Finite Group Databasebeta

← #15879590

Subgroups — #15879590

Order 3328.

1066 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718685C211yesmaximal, characteristic, complemented
2#13117793C211yesmaximal, characteristic, complemented
3#13115810C211yesmaximal, characteristic, complemented
4#13115806C211yesmaximal, characteristic, complemented
5#13115802C211yesmaximal, characteristic, complemented
6#13115794C211yesmaximal, characteristic, complemented
7#13115794C211yesmaximal, characteristic, complemented
8#13115789C211yesmaximal, characteristic, complemented
9#13114846C211yesmaximal, characteristic
10#13114846C211yesmaximal, characteristic
11#13114836C211yesmaximal, characteristic
12#13114661C211yesmaximal, characteristic
13#13114661C211yesmaximal, characteristic
14C4×#88072C211yesmaximal, characteristic
15C2×C13×#554C211yesmaximal, characteristic
16C13×#554—24no—
17C13×#554C418yescomplemented
18C2×C13×C4⋊Q8C2211yescharacteristic
19C2×C13×#125C2211yescharacteristic
20C2×C13×#125C2211yescharacteristic
21C2×C13×C22⋊Q8—21no—
22C2×C13×C22⋊Q8—21no—
23C2×C13×C22⋊Q8—21no—
24C2×C4×Q8×C13C2211yescharacteristic
25C2×C4×D4×C13C2211yescharacteristic
26C2×C4×D4×C13C2211yescharacteristic
27C2×C4×D4×C13C2211yescharacteristic
28C22×C13×C4⋊C4—21no—
29#11718891—21no—
30C2×#88072C2211yescharacteristic
31C2×#88072C2211yescharacteristic
32C2×#88072C2211yescharacteristic
33C2×#88072C2211yescharacteristic
34#11718685—24no—
35#11718642—21no—
36#11718642—21no—
37C4⋊C4×Dic13—21no—
38#11718597C2211yescharacteristic
39#11718597C2211yescharacteristic
40#11718596C2211yescharacteristic
41C4×C4⋊Dic13C2211yescharacteristic
42C4×C4⋊Dic13C2211yescharacteristic
43C4×C4⋊Dic13C2211yescharacteristic
44C2×C4⋊#1055C2211yescharacteristic
45C2×C4⋊#1055C2211yescharacteristic
46C2×C4⋊#1055C2211yescharacteristic
47C2×#88043C2211yescharacteristic
48C2×#88043C2211yescharacteristic
49C2×C4×#1055C2211yescharacteristic
50#11718121C2211yescharacteristic
51#11718121C2211yescharacteristic
52#11718121C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718121C2211yescharacteristic
60#11718121C2211yescharacteristic
61#11718121C2211yescharacteristic
62C22×Q8×C13—21no—
63C22×Q8×C13D411yescharacteristic
64C22×D4×C13C2311yescharacteristic
65C23×C4×C13—21no—
66C23×C4×C13—21no—
67C23×C4×C13—21no—
68C13×C4⋊Q8—22no—
69C13×C4⋊Q8C2×C414yes—
70C13×#125—22no—
71C13×#125—22no—
72C13×#125C2×C414yes—
73C13×#125C2×C414yes—
74C13×C22⋊Q8—28no—
75C13×C22⋊Q8—28no—
76C13×C22⋊Q8—28no—
77C4×Q8×C13C2×C414yes—
78C4×Q8×C13D414yes—
79C4×D4×C13—22no—
80C4×D4×C13—22no—
81C4×D4×C13—22no—
82C4×D4×C13C2×C414yes—
83C4×D4×C13C2×C414yes—
84C4×D4×C13C2×C414yes—
85C2×C13×C4⋊C4—21no—
86C2×C13×C4⋊C4—21no—
87C2×C13×C4⋊C4—21no—
88C2×C13×C4⋊C4—21no—
89C2×C13×C4⋊C4—21no—
90C2×C13×C4⋊C4—28no—
91C2×C13×C4⋊C4D411yescharacteristic
92C2×C13×C4⋊C4D411yescharacteristic
93C2×C13×C4⋊C4D411yescharacteristic
94C2×C13×C4⋊C4C2311yescharacteristic
95C2×C13×C4⋊C4C2311yescharacteristic
96C2×C13×C4⋊C4C2311yescharacteristic
97C2×C13×C22⋊C4—21no—
98C2×C13×C22⋊C4—21no—
99C2×C13×C22⋊C4—21no—
100C2×C42×C13C2311yescharacteristic
101C2×C42×C13C2311yescharacteristic
102C2×C42×C13C2311yescharacteristic
103C2×C4⋊Dic13—21no—
104C2×C4⋊Dic13—21no—
105C2×C4⋊Dic13C2311yescharacteristic
106C2×C4⋊Dic13C2311yescharacteristic
107C2×C4⋊Dic13C2311yescharacteristic
108C2×C4⋊Dic13C2311yescharacteristic
109C2×C4×Dic13—21no—
110C2×C4×Dic13—21no—
111C2×C4×Dic13—21no—
112C22×#1055C2311yescharacteristic
113C22×#1055C2311yescharacteristic
114C22×#1055C2311yescharacteristic
115C22×#1055C2311yescharacteristic
116#88072—22no—
117#88072—22no—
118#88072—22no—
119#88072Q814yescomplemented
120#88071—21no—
121#88071—21no—
122#88071—21no—
123#88071—21no—
124#88071—21no—
125#88071—21no—
126#88071—21no—
127C4⋊#1055—22no—
128C4⋊#1055—22no—
129C4⋊#1055—22no—
130#88043—22no—
131#88043—22no—
132C4×#1055—22no—
133#22526—131nomaximal, Sylow
134C24×C13—21no—
135C2×Q8×C13—24no—
136C2×Q8×C13—41no—
137C2×Q8×C13—41no—
138C2×Q8×C13—81no—
139C2×Q8×C13—81no—
140C2×Q8×C13C22⋊C414yes—
141C2×D4×C13—21no—
142C2×D4×C13—21no—
143C2×D4×C13—21no—
144C2×D4×C13C22×C412yes—
145C2×D4×C13C2×Q812yes—
146C2×D4×C13#4112yes—
147C22×C4×C13—21no—
148C22×C4×C13—21no—
149C22×C4×C13—21no—
150C22×C4×C13—24no—
151C22×C4×C13—24no—
152C22×C4×C13—24no—
153C22×C4×C13—42no—
154C22×C4×C13—42no—
155C22×C4×C13—81no—
156C22×C4×C13—81no—
157C22×C4×C13—81no—
158C22×C4×C13—81no—
159C22×C4×C13C2×D411yescharacteristic
160C22×C4×C13C2×D411yescharacteristic
161C22×C4×C13C2×D411yescharacteristic
162C22×C4×C13C2×D411yescharacteristic
163C22×C4×C13C2×D411yescharacteristic
164C22×C4×C13C2×D411yescharacteristic
165C22×C4×C13C2411yescharacteristic
166C22×Dic13—21no—
167C22×Dic13—21no—
168C22×Dic13—21no—
169C22×Dic13—21no—
170C13×C4⋊C4—24no—
171C13×C4⋊C4—24no—
172C13×C4⋊C4—24no—
173C13×C4⋊C4—24no—
174C13×C4⋊C4—24no—
175C13×C4⋊C4—21no—
176C13×C4⋊C4—21no—
177C13×C4⋊C4—21no—
178C13×C4⋊C4C22⋊C414yes—
179C13×C4⋊C4C22⋊C414yes—
180C13×C4⋊C4C22⋊C414yes—
181C13×C4⋊C4C22×C412yes—
182C13×C4⋊C4C22×C412yes—
183C13×C4⋊C4C22×C412yes—
184C13×C22⋊C4—24no—
185C13×C22⋊C4—24no—
186C13×C22⋊C4—24no—
187C42×C13C22×C412yes—
188C42×C13C22×C412yes—
189C42×C13C22×C412yes—
190C42×C13C2×D412yes—
191C42×C13C2×D412yes—
192C42×C13C2×D412yes—
193C4⋊Dic13—21no—
194C4⋊Dic13—21no—
195C4⋊Dic13—21no—
196C4⋊Dic13—21no—
197C4⋊Dic13—21no—
198C4⋊Dic13—21no—
199C4⋊Dic13—21no—
200C4⋊Dic13—42no—
201C4⋊Dic13—81no—
202C4⋊Dic13C2×Q812yes—
203C4×Dic13—42no—
204C4×Dic13—81no—
205C4×Dic13—81no—
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×#1055—21no—
217C2×#1055C2×Q812yes—
218C2×#554D1311yescharacteristic
219C2×#446—131no—
220#2355—131no—
221#1993—131no—
222#1992—131no—
223#1991—131no—
224#1989—131no—
225#1989—131no—
226#1988—131no—
227#1804—131no—
228#1804—131no—
229#1802—131no—
230#1762—131no—
231#1762—131no—
232C4×#102—131no—
233C23×C13—22no—
234C23×C13—22no—
235C23×C13—22no—
236C23×C13—41no—
237C23×C13—41no—
238C23×C13—41no—
239C23×C13—41no—
240C23×C13C22×D411yescharacteristic
241Q8×C13—44no—
242Q8×C13—84no—
243D4×C13—22no—
244D4×C13—22no—
245D4×C13—22no—
246D4×C13C4×Q814yes—
247C2×C4×C13—21no—
248C2×C4×C13—21no—
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—22no—
260C2×C4×C13—22no—
261C2×C4×C13—22no—
262C2×C4×C13—48no—
263C2×C4×C13—41no—
264C2×C4×C13—41no—
265C2×C4×C13—41no—
266C2×C4×C13—41no—
267C2×C4×C13—41no—
268C2×C4×C13—41no—
269C2×C4×C13—84no—
270C2×C4×C13—84no—
271C2×C4×C13C2×C22⋊C412yes—
272C2×C4×C13C2×C22⋊C412yes—
273C2×C4×C13C2×C22⋊C412yes—
274C2×C4×C13C2×C22⋊C412yes—
275C2×C4×C13C2×C22⋊C412yes—
276C2×C4×C13C2×C22⋊C412yes—
277C2×C4×C13C23×C411yescharacteristic
278C2×C4×C13C22×D411yescharacteristic
279C2×C4×C13C22×Q811yescharacteristic
280C2×C4×C13C2×#4111yescharacteristic
281C2×C4×C132−1+411yescharacteristic
282C2×C4×C132−1+411yescharacteristic
283C2×Dic13—22no—
284C2×Dic13—41no—
285C2×Dic13—41no—
286C2×Dic13—41no—
287C2×Dic13—41no—
288C2×Dic13—41no—
289C2×Dic13—41no—
290C2×Dic13—41no—
291C2×Dic13—41no—
292C2×Dic13—41no—
293C2×Dic13—41no—
294C2×Dic13—41no—
295#1055—22no—
296#1055—41no—
297#1055—41no—
298#1055—41no—
299#554—24no—
300#554Dic1318yescomplemented
301C2×C4⋊Q8C2×D1311yescharacteristic
302C2×#125C2×D1311yescharacteristic
303C2×#125C2×D1311yescharacteristic
304C2×C22⋊Q8—21no—
305C2×C22⋊Q8—21no—
306C2×C22⋊Q8—21no—
307C2×C4×Q8C2×D1311yescharacteristic
308C2×C4×D4C2×D1311yescharacteristic
309C2×C4×D4C2×D1311yescharacteristic
310C2×C4×D4C2×D1311yescharacteristic
311C22×C4⋊C4—21no—
312#446—264no—
313C2×C4⋊C8—131no—
314C2×C4⋊C8—131no—
315C2×C4⋊C8—131no—
316C2×#102—131no—
317C2×#102—131no—
318C2×#102—131no—
319C2×#102—131no—
320C2×#97—131no—
321C2×#97—131no—
322C2×C4×C8—131no—
323#391—261no—
324#387—261no—
325#387—261no—
326#384—131no—
327#382—131no—
328#382—131no—
329C4×C4⋊C4—131no—
330C4×C4⋊C4—131no—
331C4×C4⋊C4—131no—
332C4×C4⋊C4—261no—
333#340—131no—
334#340—131no—
335#340—131no—
336#340—131no—
337#340—131no—
338#340—131no—
339#340—131no—
340#340—131no—
341#340—131no—
342#340—131no—
343#340—131no—
344#340—131no—
345C22×C13—24no—
346C22×C13—42no—
347C22×C13—42no—
348C22×C13—42no—
349C22×C13—42no—
350C22×C13—42no—
351C22×C13—42no—
352C22×C13C22×C22⋊C411yescharacteristic
353C22×C13#54811yescharacteristic
354C22×C13D4×Q811yescharacteristic
355C22×C13#57511yescharacteristic
356C22×C13#57511yescharacteristic
357C22×C13#57611yescharacteristic
358C22×C13#57711yescharacteristic
359C4×C13—22no—
360C4×C13—22no—
361C4×C13—22no—
362C4×C13—22no—
363C4×C13—22no—
364C4×C13—22no—
365C4×C13—42no—
366C4×C13—42no—
367C4×C13—42no—
368C4×C13C2×C4×Q811yescharacteristic
369C4×C13#51911yescharacteristic
370C4×C13#54811yescharacteristic
371C4×C13D4×Q811yescharacteristic
372Dic13—42no—
373Dic13—81no—
374Dic13—81no—
375Dic13—81no—
376C22×Q8—21no—
377C22×Q8C22⋊D1311yescharacteristic
378C22×D4C22×D1311yescharacteristic
379C23×C4—21no—
380C23×C4—21no—
381C23×C4—21no—
382C22×C8—131no—
383C22×C8—131no—
384C22×C8—131no—
385C22×C8—131no—
386C4⋊Q8—22no—
387C4⋊Q8C2×Dic1314yes—
388#125—22no—
389#125—22no—
390#125C2×Dic1314yes—
391#125C2×Dic1314yes—
392C22⋊Q8—28no—
393C22⋊Q8—28no—
394C22⋊Q8—28no—
395C4×Q8C2×Dic1314yes—
396C4×Q8C22⋊D1314yes—
397C4×D4—22no—
398C4×D4—22no—
399C4×D4—22no—
400C4×D4C2×Dic1314yes—
401C4×D4C2×Dic1314yes—
402C4×D4C2×Dic1314yes—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—28no—
409C2×C4⋊C4—131no—
410C2×C4⋊C4—131no—
411C2×C4⋊C4—131no—
412C2×C4⋊C4—131no—
413C2×C4⋊C4—261no—
414C2×C4⋊C4—261no—
415C2×C4⋊C4C22⋊D1311yescharacteristic
416C2×C4⋊C4C22⋊D1311yescharacteristic
417C2×C4⋊C4C22⋊D1311yescharacteristic
418C2×C4⋊C4C22×D1311yescharacteristic
419C2×C4⋊C4C22×D1311yescharacteristic
420C2×C4⋊C4C22×D1311yescharacteristic
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—21no—
424C2×C42—261no—
425C2×C42—261no—
426C2×C42—261no—
427C2×C42C22×D1311yescharacteristic
428C2×C42C22×D1311yescharacteristic
429C2×C42C22×D1311yescharacteristic
430C4⋊C8—262no—
431C4⋊C8—262no—
432C4⋊C8—262no—
433#102—134no—
434#102—262no—
435#102—262no—
436#102—262no—
437#97—262no—
438#97—262no—
439C4×C8—262no—
440#95—261no—
441#95—261no—
442#95—261no—
443#95—261no—
444#95—261no—
445#95—261no—
446#95—261no—
447C2×C13—44no—
448C2×C13Q8×C22⋊C411yescharacteristic
449C2×C13#289611yescharacteristic
450C2×C13#289711yescharacteristic
451C2×C13#337011yescharacteristic
452C2×C13#337611yescharacteristic
453C2×C13#338811yescharacteristic
454C2×C13#338911yescharacteristic
455C24—21no—
456C2×Q8—24no—
457C2×Q8—41no—
458C2×Q8—41no—
459C2×Q8—81no—
460C2×Q8—81no—
461C2×Q8C22⋊Dic1314yes—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4Q8×D1312yes—
466C2×D4#613112yes—
467C2×D4C22×Dic1312yes—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—24no—
472C22×C4—24no—
473C22×C4—24no—
474C22×C4—42no—
475C22×C4—42no—
476C22×C4—81no—
477C22×C4—81no—
478C22×C4—81no—
479C22×C4—81no—
480C22×C4—261no—
481C22×C4—261no—
482C22×C4—261no—
483C22×C4—261no—
484C22×C4C2×C22⋊D1311yescharacteristic
485C22×C4C2×C22⋊D1311yescharacteristic
486C22×C4C2×C22⋊D1311yescharacteristic
487C22×C4C2×C22⋊D1311yescharacteristic
488C22×C4C2×C22⋊D1311yescharacteristic
489C22×C4C2×C22⋊D1311yescharacteristic
490C22×C4C23×D1311yescharacteristic
491C2×C8—132no—
492C2×C8—261no—
493C2×C8—261no—
494C2×C8—261no—
495C2×C8—261no—
496C2×C8—261no—
497C2×C8—261no—
498C2×C8—261no—
499C2×C8—261no—
500C2×C8—261no—
501C2×C8—261no—
502C2×C8—261no—
503C4⋊C4—24no—
504C4⋊C4—24no—
505C4⋊C4—24no—
506C4⋊C4—24no—
507C4⋊C4—24no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—132no—
512C4⋊C4—261no—
513C4⋊C4—261no—
514C4⋊C4—261no—
515C4⋊C4—261no—
516C4⋊C4—261no—
517C4⋊C4—261no—
518C4⋊C4—261no—
519C4⋊C4—522no—
520C4⋊C4—1041no—
521C4⋊C4C22⋊Dic1314yes—
522C4⋊C4C22⋊Dic1314yes—
523C4⋊C4C22⋊Dic1314yes—
524C4⋊C4C22×Dic1312yes—
525C4⋊C4C22×Dic1312yes—
526C4⋊C4C22×Dic1312yes—
527C22⋊C4—24no—
528C22⋊C4—24no—
529C22⋊C4—24no—
530C42—522no—
531C42—1041no—
532C42—1041no—
533C42C22×Dic1312yes—
534C42C22×Dic1312yes—
535C42C22×Dic1312yes—
536C42C2×C22⋊D1312yes—
537C42C2×C22⋊D1312yes—
538C42C2×C22⋊D1312yes—
539C13#2252611yescharacteristic, complemented, Sylow
540C23—22no—
541C23—22no—
542C23—22no—
543C23—41no—
544C23—41no—
545C23—41no—
546C23—41no—
547C23C22×C22⋊D1311yescharacteristic
548Q8—44no—
549Q8—84no—
550D4—22no—
551D4—22no—
552D4—22no—
553D4Q8×Dic1314yes—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—48no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—84no—
577C2×C4—84no—
578C2×C4—262no—
579C2×C4—521no—
580C2×C4—521no—
581C2×C4—521no—
582C2×C4—521no—
583C2×C4—521no—
584C2×C4—521no—
585C2×C4—521no—
586C2×C4—521no—
587C2×C4—521no—
588C2×C4—521no—
589C2×C4—521no—
590C2×C4C2×C22⋊Dic1312yes—
591C2×C4C2×C22⋊Dic1312yes—
592C2×C4C2×C22⋊Dic1312yes—
593C2×C4C2×C22⋊Dic1312yes—
594C2×C4C2×C22⋊Dic1312yes—
595C2×C4C2×C22⋊Dic1312yes—
596C2×C4C2×Q8×D1311yescharacteristic
597C2×C4C2×#613111yescharacteristic
598C2×C4#8825411yescharacteristic
599C2×C4#8825411yescharacteristic
600C2×C4C23×Dic1311yescharacteristic
601C2×C4C22×C22⋊D1311yescharacteristic
602C8—262no—
603C8—521no—
604C8—521no—
605C8—521no—
606C22—24no—
607C22—42no—
608C22—42no—
609C22—42no—
610C22—42no—
611C22—42no—
612C22—42no—
613C22Q8×C22⋊D1311yescharacteristic
614C22#1171952211yescharacteristic
615C22#1171952711yescharacteristic
616C22#1171952711yescharacteristic
617C22#1171954011yescharacteristic
618C22#1171954111yescharacteristic
619C22C22×C22⋊Dic1311yescharacteristic
620C4—22no—
621C4—22no—
622C4—22no—
623C4—22no—
624C4—22no—
625C4—22no—
626C4—42no—
627C4—42no—
628C4—42no—
629C4—522no—
630C4—1041no—
631C4—1041no—
632C4—1041no—
633C4C2×Q8×Dic1311yescharacteristic
634C4#1171951711yescharacteristic
635C4Q8×C22⋊D1311yescharacteristic
636C4#1171952211yescharacteristic
637C2—44no—
638C2Q8×C22⋊Dic1311yescharacteristic
639C2#1312335511yescharacteristic
640C2#1312336211yescharacteristic
641C2#1312758911yescharacteristic
642C2#1312766311yescharacteristic
643C2#1312778111yescharacteristic
644C2#1312779011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC2×C13×#554C2
socleC23×C13C22×D4
prime radicalC22×D4×C13C23
cosocleC22×C4×C13C24
hypercenterC2×#554D13
hypocenterC13#22526
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. C2×#11718685C2semidirect
2. #13117793C2semidirect
3. #13115810C2semidirect
4. #13115806C2semidirect
5. #13115802C2semidirect
6. #13115794C2semidirect
7. #13115794C2semidirect
8. #13115789C2semidirect
17. C13×#554C4semidirect
119. #88072Q8semidirect
300. #554Dic13semidirect
539. C13#22526semidirect

Maximal subgroups

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

subgroupindex
C2×#117186852
#131177932
#131158102
#131158062
#131158022
#131157942
#131157892
#131148462
#131148362
#131146612
C4×#880722
C2×C13×#5542
#2252613