Finite Group Databasebeta

← #15867110

Subgroups — #15867110

Order 3328.

860 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×#11718381C211yesmaximal, characteristic, complemented
2C2×#11718380C211yesmaximal, characteristic, complemented
3#13117281C211yesmaximal, characteristic
4#13115631C211yesmaximal, characteristic
5#13115559C211yesmaximal, characteristic, complemented
6#13115552C211yesmaximal, characteristic, complemented
7#13115446C211yesmaximal, characteristic, complemented
8#13115446C211yesmaximal, characteristic, complemented
9#13115445C211yesmaximal, characteristic, complemented
10#13115445C211yesmaximal, characteristic, complemented
11#13114695C211yesmaximal, characteristic, complemented
12#13114604C211yesmaximal, characteristic, complemented
13C22⋊C8×Dic13C211yesmaximal, characteristic, complemented
14#13114524C211yesmaximal, characteristic, complemented
15C13×#1955C211yesmaximal, characteristic
16C2×C4×D4×C13C2211yescharacteristic
17C2×#88180C2211yescharacteristic
18C22×C4×Dic13C2211yescharacteristic
19C2×C13×C4⋊C8C2211yescharacteristic
20C2×C13×C22⋊C8C2211yescharacteristic
21C2×C13×C22⋊C8C2211yescharacteristic
22C2×C13×C22⋊C8C2211yescharacteristic
23C2×C13×C22⋊C8C2211yescharacteristic
24C2×C13×#97C2211yescharacteristic
25#11718881C411yescharacteristic
26#11718881C411yescharacteristic
27C4×C22⋊Dic13C2211yescharacteristic
28C4×C22⋊Dic13C2211yescharacteristic
29C2×C22⋊#1055C2211yescharacteristic
30C2×C22⋊#1055C2211yescharacteristic
31C2×C22⋊#1055C2211yescharacteristic
32C2×C22⋊#1055C2211yescharacteristic
33C2×#88055C2211yescharacteristic
34C2×#88055C2211yescharacteristic
35C2×#88055C2211yescharacteristic
36C2×#88054C2211yescharacteristic
37C2×#88054C2211yescharacteristic
38C2×#88054C2211yescharacteristic
39C2×#88054C2211yescharacteristic
40C2×C8×Dic13C2211yescharacteristic
41C2×C8×Dic13C2211yescharacteristic
42C2×C8×Dic13C2211yescharacteristic
43#11718642C411yescharacteristic
44#11718642C411yescharacteristic
45#11718612C411yescharacteristic
46#11718612C411yescharacteristic
47#11718611C411yescharacteristic
48#11718611C411yescharacteristic
49C4×C4⋊Dic13C2211yescharacteristic
50#11718593C2211yescharacteristic
51C2×C4⋊#1055C2211yescharacteristic
52C2×C4×#1055C2211yescharacteristic
53#11718381—24no—
54#11718380—24no—
55#11718142C2211yescharacteristic
56#11718142C2211yescharacteristic
57#11718142C2211yescharacteristic
58#11718142C2211yescharacteristic
59#11718142C2211yescharacteristic
60#11718142C2211yescharacteristic
61C22×D4×C13C2×C411yescharacteristic
62C23×C4×C13C2311yescharacteristic
63C23×C4×C13C2311yescharacteristic
64C23×Dic13C2×C411yescharacteristic
65C23×Dic13C2×C411yescharacteristic
66C22×C8×C13C2311yescharacteristic
67C22×C8×C13C2311yescharacteristic
68C22×C8×C13C2311yescharacteristic
69C22×C8×C13C2311yescharacteristic
70C4×D4×C13—22no—
71C4×D4×C13—22no—
72C2×C13×C4⋊C4C2×C411yescharacteristic
73C2×C13×C22⋊C4C2×C411yescharacteristic
74C2×C13×C22⋊C4C2×C411yescharacteristic
75C2×C42×C13C2311yescharacteristic
76C2×C22⋊Dic13C2×C411yescharacteristic
77C2×C22⋊Dic13C2×C411yescharacteristic
78C2×C22⋊Dic13C2×C411yescharacteristic
79C2×C22⋊Dic13C2×C411yescharacteristic
80C2×C22⋊Dic13C2×C411yescharacteristic
81C2×C22⋊Dic13C2×C411yescharacteristic
82#88180—22no—
83#88180—22no—
84C2×C4⋊Dic13C2×C411yescharacteristic
85C2×C4⋊Dic13C2×C411yescharacteristic
86C2×C4⋊Dic13C2×C411yescharacteristic
87C2×C4⋊Dic13C2×C411yescharacteristic
88C2×C4×Dic13—22no—
89C2×C4×Dic13—22no—
90C2×C4×Dic13C2×C411yescharacteristic
91C2×C4×Dic13C2×C411yescharacteristic
92C2×C4×Dic13C2311yescharacteristic
93C2×C4×Dic13C2311yescharacteristic
94C2×C4×Dic13C2311yescharacteristic
95C2×C4×Dic13C2311yescharacteristic
96C22×#1055C2311yescharacteristic
97C22×#1055C2311yescharacteristic
98C22×#1055C2311yescharacteristic
99C22×#1055C2311yescharacteristic
100C13×C4⋊C8—22no—
101C13×C22⋊C8—22no—
102C13×C22⋊C8—22no—
103C13×C22⋊C8—22no—
104C13×C22⋊C8—22no—
105C13×#97—22no—
106#88071C2×C411yescharacteristic
107#88071C2×C411yescharacteristic
108#88071C2×C411yescharacteristic
109#88071C2×C411yescharacteristic
110#88071C2×C411yescharacteristic
111#88071C2×C411yescharacteristic
112#88071C2×C411yescharacteristic
113#88071C2×C411yescharacteristic
114#88071C2×C411yescharacteristic
115#88071C2×C411yescharacteristic
116C22⋊#1055—22no—
117C22⋊#1055—22no—
118C22⋊#1055—22no—
119C22⋊#1055—22no—
120#88055—22no—
121#88055—22no—
122#88055D414yescomplemented
123#88054—22no—
124#88054—22no—
125#88054—22no—
126#88054—22no—
127C8×Dic13—22no—
128C8×Dic13—22no—
129C8×Dic13—22no—
130C4⋊#1055—22no—
131C4×#1055—22no—
132#21273—131nomaximal, Sylow
133C24×C13C22×C411yescharacteristic
134C24×C13C22×C411yescharacteristic
135C2×D4×C13—22no—
136C2×D4×C13—22no—
137C2×D4×C13—41no—
138C22×C4×C13—21no—
139C22×C4×C13—21no—
140C22×C4×C13—21no—
141C22×C4×C13—21no—
142C22×C4×C13—21no—
143C22×C4×C13—21no—
144C22×C4×C13—21no—
145C22×C4×C13—21no—
146C22×C4×C13—21no—
147C22×C4×C13—21no—
148C22×C4×C13—21no—
149C22×C4×C13—21no—
150C22×C4×C13C22×C411yescharacteristic
151C22×C4×C13C22×C411yescharacteristic
152C22×C4×C13C22×C411yescharacteristic
153C22×C4×C13C22×C411yescharacteristic
154C22×C4×C13C2411yescharacteristic
155C22×Dic13—22no—
156C22×Dic13—22no—
157C22×Dic13—22no—
158C22×Dic13—22no—
159C22×Dic13—41no—
160C22×Dic13—41no—
161C22×Dic13C22×C411yescharacteristic
162C22×Dic13C22×C411yescharacteristic
163C22×Dic13C22×C411yescharacteristic
164C22×Dic13C22×C411yescharacteristic
165C22×Dic13C22×C411yescharacteristic
166C22×Dic13C22×C411yescharacteristic
167C22×Dic13C22×C411yescharacteristic
168C22×Dic13C22×C411yescharacteristic
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×C13—21no—
179C2×C8×C13C2×D412yes—
180C2×C8×C13#4112yes—
181C13×C4⋊C4—22no—
182C13×C22⋊C4—22no—
183C13×C22⋊C4—22no—
184C42×C13#4112yes—
185C42×C13#4112yes—
186C22⋊Dic13—22no—
187C22⋊Dic13—22no—
188C22⋊Dic13—22no—
189C22⋊Dic13—22no—
190C22⋊Dic13—41no—
191C22⋊Dic13—41no—
192C4⋊Dic13—22no—
193C4⋊Dic13—22no—
194C4⋊Dic13—22no—
195C4⋊Dic13—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×Dic13C2×D412yes—
205C4×Dic13#4112yes—
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×#1055#4112yes—
218C2×#433—131no—
219C2×#432—131no—
220#2290—131no—
221#1955D1311yescharacteristic
222#1954—131no—
223#1940—131no—
224#1939—131no—
225#1924—131no—
226#1924—131no—
227#1923—131no—
228#1923—131no—
229#1768—131no—
230#1750—131no—
231C4×C22⋊C8—131no—
232#1726—131no—
233C23×C13—21no—
234C23×C13—21no—
235C23×C13—21no—
236C23×C13—21no—
237C23×C13—21no—
238C23×C13—21no—
239C23×C13—21no—
240C23×C13—21no—
241C23×C13—21no—
242C23×C13—21no—
243C23×C13—21no—
244C23×C13—21no—
245C23×C13—21no—
246C23×C13#13112yes—
247C23×C13C23×C411yescharacteristic
248D4×C13—44no—
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—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×C13—41no—
267C2×C4×C13#11712yes—
268C2×C4×C13#11712yes—
269C2×C4×C13C22×D411yescharacteristic
270C2×C4×C13C2×#4111yescharacteristic
271C2×C4×C13C2×#4111yescharacteristic
272C2×C4×C13C2×#4111yescharacteristic
273C2×C4×C13C2×#4111yescharacteristic
274C2×C4×C13C2×#4111yescharacteristic
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×Dic13—21no—
289C2×Dic13—21no—
290C2×Dic13—21no—
291C2×Dic13—21no—
292C2×Dic13—21no—
293C2×Dic13—21no—
294C2×Dic13—21no—
295C2×Dic13—21no—
296C2×Dic13—44no—
297C2×Dic13—44no—
298C2×Dic13C4×D412yes—
299C2×Dic13C4×D412yes—
300C2×Dic13#13112yes—
301C8×C13—22no—
302C8×C13—22no—
303C8×C13—41no—
304C8×C13—41no—
305#1055—22no—
306#1055—22no—
307#1055—41no—
308#1055—41no—
309C2×C4×D4C2×D1311yescharacteristic
310C2×#117—131no—
311C22×C42—131no—
312#433—264no—
313#432—264no—
314C2×C4⋊C8—131no—
315C2×C4⋊C8—131no—
316C2×C4⋊C8—131no—
317C2×C4⋊C8—131no—
318C2×C4⋊C8—131no—
319C2×C4⋊C8C2×D1311yescharacteristic
320C2×C22⋊C8—131no—
321C2×C22⋊C8—131no—
322C2×C22⋊C8—131no—
323C2×C22⋊C8—131no—
324C2×C22⋊C8C2×D1311yescharacteristic
325C2×C22⋊C8C2×D1311yescharacteristic
326C2×C22⋊C8C2×D1311yescharacteristic
327C2×C22⋊C8C2×D1311yescharacteristic
328C2×#97—131no—
329C2×#97—131no—
330C2×#97—131no—
331C2×#97C2×D1311yescharacteristic
332C2×C4×C8—131no—
333C2×C4×C8—131no—
334C2×C4×C8—131no—
335C2×C4×C8—131no—
336#388—131no—
337#388—131no—
338#387—131no—
339#387—131no—
340#386—131no—
341#386—131no—
342#385—131no—
343#385—131no—
344C4×C4⋊C4—131no—
345C4×C22⋊C4—131no—
346C4×C22⋊C4—131no—
347#376—131no—
348#336—131no—
349#336—131no—
350#336—131no—
351#336—131no—
352#336—131no—
353#336—131no—
354C22×C13—22no—
355C22×C13—22no—
356C22×C13—22no—
357C22×C13—41no—
358C22×C13—41no—
359C22×C13—41no—
360C22×C13—41no—
361C22×C13—41no—
362C22×C13—41no—
363C22×C13—41no—
364C22×C13—41no—
365C22×C13—41no—
366C22×C13—41no—
367C22×C13—41no—
368C22×C13C2×#11711yescharacteristic
369C22×C13C2×C4×D411yescharacteristic
370C22×C13C4×#4111yescharacteristic
371C22×C13C2×#13111yescharacteristic
372C22×C13C2×#13111yescharacteristic
373C22×C13#56811yescharacteristic
374C22×C13#56811yescharacteristic
375C4×C13—22no—
376C4×C13—22no—
377C4×C13—41no—
378C4×C13—41no—
379C4×C13#52911yescharacteristic
380C4×C13#52911yescharacteristic
381C4×C13#53211yescharacteristic
382C4×C13#53211yescharacteristic
383Dic13—22no—
384Dic13—22no—
385Dic13—22no—
386Dic13—41no—
387Dic13—41no—
388Dic13—41no—
389Dic13—41no—
390Dic13—41no—
391C22×D4C4×D1311yescharacteristic
392C23×C4—131no—
393C23×C4—131no—
394C23×C4C22×D1311yescharacteristic
395C23×C4C22×D1311yescharacteristic
396C22×C8—131no—
397C22×C8—131no—
398C22×C8—131no—
399C22×C8—131no—
400C22×C8C22×D1311yescharacteristic
401C22×C8C22×D1311yescharacteristic
402C22×C8C22×D1311yescharacteristic
403C22×C8C22×D1311yescharacteristic
404C4×D4—22no—
405C4×D4—22no—
406#117—262no—
407#117—262no—
408C2×C4⋊C4—131no—
409C2×C4⋊C4—131no—
410C2×C4⋊C4—131no—
411C2×C4⋊C4—131no—
412C2×C4⋊C4C4×D1311yescharacteristic
413C2×C22⋊C4—131no—
414C2×C22⋊C4—131no—
415C2×C22⋊C4—131no—
416C2×C22⋊C4—131no—
417C2×C22⋊C4—131no—
418C2×C22⋊C4—131no—
419C2×C22⋊C4C4×D1311yescharacteristic
420C2×C22⋊C4C4×D1311yescharacteristic
421C2×C42—131no—
422C2×C42—131no—
423C2×C42—131no—
424C2×C42—131no—
425C2×C42—131no—
426C2×C42—131no—
427C2×C42—262no—
428C2×C42—262no—
429C2×C42C22×D1311yescharacteristic
430C4⋊C8—22no—
431C4⋊C8—262no—
432C4⋊C8—262no—
433C4⋊C8—262no—
434C4⋊C8—262no—
435C4⋊C8—262no—
436C22⋊C8—22no—
437C22⋊C8—22no—
438C22⋊C8—22no—
439C22⋊C8—22no—
440C22⋊C8—262no—
441C22⋊C8—262no—
442C22⋊C8—262no—
443C22⋊C8—262no—
444#97—22no—
445#97—134no—
446#97—262no—
447#97—262no—
448C4×C8—262no—
449C4×C8—262no—
450C4×C8—262no—
451C4×C8—262no—
452#95—131no—
453#95—131no—
454#95—131no—
455#95—131no—
456#95—131no—
457#95—131no—
458#95—131no—
459#95—131no—
460#95—131no—
461#95—131no—
462C2×C13—42no—
463C2×C13—81no—
464C2×C13#229311yescharacteristic
465C2×C13#292411yescharacteristic
466C2×C13#292511yescharacteristic
467C2×C13#293311yescharacteristic
468C2×C13#293311yescharacteristic
469C2×C13#296611yescharacteristic
470C2×C13#296711yescharacteristic
471C24C2×C4×D1311yescharacteristic
472C24C2×C4×D1311yescharacteristic
473C2×D4—22no—
474C2×D4—22no—
475C2×D4—41no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—131no—
489C22×C4—131no—
490C22×C4—131no—
491C22×C4—131no—
492C22×C4—131no—
493C22×C4—131no—
494C22×C4—131no—
495C22×C4—131no—
496C22×C4—262no—
497C22×C4—262no—
498C22×C4—262no—
499C22×C4—262no—
500C22×C4—521no—
501C22×C4—521no—
502C22×C4C2×C4×D1311yescharacteristic
503C22×C4C2×C4×D1311yescharacteristic
504C22×C4C2×C4×D1311yescharacteristic
505C22×C4C2×C4×D1311yescharacteristic
506C22×C4C23×D1311yescharacteristic
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—132no—
518C2×C8—132no—
519C2×C8—261no—
520C2×C8—261no—
521C2×C8—261no—
522C2×C8—261no—
523C2×C8—261no—
524C2×C8—261no—
525C2×C8—261no—
526C2×C8—261no—
527C2×C8—261no—
528C2×C8—261no—
529C2×C8D4×D1312yes—
530C2×C8#612912yes—
531C4⋊C4—22no—
532C4⋊C4—262no—
533C4⋊C4—262no—
534C4⋊C4—262no—
535C4⋊C4—521no—
536C22⋊C4—22no—
537C22⋊C4—22no—
538C22⋊C4—262no—
539C22⋊C4—262no—
540C22⋊C4—262no—
541C22⋊C4—262no—
542C22⋊C4—521no—
543C22⋊C4—521no—
544C42—132no—
545C42—132no—
546C42—262no—
547C42—262no—
548C42—261no—
549C42—261no—
550C42—261no—
551C42—261no—
552C42—261no—
553C42—261no—
554C42#612912yes—
555C42#612912yes—
556C13#2127311yescharacteristic, complemented, Sylow
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23#8816112yes—
571C23C22×C4×D1311yescharacteristic
572D4—44no—
573C2×C4—21no—
574C2×C4—21no—
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—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
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—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—261no—
614C2×C4—261no—
615C2×C4—524no—
616C2×C4—524no—
617C2×C4#8813112yes—
618C2×C4#8813112yes—
619C2×C4C2×D4×D1311yescharacteristic
620C2×C4C2×#612911yescharacteristic
621C2×C4C2×#612911yescharacteristic
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—22no—
634C22—22no—
635C22—22no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22—41no—
640C22—41no—
641C22—41no—
642C22—41no—
643C22—41no—
644C22—41no—
645C22—41no—
646C22—41no—
647C22C2×#8813111yescharacteristic
648C22C4×#612911yescharacteristic
649C22C4×D4×D1311yescharacteristic
650C22C2×#8816111yescharacteristic
651C22#1171945011yescharacteristic
652C22D13×#13111yescharacteristic
653C22#1171945511yescharacteristic
654C4—22no—
655C4—22no—
656C4—41no—
657C4—41no—
658C4—262no—
659C4—262no—
660C4—262no—
661C4—521no—
662C4—521no—
663C4—521no—
664C4—521no—
665C4—521no—
666C4#1171930111yescharacteristic
667C4#1171930511yescharacteristic
668C4#1171938511yescharacteristic
669C4#1171942111yescharacteristic
670C2—42no—
671C2—81no—
672C2#1311729811yescharacteristic
673C2#1312349611yescharacteristic
674C2#1312349811yescharacteristic
675C2#1312355911yescharacteristic
676C2#1312356211yescharacteristic
677C2#1312380611yescharacteristic
678C2#1312381511yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D13
commutator, socleC23×C13C23×C4
FittingC13×#1955C2
prime radicalC22×D4×C13C2×C4
cosocleC22×C4×C13C24
hypercenter#1955D13
hypocenterC13#21273
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ #1955

Complements

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

NH ≅ G/Ntype
1. C2×#11718381C2semidirect
2. C2×#11718380C2semidirect
5. #13115559C2semidirect
6. #13115552C2semidirect
7. #13115446C2semidirect
8. #13115446C2semidirect
9. #13115445C2semidirect
10. #13115445C2semidirect
11. #13114695C2semidirect
12. #13114604C2semidirect
13. C22⋊C8×Dic13C2semidirect
14. #13114524C2semidirect
122. #88055D4semidirect
556. C13#21273semidirect

Maximal subgroups

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

subgroupindex
C2×#117183812
C2×#117183802
#131172812
#131156312
#131155592
#131155522
#131154462
#131154452
#131146952
#131146042
C22⋊C8×Dic132
#131145242
C13×#19552
#2127313