Finite Group Databasebeta

← #15876864

Subgroups — #15876864

Order 3328.

722 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13118110C211yesmaximal, characteristic
2#13115772C211yesmaximal, characteristic, complemented
3#13115770C211yesmaximal, characteristic, complemented
4#13115554C211yesmaximal, characteristic, complemented
5#13115553C211yesmaximal, characteristic, complemented
6#13115396C211yesmaximal, characteristic, complemented
7#13115393C211yesmaximal, characteristic, complemented
8#13115393C211yesmaximal, characteristic, complemented
9#13115392C211yesmaximal, characteristic, complemented
10#13115021C211yesmaximal, characteristic
11#13115018C211yesmaximal, characteristic
12#13114818C211yesmaximal, characteristic
13C8×C22⋊Dic13C211yesmaximal, characteristic
14#13114532C211yesmaximal, characteristic
15C8×C13×C22⋊C4C211yesmaximal, characteristic
16C23×C8×C13C2211yescharacteristic
17C2×#88180C2211yescharacteristic
18C22×#6099C2211yescharacteristic
19C2×C4×Dic26C2211yescharacteristic
20C2×C13×C22⋊C8C2211yescharacteristic
21C2×C4×C8×C13C2211yescharacteristic
22C2×C4×C8×C13C2211yescharacteristic
23C4×C13×C22⋊C4C2211yescharacteristic
24C4×C22⋊Dic13C2211yescharacteristic
25C2×C22⋊#1055C2211yescharacteristic
26C2×#88054C2211yescharacteristic
27C2×#88054C2211yescharacteristic
28C2×#88054C2211yescharacteristic
29C2×#88054C2211yescharacteristic
30C2×C8×Dic13C2211yescharacteristic
31C2×C8×Dic13C2211yescharacteristic
32#11718610C411yescharacteristic
33#11718609C411yescharacteristic
34#11718609C411yescharacteristic
35#11718608C411yescharacteristic
36C4×C4⋊Dic13C2211yescharacteristic
37C4×#6101C2211yescharacteristic
38C4×#6101C2211yescharacteristic
39C2×C4⋊#1055C2211yescharacteristic
40C2×C4⋊#1055C2211yescharacteristic
41#11718322C411yescharacteristic
42#11718321C411yescharacteristic
43#11718318C411yescharacteristic
44#11718317C411yescharacteristic
45C13×#336C2211yescharacteristic
46C13×#336C2211yescharacteristic
47#11718142C2211yescharacteristic
48#11718142C2211yescharacteristic
49#11718142C2211yescharacteristic
50#11718142C2211yescharacteristic
51#11718142C2211yescharacteristic
52#11718142C2211yescharacteristic
53#11718142C2211yescharacteristic
54#11718142C2211yescharacteristic
55#11718142C2211yescharacteristic
56#11718142C2211yescharacteristic
57#11718116C2211yescharacteristic
58#11718116C2211yescharacteristic
59C23×C4×C13C2311yescharacteristic
60C22×Dic26C2×C411yescharacteristic
61C22×C8×C13—41no—
62C22×C8×C13—41no—
63C22×C8×C13Q814yescomplemented
64C22×C8×C13C2311yescharacteristic
65C22×C8×C13C2311yescharacteristic
66C22×C8×C13C2311yescharacteristic
67C22×C8×C13C2311yescharacteristic
68C2×C13×C22⋊C4C2×C411yescharacteristic
69C2×C13×C22⋊C4C2×C411yescharacteristic
70C2×C42×C13C2311yescharacteristic
71C2×C42×C13C2311yescharacteristic
72C2×C22⋊Dic13C2×C411yescharacteristic
73C2×C22⋊Dic13C2×C411yescharacteristic
74C2×C22⋊Dic13C2×C411yescharacteristic
75C2×C22⋊Dic13C2×C411yescharacteristic
76#88180—41no—
77#88180—41no—
78C2×C4⋊Dic13C2×C411yescharacteristic
79C2×C4⋊Dic13C2×C411yescharacteristic
80C2×C4⋊Dic13C2×C411yescharacteristic
81C2×C4⋊Dic13C2×C411yescharacteristic
82C2×C4⋊Dic13C2×C411yescharacteristic
83C2×#6101C2×C411yescharacteristic
84C2×#6101C2×C411yescharacteristic
85C2×#6101C2×C411yescharacteristic
86C2×#6101C2×C411yescharacteristic
87C2×#6101C2×C411yescharacteristic
88C2×#6101C2×C411yescharacteristic
89C2×C4×Dic13C2311yescharacteristic
90C2×C4×Dic13C2311yescharacteristic
91C2×C4×Dic13C2311yescharacteristic
92C2×C4×Dic13C2311yescharacteristic
93C2×#6099—22no—
94C2×#6099—41no—
95C2×#6099—41no—
96C22×#1055C2311yescharacteristic
97C22×#1055C2311yescharacteristic
98C22×#1055C2311yescharacteristic
99C22×#1055C2311yescharacteristic
100C4×Dic26—41no—
101C4×Dic26—41no—
102C13×C22⋊C8—22no—
103C4×C8×C13—41no—
104C4×C8×C13—41no—
105C13×#95C2×C411yescharacteristic
106C13×#95C2×C411yescharacteristic
107#88071C2×C411yescharacteristic
108#88071C2×C411yescharacteristic
109#88071C2×C411yescharacteristic
110#88071C2×C411yescharacteristic
111#88071C2×C411yescharacteristic
112#88071C2×C411yescharacteristic
113#88071C2×C411yescharacteristic
114#88071C2×C411yescharacteristic
115C22⋊#1055—22no—
116#88054—41no—
117#88054—41no—
118#88054—41no—
119#88054—41no—
120C8×Dic13—41no—
121C8×Dic13—41no—
122C4⋊#1055—41no—
123C4⋊#1055—41no—
124#22288—131nomaximal, Sylow
125C24×C13C22×C411yescharacteristic
126C22×C4×C13—21no—
127C22×C4×C13—21no—
128C22×C4×C13—21no—
129C22×C4×C13—21no—
130C22×C4×C13C22×C411yescharacteristic
131C22×C4×C13C22×C411yescharacteristic
132C22×C4×C13C22×C411yescharacteristic
133C22×C4×C13C22×C411yescharacteristic
134C22×C4×C13C22×C411yescharacteristic
135C22×C4×C13C2×Q812yes—
136C22×C4×C13#4112yes—
137C22×C4×C13C2411yescharacteristic
138C22×Dic13C22×C411yescharacteristic
139C22×Dic13C22×C411yescharacteristic
140C22×Dic13C22×C411yescharacteristic
141C22×Dic13C22×C411yescharacteristic
142C22×Dic13C22×C411yescharacteristic
143C22×Dic13C22×C411yescharacteristic
144C22×Dic13C22×C411yescharacteristic
145C22×Dic13C22×C411yescharacteristic
146C2×Dic26—22no—
147C2×Dic26—22no—
148C2×Dic26—41no—
149C2×C8×C13—21no—
150C2×C8×C13—21no—
151C2×C8×C13—21no—
152C2×C8×C13—21no—
153C2×C8×C13—21no—
154C2×C8×C13—21no—
155C2×C8×C13—21no—
156C2×C8×C13—21no—
157C2×C8×C13—21no—
158C2×C8×C13—21no—
159C2×C8×C13—44no—
160C2×C8×C13C2×Q812yes—
161C2×C8×C13C2×Q812yes—
162C13×C22⋊C4—22no—
163C13×C22⋊C4—22no—
164C42×C13—21no—
165C42×C13—21no—
166C42×C13—21no—
167C42×C13—21no—
168C22⋊Dic13—22no—
169C22⋊Dic13—22no—
170C22⋊Dic13—41no—
171C22⋊Dic13—41no—
172C4⋊Dic13—22no—
173C4⋊Dic13—22no—
174C4⋊Dic13—41no—
175C4⋊Dic13—41no—
176C4⋊Dic13—41no—
177#6101—22no—
178#6101—22no—
179#6101—22no—
180#6101—22no—
181#6101—41no—
182#6101—41no—
183C4×Dic13—21no—
184C4×Dic13—21no—
185C4×Dic13—21no—
186C4×Dic13—21no—
187C4×Dic13—21no—
188C4×Dic13—21no—
189C4×Dic13—21no—
190C4×Dic13—21no—
191#6099—44no—
192C2×#1055—21no—
193C2×#1055—21no—
194C2×#1055—21no—
195C2×#1055—21no—
196C2×#1055—21no—
197C2×#1055—21no—
198C2×#1055—21no—
199C2×#1055—21no—
200C2×#1055—21no—
201C2×#1055—21no—
202C2×#1055—21no—
203C2×#1055—21no—
204#2396—131no—
205#1984—131no—
206#1984—131no—
207#1939—131no—
208#1939—131no—
209#1916—131no—
210#1916—131no—
211#1916—131no—
212#1916—131no—
213#1851—131no—
214#1851—131no—
215#1798—131no—
216C8×C22⋊C4—131no—
217C8×C22⋊C4D1311yescharacteristic
218#1729—131no—
219C23×C13—21no—
220C23×C13—21no—
221C23×C13—21no—
222C23×C13—21no—
223C23×C13—21no—
224C23×C13—21no—
225C23×C13C4×Q812yes—
226C23×C13C23×C411yescharacteristic
227C2×C4×C13—21no—
228C2×C4×C13—21no—
229C2×C4×C13—21no—
230C2×C4×C13—21no—
231C2×C4×C13—21no—
232C2×C4×C13—21no—
233C2×C4×C13—22no—
234C2×C4×C13—22no—
235C2×C4×C13—22no—
236C2×C4×C13—22no—
237C2×C4×C13—21no—
238C2×C4×C13—21no—
239C2×C4×C13—21no—
240C2×C4×C13—21no—
241C2×C4×C13—21no—
242C2×C4×C13—21no—
243C2×C4×C13C4×Q812yes—
244C2×C4×C13#13112yes—
245C2×C4×C13#13112yes—
246C2×C4×C13C22×Q811yescharacteristic
247C2×C4×C13C2×#4111yescharacteristic
248C2×C4×C13H(5,𝔽2)11yescharacteristic
249C2×C4×C13H(5,𝔽2)11yescharacteristic
250C2×C4×C13H(5,𝔽2)11yescharacteristic
251C2×C4×C132−1+411yescharacteristic
252C2×Dic13—21no—
253C2×Dic13—21no—
254C2×Dic13—21no—
255C2×Dic13—21no—
256C2×Dic13—21no—
257C2×Dic13—21no—
258C2×Dic13—21no—
259C2×Dic13—21no—
260C2×Dic13—21no—
261C2×Dic13—21no—
262C2×Dic13—21no—
263C2×Dic13—21no—
264C2×Dic13—21no—
265C2×Dic13—21no—
266C2×Dic13—21no—
267C2×Dic13—21no—
268C2×Dic13—21no—
269C2×Dic13—21no—
270C2×Dic13—21no—
271C2×Dic13—21no—
272C2×Dic13—21no—
273C2×Dic13—21no—
274C2×Dic13#13112yes—
275C2×Dic13#13112yes—
276Dic26—44no—
277C8×C13—22no—
278C8×C13—22no—
279C8×C13—41no—
280C8×C13—41no—
281#1055—41no—
282#1055—41no—
283#1055—41no—
284#1055—41no—
285C22×M16—131no—
286C23×C8C2×D1311yescharacteristic
287C2×C4×Q8—131no—
288C2×#117—131no—
289C2×C4⋊C8—131no—
290C2×C4⋊C8—131no—
291C2×C4⋊C8—131no—
292C2×C4⋊C8—131no—
293C2×C4⋊C8—131no—
294C2×C4⋊C8—131no—
295C2×C22⋊C8—131no—
296C2×C22⋊C8C2×D1311yescharacteristic
297C2×C4×C8—131no—
298C2×C4×C8—131no—
299C2×C4×C8C2×D1311yescharacteristic
300C2×C4×C8C2×D1311yescharacteristic
301#400—131no—
302#399—131no—
303#398—131no—
304#398—131no—
305#396—131no—
306#396—131no—
307#395—131no—
308#393—131no—
309C4×C4⋊C4—131no—
310C4×C4⋊C4—131no—
311C4×C4⋊C4—131no—
312C4×C22⋊C4—131no—
313C4×C22⋊C4C2×D1311yescharacteristic
314#336—131no—
315#336—131no—
316#336—131no—
317#336—131no—
318#336—131no—
319#336—131no—
320#336—131no—
321#336—131no—
322#336—131no—
323#336—131no—
324#336—131no—
325#336—131no—
326#336C2×D1311yescharacteristic
327#336C2×D1311yescharacteristic
328C22×C13—22no—
329C22×C13—22no—
330C22×C13—22no—
331C22×C13—41no—
332C22×C13—41no—
333C22×C13—41no—
334C22×C13—41no—
335C22×C13C2×C4×Q811yescharacteristic
336C22×C13#51811yescharacteristic
337C22×C13#52011yescharacteristic
338C22×C13C2×#13111yescharacteristic
339C22×C13C2×#13111yescharacteristic
340C22×C13C2×#13111yescharacteristic
341C22×C13C2×#13111yescharacteristic
342C4×C13—22no—
343C4×C13—22no—
344C4×C13—22no—
345C4×C13—41no—
346C4×C13—41no—
347C4×C13#53811yescharacteristic
348C4×C13#53911yescharacteristic
349C4×C13#54311yescharacteristic
350C4×C13#54411yescharacteristic
351Dic13—22no—
352Dic13—22no—
353Dic13—41no—
354Dic13—41no—
355Dic13—41no—
356Dic13—41no—
357Dic13—41no—
358Dic13—41no—
359C22×Q8—131no—
360C23×C4C22×D1311yescharacteristic
361C2×M16—262no—
362C2×M16—521no—
363C2×M16—521no—
364C22×C8—41no—
365C22×C8—41no—
366C22×C8—131no—
367C22×C8—131no—
368C22×C8—131no—
369C22×C8—131no—
370C22×C8Dic2614yescomplemented
371C22×C8C22×D1311yescharacteristic
372C22×C8C22×D1311yescharacteristic
373C22×C8C22×D1311yescharacteristic
374C22×C8C22×D1311yescharacteristic
375C4×Q8—521no—
376C4×Q8—521no—
377#117—521no—
378#117—521no—
379C2×C4⋊C4—131no—
380C2×C4⋊C4—131no—
381C2×C4⋊C4—131no—
382C2×C4⋊C4—131no—
383C2×C4⋊C4—131no—
384C2×C4⋊C4—131no—
385C2×C4⋊C4—131no—
386C2×C4⋊C4—131no—
387C2×C4⋊C4—131no—
388C2×C4⋊C4—131no—
389C2×C4⋊C4—131no—
390C2×C22⋊C4—131no—
391C2×C22⋊C4—131no—
392C2×C22⋊C4—131no—
393C2×C22⋊C4—131no—
394C2×C22⋊C4C4×D1311yescharacteristic
395C2×C22⋊C4C4×D1311yescharacteristic
396C2×C42—131no—
397C2×C42—131no—
398C2×C42—131no—
399C2×C42—131no—
400C2×C42C22×D1311yescharacteristic
401C2×C42C22×D1311yescharacteristic
402C4⋊C8—521no—
403C4⋊C8—521no—
404C4⋊C8—521no—
405C4⋊C8—521no—
406C4⋊C8—521no—
407C4⋊C8—521no—
408C22⋊C8—22no—
409C22⋊C8—262no—
410C4×C8—41no—
411C4×C8—41no—
412C4×C8—521no—
413C4×C8—521no—
414#95—131no—
415#95—131no—
416#95—131no—
417#95—131no—
418#95—131no—
419#95—131no—
420#95—131no—
421#95—131no—
422#95C4×D1311yescharacteristic
423#95C4×D1311yescharacteristic
424C2×C13—42no—
425C2×C13#232911yescharacteristic
426C2×C13#296011yescharacteristic
427C2×C13#296011yescharacteristic
428C2×C13#297711yescharacteristic
429C2×C13#297911yescharacteristic
430C2×C13#299411yescharacteristic
431C2×C13#299411yescharacteristic
432C24C2×C4×D1311yescharacteristic
433C2×Q8—262no—
434C2×Q8—262no—
435C2×Q8—521no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—131no—
441C22×C4—131no—
442C22×C4—131no—
443C22×C4—131no—
444C22×C4—131no—
445C22×C4—131no—
446C22×C4—131no—
447C22×C4—131no—
448C22×C4C2×Dic2612yes—
449C22×C4C2×C4×D1311yescharacteristic
450C22×C4C2×C4×D1311yescharacteristic
451C22×C4C2×C4×D1311yescharacteristic
452C22×C4C2×C4×D1311yescharacteristic
453C22×C4C2×C4×D1311yescharacteristic
454C22×C4#612712yes—
455C22×C4C23×D1311yescharacteristic
456M16—524no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—44no—
468C2×C8—261no—
469C2×C8—261no—
470C2×C8—261no—
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×C8C2×Dic2612yes—
481C2×C8C2×Dic2612yes—
482C4⋊C4—262no—
483C4⋊C4—262no—
484C4⋊C4—262no—
485C4⋊C4—262no—
486C4⋊C4—262no—
487C4⋊C4—262no—
488C4⋊C4—521no—
489C4⋊C4—521no—
490C4⋊C4—521no—
491C4⋊C4—521no—
492C4⋊C4—521no—
493C22⋊C4—22no—
494C22⋊C4—22no—
495C22⋊C4—262no—
496C22⋊C4—262no—
497C22⋊C4—521no—
498C22⋊C4—521no—
499C42—21no—
500C42—21no—
501C42—21no—
502C42—21no—
503C42—261no—
504C42—261no—
505C42—261no—
506C42—261no—
507C42—261no—
508C42—261no—
509C42—261no—
510C42—261no—
511C13#2228811yescharacteristic, complemented, Sylow
512C23—21no—
513C23—21no—
514C23—21no—
515C23—21no—
516C23—21no—
517C23—21no—
518C23C4×Dic2612yes—
519C23C22×C4×D1311yescharacteristic
520Q8—524no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—132no—
538C2×C4—132no—
539C2×C4—261no—
540C2×C4—261no—
541C2×C4—261no—
542C2×C4—261no—
543C2×C4—261no—
544C2×C4—261no—
545C2×C4—261no—
546C2×C4—261no—
547C2×C4—261no—
548C2×C4—261no—
549C2×C4—261no—
550C2×C4—261no—
551C2×C4—261no—
552C2×C4—261no—
553C2×C4—261no—
554C2×C4—261no—
555C2×C4—261no—
556C2×C4—261no—
557C2×C4—261no—
558C2×C4—261no—
559C2×C4—261no—
560C2×C4—261no—
561C2×C4C4×Dic2612yes—
562C2×C4#8815512yes—
563C2×C4#8815512yes—
564C2×C4C22×Dic2611yescharacteristic
565C2×C4C2×#612711yescharacteristic
566C2×C4#8825111yescharacteristic
567C2×C4#8825111yescharacteristic
568C2×C4#8825611yescharacteristic
569C2×C4#8825711yescharacteristic
570C8—22no—
571C8—22no—
572C8—41no—
573C8—41no—
574C8—521no—
575C8—521no—
576C8—521no—
577C8—521no—
578C22—22no—
579C22—22no—
580C22—22no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22C2×C4×Dic2611yescharacteristic
586C22#1171925011yescharacteristic
587C22#1171925111yescharacteristic
588C22C2×#8815511yescharacteristic
589C22C2×#8815511yescharacteristic
590C22D13×#13111yescharacteristic
591C22D13×#13111yescharacteristic
592C4—22no—
593C4—22no—
594C4—22no—
595C4—41no—
596C4—41no—
597C4—262no—
598C4—262no—
599C4—521no—
600C4—521no—
601C4—521no—
602C4—521no—
603C4—521no—
604C4—521no—
605C4#1171918811yescharacteristic
606C4#1171922411yescharacteristic
607C4#1171926511yescharacteristic
608C4#1171926911yescharacteristic
609C2—42no—
610C2#1311756411yescharacteristic
611C2#1312376811yescharacteristic
612C2#1312377011yescharacteristic
613C2#1312388911yescharacteristic
614C2#1312389911yescharacteristic
615C2#1312399111yescharacteristic
616C2#1312399311yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D13
commutator, socleC23×C13C23×C4
FittingC8×C13×C22⋊C4C2
prime radicalC24×C13C22×C4
cosocleC22×C4×C13C24
hypercenterC8×C22⋊C4D13
hypocenterC13#22288
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C8×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #13115772C2semidirect
3. #13115770C2semidirect
4. #13115554C2semidirect
5. #13115553C2semidirect
6. #13115396C2semidirect
7. #13115393C2semidirect
8. #13115393C2semidirect
9. #13115392C2semidirect
63. C22×C8×C13Q8semidirect
370. C22×C8Dic26semidirect
511. C13#22288semidirect

Maximal subgroups

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

subgroupindex
#131181102
#131157722
#131157702
#131155542
#131155532
#131153962
#131153932
#131153922
#131150212
#131150182
#131148182
C8×C22⋊Dic132
#131145322
C8×C13×C22⋊C42
#2228813