Finite Group Databasebeta

← #15926035

Subgroups — #15926035

Order 3328.

828 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718683C211yesmaximal, characteristic, complemented
2C2×C4×#6106C211yesmaximal, characteristic
3#13118708C211yesmaximal, characteristic
4#13116365C211yesmaximal, characteristic
5#13116313C211yesmaximal, characteristic, complemented
6#13116221C211yesmaximal, characteristic
7#13116174C211yesmaximal, characteristic, complemented
8#13115566C211yesmaximal, characteristic, complemented
9#13115395C211yesmaximal, characteristic, complemented
10#13115191C211yesmaximal, characteristic
11#13115191C211yesmaximal, characteristic
12#13115096C211yesmaximal, characteristic
13#13115090C211yesmaximal, characteristic, complemented
14#13115090C211yesmaximal, characteristic, complemented
15Q8×C13×C4⋊C4C211yesmaximal, characteristic, complemented
16C2×C4×Q8×C13C2211yescharacteristic
17C2×C4×Q8×C13C2211yescharacteristic
18C2×C4×Q8×C13C2211yescharacteristic
19C22×#6106C2211yescharacteristic
20C2×C4×D52C2211yescharacteristic
21C2×#88124C2211yescharacteristic
22C13×#389—21no—
23C13×#389—21no—
24C13×#389C2211yescharacteristic
25C13×#389C2211yescharacteristic
26C13×#384—21no—
27C13×#384C2211yescharacteristic
28C4×C13×C4⋊C4—21no—
29C4×C13×C4⋊C4C2211yescharacteristic
30C2×#88075C2211yescharacteristic
31C2×#88075C2211yescharacteristic
32C2×#88075C2211yescharacteristic
33C4×#6106—24no—
34#11718683—24no—
35#11718653—21no—
36#11718650—21no—
37C2×#88049C2211yescharacteristic
38C2×#88049C2211yescharacteristic
39C2×#88049C2211yescharacteristic
40C2×#88048C2211yescharacteristic
41C2×#88048C2211yescharacteristic
42C2×#88047C2211yescharacteristic
43C2×#88047C2211yescharacteristic
44C2×#88047C2211yescharacteristic
45#11718600C2211yescharacteristic
46#11718600C2211yescharacteristic
47#11718589C2211yescharacteristic
48#11718589C2211yescharacteristic
49C2×C4⋊#1055C2211yescharacteristic
50C2×C4×#1055C2211yescharacteristic
51#11718337—21no—
52#11718328—21no—
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718116C2211yescharacteristic
58#11718116C2211yescharacteristic
59#11718116C2211yescharacteristic
60#11718116C2211yescharacteristic
61C22×Q8×C13C2311yescharacteristic
62C22×D52C2311yescharacteristic
63C22×C4×D13—21no—
64C4×Q8×C13—22no—
65C4×Q8×C13—22no—
66C4×Q8×C13—22no—
67C4×Q8×C13—22no—
68C4×Q8×C13—41no—
69C4×Q8×C13—41no—
70C2×C13×C4⋊C4—21no—
71C2×C13×C4⋊C4—21no—
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×#6106—22no—
89C2×#6106—22no—
90C2×#6106Q814yes—
91C2×#6103—21no—
92C2×#6103—21no—
93C2×#6103—21no—
94C2×#6103—21no—
95C2×#6103—21no—
96C2×C4⋊Dic13C2311yescharacteristic
97C2×C4⋊Dic13C2311yescharacteristic
98C2×C4⋊Dic13C2311yescharacteristic
99C2×#6101—21no—
100C2×#6101—21no—
101C2×#6101—21no—
102C2×#6101—21no—
103C22×#1055C2311yescharacteristic
104C22×#1055C2311yescharacteristic
105C22×#1055C2311yescharacteristic
106C22×#1055C2311yescharacteristic
107C4×D52—22no—
108C4×D52—41no—
109#88124—22no—
110#88124—41no—
111C13×#95—21no—
112C13×#95—21no—
113C13×#95D411yescharacteristic
114C13×#95D411yescharacteristic
115#88075—22no—
116#88075—22no—
117#88075D414yes—
118#88071—21no—
119#88071—21no—
120#88049—22no—
121#88049—22no—
122#88049—41no—
123#88048—22no—
124#88048—22no—
125#88047—22no—
126#88047—22no—
127#88047—41no—
128C4⋊#1055—22no—
129C4×#1055—22no—
130#26379—131nomaximal, Sylow
131C23×D13—21no—
132C2×Q8×C13—21no—
133C2×Q8×C13—21no—
134C2×Q8×C13—21no—
135C2×Q8×C13C2×D412yes—
136C2×Q8×C13C2×Q812yes—
137C2×Q8×C13#4112yes—
138C22×C4×C13—21no—
139C22×C4×C13—21no—
140C22×C4×C13—21no—
141C22×C4×C13—21no—
142C22×C4×C13C2×D411yescharacteristic
143C22×C4×C13C2×D411yescharacteristic
144C22×C4×C13C2×D411yescharacteristic
145C22×C4×C13C2×D411yescharacteristic
146C22×C4×C13C2×D411yescharacteristic
147C22×C4×C13C2×D411yescharacteristic
148C22×C4×C13C2411yescharacteristic
149C22×Dic13—21no—
150C22×Dic13—21no—
151C22×Dic13—21no—
152C2×D52—21no—
153C2×D52—21no—
154C2×D52—21no—
155C2×D52—21no—
156C2×D52—21no—
157C2×D52C2×Q812yes—
158C2×C4×D13—42no—
159C2×C4×D13—42no—
160C2×C4×D13—81no—
161C13×C4⋊C4—24no—
162C13×C4⋊C4—22no—
163C13×C4⋊C4—22no—
164C13×C4⋊C4—21no—
165C13×C4⋊C4—21no—
166C13×C4⋊C4—21no—
167C13×C4⋊C4—21no—
168C13×C4⋊C4—21no—
169C13×C4⋊C4—42no—
170C13×C4⋊C4—42no—
171C13×C4⋊C4—42no—
172C13×C4⋊C4—81no—
173C13×C4⋊C4—81no—
174C13×C4⋊C4—81no—
175C13×C4⋊C4#4112yes—
176C42×C13—24no—
177C42×C13—21no—
178C42×C13—21no—
179C42×C13—21no—
180C42×C13—21no—
181C42×C13—21no—
182C42×C13—21no—
183C42×C13—42no—
184C42×C13—42no—
185#6106—28no—
186#6103—42no—
187#6103—42no—
188#6103—81no—
189#6103—81no—
190#6103—81no—
191C4⋊Dic13—21no—
192C4⋊Dic13—21no—
193C4⋊Dic13—21no—
194C4⋊Dic13—21no—
195C4⋊Dic13—21no—
196C4⋊Dic13C2×D412yes—
197#6101—42no—
198#6101—42no—
199#6101—81no—
200#6101—81no—
201C2×#1055—21no—
202C2×#1055—21no—
203C2×#1055—21no—
204C2×#1055—21no—
205C2×#1055—21no—
206C2×#1055—21no—
207C2×#1055—21no—
208C2×#1055—21no—
209C2×#1055—21no—
210C2×#1055—21no—
211C2×#1055C2×D412yes—
212C2×#1055C2×Q812yes—
213C2×#479—131no—
214C2×C4×SD16—131no—
215#2454—131no—
216Q8×C4⋊C4D1311yescharacteristic, complemented
217#2093—131no—
218#2084—131no—
219#2067—131no—
220#2059—131no—
221#1942—131no—
222#1916—131no—
223#1880—131no—
224#1880—131no—
225#1864—131no—
226#1863—131no—
227#1863—131no—
228C23×C13C22×D411yescharacteristic
229C22×D13—22no—
230C22×D13—41no—
231C22×D13—41no—
232C22×D13—41no—
233C22×D13—41no—
234C22×D13—41no—
235C22×D13—41no—
236Q8×C13—22no—
237Q8×C13—22no—
238Q8×C13—22no—
239Q8×C13C22⋊Q814yes—
240C2×C4×C13—21no—
241C2×C4×C13—22no—
242C2×C4×C13—21no—
243C2×C4×C13—22no—
244C2×C4×C13—22no—
245C2×C4×C13—21no—
246C2×C4×C13—21no—
247C2×C4×C13—21no—
248C2×C4×C13—22no—
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—21no—
258C2×C4×C13—21no—
259C2×C4×C13—21no—
260C2×C4×C13—41no—
261C2×C4×C13—41no—
262C2×C4×C13—41no—
263C2×C4×C13—41no—
264C2×C4×C13—41no—
265C2×C4×C13—41no—
266C2×C4×C13—41no—
267C2×C4×C13—41no—
268C2×C4×C13#13512yes—
269C2×C4×C13#13712yes—
270C2×C4×C13C22×D411yescharacteristic
271C2×C4×C13C22×Q811yescharacteristic
272C2×C4×C13C2×#4111yescharacteristic
273C2×C4×C13C2×#4111yescharacteristic
274C2×C4×C13H(5,𝔽2)11yescharacteristic
275C2×C4×C132−1+411yescharacteristic
276C2×Dic13—22no—
277C2×Dic13—41no—
278C2×Dic13—41no—
279C2×Dic13—41no—
280C2×Dic13—41no—
281C2×Dic13—41no—
282C2×Dic13—41no—
283C2×Dic13—41no—
284C2×Dic13—41no—
285D52—22no—
286D52—22no—
287D52—41no—
288D52—41no—
289C4×D13—84no—
290#1055—22no—
291#1055—22no—
292#1055—41no—
293#1055—41no—
294C22×SD16—131no—
295C2×#125—131no—
296C2×C4×Q8C2×D1311yescharacteristic
297C2×C4×Q8C2×D1311yescharacteristic
298C2×C4×Q8C2×D1311yescharacteristic
299C2×C4×D4—131no—
300#479—264no—
301C4×SD16—264no—
302C2×#107—131no—
303C2×#107—131no—
304C2×#107—131no—
305C2×#106—131no—
306C2×#106—131no—
307C2×C4⋊C8—131no—
308C2×#103—131no—
309C2×#103—131no—
310C2×#103—131no—
311C2×#102—131no—
312C2×#102—131no—
313C2×#102—131no—
314C2×C4×C8—131no—
315#399—261no—
316#396—261no—
317#390—131no—
318#390—131no—
319#389—21no—
320#389—21no—
321#389—131no—
322#389—131no—
323#389C2×D1311yescharacteristic
324#389C2×D1311yescharacteristic
325#385—261no—
326#384—21no—
327#384C2×D1311yescharacteristic
328#380—261no—
329C4×C4⋊C4—21no—
330C4×C4⋊C4C2×D1311yescharacteristic
331#340—131no—
332#340—131no—
333#340—131no—
334#340—131no—
335#336—131no—
336#336—131no—
337#336—131no—
338#336—131no—
339C22×C13#52511yescharacteristic
340C22×C13D4211yescharacteristic
341C22×C13D4×Q811yescharacteristic
342C22×C13C2×#13511yescharacteristic
343C22×C13C2×#13711yescharacteristic
344C22×C13#57611yescharacteristic
345C22×C13#57711yescharacteristic
346C2×D13—42no—
347C2×D13—42no—
348C2×D13—42no—
349C2×D13—81no—
350C2×D13—81no—
351C2×D13—81no—
352C2×D13—81no—
353C4×C13—22no—
354C4×C13—24no—
355C4×C13—22no—
356C4×C13—41no—
357C4×C13—42no—
358C4×C13—41no—
359C4×C13—41no—
360C4×C13—41no—
361C4×C13—81no—
362C4×C13—81no—
363C4×C13C2×C22⋊Q811yescharacteristic
364C4×C13#53911yescharacteristic
365C4×C13#54711yescharacteristic
366C4×C13#55411yescharacteristic
367Dic13—42no—
368Dic13—81no—
369Dic13—81no—
370C22×Q8C22×D1311yescharacteristic
371C22×D4—131no—
372C23×C4—261no—
373C2×SD16—134no—
374C2×SD16—262no—
375C2×SD16—262no—
376C22×C8—131no—
377C22×C8—131no—
378C22×C8—131no—
379C22×C8—131no—
380#125—262no—
381#125—521no—
382C4×Q8—22no—
383C4×Q8—22no—
384C4×Q8—22no—
385C4×Q8—22no—
386C4×Q8—41no—
387C4×Q8—41no—
388C4×D4—262no—
389C4×D4—521no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—131no—
398C2×C4⋊C4—131no—
399C2×C4⋊C4—131no—
400C2×C4⋊C4—261no—
401C2×C4⋊C4—261no—
402C2×C4⋊C4—261no—
403C2×C4⋊C4—261no—
404C2×C4⋊C4C22⋊D1311yescharacteristic
405C2×C4⋊C4C22⋊D1311yescharacteristic
406C2×C4⋊C4C22×D1311yescharacteristic
407C2×C4⋊C4C22×D1311yescharacteristic
408C2×C4⋊C4C22×D1311yescharacteristic
409C2×C22⋊C4—261no—
410C2×C22⋊C4—261no—
411C2×C22⋊C4—261no—
412C2×C22⋊C4—261no—
413C2×C22⋊C4—261no—
414C2×C42—21no—
415C2×C42—21no—
416C2×C42—21no—
417C2×C42C22×D1311yescharacteristic
418C2×C42C22×D1311yescharacteristic
419C2×C42C22×D1311yescharacteristic
420#107—262no—
421#107—262no—
422#107—521no—
423#106—262no—
424#106—262no—
425C4⋊C8—262no—
426#103—134no—
427#103—262no—
428#103—262no—
429#102—262no—
430#102—262no—
431#102—521no—
432C4×C8—262no—
433#95—21no—
434#95—21no—
435#95—261no—
436#95—261no—
437#95C22⋊D1311yescharacteristic
438#95C22⋊D1311yescharacteristic
439C2×C13#244911yescharacteristic
440C2×C13#310811yescharacteristic
441C2×C13#311911yescharacteristic
442C2×C13#326611yescharacteristic
443C2×C13#328711yescharacteristic
444C2×C13#338111yescharacteristic
445C2×C13#338511yescharacteristic
446D13—82no—
447C24—261no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8#612712yes—
452C2×Q8D4×D1312yes—
453C2×Q8Q8×D1312yes—
454C2×D4—132no—
455C2×D4—261no—
456C2×D4—261no—
457C2×D4—261no—
458C2×D4—261no—
459C2×D4—261no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—261no—
465C22×C4—261no—
466C22×C4—261no—
467C22×C4—522no—
468C22×C4—522no—
469C22×C4—1041no—
470C22×C4C2×C22⋊D1311yescharacteristic
471C22×C4C2×C22⋊D1311yescharacteristic
472C22×C4C2×C22⋊D1311yescharacteristic
473C22×C4C2×C22⋊D1311yescharacteristic
474C22×C4C2×C22⋊D1311yescharacteristic
475C22×C4C2×C22⋊D1311yescharacteristic
476C22×C4C23×D1311yescharacteristic
477SD16—268no—
478C2×C8—132no—
479C2×C8—132no—
480C2×C8—261no—
481C2×C8—261no—
482C2×C8—261no—
483C2×C8—261no—
484C2×C8—261no—
485C2×C8—261no—
486C2×C8—261no—
487C2×C8—261no—
488C2×C8—261no—
489C2×C8—261no—
490C4⋊C4—24no—
491C4⋊C4—22no—
492C4⋊C4—22no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—42no—
499C4⋊C4—42no—
500C4⋊C4—42no—
501C4⋊C4—81no—
502C4⋊C4—81no—
503C4⋊C4—81no—
504C4⋊C4—132no—
505C4⋊C4—261no—
506C4⋊C4—261no—
507C4⋊C4—261no—
508C4⋊C4—261no—
509C4⋊C4—261no—
510C4⋊C4—522no—
511C4⋊C4—522no—
512C4⋊C4—1041no—
513C4⋊C4—1041no—
514C4⋊C4#612712yes—
515C22⋊C4—522no—
516C22⋊C4—522no—
517C22⋊C4—1041no—
518C22⋊C4—1041no—
519C22⋊C4—1041no—
520C42—24no—
521C42—21no—
522C42—21no—
523C42—21no—
524C42—21no—
525C42—21no—
526C42—21no—
527C42—42no—
528C42—42no—
529C13#2637911yescharacteristic, complemented, Sylow
530C23—262no—
531C23—521no—
532C23—521no—
533C23—521no—
534C23—521no—
535C23—521no—
536C23—521no—
537C23C22×C22⋊D1311yescharacteristic
538Q8—22no—
539Q8—22no—
540Q8—22no—
541Q8#8815014yes—
542D4—262no—
543D4—262no—
544D4—521no—
545D4—521no—
546C2×C4—21no—
547C2×C4—22no—
548C2×C4—21no—
549C2×C4—22no—
550C2×C4—21no—
551C2×C4—22no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—22no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—262no—
575C2×C4—521no—
576C2×C4—521no—
577C2×C4—521no—
578C2×C4—521no—
579C2×C4—521no—
580C2×C4—521no—
581C2×C4—521no—
582C2×C4—521no—
583C2×C4—1044no—
584C2×C4#8819612yes—
585C2×C4#8820412yes—
586C2×C4C2×#612711yescharacteristic
587C2×C4C2×#612711yescharacteristic
588C2×C4C2×D4×D1311yescharacteristic
589C2×C4#8825111yescharacteristic
590C2×C4C2×Q8×D1311yescharacteristic
591C2×C4#8825411yescharacteristic
592C8—262no—
593C8—262no—
594C8—521no—
595C8—521no—
596C22—522no—
597C22—522no—
598C22—522no—
599C22—1041no—
600C22—1041no—
601C22—1041no—
602C22—1041no—
603C22#1171949611yescharacteristic
604C22D4×C22⋊D1311yescharacteristic
605C22C2×#8819611yescharacteristic
606C22Q8×C22⋊D1311yescharacteristic
607C22C2×#8820411yescharacteristic
608C22#1171954011yescharacteristic
609C22#1171954211yescharacteristic
610C4—22no—
611C4—24no—
612C4—22no—
613C4—41no—
614C4—42no—
615C4—41no—
616C4—41no—
617C4—41no—
618C4—81no—
619C4—81no—
620C4—522no—
621C4—1041no—
622C4—1041no—
623C4#1171921211yescharacteristic
624C4C2×#8815011yescharacteristic
625C4#1171921611yescharacteristic
626C4#1171922011yescharacteristic
627C2—1042no—
628C2#1311864511yescharacteristic
629C2#1312491611yescharacteristic
630C2#1312503511yescharacteristic
631C2#1312634711yescharacteristic
632C2#1312659211yescharacteristic
633C2#1312770711yescharacteristic
634C2#1312774211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingQ8×C13×C4⋊C4C2
socleC23×C13C22×D4
prime radicalC22×D52C23
hypercenterQ8×C4⋊C4D13
hypocenterC13#26379
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ Q8×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#11718683C2semidirect
5. #13116313C2semidirect
7. #13116174C2semidirect
8. #13115566C2semidirect
9. #13115395C2semidirect
13. #13115090C2semidirect
14. #13115090C2semidirect
15. Q8×C13×C4⋊C4C2semidirect
216. Q8×C4⋊C4D13semidirect
529. C13#26379semidirect

Maximal subgroups

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

subgroupindex
C2×#117186832
C2×C4×#61062
#131187082
#131163652
#131163132
#131162212
#131161742
#131155662
#131153952
#131151912
#131150962
#131150902
Q8×C13×C4⋊C42
#2637913