Finite Group Databasebeta

← #15921994

Subgroups — #15921994

Order 3328.

678 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13117807C211yesmaximal, characteristic
2#13116370C211yesmaximal, characteristic
3#13116360C211yesmaximal, characteristic
4#13116221C211yesmaximal, characteristic
5#13116221C211yesmaximal, characteristic
6#13115604C211yesmaximal, characteristic, complemented
7#13115602C211yesmaximal, characteristic, complemented
8#13115592C211yesmaximal, characteristic, complemented
9#13115555C211yesmaximal, characteristic, complemented
10#13115418C211yesmaximal, characteristic, complemented
11#13115411C211yesmaximal, characteristic, complemented
12#13114998C211yesmaximal, characteristic, complemented
13#13114843C211yesmaximal, characteristic
14C4×#88049C211yesmaximal, characteristic
15C13×#2570C211yesmaximal, characteristic, complemented
16C2×C4×D52C2211yescharacteristic
17C13×#400—21no—
18C13×#398—21no—
19C13×#389C2211yescharacteristic
20C13×#389C2211yescharacteristic
21C13×#387—21no—
22C13×#387—21no—
23C13×#384C2211yescharacteristic
24C13×#382C2211yescharacteristic
25C13×#382C2211yescharacteristic
26C4×C13×C4⋊C4C2211yescharacteristic
27C4×C13×C4⋊C4C2211yescharacteristic
28#11718651—21no—
29#11718651—21no—
30C2×#88049C2211yescharacteristic
31C2×#88049C2211yescharacteristic
32C2×#88049C2211yescharacteristic
33C2×#88049C2211yescharacteristic
34C2×#88048C2211yescharacteristic
35C2×#88048C2211yescharacteristic
36C2×#88048C2211yescharacteristic
37C2×#88047C2211yescharacteristic
38C2×#88047C2211yescharacteristic
39C2×#88047C2211yescharacteristic
40#11718600C2211yescharacteristic
41#11718600C2211yescharacteristic
42#11718597C2211yescharacteristic
43C4×C4⋊Dic13C2211yescharacteristic
44C4×C4⋊Dic13C2211yescharacteristic
45C2×C4⋊#1055C2211yescharacteristic
46C2×C4⋊#1055C2211yescharacteristic
47C2×C4⋊#1055C2211yescharacteristic
48C2×C4×#1055C2211yescharacteristic
49#11718327—21no—
50#11718325—21no—
51#11718121C2211yescharacteristic
52#11718121C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718116C2211yescharacteristic
58#11718116C2211yescharacteristic
59C22×D52C2311yescharacteristic
60C22×C4×D13—21no—
61C2×C13×C4⋊C4—21no—
62C2×C13×C4⋊C4—21no—
63C2×C13×C4⋊C4—21no—
64C2×C13×C4⋊C4—21no—
65C2×C13×C4⋊C4D411yescharacteristic
66C2×C13×C4⋊C4D411yescharacteristic
67C2×C13×C4⋊C4C2311yescharacteristic
68C2×C13×C4⋊C4C2311yescharacteristic
69C2×C13×C4⋊C4C2311yescharacteristic
70C2×C13×C4⋊C4C2311yescharacteristic
71C2×C42×C13—21no—
72C2×C42×C13C2311yescharacteristic
73C2×C42×C13C2311yescharacteristic
74C2×C42×C13C2311yescharacteristic
75C2×#6103—21no—
76C2×#6103—21no—
77C2×#6103—21no—
78C2×#6103—21no—
79C2×#6103—21no—
80C2×C4⋊Dic13C2311yescharacteristic
81C2×C4⋊Dic13C2311yescharacteristic
82C2×C4⋊Dic13C2311yescharacteristic
83C2×C4×Dic13—21no—
84C2×C4×Dic13—21no—
85C22×#1055C2311yescharacteristic
86C22×#1055C2311yescharacteristic
87C22×#1055C2311yescharacteristic
88C22×#1055C2311yescharacteristic
89C4×D52—22no—
90C4×D52Q814yes—
91C13×#95—21no—
92C13×#95—21no—
93C13×#95—21no—
94C13×#95—21no—
95C13×#95—21no—
96C13×#95—21no—
97C13×#95—21no—
98C13×#95D411yescharacteristic
99C13×#95D411yescharacteristic
100#88071—21no—
101#88071—21no—
102#88071—21no—
103#88071—21no—
104#88049—22no—
105#88049—22no—
106#88049—41no—
107#88049—41no—
108#88048—22no—
109#88048—22no—
110#88048—41no—
111#88047—41no—
112#88047—41no—
113#88047—41no—
114C4⋊#1055—22no—
115C4⋊#1055—22no—
116C4⋊#1055—22no—
117C4×#1055—22no—
118#26096—131nomaximal, Sylow
119C23×D13—21no—
120C22×C4×C13—21no—
121C22×C4×C13—21no—
122C22×C4×C13—21no—
123C22×C4×C13—21no—
124C22×C4×C13C2×D411yescharacteristic
125C22×C4×C13C2×D411yescharacteristic
126C22×C4×C13C2×D411yescharacteristic
127C22×C4×C13C2×D411yescharacteristic
128C22×C4×C13C2×D411yescharacteristic
129C22×C4×C13C2×D411yescharacteristic
130C22×C4×C13C2411yescharacteristic
131C22×Dic13—21no—
132C22×Dic13—21no—
133C22×Dic13—21no—
134C2×D52—21no—
135C2×D52—21no—
136C2×D52—21no—
137C2×D52—21no—
138C2×D52—21no—
139C2×D52C2×Q812yes—
140C2×C4×D13—24no—
141C2×C4×D13—81no—
142C2×C4×D13—81no—
143C13×C4⋊C4—22no—
144C13×C4⋊C4—21no—
145C13×C4⋊C4—21no—
146C13×C4⋊C4—21no—
147C13×C4⋊C4—21no—
148C13×C4⋊C4—21no—
149C13×C4⋊C4—21no—
150C13×C4⋊C4—21no—
151C13×C4⋊C4—21no—
152C13×C4⋊C4—41no—
153C13×C4⋊C4—42no—
154C13×C4⋊C4—42no—
155C13×C4⋊C4—81no—
156C13×C4⋊C4—81no—
157C42×C13—21no—
158C42×C13—21no—
159C42×C13—21no—
160C42×C13—21no—
161C42×C13—81no—
162C42×C13C2×Q812yes—
163C42×C13#4112yes—
164#6103—24no—
165#6103—42no—
166#6103—42no—
167#6103—81no—
168#6103—81no—
169C4⋊Dic13—21no—
170C4⋊Dic13—21no—
171C4⋊Dic13—21no—
172C4⋊Dic13—21no—
173C4⋊Dic13—21no—
174C4⋊Dic13C2×Q812yes—
175C4×Dic13—81no—
176C4×Dic13—81no—
177C2×#1055—21no—
178C2×#1055—21no—
179C2×#1055—21no—
180C2×#1055—21no—
181C2×#1055—21no—
182C2×#1055—21no—
183C2×#1055—21no—
184C2×#1055—21no—
185C2×#1055—21no—
186C2×#1055—21no—
187C2×#1055#4112yes—
188C2×#1055#4112yes—
189#2570D1311yescharacteristic, complemented
190#2357—131no—
191#2094—131no—
192#2092—131no—
193#2067—131no—
194#2067—131no—
195#1949—131no—
196#1949—131no—
197#1947—131no—
198#1939—131no—
199#1920—131no—
200#1919—131no—
201#1846—131no—
202#1804—131no—
203C4×#102—131no—
204C23×C13C22×D411yescharacteristic
205C22×D13—22no—
206C22×D13—41no—
207C22×D13—41no—
208C22×D13—41no—
209C22×D13—41no—
210C22×D13—41no—
211C22×D13—41no—
212C2×C4×C13—21no—
213C2×C4×C13—21no—
214C2×C4×C13—21no—
215C2×C4×C13—21no—
216C2×C4×C13—21no—
217C2×C4×C13—21no—
218C2×C4×C13—21no—
219C2×C4×C13—21no—
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—41no—
228C2×C4×C13—41no—
229C2×C4×C13—41no—
230C2×C4×C13—41no—
231C2×C4×C13—41no—
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×C13C22⋊Q812yes—
240C2×C4×C13C22⋊Q812yes—
241C2×C4×C13#13512yes—
242C2×C4×C13C22×Q811yescharacteristic
243C2×C4×C13C2×#4111yescharacteristic
244C2×C4×C13C2×#4111yescharacteristic
245C2×C4×C13C2×#4111yescharacteristic
246C2×C4×C13H(5,𝔽2)11yescharacteristic
247C2×C4×C132−1+411yescharacteristic
248C2×Dic13—22no—
249C2×Dic13—41no—
250C2×Dic13—41no—
251C2×Dic13—41no—
252C2×Dic13—41no—
253C2×Dic13—41no—
254C2×Dic13—41no—
255C2×Dic13—41no—
256C2×Dic13—41no—
257D52—22no—
258D52—22no—
259D52—41no—
260D52—41no—
261C4×D13—84no—
262#1055—22no—
263#1055—22no—
264#1055—41no—
265#1055—41no—
266C2×C4×D4—131no—
267C2×#107—131no—
268C2×#107—131no—
269C2×#107—131no—
270C2×#106—131no—
271C2×#106—131no—
272C2×#106—131no—
273C2×C4⋊C8—131no—
274C2×C4⋊C8—131no—
275C2×C4⋊C8—131no—
276C2×#102—131no—
277C2×#102—131no—
278C2×#102—131no—
279C2×#102—131no—
280C2×C4×C8—131no—
281#400—21no—
282#398—21no—
283#390—131no—
284#390—131no—
285#389C2×D1311yescharacteristic
286#389C2×D1311yescharacteristic
287#388—261no—
288#388—261no—
289#387—21no—
290#387—21no—
291#384C2×D1311yescharacteristic
292#382—131no—
293#382C2×D1311yescharacteristic
294#382C2×D1311yescharacteristic
295#381—261no—
296C4×C4⋊C4—131no—
297C4×C4⋊C4—131no—
298C4×C4⋊C4C2×D1311yescharacteristic
299C4×C4⋊C4C2×D1311yescharacteristic
300C4×C22⋊C4—261no—
301#340—131no—
302#340—131no—
303#340—131no—
304#340—131no—
305#340—131no—
306#340—131no—
307#336—131no—
308#336—131no—
309C22×C13C2×C22⋊Q811yescharacteristic
310C22×C13#54711yescharacteristic
311C22×C13#55011yescharacteristic
312C22×C13C2×#13511yescharacteristic
313C22×C13#57511yescharacteristic
314C22×C13#57611yescharacteristic
315C22×C13#57711yescharacteristic
316C2×D13—42no—
317C2×D13—42no—
318C2×D13—42no—
319C2×D13—81no—
320C2×D13—81no—
321C2×D13—81no—
322C2×D13—81no—
323C4×C13—22no—
324C4×C13—22no—
325C4×C13—22no—
326C4×C13—41no—
327C4×C13—41no—
328C4×C13—41no—
329C4×C13—81no—
330C4×C13—81no—
331C4×C13—81no—
332C4×C13—81no—
333C4×C13#53311yescharacteristic
334C4×C13#54411yescharacteristic
335C4×C13#55211yescharacteristic
336C4×C13#55311yescharacteristic
337Dic13—42no—
338Dic13—81no—
339Dic13—81no—
340C22×D4—131no—
341C23×C4—261no—
342C22×C8—131no—
343C22×C8—131no—
344C22×C8—131no—
345C22×C8—131no—
346C4×D4—134no—
347C4×D4—262no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—131no—
353C2×C4⋊C4—131no—
354C2×C4⋊C4—131no—
355C2×C4⋊C4C22⋊D1311yescharacteristic
356C2×C4⋊C4C22⋊D1311yescharacteristic
357C2×C4⋊C4C22×D1311yescharacteristic
358C2×C4⋊C4C22×D1311yescharacteristic
359C2×C4⋊C4C22×D1311yescharacteristic
360C2×C4⋊C4C22×D1311yescharacteristic
361C2×C22⋊C4—261no—
362C2×C22⋊C4—261no—
363C2×C22⋊C4—261no—
364C2×C22⋊C4—261no—
365C2×C22⋊C4—261no—
366C2×C42—21no—
367C2×C42—261no—
368C2×C42—261no—
369C2×C42C22×D1311yescharacteristic
370C2×C42C22×D1311yescharacteristic
371C2×C42C22×D1311yescharacteristic
372#107—521no—
373#107—521no—
374#107—521no—
375#106—262no—
376#106—262no—
377#106—521no—
378C4⋊C8—262no—
379C4⋊C8—262no—
380C4⋊C8—262no—
381#102—262no—
382#102—262no—
383#102—521no—
384#102—521no—
385C4×C8—262no—
386#95—21no—
387#95—21no—
388#95—21no—
389#95—21no—
390#95—21no—
391#95—21no—
392#95—21no—
393#95—261no—
394#95—261no—
395#95—261no—
396#95—261no—
397#95C22⋊D1311yescharacteristic
398#95C22⋊D1311yescharacteristic
399C2×C13#244111yescharacteristic
400C2×C13#307611yescharacteristic
401C2×C13#308111yescharacteristic
402C2×C13#333911yescharacteristic
403C2×C13#335111yescharacteristic
404C2×C13#339411yescharacteristic
405C2×C13#340311yescharacteristic
406D13—82no—
407C24—261no—
408C2×D4—132no—
409C2×D4—261no—
410C2×D4—261no—
411C2×D4—261no—
412C2×D4—261no—
413C2×D4—261no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—261no—
419C22×C4—264no—
420C22×C4—261no—
421C22×C4—261no—
422C22×C4—1041no—
423C22×C4—1041no—
424C22×C4C2×C22⋊D1311yescharacteristic
425C22×C4C2×C22⋊D1311yescharacteristic
426C22×C4C2×C22⋊D1311yescharacteristic
427C22×C4C2×C22⋊D1311yescharacteristic
428C22×C4C2×C22⋊D1311yescharacteristic
429C22×C4C2×C22⋊D1311yescharacteristic
430C22×C4C23×D1311yescharacteristic
431C2×C8—132no—
432C2×C8—132no—
433C2×C8—261no—
434C2×C8—261no—
435C2×C8—261no—
436C2×C8—261no—
437C2×C8—261no—
438C2×C8—261no—
439C2×C8—261no—
440C2×C8—261no—
441C2×C8—261no—
442C2×C8—261no—
443C4⋊C4—22no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—41no—
453C4⋊C4—42no—
454C4⋊C4—42no—
455C4⋊C4—81no—
456C4⋊C4—81no—
457C4⋊C4—132no—
458C4⋊C4—261no—
459C4⋊C4—261no—
460C4⋊C4—261no—
461C4⋊C4—261no—
462C4⋊C4—261no—
463C22⋊C4—264no—
464C22⋊C4—522no—
465C22⋊C4—522no—
466C22⋊C4—1041no—
467C22⋊C4—1041no—
468C42—21no—
469C42—21no—
470C42—21no—
471C42—21no—
472C42—81no—
473C42—1041no—
474C42—1041no—
475C42Q8×D1312yes—
476C42#613112yes—
477C13#2609611yescharacteristic, complemented, Sylow
478C23—262no—
479C23—521no—
480C23—521no—
481C23—521no—
482C23—521no—
483C23—521no—
484C23—521no—
485C23C22×C22⋊D1311yescharacteristic
486D4—262no—
487D4—262no—
488D4—521no—
489D4—521no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—262no—
518C2×C4—521no—
519C2×C4—521no—
520C2×C4—521no—
521C2×C4—521no—
522C2×C4—521no—
523C2×C4—521no—
524C2×C4—521no—
525C2×C4—521no—
526C2×C4—1044no—
527C2×C4#8820012yes—
528C2×C4#8820012yes—
529C2×C4#8820412yes—
530C2×C4C2×Q8×D1311yescharacteristic
531C2×C4C2×#613111yescharacteristic
532C2×C4#41×D1311yescharacteristic
533C2×C4#41×D1311yescharacteristic
534C2×C4#8825611yescharacteristic
535C2×C4#8825711yescharacteristic
536C8—262no—
537C8—262no—
538C8—521no—
539C8—521no—
540C22—522no—
541C22—522no—
542C22—522no—
543C22—1041no—
544C22—1041no—
545C22—1041no—
546C22—1041no—
547C22C2×#8820011yescharacteristic
548C22C2×#8820411yescharacteristic
549C22#1171952711yescharacteristic
550C22#1171952911yescharacteristic
551C22#1171953911yescharacteristic
552C22#1171954011yescharacteristic
553C22#1171954211yescharacteristic
554C4—22no—
555C4—22no—
556C4—22no—
557C4—41no—
558C4—41no—
559C4—41no—
560C4—81no—
561C4—81no—
562C4—81no—
563C4—81no—
564C4—522no—
565C4—1041no—
566C4—1041no—
567C4#1171939311yescharacteristic
568C4#1171939411yescharacteristic
569C4#1171939911yescharacteristic
570C4#1171940011yescharacteristic
571C2—1042no—
572C2#1311854511yescharacteristic
573C2#1312461811yescharacteristic
574C2#1312466111yescharacteristic
575C2#1312723211yescharacteristic
576C2#1312739611yescharacteristic
577C2#1312783211yescharacteristic
578C2#1312792011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2570C2
socleC23×C13C22×D4
prime radicalC22×D52C23
hypercenter#2570D13
hypocenterC13#26096
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2570

Complements

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

NH ≅ G/Ntype
6. #13115604C2semidirect
7. #13115602C2semidirect
8. #13115592C2semidirect
9. #13115555C2semidirect
10. #13115418C2semidirect
11. #13115411C2semidirect
12. #13114998C2semidirect
15. C13×#2570C2semidirect
189. #2570D13semidirect
477. C13#26096semidirect

Maximal subgroups

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

subgroupindex
#131178072
#131163702
#131163602
#131162212
#131156042
#131156022
#131155922
#131155552
#131154182
#131154112
#131149982
#131148432
C4×#880492
C13×#25702
#2609613