Finite Group Databasebeta

← #15866218

Subgroups — #15866218

Order 3328.

1010 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×#11718500C211yesmaximal, characteristic
2C2×#11718500C211yesmaximal, characteristic
3C2×D13×C4⋊C8C211yesmaximal, characteristic
4C2×#11718350C211yesmaximal, characteristic
5#13117316C211yesmaximal, characteristic
6#13115560C211yesmaximal, characteristic, complemented
7#13115558C211yesmaximal, characteristic, complemented
8#13115558C211yesmaximal, characteristic, complemented
9#13115557C211yesmaximal, characteristic, complemented
10#13115554C211yesmaximal, characteristic, complemented
11#13115551C211yesmaximal, characteristic, complemented
12#13115551C211yesmaximal, characteristic, complemented
13#13114531C211yesmaximal, characteristic
14#13114528C211yesmaximal, characteristic
15C13×#1939C211yesmaximal, characteristic, complemented
16C22×#6094C2211yescharacteristic
17C22×#6094C2211yescharacteristic
18C22×C8×D13C2211yescharacteristic
19C22×C8×D13C2211yescharacteristic
20C2×#88126C2211yescharacteristic
21C2×#88126C2211yescharacteristic
22C2×C42×D13C2211yescharacteristic
23C2×C13×C4⋊C8C2211yescharacteristic
24C2×C13×C4⋊C8C2211yescharacteristic
25C2×C13×C4⋊C8C2211yescharacteristic
26C2×C4×C8×C13C2211yescharacteristic
27C4×C13×C4⋊C4C2211yescharacteristic
28C2×#88055C2211yescharacteristic
29C2×#88054C2211yescharacteristic
30C2×#88054C2211yescharacteristic
31C2×#88054C2211yescharacteristic
32C2×#88054C2211yescharacteristic
33C2×#88054C2211yescharacteristic
34C2×#88054C2211yescharacteristic
35C2×C8×Dic13C2211yescharacteristic
36#11718650C411yescharacteristic
37#11718650C411yescharacteristic
38#11718633C411yescharacteristic
39#11718633C411yescharacteristic
40C4×C4⋊Dic13C2211yescharacteristic
41C4×#6101C2211yescharacteristic
42C4×#6101C2211yescharacteristic
43C2×C4⋊#1055C2211yescharacteristic
44C2×C4⋊#1055C2211yescharacteristic
45C2×C4⋊#1055C2211yescharacteristic
46C2×#88043C2211yescharacteristic
47#11718500—24no—
48#11718500—24no—
49D13×C4⋊C8—24no—
50#11718350—24no—
51#11718329C411yescharacteristic
52#11718329C411yescharacteristic
53#11718308C411yescharacteristic
54#11718308C411yescharacteristic
55C13×#336C2211yescharacteristic
56C13×#336C2211yescharacteristic
57#11718142C2211yescharacteristic
58#11718142C2211yescharacteristic
59#11718142C2211yescharacteristic
60#11718142C2211yescharacteristic
61#11718116C2211yescharacteristic
62#11718116C2211yescharacteristic
63C22×C4×D13C2×C411yescharacteristic
64C22×C4×D13C2×C411yescharacteristic
65C22×C4×D13C2311yescharacteristic
66C22×C8×C13C2311yescharacteristic
67C22×C8×C13C2311yescharacteristic
68C22×C8×C13C2311yescharacteristic
69C22×C8×C13C2311yescharacteristic
70C2×C13×C4⋊C4C2×C411yescharacteristic
71C2×C13×C4⋊C4C2×C411yescharacteristic
72C2×C42×C13C2311yescharacteristic
73C2×C42×C13C2311yescharacteristic
74C2×C42×C13C2311yescharacteristic
75C2×#6103C2×C411yescharacteristic
76C2×#6103C2×C411yescharacteristic
77C2×#6103C2×C411yescharacteristic
78C2×#6103C2×C411yescharacteristic
79C2×C4⋊Dic13C2×C411yescharacteristic
80C2×C4⋊Dic13C2×C411yescharacteristic
81C2×#6101C2×C411yescharacteristic
82C2×#6101C2×C411yescharacteristic
83C2×#6101C2×C411yescharacteristic
84C2×#6101C2×C411yescharacteristic
85C2×#6101C2×C411yescharacteristic
86C2×#6101C2×C411yescharacteristic
87C2×#6101C2×C411yescharacteristic
88C2×#6101C2×C411yescharacteristic
89C2×C4×Dic13C2×C411yescharacteristic
90C2×C4×Dic13C2×C411yescharacteristic
91C2×C4×Dic13C2311yescharacteristic
92C2×C4×Dic13C2311yescharacteristic
93C2×C4×Dic13C2311yescharacteristic
94C22×#1055C2311yescharacteristic
95C22×#1055C2311yescharacteristic
96C22×#1055C2311yescharacteristic
97C22×#1055C2311yescharacteristic
98C2×#6094—22no—
99C2×#6094—22no—
100C2×#6094—22no—
101C2×#6094—22no—
102C2×#6094—22no—
103C2×#6094Q814yes—
104C2×C8×D13—22no—
105C2×C8×D13—22no—
106C2×C8×D13—22no—
107C2×C8×D13—22no—
108C2×C8×D13—22no—
109C2×C8×D13D414yes—
110#88126—22no—
111#88126—22no—
112#88126D414yes—
113#88126Q814yes—
114C42×D13—22no—
115C42×D13—22no—
116C13×C4⋊C8—22no—
117C13×C4⋊C8—22no—
118C13×C4⋊C8—22no—
119C4×C8×C13—22no—
120C13×#95C2×C411yescharacteristic
121C13×#95C2×C411yescharacteristic
122#88071C2×C411yescharacteristic
123#88071C2×C411yescharacteristic
124#88071C2×C411yescharacteristic
125#88071C2×C411yescharacteristic
126#88071C2×C411yescharacteristic
127#88071C2×C411yescharacteristic
128#88055—22no—
129#88054—22no—
130#88054—22no—
131#88054—22no—
132#88054—22no—
133#88054—22no—
134#88054—22no—
135C8×Dic13—22no—
136C4⋊#1055—22no—
137C4⋊#1055—22no—
138C4⋊#1055—22no—
139#88043—22no—
140#21147—131nomaximal, Sylow
141C23×D13C22×C411yescharacteristic
142C22×C4×C13C22×C411yescharacteristic
143C22×C4×C13C22×C411yescharacteristic
144C22×C4×C13C22×C411yescharacteristic
145C22×C4×C13C22×C411yescharacteristic
146C22×C4×C13C22×C411yescharacteristic
147C22×C4×C13C22×C411yescharacteristic
148C22×C4×C13C2411yescharacteristic
149C22×Dic13C22×C411yescharacteristic
150C22×Dic13C22×C411yescharacteristic
151C22×Dic13C22×C411yescharacteristic
152C22×Dic13C22×C411yescharacteristic
153C22×Dic13C22×C411yescharacteristic
154C22×Dic13C22×C411yescharacteristic
155C22×Dic13C22×C411yescharacteristic
156C2×C4×D13—22no—
157C2×C4×D13—22no—
158C2×C4×D13—22no—
159C2×C4×D13—22no—
160C2×C4×D13—41no—
161C2×C4×D13—41no—
162C2×C4×D13C2×D412yes—
163C2×C4×D13C2×D412yes—
164C2×C4×D13C2×Q812yes—
165C2×C4×D13C2×Q812yes—
166C2×C4×D13#4112yes—
167C2×C4×D13#4112yes—
168C2×C8×C13—21no—
169C2×C8×C13—21no—
170C2×C8×C13—21no—
171C2×C8×C13—21no—
172C2×C8×C13—21no—
173C2×C8×C13—21no—
174C2×C8×C13—21no—
175C2×C8×C13—21no—
176C2×C8×C13—21no—
177C2×C8×C13—21no—
178C2×C8×C13C2×D412yes—
179C2×C8×C13C2×Q812yes—
180C13×C4⋊C4—22no—
181C13×C4⋊C4—41no—
182C42×C13—21no—
183C42×C13—21no—
184C42×C13—21no—
185C42×C13—21no—
186C42×C13C2×D412yes—
187C42×C13C2×Q812yes—
188#6103—22no—
189#6103—22no—
190#6103C4⋊C414yes—
191#6103C4⋊C414yes—
192C4⋊Dic13—22no—
193C4⋊Dic13—41no—
194#6101—22no—
195#6101—22no—
196#6101—22no—
197#6101—22no—
198#6101—41no—
199#6101—41no—
200#6101C4⋊C414yes—
201#6101C4⋊C414yes—
202C4×Dic13—21no—
203C4×Dic13—21no—
204C4×Dic13—21no—
205C4×Dic13—21no—
206C4×Dic13—22no—
207C4×Dic13—22no—
208C4×Dic13C2×D412yes—
209C4×Dic13C2×Q812yes—
210C2×#1055—21no—
211C2×#1055—21no—
212C2×#1055—21no—
213C2×#1055—21no—
214C2×#1055—21no—
215C2×#1055—21no—
216C2×#1055—21no—
217C2×#1055—21no—
218C2×#1055—21no—
219C2×#1055—21no—
220C2×#1055C2×D412yes—
221C2×#1055C2×Q812yes—
222#6094—28no—
223#6094—44no—
224C8×D13—28no—
225C8×D13—44no—
226C2×#424—131no—
227C2×#424—131no—
228C22×C4⋊C8—131no—
229C2×#405—131no—
230#2296—131no—
231#1940—131no—
232#1940—131no—
233#1940—131no—
234#1940—131no—
235#1939—131no—
236#1939—131no—
237#1939—131no—
238#1939D1311yescharacteristic, complemented
239#1729—131no—
240#1728—131no—
241C23×C13C23×C411yescharacteristic
242C22×D13—21no—
243C22×D13—21no—
244C22×D13—21no—
245C22×D13—21no—
246C22×D13C2×C4⋊C412yes—
247C22×D13C4×D412yes—
248C22×D13C4×Q812yes—
249C2×C4×C13—21no—
250C2×C4×C13—21no—
251C2×C4×C13—21no—
252C2×C4×C13—21no—
253C2×C4×C13—21no—
254C2×C4×C13—21no—
255C2×C4×C13—21no—
256C2×C4×C13—21no—
257C2×C4×C13—21no—
258C2×C4×C13—21no—
259C2×C4×C13—21no—
260C2×C4×C13—21no—
261C2×C4×C13—21no—
262C2×C4×C13—21no—
263C2×C4×C13—21no—
264C2×C4×C13C2×C4⋊C412yes—
265C2×C4×C13C2×C4⋊C412yes—
266C2×C4×C13#13112yes—
267C2×C4×C13C22×D411yescharacteristic
268C2×C4×C13C22×D411yescharacteristic
269C2×C4×C13C22×Q811yescharacteristic
270C2×C4×C13C22×Q811yescharacteristic
271C2×C4×C13C2×#4111yescharacteristic
272C2×C4×C13C2×#4111yescharacteristic
273C2×Dic13—21no—
274C2×Dic13—21no—
275C2×Dic13—21no—
276C2×Dic13—21no—
277C2×Dic13—21no—
278C2×Dic13—21no—
279C2×Dic13—21no—
280C2×Dic13—21no—
281C2×Dic13—21no—
282C2×Dic13—21no—
283C2×Dic13—21no—
284C2×Dic13—21no—
285C2×Dic13—21no—
286C2×Dic13—21no—
287C2×Dic13—21no—
288C2×Dic13C2×C4⋊C412yes—
289C2×Dic13C2×C4⋊C412yes—
290C2×Dic13C2×C4⋊C412yes—
291C2×Dic13C4×D412yes—
292C2×Dic13C4×Q812yes—
293C2×Dic13#13112yes—
294C4×D13—28no—
295C4×D13—44no—
296C4×D13#12114yes—
297C4×D13C22⋊Q814yes—
298C4×D13#12514yes—
299C4×D13C4⋊Q814yes—
300C8×C13—22no—
301C8×C13—22no—
302C8×C13—41no—
303C8×C13—41no—
304#1055—22no—
305#1055—22no—
306#1055—41no—
307#1055—41no—
308C22×M16—131no—
309C22×M16—131no—
310C23×C8—131no—
311C23×C8—131no—
312C2×#117—131no—
313C2×#117—131no—
314C22×C42—131no—
315#424—264no—
316#424—264no—
317C2×C4⋊C8—131no—
318C2×C4⋊C8—131no—
319C2×C4⋊C8—131no—
320C2×C4⋊C8—131no—
321C2×C4⋊C8—131no—
322C2×C4⋊C8—131no—
323C2×C4⋊C8—131no—
324C2×C4⋊C8—131no—
325C2×C4⋊C8—131no—
326C2×C4⋊C8—264no—
327C2×C4⋊C8C2×D1311yescharacteristic
328C2×C4⋊C8C2×D1311yescharacteristic
329C2×C4⋊C8C2×D1311yescharacteristic
330#405—264no—
331C2×#97—131no—
332C2×#97—131no—
333C2×C4×C8—131no—
334C2×C4×C8C2×D1311yescharacteristic
335#389—131no—
336#389—131no—
337#389—131no—
338#389—131no—
339#385—131no—
340#385—131no—
341#385—131no—
342#385—131no—
343C4×C4⋊C4—131no—
344C4×C4⋊C4—131no—
345C4×C4⋊C4—131no—
346C4×C4⋊C4C2×D1311yescharacteristic
347#336—131no—
348#336—131no—
349#336—131no—
350#336—131no—
351#336—131no—
352#336—131no—
353#336C2×D1311yescharacteristic
354#336C2×D1311yescharacteristic
355C22×C13C22×C4⋊C411yescharacteristic
356C22×C13C2×C4×D411yescharacteristic
357C22×C13C2×C4×Q811yescharacteristic
358C22×C13C2×#13111yescharacteristic
359C22×C13C2×#13111yescharacteristic
360C22×C13#56811yescharacteristic
361C22×C13#56811yescharacteristic
362C2×D13—22no—
363C2×D13—22no—
364C2×D13—22no—
365C2×D13—22no—
366C2×D13—22no—
367C2×D13—22no—
368C2×D13#38914yes—
369C4×C13—22no—
370C4×C13—22no—
371C4×C13—22no—
372C4×C13—41no—
373C4×C13—41no—
374C4×C13—41no—
375C4×C13C2×#12111yescharacteristic
376C4×C13C2×C22⋊Q811yescharacteristic
377C4×C13C2×#12511yescharacteristic
378C4×C13C2×C4⋊Q811yescharacteristic
379Dic13—22no—
380Dic13—22no—
381Dic13—22no—
382Dic13—41no—
383Dic13—41no—
384Dic13—41no—
385Dic13#38914yes—
386C23×C4—131no—
387C23×C4—131no—
388C23×C4—131no—
389C2×M16—134no—
390C2×M16—262no—
391C2×M16—262no—
392C2×M16—262no—
393C2×M16—262no—
394C2×M16—262no—
395C22×C8—131no—
396C22×C8—131no—
397C22×C8—134no—
398C22×C8—131no—
399C22×C8—131no—
400C22×C8—262no—
401C22×C8—262no—
402C22×C8—262no—
403C22×C8—262no—
404C22×C8—262no—
405C22×C8C22×D1311yescharacteristic
406C22×C8C22×D1311yescharacteristic
407C22×C8C22×D1311yescharacteristic
408C22×C8C22×D1311yescharacteristic
409#117—134no—
410#117—134no—
411#117—262no—
412#117—262no—
413C2×C4⋊C4—131no—
414C2×C4⋊C4—131no—
415C2×C4⋊C4—131no—
416C2×C4⋊C4—131no—
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⋊C4C4×D1311yescharacteristic
424C2×C4⋊C4C4×D1311yescharacteristic
425C2×C22⋊C4—131no—
426C2×C22⋊C4—131no—
427C2×C22⋊C4—131no—
428C2×C22⋊C4—131no—
429C2×C42—131no—
430C2×C42—131no—
431C2×C42—131no—
432C2×C42—131no—
433C2×C42—131no—
434C2×C42—262no—
435C2×C42—262no—
436C2×C42C22×D1311yescharacteristic
437C2×C42C22×D1311yescharacteristic
438C2×C42C22×D1311yescharacteristic
439C4⋊C8—22no—
440C4⋊C8—22no—
441C4⋊C8—22no—
442C4⋊C8—262no—
443C4⋊C8—262no—
444C4⋊C8—262no—
445C4⋊C8—262no—
446C4⋊C8—262no—
447C4⋊C8—262no—
448C4⋊C8—262no—
449C4⋊C8—262no—
450C4⋊C8—262no—
451#97—262no—
452#97—262no—
453C4×C8—22no—
454C4×C8—262no—
455#95—131no—
456#95—131no—
457#95—131no—
458#95—131no—
459#95—131no—
460#95—131no—
461#95C4×D1311yescharacteristic
462#95C4×D1311yescharacteristic
463C2×C13C2×#38911yescharacteristic
464C2×C13#290611yescharacteristic
465C2×C13#290611yescharacteristic
466C2×C13#292911yescharacteristic
467C2×C13#293011yescharacteristic
468C2×C13#296211yescharacteristic
469C2×C13#296211yescharacteristic
470D13—24no—
471C24—131no—
472C22×C4—131no—
473C22×C4—132no—
474C22×C4—132no—
475C22×C4—132no—
476C22×C4—132no—
477C22×C4—132no—
478C22×C4—132no—
479C22×C4—131no—
480C22×C4—131no—
481C22×C4—131no—
482C22×C4—131no—
483C22×C4—131no—
484C22×C4—131no—
485C22×C4—262no—
486C22×C4—262no—
487C22×C4—262no—
488C22×C4—262no—
489C22×C4—521no—
490C22×C4—521no—
491C22×C4C2×C4×D1311yescharacteristic
492C22×C4C2×C4×D1311yescharacteristic
493C22×C4C2×C4×D1311yescharacteristic
494C22×C4C2×C4×D1311yescharacteristic
495C22×C4C2×C4×D1311yescharacteristic
496C22×C4C2×C4×D1311yescharacteristic
497C22×C4C23×D1311yescharacteristic
498M16—268no—
499M16—524no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—132no—
511C2×C8—132no—
512C2×C8—268no—
513C2×C8—261no—
514C2×C8—261no—
515C2×C8—261no—
516C2×C8—261no—
517C2×C8—261no—
518C2×C8—261no—
519C2×C8—261no—
520C2×C8—261no—
521C2×C8—261no—
522C2×C8—261no—
523C2×C8—524no—
524C2×C8D4×D1312yes—
525C2×C8Q8×D1312yes—
526C4⋊C4—22no—
527C4⋊C4—41no—
528C4⋊C4—134no—
529C4⋊C4—134no—
530C4⋊C4—262no—
531C4⋊C4—262no—
532C4⋊C4—262no—
533C4⋊C4—262no—
534C4⋊C4—262no—
535C4⋊C4—521no—
536C4⋊C4—521no—
537C4⋊C4—521no—
538C22⋊C4—134no—
539C22⋊C4—134no—
540C22⋊C4—262no—
541C22⋊C4—262no—
542C42—21no—
543C42—21no—
544C42—21no—
545C42—21no—
546C42—132no—
547C42—132no—
548C42—262no—
549C42—262no—
550C42—261no—
551C42—261no—
552C42—261no—
553C42—261no—
554C42D4×D1312yes—
555C42Q8×D1312yes—
556C13#2114711yescharacteristic, complemented, Sylow
557C23—132no—
558C23—132no—
559C23—132no—
560C23—261no—
561C23—261no—
562C23—261no—
563C23—261no—
564C23C22×C4×D1311yescharacteristic
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—132no—
581C2×C4—132no—
582C2×C4—132no—
583C2×C4—134no—
584C2×C4—134no—
585C2×C4—134no—
586C2×C4—134no—
587C2×C4—132no—
588C2×C4—132no—
589C2×C4—132no—
590C2×C4—268no—
591C2×C4—261no—
592C2×C4—261no—
593C2×C4—261no—
594C2×C4—261no—
595C2×C4—261no—
596C2×C4—261no—
597C2×C4—261no—
598C2×C4—261no—
599C2×C4—261no—
600C2×C4—261no—
601C2×C4—261no—
602C2×C4—261no—
603C2×C4—261no—
604C2×C4—261no—
605C2×C4—261no—
606C2×C4—524no—
607C2×C4C4⋊C4×D1312yes—
608C2×C4C4⋊C4×D1312yes—
609C2×C4#8815512yes—
610C2×C4C2×D4×D1311yescharacteristic
611C2×C4C2×D4×D1311yescharacteristic
612C2×C4C2×Q8×D1311yescharacteristic
613C2×C4C2×Q8×D1311yescharacteristic
614C2×C4#41×D1311yescharacteristic
615C2×C4#41×D1311yescharacteristic
616C8—22no—
617C8—22no—
618C8—41no—
619C8—41no—
620C8—262no—
621C8—262no—
622C8—521no—
623C8—521no—
624C22—134no—
625C22—262no—
626C22—262no—
627C22—262no—
628C22—262no—
629C22—262no—
630C22—262no—
631C22C2×C4⋊C4×D1311yescharacteristic
632C22C4×D4×D1311yescharacteristic
633C22C4×Q8×D1311yescharacteristic
634C22C2×#8815511yescharacteristic
635C22#1171945011yescharacteristic
636C22D13×#13111yescharacteristic
637C22#1171945511yescharacteristic
638C4—22no—
639C4—22no—
640C4—22no—
641C4—41no—
642C4—41no—
643C4—41no—
644C4—134no—
645C4—262no—
646C4—262no—
647C4—262no—
648C4—521no—
649C4—521no—
650C4—521no—
651C4D13×#12111yescharacteristic
652C4D13×C22⋊Q811yescharacteristic
653C4D13×#12511yescharacteristic
654C4D13×C4⋊Q811yescharacteristic
655C2—264no—
656C2D13×#38911yescharacteristic
657C2#1312340111yescharacteristic
658C2#1312340311yescharacteristic
659C2#1312352511yescharacteristic
660C2#1312353611yescharacteristic
661C2#1312377811yescharacteristic
662C2#1312378111yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D13
commutator, socleC23×C13C23×C4
FittingC13×#1939C2
prime radicalC23×D13C22×C4
cosocleC22×C4×C13C24
hypercenter#1939D13
hypocenterC13#21147
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ #1939

Complements

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

NH ≅ G/Ntype
6. #13115560C2semidirect
7. #13115558C2semidirect
8. #13115558C2semidirect
9. #13115557C2semidirect
10. #13115554C2semidirect
11. #13115551C2semidirect
12. #13115551C2semidirect
15. C13×#1939C2semidirect
238. #1939D13semidirect
556. C13#21147semidirect

Maximal subgroups

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

subgroupindex
C2×#117185002
C2×D13×C4⋊C82
C2×#117183502
#131173162
#131155602
#131155582
#131155572
#131155542
#131155512
#131145312
#131145282
C13×#19392
#2114713