Finite Group Databasebeta

← #16785764

Subgroups — #16785764

Order 3328.

926 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88112C211yesmaximal, characteristic
2C22×#88110C211yesmaximal, characteristic
3C2×#11718290C211yesmaximal, characteristic
4C2×#11718290C211yesmaximal, characteristic
5C2×#11718290C211yesmaximal, characteristic
6C2×#11718290C211yesmaximal, characteristic
7#95×Dic13C211yesmaximal, characteristic
8C23×#1057C2211yescharacteristic
9C23×#1057C2211yescharacteristic
10C23×#1057C2211yescharacteristic
11C23×#1057C2211yescharacteristic
12C22×C4×Dic13C2211yescharacteristic
13C22×C4×Dic13C2211yescharacteristic
14C22×C4×Dic13C2211yescharacteristic
15C2×#88112—22no—
16C2×#88112—22no—
17C2×#88112C414yescomplemented
18C2×#88110—22no—
19C2×#88110—22no—
20C2×#88110—22no—
21C2×C13×#95C411yescharacteristic
22C2×#88071C411yescharacteristic
23C2×#88071C411yescharacteristic
24C2×#88071C411yescharacteristic
25#11718290—22no—
26#11718290—22no—
27#11718290—22no—
28#11718290C414yescomplemented
29C23×C4×C13C2×C411yescharacteristic
30C23×C4×C13C2×C411yescharacteristic
31C23×C4×C13C2×C411yescharacteristic
32C23×Dic13C2×C411yescharacteristic
33C23×Dic13C2×C411yescharacteristic
34C23×Dic13C2×C411yescharacteristic
35C23×Dic13C2311yescharacteristic
36C22×#1057—21no—
37C22×#1057—21no—
38C22×#1057—21no—
39C22×#1057—21no—
40C22×#1057—21no—
41C22×#1057—21no—
42C22×#1057—21no—
43C22×#1057—21no—
44C22×#1057—21no—
45C22×#1057—21no—
46C22×#1057—21no—
47C22×#1057—21no—
48C22×#1057—21no—
49C22×#1057—21no—
50C22×#1057—21no—
51C22×#1057—21no—
52C22×#1057—21no—
53C22×#1057—21no—
54C22×#1057—21no—
55C22×#1057—21no—
56C22×#1057C2×C412yes—
57C22×#1057C2×C412yes—
58C22×#1057C2×C412yes—
59C22×#1057C2×C412yes—
60C22×#1057D412yes—
61C22×#1057D412yes—
62C22×#1057D412yes—
63C22×#1057Q812yes—
64C2×C4×Dic13—21no—
65C2×C4×Dic13—21no—
66C2×C4×Dic13—21no—
67C2×C4×Dic13—21no—
68C2×C4×Dic13—21no—
69C2×C4×Dic13—21no—
70C2×C4×Dic13—21no—
71C2×C4×Dic13—21no—
72C2×C4×Dic13—21no—
73C2×C4×Dic13—21no—
74C2×C4×Dic13—21no—
75C2×C4×Dic13—21no—
76C2×C4×Dic13—21no—
77C2×C4×Dic13—21no—
78C2×C4×Dic13C2×C412yes—
79C2×C4×Dic13C2×C412yes—
80C2×C4×Dic13D412yes—
81C2×C4×Dic13Q812yes—
82#88112—28no—
83#88110—28no—
84C13×#95—22no—
85#88071—22no—
86#88071—22no—
87#88071—22no—
88#10877—131nomaximal, Sylow
89C24×C13C22×C411yescharacteristic
90C22×C4×C13—21no—
91C22×C4×C13—21no—
92C22×C4×C13—21no—
93C22×C4×C13—21no—
94C22×C4×C13—21no—
95C22×C4×C13—21no—
96C22×C4×C13—21no—
97C22×C4×C13—21no—
98C22×C4×C13—21no—
99C22×C4×C13—21no—
100C22×C4×C13—21no—
101C22×C4×C13—21no—
102C22×C4×C13—21no—
103C22×C4×C13—21no—
104C22×C4×C13—21no—
105C22×C4×C13—21no—
106C22×C4×C13—21no—
107C22×C4×C13—21no—
108C22×C4×C13C4212yes—
109C22×C4×C13C4⋊C412yes—
110C22×C4×C13M1612yes—
111C22×Dic13—21no—
112C22×Dic13—21no—
113C22×Dic13—21no—
114C22×Dic13—21no—
115C22×Dic13—21no—
116C22×Dic13—21no—
117C22×Dic13—21no—
118C22×Dic13—21no—
119C22×Dic13—21no—
120C22×Dic13—21no—
121C22×Dic13—21no—
122C22×Dic13—21no—
123C22×Dic13—21no—
124C22×Dic13—21no—
125C22×Dic13—21no—
126C22×Dic13—21no—
127C22×Dic13C4212yes—
128C22×Dic13C4⋊C412yes—
129C22×Dic13M1612yes—
130C22×Dic13M1612yes—
131C22×Dic13M1612yes—
132C22×Dic13C22×C411yescharacteristic
133C22×Dic13C22×C411yescharacteristic
134C22×Dic13C2×D411yescharacteristic
135C22×Dic13C2×D411yescharacteristic
136C22×Dic13C2×D411yescharacteristic
137C22×Dic13C2×D411yescharacteristic
138C22×Dic13C2×Q811yescharacteristic
139C22×Dic13C2×Q811yescharacteristic
140C22×Dic13#4111yescharacteristic
141C22×Dic13#4111yescharacteristic
142C22×Dic13#4111yescharacteristic
143C22×Dic13#4111yescharacteristic
144C22×Dic13#4111yescharacteristic
145C22×Dic13#4111yescharacteristic
146C2×#1057—22no—
147C2×#1057—22no—
148C2×#1057—22no—
149C2×#1057—22no—
150C2×#1057—22no—
151C2×#1057—22no—
152C2×#1057—22no—
153C2×#1057—22no—
154C2×#1057—22no—
155C2×#1057—22no—
156C2×#1057—22no—
157C2×#1057—22no—
158C2×#1057—22no—
159C2×#1057—22no—
160C2×#1057—22no—
161C2×#1057—22no—
162C2×#1057—22no—
163C2×#1057—22no—
164C2×#1057—41no—
165C2×#1057—41no—
166C2×#1057—41no—
167C2×#1057—41no—
168C2×#1057—41no—
169C2×#1057—41no—
170C2×#1057—41no—
171C2×#1057—41no—
172C2×#1057C22⋊C414yes—
173C2×#1057C4⋊C414yes—
174C4×Dic13—22no—
175C4×Dic13—22no—
176C4×Dic13—22no—
177C4×Dic13—22no—
178C4×Dic13—22no—
179C4×Dic13—22no—
180C4×Dic13—22no—
181C4×Dic13—22no—
182C4×Dic13—41no—
183C4×Dic13—41no—
184C4×Dic13—41no—
185C4×Dic13—41no—
186C22×C4⋊C8—131no—
187C22×#97—131no—
188C2×#336—131no—
189C2×#336—131no—
190C2×#336—131no—
191C2×#336—131no—
192C4×#95—131no—
193C23×C13C2×C4211yescharacteristic
194C23×C13C2×C4⋊C411yescharacteristic
195C23×C13#11711yescharacteristic
196C23×C13C4×D411yescharacteristic
197C23×C13C4×D411yescharacteristic
198C23×C13C4×D411yescharacteristic
199C23×C13C4×Q811yescharacteristic
200C23×C13C2×M1611yescharacteristic
201C23×C13C2×M1611yescharacteristic
202C23×C13C2×M1611yescharacteristic
203C23×C13C2×M1611yescharacteristic
204C23×C13#13111yescharacteristic
205C23×C13#13111yescharacteristic
206C23×C13#13111yescharacteristic
207C23×C13#13111yescharacteristic
208C2×C4×C13—22no—
209C2×C4×C13—22no—
210C2×C4×C13—22no—
211C2×C4×C13—22no—
212C2×C4×C13—22no—
213C2×C4×C13—22no—
214C2×C4×C13—22no—
215C2×C4×C13—22no—
216C2×C4×C13—22no—
217C2×C4×C13—41no—
218C2×C4×C13—41no—
219C2×C4×C13—41no—
220C2×C4×C13—41no—
221C2×C4×C13—41no—
222C2×C4×C13—41no—
223C2×C4×C13—41no—
224C2×C4×C13—41no—
225C2×C4×C13—41no—
226C2×C4×C13—41no—
227C2×C4×C13—41no—
228C2×C4×C13—41no—
229C2×Dic13—22no—
230C2×Dic13—22no—
231C2×Dic13—22no—
232C2×Dic13—22no—
233C2×Dic13—22no—
234C2×Dic13—22no—
235C2×Dic13—22no—
236C2×Dic13—22no—
237C2×Dic13—22no—
238C2×Dic13—22no—
239C2×Dic13—22no—
240C2×Dic13—22no—
241C2×Dic13—41no—
242C2×Dic13—41no—
243C2×Dic13—41no—
244C2×Dic13—41no—
245C2×Dic13—41no—
246C2×Dic13—41no—
247C2×Dic13—41no—
248C2×Dic13—41no—
249C2×Dic13#9714yescomplemented
250C2×Dic13C2×C22⋊C411yescharacteristic
251C2×Dic13C2×C4⋊C411yescharacteristic
252C2×Dic13#11711yescharacteristic
253C2×Dic13#11711yescharacteristic
254C2×Dic13C4×D411yescharacteristic
255C2×Dic13C4×D411yescharacteristic
256C2×Dic13C4×D411yescharacteristic
257C2×Dic13C4×D411yescharacteristic
258C2×Dic13C4×D411yescharacteristic
259C2×Dic13C4×Q811yescharacteristic
260C2×Dic13C4×Q811yescharacteristic
261C2×Dic13C4×Q811yescharacteristic
262C2×Dic13#12011yescharacteristic
263C2×Dic13#12111yescharacteristic
264C2×Dic13#12111yescharacteristic
265C2×Dic13C22⋊Q811yescharacteristic
266C2×Dic13C22⋊Q811yescharacteristic
267C2×Dic13C22⋊Q811yescharacteristic
268C2×Dic13C22⋊Q811yescharacteristic
269C2×Dic13#12311yescharacteristic
270C2×Dic13#12311yescharacteristic
271C2×Dic13#12311yescharacteristic
272C2×Dic13#12411yescharacteristic
273C2×Dic13#12511yescharacteristic
274C2×Dic13#12511yescharacteristic
275C2×Dic13#12611yescharacteristic
276C2×Dic13#12611yescharacteristic
277C2×Dic13C4⋊Q811yescharacteristic
278#1057—24no—
279#1057—24no—
280#1057—42no—
281#1057—42no—
282C23×C8—131no—
283C23×C8—131no—
284C23×C8—131no—
285C23×C8—131no—
286C22×C42—131no—
287C22×C42—131no—
288C22×C42—131no—
289C2×C4⋊C8—134no—
290C2×C4⋊C8—262no—
291C2×C4⋊C8—262no—
292C2×#97—262no—
293C2×#97—262no—
294C2×#97—262no—
295C2×#95—131no—
296C2×#95—131no—
297C2×#95—131no—
298C2×#95#26111yescharacteristic
299#336—134no—
300#336—262no—
301#336—262no—
302#336—262no—
303C22×C13C4×C22⋊C411yescharacteristic
304C22×C13C4×C4⋊C411yescharacteristic
305C22×C13C4×C4⋊C411yescharacteristic
306C22×C13#38511yescharacteristic
307C22×C13#38711yescharacteristic
308C22×C13#38811yescharacteristic
309C22×C13#38911yescharacteristic
310C22×C13C2×#9711yescharacteristic
311C22×C13C4×M1611yescharacteristic
312C22×C13#40511yescharacteristic
313C22×C13#40511yescharacteristic
314C22×C13#42311yescharacteristic
315C22×C13#42311yescharacteristic
316C22×C13#42411yescharacteristic
317C22×C13#42411yescharacteristic
318C22×C13#43211yescharacteristic
319C22×C13#43211yescharacteristic
320C22×C13#43311yescharacteristic
321C22×C13#43311yescharacteristic
322C22×C13#43511yescharacteristic
323C22×C13#43511yescharacteristic
324C22×C13#43511yescharacteristic
325C22×C13#43511yescharacteristic
326C22×C13#43511yescharacteristic
327C22×C13#43511yescharacteristic
328C22×C13#43511yescharacteristic
329C22×C13#43511yescharacteristic
330C22×C13#43611yescharacteristic
331C22×C13#43611yescharacteristic
332C22×C13#43611yescharacteristic
333C22×C13#43611yescharacteristic
334C22×C13#44611yescharacteristic
335C22×C13#44611yescharacteristic
336C22×C13#44611yescharacteristic
337C22×C13#44611yescharacteristic
338C4×C13—42no—
339C4×C13—42no—
340C4×C13—42no—
341Dic13—24no—
342Dic13—42no—
343Dic13—42no—
344Dic13#38511yescharacteristic
345Dic13#38611yescharacteristic
346Dic13#38711yescharacteristic
347Dic13#38711yescharacteristic
348Dic13#38711yescharacteristic
349Dic13#38811yescharacteristic
350Dic13#38911yescharacteristic
351Dic13#39111yescharacteristic
352C23×C4—131no—
353C23×C4—131no—
354C23×C4—131no—
355C23×C4—131no—
356C23×C4C2×#26111yescharacteristic
357C23×C4C2×#26111yescharacteristic
358C23×C4C2×#26111yescharacteristic
359C22×C8—132no—
360C22×C8—132no—
361C22×C8—132no—
362C22×C8—132no—
363C22×C8—132no—
364C22×C8—132no—
365C22×C8—132no—
366C22×C8—132no—
367C22×C8—261no—
368C22×C8—261no—
369C22×C8—261no—
370C22×C8—261no—
371C22×C8—261no—
372C22×C8—261no—
373C22×C8—261no—
374C22×C8—261no—
375C22×C8—261no—
376C22×C8—261no—
377C22×C8—261no—
378C22×C8—261no—
379C22×C8—261no—
380C22×C8—261no—
381C22×C8—261no—
382C22×C8—261no—
383C22×C8—261no—
384C22×C8—261no—
385C22×C8—261no—
386C22×C8—261no—
387C2×C42—132no—
388C2×C42—132no—
389C2×C42—132no—
390C2×C42—132no—
391C2×C42—261no—
392C2×C42—261no—
393C2×C42—261no—
394C2×C42—261no—
395C2×C42—261no—
396C2×C42—261no—
397C2×C42—261no—
398C2×C42—261no—
399C2×C42—261no—
400C2×C42—261no—
401C2×C42—261no—
402C2×C42—261no—
403C2×C42—261no—
404C2×C42—261no—
405C4⋊C8—268no—
406#97—268no—
407#95—22no—
408#95—262no—
409#95—262no—
410#95—262no—
411C2×C13#143611yescharacteristic
412C2×C13#175211yescharacteristic
413C2×C13#175311yescharacteristic
414C2×C13#176711yescharacteristic
415C2×C13#176811yescharacteristic
416C2×C13#177011yescharacteristic
417C2×C13#177111yescharacteristic
418C2×C13#185111yescharacteristic
419C2×C13#185111yescharacteristic
420C2×C13#191711yescharacteristic
421C2×C13#191711yescharacteristic
422C2×C13#192411yescharacteristic
423C2×C13#192411yescharacteristic
424C2×C13#194011yescharacteristic
425C2×C13#194011yescharacteristic
426C24C22×#26111yescharacteristic
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—131no—
446C22×C4—131no—
447C22×C4—131no—
448C22×C4—131no—
449C22×C4—131no—
450C22×C4—131no—
451C22×C4—131no—
452C22×C4—131no—
453C22×C4—131no—
454C22×C4—131no—
455C22×C4—131no—
456C22×C4—131no—
457C22×C4—131no—
458C22×C4—131no—
459C22×C4—132no—
460C22×C4—132no—
461C22×C4—132no—
462C22×C4—132no—
463C22×C4—132no—
464C22×C4—261no—
465C22×C4—261no—
466C22×C4—261no—
467C22×C4—261no—
468C22×C4—261no—
469C22×C4—261no—
470C22×C4—261no—
471C22×C4—261no—
472C22×C4—261no—
473C22×C4—261no—
474C22×C4—261no—
475C22×C4—261no—
476C22×C4—261no—
477C22×C4—261no—
478C22×C4—261no—
479C22×C4—261no—
480C22×C4C4×#26112yes—
481C22×C4C4⋊#26112yes—
482C22×C4#612212yes—
483C2×C8—134no—
484C2×C8—134no—
485C2×C8—262no—
486C2×C8—262no—
487C2×C8—262no—
488C2×C8—262no—
489C2×C8—262no—
490C2×C8—262no—
491C2×C8—262no—
492C2×C8—262no—
493C2×C8—262no—
494C2×C8—262no—
495C2×C8—262no—
496C2×C8—262no—
497C2×C8—262no—
498C2×C8—262no—
499C2×C8—262no—
500C2×C8—262no—
501C2×C8—262no—
502C2×C8—262no—
503C2×C8—521no—
504C2×C8—521no—
505C2×C8—521no—
506C2×C8—521no—
507C2×C8—521no—
508C2×C8—521no—
509C2×C8—521no—
510C2×C8—521no—
511C42—262no—
512C42—262no—
513C42—262no—
514C42—262no—
515C42—262no—
516C42—262no—
517C42—262no—
518C42—262no—
519C42—521no—
520C42—521no—
521C42—521no—
522C42—521no—
523C13#1087711yescharacteristic, complemented, Sylow
524C23D13⋊M1611yescharacteristic
525C23D13⋊M1611yescharacteristic
526C23D13⋊M1611yescharacteristic
527C23C2×C4×#26111yescharacteristic
528C23C2×C4⋊#26111yescharacteristic
529C23#8823711yescharacteristic
530C23#8823811yescharacteristic
531C23#8823811yescharacteristic
532C23#8823811yescharacteristic
533C23D4×#26111yescharacteristic
534C23D4×#26111yescharacteristic
535C23D4×#26111yescharacteristic
536C23#8824011yescharacteristic
537C23Q8×#26111yescharacteristic
538C23C2×#612211yescharacteristic
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—131no—
561C2×C4—131no—
562C2×C4—131no—
563C2×C4—131no—
564C2×C4—131no—
565C2×C4—131no—
566C2×C4—131no—
567C2×C4—131no—
568C2×C4—131no—
569C2×C4—131no—
570C2×C4—131no—
571C2×C4—131no—
572C2×C4—131no—
573C2×C4—131no—
574C2×C4—131no—
575C2×C4—131no—
576C2×C4—131no—
577C2×C4—131no—
578C2×C4—131no—
579C2×C4—131no—
580C2×C4—131no—
581C2×C4—131no—
582C2×C4—131no—
583C2×C4—131no—
584C2×C4—131no—
585C2×C4—131no—
586C2×C4—131no—
587C2×C4—131no—
588C2×C4—134no—
589C2×C4—262no—
590C2×C4—262no—
591C2×C4—262no—
592C2×C4—262no—
593C2×C4—262no—
594C2×C4—262no—
595C2×C4—262no—
596C2×C4—262no—
597C2×C4—262no—
598C2×C4—262no—
599C2×C4—262no—
600C2×C4—262no—
601C2×C4—521no—
602C2×C4—521no—
603C2×C4—521no—
604C2×C4—521no—
605C2×C4—521no—
606C2×C4—521no—
607C2×C4—521no—
608C2×C4—521no—
609C8—264no—
610C8—264no—
611C8—522no—
612C8—522no—
613C22#1171904711yescharacteristic
614C22#1171905311yescharacteristic
615C22#1171905511yescharacteristic
616C22C4×C4⋊#26111yescharacteristic
617C22#1171906211yescharacteristic
618C22#1171906511yescharacteristic
619C22#1171906511yescharacteristic
620C22#1171906511yescharacteristic
621C22#1171906611yescharacteristic
622C22#1171906611yescharacteristic
623C22#1171906611yescharacteristic
624C22#1171906711yescharacteristic
625C22#1171906811yescharacteristic
626C22C22⋊C4×#26111yescharacteristic
627C22#1171907011yescharacteristic
628C22#1171907111yescharacteristic
629C22#1171907211yescharacteristic
630C22#1171907511yescharacteristic
631C22#1171907511yescharacteristic
632C22#1171907511yescharacteristic
633C22#1171907711yescharacteristic
634C22#1171907811yescharacteristic
635C22#1171907811yescharacteristic
636C22#1171907811yescharacteristic
637C22#1171907911yescharacteristic
638C22C4⋊C4×#26111yescharacteristic
639C22#1171908211yescharacteristic
640C22#1171908311yescharacteristic
641C22C4×#612211yescharacteristic
642C22#1171912811yescharacteristic
643C22#1171912911yescharacteristic
644C22#1171914411yescharacteristic
645C22#1171914411yescharacteristic
646C22#1171914511yescharacteristic
647C22#1171915811yescharacteristic
648C4—42no—
649C4—42no—
650C4—42no—
651C4—131no—
652C4—131no—
653C4—131no—
654C4—131no—
655C4—131no—
656C4—131no—
657C4—131no—
658C4—131no—
659C4—264no—
660C4—522no—
661C4—522no—
662C2#1313001611yescharacteristic
663C2#1313057411yescharacteristic
664C2#1313057811yescharacteristic
665C2#1313062111yescharacteristic
666C2#1313062411yescharacteristic
667C2#1313063111yescharacteristic
668C2#1313063611yescharacteristic
669C2#1313078311yescharacteristic
670C2#1313078411yescharacteristic
671C2#1313089511yescharacteristic
672C2#1313089611yescharacteristic
673C2#1313090911yescharacteristic
674C2#1313091211yescharacteristic
675C2#1313093711yescharacteristic
676C2#1313093811yescharacteristic
subgroupG/H
center, FrattiniC24C22×#261
commutatorC23×C13C2×C42
FittingC2×C13×#95C4
socle, prime radicalC24×C13C22×C4
cosocleC23×Dic13C23
hypercenterC2×#95#261
hypocenterC13#10877
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
17. C2×#88112C4semidirect
28. #11718290C4semidirect
249. C2×Dic13#97semidirect
523. C13#10877semidirect

Maximal subgroups

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

subgroupindex
C22×#881122
C22×#881102
C2×#117182902
#95×Dic132
#1087713