Finite Group Databasebeta

← #15881347

Subgroups — #15881347

Order 3328.

926 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#6107C211yesmaximal, characteristic
2C2×#11718451C211yesmaximal, characteristic
3C2×#11718451C211yesmaximal, characteristic
4#13117750C211yesmaximal, characteristic
5Q8×#6101C211yesmaximal, characteristic
6#13115568C211yesmaximal, characteristic
7#13115566C211yesmaximal, characteristic
8#13115093C211yesmaximal, characteristic
9#13115092C211yesmaximal, characteristic
10#13115087C211yesmaximal, characteristic
11#13114994C211yesmaximal, characteristic
12#13114840C211yesmaximal, characteristic
13#13114839C211yesmaximal, characteristic
14#13114697C211yesmaximal, characteristic
15C13×#1863C211yesmaximal, characteristic
16C2×C4×Q8×C13C2211yescharacteristic
17C2×Q8×Dic13C2211yescharacteristic
18C2×Q8×Dic13C2211yescharacteristic
19C22×#6107C2211yescharacteristic
20C2×#88141C2211yescharacteristic
21C2×#88141C2211yescharacteristic
22C2×C4×Dic26C2211yescharacteristic
23C2×C13×#107C2211yescharacteristic
24C2×C13×#103C2211yescharacteristic
25C2×C13×#103C2211yescharacteristic
26C13×#389C2211yescharacteristic
27C2×#88075C2211yescharacteristic
28C2×#88058C2211yescharacteristic
29C2×#88056C2211yescharacteristic
30C2×#88056C2211yescharacteristic
31C2×#88054C2211yescharacteristic
32C2×C8×Dic13C2211yescharacteristic
33C2×C8×Dic13C2211yescharacteristic
34C4×#6107—24no—
35#11718646C2211yescharacteristic
36#11718637—21no—
37#11718637—21no—
38#11718637C2211yescharacteristic
39#11718637C2211yescharacteristic
40#11718634—21no—
41#11718634C2211yescharacteristic
42#11718633—21no—
43C2×#88050C2211yescharacteristic
44C2×#88047C2211yescharacteristic
45C2×#88047C2211yescharacteristic
46C2×#88047C2211yescharacteristic
47C4×#6101—21no—
48C4×#6101C2211yescharacteristic
49#11718589—21no—
50#11718589C2211yescharacteristic
51C2×C4×#1055C2211yescharacteristic
52#11718451—24no—
53#11718451C418yescomplemented
54#11718310—21no—
55#11718308—21no—
56C13×#340C2211yescharacteristic
57C13×#336C2211yescharacteristic
58#11718143C2211yescharacteristic
59#11718142C2211yescharacteristic
60#11718121C2211yescharacteristic
61#11718121C2211yescharacteristic
62C22×Q8×C13C2311yescharacteristic
63C22×Dic26C2311yescharacteristic
64C22×C8×C13C2311yescharacteristic
65C22×C8×C13C2311yescharacteristic
66C4×Q8×C13—22no—
67C4×Q8×C13—41no—
68C2×C13×C4⋊C4—21no—
69C2×C13×C4⋊C4—21no—
70C2×C13×C4⋊C4C2311yescharacteristic
71C2×C13×C4⋊C4C2311yescharacteristic
72C2×C13×C4⋊C4C2311yescharacteristic
73C2×C42×C13—21no—
74C2×C42×C13C2311yescharacteristic
75Q8×Dic13—22no—
76Q8×Dic13—22no—
77Q8×Dic13—41no—
78Q8×Dic13C2×C414yes—
79C2×#6107C2×C414yes—
80C2×#6107D414yes—
81C2×#6107Q814yes—
82C2×C4⋊Dic13—21no—
83C2×C4⋊Dic13—21no—
84C2×C4⋊Dic13—21no—
85C2×C4⋊Dic13C2311yescharacteristic
86C2×C4⋊Dic13C2311yescharacteristic
87C2×C4⋊Dic13C2311yescharacteristic
88C2×#6101—21no—
89C2×#6101—21no—
90C2×#6101—21no—
91C2×#6101—21no—
92C2×#6101—21no—
93C2×#6101—21no—
94C2×#6101—21no—
95C2×#6101—21no—
96C2×#6101—21no—
97C2×#6101D411yescharacteristic
98C2×#6101D411yescharacteristic
99C2×C4×Dic13—21no—
100C2×C4×Dic13—21no—
101C2×C4×Dic13—21no—
102C2×C4×Dic13—21no—
103C2×C4×Dic13—21no—
104C2×C4×Dic13C2311yescharacteristic
105C2×C4×Dic13C2311yescharacteristic
106C22×#1055C2311yescharacteristic
107C22×#1055C2311yescharacteristic
108#88141—22no—
109#88141—22no—
110#88141—41no—
111#88141C2×C414yes—
112C4×Dic26—22no—
113C4×Dic26—41no—
114C13×#107—41no—
115C13×#103—22no—
116C13×#103C2×C414yes—
117C13×#95—21no—
118#88075—22no—
119#88071—21no—
120#88071—21no—
121#88071—21no—
122#88071D411yescharacteristic
123#88071D411yescharacteristic
124#88058—41no—
125#88056—22no—
126#88056C2×C414yes—
127#88054—22no—
128C8×Dic13—22no—
129C8×Dic13C2×C414yes—
130#88050—22no—
131#88047—22no—
132#88047—22no—
133#88047C2×C414yes—
134C4×#1055—22no—
135C4⋊C4×Q16—131nomaximal, Sylow
136C2×Q8×C13—21no—
137C2×Q8×C13—21no—
138C2×Q8×C13—21no—
139C2×Q8×C13C22×C412yes—
140C2×Q8×C13C2×D412yes—
141C2×Q8×C13C2×Q812yes—
142C22×C4×C13—21no—
143C22×C4×C13—21no—
144C22×C4×C13—21no—
145C22×C4×C13—21no—
146C22×C4×C13C2×D411yescharacteristic
147C22×C4×C13C2×D411yescharacteristic
148C22×C4×C13C2411yescharacteristic
149C22×Dic13—21no—
150C22×Dic13—21no—
151C22×Dic13—21no—
152C22×Dic13—21no—
153C22×Dic13C2×D411yescharacteristic
154C22×Dic13C2×D411yescharacteristic
155C22×Dic13C2×D411yescharacteristic
156C22×Dic13C2×D411yescharacteristic
157C2×Dic26—21no—
158C2×Dic26—21no—
159C2×Dic26—21no—
160C2×Dic26C22×C412yes—
161C2×Dic26C2×D412yes—
162C2×Dic26C2×Q812yes—
163C2×C8×C13—21no—
164C2×C8×C13—21no—
165C2×C8×C13—21no—
166C2×C8×C13—21no—
167C2×C8×C13—21no—
168C2×C8×C13C22×C412yes—
169C13×C4⋊C4—21no—
170C13×C4⋊C4—21no—
171C13×C4⋊C4—21no—
172C13×C4⋊C4—21no—
173C13×C4⋊C4—21no—
174C13×C4⋊C4—42no—
175C13×C4⋊C4—81no—
176C13×C4⋊C4C22×C412yes—
177C42×C13—21no—
178C42×C13—21no—
179C42×C13—42no—
180#6107C4⋊C4116yescomplemented
181C4⋊Dic13—21no—
182C4⋊Dic13—24no—
183C4⋊Dic13—21no—
184C4⋊Dic13—21no—
185C4⋊Dic13—21no—
186C4⋊Dic13—21no—
187C4⋊Dic13—42no—
188C4⋊Dic13—81no—
189C4⋊Dic13C22×C412yes—
190#6101—24no—
191#6101—22no—
192#6101—42no—
193#6101—42no—
194#6101—42no—
195#6101—42no—
196#6101—81no—
197#6101—81no—
198#6101—81no—
199#6101—81no—
200#6101Q1614yescomplemented
201C4×Dic13—21no—
202C4×Dic13—21no—
203C4×Dic13—24no—
204C4×Dic13—24no—
205C4×Dic13—42no—
206C4×Dic13—42no—
207C4×Dic13—42no—
208C4×Dic13C22×C412yes—
209C4×Dic13#4112yes—
210C2×#1055—21no—
211C2×#1055—21no—
212C2×#1055—21no—
213C2×#1055C22×C412yes—
214C2×#1055C2×D412yes—
215C2×#1055C2×Q812yes—
216C2×C4×Q16—131no—
217C2×C4×Q16—131no—
218C2×C4×Q16—131no—
219Q8×C4⋊C4—131no—
220Q8×C4⋊C4—131no—
221#1942—131no—
222#1942—131no—
223#1863—131no—
224#1863—131no—
225#1863—131no—
226#1863D1311yescharacteristic
227#1845—131no—
228#1803—131no—
229#1803—131no—
230C8×C4⋊C4—131no—
231C23×C13C22×D411yescharacteristic
232Q8×C13—22no—
233Q8×C13—22no—
234Q8×C13—22no—
235Q8×C13C2×C4⋊C414yes—
236C2×C4×C13—22no—
237C2×C4×C13—21no—
238C2×C4×C13—22no—
239C2×C4×C13—22no—
240C2×C4×C13—21no—
241C2×C4×C13—22no—
242C2×C4×C13—21no—
243C2×C4×C13—21no—
244C2×C4×C13—21no—
245C2×C4×C13—41no—
246C2×C4×C13—41no—
247C2×C4×C13—41no—
248C2×C4×C13—41no—
249C2×C4×C13—41no—
250C2×C4×C13—41no—
251C2×C4×C13—41no—
252C2×C4×C13—41no—
253C2×C4×C13C2×Q1612yes—
254C2×C4×C13C23×C411yescharacteristic
255C2×C4×C13C22×D411yescharacteristic
256C2×C4×C13C22×Q811yescharacteristic
257C2×C4×C13C2×#4111yescharacteristic
258C2×C4×C13H(5,𝔽2)11yescharacteristic
259C2×C4×C132−1+411yescharacteristic
260C2×Dic13—22no—
261C2×Dic13—21no—
262C2×Dic13—22no—
263C2×Dic13—22no—
264C2×Dic13—21no—
265C2×Dic13—21no—
266C2×Dic13—21no—
267C2×Dic13—22no—
268C2×Dic13—21no—
269C2×Dic13—21no—
270C2×Dic13—21no—
271C2×Dic13—41no—
272C2×Dic13—41no—
273C2×Dic13—41no—
274C2×Dic13—41no—
275C2×Dic13—41no—
276C2×Dic13—41no—
277C2×Dic13—41no—
278C2×Dic13—41no—
279C2×Dic13C4×D412yes—
280C2×Dic13C4×D412yes—
281C2×Dic13C2×Q1612yes—
282C2×Dic13C2×Q1612yes—
283C2×Dic13#13512yes—
284Dic26—22no—
285Dic26—22no—
286Dic26—22no—
287Dic26C2×C4⋊C414yes—
288C8×C13—22no—
289C8×C13—41no—
290#1055—41no—
291#1055C2×C4⋊C414yes—
292C22×Q16—131no—
293C2×C4×Q8—131no—
294C2×C4×Q8—131no—
295C2×C4×Q8—131no—
296C2×C4×Q8—131no—
297C2×C4×Q8—131no—
298C2×C4×Q8C2×D1311yescharacteristic
299C4×Q16—138no—
300C4×Q16—264no—
301C4×Q16—264no—
302C2×#107—131no—
303C2×#107—131no—
304C2×#107—131no—
305C2×#107—131no—
306C2×#107C2×D1311yescharacteristic
307C2×C4⋊C8—131no—
308C2×#103—131no—
309C2×#103—131no—
310C2×#103—131no—
311C2×#103—131no—
312C2×#103C2×D1311yescharacteristic
313C2×#103C2×D1311yescharacteristic
314C2×C4×C8—131no—
315C2×C4×C8—131no—
316C2×C4×C8—131no—
317#389—131no—
318#389—131no—
319#389—131no—
320#389—261no—
321#389—261no—
322#389—261no—
323#389—261no—
324#389C2×D1311yescharacteristic
325#384—131no—
326#384—131no—
327#384—261no—
328#384—261no—
329C4×C4⋊C4—131no—
330C4×C4⋊C4—261no—
331C4×C4⋊C4—261no—
332#340—131no—
333#340—131no—
334#340—131no—
335#340C2×D1311yescharacteristic
336#336—131no—
337#336C2×D1311yescharacteristic
338C22×C13C2×C4×D411yescharacteristic
339C22×C13D4211yescharacteristic
340C22×C13D4×Q811yescharacteristic
341C22×C13C22×Q1611yescharacteristic
342C22×C13C2×#13511yescharacteristic
343C22×C13#57611yescharacteristic
344C22×C13#57811yescharacteristic
345C4×C13—24no—
346C4×C13—22no—
347C4×C13—42no—
348C4×C13—41no—
349C4×C13—81no—
350C4×C13—81no—
351C4×C13C22×C4⋊C411yescharacteristic
352C4×C13#52011yescharacteristic
353C4×C13#54711yescharacteristic
354C4×C13#55411yescharacteristic
355Dic13—24no—
356Dic13—22no—
357Dic13—22no—
358Dic13—42no—
359Dic13—41no—
360Dic13—81no—
361Dic13—81no—
362Dic13C4×Q1614yescomplemented
363C22×Q8—131no—
364C22×Q8C22×D1311yescharacteristic
365C2×Q16—134no—
366C2×Q16—134no—
367C2×Q16—134no—
368C22×C8—131no—
369C22×C8—131no—
370C22×C8C22×D1311yescharacteristic
371C22×C8C22×D1311yescharacteristic
372C4×Q8—22no—
373C4×Q8—41no—
374C4×Q8—134no—
375C4×Q8—134no—
376C4×Q8—262no—
377C4×Q8—262no—
378C4×Q8—262no—
379C4×Q8—262no—
380C4×Q8—262no—
381C4×Q8—521no—
382C4×Q8—521no—
383C4×Q8—521no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—131no—
387C2×C4⋊C4—131no—
388C2×C4⋊C4—131no—
389C2×C4⋊C4—131no—
390C2×C4⋊C4—131no—
391C2×C4⋊C4—261no—
392C2×C4⋊C4—261no—
393C2×C4⋊C4—261no—
394C2×C4⋊C4—261no—
395C2×C4⋊C4—261no—
396C2×C4⋊C4—261no—
397C2×C4⋊C4—261no—
398C2×C4⋊C4—261no—
399C2×C4⋊C4—261no—
400C2×C4⋊C4—261no—
401C2×C4⋊C4—261no—
402C2×C4⋊C4—261no—
403C2×C4⋊C4C22×D1311yescharacteristic
404C2×C4⋊C4C22×D1311yescharacteristic
405C2×C4⋊C4C22×D1311yescharacteristic
406C2×C42—21no—
407C2×C42—131no—
408C2×C42—131no—
409C2×C42—261no—
410C2×C42—261no—
411C2×C42—261no—
412C2×C42—261no—
413C2×C42—261no—
414C2×C42C22×D1311yescharacteristic
415#107—41no—
416#107—134no—
417#107—262no—
418#107—262no—
419#107—521no—
420C4⋊C8—262no—
421#103—22no—
422#103—134no—
423#103—262no—
424#103—262no—
425#103—262no—
426#103C4×D1314yes—
427C4×C8—134no—
428C4×C8—262no—
429C4×C8—262no—
430#95—21no—
431#95—131no—
432#95—131no—
433#95—261no—
434#95—261no—
435#95—261no—
436C2×C13D4×C4⋊C411yescharacteristic
437C2×C13C2×C4×Q1611yescharacteristic
438C2×C13#295111yescharacteristic
439C2×C13D4×Q1611yescharacteristic
440C2×C13#328711yescharacteristic
441C2×C13Q8×Q1611yescharacteristic
442C2×C13#338311yescharacteristic
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—132no—
447C2×Q8—132no—
448C2×Q8—132no—
449C2×Q8—261no—
450C2×Q8—261no—
451C2×Q8—261no—
452C2×Q8C2×C4×D1312yes—
453C2×Q8D4×D1312yes—
454C2×Q8Q8×D1312yes—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—131no—
460C22×C4—131no—
461C22×C4—131no—
462C22×C4—131no—
463C22×C4—261no—
464C22×C4—261no—
465C22×C4—261no—
466C22×C4—261no—
467C22×C4D4×D1311yescharacteristic
468C22×C4D4×D1311yescharacteristic
469C22×C4C23×D1311yescharacteristic
470Q16—1316no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—132no—
477C2×C8—132no—
478C2×C8—132no—
479C2×C8—261no—
480C2×C8—261no—
481C2×C8—261no—
482C2×C8C2×C4×D1312yes—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—42no—
489C4⋊C4—81no—
490C4⋊C4—134no—
491C4⋊C4—132no—
492C4⋊C4—262no—
493C4⋊C4—264no—
494C4⋊C4—264no—
495C4⋊C4—261no—
496C4⋊C4—261no—
497C4⋊C4—261no—
498C4⋊C4—261no—
499C4⋊C4—261no—
500C4⋊C4—522no—
501C4⋊C4—522no—
502C4⋊C4—522no—
503C4⋊C4—522no—
504C4⋊C4—522no—
505C4⋊C4—1041no—
506C4⋊C4—1041no—
507C4⋊C4—1041no—
508C4⋊C4—1041no—
509C4⋊C4—1041no—
510C4⋊C4C2×C4×D1312yes—
511C42—21no—
512C42—21no—
513C42—42no—
514C42—132no—
515C42—132no—
516C42—264no—
517C42—264no—
518C42—261no—
519C42—261no—
520C42—522no—
521C42—522no—
522C42—522no—
523C13C4⋊C4×Q1611yescharacteristic, complemented, Sylow
524C23C2×D4×D1311yescharacteristic
525Q8—22no—
526Q8—22no—
527Q8—22no—
528Q8—134no—
529Q8—262no—
530Q8—262no—
531Q8—262no—
532Q8C4⋊C4×D1314yes—
533C2×C4—21no—
534C2×C4—22no—
535C2×C4—21no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—22no—
541C2×C4—21no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—132no—
551C2×C4—132no—
552C2×C4—132no—
553C2×C4—132no—
554C2×C4—132no—
555C2×C4—261no—
556C2×C4—261no—
557C2×C4—261no—
558C2×C4—262no—
559C2×C4—261no—
560C2×C4—262no—
561C2×C4—262no—
562C2×C4—261no—
563C2×C4—261no—
564C2×C4—262no—
565C2×C4—261no—
566C2×C4—521no—
567C2×C4—521no—
568C2×C4—521no—
569C2×C4—521no—
570C2×C4—521no—
571C2×C4—521no—
572C2×C4—521no—
573C2×C4—521no—
574C2×C4Q16×D1312yes—
575C2×C4C22×C4×D1311yescharacteristic
576C2×C4C2×D4×D1311yescharacteristic
577C2×C4#8825111yescharacteristic
578C2×C4C2×Q8×D1311yescharacteristic
579C2×C4#41×D1311yescharacteristic
580C2×C4#8825711yescharacteristic
581C8—22no—
582C8—41no—
583C8—134no—
584C8—521no—
585C22C4×D4×D1311yescharacteristic
586C22#1171929511yescharacteristic
587C22#1171933711yescharacteristic
588C22C2×Q16×D1311yescharacteristic
589C22D13×#13511yescharacteristic
590C22#1171947911yescharacteristic
591C22#1171948411yescharacteristic
592C4—24no—
593C4—22no—
594C4—42no—
595C4—41no—
596C4—81no—
597C4—81no—
598C4—134no—
599C4—264no—
600C4—262no—
601C4—262no—
602C4—522no—
603C4—521no—
604C4—1041no—
605C4—1041no—
606C4C2×C4⋊C4×D1311yescharacteristic
607C4#1171925111yescharacteristic
608C4#1171934111yescharacteristic
609C4#1171936011yescharacteristic
610C2#1311773411yescharacteristic
611C2C4×Q16×D1311yescharacteristic
612C2#1312370811yescharacteristic
613C2#1312658111yescharacteristic
614C2#1312658911yescharacteristic
615C2#1312771711yescharacteristic
616C2#1312772211yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1863C2
socle, prime radicalC23×C13C22×D4
cosocleC22×C4×C13C24
hypercenter#1863D13
hypocenterC13C4⋊C4×Q16
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1863

Complements

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

NH ≅ G/Ntype
53. #11718451C4semidirect
180. #6107C4⋊C4semidirect
200. #6101Q16semidirect
362. Dic13C4×Q16semidirect
523. C13C4⋊C4×Q16semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#61072
C2×#117184512
#131177502
Q8×#61012
#131155682
#131155662
#131150932
#131150922
#131150872
#131149942
#131148402
#131148392
#131146972
C13×#18632
C4⋊C4×Q1613