Finite Group Databasebeta

← #15925549

Subgroups — #15925549

Order 3328.

858 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718670C211yesmaximal, characteristic, complemented
2C2×#11718659C211yesmaximal, characteristic, complemented
3#13118549C211yesmaximal, characteristic, complemented
4#13116364C211yesmaximal, characteristic, complemented
5#13116327C211yesmaximal, characteristic, complemented
6#13116210C211yesmaximal, characteristic, complemented
7#13116174C211yesmaximal, characteristic, complemented
8#13115599C211yesmaximal, characteristic, complemented
9#13115428C211yesmaximal, characteristic, complemented
10#13115265C211yesmaximal, characteristic
11#13115159C211yesmaximal, characteristic
12#13115097C211yesmaximal, characteristic, complemented
13#13115035C211yesmaximal, characteristic, complemented
14#13115016C211yesmaximal, characteristic, complemented
15C13×#2363C211yesmaximal, characteristic
16C2×C13×#121C2211yescharacteristic
17C2×C4×D4×C13C2211yescharacteristic
18C2×C13×#117C2211yescharacteristic
19C2×#88180C2211yescharacteristic
20C23×#1055C2211yescharacteristic
21C2×#88124C2211yescharacteristic
22C13×#390—21no—
23C13×#390C2211yescharacteristic
24C13×#389C2211yescharacteristic
25C13×#388—21no—
26C13×#386—21no—
27C4×C13×C4⋊C4C2211yescharacteristic
28C4×C13×C22⋊C4—21no—
29C4×C13×C22⋊C4C2211yescharacteristic
30C2×#88072C2211yescharacteristic
31C2×#88072C2211yescharacteristic
32C2×#88072C2211yescharacteristic
33C2×#88072C2211yescharacteristic
34#11718873C2211yescharacteristic
35C2×C22⋊#1055C2211yescharacteristic
36#11718670—24no—
37#11718659—24no—
38C2×#88048C2211yescharacteristic
39C2×#88048C2211yescharacteristic
40C2×#88048C2211yescharacteristic
41C2×#88047C2211yescharacteristic
42C2×#88047C2211yescharacteristic
43C2×#88047C2211yescharacteristic
44#11718610—21no—
45#11718609—21no—
46#11718596C2211yescharacteristic
47#11718589C2211yescharacteristic
48#11718589C2211yescharacteristic
49C2×C4⋊#1055C2211yescharacteristic
50C2×C4⋊#1055C2211yescharacteristic
51#11718315—21no—
52#11718308—21no—
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718116C2211yescharacteristic
60#11718116C2211yescharacteristic
61C22×D4×C13—21no—
62C22×D4×C13C2311yescharacteristic
63C23×C4×C13—21no—
64C23×C4×C13C2311yescharacteristic
65C13×#121—22no—
66C13×#121Q814yes—
67C4×D4×C13—22no—
68C4×D4×C13—41no—
69C13×#117—22no—
70C13×#117—41no—
71C2×C13×C4⋊C4—21no—
72C2×C13×C4⋊C4C2311yescharacteristic
73C2×C13×C4⋊C4C2311yescharacteristic
74C2×C13×C4⋊C4C2311yescharacteristic
75C2×C13×C22⋊C4—21no—
76C2×C13×C22⋊C4—21no—
77C2×C13×C22⋊C4—21no—
78C2×C13×C22⋊C4—21no—
79C2×C13×C22⋊C4—21no—
80C2×C13×C22⋊C4D411yescharacteristic
81C2×C13×C22⋊C4D411yescharacteristic
82C2×C42×C13—21no—
83C2×C42×C13—21no—
84C2×C42×C13C2311yescharacteristic
85C2×C42×C13C2311yescharacteristic
86C2×C22⋊Dic13—21no—
87C2×C22⋊Dic13—21no—
88#88180—22no—
89#88180—41no—
90C2×C4⋊Dic13—21no—
91C2×C4⋊Dic13—21no—
92C2×C4⋊Dic13C2311yescharacteristic
93C2×C4⋊Dic13C2311yescharacteristic
94C2×C4⋊Dic13C2311yescharacteristic
95C2×C4⋊Dic13C2311yescharacteristic
96C2×#6101—21no—
97C2×#6101—21no—
98C2×#6101—21no—
99C2×#6101—21no—
100C2×C4×Dic13—21no—
101C22×#1055—22no—
102C22×#1055—22no—
103C22×#1055—22no—
104C22×#1055C2311yescharacteristic
105C22×#1055C2311yescharacteristic
106C22×#1055C2311yescharacteristic
107C22×#1055C2311yescharacteristic
108#88124—22no—
109#88124—41no—
110C13×#95—21no—
111C13×#95—21no—
112C13×#95D411yescharacteristic
113C13×#95D411yescharacteristic
114#88072—22no—
115#88072—22no—
116#88072—22no—
117#88072—41no—
118#88071—21no—
119#88071—21no—
120#88071—21no—
121C22⋊#1055—22no—
122#88048—22no—
123#88048—22no—
124#88048—22no—
125#88047—22no—
126#88047—41no—
127#88047D414yescomplemented
128C4⋊#1055—22no—
129C4⋊#1055—22no—
130#26347—131nomaximal, Sylow
131C24×C13—21no—
132C24×C13C2×D411yescharacteristic
133C2×D4×C13—24no—
134C2×D4×C13—21no—
135C2×D4×C13—21no—
136C2×D4×C13—21no—
137C2×D4×C13—21no—
138C2×D4×C13—21no—
139C2×D4×C13—81no—
140C2×D4×C13—81no—
141C2×D4×C13C2×Q812yes—
142C22×C4×C13—21no—
143C22×C4×C13—21no—
144C22×C4×C13—21no—
145C22×C4×C13—21no—
146C22×C4×C13—21no—
147C22×C4×C13—21no—
148C22×C4×C13—21no—
149C22×C4×C13—42no—
150C22×C4×C13—42no—
151C22×C4×C13—81no—
152C22×C4×C13C2×D411yescharacteristic
153C22×C4×C13C2×D411yescharacteristic
154C22×C4×C13C2×D411yescharacteristic
155C22×C4×C13C2×D411yescharacteristic
156C22×C4×C13C2×D411yescharacteristic
157C22×C4×C13C2×Q812yes—
158C22×C4×C13#4112yes—
159C22×C4×C13C2411yescharacteristic
160C22×Dic13—21no—
161C22×Dic13—21no—
162C22×Dic13—21no—
163C22×Dic13—21no—
164C13×C4⋊C4—21no—
165C13×C4⋊C4—21no—
166C13×C4⋊C4—21no—
167C13×C4⋊C4—21no—
168C13×C4⋊C4—81no—
169C13×C4⋊C4C2×D412yes—
170C13×C4⋊C4C2×Q812yes—
171C13×C22⋊C4—24no—
172C13×C22⋊C4—22no—
173C13×C22⋊C4—41no—
174C13×C22⋊C4—42no—
175C13×C22⋊C4—42no—
176C13×C22⋊C4—42no—
177C13×C22⋊C4—81no—
178C42×C13—21no—
179C42×C13—21no—
180C42×C13—21no—
181C42×C13—21no—
182C42×C13—42no—
183C42×C13—81no—
184C22⋊Dic13—42no—
185C22⋊Dic13—81no—
186C4⋊Dic13—21no—
187C4⋊Dic13—21no—
188C4⋊Dic13—21no—
189C4⋊Dic13—21no—
190C4⋊Dic13—21no—
191C4⋊Dic13—21no—
192C4⋊Dic13—21no—
193C4⋊Dic13—42no—
194C4⋊Dic13—81no—
195C4⋊Dic13C2×D412yes—
196#6101—42no—
197#6101—42no—
198#6101—42no—
199#6101—81no—
200C4×Dic13—42no—
201C2×#1055—28no—
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×#1055—21no—
212C2×#1055C2×D412yes—
213C2×#1055#4112yes—
214C2×#478—131no—
215C2×#427—131no—
216#2441—131no—
217#2363D1311yescharacteristic
218#2093—131no—
219#2086—131no—
220#2065—131no—
221#2059—131no—
222#1948—131no—
223#1921—131no—
224#1893—131no—
225#1875—131no—
226#1864—131no—
227#1854—131no—
228#1850—131no—
229C23×C13—21no—
230C23×C13—21no—
231C23×C13—21no—
232C23×C13—21no—
233C23×C13—21no—
234C23×C13—21no—
235C23×C13—22no—
236C23×C13—41no—
237C23×C13—41no—
238C23×C13—41no—
239C23×C13—41no—
240C23×C13—41no—
241C23×C13—41no—
242C23×C13C22⋊Q812yes—
243C23×C13C22×D411yescharacteristic
244D4×C13—22no—
245D4×C13—22no—
246D4×C13—41no—
247D4×C13—41no—
248D4×C13—84no—
249C2×C4×C13—21no—
250C2×C4×C13—21no—
251C2×C4×C13—21no—
252C2×C4×C13—21no—
253C2×C4×C13—22no—
254C2×C4×C13—22no—
255C2×C4×C13—22no—
256C2×C4×C13—22no—
257C2×C4×C13—22no—
258C2×C4×C13—21no—
259C2×C4×C13—21no—
260C2×C4×C13—22no—
261C2×C4×C13—21no—
262C2×C4×C13—21no—
263C2×C4×C13—21no—
264C2×C4×C13—21no—
265C2×C4×C13—21no—
266C2×C4×C13—21no—
267C2×C4×C13—21no—
268C2×C4×C13—41no—
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—84no—
276C2×C4×C13C22⋊Q812yes—
277C2×C4×C13#13512yes—
278C2×C4×C13C22×D411yescharacteristic
279C2×C4×C13C22×Q811yescharacteristic
280C2×C4×C13C2×#4111yescharacteristic
281C2×C4×C13C2×#4111yescharacteristic
282C2×C4×C13H(5,𝔽2)11yescharacteristic
283C2×C4×C132−1+411yescharacteristic
284C2×Dic13—22no—
285C2×Dic13—41no—
286C2×Dic13—41no—
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—
296#1055—22no—
297#1055—22no—
298#1055—41no—
299#1055—41no—
300C23×C8—131no—
301C2×#125—131no—
302C2×#121C2×D1311yescharacteristic
303C2×C4×D4C2×D1311yescharacteristic
304C2×#117—131no—
305C2×#117C2×D1311yescharacteristic
306#478—264no—
307#427—264no—
308C2×#107—131no—
309C2×#107—131no—
310C2×#107—131no—
311C2×#106—131no—
312C2×#106—131no—
313C2×#106—131no—
314C2×C4⋊C8—131no—
315C2×C4⋊C8—131no—
316C2×#102—131no—
317C2×#102—131no—
318C2×#102—131no—
319C2×#102—131no—
320C2×C22⋊C8—131no—
321#399—261no—
322#396—261no—
323#390—21no—
324#390C2×D1311yescharacteristic
325#389—131no—
326#389—131no—
327#389—261no—
328#389C2×D1311yescharacteristic
329#388—21no—
330#387—261no—
331#386—21no—
332#384—131no—
333#380—131no—
334C4×C4⋊C4C2×D1311yescharacteristic
335C4×C22⋊C4—21no—
336C4×C22⋊C4C2×D1311yescharacteristic
337#340—131no—
338#340—131no—
339#340—131no—
340#340—131no—
341#340—131no—
342#340—131no—
343#336—131no—
344#336—131no—
345C22×C13—22no—
346C22×C13—22no—
347C22×C13—22no—
348C22×C13—41no—
349C22×C13—41no—
350C22×C13—41no—
351C22×C13—41no—
352C22×C13—42no—
353C22×C13—42no—
354C22×C13—42no—
355C22×C13—81no—
356C22×C13—81no—
357C22×C13—81no—
358C22×C13—81no—
359C22×C13C2×C22⋊Q811yescharacteristic
360C22×C13D4211yescharacteristic
361C22×C13#54711yescharacteristic
362C22×C13C2×#13511yescharacteristic
363C22×C13#57511yescharacteristic
364C22×C13#57611yescharacteristic
365C22×C13#57711yescharacteristic
366C4×C13—22no—
367C4×C13—22no—
368C4×C13—42no—
369C4×C13—41no—
370C4×C13—41no—
371C4×C13—42no—
372C4×C13—41no—
373C4×C13—81no—
374C4×C13#52511yescharacteristic
375C4×C13#53911yescharacteristic
376C4×C13D4×Q811yescharacteristic
377C4×C13#55411yescharacteristic
378Dic13—42no—
379Dic13—81no—
380Dic13—81no—
381Dic13—81no—
382C22×D4—21no—
383C22×D4C22×D1311yescharacteristic
384C23×C4—21no—
385C23×C4C22×D1311yescharacteristic
386C22×C8—131no—
387C22×C8—131no—
388C22×C8—131no—
389C22×C8—131no—
390C22×C8—262no—
391C22×C8—262no—
392C22×C8—262no—
393#125—262no—
394#125—521no—
395#121—22no—
396#121Dic2614yes—
397C4×D4—22no—
398C4×D4—41no—
399#117—22no—
400#117—41no—
401#117—262no—
402#117—521no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—131no—
405C2×C4⋊C4—131no—
406C2×C4⋊C4—131no—
407C2×C4⋊C4—131no—
408C2×C4⋊C4—261no—
409C2×C4⋊C4—261no—
410C2×C4⋊C4—261no—
411C2×C4⋊C4—261no—
412C2×C4⋊C4—261no—
413C2×C4⋊C4—261no—
414C2×C4⋊C4C22×D1311yescharacteristic
415C2×C4⋊C4C22×D1311yescharacteristic
416C2×C4⋊C4C22×D1311yescharacteristic
417C2×C22⋊C4—21no—
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—21no—
422C2×C22⋊C4—261no—
423C2×C22⋊C4—261no—
424C2×C22⋊C4C22⋊D1311yescharacteristic
425C2×C22⋊C4C22⋊D1311yescharacteristic
426C2×C42—21no—
427C2×C42—21no—
428C2×C42—261no—
429C2×C42C22×D1311yescharacteristic
430C2×C42C22×D1311yescharacteristic
431#107—134no—
432#107—262no—
433#107—521no—
434#106—262no—
435#106—262no—
436#106—262no—
437C4⋊C8—262no—
438C4⋊C8—262no—
439#102—262no—
440#102—262no—
441#102—262no—
442#102—521no—
443C22⋊C8—262no—
444#95—21no—
445#95—21no—
446#95—261no—
447#95—261no—
448#95—261no—
449#95C22⋊D1311yescharacteristic
450#95C22⋊D1311yescharacteristic
451C2×C13—42no—
452C2×C13—82no—
453C2×C13#244911yescharacteristic
454C2×C13#307611yescharacteristic
455C2×C13#308111yescharacteristic
456C2×C13#326711yescharacteristic
457C2×C13#328711yescharacteristic
458C2×C13#333711yescharacteristic
459C2×C13#334711yescharacteristic
460C24—21no—
461C24C2×C22⋊D1311yescharacteristic
462C2×D4—24no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—81no—
469C2×D4—81no—
470C2×D4C2×Dic2612yes—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—42no—
479C22×C4—42no—
480C22×C4—81no—
481C22×C4—261no—
482C22×C4—261no—
483C22×C4—261no—
484C22×C4—261no—
485C22×C4C2×Dic2612yes—
486C22×C4#612712yes—
487C22×C4C2×C22⋊D1311yescharacteristic
488C22×C4C2×C22⋊D1311yescharacteristic
489C22×C4C2×C22⋊D1311yescharacteristic
490C22×C4C2×C22⋊D1311yescharacteristic
491C22×C4C2×C22⋊D1311yescharacteristic
492C22×C4C23×D1311yescharacteristic
493C2×C8—132no—
494C2×C8—132no—
495C2×C8—268no—
496C2×C8—261no—
497C2×C8—261no—
498C2×C8—261no—
499C2×C8—261no—
500C2×C8—261no—
501C2×C8—261no—
502C2×C8—261no—
503C2×C8—261no—
504C2×C8—261no—
505C2×C8—261no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—81no—
511C4⋊C4—132no—
512C4⋊C4—261no—
513C4⋊C4—261no—
514C4⋊C4—261no—
515C4⋊C4—261no—
516C4⋊C4—261no—
517C4⋊C4—261no—
518C4⋊C4—261no—
519C4⋊C4—522no—
520C4⋊C4—522no—
521C4⋊C4—522no—
522C4⋊C4—522no—
523C4⋊C4—1041no—
524C4⋊C4—1041no—
525C4⋊C4C2×Dic2612yes—
526C4⋊C4D4×D1312yes—
527C22⋊C4—24no—
528C22⋊C4—22no—
529C22⋊C4—41no—
530C22⋊C4—42no—
531C22⋊C4—42no—
532C22⋊C4—42no—
533C22⋊C4—81no—
534C22⋊C4—522no—
535C22⋊C4—1041no—
536C42—21no—
537C42—21no—
538C42—21no—
539C42—21no—
540C42—42no—
541C42—81no—
542C42—522no—
543C13#2634711yescharacteristic, complemented, Sylow
544C23—21no—
545C23—21no—
546C23—21no—
547C23—21no—
548C23—21no—
549C23—21no—
550C23—22no—
551C23—41no—
552C23—41no—
553C23—41no—
554C23—41no—
555C23—41no—
556C23—41no—
557C23#8817812yes—
558C23C22×C22⋊D1311yescharacteristic
559D4—22no—
560D4—22no—
561D4—41no—
562D4—41no—
563D4—84no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—22no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—84no—
591C2×C4—262no—
592C2×C4—521no—
593C2×C4—521no—
594C2×C4—521no—
595C2×C4—521no—
596C2×C4—521no—
597C2×C4—521no—
598C2×C4—521no—
599C2×C4—521no—
600C2×C4—521no—
601C2×C4—521no—
602C2×C4—521no—
603C2×C4#8817812yes—
604C2×C4#8820412yes—
605C2×C4C22×Dic2611yescharacteristic
606C2×C4C2×#612711yescharacteristic
607C2×C4C2×D4×D1311yescharacteristic
608C2×C4#8825111yescharacteristic
609C2×C4#41×D1311yescharacteristic
610C2×C4#8825711yescharacteristic
611C8—262no—
612C8—262no—
613C8—521no—
614C8—521no—
615C22—22no—
616C22—22no—
617C22—22no—
618C22—41no—
619C22—41no—
620C22—41no—
621C22—41no—
622C22—42no—
623C22—42no—
624C22—42no—
625C22—81no—
626C22—81no—
627C22—81no—
628C22—81no—
629C22C2×#8817811yescharacteristic
630C22D4×C22⋊D1311yescharacteristic
631C22C2×#8820411yescharacteristic
632C22#1171952711yescharacteristic
633C22#1171952911yescharacteristic
634C22#1171954011yescharacteristic
635C22#1171954111yescharacteristic
636C4—22no—
637C4—22no—
638C4—42no—
639C4—41no—
640C4—41no—
641C4—41no—
642C4—42no—
643C4—81no—
644C4—522no—
645C4—1041no—
646C4—1041no—
647C4—1041no—
648C4D4×Dic2611yescharacteristic
649C4#1171924411yescharacteristic
650C4#1171925211yescharacteristic
651C4#1171926911yescharacteristic
652C2—42no—
653C2—82no—
654C2#1311863911yescharacteristic
655C2#1312462411yescharacteristic
656C2#1312466711yescharacteristic
657C2#1312635711yescharacteristic
658C2#1312659211yescharacteristic
659C2#1312720911yescharacteristic
660C2#1312733611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2363C2
socleC23×C13C22×D4
prime radicalC2×C13×#121C22
hypercenter#2363D13
hypocenterC13#26347
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2363

Complements

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

NH ≅ G/Ntype
1. C2×#11718670C2semidirect
2. C2×#11718659C2semidirect
3. #13118549C2semidirect
4. #13116364C2semidirect
5. #13116327C2semidirect
6. #13116210C2semidirect
7. #13116174C2semidirect
8. #13115599C2semidirect
9. #13115428C2semidirect
12. #13115097C2semidirect
13. #13115035C2semidirect
14. #13115016C2semidirect
127. #88047D4semidirect
543. C13#26347semidirect

Maximal subgroups

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

subgroupindex
C2×#117186702
C2×#117186592
#131185492
#131163642
#131163272
#131162102
#131161742
#131155992
#131154282
#131152652
#131151592
#131150972
#131150352
#131150162
C13×#23632
#2634713