Finite Group Databasebeta

← #15869629

Subgroups — #15869629

Order 3328.

1002 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718713C211yesmaximal, characteristic
2C2×#11718691C211yesmaximal, characteristic, complemented
3C2×C4×#6099C211yesmaximal, characteristic
4C4×#88178C211yesmaximal, characteristic
5#13115696C211yesmaximal, characteristic, complemented
6#13115561C211yesmaximal, characteristic, complemented
7#13115515C211yesmaximal, characteristic, complemented
8#13115511C211yesmaximal, characteristic, complemented
9#13115270C211yesmaximal, characteristic
10#13115267C211yesmaximal, characteristic
11#13114867C211yesmaximal, characteristic
12#13114734C211yesmaximal, characteristic, complemented
13#13114669C211yesmaximal, characteristic, complemented
14#13114666C211yesmaximal, characteristic, complemented
15C4×C13×C22⋊Q8C211yesmaximal, characteristic
16C2×C13×C22⋊Q8C2211yescharacteristic
17C2×C4×Q8×C13C2211yescharacteristic
18C22×C42×C13C2211yescharacteristic
19C22×#6107C2211yescharacteristic
20C2×#88178C2211yescharacteristic
21C22×#6099C2211yescharacteristic
22C22×#6099C2211yescharacteristic
23C2×C4×Dic26C2211yescharacteristic
24C13×#391C2211yescharacteristic
25C13×#389C2211yescharacteristic
26C13×#387—21no—
27C13×#385—21no—
28C13×#380C2211yescharacteristic
29C4×C13×C4⋊C4—21no—
30C4×C13×C4⋊C4C2211yescharacteristic
31C4×C13×C22⋊C4—21no—
32C2×#88075C2211yescharacteristic
33C2×#88075C2211yescharacteristic
34C2×#88075C2211yescharacteristic
35#11718873C2211yescharacteristic
36#11718871—21no—
37C4×C22⋊Dic13—21no—
38#11718713C418yescomplemented
39#11718691—24no—
40C2×#88050C2211yescharacteristic
41C2×#88050C2211yescharacteristic
42C2×#88050C2211yescharacteristic
43C2×#88048C2211yescharacteristic
44C2×#88048C2211yescharacteristic
45C2×#88047C2211yescharacteristic
46C4×C4⋊Dic13C2211yescharacteristic
47#11718594—21no—
48C4×#6101—21no—
49#11718590C2211yescharacteristic
50#11718589C2211yescharacteristic
51C4×#6099—24no—
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×C13D411yescharacteristic
64C23×C4×C13D411yescharacteristic
65C23×C4×C13C2311yescharacteristic
66C22×Dic26C2311yescharacteristic
67C13×C22⋊Q8—22no—
68C13×C22⋊Q8C2×C414yes—
69C4×Q8×C13—22no—
70C4×Q8×C13—22no—
71C2×C13×C4⋊C4—21no—
72C2×C13×C4⋊C4—21no—
73C2×C13×C4⋊C4—21no—
74C2×C13×C4⋊C4C2311yescharacteristic
75C2×C13×C4⋊C4C2311yescharacteristic
76C2×C13×C4⋊C4C2311yescharacteristic
77C2×C13×C22⋊C4—21no—
78C2×C13×C22⋊C4—21no—
79C2×C42×C13—22no—
80C2×C42×C13—22no—
81C2×C42×C13—21no—
82C2×C42×C13—21no—
83C2×C42×C13D411yescharacteristic
84C2×C42×C13D411yescharacteristic
85C2×C42×C13C2311yescharacteristic
86C2×C42×C13C2311yescharacteristic
87C2×C22⋊Dic13—21no—
88C2×C22⋊Dic13—21no—
89C2×#6107—22no—
90C2×#6107—22no—
91C2×#6107C2×C414yescomplemented
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—
105C2×#6099—22no—
106C2×#6099—22no—
107C2×#6099C2×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×C414yescomplemented
122#88071—21no—
123#88071—21no—
124#88071—21no—
125#88071—21no—
126#88071—21no—
127#88050—22no—
128#88050—22no—
129#88050C2×C414yescomplemented
130#88048—22no—
131#88048C2×C414yescomplemented
132#88047—22no—
133#88043—22no—
134#88043D414yes—
135C4×#1055—22no—
136C4×#1055—22no—
137#21539—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—22no—
152C22×C4×C13—22no—
153C22×C4×C13—22no—
154C22×C4×C13—22no—
155C22×C4×C13—21no—
156C22×C4×C13—21no—
157C22×C4×C13—41no—
158C22×C4×C13—41no—
159C22×C4×C13C22×C412yes—
160C22×C4×C13C2×D411yescharacteristic
161C22×C4×C13C2×D411yescharacteristic
162C22×C4×C13C2×D411yescharacteristic
163C22×C4×C13C2×D411yescharacteristic
164C22×C4×C13C2×D411yescharacteristic
165C22×C4×C13#4112yes—
166C22×C4×C13C2411yescharacteristic
167C22×Dic13—21no—
168C22×Dic13—21no—
169C22×Dic13—21no—
170C22×Dic13—21no—
171C2×Dic26—21no—
172C2×Dic26—21no—
173C2×Dic26—21no—
174C2×Dic26—21no—
175C2×Dic26—21no—
176C2×Dic26C22×C412yes—
177C13×C4⋊C4—24no—
178C13×C4⋊C4—21no—
179C13×C4⋊C4—21no—
180C13×C4⋊C4—21no—
181C13×C4⋊C4—21no—
182C13×C4⋊C4—21no—
183C13×C4⋊C4—42no—
184C13×C4⋊C4—42no—
185C13×C4⋊C4C22×C412yes—
186C13×C22⋊C4—24no—
187C13×C22⋊C4—42no—
188C42×C13—22no—
189C42×C13—22no—
190C42×C13—21no—
191C42×C13—21no—
192C42×C13—42no—
193C42×C13—42no—
194C42×C13C2×D412yes—
195C42×C13#4112yes—
196C22⋊Dic13—24no—
197C22⋊Dic13—42no—
198#6107—28no—
199C4⋊Dic13—21no—
200C4⋊Dic13—21no—
201C4⋊Dic13—21no—
202C4⋊Dic13—21no—
203C4⋊Dic13—21no—
204C4⋊Dic13C22×C412yes—
205#6101—24no—
206#6101—42no—
207#6101—42no—
208C4×Dic13—42no—
209C4×Dic13—42no—
210#6099—28no—
211#6099—28no—
212C2×#1055—21no—
213C2×#1055—21no—
214C2×#1055—21no—
215C2×#1055—21no—
216C2×#1055—21no—
217C2×#1055—21no—
218C2×#1055C22×C412yes—
219C2×#1055C22×C412yes—
220C2×#1055C2×D412yes—
221C2×#1055C2×D412yes—
222C2×#1055#4112yes—
223C2×#1055#4112yes—
224C2×#470—131no—
225C2×#441—131no—
226C2×C4×M16—131no—
227C4×C22⋊Q8—131no—
228C4×C22⋊Q8D1311yescharacteristic
229#1969—131no—
230#1941—131no—
231#1933—131no—
232#1933—131no—
233#1894—131no—
234#1894—131no—
235#1809—131no—
236#1776—131no—
237#1763—131no—
238#1763—131no—
239C23×C13—21no—
240C23×C13—21no—
241C23×C13—21no—
242C23×C13—21no—
243C23×C13—21no—
244C23×C13—21no—
245C23×C13C4×D412yes—
246C23×C13C22×D411yescharacteristic
247Q8×C13—22no—
248Q8×C13—22no—
249Q8×C13—41no—
250Q8×C13—41no—
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—22no—
262C2×C4×C13—22no—
263C2×C4×C13—22no—
264C2×C4×C13—22no—
265C2×C4×C13—22no—
266C2×C4×C13—22no—
267C2×C4×C13—44no—
268C2×C4×C13—44no—
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×C13C4×D412yes—
280C2×C4×C13#12112yes—
281C2×C4×C13#12112yes—
282C2×C4×C13#13712yes—
283C2×C4×C13#13712yes—
284C2×C4×C13C23×C411yescharacteristic
285C2×C4×C13C22×D411yescharacteristic
286C2×C4×C13C2×#4111yescharacteristic
287C2×C4×C13C2×#4111yescharacteristic
288C2×C4×C13C2×#4111yescharacteristic
289C2×C4×C13C2×#4111yescharacteristic
290C2×Dic13—22no—
291C2×Dic13—22no—
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—
301C2×Dic13—41no—
302Dic26—22no—
303Dic26—22no—
304Dic26—41no—
305Dic26—41no—
306#1055—22no—
307#1055—22no—
308#1055—22no—
309#1055C4×D414yes—
310C22×Q16—131no—
311C22×M16—131no—
312C22×M16—131no—
313C2×C22⋊Q8—131no—
314C2×C22⋊Q8C2×D1311yescharacteristic
315C2×C4×Q8—131no—
316C2×C4×Q8C2×D1311yescharacteristic
317C22×C42C2×D1311yescharacteristic
318#470—138no—
319#441—264no—
320C2×#107—131no—
321C2×#106—131no—
322C2×#106—131no—
323C2×#103—131no—
324C2×#103—131no—
325C2×#103—131no—
326C2×#103—131no—
327C2×#103—131no—
328C2×#103—131no—
329C4×M16—264no—
330C2×#97—131no—
331C2×#97—131no—
332C2×C4×C8—131no—
333C2×C4×C8—131no—
334#391—131no—
335#391C2×D1311yescharacteristic
336#389—131no—
337#389C2×D1311yescharacteristic
338#387—21no—
339#387—261no—
340#385—21no—
341#385—261no—
342#380—131no—
343#380C2×D1311yescharacteristic
344C4×C4⋊C4—21no—
345C4×C4⋊C4—131no—
346C4×C4⋊C4—261no—
347C4×C4⋊C4C2×D1311yescharacteristic
348C4×C22⋊C4—21no—
349C4×C22⋊C4—261no—
350#340—131no—
351#340—131no—
352#340—131no—
353#340—131no—
354#340—131no—
355#340—131no—
356C22×C13—22no—
357C22×C13—22no—
358C22×C13—22no—
359C22×C13—41no—
360C22×C13—41no—
361C22×C13—41no—
362C22×C13—41no—
363C22×C13C2×C4×D411yescharacteristic
364C22×C13C2×#12111yescharacteristic
365C22×C13#53211yescharacteristic
366C22×C13C2×#13711yescharacteristic
367C22×C13C2×#13711yescharacteristic
368C22×C13#57511yescharacteristic
369C22×C13#57511yescharacteristic
370C4×C13—22no—
371C4×C13—22no—
372C4×C13—22no—
373C4×C13—22no—
374C4×C13—22no—
375C4×C13—42no—
376C4×C13—42no—
377C4×C13—81no—
378C4×C13—81no—
379C4×C13C2×C4×D411yescharacteristic
380C4×C13C4×#4111yescharacteristic
381C4×C13#52511yescharacteristic
382C4×C13#52911yescharacteristic
383Dic13—42no—
384Dic13—42no—
385Dic13—81no—
386Dic13—81no—
387C22×Q8—131no—
388C22×Q8C22×D1311yescharacteristic
389C23×C4C22⋊D1311yescharacteristic
390C23×C4C22⋊D1311yescharacteristic
391C23×C4C22×D1311yescharacteristic
392C2×Q16—134no—
393C2×Q16—262no—
394C2×Q16—262no—
395C2×M16—134no—
396C2×M16—262no—
397C2×M16—262no—
398C2×M16—262no—
399C2×M16—262no—
400C2×M16—262no—
401C22×C8—131no—
402C22×C8—131no—
403C22×C8—131no—
404C22×C8—131no—
405C22⋊Q8—22no—
406C22⋊Q8—134no—
407C22⋊Q8—262no—
408C22⋊Q8C4×D1314yes—
409C4×Q8—22no—
410C4×Q8—22no—
411C4×Q8—262no—
412C4×Q8—262no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—131no—
417C2×C4⋊C4—131no—
418C2×C4⋊C4—131no—
419C2×C4⋊C4—261no—
420C2×C4⋊C4—261no—
421C2×C4⋊C4—261no—
422C2×C4⋊C4C22×D1311yescharacteristic
423C2×C4⋊C4C22×D1311yescharacteristic
424C2×C4⋊C4C22×D1311yescharacteristic
425C2×C22⋊C4—21no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—261no—
428C2×C22⋊C4—261no—
429C2×C42—22no—
430C2×C42—22no—
431C2×C42—21no—
432C2×C42—21no—
433C2×C42—261no—
434C2×C42—261no—
435C2×C42C22⋊D1311yescharacteristic
436C2×C42C22⋊D1311yescharacteristic
437C2×C42C22×D1311yescharacteristic
438C2×C42C22×D1311yescharacteristic
439#107—262no—
440#106—134no—
441#106—262no—
442#103—134no—
443#103—134no—
444#103—262no—
445#103—262no—
446#103—262no—
447#103—262no—
448#97—134no—
449#97—262no—
450C4×C8—262no—
451C4×C8—262no—
452#95—21no—
453#95—21no—
454#95—21no—
455#95—21no—
456#95—21no—
457#95—261no—
458#95—261no—
459#95—261no—
460#95—261no—
461#95—261no—
462C2×C13—42no—
463C2×C13C4×#12111yescharacteristic
464C2×C13C4×#13711yescharacteristic
465C2×C13C4×#13711yescharacteristic
466C2×C13#305611yescharacteristic
467C2×C13#305611yescharacteristic
468C2×C13#318311yescharacteristic
469C2×C13#318511yescharacteristic
470C24C2×C22⋊D1311yescharacteristic
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—132no—
477C2×Q8—261no—
478C2×Q8—261no—
479C2×Q8—261no—
480C2×Q8—261no—
481C2×Q8—261no—
482C2×Q8C2×C4×D1312yes—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—41no—
496C22×C4—41no—
497C22×C4—261no—
498C22×C4—261no—
499C22×C4—261no—
500C22×C4—261no—
501C22×C4C2×C4×D1312yes—
502C22×C4#612712yes—
503C22×C4C2×C22⋊D1311yescharacteristic
504C22×C4C2×C22⋊D1311yescharacteristic
505C22×C4C2×C22⋊D1311yescharacteristic
506C22×C4C2×C22⋊D1311yescharacteristic
507C22×C4C2×C22⋊D1311yescharacteristic
508C22×C4C23×D1311yescharacteristic
509Q16—268no—
510M16—268no—
511M16—268no—
512C2×C8—132no—
513C2×C8—132no—
514C2×C8—132no—
515C2×C8—132no—
516C2×C8—132no—
517C2×C8—132no—
518C2×C8—261no—
519C2×C8—261no—
520C2×C8—261no—
521C2×C8—261no—
522C2×C8—261no—
523C2×C8—261no—
524C4⋊C4—24no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—42no—
531C4⋊C4—42no—
532C4⋊C4—132no—
533C4⋊C4—264no—
534C4⋊C4—261no—
535C4⋊C4—261no—
536C4⋊C4—261no—
537C4⋊C4—261no—
538C4⋊C4—261no—
539C4⋊C4—522no—
540C4⋊C4—522no—
541C4⋊C4C2×C4×D1312yes—
542C22⋊C4—24no—
543C22⋊C4—42no—
544C22⋊C4—264no—
545C22⋊C4—522no—
546C42—22no—
547C42—22no—
548C42—21no—
549C42—21no—
550C42—42no—
551C42—42no—
552C42—522no—
553C42—522no—
554C42D4×D1312yes—
555C42#612912yes—
556C13#2153911yescharacteristic, complemented, Sylow
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23C4×C22⋊D1312yes—
564C23C22×C22⋊D1311yescharacteristic
565Q8—22no—
566Q8—22no—
567Q8—41no—
568Q8—41no—
569Q8—262no—
570Q8—262no—
571Q8—521no—
572Q8—521no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—44no—
590C2×C4—44no—
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—262no—
602C2×C4—262no—
603C2×C4—521no—
604C2×C4—521no—
605C2×C4—521no—
606C2×C4—521no—
607C2×C4—521no—
608C2×C4—521no—
609C2×C4—521no—
610C2×C4—521no—
611C2×C4—521no—
612C2×C4—521no—
613C2×C4C4×C22⋊D1312yes—
614C2×C4#8819312yes—
615C2×C4#8819312yes—
616C2×C4#8819612yes—
617C2×C4#8820512yes—
618C2×C4C22×C4×D1311yescharacteristic
619C2×C4C2×#612711yescharacteristic
620C2×C4C2×D4×D1311yescharacteristic
621C2×C4C2×#612911yescharacteristic
622C2×C4#41×D1311yescharacteristic
623C2×C4#41×D1311yescharacteristic
624C8—134no—
625C8—262no—
626C8—262no—
627C8—262no—
628C22—22no—
629C22—22no—
630C22—22no—
631C22—41no—
632C22—41no—
633C22—41no—
634C22—41no—
635C22C2×C4×C22⋊D1311yescharacteristic
636C22C2×#8819311yescharacteristic
637C22C2×#8819611yescharacteristic
638C22#1171952711yescharacteristic
639C22#1171952711yescharacteristic
640C22C2×#8820511yescharacteristic
641C22#1171953711yescharacteristic
642C4—22no—
643C4—22no—
644C4—22no—
645C4—22no—
646C4—22no—
647C4—42no—
648C4—42no—
649C4—81no—
650C4—81no—
651C4—522no—
652C4—522no—
653C4—1041no—
654C4—1041no—
655C4C4×#612911yescharacteristic
656C4#1171924311yescharacteristic
657C4C4×D4×D1311yescharacteristic
658C4#1171925211yescharacteristic
659C2—42no—
660C2C4×#8819311yescharacteristic
661C2C4×#8820511yescharacteristic
662C2C4×#8819611yescharacteristic
663C2#1312446211yescharacteristic
664C2#1312446811yescharacteristic
665C2#1312555911yescharacteristic
666C2#1312557711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC4×C13×C22⋊Q8C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
cosocleC22×C4×C13C24
hypercenterC4×C22⋊Q8D13
hypocenterC13#21539
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. C2×#11718691C2semidirect
5. #13115696C2semidirect
6. #13115561C2semidirect
7. #13115515C2semidirect
8. #13115511C2semidirect
12. #13114734C2semidirect
13. #13114669C2semidirect
14. #13114666C2semidirect
38. #11718713C4semidirect
91. C2×#6107C2×C4semidirect
121. #88075C2×C4semidirect
129. #88050C2×C4semidirect
131. #88048C2×C4semidirect
556. C13#21539semidirect

Maximal subgroups

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

subgroupindex
C2×#117187132
C2×#117186912
C2×C4×#60992
C4×#881782
#131156962
#131155612
#131155152
#131155112
#131152702
#131152672
#131148672
#131147342
#131146692
#131146662
C4×C13×C22⋊Q82
#2153913