Finite Group Databasebeta

← #29609189

Subgroups — #29609189

Order 15616.

1962 conjugacy classes of subgroups.

The subgroup lattice has 1160 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519761C211yesmaximal, characteristic
2C2×#16839655C211yesmaximal, characteristic, complemented
3#21444088C211yesmaximal, characteristic, complemented
4#21444086C211yesmaximal, characteristic, complemented
5#21444065C211yesmaximal, characteristic, complemented
6#21444061C211yesmaximal, characteristic, complemented
7#21444058C211yesmaximal, characteristic
8#21444058C211yesmaximal, characteristic
9#21444057C211yesmaximal, characteristic, complemented
10#21444055C211yesmaximal, characteristic, complemented
11#21444049C211yesmaximal, characteristic, complemented
12#21444048C211yesmaximal, characteristic, complemented
13#21444041C211yesmaximal, characteristic, complemented
14#21444041C211yesmaximal, characteristic, complemented
15C2×C61×#388C211yesmaximal, characteristic, complemented
16C23×C22⋊D61C2211yescharacteristic
17C24×Dic61C2211yescharacteristic
18C2×#14519761—24no—
19C2×#14519761—24no—
20C2×#14519761C418yescomplemented
21C22×C4⋊Dic61C2211yescharacteristic
22C22×C4⋊Dic61C2211yescharacteristic
23C22×C4⋊Dic61C2211yescharacteristic
24C22×C22⋊Dic61C2211yescharacteristic
25C22×C22⋊Dic61C2211yescharacteristic
26C22×#11758198C2211yescharacteristic
27C22×#11758198C2211yescharacteristic
28C22×#11758198C2211yescharacteristic
29C22×#11758198C2211yescharacteristic
30C22×#11758198C2211yescharacteristic
31C22×#11758198C2211yescharacteristic
32C22×C4×Dic61C2211yescharacteristic
33#16839655—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×Dic61—22no—
65C23×Dic61—22no—
66C23×Dic61—41no—
67C23×Dic61—41no—
68C23×Dic61—41no—
69C23×Dic61—41no—
70C23×Dic61C2×C414yes—
71C23×Dic61C2311yescharacteristic
72C23×Dic61C2311yescharacteristic
73C23×Dic61C2311yescharacteristic
74C23×Dic61C2311yescharacteristic
75C23×Dic61C2311yescharacteristic
76C23×Dic61C2311yescharacteristic
77C23×Dic61C2311yescharacteristic
78#14519761—232no—
79C2×C4⋊Dic61—22no—
80C2×C4⋊Dic61—22no—
81C2×C4⋊Dic61—22no—
82C2×C4⋊Dic61—22no—
83C2×C4⋊Dic61—22no—
84C2×C4⋊Dic61—22no—
85C2×C4⋊Dic61—41no—
86C2×C4⋊Dic61C2×C414yes—
87C2×C4⋊Dic61C2×C414yes—
88C2×C22⋊Dic61—22no—
89C2×C22⋊Dic61—22no—
90C2×C22⋊Dic61—22no—
91C2×C22⋊Dic61—22no—
92C2×C22⋊Dic61—41no—
93C2×C22⋊Dic61—41no—
94C2×#11758198—22no—
95C2×#11758198—22no—
96C2×#11758198—22no—
97C2×#11758198—22no—
98C2×#11758198—22no—
99C2×#11758198—22no—
100C2×#11758198—22no—
101C2×#11758198—22no—
102C2×#11758198—41no—
103C2×#11758198—41no—
104C2×#11758198—41no—
105C2×#11758198—41no—
106C2×#11758198—41no—
107C2×#11758198—41no—
108C2×#11758198—41no—
109C2×#11758198—41no—
110C2×#11758198C2×C414yes—
111C2×#11758198C2×C414yes—
112C2×C4×Dic61—22no—
113C2×C4×Dic61—22no—
114C2×C4×Dic61—41no—
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#14519684—41no—
126#14519684—41no—
127#14519684—41no—
128#14519684—41no—
129C25×C61C2311yescharacteristic
130C23×C4×C61C2311yescharacteristic
131C23×C4×C61C2311yescharacteristic
132C23×C4×C61C2311yescharacteristic
133C23×C4×C61C2311yescharacteristic
134C23×C4×C61C2311yescharacteristic
135C23×C4×C61C2311yescharacteristic
136C2×C4⋊C4×C61—22no—
137C2×C4⋊C4×C61—22no—
138C2×C4⋊C4×C61—41no—
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×C61C2×C414yes—
146C2×C22⋊C4×C61D414yes—
147C2×C22⋊C4×C61D414yes—
148C2×C42×C61—22no—
149C2×C42×C61—22no—
150C2×C42×C61—41no—
151#95×C61—22no—
152#95×C61—22no—
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×C61C22×C412yes—
166C24×C61C2×D412yes—
167C24×C61C2×D412yes—
168C24×C61C2411yescharacteristic
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×D61—21no—
181C23×D61—21no—
182C23×D61—21no—
183C23×D61C22×C412yes—
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—
225C22×C4×C61#4112yes—
226C2×C22⋊D61—28no—
227C2×C22⋊D61—44no—
228C2×C22⋊D61—44no—
229C2×C22⋊D61—44no—
230C2×C22⋊D61—44no—
231C2×C22⋊D61—44no—
232C2×C22⋊D61—44no—
233C22×Dic61—28no—
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×Dic61—21no—
276C22×Dic61—21no—
277C22×Dic61—21no—
278C22×Dic61—44no—
279C22×Dic61—44no—
280C22×Dic61—44no—
281C22×Dic61—44no—
282C22×Dic61—44no—
283C22×Dic61—44no—
284C22×Dic61C22×C412yes—
285C22×Dic61C22×C412yes—
286C22×Dic61C22×C412yes—
287C22×Dic61#4112yes—
288C22×Dic61#4112yes—
289C4⋊C4×C61—44no—
290C22⋊C4×C61—44no—
291C22⋊C4×C61—44no—
292C22⋊C4×C61C22⋊C4116yescomplemented
293C42×C61—44no—
294C22⋊Dic61—44no—
295C22⋊Dic61—44no—
296#11758198—28no—
297#11758198—28no—
298#11758198—44no—
299#11758198—44no—
300#11758198—44no—
301#11758198—44no—
302C4⋊Dic61—28no—
303C4⋊Dic61—28no—
304C4⋊Dic61—44no—
305C4×Dic61—44no—
306C23×C61—22no—
307C23×C61—22no—
308C23×C61—22no—
309C23×C61—22no—
310C23×C61—22no—
311C23×C61—22no—
312C23×C61—22no—
313C23×C61—22no—
314C23×C61—22no—
315C23×C61—22no—
316C23×C61—22no—
317C23×C61—22no—
318C23×C61—22no—
319C23×C61—22no—
320C23×C61—22no—
321C23×C61—22no—
322C23×C61—22no—
323C23×C61—22no—
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×C61C2×C22⋊C414yes—
341C23×C61C23×C411yescharacteristic
342C23×C61C22×D411yescharacteristic
343C23×C61C22×D411yescharacteristic
344C23×C61C2×#4111yescharacteristic
345C23×C61C2×#4111yescharacteristic
346C23×C61C2×#4111yescharacteristic
347C23×C61C2×#4111yescharacteristic
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×C61H(5,𝔽2)11yescharacteristic
354C23×C612−1+411yescharacteristic
355C23×C612−1+411yescharacteristic
356C22×D61—22no—
357C22×D61—22no—
358C22×D61—22no—
359C22×D61—22no—
360C22×D61—22no—
361C22×D61—22no—
362C22×D61—22no—
363C22×D61—41no—
364C22×D61—41no—
365C22×D61—41no—
366C22×D61—41no—
367C22×D61—41no—
368C22×D61—41no—
369C22×D61—41no—
370C22×D61—41no—
371C22×D61—41no—
372C22×D61—41no—
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—41no—
390C22×D61—41no—
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—22no—
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×C61C2×C22⋊C414yes—
432C2×C4×C61C2×C22⋊C414yes—
433C22⋊D61—416no—
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—22no—
449C2×Dic61—416no—
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×Dic61—41no—
482C2×Dic61—41no—
483C2×Dic61—41no—
484#14506—611nomaximal, Sylow
485C22×C61—24no—
486C22×C61—24no—
487C22×C61—24no—
488C22×C61—42no—
489C22×C61—42no—
490C22×C61—42no—
491C22×C61—42no—
492C22×C61—42no—
493C22×C61—42no—
494C22×C61—42no—
495C22×C61—42no—
496C22×C61—42no—
497C22×C61—42no—
498C22×C61—42no—
499C22×C61—42no—
500C22×C61C22×C22⋊C411yescharacteristic
501C22×C61C4×#4111yescharacteristic
502C22×C61C4×#4111yescharacteristic
503C22×C61#51811yescharacteristic
504C22×C61#51811yescharacteristic
505C22×C61#52011yescharacteristic
506C22×C61#52011yescharacteristic
507C22×C61#53511yescharacteristic
508C22×C61#53511yescharacteristic
509C22×C61#53511yescharacteristic
510C22×C61#53511yescharacteristic
511C22×C61#53811yescharacteristic
512C22×C61#53811yescharacteristic
513C22×C61#53911yescharacteristic
514C22×C61#53911yescharacteristic
515C22×C61#54011yescharacteristic
516C22×C61#54011yescharacteristic
517C22×C61#54211yescharacteristic
518C22×C61#54211yescharacteristic
519C22×C61#54611yescharacteristic
520C22×C61#54611yescharacteristic
521C22×C61#54611yescharacteristic
522C22×C61#54611yescharacteristic
523C22×C61#54711yescharacteristic
524C22×C61#54711yescharacteristic
525C22×C61#54711yescharacteristic
526C22×C61#54711yescharacteristic
527C22×C61#55111yescharacteristic
528C22×C61#55311yescharacteristic
529C22×C61#55311yescharacteristic
530C22×C61#55911yescharacteristic
531C22×C61#56011yescharacteristic
532C22×C61#56211yescharacteristic
533C22×C61#56211yescharacteristic
534C22×C61#56311yescharacteristic
535C2×D61—42no—
536C2×D61—42no—
537C2×D61—42no—
538C2×D61—42no—
539C2×D61—42no—
540C2×D61—42no—
541C2×D61—42no—
542C2×D61—81no—
543C2×D61—81no—
544C2×D61—81no—
545C2×D61—81no—
546C2×D61—81no—
547C2×D61—81no—
548C2×D61—81no—
549C2×D61—81no—
550C4×C61—24no—
551C4×C61—24no—
552C4×C61—42no—
553C4×C61—42no—
554C4×C61—81no—
555C4×C61—81no—
556Dic61—42no—
557Dic61—42no—
558Dic61—42no—
559Dic61—42no—
560Dic61—42no—
561Dic61—81no—
562Dic61—81no—
563C22×#123—611no—
564C2×#388—611no—
565C2×#388D6111yescharacteristic, complemented
566#1445—611no—
567#1445—611no—
568#1439—611no—
569#1439—611no—
570#1438—611no—
571#1438—611no—
572#1437—611no—
573#1437—611no—
574C4⋊#95—611no—
575C4⋊#95—611no—
576C22⋊#95—611no—
577C22⋊#95—611no—
578C2×C61—44no—
579C2×C61#230911yescharacteristic
580C2×C61#233511yescharacteristic
581C2×C61#233511yescharacteristic
582C2×C61#233911yescharacteristic
583C2×C61#233911yescharacteristic
584C2×C61#237411yescharacteristic
585C2×C61#237611yescharacteristic
586C2×C61#270311yescharacteristic
587C2×C61#270311yescharacteristic
588C2×C61#270611yescharacteristic
589C2×C61#270611yescharacteristic
590C2×C61#271011yescharacteristic
591C2×C61#271011yescharacteristic
592C2×C61#271811yescharacteristic
593C2×C61#271811yescharacteristic
594D61—82no—
595C23×D4—611no—
596C24×C4—611no—
597C2×#123—618no—
598C2×#123—1224no—
599C2×#123—1224no—
600C22×C4⋊C4—611no—
601C22×C4⋊C4—611no—
602C22×C4⋊C4—611no—
603C22×C4⋊C4C2×D6111yescharacteristic
604C22×C22⋊C4—611no—
605C22×C22⋊C4—611no—
606C22×C22⋊C4—611no—
607C22×C22⋊C4—611no—
608C22×C22⋊C4—611no—
609C22×C22⋊C4—611no—
610C22×C22⋊C4—611no—
611C22×C22⋊C4—611no—
612C22×C22⋊C4C2×D6111yescharacteristic
613C22×C22⋊C4C2×D6111yescharacteristic
614C22×C22⋊C4C2×D6111yescharacteristic
615C22×C42—611no—
616C22×C42C2×D6111yescharacteristic
617#388—24no—
618#388—1224no—
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×#95—611no—
633C2×#95C2×D6111yescharacteristic
634C2×#95C2×D6111yescharacteristic
635C61#1450611yescharacteristic, complemented, Sylow
636C25—611no—
637C25C22×D6111yescharacteristic
638C22×D4—614no—
639C22×D4—1222no—
640C22×D4—1222no—
641C22×D4—2441no—
642C22×D4—2441no—
643C22×D4—2441no—
644C22×D4—2441no—
645C23×C4—611no—
646C23×C4—611no—
647C23×C4—611no—
648C23×C4—611no—
649C23×C4—611no—
650C23×C4—614no—
651C23×C4—611no—
652C23×C4—611no—
653C23×C4—1222no—
654C23×C4—1222no—
655C23×C4—2441no—
656C23×C4—2441no—
657C23×C4—2441no—
658C23×C4—2441no—
659C23×C4C22×D6111yescharacteristic
660C23×C4C22×D6111yescharacteristic
661C23×C4C22×D6111yescharacteristic
662C23×C4C22×D6111yescharacteristic
663C23×C4C22×D6111yescharacteristic
664C23×C4C22×D6111yescharacteristic
665#123—12232no—
666C2×C4⋊C4—22no—
667C2×C4⋊C4—22no—
668C2×C4⋊C4—41no—
669C2×C4⋊C4—614no—
670C2×C4⋊C4—614no—
671C2×C4⋊C4—1222no—
672C2×C4⋊C4—1222no—
673C2×C4⋊C4—1222no—
674C2×C4⋊C4—1222no—
675C2×C4⋊C4—1222no—
676C2×C4⋊C4—1222no—
677C2×C4⋊C4—2441no—
678C2×C22⋊C4—22no—
679C2×C22⋊C4—22no—
680C2×C22⋊C4—22no—
681C2×C22⋊C4—22no—
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—1222no—
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×C22⋊C4D24414yes—
710C2×C22⋊C4C22⋊D6114yes—
711C2×C42—22no—
712C2×C42—22no—
713C2×C42—41no—
714C2×C42—1222no—
715C2×C42—1222no—
716C2×C42—2441no—
717#95—22no—
718#95—22no—
719#95—1222no—
720#95—1222no—
721#95—2441no—
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#95—2441no—
731#95—2441no—
732#95—2441no—
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—1221no—
747C24—1221no—
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—
761C24C2×D24412yes—
762C24C2×C22⋊D6112yes—
763C24C23×D6111yescharacteristic
764C2×D4—1228no—
765C2×D4—2444no—
766C2×D4—2444no—
767C2×D4—2444no—
768C2×D4—2444no—
769C2×D4—2444no—
770C2×D4—2444no—
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—21no—
805C22×C4—612no—
806C22×C4—612no—
807C22×C4—612no—
808C22×C4—612no—
809C22×C4—612no—
810C22×C4—1221no—
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—1221no—
834C22×C4—1221no—
835C22×C4—1221no—
836C22×C4—1221no—
837C22×C4—1221no—
838C22×C4—1221no—
839C22×C4—1221no—
840C22×C4—1228no—
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×C4—2444no—
861C22×C4C2×C4×D6112yes—
862C22×C4C2×C4×D6112yes—
863C22×C4C2×D24412yes—
864C22×C4C2×D24412yes—
865C22×C4#1175822412yes—
866C22×C4#1175822412yes—
867C22×C4C2×C22⋊D6112yes—
868C22×C4C2×C22⋊D6112yes—
869C4⋊C4—44no—
870C4⋊C4—1228no—
871C4⋊C4—1228no—
872C4⋊C4—2444no—
873C22⋊C4—44no—
874C22⋊C4—44no—
875C22⋊C4—1228no—
876C22⋊C4—1228no—
877C22⋊C4—2444no—
878C22⋊C4—2444no—
879C22⋊C4—2444no—
880C22⋊C4—2444no—
881C22⋊C4—2444no—
882C22⋊C4—2444no—
883C22⋊C4#11758198116yescomplemented
884C42—44no—
885C42—2444no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—22no—
895C23—22no—
896C23—22no—
897C23—22no—
898C23—22no—
899C23—22no—
900C23—22no—
901C23—22no—
902C23—22no—
903C23—22no—
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—41no—
920C23—1222no—
921C23—1222no—
922C23—1222no—
923C23—1222no—
924C23—1222no—
925C23—1222no—
926C23—1222no—
927C23—2441no—
928C23—2441no—
929C23—2441no—
930C23—2441no—
931C23—2441no—
932C23—2441no—
933C23—2441no—
934C23—2441no—
935C23—2441no—
936C23—2441no—
937C23—2441no—
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—
954C23—2441no—
955C23C2×#1175819814yes—
956C23C22×C4×D6111yescharacteristic
957C23C22×C22⋊D6111yescharacteristic
958C23C22×D24411yescharacteristic
959C23#41×D6111yescharacteristic
960C23#41×D6111yescharacteristic
961C23C2×#1175822411yescharacteristic
962C23C2×#1175822411yescharacteristic
963C23#1451982211yescharacteristic
964C23#1451982211yescharacteristic
965C23#1451982311yescharacteristic
966C23#1451982311yescharacteristic
967C23#1451982311yescharacteristic
968C23#1451982311yescharacteristic
969C23#1451982411yescharacteristic
970C23#1451982411yescharacteristic
971D4—24416no—
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—22no—
989C2×C4—22no—
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—41no—
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—2441no—
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—24416no—
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×C4—2441no—
1062C2×C4C2×#1175819814yes—
1063C2×C4C2×#1175819814yes—
1064C22—24no—
1065C22—24no—
1066C22—24no—
1067C22—42no—
1068C22—42no—
1069C22—42no—
1070C22—42no—
1071C22—42no—
1072C22—42no—
1073C22—42no—
1074C22—42no—
1075C22—42no—
1076C22—42no—
1077C22—42no—
1078C22—42no—
1079C22—4881no—
1080C22—4881no—
1081C22—4881no—
1082C22—4881no—
1083C22—4881no—
1084C22—4881no—
1085C22—4881no—
1086C22—4881no—
1087C22—2442no—
1088C22—2442no—
1089C22—2442no—
1090C22—2442no—
1091C22—2442no—
1092C22—2442no—
1093C22—2442no—
1094C22C22×#1175819811yescharacteristic
1095C22C4×#1175822411yescharacteristic
1096C22C4×#1175822411yescharacteristic
1097C22#1684023611yescharacteristic
1098C22#1684023611yescharacteristic
1099C22#1684024111yescharacteristic
1100C22#1684024111yescharacteristic
1101C22#1684032611yescharacteristic
1102C22#1684032611yescharacteristic
1103C22#1684033111yescharacteristic
1104C22#1684033111yescharacteristic
1105C22#1684034611yescharacteristic
1106C22#1684034911yescharacteristic
1107C22#1684035311yescharacteristic
1108C22#1684035611yescharacteristic
1109C22#1684036411yescharacteristic
1110C22#1684036511yescharacteristic
1111C22#1684037811yescharacteristic
1112C22#1684038111yescharacteristic
1113C22#1684040611yescharacteristic
1114C22#1684040611yescharacteristic
1115C22#1684040711yescharacteristic
1116C22#1684040711yescharacteristic
1117C22#1684041111yescharacteristic
1118C22#1684041111yescharacteristic
1119C22#1684041611yescharacteristic
1120C22#1684041611yescharacteristic
1121C22#1684043511yescharacteristic
1122C22#1684046311yescharacteristic
1123C22#1684046411yescharacteristic
1124C22#1684049411yescharacteristic
1125C22#1684050011yescharacteristic
1126C22#1684050611yescharacteristic
1127C22#1684050911yescharacteristic
1128C22#1684051411yescharacteristic
1129C4—24no—
1130C4—24no—
1131C4—42no—
1132C4—42no—
1133C4—81no—
1134C4—81no—
1135C4—4881no—
1136C4—4881no—
1137C4—2442no—
1138C4—2442no—
1139C4—2442no—
1140C4—2442no—
1141C4—2442no—
1142C2—44no—
1143C2—4882no—
1144C2#2144839911yescharacteristic
1145C2#2144860211yescharacteristic
1146C2#2144861411yescharacteristic
1147C2#2144864411yescharacteristic
1148C2#2144864411yescharacteristic
1149C2#2144894911yescharacteristic
1150C2#2144896511yescharacteristic
1151C2#2145245811yescharacteristic
1152C2#2145246011yescharacteristic
1153C2#2145250311yescharacteristic
1154C2#2145250511yescharacteristic
1155C2#2145255511yescharacteristic
1156C2#2145255911yescharacteristic
1157C2#2145266311yescharacteristic
1158C2#2145266711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC2×C61×#388C2
socle, cosocleC24×C61C24
prime radicalC23×C22⋊D61C22
hypercenterC2×#388D61
hypocenterC61#14506
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C2×#16839655C2semidirect
3. #21444088C2semidirect
4. #21444086C2semidirect
5. #21444065C2semidirect
6. #21444061C2semidirect
9. #21444057C2semidirect
10. #21444055C2semidirect
11. #21444049C2semidirect
12. #21444048C2semidirect
13. #21444041C2semidirect
14. #21444041C2semidirect
15. C2×C61×#388C2semidirect
20. C2×#14519761C4semidirect
292. C22⋊C4×C61C22⋊C4semidirect
565. C2×#388D61semidirect
635. C61#14506semidirect
883. C22⋊C4#11758198semidirect

Maximal subgroups

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

subgroupindex
C22×#145197612
C2×#168396552
#214440882
#214440862
#214440652
#214440612
#214440582
#214440572
#214440552
#214440492
#214440482
#214440412
C2×C61×#3882
#1450661