Finite Group Databasebeta

← #15880254

Subgroups — #15880254

Order 3328.

934 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718665C211yesmaximal, characteristic
2C22⋊C4×Dic26C211yesmaximal, characteristic
3#13115525C211yesmaximal, characteristic, complemented
4#13115511C211yesmaximal, characteristic, complemented
5#13115477C211yesmaximal, characteristic, complemented
6#13115470C211yesmaximal, characteristic, complemented
7#13115103C211yesmaximal, characteristic, complemented
8#13115089C211yesmaximal, characteristic, complemented
9#13114931C211yesmaximal, characteristic
10#13114867C211yesmaximal, characteristic
11#13114770C211yesmaximal, characteristic
12#13114669C211yesmaximal, characteristic, complemented
13C4×#88050C211yesmaximal, characteristic, complemented
14#13114620C211yesmaximal, characteristic
15C13×#2346C211yesmaximal, characteristic
16C23×Dic26C2211yescharacteristic
17C2×C13×#117C2211yescharacteristic
18C22×#6099C2211yescharacteristic
19C2×C4×Dic26C2211yescharacteristic
20C2×C4×Dic26C2211yescharacteristic
21C13×#389C2211yescharacteristic
22C13×#389C2211yescharacteristic
23C13×#388—21no—
24C13×#388—21no—
25C13×#382—21no—
26C13×#380C2211yescharacteristic
27C4×C13×C4⋊C4C2211yescharacteristic
28C4×C13×C4⋊C4C2211yescharacteristic
29C4×C13×C22⋊C4C2211yescharacteristic
30C13×#376—21no—
31#11718873C2211yescharacteristic
32C2×C22⋊#1055C2211yescharacteristic
33#11718665C418yescomplemented
34C2×#88050C2211yescharacteristic
35C2×#88050C2211yescharacteristic
36C2×#88050C2211yescharacteristic
37C2×#88050C2211yescharacteristic
38C2×#88050C2211yescharacteristic
39C2×#88050C2211yescharacteristic
40C2×#88050C2211yescharacteristic
41C2×#88050C2211yescharacteristic
42C2×#88048C2211yescharacteristic
43C2×#88047C2211yescharacteristic
44#11718603—21no—
45C22⋊C4×Dic13—21no—
46#11718590C2211yescharacteristic
47#11718590C2211yescharacteristic
48C2×#88043C2211yescharacteristic
49C2×C4×#1055C2211yescharacteristic
50#11718307—21no—
51#11718307—21no—
52#11718121C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718116C2211yescharacteristic
59#11718116C2211yescharacteristic
60C23×C4×C13C2311yescharacteristic
61C23×Dic13—21no—
62C22×Dic26—22no—
63C22×Dic26—22no—
64C22×Dic26—21no—
65C22×Dic26—22no—
66C22×Dic26—41no—
67C22×Dic26—41no—
68C22×Dic26C2×C414yes—
69C22×Dic26C2311yescharacteristic
70C22×Dic26C2311yescharacteristic
71C13×#117—22no—
72C13×#117C2×C414yes—
73C2×C13×C4⋊C4—21no—
74C2×C13×C4⋊C4—21no—
75C2×C13×C4⋊C4C2311yescharacteristic
76C2×C13×C4⋊C4C2311yescharacteristic
77C2×C13×C4⋊C4C2311yescharacteristic
78C2×C13×C4⋊C4C2311yescharacteristic
79C2×C13×C22⋊C4—21no—
80C2×C13×C22⋊C4—21no—
81C2×C13×C22⋊C4D411yescharacteristic
82C2×C13×C22⋊C4D411yescharacteristic
83C2×C42×C13—21no—
84C2×C42×C13—21no—
85C2×C42×C13—21no—
86C2×C42×C13C2311yescharacteristic
87C2×C42×C13C2311yescharacteristic
88C2×C22⋊Dic13—21no—
89C2×C4⋊Dic13C2311yescharacteristic
90C2×C4⋊Dic13C2311yescharacteristic
91C2×#6101—21no—
92C2×#6101—21no—
93C2×C4×Dic13—21no—
94C2×C4×Dic13—21no—
95C2×#6099—41no—
96C2×#6099—41no—
97C2×#6099C2×C414yes—
98C22×#1055C2311yescharacteristic
99C22×#1055C2311yescharacteristic
100C22×#1055C2311yescharacteristic
101C22×#1055C2311yescharacteristic
102C4×Dic26—22no—
103C4×Dic26—22no—
104C4×Dic26—41no—
105C4×Dic26—41no—
106C13×#95—21no—
107C13×#95—21no—
108C13×#95—21no—
109C13×#95—21no—
110C13×#95—21no—
111C13×#95D411yescharacteristic
112C13×#95D411yescharacteristic
113#88071—21no—
114#88071—21no—
115#88071—21no—
116#88071—21no—
117#88071—21no—
118C22⋊#1055—22no—
119#88050—22no—
120#88050—22no—
121#88050—41no—
122#88050—41no—
123#88050C2×C414yes—
124#88050C2×C414yes—
125#88050C2×C414yes—
126#88050C2×C414yes—
127#88048—41no—
128#88047—41no—
129#88043—41no—
130C4×#1055—41no—
131#22585—131nomaximal, Sylow
132C24×C13C2×D411yescharacteristic
133C22×C4×C13—21no—
134C22×C4×C13—21no—
135C22×C4×C13—21no—
136C22×C4×C13—21no—
137C22×C4×C13—21no—
138C22×C4×C13—21no—
139C22×C4×C13—21no—
140C22×C4×C13—21no—
141C22×C4×C13C22×C412yes—
142C22×C4×C13C2×D411yescharacteristic
143C22×C4×C13C2×D411yescharacteristic
144C22×C4×C13C2×D411yescharacteristic
145C22×C4×C13C2×D411yescharacteristic
146C22×C4×C13C2×D411yescharacteristic
147C22×C4×C13#4112yes—
148C22×C4×C13C2411yescharacteristic
149C22×Dic13—21no—
150C22×Dic13—24no—
151C22×Dic13—21no—
152C22×Dic13—21no—
153C22×Dic13—21no—
154C22×Dic13—42no—
155C22×Dic13—42no—
156C2×Dic26—21no—
157C2×Dic26—21no—
158C2×Dic26—21no—
159C2×Dic26—21no—
160C2×Dic26—21no—
161C2×Dic26—21no—
162C2×Dic26—21no—
163C2×Dic26—28no—
164C2×Dic26—24no—
165C2×Dic26—21no—
166C2×Dic26—44no—
167C2×Dic26—44no—
168C2×Dic26—44no—
169C2×Dic26—42no—
170C2×Dic26—42no—
171C2×Dic26C22×C412yes—
172C2×Dic26C22×C412yes—
173C2×Dic26#4112yes—
174C2×Dic26#4112yes—
175C13×C4⋊C4—21no—
176C13×C4⋊C4—21no—
177C13×C4⋊C4—21no—
178C13×C4⋊C4—21no—
179C13×C4⋊C4—21no—
180C13×C4⋊C4—21no—
181C13×C4⋊C4—81no—
182C13×C4⋊C4—81no—
183C13×C4⋊C4C22×C412yes—
184C13×C4⋊C4C22×C412yes—
185C13×C22⋊C4—24no—
186C13×C22⋊C4—22no—
187C13×C22⋊C4—41no—
188C13×C22⋊C4—81no—
189C42×C13—24no—
190C42×C13—21no—
191C42×C13—21no—
192C42×C13—21no—
193C42×C13—21no—
194C42×C13—42no—
195C42×C13—42no—
196C22⋊Dic13—42no—
197C4⋊Dic13—21no—
198C4⋊Dic13—21no—
199C4⋊Dic13—21no—
200C4⋊Dic13—21no—
201#6101—42no—
202#6101—42no—
203C4×Dic13—42no—
204C4×Dic13—42no—
205#6099—44no—
206C2×#1055—21no—
207C2×#1055—21no—
208C2×#1055—21no—
209C2×#1055—21no—
210C2×#1055—21no—
211C2×#1055—21no—
212C2×#1055—21no—
213C2×#1055—21no—
214C2×#1055—21no—
215C2×#1055—21no—
216C2×#1055C22×C412yes—
217C2×#1055C22×C412yes—
218C2×#419—131no—
219#2346D1311yescharacteristic
220Q8×C22⋊C4—131no—
221#1935—131no—
222#1933—131no—
223#1928—131no—
224#1927—131no—
225#1865—131no—
226#1863—131no—
227#1825—131no—
228#1809—131no—
229#1787—131no—
230#1763—131no—
231C4×#103—131no—
232#1753—131no—
233C23×C13—21no—
234C23×C13—21no—
235C23×C13—21no—
236C23×C13—21no—
237C23×C13—21no—
238C23×C13—21no—
239C23×C13C4×D412yes—
240C23×C13C22×D411yescharacteristic
241C2×C4×C13—21no—
242C2×C4×C13—21no—
243C2×C4×C13—21no—
244C2×C4×C13—21no—
245C2×C4×C13—22no—
246C2×C4×C13—22no—
247C2×C4×C13—22no—
248C2×C4×C13—22no—
249C2×C4×C13—22no—
250C2×C4×C13—22no—
251C2×C4×C13—21no—
252C2×C4×C13—21no—
253C2×C4×C13—21no—
254C2×C4×C13—21no—
255C2×C4×C13—21no—
256C2×C4×C13—21no—
257C2×C4×C13—21no—
258C2×C4×C13—21no—
259C2×C4×C13—21no—
260C2×C4×C13—41no—
261C2×C4×C13—41no—
262C2×C4×C13—41no—
263C2×C4×C13—41no—
264C2×C4×C13—41no—
265C2×C4×C13—41no—
266C2×C4×C13—41no—
267C2×C4×C13—41no—
268C2×C4×C13—41no—
269C2×C4×C13—41no—
270C2×C4×C13C4×D412yes—
271C2×C4×C13#13712yes—
272C2×C4×C13C23×C411yescharacteristic
273C2×C4×C13C2×#4111yescharacteristic
274C2×C4×C13C2×#4111yescharacteristic
275C2×C4×C13C2×#4111yescharacteristic
276C2×C4×C13H(5,𝔽2)11yescharacteristic
277C2×C4×C13H(5,𝔽2)11yescharacteristic
278C2×Dic13—22no—
279C2×Dic13—22no—
280C2×Dic13—22no—
281C2×Dic13—22no—
282C2×Dic13—48no—
283C2×Dic13—41no—
284C2×Dic13—41no—
285C2×Dic13—41no—
286C2×Dic13—41no—
287C2×Dic13—41no—
288C2×Dic13—41no—
289C2×Dic13—41no—
290C2×Dic13—41no—
291Dic26—22no—
292Dic26—22no—
293Dic26—22no—
294Dic26—22no—
295Dic26—22no—
296Dic26—48no—
297Dic26—41no—
298Dic26—41no—
299Dic26#11714yes—
300#1055—22no—
301#1055—22no—
302#1055—41no—
303#1055—41no—
304C23×Q8—131no—
305C22×M16—131no—
306C2×C4×Q8—131no—
307C2×C4×Q8—131no—
308C2×#117C2×D1311yescharacteristic
309C2×#107—131no—
310C2×#106—131no—
311#419—138no—
312C2×#103—131no—
313C2×#103—131no—
314C2×#103—131no—
315C2×#103—131no—
316C2×#103—131no—
317C2×#103—131no—
318C2×#103—131no—
319C2×#103—131no—
320C2×C22⋊C8—131no—
321C2×#97—131no—
322C2×C4×C8—131no—
323#391—131no—
324#391—131no—
325#391—261no—
326#391—261no—
327#389C2×D1311yescharacteristic
328#389C2×D1311yescharacteristic
329#388—21no—
330#388—21no—
331#382—21no—
332#380—131no—
333#380—261no—
334#380C2×D1311yescharacteristic
335C4×C4⋊C4C2×D1311yescharacteristic
336C4×C4⋊C4C2×D1311yescharacteristic
337C4×C22⋊C4—261no—
338C4×C22⋊C4C2×D1311yescharacteristic
339#376—21no—
340#340—131no—
341#340—131no—
342#340—131no—
343#340—131no—
344#340—131no—
345#340—131no—
346#336—131no—
347#336—131no—
348C22×C13—22no—
349C22×C13—22no—
350C22×C13—22no—
351C22×C13—41no—
352C22×C13—41no—
353C22×C13—41no—
354C22×C13—41no—
355C22×C13C2×C4×D411yescharacteristic
356C22×C13#54611yescharacteristic
357C22×C13#54611yescharacteristic
358C22×C13C2×#13711yescharacteristic
359C22×C13#57511yescharacteristic
360C22×C13#57711yescharacteristic
361C22×C13#57811yescharacteristic
362C4×C13—22no—
363C4×C13—22no—
364C4×C13—41no—
365C4×C13—42no—
366C4×C13—42no—
367C4×C13—41no—
368C4×C13—41no—
369C4×C13—81no—
370C4×C13—81no—
371C4×C13C2×#11711yescharacteristic
372C4×C13#51811yescharacteristic
373C4×C13#55111yescharacteristic
374C4×C13#55111yescharacteristic
375Dic13—24no—
376Dic13—42no—
377Dic13—81no—
378Dic13—81no—
379C22×Q8—134no—
380C22×Q8—131no—
381C22×Q8—131no—
382C22×Q8—262no—
383C22×Q8—262no—
384C22×Q8—262no—
385C22×Q8—261no—
386C22×Q8—521no—
387C22×Q8—521no—
388C23×C4—261no—
389C23×C4C22×D1311yescharacteristic
390C2×M16—134no—
391C2×M16—521no—
392C2×M16—521no—
393C22×C8—131no—
394C22×C8—131no—
395C22×C8—131no—
396C22×C8—131no—
397C4×Q8—262no—
398C4×Q8—262no—
399C4×Q8—521no—
400C4×Q8—521no—
401#117—22no—
402#117C4×D1314yes—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—131no—
406C2×C4⋊C4—131no—
407C2×C4⋊C4—261no—
408C2×C4⋊C4—261no—
409C2×C4⋊C4C22×D1311yescharacteristic
410C2×C4⋊C4C22×D1311yescharacteristic
411C2×C4⋊C4C22×D1311yescharacteristic
412C2×C4⋊C4C22×D1311yescharacteristic
413C2×C22⋊C4—21no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—261no—
416C2×C22⋊C4C22⋊D1311yescharacteristic
417C2×C22⋊C4C22⋊D1311yescharacteristic
418C2×C42—21no—
419C2×C42—21no—
420C2×C42—21no—
421C2×C42—261no—
422C2×C42—261no—
423C2×C42C22×D1311yescharacteristic
424C2×C42C22×D1311yescharacteristic
425#107—521no—
426#106—521no—
427#103—134no—
428#103—134no—
429#103—134no—
430#103—134no—
431#103—262no—
432#103—262no—
433#103—521no—
434#103—521no—
435C22⋊C8—262no—
436#97—521no—
437C4×C8—521no—
438#95—21no—
439#95—21no—
440#95—21no—
441#95—21no—
442#95—21no—
443#95—261no—
444#95—261no—
445#95—261no—
446#95—261no—
447#95—261no—
448#95C22⋊D1311yescharacteristic
449#95C22⋊D1311yescharacteristic
450C2×C13—42no—
451C2×C13#234211yescharacteristic
452C2×C13C4×#13711yescharacteristic
453C2×C13#294711yescharacteristic
454C2×C13#331211yescharacteristic
455C2×C13#332111yescharacteristic
456C2×C13#332711yescharacteristic
457C2×C13#332911yescharacteristic
458C24C2×C22⋊D1311yescharacteristic
459C2×Q8—132no—
460C2×Q8—132no—
461C2×Q8—132no—
462C2×Q8—132no—
463C2×Q8—268no—
464C2×Q8—264no—
465C2×Q8—261no—
466C2×Q8—261no—
467C2×Q8—261no—
468C2×Q8—261no—
469C2×Q8—261no—
470C2×Q8—261no—
471C2×Q8—261no—
472C2×Q8—261no—
473C2×Q8—522no—
474C2×Q8—522no—
475C2×Q8—524no—
476C2×Q8—524no—
477C2×Q8—524no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—261no—
487C22×C4—264no—
488C22×C4—261no—
489C22×C4—261no—
490C22×C4—261no—
491C22×C4—522no—
492C22×C4—522no—
493C22×C4C2×C4×D1312yes—
494C22×C4#612712yes—
495C22×C4C2×C22⋊D1311yescharacteristic
496C22×C4C2×C22⋊D1311yescharacteristic
497C22×C4C2×C22⋊D1311yescharacteristic
498C22×C4C2×C22⋊D1311yescharacteristic
499C22×C4C2×C22⋊D1311yescharacteristic
500C22×C4C23×D1311yescharacteristic
501M16—524no—
502C2×C8—132no—
503C2×C8—132no—
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—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—81no—
521C4⋊C4—81no—
522C4⋊C4—261no—
523C4⋊C4—261no—
524C4⋊C4—261no—
525C4⋊C4—261no—
526C4⋊C4—522no—
527C4⋊C4—522no—
528C4⋊C4C2×C4×D1312yes—
529C4⋊C4C2×C4×D1312yes—
530C22⋊C4—24no—
531C22⋊C4—22no—
532C22⋊C4—41no—
533C22⋊C4—81no—
534C22⋊C4—522no—
535C42—24no—
536C42—21no—
537C42—21no—
538C42—21no—
539C42—21no—
540C42—42no—
541C42—42no—
542C42—522no—
543C42—522no—
544C13#2258511yescharacteristic, complemented, Sylow
545C23—21no—
546C23—21no—
547C23—21no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23C4×C22⋊D1312yes—
552C23C22×C22⋊D1311yescharacteristic
553Q8—134no—
554Q8—262no—
555Q8—262no—
556Q8—262no—
557Q8—262no—
558Q8—262no—
559Q8—528no—
560Q8—521no—
561Q8—521no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—262no—
592C2×C4—262no—
593C2×C4—262no—
594C2×C4—262no—
595C2×C4—528no—
596C2×C4—521no—
597C2×C4—521no—
598C2×C4—521no—
599C2×C4—521no—
600C2×C4—521no—
601C2×C4—521no—
602C2×C4—521no—
603C2×C4—521no—
604C2×C4C4×C22⋊D1312yes—
605C2×C4#8820512yes—
606C2×C4C22×C4×D1311yescharacteristic
607C2×C4C2×#612711yescharacteristic
608C2×C4#41×D1311yescharacteristic
609C2×C4#41×D1311yescharacteristic
610C2×C4#8825611yescharacteristic
611C2×C4#8825611yescharacteristic
612C8—262no—
613C8—262no—
614C8—521no—
615C8—521no—
616C22—22no—
617C22—22no—
618C22—22no—
619C22—41no—
620C22—41no—
621C22—41no—
622C22—41no—
623C22C2×C4×C22⋊D1311yescharacteristic
624C22#1171952711yescharacteristic
625C22C2×#8820511yescharacteristic
626C22#1171953411yescharacteristic
627C22#1171953411yescharacteristic
628C22#1171954111yescharacteristic
629C22#1171954311yescharacteristic
630C4—22no—
631C4—22no—
632C4—42no—
633C4—42no—
634C4—41no—
635C4—41no—
636C4—41no—
637C4—81no—
638C4—81no—
639C4—264no—
640C4—522no—
641C4—1041no—
642C4—1041no—
643C4D13×#11711yescharacteristic
644C4#1171922611yescharacteristic
645C4#1171923211yescharacteristic
646C4#1171923211yescharacteristic
647C2—42no—
648C2#1311768611yescharacteristic
649C2C4×#8820511yescharacteristic
650C2#1312367511yescharacteristic
651C2#1312688111yescharacteristic
652C2#1312701611yescharacteristic
653C2#1312709811yescharacteristic
654C2#1312712411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#2346C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
cosocleC22×C4×C13C24
hypercenter#2346D13
hypocenterC13#22585
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2346

Complements

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

NH ≅ G/Ntype
3. #13115525C2semidirect
4. #13115511C2semidirect
5. #13115477C2semidirect
6. #13115470C2semidirect
7. #13115103C2semidirect
8. #13115089C2semidirect
12. #13114669C2semidirect
13. C4×#88050C2semidirect
33. #11718665C4semidirect
544. C13#22585semidirect

Maximal subgroups

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

subgroupindex
C2×#117186652
C22⋊C4×Dic262
#131155252
#131155112
#131154772
#131154702
#131151032
#131150892
#131149312
#131148672
#131147702
#131146692
C4×#880502
#131146202
C13×#23462
#2258513