Finite Group Databasebeta

← #15899129

Subgroups — #15899129

Order 3328.

1012 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×#11719224C211yesmaximal, characteristic
2C2×#11718683C211yesmaximal, characteristic, complemented
3C2×#11718682C211yesmaximal, characteristic, complemented
4#13116174C211yesmaximal, characteristic, complemented
5#13116164C211yesmaximal, characteristic, complemented
6#13115987C211yesmaximal, characteristic, complemented
7#13115977C211yesmaximal, characteristic, complemented
8#13115793C211yesmaximal, characteristic, complemented
9#13115788C211yesmaximal, characteristic, complemented
10#13115149C211yesmaximal, characteristic
11#13115144C211yesmaximal, characteristic
12#13115033C211yesmaximal, characteristic
13#13115023C211yesmaximal, characteristic
14#13114820C211yesmaximal, characteristic
15C13×#2323C211yesmaximal, characteristic
16C2×C13×C22⋊Q8C2211yescharacteristic
17C2×C4×Q8×C13C2211yescharacteristic
18C2×C13×#117C2211yescharacteristic
19C2×#88180C2211yescharacteristic
20C22×C4⋊Dic13C2211yescharacteristic
21#11719224—24no—
22#11719224—24no—
23C2×#88144—21no—
24C2×#88142—21no—
25C2×#88132—21no—
26C2×#88132—21no—
27C2×#88124C2211yescharacteristic
28C2×#88124C2211yescharacteristic
29C2×#88123C2211yescharacteristic
30C2×#88123C2211yescharacteristic
31C13×#391C2211yescharacteristic
32C13×#389—21no—
33C13×#389C2211yescharacteristic
34C13×#388—21no—
35C13×#388—21no—
36C13×#387—21no—
37C13×#380C2211yescharacteristic
38C4×C13×C4⋊C4C2211yescharacteristic
39C2×#88075C2211yescharacteristic
40C2×#88075C2211yescharacteristic
41C2×#88075C2211yescharacteristic
42C2×#88075C2211yescharacteristic
43C2×C22⋊#1055C2211yescharacteristic
44C2×C22⋊#1055C2211yescharacteristic
45#11718683—24no—
46#11718682—24no—
47C2×#88048C2211yescharacteristic
48C2×#88047C2211yescharacteristic
49C2×#88047C2211yescharacteristic
50C2×#88047C2211yescharacteristic
51C2×C4⋊#1055C2211yescharacteristic
52C2×C4⋊#1055C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718121C2211yescharacteristic
60#11718121C2211yescharacteristic
61#11718116C2211yescharacteristic
62#11718116C2211yescharacteristic
63C22×Q8×C13C2311yescharacteristic
64C23×C4×C13C2311yescharacteristic
65C23×Dic13—21no—
66C22×Dic26—21no—
67C22×Dic26—21no—
68C13×C22⋊Q8—22no—
69C13×C22⋊Q8Q814yescomplemented
70C4×Q8×C13—22no—
71C4×Q8×C13—22no—
72C13×#117—22no—
73C13×#117—22no—
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×C13×C22⋊C4—21no—
83C2×C13×C22⋊C4—21no—
84C2×C13×C22⋊C4D411yescharacteristic
85C2×C13×C22⋊C4D411yescharacteristic
86C2×C42×C13—21no—
87C2×C42×C13—21no—
88C2×C42×C13C2311yescharacteristic
89C2×C42×C13C2311yescharacteristic
90C2×C22⋊Dic13—21no—
91#88180—22no—
92#88180—22no—
93C2×C4⋊Dic13—21no—
94C2×C4⋊Dic13—21no—
95C2×C4⋊Dic13—21no—
96C2×C4⋊Dic13—22no—
97C2×C4⋊Dic13—22no—
98C2×C4⋊Dic13C2311yescharacteristic
99C2×C4⋊Dic13C2311yescharacteristic
100C2×C4⋊Dic13C2311yescharacteristic
101C2×C4⋊Dic13C2311yescharacteristic
102C2×#6101—21no—
103C2×#6101—21no—
104C2×#6101—21no—
105C2×#6101—21no—
106C2×C4×Dic13—21no—
107C22×#1055C2311yescharacteristic
108C22×#1055C2311yescharacteristic
109C22×#1055C2311yescharacteristic
110C22×#1055C2311yescharacteristic
111#88144—28no—
112#88142—28no—
113#88132—28no—
114#88132—28no—
115#88124—22no—
116#88124—22no—
117#88124—22no—
118#88124D414yes—
119#88123—22no—
120#88123—22no—
121#88123—22no—
122#88123D414yes—
123C13×#95—21no—
124C13×#95—21no—
125C13×#95—21no—
126C13×#95—21no—
127C13×#95—21no—
128#88075—22no—
129#88075—22no—
130#88075—22no—
131#88075—22no—
132C22⋊#1055—22no—
133C22⋊#1055—22no—
134#88048—22no—
135#88047—22no—
136#88047—22no—
137#88047—22no—
138C4⋊#1055—22no—
139C4⋊#1055—22no—
140#24311—131nomaximal, Sylow
141C24×C13C2×D411yescharacteristic
142C2×Q8×C13—21no—
143C2×Q8×C13—21no—
144C2×Q8×C13—21no—
145C2×Q8×C13—21no—
146C2×Q8×C13—21no—
147C2×Q8×C13C2×Q812yes—
148C22×C4×C13—21no—
149C22×C4×C13—21no—
150C22×C4×C13—21no—
151C22×C4×C13—21no—
152C22×C4×C13—21no—
153C22×C4×C13—21no—
154C22×C4×C13—21no—
155C22×C4×C13—21no—
156C22×C4×C13C2×D411yescharacteristic
157C22×C4×C13C2×D411yescharacteristic
158C22×C4×C13C2×D411yescharacteristic
159C22×C4×C13C2×D411yescharacteristic
160C22×C4×C13C2×D411yescharacteristic
161C22×C4×C13C2×Q812yes—
162C22×C4×C13#4112yes—
163C22×C4×C13C2411yescharacteristic
164C22×Dic13—21no—
165C22×Dic13—21no—
166C22×Dic13—21no—
167C22×Dic13—21no—
168C22×Dic13—24no—
169C22×Dic13—81no—
170C22×Dic13—81no—
171C2×Dic26—24no—
172C2×Dic26—24no—
173C2×Dic26—81no—
174C2×Dic26—81no—
175C2×Dic26—81no—
176C2×Dic26—81no—
177C13×C4⋊C4—22no—
178C13×C4⋊C4—22no—
179C13×C4⋊C4—24no—
180C13×C4⋊C4—21no—
181C13×C4⋊C4—21no—
182C13×C4⋊C4—21no—
183C13×C4⋊C4—21no—
184C13×C4⋊C4—21no—
185C13×C4⋊C4—42no—
186C13×C4⋊C4—81no—
187C13×C4⋊C4C2×Q812yes—
188C13×C22⋊C4—24no—
189C13×C22⋊C4—22no—
190C13×C22⋊C4—22no—
191C13×C22⋊C4—81no—
192C42×C13—21no—
193C42×C13—21no—
194C42×C13—42no—
195C42×C13—81no—
196C42×C13C2×D412yes—
197C42×C13C2×D412yes—
198C22⋊Dic13—24no—
199C4⋊Dic13—24no—
200C4⋊Dic13—24no—
201C4⋊Dic13—24no—
202C4⋊Dic13—21no—
203C4⋊Dic13—21no—
204C4⋊Dic13—21no—
205C4⋊Dic13—21no—
206C4⋊Dic13C2×D412yes—
207C4⋊Dic13C2×D412yes—
208C4⋊Dic13C2×D412yes—
209C4⋊Dic13C2×D412yes—
210#6101—24no—
211#6101—24no—
212#6101—24no—
213#6101—24no—
214C4×Dic13—24no—
215C2×#1055—21no—
216C2×#1055—21no—
217C2×#1055—21no—
218C2×#1055—21no—
219C2×#1055—21no—
220C2×#1055—21no—
221C2×#1055—21no—
222C2×#1055—21no—
223C2×#1055—21no—
224C2×#1055—21no—
225C2×#1055—21no—
226C2×#1055—21no—
227C2×#544—131no—
228C2×#479—131no—
229C2×#477—131no—
230#2323D1311yescharacteristic
231#2059—131no—
232#2057—131no—
233#2026—131no—
234#2024—131no—
235#1989—131no—
236#1988—131no—
237#1873—131no—
238#1872—131no—
239#1854—131no—
240#1852—131no—
241#1798—131no—
242C23×C13—21no—
243C23×C13—21no—
244C23×C13—21no—
245C23×C13—21no—
246C23×C13—21no—
247C23×C13—21no—
248C23×C13C22⋊Q812yes—
249C23×C13C22×D411yescharacteristic
250Q8×C13—22no—
251Q8×C13—22no—
252Q8×C13—41no—
253Q8×C13—41no—
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—22no—
262C2×C4×C13—22no—
263C2×C4×C13—22no—
264C2×C4×C13—21no—
265C2×C4×C13—21no—
266C2×C4×C13—22no—
267C2×C4×C13—22no—
268C2×C4×C13—21no—
269C2×C4×C13—21no—
270C2×C4×C13—21no—
271C2×C4×C13—21no—
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×C13—41no—
280C2×C4×C13—41no—
281C2×C4×C13—41no—
282C2×C4×C13#12012yes—
283C2×C4×C13#12012yes—
284C2×C4×C13C22⋊Q812yes—
285C2×C4×C13C22×D411yescharacteristic
286C2×C4×C13C22×D411yescharacteristic
287C2×C4×C13C22×Q811yescharacteristic
288C2×C4×C13C2×#4111yescharacteristic
289C2×C4×C132−1+411yescharacteristic
290C2×C4×C132−1+411yescharacteristic
291C2×Dic13—22no—
292C2×Dic13—22no—
293C2×Dic13—22no—
294C2×Dic13—22no—
295C2×Dic13—41no—
296C2×Dic13—41no—
297C2×Dic13—41no—
298C2×Dic13—41no—
299C2×Dic13—41no—
300C2×Dic13—41no—
301C2×Dic13—41no—
302C2×Dic13—41no—
303C2×Dic13—84no—
304Dic26—84no—
305Dic26—84no—
306#1055—41no—
307#1055—41no—
308#1055—41no—
309#1055—41no—
310#544—264no—
311#544—264no—
312C2×C4⋊Q8—131no—
313C2×C4⋊Q8—131no—
314C2×C4⋊Q8—261no—
315C2×#125—131no—
316C2×#125—131no—
317C2×#125—261no—
318C2×C22⋊Q8—261no—
319C2×C22⋊Q8—261no—
320C2×C22⋊Q8C2×D1311yescharacteristic
321C2×C4×Q8C2×D1311yescharacteristic
322C2×#117—131no—
323C2×#117C2×D1311yescharacteristic
324C22×C4⋊C4—131no—
325#479—264no—
326#477—264no—
327C2×#107—131no—
328C2×#107—131no—
329C2×#107—131no—
330C2×#106—131no—
331C2×C4⋊C8—131no—
332C2×C4⋊C8—131no—
333C2×#103—131no—
334C2×#103—131no—
335C2×#103—131no—
336C2×#103—131no—
337C2×C22⋊C8—131no—
338C2×C22⋊C8—131no—
339#391C2×D1311yescharacteristic
340#389—21no—
341#389C2×D1311yescharacteristic
342#388—21no—
343#388—21no—
344#387—21no—
345#380C2×D1311yescharacteristic
346C4×C4⋊C4C2×D1311yescharacteristic
347#340—131no—
348#340—131no—
349#340—131no—
350#340—131no—
351#340—131no—
352#340—131no—
353#340—131no—
354#340—131no—
355#336—131no—
356#336—131no—
357C22×C13—22no—
358C22×C13—22no—
359C22×C13—22no—
360C22×C13—41no—
361C22×C13—41no—
362C22×C13—41no—
363C22×C13—41no—
364C22×C13C2×#12011yescharacteristic
365C22×C13C2×C22⋊Q811yescharacteristic
366C22×C13#53611yescharacteristic
367C22×C13#57611yescharacteristic
368C22×C13#57711yescharacteristic
369C22×C13#57811yescharacteristic
370C22×C13#57811yescharacteristic
371C4×C13—22no—
372C4×C13—22no—
373C4×C13—22no—
374C4×C13—42no—
375C4×C13—42no—
376C4×C13—41no—
377C4×C13—41no—
378C4×C13—81no—
379C4×C13—81no—
380C4×C13#54811yescharacteristic
381C4×C13#54811yescharacteristic
382C4×C13D4×Q811yescharacteristic
383C4×C13D4×Q811yescharacteristic
384Dic13—42no—
385Dic13—42no—
386Dic13—42no—
387Dic13—42no—
388C22×Q8—261no—
389C22×Q8—261no—
390C22×Q8C22×D1311yescharacteristic
391C23×C4—261no—
392C23×C4C22×D1311yescharacteristic
393C22×C8—131no—
394C22×C8—131no—
395C22×C8—131no—
396C22×C8—131no—
397C4⋊Q8—134no—
398C4⋊Q8—262no—
399C4⋊Q8—262no—
400C4⋊Q8—268no—
401C4⋊Q8—262no—
402#125—134no—
403#125—262no—
404#125—262no—
405#125—268no—
406#125—262no—
407C22⋊Q8—22no—
408C22⋊Q8—268no—
409C22⋊Q8—268no—
410C22⋊Q8Dic2614yescomplemented
411C4×Q8—22no—
412C4×Q8—22no—
413#117—22no—
414#117—22no—
415#117—262no—
416#117—262no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—131no—
421C2×C4⋊C4—131no—
422C2×C4⋊C4—131no—
423C2×C4⋊C4—131no—
424C2×C4⋊C4—262no—
425C2×C4⋊C4—262no—
426C2×C4⋊C4—261no—
427C2×C4⋊C4—261no—
428C2×C4⋊C4—261no—
429C2×C4⋊C4—261no—
430C2×C4⋊C4—261no—
431C2×C4⋊C4—261no—
432C2×C4⋊C4—261no—
433C2×C4⋊C4C22⋊D1311yescharacteristic
434C2×C4⋊C4C22⋊D1311yescharacteristic
435C2×C4⋊C4C22×D1311yescharacteristic
436C2×C4⋊C4C22×D1311yescharacteristic
437C2×C4⋊C4C22×D1311yescharacteristic
438C2×C22⋊C4—21no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4—261no—
441C2×C22⋊C4C22⋊D1311yescharacteristic
442C2×C22⋊C4C22⋊D1311yescharacteristic
443C2×C42—21no—
444C2×C42—21no—
445C2×C42—261no—
446C2×C42C22×D1311yescharacteristic
447C2×C42C22×D1311yescharacteristic
448#107—262no—
449#107—262no—
450#107—262no—
451#106—262no—
452C4⋊C8—262no—
453C4⋊C8—262no—
454#103—262no—
455#103—262no—
456#103—262no—
457#103—262no—
458C22⋊C8—262no—
459C22⋊C8—262no—
460#95—21no—
461#95—21no—
462#95—21no—
463#95—21no—
464#95—21no—
465C2×C13—42no—
466C2×C13#240911yescharacteristic
467C2×C13#301111yescharacteristic
468C2×C13#301211yescharacteristic
469C2×C13#308211yescharacteristic
470C2×C13#308311yescharacteristic
471C2×C13#324211yescharacteristic
472C2×C13#324311yescharacteristic
473C24C2×C22⋊D1311yescharacteristic
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—264no—
480C2×Q8—264no—
481C2×Q8—1041no—
482C2×Q8—1041no—
483C2×Q8—1041no—
484C2×Q8—1041no—
485C2×Q8C2×Dic2612yes—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—261no—
495C22×C4—261no—
496C22×C4—261no—
497C22×C4—261no—
498C22×C4—264no—
499C22×C4—1041no—
500C22×C4—1041no—
501C22×C4C2×Dic2612yes—
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
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—
519C2×C8—261no—
520C2×C8—261no—
521C4⋊C4—24no—
522C4⋊C4—22no—
523C4⋊C4—22no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—42no—
530C4⋊C4—81no—
531C4⋊C4—132no—
532C4⋊C4—132no—
533C4⋊C4—132no—
534C4⋊C4—132no—
535C4⋊C4—264no—
536C4⋊C4—264no—
537C4⋊C4—264no—
538C4⋊C4—264no—
539C4⋊C4—264no—
540C4⋊C4—264no—
541C4⋊C4—264no—
542C4⋊C4—261no—
543C4⋊C4—261no—
544C4⋊C4—261no—
545C4⋊C4—261no—
546C4⋊C4C2×Dic2612yes—
547C22⋊C4—24no—
548C22⋊C4—22no—
549C22⋊C4—22no—
550C22⋊C4—81no—
551C22⋊C4—264no—
552C42—21no—
553C42—21no—
554C42—42no—
555C42—81no—
556C42—264no—
557C42D4×D1312yes—
558C42D4×D1312yes—
559C13#2431111yescharacteristic, complemented, Sylow
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23#8817812yes—
567C23C22×C22⋊D1311yescharacteristic
568Q8—22no—
569Q8—22no—
570Q8—41no—
571Q8—41no—
572Q8—1044no—
573Q8—1044no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
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—41no—
602C2×C4—262no—
603C2×C4—262no—
604C2×C4—262no—
605C2×C4—262no—
606C2×C4—521no—
607C2×C4—521no—
608C2×C4—521no—
609C2×C4—521no—
610C2×C4—521no—
611C2×C4—521no—
612C2×C4—521no—
613C2×C4—521no—
614C2×C4—1044no—
615C2×C4#8817812yes—
616C2×C4#8819112yes—
617C2×C4#8819112yes—
618C2×C4C22×Dic2611yescharacteristic
619C2×C4C2×#612711yescharacteristic
620C2×C4C2×D4×D1311yescharacteristic
621C2×C4C2×D4×D1311yescharacteristic
622C2×C4#8825711yescharacteristic
623C2×C4#8825711yescharacteristic
624C8—521no—
625C8—521no—
626C8—521no—
627C8—521no—
628C22—22no—
629C22—22no—
630C22—22no—
631C22—41no—
632C22—41no—
633C22—41no—
634C22—41no—
635C22C2×#8817811yescharacteristic
636C22C2×#8819111yescharacteristic
637C22#1171953011yescharacteristic
638C22#1171954011yescharacteristic
639C22#1171954211yescharacteristic
640C22#1171954311yescharacteristic
641C22#1171954311yescharacteristic
642C4—22no—
643C4—22no—
644C4—22no—
645C4—41no—
646C4—41no—
647C4—42no—
648C4—42no—
649C4—81no—
650C4—81no—
651C4—522no—
652C4—522no—
653C4—522no—
654C4—522no—
655C4D4×Dic2611yescharacteristic
656C4D4×Dic2611yescharacteristic
657C4#1171925711yescharacteristic
658C4#1171925711yescharacteristic
659C2—42no—
660C2#1311820111yescharacteristic
661C2#1312412911yescharacteristic
662C2#1312413711yescharacteristic
663C2#1312467811yescharacteristic
664C2#1312468711yescharacteristic
665C2#1312609811yescharacteristic
666C2#1312611311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2323C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
hypercenter#2323D13
hypocenterC13#24311
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2323

Complements

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

NH ≅ G/Ntype
2. C2×#11718683C2semidirect
3. C2×#11718682C2semidirect
4. #13116174C2semidirect
5. #13116164C2semidirect
6. #13115987C2semidirect
7. #13115977C2semidirect
8. #13115793C2semidirect
9. #13115788C2semidirect
69. C13×C22⋊Q8Q8semidirect
410. C22⋊Q8Dic26semidirect
559. C13#24311semidirect

Maximal subgroups

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

subgroupindex
C2×#117192242
C2×#117186832
C2×#117186822
#131161742
#131161642
#131159872
#131159772
#131157932
#131157882
#131151492
#131151442
#131150332
#131150232
#131148202
C13×#23232
#2431113