Finite Group Databasebeta

← #15914803

Subgroups — #15914803

Order 3328.

774 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718491C211yesmaximal, characteristic, complemented
2#13120225C211yesmaximal, characteristic, complemented
3#13120190C211yesmaximal, characteristic
4#13116335C211yesmaximal, characteristic, complemented
5#13116330C211yesmaximal, characteristic, complemented
6#13116222C211yesmaximal, characteristic
7#13116208C211yesmaximal, characteristic
8#13115802C211yesmaximal, characteristic, complemented
9#13115606C211yesmaximal, characteristic, complemented
10#13115567C211yesmaximal, characteristic, complemented
11#13115562C211yesmaximal, characteristic, complemented
12#13115516C211yesmaximal, characteristic
13#13115516C211yesmaximal, characteristic
14C4×#88072C211yesmaximal, characteristic
15C2×C13×#478C211yesmaximal, characteristic
16C2×C13×#125C2211yescharacteristic
17C2×C4×D4×C13C2211yescharacteristic
18C2×C4×Dic26C2211yescharacteristic
19C13×#478—24no—
20C2×C13×#107C2211yescharacteristic
21C2×C13×#106C2211yescharacteristic
22C2×C13×C4⋊C8C2211yescharacteristic
23C2×C13×#102C2211yescharacteristic
24C2×C13×#102C2211yescharacteristic
25#11718882C2211yescharacteristic
26#11718882C2211yescharacteristic
27C2×#88072C2211yescharacteristic
28C2×#88072C2211yescharacteristic
29#11718871—21no—
30#11718871—21no—
31C2×#88058C2211yescharacteristic
32C2×#88057C2211yescharacteristic
33C2×#88054C2211yescharacteristic
34C2×#88054C2211yescharacteristic
35C2×C8×Dic13C2211yescharacteristic
36C2×C8×Dic13C2211yescharacteristic
37#11718644—21no—
38#11718640—21no—
39#11718634C2211yescharacteristic
40#11718634C2211yescharacteristic
41#11718634C2211yescharacteristic
42#11718634C2211yescharacteristic
43#11718634C2211yescharacteristic
44#11718634C2211yescharacteristic
45#11718633—21no—
46#11718633—21no—
47#11718610—21no—
48#11718608—21no—
49#11718597C2211yescharacteristic
50C4×C4⋊Dic13C2211yescharacteristic
51C2×C4×#1055C2211yescharacteristic
52#11718491—24no—
53#11718143C2211yescharacteristic
54#11718143C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718121C2211yescharacteristic
60#11718121C2211yescharacteristic
61C22×D4×C13C2311yescharacteristic
62C23×C4×C13—21no—
63C22×Dic26D411yescharacteristic
64C22×C8×C13C2311yescharacteristic
65C22×C8×C13C2311yescharacteristic
66C13×#125—22no—
67C13×#125—22no—
68C4×D4×C13—22no—
69C4×D4×C13—22no—
70C2×C13×C4⋊C4—21no—
71C2×C13×C4⋊C4—21no—
72C2×C13×C4⋊C4C2311yescharacteristic
73C2×C13×C4⋊C4C2311yescharacteristic
74C2×C13×C4⋊C4C2311yescharacteristic
75C2×C13×C22⋊C4—21no—
76C2×C42×C13C2311yescharacteristic
77C2×C22⋊Dic13—21no—
78C2×C22⋊Dic13—21no—
79C2×C22⋊Dic13—21no—
80C2×C22⋊Dic13—21no—
81C2×C4⋊Dic13D411yescharacteristic
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×#6101D411yescharacteristic
93C2×#6101D411yescharacteristic
94C2×C4×Dic13—21no—
95C2×C4×Dic13C2311yescharacteristic
96C2×C4×Dic13C2311yescharacteristic
97C22×#1055C2311yescharacteristic
98C22×#1055C2311yescharacteristic
99C4×Dic26—22no—
100C4×Dic26—22no—
101C13×#107—22no—
102C13×#106—22no—
103C13×C4⋊C8D414yes—
104C13×#102—22no—
105C13×#102—22no—
106#88072—22no—
107#88072Q814yescomplemented
108#88071—21no—
109#88071—21no—
110#88071—21no—
111#88071—21no—
112#88071—21no—
113#88071—21no—
114#88071—21no—
115#88071—21no—
116#88071—21no—
117#88058—22no—
118#88057—22no—
119#88054—22no—
120#88054—22no—
121C8×Dic13—22no—
122C8×Dic13—22no—
123C4×#1055—22no—
124#25473—131nomaximal, Sylow
125C24×C13—21no—
126C2×D4×C13—21no—
127C2×D4×C13—21no—
128C2×D4×C13—21no—
129C2×D4×C13—21no—
130C2×D4×C13—21no—
131C2×D4×C13C2×Q812yes—
132C22×C4×C13—21no—
133C22×C4×C13—21no—
134C22×C4×C13—21no—
135C22×C4×C13—42no—
136C22×C4×C13—81no—
137C22×C4×C13—81no—
138C22×C4×C13C2×D411yescharacteristic
139C22×C4×C13C2×D411yescharacteristic
140C22×C4×C13C2411yescharacteristic
141C22×Dic13—21no—
142C22×Dic13—21no—
143C22×Dic13—21no—
144C22×Dic13—21no—
145C22×Dic13C2×D411yescharacteristic
146C22×Dic13C2×D411yescharacteristic
147C22×Dic13C2×D411yescharacteristic
148C22×Dic13C2×D411yescharacteristic
149C2×Dic26—22no—
150C2×Dic26—22no—
151C2×Dic26—22no—
152C2×C8×C13—21no—
153C2×C8×C13—21no—
154C2×C8×C13—21no—
155C2×C8×C13—21no—
156C2×C8×C13C2×D412yes—
157C2×C8×C13C2×D412yes—
158C13×C4⋊C4—21no—
159C13×C4⋊C4—21no—
160C13×C4⋊C4—21no—
161C13×C4⋊C4—21no—
162C13×C4⋊C4—21no—
163C13×C4⋊C4—21no—
164C13×C4⋊C4—42no—
165C13×C4⋊C4—42no—
166C13×C22⋊C4—42no—
167C42×C13C2×D412yes—
168C42×C13#4112yes—
169C22⋊Dic13—42no—
170C22⋊Dic13—42no—
171C22⋊Dic13—81no—
172C22⋊Dic13—81no—
173C4⋊Dic13—22no—
174C4⋊Dic13—21no—
175C4⋊Dic13—21no—
176C4⋊Dic13—21no—
177C4⋊Dic13—21no—
178C4⋊Dic13—21no—
179C4⋊Dic13—21no—
180C4⋊Dic13C2×Q812yes—
181C4⋊Dic13#4112yes—
182#6101—22no—
183#6101—22no—
184#6101—42no—
185#6101—42no—
186#6101—81no—
187#6101—81no—
188#6101—81no—
189#6101—81no—
190C4×Dic13—21no—
191C4×Dic13—21no—
192C4×Dic13—21no—
193C4×Dic13—21no—
194C4×Dic13—81no—
195C2×#1055—21no—
196C2×#1055—21no—
197C2×#1055—21no—
198C2×#1055—21no—
199C2×#1055—21no—
200C2×#1055C2×Q812yes—
201C2×#478D1311yescharacteristic
202C2×C8×Q8—131no—
203#2584—131no—
204#2580—131no—
205#2088—131no—
206#2087—131no—
207#2067—131no—
208#2065—131no—
209#1991—131no—
210#1949—131no—
211#1942—131no—
212#1941—131no—
213#1934—131no—
214#1934—131no—
215C4×#102—131no—
216C23×C13—22no—
217C23×C13—41no—
218C23×C13—41no—
219C23×C13—41no—
220C23×C13—41no—
221C23×C13—41no—
222C23×C13—41no—
223C23×C13C22×D411yescharacteristic
224D4×C13—22no—
225D4×C13—22no—
226D4×C13—41no—
227D4×C13—41no—
228C2×C4×C13—21no—
229C2×C4×C13—21no—
230C2×C4×C13—21no—
231C2×C4×C13—21no—
232C2×C4×C13—41no—
233C2×C4×C13—41no—
234C2×C4×C13—41no—
235C2×C4×C13—41no—
236C2×C4×C13—41no—
237C2×C4×C13—41no—
238C2×C4×C13—41no—
239C2×C4×C13—41no—
240C2×C4×C13—41no—
241C2×C4×C13—84no—
242C2×C4×C13#12112yes—
243C2×C4×C13#12112yes—
244C2×C4×C13C22×D411yescharacteristic
245C2×C4×C13C22×Q811yescharacteristic
246C2×C4×C13C2×#4111yescharacteristic
247C2×C4×C13C2×#4111yescharacteristic
248C2×C4×C132−1+411yescharacteristic
249C2×C4×C132−1+411yescharacteristic
250C2×Dic13—21no—
251C2×Dic13—21no—
252C2×Dic13—21no—
253C2×Dic13—21no—
254C2×Dic13—21no—
255C2×Dic13—21no—
256C2×Dic13—22no—
257C2×Dic13—22no—
258C2×Dic13—21no—
259C2×Dic13—21no—
260C2×Dic13—21no—
261C2×Dic13—21no—
262C2×Dic13—41no—
263C2×Dic13—41no—
264C2×Dic13—41no—
265C2×Dic13—41no—
266C2×Dic13—41no—
267C2×Dic13—41no—
268C2×Dic13—41no—
269C2×Dic13—41no—
270C2×Dic13—41no—
271C2×Dic13—41no—
272C2×Dic13#13512yes—
273C2×Dic13#13512yes—
274Dic26—28no—
275C8×C13—22no—
276C8×C13—22no—
277#1055—22no—
278#1055—41no—
279C2×#125C2×D1311yescharacteristic
280C2×C4×Q8—131no—
281C2×C4×D4C2×D1311yescharacteristic
282#478—24no—
283C8×Q8—264no—
284C2×#107—131no—
285C2×#107C2×D1311yescharacteristic
286C2×#106—131no—
287C2×#106C2×D1311yescharacteristic
288C2×C4⋊C8—131no—
289C2×C4⋊C8—131no—
290C2×C4⋊C8C2×D1311yescharacteristic
291C2×#102—131no—
292C2×#102—131no—
293C2×#102C2×D1311yescharacteristic
294C2×#102C2×D1311yescharacteristic
295C2×C4×C8—131no—
296C2×C4×C8—131no—
297C2×C4×C8—131no—
298#399—261no—
299#398—261no—
300#395—261no—
301#393—261no—
302#390—131no—
303#390—131no—
304#389—131no—
305#389—131no—
306#389—131no—
307#389—131no—
308#389—131no—
309#389—131no—
310#389—261no—
311#389—261no—
312#385—261no—
313#385—261no—
314#382—131no—
315C4×C4⋊C4—131no—
316#340—131no—
317#340—131no—
318#340—131no—
319#340—131no—
320#340—131no—
321#340—131no—
322#340—131no—
323#340—131no—
324C22×C13—42no—
325C22×C13—42no—
326C22×C13—42no—
327C22×C13—81no—
328C22×C13—81no—
329C22×C13—81no—
330C22×C13—81no—
331C22×C13C2×#12111yescharacteristic
332C22×C13#54811yescharacteristic
333C22×C13D4×Q811yescharacteristic
334C22×C13C2×#13511yescharacteristic
335C22×C13C2×#13511yescharacteristic
336C22×C13#57611yescharacteristic
337C22×C13#57711yescharacteristic
338C4×C13—22no—
339C4×C13—22no—
340C4×C13—81no—
341C4×C13—81no—
342C4×C13—81no—
343C4×C13#53311yescharacteristic
344C4×C13#54111yescharacteristic
345C4×C13#54711yescharacteristic
346C4×C13D4×Q811yescharacteristic
347Dic13—22no—
348Dic13—22no—
349Dic13—42no—
350Dic13—42no—
351Dic13—41no—
352Dic13—41no—
353Dic13—81no—
354Dic13—81no—
355C22×Q8—131no—
356C22×D4C22×D1311yescharacteristic
357C23×C4—21no—
358C22×C8—131no—
359C22×C8—131no—
360C22×C8C22×D1311yescharacteristic
361C22×C8C22×D1311yescharacteristic
362#125—22no—
363#125—22no—
364C4×Q8—262no—
365C4×Q8—262no—
366C4×D4—22no—
367C4×D4—22no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—131no—
371C2×C4⋊C4—131no—
372C2×C4⋊C4—131no—
373C2×C4⋊C4—131no—
374C2×C4⋊C4—131no—
375C2×C4⋊C4—131no—
376C2×C4⋊C4—131no—
377C2×C4⋊C4—261no—
378C2×C4⋊C4—261no—
379C2×C4⋊C4—261no—
380C2×C4⋊C4—261no—
381C2×C4⋊C4—261no—
382C2×C4⋊C4—261no—
383C2×C4⋊C4C22×D1311yescharacteristic
384C2×C4⋊C4C22×D1311yescharacteristic
385C2×C4⋊C4C22×D1311yescharacteristic
386C2×C22⋊C4—21no—
387C2×C22⋊C4—261no—
388C2×C22⋊C4—261no—
389C2×C22⋊C4—261no—
390C2×C22⋊C4—261no—
391C2×C42—131no—
392C2×C42—131no—
393C2×C42—261no—
394C2×C42C22×D1311yescharacteristic
395#107—22no—
396#107—262no—
397#106—22no—
398#106—262no—
399C4⋊C8—262no—
400C4⋊C8—262no—
401C4⋊C8C22⋊D1314yes—
402#102—22no—
403#102—22no—
404#102—134no—
405#102—262no—
406C4×C8—262no—
407C4×C8—262no—
408C4×C8—262no—
409#95—261no—
410#95—261no—
411#95—261no—
412#95—261no—
413#95—261no—
414#95—261no—
415#95—261no—
416#95—261no—
417#95—261no—
418C2×C13—82no—
419C2×C13#242911yescharacteristic
420C2×C13#305011yescharacteristic
421C2×C13#306211yescharacteristic
422C2×C13#336111yescharacteristic
423C2×C13#336511yescharacteristic
424C2×C13#338011yescharacteristic
425C2×C13#338111yescharacteristic
426C24—21no—
427C2×Q8—262no—
428C2×Q8—262no—
429C2×Q8—262no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—21no—
434C2×D4—21no—
435C2×D4Q8×D1312yes—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—42no—
440C22×C4—81no—
441C22×C4—81no—
442C22×C4—131no—
443C22×C4—131no—
444C22×C4—131no—
445C22×C4—131no—
446C22×C4—261no—
447C22×C4—261no—
448C22×C4—261no—
449C22×C4—261no—
450C22×C4D4×D1311yescharacteristic
451C22×C4D4×D1311yescharacteristic
452C22×C4C23×D1311yescharacteristic
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—132no—
458C2×C8—261no—
459C2×C8—261no—
460C2×C8—261no—
461C2×C8—261no—
462C2×C8—261no—
463C2×C8C2×C22⋊D1312yes—
464C2×C8C2×C22⋊D1312yes—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—42no—
472C4⋊C4—42no—
473C4⋊C4—132no—
474C4⋊C4—132no—
475C4⋊C4—262no—
476C4⋊C4—262no—
477C4⋊C4—262no—
478C4⋊C4—261no—
479C4⋊C4—261no—
480C4⋊C4—261no—
481C4⋊C4—261no—
482C4⋊C4—261no—
483C4⋊C4—261no—
484C4⋊C4—522no—
485C4⋊C4—522no—
486C4⋊C4—1041no—
487C4⋊C4—1041no—
488C4⋊C4—1041no—
489C4⋊C4—1041no—
490C22⋊C4—42no—
491C22⋊C4—522no—
492C22⋊C4—522no—
493C22⋊C4—1041no—
494C22⋊C4—1041no—
495C42—261no—
496C42—261no—
497C42—261no—
498C42—261no—
499C42—1041no—
500C42#612912yes—
501C42C2×C22⋊D1312yes—
502C13#2547311yescharacteristic, complemented, Sylow
503C23—22no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23—41no—
510C23C2×D4×D1311yescharacteristic
511Q8—268no—
512D4—22no—
513D4—22no—
514D4—41no—
515D4—41no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—84no—
530C2×C4—132no—
531C2×C4—132no—
532C2×C4—261no—
533C2×C4—261no—
534C2×C4—261no—
535C2×C4—261no—
536C2×C4—261no—
537C2×C4—261no—
538C2×C4—261no—
539C2×C4—261no—
540C2×C4—261no—
541C2×C4—261no—
542C2×C4—262no—
543C2×C4—262no—
544C2×C4—521no—
545C2×C4—521no—
546C2×C4—521no—
547C2×C4—521no—
548C2×C4—521no—
549C2×C4—521no—
550C2×C4—521no—
551C2×C4—521no—
552C2×C4—521no—
553C2×C4—521no—
554C2×C4#8819212yes—
555C2×C4#8819212yes—
556C2×C4C2×#612911yescharacteristic
557C2×C4C2×Q8×D1311yescharacteristic
558C2×C4#8825411yescharacteristic
559C2×C4#41×D1311yescharacteristic
560C2×C4#8825711yescharacteristic
561C2×C4C22×C22⋊D1311yescharacteristic
562C8—22no—
563C8—22no—
564C8—262no—
565C8—521no—
566C22—42no—
567C22—42no—
568C22—42no—
569C22—81no—
570C22—81no—
571C22—81no—
572C22—81no—
573C22#1171933711yescharacteristic
574C22#1171933811yescharacteristic
575C22D13×#13511yescharacteristic
576C22D13×#13511yescharacteristic
577C22#1171947911yescharacteristic
578C22#1171948011yescharacteristic
579C22C2×#8819211yescharacteristic
580C4—22no—
581C4—22no—
582C4—81no—
583C4—81no—
584C4—81no—
585C4—262no—
586C4—262no—
587C4—522no—
588C4—522no—
589C4—521no—
590C4—521no—
591C4—1041no—
592C4—1041no—
593C4#1171932711yescharacteristic
594C4#1171933011yescharacteristic
595C4Q8×C22⋊D1311yescharacteristic
596C4#1171952911yescharacteristic
597C2—82no—
598C2#1311843111yescharacteristic
599C2#1312441311yescharacteristic
600C2#1312451011yescharacteristic
601C2#1312749911yescharacteristic
602C2#1312753511yescharacteristic
603C2#1312769811yescharacteristic
604C2#1312770611yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC2×C13×#478C2
socleC23×C13C22×D4
prime radicalC22×D4×C13C23
hypercenterC2×#478D13
hypocenterC13#25473
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#478

Complements

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

NH ≅ G/Ntype
1. C2×#11718491C2semidirect
2. #13120225C2semidirect
4. #13116335C2semidirect
5. #13116330C2semidirect
8. #13115802C2semidirect
9. #13115606C2semidirect
10. #13115567C2semidirect
11. #13115562C2semidirect
107. #88072Q8semidirect
502. C13#25473semidirect

Maximal subgroups

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

subgroupindex
C2×#117184912
#131202252
#131201902
#131163352
#131163302
#131162222
#131162082
#131158022
#131156062
#131155672
#131155622
#131155162
C4×#880722
C2×C13×#4782
#2547313