Finite Group Databasebeta

← #15879552

Subgroups — #15879552

Order 3328.

1250 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719432C211yesmaximal, characteristic
2C2×#11718362C211yesmaximal, characteristic, complemented
3#13117788C211yesmaximal, characteristic, complemented
4#13115807C211yesmaximal, characteristic, complemented
5#13115795C211yesmaximal, characteristic, complemented
6#13115786C211yesmaximal, characteristic, complemented
7#13115785C211yesmaximal, characteristic, complemented
8#13115782C211yesmaximal, characteristic, complemented
9#13114845C211yesmaximal, characteristic
10#13114843C211yesmaximal, characteristic
11#13114835C211yesmaximal, characteristic
12#13114662C211yesmaximal, characteristic
13#13114660C211yesmaximal, characteristic
14#13114650C211yesmaximal, characteristic
15C13×#1993C211yesmaximal, characteristic, complemented
16C22×Q8×D13—21no—
17C2×C13×C4⋊Q8C2211yescharacteristic
18C2×#88200—21no—
19#11719432—24no—
20#11719432C418yescomplemented
21C2×#88150—21no—
22C2×#88150—21no—
23C2×#88147C2211yescharacteristic
24C2×#88147C2211yescharacteristic
25C2×#88142C2211yescharacteristic
26C2×#88142C2211yescharacteristic
27C2×C4×D52C2211yescharacteristic
28C2×C4×Dic26C2211yescharacteristic
29C2×C13×#97C2211yescharacteristic
30C13×#382C2211yescharacteristic
31C2×#88061C2211yescharacteristic
32C2×#88061C2211yescharacteristic
33C2×#88055C2211yescharacteristic
34C2×#88054C2211yescharacteristic
35C2×#88054C2211yescharacteristic
36C2×C8×Dic13C2211yescharacteristic
37#11718638C2211yescharacteristic
38#11718637C2211yescharacteristic
39C4⋊C4×Dic13C2211yescharacteristic
40C4⋊C4×Dic13C2211yescharacteristic
41C2×#88049C2211yescharacteristic
42C2×#88049C2211yescharacteristic
43C4×C4⋊Dic13C2211yescharacteristic
44C2×C4⋊#1055C2211yescharacteristic
45#11718362—24no—
46#11718314—21no—
47#11718313—21no—
48#11718310—21no—
49#11718307—21no—
50C13×#340C2211yescharacteristic
51C13×#340C2211yescharacteristic
52C13×#340C2211yescharacteristic
53C13×#340C2211yescharacteristic
54#11718143C2211yescharacteristic
55#11718143C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718121C2211yescharacteristic
60#11718121C2211yescharacteristic
61#11718121C2211yescharacteristic
62C22×Q8×C13—21no—
63C2×Q8×D13—28no—
64C2×Q8×D13—44no—
65C2×Q8×D13—44no—
66C22×D52C2311yescharacteristic
67C22×C4×D13—21no—
68C22×C4×D13—21no—
69C22×C4×D13—21no—
70C22×Dic26—21no—
71C22×Dic26—21no—
72C22×Dic26D411yescharacteristic
73C22×C8×C13C2311yescharacteristic
74C22×C8×C13C2311yescharacteristic
75C13×C4⋊Q8—22no—
76C13×C4⋊Q8C2×C414yes—
77C2×C13×C4⋊C4—21no—
78C2×C13×C4⋊C4C2311yescharacteristic
79C2×C13×C4⋊C4C2311yescharacteristic
80C2×C13×C4⋊C4C2311yescharacteristic
81C2×C13×C4⋊C4C2311yescharacteristic
82C2×C42×C13C2311yescharacteristic
83#88200—28no—
84C2×#6103—21no—
85C2×#6103—21no—
86C2×#6103—21no—
87C2×C4⋊Dic13D411yescharacteristic
88C2×C4⋊Dic13C2311yescharacteristic
89C2×C4⋊Dic13C2311yescharacteristic
90C2×C4⋊Dic13C2311yescharacteristic
91C2×#6101—21no—
92C2×#6101—21no—
93C2×#6101—21no—
94C2×#6101—21no—
95C2×#6101D411yescharacteristic
96C2×#6101D411yescharacteristic
97C2×C4×Dic13—21no—
98C2×C4×Dic13—21no—
99C2×C4×Dic13—21no—
100C2×C4×Dic13C2311yescharacteristic
101C2×C4×Dic13C2311yescharacteristic
102C22×#1055C2311yescharacteristic
103C22×#1055C2311yescharacteristic
104#88150—28no—
105#88150—28no—
106#88147—22no—
107#88147—22no—
108#88147C2×C414yes—
109#88147C2×C414yes—
110#88142—22no—
111#88142—22no—
112#88142C2×C414yes—
113#88142C2×C414yes—
114C4×D52—22no—
115C4×D52C2×C414yes—
116C4×Dic26C2×C414yes—
117C4×Dic26D414yes—
118C13×#97—22no—
119C13×#95—21no—
120C13×#95—21no—
121#88071—21no—
122#88071—21no—
123#88071—21no—
124#88071—21no—
125#88071—21no—
126#88061—22no—
127#88061Q814yescomplemented
128#88055—22no—
129#88054—22no—
130#88054—22no—
131C8×Dic13—22no—
132#88049—22no—
133#88049—22no—
134C4⋊#1055—22no—
135#22523—131nomaximal, Sylow
136C23×D13—21no—
137C2×Q8×C13—24no—
138C2×Q8×C13—42no—
139C2×Q8×C13—42no—
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×Dic13C2×D411yescharacteristic
151C22×Dic13C2×D411yescharacteristic
152C22×Dic13C2×D411yescharacteristic
153C22×Dic13C2×D411yescharacteristic
154Q8×D13—432no—
155C2×D52—21no—
156C2×D52—21no—
157C2×D52—21no—
158C2×D52C22×C412yes—
159C2×D52C2×Q812yes—
160C2×D52#4112yes—
161C2×C4×D13—24no—
162C2×C4×D13—24no—
163C2×C4×D13—24no—
164C2×C4×D13—42no—
165C2×C4×D13—42no—
166C2×C4×D13—42no—
167C2×C4×D13—42no—
168C2×C4×D13—42no—
169C2×C4×D13—42no—
170C2×Dic26—22no—
171C2×Dic26—22no—
172C2×Dic26—24no—
173C2×Dic26—24no—
174C2×Dic26—42no—
175C2×Dic26—42no—
176C2×Dic26—42no—
177C2×Dic26—42no—
178C2×Dic26C22⋊C414yes—
179C2×C8×C13—21no—
180C2×C8×C13—21no—
181C2×C8×C13—21no—
182C2×C8×C13—21no—
183C2×C8×C13—21no—
184C2×C8×C13C2×Q812yescomplemented
185C13×C4⋊C4—24no—
186C13×C4⋊C4—21no—
187C13×C4⋊C4—21no—
188C13×C4⋊C4—21no—
189C13×C4⋊C4—21no—
190C13×C4⋊C4—21no—
191C13×C4⋊C4—21no—
192C13×C4⋊C4C22×C412yes—
193C13×C4⋊C4C22×C412yes—
194C42×C13C22×C412yes—
195C42×C13C2×D412yes—
196#6103—24no—
197#6103—24no—
198#6103—24no—
199C4⋊Dic13—21no—
200C4⋊Dic13—21no—
201C4⋊Dic13—21no—
202C4⋊Dic13—21no—
203C4⋊Dic13C22⋊C414yes—
204C4⋊Dic13C22×C412yes—
205C4⋊Dic13C2×Q812yescomplemented
206#6101—24no—
207#6101—24no—
208#6101—42no—
209#6101—81no—
210#6101C22⋊C414yes—
211#6101C22⋊C414yes—
212C4×Dic13—42no—
213C4×Dic13—81no—
214C4×Dic13—81no—
215C4×Dic13C22×C412yes—
216C4×Dic13C22×C412yes—
217C4×Dic13C2×D412yes—
218C4×Dic13C2×D412yes—
219C2×#1055—21no—
220C2×#1055—21no—
221C2×#1055—21no—
222C2×#1055—21no—
223C2×#1055—21no—
224C2×#1055—21no—
225C2×D4×Q8—131no—
226C2×#446—131no—
227#2355—131no—
228#1993—131no—
229#1993D1311yescharacteristic, complemented
230#1990—131no—
231#1988—131no—
232#1987—131no—
233#1987—131no—
234#1804—131no—
235#1804—131no—
236#1802—131no—
237#1762—131no—
238#1762—131no—
239C4×#102—131no—
240C23×C13C22×D411yescharacteristic
241C22×D13—22no—
242C22×D13—22no—
243C22×D13—22no—
244C22×D13—41no—
245C22×D13—41no—
246C22×D13—41no—
247C22×D13—41no—
248Q8×C13—48no—
249C2×C4×C13—21no—
250C2×C4×C13—21no—
251C2×C4×C13—21no—
252C2×C4×C13—21no—
253C2×C4×C13—22no—
254C2×C4×C13—22no—
255C2×C4×C13—41no—
256C2×C4×C13—41no—
257C2×C4×C13—41no—
258C2×C4×C13—41no—
259C2×C4×C13—41no—
260C2×C4×C13—41no—
261C2×C4×C13—41no—
262C2×C4×C13—41no—
263C2×C4×C13—41no—
264C2×C4×C13—41no—
265C2×C4×C13C2×C22⋊C412yes—
266C2×C4×C13C2×C22⋊C412yes—
267C2×C4×C13C23×C411yescharacteristic
268C2×C4×C13C22×D411yescharacteristic
269C2×C4×C13C22×Q811yescharacteristic
270C2×C4×C13C2×#4111yescharacteristic
271C2×C4×C132−1+411yescharacteristic
272C2×C4×C132−1+411yescharacteristic
273C2×Dic13—21no—
274C2×Dic13—21no—
275C2×Dic13—21no—
276C2×Dic13—21no—
277C2×Dic13—21no—
278C2×Dic13—21no—
279C2×Dic13—22no—
280C2×Dic13—22no—
281C2×Dic13—41no—
282C2×Dic13—41no—
283C2×Dic13—41no—
284C2×Dic13—41no—
285C2×Dic13—41no—
286C2×Dic13—41no—
287C2×Dic13—41no—
288C2×Dic13C2×C22⋊C412yes—
289C2×Dic13C2×C22⋊C412yes—
290C2×Dic13C2×C22⋊C412yes—
291C2×Dic13C2×C22⋊C412yes—
292C2×Dic13AGL(1,ℤ/8)12yes—
293C2×Dic13AGL(1,ℤ/8)12yes—
294D52—22no—
295D52—22no—
296D52—22no—
297D52C4×Q814yes—
298C4×D13—48no—
299C4×D13—48no—
300C4×D13—48no—
301Dic26—28no—
302Dic26—48no—
303Dic26—48no—
304C8×C13—22no—
305C8×C13—41no—
306#1055—41no—
307#1055—41no—
308C23×Q8—261no—
309D4×Q8—138no—
310D4×Q8—264no—
311C2×C4⋊Q8—131no—
312C2×C4⋊Q8—131no—
313C2×C4⋊Q8C2×D1311yescharacteristic
314C2×C22⋊Q8—261no—
315C2×C22⋊Q8—261no—
316C2×C22⋊Q8—261no—
317C2×C4×Q8—131no—
318C2×C4×D4—131no—
319C2×C4×D4—131no—
320C2×C4×D4—131no—
321#446—264no—
322C2×C4⋊C8—131no—
323C2×C4⋊C8—131no—
324C2×C4⋊C8—131no—
325C2×#102—131no—
326C2×#102—131no—
327C2×#102—131no—
328C2×#102—131no—
329C2×#97—131no—
330C2×#97C2×D1311yescharacteristic
331C2×C4×C8—131no—
332#391—261no—
333#387—261no—
334#387—261no—
335#384—131no—
336#382—131no—
337#382C2×D1311yescharacteristic
338C4×C4⋊C4—131no—
339C4×C4⋊C4—131no—
340C4×C4⋊C4—131no—
341C4×C4⋊C4—261no—
342#340—131no—
343#340—131no—
344#340—131no—
345#340—131no—
346#340—131no—
347#340—131no—
348#340—131no—
349#340—131no—
350#340C2×D1311yescharacteristic
351#340C2×D1311yescharacteristic
352#340C2×D1311yescharacteristic
353#340C2×D1311yescharacteristic
354C22×C13C22×C22⋊C411yescharacteristic
355C22×C13#54811yescharacteristic
356C22×C13D4×Q811yescharacteristic
357C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
358C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
359C22×C13#57711yescharacteristic
360C22×C13#57811yescharacteristic
361C2×D13—24no—
362C2×D13—42no—
363C2×D13—42no—
364C2×D13—42no—
365C2×D13—42no—
366C2×D13—42no—
367C2×D13—42no—
368C4×C13—22no—
369C4×C13—22no—
370C4×C13—42no—
371C4×C13—42no—
372C4×C13—81no—
373C4×C13—81no—
374C4×C13C2×C4×Q811yescharacteristic
375C4×C13#51911yescharacteristic
376C4×C13#54811yescharacteristic
377C4×C13D4×Q811yescharacteristic
378Dic13—22no—
379Dic13—22no—
380Dic13—22no—
381Dic13—42no—
382Dic13—42no—
383Dic13—81no—
384Dic13#41814yes—
385C22×Q8—21no—
386C22×Q8—131no—
387C22×Q8—261no—
388C22×Q8—261no—
389C22×Q8—268no—
390C22×Q8—524no—
391C22×Q8—524no—
392C22×D4—131no—
393C23×C4—261no—
394C23×C4—261no—
395C23×C4—261no—
396C22×C8—131no—
397C22×C8—131no—
398C22×C8C22×D1311yescharacteristic
399C22×C8C22×D1311yescharacteristic
400C4⋊Q8—22no—
401C4⋊Q8—134no—
402C4⋊Q8—134no—
403C4⋊Q8—262no—
404C4⋊Q8—262no—
405C4⋊Q8C4×D1314yes—
406C22⋊Q8—268no—
407C22⋊Q8—268no—
408C22⋊Q8—268no—
409C4×Q8—134no—
410C4×Q8—134no—
411C4×D4—134no—
412C4×D4—134no—
413C4×D4—134no—
414C4×D4—262no—
415C4×D4—262no—
416C4×D4—262no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—131no—
419C2×C4⋊C4—131no—
420C2×C4⋊C4—131no—
421C2×C4⋊C4—131no—
422C2×C4⋊C4—131no—
423C2×C4⋊C4—131no—
424C2×C4⋊C4—261no—
425C2×C4⋊C4—261no—
426C2×C4⋊C4—261no—
427C2×C4⋊C4—261no—
428C2×C4⋊C4C22×D1311yescharacteristic
429C2×C4⋊C4C22×D1311yescharacteristic
430C2×C4⋊C4C22×D1311yescharacteristic
431C2×C4⋊C4C22×D1311yescharacteristic
432C2×C22⋊C4—261no—
433C2×C22⋊C4—261no—
434C2×C22⋊C4—261no—
435C2×C42—131no—
436C2×C42—131no—
437C2×C42—261no—
438C2×C42—261no—
439C2×C42—261no—
440C2×C42C22×D1311yescharacteristic
441C4⋊C8—262no—
442C4⋊C8—262no—
443C4⋊C8—262no—
444#102—134no—
445#102—262no—
446#102—262no—
447#102—262no—
448#97—22no—
449#97—262no—
450C4×C8—262no—
451#95—21no—
452#95—21no—
453#95—261no—
454#95—261no—
455#95—261no—
456#95—261no—
457#95—261no—
458C2×C13Q8×C22⋊C411yescharacteristic
459C2×C13C2×#41811yescharacteristic
460C2×C13#289811yescharacteristic
461C2×C13#336711yescharacteristic
462C2×C13#337311yescharacteristic
463C2×C13#338411yescharacteristic
464C2×C13#338611yescharacteristic
465D13—44no—
466C24—261no—
467C2×Q8—24no—
468C2×Q8—42no—
469C2×Q8—42no—
470C2×Q8—134no—
471C2×Q8—262no—
472C2×Q8—262no—
473C2×Q8—264no—
474C2×Q8—264no—
475C2×Q8—522no—
476C2×Q8—522no—
477C2×Q8—522no—
478C2×Q8—522no—
479C2×Q8—5232no—
480C2×D4—132no—
481C2×D4—132no—
482C2×D4—132no—
483C2×D4—261no—
484C2×D4—261no—
485C2×D4—261no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—131no—
491C22×C4—131no—
492C22×C4—131no—
493C22×C4—131no—
494C22×C4—264no—
495C22×C4—264no—
496C22×C4—261no—
497C22×C4—261no—
498C22×C4—264no—
499C22×C4—261no—
500C22×C4—522no—
501C22×C4—522no—
502C22×C4—522no—
503C22×C4—522no—
504C22×C4—522no—
505C22×C4—522no—
506C22×C4D4×D1311yescharacteristic
507C22×C4D4×D1311yescharacteristic
508C22×C4C23×D1311yescharacteristic
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—261no—
515C2×C8—261no—
516C2×C8—261no—
517C2×C8—261no—
518C2×C8—261no—
519C2×C8—261no—
520C2×C8Q8×D1312yescomplemented
521C4⋊C4—24no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—134no—
529C4⋊C4—134no—
530C4⋊C4—134no—
531C4⋊C4—132no—
532C4⋊C4—132no—
533C4⋊C4—264no—
534C4⋊C4—264no—
535C4⋊C4—261no—
536C4⋊C4—261no—
537C4⋊C4—261no—
538C4⋊C4—261no—
539C4⋊C4—522no—
540C4⋊C4—1041no—
541C4⋊C4C2×C4×D1312yes—
542C4⋊C4C2×C4×D1312yes—
543C22⋊C4—264no—
544C22⋊C4—264no—
545C22⋊C4—264no—
546C42—132no—
547C42—132no—
548C42—132no—
549C42—132no—
550C42—522no—
551C42—1041no—
552C42—1041no—
553C42C2×C4×D1312yes—
554C42D4×D1312yes—
555C13#2252311yescharacteristic, complemented, Sylow
556C23—262no—
557C23—262no—
558C23—262no—
559C23—521no—
560C23—521no—
561C23—521no—
562C23—521no—
563C23C2×D4×D1311yescharacteristic
564Q8—48no—
565Q8—268no—
566Q8—528no—
567Q8—528no—
568D4—134no—
569D4—262no—
570D4—262no—
571D4—262no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—132no—
589C2×C4—132no—
590C2×C4—132no—
591C2×C4—132no—
592C2×C4—132no—
593C2×C4—132no—
594C2×C4—261no—
595C2×C4—261no—
596C2×C4—261no—
597C2×C4—261no—
598C2×C4—261no—
599C2×C4—261no—
600C2×C4—262no—
601C2×C4—262no—
602C2×C4—528no—
603C2×C4—528no—
604C2×C4—528no—
605C2×C4—521no—
606C2×C4—521no—
607C2×C4—521no—
608C2×C4—521no—
609C2×C4—521no—
610C2×C4—521no—
611C2×C4—521no—
612C2×C4C22⋊C4×D1312yes—
613C2×C4C22⋊C4×D1312yes—
614C2×C4C22×C4×D1311yescharacteristic
615C2×C4C2×D4×D1311yescharacteristic
616C2×C4C2×Q8×D1311yescharacteristic
617C2×C4#8825411yescharacteristic
618C2×C4#41×D1311yescharacteristic
619C2×C4#8825711yescharacteristic
620C8—22no—
621C8—41no—
622C8—521no—
623C8—521no—
624C22—264no—
625C22—522no—
626C22—522no—
627C22—522no—
628C22—522no—
629C22—522no—
630C22—522no—
631C22C2×C22⋊C4×D1311yescharacteristic
632C22#1171938211yescharacteristic
633C22#1171943211yescharacteristic
634C22D13×AGL(1,ℤ/8)11yescharacteristic
635C22D13×AGL(1,ℤ/8)11yescharacteristic
636C22#1171948311yescharacteristic
637C22#1171948411yescharacteristic
638C4—22no—
639C4—22no—
640C4—42no—
641C4—42no—
642C4—81no—
643C4—81no—
644C4—134no—
645C4—262no—
646C4—262no—
647C4—262no—
648C4—522no—
649C4—522no—
650C4—1041no—
651C4C4×Q8×D1311yescharacteristic
652C4#1171927711yescharacteristic
653C4#1171933711yescharacteristic
654C4#1171933811yescharacteristic
655C2—524no—
656C2#1311767011yescharacteristic
657C2D13×#41811yescharacteristic
658C2#1312336811yescharacteristic
659C2#1312755111yescharacteristic
660C2#1312762511yescharacteristic
661C2#1312773211yescharacteristic
662C2#1312775411yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1993C2
socleC23×C13C22×D4
prime radicalC22×D52C23
cosocleC22×C4×C13C24
hypercenter#1993D13
hypocenterC13#22523
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1993

Complements

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

NH ≅ G/Ntype
2. C2×#11718362C2semidirect
3. #13117788C2semidirect
4. #13115807C2semidirect
5. #13115795C2semidirect
6. #13115786C2semidirect
7. #13115785C2semidirect
8. #13115782C2semidirect
15. C13×#1993C2semidirect
20. #11719432C4semidirect
127. #88061Q8semidirect
184. C2×C8×C13C2×Q8semidirect
205. C4⋊Dic13C2×Q8semidirect
229. #1993D13semidirect
520. C2×C8Q8×D13semidirect
555. C13#22523semidirect

Maximal subgroups

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

subgroupindex
C2×#117194322
C2×#117183622
#131177882
#131158072
#131157952
#131157862
#131157852
#131157822
#131148452
#131148432
#131148352
#131146622
#131146602
#131146502
C13×#19932
#2252313