Finite Group Databasebeta

← #15884758

Subgroups — #15884758

Order 3328.

846 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×#11718727C211yesmaximal, characteristic
2#13117747C211yesmaximal, characteristic
3#13115802C211yesmaximal, characteristic, complemented
4#13115604C211yesmaximal, characteristic, complemented
5#13115566C211yesmaximal, characteristic, complemented
6#13115561C211yesmaximal, characteristic, complemented
7#13115428C211yesmaximal, characteristic, complemented
8#13115421C211yesmaximal, characteristic, complemented
9#13115096C211yesmaximal, characteristic
10#13115082C211yesmaximal, characteristic
11C4⋊C4×#1055C211yesmaximal, characteristic, complemented
12C4×#88049C211yesmaximal, characteristic
13C4×#88049C211yesmaximal, characteristic
14C4×#88049C211yesmaximal, characteristic
15C13×#2370C211yesmaximal, characteristic, complemented
16C2×C13×#125C2211yescharacteristic
17C2×C4×D52C2211yescharacteristic
18C2×C4×D52C2211yescharacteristic
19C2×C4×D52C2211yescharacteristic
20C13×#389—21no—
21C13×#389C2211yescharacteristic
22C13×#389C2211yescharacteristic
23C13×#387—21no—
24C13×#387—21no—
25C4×C13×C4⋊C4—21no—
26C4×C13×C4⋊C4C2211yescharacteristic
27C4×C13×C4⋊C4C2211yescharacteristic
28C4×C13×C4⋊C4C2211yescharacteristic
29C4×C13×C4⋊C4C2211yescharacteristic
30#11718727C418yescomplemented
31#11718650—21no—
32#11718650—21no—
33C2×#88049C2211yescharacteristic
34C2×#88049C2211yescharacteristic
35C2×#88049C2211yescharacteristic
36C2×#88049C2211yescharacteristic
37C2×#88048C2211yescharacteristic
38C2×#88048C2211yescharacteristic
39C2×#88047C2211yescharacteristic
40C2×#88047C2211yescharacteristic
41#11718597C2211yescharacteristic
42#11718589C2211yescharacteristic
43#11718589C2211yescharacteristic
44C2×C4⋊#1055C2211yescharacteristic
45C2×C4×#1055C2211yescharacteristic
46C2×C4×#1055C2211yescharacteristic
47C2×C4×#1055C2211yescharacteristic
48#11718328—21no—
49D13×#95—21no—
50#11718121C2211yescharacteristic
51#11718121C2211yescharacteristic
52#11718121C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718116C2211yescharacteristic
59#11718116C2211yescharacteristic
60C22×D52C2311yescharacteristic
61C22×C4×D13—21no—
62C22×C4×D13—21no—
63C22×C4×D13—21no—
64C13×#125—22no—
65C13×#125C2×C414yescomplemented
66C2×C13×C4⋊C4—21no—
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×C4⋊Dic13C2311yescharacteristic
86C2×C4⋊Dic13C2311yescharacteristic
87C2×C4⋊Dic13C2311yescharacteristic
88C2×#6101—21no—
89C2×#6101—21no—
90C22×#1055C2311yescharacteristic
91C22×#1055C2311yescharacteristic
92C22×#1055C2311yescharacteristic
93C22×#1055C2311yescharacteristic
94C4×D52—22no—
95C4×D52—22no—
96C4×D52—22no—
97C4×D52—41no—
98C4×D52—41no—
99C4×D52C2×C414yes—
100C13×#95—21no—
101C13×#95—21no—
102C13×#95—21no—
103C13×#95—21no—
104C13×#95—21no—
105C13×#95D411yescharacteristic
106C13×#95D411yescharacteristic
107#88071—21no—
108#88071—21no—
109#88071—21no—
110#88071—21no—
111#88049—22no—
112#88049C2×C414yes—
113#88049C2×C414yes—
114#88049Q814yes—
115#88048—41no—
116#88048C2×C414yescomplemented
117#88047—41no—
118#88047C2×C414yescomplemented
119C4⋊#1055C2×C414yescomplemented
120C4×#1055—22no—
121C4×#1055—41no—
122C4×#1055—41no—
123#22966—131nomaximal, Sylow
124C23×D13—21no—
125C22×C4×C13—21no—
126C22×C4×C13—21no—
127C22×C4×C13—21no—
128C22×C4×C13—21no—
129C22×C4×C13C2×D411yescharacteristic
130C22×C4×C13C2×D411yescharacteristic
131C22×C4×C13C2×D411yescharacteristic
132C22×C4×C13C2×D411yescharacteristic
133C22×C4×C13C2×D411yescharacteristic
134C22×C4×C13C2×D411yescharacteristic
135C22×C4×C13C2411yescharacteristic
136C22×Dic13—21no—
137C22×Dic13—21no—
138C22×Dic13—21no—
139C2×D52—21no—
140C2×D52—21no—
141C2×D52—21no—
142C2×D52C22×C412yes—
143C2×D52C2×Q812yes—
144C2×D52#4112yes—
145C2×C4×D13—24no—
146C2×C4×D13—42no—
147C2×C4×D13—42no—
148C2×C4×D13—42no—
149C2×C4×D13—42no—
150C2×C4×D13—81no—
151C2×C4×D13—81no—
152C2×C4×D13—81no—
153C2×C4×D13—81no—
154C13×C4⋊C4—24no—
155C13×C4⋊C4—24no—
156C13×C4⋊C4—22no—
157C13×C4⋊C4—22no—
158C13×C4⋊C4—21no—
159C13×C4⋊C4—21no—
160C13×C4⋊C4—21no—
161C13×C4⋊C4—21no—
162C13×C4⋊C4—21no—
163C13×C4⋊C4—42no—
164C13×C4⋊C4—81no—
165C13×C4⋊C4C22×C412yes—
166C13×C4⋊C4C22×C412yes—
167C13×C4⋊C4C2×Q812yes—
168C42×C13—21no—
169C42×C13—21no—
170C42×C13—21no—
171C42×C13—21no—
172C42×C13—42no—
173C42×C13—81no—
174C42×C13—81no—
175C42×C13C22×C412yes—
176C42×C13#4112yes—
177#6103—24no—
178#6103—42no—
179#6103—42no—
180C4⋊Dic13—21no—
181C4⋊Dic13—21no—
182C4⋊Dic13—21no—
183C4⋊Dic13—21no—
184C4⋊Dic13—21no—
185C4⋊Dic13C22×C412yes—
186#6101—81no—
187#6101—81no—
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—21no—
197C2×#1055C22×C412yes—
198C2×#1055C22×C412yes—
199C2×#1055C2×Q812yes—
200C2×#478—131no—
201#2370D1311yescharacteristic, complemented
202#2349—131no—
203#1991—131no—
204#1949—131no—
205#1942—131no—
206#1941—131no—
207#1921—131no—
208#1920—131no—
209#1864—131no—
210#1862—131no—
211C8×C4⋊C4—131no—
212C4×#102—131no—
213C4×#102—131no—
214C4×#102—131no—
215C23×C13C22×D411yescharacteristic
216C22×D13—22no—
217C22×D13—22no—
218C22×D13—22no—
219C22×D13—41no—
220C22×D13—41no—
221C22×D13—41no—
222C22×D13—41no—
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—22no—
232C2×C4×C13—22no—
233C2×C4×C13—21no—
234C2×C4×C13—21no—
235C2×C4×C13—22no—
236C2×C4×C13—21no—
237C2×C4×C13—21no—
238C2×C4×C13—21no—
239C2×C4×C13—21no—
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×C13C4×D412yes—
250C2×C4×C13C4×D412yes—
251C2×C4×C13#13512yes—
252C2×C4×C13#13512yes—
253C2×C4×C13C23×C411yescharacteristic
254C2×C4×C13C22×Q811yescharacteristic
255C2×C4×C13C2×#4111yescharacteristic
256C2×C4×C13C2×#4111yescharacteristic
257C2×C4×C13H(5,𝔽2)11yescharacteristic
258C2×C4×C132−1+411yescharacteristic
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—
268D52—22no—
269D52—22no—
270D52—22no—
271D52C4×Q814yes—
272C4×D13—84no—
273C4×D13—84no—
274C4×D13—84no—
275#1055—22no—
276#1055—22no—
277#1055—22no—
278#1055—41no—
279C2×#125C2×D1311yescharacteristic
280C2×C4×D4—131no—
281C2×C4×D4—131no—
282C2×C4×D4—131no—
283#478—138no—
284C2×#107—131no—
285C2×#107—131no—
286C2×#106—131no—
287C2×#106—131no—
288C2×C4⋊C8—131no—
289C2×#102—131no—
290C2×#102—131no—
291C2×#102—131no—
292C2×#102—131no—
293C2×C4×C8—131no—
294C2×C4×C8—131no—
295C2×C4×C8—131no—
296#389—21no—
297#389—131no—
298#389—131no—
299#389C2×D1311yescharacteristic
300#389C2×D1311yescharacteristic
301#387—21no—
302#387—21no—
303#385—261no—
304#385—261no—
305#382—131no—
306#380—261no—
307C4×C4⋊C4—21no—
308C4×C4⋊C4C2×D1311yescharacteristic
309C4×C4⋊C4C2×D1311yescharacteristic
310C4×C4⋊C4C2×D1311yescharacteristic
311C4×C4⋊C4C2×D1311yescharacteristic
312C2×#95—261no—
313#340—131no—
314#340—131no—
315#340—131no—
316#340—131no—
317#340—131no—
318#340—131no—
319#340—131no—
320#340—131no—
321#336—131no—
322#336—131no—
323C22×C13C2×C4×D411yescharacteristic
324C22×C13#54611yescharacteristic
325C22×C13D4×Q811yescharacteristic
326C22×C13C2×#13511yescharacteristic
327C22×C13C2×#13511yescharacteristic
328C22×C13#57611yescharacteristic
329C22×C13#57711yescharacteristic
330C2×D13—24no—
331C2×D13—42no—
332C2×D13—42no—
333C2×D13—42no—
334C2×D13—42no—
335C2×D13—42no—
336C2×D13—42no—
337C4×C13—22no—
338C4×C13—22no—
339C4×C13—22no—
340C4×C13—22no—
341C4×C13—42no—
342C4×C13—42no—
343C4×C13—42no—
344C4×C13—41no—
345C4×C13—41no—
346C4×C13—81no—
347C4×C13C2×C4×Q811yescharacteristic
348C4×C13#52011yescharacteristic
349C4×C13#55211yescharacteristic
350C4×C13#55411yescharacteristic
351Dic13—42no—
352Dic13—81no—
353Dic13—81no—
354C22×D4—131no—
355C23×C4—261no—
356C23×C4—261no—
357C23×C4—261no—
358C22×C8—131no—
359C22×C8—131no—
360C22×C8—131no—
361C22×C8—131no—
362#125—22no—
363#125C4×D1314yescomplemented
364C4×D4—134no—
365C4×D4—262no—
366C4×D4—262no—
367C4×D4—262no—
368C4×D4—521no—
369C4×D4—521no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—131no—
375C2×C4⋊C4—131no—
376C2×C4⋊C4—131no—
377C2×C4⋊C4—261no—
378C2×C4⋊C4—261no—
379C2×C4⋊C4C22⋊D1311yescharacteristic
380C2×C4⋊C4C22⋊D1311yescharacteristic
381C2×C4⋊C4C22×D1311yescharacteristic
382C2×C4⋊C4C22×D1311yescharacteristic
383C2×C4⋊C4C22×D1311yescharacteristic
384C2×C4⋊C4C22×D1311yescharacteristic
385C2×C22⋊C4—261no—
386C2×C22⋊C4—261no—
387C2×C22⋊C4—261no—
388C2×C42—21no—
389C2×C42—21no—
390C2×C42—21no—
391C2×C42C22×D1311yescharacteristic
392C2×C42C22×D1311yescharacteristic
393C2×C42C22×D1311yescharacteristic
394#107—134no—
395#107—521no—
396#106—134no—
397#106—521no—
398C4⋊C8—134no—
399#102—134no—
400#102—134no—
401#102—134no—
402#102—262no—
403C4×C8—262no—
404C4×C8—521no—
405C4×C8—521no—
406#95—21no—
407#95—21no—
408#95—21no—
409#95—21no—
410#95—21no—
411#95—261no—
412#95—261no—
413#95—261no—
414#95—261no—
415#95C22⋊D1311yescharacteristic
416#95C22⋊D1311yescharacteristic
417C2×C13#236011yescharacteristic
418C2×C13C4×#13511yescharacteristic
419C2×C13#294611yescharacteristic
420C2×C13#329611yescharacteristic
421C2×C13#329711yescharacteristic
422C2×C13#338011yescharacteristic
423C2×C13#338111yescharacteristic
424D13—44no—
425C24—261no—
426C2×D4—132no—
427C2×D4—132no—
428C2×D4—132no—
429C2×D4—261no—
430C2×D4—261no—
431C2×D4—261no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—261no—
437C22×C4—264no—
438C22×C4—261no—
439C22×C4—261no—
440C22×C4—522no—
441C22×C4—522no—
442C22×C4—522no—
443C22×C4—522no—
444C22×C4—1041no—
445C22×C4—1041no—
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—132no—
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—24no—
469C4⋊C4—22no—
470C4⋊C4—22no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—42no—
477C4⋊C4—81no—
478C4⋊C4—132no—
479C4⋊C4—261no—
480C4⋊C4—261no—
481C4⋊C4—261no—
482C4⋊C4—261no—
483C4⋊C4—261no—
484C4⋊C4—1041no—
485C4⋊C4—1041no—
486C4⋊C4C2×C4×D1312yes—
487C4⋊C4C2×C4×D1312yes—
488C4⋊C4Q8×D1312yes—
489C22⋊C4—264no—
490C22⋊C4—522no—
491C22⋊C4—522no—
492C42—21no—
493C42—21no—
494C42—21no—
495C42—21no—
496C42—42no—
497C42—81no—
498C42—81no—
499C42C2×C4×D1312yes—
500C42#612712yes—
501C13#2296611yescharacteristic, complemented, Sylow
502C23—262no—
503C23—262no—
504C23—262no—
505C23—521no—
506C23—521no—
507C23—521no—
508C23—521no—
509C23C22×C22⋊D1311yescharacteristic
510D4—134no—
511D4—262no—
512D4—262no—
513D4—262no—
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—22no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
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—41no—
540C2×C4—262no—
541C2×C4—521no—
542C2×C4—521no—
543C2×C4—521no—
544C2×C4—521no—
545C2×C4—521no—
546C2×C4—521no—
547C2×C4—521no—
548C2×C4—521no—
549C2×C4—1044no—
550C2×C4—1044no—
551C2×C4—1044no—
552C2×C4C4×C22⋊D1312yes—
553C2×C4C4×C22⋊D1312yes—
554C2×C4#8820412yes—
555C2×C4#8820412yes—
556C2×C4C22×C4×D1311yescharacteristic
557C2×C4C2×#612711yescharacteristic
558C2×C4C2×Q8×D1311yescharacteristic
559C2×C4#8825411yescharacteristic
560C2×C4#41×D1311yescharacteristic
561C2×C4#8825611yescharacteristic
562C8—262no—
563C8—262no—
564C8—262no—
565C8—521no—
566C22—264no—
567C22—522no—
568C22—522no—
569C22—522no—
570C22—522no—
571C22—522no—
572C22—522no—
573C22C2×C4×C22⋊D1311yescharacteristic
574C22Q8×C22⋊D1311yescharacteristic
575C22C2×#8820411yescharacteristic
576C22C2×#8820411yescharacteristic
577C22#1171953411yescharacteristic
578C22#1171954011yescharacteristic
579C22#1171954211yescharacteristic
580C4—22no—
581C4—22no—
582C4—22no—
583C4—22no—
584C4—41no—
585C4—42no—
586C4—42no—
587C4—41no—
588C4—42no—
589C4—81no—
590C4—522no—
591C4—1041no—
592C4—1041no—
593C4C4×Q8×D1311yescharacteristic
594C4#1171927911yescharacteristic
595C4#1171928411yescharacteristic
596C4#1171928611yescharacteristic
597C2—524no—
598C2#1311783711yescharacteristic
599C2C4×#8820411yescharacteristic
600C2#1312366411yescharacteristic
601C2#1312666511yescharacteristic
602C2#1312668011yescharacteristic
603C2#1312769911yescharacteristic
604C2#1312770711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#2370C2
socleC23×C13C22×D4
prime radicalC22×D52C23
cosocleC22×C4×C13C24
hypercenter#2370D13
hypocenterC13#22966
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2370

Complements

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

NH ≅ G/Ntype
3. #13115802C2semidirect
4. #13115604C2semidirect
5. #13115566C2semidirect
6. #13115561C2semidirect
7. #13115428C2semidirect
8. #13115421C2semidirect
11. C4⋊C4×#1055C2semidirect
15. C13×#2370C2semidirect
30. #11718727C4semidirect
65. C13×#125C2×C4semidirect
116. #88048C2×C4semidirect
118. #88047C2×C4semidirect
119. C4⋊#1055C2×C4semidirect
201. #2370D13semidirect
363. #125C4×D13semidirect
501. C13#22966semidirect

Maximal subgroups

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

subgroupindex
C2×#117187272
#131177472
#131158022
#131156042
#131155662
#131155612
#131154282
#131154212
#131150962
#131150822
C4⋊C4×#10552
C4×#880492
C13×#23702
#2296613