Finite Group Databasebeta

← #15885218

Subgroups — #15885218

Order 3328.

958 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718689C211yesmaximal, characteristic
2C2×C4×#6107C211yesmaximal, characteristic, complemented
3C2×C4×#6106C211yesmaximal, characteristic
4#13117905C211yesmaximal, characteristic
5#13115645C211yesmaximal, characteristic
6#13115602C211yesmaximal, characteristic, complemented
7#13115518C211yesmaximal, characteristic
8#13115511C211yesmaximal, characteristic, complemented
9#13115191C211yesmaximal, characteristic
10#13115177C211yesmaximal, characteristic, complemented
11#13115103C211yesmaximal, characteristic, complemented
12#13115082C211yesmaximal, characteristic
13C4⋊C4×#1055C211yesmaximal, characteristic, complemented
14C4×#88075C211yesmaximal, characteristic, complemented
15C13×#2351C211yesmaximal, characteristic, complemented
16C2×C4×Q8×C13C2211yescharacteristic
17C2×C4×Q8×C13C2211yescharacteristic
18C2×C4×Q8×C13C2211yescharacteristic
19C22×#6107C2211yescharacteristic
20C22×#6106C2211yescharacteristic
21C2×#88129C2211yescharacteristic
22C2×C4×D52C2211yescharacteristic
23C2×C4×Dic26C2211yescharacteristic
24C13×#389—21no—
25C13×#389—21no—
26C13×#389C2211yescharacteristic
27C13×#389C2211yescharacteristic
28C13×#382—21no—
29C13×#382C2211yescharacteristic
30C4×C13×C4⋊C4—21no—
31C4×C13×C4⋊C4C2211yescharacteristic
32C2×#88075C2211yescharacteristic
33C2×#88075C2211yescharacteristic
34C4×#6107—24no—
35#11718689C418yescomplemented
36C4×#6106—24no—
37#11718651—21no—
38#11718650—21no—
39C2×#88050C2211yescharacteristic
40C2×#88050C2211yescharacteristic
41C2×#88050C2211yescharacteristic
42C2×#88049C2211yescharacteristic
43C2×#88049C2211yescharacteristic
44C2×#88049C2211yescharacteristic
45C2×#88048C2211yescharacteristic
46C2×#88047C2211yescharacteristic
47#11718600C2211yescharacteristic
48C4×C4⋊Dic13C2211yescharacteristic
49#11718590C2211yescharacteristic
50C2×C4⋊#1055C2211yescharacteristic
51C2×C4×#1055C2211yescharacteristic
52C2×C4×#1055C2211yescharacteristic
53C2×C4×#1055C2211yescharacteristic
54#11718330—21no—
55#11718327—21no—
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718121C2211yescharacteristic
60#11718116C2211yescharacteristic
61#11718116C2211yescharacteristic
62C22×Q8×C13C2311yescharacteristic
63C22×D52C2311yescharacteristic
64C22×C4×D13—21no—
65C22×Dic26C2311yescharacteristic
66C4×Q8×C13—22no—
67C4×Q8×C13—22no—
68C4×Q8×C13—22no—
69C4×Q8×C13—41no—
70C4×Q8×C13—41no—
71C4×Q8×C13C2×C414yescomplemented
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⋊C4D411yescharacteristic
78C2×C13×C4⋊C4D411yescharacteristic
79C2×C13×C4⋊C4C2311yescharacteristic
80C2×C13×C4⋊C4C2311yescharacteristic
81C2×C13×C4⋊C4C2311yescharacteristic
82C2×C42×C13—21no—
83C2×C42×C13—21no—
84C2×C42×C13—21no—
85C2×C42×C13C2311yescharacteristic
86C2×C42×C13C2311yescharacteristic
87C2×C42×C13C2311yescharacteristic
88C2×#6107—22no—
89C2×#6107—22no—
90C2×#6107C2×C414yescomplemented
91C2×#6106—22no—
92C2×#6106—22no—
93C2×#6106C2×C414yes—
94C2×#6103—21no—
95C2×#6103—21no—
96C2×#6103—21no—
97C2×#6103—21no—
98C2×#6103—21no—
99C2×C4⋊Dic13C2311yescharacteristic
100C2×C4⋊Dic13C2311yescharacteristic
101C2×#6101—21no—
102C2×C4×Dic13—21no—
103C2×C4×Dic13—21no—
104C22×#1055C2311yescharacteristic
105C22×#1055C2311yescharacteristic
106C22×#1055C2311yescharacteristic
107C22×#1055C2311yescharacteristic
108#88129—22no—
109#88129C2×C414yes—
110C4×D52—22no—
111C4×D52—41no—
112C4×Dic26—22no—
113C4×Dic26—41no—
114C13×#95—21no—
115C13×#95—21no—
116C13×#95—21no—
117C13×#95—21no—
118C13×#95D411yescharacteristic
119C13×#95D411yescharacteristic
120#88075—22no—
121#88075D414yes—
122#88071—21no—
123#88071—21no—
124#88071—21no—
125#88050—22no—
126#88050—41no—
127#88050C2×C414yescomplemented
128#88049—22no—
129#88049—41no—
130#88049C2×C414yes—
131#88048—22no—
132#88047—22no—
133C4⋊#1055C2×C414yescomplemented
134C4×#1055—22no—
135C4×#1055—22no—
136C4×#1055—22no—
137#23000—131nomaximal, Sylow
138C23×D13—21no—
139C2×Q8×C13—21no—
140C2×Q8×C13—21no—
141C2×Q8×C13—21no—
142C2×Q8×C13C22×C412yes—
143C2×Q8×C13C2×D412yes—
144C2×Q8×C13#4112yes—
145C22×C4×C13—21no—
146C22×C4×C13—21no—
147C22×C4×C13—21no—
148C22×C4×C13—21no—
149C22×C4×C13C2×D411yescharacteristic
150C22×C4×C13C2×D411yescharacteristic
151C22×C4×C13C2×D411yescharacteristic
152C22×C4×C13C2×D411yescharacteristic
153C22×C4×C13C2×D411yescharacteristic
154C22×C4×C13C2×D411yescharacteristic
155C22×C4×C13C2411yescharacteristic
156C22×Dic13—21no—
157C22×Dic13—21no—
158C22×Dic13—21no—
159C2×D52—21no—
160C2×D52—21no—
161C2×D52—21no—
162C2×D52—21no—
163C2×D52—21no—
164C2×D52C22×C412yes—
165C2×C4×D13—42no—
166C2×C4×D13—42no—
167C2×C4×D13—81no—
168C2×Dic26—21no—
169C2×Dic26—21no—
170C2×Dic26—21no—
171C2×Dic26—21no—
172C2×Dic26—21no—
173C2×Dic26C22×C412yes—
174C13×C4⋊C4—24no—
175C13×C4⋊C4—22no—
176C13×C4⋊C4—22no—
177C13×C4⋊C4—21no—
178C13×C4⋊C4—21no—
179C13×C4⋊C4—21no—
180C13×C4⋊C4—21no—
181C13×C4⋊C4—21no—
182C13×C4⋊C4—42no—
183C13×C4⋊C4—42no—
184C13×C4⋊C4—42no—
185C13×C4⋊C4—42no—
186C13×C4⋊C4C22×C412yes—
187C42×C13—24no—
188C42×C13—21no—
189C42×C13—21no—
190C42×C13—21no—
191C42×C13—21no—
192C42×C13—42no—
193C42×C13—42no—
194C42×C13C22×C412yes—
195C42×C13#4112yes—
196#6107—28no—
197#6106—28no—
198#6103—24no—
199#6103—24no—
200#6103—42no—
201#6103—42no—
202#6103—81no—
203C4⋊Dic13—21no—
204C4⋊Dic13—21no—
205C4⋊Dic13—21no—
206C4⋊Dic13C2×D412yes—
207#6101—42no—
208C4×Dic13—42no—
209C4×Dic13—81no—
210C2×#1055—21no—
211C2×#1055—21no—
212C2×#1055—21no—
213C2×#1055—21no—
214C2×#1055—21no—
215C2×#1055—21no—
216C2×#1055—21no—
217C2×#1055—21no—
218C2×#1055—21no—
219C2×#1055C22×C412yes—
220C2×#1055C22×C412yes—
221C2×#1055C2×D412yes—
222C2×#464—131no—
223C2×C4×Q16—131no—
224C2×C4×SD16—131no—
225#2367—131no—
226#2351D1311yescharacteristic, complemented
227#1958—131no—
228#1949—131no—
229#1934—131no—
230#1933—131no—
231#1880—131no—
232#1878—131no—
233#1865—131no—
234#1862—131no—
235C8×C4⋊C4—131no—
236C4×#103—131no—
237C23×C13C22×D411yescharacteristic
238C22×D13—22no—
239C22×D13—41no—
240C22×D13—41no—
241C22×D13—41no—
242C22×D13—41no—
243C22×D13—41no—
244C22×D13—41no—
245Q8×C13—22no—
246Q8×C13—22no—
247Q8×C13—22no—
248Q8×C13C4×D414yes—
249C2×C4×C13—22no—
250C2×C4×C13—21no—
251C2×C4×C13—21no—
252C2×C4×C13—22no—
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—22no—
261C2×C4×C13—21no—
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×C13C4×D412yes—
276C2×C4×C13C4×D412yes—
277C2×C4×C13#13512yes—
278C2×C4×C13#13512yes—
279C2×C4×C13C23×C411yescharacteristic
280C2×C4×C13C22×D411yescharacteristic
281C2×C4×C13C2×#4111yescharacteristic
282C2×C4×C13C2×#4111yescharacteristic
283C2×C4×C13H(5,𝔽2)11yescharacteristic
284C2×C4×C132−1+411yescharacteristic
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—
294D52—22no—
295D52—22no—
296D52—41no—
297D52—41no—
298C4×D13—84no—
299Dic26—22no—
300Dic26—22no—
301Dic26—41no—
302Dic26—41no—
303#1055—22no—
304#1055—22no—
305#1055—22no—
306#1055—41no—
307C22×Q16—131no—
308C22×SD16—131no—
309C2×#124—131no—
310C2×C4×Q8—131no—
311C2×C4×Q8C2×D1311yescharacteristic
312C2×C4×Q8C2×D1311yescharacteristic
313C2×C4×Q8C2×D1311yescharacteristic
314C2×C4×D4—131no—
315#464—138no—
316C4×Q16—264no—
317C4×SD16—264no—
318C2×#107—131no—
319C2×#106—131no—
320C2×C4⋊C8—131no—
321C2×#103—131no—
322C2×#103—131no—
323C2×#103—131no—
324C2×#103—131no—
325C2×#103—131no—
326C2×#102—131no—
327C2×#102—131no—
328C2×#102—131no—
329C2×C4×C8—131no—
330C2×C4×C8—131no—
331C2×C4×C8—131no—
332#391—131no—
333#390—131no—
334#389—21no—
335#389—21no—
336#389C2×D1311yescharacteristic
337#389C2×D1311yescharacteristic
338#388—261no—
339#388—261no—
340#385—261no—
341#382—21no—
342#382C2×D1311yescharacteristic
343C4×C4⋊C4—21no—
344C4×C4⋊C4—131no—
345C4×C4⋊C4C2×D1311yescharacteristic
346C4×C22⋊C4—261no—
347#340—131no—
348#340—131no—
349#340—131no—
350#340—131no—
351#336—131no—
352#336—131no—
353C22×C13C2×C4×D411yescharacteristic
354C22×C13D4211yescharacteristic
355C22×C13#54811yescharacteristic
356C22×C13C2×#13511yescharacteristic
357C22×C13C2×#13511yescharacteristic
358C22×C13#57711yescharacteristic
359C22×C13#57811yescharacteristic
360C2×D13—42no—
361C2×D13—42no—
362C2×D13—42no—
363C2×D13—81no—
364C2×D13—81no—
365C2×D13—81no—
366C2×D13—81no—
367C4×C13—24no—
368C4×C13—22no—
369C4×C13—22no—
370C4×C13—22no—
371C4×C13—22no—
372C4×C13—42no—
373C4×C13—41no—
374C4×C13—41no—
375C4×C13—81no—
376C4×C13—81no—
377C4×C13C2×C4×D411yescharacteristic
378C4×C13#52011yescharacteristic
379C4×C13#54711yescharacteristic
380C4×C13#55311yescharacteristic
381Dic13—42no—
382Dic13—42no—
383Dic13—81no—
384C22×Q8—131no—
385C22×Q8C22×D1311yescharacteristic
386C22×D4—131no—
387C23×C4—261no—
388C2×Q16—134no—
389C2×Q16—262no—
390C2×Q16—262no—
391C2×SD16—134no—
392C2×SD16—262no—
393C2×SD16—262no—
394C22×C8—131no—
395C22×C8—131no—
396C22×C8—131no—
397C22×C8—131no—
398#124—134no—
399#124—262no—
400C4×Q8—22no—
401C4×Q8—22no—
402C4×Q8—22no—
403C4×Q8—41no—
404C4×Q8—41no—
405C4×Q8—262no—
406C4×Q8—521no—
407C4×Q8C4×D1314yescomplemented
408C4×D4—262no—
409C4×D4—521no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—131no—
416C2×C4⋊C4—131no—
417C2×C4⋊C4—261no—
418C2×C4⋊C4C22⋊D1311yescharacteristic
419C2×C4⋊C4C22⋊D1311yescharacteristic
420C2×C4⋊C4C22×D1311yescharacteristic
421C2×C4⋊C4C22×D1311yescharacteristic
422C2×C4⋊C4C22×D1311yescharacteristic
423C2×C22⋊C4—261no—
424C2×C22⋊C4—261no—
425C2×C22⋊C4—261no—
426C2×C22⋊C4—261no—
427C2×C22⋊C4—261no—
428C2×C42—21no—
429C2×C42—21no—
430C2×C42—21no—
431C2×C42—261no—
432C2×C42—261no—
433C2×C42C22×D1311yescharacteristic
434C2×C42C22×D1311yescharacteristic
435C2×C42C22×D1311yescharacteristic
436#107—262no—
437#106—262no—
438C4⋊C8—134no—
439#103—134no—
440#103—134no—
441#103—262no—
442#103—262no—
443#103—521no—
444#102—134no—
445#102—262no—
446#102—521no—
447C4×C8—262no—
448C4×C8—262no—
449C4×C8—262no—
450#95—21no—
451#95—21no—
452#95—21no—
453#95—21no—
454#95—261no—
455#95—261no—
456#95—261no—
457#95C22⋊D1311yescharacteristic
458#95C22⋊D1311yescharacteristic
459C2×C13#236111yescharacteristic
460C2×C13C4×#13511yescharacteristic
461C2×C13#294711yescharacteristic
462C2×C13#328211yescharacteristic
463C2×C13#328511yescharacteristic
464C2×C13#336411yescharacteristic
465C2×C13#336511yescharacteristic
466D13—82no—
467C24—261no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—132no—
472C2×Q8—261no—
473C2×Q8—261no—
474C2×Q8—261no—
475C2×Q8—261no—
476C2×Q8—261no—
477C2×Q8C2×C4×D1312yes—
478C2×Q8D4×D1312yes—
479C2×Q8#613112yes—
480C2×D4—132no—
481C2×D4—261no—
482C2×D4—261no—
483C2×D4—261no—
484C2×D4—261no—
485C2×D4—261no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—261no—
491C22×C4—261no—
492C22×C4—261no—
493C22×C4—522no—
494C22×C4—522no—
495C22×C4—1041no—
496C22×C4C2×C22⋊D1311yescharacteristic
497C22×C4C2×C22⋊D1311yescharacteristic
498C22×C4C2×C22⋊D1311yescharacteristic
499C22×C4C2×C22⋊D1311yescharacteristic
500C22×C4C2×C22⋊D1311yescharacteristic
501C22×C4C2×C22⋊D1311yescharacteristic
502C22×C4C23×D1311yescharacteristic
503Q16—268no—
504SD16—268no—
505C2×C8—132no—
506C2×C8—132no—
507C2×C8—132no—
508C2×C8—261no—
509C2×C8—261no—
510C2×C8—261no—
511C2×C8—261no—
512C2×C8—261no—
513C2×C8—261no—
514C2×C8—261no—
515C2×C8—261no—
516C2×C8—261no—
517C4⋊C4—24no—
518C4⋊C4—22no—
519C4⋊C4—22no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—42no—
526C4⋊C4—42no—
527C4⋊C4—42no—
528C4⋊C4—42no—
529C4⋊C4—132no—
530C4⋊C4—261no—
531C4⋊C4—261no—
532C4⋊C4—261no—
533C4⋊C4—522no—
534C4⋊C4C2×C4×D1312yes—
535C22⋊C4—264no—
536C22⋊C4—264no—
537C22⋊C4—522no—
538C22⋊C4—522no—
539C22⋊C4—1041no—
540C42—24no—
541C42—21no—
542C42—21no—
543C42—21no—
544C42—21no—
545C42—42no—
546C42—42no—
547C42—522no—
548C42—1041no—
549C42C2×C4×D1312yes—
550C42#612712yes—
551C13#2300011yescharacteristic, complemented, Sylow
552C23—262no—
553C23—521no—
554C23—521no—
555C23—521no—
556C23—521no—
557C23—521no—
558C23—521no—
559C23C22×C22⋊D1311yescharacteristic
560Q8—22no—
561Q8—22no—
562Q8—22no—
563Q8—262no—
564Q8—262no—
565Q8—521no—
566Q8—521no—
567Q8#8814714yes—
568D4—262no—
569D4—262no—
570D4—521no—
571D4—521no—
572C2×C4—22no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—22no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
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—262no—
599C2×C4—262no—
600C2×C4—521no—
601C2×C4—521no—
602C2×C4—521no—
603C2×C4—521no—
604C2×C4—521no—
605C2×C4—521no—
606C2×C4—521no—
607C2×C4—1044no—
608C2×C4C4×C22⋊D1312yes—
609C2×C4C4×C22⋊D1312yes—
610C2×C4#8820412yes—
611C2×C4#8820412yes—
612C2×C4C22×C4×D1311yescharacteristic
613C2×C4C2×#612711yescharacteristic
614C2×C4C2×D4×D1311yescharacteristic
615C2×C4#8825111yescharacteristic
616C2×C4C2×#613111yescharacteristic
617C2×C4#8825411yescharacteristic
618C8—262no—
619C8—262no—
620C8—262no—
621C8—521no—
622C22—522no—
623C22—522no—
624C22—522no—
625C22—1041no—
626C22—1041no—
627C22—1041no—
628C22—1041no—
629C22C2×C4×C22⋊D1311yescharacteristic
630C22D4×C22⋊D1311yescharacteristic
631C22#1171952211yescharacteristic
632C22C2×#8820411yescharacteristic
633C22C2×#8820411yescharacteristic
634C22#1171954211yescharacteristic
635C22#1171954311yescharacteristic
636C4—22no—
637C4—22no—
638C4—22no—
639C4—24no—
640C4—22no—
641C4—42no—
642C4—41no—
643C4—41no—
644C4—81no—
645C4—81no—
646C4—522no—
647C4—522no—
648C4—1041no—
649C4C2×#8814711yescharacteristic
650C4#1171920911yescharacteristic
651C4#1171921211yescharacteristic
652C4#1171921911yescharacteristic
653C2—1042no—
654C2#1311785211yescharacteristic
655C2C4×#8820411yescharacteristic
656C2#1312367911yescharacteristic
657C2#1312654411yescharacteristic
658C2#1312657311yescharacteristic
659C2#1312752111yescharacteristic
660C2#1312753211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#2351C2
socleC23×C13C22×D4
prime radicalC22×D52C23
cosocleC22×C4×C13C24
hypercenter#2351D13
hypocenterC13#23000
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2351

Complements

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

NH ≅ G/Ntype
2. C2×C4×#6107C2semidirect
6. #13115602C2semidirect
8. #13115511C2semidirect
10. #13115177C2semidirect
11. #13115103C2semidirect
13. C4⋊C4×#1055C2semidirect
14. C4×#88075C2semidirect
15. C13×#2351C2semidirect
35. #11718689C4semidirect
71. C4×Q8×C13C2×C4semidirect
90. C2×#6107C2×C4semidirect
127. #88050C2×C4semidirect
133. C4⋊#1055C2×C4semidirect
226. #2351D13semidirect
407. C4×Q8C4×D13semidirect
551. C13#23000semidirect

Maximal subgroups

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

subgroupindex
C2×#117186892
C2×C4×#61072
C2×C4×#61062
#131179052
#131156452
#131156022
#131155182
#131155112
#131151912
#131151772
#131151032
#131150822
C4⋊C4×#10552
C4×#880752
C13×#23512
#2300013