Finite Group Databasebeta

← #15879550

Subgroups — #15879550

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×D4×Dic26C211yesmaximal, characteristic
2C2×#11718489C211yesmaximal, characteristic, complemented
3#13117788C211yesmaximal, characteristic, complemented
4#13115808C211yesmaximal, characteristic, complemented
5#13115807C211yesmaximal, characteristic, complemented
6#13115795C211yesmaximal, characteristic, complemented
7#13115786C211yesmaximal, characteristic, complemented
8#13115783C211yesmaximal, characteristic, complemented
9#13115782C211yesmaximal, characteristic, complemented
10#13114844C211yesmaximal, characteristic
11#13114834C211yesmaximal, characteristic
12#13114663C211yesmaximal, characteristic
13#13114661C211yesmaximal, characteristic
14#102×Dic13C211yesmaximal, characteristic
15C13×#1804C211yesmaximal, characteristic
16C23×Dic26—21no—
17C2×C4×D4×C13C2211yescharacteristic
18C2×D4×Dic13C2211yescharacteristic
19C2×D4×Dic13C2211yescharacteristic
20C2×#88178—21no—
21D4×Dic26—24no—
22D4×Dic26C418yescomplemented
23C2×#88142C2211yescharacteristic
24C2×#88142C2211yescharacteristic
25C2×#88132—21no—
26C2×#88132—21no—
27C2×#88123C2211yescharacteristic
28C2×C4×Dic26C2211yescharacteristic
29C2×C13×C4⋊C8C2211yescharacteristic
30C2×C13×#102C2211yescharacteristic
31C2×C13×#102C2211yescharacteristic
32C13×#382C2211yescharacteristic
33C2×#88072C2211yescharacteristic
34C2×#88072C2211yescharacteristic
35C2×#88055C2211yescharacteristic
36C2×#88054C2211yescharacteristic
37C2×#88054C2211yescharacteristic
38C2×C8×Dic13C2211yescharacteristic
39#11718638C2211yescharacteristic
40#11718637C2211yescharacteristic
41C4⋊C4×Dic13C2211yescharacteristic
42C4⋊C4×Dic13C2211yescharacteristic
43C4×C4⋊Dic13C2211yescharacteristic
44C2×#88043C2211yescharacteristic
45#11718489—24no—
46#11718314—21no—
47#11718313—21no—
48#11718310—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×D4×C13C2311yescharacteristic
63C23×C4×C13—21no—
64C23×Dic13—21no—
65C23×Dic13—21no—
66C22×Dic26—21no—
67C22×Dic26—21no—
68C22×Dic26—21no—
69C22×Dic26—28no—
70C22×Dic26—44no—
71C22×Dic26—44no—
72C22×Dic26D411yescharacteristic
73C22×C8×C13C2311yescharacteristic
74C22×C8×C13C2311yescharacteristic
75C4×D4×C13—22no—
76C4×D4×C13C2×C414yes—
77C2×C13×C4⋊C4C2311yescharacteristic
78C2×C13×C4⋊C4C2311yescharacteristic
79C2×C13×C4⋊C4C2311yescharacteristic
80C2×C13×C22⋊C4—21no—
81C2×C42×C13C2311yescharacteristic
82C2×C22⋊Dic13—21no—
83C2×C22⋊Dic13—21no—
84D4×Dic13—22no—
85D4×Dic13—22no—
86D4×Dic13C2×C414yes—
87D4×Dic13C2×C414yes—
88C2×C4⋊Dic13—21no—
89C2×C4⋊Dic13D411yescharacteristic
90C2×C4⋊Dic13C2311yescharacteristic
91C2×C4⋊Dic13C2311yescharacteristic
92C2×C4⋊Dic13C2311yescharacteristic
93C2×C4⋊Dic13C2311yescharacteristic
94#88178—28no—
95C2×#6101—21no—
96C2×#6101—21no—
97C2×#6101—21no—
98C2×#6101—21no—
99C2×#6101D411yescharacteristic
100C2×#6101D411yescharacteristic
101C2×C4×Dic13—21no—
102C2×C4×Dic13—21no—
103C2×C4×Dic13—21no—
104C2×C4×Dic13C2311yescharacteristic
105C2×C4×Dic13C2311yescharacteristic
106C22×#1055C2311yescharacteristic
107C22×#1055C2311yescharacteristic
108#88142—22no—
109#88142—22no—
110#88142C2×C414yes—
111#88142C2×C414yes—
112#88132—28no—
113#88132—28no—
114#88123—22no—
115#88123C2×C414yes—
116C4×Dic26C2×C414yes—
117C4×Dic26D414yes—
118C13×C4⋊C8—22no—
119C13×#102—22no—
120C13×#102—22no—
121C13×#95—21no—
122C13×#95—21no—
123#88072—22no—
124#88072Q814yescomplemented
125#88071—21no—
126#88071—21no—
127#88071—21no—
128#88071—21no—
129#88071—21no—
130#88055—22no—
131#88054—22no—
132#88054—22no—
133C8×Dic13—22no—
134#88043—22no—
135#22523—131nomaximal, Sylow
136C24×C13—21no—
137C2×D4×C13—21no—
138C2×D4×C13—21no—
139C2×D4×C13—21no—
140C2×D4×C13C22×C412yes—
141C2×D4×C13C2×Q812yes—
142C2×D4×C13#4112yes—
143C22×C4×C13—21no—
144C22×C4×C13—24no—
145C22×C4×C13—21no—
146C22×C4×C13—21no—
147C22×C4×C13—42no—
148C22×C4×C13—42no—
149C22×C4×C13C2×D411yescharacteristic
150C22×C4×C13C2×D411yescharacteristic
151C22×C4×C13C2411yescharacteristic
152C22×Dic13—21no—
153C22×Dic13—21no—
154C22×Dic13—21no—
155C22×Dic13—24no—
156C22×Dic13—24no—
157C22×Dic13—21no—
158C22×Dic13—42no—
159C22×Dic13—42no—
160C22×Dic13—42no—
161C22×Dic13—42no—
162C22×Dic13C2×D411yescharacteristic
163C22×Dic13C2×D411yescharacteristic
164C22×Dic13C2×D411yescharacteristic
165C22×Dic13C2×D411yescharacteristic
166C2×Dic26—22no—
167C2×Dic26—22no—
168C2×Dic26—24no—
169C2×Dic26—24no—
170C2×Dic26—24no—
171C2×Dic26—432no—
172C2×Dic26—42no—
173C2×Dic26—42no—
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×C13—21no—
185C13×C4⋊C4—21no—
186C13×C4⋊C4—21no—
187C13×C4⋊C4—21no—
188C13×C4⋊C4—21no—
189C13×C4⋊C4—21no—
190C13×C4⋊C4C22×C412yes—
191C13×C22⋊C4—24no—
192C42×C13C22×C412yes—
193C42×C13C2×D412yes—
194C22⋊Dic13—24no—
195C22⋊Dic13—24no—
196C4⋊Dic13—24no—
197C4⋊Dic13—21no—
198C4⋊Dic13—21no—
199C4⋊Dic13—21no—
200C4⋊Dic13—21no—
201C4⋊Dic13—21no—
202C4⋊Dic13C22⋊C414yes—
203C4⋊Dic13C22×C412yes—
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×#1055C2×Q812yescomplemented
225C2×D4×Q8—131no—
226C2×#446—131no—
227#2355—131no—
228#1993—131no—
229#1993—131no—
230#1990—131no—
231#1988—131no—
232#1987—131no—
233#1987—131no—
234#1804—131no—
235#1804D1311yescharacteristic
236#1802—131no—
237#1762—131no—
238#1762—131no—
239C4×#102—131no—
240C23×C13—22no—
241C23×C13—22no—
242C23×C13—22no—
243C23×C13—41no—
244C23×C13—41no—
245C23×C13—41no—
246C23×C13—41no—
247C23×C13C22×D411yescharacteristic
248D4×C13—22no—
249D4×C13—22no—
250D4×C13—22no—
251D4×C13C4×Q814yes—
252C2×C4×C13—21no—
253C2×C4×C13—21no—
254C2×C4×C13—21no—
255C2×C4×C13—21no—
256C2×C4×C13—22no—
257C2×C4×C13—48no—
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×C13—41no—
266C2×C4×C13C2×C22⋊C412yes—
267C2×C4×C13C2×C22⋊C412yes—
268C2×C4×C13C23×C411yescharacteristic
269C2×C4×C13C22×D411yescharacteristic
270C2×C4×C13C22×Q811yescharacteristic
271C2×C4×C13C2×#4111yescharacteristic
272C2×C4×C132−1+411yescharacteristic
273C2×C4×C132−1+411yescharacteristic
274C2×Dic13—21no—
275C2×Dic13—21no—
276C2×Dic13—21no—
277C2×Dic13—21no—
278C2×Dic13—21no—
279C2×Dic13—21no—
280C2×Dic13—22no—
281C2×Dic13—22no—
282C2×Dic13—22no—
283C2×Dic13—48no—
284C2×Dic13—41no—
285C2×Dic13—41no—
286C2×Dic13—41no—
287C2×Dic13—41no—
288C2×Dic13—41no—
289C2×Dic13—41no—
290C2×Dic13—48no—
291C2×Dic13—41no—
292C2×Dic13—41no—
293C2×Dic13—41no—
294C2×Dic13C2×C22⋊C412yes—
295C2×Dic13C2×C22⋊C412yes—
296C2×Dic13C2×C22⋊C412yes—
297C2×Dic13C2×C22⋊C412yes—
298C2×Dic13AGL(1,ℤ/8)12yes—
299C2×Dic13AGL(1,ℤ/8)12yes—
300Dic26—28no—
301Dic26—48no—
302Dic26—48no—
303Dic26—48no—
304C8×C13—41no—
305C8×C13—41no—
306#1055—22no—
307#1055—41no—
308C23×Q8—261no—
309D4×Q8—138no—
310D4×Q8—264no—
311C2×C4⋊Q8—131no—
312C2×C4⋊Q8—131no—
313C2×C4⋊Q8—131no—
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×D4C2×D1311yescharacteristic
321#446—264no—
322C2×C4⋊C8—131no—
323C2×C4⋊C8—131no—
324C2×C4⋊C8C2×D1311yescharacteristic
325C2×#102—131no—
326C2×#102—131no—
327C2×#102C2×D1311yescharacteristic
328C2×#102C2×D1311yescharacteristic
329C2×#97—131no—
330C2×#97—131no—
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#340—131no—
351#340—131no—
352#340C2×D1311yescharacteristic
353#340C2×D1311yescharacteristic
354C22×C13—24no—
355C22×C13—42no—
356C22×C13—42no—
357C22×C13—42no—
358C22×C13—42no—
359C22×C13—42no—
360C22×C13—42no—
361C22×C13C22×C22⋊C411yescharacteristic
362C22×C13#54811yescharacteristic
363C22×C13D4×Q811yescharacteristic
364C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
365C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
366C22×C13#57711yescharacteristic
367C22×C13#57811yescharacteristic
368C4×C13—22no—
369C4×C13—22no—
370C4×C13—42no—
371C4×C13—81no—
372C4×C13—81no—
373C4×C13C2×C4×Q811yescharacteristic
374C4×C13#51911yescharacteristic
375C4×C13#54811yescharacteristic
376C4×C13D4×Q811yescharacteristic
377Dic13—22no—
378Dic13—22no—
379Dic13—22no—
380Dic13—42no—
381Dic13—42no—
382Dic13—42no—
383Dic13—81no—
384Dic13#41814yes—
385C22×Q8—131no—
386C22×Q8—261no—
387C22×Q8—261no—
388C22×Q8—268no—
389C22×Q8—261no—
390C22×Q8—524no—
391C22×Q8—524no—
392C22×D4C22×D1311yescharacteristic
393C23×C4—21no—
394C23×C4—261no—
395C23×C4—261no—
396C22×C8—131no—
397C22×C8—131no—
398C22×C8C22×D1311yescharacteristic
399C22×C8C22×D1311yescharacteristic
400C4⋊Q8—134no—
401C4⋊Q8—134no—
402C4⋊Q8—134no—
403C4⋊Q8—262no—
404C4⋊Q8—262no—
405C4⋊Q8—262no—
406C22⋊Q8—268no—
407C22⋊Q8—268no—
408C22⋊Q8—268no—
409C4×Q8—134no—
410C4×Q8—134no—
411C4×D4—22no—
412C4×D4—134no—
413C4×D4—134no—
414C4×D4—262no—
415C4×D4—262no—
416C4×D4C4×D1314yes—
417C2×C4⋊C4—131no—
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⋊C4—261no—
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×C42—131no—
436C2×C42—131no—
437C2×C42—261no—
438C2×C42—261no—
439C2×C42—261no—
440C2×C42C22×D1311yescharacteristic
441C4⋊C8—22no—
442C4⋊C8—262no—
443C4⋊C8—262no—
444#102—22no—
445#102—22no—
446#102—134no—
447#102—262no—
448#97—262no—
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×C13—44no—
459C2×C13Q8×C22⋊C411yescharacteristic
460C2×C13C2×#41811yescharacteristic
461C2×C13#289811yescharacteristic
462C2×C13#336711yescharacteristic
463C2×C13#337311yescharacteristic
464C2×C13#338411yescharacteristic
465C2×C13#338611yescharacteristic
466C24—21no—
467C2×Q8—134no—
468C2×Q8—262no—
469C2×Q8—262no—
470C2×Q8—264no—
471C2×Q8—264no—
472C2×Q8—264no—
473C2×Q8—522no—
474C2×Q8—522no—
475C2×Q8—522no—
476C2×Q8—522no—
477C2×Q8—522no—
478C2×Q8—522no—
479C2×Q8—5232no—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4C2×C4×D1312yes—
484C2×D4#612912yes—
485C2×D4Q8×D1312yes—
486C22×C4—21no—
487C22×C4—24no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—42no—
491C22×C4—42no—
492C22×C4—131no—
493C22×C4—131no—
494C22×C4—131no—
495C22×C4—131no—
496C22×C4—264no—
497C22×C4—264no—
498C22×C4—261no—
499C22×C4—261no—
500C22×C4—261no—
501C22×C4—261no—
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—21no—
515C2×C8—132no—
516C2×C8—261no—
517C2×C8—261no—
518C2×C8—261no—
519C2×C8—261no—
520C2×C8—261no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—134no—
527C4⋊C4—134no—
528C4⋊C4—134no—
529C4⋊C4—132no—
530C4⋊C4—132no—
531C4⋊C4—132no—
532C4⋊C4—264no—
533C4⋊C4—264no—
534C4⋊C4—264no—
535C4⋊C4—261no—
536C4⋊C4—261no—
537C4⋊C4—261no—
538C4⋊C4—261no—
539C4⋊C4—261no—
540C4⋊C4—522no—
541C4⋊C4—1041no—
542C4⋊C4C2×C4×D1312yes—
543C22⋊C4—24no—
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—22no—
557C23—22no—
558C23—22no—
559C23—41no—
560C23—41no—
561C23—41no—
562C23—41no—
563C23C2×D4×D1311yescharacteristic
564Q8—268no—
565Q8—528no—
566Q8—528no—
567Q8—528no—
568D4—22no—
569D4—22no—
570D4—22no—
571D4#8814114yes—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—22no—
577C2×C4—48no—
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—132no—
587C2×C4—132no—
588C2×C4—132no—
589C2×C4—132no—
590C2×C4—132no—
591C2×C4—132no—
592C2×C4—261no—
593C2×C4—261no—
594C2×C4—261no—
595C2×C4—261no—
596C2×C4—261no—
597C2×C4—261no—
598C2×C4—262no—
599C2×C4—262no—
600C2×C4—262no—
601C2×C4—528no—
602C2×C4—528no—
603C2×C4—521no—
604C2×C4—521no—
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×#612911yescharacteristic
617C2×C4C2×Q8×D1311yescharacteristic
618C2×C4#8825711yescharacteristic
619C2×C4#8825711yescharacteristic
620C8—41no—
621C8—41no—
622C8—262no—
623C8—521no—
624C22—24no—
625C22—42no—
626C22—42no—
627C22—42no—
628C22—42no—
629C22—42no—
630C22—42no—
631C22C2×C22⋊C4×D1311yescharacteristic
632C22#1171930311yescharacteristic
633C22#1171933711yescharacteristic
634C22#1171947511yescharacteristic
635C22#1171947611yescharacteristic
636C22D13×AGL(1,ℤ/8)11yescharacteristic
637C22D13×AGL(1,ℤ/8)11yescharacteristic
638C4—22no—
639C4—22no—
640C4—42no—
641C4—81no—
642C4—81no—
643C4—134no—
644C4—262no—
645C4—262no—
646C4—262no—
647C4—522no—
648C4—522no—
649C4—522no—
650C4—1041no—
651C4C2×#8814111yescharacteristic
652C4#1171922111yescharacteristic
653C4#1171930311yescharacteristic
654C4#1171933711yescharacteristic
655C2—44no—
656C2#1311766811yescharacteristic
657C2D13×#41811yescharacteristic
658C2#1312336511yescharacteristic
659C2#1312754911yescharacteristic
660C2#1312762311yescharacteristic
661C2#1312773811yescharacteristic
662C2#1312775211yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1804C2
socleC23×C13C22×D4
prime radicalC22×D4×C13C23
cosocleC22×C4×C13C24
hypercenter#1804D13
hypocenterC13#22523
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1804

Complements

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

NH ≅ G/Ntype
2. C2×#11718489C2semidirect
3. #13117788C2semidirect
4. #13115808C2semidirect
5. #13115807C2semidirect
6. #13115795C2semidirect
7. #13115786C2semidirect
8. #13115783C2semidirect
9. #13115782C2semidirect
22. D4×Dic26C4semidirect
124. #88072Q8semidirect
205. C4⋊Dic13C2×Q8semidirect
224. C2×#1055C2×Q8semidirect
555. C13#22523semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Dic262
C2×#117184892
#131177882
#131158082
#131158072
#131157952
#131157862
#131157832
#131157822
#131148442
#131148342
#131146632
#131146612
#102×Dic132
C13×#18042
#2252313