Finite Group Databasebeta

← #16800159

Subgroups — #16800159

Order 3328.

898 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719078C211yesmaximal, characteristic, complemented
2C22×#88110C211yesmaximal, characteristic
3#13131008C211yesmaximal, characteristic, complemented
4#13130938C211yesmaximal, characteristic, complemented
5#13130895C211yesmaximal, characteristic, complemented
6#13130894C211yesmaximal, characteristic, complemented
7#13130780C211yesmaximal, characteristic
8#13130779C211yesmaximal, characteristic
9#13130692C211yesmaximal, characteristic
10#13130636C211yesmaximal, characteristic, complemented
11#13130635C211yesmaximal, characteristic, complemented
12#13130631C211yesmaximal, characteristic, complemented
13#13130573C211yesmaximal, characteristic
14C22⋊C4×#1057C211yesmaximal, characteristic
15#13117364C211yesmaximal, characteristic
16C23×#1057C2211yescharacteristic
17C23×#1057C2211yescharacteristic
18C2×#88178C411yescharacteristic
19C22×C4×Dic13C2211yescharacteristic
20C2×#88141C2211yescharacteristic
21C2×C22⋊#1057C2211yescharacteristic
22C2×C22⋊#1057C2211yescharacteristic
23C2×#88112C2211yescharacteristic
24C2×#88112C2211yescharacteristic
25C2×#88112C2211yescharacteristic
26C2×#88112C2211yescharacteristic
27C2×#88110—24no—
28C2×#88110C2211yescharacteristic
29C2×#88110C2211yescharacteristic
30C2×#88110C2211yescharacteristic
31C2×#88110C2211yescharacteristic
32C2×#88110C2211yescharacteristic
33C2×#88110C2211yescharacteristic
34C2×C4⋊#1057C2211yescharacteristic
35C2×C4⋊#1057C2211yescharacteristic
36C2×C4×#1057C2211yescharacteristic
37C2×C4×#1057C2211yescharacteristic
38#11719078—24no—
39C13×#380C411yescharacteristic
40C4⋊C4×Dic13C2211yescharacteristic
41#11718635C411yescharacteristic
42#11718634C411yescharacteristic
43#11718607C411yescharacteristic
44#11718607C411yescharacteristic
45C22⋊C4×Dic13C2211yescharacteristic
46C22⋊C4×Dic13C2211yescharacteristic
47#11718313C411yescharacteristic
48#11718313C411yescharacteristic
49#11718310C2211yescharacteristic
50#11718310C2211yescharacteristic
51#11718290C2211yescharacteristic
52#11718290C2211yescharacteristic
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×Dic26C2×C411yescharacteristic
65C22×#1057—22no—
66C22×#1057—22no—
67C22×#1057—22no—
68C22×#1057—22no—
69C22×#1057—22no—
70C22×#1057Q814yescomplemented
71C22×#1057C2311yescharacteristic
72C22×#1057C2311yescharacteristic
73C22×#1057C2311yescharacteristic
74C22×#1057C2311yescharacteristic
75C22×#1057C2311yescharacteristic
76C22×#1057C2311yescharacteristic
77C22×#1057C2311yescharacteristic
78C22×#1057C2311yescharacteristic
79C2×C13×C4⋊C4C2×C411yescharacteristic
80C2×C13×C4⋊C4C2×C411yescharacteristic
81C2×C13×C22⋊C4C2×C411yescharacteristic
82C2×C13×C22⋊C4C2×C411yescharacteristic
83C2×C22⋊Dic13C2×C411yescharacteristic
84C2×C22⋊Dic13C2×C411yescharacteristic
85C2×C4⋊Dic13C2×C411yescharacteristic
86#88178—24no—
87C2×#6101C2×C411yescharacteristic
88C2×#6101C2×C411yescharacteristic
89C2×#6101C2×C411yescharacteristic
90C2×#6101C2×C411yescharacteristic
91C2×#6101C2×C411yescharacteristic
92C2×#6101C2×C411yescharacteristic
93C2×C4×Dic13—22no—
94C2×C4×Dic13—22no—
95C2×C4×Dic13C2×C411yescharacteristic
96C2×C4×Dic13C2×C411yescharacteristic
97C2×C4×Dic13C2311yescharacteristic
98C2×C4×Dic13C2311yescharacteristic
99C2×C4×Dic13C2311yescharacteristic
100C2×C4×Dic13C2311yescharacteristic
101C2×C4×Dic13C2311yescharacteristic
102C2×C4×Dic13C2311yescharacteristic
103#88141—22no—
104#88141—22no—
105C22⋊#1057—22no—
106C22⋊#1057—22no—
107#88112—22no—
108#88112—22no—
109#88112—22no—
110#88112—22no—
111#88110—22no—
112#88110—22no—
113#88110—22no—
114#88110—22no—
115#88110—22no—
116#88110D414yes—
117C4⋊#1057—22no—
118C4⋊#1057—22no—
119C4×#1057—22no—
120C4×#1057—22no—
121C13×#95C2×C411yescharacteristic
122C13×#95C2×C411yescharacteristic
123#88071C2×C411yescharacteristic
124#88071C2×C411yescharacteristic
125#88071C2×C411yescharacteristic
126#88071C2×C411yescharacteristic
127#88071C2×C411yescharacteristic
128#88071C2×C411yescharacteristic
129#88071C2×C411yescharacteristic
130#88071C2×C411yescharacteristic
131#21599—131nomaximal, Sylow
132C24×C13C22×C411yescharacteristic
133C22×C4×C13—22no—
134C22×C4×C13—22no—
135C22×C4×C13—41no—
136C22×C4×C13C22×C411yescharacteristic
137C22×C4×C13C22×C411yescharacteristic
138C22×C4×C13C22×C411yescharacteristic
139C22×C4×C13C22×C411yescharacteristic
140C22×C4×C13C22×C411yescharacteristic
141C22×C4×C13C22×C411yescharacteristic
142C22×Dic13—21no—
143C22×Dic13—21no—
144C22×Dic13—21no—
145C22×Dic13—21no—
146C22×Dic13—22no—
147C22×Dic13—22no—
148C22×Dic13—41no—
149C22×Dic13C22×C411yescharacteristic
150C22×Dic13C22×C411yescharacteristic
151C22×Dic13C22×C411yescharacteristic
152C22×Dic13C22×C411yescharacteristic
153C22×Dic13C22×C411yescharacteristic
154C22×Dic13C22×C411yescharacteristic
155C22×Dic13C22×C411yescharacteristic
156C22×Dic13C2×Q812yes—
157C22×Dic13#4112yes—
158C22×Dic13C2411yescharacteristic
159C2×Dic26—22no—
160C2×Dic26—22no—
161C2×Dic26—41no—
162C2×#1057—28no—
163C2×#1057—21no—
164C2×#1057—21no—
165C2×#1057—21no—
166C2×#1057—21no—
167C2×#1057—21no—
168C2×#1057—21no—
169C2×#1057—28no—
170C2×#1057—21no—
171C2×#1057—21no—
172C2×#1057—21no—
173C2×#1057—21no—
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×#1057C2×D412yes—
183C2×#1057C2×D412yes—
184C2×#1057C2×Q812yes—
185C2×#1057C2×Q812yes—
186C2×#1057#4112yes—
187C2×#1057#4112yes—
188C13×C4⋊C4—22no—
189C13×C4⋊C4—41no—
190C13×C22⋊C4—22no—
191C13×C22⋊C4—22no—
192C22⋊Dic13—22no—
193C22⋊Dic13M1614yes—
194C4⋊Dic13—22no—
195#6101—22no—
196#6101—22no—
197#6101—22no—
198#6101—22no—
199#6101—41no—
200#6101—41no—
201C4×Dic13—22no—
202C4×Dic13—22no—
203C4×Dic13—21no—
204C4×Dic13—21no—
205C4×Dic13—21no—
206C4×Dic13—21no—
207C4×Dic13—21no—
208C4×Dic13—21no—
209C4×Dic13—21no—
210C4×Dic13—21no—
211C4×Dic13—21no—
212C4×Dic13—21no—
213C4×Dic13C2×D412yes—
214C4×Dic13#4112yes—
215C2×#446—131no—
216C22×#97—131no—
217C4×C22⋊Q8—131no—
218#1985—131no—
219#1940—131no—
220#1917—131no—
221#1917—131no—
222#1850—131no—
223#1850—131no—
224#1797—131no—
225#1771—131no—
226#1771—131no—
227#1770—131no—
228#1752—131no—
229C8×C22⋊C4—131no—
230C23×C13—21no—
231C23×C13—21no—
232C23×C13—21no—
233C23×C13—21no—
234C23×C13C4×Q812yes—
235C23×C13C2×M1612yes—
236C23×C13#13112yes—
237C23×C13C23×C411yescharacteristic
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—21no—
251C2×C4×C13—21no—
252C2×C4×C13—21no—
253C2×C4×C13—21no—
254C2×C4×C13—21no—
255C2×C4×C13—44no—
256C2×C4×C13C4×D412yes—
257C2×Dic13—21no—
258C2×Dic13—21no—
259C2×Dic13—21no—
260C2×Dic13—21no—
261C2×Dic13—21no—
262C2×Dic13—21no—
263C2×Dic13—21no—
264C2×Dic13—21no—
265C2×Dic13—22no—
266C2×Dic13—22no—
267C2×Dic13—22no—
268C2×Dic13—22no—
269C2×Dic13—21no—
270C2×Dic13—21no—
271C2×Dic13—21no—
272C2×Dic13—21no—
273C2×Dic13—21no—
274C2×Dic13—21no—
275C2×Dic13—21no—
276C2×Dic13—21no—
277C2×Dic13—21no—
278C2×Dic13—44no—
279C2×Dic13C4×D412yes—
280C2×Dic13C4×Q812yes—
281C2×Dic13C2×M1612yes—
282C2×Dic13C2×M1612yes—
283C2×Dic13C22×D411yescharacteristic
284C2×Dic13C22×Q811yescharacteristic
285C2×Dic13C2×#4111yescharacteristic
286C2×Dic13C2×#4111yescharacteristic
287C2×Dic13C2×#4111yescharacteristic
288C2×Dic13C2×#4111yescharacteristic
289Dic26—44no—
290#1057—22no—
291#1057—22no—
292#1057—22no—
293#1057—41no—
294#1057—41no—
295#1057—41no—
296#1057—41no—
297#1057C22⋊Q814yescomplemented
298C23×C8—131no—
299C23×C8—131no—
300C2×C22⋊Q8—131no—
301C2×C4×Q8—131no—
302C22×C42—131no—
303#446—264no—
304C2×C4⋊C8—131no—
305C2×C4⋊C8—131no—
306C2×C4⋊C8—131no—
307C2×C4⋊C8—131no—
308C2×C4⋊C8—131no—
309C2×C4⋊C8—131no—
310C2×C22⋊C8—131no—
311C2×C22⋊C8—131no—
312C2×#97—131no—
313C2×#97—131no—
314C2×#97—131no—
315C2×#97—131no—
316C2×#97—131no—
317C2×#97—131no—
318C2×#97—264no—
319C2×C4×C8—131no—
320C2×C4×C8—131no—
321#391—131no—
322#389—131no—
323#387—131no—
324#387—131no—
325#385—131no—
326#385—131no—
327#380#26111yescharacteristic
328C4×C4⋊C4—131no—
329C4×C4⋊C4—131no—
330C4×C4⋊C4—131no—
331C4×C22⋊C4—131no—
332C4×C22⋊C4—131no—
333#336—131no—
334#336—131no—
335#336—131no—
336#336—131no—
337#336—131no—
338#336—131no—
339#336—131no—
340#336—131no—
341#336—131no—
342#336—131no—
343C22×C13—22no—
344C22×C13—22no—
345C22×C13—22no—
346C22×C13—22no—
347C22×C13—22no—
348C22×C13—22no—
349C22×C13#44614yescomplemented
350C22×C13C2×C4×D411yescharacteristic
351C22×C13C2×C4×Q811yescharacteristic
352C22×C13C4×#4111yescharacteristic
353C22×C13C22×M1611yescharacteristic
354C22×C13C2×#13111yescharacteristic
355C22×C13#56811yescharacteristic
356C22×C13#56811yescharacteristic
357C4×C13—22no—
358C4×C13—41no—
359C4×C13—41no—
360C4×C13—41no—
361C4×C13—41no—
362C4×C13—41no—
363Dic13—22no—
364Dic13—22no—
365Dic13—22no—
366Dic13—22no—
367Dic13—41no—
368Dic13—41no—
369Dic13—41no—
370Dic13C2×C22⋊Q811yescharacteristic
371Dic13#52511yescharacteristic
372Dic13#52911yescharacteristic
373Dic13#53311yescharacteristic
374C22×Q8—131no—
375C23×C4—131no—
376C23×C4—131no—
377C23×C4C2×#26111yescharacteristic
378C22×C8—131no—
379C22×C8—131no—
380C22×C8—131no—
381C22×C8—131no—
382C22×C8—134no—
383C22×C8—131no—
384C22×C8—131no—
385C22×C8—131no—
386C22×C8—131no—
387C22×C8—262no—
388C22×C8—262no—
389C22×C8—262no—
390C22×C8—262no—
391C22×C8—262no—
392C22⋊Q8—264no—
393C4×Q8—262no—
394C4×Q8—262no—
395C2×C4⋊C4—131no—
396C2×C4⋊C4—131no—
397C2×C4⋊C4—131no—
398C2×C4⋊C4—131no—
399C2×C4⋊C4—131no—
400C2×C4⋊C4—131no—
401C2×C4⋊C4—131no—
402C2×C4⋊C4C2×#26111yescharacteristic
403C2×C4⋊C4C2×#26111yescharacteristic
404C2×C22⋊C4—131no—
405C2×C22⋊C4—131no—
406C2×C22⋊C4C2×#26111yescharacteristic
407C2×C22⋊C4C2×#26111yescharacteristic
408C2×C42—131no—
409C2×C42—131no—
410C2×C42—131no—
411C2×C42—131no—
412C2×C42—131no—
413C2×C42—131no—
414C2×C42—131no—
415C2×C42—131no—
416C2×C42—262no—
417C2×C42—262no—
418C4⋊C8—262no—
419C4⋊C8—262no—
420C4⋊C8—262no—
421C4⋊C8—262no—
422C4⋊C8—262no—
423C4⋊C8—262no—
424C22⋊C8—262no—
425C22⋊C8—262no—
426#97—134no—
427#97—262no—
428#97—262no—
429#97—262no—
430#97—262no—
431#97—262no—
432C4×C8—262no—
433C4×C8—262no—
434#95—131no—
435#95—131no—
436#95—131no—
437#95—131no—
438#95—131no—
439#95—131no—
440#95—131no—
441#95—131no—
442#95C2×#26111yescharacteristic
443#95C2×#26111yescharacteristic
444C2×C13—24no—
445C2×C13C4×C22⋊Q811yescharacteristic
446C2×C13#293311yescharacteristic
447C2×C13D4×M1611yescharacteristic
448C2×C13C2×#44611yescharacteristic
449C2×C13#296111yescharacteristic
450C2×C13#296811yescharacteristic
451C2×C13#297011yescharacteristic
452C24C22×#26111yescharacteristic
453C2×Q8—262no—
454C2×Q8—262no—
455C2×Q8—521no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—41no—
459C22×C4—131no—
460C22×C4—132no—
461C22×C4—132no—
462C22×C4—131no—
463C22×C4—131no—
464C22×C4—131no—
465C22×C4—131no—
466C22×C4—131no—
467C22×C4—131no—
468C22×C4—131no—
469C22×C4—261no—
470C22×C4—261no—
471C22×C4—261no—
472C22×C4—261no—
473C22×C4—262no—
474C22×C4—262no—
475C22×C4—521no—
476C22×C4C22×#26111yescharacteristic
477C22×C4C22×#26111yescharacteristic
478C22×C4C22×#26111yescharacteristic
479C22×C4C22×#26111yescharacteristic
480C22×C4C22×#26111yescharacteristic
481C22×C4C22×#26111yescharacteristic
482C2×C8—132no—
483C2×C8—132no—
484C2×C8—132no—
485C2×C8—132no—
486C2×C8—132no—
487C2×C8—132no—
488C2×C8—268no—
489C2×C8—261no—
490C2×C8—261no—
491C2×C8—261no—
492C2×C8—261no—
493C2×C8—261no—
494C2×C8—261no—
495C2×C8—268no—
496C2×C8—261no—
497C2×C8—261no—
498C2×C8—261no—
499C2×C8—261no—
500C2×C8—261no—
501C2×C8—261no—
502C2×C8—261no—
503C2×C8—261no—
504C2×C8—261no—
505C2×C8—261no—
506C2×C8—261no—
507C2×C8—261no—
508C4⋊C4—22no—
509C4⋊C4—41no—
510C4⋊C4—262no—
511C4⋊C4—262no—
512C4⋊C4—262no—
513C4⋊C4—262no—
514C4⋊C4—262no—
515C4⋊C4—521no—
516C4⋊C4—521no—
517C22⋊C4—22no—
518C22⋊C4—22no—
519C22⋊C4—134no—
520C22⋊C4—262no—
521C42—132no—
522C42—132no—
523C42—261no—
524C42—261no—
525C42—261no—
526C42—261no—
527C42—261no—
528C42—261no—
529C42—261no—
530C42—261no—
531C42—262no—
532C42—261no—
533C42—261no—
534C42—262no—
535C13#2159911yescharacteristic, complemented, Sylow
536C23—21no—
537C23—21no—
538C23—21no—
539C23—21no—
540C23D13⋊M1612yes—
541C23#8823812yes—
542C23Q8×#26112yes—
543C23C23×#26111yescharacteristic
544Q8—524no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—44no—
563C2×C4—131no—
564C2×C4—131no—
565C2×C4—131no—
566C2×C4—131no—
567C2×C4—131no—
568C2×C4—131no—
569C2×C4—132no—
570C2×C4—132no—
571C2×C4—132no—
572C2×C4—132no—
573C2×C4—262no—
574C2×C4—262no—
575C2×C4—262no—
576C2×C4—262no—
577C2×C4—261no—
578C2×C4—261no—
579C2×C4—261no—
580C2×C4—261no—
581C2×C4—261no—
582C2×C4—261no—
583C2×C4—261no—
584C2×C4—261no—
585C2×C4—261no—
586C2×C4—261no—
587C2×C4—261no—
588C2×C4—261no—
589C2×C4—261no—
590C2×C4—261no—
591C2×C4—261no—
592C2×C4—261no—
593C2×C4—261no—
594C2×C4—524no—
595C2×C4D4×#26112yes—
596C8—134no—
597C8—262no—
598C8—262no—
599C8—262no—
600C8—521no—
601C8—521no—
602C8—521no—
603C8—521no—
604C22—22no—
605C22—22no—
606C22—22no—
607C22—22no—
608C22—22no—
609C22—22no—
610C22#1171907814yescomplemented
611C22C2×D13⋊M1611yescharacteristic
612C22C2×#8823811yescharacteristic
613C22#1171962111yescharacteristic
614C22C2×D4×#26111yescharacteristic
615C22C2×Q8×#26111yescharacteristic
616C22#1171962911yescharacteristic
617C22#41×#26111yescharacteristic
618C4—22no—
619C4—41no—
620C4—41no—
621C4—41no—
622C4—41no—
623C4—41no—
624C4—131no—
625C4—131no—
626C4—131no—
627C4—131no—
628C4—262no—
629C4—262no—
630C4—262no—
631C4—262no—
632C4—521no—
633C4—521no—
634C4—521no—
635C2—24no—
636C2C22⋊Q8×#26111yescharacteristic
637C2#1313156611yescharacteristic
638C2#1313157411yescharacteristic
639C2C2×#1171907811yescharacteristic
640C2#1313162711yescharacteristic
641C2#1313166111yescharacteristic
642C2#1313167511yescharacteristic
subgroupG/H
center, FrattiniC23C23×#261
commutator, socleC23×C13C23×C4
FittingC13×#380C4
prime radicalC24×C13C22×C4
cosocleC22×Dic13C24
hypercenter#380#261
hypocenterC13#21599
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
1. C2×#11719078C2semidirect
3. #13131008C2semidirect
4. #13130938C2semidirect
5. #13130895C2semidirect
6. #13130894C2semidirect
10. #13130636C2semidirect
11. #13130635C2semidirect
12. #13130631C2semidirect
70. C22×#1057Q8semidirect
297. #1057C22⋊Q8semidirect
349. C22×C13#446semidirect
535. C13#21599semidirect
610. C22#11719078semidirect

Maximal subgroups

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

subgroupindex
C2×#117190782
C22×#881102
#131310082
#131309382
#131308952
#131308942
#131307802
#131307792
#131306922
#131306362
#131306352
#131306312
#131305732
C22⋊C4×#10572
#131173642
#2159913