Finite Group Databasebeta

← #15870772

Subgroups — #15870772

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#13123777C211yesmaximal, characteristic, complemented
2#13123264C211yesmaximal, characteristic
3#13115781C211yesmaximal, characteristic, complemented
4#13115612C211yesmaximal, characteristic, complemented
5#13115437C211yesmaximal, characteristic, complemented
6#13115437C211yesmaximal, characteristic, complemented
7#13115113C211yesmaximal, characteristic
8#13115113C211yesmaximal, characteristic
9#13114856C211yesmaximal, characteristic
10#13114722C211yesmaximal, characteristic, complemented
11#13114717C211yesmaximal, characteristic, complemented
12#13114713C211yesmaximal, characteristic, complemented
13#13114683C211yesmaximal, characteristic
14#13114676C211yesmaximal, characteristic
15C13×#3076C211yesmaximal, characteristic
16C13×#533C2211yescharacteristic
17C4×C13×#41C2211yescharacteristic
18C2×#88202C2211yescharacteristic
19C2×#88202C2211yescharacteristic
20C13×#479C411yescharacteristic, complemented
21C13×#479C411yescharacteristic, complemented
22C13×#478C411yescharacteristic, complemented
23C13×#478C411yescharacteristic, complemented
24C13×#477C411yescharacteristic, complemented
25C13×#476C411yescharacteristic, complemented
26C13×#475C411yescharacteristic, complemented
27C13×#474C411yescharacteristic, complemented
28C13×#427C2211yescharacteristic
29C13×#427C2211yescharacteristic
30C2×C13×C4⋊C8C2211yescharacteristic
31C13×#416C2211yescharacteristic
32C13×#416C2211yescharacteristic
33C2×#88077C2211yescharacteristic
34C2×#88077C2211yescharacteristic
35C2×#88059C2211yescharacteristic
36C2×#88059C2211yescharacteristic
37C2×#88055C2211yescharacteristic
38C2×C8×Dic13C2211yescharacteristic
39#11718685—21no—
40#11718685—21no—
41#11718685—21no—
42#11718685—21no—
43#11718660C2211yescharacteristic
44#11718660C2211yescharacteristic
45#11718658—21no—
46#11718658—21no—
47#11718658C2211yescharacteristic
48#11718658C2211yescharacteristic
49#11718658C2211yescharacteristic
50#11718658C2211yescharacteristic
51C4×C4⋊Dic13C2211yescharacteristic
52#11718585C2211yescharacteristic
53C4×#6099—21no—
54C4×#6099C2211yescharacteristic
55C2×#88043—21no—
56C2×#88043C2211yescharacteristic
57#11718144C2211yescharacteristic
58#11718144C2211yescharacteristic
59#11718142C2211yescharacteristic
60#11718142C2211yescharacteristic
61#11718124C2211yescharacteristic
62#11718124C2211yescharacteristic
63#11718124C2211yescharacteristic
64#11718124C2211yescharacteristic
65#11718124C2211yescharacteristic
66#11718124C2211yescharacteristic
67C2×C13×#41C2311yescharacteristic
68C22×C8×C13C2311yescharacteristic
69C22×C8×C13C2311yescharacteristic
70C13×C4⋊Q8C2×C411yescharacteristic
71C13×C4⋊Q8C2×C411yescharacteristic
72C13×#125C2×C411yescharacteristic
73C13×#125C2×C411yescharacteristic
74C13×C22⋊Q8—21no—
75C13×C22⋊Q8—21no—
76C4×Q8×C13—21no—
77C4×Q8×C13—21no—
78C4×Q8×C13C2×C411yescharacteristic
79C4×Q8×C13C2×C411yescharacteristic
80C4×D4×C13—21no—
81C4×D4×C13—21no—
82C4×D4×C13C2×C411yescharacteristic
83C4×D4×C13C2×C411yescharacteristic
84C13×#117—21no—
85C13×#117C2311yescharacteristic
86C13×#117C2311yescharacteristic
87C13×#117C2311yescharacteristic
88C2×C42×C13—21no—
89C2×C42×C13C2311yescharacteristic
90#88202—22no—
91#88202—22no—
92#88202—22no—
93#88202Q814yescomplemented
94C2×C4⋊Dic13—21no—
95C2×C4×Dic13C2311yescharacteristic
96C2×C4×Dic13C2311yescharacteristic
97C2×#6099—21no—
98C2×#6099—21no—
99C2×#6099C2311yescharacteristic
100C2×#6099C2311yescharacteristic
101C2×#6099C2311yescharacteristic
102C2×#6099C2311yescharacteristic
103C22×#1055—21no—
104C22×#1055—21no—
105C22×#1055C2311yescharacteristic
106C22×#1055C2311yescharacteristic
107C13×#107C2×C411yescharacteristic
108C13×#107C2×C411yescharacteristic
109C13×#107C2×C411yescharacteristic
110C13×#107C2×C411yescharacteristic
111C13×#106C2×C411yescharacteristic
112C13×#106C2×C411yescharacteristic
113C13×#106C2×C411yescharacteristic
114C13×#106C2×C411yescharacteristic
115C13×C4⋊C8C2×C411yescharacteristic
116C13×C4⋊C8C2×C411yescharacteristic
117C13×C4⋊C8C2×C411yescharacteristic
118C13×C4⋊C8C2×C411yescharacteristic
119C13×#103C2×C411yescharacteristic
120C13×#103C2×C411yescharacteristic
121C13×#103C2×C411yescharacteristic
122C13×#103C2×C411yescharacteristic
123C13×#102C2×C411yescharacteristic
124C13×#102C2×C411yescharacteristic
125C13×#102C2×C411yescharacteristic
126C13×#102C2×C411yescharacteristic
127#88077—22no—
128#88077—22no—
129#88071—21no—
130#88059—22no—
131#88059—22no—
132#88055—22no—
133C8×Dic13—22no—
134C4⋊#1055—21no—
135C4⋊#1055—21no—
136C4⋊#1055—21no—
137C4⋊#1055—21no—
138C4⋊#1055—21no—
139C4⋊#1055—21no—
140#88043—21no—
141#88043—21no—
142#88043—21no—
143#88043—21no—
144#88043—21no—
145#88043D411yescharacteristic
146#88043D411yescharacteristic
147#88043D411yescharacteristic
148#88043D411yescharacteristic
149C4×#1055—21no—
150C4×#1055—21no—
151C4×#1055—21no—
152C4×#1055—21no—
153C4×#1055—21no—
154#21629—131nomaximal, Sylow
155C13×#41—21no—
156C13×#41—21no—
157C13×#41C2×Q812yes—
158C13×#41#4112yes—
159C2×Q8×C13—21no—
160C2×Q8×C13—21no—
161C2×Q8×C13C22×C411yescharacteristic
162C2×D4×C13—21no—
163C2×D4×C13C22×C411yescharacteristic
164C22×C4×C13—21no—
165C22×C4×C13—21no—
166C22×C4×C13—21no—
167C22×C4×C13#4111yescharacteristic
168C22×C4×C13#4111yescharacteristic
169C22×C4×C13C2411yescharacteristic
170C22×Dic13—21no—
171C22×Dic13—21no—
172C2×C8×C13—21no—
173C2×C8×C13—21no—
174C2×C8×C13—21no—
175C2×C8×C13—21no—
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⋊C4—21no—
183C13×C4⋊C4—21no—
184C13×C4⋊C4—21no—
185C13×C4⋊C4—21no—
186C13×C4⋊C4—21no—
187C13×C4⋊C4—21no—
188C13×C4⋊C4C22×C411yescharacteristic
189C13×C4⋊C4C22×C411yescharacteristic
190C13×C4⋊C4C22×C411yescharacteristic
191C13×C4⋊C4C22×C411yescharacteristic
192C13×C4⋊C4C22×C411yescharacteristic
193C13×C4⋊C4C22×C411yescharacteristic
194C13×C22⋊C4—21no—
195C13×C22⋊C4—21no—
196C13×C22⋊C4—21no—
197C13×C22⋊C4—21no—
198C13×C22⋊C4—21no—
199C42×C13—21no—
200C42×C13—21no—
201C42×C13—21no—
202C42×C13—21no—
203C42×C13—21no—
204C42×C13C22×C411yescharacteristic
205C42×C13C22×C411yescharacteristic
206C42×C13C2×D411yescharacteristic
207C42×C13C2×D411yescharacteristic
208C4⋊Dic13—42no—
209C4×Dic13—21no—
210C4×Dic13—21no—
211C4×Dic13—21no—
212C4×Dic13—21no—
213#6099—24no—
214#6099—21no—
215#6099—21no—
216#6099—24no—
217#6099—21no—
218#6099—21no—
219#6099—21no—
220#6099—21no—
221#6099C2×Q812yes—
222#6099#4112yes—
223C2×#1055—24no—
224C2×#1055—21no—
225C2×#1055—21no—
226C2×#1055—21no—
227C2×#1055—21no—
228C2×#1055—24no—
229C2×#1055—21no—
230C2×#1055—21no—
231C2×#1055C2×D411yescharacteristic
232C2×#1055C2×D411yescharacteristic
233C2×#1055C2×D411yescharacteristic
234C2×#1055C2×D411yescharacteristic
235C2×#1055C2×Q812yes—
236C2×#1055#4112yes—
237#3076D1311yescharacteristic
238#2961—131no—
239#2875—131no—
240#1986—131no—
241#1950—131no—
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×C13—21no—
253C23×C13C2×#4111yescharacteristic
254Q8×C13—21no—
255Q8×C13—81no—
256Q8×C13—81no—
257Q8×C13C4×Q812yes—
258D4×C13—22no—
259D4×C13—22no—
260D4×C13—21no—
261D4×C13C4×Q812yes—
262C2×C4×C13—21no—
263C2×C4×C13—22no—
264C2×C4×C13—22no—
265C2×C4×C13—21no—
266C2×C4×C13—21no—
267C2×C4×C13—21no—
268C2×C4×C13—21no—
269C2×C4×C13—21no—
270C2×C4×C13—21no—
271C2×C4×C13—41no—
272C2×C4×C13—41no—
273C2×C4×C13—81no—
274C2×C4×C13—81no—
275C2×C4×C13C4×D411yescharacteristic
276C2×C4×C13C4×D411yescharacteristic
277C2×C4×C13C4×D411yescharacteristic
278C2×C4×C13C4×D411yescharacteristic
279C2×C4×C13C23×C411yescharacteristic
280C2×C4×C13C22×D411yescharacteristic
281C2×C4×C13C22×Q811yescharacteristic
282C2×C4×C13C2×#4111yescharacteristic
283C2×C4×C13C2×#4111yescharacteristic
284C2×C4×C13C2×#4111yescharacteristic
285C2×Dic13—22no—
286C2×Dic13—41no—
287C2×Dic13—41no—
288C2×Dic13—41no—
289C2×Dic13—41no—
290C2×Dic13—41no—
291C8×C13—21no—
292C8×C13—21no—
293C8×C13—21no—
294C8×C13—21no—
295#1055—22no—
296#1055—21no—
297#1055—22no—
298#1055—21no—
299#1055—41no—
300#1055—41no—
301#1055C22⋊Q812yes—
302#1055C22⋊Q812yes—
303C2×#131—131no—
304C2×#131—131no—
305#533C2×D1311yescharacteristic
306C4×#41C2×D1311yescharacteristic
307#479Dic1311yescharacteristic, complemented
308#479Dic1311yescharacteristic, complemented
309#478Dic1311yescharacteristic, complemented
310#478Dic1311yescharacteristic, complemented
311#477Dic1311yescharacteristic, complemented
312#476Dic1311yescharacteristic, complemented
313#475Dic1311yescharacteristic, complemented
314#474Dic1311yescharacteristic, complemented
315#446—261no—
316#446—261no—
317#446—261no—
318#446—261no—
319C2×#108—131no—
320C2×#108—131no—
321#427C2×D1311yescharacteristic
322#427C2×D1311yescharacteristic
323#424—131no—
324#424—131no—
325#423—131no—
326C2×C4⋊C8C2×D1311yescharacteristic
327C2×#104—131no—
328C2×#104—131no—
329#416C2×D1311yescharacteristic
330#416C2×D1311yescharacteristic
331#405—131no—
332#405—131no—
333#405—131no—
334#405—131no—
335#405—261no—
336#405—261no—
337C4×M16—131no—
338C4×M16—261no—
339C2×#97—131no—
340C2×#97—131no—
341C2×#97—261no—
342C2×C4×C8—131no—
343C4×C4⋊C4—131no—
344#341—131no—
345#341—131no—
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×C13—22no—
357C22×C13—41no—
358C22×C13—41no—
359C22×C13C2×C4×D411yescharacteristic
360C22×C13#52911yescharacteristic
361C22×C13#53311yescharacteristic
362C4×C13—21no—
363C4×C13—21no—
364C4×C13—21no—
365C4×C13—21no—
366C4×C13—22no—
367C4×C13—41no—
368C4×C13—41no—
369C4×C13—41no—
370C4×C13—41no—
371C4×C13—41no—
372C4×C13—41no—
373C4×C13C2×C4×Q811yescharacteristic
374C4×C13C4×#4111yescharacteristic
375C4×C13C2×C22⋊Q811yescharacteristic
376C4×C13#52511yescharacteristic
377Dic13—42no—
378Dic13—81no—
379C2×#41C22×D1311yescharacteristic
380#131—134no—
381#131—262no—
382#131—262no—
383#131—262no—
384C2×M16—131no—
385C2×M16—131no—
386C2×M16—131no—
387C2×M16—131no—
388C2×M16—261no—
389C2×M16—261no—
390C22×C8—131no—
391C22×C8—131no—
392C22×C8—261no—
393C22×C8—261no—
394C22×C8C22×D1311yescharacteristic
395C22×C8C22×D1311yescharacteristic
396C4⋊Q8C2×Dic1311yescharacteristic
397C4⋊Q8C2×Dic1311yescharacteristic
398#125C2×Dic1311yescharacteristic
399#125C2×Dic1311yescharacteristic
400C22⋊Q8—21no—
401C22⋊Q8—21no—
402C4×Q8—21no—
403C4×Q8—21no—
404C4×Q8C2×Dic1311yescharacteristic
405C4×Q8C2×Dic1311yescharacteristic
406C4×D4—21no—
407C4×D4—21no—
408C4×D4C2×Dic1311yescharacteristic
409C4×D4C2×Dic1311yescharacteristic
410#117—21no—
411#117C22×D1311yescharacteristic
412#117C22×D1311yescharacteristic
413#117C22×D1311yescharacteristic
414C2×C4⋊C4—261no—
415C2×C42—21no—
416C2×C42—131no—
417C2×C42—131no—
418C2×C42C22×D1311yescharacteristic
419#108—262no—
420#108—262no—
421#107C2×Dic1311yescharacteristic
422#107C2×Dic1311yescharacteristic
423#107C2×Dic1311yescharacteristic
424#107C2×Dic1311yescharacteristic
425#106C2×Dic1311yescharacteristic
426#106C2×Dic1311yescharacteristic
427#106C2×Dic1311yescharacteristic
428#106C2×Dic1311yescharacteristic
429C4⋊C8—261no—
430C4⋊C8—261no—
431C4⋊C8—261no—
432C4⋊C8—261no—
433C4⋊C8—261no—
434C4⋊C8—261no—
435C4⋊C8C2×Dic1311yescharacteristic
436C4⋊C8C2×Dic1311yescharacteristic
437C4⋊C8C2×Dic1311yescharacteristic
438C4⋊C8C2×Dic1311yescharacteristic
439#104—262no—
440#104—262no—
441#103C2×Dic1311yescharacteristic
442#103C2×Dic1311yescharacteristic
443#103C2×Dic1311yescharacteristic
444#103C2×Dic1311yescharacteristic
445#102C2×Dic1311yescharacteristic
446#102C2×Dic1311yescharacteristic
447#102C2×Dic1311yescharacteristic
448#102C2×Dic1311yescharacteristic
449#97—131no—
450#97—131no—
451#97—131no—
452#97—131no—
453#97—261no—
454#97—261no—
455#97—261no—
456#97—261no—
457#97—262no—
458#97—261no—
459C4×C8—261no—
460C4×C8—261no—
461C4×C8—261no—
462C4×C8—261no—
463C4×C8—262no—
464C4×C8—261no—
465#95—261no—
466C2×C13—21no—
467C2×C13—21no—
468C2×C13—42no—
469C2×C13C4×C22⋊Q811yescharacteristic
470C2×C13#295611yescharacteristic
471C2×C13#295711yescharacteristic
472#41—21no—
473#41—21no—
474#41Q8×D1312yes—
475#41#613112yes—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8C22×Dic1311yescharacteristic
479C2×D4—21no—
480C2×D4C22×Dic1311yescharacteristic
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—261no—
485C22×C4—261no—
486C22×C4#612911yescharacteristic
487C22×C4#612911yescharacteristic
488C22×C4C23×D1311yescharacteristic
489M16—132no—
490M16—132no—
491M16—264no—
492M16—264no—
493M16—261no—
494M16—261no—
495M16—261no—
496M16—261no—
497M16—261no—
498M16—261no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—131no—
504C2×C8—131no—
505C2×C8—132no—
506C2×C8—132no—
507C2×C8—131no—
508C2×C8—131no—
509C2×C8—264no—
510C2×C8—264no—
511C2×C8—261no—
512C2×C8—261no—
513C2×C8—261no—
514C2×C8—261no—
515C2×C8—261no—
516C2×C8—261no—
517C2×C8C22×Dic1311yescharacteristic
518C2×C8C22×Dic1311yescharacteristic
519C2×C8C22×Dic1311yescharacteristic
520C2×C8C22×Dic1311yescharacteristic
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—522no—
530C4⋊C4C22×Dic1311yescharacteristic
531C4⋊C4C22×Dic1311yescharacteristic
532C4⋊C4C22×Dic1311yescharacteristic
533C4⋊C4C22×Dic1311yescharacteristic
534C4⋊C4C22×Dic1311yescharacteristic
535C4⋊C4C22×Dic1311yescharacteristic
536C22⋊C4—21no—
537C22⋊C4—21no—
538C22⋊C4—21no—
539C22⋊C4—21no—
540C22⋊C4—21no—
541C42—21no—
542C42—21no—
543C42—21no—
544C42—21no—
545C42—21no—
546C42—261no—
547C42—261no—
548C42—261no—
549C42—261no—
550C42D4×D1311yescharacteristic
551C42D4×D1311yescharacteristic
552C42C22×Dic1311yescharacteristic
553C42C22×Dic1311yescharacteristic
554C13#2162911yescharacteristic, complemented, Sylow
555C23—21no—
556C23C2×#612911yescharacteristic
557Q8—21no—
558Q8—81no—
559Q8—81no—
560Q8Q8×Dic1312yes—
561D4—22no—
562D4—22no—
563D4—21no—
564D4Q8×Dic1312yes—
565C2×C4—21no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—81no—
577C2×C4—81no—
578C2×C4—262no—
579C2×C4—521no—
580C2×C4—521no—
581C2×C4—521no—
582C2×C4—521no—
583C2×C4—521no—
584C2×C4D4×Dic1311yescharacteristic
585C2×C4D4×Dic1311yescharacteristic
586C2×C4D4×Dic1311yescharacteristic
587C2×C4D4×Dic1311yescharacteristic
588C2×C4C2×D4×D1311yescharacteristic
589C2×C4C2×Q8×D1311yescharacteristic
590C2×C4C2×#613111yescharacteristic
591C2×C4#41×D1311yescharacteristic
592C2×C4#41×D1311yescharacteristic
593C2×C4C23×Dic1311yescharacteristic
594C8—21no—
595C8—21no—
596C8—21no—
597C8—21no—
598C8—132no—
599C8—132no—
600C8—262no—
601C8—261no—
602C8—261no—
603C8—262no—
604C8—521no—
605C8—521no—
606C22—21no—
607C22—21no—
608C22—22no—
609C22—41no—
610C22—41no—
611C22#1171932711yescharacteristic
612C22#1171932911yescharacteristic
613C22C2×D4×Dic1311yescharacteristic
614C4—21no—
615C4—21no—
616C4—21no—
617C4—21no—
618C4—22no—
619C4—41no—
620C4—41no—
621C4—41no—
622C4—41no—
623C4—41no—
624C4—41no—
625C4—522no—
626C4—1041no—
627C4D13×C22⋊Q811yescharacteristic
628C4#1171933211yescharacteristic
629C4C2×Q8×Dic1311yescharacteristic
630C4#41×Dic1311yescharacteristic
631C2—21no—
632C2—21no—
633C2—42no—
634C2C22⋊Q8×Dic1311yescharacteristic
635C2#1312374611yescharacteristic
636C2#1312375311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#3076C2
socleC22×C13C2×C4×D4
prime radicalC2×C13×#41C23
cosocleC22×C4×C13C24
hypercenter#3076D13
hypocenterC13#21629
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3076

Complements

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

NH ≅ G/Ntype
1. #13123777C2semidirect
3. #13115781C2semidirect
4. #13115612C2semidirect
5. #13115437C2semidirect
6. #13115437C2semidirect
10. #13114722C2semidirect
11. #13114717C2semidirect
12. #13114713C2semidirect
20. C13×#479C4semidirect
21. C13×#479C4semidirect
22. C13×#478C4semidirect
23. C13×#478C4semidirect
24. C13×#477C4semidirect
25. C13×#476C4semidirect
26. C13×#475C4semidirect
27. C13×#474C4semidirect
93. #88202Q8semidirect
307. #479Dic13semidirect
308. #479Dic13semidirect
309. #478Dic13semidirect
310. #478Dic13semidirect
311. #477Dic13semidirect
312. #476Dic13semidirect
313. #475Dic13semidirect
314. #474Dic13semidirect
554. C13#21629semidirect

Maximal subgroups

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

subgroupindex
#131237772
#131232642
#131157812
#131156122
#131154372
#131151132
#131148562
#131147222
#131147172
#131147132
#131146832
#131146762
C13×#30762
#2162913