Finite Group Databasebeta

← #15913274

Subgroups — #15913274

Order 3328.

840 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718755C211yesmaximal, characteristic, complemented
2C2×#11718672C211yesmaximal, characteristic
3#13119745C211yesmaximal, characteristic
4#13116273C211yesmaximal, characteristic, complemented
5#13116272C211yesmaximal, characteristic, complemented
6#13116039C211yesmaximal, characteristic, complemented
7#13116032C211yesmaximal, characteristic, complemented
8#13115810C211yesmaximal, characteristic, complemented
9#13115604C211yesmaximal, characteristic, complemented
10#13115267C211yesmaximal, characteristic, complemented
11#13115257C211yesmaximal, characteristic, complemented
12#13114867C211yesmaximal, characteristic, complemented
13#13114859C211yesmaximal, characteristic, complemented
14#13114669C211yesmaximal, characteristic, complemented
15C13×#2563C211yesmaximal, characteristic
16C2×C13×C4⋊Q8C2211yescharacteristic
17C2×C4×D4×C13C2211yescharacteristic
18C2×#88178C2211yescharacteristic
19C2×#88178C2211yescharacteristic
20C22×#6099C2211yescharacteristic
21C23×#1055C2211yescharacteristic
22C2×C4×Dic26C2211yescharacteristic
23C13×#393—21no—
24C13×#393—21no—
25C13×#390—21no—
26C13×#382—21no—
27C13×#380C2211yescharacteristic
28C13×#380C2211yescharacteristic
29C13×#380C2211yescharacteristic
30C13×#380C2211yescharacteristic
31C4×C13×C4⋊C4C2211yescharacteristic
32#11718883—21no—
33#11718873C2211yescharacteristic
34#11718873C2211yescharacteristic
35C2×C22⋊#1055C2211yescharacteristic
36C2×C22⋊#1055C2211yescharacteristic
37#11718755—24no—
38#11718672—24no—
39#11718641—21no—
40C2×#88050C2211yescharacteristic
41C2×#88050C2211yescharacteristic
42C2×#88050C2211yescharacteristic
43C2×#88050C2211yescharacteristic
44C2×#88048C2211yescharacteristic
45C2×#88048C2211yescharacteristic
46C2×#88048C2211yescharacteristic
47C2×#88047C2211yescharacteristic
48#11718605—21no—
49#11718605—21no—
50#11718597C2211yescharacteristic
51C2×C4⋊#1055C2211yescharacteristic
52C2×#88043C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718121C2211yescharacteristic
60#11718121C2211yescharacteristic
61C22×Q8×C13—21no—
62C22×D4×C13D411yescharacteristic
63C23×C4×C13C2311yescharacteristic
64C23×C4×C13C2311yescharacteristic
65C22×Dic26C2311yescharacteristic
66C13×C4⋊Q8—22no—
67C13×C4⋊Q8—22no—
68C4×D4×C13—22no—
69C4×D4×C13—22no—
70C2×C13×C4⋊C4—21no—
71C2×C13×C4⋊C4D411yescharacteristic
72C2×C13×C4⋊C4C2311yescharacteristic
73C2×C13×C4⋊C4C2311yescharacteristic
74C2×C13×C4⋊C4C2311yescharacteristic
75C2×C13×C4⋊C4C2311yescharacteristic
76C2×C13×C22⋊C4—21no—
77C2×C13×C22⋊C4—21no—
78C2×C13×C22⋊C4—21no—
79C2×C13×C22⋊C4—21no—
80C2×C13×C22⋊C4D411yescharacteristic
81C2×C13×C22⋊C4D411yescharacteristic
82C2×C42×C13—21no—
83C2×C42×C13C2311yescharacteristic
84C2×C22⋊Dic13—21no—
85C2×C22⋊Dic13—21no—
86C2×C22⋊Dic13—21no—
87C2×C22⋊Dic13—21no—
88C2×C4⋊Dic13C2311yescharacteristic
89C2×C4⋊Dic13C2311yescharacteristic
90C2×C4⋊Dic13C2311yescharacteristic
91#88178—22no—
92#88178—22no—
93#88178—41no—
94#88178—41no—
95C2×#6101—21no—
96C2×#6101—21no—
97C2×#6101—21no—
98C2×C4×Dic13—21no—
99C2×#6099—22no—
100C2×#6099—22no—
101C2×#6099—41no—
102C22×#1055—22no—
103C22×#1055—22no—
104C22×#1055—41no—
105C22×#1055C2311yescharacteristic
106C22×#1055C2311yescharacteristic
107C22×#1055C2311yescharacteristic
108C22×#1055C2311yescharacteristic
109C4×Dic26—22no—
110C4×Dic26—22no—
111C13×#95—21no—
112C13×#95—21no—
113C13×#95—21no—
114C13×#95—21no—
115C13×#95—21no—
116#88071—21no—
117#88071—21no—
118#88071—21no—
119#88071—21no—
120C22⋊#1055—22no—
121C22⋊#1055—22no—
122#88050—22no—
123#88050—22no—
124#88050—22no—
125#88050—22no—
126#88048—22no—
127#88048—22no—
128#88048—41no—
129#88047—41no—
130C4⋊#1055D414yes—
131#88043—22no—
132#25356—131nomaximal, Sylow
133C24×C13C2×D411yescharacteristic
134C24×C13C2×D411yescharacteristic
135C2×Q8×C13—42no—
136C2×Q8×C13—81no—
137C2×Q8×C13—81no—
138C2×D4×C13—22no—
139C2×D4×C13—22no—
140C2×D4×C13—41no—
141C22×C4×C13—21no—
142C22×C4×C13—21no—
143C22×C4×C13—21no—
144C22×C4×C13—21no—
145C22×C4×C13—21no—
146C22×C4×C13—21no—
147C22×C4×C13—21no—
148C22×C4×C13—21no—
149C22×C4×C13—21no—
150C22×C4×C13—21no—
151C22×C4×C13—21no—
152C22×C4×C13—21no—
153C22×C4×C13—21no—
154C22×C4×C13—21no—
155C22×C4×C13—21no—
156C22×C4×C13—21no—
157C22×C4×C13C2×D411yescharacteristic
158C22×C4×C13C2×D411yescharacteristic
159C22×C4×C13C2×D411yescharacteristic
160C22×C4×C13C2×D411yescharacteristic
161C22×C4×C13C2411yescharacteristic
162C22×Dic13—21no—
163C22×Dic13—21no—
164C22×Dic13—21no—
165C22×Dic13—21no—
166C2×Dic26—21no—
167C2×Dic26—21no—
168C2×Dic26—21no—
169C2×Dic26—21no—
170C2×Dic26—21no—
171C2×Dic26#4112yes—
172C13×C4⋊C4—22no—
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⋊C4—21no—
180C13×C4⋊C4—21no—
181C13×C4⋊C4—42no—
182C13×C22⋊C4—22no—
183C13×C22⋊C4—22no—
184C13×C22⋊C4—81no—
185C13×C22⋊C4—81no—
186C13×C22⋊C4—81no—
187C13×C22⋊C4—81no—
188C42×C13—42no—
189C42×C13C2×D412yes—
190C42×C13#4112yes—
191C22⋊Dic13—42no—
192C22⋊Dic13—42no—
193C22⋊Dic13—42no—
194C22⋊Dic13—42no—
195C4⋊Dic13—21no—
196C4⋊Dic13—21no—
197C4⋊Dic13—21no—
198C4⋊Dic13—21no—
199C4⋊Dic13—21no—
200C4⋊Dic13—21no—
201#6101—42no—
202#6101—42no—
203#6101—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—44no—
216C2×#1055C2×D412yes—
217C2×#1055C2×D412yes—
218C2×#1055#4112yes—
219C2×#475—131no—
220C2×#435—131no—
221#2563D1311yescharacteristic
222#2536—131no—
223#2077—131no—
224#2077—131no—
225#2036—131no—
226#2035—131no—
227#1993—131no—
228#1949—131no—
229#1894—131no—
230#1892—131no—
231#1809—131no—
232#1807—131no—
233#1763—131no—
234C23×C13—21no—
235C23×C13—21no—
236C23×C13—21no—
237C23×C13—21no—
238C23×C13—21no—
239C23×C13—21no—
240C23×C13—21no—
241C23×C13—21no—
242C23×C13—21no—
243C23×C13—21no—
244C23×C13—21no—
245C23×C13—21no—
246C23×C13—21no—
247C23×C13#13712yes—
248C23×C13C22×D411yescharacteristic
249Q8×C13—84no—
250D4×C13—44no—
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—21no—
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×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—41no—
279C2×C4×C13—41no—
280C2×C4×C13—41no—
281C2×C4×C13#12112yes—
282C2×C4×C13#12112yes—
283C2×C4×C13C22×D411yescharacteristic
284C2×C4×C13C2×#4111yescharacteristic
285C2×C4×C13C2×#4111yescharacteristic
286C2×C4×C13C2×#4111yescharacteristic
287C2×C4×C13H(5,𝔽2)11yescharacteristic
288C2×C4×C132−1+411yescharacteristic
289C2×Dic13—22no—
290C2×Dic13—41no—
291C2×Dic13—41no—
292C2×Dic13—41no—
293C2×Dic13—41no—
294C2×Dic13—41no—
295C2×Dic13—41no—
296C2×Dic13—41no—
297C2×Dic13—41no—
298C2×Dic13—41no—
299C2×Dic13—41no—
300C2×Dic13—41no—
301Dic26—22no—
302Dic26—22no—
303Dic26—41no—
304Dic26—41no—
305#1055—22no—
306#1055—22no—
307#1055—22no—
308#1055—41no—
309C22×M16—131no—
310C23×C8—131no—
311C2×C4⋊Q8C2×D1311yescharacteristic
312C2×C22⋊Q8—131no—
313C2×C22⋊Q8—131no—
314C2×C4×Q8—131no—
315C2×C4×D4C2×D1311yescharacteristic
316#475—264no—
317#435—264no—
318C2×#107—131no—
319C2×#106—131no—
320C2×#106—131no—
321C2×#106—131no—
322C2×C4⋊C8—131no—
323C2×#103—131no—
324C2×#103—131no—
325C2×#103—131no—
326C2×#103—131no—
327C2×C22⋊C8—131no—
328C2×C22⋊C8—131no—
329C2×#97—131no—
330#398—261no—
331#394—261no—
332#393—21no—
333#393—21no—
334#390—21no—
335#388—261no—
336#388—261no—
337#382—21no—
338#382—131no—
339#380—131no—
340#380—131no—
341#380C2×D1311yescharacteristic
342#380C2×D1311yescharacteristic
343#380C2×D1311yescharacteristic
344#380C2×D1311yescharacteristic
345C4×C4⋊C4C2×D1311yescharacteristic
346#340—131no—
347#340—131no—
348#340—131no—
349#340—131no—
350#340—131no—
351#340—131no—
352#340—131no—
353#340—131no—
354C22×C13—22no—
355C22×C13—22no—
356C22×C13—22no—
357C22×C13—41no—
358C22×C13—41no—
359C22×C13—41no—
360C22×C13—41no—
361C22×C13—41no—
362C22×C13—41no—
363C22×C13—41no—
364C22×C13—41no—
365C22×C13—41no—
366C22×C13—41no—
367C22×C13—41no—
368C22×C13C2×#12111yescharacteristic
369C22×C13#54611yescharacteristic
370C22×C13#54711yescharacteristic
371C22×C13C2×#13711yescharacteristic
372C22×C13#57511yescharacteristic
373C22×C13#57711yescharacteristic
374C22×C13#57711yescharacteristic
375C4×C13—22no—
376C4×C13—22no—
377C4×C13—41no—
378C4×C13—41no—
379C4×C13—81no—
380C4×C13—81no—
381C4×C13—81no—
382C4×C13—81no—
383C4×C13#52911yescharacteristic
384C4×C13#54211yescharacteristic
385C4×C13#54611yescharacteristic
386C4×C13#54811yescharacteristic
387Dic13—42no—
388Dic13—81no—
389Dic13—81no—
390Dic13—81no—
391C22×Q8—21no—
392C22×Q8—131no—
393C22×D4C22⋊D1311yescharacteristic
394C23×C4C22×D1311yescharacteristic
395C23×C4C22×D1311yescharacteristic
396C2×M16—262no—
397C2×M16—262no—
398C2×M16—521no—
399C22×C8—131no—
400C22×C8—131no—
401C22×C8—131no—
402C22×C8—131no—
403C22×C8—262no—
404C22×C8—262no—
405C22×C8—521no—
406C4⋊Q8—22no—
407C4⋊Q8—22no—
408C22⋊Q8—262no—
409C22⋊Q8—262no—
410C22⋊Q8—521no—
411C22⋊Q8—521no—
412C4×Q8—262no—
413C4×Q8—262no—
414C4×D4—22no—
415C4×D4—22no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—131no—
418C2×C4⋊C4—131no—
419C2×C4⋊C4—131no—
420C2×C4⋊C4—261no—
421C2×C4⋊C4—261no—
422C2×C4⋊C4—261no—
423C2×C4⋊C4C22⋊D1311yescharacteristic
424C2×C4⋊C4C22×D1311yescharacteristic
425C2×C4⋊C4C22×D1311yescharacteristic
426C2×C4⋊C4C22×D1311yescharacteristic
427C2×C4⋊C4C22×D1311yescharacteristic
428C2×C22⋊C4—21no—
429C2×C22⋊C4—21no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
432C2×C22⋊C4—261no—
433C2×C22⋊C4—261no—
434C2×C22⋊C4—261no—
435C2×C22⋊C4—261no—
436C2×C22⋊C4C22⋊D1311yescharacteristic
437C2×C22⋊C4C22⋊D1311yescharacteristic
438C2×C42—21no—
439C2×C42—261no—
440C2×C42C22×D1311yescharacteristic
441#107—521no—
442#106—262no—
443#106—262no—
444#106—521no—
445C4⋊C8—134no—
446#103—262no—
447#103—262no—
448#103—262no—
449#103—262no—
450C22⋊C8—262no—
451C22⋊C8—262no—
452#97—262no—
453#95—21no—
454#95—21no—
455#95—21no—
456#95—21no—
457#95—21no—
458#95—261no—
459#95—261no—
460#95—261no—
461#95—261no—
462C2×C13—42no—
463C2×C13—81no—
464C2×C13#242711yescharacteristic
465C2×C13#305611yescharacteristic
466C2×C13#305711yescharacteristic
467C2×C13#331611yescharacteristic
468C2×C13#332111yescharacteristic
469C2×C13#334411yescharacteristic
470C2×C13#334811yescharacteristic
471C24C2×C22⋊D1311yescharacteristic
472C24C2×C22⋊D1311yescharacteristic
473C2×Q8—42no—
474C2×Q8—81no—
475C2×Q8—81no—
476C2×Q8—132no—
477C2×Q8—261no—
478C2×Q8—261no—
479C2×Q8—261no—
480C2×Q8—261no—
481C2×Q8—261no—
482C2×D4—22no—
483C2×D4—22no—
484C2×D4—41no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—261no—
502C22×C4—261no—
503C22×C4—261no—
504C22×C4—261no—
505C22×C4C2×C22⋊D1311yescharacteristic
506C22×C4C2×C22⋊D1311yescharacteristic
507C22×C4C2×C22⋊D1311yescharacteristic
508C22×C4C2×C22⋊D1311yescharacteristic
509C22×C4C23×D1311yescharacteristic
510M16—524no—
511C2×C8—132no—
512C2×C8—132no—
513C2×C8—132no—
514C2×C8—261no—
515C2×C8—261no—
516C2×C8—261no—
517C2×C8—261no—
518C2×C8—261no—
519C2×C8—261no—
520C2×C8—261no—
521C2×C8—261no—
522C2×C8—261no—
523C2×C8—524no—
524C4⋊C4—22no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—42no—
534C4⋊C4—261no—
535C4⋊C4—261no—
536C4⋊C4—261no—
537C4⋊C4—261no—
538C4⋊C4—261no—
539C4⋊C4—261no—
540C4⋊C4—522no—
541C4⋊C4—522no—
542C4⋊C4—522no—
543C22⋊C4—22no—
544C22⋊C4—22no—
545C22⋊C4—81no—
546C22⋊C4—81no—
547C22⋊C4—81no—
548C22⋊C4—81no—
549C22⋊C4—522no—
550C22⋊C4—522no—
551C22⋊C4—522no—
552C22⋊C4—522no—
553C42—42no—
554C42—522no—
555C42D4×D1312yes—
556C42#612912yes—
557C13#2535611yescharacteristic, complemented, Sylow
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23#8819612yes—
572C23C22×C22⋊D1311yescharacteristic
573Q8—84no—
574Q8—262no—
575Q8—262no—
576Q8—521no—
577Q8—521no—
578D4—44no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
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—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—262no—
610C2×C4—521no—
611C2×C4—521no—
612C2×C4—521no—
613C2×C4—521no—
614C2×C4—521no—
615C2×C4—521no—
616C2×C4—521no—
617C2×C4—521no—
618C2×C4—521no—
619C2×C4—521no—
620C2×C4—521no—
621C2×C4#8819312yes—
622C2×C4#8819312yes—
623C2×C4C2×D4×D1311yescharacteristic
624C2×C4C2×#612911yescharacteristic
625C2×C4#41×D1311yescharacteristic
626C2×C4#41×D1311yescharacteristic
627C2×C4#8825611yescharacteristic
628C2×C4#8825711yescharacteristic
629C8—262no—
630C8—262no—
631C8—262no—
632C8—521no—
633C22—22no—
634C22—22no—
635C22—22no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22—41no—
640C22—41no—
641C22—41no—
642C22—41no—
643C22—41no—
644C22—41no—
645C22—41no—
646C22—41no—
647C22C2×#8819311yescharacteristic
648C22C2×#8819611yescharacteristic
649C22#1171952711yescharacteristic
650C22#1171952911yescharacteristic
651C22#1171953411yescharacteristic
652C22#1171954111yescharacteristic
653C22#1171954111yescharacteristic
654C4—22no—
655C4—22no—
656C4—41no—
657C4—41no—
658C4—81no—
659C4—81no—
660C4—81no—
661C4—81no—
662C4—522no—
663C4—1041no—
664C4—1041no—
665C4—1041no—
666C4#1171938111yescharacteristic
667C4#1171938211yescharacteristic
668C4#1171938511yescharacteristic
669C4#1171938711yescharacteristic
670C2—42no—
671C2—81no—
672C2#1311841611yescharacteristic
673C2#1312446211yescharacteristic
674C2#1312447211yescharacteristic
675C2#1312694111yescharacteristic
676C2#1312701611yescharacteristic
677C2#1312728511yescharacteristic
678C2#1312735111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2563C2
socleC23×C13C22×D4
prime radicalC22×D4×C13D4
hypercenter#2563D13
hypocenterC13#25356
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2563

Complements

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

NH ≅ G/Ntype
1. C2×#11718755C2semidirect
4. #13116273C2semidirect
5. #13116272C2semidirect
6. #13116039C2semidirect
7. #13116032C2semidirect
8. #13115810C2semidirect
9. #13115604C2semidirect
10. #13115267C2semidirect
11. #13115257C2semidirect
12. #13114867C2semidirect
13. #13114859C2semidirect
14. #13114669C2semidirect
557. C13#25356semidirect

Maximal subgroups

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

subgroupindex
C2×#117187552
C2×#117186722
#131197452
#131162732
#131162722
#131160392
#131160322
#131158102
#131156042
#131152672
#131152572
#131148672
#131148592
#131146692
C13×#25632
#2535613