Finite Group Databasebeta

← #15925296

Subgroups — #15925296

Order 3328.

718 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×C4⋊Dic13C211yesmaximal, characteristic, complemented
2#13116374C211yesmaximal, characteristic, complemented
3#13116364C211yesmaximal, characteristic
4#13116244C211yesmaximal, characteristic, complemented
5#13116239C211yesmaximal, characteristic
6#13115777C211yesmaximal, characteristic, complemented
7#13115769C211yesmaximal, characteristic
8#13115653C211yesmaximal, characteristic
9#13115594C211yesmaximal, characteristic, complemented
10#13115474C211yesmaximal, characteristic, complemented
11#13115467C211yesmaximal, characteristic, complemented
12#13115460C211yesmaximal, characteristic
13#13115453C211yesmaximal, characteristic
14#13114734C211yesmaximal, characteristic, complemented
15C13×#2592C211yesmaximal, characteristic
16C2×C13×#124C2211yescharacteristic
17C2×C4×Q8×C13C2211yescharacteristic
18C2×Q8×Dic13—21no—
19C13×#397—21no—
20C13×#393—21no—
21C13×#391C2211yescharacteristic
22C13×#391C2211yescharacteristic
23C13×#390C2211yescharacteristic
24C13×#390C2211yescharacteristic
25C13×#388—21no—
26C13×#388—21no—
27C4×C13×C4⋊C4C2211yescharacteristic
28C2×#88075C2211yescharacteristic
29C2×#88075C2211yescharacteristic
30C2×#88075C2211yescharacteristic
31C2×#88075C2211yescharacteristic
32C2×#88072C2211yescharacteristic
33C2×#88072C2211yescharacteristic
34C2×#88072C2211yescharacteristic
35C2×#88072C2211yescharacteristic
36#11718646—21no—
37#11718646—21no—
38#11718646—21no—
39C2×#88048C2211yescharacteristic
40C2×#88047C2211yescharacteristic
41C2×#88047C2211yescharacteristic
42C2×#88047C2211yescharacteristic
43#11718596C2211yescharacteristic
44#11718596C2211yescharacteristic
45#11718596C2211yescharacteristic
46C4×C4⋊Dic13C2211yescharacteristic
47C4×C4⋊Dic13C2211yescharacteristic
48C4×C4⋊Dic13C2211yescharacteristic
49C2×C4⋊#1055C2211yescharacteristic
50C2×#88043C2211yescharacteristic
51#11718121C2211yescharacteristic
52#11718121C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718116C2211yescharacteristic
56#11718116C2211yescharacteristic
57#11718116C2211yescharacteristic
58#11718116C2211yescharacteristic
59C22×Q8×C13D411yescharacteristic
60C22×Q8×C13C2311yescharacteristic
61C22×D4×C13C2311yescharacteristic
62C13×#124—22no—
63C13×#124—22no—
64C4×Q8×C13—22no—
65C4×Q8×C13—22no—
66C2×C13×C4⋊C4D411yescharacteristic
67C2×C13×C4⋊C4D411yescharacteristic
68C2×C13×C4⋊C4D411yescharacteristic
69C2×C13×C4⋊C4C2311yescharacteristic
70C2×C13×C4⋊C4C2311yescharacteristic
71C2×C13×C22⋊C4—21no—
72C2×C13×C22⋊C4—21no—
73C2×C13×C22⋊C4—21no—
74C2×C13×C22⋊C4—21no—
75C2×C13×C22⋊C4—21no—
76C2×C13×C22⋊C4—21no—
77C2×C42×C13—21no—
78C2×C42×C13C2311yescharacteristic
79C2×C42×C13C2311yescharacteristic
80C2×C42×C13C2311yescharacteristic
81Q8×Dic13—44no—
82C2×C4⋊Dic13—21no—
83C2×C4⋊Dic13—21no—
84C2×C4⋊Dic13—21no—
85C2×C4⋊Dic13—21no—
86C2×C4⋊Dic13—21no—
87C2×C4⋊Dic13—21no—
88C2×C4⋊Dic13C2311yescharacteristic
89C2×C4⋊Dic13C2311yescharacteristic
90C2×C4⋊Dic13C2311yescharacteristic
91C2×C4⋊Dic13C2311yescharacteristic
92C2×C4×Dic13—21no—
93C2×C4×Dic13—21no—
94C2×C4×Dic13—21no—
95C22×#1055C2311yescharacteristic
96C22×#1055C2311yescharacteristic
97C22×#1055C2311yescharacteristic
98C22×#1055C2311yescharacteristic
99C13×#95—21no—
100C13×#95—21no—
101C13×#95—21no—
102C13×#95—21no—
103C13×#95—21no—
104#88075—22no—
105#88075—22no—
106#88075—41no—
107#88075—41no—
108#88072—22no—
109#88072—22no—
110#88072—41no—
111#88072—41no—
112#88071—21no—
113#88071—21no—
114#88071—21no—
115#88048—22no—
116#88047—22no—
117#88047—41no—
118#88047—41no—
119C4⋊#1055—22no—
120#88043—22no—
121#26330—131nomaximal, Sylow
122C24×C13—21no—
123C2×Q8×C13—22no—
124C2×Q8×C13—22no—
125C2×Q8×C13—22no—
126C2×Q8×C13—21no—
127C2×Q8×C13—21no—
128C2×Q8×C13—21no—
129C2×Q8×C13—21no—
130C2×Q8×C13—21no—
131C2×Q8×C13—21no—
132C2×D4×C13—21no—
133C2×D4×C13—21no—
134C2×D4×C13—21no—
135C2×D4×C13—21no—
136C2×D4×C13—21no—
137C2×D4×C13—21no—
138C22×C4×C13—21no—
139C22×C4×C13—21no—
140C22×C4×C13—21no—
141C22×C4×C13C2×D411yescharacteristic
142C22×C4×C13C2×D411yescharacteristic
143C22×C4×C13C2×D411yescharacteristic
144C22×C4×C13C2×D411yescharacteristic
145C22×C4×C13C2×D411yescharacteristic
146C22×C4×C13C2×D411yescharacteristic
147C22×C4×C13C2411yescharacteristic
148C22×Dic13—21no—
149C22×Dic13—21no—
150C22×Dic13—21no—
151C22×Dic13—21no—
152C13×C4⋊C4—22no—
153C13×C4⋊C4—22no—
154C13×C4⋊C4—22no—
155C13×C4⋊C4—21no—
156C13×C4⋊C4—21no—
157C13×C4⋊C4—21no—
158C13×C4⋊C4—21no—
159C13×C22⋊C4—42no—
160C13×C22⋊C4—42no—
161C13×C22⋊C4—42no—
162C13×C22⋊C4—42no—
163C13×C22⋊C4—81no—
164C13×C22⋊C4—81no—
165C42×C13—21no—
166C42×C13—21no—
167C42×C13—21no—
168C42×C13—21no—
169C42×C13—81no—
170C42×C13#4112yes—
171C42×C13#4112yes—
172C4⋊Dic13—21no—
173C4⋊Dic13—21no—
174C4⋊Dic13—21no—
175C4⋊Dic13—21no—
176C4⋊Dic13—21no—
177C4⋊Dic13—21no—
178C4⋊Dic13—21no—
179C4⋊Dic13—42no—
180C4⋊Dic13—42no—
181C4⋊Dic13—42no—
182C4⋊Dic13—81no—
183C4⋊Dic13—81no—
184C4⋊Dic13—81no—
185C4⋊Dic13#4112yes—
186C4×Dic13—42no—
187C4×Dic13—42no—
188C4×Dic13—42no—
189C2×#1055—21no—
190C2×#1055—21no—
191C2×#1055—21no—
192C2×#1055—21no—
193C2×#1055—21no—
194C2×#1055—21no—
195C2×#1055—21no—
196C2×#1055—21no—
197C2×#1055—21no—
198C2×#1055—21no—
199C2×#1055—21no—
200C2×#1055#4112yes—
201#2592D1311yescharacteristic
202Q8×C4⋊C4—131no—
203#2095—131no—
204#2093—131no—
205#2072—131no—
206#2071—131no—
207#1985—131no—
208#1983—131no—
209#1959—131no—
210#1947—131no—
211#1928—131no—
212#1927—131no—
213#1926—131no—
214#1925—131no—
215#1776—131no—
216C23×C13—41no—
217C23×C13—41no—
218C23×C13—41no—
219C23×C13—41no—
220C23×C13—41no—
221C23×C13—41no—
222C23×C13—41no—
223C23×C13C22×D411yescharacteristic
224Q8×C13—28no—
225Q8×C13—41no—
226Q8×C13—41no—
227Q8×C13—41no—
228Q8×C13—41no—
229D4×C13—41no—
230D4×C13—41no—
231D4×C13—41no—
232D4×C13—41no—
233C2×C4×C13—21no—
234C2×C4×C13—21no—
235C2×C4×C13—21no—
236C2×C4×C13—21no—
237C2×C4×C13—21no—
238C2×C4×C13—21no—
239C2×C4×C13—21no—
240C2×C4×C13—21no—
241C2×C4×C13—21no—
242C2×C4×C13—21no—
243C2×C4×C13—21no—
244C2×C4×C13—21no—
245C2×C4×C13—21no—
246C2×C4×C13—21no—
247C2×C4×C13—41no—
248C2×C4×C13—41no—
249C2×C4×C13—41no—
250C2×C4×C13—41no—
251C2×C4×C13—41no—
252C2×C4×C13—41no—
253C2×C4×C13—41no—
254C2×C4×C13—41no—
255C2×C4×C13—41no—
256C2×C4×C13#12312yes—
257C2×C4×C13#12312yes—
258C2×C4×C13AGL(1,ℤ/8)12yes—
259C2×C4×C13#13712yes—
260C2×C4×C13C2×#4111yescharacteristic
261C2×C4×C13C2×#4111yescharacteristic
262C2×C4×C13C2×#4111yescharacteristic
263C2×C4×C13C2×#4111yescharacteristic
264C2×C4×C13H(5,𝔽2)11yescharacteristic
265C2×C4×C132−1+411yescharacteristic
266C2×Dic13—22no—
267C2×Dic13—41no—
268C2×Dic13—41no—
269C2×Dic13—41no—
270C2×Dic13—41no—
271C2×Dic13—41no—
272C2×Dic13—41no—
273C2×Dic13—41no—
274C2×Dic13—41no—
275C2×Dic13—41no—
276C2×Dic13—41no—
277C2×Dic13—41no—
278#1055—22no—
279#1055—41no—
280#1055—41no—
281#1055—41no—
282C2×#124C2×D1311yescharacteristic
283C2×C4×Q8—261no—
284C2×C4×Q8C2×D1311yescharacteristic
285C2×#107—131no—
286C2×#107—131no—
287C2×#107—131no—
288C2×#106—131no—
289C2×C4⋊C8—131no—
290C2×#103—131no—
291C2×#103—131no—
292C2×#103—131no—
293C2×#103—131no—
294C2×#102—131no—
295C2×#102—131no—
296C2×#102—131no—
297C2×#102—131no—
298C2×#97—131no—
299#397—21no—
300#393—21no—
301#391C2×D1311yescharacteristic
302#391C2×D1311yescharacteristic
303#390C2×D1311yescharacteristic
304#390C2×D1311yescharacteristic
305#389—261no—
306#389—261no—
307#389—261no—
308#388—21no—
309#388—21no—
310#384—131no—
311#384—131no—
312#384—131no—
313C4×C4⋊C4—131no—
314C4×C4⋊C4—131no—
315C4×C4⋊C4—131no—
316C4×C4⋊C4C2×D1311yescharacteristic
317#340—131no—
318#340—131no—
319#340—131no—
320#340—131no—
321#336—131no—
322#336—131no—
323#336—131no—
324#336—131no—
325C22×C13—81no—
326C22×C13—81no—
327C22×C13—81no—
328C22×C13—81no—
329C22×C13—81no—
330C22×C13—81no—
331C22×C13—81no—
332C22×C13C2×#12311yescharacteristic
333C22×C13#54811yescharacteristic
334C22×C13#55011yescharacteristic
335C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
336C22×C13C2×#13711yescharacteristic
337C22×C13#57611yescharacteristic
338C22×C13#57811yescharacteristic
339C4×C13—22no—
340C4×C13—22no—
341C4×C13—22no—
342C4×C13—22no—
343C4×C13—41no—
344C4×C13—41no—
345C4×C13—81no—
346C4×C13—81no—
347C4×C13—81no—
348C4×C13#52911yescharacteristic
349C4×C13#54211yescharacteristic
350C4×C13#55611yescharacteristic
351C4×C13#55911yescharacteristic
352Dic13—42no—
353Dic13—81no—
354Dic13—81no—
355Dic13—81no—
356C22×Q8C22⋊D1311yescharacteristic
357C22×Q8C22×D1311yescharacteristic
358C22×D4C22×D1311yescharacteristic
359C22×C8—131no—
360C22×C8—131no—
361C22×C8—131no—
362C22×C8—131no—
363#124—22no—
364#124—22no—
365C4×Q8—22no—
366C4×Q8—22no—
367C4×Q8—524no—
368C2×C4⋊C4—131no—
369C2×C4⋊C4—131no—
370C2×C4⋊C4—131no—
371C2×C4⋊C4—131no—
372C2×C4⋊C4—261no—
373C2×C4⋊C4—261no—
374C2×C4⋊C4—261no—
375C2×C4⋊C4—261no—
376C2×C4⋊C4—261no—
377C2×C4⋊C4—261no—
378C2×C4⋊C4C22⋊D1311yescharacteristic
379C2×C4⋊C4C22⋊D1311yescharacteristic
380C2×C4⋊C4C22⋊D1311yescharacteristic
381C2×C4⋊C4C22×D1311yescharacteristic
382C2×C4⋊C4C22×D1311yescharacteristic
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C42—21no—
390C2×C42—261no—
391C2×C42—261no—
392C2×C42—261no—
393C2×C42C22×D1311yescharacteristic
394C2×C42C22×D1311yescharacteristic
395C2×C42C22×D1311yescharacteristic
396#107—262no—
397#107—521no—
398#107—521no—
399#106—262no—
400C4⋊C8—262no—
401#103—262no—
402#103—262no—
403#103—521no—
404#103—521no—
405#102—262no—
406#102—262no—
407#102—521no—
408#102—521no—
409#97—262no—
410#95—21no—
411#95—21no—
412#95—21no—
413#95—21no—
414#95—21no—
415#95—261no—
416#95—261no—
417#95—261no—
418C2×C13—161no—
419C2×C13#244811yescharacteristic
420C2×C13#309211yescharacteristic
421C2×C13#309811yescharacteristic
422C2×C13#336711yescharacteristic
423C2×C13#337511yescharacteristic
424C2×C13#339811yescharacteristic
425C2×C13#339911yescharacteristic
426C24—21no—
427C2×Q8—22no—
428C2×Q8—22no—
429C2×Q8—22no—
430C2×Q8—21no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—261no—
446C22×C4—261no—
447C22×C4—261no—
448C22×C4—261no—
449C22×C4C2×C22⋊D1311yescharacteristic
450C22×C4C2×C22⋊D1311yescharacteristic
451C22×C4C2×C22⋊D1311yescharacteristic
452C22×C4C2×C22⋊D1311yescharacteristic
453C22×C4C2×C22⋊D1311yescharacteristic
454C22×C4C2×C22⋊D1311yescharacteristic
455C22×C4C23×D1311yescharacteristic
456C2×C8—132no—
457C2×C8—261no—
458C2×C8—261no—
459C2×C8—261no—
460C2×C8—261no—
461C2×C8—261no—
462C2×C8—261no—
463C2×C8—261no—
464C2×C8—261no—
465C2×C8—261no—
466C2×C8—261no—
467C2×C8—261no—
468C4⋊C4—22no—
469C4⋊C4—22no—
470C4⋊C4—22no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—132no—
476C4⋊C4—261no—
477C4⋊C4—261no—
478C4⋊C4—261no—
479C4⋊C4—261no—
480C4⋊C4—261no—
481C4⋊C4—261no—
482C4⋊C4—261no—
483C4⋊C4—522no—
484C4⋊C4—522no—
485C4⋊C4—522no—
486C4⋊C4—1041no—
487C4⋊C4—1041no—
488C4⋊C4—1041no—
489C22⋊C4—42no—
490C22⋊C4—42no—
491C22⋊C4—42no—
492C22⋊C4—42no—
493C22⋊C4—81no—
494C22⋊C4—81no—
495C42—21no—
496C42—21no—
497C42—21no—
498C42—21no—
499C42—81no—
500C42—522no—
501C42—522no—
502C42—522no—
503C42#612912yes—
504C42#612912yes—
505C13#2633011yescharacteristic, complemented, Sylow
506C23—41no—
507C23—41no—
508C23—41no—
509C23—41no—
510C23—41no—
511C23—41no—
512C23—41no—
513C23C22×C22⋊D1311yescharacteristic
514Q8—28no—
515Q8—41no—
516Q8—41no—
517Q8—41no—
518Q8—41no—
519D4—41no—
520D4—41no—
521D4—41no—
522D4—41no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—262no—
547C2×C4—521no—
548C2×C4—521no—
549C2×C4—521no—
550C2×C4—521no—
551C2×C4—521no—
552C2×C4—521no—
553C2×C4—521no—
554C2×C4—521no—
555C2×C4—521no—
556C2×C4—521no—
557C2×C4—521no—
558C2×C4#8818912yes—
559C2×C4#8818912yes—
560C2×C4#8820312yes—
561C2×C4#8820512yes—
562C2×C4C2×#612911yescharacteristic
563C2×C4C2×#612911yescharacteristic
564C2×C4#41×D1311yescharacteristic
565C2×C4#41×D1311yescharacteristic
566C2×C4#8825611yescharacteristic
567C2×C4#8825711yescharacteristic
568C8—262no—
569C8—521no—
570C8—521no—
571C8—521no—
572C22—81no—
573C22—81no—
574C22—81no—
575C22—81no—
576C22—81no—
577C22—81no—
578C22—81no—
579C22C2×#8818911yescharacteristic
580C22C2×#8820311yescharacteristic
581C22C2×#8820511yescharacteristic
582C22#1171953611yescharacteristic
583C22#1171953911yescharacteristic
584C22#1171954011yescharacteristic
585C22#1171954311yescharacteristic
586C4—22no—
587C4—22no—
588C4—22no—
589C4—22no—
590C4—41no—
591C4—41no—
592C4—81no—
593C4—81no—
594C4—81no—
595C4—522no—
596C4—1041no—
597C4—1041no—
598C4—1041no—
599C4#1171937611yescharacteristic
600C4#1171938511yescharacteristic
601C4#1171938611yescharacteristic
602C4#1171938711yescharacteristic
603C2—161no—
604C2#1311863011yescharacteristic
605C2#1312475611yescharacteristic
606C2#1312481011yescharacteristic
607C2#1312755011yescharacteristic
608C2#1312764611yescharacteristic
609C2#1312786711yescharacteristic
610C2#1312787411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2592C2
socleC23×C13C22×D4
prime radicalC22×D4×C13C23
hypercenter#2592D13
hypocenterC13#26330
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ #2592

Complements

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

NH ≅ G/Ntype
1. Q8×C4⋊Dic13C2semidirect
2. #13116374C2semidirect
4. #13116244C2semidirect
6. #13115777C2semidirect
9. #13115594C2semidirect
10. #13115474C2semidirect
11. #13115467C2semidirect
14. #13114734C2semidirect
505. C13#26330semidirect

Maximal subgroups

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

subgroupindex
Q8×C4⋊Dic132
#131163742
#131163642
#131162442
#131162392
#131157772
#131157692
#131156532
#131155942
#131154742
#131154672
#131154602
#131154532
#131147342
C13×#25922
#2633013