Finite Group Databasebeta

← #15880164

Subgroups — #15880164

Order 3328.

982 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718627C211yesmaximal, characteristic
2#13117676C211yesmaximal, characteristic
3#13115532C211yesmaximal, characteristic, complemented
4#13115518C211yesmaximal, characteristic, complemented
5#13115463C211yesmaximal, characteristic, complemented
6#13115456C211yesmaximal, characteristic, complemented
7#13115103C211yesmaximal, characteristic, complemented
8#13115089C211yesmaximal, characteristic, complemented
9#13114922C211yesmaximal, characteristic, complemented
10#13114867C211yesmaximal, characteristic, complemented
11#13114774C211yesmaximal, characteristic
12#13114669C211yesmaximal, characteristic, complemented
13C4×#88050C211yesmaximal, characteristic, complemented
14#13114620C211yesmaximal, characteristic, complemented
15C13×#2345C211yesmaximal, characteristic, complemented
16C22×#6127C2211yescharacteristic
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×#6099C2211yescharacteristic
19C2×C4×Dic26C2211yescharacteristic
20C2×C4×Dic26C2211yescharacteristic
21C13×#389C2211yescharacteristic
22C13×#389C2211yescharacteristic
23C13×#387—21no—
24C13×#387—21no—
25C13×#380—21no—
26C13×#380C2211yescharacteristic
27C4×C13×C4⋊C4C2211yescharacteristic
28C4×C13×C4⋊C4C2211yescharacteristic
29C4×C13×C22⋊C4—21no—
30C4×C13×C22⋊C4C2211yescharacteristic
31#11718873C2211yescharacteristic
32C2×C22⋊#1055C2211yescharacteristic
33C2×#88050C2211yescharacteristic
34C2×#88050C2211yescharacteristic
35C2×#88050C2211yescharacteristic
36C2×#88050C2211yescharacteristic
37#11718627C418yescomplemented
38C2×#88049C2211yescharacteristic
39C2×#88049C2211yescharacteristic
40C2×#88049C2211yescharacteristic
41C2×#88049C2211yescharacteristic
42C2×#88048C2211yescharacteristic
43C2×#88047C2211yescharacteristic
44#11718618—21no—
45#11718618—21no—
46#11718600C2211yescharacteristic
47#11718600C2211yescharacteristic
48C2×#88043C2211yescharacteristic
49C2×C4×#1055C2211yescharacteristic
50#11718328—21no—
51#11718327—21no—
52#11718121C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718116C2211yescharacteristic
59#11718116C2211yescharacteristic
60C23×C4×C13—21no—
61C23×C4×C13C2311yescharacteristic
62C22×C22⋊D13—21no—
63C2×#6127—22no—
64C2×#6127—22no—
65C2×#6127—22no—
66C2×#6127—41no—
67C2×#6127—41no—
68C2×#6127C2×C414yes—
69C22×D52C2311yescharacteristic
70C22×C4×D13—21no—
71C22×Dic26C2311yescharacteristic
72C2×C13×C4⋊C4—21no—
73C2×C13×C4⋊C4—22no—
74C2×C13×C4⋊C4—21no—
75C2×C13×C4⋊C4—21no—
76C2×C13×C4⋊C4C2×C414yes—
77C2×C13×C4⋊C4C2311yescharacteristic
78C2×C13×C4⋊C4C2311yescharacteristic
79C2×C13×C4⋊C4C2311yescharacteristic
80C2×C13×C4⋊C4C2311yescharacteristic
81C2×C13×C22⋊C4—21no—
82C2×C13×C22⋊C4D411yescharacteristic
83C2×C13×C22⋊C4D411yescharacteristic
84C2×C42×C13—21no—
85C2×C42×C13—21no—
86C2×C42×C13C2311yescharacteristic
87C2×C42×C13C2311yescharacteristic
88C2×C22⋊Dic13—21no—
89C2×#6103—21no—
90C2×#6103—21no—
91C2×#6103—21no—
92C2×#6103—21no—
93C2×C4⋊Dic13C2311yescharacteristic
94C2×C4⋊Dic13C2311yescharacteristic
95C2×#6101—21no—
96C2×#6101—21no—
97C2×C4×Dic13—21no—
98C2×C4×Dic13—21no—
99C2×#6099—41no—
100C2×#6099—41no—
101C2×#6099C2×C414yes—
102C22×#1055C2311yescharacteristic
103C22×#1055C2311yescharacteristic
104C22×#1055C2311yescharacteristic
105C22×#1055C2311yescharacteristic
106C4×Dic26—22no—
107C4×Dic26—22no—
108C4×Dic26—41no—
109C4×Dic26—41no—
110C13×#95—21no—
111C13×#95—21no—
112C13×#95—21no—
113C13×#95—21no—
114C13×#95—21no—
115C13×#95D411yescharacteristic
116C13×#95D411yescharacteristic
117#88071—21no—
118C22⋊#1055—22no—
119#88050—22no—
120#88050—22no—
121#88050C2×C414yes—
122#88050C2×C414yes—
123#88049—41no—
124#88049—41no—
125#88049C2×C414yes—
126#88049C2×C414yes—
127#88048—41no—
128#88047—41no—
129#88043—41no—
130C4×#1055—41no—
131#22579—131nomaximal, Sylow
132C24×C13C2×D411yescharacteristic
133C23×D13—21no—
134C22×C4×C13—21no—
135C22×C4×C13—21no—
136C22×C4×C13—21no—
137C22×C4×C13—21no—
138C22×C4×C13—21no—
139C22×C4×C13—21no—
140C22×C4×C13—24no—
141C22×C4×C13—21no—
142C22×C4×C13—21no—
143C22×C4×C13—81no—
144C22×C4×C13—81no—
145C22×C4×C13C22×C412yes—
146C22×C4×C13C2×D411yescharacteristic
147C22×C4×C13C2×D411yescharacteristic
148C22×C4×C13C2×D411yescharacteristic
149C22×C4×C13C2×D411yescharacteristic
150C22×C4×C13C2×D411yescharacteristic
151C22×C4×C13#4112yes—
152C22×C4×C13C2411yescharacteristic
153C2×C22⋊D13—24no—
154C2×C22⋊D13—42no—
155C2×C22⋊D13—42no—
156C22×Dic13—21no—
157C22×Dic13—21no—
158C22×Dic13—21no—
159#6127—28no—
160#6127—44no—
161#6127—44no—
162#6127—44no—
163C2×D52—21no—
164C2×D52—21no—
165C2×D52—21no—
166C2×D52—21no—
167C2×D52—21no—
168C2×D52C22×C412yes—
169C2×C4×D13—24no—
170C2×C4×D13—42no—
171C2×C4×D13—42no—
172C2×Dic26—21no—
173C2×Dic26—21no—
174C2×Dic26—21no—
175C2×Dic26C22×C412yes—
176C2×Dic26#4112yes—
177C2×Dic26#4112yes—
178C13×C4⋊C4—24no—
179C13×C4⋊C4—21no—
180C13×C4⋊C4—21no—
181C13×C4⋊C4—21no—
182C13×C4⋊C4—21no—
183C13×C4⋊C4—21no—
184C13×C4⋊C4—21no—
185C13×C4⋊C4—81no—
186C13×C4⋊C4—81no—
187C13×C4⋊C4C22×C412yes—
188C13×C4⋊C4C22×C412yes—
189C13×C22⋊C4—22no—
190C13×C22⋊C4—41no—
191C13×C22⋊C4—42no—
192C42×C13—21no—
193C42×C13—21no—
194C42×C13—21no—
195C42×C13—21no—
196C42×C13—81no—
197C42×C13—81no—
198C22⋊Dic13—81no—
199#6103—42no—
200#6103—42no—
201#6103—81no—
202#6103—81no—
203C4⋊Dic13—21no—
204C4⋊Dic13—21no—
205C4⋊Dic13—21no—
206C4⋊Dic13—21no—
207#6101—42no—
208#6101—42no—
209C4×Dic13—42no—
210C4×Dic13—42no—
211#6099—44no—
212C2×#1055—21no—
213C2×#1055—21no—
214C2×#1055—21no—
215C2×#1055—21no—
216C2×#1055—21no—
217C2×#1055—21no—
218C2×#1055—21no—
219C2×#1055—21no—
220C2×#1055—21no—
221C2×#1055—21no—
222C2×#1055C22×C412yes—
223C2×#1055C22×C412yes—
224C2×#417—131no—
225#2345D1311yescharacteristic, complemented
226#2341—131no—
227#1936—131no—
228#1934—131no—
229#1926—131no—
230#1925—131no—
231#1865—131no—
232#1863—131no—
233#1823—131no—
234#1809—131no—
235#1788—131no—
236#1763—131no—
237C4×#103—131no—
238#1753—131no—
239C23×C13—21no—
240C23×C13—21no—
241C23×C13—21no—
242C23×C13—21no—
243C23×C13—21no—
244C23×C13—21no—
245C23×C13C4×D412yes—
246C23×C13C22×D411yescharacteristic
247C22×D13—22no—
248C22×D13—41no—
249C22×D13—41no—
250C22×D13—41no—
251C22×D13—41no—
252C22×D13—41no—
253C22×D13—41no—
254C2×C4×C13—21no—
255C2×C4×C13—21no—
256C2×C4×C13—21no—
257C2×C4×C13—21no—
258C2×C4×C13—22no—
259C2×C4×C13—22no—
260C2×C4×C13—22no—
261C2×C4×C13—22no—
262C2×C4×C13—22no—
263C2×C4×C13—22no—
264C2×C4×C13—21no—
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—21no—
272C2×C4×C13—21no—
273C2×C4×C13—41no—
274C2×C4×C13—41no—
275C2×C4×C13—41no—
276C2×C4×C13—41no—
277C2×C4×C13—41no—
278C2×C4×C13—41no—
279C2×C4×C13—41no—
280C2×C4×C13—41no—
281C2×C4×C13—41no—
282C2×C4×C13—41no—
283C2×C4×C13—84no—
284C2×C4×C13C4×D412yes—
285C2×C4×C13#13712yes—
286C2×C4×C13C23×C411yescharacteristic
287C2×C4×C13C2×#4111yescharacteristic
288C2×C4×C13C2×#4111yescharacteristic
289C2×C4×C13C2×#4111yescharacteristic
290C2×C4×C13H(5,𝔽2)11yescharacteristic
291C2×C4×C13H(5,𝔽2)11yescharacteristic
292C22⋊D13—48no—
293C2×Dic13—22no—
294C2×Dic13—22no—
295C2×Dic13—22no—
296C2×Dic13—41no—
297C2×Dic13—41no—
298C2×Dic13—41no—
299C2×Dic13—41no—
300C2×Dic13—41no—
301C2×Dic13—41no—
302D52—22no—
303D52—22no—
304D52—41no—
305D52—41no—
306C4×D13—48no—
307Dic26—22no—
308Dic26—22no—
309Dic26—22no—
310Dic26#11714yes—
311#1055—22no—
312#1055—22no—
313#1055—41no—
314#1055—41no—
315C22×#41—131no—
316C22×M16—131no—
317C2×C4×Q8—131no—
318C2×C4×Q8—131no—
319C22×C4⋊C4C2×D1311yescharacteristic
320C2×#107—131no—
321C2×#106—131no—
322#417—138no—
323C2×#103—131no—
324C2×#103—131no—
325C2×#103—131no—
326C2×#103—131no—
327C2×#102—131no—
328C2×#102—131no—
329C2×#102—131no—
330C2×#102—131no—
331C2×C22⋊C8—131no—
332C2×#97—131no—
333C2×C4×C8—131no—
334#390—131no—
335#390—131no—
336#390—261no—
337#390—261no—
338#389C2×D1311yescharacteristic
339#389C2×D1311yescharacteristic
340#387—21no—
341#387—21no—
342#380—21no—
343#380—131no—
344#380—261no—
345#380C2×D1311yescharacteristic
346C4×C4⋊C4C2×D1311yescharacteristic
347C4×C4⋊C4C2×D1311yescharacteristic
348C4×C22⋊C4—21no—
349C4×C22⋊C4—261no—
350C4×C22⋊C4C2×D1311yescharacteristic
351#340—131no—
352#340—131no—
353#340—131no—
354#340—131no—
355#340—131no—
356#340—131no—
357#336—131no—
358#336—131no—
359C22×C13—22no—
360C22×C13—22no—
361C22×C13—22no—
362C22×C13—41no—
363C22×C13—41no—
364C22×C13—41no—
365C22×C13—41no—
366C22×C13C2×C4×D411yescharacteristic
367C22×C13#54611yescharacteristic
368C22×C13#54611yescharacteristic
369C22×C13C2×#13711yescharacteristic
370C22×C13#57511yescharacteristic
371C22×C13#57611yescharacteristic
372C22×C13#57711yescharacteristic
373C2×D13—42no—
374C2×D13—42no—
375C2×D13—42no—
376C2×D13—81no—
377C2×D13—81no—
378C2×D13—81no—
379C2×D13—81no—
380C4×C13—22no—
381C4×C13—22no—
382C4×C13—41no—
383C4×C13—42no—
384C4×C13—42no—
385C4×C13—41no—
386C4×C13—41no—
387C4×C13—81no—
388C4×C13—81no—
389C4×C13C2×#11711yescharacteristic
390C4×C13#51811yescharacteristic
391C4×C13#55111yescharacteristic
392C4×C13#55111yescharacteristic
393Dic13—24no—
394Dic13—81no—
395Dic13—81no—
396C2×#41—134no—
397C2×#41—262no—
398C2×#41—262no—
399C2×#41—262no—
400C2×#41—521no—
401C2×#41—521no—
402C22×Q8—131no—
403C22×D4—131no—
404C22×D4—261no—
405C23×C4—21no—
406C23×C4—261no—
407C23×C4C22×D1311yescharacteristic
408C2×M16—134no—
409C2×M16—521no—
410C2×M16—521no—
411C22×C8—131no—
412C22×C8—131no—
413C22×C8—131no—
414C22×C8—131no—
415C4×Q8—262no—
416C4×Q8—262no—
417C4×Q8—521no—
418C4×Q8—521no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—131no—
424C2×C4⋊C4—131no—
425C2×C4⋊C4—261no—
426C2×C4⋊C4—261no—
427C2×C4⋊C4C4×D1314yes—
428C2×C4⋊C4C22×D1311yescharacteristic
429C2×C4⋊C4C22×D1311yescharacteristic
430C2×C4⋊C4C22×D1311yescharacteristic
431C2×C4⋊C4C22×D1311yescharacteristic
432C2×C22⋊C4—21no—
433C2×C22⋊C4—261no—
434C2×C22⋊C4—261no—
435C2×C22⋊C4—261no—
436C2×C22⋊C4—261no—
437C2×C22⋊C4—261no—
438C2×C22⋊C4C22⋊D1311yescharacteristic
439C2×C22⋊C4C22⋊D1311yescharacteristic
440C2×C42—21no—
441C2×C42—21no—
442C2×C42—261no—
443C2×C42—261no—
444C2×C42C22×D1311yescharacteristic
445C2×C42C22×D1311yescharacteristic
446#107—521no—
447#106—521no—
448#103—134no—
449#103—134no—
450#103—262no—
451#103—262no—
452#102—134no—
453#102—134no—
454#102—521no—
455#102—521no—
456C22⋊C8—262no—
457#97—521no—
458C4×C8—521no—
459#95—21no—
460#95—21no—
461#95—21no—
462#95—21no—
463#95—21no—
464#95—261no—
465#95C22⋊D1311yescharacteristic
466#95C22⋊D1311yescharacteristic
467C2×C13—42no—
468C2×C13#234211yescharacteristic
469C2×C13C4×#13711yescharacteristic
470C2×C13#294611yescharacteristic
471C2×C13#330911yescharacteristic
472C2×C13#331611yescharacteristic
473C2×C13#332611yescharacteristic
474C2×C13#333311yescharacteristic
475D13—82no—
476C24—261no—
477C24C2×C22⋊D1311yescharacteristic
478#41—268no—
479#41—524no—
480#41—524no—
481#41—524no—
482C2×Q8—132no—
483C2×Q8—132no—
484C2×Q8—132no—
485C2×Q8—261no—
486C2×Q8—261no—
487C2×Q8—261no—
488C2×D4—132no—
489C2×D4—264no—
490C2×D4—261no—
491C2×D4—261no—
492C2×D4—261no—
493C2×D4—261no—
494C2×D4—261no—
495C2×D4—522no—
496C2×D4—522no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—24no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—81no—
507C22×C4—81no—
508C22×C4—261no—
509C22×C4—264no—
510C22×C4—261no—
511C22×C4—261no—
512C22×C4—522no—
513C22×C4—522no—
514C22×C4C2×C4×D1312yes—
515C22×C4#612712yes—
516C22×C4C2×C22⋊D1311yescharacteristic
517C22×C4C2×C22⋊D1311yescharacteristic
518C22×C4C2×C22⋊D1311yescharacteristic
519C22×C4C2×C22⋊D1311yescharacteristic
520C22×C4C2×C22⋊D1311yescharacteristic
521C22×C4C23×D1311yescharacteristic
522M16—524no—
523C2×C8—132no—
524C2×C8—132no—
525C2×C8—261no—
526C2×C8—261no—
527C2×C8—261no—
528C2×C8—261no—
529C2×C8—261no—
530C2×C8—261no—
531C2×C8—261no—
532C2×C8—261no—
533C2×C8—261no—
534C2×C8—261no—
535C4⋊C4—24no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—81no—
543C4⋊C4—81no—
544C4⋊C4—261no—
545C4⋊C4—261no—
546C4⋊C4—261no—
547C4⋊C4—261no—
548C4⋊C4—522no—
549C4⋊C4—522no—
550C4⋊C4C2×C4×D1312yes—
551C4⋊C4C2×C4×D1312yes—
552C22⋊C4—22no—
553C22⋊C4—41no—
554C22⋊C4—42no—
555C22⋊C4—522no—
556C22⋊C4—522no—
557C22⋊C4—1041no—
558C22⋊C4—1041no—
559C22⋊C4—1041no—
560C42—21no—
561C42—21no—
562C42—21no—
563C42—21no—
564C42—81no—
565C42—81no—
566C42—522no—
567C42—522no—
568C13#2257911yescharacteristic, complemented, Sylow
569C23—21no—
570C23—21no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—262no—
576C23—521no—
577C23—521no—
578C23—521no—
579C23—521no—
580C23—521no—
581C23—521no—
582C23C4×C22⋊D1312yes—
583C23C22×C22⋊D1311yescharacteristic
584Q8—134no—
585Q8—262no—
586Q8—262no—
587Q8—262no—
588D4—262no—
589D4—262no—
590D4—528no—
591D4—521no—
592D4—521no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—84no—
623C2×C4—262no—
624C2×C4—262no—
625C2×C4—262no—
626C2×C4—528no—
627C2×C4—521no—
628C2×C4—521no—
629C2×C4—521no—
630C2×C4—521no—
631C2×C4—521no—
632C2×C4—521no—
633C2×C4C4×C22⋊D1312yes—
634C2×C4#8819612yes—
635C2×C4C22×C4×D1311yescharacteristic
636C2×C4C2×#612711yescharacteristic
637C2×C4#41×D1311yescharacteristic
638C2×C4#41×D1311yescharacteristic
639C2×C4#8825611yescharacteristic
640C2×C4#8825611yescharacteristic
641C8—262no—
642C8—262no—
643C8—521no—
644C8—521no—
645C22—22no—
646C22—22no—
647C22—22no—
648C22—41no—
649C22—41no—
650C22—41no—
651C22—41no—
652C22—522no—
653C22—522no—
654C22—522no—
655C22—1041no—
656C22—1041no—
657C22—1041no—
658C22—1041no—
659C22C2×C4×C22⋊D1311yescharacteristic
660C22C2×#8819611yescharacteristic
661C22#1171952711yescharacteristic
662C22#1171953411yescharacteristic
663C22#1171953411yescharacteristic
664C22#1171954011yescharacteristic
665C22#1171954111yescharacteristic
666C4—22no—
667C4—22no—
668C4—41no—
669C4—42no—
670C4—42no—
671C4—41no—
672C4—41no—
673C4—81no—
674C4—81no—
675C4—264no—
676C4—1041no—
677C4—1041no—
678C4D13×#11711yescharacteristic
679C4#1171922611yescharacteristic
680C4#1171923211yescharacteristic
681C4#1171923211yescharacteristic
682C2—42no—
683C2—1042no—
684C2#1311768611yescharacteristic
685C2C4×#8819611yescharacteristic
686C2#1312366811yescharacteristic
687C2#1312683611yescharacteristic
688C2#1312694111yescharacteristic
689C2#1312708311yescharacteristic
690C2#1312716811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#2345C2
socleC23×C13C22×D4
prime radicalC22×#6127C22
cosocleC22×C4×C13C24
hypercenter#2345D13
hypocenterC13#22579
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2345

Complements

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

NH ≅ G/Ntype
3. #13115532C2semidirect
4. #13115518C2semidirect
5. #13115463C2semidirect
6. #13115456C2semidirect
7. #13115103C2semidirect
8. #13115089C2semidirect
9. #13114922C2semidirect
10. #13114867C2semidirect
12. #13114669C2semidirect
13. C4×#88050C2semidirect
14. #13114620C2semidirect
15. C13×#2345C2semidirect
37. #11718627C4semidirect
225. #2345D13semidirect
568. C13#22579semidirect

Maximal subgroups

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

subgroupindex
C2×#117186272
#131176762
#131155322
#131155182
#131154632
#131154562
#131151032
#131150892
#131149222
#131148672
#131147742
#131146692
C4×#880502
#131146202
C13×#23452
#2257913