Finite Group Databasebeta

← #15865833

Subgroups — #15865833

Order 3328.

906 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718380C211yesmaximal, characteristic, complemented
2C2×#11718762C211yesmaximal, characteristic, complemented
3#13117281C211yesmaximal, characteristic
4#13115446C211yesmaximal, characteristic, complemented
5#13115445C211yesmaximal, characteristic, complemented
6#13115401C211yesmaximal, characteristic, complemented
7#13115392C211yesmaximal, characteristic, complemented
8#13115134C211yesmaximal, characteristic
9#13115018C211yesmaximal, characteristic, complemented
10#13115014C211yesmaximal, characteristic, complemented
11#13114692C211yesmaximal, characteristic, complemented
12#13114604C211yesmaximal, characteristic, complemented
13C22⋊C8×Dic13C211yesmaximal, characteristic, complemented
14#13114586C211yesmaximal, characteristic, complemented
15C13×#1869C211yesmaximal, characteristic
16C23×C8×C13C2211yescharacteristic
17C2×C4×D4×C13C2211yescharacteristic
18C2×#88180C2211yescharacteristic
19C22×C4×Dic13C2211yescharacteristic
20C22×#6099C2211yescharacteristic
21C2×C13×C22⋊C8C2211yescharacteristic
22C2×C13×C22⋊C8C2211yescharacteristic
23C2×C13×C22⋊C8C2211yescharacteristic
24#11718881C411yescharacteristic
25#11718881C411yescharacteristic
26C4×C22⋊Dic13C2211yescharacteristic
27C4×C22⋊Dic13C2211yescharacteristic
28C2×C22⋊#1055C2211yescharacteristic
29C2×C22⋊#1055C2211yescharacteristic
30C2×C22⋊#1055C2211yescharacteristic
31#11718762—24no—
32C2×#88055C2211yescharacteristic
33C2×#88055C2211yescharacteristic
34C2×#88055C2211yescharacteristic
35C2×#88054C2211yescharacteristic
36C2×#88054C2211yescharacteristic
37C2×#88054C2211yescharacteristic
38C2×#88054C2211yescharacteristic
39C2×C8×Dic13C2211yescharacteristic
40C2×C8×Dic13C2211yescharacteristic
41C2×C8×Dic13C2211yescharacteristic
42#11718642C411yescharacteristic
43#11718642C411yescharacteristic
44#11718612C411yescharacteristic
45#11718612C411yescharacteristic
46#11718611C411yescharacteristic
47#11718611C411yescharacteristic
48C4×C4⋊Dic13C2211yescharacteristic
49#11718593C2211yescharacteristic
50#11718380—24no—
51C13×#336C2211yescharacteristic
52C13×#336C2211yescharacteristic
53#11718142C2211yescharacteristic
54#11718142C2211yescharacteristic
55#11718142C2211yescharacteristic
56#11718142C2211yescharacteristic
57#11718142C2211yescharacteristic
58#11718142C2211yescharacteristic
59#11718116C2211yescharacteristic
60#11718116C2211yescharacteristic
61C22×D4×C13C2×C411yescharacteristic
62C23×C4×C13C2311yescharacteristic
63C23×C4×C13C2311yescharacteristic
64C23×Dic13C2×C411yescharacteristic
65C23×Dic13C2×C411yescharacteristic
66C22×C8×C13—22no—
67C22×C8×C13—22no—
68C22×C8×C13—22no—
69C22×C8×C13C2311yescharacteristic
70C22×C8×C13C2311yescharacteristic
71C22×C8×C13C2311yescharacteristic
72C22×C8×C13C2311yescharacteristic
73C4×D4×C13—22no—
74C4×D4×C13—22no—
75C2×C13×C4⋊C4C2×C411yescharacteristic
76C2×C13×C22⋊C4C2×C411yescharacteristic
77C2×C13×C22⋊C4C2×C411yescharacteristic
78C2×C42×C13C2311yescharacteristic
79C2×C22⋊Dic13C2×C411yescharacteristic
80C2×C22⋊Dic13C2×C411yescharacteristic
81C2×C22⋊Dic13C2×C411yescharacteristic
82C2×C22⋊Dic13C2×C411yescharacteristic
83C2×C22⋊Dic13C2×C411yescharacteristic
84C2×C22⋊Dic13C2×C411yescharacteristic
85#88180—22no—
86#88180—22no—
87C2×C4⋊Dic13C2×C411yescharacteristic
88C2×C4⋊Dic13C2×C411yescharacteristic
89C2×C4⋊Dic13C2×C411yescharacteristic
90C2×C4⋊Dic13C2×C411yescharacteristic
91C2×C4×Dic13—22no—
92C2×C4×Dic13—22no—
93C2×C4×Dic13C2×C411yescharacteristic
94C2×C4×Dic13C2×C411yescharacteristic
95C2×C4×Dic13C2311yescharacteristic
96C2×C4×Dic13C2311yescharacteristic
97C2×C4×Dic13C2311yescharacteristic
98C2×C4×Dic13C2311yescharacteristic
99C2×#6099—22no—
100C2×#6099—22no—
101C2×#6099—22no—
102C22×#1055C2311yescharacteristic
103C22×#1055C2311yescharacteristic
104C22×#1055C2311yescharacteristic
105C22×#1055C2311yescharacteristic
106C13×C22⋊C8—22no—
107C13×C22⋊C8—22no—
108C13×C22⋊C8—22no—
109#88071C2×C411yescharacteristic
110#88071C2×C411yescharacteristic
111#88071C2×C411yescharacteristic
112#88071C2×C411yescharacteristic
113#88071C2×C411yescharacteristic
114#88071C2×C411yescharacteristic
115#88071C2×C411yescharacteristic
116#88071C2×C411yescharacteristic
117#88071C2×C411yescharacteristic
118#88071C2×C411yescharacteristic
119C22⋊#1055—22no—
120C22⋊#1055—22no—
121C22⋊#1055—22no—
122#88055—22no—
123#88055—22no—
124#88055D414yescomplemented
125#88054—22no—
126#88054—22no—
127#88054—22no—
128#88054—22no—
129C8×Dic13—22no—
130C8×Dic13—22no—
131C8×Dic13—22no—
132#21112—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×C13C22×C411yescharacteristic
149C22×C4×C13C22×C411yescharacteristic
150C22×C4×C13C22×C411yescharacteristic
151C22×C4×C13C22×C411yescharacteristic
152C22×C4×C13#4112yes—
153C22×C4×C13#4112yes—
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—28no—
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×C13—21no—
180C2×C8×C13C2×D412yes—
181C2×C8×C13#4112yes—
182C13×C4⋊C4—22no—
183C13×C22⋊C4—22no—
184C13×C22⋊C4—22no—
185C42×C13—21no—
186C42×C13—21no—
187C22⋊Dic13—22no—
188C22⋊Dic13—22no—
189C22⋊Dic13—22no—
190C22⋊Dic13—22no—
191C22⋊Dic13—41no—
192C22⋊Dic13—41no—
193C4⋊Dic13—22no—
194C4⋊Dic13—22no—
195C4⋊Dic13—22no—
196C4⋊Dic13—41no—
197C4×Dic13—21no—
198C4×Dic13—21no—
199C4×Dic13—21no—
200C4×Dic13—21no—
201C4×Dic13—21no—
202C4×Dic13—21no—
203C4×Dic13—22no—
204C4×Dic13—22no—
205C4×Dic13C2×D412yes—
206C4×Dic13#4112yes—
207#6099—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×#432—131no—
221C2×#405—131no—
222#2290—131no—
223#1924—131no—
224#1923—131no—
225#1917—131no—
226#1916—131no—
227#1870—131no—
228#1869D1311yescharacteristic
229#1851—131no—
230#1850—131no—
231#1768—131no—
232#1750—131no—
233C4×C22⋊C8—131no—
234#1746—131no—
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—21no—
247C23×C13#11712yes—
248C23×C13#13112yes—
249C23×C13C23×C411yescharacteristic
250D4×C13—44no—
251C2×C4×C13—21no—
252C2×C4×C13—21no—
253C2×C4×C13—22no—
254C2×C4×C13—22no—
255C2×C4×C13—22no—
256C2×C4×C13—22no—
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×C13—21no—
265C2×C4×C13—21no—
266C2×C4×C13—41no—
267C2×C4×C13—41no—
268C2×C4×C13—41no—
269C2×C4×C13—41no—
270C2×C4×C13#11712yes—
271C2×C4×C13C22×D411yescharacteristic
272C2×C4×C13C2×#4111yescharacteristic
273C2×C4×C13C2×#4111yescharacteristic
274C2×C4×C13C2×#4111yescharacteristic
275C2×C4×C13C2×#4111yescharacteristic
276C2×C4×C13C2×#4111yescharacteristic
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—21no—
297C2×Dic13—21no—
298C2×Dic13—44no—
299C2×Dic13—44no—
300C2×Dic13C4×D412yes—
301C2×Dic13C4×D412yes—
302C2×Dic13#13112yes—
303C8×C13—22no—
304C8×C13—22no—
305C8×C13—41no—
306C8×C13—41no—
307#1055—22no—
308#1055—22no—
309#1055—41no—
310#1055—41no—
311C22×M16—131no—
312C23×C8C2×D1311yescharacteristic
313C2×C4×D4C2×D1311yescharacteristic
314C2×#117—131no—
315C22×C42—131no—
316#432—264no—
317C2×C4⋊C8—131no—
318C2×C4⋊C8—131no—
319C2×C4⋊C8—131no—
320C2×C4⋊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
327#405—264no—
328C2×#97—131no—
329C2×#97—131no—
330C2×#97—131no—
331C2×C4×C8—131no—
332C2×C4×C8—131no—
333C2×C4×C8—131no—
334#388—131no—
335#388—131no—
336#387—131no—
337#387—131no—
338#386—131no—
339#386—131no—
340#385—131no—
341#385—131no—
342C4×C4⋊C4—131no—
343C4×C22⋊C4—131no—
344C4×C22⋊C4—131no—
345#376—131no—
346#336—131no—
347#336—131no—
348#336—131no—
349#336—131no—
350#336—131no—
351#336—131no—
352#336—131no—
353#336—131no—
354#336C2×D1311yescharacteristic
355#336C2×D1311yescharacteristic
356C22×C13—22no—
357C22×C13—22no—
358C22×C13—22no—
359C22×C13—22no—
360C22×C13—22no—
361C22×C13—22no—
362C22×C13—41no—
363C22×C13—41no—
364C22×C13—41no—
365C22×C13—41no—
366C22×C13—41no—
367C22×C13—41no—
368C22×C13—41no—
369C22×C13—41no—
370C22×C13C2×#11711yescharacteristic
371C22×C13C2×C4×D411yescharacteristic
372C22×C13C4×#4111yescharacteristic
373C22×C13C2×#13111yescharacteristic
374C22×C13C2×#13111yescharacteristic
375C22×C13#56811yescharacteristic
376C22×C13#56811yescharacteristic
377C4×C13—22no—
378C4×C13—41no—
379C4×C13—41no—
380C4×C13—41no—
381C4×C13#52511yescharacteristic
382C4×C13#52511yescharacteristic
383C4×C13#52911yescharacteristic
384C4×C13#52911yescharacteristic
385Dic13—22no—
386Dic13—22no—
387Dic13—22no—
388Dic13—41no—
389Dic13—41no—
390Dic13—41no—
391Dic13—41no—
392Dic13—41no—
393C22×D4C4×D1311yescharacteristic
394C23×C4—131no—
395C23×C4—131no—
396C23×C4C22×D1311yescharacteristic
397C23×C4C22×D1311yescharacteristic
398C2×M16—262no—
399C2×M16—262no—
400C2×M16—262no—
401C22×C8—22no—
402C22×C8—22no—
403C22×C8—22no—
404C22×C8—131no—
405C22×C8—131no—
406C22×C8—131no—
407C22×C8—131no—
408C22×C8C22×D1311yescharacteristic
409C22×C8C22×D1311yescharacteristic
410C22×C8C22×D1311yescharacteristic
411C22×C8C22×D1311yescharacteristic
412C4×D4—22no—
413C4×D4—22no—
414#117—262no—
415#117—262no—
416C2×C4⋊C4—131no—
417C2×C4⋊C4—131no—
418C2×C4⋊C4—131no—
419C2×C4⋊C4—131no—
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⋊C4C4×D1311yescharacteristic
428C2×C22⋊C4C4×D1311yescharacteristic
429C2×C42—131no—
430C2×C42—131no—
431C2×C42—131no—
432C2×C42—131no—
433C2×C42—131no—
434C2×C42—131no—
435C2×C42—262no—
436C2×C42—262no—
437C2×C42C22×D1311yescharacteristic
438C4⋊C8—262no—
439C4⋊C8—262no—
440C4⋊C8—262no—
441C4⋊C8—262no—
442C22⋊C8—22no—
443C22⋊C8—22no—
444C22⋊C8—22no—
445C22⋊C8—262no—
446C22⋊C8—262no—
447C22⋊C8—262no—
448#97—134no—
449#97—262no—
450#97—262no—
451C4×C8—262no—
452C4×C8—262no—
453C4×C8—262no—
454#95—131no—
455#95—131no—
456#95—131no—
457#95—131no—
458#95—131no—
459#95—131no—
460#95—131no—
461#95—131no—
462#95—131no—
463#95—131no—
464C2×C13—42no—
465C2×C13—42no—
466C2×C13#229011yescharacteristic
467C2×C13#292411yescharacteristic
468C2×C13#292511yescharacteristic
469C2×C13#293311yescharacteristic
470C2×C13#293311yescharacteristic
471C2×C13#296611yescharacteristic
472C2×C13#296711yescharacteristic
473C24C2×C4×D1311yescharacteristic
474C24C2×C4×D1311yescharacteristic
475C2×D4—22no—
476C2×D4—22no—
477C2×D4—41no—
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×C4#612912yes—
507C22×C4#612912yes—
508C22×C4C23×D1311yescharacteristic
509M16—268no—
510C2×C8—28no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—132no—
522C2×C8—132no—
523C2×C8—261no—
524C2×C8—261no—
525C2×C8—261no—
526C2×C8—261no—
527C2×C8—261no—
528C2×C8—261no—
529C2×C8—261no—
530C2×C8—261no—
531C2×C8—261no—
532C2×C8—261no—
533C2×C8D4×D1312yes—
534C2×C8#612912yes—
535C4⋊C4—22no—
536C4⋊C4—262no—
537C4⋊C4—262no—
538C4⋊C4—262no—
539C4⋊C4—521no—
540C22⋊C4—22no—
541C22⋊C4—22no—
542C22⋊C4—262no—
543C22⋊C4—262no—
544C22⋊C4—262no—
545C22⋊C4—262no—
546C22⋊C4—521no—
547C22⋊C4—521no—
548C42—21no—
549C42—21no—
550C42—132no—
551C42—132no—
552C42—262no—
553C42—262no—
554C42—261no—
555C42—261no—
556C42—261no—
557C42—261no—
558C42—261no—
559C42—261no—
560C13#2111211yescharacteristic, complemented, Sylow
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23—21no—
572C23—21no—
573C23#8813112yes—
574C23#8815512yes—
575C23C22×C4×D1311yescharacteristic
576D4—44no—
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—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—132no—
597C2×C4—132no—
598C2×C4—132no—
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—261no—
616C2×C4—261no—
617C2×C4—261no—
618C2×C4—261no—
619C2×C4—261no—
620C2×C4—524no—
621C2×C4—524no—
622C2×C4#8813112yes—
623C2×C4C2×D4×D1311yescharacteristic
624C2×C4C2×#612911yescharacteristic
625C2×C4C2×#612911yescharacteristic
626C2×C4C2×#612911yescharacteristic
627C2×C4#41×D1311yescharacteristic
628C2×C4#41×D1311yescharacteristic
629C8—22no—
630C8—22no—
631C8—41no—
632C8—41no—
633C8—262no—
634C8—262no—
635C8—521no—
636C8—521no—
637C22—22no—
638C22—22no—
639C22—22no—
640C22—22no—
641C22—22no—
642C22—22no—
643C22—41no—
644C22—41no—
645C22—41no—
646C22—41no—
647C22—41no—
648C22—41no—
649C22—41no—
650C22—41no—
651C22C2×#8813111yescharacteristic
652C22C4×#612911yescharacteristic
653C22C4×D4×D1311yescharacteristic
654C22C2×#8815511yescharacteristic
655C22#1171945011yescharacteristic
656C22D13×#13111yescharacteristic
657C22#1171945511yescharacteristic
658C4—22no—
659C4—41no—
660C4—41no—
661C4—41no—
662C4—262no—
663C4—262no—
664C4—262no—
665C4—521no—
666C4—521no—
667C4—521no—
668C4—521no—
669C4—521no—
670C4#1171929111yescharacteristic
671C4#1171930511yescharacteristic
672C4#1171931111yescharacteristic
673C4#1171935411yescharacteristic
674C2—42no—
675C2—42no—
676C2#1311727611yescharacteristic
677C2#1312349011yescharacteristic
678C2#1312349811yescharacteristic
679C2#1312355611yescharacteristic
680C2#1312355911yescharacteristic
681C2#1312380411yescharacteristic
682C2#1312381511yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D13
commutator, socleC23×C13C23×C4
FittingC13×#1869C2
prime radicalC22×D4×C13C2×C4
cosocleC22×C4×C13C24
hypercenter#1869D13
hypocenterC13#21112
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ #1869

Complements

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

NH ≅ G/Ntype
1. C2×#11718380C2semidirect
2. C2×#11718762C2semidirect
4. #13115446C2semidirect
5. #13115445C2semidirect
6. #13115401C2semidirect
7. #13115392C2semidirect
9. #13115018C2semidirect
10. #13115014C2semidirect
11. #13114692C2semidirect
12. #13114604C2semidirect
13. C22⋊C8×Dic13C2semidirect
14. #13114586C2semidirect
124. #88055D4semidirect
560. C13#21112semidirect

Maximal subgroups

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

subgroupindex
C2×#117183802
C2×#117187622
#131172812
#131154462
#131154452
#131154012
#131153922
#131151342
#131150182
#131150142
#131146922
#131146042
C22⋊C8×Dic132
#131145862
C13×#18692
#2111213