Finite Group Databasebeta

← #15899565

Subgroups — #15899565

Order 3328.

1072 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×#11718724C211yesmaximal, characteristic, complemented
2C2×#11718679C211yesmaximal, characteristic
3#13120206C211yesmaximal, characteristic, complemented
4#13116171C211yesmaximal, characteristic, complemented
5#13116161C211yesmaximal, characteristic, complemented
6#13115984C211yesmaximal, characteristic, complemented
7#13115974C211yesmaximal, characteristic, complemented
8#13115806C211yesmaximal, characteristic, complemented
9#13115777C211yesmaximal, characteristic, complemented
10#13115170C211yesmaximal, characteristic
11#13115170C211yesmaximal, characteristic
12#13115097C211yesmaximal, characteristic
13#13115083C211yesmaximal, characteristic
14#13114836C211yesmaximal, characteristic
15C2×C13×#554C211yesmaximal, characteristic
16C13×#554—24no—
17C13×#554—24no—
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—
29C22×#6105C2211yescharacteristic
30C2×C4×Dic26C2211yescharacteristic
31#11718891—21no—
32C2×#88072C2211yescharacteristic
33C2×#88072C2211yescharacteristic
34C2×#88072C2211yescharacteristic
35#11718724—24no—
36#11718679—24no—
37#11718645—21no—
38#11718645—21no—
39#11718634—21no—
40C2×#88050C2211yescharacteristic
41C2×#88050C2211yescharacteristic
42C2×#88050C2211yescharacteristic
43C2×#88048C2211yescharacteristic
44C2×#88047C2211yescharacteristic
45C2×#88047C2211yescharacteristic
46#11718596C2211yescharacteristic
47#11718590C2211yescharacteristic
48#11718590C2211yescharacteristic
49#11718589C2211yescharacteristic
50#11718589C2211yescharacteristic
51C2×C4⋊#1055C2211yescharacteristic
52C2×#88043C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718116C2211yescharacteristic
60#11718116C2211yescharacteristic
61#11718116C2211yescharacteristic
62#11718116C2211yescharacteristic
63C22×Q8×C13—21no—
64C22×Q8×C13D411yescharacteristic
65C22×D4×C13C2311yescharacteristic
66C23×C4×C13—21no—
67C23×C4×C13—21no—
68C23×C4×C13—21no—
69C22×Dic26C2311yescharacteristic
70C13×C4⋊Q8—22no—
71C13×C4⋊Q8—22no—
72C13×#125—22no—
73C13×#125—22no—
74C13×#125—22no—
75C13×#125D414yes—
76C13×C22⋊Q8—28no—
77C13×C22⋊Q8—28no—
78C13×C22⋊Q8—28no—
79C4×Q8×C13—22no—
80C4×Q8×C13—22no—
81C4×D4×C13—22no—
82C4×D4×C13—22no—
83C4×D4×C13—22no—
84C4×D4×C13—22no—
85C4×D4×C13—22no—
86C4×D4×C13D414yes—
87C2×C13×C4⋊C4—28no—
88C2×C13×C4⋊C4—21no—
89C2×C13×C4⋊C4—21no—
90C2×C13×C4⋊C4—21no—
91C2×C13×C4⋊C4—21no—
92C2×C13×C4⋊C4—21no—
93C2×C13×C4⋊C4D411yescharacteristic
94C2×C13×C4⋊C4D411yescharacteristic
95C2×C13×C4⋊C4D411yescharacteristic
96C2×C13×C4⋊C4C2311yescharacteristic
97C2×C13×C4⋊C4C2311yescharacteristic
98C2×C13×C4⋊C4C2311yescharacteristic
99C2×C13×C22⋊C4—21no—
100C2×C13×C22⋊C4—21no—
101C2×C13×C22⋊C4—21no—
102C2×C42×C13C2311yescharacteristic
103C2×C42×C13C2311yescharacteristic
104C2×C42×C13C2311yescharacteristic
105C2×#6105—22no—
106C2×#6105—22no—
107C2×#6105Q814yescomplemented
108C2×C4⋊Dic13—21no—
109C2×C4⋊Dic13—21no—
110C2×C4⋊Dic13C2311yescharacteristic
111C2×C4⋊Dic13C2311yescharacteristic
112C2×C4⋊Dic13C2311yescharacteristic
113C2×#6101—21no—
114C2×#6101—21no—
115C2×#6101—21no—
116C2×C4×Dic13—21no—
117C22×#1055C2311yescharacteristic
118C22×#1055C2311yescharacteristic
119C22×#1055C2311yescharacteristic
120C22×#1055C2311yescharacteristic
121C4×Dic26—22no—
122C4×Dic26—22no—
123#88072—22no—
124#88072—22no—
125#88072—22no—
126#88071—21no—
127#88071—21no—
128#88071—21no—
129#88071—21no—
130#88071—21no—
131#88071—21no—
132#88050—22no—
133#88050—22no—
134#88050—22no—
135#88048—22no—
136#88047—22no—
137#88047—22no—
138C4⋊#1055—22no—
139#88043—22no—
140#24349—131nomaximal, Sylow
141C24×C13—21no—
142C2×Q8×C13—24no—
143C2×Q8×C13—22no—
144C2×Q8×C13—22no—
145C2×Q8×C13—41no—
146C2×Q8×C13—81no—
147C2×Q8×C13—81no—
148C2×D4×C13—21no—
149C2×D4×C13—21no—
150C2×D4×C13—21no—
151C2×D4×C13C2×D412yes—
152C2×D4×C13C2×Q812yes—
153C2×D4×C13#4112yes—
154C22×C4×C13—24no—
155C22×C4×C13—21no—
156C22×C4×C13—21no—
157C22×C4×C13—21no—
158C22×C4×C13—24no—
159C22×C4×C13—24no—
160C22×C4×C13—42no—
161C22×C4×C13—42no—
162C22×C4×C13—81no—
163C22×C4×C13—81no—
164C22×C4×C13—81no—
165C22×C4×C13—81no—
166C22×C4×C13C2×D411yescharacteristic
167C22×C4×C13C2×D411yescharacteristic
168C22×C4×C13C2×D411yescharacteristic
169C22×C4×C13C2×D411yescharacteristic
170C22×C4×C13C2×D411yescharacteristic
171C22×C4×C13C2×D411yescharacteristic
172C22×C4×C13C2411yescharacteristic
173C22×Dic13—21no—
174C22×Dic13—21no—
175C22×Dic13—21no—
176C22×Dic13—21no—
177C2×Dic26—21no—
178C2×Dic26—21no—
179C2×Dic26—21no—
180C2×Dic26—21no—
181C2×Dic26—21no—
182C2×Dic26C2×Q812yes—
183C13×C4⋊C4—24no—
184C13×C4⋊C4—24no—
185C13×C4⋊C4—24no—
186C13×C4⋊C4—22no—
187C13×C4⋊C4—24no—
188C13×C4⋊C4—24no—
189C13×C4⋊C4—22no—
190C13×C4⋊C4—22no—
191C13×C4⋊C4—21no—
192C13×C4⋊C4—21no—
193C13×C4⋊C4—21no—
194C13×C4⋊C4C2×D412yes—
195C13×C4⋊C4C2×D412yes—
196C13×C4⋊C4C2×D412yes—
197C13×C22⋊C4—24no—
198C13×C22⋊C4—24no—
199C13×C22⋊C4—24no—
200C42×C13—21no—
201C42×C13—21no—
202C42×C13—21no—
203C42×C13—21no—
204C42×C13C2×D412yes—
205C42×C13C2×D412yes—
206#6105—28no—
207C4⋊Dic13—21no—
208C4⋊Dic13—21no—
209C4⋊Dic13—21no—
210C4⋊Dic13—21no—
211C4⋊Dic13—21no—
212C4⋊Dic13—21no—
213C4⋊Dic13—42no—
214C4⋊Dic13—81no—
215#6101—42no—
216#6101—81no—
217#6101—81no—
218C4×Dic13—42no—
219C2×#1055—21no—
220C2×#1055—21no—
221C2×#1055—21no—
222C2×#1055—21no—
223C2×#1055—21no—
224C2×#1055—21no—
225C2×#1055—21no—
226C2×#1055—21no—
227C2×#1055—21no—
228C2×#1055—21no—
229C2×#1055—21no—
230C2×#1055C2×Q812yes—
231C2×#554D1311yescharacteristic
232C2×#479—131no—
233C2×#440—131no—
234#2582—131no—
235#2059—131no—
236#2057—131no—
237#2026—131no—
238#2024—131no—
239#1992—131no—
240#1985—131no—
241#1877—131no—
242#1877—131no—
243#1864—131no—
244#1862—131no—
245#1802—131no—
246C23×C13—22no—
247C23×C13—22no—
248C23×C13—22no—
249C23×C13—41no—
250C23×C13—41no—
251C23×C13—41no—
252C23×C13—41no—
253C23×C13C22×D411yescharacteristic
254Q8×C13—44no—
255Q8×C13—84no—
256D4×C13—22no—
257D4×C13—22no—
258D4×C13—22no—
259D4×C13C22⋊Q814yes—
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—21no—
268C2×C4×C13—21no—
269C2×C4×C13—22no—
270C2×C4×C13—22no—
271C2×C4×C13—22no—
272C2×C4×C13—21no—
273C2×C4×C13—21no—
274C2×C4×C13—21no—
275C2×C4×C13—21no—
276C2×C4×C13—21no—
277C2×C4×C13—21no—
278C2×C4×C13—48no—
279C2×C4×C13—41no—
280C2×C4×C13—41no—
281C2×C4×C13—41no—
282C2×C4×C13—41no—
283C2×C4×C13—41no—
284C2×C4×C13—41no—
285C2×C4×C13—84no—
286C2×C4×C13—84no—
287C2×C4×C13#12012yes—
288C2×C4×C13#12012yes—
289C2×C4×C13#13712yes—
290C2×C4×C13C22×D411yescharacteristic
291C2×C4×C13C22×D411yescharacteristic
292C2×C4×C13C22×Q811yescharacteristic
293C2×C4×C13C2×#4111yescharacteristic
294C2×C4×C132−1+411yescharacteristic
295C2×C4×C132−1+411yescharacteristic
296C2×Dic13—22no—
297C2×Dic13—41no—
298C2×Dic13—41no—
299C2×Dic13—41no—
300C2×Dic13—41no—
301C2×Dic13—41no—
302C2×Dic13—41no—
303C2×Dic13—41no—
304C2×Dic13—41no—
305C2×Dic13—41no—
306C2×Dic13—41no—
307C2×Dic13—41no—
308Dic26—22no—
309Dic26—22no—
310Dic26—41no—
311Dic26—41no—
312#1055—22no—
313#1055—41no—
314#1055—41no—
315#1055—41no—
316C22×SD16—131no—
317#554—24no—
318#554—24no—
319C2×C4⋊Q8C2×D1311yescharacteristic
320C2×#125C2×D1311yescharacteristic
321C2×#125C2×D1311yescharacteristic
322C2×C22⋊Q8—21no—
323C2×C22⋊Q8—21no—
324C2×C22⋊Q8—21no—
325C2×C4×Q8—131no—
326C2×C4×Q8C2×D1311yescharacteristic
327C2×C4×D4C2×D1311yescharacteristic
328C2×C4×D4C2×D1311yescharacteristic
329C2×C4×D4C2×D1311yescharacteristic
330C22×C4⋊C4—21no—
331#479—264no—
332#440—264no—
333C2×#107—131no—
334C2×#107—131no—
335C2×#106—131no—
336C2×C4⋊C8—131no—
337C2×#103—131no—
338C2×#103—131no—
339C2×#103—131no—
340C2×#102—131no—
341C2×#102—131no—
342C2×#102—131no—
343C2×#97—131no—
344#398—261no—
345#398—261no—
346#391—131no—
347#391—131no—
348#391—261no—
349#389—131no—
350#389—131no—
351#389—261no—
352#384—131no—
353#340—131no—
354#340—131no—
355#340—131no—
356#340—131no—
357#340—131no—
358#340—131no—
359#336—131no—
360#336—131no—
361#336—131no—
362#336—131no—
363C22×C13—24no—
364C22×C13—42no—
365C22×C13—42no—
366C22×C13—42no—
367C22×C13—42no—
368C22×C13—42no—
369C22×C13—42no—
370C22×C13C2×#12011yescharacteristic
371C22×C13#54811yescharacteristic
372C22×C13D4×Q811yescharacteristic
373C22×C13C2×#13711yescharacteristic
374C22×C13#57511yescharacteristic
375C22×C13#57611yescharacteristic
376C22×C13#57711yescharacteristic
377C4×C13—22no—
378C4×C13—22no—
379C4×C13—22no—
380C4×C13—41no—
381C4×C13—42no—
382C4×C13—41no—
383C4×C13—41no—
384C4×C13—42no—
385C4×C13—42no—
386C4×C13C2×C22⋊Q811yescharacteristic
387C4×C13#53611yescharacteristic
388C4×C13#54811yescharacteristic
389C4×C13D4×Q811yescharacteristic
390Dic13—42no—
391Dic13—81no—
392Dic13—81no—
393Dic13—81no—
394C22×Q8—21no—
395C22×Q8—131no—
396C22×Q8C22⋊D1311yescharacteristic
397C22×D4C22×D1311yescharacteristic
398C23×C4—21no—
399C23×C4—21no—
400C23×C4—21no—
401C2×SD16—134no—
402C2×SD16—262no—
403C2×SD16—262no—
404C22×C8—131no—
405C22×C8—131no—
406C22×C8—131no—
407C22×C8—131no—
408C4⋊Q8—22no—
409C4⋊Q8—22no—
410#125—22no—
411#125—22no—
412#125—22no—
413#125C22⋊D1314yes—
414C22⋊Q8—28no—
415C22⋊Q8—28no—
416C22⋊Q8—28no—
417C4×Q8—22no—
418C4×Q8—22no—
419C4×Q8—262no—
420C4×Q8—262no—
421C4×D4—22no—
422C4×D4—22no—
423C4×D4—22no—
424C4×D4—22no—
425C4×D4—22no—
426C4×D4C22⋊D1314yes—
427C2×C4⋊C4—28no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—131no—
434C2×C4⋊C4—131no—
435C2×C4⋊C4—131no—
436C2×C4⋊C4—261no—
437C2×C4⋊C4—261no—
438C2×C4⋊C4—261no—
439C2×C4⋊C4—261no—
440C2×C4⋊C4—261no—
441C2×C4⋊C4C22⋊D1311yescharacteristic
442C2×C4⋊C4C22⋊D1311yescharacteristic
443C2×C4⋊C4C22⋊D1311yescharacteristic
444C2×C4⋊C4C22×D1311yescharacteristic
445C2×C4⋊C4C22×D1311yescharacteristic
446C2×C4⋊C4C22×D1311yescharacteristic
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C42—261no—
451C2×C42C22×D1311yescharacteristic
452C2×C42C22×D1311yescharacteristic
453C2×C42C22×D1311yescharacteristic
454#107—262no—
455#107—262no—
456#106—262no—
457C4⋊C8—262no—
458#103—262no—
459#103—262no—
460#103—262no—
461#102—262no—
462#102—262no—
463#102—262no—
464#97—262no—
465#95—261no—
466#95—261no—
467#95—261no—
468#95—261no—
469#95—261no—
470#95—261no—
471C2×C13—44no—
472C2×C13#240911yescharacteristic
473C2×C13#300711yescharacteristic
474C2×C13#301211yescharacteristic
475C2×C13#337011yescharacteristic
476C2×C13#337211yescharacteristic
477C2×C13#338511yescharacteristic
478C2×C13#338811yescharacteristic
479C24—21no—
480C2×Q8—24no—
481C2×Q8—22no—
482C2×Q8—22no—
483C2×Q8—41no—
484C2×Q8—81no—
485C2×Q8—81no—
486C2×Q8—132no—
487C2×Q8—261no—
488C2×Q8—261no—
489C2×Q8—261no—
490C2×Q8—261no—
491C2×Q8—261no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4Q8×D1312yes—
496C2×D4#613112yes—
497C2×D4C2×C22⋊D1312yes—
498C22×C4—24no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—24no—
503C22×C4—24no—
504C22×C4—42no—
505C22×C4—42no—
506C22×C4—81no—
507C22×C4—81no—
508C22×C4—81no—
509C22×C4—81no—
510C22×C4—261no—
511C22×C4—261no—
512C22×C4—261no—
513C22×C4—261no—
514C22×C4C2×C22⋊D1311yescharacteristic
515C22×C4C2×C22⋊D1311yescharacteristic
516C22×C4C2×C22⋊D1311yescharacteristic
517C22×C4C2×C22⋊D1311yescharacteristic
518C22×C4C2×C22⋊D1311yescharacteristic
519C22×C4C2×C22⋊D1311yescharacteristic
520C22×C4C23×D1311yescharacteristic
521SD16—268no—
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×C8—261no—
534C4⋊C4—24no—
535C4⋊C4—24no—
536C4⋊C4—24no—
537C4⋊C4—22no—
538C4⋊C4—24no—
539C4⋊C4—24no—
540C4⋊C4—22no—
541C4⋊C4—22no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—261no—
546C4⋊C4—261no—
547C4⋊C4—261no—
548C4⋊C4—261no—
549C4⋊C4—261no—
550C4⋊C4—261no—
551C4⋊C4—522no—
552C4⋊C4—522no—
553C4⋊C4—1041no—
554C4⋊C4—1041no—
555C4⋊C4—1041no—
556C4⋊C4C2×C22⋊D1312yes—
557C4⋊C4C2×C22⋊D1312yes—
558C4⋊C4C2×C22⋊D1312yes—
559C22⋊C4—24no—
560C22⋊C4—24no—
561C22⋊C4—24no—
562C42—21no—
563C42—21no—
564C42—21no—
565C42—21no—
566C42—522no—
567C42C2×C22⋊D1312yes—
568C42C2×C22⋊D1312yes—
569C13#2434911yescharacteristic, complemented, Sylow
570C23—22no—
571C23—22no—
572C23—22no—
573C23—41no—
574C23—41no—
575C23—41no—
576C23—41no—
577C23C22×C22⋊D1311yescharacteristic
578Q8—44no—
579Q8—84no—
580Q8—262no—
581Q8—262no—
582Q8—521no—
583Q8—521no—
584D4—22no—
585D4—22no—
586D4—22no—
587D4#8820014yes—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—48no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—84no—
614C2×C4—84no—
615C2×C4—262no—
616C2×C4—521no—
617C2×C4—521no—
618C2×C4—521no—
619C2×C4—521no—
620C2×C4—521no—
621C2×C4—521no—
622C2×C4—521no—
623C2×C4—521no—
624C2×C4—521no—
625C2×C4—521no—
626C2×C4—521no—
627C2×C4#8820512yes—
628C2×C4#8820712yes—
629C2×C4#8820712yes—
630C2×C4C2×Q8×D1311yescharacteristic
631C2×C4C2×#613111yescharacteristic
632C2×C4#8825411yescharacteristic
633C2×C4#8825411yescharacteristic
634C2×C4C22×C22⋊D1311yescharacteristic
635C2×C4C22×C22⋊D1311yescharacteristic
636C8—262no—
637C8—521no—
638C8—521no—
639C8—521no—
640C22—24no—
641C22—42no—
642C22—42no—
643C22—42no—
644C22—42no—
645C22—42no—
646C22—42no—
647C22Q8×C22⋊D1311yescharacteristic
648C22#1171952211yescharacteristic
649C22#1171952711yescharacteristic
650C22C2×#8820511yescharacteristic
651C22#1171954011yescharacteristic
652C22#1171954111yescharacteristic
653C22C2×#8820711yescharacteristic
654C4—22no—
655C4—22no—
656C4—22no—
657C4—41no—
658C4—42no—
659C4—41no—
660C4—41no—
661C4—42no—
662C4—42no—
663C4—522no—
664C4—1041no—
665C4—1041no—
666C4—1041no—
667C4C2×#8820011yescharacteristic
668C4Q8×C22⋊D1311yescharacteristic
669C4#1171952111yescharacteristic
670C4#1171952211yescharacteristic
671C2—44no—
672C2#1311819511yescharacteristic
673C2#1312409611yescharacteristic
674C2#1312414011yescharacteristic
675C2#1312758911yescharacteristic
676C2#1312761711yescharacteristic
677C2#1312774611yescharacteristic
678C2#1312778111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC2×C13×#554C2
socleC23×C13C22×D4
prime radicalC22×D4×C13C23
hypercenterC2×#554D13
hypocenterC13#24349
LCSG ▷ C22×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×#11718724C2semidirect
3. #13120206C2semidirect
4. #13116171C2semidirect
5. #13116161C2semidirect
6. #13115984C2semidirect
7. #13115974C2semidirect
8. #13115806C2semidirect
9. #13115777C2semidirect
107. C2×#6105Q8semidirect
569. C13#24349semidirect

Maximal subgroups

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

subgroupindex
C2×#117187242
C2×#117186792
#131202062
#131161712
#131161612
#131159842
#131159742
#131158062
#131157772
#131151702
#131150972
#131150832
#131148362
C2×C13×#5542
#2434913