Finite Group Databasebeta

← #15883232

Subgroups — #15883232

Order 3328.

1386 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718878C211yesmaximal, characteristic
2C2×#11718675C211yesmaximal, characteristic, complemented
3C22×#88072C211yesmaximal, characteristic, complemented
4#13117850C211yesmaximal, characteristic, complemented
5#13115711C211yesmaximal, characteristic, complemented
6#13115536C211yesmaximal, characteristic, complemented
7#13115460C211yesmaximal, characteristic, complemented
8#13115262C211yesmaximal, characteristic, complemented
9#13115187C211yesmaximal, characteristic, complemented
10#13115184C211yesmaximal, characteristic, complemented
11#13115097C211yesmaximal, characteristic, complemented
12#13115028C211yesmaximal, characteristic, complemented
13#13114661C211yesmaximal, characteristic, complemented
14#13114614C211yesmaximal, characteristic, complemented
15D4×C13×C22⋊C4C211yesmaximal, characteristic, complemented
16C23×D4×C13C2211yescharacteristic
17C2×C4×D4×C13C2211yescharacteristic
18C2×C4×D4×C13C2211yescharacteristic
19C22×C13×C22⋊C4—21no—
20C22×#6104C2211yescharacteristic
21C22×#6104C2211yescharacteristic
22C2×#88184C2211yescharacteristic
23C22×C4⋊Dic13C2211yescharacteristic
24C23×#1055C2211yescharacteristic
25C2×#88135—21no—
26C2×C4×D52C2211yescharacteristic, complemented
27C13×#390C2211yescharacteristic
28C13×#390C2211yescharacteristic
29C13×#386—21no—
30C13×#386—21no—
31C13×#380C2211yescharacteristic
32C13×#379—21no—
33C4×C13×C22⋊C4C2211yescharacteristic
34#11718878C418yescomplemented
35C2×#88072—24no—
36C2×#88072C2211yescharacteristic
37C2×#88072C2211yescharacteristic
38C2×#88072C2211yescharacteristic
39C2×#88072C2211yescharacteristic
40C2×#88072C2211yescharacteristic
41C2×#88072C2211yescharacteristic
42C2×C22⋊#1055C2211yescharacteristic
43#11718675—24no—
44C2×#88049C2211yescharacteristic, complemented
45C2×#88049C2211yescharacteristic, complemented
46C2×#88048C2211yescharacteristic, complemented
47C2×#88048C2211yescharacteristic, complemented
48#11718619—21no—
49#11718600C2211yescharacteristic, complemented
50C4×C4⋊Dic13C2211yescharacteristic, complemented
51#11718589C2211yescharacteristic, complemented
52C2×#88043C2211yescharacteristic, complemented
53C2×#88043C2211yescharacteristic, complemented
54#11718331—21no—
55#11718329—21no—
56#11718121C2211yescharacteristic, complemented
57#11718121C2211yescharacteristic, complemented
58#11718121C2211yescharacteristic, complemented
59#11718121C2211yescharacteristic, complemented
60#11718116C2211yescharacteristic, complemented
61#11718116C2211yescharacteristic, complemented
62C25×C13—21no—
63C22×D4×C13—22no—
64C22×D4×C13—22no—
65C22×D4×C13—21no—
66C22×D4×C13—22no—
67C22×D4×C13—41no—
68C22×D4×C13—41no—
69C22×D4×C13C2×C414yescomplemented
70C22×D4×C13C2311yescharacteristic
71C22×D4×C13C2311yescharacteristic
72C23×C4×C13—21no—
73C23×C4×C13—21no—
74C23×C4×C13C2311yescharacteristic
75C22×C22⋊D13—21no—
76C23×Dic13—21no—
77C22×D52C2311yescharacteristic
78C22×C4×D13—21no—
79C4×D4×C13—22no—
80C4×D4×C13—22no—
81C4×D4×C13—41no—
82C4×D4×C13—41no—
83C2×C13×C4⋊C4C2311yescharacteristic
84C2×C13×C4⋊C4C2311yescharacteristic
85C2×C13×C22⋊C4—21no—
86C2×C13×C22⋊C4—21no—
87C2×C13×C22⋊C4—21no—
88C2×C13×C22⋊C4—21no—
89C2×C13×C22⋊C4—21no—
90C2×C13×C22⋊C4—21no—
91C2×C13×C22⋊C4—21no—
92C2×C13×C22⋊C4—44no—
93C2×C13×C22⋊C4D411yescharacteristic
94C2×C13×C22⋊C4D411yescharacteristic
95C2×C42×C13C2311yescharacteristic
96C2×C42×C13C2311yescharacteristic
97C2×#6104—22no—
98C2×#6104—22no—
99C2×#6104—41no—
100C2×#6104—41no—
101C2×#6104C2×C414yescomplemented
102C2×#6104C2×C414yescomplemented
103#88184—22no—
104#88184C2×C414yescomplemented
105C2×#6103—21no—
106C2×#6103—21no—
107C2×#6103—21no—
108C2×#6103—21no—
109C2×C4⋊Dic13—22no—
110C2×C4⋊Dic13—21no—
111C2×C4⋊Dic13—41no—
112C2×C4⋊Dic13C2311yescharacteristic
113C2×C4⋊Dic13C2311yescharacteristic
114C2×C4⋊Dic13C2311yescharacteristic
115C2×#6101—21no—
116C2×C4×Dic13—21no—
117C22×#1055—22no—
118C22×#1055—22no—
119C22×#1055—41no—
120C22×#1055C2311yescharacteristic
121C22×#1055C2311yescharacteristic
122C22×#1055C2311yescharacteristic
123C22×#1055C2311yescharacteristic
124#88135—44no—
125C4×D52—22no—
126C4×D52—41no—
127C13×#95—21no—
128C13×#95D411yescharacteristic
129C13×#95D411yescharacteristic
130#88072—22no—
131#88072—22no—
132#88072—22no—
133#88072C2×C414yescomplemented
134#88072C2×C414yescomplemented
135#88072D414yescomplemented
136#88071—21no—
137#88071—21no—
138C22⋊#1055C2×C414yescomplemented
139#88049—22no—
140#88049—41no—
141#88048—22no—
142#88048—41no—
143#88043—22no—
144#88043—41no—
145#22858—131nomaximal, Sylow
146C24×C13—21no—
147C24×C13—21no—
148C24×C13—24no—
149C24×C13—42no—
150C24×C13—42no—
151C24×C13—42no—
152C24×C13—42no—
153C24×C13—81no—
154C24×C13—81no—
155C24×C13C2×D411yescharacteristic
156C23×D13—21no—
157C2×D4×C13—28no—
158C2×D4×C13—24no—
159C2×D4×C13—21no—
160C2×D4×C13—21no—
161C2×D4×C13—21no—
162C2×D4×C13—21no—
163C2×D4×C13—21no—
164C2×D4×C13—21no—
165C2×D4×C13—21no—
166C2×D4×C13—21no—
167C2×D4×C13—44no—
168C2×D4×C13—44no—
169C2×D4×C13—44no—
170C2×D4×C13—42no—
171C2×D4×C13—42no—
172C2×D4×C13C22×C412yes—
173C2×D4×C13C22×C412yes—
174C2×D4×C13C2×D412yes—
175C2×D4×C13#4112yes—
176C22×C4×C13—21no—
177C22×C4×C13—21no—
178C22×C4×C13—21no—
179C22×C4×C13—21no—
180C22×C4×C13—21no—
181C22×C4×C13—21no—
182C22×C4×C13—42no—
183C22×C4×C13—42no—
184C22×C4×C13—42no—
185C22×C4×C13—42no—
186C22×C4×C13—81no—
187C22×C4×C13—81no—
188C22×C4×C13C22×C412yes—
189C22×C4×C13C2×D411yescharacteristic
190C22×C4×C13C2×D411yescharacteristic
191C22×C4×C13C2×D411yescharacteristic
192C22×C4×C13C2×D411yescharacteristic
193C22×C4×C13C2×D411yescharacteristic
194C22×C4×C13#4112yes—
195C22×C4×C13C2411yescharacteristic
196C2×C22⋊D13—24no—
197C2×C22⋊D13—42no—
198C2×C22⋊D13—42no—
199C22×Dic13—21no—
200C22×Dic13—21no—
201C22×Dic13—21no—
202C22×Dic13—42no—
203C22×Dic13—42no—
204C22×Dic13—81no—
205C2×D52—21no—
206C2×D52—21no—
207C2×D52—21no—
208C2×D52—21no—
209C2×D52—21no—
210C2×D52C22×C412yes—
211C2×C4×D13—42no—
212C2×C4×D13—42no—
213C2×C4×D13—81no—
214C13×C4⋊C4—21no—
215C13×C4⋊C4—21no—
216C13×C4⋊C4—21no—
217C13×C4⋊C4—21no—
218C13×C22⋊C4—22no—
219C13×C22⋊C4—22no—
220C13×C22⋊C4—42no—
221C13×C22⋊C4—42no—
222C13×C22⋊C4—42no—
223C13×C22⋊C4—42no—
224C13×C22⋊C4—42no—
225C13×C22⋊C4—81no—
226C13×C22⋊C4—81no—
227C42×C13—21no—
228C42×C13—21no—
229C42×C13—21no—
230C42×C13—21no—
231#6104—28no—
232#6104—44no—
233#6103—24no—
234#6103—42no—
235#6103—42no—
236#6103—81no—
237C4⋊Dic13—21no—
238C4⋊Dic13—21no—
239C4⋊Dic13—21no—
240C4⋊Dic13—21no—
241C4⋊Dic13—42no—
242C4⋊Dic13C22×C412yes—
243C4⋊Dic13C2×D412yes—
244#6101—42no—
245C4×Dic13—42no—
246C2×#1055—21no—
247C2×#1055—21no—
248C2×#1055—21no—
249C2×#1055—21no—
250C2×#1055—21no—
251C2×#1055—21no—
252C2×#1055—21no—
253C2×#1055—21no—
254C2×#1055—21no—
255C2×#1055—44no—
256C2×#1055C22×C412yes—
257C2×#1055C22×C412yes—
258C2×#1055C2×D412yes—
259C2×#447—131no—
260C2×#442—131no—
261C22×#102—131no—
262#2361—131no—
263D4×C22⋊C4D1311yescharacteristic, complemented
264#1972—131no—
265#1936—131no—
266#1926—131no—
267#1893—131no—
268#1879—131no—
269#1879—131no—
270#1864—131no—
271#1853—131no—
272#1762—131no—
273#1752—131no—
274C23×C13—21no—
275C23×C13—21no—
276C23×C13—21no—
277C23×C13—21no—
278C23×C13—22no—
279C23×C13—22no—
280C23×C13—22no—
281C23×C13—22no—
282C23×C13—48no—
283C23×C13—41no—
284C23×C13—41no—
285C23×C13—41no—
286C23×C13—41no—
287C23×C13—41no—
288C23×C13—41no—
289C23×C13—41no—
290C23×C13—41no—
291C23×C13—41no—
292C23×C13—41no—
293C23×C13—48no—
294C23×C13—84no—
295C23×C13—84no—
296C23×C13—84no—
297C23×C13—84no—
298C23×C13—84no—
299C23×C13C4×D412yes—
300C23×C13AGL(1,ℤ/8)12yes—
301C23×C13AGL(1,ℤ/8)12yes—
302C23×C13C22×D411yescharacteristic
303C22×D13—22no—
304C22×D13—41no—
305C22×D13—41no—
306C22×D13—41no—
307C22×D13—41no—
308C22×D13—41no—
309C22×D13—41no—
310D4×C13—22no—
311D4×C13—22no—
312D4×C13—22no—
313D4×C13—22no—
314D4×C13—22no—
315D4×C13—48no—
316D4×C13—41no—
317D4×C13—41no—
318D4×C13C4×D414yescomplemented
319C2×C4×C13—21no—
320C2×C4×C13—21no—
321C2×C4×C13—22no—
322C2×C4×C13—22no—
323C2×C4×C13—22no—
324C2×C4×C13—22no—
325C2×C4×C13—21no—
326C2×C4×C13—21no—
327C2×C4×C13—21no—
328C2×C4×C13—21no—
329C2×C4×C13—21no—
330C2×C4×C13—21no—
331C2×C4×C13—21no—
332C2×C4×C13—21no—
333C2×C4×C13—21no—
334C2×C4×C13—21no—
335C2×C4×C13—21no—
336C2×C4×C13—21no—
337C2×C4×C13—41no—
338C2×C4×C13—41no—
339C2×C4×C13—41no—
340C2×C4×C13—41no—
341C2×C4×C13—41no—
342C2×C4×C13—41no—
343C2×C4×C13—84no—
344C2×C4×C13—84no—
345C2×C4×C13C4×D412yes—
346C2×C4×C13C23×C411yescharacteristic
347C2×C4×C13C22×D411yescharacteristic
348C2×C4×C13C2×#4111yescharacteristic
349C2×C4×C13C2×#4111yescharacteristic
350C2×C4×C13H(5,𝔽2)11yescharacteristic
351C2×C4×C13H(5,𝔽2)11yescharacteristic
352C22⋊D13—48no—
353C2×Dic13—22no—
354C2×Dic13—22no—
355C2×Dic13—41no—
356C2×Dic13—41no—
357C2×Dic13—41no—
358C2×Dic13—41no—
359C2×Dic13—41no—
360C2×Dic13—41no—
361C2×Dic13—41no—
362C2×Dic13—84no—
363D52—22no—
364D52—22no—
365D52—41no—
366D52—41no—
367C4×D13—84no—
368#1055—22no—
369#1055—22no—
370#1055—22no—
371#1055—41no—
372C23×D4C2×D1311yescharacteristic
373C22×D8—131no—
374C22×D8—131no—
375C23×C8—131no—
376C2×#121—131no—
377C2×C4×D4—131no—
378C2×C4×D4—261no—
379C2×C4×D4C2×D1311yescharacteristic
380C2×C4×D4C2×D1311yescharacteristic
381C22×C4⋊C4—131no—
382C22×C22⋊C4—21no—
383#447—138no—
384#442—264no—
385C2×#106—131no—
386C2×#106—131no—
387C2×#102—131no—
388C2×#102—131no—
389C2×#102—131no—
390C2×#102—131no—
391C2×#102—131no—
392C2×#102—131no—
393C2×#102—131no—
394C2×#102—131no—
395C2×#102—264no—
396C2×C22⋊C8—131no—
397C2×#97—131no—
398C2×#97—131no—
399#390—131no—
400#390C2×D1311yescharacteristic
401#390C2×D1311yescharacteristic
402#389—131no—
403#388—261no—
404#386—21no—
405#386—21no—
406#386—261no—
407#385—261no—
408#380C2×D1311yescharacteristic
409#379—21no—
410C4×C4⋊C4—131no—
411C4×C22⋊C4C2×D1311yescharacteristic
412#340—131no—
413#340—131no—
414#340—131no—
415#340—131no—
416#336—131no—
417#336—131no—
418C22×C13—22no—
419C22×C13—22no—
420C22×C13—22no—
421C22×C13—22no—
422C22×C13—22no—
423C22×C13—22no—
424C22×C13—24no—
425C22×C13—42no—
426C22×C13—42no—
427C22×C13—42no—
428C22×C13—42no—
429C22×C13—42no—
430C22×C13—42no—
431C22×C13—42no—
432C22×C13—42no—
433C22×C13—42no—
434C22×C13—816no—
435C22×C13—81no—
436C22×C13—81no—
437C22×C13—81no—
438C22×C13—81no—
439C22×C13#44214yescomplemented
440C22×C13C2×C4×D411yescharacteristic
441C22×C13D4211yescharacteristic
442C22×C13#54611yescharacteristic
443C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
444C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
445C22×C13#57611yescharacteristic
446C22×C13#57711yescharacteristic
447C2×D13—42no—
448C2×D13—42no—
449C2×D13—42no—
450C2×D13—81no—
451C2×D13—81no—
452C2×D13—81no—
453C2×D13—81no—
454C4×C13—22no—
455C4×C13—41no—
456C4×C13—41no—
457C4×C13—41no—
458C4×C13—41no—
459C4×C13—81no—
460C4×C13—81no—
461C4×C13C2×C4×D411yescharacteristic
462C4×C13#51811yescharacteristic
463C4×C13#54611yescharacteristic
464C4×C13#55111yescharacteristic
465Dic13—42no—
466Dic13—42no—
467Dic13—81no—
468C25—21no—
469C22×D4—22no—
470C22×D4—22no—
471C22×D4—22no—
472C22×D4—21no—
473C22×D4—41no—
474C22×D4—41no—
475C22×D4—131no—
476C22×D4—261no—
477C22×D4C4×D1314yescomplemented
478C22×D4C22×D1311yescharacteristic
479C22×D4C22×D1311yescharacteristic
480C23×C4—21no—
481C23×C4—21no—
482C23×C4—261no—
483C23×C4—261no—
484C23×C4C22×D1311yescharacteristic
485C2×D8—134no—
486C2×D8—134no—
487C2×D8—262no—
488C2×D8—262no—
489C2×D8—521no—
490C2×D8—521no—
491C22×C8—131no—
492C22×C8—131no—
493C22×C8—131no—
494C22×C8—131no—
495C22×C8—262no—
496C22×C8—262no—
497C22×C8—521no—
498#121—134no—
499#121—262no—
500C4×D4—22no—
501C4×D4—22no—
502C4×D4—41no—
503C4×D4—41no—
504C4×D4—262no—
505C4×D4—521no—
506C4×D4—524no—
507C2×C4⋊C4—131no—
508C2×C4⋊C4—131no—
509C2×C4⋊C4—131no—
510C2×C4⋊C4—262no—
511C2×C4⋊C4—261no—
512C2×C4⋊C4—261no—
513C2×C4⋊C4—521no—
514C2×C4⋊C4C22×D1311yescharacteristic
515C2×C4⋊C4C22×D1311yescharacteristic
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—44no—
524C2×C22⋊C4—261no—
525C2×C22⋊C4—261no—
526C2×C22⋊C4—261no—
527C2×C22⋊C4—261no—
528C2×C22⋊C4C22⋊D1311yescharacteristic
529C2×C22⋊C4C22⋊D1311yescharacteristic
530C2×C42—261no—
531C2×C42C22×D1311yescharacteristic
532C2×C42C22×D1311yescharacteristic
533#106—262no—
534#106—521no—
535#102—134no—
536#102—134no—
537#102—134no—
538#102—262no—
539#102—262no—
540#102—262no—
541#102—262no—
542#102—521no—
543C22⋊C8—134no—
544#97—262no—
545#97—521no—
546#95—21no—
547#95—261no—
548#95—261no—
549#95C22⋊D1311yescharacteristic
550#95C22⋊D1311yescharacteristic
551C2×C13—24no—
552C2×C13—44no—
553C2×C13—82no—
554C2×C13#235811yescharacteristic
555C2×C13C2×#44211yescharacteristic
556C2×C13#294611yescharacteristic
557C2×C13#326411yescharacteristic
558C2×C13#326511yescharacteristic
559C2×C13#330611yescharacteristic
560C2×C13#331811yescharacteristic
561D13—82no—
562C24—21no—
563C24—21no—
564C24—24no—
565C24—42no—
566C24—42no—
567C24—42no—
568C24—42no—
569C24—81no—
570C24—81no—
571C24—261no—
572C24C2×C22⋊D1311yescharacteristic
573C2×D4—28no—
574C2×D4—24no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—44no—
584C2×D4—44no—
585C2×D4—44no—
586C2×D4—42no—
587C2×D4—42no—
588C2×D4—132no—
589C2×D4—264no—
590C2×D4—261no—
591C2×D4—261no—
592C2×D4—261no—
593C2×D4—261no—
594C2×D4—261no—
595C2×D4—522no—
596C2×D4—522no—
597C2×D4C2×C4×D1312yes—
598C2×D4C2×C4×D1312yes—
599C2×D4D4×D1312yes—
600C2×D4#612912yes—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4—42no—
610C22×C4—42no—
611C22×C4—81no—
612C22×C4—81no—
613C22×C4—261no—
614C22×C4—261no—
615C22×C4—261no—
616C22×C4—522no—
617C22×C4—522no—
618C22×C4—522no—
619C22×C4—522no—
620C22×C4—1041no—
621C22×C4—1041no—
622C22×C4C2×C4×D1312yes—
623C22×C4#612712yes—
624C22×C4C2×C22⋊D1311yescharacteristic
625C22×C4C2×C22⋊D1311yescharacteristic
626C22×C4C2×C22⋊D1311yescharacteristic
627C22×C4C2×C22⋊D1311yescharacteristic
628C22×C4C2×C22⋊D1311yescharacteristic
629C22×C4C23×D1311yescharacteristic
630D8—268no—
631D8—524no—
632C2×C8—132no—
633C2×C8—132no—
634C2×C8—132no—
635C2×C8—261no—
636C2×C8—261no—
637C2×C8—261no—
638C2×C8—261no—
639C2×C8—261no—
640C2×C8—261no—
641C2×C8—261no—
642C2×C8—261no—
643C2×C8—261no—
644C2×C8—524no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—132no—
650C4⋊C4—132no—
651C4⋊C4—261no—
652C4⋊C4—261no—
653C4⋊C4—261no—
654C4⋊C4—261no—
655C4⋊C4—522no—
656C4⋊C4—522no—
657C22⋊C4—22no—
658C22⋊C4—22no—
659C22⋊C4—42no—
660C22⋊C4—42no—
661C22⋊C4—42no—
662C22⋊C4—42no—
663C22⋊C4—42no—
664C22⋊C4—81no—
665C22⋊C4—81no—
666C22⋊C4—264no—
667C22⋊C4—522no—
668C22⋊C4—522no—
669C22⋊C4—1041no—
670C42—21no—
671C42—21no—
672C42—21no—
673C42—21no—
674C42—522no—
675C13#2285811yescharacteristic, complemented, Sylow
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—48no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—48no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—84no—
697C23—84no—
698C23—84no—
699C23—84no—
700C23—84no—
701C23—262no—
702C23—521no—
703C23—521no—
704C23—521no—
705C23—521no—
706C23—521no—
707C23—521no—
708C23C4×C22⋊D1312yes—
709C23#8818612yes—
710C23#8820312yes—
711C23C22×C22⋊D1311yescharacteristic
712D4—22no—
713D4—22no—
714D4—22no—
715D4—22no—
716D4—22no—
717D4—48no—
718D4—41no—
719D4—41no—
720D4—262no—
721D4—262no—
722D4—528no—
723D4—521no—
724D4—521no—
725D4#8813514yescomplemented
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—84no—
751C2×C4—84no—
752C2×C4—262no—
753C2×C4—262no—
754C2×C4—521no—
755C2×C4—521no—
756C2×C4—521no—
757C2×C4—521no—
758C2×C4—521no—
759C2×C4—521no—
760C2×C4—521no—
761C2×C4—1044no—
762C2×C4—1044no—
763C2×C4C4×C22⋊D1312yes—
764C2×C4C22×C4×D1311yescharacteristic
765C2×C4C2×#612711yescharacteristic
766C2×C4C2×D4×D1311yescharacteristic
767C2×C4C2×#612911yescharacteristic
768C2×C4#8825111yescharacteristic
769C2×C4#8825111yescharacteristic
770C8—262no—
771C8—262no—
772C8—262no—
773C8—521no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—22no—
780C22—24no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—816no—
791C22—81no—
792C22—81no—
793C22—81no—
794C22—81no—
795C22—522no—
796C22—522no—
797C22—522no—
798C22—1041no—
799C22—1041no—
800C22—1041no—
801C22—1041no—
802C22#1171867514yescomplemented
803C22C2×C4×C22⋊D1311yescharacteristic
804C22C2×#8818611yescharacteristic
805C22D4×C22⋊D1311yescharacteristic
806C22#1171951111yescharacteristic
807C22C2×#8820311yescharacteristic
808C22#1171954011yescharacteristic
809C22#1171954111yescharacteristic
810C4—22no—
811C4—41no—
812C4—41no—
813C4—41no—
814C4—41no—
815C4—81no—
816C4—81no—
817C4—522no—
818C4—522no—
819C4—1041no—
820C4C2×#8813511yescharacteristic
821C4#1171919111yescharacteristic
822C4#1171919511yescharacteristic
823C4#1171920011yescharacteristic
824C2—24no—
825C2—44no—
826C2—82no—
827C2—1042no—
828C2#1311781511yescharacteristic
829C2C2×#1171867511yescharacteristic
830C2#1312366811yescharacteristic
831C2#1312631711yescharacteristic
832C2#1312632711yescharacteristic
833C2#1312679711yescharacteristic
834C2#1312697711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingD4×C13×C22⋊C4C2
socleC23×C13C22×D4
prime radicalC2×#11718878C2
cosocleC22×C4×C13C24
hypercenterD4×C22⋊C4D13
hypocenterC13#22858
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ D4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#11718675C2semidirect
3. C22×#88072C2semidirect
4. #13117850C2semidirect
5. #13115711C2semidirect
6. #13115536C2semidirect
7. #13115460C2semidirect
8. #13115262C2semidirect
9. #13115187C2semidirect
10. #13115184C2semidirect
11. #13115097C2semidirect
12. #13115028C2semidirect
13. #13114661C2semidirect
14. #13114614C2semidirect
15. D4×C13×C22⋊C4C2semidirect
26. C2×C4×D52C22semidirect
34. #11718878C4semidirect
44. C2×#88049C22semidirect
45. C2×#88049C22semidirect
46. C2×#88048C22semidirect
47. C2×#88048C22semidirect
49. #11718600C22semidirect
50. C4×C4⋊Dic13C22semidirect
51. #11718589C22semidirect
52. C2×#88043C22semidirect
53. C2×#88043C22semidirect
56. #11718121C22semidirect
57. #11718121C22semidirect
58. #11718121C22semidirect
59. #11718121C22semidirect
60. #11718116C22semidirect
61. #11718116C22semidirect
69. C22×D4×C13C2×C4semidirect
101. C2×#6104C2×C4semidirect
102. C2×#6104C2×C4semidirect
104. #88184C2×C4semidirect
133. #88072C2×C4semidirect
134. #88072C2×C4semidirect
135. #88072D4semidirect
138. C22⋊#1055C2×C4semidirect
263. D4×C22⋊C4D13semidirect
318. D4×C13C4×D4semidirect
439. C22×C13#442semidirect
477. C22×D4C4×D13semidirect
675. C13#22858semidirect
725. D4#88135semidirect
802. C22#11718675semidirect

Maximal subgroups

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

subgroupindex
C2×#117188782
C2×#117186752
C22×#880722
#131178502
#131157112
#131155362
#131154602
#131152622
#131151872
#131151842
#131150972
#131150282
#131146612
#131146142
D4×C13×C22⋊C42
#2285813