Finite Group Databasebeta

← #30616067

Subgroups — #30616067

Order 15616.

1042 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462276C211yesmaximal, characteristic, complemented
2C4×D4×#6923C211yesmaximal, characteristic, complemented
3#21461897C211yesmaximal, characteristic, complemented
4#21461896C211yesmaximal, characteristic, complemented
5#21461882C211yesmaximal, characteristic, complemented
6#21461881C211yesmaximal, characteristic, complemented
7#21461814C211yesmaximal, characteristic
8#21461814C211yesmaximal, characteristic
9#21461784C211yesmaximal, characteristic, complemented
10#21461782C211yesmaximal, characteristic, complemented
11#21461633C211yesmaximal, characteristic, complemented
12#21461589C211yesmaximal, characteristic, complemented
13#21461589C211yesmaximal, characteristic, complemented
14#21461535C211yesmaximal, characteristic, complemented
15#442×D61C211yesmaximal, characteristic
16C2×D4×#6923C2211yescharacteristic
17C2×D4×#6923C2211yescharacteristic
18C2×#14519856—21no—
19C22×C4×#6923—21no—
20C2×#14519846C2211yescharacteristic
21C2×#14519845C2211yescharacteristic
22C2×#14519839C2211yescharacteristic
23C2×#14519839C2211yescharacteristic
24C2×#14519839C2211yescharacteristic
25C2×#14519839C2211yescharacteristic
26#16840721C2211yescharacteristic
27#16840714C2211yescharacteristic
28#16840714C2211yescharacteristic
29#16840713C2211yescharacteristic
30#16840713C2211yescharacteristic
31#16840712—21no—
32#16840712—21no—
33C4⋊C4×#6923C2211yescharacteristic
34C4⋊C4×#6923C2211yescharacteristic
35C4×C4⋊#6923C2211yescharacteristic
36C4×C4⋊#6923C2211yescharacteristic
37C22⋊C4×#6923—21no—
38C22⋊C4×#6923—21no—
39C4×C22⋊#6923—21no—
40C4×C22⋊#6923—21no—
41C42×#6923C2211yescharacteristic
42#16840636C2211yescharacteristic
43#16840636C2211yescharacteristic
44#16840635C2211yescharacteristic
45#16840635C2211yescharacteristic
46#16840635C2211yescharacteristic
47#16840635C2211yescharacteristic
48(C2×#6923)⋊C8C2211yescharacteristic
49(C2×#6923)⋊C8C2211yescharacteristic
50(C2×#6923)⋊C8C2211yescharacteristic
51(C2×#6923)⋊C8C2211yescharacteristic
52C2×D8×D61C2211yescharacteristic
53C4×D4×D61C2211yescharacteristic
54C4×D4×D61C2211yescharacteristic
55#16839875C411yescharacteristic, complemented
56#16839874C411yescharacteristic, complemented
57#16839873C411yescharacteristic, complemented
58#16839872C411yescharacteristic, complemented
59#16839872C411yescharacteristic, complemented
60#16839871C411yescharacteristic, complemented
61#16839871C411yescharacteristic, complemented
62#106×D61C2211yescharacteristic
63#102×D61C2211yescharacteristic
64#102×D61C2211yescharacteristic
65#97×D61C2211yescharacteristic
66C61×#442C411yescharacteristic, complemented
67C23×#6923—21no—
68C23×#6923—21no—
69C2×D61⋊C8C2311yescharacteristic
70C2×D61⋊C8C2311yescharacteristic
71D4×#6923—22no—
72D4×#6923—22no—
73D4×#6923—22no—
74D4×#6923—22no—
75#14519856—44no—
76C2×C4⋊#6923—21no—
77C2×C4⋊#6923—21no—
78C2×C4⋊#6923C2311yescharacteristic
79C2×C4⋊#6923C2311yescharacteristic
80C2×C4⋊#6923C2311yescharacteristic
81C2×C4⋊#6923C2311yescharacteristic
82C2×C22⋊#6923—21no—
83C2×C22⋊#6923—21no—
84C2×C22⋊#6923—21no—
85C2×C22⋊#6923—21no—
86C2×C22⋊#6923—21no—
87C2×C22⋊#6923—21no—
88C2×C4×#6923—21no—
89C2×C4×#6923—21no—
90C2×C4×#6923—21no—
91C2×C4×#6923—21no—
92C2×C4×#6923—44no—
93C2×C4×#6923D411yescharacteristic
94C2×C4×#6923D411yescharacteristic
95C2×C4×#6923D411yescharacteristic
96C2×C4×#6923D411yescharacteristic
97C2×C4×#6923C2311yescharacteristic
98C2×C4×#6923C2311yescharacteristic
99#14519846—22no—
100#14519845—22no—
101#14519839—22no—
102#14519839—22no—
103#14519839—22no—
104#14519839—22no—
105#14519832—21no—
106#14519832—21no—
107(C2×#6923)⋊C4—21no—
108(C2×#6923)⋊C4—21no—
109(C2×#6923)⋊C4—21no—
110(C2×#6923)⋊C4—21no—
111(C2×#6923)⋊C4—21no—
112(C2×#6923)⋊C4—21no—
113C2×D4×D61C2311yescharacteristic
114C2×D4×D61C2311yescharacteristic
115C22×C4×D61—21no—
116C22×C4×D61—21no—
117C2×D488C2×C411yescharacteristic
118C2×#11758199C2×C411yescharacteristic
119C2×#11758199C2×C411yescharacteristic
120D8×D61—22no—
121D8×D61—22no—
122C2×C8×D61C2311yescharacteristic
123C2×C8×D61C2311yescharacteristic
124C4×D244C2×C411yescharacteristic
125C4×D244C2×C411yescharacteristic, complemented
126D4×Dic61C2×C411yescharacteristic
127D4×Dic61C2×C411yescharacteristic, complemented
128#14519739C2×C411yescharacteristic
129#14519739C2×C411yescharacteristic, complemented
130C4×C22⋊D61—21no—
131C4×C22⋊D61—21no—
132#14519737—21no—
133#14519737—21no—
134C4⋊C4×D61C2311yescharacteristic
135C4⋊C4×D61C2311yescharacteristic
136C22⋊C4×D61—21no—
137C22⋊C4×D61—21no—
138C42×D61C2311yescharacteristic
139#14519709C2×C411yescharacteristic, complemented
140#14519708C2×C411yescharacteristic, complemented
141#14519708C2×C411yescharacteristic, complemented
142#14519699C2×C411yescharacteristic
143#14519699C2×C411yescharacteristic, complemented
144#14519698C2×C411yescharacteristic
145#14519698C2×C411yescharacteristic, complemented
146#14519697C2×C411yescharacteristic
147#14519697C2×C411yescharacteristic, complemented
148#14519688C2×C411yescharacteristic, complemented
149#14519687C2×C411yescharacteristic, complemented
150#14519687C2×C411yescharacteristic, complemented
151C2×D8×C61C2×C411yescharacteristic
152C4×D4×C61C2×C411yescharacteristic
153C4×D4×C61C2×C411yescharacteristic, complemented
154#106×C61C2×C411yescharacteristic, complemented
155#102×C61C2×C411yescharacteristic
156#102×C61C2×C411yescharacteristic, complemented
157#97×C61C2×C411yescharacteristic, complemented
158C23×D61—21no—
159C23×D61—21no—
160C22×#6923—24no—
161C22×#6923—24no—
162C22×#6923—21no—
163C22×#6923—21no—
164C22×#6923—21no—
165C22×#6923—21no—
166C22×#6923—42no—
167C22×#6923—42no—
168C22×#6923—42no—
169C22×#6923—42no—
170C22×#6923C2×D411yescharacteristic
171C22×#6923C2×D411yescharacteristic
172C22×#6923C2×D411yescharacteristic
173C22×#6923C2×D411yescharacteristic
174C2×D4×C61C22×C411yescharacteristic
175C2×D4×C61C22×C411yescharacteristic
176C22×C4×C61—21no—
177C22×C4×C61—21no—
178C2×C22⋊D61—21no—
179C2×C22⋊D61—21no—
180C22×Dic61—21no—
181C22×Dic61—21no—
182D4×D61—21no—
183D4×D61—21no—
184D4×D61—21no—
185D4×D61—21no—
186D4×D61—21no—
187D4×D61—21no—
188D4×D61#4112yes—
189D4×D61#4112yes—
190C2×D244C22×C411yescharacteristic
191C2×D244C22×C411yescharacteristic
192C2×C4×D61—21no—
193C2×C4×D61—21no—
194C2×C4×D61—21no—
195C2×C4×D61—21no—
196C2×C4×D61—21no—
197C2×C4×D61—21no—
198C2×C4×D61—42no—
199C2×C4×D61—42no—
200C2×C4×D61—42no—
201C2×C4×D61—42no—
202C2×C4×D61C2×D411yescharacteristic
203C2×C4×D61C2×D411yescharacteristic
204C2×C4×D61C2411yescharacteristic
205C22⋊#6923—24no—
206C22⋊#6923—24no—
207C22⋊#6923—42no—
208C22⋊#6923—42no—
209C22⋊#6923—42no—
210C22⋊#6923—42no—
211C2×#92420—21no—
212C2×#92420—21no—
213C4⋊#6923—21no—
214C4⋊#6923—21no—
215C4⋊#6923—21no—
216C4⋊#6923—21no—
217C4⋊#6923—21no—
218C4⋊#6923—21no—
219C4⋊#6923—42no—
220C4⋊#6923—42no—
221C4⋊#6923#4112yes—
222C4⋊#6923#4112yes—
223C4×#6923—22no—
224C4×#6923—22no—
225C4×#6923—21no—
226C4×#6923—21no—
227C4×#6923—21no—
228C4×#6923—21no—
229C4×#6923—41no—
230C4×#6923—41no—
231C4×#6923—42no—
232C4×#6923—42no—
233C4×#6923—42no—
234C4×#6923—42no—
235D61⋊C8—21no—
236D61⋊C8—21no—
237D61⋊C8—21no—
238D61⋊C8—21no—
239D8×C61—22no—
240C2×C8×C61C22×C411yescharacteristic
241C2×C8×C61C22×C411yescharacteristic
242C4⋊C4×C61C22×C411yescharacteristic
243C4⋊C4×C61C22×C411yescharacteristic
244C22⋊C4×C61—21no—
245C22⋊C4×C61—21no—
246C42×C61C22×C411yescharacteristic
247C22⋊Dic61—21no—
248C22⋊Dic61—21no—
249#11758199—22no—
250#11758199—22no—
251#11758198—21no—
252#11758198—21no—
253#11758198—21no—
254#11758198—21no—
255C4⋊Dic61C22×C411yescharacteristic
256C4⋊Dic61C22×C411yescharacteristic
257#11758196—21no—
258#11758196—21no—
259C4×Dic61C22×C411yescharacteristic
260C4×Dic61#4111yescharacteristic
261C4×Dic61#4111yescharacteristic
262C2×#92418C22×C411yescharacteristic
263C2×#92418C22×C411yescharacteristic
264D488—22no—
265C8×D61—21no—
266C8×D61—21no—
267C8×D61—21no—
268C8×D61—21no—
269C23×C61—21no—
270C23×C61—21no—
271C22×D61—21no—
272C22×D61—22no—
273C22×D61—22no—
274C22×D61—21no—
275C22×D61—41no—
276C22×D61—41no—
277C22×D61—41no—
278C22×D61—41no—
279C22×D61—41no—
280C22×D61—41no—
281C22×D61—41no—
282C22×D61—41no—
283C22×D61—41no—
284C22×D61—41no—
285C22×D61C22×D411yescharacteristic
286C2×#6923—21no—
287C2×#6923—21no—
288C2×#6923—21no—
289C2×#6923—21no—
290C2×#6923—21no—
291C2×#6923—21no—
292C2×#6923—22no—
293C2×#6923—22no—
294C2×#6923—21no—
295C2×#6923—21no—
296C2×#6923—21no—
297C2×#6923—21no—
298C2×#6923—48no—
299C2×#6923—48no—
300C2×#6923—41no—
301C2×#6923—41no—
302C2×#6923—41no—
303C2×#6923—41no—
304C2×#6923—41no—
305C2×#6923—41no—
306C2×#6923—41no—
307C2×#6923—41no—
308C2×#6923—41no—
309C2×#6923—41no—
310C2×#6923AGL(1,ℤ/8)12yes—
311C2×#6923AGL(1,ℤ/8)12yes—
312D4×C61—21no—
313D4×C61—21no—
314D4×C61—21no—
315D4×C61#11712yescomplemented
316C2×C4×C61—21no—
317C2×C4×C61—21no—
318C2×C4×C61—42no—
319C2×C4×C61—42no—
320C2×C4×C61C4×D411yescharacteristic
321C2×C4×C61C4×D411yescharacteristic
322C2×C4×C61C23×C411yescharacteristic
323C22⋊D61—22no—
324C22⋊D61—22no—
325C22⋊D61—41no—
326C22⋊D61—41no—
327C2×Dic61—21no—
328C2×Dic61—21no—
329C2×Dic61—42no—
330C2×Dic61—42no—
331C2×Dic61C4×D411yescharacteristic
332C2×Dic61C4×D411yescharacteristic
333C2×Dic61C2×#4111yescharacteristic
334D244—21no—
335D244—21no—
336D244—21no—
337D244#11712yescomplemented
338C4×D61—21no—
339C4×D61—21no—
340C4×D61—21no—
341C4×D61—21no—
342C4×D61—42no—
343C4×D61—42no—
344C4×D61—42no—
345C4×D61—42no—
346C4×D61—41no—
347C4×D61—41no—
348C4×D61—41no—
349C4×D61—41no—
350C4×D61C2×#4111yescharacteristic
351C4×D61C2×#4111yescharacteristic
352C4×D61C2×#4111yescharacteristic
353C4×D61C2×#4111yescharacteristic
354#92420—41no—
355#92420—41no—
356C8×C61—21no—
357C8×C61—21no—
358#92418—21no—
359#92418—21no—
360#21122—611nomaximal, Sylow
361C22×C61—22no—
362C22×C61—41no—
363C22×C61—41no—
364C22×C61—41no—
365C22×C61—41no—
366C22×C61—41no—
367C22×C61C2×C4×D411yescharacteristic
368C2×D61—22no—
369C2×D61—41no—
370C2×D61—41no—
371C2×D61—42no—
372C2×D61—42no—
373C2×D61—42no—
374C2×D61—42no—
375C2×D61—41no—
376C2×D61—41no—
377C2×D61—41no—
378C2×D61—81no—
379C2×D61—81no—
380C2×D61—81no—
381C2×D61—81no—
382C2×D61#52511yescharacteristic
383C2×D61#52511yescharacteristic
384C2×D61C2×AGL(1,ℤ/8)11yescharacteristic
385C2×D61C2×AGL(1,ℤ/8)11yescharacteristic
386C2×D61#57511yescharacteristic
387C2×D61#57511yescharacteristic
388#6923—22no—
389#6923—22no—
390#6923—42no—
391#6923—41no—
392#6923—42no—
393#6923—41no—
394#6923—81no—
395#6923—81no—
396C4×C61—21no—
397C4×C61—21no—
398C4×C61—41no—
399C4×C61—41no—
400C4×C61C2×#11711yescharacteristic
401C4×C61C4×#4111yescharacteristic
402Dic61—21no—
403Dic61—21no—
404Dic61—41no—
405Dic61—41no—
406Dic61#52911yescharacteristic
407Dic61#52911yescharacteristic
408C2×#442—611no—
409#2293—611no—
410C42×D4—611no—
411#1926—611no—
412#1925—611no—
413#1920—611no—
414#1919—611no—
415#1879—611no—
416#1879—611no—
417#1864—611no—
418#1862—611no—
419#1776—611no—
420#1762—611no—
421#1762—611no—
422#1745—611no—
423C2×C61—42no—
424C2×C61—81no—
425C2×C61#229011yescharacteristic
426C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
427C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
428D61—42no—
429D61—81no—
430D61#310911yescharacteristic
431D61#311111yescharacteristic
432D61#311411yescharacteristic
433D61#311511yescharacteristic
434C22×D8—611no—
435C2×C4×D4—611no—
436C2×C4×D4—611no—
437C2×C4×D4—611no—
438C2×C4×D4—611no—
439C2×#117—1221no—
440C22×C42—1221no—
441#442—611no—
442#442—611no—
443#442—611no—
444#442—611no—
445#442—611no—
446#442—611no—
447#442—611no—
448#442#692311yescharacteristic, complemented
449C2×#107—611no—
450C2×#106—611no—
451C2×#106—611no—
452C2×#102—611no—
453C2×#102—611no—
454C2×#102—611no—
455C2×#102—611no—
456C2×#102—611no—
457C2×#102—611no—
458C2×#97—611no—
459C2×#97—611no—
460#390—611no—
461#390—611no—
462#389—611no—
463#389—611no—
464#388—1221no—
465#388—1221no—
466C4×C4⋊C4—611no—
467C4×C4⋊C4—611no—
468C4×C4⋊C4—611no—
469C4×C4⋊C4—611no—
470C4×C22⋊C4—1221no—
471C4×C22⋊C4—1221no—
472C4×C22⋊C4—1221no—
473C4×C22⋊C4—1221no—
474C43—611no—
475#340—611no—
476#340—611no—
477#340—611no—
478#340—611no—
479#340—611no—
480#340—611no—
481#336—611no—
482#336—611no—
483#336—611no—
484#336—611no—
485C61#2112211yescharacteristic, complemented, Sylow
486C22×D4—611no—
487C22×D4—611no—
488C23×C4—1221no—
489C23×C4—1221no—
490C23×C4—1221no—
491C23×C4—1221no—
492C2×D8—611no—
493C2×D8—611no—
494C2×D8—611no—
495C2×D8—1222no—
496C2×D8—1222no—
497C2×D8C2×#692311yescharacteristic
498C22×C8—611no—
499C22×C8—611no—
500C22×C8—611no—
501C22×C8—611no—
502C4×D4—611no—
503C4×D4—611no—
504C4×D4—611no—
505C4×D4—611no—
506C4×D4—611no—
507C4×D4—611no—
508C4×D4—1221no—
509C4×D4—1221no—
510C4×D4—1221no—
511C4×D4—1221no—
512C4×D4—1222no—
513C4×D4—1222no—
514C4×D4—1222no—
515C4×D4—1222no—
516C4×D4C2×#692311yescharacteristic
517C4×D4C2×#692311yescharacteristic, complemented
518#117—2444no—
519C2×C4⋊C4—611no—
520C2×C4⋊C4—611no—
521C2×C4⋊C4—611no—
522C2×C4⋊C4—611no—
523C2×C4⋊C4—611no—
524C2×C4⋊C4—611no—
525C2×C4⋊C4—1221no—
526C2×C4⋊C4—1221no—
527C2×C22⋊C4—1221no—
528C2×C22⋊C4—1221no—
529C2×C22⋊C4—1221no—
530C2×C22⋊C4—1221no—
531C2×C22⋊C4—1221no—
532C2×C22⋊C4—1221no—
533C2×C22⋊C4—1221no—
534C2×C22⋊C4—1221no—
535C2×C42—611no—
536C2×C42—611no—
537C2×C42—611no—
538C2×C42—611no—
539C2×C42—611no—
540C2×C42—611no—
541C2×C42—611no—
542C2×C42—1221no—
543C2×C42—1221no—
544C2×C42—1221no—
545C2×C42—1221no—
546C2×C42—2444no—
547#107—1222no—
548#106—611no—
549#106—611no—
550#106—611no—
551#106—1222no—
552#106C2×#692311yescharacteristic, complemented
553#102—611no—
554#102—611no—
555#102—611no—
556#102—611no—
557#102—611no—
558#102—611no—
559#102—1222no—
560#102—1222no—
561#102—1222no—
562#102—1222no—
563#102C2×#692311yescharacteristic
564#102C2×#692311yescharacteristic, complemented
565#97—611no—
566#97—611no—
567#97—611no—
568#97—1221no—
569#97—1221no—
570#97C2×#692311yescharacteristic, complemented
571#95—1221no—
572#95—1221no—
573#95—1221no—
574#95—1221no—
575#95—1221no—
576#95—1221no—
577C24—1221no—
578C24—1221no—
579C2×D4—612no—
580C2×D4—612no—
581C2×D4—611no—
582C2×D4—611no—
583C2×D4—1221no—
584C2×D4—1221no—
585C2×D4—1221no—
586C2×D4—1221no—
587C2×D4—1221no—
588C2×D4—1221no—
589C2×D4—1221no—
590C2×D4—1221no—
591C2×D4C22×#692311yescharacteristic
592C2×D4C22×#692311yescharacteristic
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—611no—
596C22×C4—611no—
597C22×C4—611no—
598C22×C4—611no—
599C22×C4—611no—
600C22×C4—611no—
601C22×C4—611no—
602C22×C4—1221no—
603C22×C4—1221no—
604C22×C4—1221no—
605C22×C4—1221no—
606C22×C4—1221no—
607C22×C4—1221no—
608C22×C4—1221no—
609C22×C4—1221no—
610C22×C4—1224no—
611C22×C4—1224no—
612C22×C4—1221no—
613C22×C4—1221no—
614C22×C4—1221no—
615C22×C4—1221no—
616C22×C4—2442no—
617C22×C4—2442no—
618C22×C4—2442no—
619C22×C4—2442no—
620C22×C4—2442no—
621C22×C4—2442no—
622C22×C4—2442no—
623C22×C4—2442no—
624D8—22no—
625D8—1222no—
626D8—1222no—
627D8—1222no—
628C2×C8—611no—
629C2×C8—611no—
630C2×C8—1221no—
631C2×C8—1221no—
632C2×C8—1221no—
633C2×C8—1221no—
634C2×C8—1221no—
635C2×C8—1221no—
636C2×C8—1221no—
637C2×C8—1221no—
638C2×C8—1221no—
639C2×C8—1221no—
640C2×C8C22×#692311yescharacteristic
641C2×C8C22×#692311yescharacteristic
642C4⋊C4—612no—
643C4⋊C4—612no—
644C4⋊C4—611no—
645C4⋊C4—611no—
646C4⋊C4—1221no—
647C4⋊C4—1221no—
648C4⋊C4—1221no—
649C4⋊C4—1221no—
650C4⋊C4—1221no—
651C4⋊C4—1221no—
652C4⋊C4—1221no—
653C4⋊C4—1221no—
654C4⋊C4—2442no—
655C4⋊C4—2442no—
656C4⋊C4C22×#692311yescharacteristic
657C4⋊C4C22×#692311yescharacteristic
658C22⋊C4—21no—
659C22⋊C4—21no—
660C22⋊C4—1221no—
661C22⋊C4—1221no—
662C22⋊C4—1221no—
663C22⋊C4—1221no—
664C22⋊C4—1224no—
665C22⋊C4—1224no—
666C22⋊C4—1221no—
667C22⋊C4—1221no—
668C22⋊C4—2442no—
669C22⋊C4—2442no—
670C22⋊C4—2442no—
671C22⋊C4—2442no—
672C42—611no—
673C42—611no—
674C42—611no—
675C42—1222no—
676C42—1222no—
677C42—1221no—
678C42—1221no—
679C42—1221no—
680C42—1221no—
681C42—2442no—
682C42—2441no—
683C42—2441no—
684C42—2442no—
685C42—2442no—
686C42—2442no—
687C42C22×#692311yescharacteristic
688C23—21no—
689C23—21no—
690C23—611no—
691C23—1222no—
692C23—1222no—
693C23—1221no—
694C23—1221no—
695C23—2441no—
696C23—2441no—
697C23—2441no—
698C23—2441no—
699C23—2441no—
700C23—2441no—
701C23—2441no—
702C23—2441no—
703C23—2441no—
704C23—2441no—
705D4—21no—
706D4—21no—
707D4—21no—
708D4—612no—
709D4—1222no—
710D4—1222no—
711D4—1221no—
712D4—1221no—
713D4—1221no—
714D4—2441no—
715D4—2441no—
716D4#1451985612yescomplemented
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—611no—
722C2×C4—611no—
723C2×C4—611no—
724C2×C4—611no—
725C2×C4—611no—
726C2×C4—612no—
727C2×C4—612no—
728C2×C4—611no—
729C2×C4—611no—
730C2×C4—1221no—
731C2×C4—1221no—
732C2×C4—1221no—
733C2×C4—1221no—
734C2×C4—1221no—
735C2×C4—1221no—
736C2×C4—1221no—
737C2×C4—1221no—
738C2×C4—1221no—
739C2×C4—1221no—
740C2×C4—1221no—
741C2×C4—1221no—
742C2×C4—1221no—
743C2×C4—1221no—
744C2×C4—1222no—
745C2×C4—1222no—
746C2×C4—1221no—
747C2×C4—1221no—
748C2×C4—2442no—
749C2×C4—2442no—
750C2×C4—2442no—
751C2×C4—2442no—
752C2×C4—2441no—
753C2×C4—2441no—
754C2×C4—2441no—
755C2×C4—2441no—
756C2×C4—2442no—
757C2×C4—2442no—
758C2×C4—2448no—
759C2×C4—2448no—
760C2×C4—2441no—
761C2×C4—2441no—
762C2×C4—2441no—
763C2×C4—2441no—
764C2×C4—2441no—
765C2×C4—2441no—
766C2×C4—2441no—
767C2×C4—2441no—
768C2×C4—2441no—
769C2×C4—2441no—
770C2×C4D4×#692311yescharacteristic
771C2×C4D4×#692311yescharacteristic
772C2×C4C23×#692311yescharacteristic
773C8—21no—
774C8—21no—
775C8—1221no—
776C8—1221no—
777C8—2441no—
778C8—2441no—
779C22—22no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—611no—
786C22—611no—
787C22—611no—
788C22—611no—
789C22—611no—
790C22—611no—
791C22—1222no—
792C22—4881no—
793C22—4881no—
794C22—4881no—
795C22—4881no—
796C22—2442no—
797C22—2442no—
798C22—2442no—
799C22—2442no—
800C22—2441no—
801C22—2441no—
802C22—2441no—
803C22—2441no—
804C22—2441no—
805C22C2×D4×#692311yescharacteristic
806C4—21no—
807C4—21no—
808C4—41no—
809C4—41no—
810C4—611no—
811C4—611no—
812C4—1222no—
813C4—1222no—
814C4—1221no—
815C4—1221no—
816C4—4881no—
817C4—4881no—
818C4—2441no—
819C4—2441no—
820C4—2442no—
821C4—2442no—
822C4—2441no—
823C4—2441no—
824C4C2×#1451985611yescharacteristic
825C4#41×#692311yescharacteristic
826C2—42no—
827C2—81no—
828C2—611no—
829C2—611no—
830C2—611no—
831C2—611no—
832C2—4881no—
833C2—2442no—
834C2#2146227311yescharacteristic
835C2AGL(1,ℤ/8)×#692311yescharacteristic
836C2AGL(1,ℤ/8)×#692311yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#442C4
socleC22×C61C2×C4×D4
prime radicalC2×D8×D61C22
cosocleC2×C4×D61C24
hypercenter#442#6923
hypocenterC61#21122
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #21462276C2semidirect
2. C4×D4×#6923C2semidirect
3. #21461897C2semidirect
4. #21461896C2semidirect
5. #21461882C2semidirect
6. #21461881C2semidirect
9. #21461784C2semidirect
10. #21461782C2semidirect
11. #21461633C2semidirect
12. #21461589C2semidirect
13. #21461589C2semidirect
14. #21461535C2semidirect
55. #16839875C4semidirect
56. #16839874C4semidirect
57. #16839873C4semidirect
58. #16839872C4semidirect
59. #16839872C4semidirect
60. #16839871C4semidirect
61. #16839871C4semidirect
66. C61×#442C4semidirect
125. C4×D244C2×C4semidirect
127. D4×Dic61C2×C4semidirect
129. #14519739C2×C4semidirect
139. #14519709C2×C4semidirect
140. #14519708C2×C4semidirect
141. #14519708C2×C4semidirect
143. #14519699C2×C4semidirect
145. #14519698C2×C4semidirect
147. #14519697C2×C4semidirect
148. #14519688C2×C4semidirect
149. #14519687C2×C4semidirect
150. #14519687C2×C4semidirect
153. C4×D4×C61C2×C4semidirect
154. #106×C61C2×C4semidirect
156. #102×C61C2×C4semidirect
157. #97×C61C2×C4semidirect
315. D4×C61#117semidirect
337. D244#117semidirect
448. #442#6923semidirect
485. C61#21122semidirect
517. C4×D4C2×#6923semidirect
552. #106C2×#6923semidirect
564. #102C2×#6923semidirect
570. #97C2×#6923semidirect
716. D4#14519856semidirect

Maximal subgroups

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

subgroupindex
#214622762
C4×D4×#69232
#214618972
#214618962
#214618822
#214618812
#214618142
#214617842
#214617822
#214616332
#214615892
#214615352
#442×D612
#2112261