Finite Group Databasebeta

← #15899417

Subgroups — #15899417

Order 3328.

1070 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718724C211yesmaximal, characteristic, complemented
2C2×C4×#6105C211yesmaximal, characteristic
3#13120202C211yesmaximal, characteristic, complemented
4#13116171C211yesmaximal, characteristic, complemented
5#13116166C211yesmaximal, characteristic, complemented
6#13115984C211yesmaximal, characteristic, complemented
7#13115974C211yesmaximal, characteristic, complemented
8#13115802C211yesmaximal, characteristic, complemented
9#13115773C211yesmaximal, characteristic, complemented
10#13115170C211yesmaximal, characteristic
11#13115170C211yesmaximal, characteristic
12#13115097C211yesmaximal, characteristic
13#13115083C211yesmaximal, characteristic
14#13114846C211yesmaximal, 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#11718890—21no—
32C2×#88072C2211yescharacteristic
33C2×#88072C2211yescharacteristic
34C2×#88072C2211yescharacteristic
35#11718724—24no—
36C4×#6105—24no—
37#11718643—21no—
38#11718639—21no—
39#11718639—21no—
40C2×#88050C2211yescharacteristic
41C2×#88050C2211yescharacteristic
42C2×#88050C2211yescharacteristic
43C2×#88048C2211yescharacteristic
44C2×#88048C2211yescharacteristic
45C2×#88047C2211yescharacteristic
46#11718597C2211yescharacteristic
47#11718590C2211yescharacteristic
48#11718590C2211yescharacteristic
49#11718589C2211yescharacteristic
50#11718589C2211yescharacteristic
51C2×C4⋊#1055C2211yescharacteristic
52C2×C4×#1055C2211yescharacteristic
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⋊Dic13C2311yescharacteristic
109C2×C4⋊Dic13C2311yescharacteristic
110C2×C4⋊Dic13C2311yescharacteristic
111C2×#6101—21no—
112C2×#6101—21no—
113C2×#6101—21no—
114C2×C4×Dic13—21no—
115C22×#1055C2311yescharacteristic
116C22×#1055C2311yescharacteristic
117C22×#1055C2311yescharacteristic
118C22×#1055C2311yescharacteristic
119C4×Dic26—22no—
120C4×Dic26—22no—
121#88072—22no—
122#88072—22no—
123#88072—22no—
124#88071—21no—
125#88071—21no—
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#88048—22no—
137#88047—22no—
138C4⋊#1055—22no—
139C4×#1055—22no—
140#24337—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—
213#6101—42no—
214#6101—42no—
215#6101—42no—
216C4×Dic13—42no—
217C2×#1055—21no—
218C2×#1055—21no—
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×#1055C2×Q812yes—
229C2×#554D1311yescharacteristic
230C2×#479—131no—
231C2×C4×SD16—131no—
232#2581—131no—
233#2059—131no—
234#2058—131no—
235#2026—131no—
236#2024—131no—
237#1991—131no—
238#1984—131no—
239#1877—131no—
240#1877—131no—
241#1864—131no—
242#1862—131no—
243#1804—131no—
244C23×C13—22no—
245C23×C13—22no—
246C23×C13—22no—
247C23×C13—41no—
248C23×C13—41no—
249C23×C13—41no—
250C23×C13—41no—
251C23×C13C22×D411yescharacteristic
252Q8×C13—44no—
253Q8×C13—84no—
254D4×C13—22no—
255D4×C13—22no—
256D4×C13—22no—
257D4×C13C22⋊Q814yes—
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—22no—
268C2×C4×C13—22no—
269C2×C4×C13—22no—
270C2×C4×C13—21no—
271C2×C4×C13—21no—
272C2×C4×C13—21no—
273C2×C4×C13—21no—
274C2×C4×C13—21no—
275C2×C4×C13—21no—
276C2×C4×C13—48no—
277C2×C4×C13—41no—
278C2×C4×C13—41no—
279C2×C4×C13—41no—
280C2×C4×C13—41no—
281C2×C4×C13—41no—
282C2×C4×C13—41no—
283C2×C4×C13—84no—
284C2×C4×C13—84no—
285C2×C4×C13#12012yes—
286C2×C4×C13#12012yes—
287C2×C4×C13#13512yes—
288C2×C4×C13C22×D411yescharacteristic
289C2×C4×C13C22×D411yescharacteristic
290C2×C4×C13C22×Q811yescharacteristic
291C2×C4×C13C2×#4111yescharacteristic
292C2×C4×C132−1+411yescharacteristic
293C2×C4×C132−1+411yescharacteristic
294C2×Dic13—22no—
295C2×Dic13—41no—
296C2×Dic13—41no—
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—
306Dic26—22no—
307Dic26—22no—
308Dic26—41no—
309Dic26—41no—
310#1055—22no—
311#1055—41no—
312#1055—41no—
313#1055—41no—
314C22×SD16—131no—
315#554—24no—
316#554—24no—
317C2×C4⋊Q8C2×D1311yescharacteristic
318C2×#125C2×D1311yescharacteristic
319C2×#125C2×D1311yescharacteristic
320C2×C22⋊Q8—21no—
321C2×C22⋊Q8—21no—
322C2×C22⋊Q8—21no—
323C2×C4×Q8—131no—
324C2×C4×Q8C2×D1311yescharacteristic
325C2×C4×D4C2×D1311yescharacteristic
326C2×C4×D4C2×D1311yescharacteristic
327C2×C4×D4C2×D1311yescharacteristic
328C22×C4⋊C4—21no—
329#479—264no—
330C4×SD16—264no—
331C2×#107—131no—
332C2×#106—131no—
333C2×#106—131no—
334C2×C4⋊C8—131no—
335C2×#103—131no—
336C2×#103—131no—
337C2×#103—131no—
338C2×#102—131no—
339C2×#102—131no—
340C2×#102—131no—
341C2×C4×C8—131no—
342#400—261no—
343#395—261no—
344#391—131no—
345#391—131no—
346#389—131no—
347#389—131no—
348#387—261no—
349#387—261no—
350#382—131no—
351#340—131no—
352#340—131no—
353#340—131no—
354#340—131no—
355#340—131no—
356#340—131no—
357#336—131no—
358#336—131no—
359#336—131no—
360#336—131no—
361C22×C13—24no—
362C22×C13—42no—
363C22×C13—42no—
364C22×C13—42no—
365C22×C13—42no—
366C22×C13—42no—
367C22×C13—42no—
368C22×C13C2×#12011yescharacteristic
369C22×C13#54811yescharacteristic
370C22×C13D4×Q811yescharacteristic
371C22×C13C2×#13511yescharacteristic
372C22×C13#57511yescharacteristic
373C22×C13#57711yescharacteristic
374C22×C13#57711yescharacteristic
375C4×C13—22no—
376C4×C13—22no—
377C4×C13—22no—
378C4×C13—41no—
379C4×C13—42no—
380C4×C13—41no—
381C4×C13—41no—
382C4×C13—42no—
383C4×C13—42no—
384C4×C13C2×C22⋊Q811yescharacteristic
385C4×C13#53611yescharacteristic
386C4×C13#54811yescharacteristic
387C4×C13D4×Q811yescharacteristic
388Dic13—42no—
389Dic13—81no—
390Dic13—81no—
391Dic13—81no—
392C22×Q8—21no—
393C22×Q8—131no—
394C22×Q8C22⋊D1311yescharacteristic
395C22×D4C22×D1311yescharacteristic
396C23×C4—21no—
397C23×C4—21no—
398C23×C4—21no—
399C2×SD16—134no—
400C2×SD16—262no—
401C2×SD16—262no—
402C22×C8—131no—
403C22×C8—131no—
404C22×C8—131no—
405C22×C8—131no—
406C4⋊Q8—22no—
407C4⋊Q8—22no—
408#125—22no—
409#125—22no—
410#125—22no—
411#125C22⋊D1314yes—
412C22⋊Q8—28no—
413C22⋊Q8—28no—
414C22⋊Q8—28no—
415C4×Q8—22no—
416C4×Q8—22no—
417C4×Q8—262no—
418C4×Q8—262no—
419C4×D4—22no—
420C4×D4—22no—
421C4×D4—22no—
422C4×D4—22no—
423C4×D4—22no—
424C4×D4C22⋊D1314yes—
425C2×C4⋊C4—28no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—131no—
432C2×C4⋊C4—131no—
433C2×C4⋊C4—131no—
434C2×C4⋊C4—261no—
435C2×C4⋊C4—261no—
436C2×C4⋊C4—261no—
437C2×C4⋊C4C22⋊D1311yescharacteristic
438C2×C4⋊C4C22⋊D1311yescharacteristic
439C2×C4⋊C4C22⋊D1311yescharacteristic
440C2×C4⋊C4C22×D1311yescharacteristic
441C2×C4⋊C4C22×D1311yescharacteristic
442C2×C4⋊C4C22×D1311yescharacteristic
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C42—261no—
447C2×C42C22×D1311yescharacteristic
448C2×C42C22×D1311yescharacteristic
449C2×C42C22×D1311yescharacteristic
450#107—262no—
451#106—262no—
452#106—262no—
453C4⋊C8—262no—
454#103—262no—
455#103—262no—
456#103—262no—
457#102—262no—
458#102—262no—
459#102—262no—
460C4×C8—262no—
461#95—261no—
462#95—261no—
463#95—261no—
464#95—261no—
465#95—261no—
466#95—261no—
467#95—261no—
468#95—261no—
469C2×C13—44no—
470C2×C13#240911yescharacteristic
471C2×C13#300211yescharacteristic
472C2×C13#300911yescharacteristic
473C2×C13#336011yescharacteristic
474C2×C13#337611yescharacteristic
475C2×C13#338111yescharacteristic
476C2×C13#338811yescharacteristic
477C24—21no—
478C2×Q8—24no—
479C2×Q8—22no—
480C2×Q8—22no—
481C2×Q8—41no—
482C2×Q8—81no—
483C2×Q8—81no—
484C2×Q8—132no—
485C2×Q8—261no—
486C2×Q8—261no—
487C2×Q8—261no—
488C2×Q8—261no—
489C2×Q8—261no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4Q8×D1312yes—
494C2×D4#613112yes—
495C2×D4C2×C22⋊D1312yes—
496C22×C4—24no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—24no—
501C22×C4—24no—
502C22×C4—42no—
503C22×C4—42no—
504C22×C4—81no—
505C22×C4—81no—
506C22×C4—81no—
507C22×C4—81no—
508C22×C4—261no—
509C22×C4—261no—
510C22×C4—261no—
511C22×C4—261no—
512C22×C4C2×C22⋊D1311yescharacteristic
513C22×C4C2×C22⋊D1311yescharacteristic
514C22×C4C2×C22⋊D1311yescharacteristic
515C22×C4C2×C22⋊D1311yescharacteristic
516C22×C4C2×C22⋊D1311yescharacteristic
517C22×C4C2×C22⋊D1311yescharacteristic
518C22×C4C23×D1311yescharacteristic
519SD16—268no—
520C2×C8—132no—
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×C8—261no—
530C2×C8—261no—
531C2×C8—261no—
532C4⋊C4—24no—
533C4⋊C4—24no—
534C4⋊C4—24no—
535C4⋊C4—22no—
536C4⋊C4—24no—
537C4⋊C4—24no—
538C4⋊C4—22no—
539C4⋊C4—22no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—261no—
544C4⋊C4—261no—
545C4⋊C4—261no—
546C4⋊C4—261no—
547C4⋊C4—261no—
548C4⋊C4—261no—
549C4⋊C4—522no—
550C4⋊C4—522no—
551C4⋊C4—522no—
552C4⋊C4C2×C22⋊D1312yes—
553C4⋊C4C2×C22⋊D1312yes—
554C4⋊C4C2×C22⋊D1312yes—
555C22⋊C4—24no—
556C22⋊C4—24no—
557C22⋊C4—24no—
558C42—21no—
559C42—21no—
560C42—21no—
561C42—21no—
562C42—522no—
563C42C2×C22⋊D1312yes—
564C42C2×C22⋊D1312yes—
565C13#2433711yescharacteristic, complemented, Sylow
566C23—22no—
567C23—22no—
568C23—22no—
569C23—41no—
570C23—41no—
571C23—41no—
572C23—41no—
573C23C22×C22⋊D1311yescharacteristic
574Q8—44no—
575Q8—84no—
576Q8—262no—
577Q8—262no—
578Q8—521no—
579Q8—521no—
580D4—22no—
581D4—22no—
582D4—22no—
583D4#8820014yes—
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—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—48no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—84no—
610C2×C4—84no—
611C2×C4—262no—
612C2×C4—521no—
613C2×C4—521no—
614C2×C4—521no—
615C2×C4—521no—
616C2×C4—521no—
617C2×C4—521no—
618C2×C4—521no—
619C2×C4—521no—
620C2×C4—521no—
621C2×C4—521no—
622C2×C4—521no—
623C2×C4#8820412yes—
624C2×C4#8820712yes—
625C2×C4#8820712yes—
626C2×C4C2×Q8×D1311yescharacteristic
627C2×C4C2×#613111yescharacteristic
628C2×C4#8825411yescharacteristic
629C2×C4#8825411yescharacteristic
630C2×C4C22×C22⋊D1311yescharacteristic
631C2×C4C22×C22⋊D1311yescharacteristic
632C8—262no—
633C8—521no—
634C8—521no—
635C8—521no—
636C22—24no—
637C22—42no—
638C22—42no—
639C22—42no—
640C22—42no—
641C22—42no—
642C22—42no—
643C22Q8×C22⋊D1311yescharacteristic
644C22#1171952211yescharacteristic
645C22C2×#8820411yescharacteristic
646C22#1171952711yescharacteristic
647C22#1171954111yescharacteristic
648C22#1171954111yescharacteristic
649C22C2×#8820711yescharacteristic
650C4—22no—
651C4—22no—
652C4—22no—
653C4—41no—
654C4—41no—
655C4—42no—
656C4—42no—
657C4—41no—
658C4—42no—
659C4—522no—
660C4—1041no—
661C4—1041no—
662C4—1041no—
663C4C2×#8820011yescharacteristic
664C4Q8×C22⋊D1311yescharacteristic
665C4#1171952111yescharacteristic
666C4#1171952211yescharacteristic
667C2—44no—
668C2#1311819511yescharacteristic
669C2#1312405411yescharacteristic
670C2#1312411311yescharacteristic
671C2#1312748511yescharacteristic
672C2#1312766311yescharacteristic
673C2#1312771111yescharacteristic
674C2#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#24337
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. #13120202C2semidirect
4. #13116171C2semidirect
5. #13116166C2semidirect
6. #13115984C2semidirect
7. #13115974C2semidirect
8. #13115802C2semidirect
9. #13115773C2semidirect
107. C2×#6105Q8semidirect
565. C13#24337semidirect

Maximal subgroups

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

subgroupindex
C2×#117187242
C2×C4×#61052
#131202022
#131161712
#131161662
#131159842
#131159742
#131158022
#131157732
#131151702
#131150972
#131150832
#131148462
C2×C13×#5542
#2433713