Finite Group Databasebeta

← #15830762

Subgroups — #15830762

Order 3328.

1010 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13128688C211yesmaximal, characteristic
2#13123865C211yesmaximal, characteristic, complemented
3#13113390C212yesmaximal, complemented
4#13113386C211yesmaximal, characteristic, complemented
5#13113382C211yesmaximal, characteristic, complemented
6#13113377C212yesmaximal, complemented
7#13113347C211yesmaximal, characteristic, complemented
8#13113343C211yesmaximal, characteristic, complemented
9#13113338C212yesmaximal, complemented
10#13113325C212yesmaximal, complemented
11C13×#2353C211yesmaximal, characteristic, complemented
12C2×C4×D4×C13C2211yescharacteristic
13#11719510—21no—
14#11719496C2212yes—
15#11719496C2212yes—
16#11719268C412yescomplemented
17#11719264—22no—
18#11719263—22no—
19#11719258C412yescomplemented
20#11719256C412yescomplemented
21#11719247C412yescomplemented
22#11719209—21no—
23#11719199—21no—
24#11719199—21no—
25#11719182C2211yescharacteristic
26#11719175C2211yescharacteristic
27C13×#388—21no—
28C13×#387—21no—
29C13×#386—21no—
30C13×#383C2211yescharacteristic
31C13×#381C2211yescharacteristic
32C13×#380C2211yescharacteristic
33C4×C13×C22⋊C4—21no—
34C4×C13×C22⋊C4C2211yescharacteristic
35C13×#376C2211yescharacteristic
36C2×C13×#95C2211yescharacteristic
37#11718868C2212yes—
38C2×C22⋊#1055C2212yes—
39#11718672—22no—
40#11718672—22no—
41#11718587C2211yescharacteristic
42#11718587C2211yescharacteristic
43#11718044C2212yes—
44#11718044C2212yes—
45#11718044C2212yes—
46#11718044C2212yes—
47#11718043C2212yes—
48#11718043C2212yes—
49#11718043C2212yes—
50#11718043C2212yes—
51C22×D4×C13D411yescharacteristic
52C23×C4×C13—21no—
53C23×C4×C13C2311yescharacteristic
54C23×C4×C13C2311yescharacteristic
55C2×#6127—21no—
56C2×#6127C2×C412yes—
57C2×#6127C2×C412yescomplemented
58C4×D4×C13C2×C412yes—
59C4×D4×C13C2×C412yes—
60C4×D4×C13D412yes—
61C4×D4×C13D412yes—
62C2×C13×C4⋊C4—21no—
63C2×C13×C4⋊C4D411yescharacteristic
64C2×C13×C22⋊C4—21no—
65C2×C13×C22⋊C4—21no—
66C2×C13×C22⋊C4—21no—
67C2×C13×C22⋊C4D411yescharacteristic
68C2×C13×C22⋊C4D411yescharacteristic
69C2×C42×C13—21no—
70C2×C42×C13—21no—
71C2×C42×C13C2311yescharacteristic
72#88207—22no—
73#88207—22no—
74#88194—22no—
75#88192—22no—
76#88192—22no—
77#88190—22no—
78#88184—21no—
79#88184C2×C412yes—
80#88184C2×C412yescomplemented
81#88184C2312yes—
82#88183—22no—
83#88183—22no—
84C4×C22⋊D13—22no—
85C4×C22⋊D13—22no—
86C4×C22⋊D13—22no—
87C4×C22⋊D13—22no—
88#88180—21no—
89#88180C2×C412yes—
90#88180C2×C412yescomplemented
91#88178—21no—
92#88178C2×C412yes—
93#88178C2×C412yescomplemented
94#88178C2312yes—
95C2×#6099—22no—
96C22×#1055—22no—
97#88147—22no—
98#88146—22no—
99C4⋊C4×D13—22no—
100#88141—22no—
101#88139—22no—
102#88139—22no—
103#88138—22no—
104#88138—22no—
105#88137—22no—
106#88137—22no—
107#88133—22no—
108#88133—22no—
109#88129—21no—
110#88128C2×C411yescharacteristic, complemented
111C4×D52—21no—
112C4×D52C2×C412yescomplemented
113#88124—21no—
114#88123C2×C411yescharacteristic, complemented
115#88123C2×C411yescharacteristic, complemented
116#88123C2×C411yescharacteristic, complemented
117C4×Dic26—21no—
118C4×Dic26C2×C412yescomplemented
119C13×#95—21no—
120C13×#95—21no—
121C13×#95—21no—
122C13×#95—21no—
123C13×#95—21no—
124C13×#95C2311yescharacteristic
125C13×#95C2311yescharacteristic
126C13×#95C2311yescharacteristic
127C13×#95C2311yescharacteristic
128C22⋊#1055—22no—
129C22⋊#1055—22no—
130C22⋊#1055C2312yes—
131C22⋊#1055C2312yes—
132C4⋊#1055—21no—
133C4⋊#1055—21no—
134#88043—21no—
135#88043—21no—
136#17629—131nomaximal, Sylow
137C24×C13C2×D411yescharacteristic
138C24×C13C2×D411yescharacteristic
139C2×D4×C13—41no—
140C2×D4×C13—41no—
141C2×D4×C13C22⋊C412yes—
142C2×D4×C13C22⋊C412yes—
143C22×C4×C13—21no—
144C22×C4×C13—21no—
145C22×C4×C13—21no—
146C22×C4×C13—21no—
147C22×C4×C13—42no—
148C22×C4×C13—42no—
149C22×C4×C13—81no—
150C22×C4×C13—81no—
151C22×C4×C13—81no—
152C22×C4×C13C22×C412yes—
153C22×C4×C13C22×C412yes—
154C22×C4×C13C2×D412yes—
155C22×C4×C13C2×D412yes—
156C22×C4×C13C2×D411yescharacteristic
157C22×C4×C13C2×D411yescharacteristic
158C22×C4×C13C2×D411yescharacteristic
159C22×C4×C13C2×D411yescharacteristic
160C22×C4×C13C2411yescharacteristic
161C2×C22⋊D13—22no—
162C2×C22⋊D13—22no—
163C2×C22⋊D13—22no—
164C2×C22⋊D13—22no—
165C2×C22⋊D13—22no—
166#6127—42no—
167#6127—42no—
168#6127—82no—
169#6127—82no—
170C2×D52—21no—
171C2×D52—21no—
172C2×D52C22×C412yes—
173C2×C4×D13—22no—
174C2×C4×D13—22no—
175C2×C4×D13—22no—
176C2×Dic26—21no—
177C2×Dic26—21no—
178C2×Dic26C22×C412yes—
179C13×C4⋊C4—81no—
180C13×C4⋊C4C22⋊C412yes—
181C13×C4⋊C4C22⋊C412yes—
182C13×C22⋊C4—42no—
183C13×C22⋊C4—42no—
184C13×C22⋊C4—81no—
185C13×C22⋊C4C22⋊C412yes—
186C13×C22⋊C4C22⋊C412yes—
187C13×C22⋊C4C22⋊C412yes—
188C13×C22⋊C4C22⋊C412yes—
189C42×C13—42no—
190C42×C13—81no—
191C42×C13C22×C411yescharacteristic
192C42×C13C22×C411yescharacteristic
193C42×C13C2×D411yescharacteristic
194C42×C13C2×D411yescharacteristic
195C22⋊Dic13—22no—
196C22⋊Dic13—22no—
197C22⋊Dic13—22no—
198C22⋊Dic13—22no—
199C22⋊Dic13—22no—
200#6103—22no—
201#6103—22no—
202#6103—22no—
203#6103—22no—
204C4⋊Dic13—21no—
205C4⋊Dic13—21no—
206C4⋊Dic13—21no—
207C4⋊Dic13—21no—
208C4⋊Dic13C22×C412yes—
209C4⋊Dic13C22×C412yes—
210#6101—22no—
211#6101—22no—
212#6101—22no—
213#6101—22no—
214C4×Dic13—22no—
215C4×Dic13—22no—
216C4×Dic13—22no—
217#6099—82no—
218C2×#1055—22no—
219C2×#1055—22no—
220C2×#1055—82no—
221#3506—131no—
222#2973—131no—
223#2353D1311yescharacteristic, complemented
224#1516—132no—
225#1515—131no—
226#1514—131no—
227#1513—132no—
228#1506—131no—
229#1505—131no—
230#1504—132no—
231#1501—132no—
232C23×C13—21no—
233C23×C13—21no—
234C23×C13—21no—
235C23×C13—21no—
236C23×C13—41no—
237C23×C13—41no—
238C23×C13—41no—
239C23×C13—41no—
240C23×C13C2×C22⋊C412yes—
241C23×C13C2×C22⋊C412yes—
242C23×C13C22×D411yescharacteristic
243C22×D13—22no—
244D4×C13—42no—
245D4×C13—42no—
246C2×C4×C13—21no—
247C2×C4×C13—21no—
248C2×C4×C13—22no—
249C2×C4×C13—42no—
250C2×C4×C13—42no—
251C2×C4×C13—41no—
252C2×C4×C13—41no—
253C2×C4×C13—41no—
254C2×C4×C13—42no—
255C2×C4×C13—42no—
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—41no—
264C2×C4×C13—41no—
265C2×C4×C13—41no—
266C2×C4×C13—41no—
267C2×C4×C13—41no—
268C2×C4×C13—84no—
269C2×C4×C13C2×C22⋊C411yescharacteristic
270C2×C4×C13C2×C22⋊C412yes—
271C2×C4×C13C2×C22⋊C412yes—
272C2×C4×C13C2×C22⋊C411yescharacteristic
273C2×C4×C13C2×C22⋊C411yescharacteristic
274C2×C4×C13C2×C22⋊C411yescharacteristic
275C2×C4×C13C23×C411yescharacteristic
276C2×C4×C13C22×D411yescharacteristic
277C22⋊D13—42no—
278C22⋊D13—42no—
279C22⋊D13—82no—
280C22⋊D13—82no—
281C22⋊D13—82no—
282C22⋊D13—82no—
283C2×Dic13—22no—
284C2×Dic13—22no—
285C2×Dic13—22no—
286D52—42no—
287D52—42no—
288D52—81no—
289C4×D13—44no—
290C4×D13—82no—
291C4×D13—82no—
292Dic26—42no—
293Dic26—42no—
294Dic26—81no—
295#1055—42no—
296#1055—42no—
297#559—262no—
298#556—132no—
299#555—132no—
300#553—262no—
301#550—132no—
302#547—132no—
303#538—261no—
304#538—261no—
305#535—261no—
306#533—131no—
307#532—131no—
308#525—132no—
309#525—132no—
310#520—261no—
311C2×C4×D4C2×D1311yescharacteristic
312#435—262no—
313#435—262no—
314#432—131no—
315#432—131no—
316#407—132no—
317C2×C22⋊C8—132no—
318#388—21no—
319#387—21no—
320#386—21no—
321#383C2×D1311yescharacteristic
322#381C2×D1311yescharacteristic
323#380C2×D1311yescharacteristic
324C4×C22⋊C4—21no—
325C4×C22⋊C4C2×D1311yescharacteristic
326#376C2×D1311yescharacteristic
327C2×#95C2×D1311yescharacteristic
328#328—132no—
329#328—132no—
330#328—132no—
331#328—132no—
332#327—132no—
333#327—132no—
334#327—132no—
335#327—132no—
336C22×C13—21no—
337C22×C13—21no—
338C22×C13—22no—
339C22×C13—22no—
340C22×C13—22no—
341C22×C13—22no—
342C22×C13—22no—
343C22×C13—22no—
344C22×C13—42no—
345C22×C13—42no—
346C22×C13—81no—
347C22×C13—81no—
348C22×C13C22×C22⋊C411yescharacteristic
349C22×C13#57511yescharacteristic
350C22×C13#57511yescharacteristic
351C2×D13—42no—
352C2×D13—42no—
353C2×D13—42no—
354C4×C13—21no—
355C4×C13—21no—
356C4×C13—22no—
357C4×C13—22no—
358C4×C13—21no—
359C4×C13—21no—
360C4×C13—21no—
361C4×C13—21no—
362C4×C13—42no—
363C4×C13—81no—
364C4×C13—81no—
365C4×C13—81no—
366Dic13—42no—
367Dic13—42no—
368Dic13—42no—
369C2×#41—132no—
370C2×#41—132no—
371C2×#41—261no—
372C22×D4C22⋊D1311yescharacteristic
373C23×C4—21no—
374C23×C4C22×D1311yescharacteristic
375C23×C4C22×D1311yescharacteristic
376C2×M16—262no—
377C22×C8—262no—
378C4⋊Q8—131no—
379C4⋊Q8—131no—
380C4⋊Q8—131no—
381#127—131no—
382#127—262no—
383#126—262no—
384#126—262no—
385#125—261no—
386#124—262no—
387#124—262no—
388#124—262no—
389#124—261no—
390#123—262no—
391#123—262no—
392#123—262no—
393#123—262no—
394C22⋊Q8—132no—
395C22⋊Q8—132no—
396C22⋊Q8—132no—
397C22⋊Q8—261no—
398#121—132no—
399#121—132no—
400#121—132no—
401#121—262no—
402#121—262no—
403#121—261no—
404#121—262no—
405#121—262no—
406#120—262no—
407#120—262no—
408C4×Q8—132no—
409C4×Q8—262no—
410C4×Q8—261no—
411C4×D4—132no—
412C4×D4—262no—
413C4×D4—262no—
414C4×D4—262no—
415C4×D4—262no—
416C4×D4—262no—
417C4×D4—261no—
418C4×D4C4×D1312yes—
419C4×D4C4×D1312yes—
420C4×D4D5212yes—
421C4×D4D5212yes—
422#117—132no—
423#117—132no—
424#117—261no—
425#117—262no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—262no—
428C2×C4⋊C4C22⋊D1311yescharacteristic
429C2×C22⋊C4—21no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
432C2×C22⋊C4C22⋊D1311yescharacteristic
433C2×C22⋊C4C22⋊D1311yescharacteristic
434C2×C42—21no—
435C2×C42—21no—
436C2×C42C22×D1311yescharacteristic
437C4⋊C8—261no—
438C4⋊C8—261no—
439C22⋊C8—132no—
440C22⋊C8—132no—
441C22⋊C8—262no—
442C22⋊C8—262no—
443#97—261no—
444#97—261no—
445#95—21no—
446#95—21no—
447#95—21no—
448#95—21no—
449#95—21no—
450#95C22×D1311yescharacteristic
451#95C22×D1311yescharacteristic
452#95C22×D1311yescharacteristic
453#95C22×D1311yescharacteristic
454C2×C13—21no—
455C2×C13—21no—
456C2×C13—42no—
457C2×C13—42no—
458C2×C13#288311yescharacteristic
459C2×C13#289611yescharacteristic
460C2×C13#290111yescharacteristic
461D13—82no—
462C24C2×C22⋊D1311yescharacteristic
463C24C2×C22⋊D1311yescharacteristic
464#41—522no—
465#41—522no—
466#41—1042no—
467#41—1042no—
468C2×Q8—132no—
469C2×Q8—261no—
470C2×Q8—261no—
471C2×D4—41no—
472C2×D4—41no—
473C2×D4—132no—
474C2×D4—262no—
475C2×D4—262no—
476C2×D4—262no—
477C2×D4—262no—
478C2×D4—262no—
479C2×D4—261no—
480C2×D4—261no—
481C2×D4#610312yes—
482C2×D4#610312yes—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—42no—
488C22×C4—42no—
489C22×C4—81no—
490C22×C4—81no—
491C22×C4—81no—
492C22×C4—262no—
493C22×C4—262no—
494C22×C4—262no—
495C22×C4C2×C4×D1312yes—
496C22×C4C2×C4×D1312yes—
497C22×C4C2×D5212yes—
498C22×C4C2×D5212yes—
499C22×C4C2×C22⋊D1311yescharacteristic
500C22×C4C2×C22⋊D1311yescharacteristic
501C22×C4C2×C22⋊D1311yescharacteristic
502C22×C4C2×C22⋊D1311yescharacteristic
503C22×C4C23×D1311yescharacteristic
504M16—1042no—
505C2×C8—262no—
506C2×C8—262no—
507C2×C8—1042no—
508C4⋊C4—81no—
509C4⋊C4—132no—
510C4⋊C4—132no—
511C4⋊C4—261no—
512C4⋊C4—262no—
513C4⋊C4—262no—
514C4⋊C4—261no—
515C4⋊C4—261no—
516C4⋊C4—262no—
517C4⋊C4—261no—
518C4⋊C4—262no—
519C4⋊C4#610312yes—
520C4⋊C4#610312yes—
521C22⋊C4—42no—
522C22⋊C4—42no—
523C22⋊C4—81no—
524C22⋊C4—262no—
525C22⋊C4—262no—
526C22⋊C4—262no—
527C22⋊C4—262no—
528C22⋊C4—262no—
529C22⋊C4—262no—
530C22⋊C4—262no—
531C22⋊C4—262no—
532C22⋊C4—262no—
533C22⋊C4#610312yes—
534C22⋊C4#610312yes—
535C22⋊C4#610312yes—
536C22⋊C4#610312yes—
537C42—42no—
538C42—81no—
539C42—262no—
540C42—262no—
541C42—262no—
542C42C2×C4×D1311yescharacteristic
543C42C2×C4×D1311yescharacteristic
544C42C2×D5211yescharacteristic
545C42C2×D5211yescharacteristic
546C13#1762911yescharacteristic, complemented, Sylow
547C23—21no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—41no—
552C23—41no—
553C23—41no—
554C23—41no—
555C23—262no—
556C23C2×#610312yes—
557C23C2×#610312yes—
558C23C22×C22⋊D1311yescharacteristic
559Q8—522no—
560Q8—522no—
561Q8—1041no—
562D4—42no—
563D4—42no—
564D4—522no—
565D4—522no—
566D4—522no—
567D4—522no—
568D4—1041no—
569D4—1042no—
570D4—1042no—
571D4—1042no—
572D4—1042no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—22no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—41no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—84no—
596C2×C4—262no—
597C2×C4—262no—
598C2×C4—262no—
599C2×C4—524no—
600C2×C4—1042no—
601C2×C4—1042no—
602C2×C4C2×#610311yescharacteristic
603C2×C4C2×#610312yes—
604C2×C4C2×#610312yes—
605C2×C4C2×#610311yescharacteristic
606C2×C4C2×#610311yescharacteristic
607C2×C4C2×#610311yescharacteristic
608C2×C4C22×C4×D1311yescharacteristic
609C2×C4C22×D5211yescharacteristic
610C8—522no—
611C8—522no—
612C22—21no—
613C22—21no—
614C22—22no—
615C22—22no—
616C22—22no—
617C22—22no—
618C22—22no—
619C22—22no—
620C22—42no—
621C22—42no—
622C22—81no—
623C22—81no—
624C22—522no—
625C22—522no—
626C22—522no—
627C22C22×#610311yescharacteristic
628C22#1171952711yescharacteristic
629C22#1171952711yescharacteristic
630C4—21no—
631C4—21no—
632C4—21no—
633C4—21no—
634C4—21no—
635C4—21no—
636C4—22no—
637C4—22no—
638C4—42no—
639C4—81no—
640C4—81no—
641C4—81no—
642C4—522no—
643C4—522no—
644C4—522no—
645C2—21no—
646C2—21no—
647C2—42no—
648C2—42no—
649C2—1042no—
650C2#1312329611yescharacteristic
651C2#1312335311yescharacteristic
652C2#1312338411yescharacteristic
subgroupG/H
centerC22C22×#6103
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#2353C2
socleC22×C13C22×C22⋊C4
prime radical#13128688C2
cosocleC22×C4×C13C24
hypercenter#2353D13
hypocenterC13#17629
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #2353

Complements

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

NH ≅ G/Ntype
2. #13123865C2semidirect
3. #13113390C2semidirect
4. #13113386C2semidirect
5. #13113382C2semidirect
6. #13113377C2semidirect
7. #13113347C2semidirect
8. #13113343C2semidirect
9. #13113338C2semidirect
10. #13113325C2semidirect
11. C13×#2353C2semidirect
16. #11719268C4semidirect
19. #11719258C4semidirect
20. #11719256C4semidirect
21. #11719247C4semidirect
57. C2×#6127C2×C4semidirect
80. #88184C2×C4semidirect
90. #88180C2×C4semidirect
93. #88178C2×C4semidirect
110. #88128C2×C4semidirect
112. C4×D52C2×C4semidirect
114. #88123C2×C4semidirect
115. #88123C2×C4semidirect
116. #88123C2×C4semidirect
118. C4×Dic26C2×C4semidirect
223. #2353D13semidirect
546. C13#17629semidirect

Maximal subgroups

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

subgroupindex
#131286882
#131238652
#131133902
#131133862
#131133822
#131133772
#131133472
#131133432
#131133382
#131133252
C13×#23532
#1762913