Finite Group Databasebeta

← #15869318

Subgroups — #15869318

Order 3328.

1008 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×#11718680C211yesmaximal, characteristic
2C2×#11718679C211yesmaximal, characteristic
3C2×C4×#6105C211yesmaximal, characteristic
4#13117555C211yesmaximal, characteristic, complemented
5#13115759C211yesmaximal, characteristic, complemented
6#13115604C211yesmaximal, characteristic, complemented
7#13115477C211yesmaximal, characteristic, complemented
8#13115470C211yesmaximal, characteristic, complemented
9#13115170C211yesmaximal, characteristic
10#13115170C211yesmaximal, characteristic
11#13114846C211yesmaximal, characteristic
12#13114693C211yesmaximal, characteristic, complemented
13#13114669C211yesmaximal, characteristic, complemented
14C4×#88050C211yesmaximal, characteristic, complemented
15C13×#2275C211yesmaximal, characteristic
16C2×C4×D4×C13C2211yescharacteristic
17C2×C4×D4×C13C2211yescharacteristic
18C2×C4×D4×C13C2211yescharacteristic
19C22×#6105C2211yescharacteristic
20C22×#6105C2211yescharacteristic
21C2×#88123C2211yescharacteristic
22C2×C4×Dic26C2211yescharacteristic
23C2×C4×Dic26C2211yescharacteristic
24C4×C13×C4⋊C4C2211yescharacteristic
25C4×C13×C4⋊C4C2211yescharacteristic
26C4×C13×C4⋊C4C2211yescharacteristic
27C4×C13×C22⋊C4—21no—
28C4×C13×C22⋊C4—21no—
29C4×C13×C22⋊C4—21no—
30C13×#376C2211yescharacteristic
31C2×C13×#95—21no—
32C2×#88072C2211yescharacteristic
33C2×#88072C2211yescharacteristic
34#11718680C418yescomplemented
35#11718679—24no—
36C4×#6105—24no—
37C2×#88050C2211yescharacteristic
38C2×#88050C2211yescharacteristic
39C2×#88050C2211yescharacteristic
40C2×#88050C2211yescharacteristic
41C2×#88050C2211yescharacteristic
42C2×#88050C2211yescharacteristic
43C2×#88048C2211yescharacteristic
44C2×#88047C2211yescharacteristic
45#11718597C2211yescharacteristic
46#11718590C2211yescharacteristic
47#11718590C2211yescharacteristic
48C2×C4⋊#1055C2211yescharacteristic
49C2×C4⋊#1055C2211yescharacteristic
50C2×#88043C2211yescharacteristic
51C2×C4×#1055C2211yescharacteristic
52#11718314—21no—
53#11718314—21no—
54#11718314—21no—
55#11718314—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
67C22×Dic26C2311yescharacteristic
68C4×D4×C13—22no—
69C4×D4×C13—22no—
70C4×D4×C13—22no—
71C4×D4×C13—22no—
72C4×D4×C13C2×C414yes—
73C4×D4×C13D414yes—
74C2×C13×C4⋊C4C2311yescharacteristic
75C2×C13×C4⋊C4C2311yescharacteristic
76C2×C13×C4⋊C4C2311yescharacteristic
77C2×C13×C22⋊C4—21no—
78C2×C13×C22⋊C4—21no—
79C2×C13×C22⋊C4—21no—
80C2×C42×C13—21no—
81C2×C42×C13—21no—
82C2×C42×C13—21no—
83C2×C42×C13C2311yescharacteristic
84C2×C42×C13C2311yescharacteristic
85C2×C42×C13C2311yescharacteristic
86C2×#6105—22no—
87C2×#6105—22no—
88C2×#6105—22no—
89C2×#6105—22no—
90C2×#6105C2×C414yes—
91C2×#6105C2×C414yes—
92C2×C4⋊Dic13—21no—
93C2×C4⋊Dic13—21no—
94C2×C4⋊Dic13C2311yescharacteristic
95C2×C4⋊Dic13C2311yescharacteristic
96C2×#6101—21no—
97C2×#6101—21no—
98C2×C4×Dic13—21no—
99C2×C4×Dic13—21no—
100C22×#1055C2311yescharacteristic
101C22×#1055C2311yescharacteristic
102C22×#1055C2311yescharacteristic
103C22×#1055C2311yescharacteristic
104#88123—22no—
105#88123C2×C414yescomplemented
106C4×Dic26—22no—
107C4×Dic26—22no—
108C4×Dic26—22no—
109C4×Dic26—22no—
110C13×#95—21no—
111C13×#95—21no—
112C13×#95—21no—
113C13×#95D411yescharacteristic
114C13×#95D411yescharacteristic
115C13×#95D411yescharacteristic
116C13×#95D411yescharacteristic
117#88072—22no—
118#88072—22no—
119#88071—21no—
120#88071—21no—
121#88071—21no—
122#88071—21no—
123#88071—21no—
124#88071—21no—
125#88050—22no—
126#88050—22no—
127#88050—22no—
128#88050—22no—
129#88050C2×C414yescomplemented
130#88050C2×C414yescomplemented
131#88048—22no—
132#88047—22no—
133C4⋊#1055—22no—
134C4⋊#1055C2×C414yescomplemented
135#88043—22no—
136C4×#1055—22no—
137#21514—131nomaximal, Sylow
138C24×C13—21no—
139C2×D4×C13—21no—
140C2×D4×C13—21no—
141C2×D4×C13—21no—
142C2×D4×C13C22×C412yes—
143C2×D4×C13C2×D412yes—
144C2×D4×C13#4112yes—
145C22×C4×C13—21no—
146C22×C4×C13—21no—
147C22×C4×C13—21no—
148C22×C4×C13—24no—
149C22×C4×C13—24no—
150C22×C4×C13—24no—
151C22×C4×C13—81no—
152C22×C4×C13—81no—
153C22×C4×C13—81no—
154C22×C4×C13—81no—
155C22×C4×C13—81no—
156C22×C4×C13—81no—
157C22×C4×C13C2×D411yescharacteristic
158C22×C4×C13C2×D411yescharacteristic
159C22×C4×C13C2×D411yescharacteristic
160C22×C4×C13C2×D411yescharacteristic
161C22×C4×C13C2×D411yescharacteristic
162C22×C4×C13C2×D411yescharacteristic
163C22×C4×C13C2411yescharacteristic
164C22×Dic13—21no—
165C22×Dic13—21no—
166C22×Dic13—21no—
167C22×Dic13—21no—
168C2×Dic26—21no—
169C2×Dic26—21no—
170C2×Dic26—21no—
171C2×Dic26—21no—
172C2×Dic26—21no—
173C2×Dic26—21no—
174C2×Dic26—21no—
175C2×Dic26—21no—
176C2×Dic26—21no—
177C2×Dic26—21no—
178C2×Dic26C22×C412yes—
179C2×Dic26C22×C412yes—
180C13×C4⋊C4—21no—
181C13×C4⋊C4—21no—
182C13×C4⋊C4—21no—
183C13×C4⋊C4C22×C412yes—
184C13×C4⋊C4C2×D412yes—
185C13×C4⋊C4#4112yes—
186C13×C22⋊C4—24no—
187C13×C22⋊C4—24no—
188C13×C22⋊C4—24no—
189C42×C13—21no—
190C42×C13—21no—
191C42×C13—81no—
192C42×C13—81no—
193C42×C13—81no—
194C42×C13C22×C412yes—
195C42×C13C2×D412yes—
196C42×C13#4112yes—
197C42×C13#4112yes—
198#6105—28no—
199#6105—28no—
200C4⋊Dic13—24no—
201C4⋊Dic13—24no—
202C4⋊Dic13—21no—
203C4⋊Dic13—21no—
204C4⋊Dic13—21no—
205C4⋊Dic13—21no—
206#6101—42no—
207#6101—42no—
208C4×Dic13—42no—
209C4×Dic13—42no—
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×#1055—21no—
220C2×#1055C22×C412yes—
221C2×#1055C22×C412yes—
222C2×#461—131no—
223C2×#440—131no—
224C2×C4×SD16—131no—
225#2327—131no—
226#2275D1311yescharacteristic
227#1981—131no—
228#1949—131no—
229#1928—131no—
230#1927—131no—
231#1877—131no—
232#1877—131no—
233#1804—131no—
234#1768—131no—
235#1763—131no—
236C4×#103—131no—
237C23×C13—22no—
238C23×C13—22no—
239C23×C13—22no—
240C23×C13—41no—
241C23×C13—41no—
242C23×C13—41no—
243C23×C13—41no—
244C23×C13C22×D411yescharacteristic
245D4×C13—22no—
246D4×C13—22no—
247D4×C13—22no—
248D4×C13C4×D414yes—
249C2×C4×C13—21no—
250C2×C4×C13—21no—
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—22no—
258C2×C4×C13—22no—
259C2×C4×C13—21no—
260C2×C4×C13—21no—
261C2×C4×C13—22no—
262C2×C4×C13—21no—
263C2×C4×C13—21no—
264C2×C4×C13—21no—
265C2×C4×C13—21no—
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—84no—
273C2×C4×C13—84no—
274C2×C4×C13—84no—
275C2×C4×C13C4×D412yes—
276C2×C4×C13C4×D412yes—
277C2×C4×C13#12112yes—
278C2×C4×C13#12112yes—
279C2×C4×C13C23×C411yescharacteristic
280C2×C4×C13C22×D411yescharacteristic
281C2×C4×C13C2×#4111yescharacteristic
282C2×C4×C13C2×#4111yescharacteristic
283C2×C4×C13C2×#4111yescharacteristic
284C2×C4×C13C2×#4111yescharacteristic
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—
295C2×Dic13—41no—
296C2×Dic13—41no—
297Dic26—22no—
298Dic26—22no—
299Dic26—22no—
300Dic26—22no—
301Dic26—41no—
302Dic26—41no—
303Dic26—41no—
304Dic26—41no—
305#1055—22no—
306#1055—22no—
307#1055—41no—
308#1055—41no—
309C22×SD16—131no—
310C22×SD16—131no—
311C2×C4⋊Q8—131no—
312C2×C4×Q8—131no—
313C2×C4×Q8—131no—
314C2×C4×D4C2×D1311yescharacteristic
315C2×C4×D4C2×D1311yescharacteristic
316C2×C4×D4C2×D1311yescharacteristic
317#461—138no—
318#440—264no—
319C4×SD16—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×#103—131no—
330C2×#102—131no—
331C2×#102—131no—
332C2×#97—131no—
333C2×C4×C8—131no—
334#391—131no—
335#391—131no—
336#387—261no—
337#387—261no—
338#387—261no—
339#387—261no—
340#382—131no—
341C4×C4⋊C4C2×D1311yescharacteristic
342C4×C4⋊C4C2×D1311yescharacteristic
343C4×C4⋊C4C2×D1311yescharacteristic
344C4×C22⋊C4—21no—
345C4×C22⋊C4—21no—
346C4×C22⋊C4—21no—
347#376C2×D1311yescharacteristic
348C2×#95—21no—
349#340—131no—
350#340—131no—
351#340—131no—
352#340—131no—
353#336—131no—
354#336—131no—
355C22×C13—24no—
356C22×C13—42no—
357C22×C13—42no—
358C22×C13—42no—
359C22×C13—42no—
360C22×C13—42no—
361C22×C13—42no—
362C22×C13C2×C4×D411yescharacteristic
363C22×C13C2×#12111yescharacteristic
364C22×C13#52511yescharacteristic
365C22×C13#57711yescharacteristic
366C22×C13#57711yescharacteristic
367C22×C13#57711yescharacteristic
368C22×C13#57811yescharacteristic
369C4×C13—22no—
370C4×C13—22no—
371C4×C13—22no—
372C4×C13—22no—
373C4×C13—41no—
374C4×C13—41no—
375C4×C13—42no—
376C4×C13—42no—
377C4×C13—42no—
378C4×C13C2×C4×D411yescharacteristic
379C4×C13C4×#4111yescharacteristic
380C4×C13#52911yescharacteristic
381C4×C13#53211yescharacteristic
382Dic13—42no—
383Dic13—42no—
384Dic13—81no—
385Dic13—81no—
386C22×Q8—131no—
387C22×Q8—131no—
388C22×D4C22×D1311yescharacteristic
389C23×C4—21no—
390C23×C4—21no—
391C23×C4—21no—
392C2×SD16—134no—
393C2×SD16—134no—
394C2×SD16—262no—
395C2×SD16—262no—
396C2×SD16—262no—
397C2×SD16—262no—
398C22×C8—131no—
399C22×C8—131no—
400C22×C8—131no—
401C22×C8—131no—
402C4⋊Q8—134no—
403C4⋊Q8—262no—
404C4×Q8—262no—
405C4×Q8—262no—
406C4×Q8—262no—
407C4×Q8—262no—
408C4×D4—22no—
409C4×D4—22no—
410C4×D4—22no—
411C4×D4—22no—
412C4×D4C4×D1314yes—
413C4×D4D5214yes—
414C2×C4⋊C4—131no—
415C2×C4⋊C4—131no—
416C2×C4⋊C4—261no—
417C2×C4⋊C4—261no—
418C2×C4⋊C4—261no—
419C2×C4⋊C4—261no—
420C2×C4⋊C4C22×D1311yescharacteristic
421C2×C4⋊C4C22×D1311yescharacteristic
422C2×C4⋊C4C22×D1311yescharacteristic
423C2×C22⋊C4—21no—
424C2×C22⋊C4—21no—
425C2×C22⋊C4—21no—
426C2×C42—21no—
427C2×C42—21no—
428C2×C42—21no—
429C2×C42—261no—
430C2×C42—261no—
431C2×C42C22×D1311yescharacteristic
432C2×C42C22×D1311yescharacteristic
433C2×C42C22×D1311yescharacteristic
434#107—262no—
435#106—262no—
436C4⋊C8—134no—
437C4⋊C8—262no—
438#103—134no—
439#103—134no—
440#103—262no—
441#103—262no—
442#103—262no—
443#103—262no—
444#102—262no—
445#102—262no—
446#97—262no—
447C4×C8—262no—
448#95—21no—
449#95—21no—
450#95—21no—
451#95—261no—
452#95—261no—
453#95—261no—
454#95—261no—
455#95—261no—
456#95—261no—
457#95C22⋊D1311yescharacteristic
458#95C22⋊D1311yescharacteristic
459#95C22⋊D1311yescharacteristic
460#95C22⋊D1311yescharacteristic
461C2×C13—44no—
462C2×C13C4×#12111yescharacteristic
463C2×C13#294711yescharacteristic
464C2×C13#294911yescharacteristic
465C2×C13#304211yescharacteristic
466C2×C13#304611yescharacteristic
467C2×C13#312011yescharacteristic
468C2×C13#312311yescharacteristic
469C24—21no—
470C2×Q8—132no—
471C2×Q8—132no—
472C2×Q8—261no—
473C2×Q8—261no—
474C2×Q8—261no—
475C2×Q8—261no—
476C2×Q8—261no—
477C2×Q8—261no—
478C2×Q8—261no—
479C2×Q8—261no—
480C2×Q8—261no—
481C2×Q8—261no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4C2×C4×D1312yes—
486C2×D4C2×D5212yes—
487C2×D4#612712yes—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—24no—
492C22×C4—24no—
493C22×C4—24no—
494C22×C4—81no—
495C22×C4—81no—
496C22×C4—81no—
497C22×C4—81no—
498C22×C4—81no—
499C22×C4—81no—
500C22×C4—261no—
501C22×C4—261no—
502C22×C4—261no—
503C22×C4—261no—
504C22×C4C2×C22⋊D1311yescharacteristic
505C22×C4C2×C22⋊D1311yescharacteristic
506C22×C4C2×C22⋊D1311yescharacteristic
507C22×C4C2×C22⋊D1311yescharacteristic
508C22×C4C2×C22⋊D1311yescharacteristic
509C22×C4C2×C22⋊D1311yescharacteristic
510C22×C4C23×D1311yescharacteristic
511SD16—268no—
512SD16—268no—
513C2×C8—132no—
514C2×C8—132no—
515C2×C8—261no—
516C2×C8—261no—
517C2×C8—261no—
518C2×C8—261no—
519C2×C8—261no—
520C2×C8—261no—
521C2×C8—261no—
522C2×C8—261no—
523C2×C8—261no—
524C2×C8—261no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—264no—
529C4⋊C4—264no—
530C4⋊C4—261no—
531C4⋊C4—261no—
532C4⋊C4—261no—
533C4⋊C4—261no—
534C4⋊C4—522no—
535C4⋊C4—522no—
536C4⋊C4C2×C4×D1312yes—
537C4⋊C4C2×D5212yes—
538C4⋊C4#612712yes—
539C22⋊C4—24no—
540C22⋊C4—24no—
541C22⋊C4—24no—
542C42—21no—
543C42—21no—
544C42—81no—
545C42—81no—
546C42—81no—
547C42—522no—
548C42—522no—
549C42C2×C4×D1312yes—
550C42C2×D5212yes—
551C42#612712yes—
552C42#612712yes—
553C13#2151411yescharacteristic, complemented, Sylow
554C23—22no—
555C23—22no—
556C23—22no—
557C23—41no—
558C23—41no—
559C23—41no—
560C23—41no—
561C23C22×C22⋊D1311yescharacteristic
562Q8—262no—
563Q8—262no—
564Q8—262no—
565Q8—262no—
566Q8—521no—
567Q8—521no—
568Q8—521no—
569Q8—521no—
570D4—22no—
571D4—22no—
572D4—22no—
573D4C4×D5214yes—
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—22no—
583C2×C4—22no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—22no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—84no—
598C2×C4—84no—
599C2×C4—84no—
600C2×C4—262no—
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—521no—
611C2×C4—521no—
612C2×C4C4×C22⋊D1312yes—
613C2×C4C4×C22⋊D1312yes—
614C2×C4#8818412yes—
615C2×C4#8818412yes—
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—24no—
627C22—42no—
628C22—42no—
629C22—42no—
630C22—42no—
631C22—42no—
632C22—42no—
633C22C2×C4×C22⋊D1311yescharacteristic
634C22C2×#8818411yescharacteristic
635C22#1171949611yescharacteristic
636C22#1171954111yescharacteristic
637C22#1171954111yescharacteristic
638C22#1171954111yescharacteristic
639C22#1171954311yescharacteristic
640C4—22no—
641C4—22no—
642C4—22no—
643C4—22no—
644C4—42no—
645C4—41no—
646C4—41no—
647C4—42no—
648C4—42no—
649C4—522no—
650C4—522no—
651C4—1041no—
652C4—1041no—
653C4C2×C4×D5211yescharacteristic
654C4C4×#612711yescharacteristic
655C4#1171918211yescharacteristic
656C4#1171918411yescharacteristic
657C2—44no—
658C2C4×#8818411yescharacteristic
659C2#1312367511yescharacteristic
660C2#1312369311yescharacteristic
661C2#1312434811yescharacteristic
662C2#1312438611yescharacteristic
663C2#1312505011yescharacteristic
664C2#1312508811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#2275C2
socleC23×C13C22×D4
prime radicalC22×D4×C13C23
cosocleC22×C4×C13C24
hypercenter#2275D13
hypocenterC13#21514
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ #376 ◁ #2275

Complements

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

NH ≅ G/Ntype
4. #13117555C2semidirect
5. #13115759C2semidirect
6. #13115604C2semidirect
7. #13115477C2semidirect
8. #13115470C2semidirect
12. #13114693C2semidirect
13. #13114669C2semidirect
14. C4×#88050C2semidirect
34. #11718680C4semidirect
105. #88123C2×C4semidirect
129. #88050C2×C4semidirect
130. #88050C2×C4semidirect
134. C4⋊#1055C2×C4semidirect
553. C13#21514semidirect

Maximal subgroups

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

subgroupindex
C2×#117186802
C2×#117186792
C2×C4×#61052
#131175552
#131157592
#131156042
#131154772
#131154702
#131151702
#131148462
#131146932
#131146692
C4×#880502
C13×#22752
#2151413