Finite Group Databasebeta

← #30615911

Subgroups — #30615911

Order 15616.

1218 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840773C211yesmaximal, characteristic, complemented
2C2×#16840753C211yesmaximal, characteristic
3#21462280C211yesmaximal, characteristic
4C2×C4⋊C4×#6923C211yesmaximal, characteristic, complemented
5#21461899C212yesmaximal, complemented
6#21461898C212yesmaximal, complemented
7#21461897C212yesmaximal, complemented
8#21461896C212yesmaximal, complemented
9#21461506C211yesmaximal, characteristic, complemented
10#21461481C211yesmaximal, characteristic, complemented
11#417×D61C211yesmaximal, characteristic
12C2×D61⋊M16C2211yescharacteristic
13C2×#14519856C2211yescharacteristic
14C22×C4⋊#6923C2211yescharacteristic
15C22×C4×#6923—21no—
16C22×C4×#6923C2211yescharacteristic
17#16840773—24no—
18C2×#14519846C2212yes—
19C2×#14519845C2212yes—
20#16840753—24no—
21C2×#14519840C2212yes—
22C2×#14519839C2212yes—
23(C2×#6923)⋊Q8C2211yescharacteristic
24(C2×#6923)⋊Q8C2211yescharacteristic
25#16840714C2211yescharacteristic
26#16840714C2211yescharacteristic
27#16840710—21no—
28#16840710—21no—
29C4⋊C4×#6923—21no—
30C4⋊C4×#6923—21no—
31C4⋊C4×#6923C2212yes—
32C4⋊C4×#6923C2212yes—
33C4×C22⋊#6923—21no—
34C4×C22⋊#6923—21no—
35C2×(C2×#6923)⋊C4—21no—
36#16840635C2212yes—
37#16840635C2212yes—
38(C2×#6923)⋊C8C2212yes—
39(C2×#6923)⋊C8C2212yes—
40C2×#41×D61C2211yescharacteristic
41C2×M16×D61C2211yescharacteristic
42C2×C4⋊C4×D61C2211yescharacteristic
43#16839764C411yescharacteristic, complemented
44#16839763C411yescharacteristic, complemented
45#16839762C412yescomplemented
46#16839761C411yescharacteristic, complemented
47#16839760C412yescomplemented
48#103×D61C2212yes—
49#102×D61C2212yes—
50C61×#417C411yescharacteristic, complemented
51C23×#6923—21no—
52C23×#6923D411yescharacteristic
53C23×#6923D411yescharacteristic
54C2×#11758213—21no—
55D61⋊M16—22no—
56D61⋊M16—22no—
57C2×#11758217—21no—
58C2×D61⋊C8C2312yes—
59#14519856—22no—
60#14519856—22no—
61C2×C4⋊#6923—21no—
62C2×C4⋊#6923—22no—
63C2×C4⋊#6923D414yes—
64C2×C4⋊#6923C2311yescharacteristic
65C2×C4⋊#6923C2311yescharacteristic
66C2×C4⋊#6923C2312yes—
67C2×C22⋊#6923—21no—
68C2×C22⋊#6923—21no—
69C2×C22⋊#6923—21no—
70C2×C22⋊#6923—21no—
71C2×C22⋊#6923—21no—
72C2×C4×#6923—22no—
73C2×C4×#6923—22no—
74C2×C4×#6923—22no—
75C2×C4×#6923—22no—
76C2×C4×#6923—21no—
77C2×C4×#6923—44no—
78C2×C4×#6923D411yescharacteristic
79C2×C4×#6923D411yescharacteristic
80C2×C4×#6923C2311yescharacteristic
81C2×C4×#6923C2311yescharacteristic
82#14519846—24no—
83#14519845—24no—
84#14519840—24no—
85#14519839—24no—
86(C2×#6923)⋊C4—21no—
87(C2×#6923)⋊C4—21no—
88(C2×#6923)⋊C4—21no—
89(C2×#6923)⋊C4—21no—
90(C2×#6923)⋊C4—22no—
91(C2×#6923)⋊C4—22no—
92C2×#11758226C2×C411yescharacteristic
93C2×#11758222—21no—
94C2×#11758222C2×C411yescharacteristic
95C2×#11758224—21no—
96C2×#11758224C2×C411yescharacteristic
97#41×D61—22no—
98#41×D61—22no—
99#41×D61—22no—
100#41×D61—22no—
101C2×Q8×D61C2311yescharacteristic
102C2×D4×D61—21no—
103C2×D4×D61C2311yescharacteristic
104C22×C4×D61—21no—
105C22×C4×D61—21no—
106C22×C4×D61C2311yescharacteristic
107C2×#11758194C2×C411yescharacteristic
108C2×#11758189C2×C412yes—
109M16×D61—22no—
110M16×D61—22no—
111C2×C8×D61C2312yes—
112C2×C4⋊Dic61C2×C411yescharacteristic
113C2×#11758196—21no—
114C4⋊C4×D61—21no—
115C4⋊C4×D61—21no—
116C4⋊C4×D61C2×C412yes—
117C4⋊C4×D61C2312yes—
118#14519702C2×C412yescomplemented
119#14519701C2×C412yescomplemented
120#14519700C2×C412yescomplemented
121#14519699C2×C412yescomplemented
122#14519698C2×C412yescomplemented
123#14519697C2×C412yescomplemented
124C2×#41×C61C2×C411yescharacteristic
125C2×M16×C61C2×C411yescharacteristic
126C2×C4⋊C4×C61C2×C411yescharacteristic
127#103×C61C2×C412yescomplemented
128#102×C61C2×C412yescomplemented
129C23×D61—21no—
130C23×D61C2×D411yescharacteristic
131C22×#6923—22no—
132C22×#6923—22no—
133C22×#6923—22no—
134C22×#6923—24no—
135C22×#6923—22no—
136C22×#6923—22no—
137C22×#6923—21no—
138C22×#6923—21no—
139C22×#6923—41no—
140C22×#6923—41no—
141C22×#6923—42no—
142C22×#6923—42no—
143C22×#6923C2×D411yescharacteristic
144C22×#6923C2×D411yescharacteristic
145C22×#6923C2×D411yescharacteristic
146C22×#6923C2×D411yescharacteristic
147#41×C61—22no—
148#41×C61—22no—
149C2×Q8×C61C22×C411yescharacteristic
150C2×D4×C61—21no—
151C2×D4×C61C22×C411yescharacteristic
152C22×C4×C61—21no—
153C22×C4×C61—21no—
154C22×C4×C61C22×C411yescharacteristic
155C2×C22⋊D61—21no—
156C2×C22⋊D61—21no—
157C2×C22⋊D61—21no—
158C22×Dic61—21no—
159C22×Dic61—21no—
160C22×Dic61#4111yescharacteristic
161#11758226—22no—
162#11758226—22no—
163Q8×D61—21no—
164Q8×D61—21no—
165Q8×D61—21no—
166Q8×D61—21no—
167#11758224—22no—
168#11758224—22no—
169#11758224—42no—
170#11758224—42no—
171D4×D61—21no—
172D4×D61—21no—
173D4×D61—21no—
174D4×D61—21no—
175D4×D61—42no—
176D4×D61—42no—
177#11758222—22no—
178#11758222—22no—
179#11758222—42no—
180#11758222—42no—
181C2×D244—21no—
182C2×D244C22×C411yescharacteristic
183C2×C4×D61—22no—
184C2×C4×D61—21no—
185C2×C4×D61—22no—
186C2×C4×D61—21no—
187C2×C4×D61—21no—
188C2×C4×D61—42no—
189C2×C4×D61—42no—
190C2×C4×D61—42no—
191C2×C4×D61—42no—
192C2×C4×D61C22×C411yescharacteristic
193C2×C4×D61C2×D412yes—
194C2×C4×D61C2×D411yescharacteristic
195C2×C4×D61#4112yes—
196C2×C4×D61#4112yes—
197C2×C4×D61#4112yes—
198C2×C4×D61#4111yescharacteristic
199C2×C4×D61C2411yescharacteristic
200C2×Dic122—21no—
201C2×Dic122C22×C411yescharacteristic
202C22⋊#6923—42no—
203C22⋊#6923—42no—
204C22⋊#6923—42no—
205C22⋊#6923—42no—
206C22⋊#6923—42no—
207#11758217—42no—
208C2×#92420—22no—
209C4⋊#6923—24no—
210C4⋊#6923—21no—
211C4⋊#6923—21no—
212C4⋊#6923—22no—
213C4⋊#6923—21no—
214C4⋊#6923—21no—
215C4⋊#6923C2×D414yes—
216C4×#6923—22no—
217C4×#6923—22no—
218C4×#6923—21no—
219C4×#6923—21no—
220C4×#6923—21no—
221C4×#6923—21no—
222C4×#6923—44no—
223C4×#6923—44no—
224C4×#6923—42no—
225#11758213—42no—
226D61⋊C8—22no—
227D61⋊C8—22no—
228M16×C61—22no—
229C2×C8×C61C22×C412yes—
230C4⋊C4×C61—21no—
231C4⋊C4×C61C22×C412yes—
232C4⋊Dic61—21no—
233C4⋊Dic61C22×C412yes—
234#11758196—22no—
235#11758196—22no—
236#11758194—22no—
237C2×#92418C22×C412yes—
238#11758189—24no—
239C8×D61—22no—
240C8×D61—22no—
241C23×C61—21no—
242C23×C61C4×D411yescharacteristic
243C22×D61—21no—
244C22×D61—21no—
245C22×D61—21no—
246C22×D61—21no—
247C22×D61—21no—
248C22×D61—41no—
249C22×D61—41no—
250C22×D61—41no—
251C22×D61—41no—
252C22×D61—41no—
253C22×D61—41no—
254C22×D61C4×D411yescharacteristic
255C22×D61#12112yes—
256C22×D61#12312yes—
257C22×D61C22×D411yescharacteristic
258C2×#6923—28no—
259C2×#6923—21no—
260C2×#6923—21no—
261C2×#6923—21no—
262C2×#6923—21no—
263C2×#6923—24no—
264C2×#6923—21no—
265C2×#6923—21no—
266C2×#6923—21no—
267C2×#6923—21no—
268C2×#6923—21no—
269C2×#6923—21no—
270C2×#6923—44no—
271C2×#6923—48no—
272C2×#6923—42no—
273C2×#6923—42no—
274C2×#6923—41no—
275C2×#6923—41no—
276C2×#6923—41no—
277C2×#6923—41no—
278C2×#6923—41no—
279C2×#6923—41no—
280C2×#6923AGL(1,ℤ/8)12yes—
281C2×#6923#13712yes—
282Q8×C61—21no—
283Q8×C61—21no—
284D4×C61—21no—
285D4×C61—21no—
286D4×C61—42no—
287C2×C4×C61—22no—
288C2×C4×C61—21no—
289C2×C4×C61—42no—
290C2×C4×C61—42no—
291C2×C4×C61#11712yes—
292C2×C4×C61C4×D412yes—
293C2×C4×C61C4×D411yescharacteristic
294C2×C4×C61C23×C411yescharacteristic
295C22⋊D61—42no—
296C22⋊D61—42no—
297C22⋊D61—41no—
298C22⋊D61—41no—
299C2×Dic61—22no—
300C2×Dic61—21no—
301C2×Dic61—42no—
302C2×Dic61—42no—
303C2×Dic61C4×D411yescharacteristic
304C2×Dic61#12412yes—
305C2×Dic61#12612yes—
306C2×Dic61C2×#4111yescharacteristic
307D244—21no—
308D244—21no—
309D244—42no—
310C4×D61—44no—
311C4×D61—41no—
312C4×D61—41no—
313C4×D61—42no—
314C4×D61—42no—
315C4×D61—42no—
316C4×D61—42no—
317C4×D61#11712yes—
318C4×D61C4×D412yes—
319C4×D61#12112yes—
320C4×D61#12312yes—
321C4×D61#12412yes—
322C4×D61#12612yes—
323C4×D61C22×D411yescharacteristic
324C4×D61C2×#4111yescharacteristic
325C4×D61C2×#4111yescharacteristic
326C4×D61C2×#4111yescharacteristic
327Dic122—21no—
328Dic122—21no—
329Dic122—41no—
330Dic122—41no—
331#92420—42no—
332C8×C61—22no—
333#92418—22no—
334#21059—611nomaximal, Sylow
335C22×C61—21no—
336C22×C61—21no—
337C22×C61—41no—
338C22×C61—41no—
339C22×C61—41no—
340C22×C61#38812yes—
341C22×C61C2×C4×D411yescharacteristic
342C2×D61—21no—
343C2×D61—21no—
344C2×D61—22no—
345C2×D61—22no—
346C2×D61—22no—
347C2×D61—22no—
348C2×D61—41no—
349C2×D61—41no—
350C2×D61—41no—
351C2×D61—81no—
352C2×D61—81no—
353C2×D61—81no—
354C2×D61—81no—
355C2×D61#38812yes—
356C2×D61C2×#12111yescharacteristic
357C2×D61C2×#12311yescharacteristic
358C2×D61C2×AGL(1,ℤ/8)11yescharacteristic
359C2×D61C2×#13711yescharacteristic
360C2×D61#57511yescharacteristic
361C2×D61#57511yescharacteristic
362#6923—22no—
363#6923—22no—
364#6923—41no—
365#6923—41no—
366#6923—44no—
367#6923—81no—
368#6923—81no—
369C4×C61—42no—
370C4×C61—41no—
371C4×C61#38812yes—
372C4×C61C2×#11711yescharacteristic
373C4×C61C2×C4×D411yescharacteristic
374Dic61—42no—
375Dic61—41no—
376Dic61#38812yes—
377Dic61C2×#12411yescharacteristic
378Dic61C2×#12611yescharacteristic
379C2×#428—611no—
380C2×#417—611no—
381C2×#417—611no—
382#2297—611no—
383C2×C4×C4⋊C4—611no—
384#1928—612no—
385#1927—612no—
386#1926—612no—
387#1925—612no—
388#1736—611no—
389#1728—611no—
390C2×C61—22no—
391C2×C61—81no—
392C2×C61C2×#38811yescharacteristic
393C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
394C2×C61C4×#13711yescharacteristic
395D61—22no—
396D61—81no—
397D61#303611yescharacteristic
398D61#303711yescharacteristic
399D61#309211yescharacteristic
400D61#309311yescharacteristic
401C22×#41—611no—
402C22×M16—611no—
403C22×M16—611no—
404C2×#117—611no—
405C22×C4⋊C4—611no—
406C22×C4⋊C4—611no—
407C22×C42—611no—
408C22×C42—1221no—
409#428—1224no—
410C2×#107—612no—
411C2×#106—612no—
412#417—611no—
413#417—611no—
414#417—611no—
415#417—612no—
416#417—612no—
417#417—1224no—
418#417#692311yescharacteristic, complemented
419C2×#103—612no—
420C2×#103—612no—
421C2×#102—612no—
422C2×#102—612no—
423#391—611no—
424#391—611no—
425#390—611no—
426#390—611no—
427#386—1221no—
428#386—1221no—
429C4×C4⋊C4—612no—
430C4×C4⋊C4—612no—
431C4×C4⋊C4—1221no—
432C4×C4⋊C4—1221no—
433C4×C22⋊C4—1221no—
434C4×C22⋊C4—1221no—
435C2×#95—1221no—
436#340—612no—
437#340—612no—
438#336—612no—
439#336—612no—
440C61#2105911yescharacteristic, complemented, Sylow
441C2×#41—611no—
442C2×#41—611no—
443C2×#41—611no—
444C2×#41—1221no—
445C2×#41—1221no—
446C2×#41—1222no—
447C2×#41—1222no—
448C2×#41—1222no—
449C2×#41—1222no—
450C2×#41C2×#692311yescharacteristic
451C22×Q8—611no—
452C22×D4—611no—
453C22×D4—1221no—
454C23×C4—611no—
455C23×C4—611no—
456C23×C4—611no—
457C23×C4—1221no—
458C23×C4—1221no—
459C23×C4—1221no—
460C2×M16—611no—
461C2×M16—612no—
462C2×M16—1222no—
463C2×M16—1222no—
464C2×M16—1221no—
465C2×M16—1222no—
466C2×M16—1222no—
467C2×M16—1221no—
468C2×M16C2×#692311yescharacteristic
469C22×C8—612no—
470C22×C8—612no—
471#117—1222no—
472#117—1222no—
473C2×C4⋊C4—614no—
474C2×C4⋊C4—612no—
475C2×C4⋊C4—611no—
476C2×C4⋊C4—612no—
477C2×C4⋊C4—612no—
478C2×C4⋊C4—611no—
479C2×C4⋊C4—611no—
480C2×C4⋊C4—1221no—
481C2×C4⋊C4—1221no—
482C2×C4⋊C4—1221no—
483C2×C4⋊C4—1222no—
484C2×C4⋊C4—1221no—
485C2×C4⋊C4C2×#692311yescharacteristic
486C2×C22⋊C4—1221no—
487C2×C22⋊C4—1221no—
488C2×C22⋊C4—1221no—
489C2×C22⋊C4—1221no—
490C2×C22⋊C4—1221no—
491C2×C42—611no—
492C2×C42—611no—
493C2×C42—611no—
494C2×C42—611no—
495C2×C42—1222no—
496C2×C42—1222no—
497C2×C42—1221no—
498C2×C42—1222no—
499C2×C42—1222no—
500C2×C42—2444no—
501#107—1224no—
502#106—1224no—
503#103—612no—
504#103—612no—
505#103—612no—
506#103—1224no—
507#103C2×#692312yescomplemented
508#102—612no—
509#102—612no—
510#102—612no—
511#102—1224no—
512#102C2×#692312yescomplemented
513#95—1222no—
514#95—1222no—
515#95—1221no—
516#95—1221no—
517#95—1221no—
518#95—1221no—
519C24—611no—
520C24—1221no—
521#41—22no—
522#41—22no—
523#41—1222no—
524#41—1222no—
525#41—1222no—
526#41—1222no—
527#41—1222no—
528#41—1222no—
529#41—2442no—
530#41—2442no—
531#41—2442no—
532#41—2442no—
533C2×Q8—611no—
534C2×Q8—1221no—
535C2×Q8—1221no—
536C2×Q8—1221no—
537C2×Q8—1221no—
538C2×Q8—1221no—
539C2×Q8C22×#692311yescharacteristic
540C2×D4—21no—
541C2×D4—611no—
542C2×D4—1221no—
543C2×D4—1221no—
544C2×D4—1221no—
545C2×D4—1221no—
546C2×D4—1221no—
547C2×D4—1221no—
548C2×D4—1221no—
549C2×D4—1221no—
550C2×D4—2442no—
551C2×D4—2442no—
552C2×D4C22×#692311yescharacteristic
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—611no—
556C22×C4—612no—
557C22×C4—612no—
558C22×C4—611no—
559C22×C4—612no—
560C22×C4—612no—
561C22×C4—611no—
562C22×C4—611no—
563C22×C4—611no—
564C22×C4—611no—
565C22×C4—611no—
566C22×C4—611no—
567C22×C4—611no—
568C22×C4—1221no—
569C22×C4—1221no—
570C22×C4—1222no—
571C22×C4—1222no—
572C22×C4—1222no—
573C22×C4—1222no—
574C22×C4—1221no—
575C22×C4—1222no—
576C22×C4—1222no—
577C22×C4—1222no—
578C22×C4—1224no—
579C22×C4—1221no—
580C22×C4—1221no—
581C22×C4—1221no—
582C22×C4—1221no—
583C22×C4—2442no—
584C22×C4—2442no—
585C22×C4—2442no—
586C22×C4—2442no—
587C22×C4—2441no—
588C22×C4—2441no—
589C22×C4—2442no—
590C22×C4—2442no—
591C22×C4C22×#692311yescharacteristic
592M16—22no—
593M16—1224no—
594M16—1222no—
595M16—2442no—
596M16—2442no—
597C2×C8—612no—
598C2×C8—1222no—
599C2×C8—1222no—
600C2×C8—1222no—
601C2×C8—1222no—
602C2×C8—1222no—
603C2×C8C22×#692312yes—
604C4⋊C4—21no—
605C4⋊C4—614no—
606C4⋊C4—612no—
607C4⋊C4—1222no—
608C4⋊C4—1222no—
609C4⋊C4—1224no—
610C4⋊C4—1222no—
611C4⋊C4—1221no—
612C4⋊C4—1221no—
613C4⋊C4—1221no—
614C4⋊C4—1221no—
615C4⋊C4—1221no—
616C4⋊C4C22×#692312yes—
617C22⋊C4—2442no—
618C22⋊C4—2442no—
619C22⋊C4—2442no—
620C22⋊C4—2442no—
621C22⋊C4—2442no—
622C42—1222no—
623C42—1222no—
624C42—1221no—
625C42—1221no—
626C42—1221no—
627C42—1221no—
628C42—2444no—
629C42—2442no—
630C42—2444no—
631C23—21no—
632C23—611no—
633C23—612no—
634C23—612no—
635C23—611no—
636C23—1221no—
637C23—1221no—
638C23—1221no—
639C23—1221no—
640C23—1221no—
641C23—2441no—
642C23—2441no—
643C23—2441no—
644C23—2441no—
645C23—2441no—
646C23—2441no—
647C23D4×#692311yescharacteristic
648Q8—21no—
649Q8—21no—
650Q8—1221no—
651Q8—1221no—
652Q8—2441no—
653Q8—2441no—
654D4—21no—
655D4—21no—
656D4—42no—
657D4—1221no—
658D4—1221no—
659D4—2442no—
660D4—2441no—
661D4—2441no—
662D4—2442no—
663D4—2442no—
664C2×C4—22no—
665C2×C4—21no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—612no—
669C2×C4—612no—
670C2×C4—611no—
671C2×C4—611no—
672C2×C4—612no—
673C2×C4—612no—
674C2×C4—612no—
675C2×C4—612no—
676C2×C4—612no—
677C2×C4—611no—
678C2×C4—611no—
679C2×C4—612no—
680C2×C4—611no—
681C2×C4—611no—
682C2×C4—612no—
683C2×C4—612no—
684C2×C4—1221no—
685C2×C4—1221no—
686C2×C4—1221no—
687C2×C4—1221no—
688C2×C4—1228no—
689C2×C4—1221no—
690C2×C4—1221no—
691C2×C4—1221no—
692C2×C4—1221no—
693C2×C4—1224no—
694C2×C4—1221no—
695C2×C4—1221no—
696C2×C4—1222no—
697C2×C4—1221no—
698C2×C4—2442no—
699C2×C4—2442no—
700C2×C4—2442no—
701C2×C4—2441no—
702C2×C4—2441no—
703C2×C4—2444no—
704C2×C4—2442no—
705C2×C4—2441no—
706C2×C4—2441no—
707C2×C4—2441no—
708C2×C4—2441no—
709C2×C4—2441no—
710C2×C4—2441no—
711C2×C4—2442no—
712C2×C4—2442no—
713C2×C4—2442no—
714C2×C4—2444no—
715C2×C4—2448no—
716C2×C4—2442no—
717C2×C4#1451985612yes—
718C2×C4D4×#692311yescharacteristic
719C2×C4D4×#692312yes—
720C2×C4C23×#692311yescharacteristic
721C8—22no—
722C8—1222no—
723C8—2442no—
724C22—21no—
725C22—21no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—611no—
730C22—611no—
731C22—611no—
732C22—611no—
733C22—611no—
734C22—611no—
735C22—612no—
736C22—1222no—
737C22—1222no—
738C22—1222no—
739C22—1222no—
740C22—1221no—
741C22—1221no—
742C22—4881no—
743C22—4881no—
744C22—4881no—
745C22—4881no—
746C22—2441no—
747C22—2441no—
748C22—2441no—
749C22#1684071212yes—
750C22C2×D4×#692311yescharacteristic
751C4—41no—
752C4—42no—
753C4—611no—
754C4—611no—
755C4—612no—
756C4—1222no—
757C4—1222no—
758C4—4881no—
759C4—4881no—
760C4—2441no—
761C4—2441no—
762C4—2444no—
763C4—2441no—
764C4—2442no—
765C4#1684071212yes—
766C4C2×#1451985611yescharacteristic
767C4C2×D4×#692311yescharacteristic
768C2—22no—
769C2—81no—
770C2—611no—
771C2—611no—
772C2—611no—
773C2—611no—
774C2—1222no—
775C2—4881no—
776C2C2×#1684071211yescharacteristic
777C2AGL(1,ℤ/8)×#692311yescharacteristic
778C2#137×#692311yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#417C4
socleC22×C61C2×C4×D4
prime radicalC2×#41×D61C22
cosocleC2×C4×D61C24
hypercenter#417#6923
hypocenterC61#21059
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
1. C2×#16840773C2semidirect
4. C2×C4⋊C4×#6923C2semidirect
5. #21461899C2semidirect
6. #21461898C2semidirect
7. #21461897C2semidirect
8. #21461896C2semidirect
9. #21461506C2semidirect
10. #21461481C2semidirect
43. #16839764C4semidirect
44. #16839763C4semidirect
45. #16839762C4semidirect
46. #16839761C4semidirect
47. #16839760C4semidirect
50. C61×#417C4semidirect
118. #14519702C2×C4semidirect
119. #14519701C2×C4semidirect
120. #14519700C2×C4semidirect
121. #14519699C2×C4semidirect
122. #14519698C2×C4semidirect
123. #14519697C2×C4semidirect
127. #103×C61C2×C4semidirect
128. #102×C61C2×C4semidirect
418. #417#6923semidirect
440. C61#21059semidirect
507. #103C2×#6923semidirect
512. #102C2×#6923semidirect

Maximal subgroups

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

subgroupindex
C2×#168407732
C2×#168407532
#214622802
C2×C4⋊C4×#69232
#214618992
#214618982
#214618972
#214618962
#214615062
#214614812
#417×D612
#2105961