Finite Group Databasebeta

← #15899520

Subgroups — #15899520

Order 3328.

1064 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718727C211yesmaximal, characteristic
2C2×#11718687C211yesmaximal, characteristic
3#13119754C211yesmaximal, characteristic
4#13116171C211yesmaximal, characteristic, complemented
5#13116161C211yesmaximal, characteristic, complemented
6#13115979C211yesmaximal, characteristic
7#13115969C211yesmaximal, characteristic
8#13115806C211yesmaximal, characteristic, complemented
9#13115777C211yesmaximal, characteristic, complemented
10#13115191C211yesmaximal, characteristic
11#13115191C211yesmaximal, characteristic
12#13115104C211yesmaximal, characteristic, complemented
13#13115090C211yesmaximal, characteristic, complemented
14#13114841C211yesmaximal, characteristic, complemented
15C2×C13×#557C211yesmaximal, characteristic, complemented
16C13×#557—24no—
17C13×#557—24no—
18C2×C13×C4⋊Q8—21no—
19C2×C13×C4⋊Q8C2211yescharacteristic
20C2×C13×#125—21no—
21C2×C13×#125—21no—
22C2×C13×#125C2211yescharacteristic
23C2×C13×#125C2211yescharacteristic
24C2×C4×Q8×C13—21no—
25C2×C4×Q8×C13C2211yescharacteristic
26C2×C4×Q8×C13C2211yescharacteristic
27C2×C4×Q8×C13C2211yescharacteristic
28C2×C4×Q8×C13C2211yescharacteristic
29C2×#88200—21no—
30C22×#6106C2211yescharacteristic
31C2×C4×D52C2211yescharacteristic
32C2×#88075C2211yescharacteristic
33C2×#88075C2211yescharacteristic
34C2×#88075C2211yescharacteristic
35#11718727—24no—
36#11718687—24no—
37#11718655—21no—
38#11718655—21no—
39#11718648—21no—
40C2×#88049C2211yescharacteristic
41C2×#88049C2211yescharacteristic
42C2×#88049C2211yescharacteristic
43C2×#88048C2211yescharacteristic
44C2×#88047C2211yescharacteristic
45C2×#88047C2211yescharacteristic
46#11718600C2211yescharacteristic
47#11718600C2211yescharacteristic
48#11718596C2211yescharacteristic
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×Q8×C13C2311yescharacteristic
66C22×D52C2311yescharacteristic
67C22×C4×D13—21no—
68C13×C4⋊Q8—28no—
69C13×C4⋊Q8—22no—
70C13×C4⋊Q8—22no—
71C13×#125—28no—
72C13×#125—28no—
73C13×#125—22no—
74C13×#125—22no—
75C13×#125—22no—
76C13×#125D414yes—
77C4×Q8×C13—28no—
78C4×Q8×C13—22no—
79C4×Q8×C13—22no—
80C4×Q8×C13—22no—
81C4×Q8×C13—22no—
82C4×Q8×C13—22no—
83C4×Q8×C13—22no—
84C4×Q8×C13—22no—
85C4×Q8×C13D414yes—
86C2×C13×C4⋊C4—21no—
87C2×C13×C4⋊C4—21no—
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⋊C4—21no—
94C2×C13×C4⋊C4D411yescharacteristic
95C2×C13×C4⋊C4D411yescharacteristic
96C2×C13×C4⋊C4D411yescharacteristic
97C2×C13×C4⋊C4C2311yescharacteristic
98C2×C13×C4⋊C4C2311yescharacteristic
99C2×C13×C4⋊C4C2311yescharacteristic
100C2×C42×C13—21no—
101C2×C42×C13—21no—
102C2×C42×C13—21no—
103C2×C42×C13C2311yescharacteristic
104C2×C42×C13C2311yescharacteristic
105C2×C42×C13C2311yescharacteristic
106#88200—44no—
107C2×#6106—22no—
108C2×#6106—22no—
109C2×#6106Q814yescomplemented
110C2×#6103—21no—
111C2×#6103—21no—
112C2×#6103—21no—
113C2×#6103—21no—
114C2×#6103—21no—
115C2×C4⋊Dic13—21no—
116C2×C4⋊Dic13—21no—
117C2×C4⋊Dic13C2311yescharacteristic
118C2×C4⋊Dic13C2311yescharacteristic
119C2×C4⋊Dic13C2311yescharacteristic
120C2×#6101—21no—
121C2×#6101—21no—
122C22×#1055C2311yescharacteristic
123C22×#1055C2311yescharacteristic
124C22×#1055C2311yescharacteristic
125C22×#1055C2311yescharacteristic
126C4×D52—22no—
127C4×D52—22no—
128#88075—22no—
129#88075—22no—
130#88075—22no—
131#88071—21no—
132#88071—21no—
133#88049—22no—
134#88049—22no—
135#88049—22no—
136#88048—22no—
137#88047—22no—
138#88047—22no—
139C4⋊#1055—22no—
140#88043—22no—
141#24346—131nomaximal, Sylow
142C23×D13—21no—
143C2×Q8×C13—24no—
144C2×Q8×C13—22no—
145C2×Q8×C13—22no—
146C2×Q8×C13—21no—
147C2×Q8×C13—21no—
148C2×Q8×C13—21no—
149C2×Q8×C13—41no—
150C2×Q8×C13—42no—
151C2×Q8×C13—42no—
152C2×Q8×C13C2×D412yes—
153C2×Q8×C13C2×Q812yes—
154C2×Q8×C13#4112yes—
155C22×C4×C13—21no—
156C22×C4×C13—21no—
157C22×C4×C13—21no—
158C22×C4×C13—21no—
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—
169C2×D52—21no—
170C2×D52—21no—
171C2×D52—21no—
172C2×D52—21no—
173C2×D52—21no—
174C2×D52C2×Q812yes—
175C2×C4×D13—42no—
176C2×C4×D13—42no—
177C2×C4×D13—42no—
178C13×C4⋊C4—24no—
179C13×C4⋊C4—24no—
180C13×C4⋊C4—24no—
181C13×C4⋊C4—24no—
182C13×C4⋊C4—24no—
183C13×C4⋊C4—24no—
184C13×C4⋊C4—24no—
185C13×C4⋊C4—24no—
186C13×C4⋊C4—22no—
187C13×C4⋊C4—22no—
188C13×C4⋊C4—22no—
189C13×C4⋊C4—21no—
190C13×C4⋊C4—21no—
191C13×C4⋊C4—21no—
192C13×C4⋊C4C2×D412yes—
193C13×C4⋊C4C2×D412yes—
194C13×C4⋊C4C2×D412yes—
195C42×C13—24no—
196C42×C13—24no—
197C42×C13—24no—
198C42×C13—21no—
199C42×C13—21no—
200C42×C13—21no—
201C42×C13—21no—
202C42×C13C2×D412yes—
203C42×C13C2×D412yes—
204#6106—28no—
205#6103—42no—
206#6103—42no—
207#6103—42no—
208#6103—81no—
209#6103—81no—
210C4⋊Dic13—21no—
211C4⋊Dic13—21no—
212C4⋊Dic13—21no—
213C4⋊Dic13—21no—
214C4⋊Dic13—21no—
215C4⋊Dic13—21no—
216C4⋊Dic13—42no—
217C4⋊Dic13—81no—
218#6101—42no—
219#6101—42no—
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×#1055—21no—
231C2×#1055C2×Q812yes—
232C2×#557D1311yescharacteristic, complemented
233C2×#478—131no—
234C2×#440—131no—
235#2538—131no—
236#2059—131no—
237#2057—131no—
238#2025—131no—
239#2023—131no—
240#1992—131no—
241#1985—131no—
242#1880—131no—
243#1880—131no—
244#1865—131no—
245#1863—131no—
246#1803—131no—
247C23×C13C22×D411yescharacteristic
248C22×D13—22no—
249C22×D13—41no—
250C22×D13—41no—
251C22×D13—41no—
252C22×D13—41no—
253C22×D13—41no—
254C22×D13—41no—
255Q8×C13—22no—
256Q8×C13—22no—
257Q8×C13—22no—
258Q8×C13—44no—
259Q8×C13—48no—
260Q8×C13C22⋊Q814yescomplemented
261C2×C4×C13—22no—
262C2×C4×C13—21no—
263C2×C4×C13—22no—
264C2×C4×C13—22no—
265C2×C4×C13—21no—
266C2×C4×C13—21no—
267C2×C4×C13—21no—
268C2×C4×C13—21no—
269C2×C4×C13—21no—
270C2×C4×C13—21no—
271C2×C4×C13—21no—
272C2×C4×C13—22no—
273C2×C4×C13—21no—
274C2×C4×C13—22no—
275C2×C4×C13—22no—
276C2×C4×C13—21no—
277C2×C4×C13—21no—
278C2×C4×C13—21no—
279C2×C4×C13—21no—
280C2×C4×C13—21no—
281C2×C4×C13—21no—
282C2×C4×C13—41no—
283C2×C4×C13—41no—
284C2×C4×C13—41no—
285C2×C4×C13—41no—
286C2×C4×C13—41no—
287C2×C4×C13—41no—
288C2×C4×C13#12012yes—
289C2×C4×C13#12012yes—
290C2×C4×C13AGL(1,ℤ/8)12yes—
291C2×C4×C13C22×D411yescharacteristic
292C2×C4×C13C22×D411yescharacteristic
293C2×C4×C13C22×Q811yescharacteristic
294C2×C4×C13C2×#4111yescharacteristic
295C2×C4×C132−1+411yescharacteristic
296C2×C4×C132−1+411yescharacteristic
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—
306D52—22no—
307D52—22no—
308D52—41no—
309D52—41no—
310C4×D13—84no—
311#1055—22no—
312#1055—41no—
313#1055—41no—
314#1055—41no—
315C22×SD16—131no—
316#557—24no—
317#557—24no—
318C2×C4⋊Q8—21no—
319C2×C4⋊Q8C2×D1311yescharacteristic
320C2×#125—21no—
321C2×#125—21no—
322C2×#125C2×D1311yescharacteristic
323C2×#125C2×D1311yescharacteristic
324C2×C22⋊Q8—261no—
325C2×C4×Q8—21no—
326C2×C4×Q8C2×D1311yescharacteristic
327C2×C4×Q8C2×D1311yescharacteristic
328C2×C4×Q8C2×D1311yescharacteristic
329C2×C4×Q8C2×D1311yescharacteristic
330C2×C4×D4—131no—
331#478—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#396—261no—
345#396—261no—
346#390—131no—
347#390—131no—
348#389—131no—
349#389—131no—
350#384—131no—
351#380—261no—
352#340—131no—
353#340—131no—
354#340—131no—
355#340—131no—
356#340—131no—
357#340—131no—
358#336—131no—
359#336—131no—
360#336—131no—
361#336—131no—
362C22×C13C2×#12011yescharacteristic
363C22×C13#54811yescharacteristic
364C22×C13D4×Q811yescharacteristic
365C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
366C22×C13#57511yescharacteristic
367C22×C13#57711yescharacteristic
368C22×C13#57811yescharacteristic
369C2×D13—42no—
370C2×D13—42no—
371C2×D13—42no—
372C2×D13—81no—
373C2×D13—81no—
374C2×D13—81no—
375C2×D13—81no—
376C4×C13—24no—
377C4×C13—22no—
378C4×C13—22no—
379C4×C13—22no—
380C4×C13—41no—
381C4×C13—42no—
382C4×C13—42no—
383C4×C13—41no—
384C4×C13—41no—
385C4×C13—42no—
386C4×C13C2×C22⋊Q811yescharacteristic
387C4×C13#53611yescharacteristic
388C4×C13#54811yescharacteristic
389C4×C13D4×Q811yescharacteristic
390Dic13—81no—
391Dic13—81no—
392Dic13—81no—
393C22×Q8—21no—
394C22×Q8C22⋊D1311yescharacteristic
395C22×Q8C22×D1311yescharacteristic
396C22×D4—131no—
397C23×C4—261no—
398C2×SD16—134no—
399C2×SD16—262no—
400C2×SD16—262no—
401C22×C8—131no—
402C22×C8—131no—
403C22×C8—131no—
404C22×C8—131no—
405C4⋊Q8—28no—
406C4⋊Q8—22no—
407C4⋊Q8—22no—
408#125—28no—
409#125—28no—
410#125—22no—
411#125—22no—
412#125—22no—
413#125C22⋊D1314yes—
414C22⋊Q8—524no—
415C4×Q8—28no—
416C4×Q8—22no—
417C4×Q8—22no—
418C4×Q8—22no—
419C4×Q8—22no—
420C4×Q8—22no—
421C4×Q8—22no—
422C4×Q8—22no—
423C4×Q8C22⋊D1314yes—
424C4×D4—262no—
425C4×D4—262no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—131no—
435C2×C4⋊C4—131no—
436C2×C4⋊C4—131no—
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—261no—
448C2×C22⋊C4—261no—
449C2×C22⋊C4—261no—
450C2×C22⋊C4—261no—
451C2×C22⋊C4—261no—
452C2×C42—21no—
453C2×C42—21no—
454C2×C42—21no—
455C2×C42C22×D1311yescharacteristic
456C2×C42C22×D1311yescharacteristic
457C2×C42C22×D1311yescharacteristic
458#107—262no—
459#107—262no—
460#106—262no—
461C4⋊C8—262no—
462#103—262no—
463#103—262no—
464#103—262no—
465#102—262no—
466#102—262no—
467#102—262no—
468#97—262no—
469#95—261no—
470#95—261no—
471C2×C13#240911yescharacteristic
472C2×C13#300611yescharacteristic
473C2×C13#301311yescharacteristic
474C2×C13#336811yescharacteristic
475C2×C13#337711yescharacteristic
476C2×C13#338611yescharacteristic
477C2×C13#338811yescharacteristic
478D13—82no—
479C24—261no—
480C2×Q8—24no—
481C2×Q8—22no—
482C2×Q8—22no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—41no—
487C2×Q8—42no—
488C2×Q8—42no—
489C2×Q8Q8×D1312yes—
490C2×Q8#613112yes—
491C2×Q8C2×C22⋊D1312yes—
492C2×D4—132no—
493C2×D4—261no—
494C2×D4—261no—
495C2×D4—261no—
496C2×D4—261no—
497C2×D4—261no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—261no—
503C22×C4—261no—
504C22×C4—261no—
505C22×C4—522no—
506C22×C4—522no—
507C22×C4—522no—
508C22×C4C2×C22⋊D1311yescharacteristic
509C22×C4C2×C22⋊D1311yescharacteristic
510C22×C4C2×C22⋊D1311yescharacteristic
511C22×C4C2×C22⋊D1311yescharacteristic
512C22×C4C2×C22⋊D1311yescharacteristic
513C22×C4C2×C22⋊D1311yescharacteristic
514C22×C4C23×D1311yescharacteristic
515SD16—268no—
516C2×C8—132no—
517C2×C8—261no—
518C2×C8—261no—
519C2×C8—261no—
520C2×C8—261no—
521C2×C8—261no—
522C2×C8—261no—
523C2×C8—261no—
524C2×C8—261no—
525C2×C8—261no—
526C2×C8—261no—
527C2×C8—261no—
528C4⋊C4—24no—
529C4⋊C4—24no—
530C4⋊C4—24no—
531C4⋊C4—24no—
532C4⋊C4—24no—
533C4⋊C4—24no—
534C4⋊C4—24no—
535C4⋊C4—24no—
536C4⋊C4—22no—
537C4⋊C4—22no—
538C4⋊C4—22no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—261no—
543C4⋊C4—261no—
544C4⋊C4—261no—
545C4⋊C4—261no—
546C4⋊C4—261no—
547C4⋊C4—261no—
548C4⋊C4—522no—
549C4⋊C4—522no—
550C4⋊C4—522no—
551C4⋊C4—1041no—
552C4⋊C4C2×C22⋊D1312yes—
553C4⋊C4C2×C22⋊D1312yes—
554C4⋊C4C2×C22⋊D1312yes—
555C22⋊C4—522no—
556C22⋊C4—522no—
557C22⋊C4—522no—
558C22⋊C4—1041no—
559C22⋊C4—1041no—
560C42—24no—
561C42—24no—
562C42—24no—
563C42—21no—
564C42—21no—
565C42—21no—
566C42—21no—
567C42C2×C22⋊D1312yes—
568C42C2×C22⋊D1312yes—
569C13#2434611yescharacteristic, complemented, Sylow
570C23—262no—
571C23—521no—
572C23—521no—
573C23—521no—
574C23—521no—
575C23—521no—
576C23—521no—
577C23C22×C22⋊D1311yescharacteristic
578Q8—22no—
579Q8—22no—
580Q8—22no—
581Q8—44no—
582Q8—48no—
583Q8#8820014yescomplemented
584D4—262no—
585D4—262no—
586D4—521no—
587D4—521no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—22no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—22no—
606C2×C4—21no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
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#8820312yes—
626C2×C4#8820712yes—
627C2×C4#8820712yes—
628C2×C4C2×Q8×D1311yescharacteristic
629C2×C4C2×#613111yescharacteristic
630C2×C4#8825411yescharacteristic
631C2×C4#8825411yescharacteristic
632C2×C4C22×C22⋊D1311yescharacteristic
633C2×C4C22×C22⋊D1311yescharacteristic
634C8—262no—
635C8—521no—
636C8—521no—
637C8—521no—
638C22—522no—
639C22—522no—
640C22—522no—
641C22—1041no—
642C22—1041no—
643C22—1041no—
644C22—1041no—
645C22Q8×C22⋊D1311yescharacteristic
646C22#1171952211yescharacteristic
647C22C2×#8820311yescharacteristic
648C22#1171952711yescharacteristic
649C22#1171954211yescharacteristic
650C22#1171954311yescharacteristic
651C22C2×#8820711yescharacteristic
652C4—22no—
653C4—24no—
654C4—22no—
655C4—22no—
656C4—41no—
657C4—41no—
658C4—42no—
659C4—41no—
660C4—42no—
661C4—42no—
662C4—1041no—
663C4—1041no—
664C4—1041no—
665C4C2×#8820011yescharacteristic
666C4Q8×C22⋊D1311yescharacteristic
667C4#1171952111yescharacteristic
668C4#1171952211yescharacteristic
669C2—1042no—
670C2#1311819511yescharacteristic
671C2#1312408811yescharacteristic
672C2#1312415111yescharacteristic
673C2#1312756511yescharacteristic
674C2#1312767811yescharacteristic
675C2#1312775311yescharacteristic
676C2#1312777511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC2×C13×#557C2
socleC23×C13C22×D4
prime radicalC22×D52C23
hypercenterC2×#557D13
hypocenterC13#24346
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
4. #13116171C2semidirect
5. #13116161C2semidirect
8. #13115806C2semidirect
9. #13115777C2semidirect
12. #13115104C2semidirect
13. #13115090C2semidirect
14. #13114841C2semidirect
15. C2×C13×#557C2semidirect
109. C2×#6106Q8semidirect
232. C2×#557D13semidirect
260. Q8×C13C22⋊Q8semidirect
569. C13#24346semidirect
583. Q8#88200semidirect

Maximal subgroups

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

subgroupindex
C2×#117187272
C2×#117186872
#131197542
#131161712
#131161612
#131159792
#131159692
#131158062
#131157772
#131151912
#131151042
#131150902
#131148412
C2×C13×#5572
#2434613