Finite Group Databasebeta

← #15935662

Subgroups — #15935662

Order 3328.

708 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13117839C211yesmaximal, characteristic
2#13116245C211yesmaximal, characteristic, complemented
3#13116228C211yesmaximal, characteristic, complemented
4#13116039C211yesmaximal, characteristic
5#13116039C211yesmaximal, characteristic
6#13115592C211yesmaximal, characteristic, complemented
7#13115566C211yesmaximal, characteristic, complemented
8#13115444C211yesmaximal, characteristic
9#13115428C211yesmaximal, characteristic, complemented
10#13115425C211yesmaximal, characteristic, complemented
11#13115089C211yesmaximal, characteristic, complemented
12#13115023C211yesmaximal, characteristic
13#13114924C211yesmaximal, characteristic
14C4×#88050C211yesmaximal, characteristic, complemented
15C13×#2497C211yesmaximal, characteristic
16C22×C4⋊Dic13C2211yescharacteristic
17C2×#88178C2211yescharacteristic
18C2×C4×Dic26C2211yescharacteristic
19C13×#400—21no—
20C13×#396—21no—
21C13×#389C2211yescharacteristic
22C13×#389C2211yescharacteristic
23C13×#388—21no—
24C13×#387—21no—
25C13×#384C2211yescharacteristic
26C13×#380C2211yescharacteristic
27C13×#380C2211yescharacteristic
28C4×C13×C4⋊C4C2211yescharacteristic
29C4×C13×C22⋊C4C2211yescharacteristic
30C2×C22⋊#1055C2211yescharacteristic
31C2×C22⋊#1055C2211yescharacteristic
32C2×#88050C2211yescharacteristic
33C2×#88050C2211yescharacteristic
34C2×#88050C2211yescharacteristic
35C2×#88050C2211yescharacteristic
36C2×#88047C2211yescharacteristic
37C2×#88047C2211yescharacteristic
38C2×#88047C2211yescharacteristic
39C2×#88047C2211yescharacteristic
40#11718607—21no—
41C22⋊C4×Dic13—21no—
42C4×C4⋊Dic13C2211yescharacteristic
43#11718590C2211yescharacteristic
44#11718589C2211yescharacteristic
45C2×C4⋊#1055C2211yescharacteristic
46C2×C4×#1055C2211yescharacteristic
47#11718316—21no—
48#11718308—21no—
49#11718121C2211yescharacteristic
50#11718121C2211yescharacteristic
51#11718121C2211yescharacteristic
52#11718121C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718116C2211yescharacteristic
58#11718116C2211yescharacteristic
59C23×C4×C13C2311yescharacteristic
60C23×Dic13—21no—
61C22×Dic26C2311yescharacteristic
62C2×C13×C4⋊C4—21no—
63C2×C13×C4⋊C4—21no—
64C2×C13×C4⋊C4—21no—
65C2×C13×C4⋊C4—21no—
66C2×C13×C4⋊C4C2311yescharacteristic
67C2×C13×C4⋊C4C2311yescharacteristic
68C2×C13×C4⋊C4C2311yescharacteristic
69C2×C13×C4⋊C4C2311yescharacteristic
70C2×C13×C22⋊C4—21no—
71C2×C13×C22⋊C4—21no—
72C2×C13×C22⋊C4D411yescharacteristic
73C2×C13×C22⋊C4D411yescharacteristic
74C2×C42×C13—21no—
75C2×C42×C13C2311yescharacteristic
76C2×C42×C13C2311yescharacteristic
77C2×C22⋊Dic13—21no—
78C2×C4⋊Dic13—22no—
79C2×C4⋊Dic13—21no—
80C2×C4⋊Dic13—41no—
81C2×C4⋊Dic13C2311yescharacteristic
82C2×C4⋊Dic13C2311yescharacteristic
83C2×C4⋊Dic13C2311yescharacteristic
84#88178—22no—
85#88178—22no—
86C2×#6101—21no—
87C2×#6101—21no—
88C2×#6101—21no—
89C2×C4×Dic13—21no—
90C2×C4×Dic13—21no—
91C22×#1055C2311yescharacteristic
92C22×#1055C2311yescharacteristic
93C22×#1055C2311yescharacteristic
94C22×#1055C2311yescharacteristic
95C4×Dic26—22no—
96C4×Dic26—41no—
97C13×#95—21no—
98C13×#95—21no—
99C13×#95—21no—
100C13×#95—21no—
101C13×#95—21no—
102C13×#95D411yescharacteristic
103C13×#95D411yescharacteristic
104#88071—21no—
105#88071—21no—
106#88071—21no—
107#88071—21no—
108C22⋊#1055—22no—
109C22⋊#1055—41no—
110#88050—22no—
111#88050—22no—
112#88050—22no—
113#88050—41no—
114#88047—22no—
115#88047—22no—
116#88047—22no—
117#88047—41no—
118C4⋊#1055—22no—
119C4×#1055—41no—
120#27036—131nomaximal, Sylow
121C24×C13C2×D411yescharacteristic
122C22×C4×C13—21no—
123C22×C4×C13—21no—
124C22×C4×C13—21no—
125C22×C4×C13—21no—
126C22×C4×C13—21no—
127C22×C4×C13—21no—
128C22×C4×C13—21no—
129C22×C4×C13—21no—
130C22×C4×C13—21no—
131C22×C4×C13—21no—
132C22×C4×C13C2×D411yescharacteristic
133C22×C4×C13C2×D411yescharacteristic
134C22×C4×C13C2×D411yescharacteristic
135C22×C4×C13C2×D411yescharacteristic
136C22×C4×C13C2×D411yescharacteristic
137C22×C4×C13C2411yescharacteristic
138C22×Dic13—21no—
139C22×Dic13—21no—
140C22×Dic13—21no—
141C22×Dic13—21no—
142C22×Dic13—42no—
143C22×Dic13—42no—
144C22×Dic13—81no—
145C2×Dic26—21no—
146C2×Dic26—21no—
147C2×Dic26—21no—
148C2×Dic26—21no—
149C2×Dic26—21no—
150C2×Dic26#4112yes—
151C13×C4⋊C4—21no—
152C13×C4⋊C4—21no—
153C13×C4⋊C4—21no—
154C13×C4⋊C4—21no—
155C13×C4⋊C4—21no—
156C13×C4⋊C4—21no—
157C13×C4⋊C4—21no—
158C13×C4⋊C4—21no—
159C13×C4⋊C4—42no—
160C13×C4⋊C4—81no—
161C13×C4⋊C4—81no—
162C13×C4⋊C4—81no—
163C13×C22⋊C4—41no—
164C13×C22⋊C4—81no—
165C13×C22⋊C4—81no—
166C13×C22⋊C4Q1614yes—
167C42×C13—21no—
168C42×C13—21no—
169C42×C13—21no—
170C42×C13—21no—
171C42×C13—81no—
172C22⋊Dic13—24no—
173C4⋊Dic13—21no—
174C4⋊Dic13—21no—
175C4⋊Dic13—21no—
176C4⋊Dic13—21no—
177C4⋊Dic13—42no—
178C4⋊Dic13#4112yes—
179C4⋊Dic13#4112yes—
180#6101—24no—
181#6101—42no—
182#6101—81no—
183C4×Dic13—42no—
184C4×Dic13—81no—
185C2×#1055—21no—
186C2×#1055—21no—
187C2×#1055—21no—
188C2×#1055—21no—
189C2×#1055—21no—
190C2×#1055—21no—
191C2×#1055—21no—
192C2×#1055—21no—
193C2×#1055—21no—
194C2×#1055—21no—
195C2×#1055—21no—
196C2×#1055#4112yes—
197#2497D1311yescharacteristic
198#2360—131no—
199#2072—131no—
200#2068—131no—
201#2036—131no—
202#2036—131no—
203#1947—131no—
204#1942—131no—
205#1923—131no—
206#1921—131no—
207#1921—131no—
208#1863—131no—
209#1852—131no—
210#1824—131no—
211C4×#103—131no—
212C23×C13—21no—
213C23×C13—21no—
214C23×C13—21no—
215C23×C13—21no—
216C23×C13—21no—
217C23×C13—21no—
218C23×C13C2×Q1612yes—
219C23×C13C22×D411yescharacteristic
220C2×C4×C13—21no—
221C2×C4×C13—21no—
222C2×C4×C13—21no—
223C2×C4×C13—21no—
224C2×C4×C13—21no—
225C2×C4×C13—21no—
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—21no—
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—41no—
242C2×C4×C13—41no—
243C2×C4×C13—41no—
244C2×C4×C13—41no—
245C2×C4×C13—41no—
246C2×C4×C13—41no—
247C2×C4×C13—41no—
248C2×C4×C13—41no—
249C2×C4×C13C2×Q1612yes—
250C2×C4×C13C2×Q1612yes—
251C2×C4×C13C2×#4111yescharacteristic
252C2×C4×C13C2×#4111yescharacteristic
253C2×C4×C13C2×#4111yescharacteristic
254C2×C4×C13C2×#4111yescharacteristic
255C2×C4×C13H(5,𝔽2)11yescharacteristic
256C2×C4×C132−1+411yescharacteristic
257C2×Dic13—22no—
258C2×Dic13—22no—
259C2×Dic13—22no—
260C2×Dic13—41no—
261C2×Dic13—41no—
262C2×Dic13—41no—
263C2×Dic13—41no—
264C2×Dic13—41no—
265C2×Dic13—41no—
266C2×Dic13—41no—
267C2×Dic13—41no—
268C2×Dic13—41no—
269C2×Dic13—84no—
270Dic26—22no—
271Dic26—22no—
272Dic26—41no—
273Dic26—41no—
274#1055—22no—
275#1055—41no—
276#1055—41no—
277#1055—41no—
278C2×C22⋊Q8—131no—
279C2×C4×Q8—131no—
280C22×C4⋊C4—131no—
281C2×#107—131no—
282C2×#107—131no—
283C2×#107—131no—
284C2×#107—131no—
285C2×C4⋊C8—131no—
286C2×#103—131no—
287C2×#103—131no—
288C2×#103—131no—
289C2×#103—131no—
290C2×C22⋊C8—131no—
291C2×C22⋊C8—131no—
292C2×C4×C8—131no—
293#400—21no—
294#396—21no—
295#391—131no—
296#389—131no—
297#389—261no—
298#389C2×D1311yescharacteristic
299#389C2×D1311yescharacteristic
300#388—21no—
301#387—21no—
302#387—261no—
303#385—261no—
304#384C2×D1311yescharacteristic
305#380C2×D1311yescharacteristic
306#380C2×D1311yescharacteristic
307C4×C4⋊C4—131no—
308C4×C4⋊C4C2×D1311yescharacteristic
309C4×C22⋊C4—261no—
310C4×C22⋊C4C2×D1311yescharacteristic
311#340—131no—
312#340—131no—
313#340—131no—
314#340—131no—
315#340—131no—
316#340—131no—
317#340—131no—
318#340—131no—
319#336—131no—
320#336—131no—
321C22×C13—22no—
322C22×C13—22no—
323C22×C13—22no—
324C22×C13—41no—
325C22×C13—41no—
326C22×C13—41no—
327C22×C13—41no—
328C22×C13#52511yescharacteristic
329C22×C13#54611yescharacteristic
330C22×C13#54711yescharacteristic
331C22×C13C22×Q1611yescharacteristic
332C22×C13#57511yescharacteristic
333C22×C13#57611yescharacteristic
334C22×C13#57711yescharacteristic
335C4×C13—22no—
336C4×C13—22no—
337C4×C13—41no—
338C4×C13—41no—
339C4×C13—41no—
340C4×C13—81no—
341C4×C13—81no—
342C4×C13—81no—
343C4×C13—81no—
344C4×C13#52911yescharacteristic
345C4×C13#53911yescharacteristic
346C4×C13#55311yescharacteristic
347C4×C13#55611yescharacteristic
348Dic13—42no—
349Dic13—42no—
350Dic13—42no—
351Dic13—81no—
352C22×Q8—131no—
353C23×C4—261no—
354C23×C4C22×D1311yescharacteristic
355C22×C8—131no—
356C22×C8—131no—
357C22×C8—131no—
358C22×C8—131no—
359C22⋊Q8—262no—
360C22⋊Q8—262no—
361C4×Q8—262no—
362C4×Q8—521no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—131no—
368C2×C4⋊C4—131no—
369C2×C4⋊C4—131no—
370C2×C4⋊C4—262no—
371C2×C4⋊C4—261no—
372C2×C4⋊C4—261no—
373C2×C4⋊C4—261no—
374C2×C4⋊C4—261no—
375C2×C4⋊C4—521no—
376C2×C4⋊C4C22×D1311yescharacteristic
377C2×C4⋊C4C22×D1311yescharacteristic
378C2×C4⋊C4C22×D1311yescharacteristic
379C2×C4⋊C4C22×D1311yescharacteristic
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—261no—
383C2×C22⋊C4C22⋊D1311yescharacteristic
384C2×C22⋊C4C22⋊D1311yescharacteristic
385C2×C42—21no—
386C2×C42—261no—
387C2×C42—261no—
388C2×C42C22×D1311yescharacteristic
389C2×C42C22×D1311yescharacteristic
390#107—262no—
391#107—262no—
392#107—262no—
393#107—521no—
394C4⋊C8—262no—
395#103—262no—
396#103—262no—
397#103—262no—
398#103—521no—
399C22⋊C8—262no—
400C22⋊C8—521no—
401C4×C8—521no—
402#95—21no—
403#95—21no—
404#95—21no—
405#95—21no—
406#95—21no—
407#95—261no—
408#95—261no—
409#95—261no—
410#95—261no—
411#95C22⋊D1311yescharacteristic
412#95C22⋊D1311yescharacteristic
413C2×C13—42no—
414C2×C13#246611yescharacteristic
415C2×C13#310411yescharacteristic
416C2×C13#311911yescharacteristic
417C2×C13#329911yescharacteristic
418C2×C13#331911yescharacteristic
419C2×C13#333811yescharacteristic
420C2×C13#335111yescharacteristic
421C24C2×C22⋊D1311yescharacteristic
422C2×Q8—132no—
423C2×Q8—261no—
424C2×Q8—261no—
425C2×Q8—261no—
426C2×Q8—261no—
427C2×Q8—261no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—261no—
439C22×C4—261no—
440C22×C4—261no—
441C22×C4—261no—
442C22×C4—522no—
443C22×C4—522no—
444C22×C4—1041no—
445C22×C4C2×C22⋊D1311yescharacteristic
446C22×C4C2×C22⋊D1311yescharacteristic
447C22×C4C2×C22⋊D1311yescharacteristic
448C22×C4C2×C22⋊D1311yescharacteristic
449C22×C4C2×C22⋊D1311yescharacteristic
450C22×C4C23×D1311yescharacteristic
451C2×C8—132no—
452C2×C8—261no—
453C2×C8—261no—
454C2×C8—261no—
455C2×C8—261no—
456C2×C8—261no—
457C2×C8—261no—
458C2×C8—261no—
459C2×C8—261no—
460C2×C8—261no—
461C2×C8—261no—
462C2×C8—261no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—42no—
472C4⋊C4—81no—
473C4⋊C4—81no—
474C4⋊C4—81no—
475C4⋊C4—132no—
476C4⋊C4—132no—
477C4⋊C4—264no—
478C4⋊C4—261no—
479C4⋊C4—261no—
480C4⋊C4—261no—
481C4⋊C4—261no—
482C4⋊C4—522no—
483C4⋊C4—522no—
484C4⋊C4—1041no—
485C22⋊C4—41no—
486C22⋊C4—81no—
487C22⋊C4—81no—
488C22⋊C4—264no—
489C22⋊C4#610714yes—
490C42—21no—
491C42—21no—
492C42—21no—
493C42—21no—
494C42—81no—
495C42—522no—
496C42—1041no—
497C13#2703611yescharacteristic, complemented, Sylow
498C23—21no—
499C23—21no—
500C23—21no—
501C23—21no—
502C23—21no—
503C23—21no—
504C23C2×#610712yes—
505C23C22×C22⋊D1311yescharacteristic
506Q8—262no—
507Q8—262no—
508Q8—521no—
509Q8—521no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—262no—
540C2×C4—262no—
541C2×C4—262no—
542C2×C4—521no—
543C2×C4—521no—
544C2×C4—521no—
545C2×C4—521no—
546C2×C4—521no—
547C2×C4—521no—
548C2×C4—521no—
549C2×C4—521no—
550C2×C4—521no—
551C2×C4—1044no—
552C2×C4C2×#610712yes—
553C2×C4C2×#610712yes—
554C2×C4#41×D1311yescharacteristic
555C2×C4#41×D1311yescharacteristic
556C2×C4#41×D1311yescharacteristic
557C2×C4#41×D1311yescharacteristic
558C2×C4#8825611yescharacteristic
559C2×C4#8825711yescharacteristic
560C8—262no—
561C8—521no—
562C8—521no—
563C8—521no—
564C22—22no—
565C22—22no—
566C22—22no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22C22×#610711yescharacteristic
572C22#1171952711yescharacteristic
573C22#1171952911yescharacteristic
574C22#1171953311yescharacteristic
575C22#1171953411yescharacteristic
576C22#1171954011yescharacteristic
577C22#1171954111yescharacteristic
578C4—22no—
579C4—22no—
580C4—41no—
581C4—41no—
582C4—41no—
583C4—81no—
584C4—81no—
585C4—81no—
586C4—81no—
587C4—522no—
588C4—522no—
589C4—522no—
590C4—1041no—
591C4#1171940711yescharacteristic
592C4#1171941111yescharacteristic
593C4#1171941211yescharacteristic
594C4#1171941411yescharacteristic
595C2—42no—
596C2#1311886811yescharacteristic
597C2#1312487111yescharacteristic
598C2#1312502911yescharacteristic
599C2#1312670611yescharacteristic
600C2#1312698611yescharacteristic
601C2#1312722411yescharacteristic
602C2#1312739011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2497C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
hypercenter#2497D13
hypocenterC13#27036
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2497

Complements

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

NH ≅ G/Ntype
2. #13116245C2semidirect
3. #13116228C2semidirect
6. #13115592C2semidirect
7. #13115566C2semidirect
9. #13115428C2semidirect
10. #13115425C2semidirect
11. #13115089C2semidirect
14. C4×#88050C2semidirect
497. C13#27036semidirect

Maximal subgroups

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

subgroupindex
#131178392
#131162452
#131162282
#131160392
#131155922
#131155662
#131154442
#131154282
#131154252
#131150892
#131150232
#131149242
C4×#880502
C13×#24972
#2703613