Finite Group Databasebeta

← #16797559

Subgroups — #16797559

Order 3328.

886 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719068C211yesmaximal, characteristic
2C2×#11719068C211yesmaximal, characteristic
3#13130636C211yesmaximal, characteristic, complemented
4#13130636C211yesmaximal, characteristic, complemented
5#13130635C211yesmaximal, characteristic, complemented
6#13130635C211yesmaximal, characteristic, complemented
7#13130632C211yesmaximal, characteristic, complemented
8#13130631C211yesmaximal, characteristic, complemented
9#13130628C211yesmaximal, characteristic, complemented
10C4⋊C4×#1057C211yesmaximal, characteristic, complemented
11#13130566C211yesmaximal, characteristic
12#13130566C211yesmaximal, characteristic
13#13130562C211yesmaximal, characteristic
14C4×C22⋊#1057C211yesmaximal, characteristic
15#13117315C211yesmaximal, characteristic
16C22×C4×Dic13C2211yescharacteristic
17C2×#88131C2211yescharacteristic
18C2×#88131C2211yescharacteristic
19C2×C22⋊#1057C2211yescharacteristic
20C2×C22⋊#1057C2211yescharacteristic
21C2×C22⋊#1057C2211yescharacteristic
22C2×C22⋊#1057C2211yescharacteristic
23C2×#88112C2211yescharacteristic
24C2×#88112C2211yescharacteristic
25C2×#88110C2211yescharacteristic
26C2×#88110C2211yescharacteristic
27C2×#88110C2211yescharacteristic
28C2×#88110C2211yescharacteristic
29C2×#88110C2211yescharacteristic
30C2×#88110C2211yescharacteristic
31C2×C4⋊#1057C2211yescharacteristic
32C2×C4⋊#1057C2211yescharacteristic
33C2×C4×#1057C2211yescharacteristic
34C2×C4×#1057C2211yescharacteristic
35C2×C4×#1057C2211yescharacteristic
36C2×C4×#1057C2211yescharacteristic
37C2×C4×#1057C2211yescharacteristic
38C2×C4×#1057C2211yescharacteristic
39#11719068C418yescomplemented
40#11719068C418yescomplemented
41C13×#385C411yescharacteristic
42#11718871C411yescharacteristic
43C4⋊C4×Dic13C2211yescharacteristic
44C4⋊C4×Dic13C2211yescharacteristic
45#11718633C411yescharacteristic
46#11718633C411yescharacteristic
47#11718611C411yescharacteristic
48#11718607C411yescharacteristic
49#11718310C2211yescharacteristic
50#11718310C2211yescharacteristic
51#11718308C411yescharacteristic
52#11718308C411yescharacteristic
53#11718290C2211yescharacteristic
54#11718290C2211yescharacteristic
55#11718290C2211yescharacteristic
56#11718290C2211yescharacteristic
57#11718290C2211yescharacteristic
58#11718290C2211yescharacteristic
59#11718290C2211yescharacteristic
60#11718290C2211yescharacteristic
61C23×C4×C13C2×C411yescharacteristic
62C23×Dic13C2×C411yescharacteristic
63C23×Dic13C2311yescharacteristic
64C22×#1057C2311yescharacteristic
65C22×#1057C2311yescharacteristic
66C22×#1057C2311yescharacteristic
67C22×#1057C2311yescharacteristic
68C22×#1057C2311yescharacteristic
69C22×#1057C2311yescharacteristic
70C22×#1057C2311yescharacteristic
71C22×#1057C2311yescharacteristic
72C2×C13×C4⋊C4C2×C411yescharacteristic
73C2×C13×C4⋊C4C2×C411yescharacteristic
74C2×C13×C22⋊C4C2×C411yescharacteristic
75C2×C13×C22⋊C4C2×C411yescharacteristic
76C2×C22⋊Dic13C2×C411yescharacteristic
77C2×C22⋊Dic13C2×C411yescharacteristic
78C2×C4⋊Dic13C2×C411yescharacteristic
79C2×C4⋊Dic13C2×C411yescharacteristic
80C2×#6101C2×C411yescharacteristic
81C2×#6101C2×C411yescharacteristic
82C2×#6101C2×C411yescharacteristic
83C2×#6101C2×C411yescharacteristic
84C2×#6101C2×C411yescharacteristic
85C2×#6101C2×C411yescharacteristic
86C2×#6101C2×C411yescharacteristic
87C2×#6101C2×C411yescharacteristic
88C2×C4×Dic13—41no—
89C2×C4×Dic13—41no—
90C2×C4×Dic13C2×C411yescharacteristic
91C2×C4×Dic13C2×C411yescharacteristic
92C2×C4×Dic13C2311yescharacteristic
93C2×C4×Dic13C2311yescharacteristic
94C2×C4×Dic13C2311yescharacteristic
95C2×C4×Dic13C2311yescharacteristic
96C2×C4×Dic13C2311yescharacteristic
97C2×C4×Dic13C2311yescharacteristic
98#88131—41no—
99#88131—41no—
100#88131C2×C414yes—
101#88131C2×C414yes—
102C22⋊#1057C2×C414yes—
103C22⋊#1057C2×C414yes—
104C22⋊#1057C2×C414yes—
105C22⋊#1057C2×C414yes—
106#88112C2×C414yescomplemented
107#88112C2×C414yescomplemented
108#88110—41no—
109#88110—41no—
110#88110—41no—
111#88110—41no—
112#88110C2×C414yescomplemented
113#88110C2×C414yescomplemented
114C4⋊#1057C2×C414yescomplemented
115C4⋊#1057C2×C414yescomplemented
116C4×#1057—41no—
117C4×#1057—41no—
118C4×#1057—41no—
119C4×#1057—41no—
120C4×#1057C2×C414yescomplemented
121C4×#1057C2×C414yescomplemented
122C13×#95C2×C411yescharacteristic
123C13×#95C2×C411yescharacteristic
124#88071C2×C411yescharacteristic
125#88071C2×C411yescharacteristic
126#88071C2×C411yescharacteristic
127#88071C2×C411yescharacteristic
128#88071C2×C411yescharacteristic
129#88071C2×C411yescharacteristic
130#20541—131nomaximal, Sylow
131C24×C13C22×C411yescharacteristic
132C22×C4×C13—22no—
133C22×C4×C13—41no—
134C22×C4×C13—41no—
135C22×C4×C13C22×C411yescharacteristic
136C22×C4×C13C22×C411yescharacteristic
137C22×C4×C13C22×C411yescharacteristic
138C22×C4×C13C22×C411yescharacteristic
139C22×C4×C13C22×C411yescharacteristic
140C22×C4×C13C22×C411yescharacteristic
141C22×Dic13—21no—
142C22×Dic13—21no—
143C22×Dic13—21no—
144C22×Dic13—21no—
145C22×Dic13—22no—
146C22×Dic13—41no—
147C22×Dic13—41no—
148C22×Dic13C22×C411yescharacteristic
149C22×Dic13C22×C411yescharacteristic
150C22×Dic13C22×C411yescharacteristic
151C22×Dic13C22×C411yescharacteristic
152C22×Dic13C22×C411yescharacteristic
153C22×Dic13C22×C411yescharacteristic
154C22×Dic13C22×C412yes—
155C22×Dic13C22×C412yes—
156C22×Dic13C22×C411yescharacteristic
157C22×Dic13C2411yescharacteristic
158C2×#1057—21no—
159C2×#1057—21no—
160C2×#1057—21no—
161C2×#1057—21no—
162C2×#1057—21no—
163C2×#1057—21no—
164C2×#1057—21no—
165C2×#1057—21no—
166C2×#1057—21no—
167C2×#1057—21no—
168C2×#1057—21no—
169C2×#1057—21no—
170C2×#1057—21no—
171C2×#1057—21no—
172C2×#1057—21no—
173C2×#1057—21no—
174C2×#1057C22×C412yes—
175C2×#1057C22×C412yes—
176C2×#1057C22×C412yes—
177C2×#1057C22×C412yes—
178C2×#1057C22×C412yes—
179C2×#1057C22×C412yes—
180C2×#1057C22×C412yes—
181C2×#1057C22×C412yes—
182C13×C4⋊C4—22no—
183C13×C4⋊C4—41no—
184C13×C22⋊C4—41no—
185C13×C22⋊C4C4214yes—
186C22⋊Dic13—41no—
187C22⋊Dic13C4214yes—
188C4⋊Dic13—22no—
189C4⋊Dic13—41no—
190#6101—22no—
191#6101—22no—
192#6101—41no—
193#6101—41no—
194#6101—41no—
195#6101—41no—
196#6101C4214yes—
197#6101C4214yes—
198C4×Dic13—21no—
199C4×Dic13—21no—
200C4×Dic13—21no—
201C4×Dic13—21no—
202C4×Dic13—21no—
203C4×Dic13—21no—
204C4×Dic13—21no—
205C4×Dic13—21no—
206C4×Dic13—41no—
207C4×Dic13—41no—
208C4×Dic13C22×C412yes—
209C4×Dic13C22×C412yes—
210C4×Dic13C22×C412yes—
211C4×Dic13C22×C412yes—
212C2×#433—131no—
213C2×#433—131no—
214#2296—131no—
215#1771—131no—
216#1771—131no—
217#1771—131no—
218#1771—131no—
219#1770—131no—
220#1770—131no—
221C8×C4⋊C4—131no—
222C8×C4⋊C4—131no—
223#1750—131no—
224#1750—131no—
225#1749—131no—
226C4×C22⋊C8—131no—
227C23×C13—21no—
228C23×C13—21no—
229C23×C13—21no—
230C23×C13—21no—
231C23×C13—21no—
232C23×C13—21no—
233C23×C13C2×C4212yes—
234C23×C13C23×C411yescharacteristic
235C2×C4×C13—21no—
236C2×C4×C13—21no—
237C2×C4×C13—21no—
238C2×C4×C13—21no—
239C2×C4×C13—21no—
240C2×C4×C13—21no—
241C2×C4×C13—21no—
242C2×C4×C13—21no—
243C2×C4×C13—21no—
244C2×C4×C13—21no—
245C2×C4×C13—21no—
246C2×C4×C13—21no—
247C2×C4×C13—21no—
248C2×C4×C13—21no—
249C2×C4×C13—21no—
250C2×C4×C13—44no—
251C2×C4×C13C2×C4212yes—
252C2×C4×C13C2×C4212yes—
253C2×C4×C13#13112yes—
254C2×Dic13—21no—
255C2×Dic13—21no—
256C2×Dic13—21no—
257C2×Dic13—21no—
258C2×Dic13—21no—
259C2×Dic13—21no—
260C2×Dic13—21no—
261C2×Dic13—21no—
262C2×Dic13—22no—
263C2×Dic13—22no—
264C2×Dic13—22no—
265C2×Dic13—22no—
266C2×Dic13—21no—
267C2×Dic13—21no—
268C2×Dic13—21no—
269C2×Dic13—21no—
270C2×Dic13—21no—
271C2×Dic13—21no—
272C2×Dic13—21no—
273C2×Dic13—21no—
274C2×Dic13—21no—
275C2×Dic13—44no—
276C2×Dic13C2×C4212yes—
277C2×Dic13C2×C4212yes—
278C2×Dic13C2×C4212yes—
279C2×Dic13#13112yes—
280C2×Dic13C23×C411yescharacteristic
281C2×Dic13C23×C411yescharacteristic
282C2×Dic13H(5,𝔽2)11yescharacteristic
283C2×Dic13H(5,𝔽2)11yescharacteristic
284C2×Dic132−1+411yescharacteristic
285C2×Dic132−1+411yescharacteristic
286#1057—22no—
287#1057—22no—
288#1057—22no—
289#1057—22no—
290#1057—22no—
291#1057—22no—
292#1057—22no—
293#1057—22no—
294C2×#117—131no—
295C2×#117—131no—
296C22×C42—131no—
297#433—138no—
298#433—138no—
299C2×C4⋊C8—131no—
300C2×C4⋊C8—131no—
301C2×C4⋊C8—131no—
302C2×C4⋊C8—131no—
303C2×C22⋊C8—131no—
304C2×C22⋊C8—131no—
305C2×C22⋊C8—131no—
306C2×C22⋊C8—131no—
307C2×#97—131no—
308C2×#97—131no—
309C2×#97—131no—
310C2×#97—131no—
311C2×#97—131no—
312C2×#97—131no—
313C2×C4×C8—131no—
314C2×C4×C8—131no—
315C2×C4×C8—131no—
316C2×C4×C8—131no—
317C2×C4×C8—131no—
318C2×C4×C8—131no—
319#389—131no—
320#389—131no—
321#389—131no—
322#389—131no—
323#385—131no—
324#385—131no—
325#385—131no—
326#385#26111yescharacteristic
327C4×C4⋊C4—131no—
328C4×C4⋊C4—131no—
329C4×C4⋊C4—131no—
330C4×C4⋊C4—131no—
331#336—131no—
332#336—131no—
333#336—131no—
334#336—131no—
335#336—131no—
336#336—131no—
337#336—131no—
338#336—131no—
339C22×C13—22no—
340C22×C13—22no—
341C22×C13—22no—
342C22×C13—41no—
343C22×C13—41no—
344C22×C13—41no—
345C22×C13—41no—
346C22×C13C22×C4211yescharacteristic
347C22×C13#51811yescharacteristic
348C22×C13#51911yescharacteristic
349C22×C13C2×#13111yescharacteristic
350C22×C13C2×#13111yescharacteristic
351C22×C13#56811yescharacteristic
352C22×C13#56811yescharacteristic
353C4×C13—22no—
354C4×C13—22no—
355C4×C13—22no—
356C4×C13—41no—
357C4×C13—41no—
358C4×C13—41no—
359Dic13—22no—
360Dic13—22no—
361Dic13—22no—
362Dic13—22no—
363Dic13—41no—
364Dic13—41no—
365Dic13—41no—
366Dic13#52011yescharacteristic
367Dic13#52011yescharacteristic
368Dic13#52011yescharacteristic
369Dic13#52011yescharacteristic
370C23×C4—131no—
371C23×C4—131no—
372C23×C4C2×#26111yescharacteristic
373C22×C8—131no—
374C22×C8—131no—
375C22×C8—131no—
376C22×C8—131no—
377C22×C8—131no—
378C22×C8—131no—
379C22×C8—131no—
380C22×C8—131no—
381#117—134no—
382#117—134no—
383#117—521no—
384#117—521no—
385C2×C4⋊C4—131no—
386C2×C4⋊C4—131no—
387C2×C4⋊C4—131no—
388C2×C4⋊C4—131no—
389C2×C4⋊C4—131no—
390C2×C4⋊C4—131no—
391C2×C4⋊C4—131no—
392C2×C4⋊C4—131no—
393C2×C4⋊C4—131no—
394C2×C4⋊C4—131no—
395C2×C4⋊C4C2×#26111yescharacteristic
396C2×C4⋊C4C2×#26111yescharacteristic
397C2×C22⋊C4—131no—
398C2×C22⋊C4—131no—
399C2×C22⋊C4C2×#26111yescharacteristic
400C2×C22⋊C4C2×#26111yescharacteristic
401C2×C42—131no—
402C2×C42—131no—
403C2×C42—131no—
404C2×C42—131no—
405C2×C42—131no—
406C2×C42—131no—
407C2×C42—131no—
408C2×C42—131no—
409C2×C42—521no—
410C2×C42—521no—
411C4⋊C8—134no—
412C4⋊C8—134no—
413C4⋊C8—134no—
414C4⋊C8—134no—
415C22⋊C8—134no—
416C22⋊C8—134no—
417C22⋊C8—134no—
418C22⋊C8—134no—
419#97—134no—
420#97—134no—
421#97—521no—
422#97—521no—
423#97—521no—
424#97—521no—
425C4×C8—134no—
426C4×C8—134no—
427C4×C8—521no—
428C4×C8—521no—
429C4×C8—521no—
430C4×C8—521no—
431#95—131no—
432#95—131no—
433#95—131no—
434#95—131no—
435#95—131no—
436#95—131no—
437#95C2×#26111yescharacteristic
438#95C2×#26111yescharacteristic
439C2×C13—42no—
440C2×C13#227411yescharacteristic
441C2×C13C4×#13111yescharacteristic
442C2×C13#287511yescharacteristic
443C2×C13#297611yescharacteristic
444C2×C13#297611yescharacteristic
445C2×C13#298511yescharacteristic
446C2×C13#298511yescharacteristic
447C24C22×#26111yescharacteristic
448C22×C4—22no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—131no—
452C22×C4—132no—
453C22×C4—132no—
454C22×C4—131no—
455C22×C4—131no—
456C22×C4—131no—
457C22×C4—131no—
458C22×C4—131no—
459C22×C4—131no—
460C22×C4—131no—
461C22×C4—261no—
462C22×C4—261no—
463C22×C4—261no—
464C22×C4—261no—
465C22×C4—262no—
466C22×C4—521no—
467C22×C4—521no—
468C22×C4C22×#26111yescharacteristic
469C22×C4C22×#26111yescharacteristic
470C22×C4C22×#26111yescharacteristic
471C22×C4C22×#26111yescharacteristic
472C22×C4C22×#26111yescharacteristic
473C22×C4C22×#26111yescharacteristic
474C2×C8—132no—
475C2×C8—132no—
476C2×C8—132no—
477C2×C8—132no—
478C2×C8—132no—
479C2×C8—132no—
480C2×C8—132no—
481C2×C8—132no—
482C2×C8—261no—
483C2×C8—261no—
484C2×C8—261no—
485C2×C8—261no—
486C2×C8—261no—
487C2×C8—261no—
488C2×C8—261no—
489C2×C8—261no—
490C2×C8—261no—
491C2×C8—261no—
492C2×C8—261no—
493C2×C8—261no—
494C2×C8—261no—
495C2×C8—261no—
496C2×C8—261no—
497C2×C8—261no—
498C4⋊C4—22no—
499C4⋊C4—41no—
500C4⋊C4—134no—
501C4⋊C4—134no—
502C4⋊C4—262no—
503C4⋊C4—262no—
504C4⋊C4—262no—
505C4⋊C4—521no—
506C4⋊C4—521no—
507C4⋊C4—521no—
508C4⋊C4—521no—
509C4⋊C4—521no—
510C22⋊C4—41no—
511C22⋊C4—134no—
512C22⋊C4—521no—
513C22⋊C4C4×#26114yes—
514C42—132no—
515C42—132no—
516C42—132no—
517C42—132no—
518C42—261no—
519C42—261no—
520C42—261no—
521C42—261no—
522C42—261no—
523C42—261no—
524C42—261no—
525C42—261no—
526C42—521no—
527C42—521no—
528C13#2054111yescharacteristic, complemented, Sylow
529C23—21no—
530C23—21no—
531C23—21no—
532C23—21no—
533C23—21no—
534C23—21no—
535C23C2×C4×#26112yes—
536C23C23×#26111yescharacteristic
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—44no—
553C2×C4—131no—
554C2×C4—131no—
555C2×C4—131no—
556C2×C4—131no—
557C2×C4—131no—
558C2×C4—131no—
559C2×C4—132no—
560C2×C4—132no—
561C2×C4—132no—
562C2×C4—132no—
563C2×C4—262no—
564C2×C4—262no—
565C2×C4—262no—
566C2×C4—262no—
567C2×C4—261no—
568C2×C4—261no—
569C2×C4—261no—
570C2×C4—261no—
571C2×C4—261no—
572C2×C4—261no—
573C2×C4—261no—
574C2×C4—261no—
575C2×C4—261no—
576C2×C4—261no—
577C2×C4—261no—
578C2×C4—261no—
579C2×C4—261no—
580C2×C4—261no—
581C2×C4—261no—
582C2×C4—261no—
583C2×C4—261no—
584C2×C4—524no—
585C2×C4C2×C4×#26112yes—
586C2×C4C2×C4×#26112yes—
587C2×C4#8823812yes—
588C8—262no—
589C8—262no—
590C8—262no—
591C8—262no—
592C8—262no—
593C8—262no—
594C8—262no—
595C8—262no—
596C22—22no—
597C22—22no—
598C22—22no—
599C22—41no—
600C22—41no—
601C22—41no—
602C22—41no—
603C22C22×C4×#26111yescharacteristic
604C22C2×#8823811yescharacteristic
605C22#1171962111yescharacteristic
606C22#1171962311yescharacteristic
607C22#1171962711yescharacteristic
608C22D13⋊#13111yescharacteristic
609C22#1171962911yescharacteristic
610C4—22no—
611C4—22no—
612C4—22no—
613C4—41no—
614C4—41no—
615C4—41no—
616C4—131no—
617C4—131no—
618C4—131no—
619C4—131no—
620C4—262no—
621C4—262no—
622C4—262no—
623C4—262no—
624C4—521no—
625C4—521no—
626C4—521no—
627C2—42no—
628C2#1313127411yescharacteristic
629C2C4×#8823811yescharacteristic
630C2#1313140711yescharacteristic
631C2#1313170211yescharacteristic
632C2#1313170411yescharacteristic
633C2#1313174011yescharacteristic
634C2#1313174211yescharacteristic
subgroupG/H
center, FrattiniC23C23×#261
commutatorC22×C13C22×C42
FittingC13×#385C4
socleC23×C13C23×C4
prime radicalC24×C13C22×C4
cosocleC22×Dic13C24
hypercenter#385#261
hypocenterC13#20541
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
3. #13130636C2semidirect
4. #13130636C2semidirect
5. #13130635C2semidirect
6. #13130635C2semidirect
7. #13130632C2semidirect
8. #13130631C2semidirect
9. #13130628C2semidirect
10. C4⋊C4×#1057C2semidirect
39. #11719068C4semidirect
40. #11719068C4semidirect
106. #88112C2×C4semidirect
107. #88112C2×C4semidirect
112. #88110C2×C4semidirect
113. #88110C2×C4semidirect
114. C4⋊#1057C2×C4semidirect
115. C4⋊#1057C2×C4semidirect
120. C4×#1057C2×C4semidirect
121. C4×#1057C2×C4semidirect
528. C13#20541semidirect

Maximal subgroups

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

subgroupindex
C2×#117190682
#131306362
#131306352
#131306322
#131306312
#131306282
C4⋊C4×#10572
#131305662
#131305622
C4×C22⋊#10572
#131173152
#2054113