Finite Group Databasebeta

← #15907268

Subgroups — #15907268

Order 3328.

754 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
1#13119133C211yesmaximal, characteristic
2#13116403C211yesmaximal, characteristic, complemented
3#13116318C211yesmaximal, characteristic, complemented
4#13116272C211yesmaximal, characteristic, complemented
5#13116262C211yesmaximal, characteristic, complemented
6#13115428C211yesmaximal, characteristic, complemented
7#13115407C211yesmaximal, characteristic, complemented
8#13115129C211yesmaximal, characteristic
9#13115035C211yesmaximal, characteristic, complemented
10#13115024C211yesmaximal, characteristic, complemented
11#13114928C211yesmaximal, characteristic, complemented
12#13114926C211yesmaximal, characteristic, complemented
13#13114863C211yesmaximal, characteristic, complemented
14#13114552C211yesmaximal, characteristic, complemented
15C13×#2352C211yesmaximal, characteristic
16C2×C4×D4×C13C2211yescharacteristic
17C2×C13×#117C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C2×#88180C2211yescharacteristic
20C23×#1055C2211yescharacteristic
21C13×#388—21no—
22C13×#387—21no—
23C13×#386—21no—
24C13×#382C2211yescharacteristic
25C13×#380C2211yescharacteristic
26C13×#380C2211yescharacteristic
27C4×C13×C4⋊C4C2211yescharacteristic
28C4×C13×C22⋊C4—21no—
29#11718883—21no—
30#11718873C2211yescharacteristic
31#11718873C2211yescharacteristic
32#11718873C2211yescharacteristic
33C2×C22⋊#1055C2211yescharacteristic
34C2×C22⋊#1055C2211yescharacteristic
35C2×C22⋊#1055C2211yescharacteristic
36#11718639—21no—
37C2×#88048C2211yescharacteristic
38C2×#88047C2211yescharacteristic
39C2×#88047C2211yescharacteristic
40C2×#88047C2211yescharacteristic
41#11718613—21no—
42#11718605—21no—
43#11718589C2211yescharacteristic
44#11718589C2211yescharacteristic
45#11718121C2211yescharacteristic
46#11718121C2211yescharacteristic
47#11718121C2211yescharacteristic
48#11718121C2211yescharacteristic
49#11718121C2211yescharacteristic
50#11718121C2211yescharacteristic
51#11718121C2211yescharacteristic
52#11718121C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718116C2211yescharacteristic
58#11718116C2211yescharacteristic
59C22×D4×C13D411yescharacteristic
60C23×C4×C13—21no—
61C23×C4×C13C2311yescharacteristic
62C23×C4×C13C2311yescharacteristic
63C4×D4×C13—22no—
64C4×D4×C13—22no—
65C13×#117—22no—
66C13×#117—41no—
67C2×C13×C4⋊C4—22no—
68C2×C13×C4⋊C4—21no—
69C2×C13×C4⋊C4—41no—
70C2×C13×C4⋊C4D411yescharacteristic
71C2×C13×C4⋊C4C2311yescharacteristic
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⋊C4D411yescharacteristic
79C2×C13×C22⋊C4D411yescharacteristic
80C2×C42×C13—21no—
81C2×C42×C13—21no—
82C2×C42×C13C2311yescharacteristic
83C2×C22⋊Dic13—21no—
84C2×C22⋊Dic13—21no—
85C2×C22⋊Dic13—21no—
86C2×C22⋊Dic13—21no—
87#88180—22no—
88#88180—22no—
89C2×C4⋊Dic13C2311yescharacteristic
90C2×C4⋊Dic13C2311yescharacteristic
91C2×C4⋊Dic13C2311yescharacteristic
92C2×C4⋊Dic13C2311yescharacteristic
93C2×#6101—21no—
94C2×#6101—21no—
95C2×C4×Dic13—21no—
96C22×#1055—22no—
97C22×#1055—22no—
98C22×#1055—41no—
99C22×#1055C2311yescharacteristic
100C22×#1055C2311yescharacteristic
101C22×#1055C2311yescharacteristic
102C22×#1055C2311yescharacteristic
103C13×#95—21no—
104C13×#95—21no—
105C13×#95—21no—
106C13×#95—21no—
107C13×#95—21no—
108#88071—21no—
109#88071—21no—
110#88071—21no—
111#88071—21no—
112#88071—21no—
113C22⋊#1055—22no—
114C22⋊#1055—22no—
115C22⋊#1055—41no—
116#88048—41no—
117#88047—22no—
118#88047—22no—
119#88047—41no—
120#24934—131nomaximal, Sylow
121C24×C13C2×D411yescharacteristic
122C24×C13C2×D411yescharacteristic
123C2×D4×C13—22no—
124C2×D4×C13—22no—
125C2×D4×C13—41no—
126C22×C4×C13—21no—
127C22×C4×C13—21no—
128C22×C4×C13—21no—
129C22×C4×C13—21no—
130C22×C4×C13—21no—
131C22×C4×C13—21no—
132C22×C4×C13—21no—
133C22×C4×C13—21no—
134C22×C4×C13—21no—
135C22×C4×C13—21no—
136C22×C4×C13—21no—
137C22×C4×C13—21no—
138C22×C4×C13—21no—
139C22×C4×C13—21no—
140C22×C4×C13—42no—
141C22×C4×C13—42no—
142C22×C4×C13—81no—
143C22×C4×C13C2×D411yescharacteristic
144C22×C4×C13C2×D411yescharacteristic
145C22×C4×C13C2×D411yescharacteristic
146C22×C4×C13C2×D411yescharacteristic
147C22×C4×C13#4112yes—
148C22×C4×C13#4112yes—
149C22×C4×C13C2411yescharacteristic
150C22×Dic13—21no—
151C22×Dic13—21no—
152C22×Dic13—21no—
153C22×Dic13—21no—
154C13×C4⋊C4—22no—
155C13×C4⋊C4—21no—
156C13×C4⋊C4—21no—
157C13×C4⋊C4—21no—
158C13×C4⋊C4—21no—
159C13×C4⋊C4—21no—
160C13×C4⋊C4—21no—
161C13×C4⋊C4—21no—
162C13×C4⋊C4—42no—
163C13×C4⋊C4#4112yes—
164C13×C22⋊C4—22no—
165C13×C22⋊C4—22no—
166C13×C22⋊C4—42no—
167C13×C22⋊C4—42no—
168C13×C22⋊C4—81no—
169C42×C13—21no—
170C42×C13—21no—
171C42×C13—42no—
172C42×C13—81no—
173C22⋊Dic13—42no—
174C22⋊Dic13—42no—
175C22⋊Dic13—81no—
176C22⋊Dic13—81no—
177C4⋊Dic13—21no—
178C4⋊Dic13—21no—
179C4⋊Dic13—21no—
180C4⋊Dic13—21no—
181C4⋊Dic13—21no—
182C4⋊Dic13—21no—
183C4⋊Dic13—21no—
184C4⋊Dic13—21no—
185#6101—42no—
186#6101—81no—
187C4×Dic13—42no—
188C2×#1055—21no—
189C2×#1055—21no—
190C2×#1055—21no—
191C2×#1055—21no—
192C2×#1055—21no—
193C2×#1055—21no—
194C2×#1055—21no—
195C2×#1055—21no—
196C2×#1055—21no—
197C2×#1055—21no—
198C2×#1055—21no—
199C2×#1055—44no—
200C2×#1055#4112yes—
201#2485—131no—
202#2352D1311yescharacteristic
203#2101—131no—
204#2085—131no—
205#2077—131no—
206#2075—131no—
207#1921—131no—
208#1918—131no—
209#1869—131no—
210#1854—131no—
211#1852—131no—
212#1825—131no—
213#1824—131no—
214#1808—131no—
215#1735—131no—
216C23×C13—21no—
217C23×C13—21no—
218C23×C13—21no—
219C23×C13—21no—
220C23×C13—21no—
221C23×C13—21no—
222C23×C13—21no—
223C23×C13—21no—
224C23×C13—21no—
225C23×C13—21no—
226C23×C13—21no—
227C23×C13—21no—
228C23×C13#12312yes—
229C23×C13#13512yes—
230C23×C13C22×D411yescharacteristic
231D4×C13—44no—
232C2×C4×C13—21no—
233C2×C4×C13—21no—
234C2×C4×C13—22no—
235C2×C4×C13—22no—
236C2×C4×C13—22no—
237C2×C4×C13—22no—
238C2×C4×C13—21no—
239C2×C4×C13—21no—
240C2×C4×C13—21no—
241C2×C4×C13—22no—
242C2×C4×C13—21no—
243C2×C4×C13—21no—
244C2×C4×C13—21no—
245C2×C4×C13—21no—
246C2×C4×C13—21no—
247C2×C4×C13—21no—
248C2×C4×C13—41no—
249C2×C4×C13—41no—
250C2×C4×C13—41no—
251C2×C4×C13—41no—
252C2×C4×C13—41no—
253C2×C4×C13—41no—
254C2×C4×C13—41no—
255C2×C4×C13—41no—
256C2×C4×C13—41no—
257C2×C4×C13—41no—
258C2×C4×C13—41no—
259C2×C4×C13—41no—
260C2×C4×C13—41no—
261C2×C4×C13—41no—
262C2×C4×C13—41no—
263C2×C4×C13—84no—
264C2×C4×C13#12312yes—
265C2×C4×C13C2×#4111yescharacteristic
266C2×C4×C13C2×#4111yescharacteristic
267C2×C4×C13C2×#4111yescharacteristic
268C2×C4×C13C2×#4111yescharacteristic
269C2×C4×C13H(5,𝔽2)11yescharacteristic
270C2×C4×C132−1+411yescharacteristic
271C2×Dic13—41no—
272C2×Dic13—41no—
273C2×Dic13—41no—
274C2×Dic13—41no—
275C2×Dic13—41no—
276C2×Dic13—41no—
277C2×Dic13—41no—
278C2×Dic13—41no—
279C2×Dic13—41no—
280C2×Dic13—41no—
281C2×Dic13—41no—
282C2×Dic13—41no—
283#1055—22no—
284#1055—41no—
285#1055—41no—
286#1055—41no—
287C23×C8—131no—
288C2×C4×D4C2×D1311yescharacteristic
289C2×#117—131no—
290C2×#117C2×D1311yescharacteristic
291C22×C4⋊C4C2×D1311yescharacteristic
292C2×#107—131no—
293C2×#107—131no—
294C2×#107—131no—
295C2×#106—131no—
296C2×C22⋊C8—131no—
297C2×C22⋊C8—131no—
298C2×C22⋊C8—131no—
299#397—261no—
300#394—261no—
301#389—131no—
302#389—131no—
303#388—21no—
304#388—261no—
305#387—21no—
306#387—261no—
307#386—21no—
308#382C2×D1311yescharacteristic
309#380—131no—
310#380—131no—
311#380—131no—
312#380C2×D1311yescharacteristic
313#380C2×D1311yescharacteristic
314C4×C4⋊C4C2×D1311yescharacteristic
315C4×C22⋊C4—21no—
316#340—131no—
317#340—131no—
318#340—131no—
319#340—131no—
320#340—131no—
321#340—131no—
322#340—131no—
323#340—131no—
324#340—131no—
325#340—131no—
326#340—131no—
327#340—131no—
328#336—131no—
329#336—131no—
330C22×C13—22no—
331C22×C13—22no—
332C22×C13—22no—
333C22×C13—22no—
334C22×C13—22no—
335C22×C13—22no—
336C22×C13—41no—
337C22×C13—41no—
338C22×C13—41no—
339C22×C13—41no—
340C22×C13—41no—
341C22×C13—41no—
342C22×C13—41no—
343C22×C13—41no—
344C22×C13C2×#12311yescharacteristic
345C22×C13#54611yescharacteristic
346C22×C13#54711yescharacteristic
347C22×C13C2×#13511yescharacteristic
348C22×C13#57511yescharacteristic
349C22×C13#57611yescharacteristic
350C22×C13#57811yescharacteristic
351C4×C13—22no—
352C4×C13—41no—
353C4×C13—41no—
354C4×C13—41no—
355C4×C13—42no—
356C4×C13—81no—
357C4×C13—81no—
358C4×C13—81no—
359C4×C13#52911yescharacteristic
360C4×C13#53911yescharacteristic
361C4×C13#55111yescharacteristic
362C4×C13#55211yescharacteristic
363Dic13—81no—
364Dic13—81no—
365Dic13—81no—
366Dic13—81no—
367C22×D4C22⋊D1311yescharacteristic
368C23×C4—21no—
369C23×C4C22×D1311yescharacteristic
370C23×C4C22×D1311yescharacteristic
371C22×C8—131no—
372C22×C8—131no—
373C22×C8—131no—
374C22×C8—131no—
375C22×C8—262no—
376C22×C8—262no—
377C22×C8—521no—
378C4×D4—22no—
379C4×D4—22no—
380#117—22no—
381#117—41no—
382#117—262no—
383#117—262no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—41no—
387C2×C4⋊C4—131no—
388C2×C4⋊C4—131no—
389C2×C4⋊C4—131no—
390C2×C4⋊C4—131no—
391C2×C4⋊C4—261no—
392C2×C4⋊C4—261no—
393C2×C4⋊C4C22⋊D1311yescharacteristic
394C2×C4⋊C4C22×D1311yescharacteristic
395C2×C4⋊C4C22×D1311yescharacteristic
396C2×C4⋊C4C22×D1311yescharacteristic
397C2×C4⋊C4C22×D1311yescharacteristic
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—261no—
402C2×C22⋊C4—261no—
403C2×C22⋊C4—261no—
404C2×C22⋊C4—261no—
405C2×C22⋊C4C22⋊D1311yescharacteristic
406C2×C22⋊C4C22⋊D1311yescharacteristic
407C2×C42—21no—
408C2×C42—21no—
409C2×C42—261no—
410C2×C42C22×D1311yescharacteristic
411#107—262no—
412#107—262no—
413#107—521no—
414#106—521no—
415C22⋊C8—262no—
416C22⋊C8—262no—
417C22⋊C8—521no—
418#95—21no—
419#95—21no—
420#95—21no—
421#95—21no—
422#95—21no—
423#95—261no—
424#95—261no—
425#95—261no—
426#95—261no—
427#95—261no—
428C2×C13—42no—
429C2×C13—42no—
430C2×C13#241911yescharacteristic
431C2×C13#309111yescharacteristic
432C2×C13#309811yescharacteristic
433C2×C13#330011yescharacteristic
434C2×C13#331911yescharacteristic
435C2×C13#333911yescharacteristic
436C2×C13#334911yescharacteristic
437C24C2×C22⋊D1311yescharacteristic
438C24C2×C22⋊D1311yescharacteristic
439C2×D4—22no—
440C2×D4—22no—
441C2×D4—41no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—42no—
457C22×C4—42no—
458C22×C4—81no—
459C22×C4—261no—
460C22×C4—261no—
461C22×C4—261no—
462C22×C4—261no—
463C22×C4#612712yes—
464C22×C4#612712yes—
465C22×C4C2×C22⋊D1311yescharacteristic
466C22×C4C2×C22⋊D1311yescharacteristic
467C22×C4C2×C22⋊D1311yescharacteristic
468C22×C4C2×C22⋊D1311yescharacteristic
469C22×C4C23×D1311yescharacteristic
470C2×C8—132no—
471C2×C8—261no—
472C2×C8—261no—
473C2×C8—261no—
474C2×C8—261no—
475C2×C8—261no—
476C2×C8—261no—
477C2×C8—261no—
478C2×C8—261no—
479C2×C8—261no—
480C2×C8—261no—
481C2×C8—261no—
482C2×C8—524no—
483C4⋊C4—22no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—42no—
492C4⋊C4—261no—
493C4⋊C4—261no—
494C4⋊C4—261no—
495C4⋊C4—261no—
496C4⋊C4—261no—
497C4⋊C4—261no—
498C4⋊C4—261no—
499C4⋊C4—261no—
500C4⋊C4—522no—
501C4⋊C4—1041no—
502C4⋊C4#612912yes—
503C22⋊C4—22no—
504C22⋊C4—22no—
505C22⋊C4—42no—
506C22⋊C4—42no—
507C22⋊C4—81no—
508C22⋊C4—522no—
509C22⋊C4—522no—
510C22⋊C4—1041no—
511C22⋊C4—1041no—
512C42—21no—
513C42—21no—
514C42—42no—
515C42—81no—
516C42—522no—
517C13#2493411yescharacteristic, complemented, Sylow
518C23—21no—
519C23—21no—
520C23—21no—
521C23—21no—
522C23—21no—
523C23—21no—
524C23—21no—
525C23—21no—
526C23—21no—
527C23—21no—
528C23—21no—
529C23—21no—
530C23#8818312yes—
531C23#8820412yes—
532C23C22×C22⋊D1311yescharacteristic
533D4—44no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—22no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—84no—
566C2×C4—521no—
567C2×C4—521no—
568C2×C4—521no—
569C2×C4—521no—
570C2×C4—521no—
571C2×C4—521no—
572C2×C4—521no—
573C2×C4—521no—
574C2×C4—521no—
575C2×C4—521no—
576C2×C4—521no—
577C2×C4—521no—
578C2×C4#8818312yes—
579C2×C4C2×#612711yescharacteristic
580C2×C4C2×#612711yescharacteristic
581C2×C4C2×#612911yescharacteristic
582C2×C4#8825111yescharacteristic
583C2×C4#41×D1311yescharacteristic
584C2×C4#8825711yescharacteristic
585C8—262no—
586C8—521no—
587C8—521no—
588C8—521no—
589C22—22no—
590C22—22no—
591C22—22no—
592C22—22no—
593C22—22no—
594C22—22no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—41no—
600C22—41no—
601C22—41no—
602C22—41no—
603C22C2×#8818311yescharacteristic
604C22#1171951111yescharacteristic
605C22C2×#8820411yescharacteristic
606C22#1171952711yescharacteristic
607C22#1171952911yescharacteristic
608C22#1171954011yescharacteristic
609C22#1171954311yescharacteristic
610C4—22no—
611C4—42no—
612C4—41no—
613C4—41no—
614C4—41no—
615C4—81no—
616C4—81no—
617C4—81no—
618C4—1041no—
619C4—1041no—
620C4—1041no—
621C4—1041no—
622C4#1171924311yescharacteristic
623C4#1171924611yescharacteristic
624C4#1171926111yescharacteristic
625C4#1171926911yescharacteristic
626C2—42no—
627C2—42no—
628C2#1311830711yescharacteristic
629C2#1312474911yescharacteristic
630C2#1312481411yescharacteristic
631C2#1312672311yescharacteristic
632C2#1312699211yescharacteristic
633C2#1312723211yescharacteristic
634C2#1312736611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2352C2
socleC23×C13C22×D4
prime radicalC22×D4×C13D4
hypercenter#2352D13
hypocenterC13#24934
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2352

Complements

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

NH ≅ G/Ntype
2. #13116403C2semidirect
3. #13116318C2semidirect
4. #13116272C2semidirect
5. #13116262C2semidirect
6. #13115428C2semidirect
7. #13115407C2semidirect
9. #13115035C2semidirect
10. #13115024C2semidirect
11. #13114928C2semidirect
12. #13114926C2semidirect
13. #13114863C2semidirect
14. #13114552C2semidirect
517. C13#24934semidirect

Maximal subgroups

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

subgroupindex
#131191332
#131164032
#131163182
#131162722
#131162622
#131154282
#131154072
#131151292
#131150352
#131150242
#131149282
#131149262
#131148632
#131145522
C13×#23522
#2493413