Finite Group Databasebeta

← #15881280

Subgroups — #15881280

Order 3328.

982 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718679C211yesmaximal, characteristic
2C2×#11718679C211yesmaximal, characteristic
3C2×C4×#6105C211yesmaximal, characteristic
4C4⋊C4×Dic26C211yesmaximal, characteristic, complemented
5#13115571C211yesmaximal, characteristic, complemented
6#13115566C211yesmaximal, characteristic, complemented
7#13115103C211yesmaximal, characteristic, complemented
8#13115097C211yesmaximal, characteristic
9#13115089C211yesmaximal, characteristic, complemented
10#13115083C211yesmaximal, characteristic
11#13115005C211yesmaximal, characteristic, complemented
12#13114848C211yesmaximal, characteristic, complemented
13#13114836C211yesmaximal, characteristic
14#13114711C211yesmaximal, characteristic, complemented
15C13×#2349C211yesmaximal, characteristic
16C2×C4×D4×C13C2211yescharacteristic
17C2×C4×D4×C13C2211yescharacteristic
18C2×C4×D4×C13C2211yescharacteristic
19C22×#6105C2211yescharacteristic
20C2×C4×Dic26C2211yescharacteristic
21C2×C4×Dic26C2211yescharacteristic
22C2×C4×Dic26C2211yescharacteristic
23C13×#389C2211yescharacteristic
24C13×#389C2211yescharacteristic
25C13×#385—21no—
26C13×#385—21no—
27C13×#382C2211yescharacteristic
28C13×#380—21no—
29C4×C13×C4⋊C4C2211yescharacteristic
30C2×C13×#95—21no—
31C2×#88072C2211yescharacteristic
32C2×#88072C2211yescharacteristic
33C2×#88072C2211yescharacteristic
34#11718679—24no—
35#11718679C418yescomplemented
36C4×#6105—24no—
37#11718637—21no—
38C4⋊C4×Dic13—21no—
39C2×#88050C2211yescharacteristic
40C2×#88050C2211yescharacteristic
41C2×#88050C2211yescharacteristic
42C2×#88048C2211yescharacteristic
43C2×#88048C2211yescharacteristic
44C2×#88047C2211yescharacteristic
45C2×#88047C2211yescharacteristic
46C2×#88047C2211yescharacteristic
47#11718596C2211yescharacteristic
48#11718589C2211yescharacteristic
49#11718589C2211yescharacteristic
50C2×C4⋊#1055C2211yescharacteristic
51C2×#88043C2211yescharacteristic
52C2×#88043C2211yescharacteristic
53C2×C4×#1055C2211yescharacteristic
54#11718308—21no—
55#11718308—21no—
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718121C2211yescharacteristic
60#11718116C2211yescharacteristic
61#11718116C2211yescharacteristic
62C22×D4×C13C2311yescharacteristic
63C23×C4×C13—21no—
64C23×C4×C13—21no—
65C23×C4×C13—21no—
66C22×Dic26C2311yescharacteristic
67C4×D4×C13—22no—
68C4×D4×C13—22no—
69C4×D4×C13—22no—
70C4×D4×C13—41no—
71C4×D4×C13—41no—
72C4×D4×C13C2×C414yes—
73C2×C13×C4⋊C4—21no—
74C2×C13×C4⋊C4—21no—
75C2×C13×C4⋊C4D411yescharacteristic
76C2×C13×C4⋊C4D411yescharacteristic
77C2×C13×C4⋊C4C2311yescharacteristic
78C2×C13×C4⋊C4C2311yescharacteristic
79C2×C13×C4⋊C4C2311yescharacteristic
80C2×C13×C22⋊C4—21no—
81C2×C13×C22⋊C4—21no—
82C2×C13×C22⋊C4—21no—
83C2×C42×C13C2311yescharacteristic
84C2×C42×C13C2311yescharacteristic
85C2×C42×C13C2311yescharacteristic
86C2×#6105C2×C414yes—
87C2×#6105D414yes—
88C2×#6105Q814yes—
89C2×C4⋊Dic13—21no—
90C2×C4⋊Dic13—21no—
91C2×C4⋊Dic13C2311yescharacteristic
92C2×C4⋊Dic13C2311yescharacteristic
93C2×C4⋊Dic13C2311yescharacteristic
94C2×#6101—21no—
95C2×#6101—21no—
96C2×#6101—21no—
97C2×#6101—21no—
98C2×#6101—21no—
99C2×C4×Dic13—21no—
100C2×C4×Dic13—21no—
101C2×C4×Dic13—21no—
102C22×#1055C2311yescharacteristic
103C22×#1055C2311yescharacteristic
104C22×#1055C2311yescharacteristic
105C22×#1055C2311yescharacteristic
106C4×Dic26—22no—
107C4×Dic26—22no—
108C4×Dic26—22no—
109C4×Dic26—41no—
110C4×Dic26—41no—
111C4×Dic26C2×C414yescomplemented
112C13×#95—21no—
113C13×#95—21no—
114C13×#95—21no—
115C13×#95—21no—
116C13×#95D411yescharacteristic
117C13×#95D411yescharacteristic
118#88072—22no—
119#88072—22no—
120#88072C2×C414yes—
121#88071—21no—
122#88071—21no—
123#88050—22no—
124#88050—22no—
125#88050C2×C414yescomplemented
126#88048—22no—
127#88048—41no—
128#88047—22no—
129#88047—41no—
130#88047C2×C414yescomplemented
131C4⋊#1055—22no—
132#88043—22no—
133#88043C2×C414yescomplemented
134C4×#1055—22no—
135#22678—131nomaximal, Sylow
136C24×C13—21no—
137C2×D4×C13—21no—
138C2×D4×C13—21no—
139C2×D4×C13—21no—
140C2×D4×C13C22×C412yes—
141C2×D4×C13C2×D412yes—
142C2×D4×C13C2×Q812yes—
143C22×C4×C13—21no—
144C22×C4×C13—24no—
145C22×C4×C13—21no—
146C22×C4×C13—21no—
147C22×C4×C13—42no—
148C22×C4×C13—42no—
149C22×C4×C13—42no—
150C22×C4×C13—42no—
151C22×C4×C13—81no—
152C22×C4×C13—81no—
153C22×C4×C13—81no—
154C22×C4×C13—81no—
155C22×C4×C13C2×D411yescharacteristic
156C22×C4×C13C2×D411yescharacteristic
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×Dic26C22×C412yes—
170C2×Dic26C2×D412yes—
171C2×Dic26C2×Q812yes—
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—41no—
179C13×C4⋊C4—81no—
180C13×C4⋊C4—81no—
181C13×C4⋊C4C22×C412yes—
182C13×C22⋊C4—24no—
183C13×C22⋊C4—42no—
184C13×C22⋊C4—42no—
185C42×C13—21no—
186C42×C13—21no—
187C42×C13—21no—
188C42×C13—21no—
189C42×C13C22×C412yes—
190C42×C13#4112yes—
191#6105C4⋊C4116yescomplemented
192C4⋊Dic13—21no—
193C4⋊Dic13—21no—
194C4⋊Dic13—21no—
195C4⋊Dic13—21no—
196C4⋊Dic13—21no—
197C4⋊Dic13—42no—
198C4⋊Dic13—81no—
199C4⋊Dic13C22×C412yes—
200#6101—24no—
201#6101—42no—
202#6101—42no—
203#6101—81no—
204#6101—81no—
205C4×Dic13—24no—
206C4×Dic13—42no—
207C4×Dic13—42no—
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×#1055C2×D412yes—
219C2×#1055C2×Q812yes—
220C2×#440—131no—
221C2×#440—131no—
222C2×C4×SD16—131no—
223Q8×C4⋊C4—131no—
224#2349D1311yescharacteristic
225#1943—131no—
226#1942—131no—
227#1865—131no—
228#1864—131no—
229#1863—131no—
230#1862—131no—
231#1847—131no—
232#1805—131no—
233#1802—131no—
234#1771—131no—
235C23×C13—22no—
236C23×C13—22no—
237C23×C13—22no—
238C23×C13—41no—
239C23×C13—41no—
240C23×C13—41no—
241C23×C13—41no—
242C23×C13C22×D411yescharacteristic
243D4×C13—22no—
244D4×C13—22no—
245D4×C13—22no—
246D4×C13C2×C4⋊C414yes—
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—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—21no—
262C2×C4×C13—21no—
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—84no—
272C2×C4×C13—84no—
273C2×C4×C13—84no—
274C2×C4×C13C4×D412yes—
275C2×C4×C13C4×D412yes—
276C2×C4×C13#13712yes—
277C2×C4×C13C23×C411yescharacteristic
278C2×C4×C13C22×D411yescharacteristic
279C2×C4×C13C22×Q811yescharacteristic
280C2×C4×C13C2×#4111yescharacteristic
281C2×C4×C13H(5,𝔽2)11yescharacteristic
282C2×C4×C132−1+411yescharacteristic
283C2×Dic13—22no—
284C2×Dic13—22no—
285C2×Dic13—22no—
286C2×Dic13—22no—
287C2×Dic13—41no—
288C2×Dic13—41no—
289C2×Dic13—41no—
290C2×Dic13—41no—
291C2×Dic13—41no—
292C2×Dic13—41no—
293C2×Dic13—41no—
294C2×Dic13—41no—
295Dic26—22no—
296Dic26—22no—
297Dic26—22no—
298Dic26C2×C4⋊C414yes—
299#1055—22no—
300#1055—41no—
301#1055—41no—
302#1055C2×C4⋊C414yes—
303C22×SD16—131no—
304C2×C4×Q8—131no—
305C2×C4×Q8—131no—
306C2×C4×Q8—131no—
307C2×C4×D4C2×D1311yescharacteristic
308C2×C4×D4C2×D1311yescharacteristic
309C2×C4×D4C2×D1311yescharacteristic
310#440—138no—
311#440—264no—
312C4×SD16—264no—
313C2×#107—131no—
314C2×#107—131no—
315C2×#107—131no—
316C2×#106—131no—
317C2×#106—131no—
318C2×C4⋊C8—131no—
319C2×#103—131no—
320C2×#103—131no—
321C2×#103—131no—
322C2×#102—131no—
323C2×#102—131no—
324C2×#102—131no—
325C2×#97—131no—
326C2×#97—131no—
327C2×C4×C8—131no—
328#389—131no—
329#389—131no—
330#389—261no—
331#389—261no—
332#389C2×D1311yescharacteristic
333#389C2×D1311yescharacteristic
334#385—21no—
335#385—21no—
336#384—131no—
337#384—261no—
338#382C2×D1311yescharacteristic
339#380—21no—
340C4×C4⋊C4—261no—
341C4×C4⋊C4C2×D1311yescharacteristic
342C2×#95—21no—
343#340—131no—
344#340—131no—
345#340—131no—
346#340—131no—
347#336—131no—
348#336—131no—
349C22×C13—24no—
350C22×C13—42no—
351C22×C13—42no—
352C22×C13—42no—
353C22×C13—42no—
354C22×C13—42no—
355C22×C13—42no—
356C22×C13C2×C4×D411yescharacteristic
357C22×C13D4211yescharacteristic
358C22×C13D4×Q811yescharacteristic
359C22×C13C2×#13711yescharacteristic
360C22×C13#57511yescharacteristic
361C22×C13#57611yescharacteristic
362C22×C13#57711yescharacteristic
363C4×C13—22no—
364C4×C13—22no—
365C4×C13—22no—
366C4×C13—42no—
367C4×C13—41no—
368C4×C13—41no—
369C4×C13—41no—
370C4×C13—81no—
371C4×C13—81no—
372C4×C13C22×C4⋊C411yescharacteristic
373C4×C13#52011yescharacteristic
374C4×C13#54711yescharacteristic
375C4×C13#55411yescharacteristic
376Dic13—24no—
377Dic13—42no—
378Dic13—81no—
379Dic13—81no—
380C22×Q8—131no—
381C22×D4C22×D1311yescharacteristic
382C23×C4—21no—
383C23×C4—21no—
384C23×C4—21no—
385C2×SD16—134no—
386C2×SD16—134no—
387C2×SD16—134no—
388C22×C8—131no—
389C22×C8—131no—
390C22×C8—131no—
391C22×C8—131no—
392C4×Q8—134no—
393C4×Q8—262no—
394C4×Q8—262no—
395C4×Q8—262no—
396C4×Q8—521no—
397C4×Q8—521no—
398C4×D4—22no—
399C4×D4—22no—
400C4×D4—22no—
401C4×D4—41no—
402C4×D4—41no—
403C4×D4C4×D1314yes—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—131no—
407C2×C4⋊C4—131no—
408C2×C4⋊C4—131no—
409C2×C4⋊C4—261no—
410C2×C4⋊C4—261no—
411C2×C4⋊C4—261no—
412C2×C4⋊C4—261no—
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—21no—
424C2×C42—261no—
425C2×C42—261no—
426C2×C42—261no—
427C2×C42C22×D1311yescharacteristic
428C2×C42C22×D1311yescharacteristic
429C2×C42C22×D1311yescharacteristic
430#107—134no—
431#107—262no—
432#107—521no—
433#106—262no—
434#106—521no—
435C4⋊C8—262no—
436#103—134no—
437#103—262no—
438#103—262no—
439#102—134no—
440#102—262no—
441#102—262no—
442#97—134no—
443#97—262no—
444C4×C8—262no—
445#95—21no—
446#95—21no—
447#95—21no—
448#95—21no—
449#95—261no—
450#95—261no—
451#95C22⋊D1311yescharacteristic
452#95C22⋊D1311yescharacteristic
453C2×C13—44no—
454C2×C13D4×C4⋊C411yescharacteristic
455C2×C13C4×#13711yescharacteristic
456C2×C13#294611yescharacteristic
457C2×C13#326611yescharacteristic
458C2×C13#326811yescharacteristic
459C2×C13#338511yescharacteristic
460C2×C13#338811yescharacteristic
461C24—21no—
462C2×Q8—132no—
463C2×Q8—132no—
464C2×Q8—132no—
465C2×Q8—261no—
466C2×Q8—261no—
467C2×Q8—261no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4C2×C4×D1312yes—
472C2×D4D4×D1312yes—
473C2×D4Q8×D1312yes—
474C22×C4—21no—
475C22×C4—24no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—42no—
479C22×C4—42no—
480C22×C4—42no—
481C22×C4—42no—
482C22×C4—81no—
483C22×C4—81no—
484C22×C4—81no—
485C22×C4—81no—
486C22×C4—261no—
487C22×C4—261no—
488C22×C4—261no—
489C22×C4—261no—
490C22×C4C2×C22⋊D1311yescharacteristic
491C22×C4C2×C22⋊D1311yescharacteristic
492C22×C4C2×C22⋊D1311yescharacteristic
493C22×C4C2×C22⋊D1311yescharacteristic
494C22×C4C2×C22⋊D1311yescharacteristic
495C22×C4C2×C22⋊D1311yescharacteristic
496C22×C4C23×D1311yescharacteristic
497SD16—1316no—
498C2×C8—132no—
499C2×C8—132no—
500C2×C8—132no—
501C2×C8—132no—
502C2×C8—261no—
503C2×C8—261no—
504C2×C8—261no—
505C2×C8—261no—
506C2×C8—261no—
507C2×C8—261no—
508C2×C8—261no—
509C2×C8—261no—
510C4⋊C4—22no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—41no—
517C4⋊C4—81no—
518C4⋊C4—81no—
519C4⋊C4—132no—
520C4⋊C4—264no—
521C4⋊C4—261no—
522C4⋊C4—261no—
523C4⋊C4—261no—
524C4⋊C4—261no—
525C4⋊C4—261no—
526C4⋊C4—522no—
527C4⋊C4—522no—
528C4⋊C4—522no—
529C4⋊C4—1041no—
530C4⋊C4—1041no—
531C4⋊C4—1041no—
532C4⋊C4C2×C4×D1312yes—
533C22⋊C4—24no—
534C22⋊C4—42no—
535C22⋊C4—42no—
536C42—21no—
537C42—21no—
538C42—21no—
539C42—21no—
540C42—264no—
541C42—522no—
542C42—522no—
543C42C2×C4×D1312yes—
544C42#612712yes—
545C13#2267811yescharacteristic, complemented, Sylow
546C23—22no—
547C23—22no—
548C23—22no—
549C23—41no—
550C23—41no—
551C23—41no—
552C23—41no—
553C23C22×C22⋊D1311yescharacteristic
554Q8—134no—
555Q8—262no—
556Q8—262no—
557Q8—262no—
558D4—22no—
559D4—22no—
560D4—22no—
561D4C4⋊C4×D1314yes—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—22no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
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—84no—
587C2×C4—84no—
588C2×C4—84no—
589C2×C4—262no—
590C2×C4—262no—
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×C4C4×C22⋊D1312yes—
602C2×C4C4×C22⋊D1312yes—
603C2×C4#8820512yes—
604C2×C4C22×C4×D1311yescharacteristic
605C2×C4C2×#612711yescharacteristic
606C2×C4C2×D4×D1311yescharacteristic
607C2×C4#8825111yescharacteristic
608C2×C4C2×Q8×D1311yescharacteristic
609C2×C4#8825411yescharacteristic
610C8—134no—
611C8—262no—
612C8—521no—
613C8—521no—
614C22—24no—
615C22—42no—
616C22—42no—
617C22—42no—
618C22—42no—
619C22—42no—
620C22—42no—
621C22C2×C4×C22⋊D1311yescharacteristic
622C22D4×C22⋊D1311yescharacteristic
623C22Q8×C22⋊D1311yescharacteristic
624C22#1171952711yescharacteristic
625C22C2×#8820511yescharacteristic
626C22#1171954011yescharacteristic
627C22#1171954111yescharacteristic
628C4—22no—
629C4—22no—
630C4—22no—
631C4—42no—
632C4—41no—
633C4—41no—
634C4—41no—
635C4—81no—
636C4—81no—
637C4—264no—
638C4—522no—
639C4—1041no—
640C4—1041no—
641C4C2×C4⋊C4×D1311yescharacteristic
642C4#1171920911yescharacteristic
643C4#1171921211yescharacteristic
644C4#1171921611yescharacteristic
645C2—44no—
646C2C4⋊C4×C22⋊D1311yescharacteristic
647C2C4×#8820511yescharacteristic
648C2#1312366811yescharacteristic
649C2#1312634211yescharacteristic
650C2#1312637211yescharacteristic
651C2#1312774611yescharacteristic
652C2#1312778111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#2349C2
socleC23×C13C22×D4
prime radicalC22×D4×C13C23
cosocleC22×C4×C13C24
hypercenter#2349D13
hypocenterC13#22678
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2349

Complements

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

NH ≅ G/Ntype
4. C4⋊C4×Dic26C2semidirect
5. #13115571C2semidirect
6. #13115566C2semidirect
7. #13115103C2semidirect
9. #13115089C2semidirect
11. #13115005C2semidirect
12. #13114848C2semidirect
14. #13114711C2semidirect
35. #11718679C4semidirect
111. C4×Dic26C2×C4semidirect
125. #88050C2×C4semidirect
130. #88047C2×C4semidirect
133. #88043C2×C4semidirect
191. #6105C4⋊C4semidirect
545. C13#22678semidirect

Maximal subgroups

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

subgroupindex
C2×#117186792
C2×C4×#61052
C4⋊C4×Dic262
#131155712
#131155662
#131151032
#131150972
#131150892
#131150832
#131150052
#131148482
#131148362
#131147112
C13×#23492
#2267813