Finite Group Databasebeta

← #15865822

Subgroups — #15865822

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×#11718501C211yesmaximal, characteristic, complemented
2C2×#11718783C211yesmaximal, characteristic, complemented
3#13117299C211yesmaximal, characteristic
4#13115448C211yesmaximal, characteristic, complemented
5#13115443C211yesmaximal, characteristic, complemented
6#13115403C211yesmaximal, characteristic, complemented
7#13115390C211yesmaximal, characteristic, complemented
8#13115133C211yesmaximal, characteristic
9#13115126C211yesmaximal, characteristic
10#13115016C211yesmaximal, characteristic, complemented
11C4⋊C8×Dic13C211yesmaximal, characteristic, complemented
12#13114604C211yesmaximal, characteristic, complemented
13#13114601C211yesmaximal, characteristic, complemented
14#13114583C211yesmaximal, characteristic, complemented
15C13×#1851C211yesmaximal, characteristic, complemented
16C22×C13×M16C2211yescharacteristic
17C2×C4×C22⋊D13C2211yescharacteristic
18C2×#88180C2211yescharacteristic
19C23×#1055C2211yescharacteristic
20C2×#88126C2211yescharacteristic
21C2×C13×C4⋊C8C2211yescharacteristic
22C2×C13×C4⋊C8C2211yescharacteristic
23C2×C13×C22⋊C8C2211yescharacteristic
24C4×C13×C22⋊C4C2211yescharacteristic
25C2×C22⋊#1055C2211yescharacteristic
26#11718783—24no—
27C2×#88060C2211yescharacteristic
28C2×#88060C2211yescharacteristic
29C2×#88060C2211yescharacteristic
30C2×#88060C2211yescharacteristic
31C2×#88055C2211yescharacteristic
32C2×#88055C2211yescharacteristic
33C2×#88055C2211yescharacteristic
34C2×C8×Dic13C2211yescharacteristic
35C2×C8×Dic13C2211yescharacteristic
36C2×C8×Dic13C2211yescharacteristic
37#11718618C411yescharacteristic
38#11718618C411yescharacteristic
39#11718605C411yescharacteristic
40#11718605C411yescharacteristic
41C4×#6103C2211yescharacteristic
42C4×#6101C2211yescharacteristic
43C42×Dic13C2211yescharacteristic
44C2×C4⋊#1055C2211yescharacteristic
45C2×C4⋊#1055C2211yescharacteristic
46#11718501—24no—
47#11718331C411yescharacteristic
48#11718331C411yescharacteristic
49#11718308C411yescharacteristic
50#11718308C411yescharacteristic
51C13×#336C2211yescharacteristic
52C13×#336C2211yescharacteristic
53#11718142C2211yescharacteristic
54#11718142C2211yescharacteristic
55#11718142C2211yescharacteristic
56#11718142C2211yescharacteristic
57#11718142C2211yescharacteristic
58#11718142C2211yescharacteristic
59#11718116C2211yescharacteristic
60#11718116C2211yescharacteristic
61C23×C4×C13C2311yescharacteristic
62C22×C22⋊D13C2×C411yescharacteristic
63C22×C4×D13C2311yescharacteristic
64C2×C13×M16—22no—
65C2×C13×M16—22no—
66C2×C13×M16—22no—
67C22×C8×C13C2311yescharacteristic
68C22×C8×C13C2311yescharacteristic
69C22×C8×C13C2311yescharacteristic
70C22×C8×C13C2311yescharacteristic
71C2×C13×C22⋊C4C2×C411yescharacteristic
72C2×C13×C22⋊C4C2×C411yescharacteristic
73C2×C42×C13C2311yescharacteristic
74C2×C42×C13C2311yescharacteristic
75C2×C22⋊Dic13C2×C411yescharacteristic
76C2×C22⋊Dic13C2×C411yescharacteristic
77C2×C22⋊Dic13C2×C411yescharacteristic
78C4×C22⋊D13—22no—
79C4×C22⋊D13—22no—
80C2×#6103C2×C411yescharacteristic
81C2×#6103C2×C411yescharacteristic
82C2×#6103C2×C411yescharacteristic
83C2×#6103C2×C411yescharacteristic
84C2×#6103C2×C411yescharacteristic
85#88180—22no—
86#88180—22no—
87C2×C4⋊Dic13C2×C411yescharacteristic
88C2×C4⋊Dic13C2×C411yescharacteristic
89C2×#6101C2×C411yescharacteristic
90C2×#6101C2×C411yescharacteristic
91C2×#6101C2×C411yescharacteristic
92C2×#6101C2×C411yescharacteristic
93C2×#6101C2×C411yescharacteristic
94C2×C4×Dic13C2×C411yescharacteristic
95C2×C4×Dic13C2×C411yescharacteristic
96C2×C4×Dic13C2×C411yescharacteristic
97C2×C4×Dic13C2×C411yescharacteristic
98C2×C4×Dic13C2311yescharacteristic
99C2×C4×Dic13C2311yescharacteristic
100C2×C4×Dic13C2311yescharacteristic
101C22×#1055—22no—
102C22×#1055—22no—
103C22×#1055—22no—
104C22×#1055C2311yescharacteristic
105C22×#1055C2311yescharacteristic
106C22×#1055C2311yescharacteristic
107C22×#1055C2311yescharacteristic
108#88126—22no—
109#88126—22no—
110C13×C4⋊C8—22no—
111C13×C4⋊C8—22no—
112C13×C22⋊C8—22no—
113C13×#95C2×C411yescharacteristic
114C13×#95C2×C411yescharacteristic
115#88071C2×C411yescharacteristic
116#88071C2×C411yescharacteristic
117#88071C2×C411yescharacteristic
118#88071C2×C411yescharacteristic
119C22⋊#1055—22no—
120#88060—22no—
121#88060—22no—
122#88060—22no—
123#88060—22no—
124#88055—22no—
125#88055—22no—
126#88055D414yescomplemented
127C8×Dic13—22no—
128C8×Dic13—22no—
129C8×Dic13—22no—
130C4⋊#1055—22no—
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×C13C22×C411yescharacteristic
140C22×C4×C13C22×C411yescharacteristic
141C22×C4×C13C22×C411yescharacteristic
142C22×C4×C13C22×C411yescharacteristic
143C22×C4×C13C22×C411yescharacteristic
144C22×C4×C13#4112yes—
145C22×C4×C13#4112yes—
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—21no—
162C2×C4×D13—21no—
163C13×M16—28no—
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—21no—
174C2×C8×C13C2×D412yes—
175C2×C8×C13#4112yes—
176C13×C22⋊C4—22no—
177C13×C22⋊C4—41no—
178C42×C13—21no—
179C42×C13—21no—
180C42×C13—21no—
181C42×C13—21no—
182C22⋊Dic13—22no—
183C22⋊Dic13—22no—
184C22⋊Dic13—22no—
185#6103—22no—
186#6103—22no—
187#6103—22no—
188#6103—22no—
189#6103—41no—
190C4⋊Dic13—22no—
191C4⋊Dic13—22no—
192#6101—22no—
193#6101—22no—
194#6101—22no—
195#6101—22no—
196#6101—41no—
197C4×Dic13—22no—
198C4×Dic13—21no—
199C4×Dic13—21no—
200C4×Dic13—21no—
201C4×Dic13—21no—
202C4×Dic13—22no—
203C4×Dic13—41no—
204C4×Dic13—41no—
205C4×Dic13C2×D412yes—
206C4×Dic13#4112yes—
207C2×#1055—28no—
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×#1055—21no—
217C2×#1055—21no—
218C2×#1055C2×D412yes—
219C2×#1055#4112yes—
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#1851D1311yescharacteristic, complemented
230#1850—131no—
231C4×C4⋊C8—131no—
232#1750—131no—
233#1750—131no—
234#1745—131no—
235C23×C13—21no—
236C23×C13—21no—
237C23×C13—21no—
238C23×C13—21no—
239C23×C13—21no—
240C23×C13—21no—
241C23×C13#11712yes—
242C23×C13C23×C411yescharacteristic
243C22×D13—21no—
244C22×D13—21no—
245C22×D13—21no—
246C22×D13—21no—
247C22×D13—21no—
248C22×D13—21no—
249C22×D13—21no—
250C2×C4×C13—21no—
251C2×C4×C13—21no—
252C2×C4×C13—21no—
253C2×C4×C13—21no—
254C2×C4×C13—22no—
255C2×C4×C13—22no—
256C2×C4×C13—22no—
257C2×C4×C13—22no—
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×C13—21no—
265C2×C4×C13—21no—
266C2×C4×C13—21no—
267C2×C4×C13#11712yes—
268C2×C4×C13#13112yes—
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×Dic13C4×D412yes—
295C2×Dic13C4×D412yes—
296C2×Dic13#13112yes—
297C4×D13—41no—
298C4×D13—41no—
299C4×D13—41no—
300C4×D13—41no—
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×M16C2×D1311yescharacteristic
310C23×C8—131no—
311C2×C4×D4—131no—
312C2×#117—131no—
313C2×#117—131no—
314#433—264no—
315C2×C4⋊C8—131no—
316C2×C4⋊C8—131no—
317C2×C4⋊C8C2×D1311yescharacteristic
318C2×C4⋊C8C2×D1311yescharacteristic
319C2×C22⋊C8—131no—
320C2×C22⋊C8—131no—
321C2×C22⋊C8—131no—
322C2×C22⋊C8—131no—
323C2×C22⋊C8—131no—
324C2×C22⋊C8C2×D1311yescharacteristic
325#405—264no—
326C2×#97—131no—
327C2×#97—131no—
328C2×#97—131no—
329C2×C4×C8—131no—
330C2×C4×C8—131no—
331C2×C4×C8—131no—
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⋊C4C2×D1311yescharacteristic
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—22no—
355C22×C13—22no—
356C22×C13—22no—
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—41no—
369C2×D13—41no—
370C2×D13—41no—
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—22no—
395C2×M16—22no—
396C2×M16—22no—
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—262no—
411#117—262no—
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⋊C4—131no—
420C2×C4⋊C4—131no—
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—22no—
441C4⋊C8—22no—
442C4⋊C8—262no—
443C4⋊C8—262no—
444C22⋊C8—22no—
445C22⋊C8—262no—
446C22⋊C8—262no—
447C22⋊C8—262no—
448C22⋊C8—262no—
449C22⋊C8—262no—
450#97—134no—
451#97—262no—
452#97—262no—
453C4×C8—262no—
454C4×C8—262no—
455C4×C8—262no—
456#95—131no—
457#95—131no—
458#95—131no—
459#95—131no—
460#95C4×D1311yescharacteristic
461#95C4×D1311yescharacteristic
462C2×C13—42no—
463C2×C13#229011yescharacteristic
464C2×C13#292411yescharacteristic
465C2×C13#292511yescharacteristic
466C2×C13#293511yescharacteristic
467C2×C13#293511yescharacteristic
468C2×C13#296611yescharacteristic
469C2×C13#296711yescharacteristic
470D13—81no—
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—131no—
481C22×C4—131no—
482C22×C4—131no—
483C22×C4—131no—
484C22×C4—131no—
485C22×C4—131no—
486C22×C4—131no—
487C22×C4—261no—
488C22×C4—261no—
489C22×C4—261no—
490C22×C4—261no—
491C22×C4—261no—
492C22×C4—261no—
493C22×C4C2×C4×D1311yescharacteristic
494C22×C4C2×C4×D1311yescharacteristic
495C22×C4C2×C4×D1311yescharacteristic
496C22×C4C2×C4×D1311yescharacteristic
497C22×C4C2×C4×D1311yescharacteristic
498C22×C4#612912yes—
499C22×C4#613112yes—
500C22×C4C23×D1311yescharacteristic
501M16—28no—
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×C8D4×D1312yes—
526C2×C8#612912yes—
527C4⋊C4—262no—
528C4⋊C4—262no—
529C4⋊C4—262no—
530C4⋊C4—262no—
531C4⋊C4—262no—
532C4⋊C4—262no—
533C4⋊C4—521no—
534C22⋊C4—22no—
535C22⋊C4—41no—
536C22⋊C4—262no—
537C22⋊C4—262no—
538C22⋊C4—262no—
539C22⋊C4—262no—
540C22⋊C4—262no—
541C22⋊C4—262no—
542C22⋊C4—262no—
543C22⋊C4—521no—
544C42—21no—
545C42—21no—
546C42—21no—
547C42—21no—
548C42—132no—
549C42—132no—
550C42—262no—
551C42—262no—
552C42—261no—
553C42—261no—
554C42—261no—
555C42—261no—
556C42—521no—
557C42—521no—
558C13#2111111yescharacteristic, complemented, Sylow
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—261no—
566C23—261no—
567C23—261no—
568C23—261no—
569C23—261no—
570C23—261no—
571C23—261no—
572C23#8814612yes—
573C23C22×C4×D1311yescharacteristic
574D4—524no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
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—261no—
602C2×C4—261no—
603C2×C4—261no—
604C2×C4—261no—
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—521no—
614C2×C4—521no—
615C2×C4—521no—
616C2×C4—521no—
617C2×C4#8814612yes—
618C2×C4#8816112yes—
619C2×C4C2×D4×D1311yescharacteristic
620C2×C4C2×#612911yescharacteristic
621C2×C4C2×#612911yescharacteristic
622C2×C4C2×#613111yescharacteristic
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—22no—
634C22—22no—
635C22—22no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22—41no—
640C22—521no—
641C22—521no—
642C22—521no—
643C22—521no—
644C22—521no—
645C22—521no—
646C22—521no—
647C22C2×#8814611yescharacteristic
648C22C4×#612911yescharacteristic
649C22C4×D4×D1311yescharacteristic
650C22C2×#8816111yescharacteristic
651C22#1171945011yescharacteristic
652C22D13×#13111yescharacteristic
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#1171929111yescharacteristic
667C4#1171932911yescharacteristic
668C4#1171933211yescharacteristic
669C4#1171935411yescharacteristic
670C2—42no—
671C2—1041no—
672C2#1311727211yescharacteristic
673C2#1312349311yescharacteristic
674C2#1312350411yescharacteristic
675C2#1312357711yescharacteristic
676C2#1312358111yescharacteristic
677C2#1312380611yescharacteristic
678C2#1312382211yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D13
commutator, socleC23×C13C23×C4
FittingC13×#1851C2
prime radicalC22×C22⋊D13C2×C4
cosocleC22×C4×C13C24
hypercenter#1851D13
hypocenterC13#21111
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ #1851

Complements

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

NH ≅ G/Ntype
1. C2×#11718501C2semidirect
2. C2×#11718783C2semidirect
4. #13115448C2semidirect
5. #13115443C2semidirect
6. #13115403C2semidirect
7. #13115390C2semidirect
10. #13115016C2semidirect
11. C4⋊C8×Dic13C2semidirect
12. #13114604C2semidirect
13. #13114601C2semidirect
14. #13114583C2semidirect
15. C13×#1851C2semidirect
126. #88055D4semidirect
229. #1851D13semidirect
558. C13#21111semidirect

Maximal subgroups

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

subgroupindex
C2×#117185012
C2×#117187832
#131172992
#131154482
#131154432
#131154032
#131153902
#131151332
#131151262
#131150162
C4⋊C8×Dic132
#131146042
#131146012
#131145832
C13×#18512
#2111113