Finite Group Databasebeta

← #15879561

Subgroups — #15879561

Order 3328.

1034 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719274C211yesmaximal, characteristic
2C2×#11718489C211yesmaximal, characteristic
3#13117748C211yesmaximal, characteristic
4#13115804C211yesmaximal, characteristic
5#13115803C211yesmaximal, characteristic
6#13115795C211yesmaximal, characteristic
7#13115791C211yesmaximal, characteristic
8#13115790C211yesmaximal, characteristic
9#13115786C211yesmaximal, characteristic
10#13114839C211yesmaximal, characteristic
11#13114839C211yesmaximal, characteristic
12#13114668C211yesmaximal, characteristic
13#13114666C211yesmaximal, characteristic
14#103×Dic13C211yesmaximal, characteristic
15C13×#1803C211yesmaximal, characteristic
16C2×C4×Q8×C13C2211yescharacteristic
17C2×Q8×Dic13C2211yescharacteristic
18C2×Q8×Dic13C2211yescharacteristic
19#11719274—24no—
20#11719274C418yescomplemented
21C2×#88144—21no—
22C2×#88144C2211yescharacteristic
23C2×#88142—21no—
24C2×#88142C2211yescharacteristic
25C2×#88141—21no—
26C2×#88124—21no—
27C2×#88124C2211yescharacteristic
28C2×C4×Dic26—21no—
29C2×C4×Dic26C2211yescharacteristic
30C2×C13×C4⋊C8C2211yescharacteristic
31C2×C13×#103C2211yescharacteristic
32C2×C13×#103C2211yescharacteristic
33C13×#384C2211yescharacteristic
34C2×#88075C2211yescharacteristic
35C2×#88075C2211yescharacteristic
36C2×#88055C2211yescharacteristic
37C2×#88054C2211yescharacteristic
38C2×#88054C2211yescharacteristic
39C2×C8×Dic13C2211yescharacteristic
40#11718637C2211yescharacteristic
41#11718637C2211yescharacteristic
42C4⋊C4×Dic13C2211yescharacteristic
43C4⋊C4×Dic13C2211yescharacteristic
44#11718634—21no—
45#11718633—21no—
46#11718633—21no—
47C4×C4⋊Dic13C2211yescharacteristic
48C2×#88043C2211yescharacteristic
49#11718489—24no—
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×Dic26D411yescharacteristic
65C22×C8×C13C2311yescharacteristic
66C22×C8×C13C2311yescharacteristic
67C4×Q8×C13—22no—
68C4×Q8×C13C2×C414yes—
69C2×C13×C4⋊C4—21no—
70C2×C13×C4⋊C4—21no—
71C2×C13×C4⋊C4—21no—
72C2×C13×C4⋊C4C2311yescharacteristic
73C2×C13×C4⋊C4C2311yescharacteristic
74C2×C13×C4⋊C4C2311yescharacteristic
75C2×C42×C13—21no—
76C2×C42×C13C2311yescharacteristic
77Q8×Dic13—22no—
78Q8×Dic13—22no—
79Q8×Dic13C2×C414yes—
80Q8×Dic13C2×C414yes—
81C2×C4⋊Dic13—21no—
82C2×C4⋊Dic13—21no—
83C2×C4⋊Dic13—21no—
84C2×C4⋊Dic13D411yescharacteristic
85C2×C4⋊Dic13C2311yescharacteristic
86C2×C4⋊Dic13C2311yescharacteristic
87C2×C4⋊Dic13C2311yescharacteristic
88C2×C4⋊Dic13C2311yescharacteristic
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#88144—28no—
109#88144—22no—
110#88144C2×C414yes—
111#88142—28no—
112#88142—22no—
113#88142C2×C414yes—
114#88141—44no—
115#88124—22no—
116#88124—28no—
117#88124C2×C414yes—
118C4×Dic26—28no—
119C4×Dic26C2×C414yes—
120C4×Dic26D414yes—
121C13×C4⋊C8—22no—
122C13×#103—22no—
123C13×#103—22no—
124#88075—22no—
125#88075Q814yescomplemented
126#88071—21no—
127#88071—21no—
128#88071—21no—
129#88055—22no—
130#88054—22no—
131#88054—22no—
132C8×Dic13—22no—
133#88043—22no—
134#22524—131nomaximal, Sylow
135C2×Q8×C13—21no—
136C2×Q8×C13—21no—
137C2×Q8×C13—21no—
138C2×Q8×C13C22×C412yes—
139C2×Q8×C13C2×Q812yes—
140C2×Q8×C13#4112yes—
141C22×C4×C13—21no—
142C22×C4×C13—21no—
143C22×C4×C13—21no—
144C22×C4×C13—21no—
145C22×C4×C13C2×D411yescharacteristic
146C22×C4×C13C2×D411yescharacteristic
147C22×C4×C13C2411yescharacteristic
148C22×Dic13—21no—
149C22×Dic13—21no—
150C22×Dic13—21no—
151C22×Dic13—21no—
152C22×Dic13C2×D411yescharacteristic
153C22×Dic13C2×D411yescharacteristic
154C22×Dic13C2×D411yescharacteristic
155C22×Dic13C2×D411yescharacteristic
156C2×Dic26—22no—
157C2×Dic26—22no—
158C2×Dic26—24no—
159C2×Dic26—42no—
160C2×Dic26—42no—
161C2×Dic26C22⋊C414yes—
162C2×C8×C13—21no—
163C2×C8×C13—21no—
164C2×C8×C13—21no—
165C2×C8×C13—21no—
166C2×C8×C13—21no—
167C2×C8×C13—21no—
168C13×C4⋊C4—24no—
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—24no—
178C42×C13C22×C412yes—
179C42×C13C2×D412yes—
180C4⋊Dic13—21no—
181C4⋊Dic13—21no—
182C4⋊Dic13—21no—
183C4⋊Dic13—24no—
184C4⋊Dic13—24no—
185C4⋊Dic13—24no—
186C4⋊Dic13—21no—
187C4⋊Dic13—21no—
188C4⋊Dic13C22⋊C414yes—
189C4⋊Dic13C22×C412yes—
190C4⋊Dic13C22×C412yes—
191C4⋊Dic13C2×Q812yes—
192#6101—24no—
193#6101—24no—
194#6101—24no—
195#6101—24no—
196#6101—42no—
197#6101—42no—
198#6101—81no—
199#6101—81no—
200#6101C22⋊C414yes—
201#6101C22⋊C414yes—
202C4×Dic13—24no—
203C4×Dic13—24no—
204C4×Dic13—42no—
205C4×Dic13—42no—
206C4×Dic13—42no—
207C4×Dic13C22×C412yes—
208C4×Dic13C22×C412yes—
209C4×Dic13C2×D412yes—
210C4×Dic13C2×D412yes—
211C2×#1055—21no—
212C2×#1055—21no—
213C2×#1055—21no—
214C2×#1055—21no—
215C2×#1055—21no—
216C2×#1055C2×Q812yes—
217C2×#557—131no—
218C2×#446—131no—
219Q8×C4⋊C4—131no—
220#1992—131no—
221#1992—131no—
222#1990—131no—
223#1989—131no—
224#1989—131no—
225#1988—131no—
226#1803—131no—
227#1803—131no—
228#1803D1311yescharacteristic
229#1763—131no—
230#1763—131no—
231C4×#103—131no—
232C23×C13C22×D411yescharacteristic
233Q8×C13—22no—
234Q8×C13—22no—
235Q8×C13—22no—
236Q8×C13C4×Q814yescomplemented
237C2×C4×C13—22no—
238C2×C4×C13—22no—
239C2×C4×C13—22no—
240C2×C4×C13—21no—
241C2×C4×C13—21no—
242C2×C4×C13—21no—
243C2×C4×C13—21no—
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×C13—41no—
253C2×C4×C13C2×C22⋊C412yes—
254C2×C4×C13C2×C22⋊C412yes—
255C2×C4×C13C23×C411yescharacteristic
256C2×C4×C13C22×D411yescharacteristic
257C2×C4×C13C22×Q811yescharacteristic
258C2×C4×C13C2×#4111yescharacteristic
259C2×C4×C132−1+411yescharacteristic
260C2×C4×C132−1+411yescharacteristic
261C2×Dic13—21no—
262C2×Dic13—21no—
263C2×Dic13—21no—
264C2×Dic13—21no—
265C2×Dic13—21no—
266C2×Dic13—21no—
267C2×Dic13—22no—
268C2×Dic13—22no—
269C2×Dic13—22no—
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×Dic13—41no—
279C2×Dic13C2×C22⋊C412yes—
280C2×Dic13C2×C22⋊C412yes—
281C2×Dic13C2×C22⋊C412yes—
282C2×Dic13C2×C22⋊C412yes—
283C2×Dic13AGL(1,ℤ/8)12yes—
284C2×Dic13#13712yes—
285Dic26—28no—
286Dic26—48no—
287C8×C13—41no—
288C8×C13—41no—
289#1055—22no—
290#1055—41no—
291#557—138no—
292#557—264no—
293C2×C4⋊Q8—131no—
294C2×C4⋊Q8—261no—
295C2×#125—131no—
296C2×#125—131no—
297C2×#125—261no—
298C2×#125—261no—
299C2×C4×Q8—131no—
300C2×C4×Q8—131no—
301C2×C4×Q8—131no—
302C2×C4×Q8—261no—
303C2×C4×Q8—261no—
304C2×C4×Q8C2×D1311yescharacteristic
305#446—264no—
306C2×C4⋊C8—131no—
307C2×C4⋊C8—131no—
308C2×C4⋊C8C2×D1311yescharacteristic
309C2×#103—131no—
310C2×#103—131no—
311C2×#103C2×D1311yescharacteristic
312C2×#103C2×D1311yescharacteristic
313C2×#97—131no—
314C2×#97—131no—
315C2×C4×C8—131no—
316#389—261no—
317#389—261no—
318#389—261no—
319#384—131no—
320#384—131no—
321#384C2×D1311yescharacteristic
322C4×C4⋊C4—131no—
323C4×C4⋊C4—131no—
324C4×C4⋊C4—131no—
325#340—131no—
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#340C2×D1311yescharacteristic
336#340C2×D1311yescharacteristic
337C22×C13C22×C22⋊C411yescharacteristic
338C22×C13#54811yescharacteristic
339C22×C13D4×Q811yescharacteristic
340C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
341C22×C13C2×#13711yescharacteristic
342C22×C13#57711yescharacteristic
343C22×C13#57811yescharacteristic
344C4×C13—24no—
345C4×C13—22no—
346C4×C13—22no—
347C4×C13—42no—
348C4×C13—81no—
349C4×C13—81no—
350C4×C13C2×C4×Q811yescharacteristic
351C4×C13#51911yescharacteristic
352C4×C13#54811yescharacteristic
353C4×C13D4×Q811yescharacteristic
354Dic13—22no—
355Dic13—22no—
356Dic13—22no—
357Dic13—42no—
358Dic13—42no—
359Dic13—42no—
360Dic13—81no—
361Dic13#41714yes—
362C22×Q8—131no—
363C22×Q8—261no—
364C22×Q8C22×D1311yescharacteristic
365C22×C8—131no—
366C22×C8—131no—
367C22×C8C22×D1311yescharacteristic
368C22×C8C22×D1311yescharacteristic
369C4⋊Q8—134no—
370C4⋊Q8—262no—
371C4⋊Q8—268no—
372#125—134no—
373#125—134no—
374#125—268no—
375#125—262no—
376#125—268no—
377#125—262no—
378C4×Q8—22no—
379C4×Q8—134no—
380C4×Q8—134no—
381C4×Q8—134no—
382C4×Q8—134no—
383C4×Q8—268no—
384C4×Q8—262no—
385C4×Q8—262no—
386C4×Q8—524no—
387C4×Q8C4×D1314yes—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
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⋊C4—261no—
406C2×C4⋊C4—261no—
407C2×C4⋊C4—261no—
408C2×C4⋊C4—261no—
409C2×C4⋊C4C22×D1311yescharacteristic
410C2×C4⋊C4C22×D1311yescharacteristic
411C2×C4⋊C4C22×D1311yescharacteristic
412C2×C42—21no—
413C2×C42—131no—
414C2×C42—131no—
415C2×C42—261no—
416C2×C42—261no—
417C2×C42—261no—
418C2×C42—261no—
419C2×C42—261no—
420C2×C42C22×D1311yescharacteristic
421C4⋊C8—22no—
422C4⋊C8—262no—
423C4⋊C8—262no—
424#103—22no—
425#103—22no—
426#103—134no—
427#103—262no—
428#97—262no—
429#97—262no—
430C4×C8—262no—
431#95—261no—
432#95—261no—
433#95—261no—
434C2×C13Q8×C22⋊C411yescharacteristic
435C2×C13C2×#41711yescharacteristic
436C2×C13#289811yescharacteristic
437C2×C13#336811yescharacteristic
438C2×C13#337411yescharacteristic
439C2×C13#338611yescharacteristic
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—522no—
449C2×Q8—522no—
450C2×Q8C2×C4×D1312yes—
451C2×Q8#612912yes—
452C2×Q8Q8×D1312yes—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—131no—
458C22×C4—131no—
459C22×C4—131no—
460C22×C4—131no—
461C22×C4—261no—
462C22×C4—261no—
463C22×C4—261no—
464C22×C4—261no—
465C22×C4D4×D1311yescharacteristic
466C22×C4D4×D1311yescharacteristic
467C22×C4C23×D1311yescharacteristic
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—132no—
475C2×C8—261no—
476C2×C8—261no—
477C2×C8—261no—
478C2×C8—261no—
479C2×C8—261no—
480C4⋊C4—24no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—42no—
487C4⋊C4—81no—
488C4⋊C4—134no—
489C4⋊C4—134no—
490C4⋊C4—134no—
491C4⋊C4—132no—
492C4⋊C4—132no—
493C4⋊C4—132no—
494C4⋊C4—264no—
495C4⋊C4—264no—
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—522no—
507C4⋊C4—522no—
508C4⋊C4—1041no—
509C4⋊C4—1041no—
510C4⋊C4C2×C4×D1312yes—
511C42—24no—
512C42—132no—
513C42—132no—
514C42—132no—
515C42—132no—
516C42—264no—
517C42—264no—
518C42—522no—
519C42—522no—
520C42—522no—
521C42C2×C4×D1312yes—
522C42D4×D1312yes—
523C13#2252411yescharacteristic, complemented, Sylow
524C23C2×D4×D1311yescharacteristic
525Q8—22no—
526Q8—22no—
527Q8—22no—
528Q8—268no—
529Q8—528no—
530Q8#8814114yescomplemented
531C2×C4—22no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—132no—
548C2×C4—132no—
549C2×C4—132no—
550C2×C4—132no—
551C2×C4—132no—
552C2×C4—132no—
553C2×C4—261no—
554C2×C4—261no—
555C2×C4—261no—
556C2×C4—261no—
557C2×C4—261no—
558C2×C4—261no—
559C2×C4—262no—
560C2×C4—262no—
561C2×C4—262no—
562C2×C4—521no—
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×C4C22⋊C4×D1312yes—
572C2×C4C22⋊C4×D1312yes—
573C2×C4C22×C4×D1311yescharacteristic
574C2×C4C2×D4×D1311yescharacteristic
575C2×C4C2×#612911yescharacteristic
576C2×C4C2×Q8×D1311yescharacteristic
577C2×C4#8825711yescharacteristic
578C2×C4#8825711yescharacteristic
579C8—41no—
580C8—41no—
581C8—262no—
582C8—521no—
583C22C2×C22⋊C4×D1311yescharacteristic
584C22#1171930311yescharacteristic
585C22#1171933711yescharacteristic
586C22#1171946711yescharacteristic
587C22#1171947111yescharacteristic
588C22D13×AGL(1,ℤ/8)11yescharacteristic
589C22D13×#13711yescharacteristic
590C4—22no—
591C4—22no—
592C4—24no—
593C4—42no—
594C4—81no—
595C4—81no—
596C4—134no—
597C4—262no—
598C4—262no—
599C4—262no—
600C4—522no—
601C4—522no—
602C4—522no—
603C4—1041no—
604C4C2×#8814111yescharacteristic
605C4#1171922111yescharacteristic
606C4#1171930311yescharacteristic
607C4#1171933711yescharacteristic
608C2#1311766811yescharacteristic
609C2D13×#41711yescharacteristic
610C2#1312336411yescharacteristic
611C2#1312756011yescharacteristic
612C2#1312763411yescharacteristic
613C2#1312776011yescharacteristic
614C2#1312776311yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1803C2
socle, prime radicalC23×C13C22×D4
cosocleC22×C4×C13C24
hypercenter#1803D13
hypocenterC13#22524
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1803

Complements

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

NH ≅ G/Ntype
20. #11719274C4semidirect
125. #88075Q8semidirect
236. Q8×C13C4×Q8semidirect
523. C13#22524semidirect
530. Q8#88141semidirect

Maximal subgroups

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

subgroupindex
C2×#117192742
C2×#117184892
#131177482
#131158042
#131158032
#131157952
#131157912
#131157902
#131157862
#131148392
#131146682
#131146662
#103×Dic132
C13×#18032
#2252413