Finite Group Databasebeta

← #15881060

Subgroups — #15881060

Order 3328.

982 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718386C211yesmaximal, characteristic
2C2×#11718659C211yesmaximal, characteristic, complemented
3C2×#11718521C211yesmaximal, characteristic, complemented
4#13117786C211yesmaximal, characteristic
5#13117780C211yesmaximal, characteristic
6#13115598C211yesmaximal, characteristic, complemented
7#13115596C211yesmaximal, characteristic, complemented
8#13115038C211yesmaximal, characteristic, complemented
9#13115037C211yesmaximal, characteristic, complemented
10#13115032C211yesmaximal, characteristic, complemented
11#13114994C211yesmaximal, characteristic, complemented
12#13114864C211yesmaximal, characteristic, complemented
13#13114863C211yesmaximal, characteristic, complemented
14#13114728C211yesmaximal, characteristic, complemented
15C13×#1854C211yesmaximal, characteristic, complemented
16C2×C13×#117C2211yescharacteristic
17C2×C4×C22⋊D13C2211yescharacteristic
18C2×#88180C2211yescharacteristic
19C23×#1055C2211yescharacteristic
20C22×C8×D13C2211yescharacteristic
21C2×#88146C2211yescharacteristic
22C2×#88146C2211yescharacteristic
23C2×C13×#107C2211yescharacteristic
24C2×C13×#106C2211yescharacteristic
25C2×C13×C22⋊C8C2211yescharacteristic
26C13×#380C2211yescharacteristic
27#11718873C2211yescharacteristic
28C2×#88060C2211yescharacteristic
29C2×#88058C2211yescharacteristic
30C2×#88057C2211yescharacteristic
31C2×#88054C2211yescharacteristic
32C2×C8×Dic13C2211yescharacteristic
33#11718659—24no—
34#11718648C2211yescharacteristic
35#11718648C2211yescharacteristic
36#11718637C2211yescharacteristic
37#11718637C2211yescharacteristic
38C4⋊C4×Dic13C2211yescharacteristic
39C4⋊C4×Dic13C2211yescharacteristic
40C2×#88048C2211yescharacteristic
41C2×#88048C2211yescharacteristic
42C2×#88047C2211yescharacteristic
43C2×#88047C2211yescharacteristic
44C2×#88047C2211yescharacteristic
45C2×#88047C2211yescharacteristic
46#11718618—21no—
47#11718618—21no—
48#11718606—21no—
49#11718605—21no—
50#11718601—21no—
51C4×#6101—21no—
52#11718521—24no—
53#11718386C418yescomplemented
54#11718330—21no—
55#11718310—21no—
56C13×#340C2211yescharacteristic
57C13×#340C2211yescharacteristic
58#11718143C2211yescharacteristic
59#11718143C2211yescharacteristic
60#11718121C2211yescharacteristic
61#11718121C2211yescharacteristic
62C23×C4×C13C2311yescharacteristic
63C22×C22⋊D13D411yescharacteristic
64C22×C4×D13C2311yescharacteristic
65C22×C8×C13C2311yescharacteristic
66C22×C8×C13C2311yescharacteristic
67C13×#117—22no—
68C13×#117—41no—
69C2×C13×C4⋊C4C2311yescharacteristic
70C2×C13×C4⋊C4C2311yescharacteristic
71C2×C13×C4⋊C4C2311yescharacteristic
72C2×C13×C4⋊C4C2311yescharacteristic
73C2×C13×C22⋊C4—21no—
74C2×C13×C22⋊C4—21no—
75C2×C42×C13—21no—
76C2×C22⋊Dic13—21no—
77C2×C22⋊Dic13—21no—
78C2×C22⋊Dic13D411yescharacteristic
79C4×C22⋊D13C2×C414yes—
80C4×C22⋊D13Q814yes—
81C2×#6103—21no—
82C2×#6103—21no—
83C2×#6103—21no—
84C2×#6103—21no—
85C2×#6103D411yescharacteristic
86#88180—22no—
87#88180—41no—
88C2×C4⋊Dic13C2311yescharacteristic
89C2×C4⋊Dic13C2311yescharacteristic
90C2×C4⋊Dic13C2311yescharacteristic
91C2×C4⋊Dic13C2311yescharacteristic
92C2×#6101—21no—
93C2×#6101—21no—
94C2×#6101—21no—
95C2×#6101—21no—
96C2×#6101D411yescharacteristic
97C2×C4×Dic13—21no—
98C2×C4×Dic13—21no—
99C2×C4×Dic13—21no—
100C2×C4×Dic13—21no—
101C2×C4×Dic13—21no—
102C2×C4×Dic13C2311yescharacteristic
103C22×#1055—22no—
104C22×#1055—22no—
105C22×#1055C2×C414yes—
106C22×#1055C2311yescharacteristic
107C22×#1055C2311yescharacteristic
108C2×C8×D13—22no—
109C2×C8×D13—22no—
110C2×C8×D13C2×C414yes—
111#88146—22no—
112#88146—22no—
113#88146—41no—
114#88146—41no—
115C13×#107—41no—
116C13×#106—22no—
117C13×C22⋊C8C2×C414yes—
118C13×#95—21no—
119#88071—21no—
120#88071—21no—
121#88071—21no—
122#88071—21no—
123#88071—21no—
124#88060C2×C414yes—
125#88058—41no—
126#88057—22no—
127#88054C2×C414yes—
128C8×Dic13C2×C414yes—
129#88048—22no—
130#88048—22no—
131#88047—22no—
132#88047—22no—
133#88047—22no—
134#88047D414yescomplemented
135#22658—131nomaximal, Sylow
136C24×C13C2×D411yescharacteristic
137C23×D13C2×D411yescharacteristic
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—21no—
146C22×C4×C13C22×C412yes—
147C22×C4×C13C2×D411yescharacteristic
148C22×C4×C13C2×Q812yes—
149C22×C4×C13C2411yescharacteristic
150C2×C22⋊D13—22no—
151C2×C22⋊D13—22no—
152C2×C22⋊D13C4⋊C414yes—
153C22×Dic13—21no—
154C22×Dic13—21no—
155C22×Dic13—21no—
156C22×Dic13—21no—
157C22×Dic13C2×D411yescharacteristic
158C22×Dic13C2×D411yescharacteristic
159C22×Dic13C2×D411yescharacteristic
160C2×C4×D13—21no—
161C2×C4×D13—21no—
162C2×C4×D13—21no—
163C2×C4×D13—21no—
164C2×C4×D13C22×C412yes—
165C2×C4×D13C2×Q812yes—
166C2×C8×C13—21no—
167C2×C8×C13—21no—
168C2×C8×C13—21no—
169C2×C8×C13—21no—
170C2×C8×C13C22×C412yes—
171C2×C8×C13C22×C412yes—
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—21no—
179C13×C4⋊C4C2×D412yes—
180C13×C22⋊C4—42no—
181C13×C22⋊C4—81no—
182C42×C13—42no—
183C22⋊Dic13—42no—
184C22⋊Dic13—81no—
185C22⋊Dic13C4⋊C414yes—
186#6103—42no—
187#6103—42no—
188#6103—81no—
189#6103—81no—
190#6103C4⋊C414yes—
191C4⋊Dic13—21no—
192C4⋊Dic13—21no—
193C4⋊Dic13—21no—
194C4⋊Dic13—21no—
195C4⋊Dic13—21no—
196C4⋊Dic13—21no—
197C4⋊Dic13—21no—
198C4⋊Dic13C2×D412yes—
199#6101—42no—
200#6101—42no—
201#6101—81no—
202#6101—81no—
203#6101C4⋊C414yes—
204C4×Dic13—42no—
205C4×Dic13—42no—
206C4×Dic13—42no—
207C4×Dic13—42no—
208C4×Dic13—42no—
209C4×Dic13C22×C412yes—
210C4×Dic13C2×Q812yes—
211C2×#1055—21no—
212C2×#1055—21no—
213C2×#1055—28no—
214C2×#1055C22×C412yes—
215C2×#1055C22×C412yes—
216C2×#1055C2×D412yes—
217C2×#1055#4112yes—
218C8×D13—28no—
219C2×C8×D4—131no—
220C2×#427—131no—
221C2×#427—131no—
222#2354—131no—
223#2354—131no—
224#1948—131no—
225#1948—131no—
226#1854—131no—
227#1854—131no—
228#1854—131no—
229#1854D1311yescharacteristic, complemented
230#1845—131no—
231#1808—131no—
232#1808—131no—
233C4×#107—131no—
234C23×C13—21no—
235C23×C13—21no—
236C23×C13—21no—
237C23×C13—21no—
238C23×C13—21no—
239C23×C13—21no—
240C23×C13C2×C4⋊C412yes—
241C23×C13C22×D411yescharacteristic
242C22×D13—21no—
243C22×D13—21no—
244C22×D13—21no—
245C22×D13—21no—
246C22×D13—21no—
247C22×D13—21no—
248C22×D13C2×C4⋊C412yes—
249C2×C4×C13—21no—
250C2×C4×C13—21no—
251C2×C4×C13—22no—
252C2×C4×C13—22no—
253C2×C4×C13—22no—
254C2×C4×C13—22no—
255C2×C4×C13—22no—
256C2×C4×C13—41no—
257C2×C4×C13—41no—
258C2×C4×C13—41no—
259C2×C4×C13—41no—
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×C13C2×C4⋊C412yes—
268C2×C4×C13C23×C411yescharacteristic
269C2×C4×C13C22×D411yescharacteristic
270C2×C4×C13C22×Q811yescharacteristic
271C2×C4×C13C2×#4111yescharacteristic
272C2×C4×C13H(5,𝔽2)11yescharacteristic
273C2×C4×C132−1+411yescharacteristic
274C22⋊D13—28no—
275C2×Dic13—21no—
276C2×Dic13—21no—
277C2×Dic13—21no—
278C2×Dic13—21no—
279C2×Dic13—22no—
280C2×Dic13—41no—
281C2×Dic13—41no—
282C2×Dic13—41no—
283C2×Dic13—41no—
284C2×Dic13—41no—
285C2×Dic13—41no—
286C2×Dic13—41no—
287C2×Dic13—41no—
288C2×Dic13—41no—
289C2×Dic13—41no—
290C2×Dic13—41no—
291C2×Dic13C2×C4⋊C412yes—
292C2×Dic13C2×C4⋊C412yes—
293C2×Dic13C2×C4⋊C412yes—
294C2×Dic13#13512yes—
295C2×Dic13#13512yes—
296C4×D13—22no—
297C4×D13—22no—
298C4×D13—22no—
299C4×D13—22no—
300C8×C13—22no—
301C8×C13—22no—
302#1055—22no—
303#1055C4×D414yes—
304C23×C8—131no—
305C23×C8—131no—
306C2×C4×D4—131no—
307C2×#117—131no—
308C2×#117—131no—
309C2×#117—131no—
310C2×#117C2×D1311yescharacteristic
311C8×D4—138no—
312#427—264no—
313#427—264no—
314C2×#107—131no—
315C2×#107—131no—
316C2×#107—131no—
317C2×#107—131no—
318C2×#107—131no—
319C2×#107C2×D1311yescharacteristic
320C2×#106—131no—
321C2×#106—131no—
322C2×#106—131no—
323C2×#106C2×D1311yescharacteristic
324C2×C4⋊C8—131no—
325C2×C22⋊C8—131no—
326C2×C22⋊C8C2×D1311yescharacteristic
327C2×C4×C8—131no—
328#390—261no—
329#390—261no—
330#388—261no—
331#388—261no—
332#388—261no—
333#388—261no—
334#384—131no—
335#384—131no—
336#380—131no—
337#380—131no—
338#380—131no—
339#380C2×D1311yescharacteristic
340C4×C4⋊C4—131no—
341C4×C4⋊C4—131no—
342C4×C4⋊C4—261no—
343C4×C4⋊C4—261no—
344#340—131no—
345#340—131no—
346#340—131no—
347#340—131no—
348#340C2×D1311yescharacteristic
349#340C2×D1311yescharacteristic
350C22×C13—22no—
351C22×C13—22no—
352C22×C13—22no—
353C22×C13—41no—
354C22×C13—41no—
355C22×C13—41no—
356C22×C13—41no—
357C22×C13C22×C4⋊C411yescharacteristic
358C22×C13D4211yescharacteristic
359C22×C13#54711yescharacteristic
360C22×C13C2×#13511yescharacteristic
361C22×C13C2×#13511yescharacteristic
362C22×C13#57611yescharacteristic
363C22×C13#57811yescharacteristic
364C2×D13—22no—
365C2×D13—22no—
366C2×D13—22no—
367C2×D13—41no—
368C2×D13—41no—
369C2×D13—41no—
370C2×D13—41no—
371C4×C13—22no—
372C4×C13—42no—
373C4×C13—81no—
374C4×C13—81no—
375C4×C13—81no—
376C4×C13C2×C4×D411yescharacteristic
377C4×C13#52011yescharacteristic
378C4×C13D4×Q811yescharacteristic
379C4×C13#55411yescharacteristic
380Dic13—22no—
381Dic13—22no—
382Dic13—42no—
383Dic13—81no—
384Dic13—81no—
385Dic13—81no—
386Dic13#42714yescomplemented
387C22×D4—131no—
388C23×C4—131no—
389C23×C4C22×D1311yescharacteristic
390C22×C8—131no—
391C22×C8—134no—
392C22×C8—131no—
393C22×C8—134no—
394C22×C8—262no—
395C22×C8—262no—
396C22×C8—262no—
397C22×C8—262no—
398C22×C8C22×D1311yescharacteristic
399C22×C8C22×D1311yescharacteristic
400C4×D4—134no—
401C4×D4—134no—
402#117—22no—
403#117—41no—
404#117—262no—
405#117—262no—
406#117—262no—
407#117—521no—
408#117—521no—
409#117—521no—
410C2×C4⋊C4—131no—
411C2×C4⋊C4—131no—
412C2×C4⋊C4—131no—
413C2×C4⋊C4—131no—
414C2×C4⋊C4—131no—
415C2×C4⋊C4—261no—
416C2×C4⋊C4—261no—
417C2×C4⋊C4—261no—
418C2×C4⋊C4—261no—
419C2×C4⋊C4C22×D1311yescharacteristic
420C2×C4⋊C4C22×D1311yescharacteristic
421C2×C4⋊C4C22×D1311yescharacteristic
422C2×C4⋊C4C22×D1311yescharacteristic
423C2×C22⋊C4—21no—
424C2×C22⋊C4—21no—
425C2×C22⋊C4—131no—
426C2×C22⋊C4—131no—
427C2×C22⋊C4—261no—
428C2×C22⋊C4—261no—
429C2×C22⋊C4—261no—
430C2×C22⋊C4—261no—
431C2×C22⋊C4—261no—
432C2×C22⋊C4—261no—
433C2×C42—21no—
434C2×C42—131no—
435C2×C42—261no—
436C2×C42—261no—
437C2×C42—261no—
438C2×C42—261no—
439C2×C42—261no—
440#107—41no—
441#107—134no—
442#107—262no—
443#107—262no—
444#107—262no—
445#107—521no—
446#106—22no—
447#106—262no—
448#106—262no—
449#106—262no—
450C4⋊C8—134no—
451C22⋊C8—134no—
452C22⋊C8C4×D1314yes—
453C4×C8—134no—
454#95—21no—
455#95—261no—
456#95—261no—
457#95—261no—
458#95—261no—
459#95—261no—
460C2×C13—42no—
461C2×C13D4×C4⋊C411yescharacteristic
462C2×C13C2×#42711yescharacteristic
463C2×C13#291311yescharacteristic
464C2×C13#328311yescharacteristic
465C2×C13#328711yescharacteristic
466C2×C13#334111yescharacteristic
467C2×C13#334211yescharacteristic
468D13—42no—
469C24—131no—
470C24D4×D1311yescharacteristic
471C2×D4—134no—
472C2×D4—262no—
473C2×D4—262no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—131no—
483C22×C4—131no—
484C22×C4—131no—
485C22×C4—132no—
486C22×C4—132no—
487C22×C4—261no—
488C22×C4—261no—
489C22×C4—261no—
490C22×C4—261no—
491C22×C4—261no—
492C22×C4—261no—
493C22×C4—261no—
494C22×C4—261no—
495C22×C4C2×C4×D1312yes—
496C22×C4D4×D1311yescharacteristic
497C22×C4Q8×D1312yes—
498C22×C4C23×D1311yescharacteristic
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—132no—
504C2×C8—132no—
505C2×C8—132no—
506C2×C8—132no—
507C2×C8—268no—
508C2×C8—268no—
509C2×C8—261no—
510C2×C8—261no—
511C2×C8C2×C4×D1312yes—
512C2×C8C2×C4×D1312yes—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—134no—
521C4⋊C4—132no—
522C4⋊C4—261no—
523C4⋊C4—261no—
524C4⋊C4—261no—
525C4⋊C4—261no—
526C4⋊C4—261no—
527C4⋊C4—261no—
528C4⋊C4—261no—
529C4⋊C4—522no—
530C4⋊C4—522no—
531C4⋊C4—1041no—
532C4⋊C4—1041no—
533C4⋊C4D4×D1312yes—
534C22⋊C4—42no—
535C22⋊C4—81no—
536C22⋊C4—134no—
537C22⋊C4—134no—
538C22⋊C4—522no—
539C22⋊C4—522no—
540C22⋊C4—522no—
541C22⋊C4—1041no—
542C22⋊C4—1041no—
543C22⋊C4—1041no—
544C42—42no—
545C42—132no—
546C42—132no—
547C42—522no—
548C42—522no—
549C42—522no—
550C42—522no—
551C42—522no—
552C13#2265811yescharacteristic, complemented, Sylow
553C23—21no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—132no—
560C23—261no—
561C23—261no—
562C23—261no—
563C23—261no—
564C23—261no—
565C23—261no—
566C23C4⋊C4×D1312yes—
567C23C2×D4×D1311yescharacteristic
568D4—268no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—132no—
588C2×C4—132no—
589C2×C4—132no—
590C2×C4—132no—
591C2×C4—132no—
592C2×C4—261no—
593C2×C4—261no—
594C2×C4—261no—
595C2×C4—261no—
596C2×C4—262no—
597C2×C4—262no—
598C2×C4—262no—
599C2×C4—262no—
600C2×C4—262no—
601C2×C4—521no—
602C2×C4—521no—
603C2×C4—521no—
604C2×C4—521no—
605C2×C4—521no—
606C2×C4—521no—
607C2×C4—521no—
608C2×C4—521no—
609C2×C4—521no—
610C2×C4—521no—
611C2×C4—521no—
612C2×C4C4⋊C4×D1312yes—
613C2×C4C22×C4×D1311yescharacteristic
614C2×C4C2×D4×D1311yescharacteristic
615C2×C4#8825111yescharacteristic
616C2×C4C2×Q8×D1311yescharacteristic
617C2×C4#41×D1311yescharacteristic
618C2×C4#8825711yescharacteristic
619C8—22no—
620C8—22no—
621C8—134no—
622C8—262no—
623C22—22no—
624C22—22no—
625C22—22no—
626C22—41no—
627C22—41no—
628C22—41no—
629C22—41no—
630C22—262no—
631C22—262no—
632C22—262no—
633C22—521no—
634C22—521no—
635C22—521no—
636C22—521no—
637C22C2×C4⋊C4×D1311yescharacteristic
638C22#1171929511yescharacteristic
639C22#1171936011yescharacteristic
640C22D13×#13511yescharacteristic
641C22D13×#13511yescharacteristic
642C22#1171947911yescharacteristic
643C22#1171948411yescharacteristic
644C4—22no—
645C4—42no—
646C4—81no—
647C4—81no—
648C4—81no—
649C4—134no—
650C4—262no—
651C4—262no—
652C4—522no—
653C4—1041no—
654C4—1041no—
655C4—1041no—
656C4C4×D4×D1311yescharacteristic
657C4#1171925111yescharacteristic
658C4#1171933711yescharacteristic
659C4#1171934111yescharacteristic
660C2—42no—
661C2—522no—
662C2#1311773411yescharacteristic
663C2D13×#42711yescharacteristic
664C2#1312343511yescharacteristic
665C2#1312655111yescharacteristic
666C2#1312658911yescharacteristic
667C2#1312725311yescharacteristic
668C2#1312726111yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1854C2
socleC23×C13C22×D4
prime radicalC22×C22⋊D13D4
cosocleC22×C4×C13C24
hypercenter#1854D13
hypocenterC13#22658
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1854

Complements

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

NH ≅ G/Ntype
2. C2×#11718659C2semidirect
3. C2×#11718521C2semidirect
6. #13115598C2semidirect
7. #13115596C2semidirect
8. #13115038C2semidirect
9. #13115037C2semidirect
10. #13115032C2semidirect
11. #13114994C2semidirect
12. #13114864C2semidirect
13. #13114863C2semidirect
14. #13114728C2semidirect
15. C13×#1854C2semidirect
53. #11718386C4semidirect
134. #88047D4semidirect
229. #1854D13semidirect
386. Dic13#427semidirect
552. C13#22658semidirect

Maximal subgroups

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

subgroupindex
C2×#117183862
C2×#117186592
C2×#117185212
#131177862
#131177802
#131155982
#131155962
#131150382
#131150372
#131150322
#131149942
#131148642
#131148632
#131147282
C13×#18542
#2265813