Finite Group Databasebeta

← #15869228

Subgroups — #15869228

Order 3328.

1004 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718689C211yesmaximal, characteristic
2C2×#11718691C211yesmaximal, characteristic, complemented
3C2×#11718687C211yesmaximal, characteristic
4C4×#88129C211yesmaximal, characteristic
5#13115768C211yesmaximal, characteristic
6#13115604C211yesmaximal, characteristic, complemented
7#13115477C211yesmaximal, characteristic, complemented
8#13115463C211yesmaximal, characteristic
9#13115191C211yesmaximal, characteristic
10#13115177C211yesmaximal, characteristic, complemented
11#13114851C211yesmaximal, characteristic, complemented
12#13114689C211yesmaximal, characteristic, complemented
13#13114669C211yesmaximal, characteristic, complemented
14#13114664C211yesmaximal, characteristic
15C42×Q8×C13C211yesmaximal, 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
24C4×C13×C4⋊C4—21no—
25C4×C13×C4⋊C4—21no—
26C4×C13×C4⋊C4—21no—
27C4×C13×C4⋊C4C2211yescharacteristic
28C4×C13×C4⋊C4C2211yescharacteristic
29C4×C13×C4⋊C4C2211yescharacteristic
30C43×C13—21no—
31C43×C13C2211yescharacteristic
32C2×#88075C2211yescharacteristic
33C2×#88075C2211yescharacteristic
34#11718691—24no—
35#11718689C418yescomplemented
36#11718687—24no—
37C2×#88050C2211yescharacteristic
38C2×#88050C2211yescharacteristic
39C2×#88050C2211yescharacteristic
40C2×#88049C2211yescharacteristic
41C2×#88049C2211yescharacteristic
42C2×#88049C2211yescharacteristic
43C2×#88048C2211yescharacteristic
44C2×#88047C2211yescharacteristic
45#11718601—21no—
46#11718601—21no—
47#11718600C2211yescharacteristic
48C4×#6103—21no—
49C4×#6103—21no—
50#11718597C2211yescharacteristic
51#11718590C2211yescharacteristic
52C2×C4⋊#1055C2211yescharacteristic
53C2×C4⋊#1055C2211yescharacteristic
54C2×#88043C2211yescharacteristic
55C2×#88043C2211yescharacteristic
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—22no—
70C4×Q8×C13C2×C414yescomplemented
71C4×Q8×C13D414yes—
72C2×C13×C4⋊C4—21no—
73C2×C13×C4⋊C4—21no—
74C2×C13×C4⋊C4—21no—
75C2×C13×C4⋊C4C2311yescharacteristic
76C2×C13×C4⋊C4C2311yescharacteristic
77C2×C13×C4⋊C4C2311yescharacteristic
78C2×C42×C13—21no—
79C2×C42×C13—21no—
80C2×C42×C13—21no—
81C2×C42×C13—21no—
82C2×C42×C13—21no—
83C2×C42×C13—21no—
84C2×C42×C13D411yescharacteristic
85C2×C42×C13D411yescharacteristic
86C2×C42×C13D411yescharacteristic
87C2×C42×C13D411yescharacteristic
88C2×C42×C13C2311yescharacteristic
89C2×C42×C13C2311yescharacteristic
90C2×C42×C13C2311yescharacteristic
91C2×#6107—22no—
92C2×#6107—22no—
93C2×#6107C2×C414yescomplemented
94C2×#6106—22no—
95C2×#6106—22no—
96C2×#6106C2×C414yes—
97C2×#6103—21no—
98C2×#6103—21no—
99C2×#6103—21no—
100C2×#6103—21no—
101C2×#6103—21no—
102C2×C4⋊Dic13C2311yescharacteristic
103C2×C4⋊Dic13C2311yescharacteristic
104C2×#6101—21no—
105C2×C4×Dic13—21no—
106C22×#1055C2311yescharacteristic
107C22×#1055C2311yescharacteristic
108C22×#1055C2311yescharacteristic
109C22×#1055C2311yescharacteristic
110#88129—22no—
111#88129C2×C414yes—
112C4×D52—22no—
113C4×D52—22no—
114C4×Dic26—22no—
115C4×Dic26—22no—
116C13×#95—21no—
117C13×#95—21no—
118C13×#95—21no—
119#88075—22no—
120#88075—22no—
121#88071—21no—
122#88071—21no—
123#88071—21no—
124#88071—21no—
125#88050—22no—
126#88050—22no—
127#88050C2×C414yescomplemented
128#88049—22no—
129#88049—22no—
130#88049C2×C414yes—
131#88048—22no—
132#88047—22no—
133C4⋊#1055—22no—
134C4⋊#1055C2×C414yescomplemented
135#88043—22no—
136#88043—22no—
137#21508—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—42no—
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—24no—
176C13×C4⋊C4—24no—
177C13×C4⋊C4—21no—
178C13×C4⋊C4—21no—
179C13×C4⋊C4—21no—
180C13×C4⋊C4C22×C412yes—
181C13×C4⋊C4C2×D412yes—
182C13×C4⋊C4#4112yes—
183C42×C13—24no—
184C42×C13—24no—
185C42×C13—24no—
186C42×C13—22no—
187C42×C13—21no—
188C42×C13—21no—
189C42×C13—41no—
190C42×C13—41no—
191C42×C13—41no—
192C42×C13—42no—
193C42×C13—42no—
194C42×C13—42no—
195C42×C13C22×C412yes—
196C42×C13C2×D412yes—
197C42×C13#4112yes—
198C42×C13#4112yes—
199#6107—28no—
200#6106—28no—
201#6103—24no—
202#6103—24no—
203#6103—42no—
204#6103—42no—
205#6103—42no—
206C4⋊Dic13—21no—
207C4⋊Dic13—21no—
208C4⋊Dic13—21no—
209C4⋊Dic13—21no—
210#6101—42no—
211C4×Dic13—42no—
212C2×#1055—21no—
213C2×#1055—21no—
214C2×#1055—21no—
215C2×#1055—21no—
216C2×#1055—21no—
217C2×#1055—21no—
218C2×#1055—21no—
219C2×#1055—21no—
220C2×#1055—21no—
221C2×#1055—21no—
222C2×#1055C22×C412yes—
223C2×#1055C22×C412yes—
224C2×#464—131no—
225C2×#441—131no—
226C2×#440—131no—
227C4×#124—131no—
228C42×Q8D1311yescharacteristic, complemented
229#1983—131no—
230#1949—131no—
231#1928—131no—
232#1926—131no—
233#1880—131no—
234#1878—131no—
235#1805—131no—
236#1767—131no—
237#1763—131no—
238#1762—131no—
239C23×C13C22×D411yescharacteristic
240C22×D13—22no—
241C22×D13—41no—
242C22×D13—41no—
243C22×D13—41no—
244C22×D13—41no—
245C22×D13—41no—
246C22×D13—41no—
247Q8×C13—22no—
248Q8×C13—22no—
249Q8×C13—22no—
250Q8×C13C4×D414yes—
251C2×C4×C13—22no—
252C2×C4×C13—22no—
253C2×C4×C13—21no—
254C2×C4×C13—22no—
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—21no—
264C2×C4×C13—22no—
265C2×C4×C13—22no—
266C2×C4×C13—21no—
267C2×C4×C13—22no—
268C2×C4×C13—21no—
269C2×C4×C13—21no—
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×C13C4×D412yes—
277C2×C4×C13C4×D412yes—
278C2×C4×C13#12112yes—
279C2×C4×C13#12112yes—
280C2×C4×C13#13712yes—
281C2×C4×C13C23×C411yescharacteristic
282C2×C4×C13C22×D411yescharacteristic
283C2×C4×C13C2×#4111yescharacteristic
284C2×C4×C13C2×#4111yescharacteristic
285C2×C4×C13C2×#4111yescharacteristic
286C2×C4×C13C2×#4111yescharacteristic
287C2×Dic13—22no—
288C2×Dic13—41no—
289C2×Dic13—41no—
290C2×Dic13—41no—
291C2×Dic13—41no—
292C2×Dic13—41no—
293C2×Dic13—41no—
294C2×Dic13—41no—
295C2×Dic13—41no—
296D52—22no—
297D52—22no—
298D52—41no—
299D52—41no—
300C4×D13—84no—
301Dic26—22no—
302Dic26—22no—
303Dic26—41no—
304Dic26—41no—
305#1055—22no—
306#1055—22no—
307#1055—41no—
308#1055—41no—
309C22×Q16—131no—
310C22×SD16—131no—
311C2×#124—131no—
312C2×C4×Q8—131no—
313C2×C4×Q8C2×D1311yescharacteristic
314C2×C4×Q8C2×D1311yescharacteristic
315C2×C4×Q8C2×D1311yescharacteristic
316C2×C4×D4—131no—
317#464—138no—
318#441—264no—
319#440—264no—
320C2×#107—131no—
321C2×#106—131no—
322C2×C4⋊C8—131no—
323C2×C4⋊C8—131no—
324C2×#103—131no—
325C2×#103—131no—
326C2×#103—131no—
327C2×#103—131no—
328C2×#103—131no—
329C2×#102—131no—
330C2×#102—131no—
331C2×#102—131no—
332C2×#97—131no—
333C2×#97—131no—
334#391—131no—
335#390—131no—
336#388—261no—
337#388—261no—
338#382—131no—
339C4×C4⋊C4—21no—
340C4×C4⋊C4—21no—
341C4×C4⋊C4—21no—
342C4×C4⋊C4C2×D1311yescharacteristic
343C4×C4⋊C4C2×D1311yescharacteristic
344C4×C4⋊C4C2×D1311yescharacteristic
345C4×C22⋊C4—261no—
346C4×C22⋊C4—261no—
347C43—21no—
348C43C2×D1311yescharacteristic
349#340—131no—
350#340—131no—
351#340—131no—
352#340—131no—
353#336—131no—
354#336—131no—
355C22×C13C2×C4×D411yescharacteristic
356C22×C13C2×#12111yescharacteristic
357C22×C13#52511yescharacteristic
358C22×C13C2×#13711yescharacteristic
359C22×C13#57511yescharacteristic
360C22×C13#57511yescharacteristic
361C22×C13#57511yescharacteristic
362C2×D13—42no—
363C2×D13—42no—
364C2×D13—42no—
365C2×D13—81no—
366C2×D13—81no—
367C2×D13—81no—
368C2×D13—81no—
369C4×C13—22no—
370C4×C13—22no—
371C4×C13—22no—
372C4×C13—22no—
373C4×C13—22no—
374C4×C13—24no—
375C4×C13—41no—
376C4×C13—42no—
377C4×C13—42no—
378C4×C13—42no—
379C4×C13C2×C4×D411yescharacteristic
380C4×C13C4×#4111yescharacteristic
381C4×C13#52911yescharacteristic
382C4×C13#53211yescharacteristic
383Dic13—42no—
384Dic13—81no—
385Dic13—81no—
386C22×Q8—131no—
387C22×Q8C22×D1311yescharacteristic
388C22×D4—131no—
389C23×C4—261no—
390C2×Q16—134no—
391C2×Q16—262no—
392C2×Q16—262no—
393C2×SD16—134no—
394C2×SD16—262no—
395C2×SD16—262no—
396C22×C8—131no—
397C22×C8—131no—
398C22×C8—131no—
399C22×C8—131no—
400#124—134no—
401#124—262no—
402C4×Q8—22no—
403C4×Q8—22no—
404C4×Q8—22no—
405C4×Q8—22no—
406C4×Q8—262no—
407C4×Q8—262no—
408C4×Q8C4×D1314yescomplemented
409C4×Q8D5214yes—
410C4×D4—262no—
411C4×D4—262no—
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×C22⋊C4—261no—
422C2×C22⋊C4—261no—
423C2×C22⋊C4—261no—
424C2×C22⋊C4—261no—
425C2×C22⋊C4—261no—
426C2×C42—21no—
427C2×C42—21no—
428C2×C42—21no—
429C2×C42—21no—
430C2×C42—21no—
431C2×C42—21no—
432C2×C42—261no—
433C2×C42C22⋊D1311yescharacteristic
434C2×C42C22⋊D1311yescharacteristic
435C2×C42C22⋊D1311yescharacteristic
436C2×C42C22⋊D1311yescharacteristic
437C2×C42C22×D1311yescharacteristic
438C2×C42C22×D1311yescharacteristic
439C2×C42C22×D1311yescharacteristic
440#107—262no—
441#106—262no—
442C4⋊C8—134no—
443C4⋊C8—262no—
444#103—134no—
445#103—262no—
446#103—262no—
447#103—262no—
448#103—262no—
449#102—134no—
450#102—262no—
451#102—262no—
452#97—262no—
453#97—262no—
454#95—21no—
455#95—21no—
456#95—21no—
457#95—261no—
458#95—261no—
459#95—261no—
460#95—261no—
461C2×C13C4×#12111yescharacteristic
462C2×C13#294311yescharacteristic
463C2×C13C4×#13711yescharacteristic
464C2×C13#303711yescharacteristic
465C2×C13#304011yescharacteristic
466C2×C13#311111yescharacteristic
467C2×C13#311711yescharacteristic
468D13—82no—
469C24—261no—
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—132no—
474C2×Q8—261no—
475C2×Q8—261no—
476C2×Q8—261no—
477C2×Q8—261no—
478C2×Q8—261no—
479C2×Q8C2×C4×D1312yes—
480C2×Q8C2×D5212yes—
481C2×Q8#612712yes—
482C2×D4—132no—
483C2×D4—261no—
484C2×D4—261no—
485C2×D4—261no—
486C2×D4—261no—
487C2×D4—261no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—261no—
493C22×C4—261no—
494C22×C4—261no—
495C22×C4—522no—
496C22×C4—522no—
497C22×C4—522no—
498C22×C4C2×C22⋊D1311yescharacteristic
499C22×C4C2×C22⋊D1311yescharacteristic
500C22×C4C2×C22⋊D1311yescharacteristic
501C22×C4C2×C22⋊D1311yescharacteristic
502C22×C4C2×C22⋊D1311yescharacteristic
503C22×C4C2×C22⋊D1311yescharacteristic
504C22×C4C23×D1311yescharacteristic
505Q16—268no—
506SD16—268no—
507C2×C8—132no—
508C2×C8—132no—
509C2×C8—261no—
510C2×C8—261no—
511C2×C8—261no—
512C2×C8—261no—
513C2×C8—261no—
514C2×C8—261no—
515C2×C8—261no—
516C2×C8—261no—
517C2×C8—261no—
518C2×C8—261no—
519C4⋊C4—24no—
520C4⋊C4—24no—
521C4⋊C4—24no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—261no—
526C4⋊C4—261no—
527C4⋊C4—261no—
528C4⋊C4—261no—
529C4⋊C4—522no—
530C4⋊C4C2×C4×D1312yes—
531C4⋊C4C2×D5212yes—
532C4⋊C4#612712yes—
533C22⋊C4—264no—
534C22⋊C4—264no—
535C22⋊C4—522no—
536C22⋊C4—522no—
537C22⋊C4—522no—
538C42—24no—
539C42—24no—
540C42—24no—
541C42—22no—
542C42—21no—
543C42—21no—
544C42—41no—
545C42—41no—
546C42—41no—
547C42—42no—
548C42—42no—
549C42—42no—
550C42—522no—
551C42C2×C4×D1312yes—
552C42C2×D5212yes—
553C42#612712yes—
554C42#612712yes—
555C13#2150811yescharacteristic, complemented, Sylow
556C23—262no—
557C23—521no—
558C23—521no—
559C23—521no—
560C23—521no—
561C23—521no—
562C23—521no—
563C23C22×C22⋊D1311yescharacteristic
564Q8—22no—
565Q8—22no—
566Q8—22no—
567Q8—262no—
568Q8—262no—
569Q8—521no—
570Q8—521no—
571Q8C4×D5214yes—
572D4—262no—
573D4—262no—
574D4—521no—
575D4—521no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—21no—
579C2×C4—22no—
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—22no—
590C2×C4—22no—
591C2×C4—21no—
592C2×C4—22no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—262no—
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—1044no—
611C2×C4C4×C22⋊D1312yes—
612C2×C4C4×C22⋊D1312yes—
613C2×C4#8818412yes—
614C2×C4#8818412yes—
615C2×C4#8819612yes—
616C2×C4C22×C4×D1311yescharacteristic
617C2×C4C22×D5211yescharacteristic
618C2×C4C2×#612711yescharacteristic
619C2×C4C2×#612711yescharacteristic
620C2×C4C2×#612711yescharacteristic
621C2×C4C2×#612711yescharacteristic
622C8—262no—
623C8—262no—
624C8—521no—
625C8—521no—
626C22—522no—
627C22—522no—
628C22—522no—
629C22—1041no—
630C22—1041no—
631C22—1041no—
632C22—1041no—
633C22C2×C4×C22⋊D1311yescharacteristic
634C22C2×#8818411yescharacteristic
635C22#1171949611yescharacteristic
636C22C2×#8819611yescharacteristic
637C22#1171952711yescharacteristic
638C22#1171952711yescharacteristic
639C22#1171952711yescharacteristic
640C4—22no—
641C4—22no—
642C4—22no—
643C4—24no—
644C4—22no—
645C4—22no—
646C4—42no—
647C4—41no—
648C4—42no—
649C4—42no—
650C4—522no—
651C4—1041no—
652C4—1041no—
653C4C2×C4×D5211yescharacteristic
654C4C4×#612711yescharacteristic
655C4#1171918211yescharacteristic
656C4#1171918411yescharacteristic
657C2—1042no—
658C2C4×#8818411yescharacteristic
659C2#1312363411yescharacteristic
660C2C4×#8819611yescharacteristic
661C2#1312430811yescharacteristic
662C2#1312433011yescharacteristic
663C2#1312494511yescharacteristic
664C2#1312500711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC42×Q8×C13C2
socleC23×C13C22×D4
prime radicalC22×D52C23
cosocleC22×C4×C13C24
hypercenterC42×Q8D13
hypocenterC13#21508
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C43 ◁ C42×Q8

Complements

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

NH ≅ G/Ntype
2. C2×#11718691C2semidirect
6. #13115604C2semidirect
7. #13115477C2semidirect
10. #13115177C2semidirect
11. #13114851C2semidirect
12. #13114689C2semidirect
13. #13114669C2semidirect
15. C42×Q8×C13C2semidirect
35. #11718689C4semidirect
70. C4×Q8×C13C2×C4semidirect
93. C2×#6107C2×C4semidirect
127. #88050C2×C4semidirect
134. C4⋊#1055C2×C4semidirect
228. C42×Q8D13semidirect
408. C4×Q8C4×D13semidirect
555. C13#21508semidirect

Maximal subgroups

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

subgroupindex
C2×#117186892
C2×#117186912
C2×#117186872
C4×#881292
#131157682
#131156042
#131154772
#131154632
#131151912
#131151772
#131148512
#131146892
#131146692
#131146642
C42×Q8×C132
#2150813