Finite Group Databasebeta

← #29685726

Subgroups — #29685726

Order 15616.

1616 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840234C211yesmaximal, characteristic, complemented
2C2×#16839894C211yesmaximal, characteristic
3C2×#16839872C211yesmaximal, characteristic, complemented
4#21448506C211yesmaximal, characteristic, complemented
5#21446169C211yesmaximal, characteristic, complemented
6#21446164C211yesmaximal, characteristic, complemented
7#21446138C211yesmaximal, characteristic, complemented
8#21446078C211yesmaximal, characteristic, complemented
9#21446063C211yesmaximal, characteristic, complemented
10#21446015C211yesmaximal, characteristic, complemented
11#21445748C211yesmaximal, characteristic, complemented
12#21445644C211yesmaximal, characteristic, complemented
13C4×#14519699C211yesmaximal, characteristic, complemented
14#21445586C211yesmaximal, characteristic, complemented
15C2×C4×D8×C61C211yesmaximal, characteristic, complemented
16C22×D4×D61C2211yescharacteristic
17C22×#11758199C2211yescharacteristic
18C2×#14519748C2211yescharacteristic
19#16840234—24no—
20#16840234—24no—
21C2×C4×D244C2211yescharacteristic
22C2×D4×Dic61C2211yescharacteristic
23C2×#14519739C2211yescharacteristic
24C2×C4×C22⋊D61—21no—
25C2×#14519737—21no—
26C2×#14519735C2211yescharacteristic
27C2×#14519734C2211yescharacteristic
28C22×#11758198—21no—
29C2×C22⋊C4×D61—21no—
30#16839894C418yescomplemented
31#16839872—24no—
32C2×#14519708C2211yescharacteristic, complemented
33C2×#14519699C2211yescharacteristic
34C2×#14519699C2211yescharacteristic
35C2×#14519698C2211yescharacteristic
36C2×#14519698C2211yescharacteristic
37C2×#14519698C2211yescharacteristic, complemented
38C2×#14519697C2211yescharacteristic
39C2×#14519689C2211yescharacteristic
40C2×#14519689C2211yescharacteristic
41C2×#14519688C2211yescharacteristic, complemented
42#16839665C2211yescharacteristic, complemented
43#16839662—21no—
44#16839658C2211yescharacteristic, complemented
45#16839656—21no—
46#16839641—21no—
47#16839635—21no—
48#16839619C2211yescharacteristic
49C4×C4⋊Dic61C2211yescharacteristic, complemented
50#16839525C2211yescharacteristic, complemented
51#16839525C2211yescharacteristic, complemented
52#16839524C2211yescharacteristic, complemented
53#16839524C2211yescharacteristic, complemented
54#16839516C2211yescharacteristic, complemented
55#16839516C2211yescharacteristic, complemented
56C22×D8×C61C2211yescharacteristic
57C2×C4×D4×C61C2211yescharacteristic
58C2×C4×D4×C61C2211yescharacteristic, complemented
59C4×D8×C61—24no—
60C2×#107×C61C2211yescharacteristic, complemented
61C2×#102×C61C2211yescharacteristic
62C2×#102×C61C2211yescharacteristic, complemented
63C2×C4×C8×C61C2211yescharacteristic, complemented
64C24×D61—21no—
65C22×D244C2311yescharacteristic
66C22×C22⋊D61—21no—
67C22×C22⋊D61—21no—
68C2×D4×D61—22no—
69C2×D4×D61—22no—
70C2×D4×D61—22no—
71C2×D4×D61—22no—
72C2×D4×D61—22no—
73C2×D4×D61C2×C414yescomplemented
74C23×Dic61—21no—
75C22×C4×D61—21no—
76C22×C4×D61—21no—
77C22×C4×D61C2311yescharacteristic
78C2×#11758199—22no—
79C2×#11758199—22no—
80C2×#11758199C2×C414yescomplemented
81C22×#92418C2311yescharacteristic
82C22×#92418C2311yescharacteristic
83#14519748—22no—
84#14519748C2×C414yescomplemented
85C4×D244—22no—
86C4×D244D414yescomplemented
87D4×Dic61—22no—
88D4×Dic61—22no—
89#14519739—22no—
90#14519739—22no—
91C4×C22⋊D61—28no—
92#14519737—28no—
93#14519735—22no—
94#14519735—22no—
95#14519734—22no—
96#14519734—22no—
97C2×C4⋊Dic61C2311yescharacteristic
98C2×C4⋊Dic61C2311yescharacteristic
99C2×C4⋊Dic61C2311yescharacteristic
100C2×#11758196—21no—
101C2×#11758196D411yescharacteristic
102C2×#11758196D411yescharacteristic
103C2×C22⋊Dic61—21no—
104C2×C22⋊Dic61—21no—
105C2×C22⋊Dic61—21no—
106C2×C22⋊Dic61—21no—
107C2×#11758198—28no—
108C2×#11758198—21no—
109C2×#11758198—21no—
110C2×#11758198—21no—
111C2×#11758198—21no—
112C2×#11758198D411yescharacteristic
113C2×#11758198D411yescharacteristic
114C22⋊C4×D61—28no—
115C2×C4×Dic61—21no—
116C2×C4×Dic61—21no—
117C2×C4×Dic61C2311yescharacteristic
118#14519708—22no—
119#14519699—22no—
120#14519699C2×C414yescomplemented
121#14519698—22no—
122#14519698—22no—
123#14519698C2×C414yescomplemented
124#14519697—22no—
125#14519689—22no—
126#14519689C2×C414yescomplemented
127#14519688—22no—
128#14519684—21no—
129#14519684—21no—
130#14519684—21no—
131C22×D4×C61C2311yescharacteristic
132C22×D4×C61C2311yescharacteristic
133C23×C4×C61—21no—
134C23×C4×C61—21no—
135C2×D8×C61—22no—
136C2×D8×C61—22no—
137C2×D8×C61C2×C414yescomplemented
138C22×C8×C61C2311yescharacteristic
139C22×C8×C61C2311yescharacteristic
140C4×D4×C61—22no—
141C4×D4×C61—22no—
142C4×D4×C61—22no—
143C4×D4×C61D414yescomplemented
144C2×C4⋊C4×C61C2311yescharacteristic
145C2×C4⋊C4×C61C2311yescharacteristic
146C2×C22⋊C4×C61—21no—
147C2×C22⋊C4×C61—21no—
148C2×C42×C61C2311yescharacteristic
149#107×C61—22no—
150#102×C61—22no—
151#102×C61—22no—
152C4×C8×C61—22no—
153C24×C61—21no—
154C24×C61—21no—
155C23×D61—21no—
156C23×D61—24no—
157C23×D61—24no—
158C23×D61—24no—
159C23×D61—81no—
160C23×D61—81no—
161C23×D61—81no—
162C23×D61—81no—
163C23×D61C2×D411yescharacteristic
164C2×D4×C61—21no—
165C2×D4×C61—21no—
166C2×D4×C61—21no—
167C2×D4×C61—21no—
168C2×D4×C61—21no—
169C2×D4×C61—21no—
170C2×D4×C61—21no—
171C2×D4×C61—21no—
172C2×D4×C61C22×C412yes—
173C2×D4×C61C22×C412yes—
174C2×D4×C61C2×D412yes—
175C2×D4×C61#4112yes—
176C22×C4×C61—21no—
177C22×C4×C61—24no—
178C22×C4×C61—21no—
179C22×C4×C61—42no—
180C22×C4×C61—81no—
181C22×C4×C61—81no—
182C22×C4×C61—81no—
183C22×C4×C61—81no—
184C22×C4×C61C2×D411yescharacteristic
185C22×C4×C61C2×D411yescharacteristic
186C22×C4×C61C2411yescharacteristic
187C2×C22⋊D61—24no—
188C2×C22⋊D61—24no—
189C2×C22⋊D61—24no—
190C2×C22⋊D61—24no—
191C2×C22⋊D61—81no—
192C2×C22⋊D61—81no—
193C22×Dic61—21no—
194C22×Dic61—21no—
195C22×Dic61—24no—
196C22×Dic61—21no—
197C22×Dic61—81no—
198C22×Dic61—81no—
199C22×Dic61C2×D411yescharacteristic
200C22×Dic61C2×D411yescharacteristic
201C22×Dic61C2×D411yescharacteristic
202D4×D61—28no—
203D4×D61—28no—
204D4×D61—28no—
205D4×D61—28no—
206C2×D244—21no—
207C2×D244—21no—
208C2×D244—21no—
209C2×D244C22×C412yes—
210C2×D244C2×D412yes—
211C2×D244#4112yes—
212C2×C4×D61—21no—
213C2×C4×D61—21no—
214C2×C4×D61—21no—
215C2×C4×D61—21no—
216C2×C4×D61—24no—
217C2×C4×D61—24no—
218C2×C4×D61—81no—
219C2×C4×D61—81no—
220C2×C4×D61—81no—
221C2×C4×D61—81no—
222C2×C4×D61C22×C412yes—
223C2×C4×D61#4112yes—
224D8×C61—28no—
225C2×C8×C61—21no—
226C2×C8×C61—21no—
227C2×C8×C61—21no—
228C2×C8×C61—21no—
229C2×C8×C61—21no—
230C2×C8×C61C22×C412yes—
231C4⋊C4×C61—21no—
232C4⋊C4×C61—21no—
233C4⋊C4×C61—21no—
234C4⋊C4×C61C2×D412yes—
235C22⋊C4×C61—24no—
236C22⋊C4×C61—42no—
237C42×C61C2×D412yes—
238C42×C61C2×D412yes—
239C22⋊Dic61—24no—
240C22⋊Dic61—24no—
241C22⋊Dic61—81no—
242C22⋊Dic61—81no—
243#11758199—28no—
244#11758198—24no—
245#11758198—24no—
246#11758198—22no—
247#11758198—22no—
248#11758198—24no—
249#11758198—81no—
250C4⋊Dic61—21no—
251C4⋊Dic61—21no—
252C4⋊Dic61—21no—
253C4⋊Dic61—21no—
254C4⋊Dic61C22×C412yes—
255C4⋊Dic61C2×D412yes—
256#11758196—22no—
257#11758196—22no—
258#11758196—81no—
259C4×Dic61—24no—
260C4×Dic61—21no—
261C4×Dic61—21no—
262C4×Dic61—81no—
263C2×#92418—21no—
264C2×#92418—21no—
265C2×#92418—21no—
266C2×#92418—21no—
267C2×#92418—21no—
268C2×#92418C22×C412yes—
269C23×C61—22no—
270C23×C61—22no—
271C23×C61—22no—
272C23×C61—22no—
273C23×C61—41no—
274C23×C61—41no—
275C23×C61—41no—
276C23×C61—41no—
277C23×C61—41no—
278C23×C61—41no—
279C23×C61—41no—
280C23×C61—41no—
281C23×C61—41no—
282C23×C61—41no—
283C23×C61C22×D411yescharacteristic
284C22×D61—22no—
285C22×D61—21no—
286C22×D61—22no—
287C22×D61—21no—
288C22×D61—22no—
289C22×D61—21no—
290C22×D61—21no—
291C22×D61—21no—
292C22×D61—21no—
293C22×D61—216no—
294C22×D61—41no—
295C22×D61—41no—
296C22×D61—41no—
297C22×D61—41no—
298C22×D61—84no—
299C22×D61—84no—
300C22×D61—84no—
301C22×D61—84no—
302C22×D61—84no—
303C22×D61—84no—
304C22×D61C4×D412yes—
305D4×C61—22no—
306D4×C61—22no—
307D4×C61—22no—
308D4×C61—22no—
309D4×C61—22no—
310D4×C61—41no—
311D4×C61—41no—
312D4×C61C4×D414yes—
313C2×C4×C61—21no—
314C2×C4×C61—21no—
315C2×C4×C61—21no—
316C2×C4×C61—21no—
317C2×C4×C61—22no—
318C2×C4×C61—41no—
319C2×C4×C61—41no—
320C2×C4×C61—41no—
321C2×C4×C61—41no—
322C2×C4×C61—41no—
323C2×C4×C61—84no—
324C2×C4×C61—84no—
325C2×C4×C61#12012yes—
326C2×C4×C61#12012yes—
327C2×C4×C61C23×C411yescharacteristic
328C2×C4×C61C22×D411yescharacteristic
329C2×C4×C61C22×D411yescharacteristic
330C2×C4×C61C2×#4111yescharacteristic
331C2×C4×C61C2×#4111yescharacteristic
332C2×C4×C61C2×#4111yescharacteristic
333C22⋊D61—216no—
334C22⋊D61—84no—
335C2×Dic61—21no—
336C2×Dic61—21no—
337C2×Dic61—22no—
338C2×Dic61—21no—
339C2×Dic61—21no—
340C2×Dic61—22no—
341C2×Dic61—21no—
342C2×Dic61—21no—
343C2×Dic61—21no—
344C2×Dic61—21no—
345C2×Dic61—41no—
346C2×Dic61—41no—
347C2×Dic61—41no—
348C2×Dic61—41no—
349C2×Dic61—41no—
350C2×Dic61—41no—
351C2×Dic61—41no—
352C2×Dic61—84no—
353C2×Dic61C4×D412yes—
354D244—22no—
355D244—22no—
356D244—22no—
357D244C4×D414yes—
358C4×D61—22no—
359C4×D61—22no—
360C4×D61—22no—
361C4×D61—22no—
362C4×D61—84no—
363C4×D61—84no—
364C8×C61—22no—
365C8×C61—41no—
366#92418—22no—
367#92418—41no—
368#21458—611nomaximal, Sylow
369C22×C61—24no—
370C22×C61—42no—
371C22×C61—42no—
372C22×C61—42no—
373C22×C61—42no—
374C22×C61—42no—
375C22×C61—42no—
376C22×C61—42no—
377C22×C61—42no—
378C22×C61—42no—
379C22×C61—81no—
380C22×C61—81no—
381C22×C61—81no—
382C22×C61—81no—
383C22×C61C2×C4×D411yescharacteristic
384C22×C61C2×#12011yescharacteristic
385C22×C61#52511yescharacteristic
386C22×C61#57611yescharacteristic
387C22×C61#57611yescharacteristic
388C22×C61#57611yescharacteristic
389C22×C61#57711yescharacteristic
390C2×D61—22no—
391C2×D61—22no—
392C2×D61—22no—
393C2×D61—24no—
394C2×D61—41no—
395C2×D61—42no—
396C2×D61—41no—
397C2×D61—42no—
398C2×D61—42no—
399C2×D61—42no—
400C2×D61—42no—
401C2×D61—41no—
402C2×D61—42no—
403C2×D61—41no—
404C2×D61—816no—
405C4×C61—22no—
406C4×C61—22no—
407C4×C61—42no—
408C4×C61—81no—
409C4×C61C2×C4×D411yescharacteristic
410C4×C61C2×C4×D411yescharacteristic
411C4×C61#52511yescharacteristic
412C4×C61#52511yescharacteristic
413Dic61—22no—
414Dic61—42no—
415Dic61—41no—
416Dic61—42no—
417Dic61—41no—
418Dic61—81no—
419C2×#518—611no—
420C2×#447—611no—
421C2×#442—611no—
422C2×C4×D8D6111yescharacteristic, complemented
423#2324—611no—
424#1879—611no—
425#1879—611no—
426#1875—611no—
427#1864—611no—
428#1862—611no—
429#1854—611no—
430#1786—611no—
431#1762—611no—
432C4×#102—611no—
433#1750—611no—
434C2×C61—44no—
435C2×C61—82no—
436C2×C61C4×#12011yescharacteristic
437C2×C61#294611yescharacteristic
438C2×C61#294811yescharacteristic
439C2×C61#300811yescharacteristic
440C2×C61#301211yescharacteristic
441C2×C61#311811yescharacteristic
442C2×C61#312211yescharacteristic
443D61—42no—
444D61—44no—
445C23×D4—611no—
446C22×D8—611no—
447C22×D8C2×D6111yescharacteristic
448C2×#121—611no—
449#518—1224no—
450#518—1224no—
451C2×C4×D4—611no—
452C2×C4×D4—611no—
453C2×C4×D4—611no—
454C2×C4×D4—1221no—
455C2×C4×D4—1221no—
456C2×C4×D4C2×D6111yescharacteristic
457C2×C4×D4C2×D6111yescharacteristic, complemented
458C2×#117—611no—
459C2×#117—611no—
460C22×C22⋊C4—1221no—
461C22×C22⋊C4—1221no—
462#447—618no—
463#442—1224no—
464C4×D8—24no—
465C2×#107C2×D6111yescharacteristic, complemented
466C2×#106—611no—
467C2×#102—611no—
468C2×#102—611no—
469C2×#102—611no—
470C2×#102—611no—
471C2×#102—611no—
472C2×#102—611no—
473C2×#102C2×D6111yescharacteristic
474C2×#102C2×D6111yescharacteristic, complemented
475C2×C22⋊C8—611no—
476C2×C22⋊C8—611no—
477C2×#97—611no—
478C2×C4×C8C2×D6111yescharacteristic, complemented
479#390—611no—
480#390—1221no—
481#389—611no—
482#388—1221no—
483#386—1221no—
484#385—1221no—
485#380—611no—
486C4×C4⋊C4—611no—
487#340—611no—
488#340—611no—
489#340—611no—
490#340—611no—
491#336—611no—
492#336—611no—
493C61#2145811yescharacteristic, complemented, Sylow
494C25—1221no—
495C22×D4—614no—
496C22×D4—611no—
497C22×D4—1222no—
498C22×D4—1221no—
499C22×D4—1222no—
500C22×D4—1222no—
501C22×D4—1222no—
502C22×D4—1222no—
503C22×D4—1221no—
504C22×D4C22×D6111yescharacteristic
505C22×D4C22×D6111yescharacteristic
506C23×C4—21no—
507C23×C4—21no—
508C23×C4—611no—
509C23×C4—1221no—
510C23×C4—1221no—
511C23×C4—1221no—
512C2×D8—22no—
513C2×D8—22no—
514C2×D8—614no—
515C2×D8—1222no—
516C2×D8—1222no—
517C2×D8C4×D6114yescomplemented
518C22×C8—611no—
519C22×C8—611no—
520C22×C8C22×D6111yescharacteristic
521C22×C8C22×D6111yescharacteristic
522#121—614no—
523#121—1222no—
524C4×D4—22no—
525C4×D4—22no—
526C4×D4—22no—
527C4×D4—614no—
528C4×D4—1228no—
529C4×D4—1222no—
530C4×D4—1222no—
531C4×D4—1228no—
532C4×D4—1222no—
533C4×D4—1222no—
534C4×D4—1222no—
535C4×D4C22⋊D6114yescomplemented
536#117—1222no—
537#117—1222no—
538#117—1222no—
539#117—1222no—
540C2×C4⋊C4—611no—
541C2×C4⋊C4—611no—
542C2×C4⋊C4—611no—
543C2×C4⋊C4—611no—
544C2×C4⋊C4—611no—
545C2×C4⋊C4—1221no—
546C2×C4⋊C4C22×D6111yescharacteristic
547C2×C4⋊C4C22×D6111yescharacteristic
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—611no—
551C2×C22⋊C4—611no—
552C2×C22⋊C4—1228no—
553C2×C22⋊C4—1221no—
554C2×C22⋊C4—1221no—
555C2×C22⋊C4—1228no—
556C2×C22⋊C4—1221no—
557C2×C22⋊C4—1221no—
558C2×C22⋊C4—1221no—
559C2×C22⋊C4—1221no—
560C2×C22⋊C4—1221no—
561C2×C22⋊C4—1221no—
562C2×C42—611no—
563C2×C42—1221no—
564C2×C42—1221no—
565C2×C42C22×D6111yescharacteristic
566#107—22no—
567#106—1222no—
568#102—22no—
569#102—22no—
570#102—614no—
571#102—614no—
572#102—1222no—
573#102—1222no—
574#102—1222no—
575#102—1222no—
576C22⋊C8—614no—
577C22⋊C8—1222no—
578#97—1222no—
579C4×C8—22no—
580#95—1221no—
581#95—1221no—
582#95—1221no—
583C24—21no—
584C24—21no—
585C24—611no—
586C24—1224no—
587C24—1224no—
588C24—1224no—
589C24—1221no—
590C24—4881no—
591C24—4881no—
592C24—4881no—
593C24—4881no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—612no—
603C2×D4—612no—
604C2×D4—612no—
605C2×D4—1224no—
606C2×D4—1228no—
607C2×D4—1228no—
608C2×D4—1228no—
609C2×D4—1224no—
610C2×D4—1224no—
611C2×D4—1228no—
612C2×D4—1224no—
613C2×D4—1221no—
614C2×D4—1221no—
615C2×D4—1221no—
616C2×D4—4881no—
617C2×D4—4881no—
618C2×D4C2×C4×D6112yes—
619C2×D4C2×C4×D6112yes—
620C2×D4#1175822212yes—
621C2×D4C2×C22⋊D6112yes—
622C22×C4—21no—
623C22×C4—24no—
624C22×C4—21no—
625C22×C4—42no—
626C22×C4—81no—
627C22×C4—81no—
628C22×C4—81no—
629C22×C4—81no—
630C22×C4—611no—
631C22×C4—612no—
632C22×C4—612no—
633C22×C4—611no—
634C22×C4—611no—
635C22×C4—1224no—
636C22×C4—1221no—
637C22×C4—1221no—
638C22×C4—1221no—
639C22×C4—1221no—
640C22×C4—1224no—
641C22×C4—1221no—
642C22×C4—1221no—
643C22×C4—1224no—
644C22×C4—1221no—
645C22×C4—4881no—
646C22×C4—4881no—
647C22×C4—4881no—
648C22×C4—4881no—
649C22×C4—4881no—
650C22×C4—4881no—
651C22×C4D4×D6111yescharacteristic
652C22×C4D4×D6111yescharacteristic
653C22×C4C23×D6111yescharacteristic
654D8—28no—
655D8—1228no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—612no—
662C2×C8—1221no—
663C2×C8—1221no—
664C2×C8—1221no—
665C2×C8—1221no—
666C2×C8—1221no—
667C2×C8C2×C4×D6112yes—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—612no—
672C4⋊C4—612no—
673C4⋊C4—1221no—
674C4⋊C4—1221no—
675C4⋊C4—1222no—
676C4⋊C4—1222no—
677C4⋊C4—1221no—
678C4⋊C4—1221no—
679C4⋊C4—4881no—
680C4⋊C4C2×C22⋊D6112yes—
681C22⋊C4—24no—
682C22⋊C4—42no—
683C22⋊C4—1224no—
684C22⋊C4—1224no—
685C22⋊C4—1224no—
686C22⋊C4—1224no—
687C22⋊C4—1222no—
688C22⋊C4—1222no—
689C22⋊C4—1224no—
690C22⋊C4—4881no—
691C22⋊C4—4881no—
692C22⋊C4—4881no—
693C42—1224no—
694C42—1221no—
695C42—1221no—
696C42—4881no—
697C42D4×D6112yes—
698C42C2×C22⋊D6112yes—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—612no—
714C23—12216no—
715C23—1222no—
716C23—1221no—
717C23—1222no—
718C23—1221no—
719C23—1222no—
720C23—1221no—
721C23—1221no—
722C23—1221no—
723C23—1221no—
724C23—4884no—
725C23—4884no—
726C23—4884no—
727C23—4884no—
728C23—4884no—
729C23—4884no—
730C23—2441no—
731C23—2441no—
732C23—2441no—
733C23—2441no—
734C23C2×D4×D6111yescharacteristic
735D4—22no—
736D4—22no—
737D4—22no—
738D4—22no—
739D4—22no—
740D4—41no—
741D4—41no—
742D4—614no—
743D4—12216no—
744D4—1222no—
745D4—1222no—
746D4—1222no—
747D4—4884no—
748D4C4×C22⋊D6114yes—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—22no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—84no—
760C2×C4—84no—
761C2×C4—612no—
762C2×C4—1221no—
763C2×C4—1221no—
764C2×C4—1222no—
765C2×C4—1222no—
766C2×C4—1222no—
767C2×C4—1222no—
768C2×C4—1222no—
769C2×C4—1222no—
770C2×C4—1221no—
771C2×C4—1221no—
772C2×C4—1221no—
773C2×C4—1221no—
774C2×C4—1221no—
775C2×C4—1221no—
776C2×C4—4884no—
777C2×C4—4884no—
778C2×C4—4884no—
779C2×C4—2441no—
780C2×C4—2441no—
781C2×C4—2441no—
782C2×C4—2441no—
783C2×C4—2441no—
784C2×C4—2441no—
785C2×C4—2441no—
786C2×C4#1451974512yes—
787C2×C4#1451974512yes—
788C2×C4C22×C4×D6111yescharacteristic
789C2×C4C2×D4×D6111yescharacteristic
790C2×C4C22×C22⋊D6111yescharacteristic
791C2×C4#41×D6111yescharacteristic
792C2×C4#41×D6111yescharacteristic
793C2×C4C2×#1175822211yescharacteristic
794C8—22no—
795C8—41no—
796C8—1222no—
797C8—2441no—
798C22—24no—
799C22—42no—
800C22—42no—
801C22—42no—
802C22—42no—
803C22—42no—
804C22—42no—
805C22—42no—
806C22—42no—
807C22—42no—
808C22—81no—
809C22—81no—
810C22—81no—
811C22—81no—
812C22—1222no—
813C22—1222no—
814C22—1222no—
815C22—1224no—
816C22—48816no—
817C22—2442no—
818C22—2441no—
819C22—2442no—
820C22—2442no—
821C22—2441no—
822C22—2442no—
823C22—2441no—
824C22—2442no—
825C22—2442no—
826C22—2441no—
827C22C4×D4×D6111yescharacteristic
828C22C2×#1451974511yescharacteristic
829C22#1684027111yescharacteristic
830C22#1684056311yescharacteristic
831C22#1684056311yescharacteristic
832C22#1684056411yescharacteristic
833C22#1684056911yescharacteristic
834C4—22no—
835C4—22no—
836C4—42no—
837C4—81no—
838C4—1222no—
839C4—4881no—
840C4—2441no—
841C4—2442no—
842C4—2442no—
843C4—2441no—
844C4C4×D4×D6111yescharacteristic
845C4C2×C4×C22⋊D6111yescharacteristic
846C4#1684026911yescharacteristic
847C4#1684027111yescharacteristic
848C2—44no—
849C2—82no—
850C2—2442no—
851C2—2444no—
852C2C4×#1451974511yescharacteristic
853C2#2145464411yescharacteristic
854C2#2145466611yescharacteristic
855C2#2145508311yescharacteristic
856C2#2145511911yescharacteristic
857C2#2145599911yescharacteristic
858C2#2145605911yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C4×D8×C61C2
socleC23×C61C22×D4
prime radicalC2×#16839894C2
cosocleC22×C4×C61C24
hypercenterC2×C4×D8D61
hypocenterC61#21458
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×D8

Complements

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

NH ≅ G/Ntype
1. C2×#16840234C2semidirect
3. C2×#16839872C2semidirect
4. #21448506C2semidirect
5. #21446169C2semidirect
6. #21446164C2semidirect
7. #21446138C2semidirect
8. #21446078C2semidirect
9. #21446063C2semidirect
10. #21446015C2semidirect
11. #21445748C2semidirect
12. #21445644C2semidirect
13. C4×#14519699C2semidirect
14. #21445586C2semidirect
15. C2×C4×D8×C61C2semidirect
30. #16839894C4semidirect
32. C2×#14519708C22semidirect
37. C2×#14519698C22semidirect
41. C2×#14519688C22semidirect
42. #16839665C22semidirect
44. #16839658C22semidirect
49. C4×C4⋊Dic61C22semidirect
50. #16839525C22semidirect
51. #16839525C22semidirect
52. #16839524C22semidirect
53. #16839524C22semidirect
54. #16839516C22semidirect
55. #16839516C22semidirect
58. C2×C4×D4×C61C22semidirect
60. C2×#107×C61C22semidirect
62. C2×#102×C61C22semidirect
63. C2×C4×C8×C61C22semidirect
73. C2×D4×D61C2×C4semidirect
80. C2×#11758199C2×C4semidirect
84. #14519748C2×C4semidirect
86. C4×D244D4semidirect
120. #14519699C2×C4semidirect
123. #14519698C2×C4semidirect
126. #14519689C2×C4semidirect
137. C2×D8×C61C2×C4semidirect
143. C4×D4×C61D4semidirect
422. C2×C4×D8D61semidirect
457. C2×C4×D4C2×D61semidirect
465. C2×#107C2×D61semidirect
474. C2×#102C2×D61semidirect
478. C2×C4×C8C2×D61semidirect
493. C61#21458semidirect
517. C2×D8C4×D61semidirect
535. C4×D4C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168402342
C2×#168398942
C2×#168398722
#214485062
#214461692
#214461642
#214461382
#214460782
#214460632
#214460152
#214457482
#214456442
C4×#145196992
#214455862
C2×C4×D8×C612
#2145861