Finite Group Databasebeta

← #29603189

Subgroups — #29603189

Order 15616.

2038 conjugacy classes of subgroups.

The subgroup lattice has 1180 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839662C211yesmaximal, characteristic
2C2×#16839662C211yesmaximal, characteristic
3C2×#16839662C211yesmaximal, characteristic
4C2×#16839654C211yesmaximal, characteristic, complemented
5C2×#16839653C211yesmaximal, characteristic, complemented
6C2×#16839650C211yesmaximal, characteristic, complemented
7C2×#16839631C211yesmaximal, characteristic, complemented
8C2×C4×#11758196C211yesmaximal, characteristic, complemented
9#21444064C211yesmaximal, characteristic, complemented
10#21444063C211yesmaximal, characteristic, complemented
11#21444062C211yesmaximal, characteristic, complemented
12#21444061C211yesmaximal, characteristic, complemented
13#21444047C211yesmaximal, characteristic, complemented
14#95×Dic61C211yesmaximal, characteristic, complemented
15C2×C61×#388C211yesmaximal, characteristic, complemented
16C23×C22⋊D61C2211yescharacteristic
17C22×C4⋊Dic61C2211yescharacteristic
18C22×#11758196C2211yescharacteristic
19C22×#11758196C2211yescharacteristic
20C22×#11758196C2211yescharacteristic
21C22×#11758196C2211yescharacteristic
22C22×#11758196C2211yescharacteristic
23C22×C22⋊Dic61C2211yescharacteristic
24C22×C22⋊Dic61C2211yescharacteristic
25C22×C22⋊Dic61C2211yescharacteristic
26C22×#11758198C2211yescharacteristic
27C22×#11758198C2211yescharacteristic
28C22×#11758198C2211yescharacteristic
29C22×#11758198C2211yescharacteristic
30C22×#11758198C2211yescharacteristic
31C22×#11758198C2211yescharacteristic
32C22×C4×Dic61C2211yescharacteristic
33C22×C4×Dic61C2211yescharacteristic
34C22×C4×Dic61C2211yescharacteristic
35C22×C4×Dic61C2211yescharacteristic
36#16839662—24no—
37#16839662—24no—
38#16839662C418yescomplemented
39#16839654—24no—
40#16839653—24no—
41#16839650—24no—
42#16839631—24no—
43C4×#11758196—24no—
44C2×#14519684C2211yescharacteristic
45C2×#14519684C2211yescharacteristic
46C2×#14519684C2211yescharacteristic
47C2×#14519684C2211yescharacteristic
48C2×#14519684C2211yescharacteristic
49C2×#14519684C2211yescharacteristic
50C2×#14519684C2211yescharacteristic
51C2×#14519684C2211yescharacteristic
52C22×C4⋊C4×C61C2211yescharacteristic
53C22×C22⋊C4×C61C2211yescharacteristic
54C22×C22⋊C4×C61C2211yescharacteristic
55C22×C22⋊C4×C61C2211yescharacteristic
56C22×C42×C61C2211yescharacteristic
57C61×#388—24no—
58C2×#95×C61C2211yescharacteristic
59C2×#95×C61C2211yescharacteristic
60C24×D61C2311yescharacteristic
61C22×C22⋊D61—22no—
62C22×C22⋊D61—22no—
63C22×C22⋊D61—22no—
64C22×C22⋊D61—22no—
65C22×C22⋊D61—22no—
66C22×C22⋊D61—22no—
67C22×C22⋊D61C2×C414yes—
68C23×Dic61C2311yescharacteristic
69C23×Dic61C2311yescharacteristic
70C23×Dic61C2311yescharacteristic
71C23×Dic61C2311yescharacteristic
72C23×Dic61C2311yescharacteristic
73C23×Dic61C2311yescharacteristic
74C23×Dic61C2311yescharacteristic
75C2×C4⋊Dic61—22no—
76C2×C4⋊Dic61—22no—
77C2×C4⋊Dic61—41no—
78C2×#11758196—22no—
79C2×#11758196—22no—
80C2×#11758196—22no—
81C2×#11758196—22no—
82C2×#11758196—22no—
83C2×#11758196—22no—
84C2×#11758196—22no—
85C2×#11758196—22no—
86C2×#11758196—22no—
87C2×#11758196—22no—
88C2×#11758196—22no—
89C2×#11758196—41no—
90C2×#11758196—41no—
91C2×#11758196C2×C414yes—
92C2×#11758196D414yes—
93C2×C22⋊Dic61—22no—
94C2×C22⋊Dic61—22no—
95C2×C22⋊Dic61—22no—
96C2×C22⋊Dic61—22no—
97C2×C22⋊Dic61—22no—
98C2×C22⋊Dic61—41no—
99C2×C22⋊Dic61—41no—
100C2×C22⋊Dic61—41no—
101C2×C22⋊Dic61C2×C414yes—
102C2×#11758198—22no—
103C2×#11758198—22no—
104C2×#11758198—22no—
105C2×#11758198—22no—
106C2×#11758198—22no—
107C2×#11758198—22no—
108C2×#11758198—22no—
109C2×#11758198—22no—
110C2×#11758198—22no—
111C2×#11758198—22no—
112C2×#11758198—22no—
113C2×#11758198—22no—
114C2×#11758198—41no—
115C2×#11758198—41no—
116C2×#11758198—41no—
117C2×#11758198—41no—
118C2×#11758198C2×C414yes—
119C2×#11758198C2×C414yes—
120C2×C4×Dic61—22no—
121C2×C4×Dic61—22no—
122C2×C4×Dic61—22no—
123C2×C4×Dic61—22no—
124C2×C4×Dic61—22no—
125C2×C4×Dic61—22no—
126C2×C4×Dic61—22no—
127C2×C4×Dic61—22no—
128C2×C4×Dic61—22no—
129C2×C4×Dic61—22no—
130C2×C4×Dic61C2×C414yes—
131C2×C4×Dic61D414yes—
132#14519684—22no—
133#14519684—22no—
134#14519684—22no—
135#14519684—22no—
136#14519684—22no—
137#14519684—22no—
138#14519684—22no—
139#14519684D414yescomplemented
140C25×C61C2311yescharacteristic
141C23×C4×C61C2311yescharacteristic
142C23×C4×C61C2311yescharacteristic
143C23×C4×C61C2311yescharacteristic
144C23×C4×C61C2311yescharacteristic
145C23×C4×C61C2311yescharacteristic
146C23×C4×C61C2311yescharacteristic
147C2×C4⋊C4×C61—22no—
148C2×C4⋊C4×C61—22no—
149C2×C4⋊C4×C61—41no—
150C2×C22⋊C4×C61—22no—
151C2×C22⋊C4×C61—22no—
152C2×C22⋊C4×C61—22no—
153C2×C22⋊C4×C61—22no—
154C2×C22⋊C4×C61—22no—
155C2×C22⋊C4×C61—22no—
156C2×C22⋊C4×C61—22no—
157C2×C22⋊C4×C61—41no—
158C2×C22⋊C4×C61C2×C414yes—
159C2×C42×C61—22no—
160C2×C42×C61—22no—
161C2×C42×C61—22no—
162#95×C61—22no—
163#95×C61D414yescomplemented
164C24×C61—21no—
165C24×C61—21no—
166C24×C61—21no—
167C24×C61—21no—
168C24×C61—21no—
169C24×C61—21no—
170C24×C61—21no—
171C24×C61—21no—
172C24×C61—21no—
173C24×C61—21no—
174C24×C61—21no—
175C24×C61—21no—
176C24×C61—21no—
177C24×C61—21no—
178C24×C61C22×C412yes—
179C24×C61C2411yescharacteristic
180C23×D61—21no—
181C23×D61—21no—
182C23×D61—21no—
183C23×D61—21no—
184C23×D61—21no—
185C23×D61—21no—
186C23×D61—21no—
187C23×D61—21no—
188C23×D61—21no—
189C23×D61—21no—
190C23×D61—21no—
191C23×D61—21no—
192C23×D61—21no—
193C23×D61—21no—
194C23×D61C22×C412yes—
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×C61—21no—
219C22×C4×C61—21no—
220C22×C4×C61—21no—
221C22×C4×C61—21no—
222C22×C4×C61—21no—
223C22×C4×C61—21no—
224C22×C4×C61—21no—
225C22×C4×C61—21no—
226C22×C4×C61—21no—
227C22×C4×C61—21no—
228C22×C4×C61C22×C412yes—
229C22×C4×C61C22×C412yes—
230C22×C4×C61C2×D412yes—
231C22×C4×C61C2×D412yes—
232C22×C4×C61C2×D412yes—
233C22×C4×C61C2×D412yes—
234C22×C4×C61C2×D412yes—
235C22×C4×C61C2×D412yes—
236C22×C4×C61#4112yes—
237C2×C22⋊D61—28no—
238C2×C22⋊D61—28no—
239C2×C22⋊D61—28no—
240C2×C22⋊D61—44no—
241C2×C22⋊D61—44no—
242C2×C22⋊D61—44no—
243C2×C22⋊D61—44no—
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—21no—
279C22×Dic61C22×C412yes—
280C22×Dic61C22×C412yes—
281C22×Dic61C22×C412yes—
282C22×Dic61C2×D412yes—
283C22×Dic61C2×D412yes—
284C22×Dic61C2×D412yes—
285C22×Dic61C2×D412yes—
286C22×Dic61C2×D412yes—
287C22×Dic61C2×D412yes—
288C22×Dic61#4112yes—
289C22×Dic61#4112yes—
290C22×Dic61#4112yes—
291C22×Dic61#4112yes—
292C22×Dic61#4112yes—
293C4⋊C4×C61—44no—
294C22⋊C4×C61—28no—
295C22⋊C4×C61—44no—
296C22⋊C4×C61—44no—
297C42×C61—44no—
298C22⋊Dic61—28no—
299C22⋊Dic61—44no—
300C22⋊Dic61—44no—
301#11758198—28no—
302#11758198—28no—
303#11758198—44no—
304#11758198—44no—
305#11758198—44no—
306#11758198—44no—
307C4⋊Dic61—44no—
308#11758196—28no—
309#11758196—28no—
310#11758196—44no—
311#11758196—44no—
312#11758196—44no—
313C4×Dic61—28no—
314C4×Dic61—28no—
315C4×Dic61—44no—
316C4×Dic61—44no—
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×C61—41no—
341C23×C61—41no—
342C23×C61—41no—
343C23×C61—41no—
344C23×C61—41no—
345C23×C61—41no—
346C23×C61—41no—
347C23×C61—41no—
348C23×C61—41no—
349C23×C61—41no—
350C23×C61—41no—
351C23×C61—41no—
352C23×C61C23×C411yescharacteristic
353C23×C61C22×D411yescharacteristic
354C23×C61C22×D411yescharacteristic
355C23×C61C22×D411yescharacteristic
356C23×C61C22×D411yescharacteristic
357C23×C61C2×#4111yescharacteristic
358C23×C61C2×#4111yescharacteristic
359C23×C61C2×#4111yescharacteristic
360C23×C61C2×#4111yescharacteristic
361C23×C61C2×#4111yescharacteristic
362C23×C61C2×#4111yescharacteristic
363C23×C61H(5,𝔽2)11yescharacteristic
364C23×C61H(5,𝔽2)11yescharacteristic
365C23×C612−1+411yescharacteristic
366C23×C612−1+411yescharacteristic
367C22×D61—22no—
368C22×D61—22no—
369C22×D61—22no—
370C22×D61—22no—
371C22×D61—22no—
372C22×D61—22no—
373C22×D61—22no—
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—
391C22×D61—41no—
392C22×D61—41no—
393C22×D61—41no—
394C22×D61—41no—
395C22×D61—41no—
396C22×D61—41no—
397C22×D61—41no—
398C22×D61—41no—
399C22×D61—41no—
400C22×D61—41no—
401C22×D61—41no—
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—22no—
410C2×C4×C61—22no—
411C2×C4×C61—22no—
412C2×C4×C61—22no—
413C2×C4×C61—22no—
414C2×C4×C61—22no—
415C2×C4×C61—22no—
416C2×C4×C61—22no—
417C2×C4×C61—22no—
418C2×C4×C61—22no—
419C2×C4×C61—22no—
420C2×C4×C61—22no—
421C2×C4×C61—22no—
422C2×C4×C61—22no—
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×C61—41no—
432C2×C4×C61—41no—
433C2×C4×C61—41no—
434C2×C4×C61—41no—
435C2×C4×C61—41no—
436C2×C4×C61—41no—
437C2×C4×C61—41no—
438C2×C4×C61—41no—
439C2×C4×C61—41no—
440C2×C4×C61—41no—
441C2×C4×C61—41no—
442C2×C4×C61C4×D414yes—
443C2×C4×C61#12714yes—
444C22⋊D61—416no—
445C2×Dic61—22no—
446C2×Dic61—22no—
447C2×Dic61—22no—
448C2×Dic61—22no—
449C2×Dic61—22no—
450C2×Dic61—22no—
451C2×Dic61—22no—
452C2×Dic61—22no—
453C2×Dic61—22no—
454C2×Dic61—22no—
455C2×Dic61—22no—
456C2×Dic61—22no—
457C2×Dic61—22no—
458C2×Dic61—22no—
459C2×Dic61—22no—
460C2×Dic61—22no—
461C2×Dic61—22no—
462C2×Dic61—22no—
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—
484C2×Dic61—41no—
485C2×Dic61—41no—
486C2×Dic61#11714yes—
487C2×Dic61C4×D414yes—
488C2×Dic61C4×D414yes—
489C2×Dic61C4×D414yes—
490C2×Dic61#12114yes—
491C2×Dic61#12314yes—
492C2×Dic61#12414yes—
493C2×Dic61#12614yes—
494#14001—611nomaximal, Sylow
495C22×C61—42no—
496C22×C61—42no—
497C22×C61—42no—
498C22×C61—42no—
499C22×C61—42no—
500C22×C61—42no—
501C22×C61—42no—
502C22×C61—81no—
503C22×C61—81no—
504C22×C61—81no—
505C22×C61—81no—
506C22×C61—81no—
507C22×C61—81no—
508C22×C61—81no—
509C22×C61—81no—
510C22×C61C2×#11711yescharacteristic
511C22×C61C2×C4×D411yescharacteristic
512C22×C61C2×C4×D411yescharacteristic
513C22×C61C2×C4×D411yescharacteristic
514C22×C61C2×C4×D411yescharacteristic
515C22×C61#52011yescharacteristic
516C22×C61#52011yescharacteristic
517C22×C61C2×#12111yescharacteristic
518C22×C61C2×#12311yescharacteristic
519C22×C61C2×#12411yescharacteristic
520C22×C61C2×#12611yescharacteristic
521C22×C61C2×#12711yescharacteristic
522C22×C61#53211yescharacteristic
523C22×C61#53211yescharacteristic
524C22×C61#53211yescharacteristic
525C22×C61#53511yescharacteristic
526C22×C61#53611yescharacteristic
527C22×C61#54211yescharacteristic
528C22×C61#54211yescharacteristic
529C22×C61D4211yescharacteristic
530C22×C61D4211yescharacteristic
531C22×C61#54711yescharacteristic
532C22×C61#54711yescharacteristic
533C22×C61#54711yescharacteristic
534C22×C61#54711yescharacteristic
535C22×C61#54811yescharacteristic
536C22×C61#54811yescharacteristic
537C22×C61#55011yescharacteristic
538C22×C61#55011yescharacteristic
539C22×C61#55311yescharacteristic
540C22×C61#55311yescharacteristic
541C22×C61#55511yescharacteristic
542C22×C61#55511yescharacteristic
543C22×C61#55611yescharacteristic
544C22×C61#55611yescharacteristic
545C2×D61—42no—
546C2×D61—42no—
547C2×D61—42no—
548C2×D61—42no—
549C2×D61—42no—
550C2×D61—42no—
551C2×D61—42no—
552C2×D61—81no—
553C2×D61—81no—
554C2×D61—81no—
555C2×D61—81no—
556C2×D61—81no—
557C2×D61—81no—
558C2×D61—81no—
559C2×D61—81no—
560C4×C61—24no—
561C4×C61—24no—
562C4×C61—42no—
563C4×C61—42no—
564C4×C61—42no—
565C4×C61—81no—
566Dic61—24no—
567Dic61—42no—
568Dic61—42no—
569Dic61—42no—
570Dic61—42no—
571Dic61—81no—
572Dic61#38818yescomplemented
573C2×#390—611no—
574C2×#390—611no—
575C2×#390—611no—
576C2×#388—611no—
577C2×#388—611no—
578C2×#388—611no—
579C2×#388D6111yescharacteristic, complemented
580C2×#384—611no—
581C2×C4×C4⋊C4—611no—
582#1439—611no—
583#1439—611no—
584#1439—611no—
585#1439—611no—
586C4⋊#95—611no—
587C4×#95—611no—
588C2×C61—82no—
589C2×C61C2×#38811yescharacteristic
590C2×C61C4×#12711yescharacteristic
591C2×C61#232611yescharacteristic
592C2×C61#235411yescharacteristic
593C2×C61#235411yescharacteristic
594C2×C61#236111yescharacteristic
595C2×C61#236111yescharacteristic
596C2×C61#249111yescharacteristic
597C2×C61#249111yescharacteristic
598C2×C61#250011yescharacteristic
599C2×C61#250111yescharacteristic
600C2×C61#251211yescharacteristic
601C2×C61#251211yescharacteristic
602C2×C61#254111yescharacteristic
603C2×C61#254511yescharacteristic
604D61—82no—
605C23×D4—611no—
606C22×C4⋊C4—611no—
607C22×C4⋊C4—611no—
608C22×C4⋊C4—611no—
609C22×C4⋊C4—611no—
610C22×C4⋊C4—611no—
611C22×C4⋊C4—611no—
612C22×C4⋊C4C2×D6111yescharacteristic
613C22×C22⋊C4—611no—
614C22×C22⋊C4—611no—
615C22×C22⋊C4—611no—
616C22×C22⋊C4—611no—
617C22×C22⋊C4—611no—
618C22×C22⋊C4—611no—
619C22×C22⋊C4—611no—
620C22×C22⋊C4—611no—
621C22×C22⋊C4—611no—
622C22×C22⋊C4C2×D6111yescharacteristic
623C22×C22⋊C4C2×D6111yescharacteristic
624C22×C22⋊C4C2×D6111yescharacteristic
625C22×C42—611no—
626C22×C42—611no—
627C22×C42—611no—
628C22×C42—611no—
629C22×C42C2×D6111yescharacteristic
630#390—618no—
631#390—1224no—
632#390—1224no—
633#388—24no—
634#388—1224no—
635#388—1224no—
636#388—1224no—
637#384—1224no—
638C4×C4⋊C4—1224no—
639C2×#95—611no—
640C2×#95—611no—
641C2×#95—611no—
642C2×#95—611no—
643C2×#95—611no—
644C2×#95—611no—
645C2×#95—611no—
646C2×#95—611no—
647C2×#95C2×D6111yescharacteristic
648C2×#95C2×D6111yescharacteristic
649C61#1400111yescharacteristic, complemented, Sylow
650C25—611no—
651C25C22×D6111yescharacteristic
652C22×D4—614no—
653C22×D4—1222no—
654C22×D4—1222no—
655C22×D4—1222no—
656C22×D4—1222no—
657C22×D4—1222no—
658C22×D4—1222no—
659C23×C4—611no—
660C23×C4—611no—
661C23×C4—611no—
662C23×C4—611no—
663C23×C4—611no—
664C23×C4—611no—
665C23×C4—611no—
666C23×C4C22×D6111yescharacteristic
667C23×C4C22×D6111yescharacteristic
668C23×C4C22×D6111yescharacteristic
669C23×C4C22×D6111yescharacteristic
670C23×C4C22×D6111yescharacteristic
671C23×C4C22×D6111yescharacteristic
672C2×C4⋊C4—22no—
673C2×C4⋊C4—22no—
674C2×C4⋊C4—41no—
675C2×C4⋊C4—614no—
676C2×C4⋊C4—614no—
677C2×C4⋊C4—1222no—
678C2×C4⋊C4—1222no—
679C2×C4⋊C4—1222no—
680C2×C4⋊C4—1222no—
681C2×C4⋊C4—1222no—
682C2×C4⋊C4—1222no—
683C2×C4⋊C4—1222no—
684C2×C4⋊C4—1222no—
685C2×C4⋊C4—1222no—
686C2×C4⋊C4—1222no—
687C2×C4⋊C4—1222no—
688C2×C4⋊C4—1222no—
689C2×C4⋊C4—1222no—
690C2×C4⋊C4—2441no—
691C2×C4⋊C4—2441no—
692C2×C4⋊C4—2441no—
693C2×C22⋊C4—22no—
694C2×C22⋊C4—22no—
695C2×C22⋊C4—22no—
696C2×C22⋊C4—22no—
697C2×C22⋊C4—22no—
698C2×C22⋊C4—22no—
699C2×C22⋊C4—22no—
700C2×C22⋊C4—41no—
701C2×C22⋊C4—614no—
702C2×C22⋊C4—614no—
703C2×C22⋊C4—614no—
704C2×C22⋊C4—1222no—
705C2×C22⋊C4—1222no—
706C2×C22⋊C4—1222no—
707C2×C22⋊C4—1222no—
708C2×C22⋊C4—1222no—
709C2×C22⋊C4—1222no—
710C2×C22⋊C4—1222no—
711C2×C22⋊C4—1222no—
712C2×C22⋊C4—1222no—
713C2×C22⋊C4—1222no—
714C2×C22⋊C4—1222no—
715C2×C22⋊C4—1222no—
716C2×C22⋊C4—1222no—
717C2×C22⋊C4—1222no—
718C2×C22⋊C4—1222no—
719C2×C22⋊C4—1222no—
720C2×C22⋊C4—1222no—
721C2×C22⋊C4—2441no—
722C2×C22⋊C4—2441no—
723C2×C22⋊C4—2441no—
724C2×C22⋊C4—2441no—
725C2×C22⋊C4—2441no—
726C2×C22⋊C4—2441no—
727C2×C22⋊C4—2441no—
728C2×C22⋊C4C4×D6114yes—
729C2×C42—22no—
730C2×C42—22no—
731C2×C42—22no—
732C2×C42—614no—
733C2×C42—614no—
734C2×C42—1222no—
735C2×C42—1222no—
736C2×C42—1222no—
737C2×C42—1222no—
738C2×C42—1222no—
739C2×C42—1222no—
740C2×C42—1222no—
741C2×C42—1222no—
742C2×C42—1222no—
743C2×C42—1222no—
744#95—22no—
745#95—614no—
746#95—1222no—
747#95—1222no—
748#95—1222no—
749#95—1222no—
750#95—1222no—
751#95—1222no—
752#95—1222no—
753#95C22⋊D6114yescomplemented
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24—612no—
769C24—1221no—
770C24—1221no—
771C24—1221no—
772C24—1221no—
773C24—1221no—
774C24—1221no—
775C24—1221no—
776C24—1221no—
777C24—1221no—
778C24—1221no—
779C24—1221no—
780C24—1221no—
781C24—1221no—
782C24—1221no—
783C24C2×C4×D6112yes—
784C24C23×D6111yescharacteristic
785C2×D4—1228no—
786C2×D4—1228no—
787C2×D4—1228no—
788C2×D4—2444no—
789C2×D4—2444no—
790C2×D4—2444no—
791C2×D4—2444no—
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—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—612no—
826C22×C4—612no—
827C22×C4—612no—
828C22×C4—612no—
829C22×C4—612no—
830C22×C4—612no—
831C22×C4—612no—
832C22×C4—612no—
833C22×C4—612no—
834C22×C4—612no—
835C22×C4—612no—
836C22×C4—612no—
837C22×C4—612no—
838C22×C4—612no—
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—1221no—
856C22×C4—1221no—
857C22×C4—1221no—
858C22×C4—1221no—
859C22×C4—1221no—
860C22×C4—1221no—
861C22×C4—1221no—
862C22×C4—1221no—
863C22×C4—1221no—
864C22×C4—1221no—
865C22×C4—1221no—
866C22×C4—1221no—
867C22×C4—1221no—
868C22×C4—1221no—
869C22×C4—1221no—
870C22×C4—1221no—
871C22×C4—1221no—
872C22×C4—1221no—
873C22×C4—1221no—
874C22×C4C2×C4×D6112yes—
875C22×C4C2×C4×D6112yes—
876C22×C4#1175822212yes—
877C22×C4D4×D6112yes—
878C22×C4D4×D6112yes—
879C22×C4D4×D6112yes—
880C22×C4C2×C22⋊D6112yes—
881C22×C4C2×C22⋊D6112yes—
882C22×C4C2×C22⋊D6112yes—
883C4⋊C4—44no—
884C4⋊C4—1228no—
885C4⋊C4—1228no—
886C4⋊C4—2444no—
887C4⋊C4—2444no—
888C4⋊C4—2444no—
889C4⋊C4—2444no—
890C22⋊C4—28no—
891C22⋊C4—44no—
892C22⋊C4—44no—
893C22⋊C4—1228no—
894C22⋊C4—1228no—
895C22⋊C4—1228no—
896C22⋊C4—2444no—
897C22⋊C4—2444no—
898C22⋊C4—2444no—
899C22⋊C4—2444no—
900C22⋊C4—2444no—
901C22⋊C4—2444no—
902C42—44no—
903C42—1228no—
904C42—1228no—
905C42—2444no—
906C42—2444no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—41no—
926C23—41no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—1222no—
943C23—1222no—
944C23—1222no—
945C23—1222no—
946C23—1222no—
947C23—1222no—
948C23—1222no—
949C23—2441no—
950C23—2441no—
951C23—2441no—
952C23—2441no—
953C23—2441no—
954C23—2441no—
955C23—2441no—
956C23—2441no—
957C23—2441no—
958C23—2441no—
959C23—2441no—
960C23—2441no—
961C23—2441no—
962C23—2441no—
963C23—2441no—
964C23—2441no—
965C23—2441no—
966C23—2441no—
967C23—2441no—
968C23—2441no—
969C23—2441no—
970C23—2441no—
971C23—2441no—
972C23—2441no—
973C23—2441no—
974C23—2441no—
975C23—2441no—
976C23—2441no—
977C23C22×C4×D6111yescharacteristic
978C23C2×D4×D6111yescharacteristic
979C23C2×D4×D6111yescharacteristic
980C23C2×D4×D6111yescharacteristic
981C23C22×C22⋊D6111yescharacteristic
982C23#41×D6111yescharacteristic
983C23#41×D6111yescharacteristic
984C23#41×D6111yescharacteristic
985C23#41×D6111yescharacteristic
986C23#41×D6111yescharacteristic
987C23C2×#1175822211yescharacteristic
988C23#1451982211yescharacteristic
989C23#1451982311yescharacteristic
990C23#1451982411yescharacteristic
991C23#1451982411yescharacteristic
992D4—24416no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—614no—
1034C2×C4—614no—
1035C2×C4—614no—
1036C2×C4—614no—
1037C2×C4—614no—
1038C2×C4—614no—
1039C2×C4—614no—
1040C2×C4—614no—
1041C2×C4—1222no—
1042C2×C4—1222no—
1043C2×C4—1222no—
1044C2×C4—1222no—
1045C2×C4—1222no—
1046C2×C4—1222no—
1047C2×C4—1222no—
1048C2×C4—1222no—
1049C2×C4—1222no—
1050C2×C4—1222no—
1051C2×C4—1222no—
1052C2×C4—1222no—
1053C2×C4—1222no—
1054C2×C4—1222no—
1055C2×C4—1222no—
1056C2×C4—1222no—
1057C2×C4—1222no—
1058C2×C4—1222no—
1059C2×C4—2441no—
1060C2×C4—2441no—
1061C2×C4—2441no—
1062C2×C4—2441no—
1063C2×C4—2441no—
1064C2×C4—2441no—
1065C2×C4—2441no—
1066C2×C4—2441no—
1067C2×C4—2441no—
1068C2×C4—2441no—
1069C2×C4—2441no—
1070C2×C4—2441no—
1071C2×C4—2441no—
1072C2×C4—2441no—
1073C2×C4—2441no—
1074C2×C4—2441no—
1075C2×C4—2441no—
1076C2×C4—2441no—
1077C2×C4—2441no—
1078C2×C4—2441no—
1079C2×C4—2441no—
1080C2×C4—2441no—
1081C2×C4—2441no—
1082C2×C4C4×C22⋊D6114yes—
1083C2×C4#1451977314yes—
1084C22—42no—
1085C22—42no—
1086C22—42no—
1087C22—42no—
1088C22—42no—
1089C22—42no—
1090C22—42no—
1091C22—81no—
1092C22—81no—
1093C22—81no—
1094C22—81no—
1095C22—81no—
1096C22—81no—
1097C22—81no—
1098C22—81no—
1099C22—4881no—
1100C22—4881no—
1101C22—4881no—
1102C22—4881no—
1103C22—4881no—
1104C22—4881no—
1105C22—4881no—
1106C22—4881no—
1107C22—2442no—
1108C22—2442no—
1109C22—2442no—
1110C22—2442no—
1111C22—2442no—
1112C22—2442no—
1113C22—2442no—
1114C22#117×D6111yescharacteristic
1115C22C4×D4×D6111yescharacteristic
1116C22C4×D4×D6111yescharacteristic
1117C22C4×D4×D6111yescharacteristic
1118C22C2×C4×C22⋊D6111yescharacteristic
1119C22#1684024111yescharacteristic
1120C22#1684024211yescharacteristic
1121C22#121×D6111yescharacteristic
1122C22#123×D6111yescharacteristic
1123C22#124×D6111yescharacteristic
1124C22#126×D6111yescharacteristic
1125C22C2×#1451977311yescharacteristic
1126C22#1684030811yescharacteristic
1127C22#1684030911yescharacteristic
1128C22#1684030911yescharacteristic
1129C22#1684032811yescharacteristic
1130C22#1684033411yescharacteristic
1131C22#1684037611yescharacteristic
1132C22#1684037811yescharacteristic
1133C22D4×C22⋊D6111yescharacteristic
1134C22#1684039611yescharacteristic
1135C22#1684041011yescharacteristic
1136C22#1684041011yescharacteristic
1137C22#1684041111yescharacteristic
1138C22#1684041111yescharacteristic
1139C22#1684042011yescharacteristic
1140C22#1684042111yescharacteristic
1141C22#1684043011yescharacteristic
1142C22#1684043111yescharacteristic
1143C22#1684046111yescharacteristic
1144C22#1684046311yescharacteristic
1145C22#1684047411yescharacteristic
1146C22#1684047511yescharacteristic
1147C22#1684047911yescharacteristic
1148C22#1684048011yescharacteristic
1149C4—24no—
1150C4—24no—
1151C4—42no—
1152C4—42no—
1153C4—42no—
1154C4—81no—
1155C4—618no—
1156C4—1224no—
1157C4—4881no—
1158C4—2442no—
1159C4—2442no—
1160C4—2442no—
1161C4—2442no—
1162C2—82no—
1163C2—4882no—
1164C2#388×D6111yescharacteristic
1165C2C4×#1451977311yescharacteristic
1166C2#2144852811yescharacteristic
1167C2#2144876511yescharacteristic
1168C2#2144876911yescharacteristic
1169C2#2144883211yescharacteristic
1170C2#2144883611yescharacteristic
1171C2#2145017911yescharacteristic
1172C2#2145018111yescharacteristic
1173C2#2145027911yescharacteristic
1174C2#2145028811yescharacteristic
1175C2#2145040211yescharacteristic
1176C2#2145040411yescharacteristic
1177C2#2145076211yescharacteristic
1178C2#2145079711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC2×C61×#388C2
socle, cosocleC24×C61C24
prime radicalC23×C22⋊D61C22
hypercenterC2×#388D61
hypocenterC61#14001
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
4. C2×#16839654C2semidirect
5. C2×#16839653C2semidirect
6. C2×#16839650C2semidirect
7. C2×#16839631C2semidirect
8. C2×C4×#11758196C2semidirect
9. #21444064C2semidirect
10. #21444063C2semidirect
11. #21444062C2semidirect
12. #21444061C2semidirect
13. #21444047C2semidirect
14. #95×Dic61C2semidirect
15. C2×C61×#388C2semidirect
38. #16839662C4semidirect
139. #14519684D4semidirect
163. #95×C61D4semidirect
572. Dic61#388semidirect
579. C2×#388D61semidirect
649. C61#14001semidirect
753. #95C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168396622
C2×#168396542
C2×#168396532
C2×#168396502
C2×#168396312
C2×C4×#117581962
#214440642
#214440632
#214440622
#214440612
#214440472
#95×Dic612
C2×C61×#3882
#1400161