Finite Group Databasebeta

← #15889461

Subgroups — #15889461

Order 3328.

702 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13118123C211yesmaximal, characteristic
2#13115775C211yesmaximal, characteristic, complemented
3#13115774C211yesmaximal, characteristic, complemented
4#13115452C211yesmaximal, characteristic, complemented
5#13115451C211yesmaximal, characteristic, complemented
6#13115450C211yesmaximal, characteristic, complemented
7#13115447C211yesmaximal, characteristic, complemented
8#13115130C211yesmaximal, characteristic
9#13115128C211yesmaximal, characteristic
10#13115017C211yesmaximal, characteristic, complemented
11#13115017C211yesmaximal, characteristic, complemented
12#13115014C211yesmaximal, characteristic, complemented
13#13114955C211yesmaximal, characteristic, complemented
14#13114954C211yesmaximal, characteristic, complemented
15C13×#1850C211yesmaximal, characteristic, complemented
16C23×C8×C13C2211yescharacteristic
17C2×C4×C22⋊D13C2211yescharacteristic
18C22×#6094C2211yescharacteristic
19C2×C4×Dic26C2211yescharacteristic
20C2×C13×C4⋊C8C2211yescharacteristic
21C2×C13×C4⋊C8C2211yescharacteristic
22C2×C13×C22⋊C8C2211yescharacteristic
23C4×C13×C22⋊C4C2211yescharacteristic
24C4×C22⋊Dic13C2211yescharacteristic
25C2×C22⋊#1055C2211yescharacteristic
26C2×C22⋊#1055C2211yescharacteristic
27C2×#88060C2211yescharacteristic
28C2×#88060C2211yescharacteristic
29C2×#88060C2211yescharacteristic
30C2×#88055C2211yescharacteristic
31C2×#88054C2211yescharacteristic
32C2×#88054C2211yescharacteristic
33C2×#88054C2211yescharacteristic
34#11718622C411yescharacteristic
35#11718620C411yescharacteristic
36#11718613C411yescharacteristic
37#11718608C411yescharacteristic
38C4×#6103C2211yescharacteristic
39C4×#6103C2211yescharacteristic
40#11718593C2211yescharacteristic
41C2×C4⋊#1055C2211yescharacteristic
42C2×#88043C2211yescharacteristic
43#11718336C411yescharacteristic
44#11718334C411yescharacteristic
45#11718321C411yescharacteristic
46#11718319C411yescharacteristic
47C13×#336C2211yescharacteristic
48C13×#336C2211yescharacteristic
49#11718142C2211yescharacteristic
50#11718142C2211yescharacteristic
51#11718142C2211yescharacteristic
52#11718142C2211yescharacteristic
53#11718142C2211yescharacteristic
54#11718142C2211yescharacteristic
55#11718142C2211yescharacteristic
56#11718142C2211yescharacteristic
57#11718116C2211yescharacteristic
58#11718116C2211yescharacteristic
59C23×C4×C13C2311yescharacteristic
60C22×C22⋊D13C2×C411yescharacteristic
61C22×C4×D13C2311yescharacteristic
62C22×Dic26C2×C411yescharacteristic
63C22×C8×C13—41no—
64C22×C8×C13—41no—
65C22×C8×C13—41no—
66C22×C8×C13C2311yescharacteristic
67C22×C8×C13C2311yescharacteristic
68C22×C8×C13C2311yescharacteristic
69C22×C8×C13C2311yescharacteristic
70C2×C13×C22⋊C4C2×C411yescharacteristic
71C2×C13×C22⋊C4C2×C411yescharacteristic
72C2×C42×C13C2311yescharacteristic
73C2×C42×C13C2311yescharacteristic
74C2×C22⋊Dic13C2×C411yescharacteristic
75C2×C22⋊Dic13C2×C411yescharacteristic
76C2×C22⋊Dic13C2×C411yescharacteristic
77C4×C22⋊D13—41no—
78C4×C22⋊D13—41no—
79C2×#6103C2×C411yescharacteristic
80C2×#6103C2×C411yescharacteristic
81C2×#6103C2×C411yescharacteristic
82C2×#6103C2×C411yescharacteristic
83C2×#6103C2×C411yescharacteristic
84C2×C4⋊Dic13C2×C411yescharacteristic
85C2×#6101C2×C411yescharacteristic
86C2×#6101C2×C411yescharacteristic
87C2×#6101C2×C411yescharacteristic
88C2×C4×Dic13C2311yescharacteristic
89C2×C4×Dic13C2311yescharacteristic
90C2×C4×Dic13C2311yescharacteristic
91C22×#1055C2311yescharacteristic
92C22×#1055C2311yescharacteristic
93C22×#1055C2311yescharacteristic
94C22×#1055C2311yescharacteristic
95C2×#6094—41no—
96C2×#6094—41no—
97C2×#6094—41no—
98C4×Dic26—41no—
99C4×Dic26—41no—
100C13×C4⋊C8—41no—
101C13×C4⋊C8—41no—
102C13×C22⋊C8—41no—
103C13×#95C2×C411yescharacteristic
104C13×#95C2×C411yescharacteristic
105#88071C2×C411yescharacteristic
106#88071C2×C411yescharacteristic
107#88071C2×C411yescharacteristic
108#88071C2×C411yescharacteristic
109#88071C2×C411yescharacteristic
110#88071C2×C411yescharacteristic
111#88071C2×C411yescharacteristic
112#88071C2×C411yescharacteristic
113#88071C2×C411yescharacteristic
114#88071C2×C411yescharacteristic
115C22⋊#1055—41no—
116C22⋊#1055—41no—
117#88060—41no—
118#88060—41no—
119#88060—41no—
120#88055—41no—
121#88054—41no—
122#88054—41no—
123#88054—41no—
124C4⋊#1055—41no—
125#88043—41no—
126#23354—131nomaximal, Sylow
127C24×C13C22×C411yescharacteristic
128C23×D13C22×C411yescharacteristic
129C22×C4×C13—21no—
130C22×C4×C13—21no—
131C22×C4×C13—21no—
132C22×C4×C13—21no—
133C22×C4×C13—21no—
134C22×C4×C13—21no—
135C22×C4×C13C22×C411yescharacteristic
136C22×C4×C13C22×C411yescharacteristic
137C22×C4×C13C22×C411yescharacteristic
138C22×C4×C13C22×C411yescharacteristic
139C22×C4×C13C22×C411yescharacteristic
140C22×C4×C13C2411yescharacteristic
141C2×C22⋊D13—22no—
142C2×C22⋊D13—41no—
143C2×C22⋊D13—41no—
144C22×Dic13C22×C411yescharacteristic
145C22×Dic13C22×C411yescharacteristic
146C22×Dic13C22×C411yescharacteristic
147C22×Dic13C22×C411yescharacteristic
148C22×Dic13C22×C411yescharacteristic
149C22×Dic13C22×C411yescharacteristic
150C22×Dic13C22×C411yescharacteristic
151C2×C4×D13—21no—
152C2×C4×D13—21no—
153C2×C4×D13—21no—
154C2×C4×D13—21no—
155C2×C4×D13—21no—
156C2×C4×D13—21no—
157C2×Dic26—41no—
158C2×Dic26—41no—
159C2×Dic26—41no—
160C2×C8×C13—21no—
161C2×C8×C13—21no—
162C2×C8×C13—21no—
163C2×C8×C13—21no—
164C2×C8×C13—21no—
165C2×C8×C13—21no—
166C2×C8×C13—21no—
167C2×C8×C13—21no—
168C2×C8×C13—21no—
169C2×C8×C13—21no—
170C2×C8×C13—21no—
171C2×C8×C13—21no—
172C2×C8×C13—44no—
173C13×C22⋊C4—22no—
174C13×C22⋊C4—41no—
175C42×C13—21no—
176C42×C13—21no—
177C42×C13—21no—
178C42×C13—21no—
179C22⋊Dic13—22no—
180C22⋊Dic13—41no—
181C22⋊Dic13—41no—
182#6103—41no—
183#6103—41no—
184#6103—41no—
185#6103—41no—
186#6103—41no—
187C4⋊Dic13—41no—
188#6101—41no—
189#6101—41no—
190#6101—41no—
191C4×Dic13—21no—
192C4×Dic13—21no—
193C4×Dic13—21no—
194C4×Dic13—21no—
195C4×Dic13—21no—
196C4×Dic13—21no—
197C2×#1055—21no—
198C2×#1055—21no—
199C2×#1055—21no—
200C2×#1055—21no—
201C2×#1055—21no—
202C2×#1055—21no—
203C2×#1055—21no—
204C2×#1055—21no—
205C2×#1055—21no—
206C2×#1055—21no—
207C2×#1055—21no—
208C2×#1055—21no—
209#6094—44no—
210#2398—131no—
211#1985—131no—
212#1985—131no—
213#1924—131no—
214#1924—131no—
215#1924—131no—
216#1924—131no—
217#1870—131no—
218#1869—131no—
219#1851—131no—
220#1851—131no—
221#1850—131no—
222#1850D1311yescharacteristic, complemented
223#1832—131no—
224#1832—131no—
225C23×C13—21no—
226C23×C13—21no—
227C23×C13—21no—
228C23×C13—21no—
229C23×C13—21no—
230C23×C13—21no—
231C23×C13#13112yes—
232C23×C13C23×C411yescharacteristic
233C22×D13—21no—
234C22×D13—21no—
235C22×D13—21no—
236C22×D13—21no—
237C22×D13—21no—
238C22×D13—21no—
239C22×D13—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—41no—
256C2×C4×C13—41no—
257C2×C4×C13—41no—
258C2×C4×C13—41no—
259C2×C4×C13H(5,𝔽2)11yescharacteristic
260C2×C4×C13H(5,𝔽2)11yescharacteristic
261C2×C4×C13H(5,𝔽2)11yescharacteristic
262C2×C4×C13H(5,𝔽2)11yescharacteristic
263C2×C4×C132−1+411yescharacteristic
264C2×C4×C132−1+411yescharacteristic
265C22⋊D13—44no—
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—21no—
276C2×Dic13—21no—
277C2×Dic13—21no—
278C2×Dic13—21no—
279C2×Dic13—21no—
280C2×Dic13—21no—
281C2×Dic13—21no—
282C2×Dic13—21no—
283C2×Dic13—21no—
284C2×Dic13—21no—
285C2×Dic13—21no—
286C2×Dic13—21no—
287C4×D13—41no—
288C4×D13—41no—
289C4×D13—41no—
290C4×D13—41no—
291Dic26—44no—
292C8×C13—41no—
293C8×C13—41no—
294C8×C13—41no—
295C8×C13—41no—
296#1055—41no—
297#1055—41no—
298#1055—41no—
299#1055—41no—
300C22×M16—131no—
301C23×C8C2×D1311yescharacteristic
302C2×C4×Q8—131no—
303C2×C4×D4—131no—
304C2×C4⋊C8—131no—
305C2×C4⋊C8—131no—
306C2×C4⋊C8—131no—
307C2×C4⋊C8—131no—
308C2×C4⋊C8C2×D1311yescharacteristic
309C2×C4⋊C8C2×D1311yescharacteristic
310C2×C22⋊C8—131no—
311C2×C22⋊C8—131no—
312C2×C22⋊C8—131no—
313C2×C22⋊C8—131no—
314C2×C22⋊C8—131no—
315C2×C22⋊C8C2×D1311yescharacteristic
316C2×#97—131no—
317C2×#97—131no—
318#400—131no—
319#400—131no—
320#397—131no—
321#397—131no—
322#394—131no—
323#394—131no—
324#393—131no—
325#393—131no—
326C4×C22⋊C4—131no—
327C4×C22⋊C4—131no—
328C4×C22⋊C4—131no—
329C4×C22⋊C4C2×D1311yescharacteristic
330#376—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—
339#336—131no—
340#336—131no—
341#336C2×D1311yescharacteristic
342#336C2×D1311yescharacteristic
343C22×C13—22no—
344C22×C13—22no—
345C22×C13—22no—
346C22×C13—41no—
347C22×C13—41no—
348C22×C13—41no—
349C22×C13—41no—
350C22×C13#51811yescharacteristic
351C22×C13#52011yescharacteristic
352C22×C13#52011yescharacteristic
353C22×C13C2×#13111yescharacteristic
354C22×C13#56811yescharacteristic
355C22×C13#56811yescharacteristic
356C22×C13#56811yescharacteristic
357C2×D13—41no—
358C2×D13—41no—
359C2×D13—41no—
360C2×D13—41no—
361C2×D13—41no—
362C2×D13—41no—
363C2×D13—41no—
364C4×C13—41no—
365C4×C13—41no—
366C4×C13—41no—
367C4×C13—41no—
368C4×C13—41no—
369C4×C13H(3,𝔽4)11yescharacteristic
370C4×C13#56211yescharacteristic
371C4×C13#56211yescharacteristic
372C4×C13#56311yescharacteristic
373Dic13—41no—
374Dic13—41no—
375Dic13—41no—
376Dic13—41no—
377Dic13—41no—
378Dic13—41no—
379Dic13—41no—
380C22×Q8—131no—
381C22×D4—131no—
382C23×C4—131no—
383C23×C4C22×D1311yescharacteristic
384C2×M16—521no—
385C2×M16—521no—
386C2×M16—521no—
387C22×C8—41no—
388C22×C8—41no—
389C22×C8—41no—
390C22×C8—131no—
391C22×C8—131no—
392C22×C8—131no—
393C22×C8—131no—
394C22×C8C22×D1311yescharacteristic
395C22×C8C22×D1311yescharacteristic
396C22×C8C22×D1311yescharacteristic
397C22×C8C22×D1311yescharacteristic
398C4×Q8—521no—
399C4×Q8—521no—
400C4×D4—521no—
401C4×D4—521no—
402C2×C4⋊C4—131no—
403C2×C4⋊C4—131no—
404C2×C4⋊C4—131no—
405C2×C4⋊C4—131no—
406C2×C22⋊C4—131no—
407C2×C22⋊C4—131no—
408C2×C22⋊C4—131no—
409C2×C22⋊C4—131no—
410C2×C22⋊C4—131no—
411C2×C22⋊C4—131no—
412C2×C22⋊C4—131no—
413C2×C22⋊C4—131no—
414C2×C22⋊C4C4×D1311yescharacteristic
415C2×C22⋊C4C4×D1311yescharacteristic
416C2×C42—131no—
417C2×C42—131no—
418C2×C42—131no—
419C2×C42C22×D1311yescharacteristic
420C2×C42C22×D1311yescharacteristic
421C4⋊C8—41no—
422C4⋊C8—41no—
423C4⋊C8—521no—
424C4⋊C8—521no—
425C4⋊C8—521no—
426C4⋊C8—521no—
427C22⋊C8—41no—
428C22⋊C8—521no—
429C22⋊C8—521no—
430C22⋊C8—521no—
431C22⋊C8—521no—
432C22⋊C8—521no—
433#97—521no—
434#97—521no—
435#95—131no—
436#95—131no—
437#95—131no—
438#95—131no—
439#95—131no—
440#95—131no—
441#95—131no—
442#95—131no—
443#95—131no—
444#95—131no—
445#95C4×D1311yescharacteristic
446#95C4×D1311yescharacteristic
447C2×C13—42no—
448C2×C13#237911yescharacteristic
449C2×C13#297611yescharacteristic
450C2×C13#297811yescharacteristic
451C2×C13#299211yescharacteristic
452C2×C13#299211yescharacteristic
453C2×C13#299511yescharacteristic
454C2×C13#299511yescharacteristic
455D13—81no—
456C24—131no—
457C24C2×C4×D1311yescharacteristic
458C2×Q8—521no—
459C2×Q8—521no—
460C2×Q8—521no—
461C2×D4—262no—
462C2×D4—521no—
463C2×D4—521no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—131no—
471C22×C4—131no—
472C22×C4—131no—
473C22×C4—131no—
474C22×C4—131no—
475C22×C4—131no—
476C22×C4—131no—
477C22×C4—261no—
478C22×C4—261no—
479C22×C4—261no—
480C22×C4—261no—
481C22×C4—261no—
482C22×C4—261no—
483C22×C4C2×C4×D1311yescharacteristic
484C22×C4C2×C4×D1311yescharacteristic
485C22×C4C2×C4×D1311yescharacteristic
486C22×C4C2×C4×D1311yescharacteristic
487C22×C4C2×C4×D1311yescharacteristic
488C22×C4C23×D1311yescharacteristic
489M16—524no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—44no—
503C2×C8—261no—
504C2×C8—261no—
505C2×C8—261no—
506C2×C8—261no—
507C2×C8—261no—
508C2×C8—261no—
509C2×C8—261no—
510C2×C8—261no—
511C2×C8—261no—
512C2×C8—261no—
513C2×C8—261no—
514C2×C8—261no—
515C4⋊C4—521no—
516C4⋊C4—521no—
517C4⋊C4—521no—
518C4⋊C4—521no—
519C22⋊C4—22no—
520C22⋊C4—41no—
521C22⋊C4—262no—
522C22⋊C4—521no—
523C22⋊C4—521no—
524C22⋊C4—521no—
525C22⋊C4—521no—
526C22⋊C4—521no—
527C22⋊C4—521no—
528C22⋊C4—521no—
529C42—21no—
530C42—21no—
531C42—21no—
532C42—21no—
533C42—261no—
534C42—261no—
535C42—261no—
536C42—261no—
537C42—261no—
538C42—261no—
539C13#2335411yescharacteristic, complemented, Sylow
540C23—21no—
541C23—21no—
542C23—21no—
543C23—21no—
544C23—21no—
545C23—21no—
546C23—261no—
547C23—261no—
548C23—261no—
549C23—261no—
550C23—261no—
551C23—261no—
552C23—261no—
553C23#8815512yes—
554C23C22×C4×D1311yescharacteristic
555Q8—524no—
556D4—524no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
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—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—261no—
595C2×C4—261no—
596C2×C4—261no—
597C2×C4—521no—
598C2×C4—521no—
599C2×C4—521no—
600C2×C4—521no—
601C2×C4#8825111yescharacteristic
602C2×C4#8825111yescharacteristic
603C2×C4#8825111yescharacteristic
604C2×C4#8825411yescharacteristic
605C2×C4#8825611yescharacteristic
606C2×C4#8825711yescharacteristic
607C8—41no—
608C8—41no—
609C8—41no—
610C8—41no—
611C8—521no—
612C8—521no—
613C8—521no—
614C8—521no—
615C22—22no—
616C22—22no—
617C22—22no—
618C22—41no—
619C22—41no—
620C22—41no—
621C22—41no—
622C22—521no—
623C22—521no—
624C22—521no—
625C22—521no—
626C22—521no—
627C22—521no—
628C22—521no—
629C22#1171920911yescharacteristic
630C22#1171925011yescharacteristic
631C22#1171925111yescharacteristic
632C22C2×#8815511yescharacteristic
633C22#1171945011yescharacteristic
634C22#1171945511yescharacteristic
635C22#1171945511yescharacteristic
636C4—41no—
637C4—41no—
638C4—41no—
639C4—41no—
640C4—41no—
641C4—521no—
642C4—521no—
643C4—521no—
644C4—521no—
645C4—521no—
646C4—521no—
647C4—521no—
648C4#1171929911yescharacteristic
649C4#1171935111yescharacteristic
650C4#1171935211yescharacteristic
651C4#1171937211yescharacteristic
652C2—42no—
653C2—1041no—
654C2#1311800911yescharacteristic
655C2#1312387811yescharacteristic
656C2#1312389511yescharacteristic
657C2#1312396911yescharacteristic
658C2#1312397211yescharacteristic
659C2#1312400211yescharacteristic
660C2#1312400411yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D13
commutator, socleC23×C13C23×C4
FittingC13×#1850C2
prime radicalC22×C22⋊D13C2×C4
cosocleC22×C4×C13C24
hypercenter#1850D13
hypocenterC13#23354
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ #1850

Complements

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

NH ≅ G/Ntype
2. #13115775C2semidirect
3. #13115774C2semidirect
4. #13115452C2semidirect
5. #13115451C2semidirect
6. #13115450C2semidirect
7. #13115447C2semidirect
10. #13115017C2semidirect
11. #13115017C2semidirect
12. #13115014C2semidirect
13. #13114955C2semidirect
14. #13114954C2semidirect
15. C13×#1850C2semidirect
222. #1850D13semidirect
539. C13#23354semidirect

Maximal subgroups

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

subgroupindex
#131181232
#131157752
#131157742
#131154522
#131154512
#131154502
#131154472
#131151302
#131151282
#131150172
#131150142
#131149552
#131149542
C13×#18502
#2335413