C22⋊D1311yescharacteristic
487#41—28no—
488#41—44no—
489#41—44no—
490#41—44no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8C2×Dic2612yes—
495C2×Q8D4×D1312yes—
496C2×Q8#612912yes—
497C2×D4—24no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—42no—
504C2×D4—42no—
505C2×D4C2×Dic2612yes—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—24no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—42no—
515C22×C4—42no—
516C22×C4—261no—
517C22×C4—261no—
518C22×C4—261no—
519C22×C4—261no—
520C22×C4C2×Dic2612yes—
521C22×C4#612712yes—
522C22×C4C2×C22⋊D1311yescharacteristic
523C22×C4C2×C22⋊D1311yescharacteristic
524C22×C4C2×C22⋊D1311yescharacteristic
525C22×C4C2×C22⋊D1311yescharacteristic
526C22×C4C2×C22⋊D1311yescharacteristic
527C22×C4C23×D1311yescharacteristic
528C2×C8—132no—
529C2×C8—261no—
530C2×C8—261no—
531C2×C8—261no—
532C2×C8—261no—
533C2×C8—261no—
534C2×C8—261no—
535C2×C8—261no—
536C2×C8—261no—
537C2×C8—261no—
538C2×C8—261no—
539C2×C8—261no—
540C2×C8—524no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—42no—
546C4⋊C4—42no—
547C4⋊C4—132no—
548C4⋊C4—261no—
549C4⋊C4—261no—
550C4⋊C4—261no—
551C4⋊C4—261no—
552C4⋊C4—261no—
553C4⋊C4—261no—
554C4⋊C4—261no—
555C4⋊C4—522no—
556C4⋊C4—522no—
557C4⋊C4—522no—
558C4⋊C4—522no—
559C4⋊C4—1041no—
560C4⋊C4—1041no—
561C22⋊C4—22no—
562C22⋊C4—41no—
563C22⋊C4—42no—
564C22⋊C4—42no—
565C22⋊C4—81no—
566C22⋊C4—81no—
567C22⋊C4—81no—
568C22⋊C4—522no—
569C22⋊C4—1041no—
570C42—21no—
571C42—21no—
572C42—21no—
573C42—21no—
574C42—42no—
575C42—42no—
576C42—522no—
577C13#2595311yescharacteristic, complemented, Sylow
578C23—21no—
579C23—21no—
580C23—21no—
581C23—21no—
582C23—21no—
583C23—21no—
584C23—22no—
585C23—41no—
586C23—41no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23#8817812yes—
592C23C22×C22⋊D1311yescharacteristic
593Q8—22no—
594Q8—22no—
595Q8—22no—
596Q8#8813214yes—
597D4—22no—
598D4—22no—
599D4—48no—
600D4—41no—
601D4—41no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—22no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—48no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—262no—
630C2×C4—521no—
631C2×C4—521no—
632C2×C4—521no—
633C2×C4—521no—
634C2×C4—521no—
635C2×C4—521no—
636C2×C4—521no—
637C2×C4—521no—
638C2×C4—521no—
639C2×C4—521no—
640C2×C4—521no—
641C2×C4#8817812yes—
642C2×C4#8820412yes—
643C2×C4C22×Dic2611yescharacteristic
644C2×C4C2×#612711yescharacteristic
645C2×C4C2×D4×D1311yescharacteristic
646C2×C4C2×#612911yescharacteristic
647C2×C4#8825111yescharacteristic
648C2×C4#8825111yescharacteristic
649C8—262no—
650C8—521no—
651C8—521no—
652C8—521no—
653C22—22no—
654C22—22no—
655C22—22no—
656C22—41no—
657C22—41no—
658C22—41no—
659C22—41no—
660C22—42no—
661C22—42no—
662C22—42no—
663C22—81no—
664C22—81no—
665C22—81no—
666C22—81no—
667C22C2×#8817811yescharacteristic
668C22D4×C22⋊D1311yescharacteristic
669C22#1171951111yescharacteristic
670C22C2×#8820411yescharacteristic
671C22#1171952711yescharacteristic
672C22#1171954111yescharacteristic
673C22#1171954211yescharacteristic
674C4—22no—
675C4—24no—
676C4—22no—
677C4—41no—
678C4—41no—
679C4—41no—
680C4—81no—
681C4—81no—
682C4—522no—
683C4—1041no—
684C4—1041no—
685C4—1041no—
686C4C2×#8813211yescharacteristic
687C4#1171918811yescharacteristic
688C4#1171919511yescharacteristic
689C4#1171920011yescharacteristic
690C2—42no—
691C2—82no—
692C2#1311849711yescharacteristic
693C2#1312462411yescharacteristic
694C2#1312469811yescharacteristic
695C2#1312642211yescharacteristic
696C2#1312656611yescharacteristic
697C2#1312673811yescharacteristic
698C2#1312696211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2341C2
socleC23×C13C22×D4
prime radicalC22×C13×#41C22
hypercenter#2341D13
hypocenterC13#25953
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2341

Complements

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

NH ≅ G/Ntype
1. C2×#11718683C2semidirect
3. #13118549C2semidirect
4. #13116369C2semidirect
5. #13116224C2semidirect
6. #13116210C2semidirect
7. #13115982C2semidirect
8. #13115104C2semidirect
9. #13115104C2semidirect
10. #13115033C2semidirect
11. #13115016C2semidirect
12. #13114859C2semidirect
13. #13114841C2semidirect
577. C13#25953semidirect

Maximal subgroups

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

subgroupindex
C2×#117186832
C2×#117188942
#131185492
#131163692
#131162242
#131162102
#131159822
#131151042
#131150332
#131150162
#131148592
#131148412
#131147762
C13×#23412
#2595313