Finite Group Databasebeta

← #15925701

Subgroups — #15925701

Order 3328.

904 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718748C211yesmaximal, characteristic, complemented
2C2×#11718625C211yesmaximal, characteristic, complemented
3#13117872C211yesmaximal, characteristic
4#13116370C211yesmaximal, characteristic, complemented
5#13116337C211yesmaximal, characteristic, complemented
6#13116207C211yesmaximal, characteristic, complemented
7#13116166C211yesmaximal, characteristic, complemented
8#13115592C211yesmaximal, characteristic, complemented
9#13115425C211yesmaximal, characteristic, complemented
10#13115272C211yesmaximal, characteristic
11#13115153C211yesmaximal, characteristic
12#13115082C211yesmaximal, characteristic, complemented
13#13115033C211yesmaximal, characteristic, complemented
14#13115021C211yesmaximal, characteristic, complemented
15C13×#2440C211yesmaximal, characteristic, complemented
16C2×C13×C4⋊Q8C2211yescharacteristic
17C2×C13×C22⋊Q8—21no—
18C22×C13×C4⋊C4C2211yescharacteristic
19C2×#88184C2211yescharacteristic
20C2×#88180C2211yescharacteristic
21C22×#6099C2211yescharacteristic
22C2×C4×D52C2211yescharacteristic
23C13×#398—21no—
24C13×#395—21no—
25C13×#389C2211yescharacteristic
26C13×#389C2211yescharacteristic
27C13×#385—21no—
28C13×#384C2211yescharacteristic
29C13×#380C2211yescharacteristic
30C4×C13×C22⋊C4C2211yescharacteristic
31C2×C22⋊#1055C2211yescharacteristic
32#11718748—24no—
33C2×#88049C2211yescharacteristic
34C2×#88049C2211yescharacteristic
35C2×#88049C2211yescharacteristic
36C2×#88049C2211yescharacteristic
37#11718625—24no—
38C2×#88048C2211yescharacteristic
39C2×#88048C2211yescharacteristic
40C2×#88048C2211yescharacteristic
41C2×#88047C2211yescharacteristic
42C2×#88047C2211yescharacteristic
43C2×#88047C2211yescharacteristic
44#11718618—21no—
45#11718617—21no—
46#11718600C2211yescharacteristic
47C4×C4⋊Dic13C2211yescharacteristic
48#11718589C2211yescharacteristic
49C2×C4⋊#1055C2211yescharacteristic
50C2×C4⋊#1055C2211yescharacteristic
51#11718330—21no—
52#11718327—21no—
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718116C2211yescharacteristic
60#11718116C2211yescharacteristic
61C22×Q8×C13—21no—
62C23×C4×C13—21no—
63C23×C4×C13C2311yescharacteristic
64C22×C22⋊D13—21no—
65C22×D52C2311yescharacteristic
66C22×C4×D13—21no—
67C13×C4⋊Q8—22no—
68C13×C4⋊Q8—41no—
69C13×C22⋊Q8—44no—
70C2×C13×C4⋊C4—22no—
71C2×C13×C4⋊C4—21no—
72C2×C13×C4⋊C4—21no—
73C2×C13×C4⋊C4—21no—
74C2×C13×C4⋊C4—21no—
75C2×C13×C4⋊C4—21no—
76C2×C13×C4⋊C4—21no—
77C2×C13×C4⋊C4—41no—
78C2×C13×C4⋊C4C2311yescharacteristic
79C2×C13×C4⋊C4C2311yescharacteristic
80C2×C13×C4⋊C4C2311yescharacteristic
81C2×C13×C4⋊C4C2311yescharacteristic
82C2×C13×C22⋊C4—21no—
83C2×C13×C22⋊C4D411yescharacteristic
84C2×C13×C22⋊C4D411yescharacteristic
85C2×C42×C13C2311yescharacteristic
86C2×C42×C13C2311yescharacteristic
87C2×C22⋊Dic13—21no—
88#88184—22no—
89#88184Q814yescomplemented
90C2×#6103—21no—
91C2×#6103—21no—
92C2×#6103—21no—
93C2×#6103—21no—
94#88180—22no—
95#88180—41no—
96C2×C4⋊Dic13C2311yescharacteristic
97C2×C4⋊Dic13C2311yescharacteristic
98C2×C4⋊Dic13C2311yescharacteristic
99C2×#6101—21no—
100C2×C4×Dic13—21no—
101C2×C4×Dic13—21no—
102C2×#6099—22no—
103C2×#6099—22no—
104C2×#6099—22no—
105C22×#1055C2311yescharacteristic
106C22×#1055C2311yescharacteristic
107C22×#1055C2311yescharacteristic
108C22×#1055C2311yescharacteristic
109C4×D52—22no—
110C4×D52—41no—
111C13×#95—21no—
112C13×#95—21no—
113C13×#95—21no—
114C13×#95D411yescharacteristic
115C13×#95D411yescharacteristic
116#88071—21no—
117#88071—21no—
118C22⋊#1055—22no—
119#88049—22no—
120#88049—22no—
121#88049—22no—
122#88049—41no—
123#88048—22no—
124#88048—22no—
125#88048—41no—
126#88047—22no—
127#88047—22no—
128#88047D414yescomplemented
129C4⋊#1055—22no—
130C4⋊#1055—22no—
131#26357—131nomaximal, Sylow
132C24×C13C2×D411yescharacteristic
133C23×D13—21no—
134C2×Q8×C13—42no—
135C2×Q8×C13—42no—
136C2×Q8×C13—81no—
137C22×C4×C13—21no—
138C22×C4×C13—21no—
139C22×C4×C13—21no—
140C22×C4×C13—21no—
141C22×C4×C13—21no—
142C22×C4×C13—21no—
143C22×C4×C13—21no—
144C22×C4×C13—21no—
145C22×C4×C13—42no—
146C22×C4×C13—42no—
147C22×C4×C13—81no—
148C22×C4×C13C2×D411yescharacteristic
149C22×C4×C13C2×D411yescharacteristic
150C22×C4×C13C2×D411yescharacteristic
151C22×C4×C13C2×D411yescharacteristic
152C22×C4×C13C2×D411yescharacteristic
153C22×C4×C13C2×Q812yes—
154C22×C4×C13#4112yes—
155C22×C4×C13C2411yescharacteristic
156C2×C22⋊D13—24no—
157C2×C22⋊D13—81no—
158C2×C22⋊D13—81no—
159C22×Dic13—21no—
160C22×Dic13—21no—
161C22×Dic13—21no—
162C2×D52—21no—
163C2×D52—21no—
164C2×D52—21no—
165C2×D52—21no—
166C2×D52—21no—
167C2×D52C2×Q812yes—
168C2×C4×D13—42no—
169C2×C4×D13—42no—
170C2×C4×D13—81no—
171C13×C4⋊C4—21no—
172C13×C4⋊C4—21no—
173C13×C4⋊C4—21no—
174C13×C4⋊C4—21no—
175C13×C4⋊C4—21no—
176C13×C4⋊C4—21no—
177C13×C4⋊C4—21no—
178C13×C4⋊C4—42no—
179C13×C4⋊C4—42no—
180C13×C4⋊C4—42no—
181C13×C4⋊C4—42no—
182C13×C4⋊C4—42no—
183C13×C4⋊C4—81no—
184C13×C4⋊C4C2×D412yes—
185C13×C22⋊C4—22no—
186C13×C22⋊C4—22no—
187C13×C22⋊C4—42no—
188C42×C13—21no—
189C42×C13—21no—
190C42×C13—21no—
191C42×C13—21no—
192C22⋊Dic13—42no—
193#6103—24no—
194#6103—42no—
195#6103—42no—
196#6103—81no—
197C4⋊Dic13—21no—
198C4⋊Dic13—21no—
199C4⋊Dic13—21no—
200C4⋊Dic13—21no—
201C4⋊Dic13C2×D412yes—
202C4⋊Dic13C2×Q812yes—
203#6101—81no—
204C4×Dic13—42no—
205C4×Dic13—81no—
206#6099—28no—
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×#1055—21no—
217C2×#1055C2×D412yes—
218C2×#1055#4112yes—
219C2×#474—131no—
220C2×#428—131no—
221#2440D1311yescharacteristic, complemented
222#2363—131no—
223#2094—131no—
224#2088—131no—
225#2065—131no—
226#2058—131no—
227#1947—131no—
228#1921—131no—
229#1895—131no—
230#1874—131no—
231#1862—131no—
232#1854—131no—
233#1851—131no—
234C23×C13—21no—
235C23×C13—21no—
236C23×C13—21no—
237C23×C13—21no—
238C23×C13—21no—
239C23×C13—21no—
240C23×C13C22⋊Q812yes—
241C23×C13C22×D411yescharacteristic
242C22×D13—22no—
243C22×D13—41no—
244C22×D13—41no—
245C22×D13—41no—
246C22×D13—41no—
247C22×D13—41no—
248C22×D13—41no—
249Q8×C13—84no—
250C2×C4×C13—21no—
251C2×C4×C13—21no—
252C2×C4×C13—21no—
253C2×C4×C13—21no—
254C2×C4×C13—21no—
255C2×C4×C13—21no—
256C2×C4×C13—22no—
257C2×C4×C13—22no—
258C2×C4×C13—22no—
259C2×C4×C13—22no—
260C2×C4×C13—21no—
261C2×C4×C13—22no—
262C2×C4×C13—21no—
263C2×C4×C13—21no—
264C2×C4×C13—21no—
265C2×C4×C13—21no—
266C2×C4×C13—21no—
267C2×C4×C13—41no—
268C2×C4×C13—41no—
269C2×C4×C13—41no—
270C2×C4×C13—41no—
271C2×C4×C13—41no—
272C2×C4×C13—41no—
273C2×C4×C13—41no—
274C2×C4×C13—41no—
275C2×C4×C13—41no—
276C2×C4×C13—41no—
277C2×C4×C13—41no—
278C2×C4×C13—84no—
279C2×C4×C13C22⋊Q812yes—
280C2×C4×C13AGL(1,ℤ/8)12yes—
281C2×C4×C13#13712yes—
282C2×C4×C13C22×D411yescharacteristic
283C2×C4×C13C22×Q811yescharacteristic
284C2×C4×C13C2×#4111yescharacteristic
285C2×C4×C13C2×#4111yescharacteristic
286C2×C4×C13H(5,𝔽2)11yescharacteristic
287C2×C4×C132−1+411yescharacteristic
288C22⋊D13—84no—
289C2×Dic13—22no—
290C2×Dic13—22no—
291C2×Dic13—41no—
292C2×Dic13—41no—
293C2×Dic13—41no—
294C2×Dic13—41no—
295C2×Dic13—41no—
296C2×Dic13—41no—
297C2×Dic13—41no—
298D52—22no—
299D52—22no—
300D52—41no—
301D52—41no—
302C4×D13—84no—
303#1055—22no—
304#1055—22no—
305#1055—41no—
306#1055—41no—
307C22×M16—131no—
308C2×C4⋊Q8C2×D1311yescharacteristic
309C2×C22⋊Q8—21no—
310C2×#121—131no—
311C2×C4×D4—131no—
312C2×#117—131no—
313C22×C4⋊C4C2×D1311yescharacteristic
314#474—264no—
315#428—264no—
316C2×#107—131no—
317C2×#107—131no—
318C2×#107—131no—
319C2×#106—131no—
320C2×#106—131no—
321C2×#106—131no—
322C2×C4⋊C8—131no—
323C2×C4⋊C8—131no—
324C2×#102—131no—
325C2×#102—131no—
326C2×#102—131no—
327C2×#102—131no—
328C2×C22⋊C8—131no—
329#398—21no—
330#395—21no—
331#390—131no—
332#390—261no—
333#389—131no—
334#389C2×D1311yescharacteristic
335#389C2×D1311yescharacteristic
336#388—261no—
337#386—261no—
338#385—21no—
339#384C2×D1311yescharacteristic
340#380C2×D1311yescharacteristic
341C4×C4⋊C4—131no—
342C4×C22⋊C4—261no—
343C4×C22⋊C4C2×D1311yescharacteristic
344#340—131no—
345#340—131no—
346#340—131no—
347#340—131no—
348#340—131no—
349#340—131no—
350#336—131no—
351#336—131no—
352C22×C13—22no—
353C22×C13—22no—
354C22×C13—22no—
355C22×C13—41no—
356C22×C13—41no—
357C22×C13—41no—
358C22×C13—41no—
359C22×C13C2×C22⋊Q811yescharacteristic
360C22×C13D4211yescharacteristic
361C22×C13#54711yescharacteristic
362C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
363C22×C13C2×#13711yescharacteristic
364C22×C13#57611yescharacteristic
365C22×C13#57711yescharacteristic
366C2×D13—42no—
367C2×D13—42no—
368C2×D13—42no—
369C2×D13—81no—
370C2×D13—81no—
371C2×D13—81no—
372C2×D13—81no—
373C4×C13—22no—
374C4×C13—22no—
375C4×C13—22no—
376C4×C13—41no—
377C4×C13—42no—
378C4×C13—41no—
379C4×C13—81no—
380C4×C13—81no—
381C4×C13—81no—
382C4×C13#52511yescharacteristic
383C4×C13#53911yescharacteristic
384C4×C13D4×Q811yescharacteristic
385C4×C13#55411yescharacteristic
386Dic13—42no—
387Dic13—42no—
388Dic13—81no—
389C22×Q8—21no—
390C22×D4—131no—
391C22×D4—261no—
392C23×C4—21no—
393C23×C4—261no—
394C23×C4C22×D1311yescharacteristic
395C2×M16—262no—
396C2×M16—262no—
397C2×M16—262no—
398C22×C8—131no—
399C22×C8—131no—
400C22×C8—131no—
401C22×C8—131no—
402C4⋊Q8—22no—
403C4⋊Q8—41no—
404C22⋊Q8—44no—
405#121—134no—
406#121—262no—
407C4×D4—262no—
408C4×D4—521no—
409#117—262no—
410#117—521no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—41no—
419C2×C4⋊C4—131no—
420C2×C4⋊C4—131no—
421C2×C4⋊C4—131no—
422C2×C4⋊C4—261no—
423C2×C4⋊C4C22×D1311yescharacteristic
424C2×C4⋊C4C22×D1311yescharacteristic
425C2×C4⋊C4C22×D1311yescharacteristic
426C2×C4⋊C4C22×D1311yescharacteristic
427C2×C22⋊C4—21no—
428C2×C22⋊C4—261no—
429C2×C22⋊C4—261no—
430C2×C22⋊C4—261no—
431C2×C22⋊C4—261no—
432C2×C22⋊C4—261no—
433C2×C22⋊C4C22⋊D1311yescharacteristic
434C2×C22⋊C4C22⋊D1311yescharacteristic
435C2×C42—261no—
436C2×C42—261no—
437C2×C42C22×D1311yescharacteristic
438C2×C42C22×D1311yescharacteristic
439#107—134no—
440#107—262no—
441#107—262no—
442#106—262no—
443#106—262no—
444#106—521no—
445C4⋊C8—262no—
446C4⋊C8—262no—
447#102—262no—
448#102—262no—
449#102—262no—
450#102—521no—
451C22⋊C8—262no—
452#95—21no—
453#95—21no—
454#95—21no—
455#95—261no—
456#95—261no—
457#95C22⋊D1311yescharacteristic
458#95C22⋊D1311yescharacteristic
459C2×C13—42no—
460C2×C13#244911yescharacteristic
461C2×C13#307911yescharacteristic
462C2×C13#308111yescharacteristic
463C2×C13#326411yescharacteristic
464C2×C13#327811yescharacteristic
465C2×C13#334611yescharacteristic
466C2×C13#335411yescharacteristic
467D13—82no—
468C24—261no—
469C24C2×C22⋊D1311yescharacteristic
470C2×Q8—42no—
471C2×Q8—42no—
472C2×Q8—81no—
473C2×D4—132no—
474C2×D4—264no—
475C2×D4—261no—
476C2×D4—261no—
477C2×D4—261no—
478C2×D4—261no—
479C2×D4—261no—
480C2×D4—1041no—
481C2×D4—1041no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—42no—
491C22×C4—42no—
492C22×C4—81no—
493C22×C4—261no—
494C22×C4—261no—
495C22×C4—261no—
496C22×C4—522no—
497C22×C4—522no—
498C22×C4—1041no—
499C22×C4Q8×D1312yes—
500C22×C4#613112yes—
501C22×C4C2×C22⋊D1311yescharacteristic
502C22×C4C2×C22⋊D1311yescharacteristic
503C22×C4C2×C22⋊D1311yescharacteristic
504C22×C4C2×C22⋊D1311yescharacteristic
505C22×C4C2×C22⋊D1311yescharacteristic
506C22×C4C23×D1311yescharacteristic
507M16—268no—
508C2×C8—132no—
509C2×C8—132no—
510C2×C8—261no—
511C2×C8—261no—
512C2×C8—261no—
513C2×C8—261no—
514C2×C8—261no—
515C2×C8—261no—
516C2×C8—261no—
517C2×C8—261no—
518C2×C8—261no—
519C2×C8—261no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—42no—
528C4⋊C4—42no—
529C4⋊C4—42no—
530C4⋊C4—42no—
531C4⋊C4—42no—
532C4⋊C4—81no—
533C4⋊C4—132no—
534C4⋊C4—132no—
535C4⋊C4—261no—
536C4⋊C4—261no—
537C4⋊C4—261no—
538C4⋊C4—261no—
539C4⋊C4—1041no—
540C4⋊C4D4×D1312yes—
541C22⋊C4—22no—
542C22⋊C4—22no—
543C22⋊C4—42no—
544C22⋊C4—264no—
545C22⋊C4—522no—
546C22⋊C4—522no—
547C22⋊C4—522no—
548C22⋊C4—1041no—
549C42—21no—
550C42—21no—
551C42—21no—
552C42—21no—
553C42—522no—
554C42—1041no—
555C13#2635711yescharacteristic, complemented, Sylow
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—262no—
563C23—521no—
564C23—521no—
565C23—521no—
566C23—521no—
567C23—521no—
568C23—521no—
569C23#8820012yes—
570C23C22×C22⋊D1311yescharacteristic
571Q8—84no—
572D4—262no—
573D4—262no—
574D4—521no—
575D4—521no—
576D4—1044no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—22no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—84no—
606C2×C4—262no—
607C2×C4—262no—
608C2×C4—521no—
609C2×C4—521no—
610C2×C4—521no—
611C2×C4—521no—
612C2×C4—521no—
613C2×C4—521no—
614C2×C4—521no—
615C2×C4—1044no—
616C2×C4#8818612yes—
617C2×C4#8819612yes—
618C2×C4#8820012yes—
619C2×C4C2×D4×D1311yescharacteristic
620C2×C4#8825111yescharacteristic
621C2×C4C2×Q8×D1311yescharacteristic
622C2×C4C2×#613111yescharacteristic
623C2×C4#41×D1311yescharacteristic
624C2×C4#8825711yescharacteristic
625C8—262no—
626C8—262no—
627C8—521no—
628C8—521no—
629C22—22no—
630C22—22no—
631C22—22no—
632C22—41no—
633C22—41no—
634C22—41no—
635C22—41no—
636C22—522no—
637C22—522no—
638C22—522no—
639C22—1041no—
640C22—1041no—
641C22—1041no—
642C22—1041no—
643C22C2×#8818611yescharacteristic
644C22D4×C22⋊D1311yescharacteristic
645C22C2×#8819611yescharacteristic
646C22C2×#8820011yescharacteristic
647C22#1171952911yescharacteristic
648C22#1171954011yescharacteristic
649C22#1171954211yescharacteristic
650C4—22no—
651C4—22no—
652C4—22no—
653C4—41no—
654C4—41no—
655C4—42no—
656C4—81no—
657C4—81no—
658C4—81no—
659C4—522no—
660C4—522no—
661C4—1041no—
662C4#1171933211yescharacteristic
663C4#1171933711yescharacteristic
664C4#1171934111yescharacteristic
665C4#1171935011yescharacteristic
666C2—42no—
667C2—1042no—
668C2#1311864111yescharacteristic
669C2#1312464511yescharacteristic
670C2#1312466111yescharacteristic
671C2#1312631211yescharacteristic
672C2#1312649811yescharacteristic
673C2#1312731511yescharacteristic
674C2#1312743111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2440C2
socleC23×C13C22×D4
prime radicalC2×#88184C22
hypercenter#2440D13
hypocenterC13#26357
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2440

Complements

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

NH ≅ G/Ntype
1. C2×#11718748C2semidirect
2. C2×#11718625C2semidirect
4. #13116370C2semidirect
5. #13116337C2semidirect
6. #13116207C2semidirect
7. #13116166C2semidirect
8. #13115592C2semidirect
9. #13115425C2semidirect
12. #13115082C2semidirect
13. #13115033C2semidirect
14. #13115021C2semidirect
15. C13×#2440C2semidirect
89. #88184Q8semidirect
128. #88047D4semidirect
221. #2440D13semidirect
555. C13#26357semidirect

Maximal subgroups

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

subgroupindex
C2×#117187482
C2×#117186252
#131178722
#131163702
#131163372
#131162072
#131161662
#131155922
#131154252
#131152722
#131151532
#131150822
#131150332
#131150212
C13×#24402
#2635713