Finite Group Databasebeta

← #15925975

Subgroups — #15925975

Order 3328.

820 conjugacy classes of subgroups.

The subgroup lattice has 632 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#13116360C211yesmaximal, characteristic
5#13116318C211yesmaximal, characteristic, complemented
6#13116207C211yesmaximal, characteristic
7#13116174C211yesmaximal, characteristic, complemented
8#13115561C211yesmaximal, characteristic, complemented
9#13115395C211yesmaximal, characteristic, complemented
10#13115191C211yesmaximal, characteristic
11#13115191C211yesmaximal, characteristic
12#13115104C211yesmaximal, characteristic, complemented
13#13115090C211yesmaximal, characteristic, complemented
14#13115082C211yesmaximal, characteristic
15C13×#2351C211yesmaximal, 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×#382—21no—
27C13×#382C2211yescharacteristic
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×#88048C2211yescharacteristic
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⋊C4D411yescharacteristic
76C2×C13×C4⋊C4D411yescharacteristic
77C2×C13×C4⋊C4C2311yescharacteristic
78C2×C13×C4⋊C4C2311yescharacteristic
79C2×C13×C4⋊C4C2311yescharacteristic
80C2×C42×C13—21no—
81C2×C42×C13—21no—
82C2×C42×C13—21no—
83C2×C42×C13C2311yescharacteristic
84C2×C42×C13C2311yescharacteristic
85C2×C42×C13C2311yescharacteristic
86C2×#6106—22no—
87C2×#6106—22no—
88C2×#6106Q814yes—
89C2×#6103—21no—
90C2×#6103—21no—
91C2×#6103—21no—
92C2×#6103—21no—
93C2×#6103—21no—
94C2×C4⋊Dic13C2311yescharacteristic
95C2×C4⋊Dic13C2311yescharacteristic
96C2×C4⋊Dic13C2311yescharacteristic
97C2×#6101—21no—
98C2×#6101—21no—
99C2×#6101—21no—
100C2×#6101—21no—
101C22×#1055C2311yescharacteristic
102C22×#1055C2311yescharacteristic
103C22×#1055C2311yescharacteristic
104C22×#1055C2311yescharacteristic
105C4×D52—22no—
106C4×D52—41no—
107#88124—22no—
108#88124—41no—
109C13×#95—21no—
110C13×#95—21no—
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#88048—22no—
126#88047—22no—
127#88047—41no—
128C4⋊#1055—22no—
129C4×#1055—22no—
130#26375—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—21no—
164C13×C4⋊C4—21no—
165C13×C4⋊C4—21no—
166C13×C4⋊C4—21no—
167C13×C4⋊C4—21no—
168C13×C4⋊C4—41no—
169C13×C4⋊C4—42no—
170C13×C4⋊C4—42no—
171C13×C4⋊C4—42no—
172C13×C4⋊C4—42no—
173C13×C4⋊C4#4112yes—
174C42×C13—24no—
175C42×C13—21no—
176C42×C13—21no—
177C42×C13—21no—
178C42×C13—21no—
179C42×C13—21no—
180C42×C13—21no—
181C42×C13—42no—
182C42×C13—42no—
183#6106—28no—
184#6103—42no—
185#6103—42no—
186#6103—81no—
187#6103—81no—
188#6103—81no—
189C4⋊Dic13—21no—
190C4⋊Dic13—21no—
191C4⋊Dic13—21no—
192C4⋊Dic13—21no—
193C4⋊Dic13—21no—
194C4⋊Dic13C2×D412yes—
195#6101—42no—
196#6101—42no—
197#6101—81no—
198#6101—81no—
199C2×#1055—21no—
200C2×#1055—21no—
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×#1055C2×D412yes—
210C2×#1055C2×Q812yes—
211C2×#479—131no—
212C2×C4×SD16—131no—
213#2454—131no—
214#2351D1311yescharacteristic, complemented
215#2092—131no—
216#2085—131no—
217#2065—131no—
218#2059—131no—
219#1941—131no—
220#1916—131no—
221#1880—131no—
222#1880—131no—
223#1865—131no—
224#1863—131no—
225#1862—131no—
226C23×C13C22×D411yescharacteristic
227C22×D13—22no—
228C22×D13—41no—
229C22×D13—41no—
230C22×D13—41no—
231C22×D13—41no—
232C22×D13—41no—
233C22×D13—41no—
234Q8×C13—22no—
235Q8×C13—22no—
236Q8×C13—22no—
237Q8×C13C22⋊Q814yes—
238C2×C4×C13—22no—
239C2×C4×C13—21no—
240C2×C4×C13—22no—
241C2×C4×C13—22no—
242C2×C4×C13—21no—
243C2×C4×C13—21no—
244C2×C4×C13—21no—
245C2×C4×C13—22no—
246C2×C4×C13—21no—
247C2×C4×C13—21no—
248C2×C4×C13—21no—
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—41no—
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#13512yes—
268C2×C4×C13C22×D411yescharacteristic
269C2×C4×C13C22×Q811yescharacteristic
270C2×C4×C13C2×#4111yescharacteristic
271C2×C4×C13C2×#4111yescharacteristic
272C2×C4×C13H(5,𝔽2)11yescharacteristic
273C2×C4×C132−1+411yescharacteristic
274C2×Dic13—22no—
275C2×Dic13—41no—
276C2×Dic13—41no—
277C2×Dic13—41no—
278C2×Dic13—41no—
279C2×Dic13—41no—
280C2×Dic13—41no—
281C2×Dic13—41no—
282C2×Dic13—41no—
283D52—22no—
284D52—22no—
285D52—41no—
286D52—41no—
287C4×D13—84no—
288#1055—22no—
289#1055—22no—
290#1055—41no—
291#1055—41no—
292C22×SD16—131no—
293C2×#125—131no—
294C2×C4×Q8C2×D1311yescharacteristic
295C2×C4×Q8C2×D1311yescharacteristic
296C2×C4×Q8C2×D1311yescharacteristic
297C2×C4×D4—131no—
298#479—264no—
299C4×SD16—264no—
300C2×#107—131no—
301C2×#107—131no—
302C2×#106—131no—
303C2×#106—131no—
304C2×#106—131no—
305C2×C4⋊C8—131no—
306C2×#103—131no—
307C2×#103—131no—
308C2×#103—131no—
309C2×#102—131no—
310C2×#102—131no—
311C2×#102—131no—
312C2×C4×C8—131no—
313#399—261no—
314#396—261no—
315#390—131no—
316#390—131no—
317#389—21no—
318#389—21no—
319#389—131no—
320#389—131no—
321#389C2×D1311yescharacteristic
322#389C2×D1311yescharacteristic
323#385—261no—
324#382—21no—
325#382C2×D1311yescharacteristic
326#380—261no—
327C4×C4⋊C4—21no—
328C4×C4⋊C4C2×D1311yescharacteristic
329#340—131no—
330#340—131no—
331#340—131no—
332#340—131no—
333#336—131no—
334#336—131no—
335#336—131no—
336#336—131no—
337C22×C13#52511yescharacteristic
338C22×C13D4211yescharacteristic
339C22×C13D4×Q811yescharacteristic
340C22×C13C2×#13511yescharacteristic
341C22×C13#57511yescharacteristic
342C22×C13#57711yescharacteristic
343C22×C13#57711yescharacteristic
344C2×D13—42no—
345C2×D13—42no—
346C2×D13—42no—
347C2×D13—81no—
348C2×D13—81no—
349C2×D13—81no—
350C2×D13—81no—
351C4×C13—24no—
352C4×C13—22no—
353C4×C13—41no—
354C4×C13—42no—
355C4×C13—41no—
356C4×C13—41no—
357C4×C13—41no—
358C4×C13—41no—
359C4×C13—81no—
360C4×C13—81no—
361C4×C13C2×C22⋊Q811yescharacteristic
362C4×C13#53911yescharacteristic
363C4×C13#54711yescharacteristic
364C4×C13#55411yescharacteristic
365Dic13—42no—
366Dic13—81no—
367Dic13—81no—
368C22×Q8C22×D1311yescharacteristic
369C22×D4—131no—
370C23×C4—261no—
371C2×SD16—134no—
372C2×SD16—262no—
373C2×SD16—262no—
374C22×C8—131no—
375C22×C8—131no—
376C22×C8—131no—
377C22×C8—131no—
378#125—262no—
379#125—521no—
380C4×Q8—22no—
381C4×Q8—22no—
382C4×Q8—22no—
383C4×Q8—22no—
384C4×Q8—41no—
385C4×Q8—41no—
386C4×D4—262no—
387C4×D4—521no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—131no—
394C2×C4⋊C4—131no—
395C2×C4⋊C4—131no—
396C2×C4⋊C4—261no—
397C2×C4⋊C4—261no—
398C2×C4⋊C4—261no—
399C2×C4⋊C4—261no—
400C2×C4⋊C4C22⋊D1311yescharacteristic
401C2×C4⋊C4C22⋊D1311yescharacteristic
402C2×C4⋊C4C22×D1311yescharacteristic
403C2×C4⋊C4C22×D1311yescharacteristic
404C2×C4⋊C4C22×D1311yescharacteristic
405C2×C22⋊C4—261no—
406C2×C22⋊C4—261no—
407C2×C22⋊C4—261no—
408C2×C22⋊C4—261no—
409C2×C22⋊C4—261no—
410C2×C42—21no—
411C2×C42—21no—
412C2×C42—21no—
413C2×C42C22×D1311yescharacteristic
414C2×C42C22×D1311yescharacteristic
415C2×C42C22×D1311yescharacteristic
416#107—262no—
417#107—521no—
418#106—262no—
419#106—262no—
420#106—262no—
421C4⋊C8—262no—
422#103—134no—
423#103—262no—
424#103—262no—
425#102—262no—
426#102—262no—
427#102—521no—
428C4×C8—262no—
429#95—21no—
430#95—21no—
431#95—21no—
432#95—21no—
433#95—261no—
434#95—261no—
435#95C22⋊D1311yescharacteristic
436#95C22⋊D1311yescharacteristic
437C2×C13#244911yescharacteristic
438C2×C13#310211yescharacteristic
439C2×C13#312611yescharacteristic
440C2×C13#327111yescharacteristic
441C2×C13#328211yescharacteristic
442C2×C13#338111yescharacteristic
443C2×C13#338811yescharacteristic
444D13—82no—
445C24—261no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8#612712yes—
450C2×Q8D4×D1312yes—
451C2×Q8Q8×D1312yes—
452C2×D4—132no—
453C2×D4—261no—
454C2×D4—261no—
455C2×D4—261no—
456C2×D4—261no—
457C2×D4—261no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—261no—
463C22×C4—261no—
464C22×C4—261no—
465C22×C4—522no—
466C22×C4—522no—
467C22×C4—1041no—
468C22×C4C2×C22⋊D1311yescharacteristic
469C22×C4C2×C22⋊D1311yescharacteristic
470C22×C4C2×C22⋊D1311yescharacteristic
471C22×C4C2×C22⋊D1311yescharacteristic
472C22×C4C2×C22⋊D1311yescharacteristic
473C22×C4C2×C22⋊D1311yescharacteristic
474C22×C4C23×D1311yescharacteristic
475SD16—268no—
476C2×C8—132no—
477C2×C8—132no—
478C2×C8—261no—
479C2×C8—261no—
480C2×C8—261no—
481C2×C8—261no—
482C2×C8—261no—
483C2×C8—261no—
484C2×C8—261no—
485C2×C8—261no—
486C2×C8—261no—
487C2×C8—261no—
488C4⋊C4—24no—
489C4⋊C4—22no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—41no—
496C4⋊C4—42no—
497C4⋊C4—42no—
498C4⋊C4—42no—
499C4⋊C4—42no—
500C4⋊C4—132no—
501C4⋊C4—261no—
502C4⋊C4—261no—
503C4⋊C4—261no—
504C4⋊C4—261no—
505C4⋊C4—261no—
506C4⋊C4—522no—
507C4⋊C4—522no—
508C4⋊C4—1041no—
509C4⋊C4—1041no—
510C4⋊C4#612712yes—
511C22⋊C4—522no—
512C22⋊C4—522no—
513C22⋊C4—1041no—
514C22⋊C4—1041no—
515C22⋊C4—1041no—
516C42—24no—
517C42—21no—
518C42—21no—
519C42—21no—
520C42—21no—
521C42—21no—
522C42—21no—
523C42—42no—
524C42—42no—
525C13#2637511yescharacteristic, complemented, Sylow
526C23—262no—
527C23—521no—
528C23—521no—
529C23—521no—
530C23—521no—
531C23—521no—
532C23—521no—
533C23C22×C22⋊D1311yescharacteristic
534Q8—22no—
535Q8—22no—
536Q8—22no—
537Q8#8815014yes—
538D4—262no—
539D4—262no—
540D4—521no—
541D4—521no—
542C2×C4—22no—
543C2×C4—21no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—22no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
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—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—262no—
572C2×C4—521no—
573C2×C4—521no—
574C2×C4—521no—
575C2×C4—521no—
576C2×C4—521no—
577C2×C4—521no—
578C2×C4—521no—
579C2×C4—521no—
580C2×C4—1044no—
581C2×C4#8820412yes—
582C2×C4C2×#612711yescharacteristic
583C2×C4C2×#612711yescharacteristic
584C2×C4C2×D4×D1311yescharacteristic
585C2×C4#8825111yescharacteristic
586C2×C4C2×Q8×D1311yescharacteristic
587C2×C4#8825411yescharacteristic
588C8—262no—
589C8—262no—
590C8—521no—
591C8—521no—
592C22—522no—
593C22—522no—
594C22—522no—
595C22—1041no—
596C22—1041no—
597C22—1041no—
598C22—1041no—
599C22#1171949611yescharacteristic
600C22D4×C22⋊D1311yescharacteristic
601C22Q8×C22⋊D1311yescharacteristic
602C22C2×#8820411yescharacteristic
603C22#1171952711yescharacteristic
604C22#1171954211yescharacteristic
605C22#1171954211yescharacteristic
606C4—22no—
607C4—24no—
608C4—41no—
609C4—41no—
610C4—41no—
611C4—41no—
612C4—41no—
613C4—42no—
614C4—81no—
615C4—81no—
616C4—522no—
617C4—1041no—
618C4—1041no—
619C4#1171921211yescharacteristic
620C4C2×#8815011yescharacteristic
621C4#1171921611yescharacteristic
622C4#1171922011yescharacteristic
623C2—1042no—
624C2#1311864511yescharacteristic
625C2#1312485411yescharacteristic
626C2#1312512711yescharacteristic
627C2#1312642211yescharacteristic
628C2#1312654411yescharacteristic
629C2#1312770711yescharacteristic
630C2#1312777511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2351C2
socleC23×C13C22×D4
prime radicalC22×D52C23
hypercenter#2351D13
hypocenterC13#26375
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2351

Complements

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

NH ≅ G/Ntype
1. C2×#11718683C2semidirect
5. #13116318C2semidirect
7. #13116174C2semidirect
8. #13115561C2semidirect
9. #13115395C2semidirect
12. #13115104C2semidirect
13. #13115090C2semidirect
15. C13×#2351C2semidirect
214. #2351D13semidirect
525. C13#26375semidirect

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
#131163602
#131163182
#131162072
#131161742
#131155612
#131153952
#131151912
#131151042
#131150902
#131150822
C13×#23512
#2637513