Finite Group Databasebeta

← #15884719

Subgroups — #15884719

Order 3328.

926 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718420C211yesmaximal, characteristic
2#13117895C211yesmaximal, characteristic, complemented
3D4×#6101C211yesmaximal, characteristic
4#13115795C211yesmaximal, characteristic, complemented
5#13115593C211yesmaximal, characteristic, complemented
6#13115569C211yesmaximal, characteristic, complemented
7#13115568C211yesmaximal, characteristic, complemented
8#13115407C211yesmaximal, characteristic, complemented
9#13115406C211yesmaximal, characteristic, complemented
10#13115085C211yesmaximal, characteristic
11#13115083C211yesmaximal, characteristic
12C8×#6101C211yesmaximal, characteristic, complemented
13#102×Dic13C211yesmaximal, characteristic
14#102×Dic13C211yesmaximal, characteristic
15C4×C13×#102C211yesmaximal, characteristic
16C2×C4×D4×C13C2211yescharacteristic
17C2×D4×Dic13C2211yescharacteristic
18C2×D4×Dic13C2211yescharacteristic
19C22×#6101—21no—
20C2×#88142C2211yescharacteristic
21C2×C4×Dic26—21no—
22C2×C13×#102C2211yescharacteristic
23C2×C13×#102C2211yescharacteristic
24C2×C4×C8×C13C2211yescharacteristic
25C4×C13×C4⋊C4C2211yescharacteristic
26C2×#88072C2211yescharacteristic
27C2×#88072C2211yescharacteristic
28#11718871—21no—
29C2×#88058C2211yescharacteristic
30C2×#88058C2211yescharacteristic
31C2×#88054C2211yescharacteristic
32C2×C8×Dic13C2211yescharacteristic
33C2×C8×Dic13C2211yescharacteristic
34#11718646C2211yescharacteristic
35#11718637C2211yescharacteristic
36C4⋊C4×Dic13C2211yescharacteristic
37C4⋊C4×Dic13C2211yescharacteristic
38#11718634C2211yescharacteristic
39C2×#88047C2211yescharacteristic
40C2×#88047C2211yescharacteristic
41#11718607—21no—
42#11718603—21no—
43#11718594—21no—
44C4×#6101C2211yescharacteristic
45#11718589C2211yescharacteristic
46#11718589C2211yescharacteristic
47#11718420C418yescomplemented
48#11718316—21no—
49#11718307—21no—
50C13×#340C2211yescharacteristic
51C13×#340C2211yescharacteristic
52#11718143C2211yescharacteristic
53#11718143C2211yescharacteristic
54#11718142C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718116C2211yescharacteristic
60C22×D4×C13C2311yescharacteristic
61C23×C4×C13—21no—
62C23×Dic13—21no—
63C23×Dic13—21no—
64C22×Dic26—21no—
65C22×C8×C13C2311yescharacteristic
66C22×C8×C13C2311yescharacteristic
67C4×D4×C13—22no—
68C4×D4×C13—41no—
69C2×C13×C4⋊C4C2311yescharacteristic
70C2×C13×C4⋊C4C2311yescharacteristic
71C2×C13×C4⋊C4C2311yescharacteristic
72C2×C13×C22⋊C4—21no—
73C2×C42×C13—21no—
74C2×C42×C13C2311yescharacteristic
75C2×C22⋊Dic13—21no—
76C2×C22⋊Dic13—21no—
77D4×Dic13—22no—
78D4×Dic13—22no—
79D4×Dic13—41no—
80D4×Dic13C2×C414yes—
81C2×C4⋊Dic13—21no—
82C2×C4⋊Dic13C2311yescharacteristic
83C2×C4⋊Dic13C2311yescharacteristic
84C2×C4⋊Dic13C2311yescharacteristic
85C2×C4⋊Dic13C2311yescharacteristic
86C2×#6101—21no—
87C2×#6101—21no—
88C2×#6101—21no—
89C2×#6101—21no—
90C2×#6101—21no—
91C2×#6101—21no—
92C2×#6101—44no—
93C2×#6101D411yescharacteristic
94C2×#6101D411yescharacteristic
95C2×C4×Dic13—21no—
96C2×C4×Dic13—21no—
97C2×C4×Dic13C2311yescharacteristic
98C2×C4×Dic13C2311yescharacteristic
99C22×#1055C2311yescharacteristic
100C22×#1055C2311yescharacteristic
101#88142—22no—
102#88142C2×C414yescomplemented
103C4×Dic26—44no—
104C13×#102C2×C414yes—
105C13×#102Q814yescomplemented
106C4×C8×C13—41no—
107C13×#95—21no—
108#88072—22no—
109#88072C2×C414yes—
110#88071—21no—
111#88071—21no—
112#88071—21no—
113#88071—21no—
114#88071—21no—
115#88071—21no—
116#88071D411yescharacteristic
117#88071D411yescharacteristic
118#88058—41no—
119#88058C2×C414yescomplemented
120#88054C2×C414yescomplemented
121C8×Dic13—22no—
122C8×Dic13—41no—
123#88047—41no—
124#88047C2×C414yescomplemented
125#22962—131nomaximal, Sylow
126C24×C13—21no—
127C2×D4×C13—21no—
128C2×D4×C13—21no—
129C2×D4×C13—21no—
130C2×D4×C13C22×C412yes—
131C2×D4×C13C2×Q812yes—
132C2×D4×C13#4112yes—
133C22×C4×C13—21no—
134C22×C4×C13—21no—
135C22×C4×C13—21no—
136C22×C4×C13—42no—
137C22×C4×C13—42no—
138C22×C4×C13—81no—
139C22×C4×C13C2×D411yescharacteristic
140C22×C4×C13C2×D411yescharacteristic
141C22×C4×C13C2411yescharacteristic
142C22×Dic13—21no—
143C22×Dic13—21no—
144C22×Dic13—24no—
145C22×Dic13—21no—
146C22×Dic13—21no—
147C22×Dic13—42no—
148C22×Dic13—42no—
149C22×Dic13—42no—
150C22×Dic13—42no—
151C22×Dic13—81no—
152C22×Dic13C2×D411yescharacteristic
153C22×Dic13C2×D411yescharacteristic
154C22×Dic13C2×D411yescharacteristic
155C22×Dic13C2×D411yescharacteristic
156C2×Dic26—24no—
157C2×Dic26—42no—
158C2×Dic26—42no—
159C2×C8×C13—21no—
160C2×C8×C13—21no—
161C2×C8×C13—21no—
162C2×C8×C13—21no—
163C2×C8×C13C22×C412yes—
164C2×C8×C13C2×Q812yes—
165C13×C4⋊C4—21no—
166C13×C4⋊C4—21no—
167C13×C4⋊C4—21no—
168C13×C4⋊C4—21no—
169C13×C4⋊C4C22×C412yes—
170C13×C4⋊C4C2×Q812yes—
171C13×C22⋊C4—42no—
172C42×C13—21no—
173C42×C13—21no—
174C42×C13—42no—
175C22⋊Dic13—24no—
176C22⋊Dic13—42no—
177C4⋊Dic13—21no—
178C4⋊Dic13—21no—
179C4⋊Dic13—21no—
180C4⋊Dic13—21no—
181C4⋊Dic13—21no—
182C4⋊Dic13—21no—
183C4⋊Dic13—42no—
184C4⋊Dic13C22×C412yes—
185C4⋊Dic13C22×C412yes—
186#6101—24no—
187#6101—22no—
188#6101—42no—
189#6101—42no—
190#6101—42no—
191#6101—42no—
192#6101—81no—
193#6101D814yes—
194C4×Dic13—21no—
195C4×Dic13—21no—
196C4×Dic13—42no—
197C4×Dic13—42no—
198C4×Dic13C22×C412yes—
199C4×Dic13#4112yes—
200C2×#1055—21no—
201C2×#1055—21no—
202C2×#1055—21no—
203C2×#1055—21no—
204C2×#1055—21no—
205C2×#1055C22×C412yes—
206C2×#474—131no—
207#2365—131no—
208D4×C4⋊C4—131no—
209#1990—131no—
210#1947—131no—
211#1942—131no—
212#1942—131no—
213#1918—131no—
214#1918—131no—
215#1862—131no—
216#1862—131no—
217C8×C4⋊C4—131no—
218C4×#102—131no—
219C4×#102—131no—
220C4×#102D1311yescharacteristic
221C23×C13—22no—
222C23×C13—22no—
223C23×C13—22no—
224C23×C13—41no—
225C23×C13—41no—
226C23×C13—41no—
227C23×C13—41no—
228C23×C13C22×D411yescharacteristic
229D4×C13—22no—
230D4×C13—22no—
231D4×C13—22no—
232D4×C13C4×Q814yescomplemented
233C2×C4×C13—21no—
234C2×C4×C13—21no—
235C2×C4×C13—22no—
236C2×C4×C13—21no—
237C2×C4×C13—22no—
238C2×C4×C13—21no—
239C2×C4×C13—21no—
240C2×C4×C13—41no—
241C2×C4×C13—41no—
242C2×C4×C13—41no—
243C2×C4×C13—41no—
244C2×C4×C13—41no—
245C2×C4×C13—41no—
246C2×C4×C13—41no—
247C2×C4×C13—84no—
248C2×C4×C13C2×D812yes—
249C2×C4×C13C23×C411yescharacteristic
250C2×C4×C13C22×Q811yescharacteristic
251C2×C4×C13C2×#4111yescharacteristic
252C2×C4×C13C2×#4111yescharacteristic
253C2×C4×C13H(5,𝔽2)11yescharacteristic
254C2×C4×C132−1+411yescharacteristic
255C2×Dic13—21no—
256C2×Dic13—21no—
257C2×Dic13—21no—
258C2×Dic13—21no—
259C2×Dic13—22no—
260C2×Dic13—22no—
261C2×Dic13—21no—
262C2×Dic13—21no—
263C2×Dic13—21no—
264C2×Dic13—41no—
265C2×Dic13—41no—
266C2×Dic13—41no—
267C2×Dic13—41no—
268C2×Dic13—48no—
269C2×Dic13—41no—
270C2×Dic13—41no—
271C2×Dic13—41no—
272C2×Dic13—41no—
273C2×Dic13—41no—
274C2×Dic13—41no—
275C2×Dic13—84no—
276C2×Dic13C4×D412yes—
277C2×Dic13C4×D412yes—
278C2×Dic13C2×D812yes—
279C2×Dic13C2×D812yes—
280C2×Dic13#13512yes—
281Dic26—48no—
282C8×C13—22no—
283C8×C13—22no—
284#1055—22no—
285#1055—41no—
286C2×C4⋊Q8—131no—
287C2×C4×Q8—261no—
288C2×C4×D4—131no—
289C2×C4×D4—131no—
290C2×C4×D4C2×D1311yescharacteristic
291C22×C4⋊C4—261no—
292#474—138no—
293C2×#107—131no—
294C2×#107—131no—
295C2×#107—131no—
296C2×#107—131no—
297C2×C4⋊C8—131no—
298C2×#102—131no—
299C2×#102—131no—
300C2×#102C2×D1311yescharacteristic
301C2×#102C2×D1311yescharacteristic
302C2×C4×C8—131no—
303C2×C4×C8—131no—
304C2×C4×C8C2×D1311yescharacteristic
305#391—261no—
306#389—131no—
307#389—131no—
308#389—131no—
309#389—131no—
310#387—261no—
311#387—261no—
312#385—261no—
313#385—261no—
314#384—131no—
315#380—261no—
316C4×C4⋊C4—131no—
317C4×C4⋊C4—131no—
318C4×C4⋊C4—131no—
319C4×C4⋊C4C2×D1311yescharacteristic
320#340—131no—
321#340—131no—
322#340—131no—
323#340—131no—
324#340—131no—
325#340—131no—
326#340C2×D1311yescharacteristic
327#340C2×D1311yescharacteristic
328#336—131no—
329#336—131no—
330C22×C13—24no—
331C22×C13—42no—
332C22×C13—42no—
333C22×C13—42no—
334C22×C13—42no—
335C22×C13—42no—
336C22×C13—42no—
337C22×C13C2×C4×D411yescharacteristic
338C22×C13#54611yescharacteristic
339C22×C13D4×Q811yescharacteristic
340C22×C13C22×D811yescharacteristic
341C22×C13C2×#13511yescharacteristic
342C22×C13#57711yescharacteristic
343C22×C13#57811yescharacteristic
344C4×C13—22no—
345C4×C13—42no—
346C4×C13—42no—
347C4×C13—41no—
348C4×C13—81no—
349C4×C13C2×C4×Q811yescharacteristic
350C4×C13#52011yescharacteristic
351C4×C13#55211yescharacteristic
352C4×C13#55411yescharacteristic
353Dic13—22no—
354Dic13—22no—
355Dic13—42no—
356Dic13—42no—
357Dic13—41no—
358Dic13—81no—
359Dic13—81no—
360Dic13C4×D814yes—
361C22×Q8—261no—
362C22×D4C22×D1311yescharacteristic
363C23×C4—21no—
364C23×C4—261no—
365C23×C4—261no—
366C22×C8—131no—
367C22×C8—131no—
368C22×C8C22×D1311yescharacteristic
369C22×C8C22×D1311yescharacteristic
370C4⋊Q8—134no—
371C4⋊Q8—262no—
372C4×Q8—524no—
373C4×D4—22no—
374C4×D4—41no—
375C4×D4—134no—
376C4×D4—262no—
377C4×D4—262no—
378C4×D4—521no—
379C2×C4⋊C4—131no—
380C2×C4⋊C4—131no—
381C2×C4⋊C4—131no—
382C2×C4⋊C4—131no—
383C2×C4⋊C4—131no—
384C2×C4⋊C4—131no—
385C2×C4⋊C4—261no—
386C2×C4⋊C4—261no—
387C2×C4⋊C4—261no—
388C2×C4⋊C4—261no—
389C2×C4⋊C4—261no—
390C2×C4⋊C4—261no—
391C2×C4⋊C4—261no—
392C2×C4⋊C4—524no—
393C2×C4⋊C4C22×D1311yescharacteristic
394C2×C4⋊C4C22×D1311yescharacteristic
395C2×C4⋊C4C22×D1311yescharacteristic
396C2×C22⋊C4—21no—
397C2×C22⋊C4—261no—
398C2×C22⋊C4—261no—
399C2×C42—21no—
400C2×C42—131no—
401C2×C42—131no—
402C2×C42—261no—
403C2×C42—261no—
404C2×C42C22×D1311yescharacteristic
405#107—134no—
406#107—134no—
407#107—521no—
408#107—521no—
409C4⋊C8—134no—
410#102—134no—
411#102—262no—
412#102Dic2614yescomplemented
413#102C4×D1314yes—
414C4×C8—41no—
415C4×C8—262no—
416C4×C8—521no—
417#95—21no—
418#95—131no—
419#95—131no—
420#95—261no—
421#95—261no—
422#95—261no—
423#95—261no—
424#95—261no—
425#95—261no—
426C2×C13—44no—
427C2×C13#236011yescharacteristic
428C2×C13C2×C4×D811yescharacteristic
429C2×C13#294711yescharacteristic
430C2×C13#329411yescharacteristic
431C2×C13#330211yescharacteristic
432C2×C13Q8×D811yescharacteristic
433C2×C13#338111yescharacteristic
434C24—21no—
435C2×Q8—264no—
436C2×Q8—522no—
437C2×Q8—522no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4C2×Dic2612yes—
442C2×D4C2×C4×D1312yes—
443C2×D4#612712yes—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—42no—
448C22×C4—42no—
449C22×C4—81no—
450C22×C4—131no—
451C22×C4—131no—
452C22×C4—131no—
453C22×C4—131no—
454C22×C4—264no—
455C22×C4—261no—
456C22×C4—261no—
457C22×C4—261no—
458C22×C4—261no—
459C22×C4—522no—
460C22×C4—522no—
461C22×C4—522no—
462C22×C4—522no—
463C22×C4—1041no—
464C22×C4D4×D1311yescharacteristic
465C22×C4D4×D1311yescharacteristic
466C22×C4C23×D1311yescharacteristic
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—132no—
472C2×C8—261no—
473C2×C8—261no—
474C2×C8—261no—
475C2×C8—261no—
476C2×C8—261no—
477C2×C8C2×Dic2612yes—
478C2×C8C2×C4×D1312yes—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—134no—
484C4⋊C4—132no—
485C4⋊C4—132no—
486C4⋊C4—262no—
487C4⋊C4—264no—
488C4⋊C4—261no—
489C4⋊C4—261no—
490C4⋊C4—261no—
491C4⋊C4—261no—
492C4⋊C4—261no—
493C4⋊C4—261no—
494C4⋊C4—522no—
495C4⋊C4—522no—
496C4⋊C4—522no—
497C4⋊C4—522no—
498C4⋊C4—522no—
499C4⋊C4—1041no—
500C4⋊C4C2×Dic2612yes—
501C4⋊C4C2×C4×D1312yes—
502C22⋊C4—42no—
503C22⋊C4—264no—
504C22⋊C4—522no—
505C42—21no—
506C42—21no—
507C42—42no—
508C42—132no—
509C42—132no—
510C42—261no—
511C42—261no—
512C42—522no—
513C42—522no—
514C13#2296211yescharacteristic, complemented, Sylow
515C23—22no—
516C23—22no—
517C23—22no—
518C23—41no—
519C23—41no—
520C23—41no—
521C23—41no—
522C23C2×D4×D1311yescharacteristic
523Q8—528no—
524D4—22no—
525D4—22no—
526D4—22no—
527D4C4×Dic2614yescomplemented
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—84no—
543C2×C4—132no—
544C2×C4—132no—
545C2×C4—132no—
546C2×C4—132no—
547C2×C4—132no—
548C2×C4—261no—
549C2×C4—261no—
550C2×C4—261no—
551C2×C4—261no—
552C2×C4—261no—
553C2×C4—261no—
554C2×C4—261no—
555C2×C4—262no—
556C2×C4—262no—
557C2×C4—528no—
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—1044no—
569C2×C4D8×D1312yes—
570C2×C4C22×Dic2611yescharacteristic
571C2×C4C22×C4×D1311yescharacteristic
572C2×C4C2×#612711yescharacteristic
573C2×C4#8825111yescharacteristic
574C2×C4#41×D1311yescharacteristic
575C2×C4#8825711yescharacteristic
576C8—22no—
577C8—22no—
578C8—262no—
579C8—521no—
580C22—24no—
581C22—42no—
582C22—42no—
583C22—42no—
584C22—42no—
585C22—42no—
586C22—42no—
587C22#1171919511yescharacteristic
588C22D4×Dic2611yescharacteristic
589C22C4×D4×D1311yescharacteristic
590C22C2×D8×D1311yescharacteristic
591C22#1171946711yescharacteristic
592C22D13×#13511yescharacteristic
593C22#1171947611yescharacteristic
594C4—22no—
595C4—42no—
596C4—41no—
597C4—42no—
598C4—81no—
599C4—134no—
600C4—262no—
601C4—262no—
602C4—521no—
603C4—522no—
604C4—522no—
605C4—1041no—
606C4—1041no—
607C4C2×C4×Dic2611yescharacteristic
608C4#1171923611yescharacteristic
609C4#1171924411yescharacteristic
610C4#1171925111yescharacteristic
611C2—44no—
612C2#1311784211yescharacteristic
613C2C4×D8×D1311yescharacteristic
614C2#1312367211yescharacteristic
615C2#1312664511yescharacteristic
616C2#1312674911yescharacteristic
617C2D8×Dic2611yescharacteristic
618C2#1312771211yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC4×C13×#102C2
socleC23×C13C22×D4
prime radicalC22×D4×C13C23
cosocleC22×C4×C13C24
hypercenterC4×#102D13
hypocenterC13#22962
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#102

Complements

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

NH ≅ G/Ntype
2. #13117895C2semidirect
4. #13115795C2semidirect
5. #13115593C2semidirect
6. #13115569C2semidirect
7. #13115568C2semidirect
8. #13115407C2semidirect
9. #13115406C2semidirect
12. C8×#6101C2semidirect
47. #11718420C4semidirect
102. #88142C2×C4semidirect
105. C13×#102Q8semidirect
119. #88058C2×C4semidirect
120. #88054C2×C4semidirect
124. #88047C2×C4semidirect
232. D4×C13C4×Q8semidirect
412. #102Dic26semidirect
514. C13#22962semidirect
527. D4C4×Dic26semidirect

Maximal subgroups

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

subgroupindex
C2×#117184202
#131178952
D4×#61012
#131157952
#131155932
#131155692
#131155682
#131154072
#131154062
#131150852
#131150832
C8×#61012
#102×Dic132
C4×C13×#1022
#2296213