Finite Group Databasebeta

← #15881299

Subgroups — #15881299

Order 3328.

906 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718845C211yesmaximal, characteristic
2C2×Q16×Dic13C211yesmaximal, characteristic
3#13117757C211yesmaximal, characteristic
4Q8×C4⋊Dic13C211yesmaximal, characteristic
5#13115580C211yesmaximal, characteristic
6#13115565C211yesmaximal, characteristic
7#13115106C211yesmaximal, characteristic
8#13115106C211yesmaximal, characteristic
9#13115092C211yesmaximal, characteristic
10#13115092C211yesmaximal, characteristic
11#13115004C211yesmaximal, characteristic
12#13114851C211yesmaximal, characteristic
13#13114841C211yesmaximal, characteristic
14#13114708C211yesmaximal, characteristic
15C2×C13×#441C211yesmaximal, characteristic
16C22×C13×Q16C2211yescharacteristic
17C2×C4×Q8×C13C2211yescharacteristic
18C2×C4×Q8×C13C2211yescharacteristic
19C2×Q8×Dic13C2211yescharacteristic
20C2×Q8×Dic13C2211yescharacteristic
21C2×Q8×Dic13C2211yescharacteristic
22C2×Q8×Dic13C2211yescharacteristic
23C13×#441C418yescomplemented
24C2×C13×#106C2211yescharacteristic
25C2×C13×#103C2211yescharacteristic
26C2×C13×#103C2211yescharacteristic
27C2×C13×#97C2211yescharacteristic
28C2×#88075C2211yescharacteristic
29C2×#88075C2211yescharacteristic
30C2×#88075C2211yescharacteristic
31C2×#88075C2211yescharacteristic
32#11718845—24no—
33Q16×Dic13—24no—
34C2×#88058C2211yescharacteristic
35C2×#88058C2211yescharacteristic
36C2×#88057C2211yescharacteristic
37C2×#88057C2211yescharacteristic
38C2×#88055C2211yescharacteristic
39C2×C8×Dic13C2211yescharacteristic
40#11718646—21no—
41#11718646—21no—
42#11718646—21no—
43#11718646—21no—
44#11718646C2211yescharacteristic
45#11718646C2211yescharacteristic
46#11718646C2211yescharacteristic
47#11718646C2211yescharacteristic
48#11718597—21no—
49#11718597C2211yescharacteristic
50#11718596—21no—
51#11718596C2211yescharacteristic
52C4×C4⋊Dic13—21no—
53C4×C4⋊Dic13—21no—
54C4×C4⋊Dic13C2211yescharacteristic
55C2×C4⋊#1055C2211yescharacteristic
56#11718142C2211yescharacteristic
57#11718142C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718121C2211yescharacteristic
60#11718121C2211yescharacteristic
61#11718121C2211yescharacteristic
62C22×Q8×C13C2311yescharacteristic
63C22×Q8×C13C2311yescharacteristic
64C2×C13×Q16C2×C414yes—
65C2×C13×Q16D414yes—
66C2×C13×Q16Q814yes—
67C22×C8×C13C2311yescharacteristic
68C22×C8×C13C2311yescharacteristic
69C4×Q8×C13—22no—
70C4×Q8×C13—22no—
71C4×Q8×C13C2×C414yes—
72C4×Q8×C13C2×C414yes—
73C2×C13×C4⋊C4—21no—
74C2×C13×C4⋊C4—21no—
75C2×C13×C4⋊C4C2311yescharacteristic
76C2×C13×C4⋊C4C2311yescharacteristic
77C2×C42×C13—21no—
78C2×C42×C13—21no—
79C2×C42×C13C2311yescharacteristic
80Q8×Dic13—22no—
81Q8×Dic13—22no—
82Q8×Dic13—22no—
83Q8×Dic13—22no—
84Q8×Dic13—41no—
85Q8×Dic13—41no—
86Q8×Dic13—41no—
87Q8×Dic13—41no—
88C2×C4⋊Dic13—21no—
89C2×C4⋊Dic13—21no—
90C2×C4⋊Dic13—21no—
91C2×C4⋊Dic13—21no—
92C2×C4⋊Dic13—21no—
93C2×C4⋊Dic13—21no—
94C2×C4⋊Dic13—21no—
95C2×C4⋊Dic13—21no—
96C2×C4⋊Dic13—21no—
97C2×C4⋊Dic13—21no—
98C2×C4⋊Dic13D411yescharacteristic
99C2×C4⋊Dic13D411yescharacteristic
100C2×C4⋊Dic13C2311yescharacteristic
101C2×C4⋊Dic13C2311yescharacteristic
102C2×C4⋊Dic13C2311yescharacteristic
103C2×C4⋊Dic13C2311yescharacteristic
104C2×C4×Dic13—21no—
105C2×C4×Dic13—21no—
106C2×C4×Dic13—21no—
107C2×C4×Dic13—21no—
108C2×C4×Dic13C2311yescharacteristic
109C2×C4×Dic13C2311yescharacteristic
110C22×#1055C2311yescharacteristic
111C22×#1055C2311yescharacteristic
112C13×#106C2×C414yes—
113C13×#103C2×C414yes—
114C13×#103C2×C414yes—
115C13×#97C2×C414yes—
116#88075—22no—
117#88075—22no—
118#88075—22no—
119#88075—22no—
120#88071—21no—
121#88071—21no—
122#88071—21no—
123#88071—21no—
124#88071—21no—
125#88071—21no—
126#88071D411yescharacteristic
127#88071D411yescharacteristic
128#88058—22no—
129#88058—41no—
130#88057—22no—
131#88057—41no—
132#88055—22no—
133C8×Dic13—22no—
134C4⋊#1055—22no—
135#22679—131nomaximal, Sylow
136C2×Q8×C13—21no—
137C2×Q8×C13—21no—
138C2×Q8×C13—21no—
139C2×Q8×C13—21no—
140C2×Q8×C13—21no—
141C2×Q8×C13—21no—
142C2×Q8×C13C22×C412yes—
143C2×Q8×C13C22×C412yes—
144C2×Q8×C13C2×D412yes—
145C2×Q8×C13C2×D412yes—
146C2×Q8×C13C2×Q812yes—
147C2×Q8×C13C2×Q812yes—
148C22×C4×C13—21no—
149C22×C4×C13—21no—
150C22×C4×C13—21no—
151C22×C4×C13—21no—
152C22×C4×C13C2×D411yescharacteristic
153C22×C4×C13C2×D411yescharacteristic
154C22×C4×C13C2411yescharacteristic
155C22×Dic13—21no—
156C22×Dic13—21no—
157C22×Dic13—21no—
158C22×Dic13—21no—
159C22×Dic13C2×D411yescharacteristic
160C22×Dic13C2×D411yescharacteristic
161C22×Dic13C2×D411yescharacteristic
162C22×Dic13C2×D411yescharacteristic
163C13×Q16C4⋊C4116yescomplemented
164C2×C8×C13—21no—
165C2×C8×C13—21no—
166C2×C8×C13C22×C412yes—
167C2×C8×C13C22×C412yes—
168C2×C8×C13C2×D412yes—
169C2×C8×C13C2×Q812yes—
170C13×C4⋊C4—24no—
171C13×C4⋊C4—24no—
172C13×C4⋊C4—21no—
173C13×C4⋊C4—21no—
174C13×C4⋊C4C22×C412yes—
175C13×C4⋊C4C22×C412yes—
176C42×C13—24no—
177C42×C13—24no—
178C42×C13C22×C412yes—
179C42×C13#4112yes—
180C4⋊Dic13—22no—
181C4⋊Dic13—21no—
182C4⋊Dic13—21no—
183C4⋊Dic13—21no—
184C4⋊Dic13—21no—
185C4⋊Dic13—21no—
186C4⋊Dic13—21no—
187C4⋊Dic13—21no—
188C4⋊Dic13—21no—
189C4⋊Dic13—41no—
190C4⋊Dic13—42no—
191C4⋊Dic13—42no—
192C4⋊Dic13—42no—
193C4⋊Dic13—42no—
194C4⋊Dic13—42no—
195C4⋊Dic13—42no—
196C4⋊Dic13—42no—
197C4⋊Dic13—81no—
198C4⋊Dic13—81no—
199C4⋊Dic13—81no—
200C4×Dic13—21no—
201C4×Dic13—21no—
202C4×Dic13—21no—
203C4×Dic13—21no—
204C4×Dic13—42no—
205C4×Dic13—42no—
206C4×Dic13—42no—
207C4×Dic13—42no—
208C2×#1055—21no—
209C2×#1055—21no—
210C2×#1055—21no—
211C2×#1055—21no—
212C2×#1055—21no—
213C2×#1055—21no—
214C2×#441—131no—
215C2×#441D1311yescharacteristic
216C2×C4×Q16—131no—
217#2351—131no—
218Q8×C4⋊C4—131no—
219#1944—131no—
220#1941—131no—
221#1865—131no—
222#1865—131no—
223#1863—131no—
224#1863—131no—
225#1847—131no—
226#1805—131no—
227#1803—131no—
228#1771—131no—
229C23×C13C22×D411yescharacteristic
230Q8×C13—22no—
231Q8×C13—22no—
232Q8×C13—22no—
233Q8×C13—22no—
234Q8×C13—22no—
235Q8×C13—22no—
236Q8×C13C2×C4⋊C414yes—
237Q8×C13C2×C4⋊C414yes—
238C2×C4×C13—22no—
239C2×C4×C13—22no—
240C2×C4×C13—22no—
241C2×C4×C13—22no—
242C2×C4×C13—22no—
243C2×C4×C13—22no—
244C2×C4×C13—21no—
245C2×C4×C13—21no—
246C2×C4×C13—21no—
247C2×C4×C13—21no—
248C2×C4×C13—22no—
249C2×C4×C13—22no—
250C2×C4×C13—41no—
251C2×C4×C13—41no—
252C2×C4×C13—41no—
253C2×C4×C13—41no—
254C2×C4×C13C4×D412yes—
255C2×C4×C13C4×D412yes—
256C2×C4×C13C23×C411yescharacteristic
257C2×C4×C13C22×D411yescharacteristic
258C2×C4×C13C22×Q811yescharacteristic
259C2×C4×C13C2×#4111yescharacteristic
260C2×C4×C13H(5,𝔽2)11yescharacteristic
261C2×C4×C132−1+411yescharacteristic
262C2×Dic13—21no—
263C2×Dic13—21no—
264C2×Dic13—21no—
265C2×Dic13—21no—
266C2×Dic13—21no—
267C2×Dic13—21no—
268C2×Dic13—21no—
269C2×Dic13—21no—
270C2×Dic13—21no—
271C2×Dic13—21no—
272C2×Dic13—21no—
273C2×Dic13—41no—
274C2×Dic13—41no—
275C2×Dic13—41no—
276C2×Dic13—41no—
277C2×Dic13—41no—
278C2×Dic13—41no—
279C2×Dic13—41no—
280C2×Dic13—41no—
281C2×Dic13—41no—
282C2×Dic13—41no—
283C2×Dic13—41no—
284C2×Dic13—41no—
285C2×Dic13#13712yes—
286C8×C13—22no—
287C8×C13C2×C4⋊C414yes—
288#1055—41no—
289#1055—41no—
290C22×Q16C2×D1311yescharacteristic
291C2×C4×Q8—131no—
292C2×C4×Q8—131no—
293C2×C4×Q8—131no—
294C2×C4×Q8—131no—
295C2×C4×Q8C2×D1311yescharacteristic
296C2×C4×Q8C2×D1311yescharacteristic
297#441—264no—
298#441Dic1318yescomplemented
299C4×Q16—264no—
300C2×#107—131no—
301C2×#107—131no—
302C2×#106—131no—
303C2×#106—131no—
304C2×#106C2×D1311yescharacteristic
305C2×C4⋊C8—131no—
306C2×#103—131no—
307C2×#103—131no—
308C2×#103—131no—
309C2×#103—131no—
310C2×#103C2×D1311yescharacteristic
311C2×#103C2×D1311yescharacteristic
312C2×#97—131no—
313C2×#97C2×D1311yescharacteristic
314C2×C4×C8—131no—
315#389—131no—
316#389—131no—
317#389—131no—
318#389—131no—
319#389—261no—
320#389—261no—
321#389—261no—
322#389—261no—
323#384—131no—
324#384—261no—
325#382—131no—
326#382—261no—
327C4×C4⋊C4—131no—
328C4×C4⋊C4—261no—
329C4×C4⋊C4—261no—
330#340—131no—
331#340—131no—
332#340—131no—
333#340—131no—
334#336—131no—
335#336—131no—
336C22×C13C2×C4×D411yescharacteristic
337C22×C13D4211yescharacteristic
338C22×C13D4×Q811yescharacteristic
339C22×C13C2×#13711yescharacteristic
340C22×C13#57511yescharacteristic
341C22×C13#57711yescharacteristic
342C22×C13#57811yescharacteristic
343C4×C13—24no—
344C4×C13—24no—
345C4×C13—22no—
346C4×C13—22no—
347C4×C13—42no—
348C4×C13—42no—
349C4×C13C22×C4⋊C411yescharacteristic
350C4×C13#52011yescharacteristic
351C4×C13#54711yescharacteristic
352C4×C13#55411yescharacteristic
353Dic13—22no—
354Dic13—41no—
355Dic13—41no—
356Dic13—41no—
357Dic13—81no—
358Dic13—81no—
359Dic13—81no—
360Dic13—81no—
361C22×Q8C22×D1311yescharacteristic
362C22×Q8C22×D1311yescharacteristic
363C2×Q16Dic2614yes—
364C2×Q16D5214yes—
365C2×Q16C2×Dic1314yes—
366C22×C8—131no—
367C22×C8—131no—
368C22×C8C22×D1311yescharacteristic
369C22×C8C22×D1311yescharacteristic
370C4×Q8—22no—
371C4×Q8—22no—
372C4×Q8—262no—
373C4×Q8—262no—
374C4×Q8—262no—
375C4×Q8—262no—
376C4×Q8—521no—
377C4×Q8—521no—
378C4×Q8—521no—
379C4×Q8—521no—
380C4×Q8C2×Dic1314yes—
381C4×Q8C2×Dic1314yes—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—131no—
385C2×C4⋊C4—131no—
386C2×C4⋊C4—131no—
387C2×C4⋊C4—131no—
388C2×C4⋊C4—131no—
389C2×C4⋊C4—131no—
390C2×C4⋊C4—261no—
391C2×C4⋊C4—261no—
392C2×C4⋊C4—261no—
393C2×C4⋊C4—261no—
394C2×C4⋊C4—261no—
395C2×C4⋊C4—261no—
396C2×C4⋊C4—261no—
397C2×C4⋊C4—261no—
398C2×C4⋊C4—261no—
399C2×C4⋊C4—261no—
400C2×C4⋊C4C22×D1311yescharacteristic
401C2×C4⋊C4C22×D1311yescharacteristic
402C2×C42—21no—
403C2×C42—21no—
404C2×C42—131no—
405C2×C42—131no—
406C2×C42—261no—
407C2×C42—261no—
408C2×C42—261no—
409C2×C42—261no—
410C2×C42C22×D1311yescharacteristic
411#107—262no—
412#107—521no—
413#106—262no—
414#106—521no—
415#106C2×Dic1314yes—
416C4⋊C8—262no—
417#103—262no—
418#103—262no—
419#103—262no—
420#103—262no—
421#103C2×Dic1314yes—
422#103C2×Dic1314yes—
423#97—262no—
424#97C2×Dic1314yes—
425C4×C8—262no—
426#95—131no—
427#95—131no—
428#95—261no—
429#95—261no—
430#95—261no—
431#95—261no—
432#95—261no—
433#95—261no—
434C2×C13D4×C4⋊C411yescharacteristic
435C2×C13C4×#13711yescharacteristic
436C2×C13#294711yescharacteristic
437C2×C13#327011yescharacteristic
438C2×C13#327111yescharacteristic
439C2×C13#338711yescharacteristic
440C2×C13#339011yescharacteristic
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8C2×Dic2612yes—
448C2×Q8C2×Dic2612yes—
449C2×Q8C2×D5212yes—
450C2×Q8C2×D5212yes—
451C2×Q8C22×Dic1312yes—
452C2×Q8C22×Dic1312yes—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—131no—
458C22×C4—131no—
459C22×C4—131no—
460C22×C4—131no—
461C22×C4—261no—
462C22×C4—261no—
463C22×C4—261no—
464C22×C4—261no—
465C22×C4D4×D1311yescharacteristic
466C22×C4D4×D1311yescharacteristic
467C22×C4C23×D1311yescharacteristic
468Q16C4⋊Dic13116yescomplemented
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—261no—
472C2×C8—261no—
473C2×C8—261no—
474C2×C8—261no—
475C2×C8—261no—
476C2×C8—261no—
477C2×C8C2×Dic2612yes—
478C2×C8C2×D5212yes—
479C2×C8C22×Dic1312yes—
480C2×C8C22×Dic1312yes—
481C4⋊C4—24no—
482C4⋊C4—24no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—262no—
486C4⋊C4—261no—
487C4⋊C4—261no—
488C4⋊C4—261no—
489C4⋊C4—261no—
490C4⋊C4—261no—
491C4⋊C4—261no—
492C4⋊C4—261no—
493C4⋊C4—261no—
494C4⋊C4—521no—
495C4⋊C4—522no—
496C4⋊C4—522no—
497C4⋊C4—522no—
498C4⋊C4—522no—
499C4⋊C4—522no—
500C4⋊C4—522no—
501C4⋊C4—522no—
502C4⋊C4—1041no—
503C4⋊C4—1041no—
504C4⋊C4—1041no—
505C4⋊C4C22×Dic1312yes—
506C4⋊C4C22×Dic1312yes—
507C42—24no—
508C42—24no—
509C42—261no—
510C42—261no—
511C42—261no—
512C42—261no—
513C42—522no—
514C42—522no—
515C42—522no—
516C42—522no—
517C42#612912yes—
518C42C22×Dic1312yes—
519C13#2267911yescharacteristic, complemented, Sylow
520C23C2×D4×D1311yescharacteristic
521Q8—22no—
522Q8—22no—
523Q8—22no—
524Q8—22no—
525Q8—22no—
526Q8—22no—
527Q8C2×C4⋊Dic1314yes—
528Q8C2×C4⋊Dic1314yes—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—132no—
546C2×C4—261no—
547C2×C4—261no—
548C2×C4—261no—
549C2×C4—261no—
550C2×C4—261no—
551C2×C4—261no—
552C2×C4—261no—
553C2×C4—261no—
554C2×C4—261no—
555C2×C4—261no—
556C2×C4—261no—
557C2×C4—521no—
558C2×C4—521no—
559C2×C4—521no—
560C2×C4—521no—
561C2×C4—521no—
562C2×C4—521no—
563C2×C4—521no—
564C2×C4—521no—
565C2×C4—521no—
566C2×C4—521no—
567C2×C4—521no—
568C2×C4—521no—
569C2×C4D4×Dic1312yes—
570C2×C4D4×Dic1312yes—
571C2×C4C22×Dic2611yescharacteristic
572C2×C4C22×D5211yescharacteristic
573C2×C4C2×#612911yescharacteristic
574C2×C4#8825611yescharacteristic
575C2×C4#8825711yescharacteristic
576C2×C4C23×Dic1311yescharacteristic
577C8—22no—
578C8—521no—
579C8—521no—
580C8C2×C4⋊Dic1314yes—
581C22D4×Dic2611yescharacteristic
582C22D4×D5211yescharacteristic
583C22D13×#13711yescharacteristic
584C22#1171948211yescharacteristic
585C22#1171948311yescharacteristic
586C22#1171948411yescharacteristic
587C22C2×D4×Dic1311yescharacteristic
588C4—24no—
589C4—24no—
590C4—22no—
591C4—22no—
592C4—42no—
593C4—42no—
594C4—262no—
595C4—521no—
596C4—521no—
597C4—521no—
598C4—1041no—
599C4—1041no—
600C4—1041no—
601C4—1041no—
602C4#1171924811yescharacteristic
603C4#1171926011yescharacteristic
604C4C22×C4⋊Dic1311yescharacteristic
605C4#1171953211yescharacteristic
606C2D4×C4⋊Dic1311yescharacteristic
607C2#137×Dic1311yescharacteristic
608C2#1312368011yescharacteristic
609C2#1312640811yescharacteristic
610C2#1312642311yescharacteristic
611C2#1312776911yescharacteristic
612C2#1312780411yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC2×C13×#441C2
socle, prime radicalC23×C13C22×D4
cosocleC22×C4×C13C24
hypercenterC2×#441D13
hypocenterC13#22679
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#441

Complements

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

NH ≅ G/Ntype
23. C13×#441C4semidirect
163. C13×Q16C4⋊C4semidirect
298. #441Dic13semidirect
468. Q16C4⋊Dic13semidirect
519. C13#22679semidirect

Maximal subgroups

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

subgroupindex
C2×#117188452
C2×Q16×Dic132
#131177572
Q8×C4⋊Dic132
#131155802
#131155652
#131151062
#131150922
#131150042
#131148512
#131148412
#131147082
C2×C13×#4412
#2267913