Finite Group Databasebeta

← #15865823

Subgroups — #15865823

Order 3328.

884 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718661C211yesmaximal, characteristic, complemented
2C2×#11718350C211yesmaximal, characteristic, complemented
3#13117295C211yesmaximal, characteristic
4#13115452C211yesmaximal, characteristic, complemented
5#13115445C211yesmaximal, characteristic, complemented
6#13115403C211yesmaximal, characteristic, complemented
7#13115396C211yesmaximal, characteristic, complemented
8#13115130C211yesmaximal, characteristic
9#13115125C211yesmaximal, characteristic
10#13115020C211yesmaximal, characteristic, complemented
11#13115015C211yesmaximal, characteristic, complemented
12C4×#88054C211yesmaximal, characteristic, complemented
13#13114605C211yesmaximal, characteristic, complemented
14#13114584C211yesmaximal, characteristic, complemented
15C13×#1750C211yesmaximal, characteristic, complemented
16C2×C13×#117C2211yescharacteristic
17C2×C4×C22⋊D13C2211yescharacteristic
18C22×#6094C2211yescharacteristic
19C22×C8×D13C2211yescharacteristic
20C2×#88126C2211yescharacteristic
21C2×C13×C22⋊C8C2211yescharacteristic
22C2×C13×C22⋊C8C2211yescharacteristic
23C2×C13×#97C2211yescharacteristic
24C2×C4×C8×C13C2211yescharacteristic
25C4×C22⋊Dic13C2211yescharacteristic
26C2×C22⋊#1055C2211yescharacteristic
27C2×C22⋊#1055C2211yescharacteristic
28C2×#88060C2211yescharacteristic
29C2×#88060C2211yescharacteristic
30C2×#88055C2211yescharacteristic
31C2×#88054C2211yescharacteristic
32C2×#88054C2211yescharacteristic
33C2×C8×Dic13C2211yescharacteristic
34#11718661—24no—
35#11718651C411yescharacteristic
36#11718651C411yescharacteristic
37#11718633C411yescharacteristic
38#11718633C411yescharacteristic
39#11718618C411yescharacteristic
40#11718618C411yescharacteristic
41#11718606C411yescharacteristic
42#11718606C411yescharacteristic
43C4×#6103C2211yescharacteristic
44C4×#6101C2211yescharacteristic
45C42×Dic13C2211yescharacteristic
46C2×C4⋊#1055C2211yescharacteristic
47C2×C4⋊#1055C2211yescharacteristic
48C2×#88043C2211yescharacteristic
49C2×C4×#1055C2211yescharacteristic
50#11718350—24no—
51C13×#336C2211yescharacteristic
52C13×#336C2211yescharacteristic
53#11718142C2211yescharacteristic
54#11718142C2211yescharacteristic
55#11718142C2211yescharacteristic
56#11718142C2211yescharacteristic
57#11718142C2211yescharacteristic
58#11718142C2211yescharacteristic
59#11718142C2211yescharacteristic
60#11718142C2211yescharacteristic
61C23×C4×C13C2311yescharacteristic
62C22×C22⋊D13C2×C411yescharacteristic
63C22×C4×D13C2311yescharacteristic
64C22×C8×C13C2311yescharacteristic
65C22×C8×C13C2311yescharacteristic
66C22×C8×C13C2311yescharacteristic
67C22×C8×C13C2311yescharacteristic
68C13×#117—22no—
69C13×#117—22no—
70C2×C13×C4⋊C4C2×C411yescharacteristic
71C2×C13×C4⋊C4C2×C411yescharacteristic
72C2×C13×C22⋊C4C2×C411yescharacteristic
73C2×C13×C22⋊C4C2×C411yescharacteristic
74C2×C42×C13C2311yescharacteristic
75C2×C42×C13C2311yescharacteristic
76C2×C22⋊Dic13C2×C411yescharacteristic
77C2×C22⋊Dic13C2×C411yescharacteristic
78C2×C22⋊Dic13C2×C411yescharacteristic
79C4×C22⋊D13—22no—
80C4×C22⋊D13—22no—
81C2×#6103C2×C411yescharacteristic
82C2×#6103C2×C411yescharacteristic
83C2×#6103C2×C411yescharacteristic
84C2×#6103C2×C411yescharacteristic
85C2×#6103C2×C411yescharacteristic
86C2×#6101C2×C411yescharacteristic
87C2×#6101C2×C411yescharacteristic
88C2×#6101C2×C411yescharacteristic
89C2×#6101C2×C411yescharacteristic
90C2×#6101C2×C411yescharacteristic
91C2×C4×Dic13C2×C411yescharacteristic
92C2×C4×Dic13C2×C411yescharacteristic
93C2×C4×Dic13C2×C411yescharacteristic
94C2×C4×Dic13C2×C411yescharacteristic
95C2×C4×Dic13C2311yescharacteristic
96C2×C4×Dic13C2311yescharacteristic
97C2×C4×Dic13C2311yescharacteristic
98C22×#1055C2311yescharacteristic
99C22×#1055C2311yescharacteristic
100C22×#1055C2311yescharacteristic
101C22×#1055C2311yescharacteristic
102C2×#6094—22no—
103C2×#6094—22no—
104C2×#6094—22no—
105C2×C8×D13—22no—
106C2×C8×D13—22no—
107C2×C8×D13—22no—
108#88126—22no—
109#88126—22no—
110C13×C22⋊C8—22no—
111C13×C22⋊C8—22no—
112C13×#97—22no—
113C4×C8×C13—22no—
114#88071C2×C411yescharacteristic
115#88071C2×C411yescharacteristic
116#88071C2×C411yescharacteristic
117#88071C2×C411yescharacteristic
118#88071C2×C411yescharacteristic
119#88071C2×C411yescharacteristic
120C22⋊#1055—22no—
121C22⋊#1055—22no—
122#88060—22no—
123#88060—22no—
124#88055—22no—
125#88054—22no—
126#88054—22no—
127C8×Dic13—22no—
128C4⋊#1055—22no—
129C4⋊#1055—22no—
130#88043D414yescomplemented
131C4×#1055—22no—
132#21111—131nomaximal, Sylow
133C24×C13C22×C411yescharacteristic
134C23×D13C22×C411yescharacteristic
135C22×C4×C13—21no—
136C22×C4×C13—21no—
137C22×C4×C13—21no—
138C22×C4×C13—21no—
139C22×C4×C13—21no—
140C22×C4×C13—21no—
141C22×C4×C13C22×C411yescharacteristic
142C22×C4×C13C22×C411yescharacteristic
143C22×C4×C13C22×C411yescharacteristic
144C22×C4×C13C22×C411yescharacteristic
145C22×C4×C13C22×C411yescharacteristic
146C22×C4×C13C2411yescharacteristic
147C2×C22⋊D13—22no—
148C2×C22⋊D13—22no—
149C2×C22⋊D13—41no—
150C22×Dic13C22×C411yescharacteristic
151C22×Dic13C22×C411yescharacteristic
152C22×Dic13C22×C411yescharacteristic
153C22×Dic13C22×C411yescharacteristic
154C22×Dic13C22×C411yescharacteristic
155C22×Dic13C22×C411yescharacteristic
156C22×Dic13C22×C411yescharacteristic
157C2×C4×D13—21no—
158C2×C4×D13—21no—
159C2×C4×D13—21no—
160C2×C4×D13—21no—
161C2×C4×D13#4112yes—
162C2×C4×D13#4112yes—
163C2×C8×C13—21no—
164C2×C8×C13—21no—
165C2×C8×C13—21no—
166C2×C8×C13—21no—
167C2×C8×C13—21no—
168C2×C8×C13—21no—
169C2×C8×C13—21no—
170C2×C8×C13—21no—
171C2×C8×C13—21no—
172C2×C8×C13—21no—
173C2×C8×C13#4112yes—
174C2×C8×C13#4112yes—
175C13×C4⋊C4—22no—
176C13×C4⋊C4—22no—
177C13×C22⋊C4—22no—
178C13×C22⋊C4—22no—
179C42×C13—21no—
180C42×C13—21no—
181C42×C13C2×D412yes—
182C42×C13#4112yes—
183C22⋊Dic13—22no—
184C22⋊Dic13—22no—
185C22⋊Dic13—41no—
186#6103—22no—
187#6103—22no—
188#6103—22no—
189#6103—22no—
190#6103—41no—
191#6101—22no—
192#6101—22no—
193#6101—22no—
194#6101—22no—
195#6101—41no—
196C4×Dic13—21no—
197C4×Dic13—21no—
198C4×Dic13—21no—
199C4×Dic13—21no—
200C4×Dic13—21no—
201C4×Dic13—21no—
202C4×Dic13—22no—
203C4×Dic13—22no—
204C4×Dic13—41no—
205C4×Dic13—41no—
206C2×#1055—21no—
207C2×#1055—21no—
208C2×#1055—21no—
209C2×#1055—21no—
210C2×#1055—21no—
211C2×#1055—21no—
212C2×#1055—21no—
213C2×#1055—21no—
214C2×#1055—21no—
215C2×#1055—21no—
216C2×#1055C2×D412yes—
217C2×#1055C2×D412yes—
218#6094—28no—
219C8×D13—28no—
220C2×#433—131no—
221C2×#405—131no—
222#2293—131no—
223#1924—131no—
224#1923—131no—
225#1917—131no—
226#1916—131no—
227#1870—131no—
228#1869—131no—
229#1851—131no—
230#1850—131no—
231C4×C4⋊C8—131no—
232#1750—131no—
233#1750D1311yescharacteristic, complemented
234#1745—131no—
235C23×C13—21no—
236C23×C13—21no—
237C23×C13—21no—
238C23×C13—21no—
239C23×C13—21no—
240C23×C13—21no—
241C23×C13—21no—
242C23×C13C23×C411yescharacteristic
243C22×D13—21no—
244C22×D13—21no—
245C22×D13—21no—
246C22×D13—21no—
247C22×D13—21no—
248C22×D13—21no—
249C22×D13#11712yes—
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—41no—
264C2×C4×C13—41no—
265C2×C4×C13—41no—
266C2×C4×C13—41no—
267C2×C4×C13C4×D412yes—
268C2×C4×C13C4×D412yes—
269C2×C4×C13C22×D411yescharacteristic
270C2×C4×C13C2×#4111yescharacteristic
271C2×C4×C13C2×#4111yescharacteristic
272C2×C4×C13C2×#4111yescharacteristic
273C2×C4×C13C2×#4111yescharacteristic
274C2×C4×C13C2×#4111yescharacteristic
275C22⋊D13—44no—
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×Dic13—21no—
289C2×Dic13—21no—
290C2×Dic13—21no—
291C2×Dic13—21no—
292C2×Dic13—21no—
293C2×Dic13—21no—
294C2×Dic13#11712yes—
295C2×Dic13#13112yes—
296C2×Dic13#13112yes—
297C4×D13—22no—
298C4×D13—22no—
299C4×D13—22no—
300C4×D13—22no—
301C8×C13—22no—
302C8×C13—22no—
303C8×C13—41no—
304C8×C13—41no—
305#1055—22no—
306#1055—22no—
307#1055—41no—
308#1055—41no—
309C22×M16—131no—
310C23×C8—131no—
311C2×C4×D4—131no—
312C2×#117—131no—
313C2×#117C2×D1311yescharacteristic
314#433—264no—
315C2×C4⋊C8—131no—
316C2×C4⋊C8—131no—
317C2×C4⋊C8—131no—
318C2×C4⋊C8—131no—
319C2×C22⋊C8—131no—
320C2×C22⋊C8—131no—
321C2×C22⋊C8—131no—
322C2×C22⋊C8—131no—
323C2×C22⋊C8C2×D1311yescharacteristic
324C2×C22⋊C8C2×D1311yescharacteristic
325#405—264no—
326C2×#97—131no—
327C2×#97—131no—
328C2×#97C2×D1311yescharacteristic
329C2×C4×C8—131no—
330C2×C4×C8—131no—
331C2×C4×C8C2×D1311yescharacteristic
332#390—131no—
333#390—131no—
334#389—131no—
335#389—131no—
336#388—131no—
337#388—131no—
338#388—131no—
339#388—131no—
340C4×C4⋊C4—131no—
341C4×C22⋊C4—131no—
342C4×C22⋊C4—131no—
343C43—131no—
344#336—131no—
345#336—131no—
346#336—131no—
347#336—131no—
348#336—131no—
349#336—131no—
350#336—131no—
351#336—131no—
352#336C2×D1311yescharacteristic
353#336C2×D1311yescharacteristic
354C22×C13—41no—
355C22×C13—41no—
356C22×C13—41no—
357C22×C13—41no—
358C22×C13—41no—
359C22×C13—41no—
360C22×C13—41no—
361C22×C13C2×#11711yescharacteristic
362C22×C13C2×C4×D411yescharacteristic
363C22×C13C4×#4111yescharacteristic
364C22×C13C2×#13111yescharacteristic
365C22×C13C2×#13111yescharacteristic
366C22×C13#56811yescharacteristic
367C22×C13#56811yescharacteristic
368C2×D13—22no—
369C2×D13—22no—
370C2×D13—22no—
371C2×D13—41no—
372C2×D13—41no—
373C2×D13—41no—
374C2×D13—41no—
375C4×C13—22no—
376C4×C13—22no—
377C4×C13—41no—
378C4×C13—41no—
379C4×C13—41no—
380C4×C13#52511yescharacteristic
381C4×C13#52511yescharacteristic
382C4×C13#52911yescharacteristic
383C4×C13#52911yescharacteristic
384Dic13—22no—
385Dic13—22no—
386Dic13—22no—
387Dic13—41no—
388Dic13—41no—
389Dic13—41no—
390Dic13—41no—
391C22×D4—131no—
392C23×C4—131no—
393C23×C4C22×D1311yescharacteristic
394C2×M16—262no—
395C2×M16—262no—
396C2×M16—262no—
397C22×C8—131no—
398C22×C8—131no—
399C22×C8—131no—
400C22×C8—131no—
401C22×C8—262no—
402C22×C8—262no—
403C22×C8—262no—
404C22×C8C22×D1311yescharacteristic
405C22×C8C22×D1311yescharacteristic
406C22×C8C22×D1311yescharacteristic
407C22×C8C22×D1311yescharacteristic
408C4×D4—262no—
409C4×D4—262no—
410#117—22no—
411#117—22no—
412#117—262no—
413#117—262no—
414C2×C4⋊C4—131no—
415C2×C4⋊C4—131no—
416C2×C4⋊C4—131no—
417C2×C4⋊C4—131no—
418C2×C4⋊C4—131no—
419C2×C4⋊C4C4×D1311yescharacteristic
420C2×C4⋊C4C4×D1311yescharacteristic
421C2×C22⋊C4—131no—
422C2×C22⋊C4—131no—
423C2×C22⋊C4—131no—
424C2×C22⋊C4—131no—
425C2×C22⋊C4—131no—
426C2×C22⋊C4—131no—
427C2×C22⋊C4—131no—
428C2×C22⋊C4—131no—
429C2×C22⋊C4C4×D1311yescharacteristic
430C2×C22⋊C4C4×D1311yescharacteristic
431C2×C42—131no—
432C2×C42—131no—
433C2×C42—131no—
434C2×C42—131no—
435C2×C42—131no—
436C2×C42—131no—
437C2×C42—131no—
438C2×C42C22×D1311yescharacteristic
439C2×C42C22×D1311yescharacteristic
440C4⋊C8—262no—
441C4⋊C8—262no—
442C4⋊C8—262no—
443C4⋊C8—262no—
444C22⋊C8—22no—
445C22⋊C8—22no—
446C22⋊C8—262no—
447C22⋊C8—262no—
448C22⋊C8—262no—
449C22⋊C8—262no—
450#97—22no—
451#97—134no—
452#97—262no—
453C4×C8—22no—
454C4×C8—262no—
455C4×C8—262no—
456#95—131no—
457#95—131no—
458#95—131no—
459#95—131no—
460#95—131no—
461#95—131no—
462C2×C13—81no—
463C2×C13#229011yescharacteristic
464C2×C13#292411yescharacteristic
465C2×C13#292511yescharacteristic
466C2×C13#293511yescharacteristic
467C2×C13#293511yescharacteristic
468C2×C13#296611yescharacteristic
469C2×C13#296711yescharacteristic
470D13—42no—
471C24—131no—
472C24C2×C4×D1311yescharacteristic
473C2×D4—262no—
474C2×D4—262no—
475C2×D4—521no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—131no—
483C22×C4—131no—
484C22×C4—131no—
485C22×C4—132no—
486C22×C4—132no—
487C22×C4—131no—
488C22×C4—131no—
489C22×C4—131no—
490C22×C4—131no—
491C22×C4—261no—
492C22×C4—261no—
493C22×C4—261no—
494C22×C4—261no—
495C22×C4C2×C4×D1311yescharacteristic
496C22×C4C2×C4×D1311yescharacteristic
497C22×C4C2×C4×D1311yescharacteristic
498C22×C4C2×C4×D1311yescharacteristic
499C22×C4C2×C4×D1311yescharacteristic
500C22×C4C23×D1311yescharacteristic
501M16—268no—
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—21no—
511C2×C8—21no—
512C2×C8—132no—
513C2×C8—132no—
514C2×C8—268no—
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—261no—
524C2×C8—261no—
525C2×C8#612712yes—
526C2×C8#612712yes—
527C4⋊C4—22no—
528C4⋊C4—22no—
529C4⋊C4—262no—
530C4⋊C4—262no—
531C4⋊C4—262no—
532C4⋊C4—262no—
533C4⋊C4—521no—
534C22⋊C4—22no—
535C22⋊C4—22no—
536C22⋊C4—262no—
537C22⋊C4—262no—
538C22⋊C4—262no—
539C22⋊C4—262no—
540C22⋊C4—262no—
541C22⋊C4—262no—
542C22⋊C4—521no—
543C22⋊C4—521no—
544C42—21no—
545C42—21no—
546C42—262no—
547C42—262no—
548C42—261no—
549C42—261no—
550C42—261no—
551C42—261no—
552C42—261no—
553C42—261no—
554C42—521no—
555C42—521no—
556C42D4×D1312yes—
557C42#612912yes—
558C13#2111111yescharacteristic, complemented, Sylow
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23—132no—
567C23—261no—
568C23—261no—
569C23—261no—
570C23—261no—
571C23—261no—
572C23—261no—
573C23C22×C4×D1311yescharacteristic
574D4—524no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—132no—
593C2×C4—132no—
594C2×C4—132no—
595C2×C4—261no—
596C2×C4—261no—
597C2×C4—261no—
598C2×C4—261no—
599C2×C4—261no—
600C2×C4—261no—
601C2×C4—262no—
602C2×C4—262no—
603C2×C4—262no—
604C2×C4—262no—
605C2×C4—261no—
606C2×C4—261no—
607C2×C4—261no—
608C2×C4—261no—
609C2×C4—261no—
610C2×C4—261no—
611C2×C4—261no—
612C2×C4—261no—
613C2×C4—261no—
614C2×C4—261no—
615C2×C4—261no—
616C2×C4—261no—
617C2×C4#8813512yes—
618C2×C4#8813512yes—
619C2×C4C2×#612711yescharacteristic
620C2×C4C2×#612711yescharacteristic
621C2×C4C2×D4×D1311yescharacteristic
622C2×C4C2×#612911yescharacteristic
623C2×C4#41×D1311yescharacteristic
624C2×C4#41×D1311yescharacteristic
625C8—22no—
626C8—22no—
627C8—41no—
628C8—41no—
629C8—262no—
630C8—262no—
631C8—521no—
632C8—521no—
633C22—41no—
634C22—41no—
635C22—41no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22—41no—
640C22—262no—
641C22—262no—
642C22—262no—
643C22—521no—
644C22—521no—
645C22—521no—
646C22—521no—
647C22C4×#612711yescharacteristic
648C22C2×#8813511yescharacteristic
649C22D13×#11711yescharacteristic
650C22D13×#13111yescharacteristic
651C22D13×#13111yescharacteristic
652C22#1171945511yescharacteristic
653C22#1171945511yescharacteristic
654C4—22no—
655C4—22no—
656C4—41no—
657C4—41no—
658C4—41no—
659C4—262no—
660C4—262no—
661C4—262no—
662C4—521no—
663C4—521no—
664C4—521no—
665C4—521no—
666C4#1171925211yescharacteristic
667C4#1171925211yescharacteristic
668C4#1171926211yescharacteristic
669C4#1171926211yescharacteristic
670C2—81no—
671C2—522no—
672C2#1311728211yescharacteristic
673C2#1312349211yescharacteristic
674C2#1312349911yescharacteristic
675C2#1312357611yescharacteristic
676C2#1312357611yescharacteristic
677C2#1312380711yescharacteristic
678C2#1312381711yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D13
commutator, socleC23×C13C23×C4
FittingC13×#1750C2
prime radicalC22×C22⋊D13C2×C4
cosocleC22×C4×C13C24
hypercenter#1750D13
hypocenterC13#21111
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ #1750

Complements

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

NH ≅ G/Ntype
1. C2×#11718661C2semidirect
2. C2×#11718350C2semidirect
4. #13115452C2semidirect
5. #13115445C2semidirect
6. #13115403C2semidirect
7. #13115396C2semidirect
10. #13115020C2semidirect
11. #13115015C2semidirect
12. C4×#88054C2semidirect
13. #13114605C2semidirect
14. #13114584C2semidirect
15. C13×#1750C2semidirect
130. #88043D4semidirect
233. #1750D13semidirect
558. C13#21111semidirect

Maximal subgroups

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

subgroupindex
C2×#117186612
C2×#117183502
#131172952
#131154522
#131154452
#131154032
#131153962
#131151302
#131151252
#131150202
#131150152
C4×#880542
#131146052
#131145842
C13×#17502
#2111113