Finite Group Databasebeta

← #15925394

Subgroups — #15925394

Order 3328.

966 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×#11718420C211yesmaximal, characteristic, complemented
2C22×#88047C211yesmaximal, characteristic, complemented
3#13118532C211yesmaximal, characteristic, complemented
4#13117856C211yesmaximal, characteristic
5#13116362C211yesmaximal, characteristic, complemented
6#13116328C211yesmaximal, characteristic, complemented
7#13116220C211yesmaximal, characteristic, complemented
8#13116163C211yesmaximal, characteristic, complemented
9#13115593C211yesmaximal, characteristic, complemented
10#13115410C211yesmaximal, characteristic, complemented
11#13115265C211yesmaximal, characteristic
12#13115081C211yesmaximal, characteristic, complemented
13#13115026C211yesmaximal, characteristic, complemented
14#13115013C211yesmaximal, characteristic, complemented
15C13×#1874C211yesmaximal, characteristic
16C2×C13×#121C2211yescharacteristic
17C22×C13×C4⋊C4C2211yescharacteristic
18C2×D4×Dic13—21no—
19C2×D4×Dic13C2211yescharacteristic
20C22×C4⋊Dic13C2211yescharacteristic
21C2×#88178—21no—
22C23×#1055C2211yescharacteristic
23C2×#88142C2211yescharacteristic
24C2×C13×#102C2211yescharacteristic
25C2×C13×#102C2211yescharacteristic
26C2×C13×C22⋊C8C2211yescharacteristic
27#11718882C2211yescharacteristic
28#11718881—21no—
29C2×#88072C2211yescharacteristic
30C2×#88072C2211yescharacteristic
31#11718873C2211yescharacteristic
32#11718871—21no—
33C4×C22⋊Dic13C2211yescharacteristic
34C2×#88058C2211yescharacteristic
35C2×#88058C2211yescharacteristic
36C2×#88054C2211yescharacteristic
37C2×#88054C2211yescharacteristic
38#11718646C2211yescharacteristic
39#11718646C2211yescharacteristic
40#11718645—21no—
41#11718640—21no—
42#11718637C2211yescharacteristic
43C4⋊C4×Dic13C2211yescharacteristic
44#11718634C2211yescharacteristic
45C2×#88047—24no—
46C2×#88047C2211yescharacteristic
47C2×#88047C2211yescharacteristic
48C2×#88047C2211yescharacteristic
49C2×#88047C2211yescharacteristic
50#11718612—21no—
51#11718611—21no—
52#11718420—24no—
53C13×#340C2211yescharacteristic
54C13×#340C2211yescharacteristic
55#11718143C2211yescharacteristic
56#11718143C2211yescharacteristic
57#11718142C2211yescharacteristic
58#11718142C2211yescharacteristic
59#11718121C2211yescharacteristic
60#11718121C2211yescharacteristic
61C22×D4×C13—21no—
62C22×D4×C13C2311yescharacteristic
63C23×C4×C13—21no—
64C23×C4×C13C2311yescharacteristic
65C23×Dic13—21no—
66C23×Dic13—21no—
67C22×Dic26—21no—
68C22×C8×C13C2311yescharacteristic
69C22×C8×C13C2311yescharacteristic
70C13×#121—22no—
71C13×#121Q814yescomplemented
72C2×C13×C4⋊C4—22no—
73C2×C13×C4⋊C4—21no—
74C2×C13×C4⋊C4—41no—
75C2×C13×C4⋊C4C2311yescharacteristic
76C2×C13×C4⋊C4C2311yescharacteristic
77C2×C13×C4⋊C4C2311yescharacteristic
78C2×C13×C22⋊C4—21no—
79C2×C22⋊Dic13—21no—
80C2×C22⋊Dic13—21no—
81C2×C22⋊Dic13—21no—
82C2×C22⋊Dic13—21no—
83C2×C22⋊Dic13D411yescharacteristic
84C2×C22⋊Dic13D411yescharacteristic
85D4×Dic13—22no—
86D4×Dic13—41no—
87D4×Dic13—44no—
88C2×C4⋊Dic13—22no—
89C2×C4⋊Dic13—21no—
90C2×C4⋊Dic13—21no—
91C2×C4⋊Dic13—21no—
92C2×C4⋊Dic13—41no—
93C2×C4⋊Dic13C2311yescharacteristic
94C2×C4⋊Dic13C2311yescharacteristic
95C2×C4⋊Dic13C2311yescharacteristic
96C2×C4⋊Dic13C2311yescharacteristic
97#88178—44no—
98C2×#6101—21no—
99C2×#6101—21no—
100C2×#6101—21no—
101C2×#6101—21no—
102C2×C4×Dic13—21no—
103C2×C4×Dic13C2311yescharacteristic
104C2×C4×Dic13C2311yescharacteristic
105C22×#1055—22no—
106C22×#1055—22no—
107C22×#1055—22no—
108C22×#1055C2311yescharacteristic
109C22×#1055C2311yescharacteristic
110#88142—22no—
111#88142—41no—
112C13×#102—22no—
113C13×#102—41no—
114C13×C22⋊C8—22no—
115#88072—22no—
116#88072—22no—
117#88071—21no—
118#88071—21no—
119#88071—21no—
120#88071—21no—
121#88071—21no—
122#88071D411yescharacteristic
123#88071D411yescharacteristic
124#88058—22no—
125#88058—41no—
126#88054—22no—
127#88054—22no—
128#88047—22no—
129#88047—22no—
130#88047—22no—
131#88047D414yescomplemented
132#26336—131nomaximal, Sylow
133C24×C13—21no—
134C24×C13C2×D411yescharacteristic
135C2×D4×C13—24no—
136C2×D4×C13—21no—
137C2×D4×C13—21no—
138C2×D4×C13—21no—
139C2×D4×C13—21no—
140C2×D4×C13—21no—
141C2×D4×C13—42no—
142C2×D4×C13—42no—
143C2×D4×C13C2×Q812yes—
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×C13—21no—
151C22×C4×C13—42no—
152C22×C4×C13—42no—
153C22×C4×C13—81no—
154C22×C4×C13C2×D411yescharacteristic
155C22×C4×C13C2×Q812yes—
156C22×C4×C13#4112yes—
157C22×C4×C13C2411yescharacteristic
158C22×Dic13—21no—
159C22×Dic13—21no—
160C22×Dic13—21no—
161C22×Dic13—21no—
162C22×Dic13—42no—
163C22×Dic13—42no—
164C22×Dic13—42no—
165C22×Dic13—42no—
166C22×Dic13—81no—
167C22×Dic13—81no—
168C22×Dic13C2×D411yescharacteristic
169C22×Dic13C2×D411yescharacteristic
170C22×Dic13C2×D411yescharacteristic
171C22×Dic13C2×D411yescharacteristic
172C2×Dic26—42no—
173C2×Dic26—42no—
174C2×Dic26—81no—
175C2×C8×C13—21no—
176C2×C8×C13—21no—
177C2×C8×C13—21no—
178C2×C8×C13—21no—
179C2×C8×C13—21no—
180C2×C8×C13—21no—
181C13×C4⋊C4—21no—
182C13×C4⋊C4—21no—
183C13×C4⋊C4—21no—
184C13×C4⋊C4—21no—
185C13×C4⋊C4—42no—
186C13×C4⋊C4C2×D412yes—
187C13×C4⋊C4C2×Q812yes—
188C13×C22⋊C4—24no—
189C22⋊Dic13—22no—
190C22⋊Dic13—42no—
191C22⋊Dic13—42no—
192C22⋊Dic13—42no—
193C22⋊Dic13—81no—
194C22⋊Dic13D814yes—
195C4⋊Dic13—21no—
196C4⋊Dic13—21no—
197C4⋊Dic13—21no—
198C4⋊Dic13—21no—
199C4⋊Dic13—21no—
200C4⋊Dic13—21no—
201C4⋊Dic13—21no—
202C4⋊Dic13—42no—
203C4⋊Dic13—42no—
204C4⋊Dic13—42no—
205C4⋊Dic13C2×D412yes—
206#6101—42no—
207#6101—42no—
208#6101—42no—
209#6101—81no—
210C4×Dic13—21no—
211C4×Dic13—21no—
212C4×Dic13—21no—
213C4×Dic13—21no—
214C4×Dic13—42no—
215C2×#1055—28no—
216C2×#1055—21no—
217C2×#1055—21no—
218C2×#1055—21no—
219C2×#1055—21no—
220C2×#1055C2×D412yes—
221C2×#1055#4112yes—
222C2×#474—131no—
223C22×#107—131no—
224#2440—131no—
225#2361—131no—
226#2093—131no—
227#2086—131no—
228#2067—131no—
229#2057—131no—
230#1947—131no—
231#1918—131no—
232#1893—131no—
233#1874D1311yescharacteristic
234#1862—131no—
235#1852—131no—
236#1850—131no—
237C23×C13—21no—
238C23×C13—21no—
239C23×C13—21no—
240C23×C13—21no—
241C23×C13—22no—
242C23×C13—41no—
243C23×C13—41no—
244C23×C13—41no—
245C23×C13—41no—
246C23×C13—41no—
247C23×C13—41no—
248C23×C13C22⋊Q812yes—
249C23×C13C2×D812yes—
250C23×C13#13712yes—
251C23×C13C22×D411yescharacteristic
252D4×C13—22no—
253D4×C13—22no—
254D4×C13—48no—
255D4×C13—41no—
256D4×C13—41no—
257C2×C4×C13—21no—
258C2×C4×C13—21no—
259C2×C4×C13—22no—
260C2×C4×C13—22no—
261C2×C4×C13—22no—
262C2×C4×C13—22no—
263C2×C4×C13—22no—
264C2×C4×C13—22no—
265C2×C4×C13—41no—
266C2×C4×C13—41no—
267C2×C4×C13—41no—
268C2×C4×C13—41no—
269C2×C4×C13—41no—
270C2×C4×C13—41no—
271C2×C4×C13—41no—
272C2×C4×C13—84no—
273C2×C4×C13C22⋊Q812yes—
274C2×C4×C13C22×D411yescharacteristic
275C2×C4×C13C22×Q811yescharacteristic
276C2×C4×C13C2×#4111yescharacteristic
277C2×C4×C13C2×#4111yescharacteristic
278C2×C4×C13H(5,𝔽2)11yescharacteristic
279C2×C4×C132−1+411yescharacteristic
280C2×Dic13—21no—
281C2×Dic13—21no—
282C2×Dic13—21no—
283C2×Dic13—21no—
284C2×Dic13—21no—
285C2×Dic13—22no—
286C2×Dic13—21no—
287C2×Dic13—21no—
288C2×Dic13—21no—
289C2×Dic13—21no—
290C2×Dic13—21no—
291C2×Dic13—41no—
292C2×Dic13—41no—
293C2×Dic13—41no—
294C2×Dic13—41no—
295C2×Dic13—41no—
296C2×Dic13—41no—
297C2×Dic13—41no—
298C2×Dic13—41no—
299C2×Dic13—41no—
300C2×Dic13—41no—
301C2×Dic13—41no—
302C2×Dic13—84no—
303C2×Dic13—84no—
304C2×Dic13C2×D812yes—
305C2×Dic13C2×D812yes—
306Dic26—84no—
307C8×C13—41no—
308C8×C13—41no—
309#1055—22no—
310#1055—22no—
311C23×C8—131no—
312C2×C4⋊Q8—131no—
313C2×C22⋊Q8—261no—
314C2×#121C2×D1311yescharacteristic
315C2×C4×D4—131no—
316C2×C4×D4—261no—
317C22×C4⋊C4—131no—
318C22×C4⋊C4C2×D1311yescharacteristic
319#474—264no—
320C2×#107—131no—
321C2×#107—131no—
322C2×#107—131no—
323C2×#107—131no—
324C2×#107—131no—
325C2×#107—131no—
326C2×#107—264no—
327C2×C4⋊C8—131no—
328C2×C4⋊C8—131no—
329C2×#102—131no—
330C2×#102—131no—
331C2×#102C2×D1311yescharacteristic
332C2×#102C2×D1311yescharacteristic
333C2×C22⋊C8C2×D1311yescharacteristic
334#398—261no—
335#395—261no—
336#390—131no—
337#389—131no—
338#389—131no—
339#389—131no—
340#388—261no—
341#386—261no—
342#385—261no—
343#385—261no—
344#384—131no—
345#380—131no—
346C4×C4⋊C4—131no—
347C4×C22⋊C4—131no—
348#340—131no—
349#340—131no—
350#340—131no—
351#340—131no—
352#340C2×D1311yescharacteristic
353#340C2×D1311yescharacteristic
354#336—131no—
355#336—131no—
356C22×C13—22no—
357C22×C13—22no—
358C22×C13—22no—
359C22×C13—22no—
360C22×C13—22no—
361C22×C13—22no—
362C22×C13—42no—
363C22×C13—42no—
364C22×C13—42no—
365C22×C13—81no—
366C22×C13—81no—
367C22×C13—81no—
368C22×C13—81no—
369C22×C13#47414yescomplemented
370C22×C13C2×C22⋊Q811yescharacteristic
371C22×C13D4211yescharacteristic
372C22×C13#54711yescharacteristic
373C22×C13C22×D811yescharacteristic
374C22×C13C2×#13711yescharacteristic
375C22×C13#57611yescharacteristic
376C22×C13#57811yescharacteristic
377C4×C13—22no—
378C4×C13—42no—
379C4×C13—42no—
380C4×C13—81no—
381C4×C13#52511yescharacteristic
382C4×C13#53911yescharacteristic
383C4×C13D4×Q811yescharacteristic
384C4×C13#55411yescharacteristic
385Dic13—22no—
386Dic13—22no—
387Dic13—41no—
388Dic13—41no—
389Dic13—42no—
390Dic13—81no—
391Dic13—81no—
392Dic13—81no—
393C22×Q8—261no—
394C22×D4—21no—
395C22×D4C22×D1311yescharacteristic
396C23×C4—21no—
397C23×C4—261no—
398C23×C4—261no—
399C23×C4C22×D1311yescharacteristic
400C22×C8—131no—
401C22×C8—131no—
402C22×C8—262no—
403C22×C8—262no—
404C22×C8—262no—
405C22×C8C22×D1311yescharacteristic
406C22×C8C22×D1311yescharacteristic
407C4⋊Q8—262no—
408C4⋊Q8—521no—
409C22⋊Q8—524no—
410#121—22no—
411#121Dic2614yescomplemented
412C4×D4—262no—
413C4×D4—521no—
414C4×D4—524no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—41no—
418C2×C4⋊C4—131no—
419C2×C4⋊C4—131no—
420C2×C4⋊C4—131no—
421C2×C4⋊C4—131no—
422C2×C4⋊C4—262no—
423C2×C4⋊C4—261no—
424C2×C4⋊C4—261no—
425C2×C4⋊C4—261no—
426C2×C4⋊C4—261no—
427C2×C4⋊C4—261no—
428C2×C4⋊C4—261no—
429C2×C4⋊C4—261no—
430C2×C4⋊C4—521no—
431C2×C4⋊C4C22×D1311yescharacteristic
432C2×C4⋊C4C22×D1311yescharacteristic
433C2×C4⋊C4C22×D1311yescharacteristic
434C2×C22⋊C4—21no—
435C2×C22⋊C4—131no—
436C2×C22⋊C4—131no—
437C2×C22⋊C4—261no—
438C2×C22⋊C4—261no—
439C2×C22⋊C4—261no—
440C2×C22⋊C4—261no—
441C2×C42—131no—
442C2×C42—131no—
443C2×C42—261no—
444#107—134no—
445#107—262no—
446#107—262no—
447#107—262no—
448#107—262no—
449#107—521no—
450C4⋊C8—262no—
451C4⋊C8—262no—
452#102—22no—
453#102—41no—
454#102—262no—
455#102—262no—
456C22⋊C8—22no—
457#95—131no—
458#95—131no—
459#95—261no—
460#95—261no—
461#95—261no—
462#95—261no—
463#95—261no—
464C2×C13—24no—
465C2×C13—82no—
466C2×C13#244911yescharacteristic
467C2×C13C2×#47411yescharacteristic
468C2×C13#308311yescharacteristic
469C2×C13#327011yescharacteristic
470C2×C13D4×D811yescharacteristic
471C2×C13#333411yescharacteristic
472C2×C13#334611yescharacteristic
473C24—21no—
474C24D4×D1311yescharacteristic
475C2×Q8—522no—
476C2×Q8—522no—
477C2×Q8—1041no—
478C2×D4—24no—
479C2×D4—21no—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—42no—
485C2×D4—42no—
486C2×D4C2×Dic2612yes—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—42no—
495C22×C4—42no—
496C22×C4—81no—
497C22×C4—131no—
498C22×C4—131no—
499C22×C4—131no—
500C22×C4—131no—
501C22×C4—261no—
502C22×C4—261no—
503C22×C4—261no—
504C22×C4—261no—
505C22×C4—522no—
506C22×C4—522no—
507C22×C4—522no—
508C22×C4—522no—
509C22×C4—1041no—
510C22×C4—1041no—
511C22×C4C2×Dic2612yes—
512C22×C4D4×D1311yescharacteristic
513C22×C4#612912yes—
514C22×C4C23×D1311yescharacteristic
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—268no—
524C2×C8—261no—
525C2×C8—261no—
526C2×C8—261no—
527C2×C8—261no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—42no—
533C4⋊C4—132no—
534C4⋊C4—261no—
535C4⋊C4—261no—
536C4⋊C4—261no—
537C4⋊C4—261no—
538C4⋊C4—261no—
539C4⋊C4—261no—
540C4⋊C4—261no—
541C4⋊C4—522no—
542C4⋊C4—522no—
543C4⋊C4—522no—
544C4⋊C4—522no—
545C4⋊C4—522no—
546C4⋊C4—522no—
547C4⋊C4—1041no—
548C4⋊C4C2×Dic2612yes—
549C4⋊C4D4×D1312yes—
550C22⋊C4—24no—
551C22⋊C4—134no—
552C22⋊C4—262no—
553C22⋊C4—522no—
554C22⋊C4—522no—
555C22⋊C4—522no—
556C22⋊C4—1041no—
557C42—261no—
558C42—261no—
559C42—261no—
560C42—261no—
561C42—522no—
562C13#2633611yescharacteristic, complemented, Sylow
563C23—21no—
564C23—21no—
565C23—21no—
566C23—21no—
567C23—22no—
568C23—41no—
569C23—41no—
570C23—41no—
571C23—41no—
572C23—41no—
573C23—41no—
574C23#8813212yes—
575C23D8×D1312yes—
576C23#8816912yes—
577C23C2×D4×D1311yescharacteristic
578Q8—1044no—
579D4—22no—
580D4—22no—
581D4—48no—
582D4—41no—
583D4—41no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—84no—
600C2×C4—132no—
601C2×C4—132no—
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—262no—
612C2×C4—261no—
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—521no—
624C2×C4—1044no—
625C2×C4—1044no—
626C2×C4#8813212yes—
627C2×C4C22×Dic2611yescharacteristic
628C2×C4C2×D4×D1311yescharacteristic
629C2×C4C2×#612911yescharacteristic
630C2×C4#8825111yescharacteristic
631C2×C4#41×D1311yescharacteristic
632C2×C4#8825711yescharacteristic
633C8—41no—
634C8—41no—
635C8—262no—
636C8—262no—
637C22—22no—
638C22—22no—
639C22—22no—
640C22—22no—
641C22—22no—
642C22—22no—
643C22—42no—
644C22—42no—
645C22—42no—
646C22—81no—
647C22—81no—
648C22—81no—
649C22—81no—
650C22#1171842014yescomplemented
651C22C2×#8813211yescharacteristic
652C22#1171929511yescharacteristic
653C22#1171936011yescharacteristic
654C22C2×D8×D1311yescharacteristic
655C22C2×#8816911yescharacteristic
656C22#1171947911yescharacteristic
657C22#1171948411yescharacteristic
658C4—22no—
659C4—42no—
660C4—42no—
661C4—81no—
662C4—262no—
663C4—262no—
664C4—522no—
665C4—521no—
666C4—521no—
667C4—1041no—
668C4—1041no—
669C4—1041no—
670C4D4×Dic2611yescharacteristic
671C4#1171924411yescharacteristic
672C4#1171930711yescharacteristic
673C4#1171931111yescharacteristic
674C2—24no—
675C2—82no—
676C2#1311864911yescharacteristic
677C2C2×#1171842011yescharacteristic
678C2#1312469111yescharacteristic
679C2#1312639911yescharacteristic
680C2#1312650611yescharacteristic
681C2#1312717811yescharacteristic
682C2#1312731911yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#1874C2
socleC23×C13C22×D4
prime radicalC2×C13×#121C22
hypercenter#1874D13
hypocenterC13#26336
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1874

Complements

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

NH ≅ G/Ntype
1. C2×#11718420C2semidirect
2. C22×#88047C2semidirect
3. #13118532C2semidirect
5. #13116362C2semidirect
6. #13116328C2semidirect
7. #13116220C2semidirect
8. #13116163C2semidirect
9. #13115593C2semidirect
10. #13115410C2semidirect
12. #13115081C2semidirect
13. #13115026C2semidirect
14. #13115013C2semidirect
71. C13×#121Q8semidirect
131. #88047D4semidirect
369. C22×C13#474semidirect
411. #121Dic26semidirect
562. C13#26336semidirect
650. C22#11718420semidirect

Maximal subgroups

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

subgroupindex
C2×#117184202
C22×#880472
#131185322
#131178562
#131163622
#131163282
#131162202
#131161632
#131155932
#131154102
#131152652
#131150812
#131150262
#131150132
C13×#18742
#2633613