Finite Group Databasebeta

← #15919829

Subgroups — #15919829

Order 3328.

1028 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718729C211yesmaximal, characteristic
2C2×#11718689C211yesmaximal, characteristic
3#13120324C211yesmaximal, characteristic
4#13115984C211yesmaximal, characteristic, complemented
5#13115979C211yesmaximal, characteristic
6#13115974C211yesmaximal, characteristic, complemented
7#13115969C211yesmaximal, characteristic
8#13115794C211yesmaximal, characteristic, complemented
9#13115773C211yesmaximal, characteristic, complemented
10#13115191C211yesmaximal, characteristic
11#13115191C211yesmaximal, characteristic
12#13115177C211yesmaximal, characteristic, complemented
13#13115177C211yesmaximal, characteristic, complemented
14C4×#88075C211yesmaximal, characteristic, complemented
15C2×C13×#557C211yesmaximal, characteristic, complemented
16C13×#557—24no—
17C13×#557—24no—
18C2×C13×C4⋊Q8—21no—
19C2×C13×C4⋊Q8C2211yescharacteristic
20C2×C13×#125—21no—
21C2×C13×#125—21no—
22C2×C13×#125C2211yescharacteristic
23C2×C13×#125C2211yescharacteristic
24C2×C4×Q8×C13—21no—
25C2×C4×Q8×C13C2211yescharacteristic
26C2×C4×Q8×C13C2211yescharacteristic
27C2×C4×Q8×C13C2211yescharacteristic
28C2×C4×Q8×C13C2211yescharacteristic
29C22×#6107C2211yescharacteristic
30C22×#6106C2211yescharacteristic
31C2×#88129C2211yescharacteristic
32#11718892—21no—
33C2×#88075C2211yescharacteristic
34C2×#88075C2211yescharacteristic
35#11718729—24no—
36#11718689—24no—
37#11718654—21no—
38#11718651—21no—
39#11718651—21no—
40C2×#88050C2211yescharacteristic
41C2×#88050C2211yescharacteristic
42C2×#88050C2211yescharacteristic
43C2×#88049C2211yescharacteristic
44C2×#88049C2211yescharacteristic
45C2×#88049C2211yescharacteristic
46#11718600C2211yescharacteristic
47#11718600C2211yescharacteristic
48C4×C4⋊Dic13C2211yescharacteristic
49#11718590C2211yescharacteristic
50#11718590C2211yescharacteristic
51C2×C4⋊#1055C2211yescharacteristic
52C2×C4×#1055C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718116C2211yescharacteristic
60#11718116C2211yescharacteristic
61#11718116C2211yescharacteristic
62#11718116C2211yescharacteristic
63C22×Q8×C13—21no—
64C22×Q8×C13D411yescharacteristic
65C22×Q8×C13C2311yescharacteristic
66C22×D52C2311yescharacteristic
67C22×Dic26C2311yescharacteristic
68C13×C4⋊Q8—28no—
69C13×C4⋊Q8—22no—
70C13×C4⋊Q8—22no—
71C13×#125—28no—
72C13×#125—28no—
73C13×#125—22no—
74C13×#125—22no—
75C13×#125—22no—
76C13×#125D414yes—
77C4×Q8×C13—28no—
78C4×Q8×C13—22no—
79C4×Q8×C13—22no—
80C4×Q8×C13—22no—
81C4×Q8×C13—22no—
82C4×Q8×C13—22no—
83C4×Q8×C13—22no—
84C4×Q8×C13—22no—
85C4×Q8×C13D414yes—
86C2×C13×C4⋊C4—21no—
87C2×C13×C4⋊C4—21no—
88C2×C13×C4⋊C4—21no—
89C2×C13×C4⋊C4—21no—
90C2×C13×C4⋊C4—21no—
91C2×C13×C4⋊C4—21no—
92C2×C13×C4⋊C4—21no—
93C2×C13×C4⋊C4—21no—
94C2×C13×C4⋊C4D411yescharacteristic
95C2×C13×C4⋊C4D411yescharacteristic
96C2×C13×C4⋊C4D411yescharacteristic
97C2×C13×C4⋊C4C2311yescharacteristic
98C2×C13×C4⋊C4C2311yescharacteristic
99C2×C13×C4⋊C4C2311yescharacteristic
100C2×C42×C13—21no—
101C2×C42×C13—21no—
102C2×C42×C13—21no—
103C2×C42×C13C2311yescharacteristic
104C2×C42×C13C2311yescharacteristic
105C2×C42×C13C2311yescharacteristic
106C2×#6107—22no—
107C2×#6107—22no—
108C2×#6107—22no—
109C2×#6106—22no—
110C2×#6106—22no—
111C2×#6106—22no—
112C2×#6103—21no—
113C2×#6103—21no—
114C2×#6103—21no—
115C2×#6103—21no—
116C2×#6103—21no—
117C2×#6103—21no—
118C2×C4⋊Dic13C2311yescharacteristic
119C2×C4⋊Dic13C2311yescharacteristic
120C2×C4×Dic13—21no—
121C22×#1055C2311yescharacteristic
122C22×#1055C2311yescharacteristic
123C22×#1055C2311yescharacteristic
124C22×#1055C2311yescharacteristic
125#88129—22no—
126#88129—22no—
127#88075—22no—
128#88075—22no—
129#88071—21no—
130#88071—21no—
131#88071—21no—
132#88071—21no—
133#88071—21no—
134#88050—22no—
135#88050—22no—
136#88050—22no—
137#88049—22no—
138#88049—22no—
139#88049—22no—
140C4⋊#1055—22no—
141C4×#1055—22no—
142#25937—131nomaximal, Sylow
143C23×D13—21no—
144C2×Q8×C13—24no—
145C2×Q8×C13—22no—
146C2×Q8×C13—22no—
147C2×Q8×C13—21no—
148C2×Q8×C13—21no—
149C2×Q8×C13—21no—
150C2×Q8×C13—41no—
151C2×Q8×C13—42no—
152C2×Q8×C13—42no—
153C2×Q8×C13C2×D412yes—
154C2×Q8×C13#4112yes—
155C2×Q8×C13#4112yes—
156C22×C4×C13—21no—
157C22×C4×C13—21no—
158C22×C4×C13—21no—
159C22×C4×C13—21no—
160C22×C4×C13C2×D411yescharacteristic
161C22×C4×C13C2×D411yescharacteristic
162C22×C4×C13C2×D411yescharacteristic
163C22×C4×C13C2×D411yescharacteristic
164C22×C4×C13C2×D411yescharacteristic
165C22×C4×C13C2×D411yescharacteristic
166C22×C4×C13C2411yescharacteristic
167C22×Dic13—21no—
168C22×Dic13—21no—
169C22×Dic13—21no—
170C2×D52—21no—
171C2×D52—21no—
172C2×D52—21no—
173C2×D52—21no—
174C2×D52—21no—
175C2×D52—21no—
176C2×Dic26—21no—
177C2×Dic26—21no—
178C2×Dic26—21no—
179C2×Dic26—21no—
180C2×Dic26—21no—
181C2×Dic26—21no—
182C13×C4⋊C4—24no—
183C13×C4⋊C4—24no—
184C13×C4⋊C4—24no—
185C13×C4⋊C4—24no—
186C13×C4⋊C4—24no—
187C13×C4⋊C4—24no—
188C13×C4⋊C4—24no—
189C13×C4⋊C4—24no—
190C13×C4⋊C4—22no—
191C13×C4⋊C4—22no—
192C13×C4⋊C4—22no—
193C13×C4⋊C4—21no—
194C13×C4⋊C4—21no—
195C13×C4⋊C4—21no—
196C13×C4⋊C4C2×D412yes—
197C13×C4⋊C4C2×D412yes—
198C13×C4⋊C4C2×D412yes—
199C42×C13—24no—
200C42×C13—24no—
201C42×C13—24no—
202C42×C13—21no—
203C42×C13—21no—
204C42×C13—21no—
205C42×C13—21no—
206C42×C13C2×D412yes—
207C42×C13C2×D412yes—
208#6107—44no—
209#6106—44no—
210#6103—42no—
211#6103—42no—
212#6103—42no—
213#6103—42no—
214#6103—81no—
215#6103—81no—
216C4⋊Dic13—21no—
217C4⋊Dic13—21no—
218C4⋊Dic13—21no—
219C4⋊Dic13—21no—
220C4×Dic13—81no—
221C2×#1055—21no—
222C2×#1055—21no—
223C2×#1055—21no—
224C2×#1055—21no—
225C2×#1055—21no—
226C2×#1055—21no—
227C2×#1055—21no—
228C2×#1055—21no—
229C2×#1055—21no—
230C2×#1055—21no—
231C2×#1055—21no—
232C2×#1055—21no—
233C2×#557D1311yescharacteristic, complemented
234C2×#488—131no—
235C2×#464—131no—
236#2592—131no—
237#2026—131no—
238#2025—131no—
239#2024—131no—
240#2023—131no—
241#1989—131no—
242#1984—131no—
243#1880—131no—
244#1880—131no—
245#1878—131no—
246#1878—131no—
247C4×#103—131no—
248C23×C13C22×D411yescharacteristic
249C22×D13—41no—
250C22×D13—41no—
251C22×D13—41no—
252C22×D13—41no—
253C22×D13—41no—
254C22×D13—41no—
255C22×D13—41no—
256Q8×C13—22no—
257Q8×C13—22no—
258Q8×C13—22no—
259Q8×C13—44no—
260Q8×C13—48no—
261Q8×C13#12414yes—
262C2×C4×C13—22no—
263C2×C4×C13—21no—
264C2×C4×C13—22no—
265C2×C4×C13—22no—
266C2×C4×C13—21no—
267C2×C4×C13—21no—
268C2×C4×C13—21no—
269C2×C4×C13—21no—
270C2×C4×C13—21no—
271C2×C4×C13—21no—
272C2×C4×C13—21no—
273C2×C4×C13—22no—
274C2×C4×C13—21no—
275C2×C4×C13—22no—
276C2×C4×C13—22no—
277C2×C4×C13—21no—
278C2×C4×C13—21no—
279C2×C4×C13—21no—
280C2×C4×C13—21no—
281C2×C4×C13—21no—
282C2×C4×C13—21no—
283C2×C4×C13—41no—
284C2×C4×C13—41no—
285C2×C4×C13—41no—
286C2×C4×C13—41no—
287C2×C4×C13—41no—
288C2×C4×C13—41no—
289C2×C4×C13#12012yes—
290C2×C4×C13#12012yes—
291C2×C4×C13#13512yes—
292C2×C4×C13C22×D411yescharacteristic
293C2×C4×C13C22×D411yescharacteristic
294C2×C4×C13C2×#4111yescharacteristic
295C2×C4×C13C2×#4111yescharacteristic
296C2×C4×C132−1+411yescharacteristic
297C2×C4×C132−1+411yescharacteristic
298C2×Dic13—41no—
299C2×Dic13—41no—
300C2×Dic13—41no—
301C2×Dic13—41no—
302C2×Dic13—41no—
303C2×Dic13—41no—
304C2×Dic13—41no—
305C2×Dic13—41no—
306C2×Dic13—41no—
307D52—41no—
308D52—41no—
309D52—41no—
310D52—41no—
311Dic26—41no—
312Dic26—41no—
313Dic26—41no—
314Dic26—41no—
315#1055—41no—
316#1055—41no—
317#1055—41no—
318#1055—41no—
319C22×Q16—131no—
320C22×SD16—131no—
321#557—24no—
322#557—24no—
323C2×C4⋊Q8—21no—
324C2×C4⋊Q8C2×D1311yescharacteristic
325C2×#125—21no—
326C2×#125—21no—
327C2×#125C2×D1311yescharacteristic
328C2×#125C2×D1311yescharacteristic
329C2×#124—131no—
330C2×C4×Q8—21no—
331C2×C4×Q8C2×D1311yescharacteristic
332C2×C4×Q8C2×D1311yescharacteristic
333C2×C4×Q8C2×D1311yescharacteristic
334C2×C4×Q8C2×D1311yescharacteristic
335#488—264no—
336#464—264no—
337C2×C4⋊C8—131no—
338C2×#103—131no—
339C2×#103—131no—
340C2×#103—131no—
341C2×#103—131no—
342C2×#103—131no—
343C2×#102—131no—
344C2×#102—131no—
345C2×#102—131no—
346C2×C4×C8—131no—
347#397—261no—
348#393—261no—
349#391—131no—
350#391—131no—
351#390—131no—
352#390—131no—
353#388—261no—
354#388—261no—
355C4×C4⋊C4—131no—
356#340—131no—
357#340—131no—
358#340—131no—
359#340—131no—
360#340—131no—
361#340—131no—
362#336—131no—
363#336—131no—
364#336—131no—
365#336—131no—
366C22×C13C2×#12011yescharacteristic
367C22×C13#54811yescharacteristic
368C22×C13#54811yescharacteristic
369C22×C13C2×#13511yescharacteristic
370C22×C13#57511yescharacteristic
371C22×C13#57711yescharacteristic
372C22×C13#57811yescharacteristic
373C2×D13—81no—
374C2×D13—81no—
375C2×D13—81no—
376C2×D13—81no—
377C2×D13—81no—
378C2×D13—81no—
379C2×D13—81no—
380C4×C13—24no—
381C4×C13—22no—
382C4×C13—22no—
383C4×C13—22no—
384C4×C13—41no—
385C4×C13—42no—
386C4×C13—42no—
387C4×C13—41no—
388C4×C13—41no—
389C4×C13—42no—
390C4×C13C2×#12411yescharacteristic
391C4×C13#53611yescharacteristic
392C4×C13#54811yescharacteristic
393C4×C13#54811yescharacteristic
394Dic13—81no—
395Dic13—81no—
396Dic13—81no—
397C22×Q8—21no—
398C22×Q8—131no—
399C22×Q8C22⋊D1311yescharacteristic
400C22×Q8C22×D1311yescharacteristic
401C22×D4—131no—
402C2×Q16—262no—
403C2×Q16—262no—
404C2×Q16—262no—
405C2×SD16—262no—
406C2×SD16—262no—
407C2×SD16—262no—
408C22×C8—131no—
409C22×C8—131no—
410C22×C8—131no—
411C22×C8—131no—
412C4⋊Q8—28no—
413C4⋊Q8—22no—
414C4⋊Q8—22no—
415#125—28no—
416#125—28no—
417#125—22no—
418#125—22no—
419#125—22no—
420#125C22⋊D1314yes—
421#124—262no—
422#124—262no—
423C4×Q8—28no—
424C4×Q8—22no—
425C4×Q8—22no—
426C4×Q8—22no—
427C4×Q8—22no—
428C4×Q8—22no—
429C4×Q8—22no—
430C4×Q8—22no—
431C4×Q8C22⋊D1314yes—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—131no—
441C2×C4⋊C4—131no—
442C2×C4⋊C4C22⋊D1311yescharacteristic
443C2×C4⋊C4C22⋊D1311yescharacteristic
444C2×C4⋊C4C22⋊D1311yescharacteristic
445C2×C4⋊C4C22×D1311yescharacteristic
446C2×C4⋊C4C22×D1311yescharacteristic
447C2×C4⋊C4C22×D1311yescharacteristic
448C2×C22⋊C4—261no—
449C2×C22⋊C4—261no—
450C2×C22⋊C4—261no—
451C2×C22⋊C4—261no—
452C2×C22⋊C4—261no—
453C2×C22⋊C4—261no—
454C2×C42—21no—
455C2×C42—21no—
456C2×C42—21no—
457C2×C42—261no—
458C2×C42C22×D1311yescharacteristic
459C2×C42C22×D1311yescharacteristic
460C2×C42C22×D1311yescharacteristic
461C4⋊C8—262no—
462#103—262no—
463#103—262no—
464#103—262no—
465#103—262no—
466#103—262no—
467#102—262no—
468#102—262no—
469#102—262no—
470C4×C8—262no—
471#95—261no—
472#95—261no—
473#95—261no—
474#95—261no—
475#95—261no—
476C2×C13#243611yescharacteristic
477C2×C13#300211yescharacteristic
478C2×C13#301311yescharacteristic
479C2×C13#336411yescharacteristic
480C2×C13#336511yescharacteristic
481C2×C13#337111yescharacteristic
482C2×C13#337711yescharacteristic
483D13—161no—
484C24—261no—
485C2×Q8—24no—
486C2×Q8—22no—
487C2×Q8—22no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—41no—
492C2×Q8—42no—
493C2×Q8—42no—
494C2×Q8—261no—
495C2×Q8—261no—
496C2×Q8—261no—
497C2×Q8—261no—
498C2×Q8—261no—
499C2×Q8—261no—
500C2×Q8#613112yes—
501C2×Q8#613112yes—
502C2×Q8C2×C22⋊D1312yes—
503C2×D4—261no—
504C2×D4—261no—
505C2×D4—261no—
506C2×D4—261no—
507C2×D4—261no—
508C2×D4—261no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—261no—
514C22×C4—261no—
515C22×C4—261no—
516C22×C4C2×C22⋊D1311yescharacteristic
517C22×C4C2×C22⋊D1311yescharacteristic
518C22×C4C2×C22⋊D1311yescharacteristic
519C22×C4C2×C22⋊D1311yescharacteristic
520C22×C4C2×C22⋊D1311yescharacteristic
521C22×C4C2×C22⋊D1311yescharacteristic
522C22×C4C23×D1311yescharacteristic
523Q16—524no—
524SD16—524no—
525C2×C8—261no—
526C2×C8—261no—
527C2×C8—261no—
528C2×C8—261no—
529C2×C8—261no—
530C2×C8—261no—
531C2×C8—261no—
532C2×C8—261no—
533C2×C8—261no—
534C2×C8—261no—
535C2×C8—261no—
536C2×C8—261no—
537C4⋊C4—24no—
538C4⋊C4—24no—
539C4⋊C4—24no—
540C4⋊C4—24no—
541C4⋊C4—24no—
542C4⋊C4—24no—
543C4⋊C4—24no—
544C4⋊C4—24no—
545C4⋊C4—22no—
546C4⋊C4—22no—
547C4⋊C4—22no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—261no—
552C4⋊C4—261no—
553C4⋊C4—261no—
554C4⋊C4—261no—
555C4⋊C4C2×C22⋊D1312yes—
556C4⋊C4C2×C22⋊D1312yes—
557C4⋊C4C2×C22⋊D1312yes—
558C22⋊C4—522no—
559C22⋊C4—522no—
560C22⋊C4—522no—
561C22⋊C4—522no—
562C22⋊C4—1041no—
563C22⋊C4—1041no—
564C42—24no—
565C42—24no—
566C42—24no—
567C42—21no—
568C42—21no—
569C42—21no—
570C42—21no—
571C42—1041no—
572C42C2×C22⋊D1312yes—
573C42C2×C22⋊D1312yes—
574C13#2593711yescharacteristic, complemented, Sylow
575C23—521no—
576C23—521no—
577C23—521no—
578C23—521no—
579C23—521no—
580C23—521no—
581C23—521no—
582C23C22×C22⋊D1311yescharacteristic
583Q8—22no—
584Q8—22no—
585Q8—22no—
586Q8—44no—
587Q8—48no—
588Q8—521no—
589Q8—521no—
590Q8—521no—
591Q8—521no—
592Q8#8820114yes—
593D4—521no—
594D4—521no—
595D4—521no—
596D4—521no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—22no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—22no—
615C2×C4—21no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—521no—
625C2×C4—521no—
626C2×C4—521no—
627C2×C4—521no—
628C2×C4—521no—
629C2×C4—521no—
630C2×C4—521no—
631C2×C4—521no—
632C2×C4—521no—
633C2×C4#8820412yes—
634C2×C4#8820712yes—
635C2×C4#8820712yes—
636C2×C4C2×#613111yescharacteristic
637C2×C4C2×#613111yescharacteristic
638C2×C4#8825411yescharacteristic
639C2×C4#8825411yescharacteristic
640C2×C4C22×C22⋊D1311yescharacteristic
641C2×C4C22×C22⋊D1311yescharacteristic
642C8—521no—
643C8—521no—
644C8—521no—
645C8—521no—
646C22—1041no—
647C22—1041no—
648C22—1041no—
649C22—1041no—
650C22—1041no—
651C22—1041no—
652C22—1041no—
653C22#1171952211yescharacteristic
654C22#1171952211yescharacteristic
655C22C2×#8820411yescharacteristic
656C22#1171952711yescharacteristic
657C22#1171954211yescharacteristic
658C22#1171954311yescharacteristic
659C22C2×#8820711yescharacteristic
660C4—24no—
661C4—22no—
662C4—22no—
663C4—22no—
664C4—41no—
665C4—41no—
666C4—42no—
667C4—41no—
668C4—42no—
669C4—42no—
670C4—1041no—
671C4—1041no—
672C4—1041no—
673C4C2×#8820111yescharacteristic
674C4#1171952111yescharacteristic
675C4#1171952211yescharacteristic
676C4#1171952211yescharacteristic
677C2—2081no—
678C2#1311849011yescharacteristic
679C2#1312405411yescharacteristic
680C2#1312415111yescharacteristic
681C2#1312752111yescharacteristic
682C2#1312753211yescharacteristic
683C2#1312760411yescharacteristic
684C2#1312767811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC2×C13×#557C2
socleC23×C13C22×D4
prime radicalC22×D52C23
hypercenterC2×#557D13
hypocenterC13#25937
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
4. #13115984C2semidirect
6. #13115974C2semidirect
8. #13115794C2semidirect
9. #13115773C2semidirect
12. #13115177C2semidirect
13. #13115177C2semidirect
14. C4×#88075C2semidirect
15. C2×C13×#557C2semidirect
233. C2×#557D13semidirect
574. C13#25937semidirect

Maximal subgroups

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

subgroupindex
C2×#117187292
C2×#117186892
#131203242
#131159842
#131159792
#131159742
#131159692
#131157942
#131157732
#131151912
#131151772
C4×#880752
C2×C13×#5572
#2593713