Finite Group Databasebeta

← #15879578

Subgroups — #15879578

Order 3328.

1022 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×Q8×Dic26C211yesmaximal, characteristic
2C2×#11718362C211yesmaximal, characteristic
3#13117794C211yesmaximal, characteristic
4#13115809C211yesmaximal, characteristic
5#13115807C211yesmaximal, characteristic
6#13115795C211yesmaximal, characteristic
7#13115788C211yesmaximal, characteristic
8#13115786C211yesmaximal, characteristic
9#13115782C211yesmaximal, characteristic
10#13114851C211yesmaximal, characteristic
11#13114849C211yesmaximal, characteristic
12#13114839C211yesmaximal, characteristic
13#13114668C211yesmaximal, characteristic
14#103×Dic13C211yesmaximal, characteristic
15C13×#1763C211yesmaximal, characteristic
16C2×C4×Q8×C13C2211yescharacteristic
17C2×Q8×Dic13C2211yescharacteristic
18C2×Q8×Dic13C2211yescharacteristic
19Q8×Dic26—24no—
20Q8×Dic26C418yescomplemented
21C2×#88142—21no—
22C2×#88142—21no—
23C2×#88142C2211yescharacteristic
24C2×#88142C2211yescharacteristic
25C2×#88123—21no—
26C2×#88123C2211yescharacteristic
27C2×C4×Dic26—21no—
28C2×C4×Dic26C2211yescharacteristic
29C2×C13×#103C2211yescharacteristic
30C2×C13×#103C2211yescharacteristic
31C2×C13×#97C2211yescharacteristic
32C4×C13×C4⋊C4C2211yescharacteristic
33C2×#88075C2211yescharacteristic
34C2×#88075C2211yescharacteristic
35C2×#88055C2211yescharacteristic
36C2×#88054C2211yescharacteristic
37C2×#88054C2211yescharacteristic
38C2×C8×Dic13C2211yescharacteristic
39#11718638C2211yescharacteristic
40#11718637C2211yescharacteristic
41C4⋊C4×Dic13C2211yescharacteristic
42C4⋊C4×Dic13C2211yescharacteristic
43#11718597C2211yescharacteristic
44#11718594—21no—
45C4×#6101—21no—
46C2×C4⋊#1055C2211yescharacteristic
47#11718362—24no—
48#11718315—21no—
49#11718307—21no—
50C13×#340C2211yescharacteristic
51C13×#340C2211yescharacteristic
52#11718143C2211yescharacteristic
53#11718143C2211yescharacteristic
54#11718143C2211yescharacteristic
55#11718143C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718121C2211yescharacteristic
60#11718121C2211yescharacteristic
61#11718121C2211yescharacteristic
62C22×Q8×C13C2311yescharacteristic
63C22×Dic26—21no—
64C22×Dic26—21no—
65C22×Dic26—21no—
66C22×Dic26D411yescharacteristic
67C22×C8×C13C2311yescharacteristic
68C22×C8×C13C2311yescharacteristic
69C4×Q8×C13—22no—
70C4×Q8×C13C2×C414yes—
71C2×C13×C4⋊C4—21no—
72C2×C13×C4⋊C4C2311yescharacteristic
73C2×C13×C4⋊C4C2311yescharacteristic
74C2×C13×C4⋊C4C2311yescharacteristic
75C2×C42×C13—21no—
76C2×C42×C13—21no—
77C2×C42×C13C2311yescharacteristic
78Q8×Dic13—22no—
79Q8×Dic13—22no—
80Q8×Dic13C2×C414yes—
81Q8×Dic13C2×C414yes—
82C2×C4⋊Dic13—21no—
83C2×C4⋊Dic13—21no—
84C2×C4⋊Dic13—21no—
85C2×C4⋊Dic13D411yescharacteristic
86C2×C4⋊Dic13C2311yescharacteristic
87C2×C4⋊Dic13C2311yescharacteristic
88C2×C4⋊Dic13C2311yescharacteristic
89C2×C4⋊Dic13C2311yescharacteristic
90C2×#6101—21no—
91C2×#6101—21no—
92C2×#6101—21no—
93C2×#6101—21no—
94C2×#6101D411yescharacteristic
95C2×#6101D411yescharacteristic
96C2×C4×Dic13—21no—
97C2×C4×Dic13—21no—
98C2×C4×Dic13—21no—
99C2×C4×Dic13—21no—
100C2×C4×Dic13C2311yescharacteristic
101C2×C4×Dic13C2311yescharacteristic
102C22×#1055C2311yescharacteristic
103C22×#1055C2311yescharacteristic
104#88142—28no—
105#88142—28no—
106#88142—22no—
107#88142—22no—
108#88142C2×C414yes—
109#88142C2×C414yes—
110#88123—22no—
111#88123—28no—
112#88123C2×C414yes—
113C4×Dic26—28no—
114C4×Dic26C2×C414yes—
115C4×Dic26D414yes—
116C13×#103—22no—
117C13×#103Q814yescomplemented
118C13×#97—22no—
119C13×#95—21no—
120#88075—22no—
121#88075—22no—
122#88071—21no—
123#88071—21no—
124#88071—21no—
125#88071—21no—
126#88071—21no—
127#88071—21no—
128#88055—22no—
129#88054—22no—
130#88054—22no—
131C8×Dic13—22no—
132C4⋊#1055—22no—
133#22525—131nomaximal, Sylow
134C2×Q8×C13—21no—
135C2×Q8×C13—21no—
136C2×Q8×C13—21no—
137C2×Q8×C13C22×C412yes—
138C2×Q8×C13C2×Q812yes—
139C2×Q8×C13#4112yes—
140C22×C4×C13—21no—
141C22×C4×C13—21no—
142C22×C4×C13—21no—
143C22×C4×C13—21no—
144C22×C4×C13C2×D411yescharacteristic
145C22×C4×C13C2×D411yescharacteristic
146C22×C4×C13C2411yescharacteristic
147C22×Dic13—21no—
148C22×Dic13—21no—
149C22×Dic13—21no—
150C22×Dic13—21no—
151C22×Dic13C2×D411yescharacteristic
152C22×Dic13C2×D411yescharacteristic
153C22×Dic13C2×D411yescharacteristic
154C22×Dic13C2×D411yescharacteristic
155C2×Dic26—22no—
156C2×Dic26—22no—
157C2×Dic26—24no—
158C2×Dic26—24no—
159C2×Dic26—24no—
160C2×Dic26—81no—
161C2×Dic26—81no—
162C2×Dic26—81no—
163C2×Dic26—81no—
164C2×Dic26—81no—
165C2×Dic26—81no—
166C2×Dic26C22⋊C414yes—
167C2×C8×C13—21no—
168C2×C8×C13—21no—
169C2×C8×C13—21no—
170C2×C8×C13—21no—
171C2×C8×C13—21no—
172C2×C8×C13C2×Q812yes—
173C13×C4⋊C4—24no—
174C13×C4⋊C4—21no—
175C13×C4⋊C4—21no—
176C13×C4⋊C4—21no—
177C13×C4⋊C4—21no—
178C13×C4⋊C4C22×C412yes—
179C13×C4⋊C4C2×Q812yes—
180C42×C13—24no—
181C42×C13—81no—
182C42×C13C22×C412yes—
183C42×C13C2×D412yes—
184C4⋊Dic13—24no—
185C4⋊Dic13—21no—
186C4⋊Dic13—21no—
187C4⋊Dic13—24no—
188C4⋊Dic13—24no—
189C4⋊Dic13—21no—
190C4⋊Dic13—21no—
191C4⋊Dic13—21no—
192C4⋊Dic13—21no—
193C4⋊Dic13C22⋊C414yes—
194C4⋊Dic13C22×C412yes—
195C4⋊Dic13C22×C412yes—
196#6101—24no—
197#6101—24no—
198#6101—42no—
199#6101—81no—
200#6101C22⋊C414yes—
201#6101C22⋊C414yes—
202C4×Dic13—24no—
203C4×Dic13—24no—
204C4×Dic13—42no—
205C4×Dic13—81no—
206C4×Dic13C22×C412yes—
207C4×Dic13C22×C412yes—
208C4×Dic13C2×D412yes—
209C4×Dic13C2×D412yes—
210C2×#1055—21no—
211C2×#1055—21no—
212C2×#1055—21no—
213C2×#1055—21no—
214C2×#1055—21no—
215C2×#1055—21no—
216C2×Q82—131no—
217C2×#446—131no—
218#2355—131no—
219#1993—131no—
220#1993—131no—
221#1990—131no—
222#1988—131no—
223#1988—131no—
224#1987—131no—
225#1805—131no—
226#1805—131no—
227#1803—131no—
228#1763—131no—
229#1763D1311yescharacteristic
230C4×#103—131no—
231C23×C13C22×D411yescharacteristic
232Q8×C13—22no—
233Q8×C13—22no—
234Q8×C13—22no—
235Q8×C13C4×Q814yes—
236C2×C4×C13—22no—
237C2×C4×C13—22no—
238C2×C4×C13—22no—
239C2×C4×C13—21no—
240C2×C4×C13—21no—
241C2×C4×C13—21no—
242C2×C4×C13—21no—
243C2×C4×C13—22no—
244C2×C4×C13—22no—
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×C13C2×C22⋊C412yes—
253C2×C4×C13C2×C22⋊C412yes—
254C2×C4×C13C23×C411yescharacteristic
255C2×C4×C13C22×D411yescharacteristic
256C2×C4×C13C22×Q811yescharacteristic
257C2×C4×C13C2×#4111yescharacteristic
258C2×C4×C132−1+411yescharacteristic
259C2×C4×C132−1+411yescharacteristic
260C2×Dic13—21no—
261C2×Dic13—21no—
262C2×Dic13—21no—
263C2×Dic13—21no—
264C2×Dic13—21no—
265C2×Dic13—21no—
266C2×Dic13—22no—
267C2×Dic13—22no—
268C2×Dic13—41no—
269C2×Dic13—41no—
270C2×Dic13—41no—
271C2×Dic13—41no—
272C2×Dic13—41no—
273C2×Dic13—41no—
274C2×Dic13—41no—
275C2×Dic13—41no—
276C2×Dic13—41no—
277C2×Dic13—41no—
278C2×Dic13C2×C22⋊C412yes—
279C2×Dic13C2×C22⋊C412yes—
280C2×Dic13C2×C22⋊C412yes—
281C2×Dic13C2×C22⋊C412yes—
282C2×Dic13#13712yes—
283C2×Dic13#13712yes—
284Dic26—28no—
285Dic26—84no—
286Dic26—84no—
287Dic26—84no—
288C8×C13—22no—
289C8×C13—41no—
290#1055—41no—
291#1055—41no—
292Q82—138no—
293Q82—264no—
294C2×C4⋊Q8—131no—
295C2×C4⋊Q8—131no—
296C2×C4⋊Q8—131no—
297C2×C4⋊Q8—261no—
298C2×C4⋊Q8—261no—
299C2×C4⋊Q8—261no—
300C2×C4×Q8—131no—
301C2×C4×Q8—131no—
302C2×C4×Q8—131no—
303C2×C4×Q8—261no—
304C2×C4×Q8C2×D1311yescharacteristic
305#446—264no—
306C2×C4⋊C8—131no—
307C2×C4⋊C8—131no—
308C2×C4⋊C8—131no—
309C2×#103—131no—
310C2×#103—131no—
311C2×#103C2×D1311yescharacteristic
312C2×#103C2×D1311yescharacteristic
313C2×#97—131no—
314C2×#97C2×D1311yescharacteristic
315C2×C4×C8—131no—
316#391—261no—
317#387—261no—
318#387—261no—
319#384—131no—
320#382—131no—
321#382—131no—
322C4×C4⋊C4—131no—
323C4×C4⋊C4—131no—
324C4×C4⋊C4—261no—
325C4×C4⋊C4C2×D1311yescharacteristic
326#340—131no—
327#340—131no—
328#340—131no—
329#340—131no—
330#340—131no—
331#340—131no—
332#340—131no—
333#340—131no—
334#340—131no—
335#340—131no—
336#340C2×D1311yescharacteristic
337#340C2×D1311yescharacteristic
338C22×C13C22×C22⋊C411yescharacteristic
339C22×C13#54811yescharacteristic
340C22×C13D4×Q811yescharacteristic
341C22×C13C2×#13711yescharacteristic
342C22×C13C2×#13711yescharacteristic
343C22×C13#57611yescharacteristic
344C22×C13#57711yescharacteristic
345C4×C13—24no—
346C4×C13—22no—
347C4×C13—22no—
348C4×C13—42no—
349C4×C13—42no—
350C4×C13—81no—
351C4×C13C2×C4×Q811yescharacteristic
352C4×C13#51911yescharacteristic
353C4×C13#54811yescharacteristic
354C4×C13D4×Q811yescharacteristic
355Dic13—22no—
356Dic13—22no—
357Dic13—22no—
358Dic13—42no—
359Dic13—42no—
360Dic13—81no—
361Dic13—81no—
362Dic13#41914yes—
363C22×Q8—131no—
364C22×Q8—261no—
365C22×Q8—261no—
366C22×Q8—261no—
367C22×Q8C22×D1311yescharacteristic
368C22×C8—131no—
369C22×C8—131no—
370C22×C8C22×D1311yescharacteristic
371C22×C8C22×D1311yescharacteristic
372C4⋊Q8—134no—
373C4⋊Q8—134no—
374C4⋊Q8—134no—
375C4⋊Q8—268no—
376C4⋊Q8—262no—
377C4⋊Q8—262no—
378C4⋊Q8—268no—
379C4⋊Q8—268no—
380C4⋊Q8—262no—
381C4×Q8—22no—
382C4×Q8—134no—
383C4×Q8—134no—
384C4×Q8—134no—
385C4×Q8—134no—
386C4×Q8—268no—
387C4×Q8—262no—
388C4×Q8—262no—
389C4×Q8C4×D1314yes—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—131no—
392C2×C4⋊C4—131no—
393C2×C4⋊C4—131no—
394C2×C4⋊C4—131no—
395C2×C4⋊C4—131no—
396C2×C4⋊C4—131no—
397C2×C4⋊C4—131no—
398C2×C4⋊C4—261no—
399C2×C4⋊C4—261no—
400C2×C4⋊C4—261no—
401C2×C4⋊C4—261no—
402C2×C4⋊C4—261no—
403C2×C4⋊C4—261no—
404C2×C4⋊C4—261no—
405C2×C4⋊C4C22×D1311yescharacteristic
406C2×C4⋊C4C22×D1311yescharacteristic
407C2×C4⋊C4C22×D1311yescharacteristic
408C2×C42—21no—
409C2×C42—21no—
410C2×C42—131no—
411C2×C42—131no—
412C2×C42—261no—
413C2×C42—261no—
414C2×C42—261no—
415C2×C42—261no—
416C2×C42C22×D1311yescharacteristic
417C4⋊C8—262no—
418C4⋊C8—262no—
419C4⋊C8—262no—
420#103—22no—
421#103—262no—
422#103—262no—
423#103Dic2614yescomplemented
424#97—22no—
425#97—262no—
426C4×C8—262no—
427#95—21no—
428#95—261no—
429#95—261no—
430#95—261no—
431#95—261no—
432#95—261no—
433#95—261no—
434C2×C13Q8×C22⋊C411yescharacteristic
435C2×C13C2×#41911yescharacteristic
436C2×C13#289711yescharacteristic
437C2×C13#336911yescharacteristic
438C2×C13#337511yescharacteristic
439C2×C13#338511yescharacteristic
440C2×C13#338711yescharacteristic
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—134no—
445C2×Q8—262no—
446C2×Q8—262no—
447C2×Q8—264no—
448C2×Q8—264no—
449C2×Q8—264no—
450C2×Q8—1041no—
451C2×Q8—1041no—
452C2×Q8—1041no—
453C2×Q8—1041no—
454C2×Q8—1041no—
455C2×Q8—1041no—
456C2×Q8C2×Dic2612yes—
457C2×Q8C2×C4×D1312yes—
458C2×Q8#612712yes—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—131no—
464C22×C4—131no—
465C22×C4—131no—
466C22×C4—131no—
467C22×C4—261no—
468C22×C4—261no—
469C22×C4—261no—
470C22×C4—261no—
471C22×C4D4×D1311yescharacteristic
472C22×C4D4×D1311yescharacteristic
473C22×C4C23×D1311yescharacteristic
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—261no—
480C2×C8—261no—
481C2×C8—261no—
482C2×C8—261no—
483C2×C8—261no—
484C2×C8—261no—
485C2×C8C2×Dic2612yes—
486C4⋊C4—24no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—134no—
492C4⋊C4—134no—
493C4⋊C4—134no—
494C4⋊C4—132no—
495C4⋊C4—132no—
496C4⋊C4—264no—
497C4⋊C4—264no—
498C4⋊C4—264no—
499C4⋊C4—264no—
500C4⋊C4—264no—
501C4⋊C4—261no—
502C4⋊C4—261no—
503C4⋊C4—261no—
504C4⋊C4—261no—
505C4⋊C4—261no—
506C4⋊C4—261no—
507C4⋊C4—522no—
508C4⋊C4—1041no—
509C4⋊C4C2×Dic2612yes—
510C4⋊C4C2×C4×D1312yes—
511C42—24no—
512C42—81no—
513C42—132no—
514C42—132no—
515C42—132no—
516C42—132no—
517C42—264no—
518C42—264no—
519C42—522no—
520C42—1041no—
521C42C2×C4×D1312yes—
522C42D4×D1312yes—
523C13#2252511yescharacteristic, complemented, Sylow
524C23C2×D4×D1311yescharacteristic
525Q8—22no—
526Q8—22no—
527Q8—22no—
528Q8—268no—
529Q8—1044no—
530Q8—1044no—
531Q8—1044no—
532Q8C4×Dic2614yes—
533C2×C4—22no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—132no—
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—261no—
559C2×C4—261no—
560C2×C4—261no—
561C2×C4—262no—
562C2×C4—262no—
563C2×C4—521no—
564C2×C4—521no—
565C2×C4—521no—
566C2×C4—521no—
567C2×C4—521no—
568C2×C4—521no—
569C2×C4—521no—
570C2×C4—521no—
571C2×C4—521no—
572C2×C4—521no—
573C2×C4C22⋊C4×D1312yes—
574C2×C4C22⋊C4×D1312yes—
575C2×C4C22×Dic2611yescharacteristic
576C2×C4C22×C4×D1311yescharacteristic
577C2×C4C2×#612711yescharacteristic
578C2×C4C2×D4×D1311yescharacteristic
579C2×C4#8825711yescharacteristic
580C2×C4#8825711yescharacteristic
581C8—22no—
582C8—41no—
583C8—521no—
584C8—521no—
585C22C2×C22⋊C4×D1311yescharacteristic
586C22D4×Dic2611yescharacteristic
587C22#1171925711yescharacteristic
588C22#1171947911yescharacteristic
589C22D13×#13711yescharacteristic
590C22D13×#13711yescharacteristic
591C22#1171948311yescharacteristic
592C4—22no—
593C4—22no—
594C4—24no—
595C4—42no—
596C4—42no—
597C4—81no—
598C4—134no—
599C4—262no—
600C4—262no—
601C4—262no—
602C4—522no—
603C4—522no—
604C4—1041no—
605C4—1041no—
606C4C2×C4×Dic2611yescharacteristic
607C4#1171922111yescharacteristic
608C4D4×Dic2611yescharacteristic
609C4#1171925711yescharacteristic
610C2C22⋊C4×Dic2611yescharacteristic
611C2D13×#41911yescharacteristic
612C2#1312336011yescharacteristic
613C2#1312757711yescharacteristic
614C2#1312765111yescharacteristic
615C2#1312774711yescharacteristic
616C2#1312776911yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1763C2
socle, prime radicalC23×C13C22×D4
cosocleC22×C4×C13C24
hypercenter#1763D13
hypocenterC13#22525
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1763

Complements

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

NH ≅ G/Ntype
20. Q8×Dic26C4semidirect
117. C13×#103Q8semidirect
423. #103Dic26semidirect
523. C13#22525semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×Dic262
C2×#117183622
#131177942
#131158092
#131158072
#131157952
#131157882
#131157862
#131157822
#131148512
#131148492
#131148392
#131146682
#103×Dic132
C13×#17632
#2252513