Finite Group Databasebeta

← #29608048

Subgroups — #29608048

Order 15616.

1866 conjugacy classes of subgroups.

The subgroup lattice has 1158 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839656C211yesmaximal, characteristic, complemented
2C2×#16839638C211yesmaximal, characteristic
3C2×#16839621C211yesmaximal, characteristic, complemented
4C2×#16839619C211yesmaximal, characteristic, complemented
5#21444078C211yesmaximal, characteristic, complemented
6#21444077C211yesmaximal, characteristic, complemented
7#21444064C211yesmaximal, characteristic, complemented
8#21444062C211yesmaximal, characteristic, complemented
9#21444058C211yesmaximal, characteristic
10#21444058C211yesmaximal, characteristic
11#21444057C211yesmaximal, characteristic, complemented
12#21444055C211yesmaximal, characteristic, complemented
13#21444053C211yesmaximal, characteristic, complemented
14#21444052C211yesmaximal, characteristic, complemented
15C2×C61×#388C211yesmaximal, characteristic, complemented
16C23×C22⋊D61C2211yescharacteristic
17C23×C4×D61C2211yescharacteristic
18C22×C4⋊Dic61C2211yescharacteristic
19C22×#11758196C2211yescharacteristic
20C22×#11758196C2211yescharacteristic
21C22×C22⋊Dic61C2211yescharacteristic
22C22×C22⋊Dic61C2211yescharacteristic
23C22×C22⋊Dic61C2211yescharacteristic
24C22×#11758198C2211yescharacteristic
25C22×#11758198C2211yescharacteristic
26C22×#11758198C2211yescharacteristic
27C22×#11758198C2211yescharacteristic
28C22×#11758198C2211yescharacteristic
29C22×C4×Dic61C2211yescharacteristic
30#16839656—24no—
31#16839638C418yescomplemented
32#16839621—24no—
33#16839619—24no—
34C2×#14519684C2211yescharacteristic
35C2×#14519684C2211yescharacteristic
36C2×#14519684C2211yescharacteristic
37C2×#14519684C2211yescharacteristic
38C2×#14519684C2211yescharacteristic
39C2×#14519684C2211yescharacteristic
40C2×#14519684C2211yescharacteristic
41C2×#14519684C2211yescharacteristic
42C2×#14519684C2211yescharacteristic
43C2×#14519684C2211yescharacteristic
44C2×#14519684C2211yescharacteristic
45C2×#14519684C2211yescharacteristic
46C2×#14519684C2211yescharacteristic
47C2×#14519684C2211yescharacteristic
48C22×C4⋊C4×C61C2211yescharacteristic
49C22×C22⋊C4×C61C2211yescharacteristic
50C22×C22⋊C4×C61C2211yescharacteristic
51C22×C22⋊C4×C61C2211yescharacteristic
52C22×C42×C61C2211yescharacteristic
53C61×#388—24no—
54C2×#95×C61C2211yescharacteristic
55C2×#95×C61C2211yescharacteristic
56C24×D61C2311yescharacteristic
57C22×C22⋊D61—22no—
58C22×C22⋊D61—22no—
59C22×C22⋊D61—41no—
60C22×C22⋊D61—41no—
61C22×C22⋊D61—41no—
62C22×C22⋊D61—41no—
63C22×C22⋊D61C2×C414yes—
64C23×Dic61C2311yescharacteristic
65C23×Dic61C2311yescharacteristic
66C23×Dic61C2311yescharacteristic
67C23×Dic61C2311yescharacteristic
68C23×Dic61C2311yescharacteristic
69C23×Dic61C2311yescharacteristic
70C23×Dic61C2311yescharacteristic
71C22×C4×D61—22no—
72C22×C4×D61—22no—
73C22×C4×D61—22no—
74C22×C4×D61—22no—
75C22×C4×D61—41no—
76C22×C4×D61—41no—
77C22×C4×D61C2×C414yes—
78C2×C4⋊Dic61—22no—
79C2×C4⋊Dic61—22no—
80C2×C4⋊Dic61—41no—
81C2×#11758196—22no—
82C2×#11758196—22no—
83C2×#11758196—22no—
84C2×#11758196—22no—
85C2×#11758196—41no—
86C2×#11758196—41no—
87C2×C22⋊Dic61—22no—
88C2×C22⋊Dic61—22no—
89C2×C22⋊Dic61—22no—
90C2×C22⋊Dic61—41no—
91C2×C22⋊Dic61—41no—
92C2×C22⋊Dic61—41no—
93C2×C22⋊Dic61—41no—
94C2×C22⋊Dic61—41no—
95C2×C22⋊Dic61C2×C414yes—
96C2×#11758198—22no—
97C2×#11758198—22no—
98C2×#11758198—22no—
99C2×#11758198—22no—
100C2×#11758198—22no—
101C2×#11758198—22no—
102C2×#11758198—22no—
103C2×#11758198—22no—
104C2×#11758198—41no—
105C2×#11758198—41no—
106C2×#11758198—41no—
107C2×#11758198—41no—
108C2×#11758198—41no—
109C2×#11758198—41no—
110C2×#11758198C2×C414yes—
111C2×C4×Dic61—22no—
112C2×C4×Dic61—41no—
113C2×C4×Dic61—41no—
114#14519684—22no—
115#14519684—22no—
116#14519684—22no—
117#14519684—41no—
118#14519684—41no—
119#14519684—41no—
120#14519684—41no—
121#14519684—41no—
122#14519684—41no—
123#14519684—41no—
124#14519684—41no—
125#14519684C2×C414yes—
126#14519684C2×C414yes—
127#14519684D414yescomplemented
128C25×C61C2311yescharacteristic
129C23×C4×C61C2311yescharacteristic
130C23×C4×C61C2311yescharacteristic
131C23×C4×C61C2311yescharacteristic
132C23×C4×C61C2311yescharacteristic
133C23×C4×C61C2311yescharacteristic
134C23×C4×C61C2311yescharacteristic
135C2×C4⋊C4×C61—22no—
136C2×C4⋊C4×C61—22no—
137C2×C4⋊C4×C61—41no—
138C2×C22⋊C4×C61—22no—
139C2×C22⋊C4×C61—22no—
140C2×C22⋊C4×C61—22no—
141C2×C22⋊C4×C61—22no—
142C2×C22⋊C4×C61—22no—
143C2×C22⋊C4×C61—41no—
144C2×C22⋊C4×C61—41no—
145C2×C22⋊C4×C61—41no—
146C2×C22⋊C4×C61C2×C414yes—
147C2×C42×C61—22no—
148C2×C42×C61—41no—
149C2×C42×C61—41no—
150#95×C61—22no—
151#95×C61D414yescomplemented
152C24×C61—21no—
153C24×C61—21no—
154C24×C61—21no—
155C24×C61—21no—
156C24×C61—21no—
157C24×C61—21no—
158C24×C61—21no—
159C24×C61—21no—
160C24×C61—21no—
161C24×C61—21no—
162C24×C61—21no—
163C24×C61—21no—
164C24×C61—21no—
165C24×C61—21no—
166C24×C61C22×C412yes—
167C24×C61C2411yescharacteristic
168C23×D61—21no—
169C23×D61—21no—
170C23×D61—21no—
171C23×D61—21no—
172C23×D61—21no—
173C23×D61—21no—
174C23×D61—21no—
175C23×D61—21no—
176C23×D61—21no—
177C23×D61—21no—
178C23×D61—21no—
179C23×D61—21no—
180C23×D61C22×C412yes—
181C23×D61#4112yes—
182C23×D61#4112yes—
183C22×C4×C61—21no—
184C22×C4×C61—21no—
185C22×C4×C61—21no—
186C22×C4×C61—21no—
187C22×C4×C61—21no—
188C22×C4×C61—21no—
189C22×C4×C61—21no—
190C22×C4×C61—21no—
191C22×C4×C61—21no—
192C22×C4×C61—21no—
193C22×C4×C61—21no—
194C22×C4×C61—21no—
195C22×C4×C61—21no—
196C22×C4×C61—21no—
197C22×C4×C61—21no—
198C22×C4×C61—21no—
199C22×C4×C61—21no—
200C22×C4×C61—21no—
201C22×C4×C61—21no—
202C22×C4×C61—21no—
203C22×C4×C61—21no—
204C22×C4×C61—21no—
205C22×C4×C61—21no—
206C22×C4×C61—21no—
207C22×C4×C61—21no—
208C22×C4×C61—21no—
209C22×C4×C61—21no—
210C22×C4×C61—21no—
211C22×C4×C61—21no—
212C22×C4×C61—21no—
213C22×C4×C61—21no—
214C22×C4×C61—21no—
215C22×C4×C61—21no—
216C22×C4×C61—21no—
217C22×C4×C61—21no—
218C22×C4×C61C22×C412yes—
219C22×C4×C61C22×C412yes—
220C22×C4×C61C2×D412yes—
221C22×C4×C61C2×D412yes—
222C22×C4×C61C2×D412yes—
223C22×C4×C61C2×D412yes—
224C22×C4×C61#4112yes—
225C2×C22⋊D61—28no—
226C2×C22⋊D61—44no—
227C2×C22⋊D61—44no—
228C2×C22⋊D61—44no—
229C2×C22⋊D61—44no—
230C2×C22⋊D61—44no—
231C2×C22⋊D61—44no—
232C22×Dic61—21no—
233C22×Dic61—21no—
234C22×Dic61—21no—
235C22×Dic61—21no—
236C22×Dic61—21no—
237C22×Dic61—21no—
238C22×Dic61—21no—
239C22×Dic61—21no—
240C22×Dic61—21no—
241C22×Dic61—21no—
242C22×Dic61—21no—
243C22×Dic61—21no—
244C22×Dic61—21no—
245C22×Dic61—21no—
246C22×Dic61—21no—
247C22×Dic61—21no—
248C22×Dic61—21no—
249C22×Dic61—21no—
250C22×Dic61—21no—
251C22×Dic61—21no—
252C22×Dic61—21no—
253C22×Dic61—21no—
254C22×Dic61—21no—
255C22×Dic61—21no—
256C22×Dic61—21no—
257C22×Dic61—21no—
258C22×Dic61—21no—
259C22×Dic61—21no—
260C22×Dic61—21no—
261C22×Dic61—21no—
262C22×Dic61—21no—
263C22×Dic61—21no—
264C22×Dic61—21no—
265C22×Dic61—21no—
266C22×Dic61—21no—
267C22×Dic61—21no—
268C22×Dic61—21no—
269C22×Dic61—21no—
270C22×Dic61—21no—
271C22×Dic61—21no—
272C22×Dic61—21no—
273C22×Dic61—21no—
274C22×Dic61—21no—
275C22×Dic61C22×C412yes—
276C22×Dic61C22×C412yes—
277C22×Dic61C22×C412yes—
278C22×Dic61C2×D412yes—
279C22×Dic61C2×D412yes—
280C22×Dic61#4112yes—
281C2×C4×D61—28no—
282C2×C4×D61—28no—
283C2×C4×D61—44no—
284C2×C4×D61—44no—
285C2×C4×D61—44no—
286C2×C4×D61—44no—
287C2×C4×D61—44no—
288C4⋊C4×C61—44no—
289C22⋊C4×C61—28no—
290C22⋊C4×C61—44no—
291C22⋊C4×C61—44no—
292C42×C61—44no—
293C22⋊Dic61—28no—
294C22⋊Dic61—44no—
295C22⋊Dic61—44no—
296#11758198—44no—
297#11758198—44no—
298#11758198—44no—
299#11758198—44no—
300#11758198—44no—
301C4⋊Dic61—44no—
302#11758196—44no—
303#11758196—44no—
304C4×Dic61—44no—
305C23×C61—22no—
306C23×C61—22no—
307C23×C61—22no—
308C23×C61—22no—
309C23×C61—22no—
310C23×C61—22no—
311C23×C61—22no—
312C23×C61—41no—
313C23×C61—41no—
314C23×C61—41no—
315C23×C61—41no—
316C23×C61—41no—
317C23×C61—41no—
318C23×C61—41no—
319C23×C61—41no—
320C23×C61—41no—
321C23×C61—41no—
322C23×C61—41no—
323C23×C61—41no—
324C23×C61—41no—
325C23×C61—41no—
326C23×C61—41no—
327C23×C61—41no—
328C23×C61—41no—
329C23×C61—41no—
330C23×C61—41no—
331C23×C61—41no—
332C23×C61—41no—
333C23×C61—41no—
334C23×C61—41no—
335C23×C61—41no—
336C23×C61—41no—
337C23×C61—41no—
338C23×C61—41no—
339C23×C61—41no—
340C23×C61C23×C411yescharacteristic
341C23×C61C22×D411yescharacteristic
342C23×C61C22×D411yescharacteristic
343C23×C61C2×#4111yescharacteristic
344C23×C61C2×#4111yescharacteristic
345C23×C61C2×#4111yescharacteristic
346C23×C61C2×#4111yescharacteristic
347C23×C61H(5,𝔽2)11yescharacteristic
348C23×C61H(5,𝔽2)11yescharacteristic
349C23×C61H(5,𝔽2)11yescharacteristic
350C23×C61H(5,𝔽2)11yescharacteristic
351C23×C61H(5,𝔽2)11yescharacteristic
352C23×C61H(5,𝔽2)11yescharacteristic
353C23×C612−1+411yescharacteristic
354C23×C612−1+411yescharacteristic
355C22×D61—22no—
356C22×D61—22no—
357C22×D61—22no—
358C22×D61—22no—
359C22×D61—22no—
360C22×D61—22no—
361C22×D61—22no—
362C22×D61—22no—
363C22×D61—22no—
364C22×D61—22no—
365C22×D61—22no—
366C22×D61—22no—
367C22×D61—22no—
368C22×D61—22no—
369C22×D61—22no—
370C22×D61—22no—
371C22×D61—22no—
372C22×D61—22no—
373C22×D61—41no—
374C22×D61—41no—
375C22×D61—41no—
376C22×D61—41no—
377C22×D61—41no—
378C22×D61—41no—
379C22×D61—41no—
380C22×D61—41no—
381C22×D61—41no—
382C22×D61—41no—
383C22×D61—41no—
384C22×D61—41no—
385C22×D61—41no—
386C22×D61—41no—
387C22×D61—41no—
388C22×D61—41no—
389C22×D61#11714yes—
390C2×C4×C61—22no—
391C2×C4×C61—22no—
392C2×C4×C61—22no—
393C2×C4×C61—22no—
394C2×C4×C61—22no—
395C2×C4×C61—22no—
396C2×C4×C61—22no—
397C2×C4×C61—22no—
398C2×C4×C61—22no—
399C2×C4×C61—22no—
400C2×C4×C61—22no—
401C2×C4×C61—22no—
402C2×C4×C61—22no—
403C2×C4×C61—22no—
404C2×C4×C61—22no—
405C2×C4×C61—22no—
406C2×C4×C61—22no—
407C2×C4×C61—22no—
408C2×C4×C61—41no—
409C2×C4×C61—41no—
410C2×C4×C61—41no—
411C2×C4×C61—41no—
412C2×C4×C61—41no—
413C2×C4×C61—41no—
414C2×C4×C61—41no—
415C2×C4×C61—41no—
416C2×C4×C61—41no—
417C2×C4×C61—41no—
418C2×C4×C61—41no—
419C2×C4×C61—41no—
420C2×C4×C61—41no—
421C2×C4×C61—41no—
422C2×C4×C61—41no—
423C2×C4×C61—41no—
424C2×C4×C61—41no—
425C2×C4×C61—41no—
426C2×C4×C61—41no—
427C2×C4×C61—41no—
428C2×C4×C61—41no—
429C2×C4×C61—41no—
430C2×C4×C61—41no—
431C2×C4×C61C4×D414yes—
432C22⋊D61—416no—
433C2×Dic61—22no—
434C2×Dic61—22no—
435C2×Dic61—22no—
436C2×Dic61—22no—
437C2×Dic61—22no—
438C2×Dic61—22no—
439C2×Dic61—22no—
440C2×Dic61—22no—
441C2×Dic61—22no—
442C2×Dic61—22no—
443C2×Dic61—22no—
444C2×Dic61—22no—
445C2×Dic61—22no—
446C2×Dic61—22no—
447C2×Dic61—22no—
448C2×Dic61—41no—
449C2×Dic61—41no—
450C2×Dic61—41no—
451C2×Dic61—41no—
452C2×Dic61—41no—
453C2×Dic61—41no—
454C2×Dic61—41no—
455C2×Dic61—41no—
456C2×Dic61—41no—
457C2×Dic61—41no—
458C2×Dic61—41no—
459C2×Dic61—41no—
460C2×Dic61—41no—
461C2×Dic61—41no—
462C2×Dic61—41no—
463C2×Dic61—41no—
464C2×Dic61—41no—
465C2×Dic61—41no—
466C2×Dic61—41no—
467C2×Dic61—41no—
468C2×Dic61—41no—
469C2×Dic61—41no—
470C2×Dic61—41no—
471C2×Dic61—41no—
472C2×Dic61—41no—
473C2×Dic61—41no—
474C2×Dic61—41no—
475C2×Dic61—41no—
476C2×Dic61—41no—
477C2×Dic61—41no—
478C2×Dic61—41no—
479C2×Dic61—41no—
480C2×Dic61—41no—
481C2×Dic61C4×D414yes—
482C4×D61—416no—
483#14410—611nomaximal, Sylow
484C22×C61—42no—
485C22×C61—42no—
486C22×C61—42no—
487C22×C61—42no—
488C22×C61—42no—
489C22×C61—42no—
490C22×C61—42no—
491C22×C61—81no—
492C22×C61—81no—
493C22×C61—81no—
494C22×C61—81no—
495C22×C61—81no—
496C22×C61—81no—
497C22×C61—81no—
498C22×C61—81no—
499C22×C61C2×#11711yescharacteristic
500C22×C61C2×C4×D411yescharacteristic
501C22×C61C2×C4×D411yescharacteristic
502C22×C61#51811yescharacteristic
503C22×C61#51811yescharacteristic
504C22×C61#52011yescharacteristic
505C22×C61#52011yescharacteristic
506C22×C61#53511yescharacteristic
507C22×C61#53511yescharacteristic
508C22×C61#53711yescharacteristic
509C22×C61#53711yescharacteristic
510C22×C61#53811yescharacteristic
511C22×C61#53811yescharacteristic
512C22×C61#53811yescharacteristic
513C22×C61#53811yescharacteristic
514C22×C61#54011yescharacteristic
515C22×C61#54011yescharacteristic
516C22×C61#54211yescharacteristic
517C22×C61#54211yescharacteristic
518C22×C61D4211yescharacteristic
519C22×C61#54611yescharacteristic
520C22×C61#54611yescharacteristic
521C22×C61#54611yescharacteristic
522C22×C61#54611yescharacteristic
523C22×C61#54811yescharacteristic
524C22×C61#54811yescharacteristic
525C22×C61#55111yescharacteristic
526C22×C61#55211yescharacteristic
527C22×C61#55211yescharacteristic
528C22×C61#55311yescharacteristic
529C22×C61#55311yescharacteristic
530C22×C61#56011yescharacteristic
531C22×C61#56211yescharacteristic
532C22×C61#56211yescharacteristic
533C22×C61#56311yescharacteristic
534C2×D61—24no—
535C2×D61—24no—
536C2×D61—24no—
537C2×D61—42no—
538C2×D61—42no—
539C2×D61—42no—
540C2×D61—42no—
541C2×D61—42no—
542C2×D61—42no—
543C2×D61—42no—
544C2×D61—42no—
545C2×D61—42no—
546C2×D61—42no—
547C2×D61—42no—
548C2×D61—42no—
549C4×C61—24no—
550C4×C61—42no—
551C4×C61—42no—
552C4×C61—42no—
553C4×C61—42no—
554C4×C61—81no—
555Dic61—24no—
556Dic61—42no—
557Dic61—42no—
558Dic61—42no—
559Dic61—81no—
560Dic61—81no—
561Dic61—81no—
562C2×#388—611no—
563C2×#388D6111yescharacteristic, complemented
564C2×#386—611no—
565C2×#380—611no—
566C2×#380—611no—
567#1442—611no—
568#1442—611no—
569#1439—611no—
570#1439—611no—
571#1438—611no—
572#1438—611no—
573#1437—611no—
574#1437—611no—
575#1436—611no—
576#1436—611no—
577C2×C61—82no—
578C2×C61#231211yescharacteristic
579C2×C61#232411yescharacteristic
580C2×C61#232411yescharacteristic
581C2×C61#235211yescharacteristic
582C2×C61#235211yescharacteristic
583C2×C61#235811yescharacteristic
584C2×C61#237611yescharacteristic
585C2×C61#267611yescharacteristic
586C2×C61#267611yescharacteristic
587C2×C61#270211yescharacteristic
588C2×C61#270211yescharacteristic
589C2×C61#270311yescharacteristic
590C2×C61#270311yescharacteristic
591C2×C61#274111yescharacteristic
592C2×C61#274111yescharacteristic
593D61—44no—
594C23×D4—611no—
595C24×C4—611no—
596C22×C4⋊C4—611no—
597C22×C4⋊C4—611no—
598C22×C4⋊C4—611no—
599C22×C4⋊C4C2×D6111yescharacteristic
600C22×C22⋊C4—611no—
601C22×C22⋊C4—611no—
602C22×C22⋊C4—611no—
603C22×C22⋊C4—611no—
604C22×C22⋊C4—611no—
605C22×C22⋊C4—611no—
606C22×C22⋊C4—611no—
607C22×C22⋊C4—611no—
608C22×C22⋊C4C2×D6111yescharacteristic
609C22×C22⋊C4C2×D6111yescharacteristic
610C22×C22⋊C4C2×D6111yescharacteristic
611C22×C42—611no—
612C22×C42C2×D6111yescharacteristic
613#388—24no—
614#388—1224no—
615#386—618no—
616#380—1224no—
617#380—1224no—
618C2×#95—611no—
619C2×#95—611no—
620C2×#95—611no—
621C2×#95—611no—
622C2×#95—611no—
623C2×#95—611no—
624C2×#95—611no—
625C2×#95—611no—
626C2×#95—611no—
627C2×#95—611no—
628C2×#95—611no—
629C2×#95—611no—
630C2×#95—611no—
631C2×#95—611no—
632C2×#95C2×D6111yescharacteristic
633C2×#95C2×D6111yescharacteristic
634C61#1441011yescharacteristic, complemented, Sylow
635C25—611no—
636C25C22×D6111yescharacteristic
637C22×D4—614no—
638C22×D4—1222no—
639C22×D4—1222no—
640C22×D4—2441no—
641C22×D4—2441no—
642C22×D4—2441no—
643C22×D4—2441no—
644C23×C4—611no—
645C23×C4—611no—
646C23×C4—611no—
647C23×C4—611no—
648C23×C4—614no—
649C23×C4—611no—
650C23×C4—611no—
651C23×C4—611no—
652C23×C4—1222no—
653C23×C4—1222no—
654C23×C4—1222no—
655C23×C4—1222no—
656C23×C4—2441no—
657C23×C4—2441no—
658C23×C4C22×D6111yescharacteristic
659C23×C4C22×D6111yescharacteristic
660C23×C4C22×D6111yescharacteristic
661C23×C4C22×D6111yescharacteristic
662C23×C4C22×D6111yescharacteristic
663C23×C4C22×D6111yescharacteristic
664C2×C4⋊C4—22no—
665C2×C4⋊C4—22no—
666C2×C4⋊C4—41no—
667C2×C4⋊C4—1222no—
668C2×C4⋊C4—1222no—
669C2×C4⋊C4—1222no—
670C2×C4⋊C4—1222no—
671C2×C4⋊C4—1222no—
672C2×C4⋊C4—1222no—
673C2×C4⋊C4—2441no—
674C2×C4⋊C4—2441no—
675C2×C4⋊C4—2441no—
676C2×C22⋊C4—22no—
677C2×C22⋊C4—22no—
678C2×C22⋊C4—22no—
679C2×C22⋊C4—22no—
680C2×C22⋊C4—22no—
681C2×C22⋊C4—41no—
682C2×C22⋊C4—41no—
683C2×C22⋊C4—41no—
684C2×C22⋊C4—614no—
685C2×C22⋊C4—614no—
686C2×C22⋊C4—1222no—
687C2×C22⋊C4—1222no—
688C2×C22⋊C4—1222no—
689C2×C22⋊C4—1222no—
690C2×C22⋊C4—1222no—
691C2×C22⋊C4—1222no—
692C2×C22⋊C4—1222no—
693C2×C22⋊C4—1222no—
694C2×C22⋊C4—1222no—
695C2×C22⋊C4—1222no—
696C2×C22⋊C4—1222no—
697C2×C22⋊C4—2441no—
698C2×C22⋊C4—2441no—
699C2×C22⋊C4—2441no—
700C2×C22⋊C4—2441no—
701C2×C22⋊C4—2441no—
702C2×C22⋊C4—2441no—
703C2×C22⋊C4—2441no—
704C2×C22⋊C4—2441no—
705C2×C22⋊C4—2441no—
706C2×C22⋊C4—2441no—
707C2×C22⋊C4—2441no—
708C2×C22⋊C4C4×D6114yes—
709C2×C42—22no—
710C2×C42—41no—
711C2×C42—41no—
712C2×C42—1222no—
713C2×C42—2441no—
714C2×C42—2441no—
715#95—22no—
716#95—614no—
717#95—614no—
718#95—614no—
719#95—1222no—
720#95—1222no—
721#95—1222no—
722#95—2441no—
723#95—2441no—
724#95—2441no—
725#95—2441no—
726#95—2441no—
727#95—2441no—
728#95—2441no—
729#95—2441no—
730#95C22⋊D6114yescomplemented
731C24—21no—
732C24—21no—
733C24—21no—
734C24—21no—
735C24—21no—
736C24—21no—
737C24—21no—
738C24—21no—
739C24—21no—
740C24—21no—
741C24—21no—
742C24—21no—
743C24—21no—
744C24—21no—
745C24—612no—
746C24—612no—
747C24—612no—
748C24—1221no—
749C24—1221no—
750C24—1221no—
751C24—1221no—
752C24—1221no—
753C24—1221no—
754C24—1221no—
755C24—1221no—
756C24—1221no—
757C24—1221no—
758C24—1221no—
759C24—1221no—
760C24C2×C4×D6112yes—
761C24C23×D6111yescharacteristic
762C2×D4—1228no—
763C2×D4—2444no—
764C2×D4—2444no—
765C2×D4—2444no—
766C2×D4—2444no—
767C2×D4—2444no—
768C2×D4—2444no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—612no—
805C22×C4—612no—
806C22×C4—612no—
807C22×C4—612no—
808C22×C4—612no—
809C22×C4—612no—
810C22×C4—1228no—
811C22×C4—1221no—
812C22×C4—1221no—
813C22×C4—1221no—
814C22×C4—1221no—
815C22×C4—1221no—
816C22×C4—1221no—
817C22×C4—1221no—
818C22×C4—1221no—
819C22×C4—1221no—
820C22×C4—1221no—
821C22×C4—1221no—
822C22×C4—1221no—
823C22×C4—1221no—
824C22×C4—1221no—
825C22×C4—1221no—
826C22×C4—1221no—
827C22×C4—1221no—
828C22×C4—1221no—
829C22×C4—1221no—
830C22×C4—1221no—
831C22×C4—1221no—
832C22×C4—1221no—
833C22×C4—1228no—
834C22×C4—1221no—
835C22×C4—1221no—
836C22×C4—1221no—
837C22×C4—1221no—
838C22×C4—1221no—
839C22×C4—1221no—
840C22×C4—1221no—
841C22×C4—1221no—
842C22×C4—1221no—
843C22×C4—1221no—
844C22×C4—1221no—
845C22×C4—1221no—
846C22×C4—1221no—
847C22×C4—1221no—
848C22×C4—1221no—
849C22×C4—1221no—
850C22×C4—1221no—
851C22×C4—1221no—
852C22×C4—1221no—
853C22×C4—1221no—
854C22×C4—1221no—
855C22×C4—2444no—
856C22×C4—2444no—
857C22×C4—2444no—
858C22×C4—2444no—
859C22×C4—2444no—
860C22×C4C2×C4×D6112yes—
861C22×C4C2×C4×D6112yes—
862C22×C4#1175822212yes—
863C22×C4D4×D6112yes—
864C22×C4C2×C22⋊D6112yes—
865C22×C4C2×C22⋊D6112yes—
866C22×C4C2×C22⋊D6112yes—
867C4⋊C4—44no—
868C4⋊C4—2444no—
869C4⋊C4—2444no—
870C4⋊C4—2444no—
871C22⋊C4—28no—
872C22⋊C4—44no—
873C22⋊C4—44no—
874C22⋊C4—1228no—
875C22⋊C4—2444no—
876C22⋊C4—2444no—
877C22⋊C4—2444no—
878C22⋊C4—2444no—
879C22⋊C4—2444no—
880C22⋊C4—2444no—
881C22⋊C4—2444no—
882C42—44no—
883C42—2444no—
884C23—22no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—41no—
892C23—41no—
893C23—41no—
894C23—41no—
895C23—41no—
896C23—41no—
897C23—41no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—41no—
911C23—41no—
912C23—41no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—614no—
920C23—1222no—
921C23—1222no—
922C23—1222no—
923C23—1222no—
924C23—1222no—
925C23—1222no—
926C23—1222no—
927C23—1222no—
928C23—1222no—
929C23—1222no—
930C23—1222no—
931C23—1222no—
932C23—1222no—
933C23—1222no—
934C23—1222no—
935C23—1222no—
936C23—1222no—
937C23—1222no—
938C23—2441no—
939C23—2441no—
940C23—2441no—
941C23—2441no—
942C23—2441no—
943C23—2441no—
944C23—2441no—
945C23—2441no—
946C23—2441no—
947C23—2441no—
948C23—2441no—
949C23—2441no—
950C23—2441no—
951C23—2441no—
952C23—2441no—
953C23—2441no—
954C23C22×C4×D6111yescharacteristic
955C23C2×D4×D6111yescharacteristic
956C23C22×C22⋊D6111yescharacteristic
957C23#41×D6111yescharacteristic
958C23#41×D6111yescharacteristic
959C23#41×D6111yescharacteristic
960C23C2×#1175822211yescharacteristic
961C23#1451982211yescharacteristic
962C23#1451982211yescharacteristic
963C23#1451982211yescharacteristic
964C23#1451982311yescharacteristic
965C23#1451982311yescharacteristic
966C23#1451982311yescharacteristic
967C23#1451982411yescharacteristic
968C23#1451982411yescharacteristic
969D4—24416no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—614no—
1012C2×C4—1222no—
1013C2×C4—1222no—
1014C2×C4—1222no—
1015C2×C4—1222no—
1016C2×C4—1222no—
1017C2×C4—1222no—
1018C2×C4—1222no—
1019C2×C4—1222no—
1020C2×C4—1222no—
1021C2×C4—1222no—
1022C2×C4—1222no—
1023C2×C4—1222no—
1024C2×C4—1222no—
1025C2×C4—1222no—
1026C2×C4—1222no—
1027C2×C4—24416no—
1028C2×C4—2441no—
1029C2×C4—2441no—
1030C2×C4—2441no—
1031C2×C4—2441no—
1032C2×C4—2441no—
1033C2×C4—2441no—
1034C2×C4—2441no—
1035C2×C4—2441no—
1036C2×C4—2441no—
1037C2×C4—2441no—
1038C2×C4—2441no—
1039C2×C4—2441no—
1040C2×C4—2441no—
1041C2×C4—2441no—
1042C2×C4—2441no—
1043C2×C4—2441no—
1044C2×C4—2441no—
1045C2×C4—2441no—
1046C2×C4—2441no—
1047C2×C4—2441no—
1048C2×C4—2441no—
1049C2×C4—2441no—
1050C2×C4—2441no—
1051C2×C4—2441no—
1052C2×C4—2441no—
1053C2×C4—2441no—
1054C2×C4—2441no—
1055C2×C4—2441no—
1056C2×C4—2441no—
1057C2×C4—2441no—
1058C2×C4—2441no—
1059C2×C4—2441no—
1060C2×C4—2441no—
1061C2×C4C4×C22⋊D6114yes—
1062C22—42no—
1063C22—42no—
1064C22—42no—
1065C22—42no—
1066C22—42no—
1067C22—42no—
1068C22—42no—
1069C22—81no—
1070C22—81no—
1071C22—81no—
1072C22—81no—
1073C22—81no—
1074C22—81no—
1075C22—81no—
1076C22—81no—
1077C22—1224no—
1078C22—1224no—
1079C22—1224no—
1080C22—2442no—
1081C22—2442no—
1082C22—2442no—
1083C22—2442no—
1084C22—2442no—
1085C22—2442no—
1086C22—2442no—
1087C22—2442no—
1088C22—2442no—
1089C22—2442no—
1090C22—2442no—
1091C22—2442no—
1092C22#117×D6111yescharacteristic
1093C22C4×D4×D6111yescharacteristic
1094C22C2×C4×C22⋊D6111yescharacteristic
1095C22#1684023411yescharacteristic
1096C22#1684023411yescharacteristic
1097C22#1684024111yescharacteristic
1098C22#1684024211yescharacteristic
1099C22#1684032911yescharacteristic
1100C22#1684033011yescharacteristic
1101C22#1684033911yescharacteristic
1102C22#1684034011yescharacteristic
1103C22#1684034411yescharacteristic
1104C22#1684034611yescharacteristic
1105C22#1684034811yescharacteristic
1106C22#1684035111yescharacteristic
1107C22#1684036311yescharacteristic
1108C22#1684036411yescharacteristic
1109C22#1684037711yescharacteristic
1110C22#1684037811yescharacteristic
1111C22D4×C22⋊D6111yescharacteristic
1112C22#1684040011yescharacteristic
1113C22#1684040011yescharacteristic
1114C22#1684040111yescharacteristic
1115C22#1684040811yescharacteristic
1116C22#1684041911yescharacteristic
1117C22#1684042011yescharacteristic
1118C22#1684044111yescharacteristic
1119C22#1684044811yescharacteristic
1120C22#1684045111yescharacteristic
1121C22#1684045611yescharacteristic
1122C22#1684045711yescharacteristic
1123C22#1684050211yescharacteristic
1124C22#1684050611yescharacteristic
1125C22#1684050711yescharacteristic
1126C22#1684051411yescharacteristic
1127C4—24no—
1128C4—42no—
1129C4—42no—
1130C4—42no—
1131C4—42no—
1132C4—81no—
1133C4—1224no—
1134C4—4881no—
1135C4—4881no—
1136C4—4881no—
1137C4—2442no—
1138C4—2442no—
1139C4—2442no—
1140C2—82no—
1141C2—2444no—
1142C2#2144841311yescharacteristic
1143C2#2144850611yescharacteristic
1144C2#2144850711yescharacteristic
1145C2#2144874711yescharacteristic
1146C2#2144874911yescharacteristic
1147C2#2144879611yescharacteristic
1148C2#2144896111yescharacteristic
1149C2#2145211411yescharacteristic
1150C2#2145211511yescharacteristic
1151C2#2145244111yescharacteristic
1152C2#2145244211yescharacteristic
1153C2#2145245611yescharacteristic
1154C2#2145245711yescharacteristic
1155C2#2145293211yescharacteristic
1156C2#2145293711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC2×C61×#388C2
socle, cosocleC24×C61C24
prime radicalC23×C22⋊D61C22
hypercenterC2×#388D61
hypocenterC61#14410
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. C2×#16839656C2semidirect
3. C2×#16839621C2semidirect
4. C2×#16839619C2semidirect
5. #21444078C2semidirect
6. #21444077C2semidirect
7. #21444064C2semidirect
8. #21444062C2semidirect
11. #21444057C2semidirect
12. #21444055C2semidirect
13. #21444053C2semidirect
14. #21444052C2semidirect
15. C2×C61×#388C2semidirect
31. #16839638C4semidirect
127. #14519684D4semidirect
151. #95×C61D4semidirect
563. C2×#388D61semidirect
634. C61#14410semidirect
730. #95C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168396562
C2×#168396382
C2×#168396212
C2×#168396192
#214440782
#214440772
#214440642
#214440622
#214440582
#214440572
#214440552
#214440532
#214440522
C2×C61×#3882
#1441061