Finite Group Databasebeta

← #15870766

Subgroups — #15870766

Order 3328.

730 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124626C211yesmaximal, characteristic
2#13123773C211yesmaximal, characteristic, complemented
3#13123265C211yesmaximal, characteristic
4#13115780C211yesmaximal, characteristic, complemented
5#13115434C211yesmaximal, characteristic, complemented
6#13115434C211yesmaximal, characteristic, complemented
7#13115108C211yesmaximal, characteristic
8#13115108C211yesmaximal, characteristic
9#13114853C211yesmaximal, characteristic
10#13114723C211yesmaximal, characteristic, complemented
11#13114718C211yesmaximal, characteristic, complemented
12#13114713C211yesmaximal, characteristic, complemented
13#13114679C211yesmaximal, characteristic
14#13114672C211yesmaximal, characteristic
15C13×#1950C211yesmaximal, characteristic, complemented
16C2×#88161C2211yescharacteristic
17C2×#88161C2211yescharacteristic
18C4×#6127C2211yescharacteristic
19#11719175C2211yescharacteristic
20C2×C13×#108C2211yescharacteristic
21C2×C13×#108C2211yescharacteristic
22C13×#423C2211yescharacteristic
23C2×C13×C4⋊C8C2211yescharacteristic
24C4×C13×M16C2211yescharacteristic
25C2×#88065C2211yescharacteristic
26C2×#88065C2211yescharacteristic
27#11718783C2211yescharacteristic
28#11718783C2211yescharacteristic
29#11718783C2211yescharacteristic
30#11718783C2211yescharacteristic
31#11718780C2211yescharacteristic
32#11718780C2211yescharacteristic
33#11718774C2211yescharacteristic
34#11718774C2211yescharacteristic
35#11718767C2211yescharacteristic
36#11718767C2211yescharacteristic
37C2×#88055C2211yescharacteristic
38C2×C8×Dic13C2211yescharacteristic
39C4×C4⋊Dic13C2211yescharacteristic
40C2×#88043C2211yescharacteristic
41#11718512C411yescharacteristic, complemented
42#11718511C411yescharacteristic, complemented
43#11718508C411yescharacteristic, complemented
44#11718508C411yescharacteristic, complemented
45#11718507C411yescharacteristic, complemented
46#11718503C411yescharacteristic, complemented
47#11718490C411yescharacteristic, complemented
48#11718490C411yescharacteristic, complemented
49#11718489—21no—
50#11718489—21no—
51#11718489—21no—
52#11718489—21no—
53#11718368—21no—
54D13×#97—21no—
55#11718350—21no—
56#11718350—21no—
57C13×#341C2211yescharacteristic
58C13×#341C2211yescharacteristic
59#11718147C2211yescharacteristic
60#11718147C2211yescharacteristic
61#11718147C2211yescharacteristic
62#11718147C2211yescharacteristic
63#11718147C2211yescharacteristic
64#11718147C2211yescharacteristic
65#11718142C2211yescharacteristic
66#11718142C2211yescharacteristic
67C2×#6127C2311yescharacteristic
68C2×C13×M16C2311yescharacteristic
69C2×C13×M16C2311yescharacteristic
70C2×C13×M16C2311yescharacteristic
71C2×C13×M16C2311yescharacteristic
72C22×C8×C13C2311yescharacteristic
73C22×C8×C13C2311yescharacteristic
74C2×C42×C13C2311yescharacteristic
75C4×C22⋊D13—21no—
76C4×C22⋊D13—21no—
77#88180C2311yescharacteristic
78#88180C2311yescharacteristic
79#88180C2311yescharacteristic
80C2×C4⋊Dic13—21no—
81#88178—21no—
82#88178—21no—
83C2×C4×Dic13C2311yescharacteristic
84C2×C4×Dic13C2311yescharacteristic
85C22×#1055C2311yescharacteristic
86C22×#1055C2311yescharacteristic
87#88161—22no—
88#88161—22no—
89#88161—22no—
90#88161Q814yescomplemented
91C2×#6094—21no—
92C2×#6094—21no—
93C2×C8×D13—21no—
94C2×C8×D13—21no—
95C4×D52C2×C411yescharacteristic
96C4×D52C2×C411yescharacteristic
97#88126—21no—
98C42×D13—21no—
99#88124C2×C411yescharacteristic
100#88124C2×C411yescharacteristic
101#88123C2×C411yescharacteristic
102#88123C2×C411yescharacteristic
103C4×Dic26—21no—
104C4×Dic26—21no—
105C4×Dic26C2×C411yescharacteristic
106C4×Dic26C2×C411yescharacteristic
107C13×#108—22no—
108C13×#108—22no—
109C13×C4⋊C8—21no—
110C13×C4⋊C8—21no—
111C13×C4⋊C8C2×C411yescharacteristic
112C13×C4⋊C8C2×C411yescharacteristic
113C13×C4⋊C8C2×C411yescharacteristic
114C13×C4⋊C8C2×C411yescharacteristic
115C13×#97—21no—
116C4×C8×C13—21no—
117#88071—21no—
118#88065—22no—
119#88065—22no—
120#88061C2×C411yescharacteristic
121#88061C2×C411yescharacteristic
122#88061C2×C411yescharacteristic
123#88061C2×C411yescharacteristic
124#88058C2×C411yescharacteristic
125#88058C2×C411yescharacteristic
126#88058C2×C411yescharacteristic
127#88058C2×C411yescharacteristic
128#88057C2×C411yescharacteristic
129#88057C2×C411yescharacteristic
130#88057C2×C411yescharacteristic
131#88057C2×C411yescharacteristic
132#88056C2×C411yescharacteristic
133#88056C2×C411yescharacteristic
134#88056C2×C411yescharacteristic
135#88056C2×C411yescharacteristic
136#88055—21no—
137#88055—21no—
138#88055—21no—
139#88055—21no—
140#88055—22no—
141#88054—21no—
142#88054—21no—
143#88054—21no—
144#88054—21no—
145C8×Dic13—21no—
146C8×Dic13—21no—
147C8×Dic13—21no—
148C8×Dic13—21no—
149C8×Dic13—22no—
150#88043D411yescharacteristic
151#88043D411yescharacteristic
152#88043D411yescharacteristic
153#88043D411yescharacteristic
154#21629—131nomaximal, Sylow
155C22×C4×C13#4111yescharacteristic
156C22×C4×C13#4111yescharacteristic
157C22×C4×C13C2411yescharacteristic
158C2×C22⋊D13—21no—
159C22×Dic13—21no—
160C22×Dic13—21no—
161#6127—21no—
162#6127—21no—
163#6127C2×Q812yes—
164#6127#4112yes—
165C2×D52C22×C411yescharacteristic
166C2×C4×D13—21no—
167C2×C4×D13—21no—
168C2×C4×D13—21no—
169C2×Dic26—21no—
170C2×Dic26—21no—
171C2×Dic26C22×C411yescharacteristic
172C13×M16—21no—
173C13×M16—21no—
174C13×M16—21no—
175C13×M16—21no—
176C13×M16—21no—
177C13×M16—21no—
178C13×M16C2×Q812yes—
179C13×M16#4112yes—
180C2×C8×C13—21no—
181C2×C8×C13—21no—
182C2×C8×C13—21no—
183C2×C8×C13—21no—
184C2×C8×C13—21no—
185C2×C8×C13—21no—
186C2×C8×C13—21no—
187C2×C8×C13—21no—
188C2×C8×C13C22×C411yescharacteristic
189C2×C8×C13C22×C411yescharacteristic
190C2×C8×C13C22×C411yescharacteristic
191C2×C8×C13C22×C411yescharacteristic
192C42×C13C22×C411yescharacteristic
193C42×C13C22×C411yescharacteristic
194C42×C13C2×D411yescharacteristic
195C42×C13C2×D411yescharacteristic
196C22⋊Dic13—21no—
197C22⋊Dic13—21no—
198C22⋊Dic13—21no—
199#6103—21no—
200#6103—21no—
201C4⋊Dic13—21no—
202C4⋊Dic13—21no—
203C4⋊Dic13—42no—
204C4⋊Dic13C22×C411yescharacteristic
205C4⋊Dic13C22×C411yescharacteristic
206C4⋊Dic13C22×C411yescharacteristic
207C4⋊Dic13C22×C411yescharacteristic
208C4⋊Dic13C22×C411yescharacteristic
209C4⋊Dic13C22×C411yescharacteristic
210#6101—21no—
211#6101—21no—
212#6101—21no—
213#6101—21no—
214#6101—21no—
215#6101—21no—
216C4×Dic13—21no—
217C4×Dic13—21no—
218C4×Dic13—21no—
219C4×Dic13—21no—
220C4×Dic13—21no—
221C4×Dic13—21no—
222C4×Dic13—21no—
223C4×Dic13—21no—
224C4×Dic13—21no—
225C2×#1055—21no—
226C2×#1055—21no—
227C2×#1055C2×D411yescharacteristic
228C2×#1055C2×D411yescharacteristic
229C2×#1055C2×D411yescharacteristic
230C2×#1055C2×D411yescharacteristic
231C2×#1055C2×Q812yes—
232C2×#1055#4112yes—
233#6094—24no—
234#6094—24no—
235C8×D13—24no—
236C8×D13—24no—
237#3076—131no—
238#2961—131no—
239#2875—131no—
240#1986—131no—
241#1950D1311yescharacteristic, complemented
242#1922—131no—
243#1922—131no—
244#1866—131no—
245#1866—131no—
246#1806—131no—
247#1773—131no—
248#1772—131no—
249#1771—131no—
250#1765—131no—
251#1764—131no—
252C23×C13C2×#4111yescharacteristic
253C22×D13—21no—
254C2×C4×C13—41no—
255C2×C4×C13—41no—
256C2×C4×C13C4×D411yescharacteristic
257C2×C4×C13C4×D411yescharacteristic
258C2×C4×C13C4×D411yescharacteristic
259C2×C4×C13C4×D411yescharacteristic
260C2×C4×C13C23×C411yescharacteristic
261C2×C4×C13C22×D411yescharacteristic
262C2×C4×C13C22×Q811yescharacteristic
263C2×C4×C13C2×#4111yescharacteristic
264C2×C4×C13C2×#4111yescharacteristic
265C2×C4×C13C2×#4111yescharacteristic
266C22⋊D13—22no—
267C22⋊D13—22no—
268C2×Dic13—21no—
269C2×Dic13—22no—
270C2×Dic13—21no—
271C2×Dic13—21no—
272C2×Dic13—21no—
273C2×Dic13—21no—
274C2×Dic13—21no—
275C2×Dic13—21no—
276C2×Dic13—41no—
277C2×Dic13—41no—
278C2×Dic13—41no—
279C2×Dic13—41no—
280C2×Dic13—41no—
281D52—21no—
282D52C4×Q812yes—
283C4×D13—22no—
284C4×D13—22no—
285C4×D13—81no—
286C4×D13—81no—
287Dic26—21no—
288Dic26—81no—
289Dic26—81no—
290Dic26C4×Q812yes—
291C8×C13—21no—
292C8×C13—21no—
293C8×C13—21no—
294C8×C13—21no—
295C8×C13—22no—
296C8×C13—22no—
297C8×C13—41no—
298C8×C13—41no—
299#1055—21no—
300#1055—21no—
301#1055C22⋊Q812yes—
302#1055C22⋊Q812yes—
303C2×#131—131no—
304C2×#131—131no—
305#533—131no—
306C4×#41—131no—
307#479—131no—
308#479—131no—
309#478—131no—
310#478—131no—
311#477—131no—
312#476—131no—
313#475—131no—
314#474—131no—
315#446—261no—
316#446—261no—
317#446—261no—
318#446—261no—
319C2×#108C2×D1311yescharacteristic
320C2×#108C2×D1311yescharacteristic
321#427—131no—
322#427—131no—
323#424—131no—
324#424—131no—
325#423C2×D1311yescharacteristic
326C2×C4⋊C8C2×D1311yescharacteristic
327C2×#104—131no—
328C2×#104—131no—
329#416—131no—
330#416—131no—
331#405—131no—
332#405—131no—
333#405—131no—
334#405—131no—
335#405—261no—
336#405—261no—
337C4×M16—261no—
338C4×M16C2×D1311yescharacteristic
339C2×#97—131no—
340C2×#97—131no—
341C2×#97—261no—
342C2×C4×C8—131no—
343C4×C4⋊C4—131no—
344#341C2×D1311yescharacteristic
345#341C2×D1311yescharacteristic
346#339—131no—
347#339—131no—
348#339—131no—
349#339—131no—
350#339—131no—
351#339—131no—
352#336—131no—
353#336—131no—
354C22×C13—21no—
355C22×C13—21no—
356C22×C13C2×C4×D411yescharacteristic
357C22×C13#52911yescharacteristic
358C22×C13#53311yescharacteristic
359C2×D13—22no—
360C2×D13—41no—
361C2×D13—41no—
362C4×C13—21no—
363C4×C13—21no—
364C4×C13—21no—
365C4×C13—21no—
366C4×C13C2×C4×Q811yescharacteristic
367C4×C13C4×#4111yescharacteristic
368C4×C13C2×C22⋊Q811yescharacteristic
369C4×C13#52511yescharacteristic
370Dic13—22no—
371Dic13—42no—
372Dic13—41no—
373Dic13—41no—
374Dic13—41no—
375Dic13—41no—
376Dic13—41no—
377Dic13—41no—
378Dic13—81no—
379C2×#41—131no—
380#131—134no—
381#131—262no—
382#131—262no—
383#131—262no—
384C2×M16—261no—
385C2×M16—261no—
386C2×M16C22×D1311yescharacteristic
387C2×M16C22×D1311yescharacteristic
388C2×M16C22×D1311yescharacteristic
389C2×M16C22×D1311yescharacteristic
390C22×C8—131no—
391C22×C8—131no—
392C22×C8—261no—
393C22×C8—261no—
394C22×C8C22×D1311yescharacteristic
395C22×C8C22×D1311yescharacteristic
396C4⋊Q8—131no—
397C4⋊Q8—131no—
398#125—131no—
399#125—131no—
400C22⋊Q8—261no—
401C22⋊Q8—261no—
402C4×Q8—131no—
403C4×Q8—131no—
404C4×Q8—261no—
405C4×Q8—261no—
406C4×D4—131no—
407C4×D4—131no—
408C4×D4—261no—
409C4×D4—261no—
410#117—131no—
411#117—131no—
412#117—131no—
413#117—261no—
414C2×C4⋊C4—261no—
415C2×C42—131no—
416C2×C42—131no—
417C2×C42—261no—
418C2×C42C22×D1311yescharacteristic
419#108—22no—
420#108—22no—
421#107—131no—
422#107—131no—
423#107—131no—
424#107—131no—
425#106—131no—
426#106—131no—
427#106—131no—
428#106—131no—
429C4⋊C8—21no—
430C4⋊C8—21no—
431C4⋊C8—261no—
432C4⋊C8—261no—
433C4⋊C8—261no—
434C4⋊C8—261no—
435C4⋊C8C4×D1311yescharacteristic
436C4⋊C8C4×D1311yescharacteristic
437C4⋊C8C4×D1311yescharacteristic
438C4⋊C8C4×D1311yescharacteristic
439#104—262no—
440#104—262no—
441#103—131no—
442#103—131no—
443#103—131no—
444#103—131no—
445#102—131no—
446#102—131no—
447#102—131no—
448#102—131no—
449#97—21no—
450#97—131no—
451#97—131no—
452#97—131no—
453#97—131no—
454#97—262no—
455#97—261no—
456#97—261no—
457#97—261no—
458#97—261no—
459C4×C8—21no—
460C4×C8—262no—
461C4×C8—261no—
462C4×C8—261no—
463C4×C8—261no—
464C4×C8—261no—
465#95—261no—
466C2×C13—21no—
467C2×C13—21no—
468C2×C13C4×C22⋊Q811yescharacteristic
469C2×C13#295611yescharacteristic
470C2×C13#295711yescharacteristic
471D13—42no—
472#41—132no—
473#41—132no—
474#41—261no—
475#41—261no—
476C2×Q8—131no—
477C2×Q8—261no—
478C2×Q8—261no—
479C2×D4—131no—
480C2×D4—261no—
481C22×C4—261no—
482C22×C4—261no—
483C22×C4—261no—
484C22×C4—261no—
485C22×C4—261no—
486C22×C4#613111yescharacteristic
487C22×C4#613111yescharacteristic
488C22×C4C23×D1311yescharacteristic
489M16—21no—
490M16—21no—
491M16—21no—
492M16—21no—
493M16—21no—
494M16—21no—
495M16—264no—
496M16—264no—
497M16#612912yes—
498M16Q8×D1312yes—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—131no—
508C2×C8—131no—
509C2×C8—132no—
510C2×C8—132no—
511C2×C8—131no—
512C2×C8—131no—
513C2×C8—264no—
514C2×C8—264no—
515C2×C8—261no—
516C2×C8—261no—
517C2×C8C2×C4×D1311yescharacteristic
518C2×C8C2×C4×D1311yescharacteristic
519C2×C8C2×C4×D1311yescharacteristic
520C2×C8C2×C4×D1311yescharacteristic
521C4⋊C4—131no—
522C4⋊C4—131no—
523C4⋊C4—131no—
524C4⋊C4—131no—
525C4⋊C4—131no—
526C4⋊C4—131no—
527C4⋊C4—261no—
528C4⋊C4—261no—
529C4⋊C4—261no—
530C4⋊C4—261no—
531C4⋊C4—261no—
532C4⋊C4—261no—
533C4⋊C4—261no—
534C4⋊C4—261no—
535C4⋊C4—522no—
536C22⋊C4—261no—
537C22⋊C4—261no—
538C22⋊C4—261no—
539C22⋊C4—261no—
540C22⋊C4—261no—
541C42—261no—
542C42—261no—
543C42—261no—
544C42—261no—
545C42—261no—
546C42—261no—
547C42—261no—
548C42—261no—
549C42—261no—
550C42C2×C4×D1311yescharacteristic
551C42C2×C4×D1311yescharacteristic
552C42D4×D1311yescharacteristic
553C42D4×D1311yescharacteristic
554C13#2162911yescharacteristic, complemented, Sylow
555C23—261no—
556C23C2×#613111yescharacteristic
557Q8—132no—
558Q8—261no—
559Q8—1041no—
560Q8—1041no—
561D4—132no—
562D4—262no—
563D4—262no—
564D4—261no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—261no—
568C2×C4—262no—
569C2×C4—262no—
570C2×C4—262no—
571C2×C4—261no—
572C2×C4—261no—
573C2×C4—261no—
574C2×C4—261no—
575C2×C4—261no—
576C2×C4—261no—
577C2×C4—521no—
578C2×C4—521no—
579C2×C4—521no—
580C2×C4—521no—
581C2×C4—521no—
582C2×C4—1041no—
583C2×C4—1041no—
584C2×C4#8814711yescharacteristic
585C2×C4#8814711yescharacteristic
586C2×C4#8814711yescharacteristic
587C2×C4#8814711yescharacteristic
588C2×C4C22×C4×D1311yescharacteristic
589C2×C4C2×D4×D1311yescharacteristic
590C2×C4C2×#612911yescharacteristic
591C2×C4C2×Q8×D1311yescharacteristic
592C2×C4#41×D1311yescharacteristic
593C2×C4#41×D1311yescharacteristic
594C8—21no—
595C8—21no—
596C8—21no—
597C8—21no—
598C8—22no—
599C8—22no—
600C8—41no—
601C8—41no—
602C8—132no—
603C8—132no—
604C8—261no—
605C8—261no—
606C22—21no—
607C22—21no—
608C22—262no—
609C22—521no—
610C22—521no—
611C22C2×#8814711yescharacteristic
612C22#1171939611yescharacteristic
613C22#1171943311yescharacteristic
614C4—21no—
615C4—21no—
616C4—21no—
617C4—21no—
618C4—262no—
619C4—522no—
620C4—521no—
621C4—521no—
622C4—521no—
623C4—521no—
624C4—521no—
625C4—521no—
626C4—1041no—
627C4C4×#612911yescharacteristic
628C4C4×Q8×D1311yescharacteristic
629C4#1171931111yescharacteristic
630C4D13×C22⋊Q811yescharacteristic
631C2—21no—
632C2—21no—
633C2—522no—
634C2#1311736611yescharacteristic
635C2#1312374511yescharacteristic
636C2#1312375211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1950C2
socleC22×C13C2×C4×D4
prime radicalC2×#6127C23
cosocleC22×C4×C13C24
hypercenter#1950D13
hypocenterC13#21629
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1950

Complements

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

NH ≅ G/Ntype
2. #13123773C2semidirect
4. #13115780C2semidirect
5. #13115434C2semidirect
6. #13115434C2semidirect
10. #13114723C2semidirect
11. #13114718C2semidirect
12. #13114713C2semidirect
15. C13×#1950C2semidirect
41. #11718512C4semidirect
42. #11718511C4semidirect
43. #11718508C4semidirect
44. #11718508C4semidirect
45. #11718507C4semidirect
46. #11718503C4semidirect
47. #11718490C4semidirect
48. #11718490C4semidirect
90. #88161Q8semidirect
241. #1950D13semidirect
554. C13#21629semidirect

Maximal subgroups

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

subgroupindex
#131246262
#131237732
#131232652
#131157802
#131154342
#131151082
#131148532
#131147232
#131147182
#131147132
#131146792
#131146722
C13×#19502
#2162913