Finite Group Databasebeta

← #15869459

Subgroups — #15869459

Order 3328.

954 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×#11718712C211yesmaximal, characteristic
2C2×C4×#6107C211yesmaximal, characteristic, complemented
3C2×#11718658C211yesmaximal, characteristic
4#13117518C211yesmaximal, characteristic
5#13115696C211yesmaximal, characteristic, complemented
6#13115566C211yesmaximal, characteristic, complemented
7#13115529C211yesmaximal, characteristic, complemented
8#13115525C211yesmaximal, characteristic, complemented
9#13115270C211yesmaximal, characteristic
10#13115267C211yesmaximal, characteristic
11#13114863C211yesmaximal, characteristic
12C4×#88047C211yesmaximal, characteristic, complemented
13#13114669C211yesmaximal, characteristic, complemented
14#13114666C211yesmaximal, characteristic, complemented
15C13×#2323C211yesmaximal, characteristic
16C2×C13×C22⋊Q8C2211yescharacteristic
17C2×C4×Q8×C13C2211yescharacteristic
18C2×C13×#117C2211yescharacteristic
19C22×#6107C2211yescharacteristic
20C2×#88178C2211yescharacteristic
21C22×#6099C2211yescharacteristic
22C23×#1055C2211yescharacteristic
23C2×C4×Dic26C2211yescharacteristic
24C13×#391C2211yescharacteristic
25C13×#389—21no—
26C13×#389C2211yescharacteristic
27C13×#388—21no—
28C13×#388—21no—
29C13×#387—21no—
30C13×#380C2211yescharacteristic
31C4×C13×C4⋊C4C2211yescharacteristic
32C2×#88075C2211yescharacteristic
33C2×#88075C2211yescharacteristic
34C2×#88075C2211yescharacteristic
35#11718873C2211yescharacteristic
36#11718712C418yescomplemented
37C4×#6107—24no—
38#11718658—24no—
39#11718639—21no—
40#11718633—21no—
41C2×#88050C2211yescharacteristic
42C2×#88050C2211yescharacteristic
43C2×#88050C2211yescharacteristic
44C2×#88047C2211yescharacteristic
45C2×#88047C2211yescharacteristic
46C2×#88047C2211yescharacteristic
47#11718606—21no—
48#11718605—21no—
49C4×C4⋊Dic13C2211yescharacteristic
50#11718590C2211yescharacteristic
51#11718589C2211yescharacteristic
52C2×#88043C2211yescharacteristic
53C2×#88043C2211yescharacteristic
54C2×C4×#1055C2211yescharacteristic
55C2×C4×#1055C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718121C2211yescharacteristic
60#11718121C2211yescharacteristic
61#11718121C2211yescharacteristic
62C22×Q8×C13C2311yescharacteristic
63C23×C4×C13C2311yescharacteristic
64C22×Dic26C2311yescharacteristic
65C13×C22⋊Q8—22no—
66C13×C22⋊Q8C2×C414yes—
67C4×Q8×C13—22no—
68C4×Q8×C13—22no—
69C13×#117—22no—
70C13×#117—22no—
71C2×C13×C4⋊C4—21no—
72C2×C13×C4⋊C4—21no—
73C2×C13×C4⋊C4—21no—
74C2×C13×C4⋊C4D411yescharacteristic
75C2×C13×C4⋊C4D411yescharacteristic
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×C13C2311yescharacteristic
86C2×C42×C13C2311yescharacteristic
87C2×C22⋊Dic13—21no—
88C2×C22⋊Dic13—21no—
89C2×#6107—22no—
90C2×#6107—22no—
91C2×#6107C2×C414yes—
92C2×C4⋊Dic13C2311yescharacteristic
93C2×C4⋊Dic13C2311yescharacteristic
94C2×C4⋊Dic13C2311yescharacteristic
95#88178—22no—
96#88178C2×C414yes—
97C2×#6101—21no—
98C2×#6101—21no—
99C2×#6101—21no—
100C2×C4×Dic13—21no—
101C2×C4×Dic13—21no—
102C2×#6099—22no—
103C2×#6099—22no—
104C2×#6099—22no—
105C22×#1055—22no—
106C22×#1055—22no—
107C22×#1055C2×C414yes—
108C22×#1055C2311yescharacteristic
109C22×#1055C2311yescharacteristic
110C22×#1055C2311yescharacteristic
111C22×#1055C2311yescharacteristic
112C4×Dic26—22no—
113C4×Dic26—22no—
114C13×#95—21no—
115C13×#95—21no—
116C13×#95—21no—
117C13×#95—21no—
118C13×#95—21no—
119#88075—22no—
120#88075—22no—
121#88075C2×C414yes—
122#88071—21no—
123#88071—21no—
124#88071—21no—
125#88071—21no—
126#88071—21no—
127#88050—22no—
128#88050—22no—
129#88050C2×C414yes—
130#88047—22no—
131#88047—22no—
132#88047C2×C414yes—
133#88043—22no—
134#88043—22no—
135C4×#1055—22no—
136C4×#1055D414yes—
137#21525—131nomaximal, Sylow
138C24×C13C2×D411yescharacteristic
139C2×Q8×C13—21no—
140C2×Q8×C13—21no—
141C2×Q8×C13—21no—
142C2×Q8×C13—21no—
143C2×Q8×C13—21no—
144C2×Q8×C13C22×C412yes—
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×C13C22×C412yes—
154C22×C4×C13C2×D411yescharacteristic
155C22×C4×C13C2×D411yescharacteristic
156C22×C4×C13C2×D411yescharacteristic
157C22×C4×C13C2×D411yescharacteristic
158C22×C4×C13C2×D411yescharacteristic
159C22×C4×C13#4112yes—
160C22×C4×C13C2411yescharacteristic
161C22×Dic13—21no—
162C22×Dic13—21no—
163C22×Dic13—21no—
164C22×Dic13—21no—
165C2×Dic26—21no—
166C2×Dic26—21no—
167C2×Dic26—21no—
168C2×Dic26—21no—
169C2×Dic26—21no—
170C2×Dic26C22×C412yes—
171C13×C4⋊C4—24no—
172C13×C4⋊C4—22no—
173C13×C4⋊C4—22no—
174C13×C4⋊C4—21no—
175C13×C4⋊C4—21no—
176C13×C4⋊C4—21no—
177C13×C4⋊C4—21no—
178C13×C4⋊C4—21no—
179C13×C4⋊C4—42no—
180C13×C4⋊C4—81no—
181C13×C4⋊C4C22×C412yes—
182C13×C22⋊C4—24no—
183C13×C22⋊C4—22no—
184C13×C22⋊C4—22no—
185C13×C22⋊C4—81no—
186C42×C13—21no—
187C42×C13—21no—
188C42×C13—42no—
189C42×C13—81no—
190C42×C13C2×D412yes—
191C42×C13#4112yes—
192C22⋊Dic13—24no—
193C22⋊Dic13—81no—
194#6107—28no—
195C4⋊Dic13—21no—
196C4⋊Dic13—21no—
197C4⋊Dic13—21no—
198C4⋊Dic13—21no—
199C4⋊Dic13—21no—
200C4⋊Dic13C22×C412yes—
201#6101—24no—
202#6101—42no—
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—28no—
214C2×#1055C22×C412yes—
215C2×#1055C22×C412yes—
216C2×#1055C2×D412yes—
217C2×#1055C2×D412yes—
218C2×#1055#4112yes—
219C2×#1055#4112yes—
220C2×#467—131no—
221C2×C4×Q16—131no—
222C2×#405—131no—
223#2323—131no—
224#2323D1311yescharacteristic
225#1969—131no—
226#1942—131no—
227#1935—131no—
228#1935—131no—
229#1894—131no—
230#1894—131no—
231#1808—131no—
232C4×#107—131no—
233#1763—131no—
234#1763—131no—
235C23×C13—21no—
236C23×C13—21no—
237C23×C13—21no—
238C23×C13—21no—
239C23×C13—21no—
240C23×C13—21no—
241C23×C13C4×D412yes—
242C23×C13C22×D411yescharacteristic
243Q8×C13—22no—
244Q8×C13—22no—
245Q8×C13—41no—
246Q8×C13—41no—
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—22no—
254C2×C4×C13—22no—
255C2×C4×C13—22no—
256C2×C4×C13—22no—
257C2×C4×C13—22no—
258C2×C4×C13—22no—
259C2×C4×C13—21no—
260C2×C4×C13—21no—
261C2×C4×C13—21no—
262C2×C4×C13—21no—
263C2×C4×C13—21no—
264C2×C4×C13—21no—
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×C13C4×D412yes—
276C2×C4×C13#12112yes—
277C2×C4×C13#12112yes—
278C2×C4×C13C23×C411yescharacteristic
279C2×C4×C13C22×D411yescharacteristic
280C2×C4×C13C2×#4111yescharacteristic
281C2×C4×C13C2×#4111yescharacteristic
282C2×C4×C13C2×#4111yescharacteristic
283C2×C4×C13C2×#4111yescharacteristic
284C2×Dic13—22no—
285C2×Dic13—22no—
286C2×Dic13—41no—
287C2×Dic13—41no—
288C2×Dic13—41no—
289C2×Dic13—41no—
290C2×Dic13—41no—
291C2×Dic13—41no—
292C2×Dic13—41no—
293C2×Dic13—41no—
294C2×Dic13—41no—
295C2×Dic13—41no—
296Dic26—22no—
297Dic26—22no—
298Dic26—41no—
299Dic26—41no—
300#1055—22no—
301#1055—22no—
302#1055—22no—
303#1055C4×D414yes—
304C22×Q16—131no—
305C22×M16—131no—
306C23×C8—131no—
307C2×C22⋊Q8—131no—
308C2×C22⋊Q8C2×D1311yescharacteristic
309C2×C4×Q8—131no—
310C2×C4×Q8C2×D1311yescharacteristic
311C2×#117C2×D1311yescharacteristic
312#467—138no—
313C4×Q16—264no—
314C2×#107—131no—
315C2×#107—131no—
316C2×#107—131no—
317C2×#103—131no—
318C2×#103—131no—
319C2×#103—131no—
320C2×#103—131no—
321C2×#103—131no—
322C2×#103—131no—
323#405—264no—
324C2×#97—131no—
325C2×#97—131no—
326C2×C4×C8—131no—
327C2×C4×C8—131no—
328#391—131no—
329#391C2×D1311yescharacteristic
330#389—21no—
331#389—131no—
332#389—261no—
333#389C2×D1311yescharacteristic
334#388—21no—
335#388—21no—
336#388—261no—
337#388—261no—
338#387—21no—
339#387—261no—
340#380—131no—
341#380C2×D1311yescharacteristic
342C4×C4⋊C4—131no—
343C4×C4⋊C4C2×D1311yescharacteristic
344#340—131no—
345#340—131no—
346#340—131no—
347#340—131no—
348#340—131no—
349#340—131no—
350C22×C13—22no—
351C22×C13—22no—
352C22×C13—22no—
353C22×C13—41no—
354C22×C13—41no—
355C22×C13—41no—
356C22×C13—41no—
357C22×C13C2×C4×D411yescharacteristic
358C22×C13C2×#12111yescharacteristic
359C22×C13#53211yescharacteristic
360C22×C13#57611yescharacteristic
361C22×C13#57811yescharacteristic
362C22×C13#57811yescharacteristic
363C22×C13#57811yescharacteristic
364C4×C13—22no—
365C4×C13—22no—
366C4×C13—22no—
367C4×C13—42no—
368C4×C13—41no—
369C4×C13—41no—
370C4×C13—42no—
371C4×C13—81no—
372C4×C13—81no—
373C4×C13C2×C4×D411yescharacteristic
374C4×C13C4×#4111yescharacteristic
375C4×C13#52511yescharacteristic
376C4×C13#52911yescharacteristic
377Dic13—42no—
378Dic13—42no—
379Dic13—81no—
380Dic13—81no—
381C22×Q8—131no—
382C22×Q8C22×D1311yescharacteristic
383C23×C4C22×D1311yescharacteristic
384C2×Q16—134no—
385C2×Q16—262no—
386C2×Q16—262no—
387C2×M16—262no—
388C2×M16—262no—
389C2×M16—262no—
390C22×C8—131no—
391C22×C8—134no—
392C22×C8—131no—
393C22×C8—131no—
394C22×C8—131no—
395C22×C8—262no—
396C22×C8—262no—
397C22⋊Q8—22no—
398C22⋊Q8—134no—
399C22⋊Q8—262no—
400C22⋊Q8C4×D1314yes—
401C4×Q8—22no—
402C4×Q8—22no—
403C4×Q8—262no—
404C4×Q8—262no—
405#117—22no—
406#117—22no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—131no—
411C2×C4⋊C4—131no—
412C2×C4⋊C4—131no—
413C2×C4⋊C4—261no—
414C2×C4⋊C4—261no—
415C2×C4⋊C4—261no—
416C2×C4⋊C4C22⋊D1311yescharacteristic
417C2×C4⋊C4C22⋊D1311yescharacteristic
418C2×C4⋊C4C22×D1311yescharacteristic
419C2×C4⋊C4C22×D1311yescharacteristic
420C2×C4⋊C4C22×D1311yescharacteristic
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—261no—
424C2×C22⋊C4—261no—
425C2×C22⋊C4C22⋊D1311yescharacteristic
426C2×C22⋊C4C22⋊D1311yescharacteristic
427C2×C42—21no—
428C2×C42—21no—
429C2×C42—261no—
430C2×C42—261no—
431C2×C42C22×D1311yescharacteristic
432C2×C42C22×D1311yescharacteristic
433#107—134no—
434#107—262no—
435#107—262no—
436#103—134no—
437#103—134no—
438#103—262no—
439#103—262no—
440#103—262no—
441#103—262no—
442#97—262no—
443#97—262no—
444C4×C8—134no—
445C4×C8—262no—
446#95—21no—
447#95—21no—
448#95—21no—
449#95—21no—
450#95—21no—
451#95—261no—
452#95—261no—
453#95—261no—
454#95—261no—
455#95—261no—
456C2×C13—42no—
457C2×C13C4×#12111yescharacteristic
458C2×C13#295011yescharacteristic
459C2×C13#295111yescharacteristic
460C2×C13#305911yescharacteristic
461C2×C13#306111yescharacteristic
462C2×C13#317511yescharacteristic
463C2×C13#317711yescharacteristic
464C24C2×C22⋊D1311yescharacteristic
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—132no—
471C2×Q8—261no—
472C2×Q8—261no—
473C2×Q8—261no—
474C2×Q8—261no—
475C2×Q8—261no—
476C2×Q8C2×C4×D1312yes—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—261no—
486C22×C4—261no—
487C22×C4—261no—
488C22×C4—261no—
489C22×C4C2×C4×D1312yes—
490C22×C4#612712yes—
491C22×C4C2×C22⋊D1311yescharacteristic
492C22×C4C2×C22⋊D1311yescharacteristic
493C22×C4C2×C22⋊D1311yescharacteristic
494C22×C4C2×C22⋊D1311yescharacteristic
495C22×C4C2×C22⋊D1311yescharacteristic
496C22×C4C23×D1311yescharacteristic
497Q16—268no—
498M16—268no—
499C2×C8—132no—
500C2×C8—132no—
501C2×C8—132no—
502C2×C8—132no—
503C2×C8—132no—
504C2×C8—132no—
505C2×C8—268no—
506C2×C8—261no—
507C2×C8—261no—
508C2×C8—261no—
509C2×C8—261no—
510C2×C8—261no—
511C2×C8—261no—
512C4⋊C4—24no—
513C4⋊C4—22no—
514C4⋊C4—22no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—42no—
521C4⋊C4—81no—
522C4⋊C4—132no—
523C4⋊C4—264no—
524C4⋊C4—261no—
525C4⋊C4—261no—
526C4⋊C4—261no—
527C4⋊C4—261no—
528C4⋊C4—261no—
529C4⋊C4—522no—
530C4⋊C4—1041no—
531C4⋊C4C2×C4×D1312yes—
532C22⋊C4—24no—
533C22⋊C4—22no—
534C22⋊C4—22no—
535C22⋊C4—81no—
536C22⋊C4—264no—
537C22⋊C4—1041no—
538C42—21no—
539C42—21no—
540C42—42no—
541C42—81no—
542C42—522no—
543C42—1041no—
544C42D4×D1312yes—
545C42#612912yes—
546C13#2152511yescharacteristic, complemented, Sylow
547C23—21no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—21no—
552C23—21no—
553C23C4×C22⋊D1312yes—
554C23C22×C22⋊D1311yescharacteristic
555Q8—22no—
556Q8—22no—
557Q8—41no—
558Q8—41no—
559Q8—262no—
560Q8—262no—
561Q8—521no—
562Q8—521no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
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—521no—
594C2×C4—521no—
595C2×C4—521no—
596C2×C4—521no—
597C2×C4—521no—
598C2×C4—521no—
599C2×C4—521no—
600C2×C4—521no—
601C2×C4—521no—
602C2×C4—521no—
603C2×C4C4×C22⋊D1312yes—
604C2×C4#8819312yes—
605C2×C4#8819312yes—
606C2×C4C22×C4×D1311yescharacteristic
607C2×C4C2×#612711yescharacteristic
608C2×C4C2×D4×D1311yescharacteristic
609C2×C4C2×#612911yescharacteristic
610C2×C4#41×D1311yescharacteristic
611C2×C4#41×D1311yescharacteristic
612C8—134no—
613C8—262no—
614C8—262no—
615C8—262no—
616C22—22no—
617C22—22no—
618C22—22no—
619C22—41no—
620C22—41no—
621C22—41no—
622C22—41no—
623C22C2×C4×C22⋊D1311yescharacteristic
624C22C2×#8819311yescharacteristic
625C22#1171953711yescharacteristic
626C22#1171954011yescharacteristic
627C22#1171954311yescharacteristic
628C22#1171954311yescharacteristic
629C22#1171954311yescharacteristic
630C4—22no—
631C4—22no—
632C4—22no—
633C4—42no—
634C4—41no—
635C4—41no—
636C4—42no—
637C4—81no—
638C4—81no—
639C4—522no—
640C4—522no—
641C4—1041no—
642C4—1041no—
643C4C4×#612911yescharacteristic
644C4#1171924311yescharacteristic
645C4C4×D4×D1311yescharacteristic
646C4#1171925211yescharacteristic
647C2—42no—
648C2C4×#8819311yescharacteristic
649C2#1312370211yescharacteristic
650C2#1312370911yescharacteristic
651C2#1312448811yescharacteristic
652C2#1312450311yescharacteristic
653C2#1312546911yescharacteristic
654C2#1312548911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#2323C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
cosocleC22×C4×C13C24
hypercenter#2323D13
hypocenterC13#21525
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2323

Complements

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

NH ≅ G/Ntype
2. C2×C4×#6107C2semidirect
5. #13115696C2semidirect
6. #13115566C2semidirect
7. #13115529C2semidirect
8. #13115525C2semidirect
12. C4×#88047C2semidirect
13. #13114669C2semidirect
14. #13114666C2semidirect
36. #11718712C4semidirect
546. C13#21525semidirect

Maximal subgroups

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

subgroupindex
C2×#117187122
C2×C4×#61072
C2×#117186582
#131175182
#131156962
#131155662
#131155292
#131155252
#131152702
#131152672
#131148632
C4×#880472
#131146692
#131146662
C13×#23232
#2152513