Finite Group Databasebeta

← #15914637

Subgroups — #15914637

Order 3328.

792 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718741C211yesmaximal, characteristic, complemented
2C2×#11718745C211yesmaximal, characteristic
3#13120036C211yesmaximal, characteristic
4#13116317C211yesmaximal, characteristic, complemented
5#13116312C211yesmaximal, characteristic, complemented
6#13116221C211yesmaximal, characteristic
7#13116207C211yesmaximal, characteristic
8#13115793C211yesmaximal, characteristic, complemented
9#13115604C211yesmaximal, characteristic, complemented
10#13115599C211yesmaximal, characteristic, complemented
11#13115560C211yesmaximal, characteristic, complemented
12#13115463C211yesmaximal, characteristic
13#13115456C211yesmaximal, characteristic
14#13114664C211yesmaximal, characteristic
15C13×#2365C211yesmaximal, characteristic, complemented
16C2×C13×C4⋊Q8C2211yescharacteristic
17C2×C4×Q8×C13—21no—
18C2×C4×D52C2211yescharacteristic
19C2×#88124C2211yescharacteristic
20C13×#391—21no—
21C13×#389C2211yescharacteristic
22C13×#389C2211yescharacteristic
23C13×#387—21no—
24C13×#387—21no—
25C4×C13×C4⋊C4C2211yescharacteristic
26C4×C13×C4⋊C4C2211yescharacteristic
27C4×C13×C4⋊C4C2211yescharacteristic
28C4×C13×C4⋊C4C2211yescharacteristic
29#11718745—24no—
30#11718741—24no—
31#11718655—21no—
32#11718655—21no—
33C2×#88049C2211yescharacteristic
34C2×#88049C2211yescharacteristic
35C2×#88049C2211yescharacteristic
36C2×#88049C2211yescharacteristic
37C2×#88048C2211yescharacteristic
38C2×#88048C2211yescharacteristic
39C2×#88048C2211yescharacteristic
40C2×#88048C2211yescharacteristic
41C2×#88047C2211yescharacteristic
42C2×#88047C2211yescharacteristic
43#11718600C2211yescharacteristic
44#11718600C2211yescharacteristic
45#11718597C2211yescharacteristic
46#11718596C2211yescharacteristic
47C2×C4⋊#1055C2211yescharacteristic
48C2×C4⋊#1055C2211yescharacteristic
49C2×C4⋊#1055C2211yescharacteristic
50C2×#88043C2211yescharacteristic
51#11718329—21no—
52#11718329—21no—
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718116C2211yescharacteristic
60#11718116C2211yescharacteristic
61C22×Q8×C13—21no—
62C22×D52C2311yescharacteristic
63C22×C4×D13—21no—
64C13×C4⋊Q8—22no—
65C13×C4⋊Q8D414yes—
66C4×Q8×C13—44no—
67C2×C13×C4⋊C4—21no—
68C2×C13×C4⋊C4—21no—
69C2×C13×C4⋊C4—21no—
70C2×C13×C4⋊C4D411yescharacteristic
71C2×C13×C4⋊C4D411yescharacteristic
72C2×C13×C4⋊C4C2311yescharacteristic
73C2×C13×C4⋊C4C2311yescharacteristic
74C2×C13×C4⋊C4C2311yescharacteristic
75C2×C13×C4⋊C4C2311yescharacteristic
76C2×C42×C13—21no—
77C2×C42×C13—21no—
78C2×C42×C13—21no—
79C2×C42×C13C2311yescharacteristic
80C2×C42×C13C2311yescharacteristic
81C2×C42×C13C2311yescharacteristic
82C2×#6103—21no—
83C2×#6103—21no—
84C2×#6103—21no—
85C2×#6103—21no—
86C2×#6103—21no—
87C2×C4⋊Dic13—21no—
88C2×C4⋊Dic13—21no—
89C2×C4⋊Dic13C2311yescharacteristic
90C2×C4⋊Dic13C2311yescharacteristic
91C2×C4⋊Dic13C2311yescharacteristic
92C2×#6101—21no—
93C2×#6101—21no—
94C22×#1055C2311yescharacteristic
95C22×#1055C2311yescharacteristic
96C22×#1055C2311yescharacteristic
97C22×#1055C2311yescharacteristic
98C4×D52—22no—
99C4×D52—22no—
100#88124—22no—
101#88124—22no—
102C13×#95—21no—
103C13×#95—21no—
104C13×#95—21no—
105C13×#95—21no—
106C13×#95—21no—
107C13×#95D411yescharacteristic
108C13×#95D411yescharacteristic
109#88071—21no—
110#88071—21no—
111#88049—22no—
112#88049—22no—
113#88049—22no—
114#88049Q814yescomplemented
115#88048—22no—
116#88048—22no—
117#88048—22no—
118#88048—22no—
119#88047—22no—
120#88047—22no—
121C4⋊#1055—22no—
122C4⋊#1055—22no—
123C4⋊#1055—22no—
124#88043—22no—
125#25461—131nomaximal, Sylow
126C23×D13—21no—
127C2×Q8×C13—24no—
128C2×Q8×C13—42no—
129C2×Q8×C13—42no—
130C22×C4×C13—21no—
131C22×C4×C13—21no—
132C22×C4×C13—21no—
133C22×C4×C13—21no—
134C22×C4×C13C2×D411yescharacteristic
135C22×C4×C13C2×D411yescharacteristic
136C22×C4×C13C2×D411yescharacteristic
137C22×C4×C13C2×D411yescharacteristic
138C22×C4×C13C2×D411yescharacteristic
139C22×C4×C13C2×D411yescharacteristic
140C22×C4×C13C2411yescharacteristic
141C22×Dic13—21no—
142C22×Dic13—21no—
143C22×Dic13—21no—
144C2×D52—21no—
145C2×D52—21no—
146C2×D52—21no—
147C2×D52—21no—
148C2×D52—21no—
149C2×D52C2×Q812yes—
150C2×C4×D13—42no—
151C2×C4×D13—81no—
152C2×C4×D13—81no—
153C13×C4⋊C4—24no—
154C13×C4⋊C4—22no—
155C13×C4⋊C4—21no—
156C13×C4⋊C4—21no—
157C13×C4⋊C4—21no—
158C13×C4⋊C4—21no—
159C13×C4⋊C4—21no—
160C13×C4⋊C4—41no—
161C13×C4⋊C4—42no—
162C13×C4⋊C4—42no—
163C13×C4⋊C4C2×D412yes—
164C13×C4⋊C4C2×D412yes—
165C13×C4⋊C4C2×Q812yes—
166C42×C13—21no—
167C42×C13—21no—
168C42×C13—21no—
169C42×C13—21no—
170C42×C13—42no—
171C42×C13—42no—
172C42×C13—42no—
173C42×C13C2×D412yes—
174C42×C13#4112yes—
175#6103—42no—
176#6103—42no—
177#6103—42no—
178#6103—81no—
179#6103—81no—
180C4⋊Dic13—21no—
181C4⋊Dic13—21no—
182C4⋊Dic13—21no—
183C4⋊Dic13—21no—
184C4⋊Dic13—21no—
185C4⋊Dic13—21no—
186C4⋊Dic13—81no—
187C4⋊Dic13—81no—
188#6101—42no—
189#6101—42no—
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×#1055C2×Q812yes—
201C2×#1055#4112yes—
202C2×#501—131no—
203C2×#476—131no—
204#2566—131no—
205#2365D1311yescharacteristic, complemented
206#2085—131no—
207#2084—131no—
208#2067—131no—
209#2065—131no—
210#1989—131no—
211#1949—131no—
212#1948—131no—
213#1940—131no—
214#1926—131no—
215#1925—131no—
216#1762—131no—
217C23×C13C22×D411yescharacteristic
218C22×D13—22no—
219C22×D13—41no—
220C22×D13—41no—
221C22×D13—41no—
222C22×D13—41no—
223C22×D13—41no—
224C22×D13—41no—
225Q8×C13—48no—
226C2×C4×C13—21no—
227C2×C4×C13—21no—
228C2×C4×C13—21no—
229C2×C4×C13—21no—
230C2×C4×C13—21no—
231C2×C4×C13—21no—
232C2×C4×C13—22no—
233C2×C4×C13—22no—
234C2×C4×C13—21no—
235C2×C4×C13—21no—
236C2×C4×C13—21no—
237C2×C4×C13—22no—
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—41no—
245C2×C4×C13—41no—
246C2×C4×C13—41no—
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#12112yes—
254C2×C4×C13#12112yes—
255C2×C4×C13AGL(1,ℤ/8)12yes—
256C2×C4×C13C22×D411yescharacteristic
257C2×C4×C13C22×Q811yescharacteristic
258C2×C4×C13C2×#4111yescharacteristic
259C2×C4×C13C2×#4111yescharacteristic
260C2×C4×C132−1+411yescharacteristic
261C2×C4×C132−1+411yescharacteristic
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—
271D52—22no—
272D52—22no—
273D52—41no—
274D52—41no—
275C4×D13—84no—
276#1055—22no—
277#1055—22no—
278#1055—41no—
279#1055—41no—
280C2×C4⋊Q8C2×D1311yescharacteristic
281C2×#125—131no—
282C2×C4×Q8—21no—
283C2×C4×D4—131no—
284#501—264no—
285#476—264no—
286C2×#107—131no—
287C2×#107—131no—
288C2×#106—131no—
289C2×#106—131no—
290C2×#106—131no—
291C2×#106—131no—
292C2×C4⋊C8—131no—
293C2×C4⋊C8—131no—
294C2×C4⋊C8—131no—
295C2×#102—131no—
296C2×#102—131no—
297C2×#102—131no—
298C2×#102—131no—
299C2×#97—131no—
300#396—261no—
301#396—261no—
302#391—21no—
303#390—131no—
304#390—131no—
305#389C2×D1311yescharacteristic
306#389C2×D1311yescharacteristic
307#387—21no—
308#387—21no—
309#385—261no—
310#385—261no—
311#384—131no—
312#382—131no—
313C4×C4⋊C4C2×D1311yescharacteristic
314C4×C4⋊C4C2×D1311yescharacteristic
315C4×C4⋊C4C2×D1311yescharacteristic
316C4×C4⋊C4C2×D1311yescharacteristic
317#340—131no—
318#340—131no—
319#340—131no—
320#340—131no—
321#340—131no—
322#340—131no—
323#336—131no—
324#336—131no—
325C22×C13C2×#12111yescharacteristic
326C22×C13#54711yescharacteristic
327C22×C13D4×Q811yescharacteristic
328C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
329C22×C13#57511yescharacteristic
330C22×C13#57711yescharacteristic
331C22×C13#57711yescharacteristic
332C2×D13—42no—
333C2×D13—42no—
334C2×D13—42no—
335C2×D13—81no—
336C2×D13—81no—
337C2×D13—81no—
338C2×D13—81no—
339C4×C13—22no—
340C4×C13—22no—
341C4×C13—22no—
342C4×C13—41no—
343C4×C13—41no—
344C4×C13—41no—
345C4×C13—42no—
346C4×C13—42no—
347C4×C13—42no—
348C4×C13—81no—
349C4×C13#53311yescharacteristic
350C4×C13#54111yescharacteristic
351C4×C13#54811yescharacteristic
352C4×C13D4×Q811yescharacteristic
353Dic13—81no—
354Dic13—81no—
355Dic13—81no—
356C22×Q8—21no—
357C22×D4—131no—
358C23×C4—261no—
359C22×C8—131no—
360C22×C8—131no—
361C22×C8—131no—
362C22×C8—131no—
363C4⋊Q8—22no—
364C4⋊Q8D5214yes—
365#125—262no—
366#125—262no—
367C4×Q8—44no—
368C4×D4—262no—
369C4×D4—262no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—131no—
374C2×C4⋊C4—131no—
375C2×C4⋊C4—131no—
376C2×C4⋊C4—261no—
377C2×C4⋊C4—261no—
378C2×C4⋊C4—261no—
379C2×C4⋊C4—261no—
380C2×C4⋊C4C22⋊D1311yescharacteristic
381C2×C4⋊C4C22⋊D1311yescharacteristic
382C2×C4⋊C4C22×D1311yescharacteristic
383C2×C4⋊C4C22×D1311yescharacteristic
384C2×C4⋊C4C22×D1311yescharacteristic
385C2×C4⋊C4C22×D1311yescharacteristic
386C2×C22⋊C4—261no—
387C2×C22⋊C4—261no—
388C2×C22⋊C4—261no—
389C2×C22⋊C4—261no—
390C2×C22⋊C4—261no—
391C2×C42—21no—
392C2×C42—21no—
393C2×C42—21no—
394C2×C42C22×D1311yescharacteristic
395C2×C42C22×D1311yescharacteristic
396C2×C42C22×D1311yescharacteristic
397#107—262no—
398#107—262no—
399#106—262no—
400#106—262no—
401#106—262no—
402#106—262no—
403C4⋊C8—262no—
404C4⋊C8—262no—
405C4⋊C8—262no—
406#102—134no—
407#102—262no—
408#102—262no—
409#102—262no—
410#97—262no—
411#95—21no—
412#95—21no—
413#95—21no—
414#95—21no—
415#95—21no—
416#95—261no—
417#95—261no—
418#95C22⋊D1311yescharacteristic
419#95C22⋊D1311yescharacteristic
420C2×C13#242911yescharacteristic
421C2×C13#303611yescharacteristic
422C2×C13#304311yescharacteristic
423C2×C13#334511yescharacteristic
424C2×C13#335011yescharacteristic
425C2×C13#338411yescharacteristic
426C2×C13#338811yescharacteristic
427D13—82no—
428C24—261no—
429C2×Q8—24no—
430C2×Q8—42no—
431C2×Q8—42no—
432C2×D4—132no—
433C2×D4—261no—
434C2×D4—261no—
435C2×D4—261no—
436C2×D4—261no—
437C2×D4—261no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—261no—
443C22×C4—261no—
444C22×C4—261no—
445C22×C4—522no—
446C22×C4—1041no—
447C22×C4—1041no—
448C22×C4C2×C22⋊D1311yescharacteristic
449C22×C4C2×C22⋊D1311yescharacteristic
450C22×C4C2×C22⋊D1311yescharacteristic
451C22×C4C2×C22⋊D1311yescharacteristic
452C22×C4C2×C22⋊D1311yescharacteristic
453C22×C4C2×C22⋊D1311yescharacteristic
454C22×C4C23×D1311yescharacteristic
455C2×C8—132no—
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—
467C4⋊C4—24no—
468C4⋊C4—22no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—41no—
475C4⋊C4—42no—
476C4⋊C4—42no—
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—1041no—
486C4⋊C4—1041no—
487C4⋊C4C2×D5212yes—
488C4⋊C4C2×D5212yes—
489C4⋊C4Q8×D1312yes—
490C22⋊C4—522no—
491C22⋊C4—522no—
492C22⋊C4—522no—
493C22⋊C4—1041no—
494C22⋊C4—1041no—
495C42—21no—
496C42—21no—
497C42—21no—
498C42—21no—
499C42—42no—
500C42—42no—
501C42—42no—
502C42C2×D5212yes—
503C42#612712yes—
504C13#2546111yescharacteristic, complemented, Sylow
505C23—262no—
506C23—521no—
507C23—521no—
508C23—521no—
509C23—521no—
510C23—521no—
511C23—521no—
512C23C22×C22⋊D1311yescharacteristic
513Q8—48no—
514D4—262no—
515D4—262no—
516D4—521no—
517D4—521no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—21no—
527C2×C4—22no—
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—41no—
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—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—1044no—
555C2×C4#8818412yes—
556C2×C4#8818412yes—
557C2×C4#8818612yes—
558C2×C4C22×D5211yescharacteristic
559C2×C4C2×#612711yescharacteristic
560C2×C4C2×Q8×D1311yescharacteristic
561C2×C4#8825411yescharacteristic
562C2×C4#41×D1311yescharacteristic
563C2×C4#8825711yescharacteristic
564C8—262no—
565C8—262no—
566C8—521no—
567C8—521no—
568C22—522no—
569C22—522no—
570C22—522no—
571C22—1041no—
572C22—1041no—
573C22—1041no—
574C22—1041no—
575C22C2×#8818411yescharacteristic
576C22C2×#8818611yescharacteristic
577C22Q8×C22⋊D1311yescharacteristic
578C22#1171952711yescharacteristic
579C22#1171952911yescharacteristic
580C22#1171954211yescharacteristic
581C22#1171954211yescharacteristic
582C4—22no—
583C4—22no—
584C4—22no—
585C4—42no—
586C4—41no—
587C4—42no—
588C4—42no—
589C4—41no—
590C4—41no—
591C4—81no—
592C4—1041no—
593C4—1041no—
594C4—1041no—
595C4Q8×D5211yescharacteristic
596C4#1171928111yescharacteristic
597C4#1171928311yescharacteristic
598C4#1171928811yescharacteristic
599C2—1042no—
600C2#1311842911yescharacteristic
601C2#1312430011yescharacteristic
602C2#1312435711yescharacteristic
603C2#1312730611yescharacteristic
604C2#1312738111yescharacteristic
605C2#1312773111yescharacteristic
606C2#1312777511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2365C2
socleC23×C13C22×D4
prime radicalC22×D52C23
hypercenter#2365D13
hypocenterC13#25461
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2365

Complements

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

NH ≅ G/Ntype
1. C2×#11718741C2semidirect
4. #13116317C2semidirect
5. #13116312C2semidirect
8. #13115793C2semidirect
9. #13115604C2semidirect
10. #13115599C2semidirect
11. #13115560C2semidirect
15. C13×#2365C2semidirect
114. #88049Q8semidirect
205. #2365D13semidirect
504. C13#25461semidirect

Maximal subgroups

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

subgroupindex
C2×#117187412
C2×#117187452
#131200362
#131163172
#131163122
#131162212
#131162072
#131157932
#131156042
#131155992
#131155602
#131154632
#131154562
#131146642
C13×#23652
#2546113