Finite Group Databasebeta

← #15834225

Subgroups — #15834225

Order 3328.

656 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123903C211yesmaximal, characteristic, complemented
2#13123871C211yesmaximal, characteristic, complemented
3#13113750C211yesmaximal, characteristic, complemented
4#13113721C211yesmaximal, characteristic, complemented
5#13113701C211yesmaximal, characteristic, complemented
6#13113701C211yesmaximal, characteristic, complemented
7#13113666C211yesmaximal, characteristic, complemented
8#13113666C211yesmaximal, characteristic, complemented
9#13113660C211yesmaximal, characteristic, complemented
10D8×#1055C211yesmaximal, characteristic, complemented
11#13113616C211yesmaximal, characteristic, complemented
12#13113305C211yesmaximal, characteristic, complemented
13#13113227C211yesmaximal, characteristic, complemented
14#13113136C211yesmaximal, characteristic, complemented
15C13×#3100C211yesmaximal, characteristic
16C13×#532C2211yescharacteristic
17C2×C4×D4×C13C2211yescharacteristic
18C13×#480C411yescharacteristic
19C13×#480C411yescharacteristic
20C13×#474C411yescharacteristic
21C13×#474C411yescharacteristic
22C13×#459C411yescharacteristic
23C13×#459C411yescharacteristic
24C13×#447C411yescharacteristic
25C13×#447C411yescharacteristic
26C4×C13×D8C2211yescharacteristic
27C4×C13×D8C2211yescharacteristic
28C4×C13×D8C2211yescharacteristic
29C4×C13×D8C2211yescharacteristic
30C13×#431C2211yescharacteristic
31#11718895—21no—
32#11718895—21no—
33#11718868—21no—
34C2×C22⋊#1055—21no—
35#11718673—21no—
36#11718673C2211yescharacteristic
37#11718673C2211yescharacteristic
38#11718673C2211yescharacteristic, complemented
39#11718673C2211yescharacteristic, complemented
40#11718672—21no—
41#11718672—21no—
42D4×#1055—21no—
43D4×#1055C2211yescharacteristic
44D4×#1055C2211yescharacteristic
45D4×#1055C2211yescharacteristic, complemented
46D4×#1055C2211yescharacteristic, complemented
47#11718587C2211yescharacteristic
48#11718586C2211yescharacteristic
49#11718586C2211yescharacteristic
50#11718586C2211yescharacteristic
51D4⋊#1055C2211yescharacteristic
52D4⋊#1055C2211yescharacteristic
53D4⋊#1055C2211yescharacteristic
54D4⋊#1055C2211yescharacteristic
55D4⋊#1055C2211yescharacteristic, complemented
56D4⋊#1055C2211yescharacteristic, complemented
57D4⋊#1055C2211yescharacteristic, complemented
58D4⋊#1055C2211yescharacteristic, complemented
59#11718050C2211yescharacteristic, complemented
60#11718050C2211yescharacteristic, complemented
61#11718049C2211yescharacteristic, complemented
62#11718049C2211yescharacteristic, complemented
63#11718047C2211yescharacteristic, complemented
64#11718046C2211yescharacteristic, complemented
65#11718046C2211yescharacteristic, complemented
66C8×#1055C2211yescharacteristic, complemented
67C2×C13×#41—21no—
68C22×D4×C13C2×C411yescharacteristic
69C23×C4×C13—21no—
70C2×C13×D8C2×C411yescharacteristic
71C2×C13×D8C2×C411yescharacteristic
72C2×C13×D8C2×C411yescharacteristic
73C2×C13×D8C2×C411yescharacteristic
74C13×C4⋊Q8C2×C411yescharacteristic
75C13×#127C2×C411yescharacteristic
76C13×#124—21no—
77C13×#121—21no—
78C13×#121C2×C411yescharacteristic
79C13×#121C2×C411yescharacteristic
80C4×D4×C13—21no—
81C4×D4×C13—21no—
82C4×D4×C13—21no—
83C4×D4×C13C2×C411yescharacteristic
84C4×D4×C13C2×C411yescharacteristic
85C4×D4×C13C2311yescharacteristic
86C4×D4×C13C2311yescharacteristic
87C4×D4×C13C2311yescharacteristic
88C4×D4×C13C2311yescharacteristic
89C2×C13×C4⋊C4C2×C411yescharacteristic
90C2×C13×C22⋊C4—21no—
91C2×C42×C13C2311yescharacteristic
92C2×#6099—21no—
93C2×#6099—21no—
94C2×#6099—21no—
95C2×#6099—21no—
96C22×#1055—21no—
97C22×#1055—21no—
98C22×#1055—21no—
99C22×#1055—21no—
100C13×#107C2×C411yescharacteristic
101C13×#107C2×C411yescharacteristic
102C13×#107C2×C411yescharacteristic
103C13×#107C2×C411yescharacteristic
104C13×C4⋊C8C2×C411yescharacteristic
105C13×C4⋊C8C2×C411yescharacteristic
106C13×#102C2×C411yescharacteristic
107C13×#102C2×C411yescharacteristic
108C13×#102C2×C411yescharacteristic
109C13×#102C2×C411yescharacteristic
110C13×#102C2×C411yescharacteristic
111C13×#102C2×C411yescharacteristic
112C13×#102C2×C411yescharacteristic
113C13×#102C2×C411yescharacteristic
114C13×C22⋊C8C2×C411yescharacteristic
115C13×C22⋊C8C2×C411yescharacteristic
116C4×C8×C13C2311yescharacteristic
117C4×C8×C13C2311yescharacteristic
118C22⋊#1055—21no—
119C22⋊#1055—21no—
120C22⋊#1055—21no—
121C22⋊#1055—21no—
122C22⋊#1055—21no—
123C22⋊#1055—21no—
124C22⋊#1055—21no—
125C22⋊#1055—21no—
126C22⋊#1055—21no—
127C22⋊#1055—21no—
128C22⋊#1055—21no—
129C22⋊#1055D411yescharacteristic
130C22⋊#1055D411yescharacteristic
131C4⋊#1055—21no—
132C4⋊#1055D411yescharacteristic
133C4⋊#1055D411yescharacteristic
134C4⋊#1055C2311yescharacteristic
135C4⋊#1055C2311yescharacteristic
136C4⋊#1055C2311yescharacteristic
137C4⋊#1055C2311yescharacteristic
138#88043—21no—
139C4×#1055—21no—
140C4×#1055C2311yescharacteristic
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144#18026—131nomaximal, Sylow
145C24×C13—21no—
146C13×#41—81no—
147C13×#41—81no—
148C2×Q8×C13—21no—
149C2×D4×C13—22no—
150C2×D4×C13—21no—
151C2×D4×C13—21no—
152C2×D4×C13—21no—
153C2×D4×C13—21no—
154C2×D4×C13—21no—
155C2×D4×C13—41no—
156C2×D4×C13C22×C411yescharacteristic
157C2×D4×C13C22×C411yescharacteristic
158C2×D4×C13C22×C411yescharacteristic
159C2×D4×C13C22×C411yescharacteristic
160C22×C4×C13—21no—
161C22×C4×C13—21no—
162C22×C4×C13—21no—
163C22×C4×C13—21no—
164C22×C4×C13—21no—
165C22×C4×C13—21no—
166C22×C4×C13—21no—
167C22×C4×C13—81no—
168C22×C4×C13—81no—
169C22×C4×C13C22×C411yescharacteristic
170C22×C4×C13C2×D411yescharacteristic
171C22×C4×C13#4111yescharacteristic
172C13×D8—22no—
173C13×D8—22no—
174C13×D8—41no—
175C13×D8—41no—
176C2×C8×C13C22×C411yescharacteristic
177C2×C8×C13C22×C411yescharacteristic
178C2×C8×C13C22×C411yescharacteristic
179C2×C8×C13C22×C411yescharacteristic
180C13×C4⋊C4—21no—
181C13×C4⋊C4—21no—
182C13×C4⋊C4C22×C411yescharacteristic
183C13×C4⋊C4C22×C411yescharacteristic
184C13×C4⋊C4C22×C411yescharacteristic
185C13×C4⋊C4C22×C411yescharacteristic
186C13×C22⋊C4—21no—
187C13×C22⋊C4—21no—
188C13×C22⋊C4—21no—
189C13×C22⋊C4—21no—
190C13×C22⋊C4—21no—
191C13×C22⋊C4—21no—
192C13×C22⋊C4—21no—
193C13×C22⋊C4—21no—
194C42×C13C22×C411yescharacteristic
195C42×C13C2×D411yescharacteristic
196C42×C13#4111yescharacteristic
197C42×C13C2411yescharacteristic
198#6099—81no—
199#6099—81no—
200#6099—81no—
201#6099—81no—
202C2×#1055—21no—
203C2×#1055—21no—
204C2×#1055—21no—
205C2×#1055—21no—
206C2×#1055—21no—
207C2×#1055—21no—
208C2×#1055—81no—
209C2×#1055—81no—
210C2×#1055—81no—
211C2×#1055—81no—
212C2×#1055C2×D411yescharacteristic
213C2×#1055C2×D411yescharacteristic
214C2×#1055C2×D411yescharacteristic
215C2×#1055C2×D411yescharacteristic
216#3100D1311yescharacteristic
217#2979—131no—
218#2974—131no—
219#1594—131no—
220#1589—131no—
221#1586—131no—
222#1586—131no—
223#1581—131no—
224#1581—131no—
225#1580—131no—
226C8×D8—131no—
227#1572—131no—
228#1496—131no—
229#1478—131no—
230#1454—131no—
231C23×C13—21no—
232C23×C13—21no—
233C23×C13—21no—
234C23×C13—21no—
235C23×C13—42no—
236C23×C13—42no—
237C23×C13—81no—
238C23×C13C4×D411yescharacteristic
239Q8×C13—81no—
240D4×C13—21no—
241D4×C13—21no—
242D4×C13—21no—
243D4×C13—21no—
244D4×C13—21no—
245D4×C13—21no—
246D4×C13—21no—
247D4×C13—42no—
248D4×C13—42no—
249D4×C13—81no—
250D4×C13—81no—
251D4×C13—81no—
252D4×C13#13112yes—
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—21no—
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—41no—
269C2×C4×C13—41no—
270C2×C4×C13—81no—
271C2×C4×C13—81no—
272C2×C4×C13—81no—
273C2×C4×C13C4×D411yescharacteristic
274C2×C4×C13C4×D411yescharacteristic
275C2×C4×C13C4×D411yescharacteristic
276C2×C4×C13C23×C411yescharacteristic
277C2×C4×C13C22×D411yescharacteristic
278C2×C4×C13C2×#4111yescharacteristic
279C8×C13—21no—
280C8×C13—21no—
281C8×C13—21no—
282C8×C13—21no—
283#1055—21no—
284#1055—21no—
285#1055—21no—
286#1055—21no—
287#1055—41no—
288#1055—41no—
289#1055—41no—
290#1055—41no—
291#1055—41no—
292#1055—41no—
293#532C2×D1311yescharacteristic
294C2×C4×D4C2×D1311yescharacteristic
295#480Dic1311yescharacteristic
296#480Dic1311yescharacteristic
297#474Dic1311yescharacteristic
298#474Dic1311yescharacteristic
299#459Dic1311yescharacteristic
300#459Dic1311yescharacteristic
301#447Dic1311yescharacteristic
302#447Dic1311yescharacteristic
303C4×D8C2×D1311yescharacteristic
304C4×D8C2×D1311yescharacteristic
305C4×D8C2×D1311yescharacteristic
306C4×D8C2×D1311yescharacteristic
307#436—131no—
308#436—131no—
309#436—131no—
310#436—131no—
311#436—261no—
312#435—261no—
313#435—261no—
314C8×D4—131no—
315C8×D4—131no—
316C8×D4—131no—
317C8×D4—131no—
318C8×D4—261no—
319#432—131no—
320#431—131no—
321#431—131no—
322#431—131no—
323#431C2×D1311yescharacteristic
324#408—261no—
325#408—261no—
326#407—261no—
327C2×C22⋊C8—261no—
328#335—131no—
329#335—131no—
330#334—131no—
331#334—131no—
332D4⋊C8—131no—
333D4⋊C8—131no—
334D4⋊C8—131no—
335D4⋊C8—131no—
336D4⋊C8—131no—
337D4⋊C8—131no—
338D4⋊C8—131no—
339D4⋊C8—131no—
340#322—131no—
341#322—131no—
342#322—131no—
343C82—131no—
344C22×C13—21no—
345C22×C13—22no—
346C22×C13—21no—
347C22×C13—21no—
348C22×C13—41no—
349C22×C13—41no—
350C22×C13—41no—
351C22×C13—41no—
352C22×C13—41no—
353C22×C13—41no—
354C22×C13—41no—
355C22×C13—41no—
356C22×C13—41no—
357C22×C13—41no—
358C22×C13—41no—
359C22×C13—84no—
360C22×C13C2×C4×D411yescharacteristic
361C4×C13—21no—
362C4×C13—21no—
363C4×C13—21no—
364C4×C13—21no—
365C4×C13—41no—
366C4×C13—41no—
367C4×C13—41no—
368C4×C13—41no—
369C4×C13C2×#13111yescharacteristic
370C4×C13#56811yescharacteristic
371C4×C13#57611yescharacteristic
372C4×C13#57611yescharacteristic
373C2×#41—21no—
374C22×D4C2×Dic1311yescharacteristic
375C23×C4—21no—
376C2×D8C2×Dic1311yescharacteristic
377C2×D8C2×Dic1311yescharacteristic
378C2×D8C2×Dic1311yescharacteristic
379C2×D8C2×Dic1311yescharacteristic
380C2×M16—261no—
381C2×M16—261no—
382C2×M16—261no—
383C2×M16—261no—
384C22×C8—261no—
385C22×C8—261no—
386C22×C8—261no—
387C22×C8—261no—
388C4⋊Q8C2×Dic1311yescharacteristic
389#127C2×Dic1311yescharacteristic
390#124—21no—
391#121—21no—
392#121C2×Dic1311yescharacteristic
393#121C2×Dic1311yescharacteristic
394C4×D4—21no—
395C4×D4—21no—
396C4×D4—21no—
397C4×D4C2×Dic1311yescharacteristic
398C4×D4C2×Dic1311yescharacteristic
399C4×D4C22×D1311yescharacteristic
400C4×D4C22×D1311yescharacteristic
401C4×D4C22×D1311yescharacteristic
402C4×D4C22×D1311yescharacteristic
403C2×C4⋊C4C2×Dic1311yescharacteristic
404C2×C22⋊C4—21no—
405C2×C42C22×D1311yescharacteristic
406#107C2×Dic1311yescharacteristic
407#107C2×Dic1311yescharacteristic
408#107C2×Dic1311yescharacteristic
409#107C2×Dic1311yescharacteristic
410C4⋊C8—131no—
411C4⋊C8—131no—
412C4⋊C8—131no—
413C4⋊C8—131no—
414C4⋊C8—131no—
415C4⋊C8—131no—
416C4⋊C8—261no—
417C4⋊C8C2×Dic1311yescharacteristic
418C4⋊C8C2×Dic1311yescharacteristic
419#102C2×Dic1311yescharacteristic
420#102C2×Dic1311yescharacteristic
421#102C2×Dic1311yescharacteristic
422#102C2×Dic1311yescharacteristic
423#102C2×Dic1311yescharacteristic
424#102C2×Dic1311yescharacteristic
425#102C2×Dic1311yescharacteristic
426#102C2×Dic1311yescharacteristic
427C22⋊C8—131no—
428C22⋊C8—131no—
429C22⋊C8—261no—
430C22⋊C8—261no—
431C22⋊C8—261no—
432C22⋊C8—261no—
433C22⋊C8—261no—
434C22⋊C8—261no—
435C22⋊C8—261no—
436C22⋊C8—261no—
437C22⋊C8—261no—
438C22⋊C8—261no—
439C22⋊C8—261no—
440C22⋊C8C2×Dic1311yescharacteristic
441C22⋊C8C2×Dic1311yescharacteristic
442#97—261no—
443C4×C8—131no—
444C4×C8—131no—
445C4×C8—131no—
446C4×C8—131no—
447C4×C8—261no—
448C4×C8C22×D1311yescharacteristic
449C4×C8C22×D1311yescharacteristic
450C2×C13—41no—
451C2×C13—42no—
452C2×C13—81no—
453C2×C13—81no—
454C2×C13—81no—
455C2×C13#293311yescharacteristic
456C2×C13#294811yescharacteristic
457C2×C13#295511yescharacteristic
458C24—21no—
459#41—81no—
460#41—81no—
461C2×Q8—21no—
462C2×D4—22no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—41no—
469C2×D4C22×Dic1311yescharacteristic
470C2×D4C22×Dic1311yescharacteristic
471C2×D4C22×Dic1311yescharacteristic
472C2×D4C22×Dic1311yescharacteristic
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—81no—
481C22×C4—81no—
482C22×C4D4×D1311yescharacteristic
483C22×C4#612911yescharacteristic
484C22×C4C22×Dic1311yescharacteristic
485D8—22no—
486D8—22no—
487D8—41no—
488D8—41no—
489M16—1041no—
490M16—1041no—
491M16—1041no—
492M16—1041no—
493C2×C8—131no—
494C2×C8—131no—
495C2×C8—131no—
496C2×C8—131no—
497C2×C8—261no—
498C2×C8—261no—
499C2×C8—261no—
500C2×C8—261no—
501C2×C8—261no—
502C2×C8—261no—
503C2×C8—1041no—
504C2×C8—1041no—
505C2×C8—1041no—
506C2×C8—1041no—
507C2×C8C22×Dic1311yescharacteristic
508C2×C8C22×Dic1311yescharacteristic
509C2×C8C22×Dic1311yescharacteristic
510C2×C8C22×Dic1311yescharacteristic
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4C22×Dic1311yescharacteristic
514C4⋊C4C22×Dic1311yescharacteristic
515C4⋊C4C22×Dic1311yescharacteristic
516C4⋊C4C22×Dic1311yescharacteristic
517C22⋊C4—21no—
518C22⋊C4—21no—
519C22⋊C4—21no—
520C22⋊C4—21no—
521C22⋊C4—21no—
522C22⋊C4—21no—
523C22⋊C4—21no—
524C22⋊C4—21no—
525C42D4×D1311yescharacteristic
526C42#612911yescharacteristic
527C42C22×Dic1311yescharacteristic
528C42C23×D1311yescharacteristic
529C13#1802611yescharacteristic, complemented, Sylow
530C23—21no—
531C23—21no—
532C23—21no—
533C23—21no—
534C23—42no—
535C23—42no—
536C23—81no—
537C23D4×Dic1311yescharacteristic
538Q8—81no—
539D4—21no—
540D4—21no—
541D4—21no—
542D4—21no—
543D4—21no—
544D4—21no—
545D4—21no—
546D4—42no—
547D4—42no—
548D4—81no—
549D4—81no—
550D4—81no—
551D4#8820212yes—
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—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—81no—
570C2×C4—81no—
571C2×C4—81no—
572C2×C4D4×Dic1311yescharacteristic
573C2×C4D4×Dic1311yescharacteristic
574C2×C4D4×Dic1311yescharacteristic
575C2×C4C2×D4×D1311yescharacteristic
576C2×C4C2×#612911yescharacteristic
577C2×C4C23×Dic1311yescharacteristic
578C8—21no—
579C8—21no—
580C8—21no—
581C8—21no—
582C8—261no—
583C8—261no—
584C8—261no—
585C8—261no—
586C8—521no—
587C8—521no—
588C8—521no—
589C8—521no—
590C8—521no—
591C8—521no—
592C22—21no—
593C22—21no—
594C22—21no—
595C22—22no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—41no—
600C22—41no—
601C22—41no—
602C22—41no—
603C22—41no—
604C22—41no—
605C22—41no—
606C22—41no—
607C22—84no—
608C22C2×D4×Dic1311yescharacteristic
609C4—21no—
610C4—21no—
611C4—21no—
612C4—21no—
613C4—41no—
614C4—41no—
615C4—41no—
616C4—41no—
617C4#1171946211yescharacteristic
618C4#1171946211yescharacteristic
619C4C2×#8820211yescharacteristic
620C4#1171952411yescharacteristic
621C2—41no—
622C2—42no—
623C2—81no—
624C2—81no—
625C2—81no—
626C2#1312356311yescharacteristic
627C2#1312368811yescharacteristic
628C2#1312373911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
Fitting, prime radicalC13×#3100C2
socleC22×C13C2×C4×D4
cosocleC42×C13C24
hypercenter#3100D13
hypocenterC13#18026
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3100

Complements

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

NH ≅ G/Ntype
1. #13123903C2semidirect
2. #13123871C2semidirect
3. #13113750C2semidirect
4. #13113721C2semidirect
5. #13113701C2semidirect
6. #13113701C2semidirect
7. #13113666C2semidirect
8. #13113666C2semidirect
9. #13113660C2semidirect
10. D8×#1055C2semidirect
11. #13113616C2semidirect
12. #13113305C2semidirect
13. #13113227C2semidirect
14. #13113136C2semidirect
38. #11718673C22semidirect
39. #11718673C22semidirect
45. D4×#1055C22semidirect
46. D4×#1055C22semidirect
55. D4⋊#1055C22semidirect
56. D4⋊#1055C22semidirect
57. D4⋊#1055C22semidirect
58. D4⋊#1055C22semidirect
59. #11718050C22semidirect
60. #11718050C22semidirect
61. #11718049C22semidirect
62. #11718049C22semidirect
63. #11718047C22semidirect
64. #11718046C22semidirect
65. #11718046C22semidirect
66. C8×#1055C22semidirect
529. C13#18026semidirect

Maximal subgroups

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

subgroupindex
#131239032
#131238712
#131137502
#131137212
#131137012
#131136662
#131136602
D8×#10552
#131136162
#131133052
#131132272
#131131362
C13×#31002
#1802613