Finite Group Databasebeta

← #16797363

Subgroups — #16797363

Order 3328.

1102 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719065C211yesmaximal, characteristic
2C2×#11719064C211yesmaximal, characteristic
3C2×#11719072C211yesmaximal, characteristic, complemented
4C2×#11719062C211yesmaximal, characteristic, complemented
5#13130635C211yesmaximal, characteristic, complemented
6#13130635C211yesmaximal, characteristic, complemented
7#13130622C211yesmaximal, characteristic, complemented
8#13130578C211yesmaximal, characteristic, complemented
9#13130577C211yesmaximal, characteristic, complemented
10#13130574C211yesmaximal, characteristic, complemented
11#13130573C211yesmaximal, characteristic, complemented
12#13130566C211yesmaximal, characteristic, complemented
13#13130565C211yesmaximal, characteristic, complemented
14C4×#88110C211yesmaximal, characteristic, complemented
15#13117296C211yesmaximal, characteristic
16C22×#6122C2211yescharacteristic
17C23×#1057C2211yescharacteristic
18C22×#6118C2211yescharacteristic
19C22×D13⋊C8C2211yescharacteristic
20C2×#88146C2211yescharacteristic
21C2×#88135C2211yescharacteristic
22C2×#88131C2211yescharacteristic
23C2×C22⋊#1057C2211yescharacteristic
24C2×C22⋊#1057C2211yescharacteristic
25C2×#88111C2211yescharacteristic
26C2×#88111C2211yescharacteristic
27C2×#88110C2211yescharacteristic
28C2×#88110C2211yescharacteristic
29C2×#88110C2211yescharacteristic
30C2×#88110C2211yescharacteristic
31C2×#88110C2211yescharacteristic
32C2×#88110C2211yescharacteristic
33C2×#88110C2211yescharacteristic
34C2×#88110C2211yescharacteristic
35C2×C4⋊#1057C2211yescharacteristic
36C2×C4⋊#1057C2211yescharacteristic
37C2×C4×#1057C2211yescharacteristic
38C2×C4×#1057C2211yescharacteristic
39C2×C4×#1057C2211yescharacteristic
40C2×C4×#1057C2211yescharacteristic
41#11719072—24no—
42#11719065C418yescomplemented
43#11719064C418yescomplemented
44#11719062—24no—
45C13×#388C411yescharacteristic
46#11718633C411yescharacteristic
47#11718618C411yescharacteristic
48#11718618C411yescharacteristic
49#11718612C411yescharacteristic
50C22⋊C4×Dic13C2211yescharacteristic
51#11718601C411yescharacteristic
52C42×Dic13C2211yescharacteristic
53#11718330C411yescharacteristic
54#11718327C2211yescharacteristic
55#11718310C2211yescharacteristic
56#11718308C411yescharacteristic
57#11718290C2211yescharacteristic
58#11718290C2211yescharacteristic
59#11718290C2211yescharacteristic
60#11718290C2211yescharacteristic
61#11718290C2211yescharacteristic
62#11718290C2211yescharacteristic
63C22×C22⋊D13C2×C411yescharacteristic
64C23×Dic13C2311yescharacteristic
65C22×C4×D13C2311yescharacteristic
66C2×#6122—22no—
67C2×#6122—22no—
68C2×#6122C2×C414yes—
69C22×#1057—22no—
70C22×#1057—22no—
71C22×#1057C2×C414yes—
72C22×#1057C2311yescharacteristic
73C22×#1057C2311yescharacteristic
74C22×#1057C2311yescharacteristic
75C22×#1057C2311yescharacteristic
76C22×#1057C2311yescharacteristic
77C22×#1057C2311yescharacteristic
78C22×#1057C2311yescharacteristic
79C22×#1057C2311yescharacteristic
80C2×#6118—22no—
81C2×#6118—22no—
82C2×#6118C2×C414yes—
83C2×D13⋊C8—22no—
84C2×D13⋊C8—22no—
85C2×D13⋊C8C2×C414yes—
86C2×C13×C4⋊C4C2×C411yescharacteristic
87C2×C13×C22⋊C4C2×C411yescharacteristic
88C2×C13×C22⋊C4C2×C411yescharacteristic
89C2×C13×C22⋊C4C2×C411yescharacteristic
90C2×C42×C13C2×C411yescharacteristic
91C2×C22⋊Dic13C2×C411yescharacteristic
92C2×C22⋊Dic13C2×C411yescharacteristic
93C2×#6103C2×C411yescharacteristic
94C2×#6103C2×C411yescharacteristic
95C2×#6103C2×C411yescharacteristic
96C2×#6103C2×C411yescharacteristic
97C2×#6103C2×C411yescharacteristic
98C2×C4⋊Dic13C2×C411yescharacteristic
99C2×#6101C2×C411yescharacteristic
100C2×#6101C2×C411yescharacteristic
101C2×#6101C2×C411yescharacteristic
102C2×#6101C2×C411yescharacteristic
103C2×#6101C2×C411yescharacteristic
104C2×C4×Dic13C2×C411yescharacteristic
105C2×C4×Dic13C2×C411yescharacteristic
106C2×C4×Dic13C2×C411yescharacteristic
107C2×C4×Dic13C2311yescharacteristic
108C2×C4×Dic13C2311yescharacteristic
109C2×C4×Dic13C2311yescharacteristic
110C2×C4×Dic13C2311yescharacteristic
111C2×C4×Dic13C2311yescharacteristic
112#88146—22no—
113#88146—22no—
114#88135C2×C414yes—
115#88135C2×C414yes—
116#88131—22no—
117#88131—22no—
118C22⋊#1057C2×C414yes—
119C22⋊#1057C2×C414yes—
120#88111C2×C414yes—
121#88111C2×C414yes—
122#88110—22no—
123#88110—22no—
124#88110—22no—
125#88110—22no—
126#88110—22no—
127#88110—22no—
128#88110C2×C414yes—
129#88110C2×C414yes—
130C4⋊#1057C2×C414yes—
131C4⋊#1057C2×C414yes—
132C4×#1057—22no—
133C4×#1057—22no—
134C4×#1057—22no—
135C4×#1057D414yescomplemented
136C13×#95C2×C411yescharacteristic
137C13×#95C2×C411yescharacteristic
138#88071C2×C411yescharacteristic
139#88071C2×C411yescharacteristic
140#88071C2×C411yescharacteristic
141#88071C2×C411yescharacteristic
142#20488—131nomaximal, Sylow
143C24×C13C22×C411yescharacteristic
144C23×D13C22×C411yescharacteristic
145C22×C4×C13C22×C411yescharacteristic
146C22×C4×C13C22×C411yescharacteristic
147C22×C4×C13C22×C411yescharacteristic
148C22×C4×C13C22×C411yescharacteristic
149C22×C4×C13C22×C411yescharacteristic
150C22×C4×C13C22×C411yescharacteristic
151C2×C22⋊D13—41no—
152C2×C22⋊D13—41no—
153C2×C22⋊D13C4214yes—
154C22×Dic13—21no—
155C22×Dic13—21no—
156C22×Dic13—21no—
157C22×Dic13—21no—
158C22×Dic13C22×C411yescharacteristic
159C22×Dic13C22×C411yescharacteristic
160C22×Dic13C22×C411yescharacteristic
161C22×Dic13C22×C411yescharacteristic
162C22×Dic13C22×C411yescharacteristic
163C22×Dic13C22×C412yes—
164C22×Dic13C22×C412yes—
165C22×Dic13C22×C411yescharacteristic
166C22×Dic13C2411yescharacteristic
167C2×C4×D13—21no—
168C2×C4×D13—21no—
169C2×C4×D13—21no—
170C2×C4×D13—21no—
171C2×C4×D13C22×C412yes—
172C2×C4×D13C22×C412yes—
173#6122—28no—
174C2×#1057—21no—
175C2×#1057—21no—
176C2×#1057—21no—
177C2×#1057—21no—
178C2×#1057—21no—
179C2×#1057—21no—
180C2×#1057—21no—
181C2×#1057—21no—
182C2×#1057—21no—
183C2×#1057—21no—
184C2×#1057—21no—
185C2×#1057—21no—
186C2×#1057—28no—
187C2×#1057C22×C412yes—
188C2×#1057C22×C412yes—
189C2×#1057C22×C412yes—
190C2×#1057C22×C412yes—
191C2×#1057C22×C412yes—
192C2×#1057C22×C412yes—
193C2×#1057C22×C412yes—
194C2×#1057C22×C412yes—
195C2×#1057C2×D412yes—
196C2×#1057C2×D412yes—
197C2×#1057#4112yes—
198C2×#1057#4112yes—
199#6118—28no—
200D13⋊C8—28no—
201C13×C4⋊C4—22no—
202C13×C22⋊C4—22no—
203C13×C22⋊C4—41no—
204C13×C22⋊C4C4214yes—
205C42×C13—41no—
206C22⋊Dic13—22no—
207C22⋊Dic13—41no—
208#6103—22no—
209#6103—22no—
210#6103—41no—
211#6103—41no—
212#6103C4214yes—
213C4⋊Dic13—22no—
214#6101—22no—
215#6101—22no—
216#6101—41no—
217#6101—41no—
218#6101C4214yes—
219C4×Dic13—21no—
220C4×Dic13—21no—
221C4×Dic13—21no—
222C4×Dic13—21no—
223C4×Dic13—21no—
224C4×Dic13—21no—
225C4×Dic13—41no—
226C4×Dic13—41no—
227C4×Dic13—41no—
228C4×Dic13C22×C412yes—
229C4×Dic13C22×C412yes—
230C4×Dic13C2×D412yes—
231C4×Dic13#4112yes—
232C2×#435—131no—
233C2×#435—131no—
234C2×#405—131no—
235C2×#405—131no—
236#2293—131no—
237#1771—131no—
238#1771—131no—
239#1767—131no—
240#1753—131no—
241#1753—131no—
242#1752—131no—
243#1752—131no—
244#1750—131no—
245#1750—131no—
246C4×#97—131no—
247C23×C13—21no—
248C23×C13—21no—
249C23×C13—21no—
250C23×C13—21no—
251C23×C13—21no—
252C23×C13—21no—
253C23×C13C2×C4212yes—
254C23×C13C23×C411yescharacteristic
255C22×D13—21no—
256C22×D13—21no—
257C22×D13—21no—
258C22×D13—21no—
259C22×D13—21no—
260C22×D13—21no—
261C22×D13C2×C4212yes—
262C2×C4×C13—21no—
263C2×C4×C13—21no—
264C2×C4×C13—21no—
265C2×C4×C13—21no—
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—21no—
274C2×C4×C13—21no—
275C2×C4×C13—21no—
276C2×C4×C13—21no—
277C2×C4×C13C2×C4212yes—
278C2×C4×C13C2×C4212yes—
279C2×C4×C13C4×D412yes—
280C22⋊D13—44no—
281C2×Dic13—21no—
282C2×Dic13—21no—
283C2×Dic13—21no—
284C2×Dic13—21no—
285C2×Dic13—21no—
286C2×Dic13—21no—
287C2×Dic13—22no—
288C2×Dic13—22no—
289C2×Dic13—22no—
290C2×Dic13—22no—
291C2×Dic13—21no—
292C2×Dic13—21no—
293C2×Dic13—21no—
294C2×Dic13—21no—
295C2×Dic13—21no—
296C2×Dic13—21no—
297C2×Dic13—21no—
298C2×Dic13—21no—
299C2×Dic13—21no—
300C2×Dic13C2×C4212yes—
301C2×Dic13C2×C4212yes—
302C2×Dic13C4×D412yes—
303C2×Dic13C23×C411yescharacteristic
304C2×Dic13C23×C411yescharacteristic
305C2×Dic13C22×D411yescharacteristic
306C2×Dic13C2×#4111yescharacteristic
307C2×Dic13C2×#4111yescharacteristic
308C2×Dic13C2×#4111yescharacteristic
309C4×D13—22no—
310C4×D13—22no—
311C4×D13—22no—
312C4×D13—22no—
313#1057—22no—
314#1057—22no—
315#1057—22no—
316#1057—22no—
317#1057—22no—
318#1057—22no—
319#1057C4×D414yes—
320#1057C4×D414yes—
321C22×M16—131no—
322C22×M16—131no—
323C23×C8—131no—
324C23×C8—131no—
325C2×C4×D4—131no—
326C2×#117—131no—
327C2×#117—131no—
328#435—138no—
329#435—138no—
330C2×C4⋊C8—131no—
331C2×C4⋊C8—131no—
332C2×C22⋊C8—131no—
333C2×C22⋊C8—131no—
334C2×C22⋊C8—131no—
335C2×C22⋊C8—131no—
336#405—264no—
337#405—264no—
338C2×#97—131no—
339C2×#97—131no—
340C2×#97—131no—
341C2×#97—131no—
342C2×#97—131no—
343C2×#97—131no—
344C2×#97—131no—
345C2×#97—131no—
346C2×C4×C8—131no—
347C2×C4×C8—131no—
348C2×C4×C8—131no—
349C2×C4×C8—131no—
350#390—131no—
351#390—131no—
352#389—131no—
353#389—131no—
354#388—131no—
355#388—131no—
356#388—131no—
357#388#26111yescharacteristic
358C4×C4⋊C4—131no—
359C4×C22⋊C4—131no—
360C4×C22⋊C4—131no—
361C43—131no—
362#336—131no—
363#336—131no—
364#336—131no—
365#336—131no—
366#336—131no—
367#336—131no—
368C22×C13—22no—
369C22×C13—22no—
370C22×C13—22no—
371C22×C13—41no—
372C22×C13—41no—
373C22×C13—41no—
374C22×C13—41no—
375C22×C13C22×C4211yescharacteristic
376C22×C13C2×C4×D411yescharacteristic
377C22×C13C4×#4111yescharacteristic
378C22×C13#56811yescharacteristic
379C22×C13#56811yescharacteristic
380C22×C13#56811yescharacteristic
381C22×C13#56811yescharacteristic
382C2×D13—22no—
383C2×D13—22no—
384C2×D13—22no—
385C2×D13—41no—
386C2×D13—41no—
387C2×D13—41no—
388C2×D13—41no—
389C4×C13—22no—
390C4×C13—22no—
391C4×C13—22no—
392C4×C13—41no—
393C4×C13—41no—
394C4×C13—41no—
395Dic13—22no—
396Dic13—22no—
397Dic13—22no—
398Dic13—41no—
399Dic13—41no—
400Dic13—41no—
401Dic13C2×C4×D411yescharacteristic
402Dic13C2×C4×D411yescharacteristic
403Dic13C4×#4111yescharacteristic
404Dic13C4×#4111yescharacteristic
405C22×D4—131no—
406C23×C4—131no—
407C23×C4—131no—
408C2×M16—134no—
409C2×M16—134no—
410C2×M16—262no—
411C2×M16—262no—
412C2×M16—262no—
413C2×M16—262no—
414C22×C8—131no—
415C22×C8—131no—
416C22×C8—131no—
417C22×C8—131no—
418C22×C8—134no—
419C22×C8—134no—
420C22×C8—131no—
421C22×C8—131no—
422C22×C8—131no—
423C22×C8—131no—
424C22×C8—262no—
425C22×C8—262no—
426C22×C8—262no—
427C22×C8—262no—
428C4×D4—134no—
429C4×D4—134no—
430#117—262no—
431#117—262no—
432#117—262no—
433#117—262no—
434C2×C4⋊C4—131no—
435C2×C4⋊C4—131no—
436C2×C4⋊C4—131no—
437C2×C4⋊C4—131no—
438C2×C4⋊C4—131no—
439C2×C4⋊C4—131no—
440C2×C4⋊C4C2×#26111yescharacteristic
441C2×C22⋊C4—131no—
442C2×C22⋊C4—131no—
443C2×C22⋊C4—131no—
444C2×C22⋊C4—131no—
445C2×C22⋊C4—131no—
446C2×C22⋊C4—131no—
447C2×C22⋊C4—131no—
448C2×C22⋊C4C2×#26111yescharacteristic
449C2×C22⋊C4C2×#26111yescharacteristic
450C2×C22⋊C4C2×#26111yescharacteristic
451C2×C42—131no—
452C2×C42—131no—
453C2×C42—131no—
454C2×C42—131no—
455C2×C42—131no—
456C2×C42—131no—
457C2×C42—131no—
458C2×C42—131no—
459C2×C42C2×#26111yescharacteristic
460C4⋊C8—134no—
461C4⋊C8—134no—
462C22⋊C8—134no—
463C22⋊C8—134no—
464C22⋊C8—134no—
465C22⋊C8—134no—
466#97—134no—
467#97—134no—
468#97—262no—
469#97—262no—
470#97—262no—
471#97—262no—
472#97—262no—
473#97—262no—
474C4×C8—134no—
475C4×C8—262no—
476C4×C8—262no—
477C4×C8—262no—
478#95—131no—
479#95—131no—
480#95—131no—
481#95—131no—
482#95C2×#26111yescharacteristic
483#95C2×#26111yescharacteristic
484C2×C13—42no—
485C2×C13C42×D411yescharacteristic
486C2×C13#287311yescharacteristic
487C2×C13#287511yescharacteristic
488C2×C13#293211yescharacteristic
489C2×C13#293211yescharacteristic
490C2×C13#296711yescharacteristic
491C2×C13#296711yescharacteristic
492D13—42no—
493C24—131no—
494C24C22×#26111yescharacteristic
495C2×D4—134no—
496C2×D4—521no—
497C2×D4—521no—
498C22×C4—131no—
499C22×C4—132no—
500C22×C4—132no—
501C22×C4—131no—
502C22×C4—131no—
503C22×C4—131no—
504C22×C4—132no—
505C22×C4—132no—
506C22×C4—131no—
507C22×C4—131no—
508C22×C4—131no—
509C22×C4—261no—
510C22×C4—261no—
511C22×C4—261no—
512C22×C4—261no—
513C22×C4—261no—
514C22×C4—261no—
515C22×C4—261no—
516C22×C4—261no—
517C22×C4C22×#26111yescharacteristic
518C22×C4C22×#26111yescharacteristic
519C22×C4C22×#26111yescharacteristic
520C22×C4C22×#26111yescharacteristic
521C22×C4C22×#26111yescharacteristic
522C22×C4C22×#26111yescharacteristic
523M16—268no—
524M16—268no—
525C2×C8—132no—
526C2×C8—132no—
527C2×C8—132no—
528C2×C8—132no—
529C2×C8—132no—
530C2×C8—132no—
531C2×C8—132no—
532C2×C8—132no—
533C2×C8—132no—
534C2×C8—132no—
535C2×C8—132no—
536C2×C8—132no—
537C2×C8—268no—
538C2×C8—268no—
539C2×C8—261no—
540C2×C8—261no—
541C2×C8—261no—
542C2×C8—261no—
543C2×C8—261no—
544C2×C8—261no—
545C2×C8—261no—
546C2×C8—261no—
547C2×C8—261no—
548C2×C8—261no—
549C2×C8—261no—
550C2×C8—261no—
551C4⋊C4—22no—
552C4⋊C4—134no—
553C4⋊C4—262no—
554C4⋊C4—262no—
555C4⋊C4—262no—
556C4⋊C4—521no—
557C4⋊C4—521no—
558C22⋊C4—22no—
559C22⋊C4—41no—
560C22⋊C4—134no—
561C22⋊C4—262no—
562C22⋊C4—262no—
563C22⋊C4—262no—
564C22⋊C4—521no—
565C22⋊C4—521no—
566C22⋊C4—521no—
567C22⋊C4C4×#26114yes—
568C42—41no—
569C42—132no—
570C42—132no—
571C42—132no—
572C42—132no—
573C42—261no—
574C42—261no—
575C42—261no—
576C42—261no—
577C42—261no—
578C42—261no—
579C42—521no—
580C42—521no—
581C42—521no—
582C13#2048811yescharacteristic, complemented, Sylow
583C23—21no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—132no—
590C23—261no—
591C23—261no—
592C23—261no—
593C23—261no—
594C23—261no—
595C23—261no—
596C23C2×C4×#26112yes—
597C23C23×#26111yescharacteristic
598D4—524no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
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—131no—
615C2×C4—131no—
616C2×C4—131no—
617C2×C4—131no—
618C2×C4—131no—
619C2×C4—131no—
620C2×C4—132no—
621C2×C4—132no—
622C2×C4—132no—
623C2×C4—262no—
624C2×C4—262no—
625C2×C4—262no—
626C2×C4—262no—
627C2×C4—262no—
628C2×C4—262no—
629C2×C4—262no—
630C2×C4—262no—
631C2×C4—261no—
632C2×C4—261no—
633C2×C4—261no—
634C2×C4—261no—
635C2×C4—261no—
636C2×C4—261no—
637C2×C4—261no—
638C2×C4—261no—
639C2×C4—261no—
640C2×C4—261no—
641C2×C4—261no—
642C2×C4—261no—
643C2×C4—261no—
644C2×C4—261no—
645C2×C4—261no—
646C2×C4C2×C4×#26112yes—
647C2×C4C2×C4×#26112yes—
648C2×C4D4×#26112yes—
649C8—134no—
650C8—134no—
651C8—262no—
652C8—262no—
653C8—262no—
654C8—262no—
655C8—262no—
656C8—262no—
657C22—22no—
658C22—22no—
659C22—22no—
660C22—41no—
661C22—41no—
662C22—41no—
663C22—41no—
664C22—262no—
665C22—262no—
666C22—262no—
667C22—521no—
668C22—521no—
669C22—521no—
670C22—521no—
671C22C22×C4×#26111yescharacteristic
672C22#1171962111yescharacteristic
673C22C2×D4×#26111yescharacteristic
674C22#1171962911yescharacteristic
675C22#1171962911yescharacteristic
676C22#1171962911yescharacteristic
677C22#41×#26111yescharacteristic
678C4—22no—
679C4—22no—
680C4—22no—
681C4—41no—
682C4—41no—
683C4—41no—
684C4—131no—
685C4—131no—
686C4—131no—
687C4—131no—
688C4—262no—
689C4—262no—
690C4—262no—
691C4—521no—
692C4—521no—
693C4—521no—
694C2—42no—
695C2—522no—
696C2C4×D4×#26111yescharacteristic
697C2#1313140111yescharacteristic
698C2#1313140711yescharacteristic
699C2#1313156211yescharacteristic
700C2#1313156411yescharacteristic
701C2#1313165811yescharacteristic
702C2#1313165911yescharacteristic
subgroupG/H
center, FrattiniC23C23×#261
commutatorC22×C13C22×C42
FittingC13×#388C4
socleC23×C13C23×C4
prime radicalC22×C22⋊D13C2×C4
cosocleC22×Dic13C24
hypercenter#388#261
hypocenterC13#20488
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
3. C2×#11719072C2semidirect
4. C2×#11719062C2semidirect
5. #13130635C2semidirect
6. #13130635C2semidirect
7. #13130622C2semidirect
8. #13130578C2semidirect
9. #13130577C2semidirect
10. #13130574C2semidirect
11. #13130573C2semidirect
12. #13130566C2semidirect
13. #13130565C2semidirect
14. C4×#88110C2semidirect
42. #11719065C4semidirect
43. #11719064C4semidirect
135. C4×#1057D4semidirect
582. C13#20488semidirect

Maximal subgroups

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

subgroupindex
C2×#117190652
C2×#117190642
C2×#117190722
C2×#117190622
#131306352
#131306222
#131305782
#131305772
#131305742
#131305732
#131305662
#131305652
C4×#881102
#131172962
#2048813