Finite Group Databasebeta

← #29603339

Subgroups — #29603339

Order 15616.

2046 conjugacy classes of subgroups.

The subgroup lattice has 1174 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839662C211yesmaximal, characteristic
2C2×#16839653C211yesmaximal, characteristic, complemented
3C2×#16839650C211yesmaximal, characteristic, complemented
4C2×#16839638C211yesmaximal, characteristic
5C2×#16839619C211yesmaximal, characteristic, complemented
6C2×#16839609C211yesmaximal, characteristic, complemented
7#21444082C211yesmaximal, characteristic, complemented
8#21444067C211yesmaximal, characteristic, complemented
9#21444064C211yesmaximal, characteristic, complemented
10#21444058C211yesmaximal, characteristic
11#21444056C211yesmaximal, characteristic, complemented
12#21444053C211yesmaximal, characteristic, complemented
13#21444050C211yesmaximal, characteristic, complemented
14C4×#14519684C211yesmaximal, 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
30C22×C4×Dic61C2211yescharacteristic
31C22×C4×Dic61C2211yescharacteristic
32#16839662—24no—
33#16839653—24no—
34#16839650—24no—
35#16839638C418yescomplemented
36#16839619—24no—
37#16839609—24no—
38C2×#14519684C2211yescharacteristic
39C2×#14519684C2211yescharacteristic
40C2×#14519684C2211yescharacteristic
41C2×#14519684C2211yescharacteristic
42C2×#14519684C2211yescharacteristic
43C2×#14519684C2211yescharacteristic
44C2×#14519684C2211yescharacteristic
45C2×#14519684C2211yescharacteristic
46C2×#14519684C2211yescharacteristic
47C2×#14519684C2211yescharacteristic
48C2×#14519684C2211yescharacteristic
49C2×#14519684C2211yescharacteristic
50C22×C4⋊C4×C61C2211yescharacteristic
51C22×C22⋊C4×C61C2211yescharacteristic
52C22×C22⋊C4×C61C2211yescharacteristic
53C22×C22⋊C4×C61C2211yescharacteristic
54C22×C42×C61C2211yescharacteristic
55C61×#388—24no—
56C2×#95×C61C2211yescharacteristic
57C2×#95×C61C2211yescharacteristic
58C24×D61C2311yescharacteristic
59C22×C22⋊D61—22no—
60C22×C22⋊D61—22no—
61C22×C22⋊D61—22no—
62C22×C22⋊D61—22no—
63C22×C22⋊D61—41no—
64C22×C22⋊D61—41no—
65C22×C22⋊D61C2×C414yes—
66C23×Dic61C2311yescharacteristic
67C23×Dic61C2311yescharacteristic
68C23×Dic61C2311yescharacteristic
69C23×Dic61C2311yescharacteristic
70C23×Dic61C2311yescharacteristic
71C23×Dic61C2311yescharacteristic
72C23×Dic61C2311yescharacteristic
73C22×C4×D61—22no—
74C22×C4×D61—22no—
75C22×C4×D61—22no—
76C22×C4×D61—22no—
77C22×C4×D61—41no—
78C22×C4×D61—41no—
79C22×C4×D61C2×C414yes—
80C2×C4⋊Dic61—22no—
81C2×C4⋊Dic61—22no—
82C2×C4⋊Dic61—41no—
83C2×#11758196—22no—
84C2×#11758196—22no—
85C2×#11758196—22no—
86C2×#11758196—22no—
87C2×#11758196—41no—
88C2×#11758196—41no—
89C2×C22⋊Dic61—22no—
90C2×C22⋊Dic61—22no—
91C2×C22⋊Dic61—22no—
92C2×C22⋊Dic61—22no—
93C2×C22⋊Dic61—22no—
94C2×C22⋊Dic61—41no—
95C2×C22⋊Dic61—41no—
96C2×C22⋊Dic61—41no—
97C2×C22⋊Dic61C2×C414yes—
98C2×#11758198—22no—
99C2×#11758198—22no—
100C2×#11758198—22no—
101C2×#11758198—22no—
102C2×#11758198—22no—
103C2×#11758198—22no—
104C2×#11758198—22no—
105C2×#11758198—22no—
106C2×#11758198—22no—
107C2×#11758198—22no—
108C2×#11758198—22no—
109C2×#11758198—41no—
110C2×#11758198—41no—
111C2×#11758198C2×C414yes—
112C2×#11758198D414yes—
113C2×C4×Dic61—22no—
114C2×C4×Dic61—22no—
115C2×C4×Dic61—22no—
116C2×C4×Dic61—22no—
117C2×C4×Dic61—22no—
118C2×C4×Dic61—22no—
119C2×C4×Dic61—41no—
120C2×C4×Dic61—41no—
121C2×C4×Dic61—41no—
122#14519684—22no—
123#14519684—22no—
124#14519684—22no—
125#14519684—22no—
126#14519684—22no—
127#14519684—22no—
128#14519684—22no—
129#14519684—22no—
130#14519684—41no—
131#14519684C2×C414yes—
132#14519684C2×C414yes—
133#14519684D414yescomplemented
134C25×C61C2311yescharacteristic
135C23×C4×C61C2311yescharacteristic
136C23×C4×C61C2311yescharacteristic
137C23×C4×C61C2311yescharacteristic
138C23×C4×C61C2311yescharacteristic
139C23×C4×C61C2311yescharacteristic
140C23×C4×C61C2311yescharacteristic
141C2×C4⋊C4×C61—22no—
142C2×C4⋊C4×C61—22no—
143C2×C4⋊C4×C61—41no—
144C2×C22⋊C4×C61—22no—
145C2×C22⋊C4×C61—22no—
146C2×C22⋊C4×C61—22no—
147C2×C22⋊C4×C61—22no—
148C2×C22⋊C4×C61—22no—
149C2×C22⋊C4×C61—22no—
150C2×C22⋊C4×C61—22no—
151C2×C22⋊C4×C61—41no—
152C2×C22⋊C4×C61C2×C414yes—
153C2×C42×C61—22no—
154C2×C42×C61—22no—
155C2×C42×C61—22no—
156#95×C61—22no—
157#95×C61D414yescomplemented
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×C61—21no—
167C24×C61—21no—
168C24×C61—21no—
169C24×C61—21no—
170C24×C61—21no—
171C24×C61—21no—
172C24×C61C22×C412yes—
173C24×C61C2411yescharacteristic
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×D61—21no—
184C23×D61—21no—
185C23×D61—21no—
186C23×D61C22×C412yes—
187C23×D61C2×D412yes—
188C23×D61#4112yes—
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×C61—21no—
219C22×C4×C61—21no—
220C22×C4×C61—21no—
221C22×C4×C61—21no—
222C22×C4×C61C22×C412yes—
223C22×C4×C61C22×C412yes—
224C22×C4×C61C2×D412yes—
225C22×C4×C61C2×D412yes—
226C22×C4×C61C2×D412yes—
227C22×C4×C61C2×D412yes—
228C22×C4×C61C2×D412yes—
229C22×C4×C61#4112yes—
230C22×C4×C61#4112yes—
231C2×C22⋊D61—28no—
232C2×C22⋊D61—28no—
233C2×C22⋊D61—44no—
234C2×C22⋊D61—44no—
235C2×C22⋊D61—44no—
236C2×C22⋊D61—44no—
237C2×C22⋊D61—44no—
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×Dic61C22×C412yes—
278C22×Dic61C22×C412yes—
279C22×Dic61C22×C412yes—
280C22×Dic61C2×D412yes—
281C22×Dic61C2×D412yes—
282C22×Dic61C2×D412yes—
283C22×Dic61#4112yes—
284C22×Dic61#4112yes—
285C22×Dic61#4112yes—
286C22×Dic61#4112yes—
287C2×C4×D61—28no—
288C2×C4×D61—28no—
289C2×C4×D61—44no—
290C2×C4×D61—44no—
291C2×C4×D61—44no—
292C2×C4×D61—44no—
293C2×C4×D61—44no—
294C4⋊C4×C61—44no—
295C22⋊C4×C61—28no—
296C22⋊C4×C61—44no—
297C22⋊C4×C61—44no—
298C42×C61—44no—
299C22⋊Dic61—28no—
300C22⋊Dic61—44no—
301C22⋊Dic61—44no—
302#11758198—28no—
303#11758198—28no—
304#11758198—28no—
305#11758198—44no—
306#11758198—44no—
307C4⋊Dic61—44no—
308#11758196—44no—
309#11758196—44no—
310C4×Dic61—44no—
311C4×Dic61—44no—
312C4×Dic61—44no—
313C23×C61—22no—
314C23×C61—22no—
315C23×C61—22no—
316C23×C61—22no—
317C23×C61—22no—
318C23×C61—22no—
319C23×C61—22no—
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×C61—41no—
341C23×C61—41no—
342C23×C61—41no—
343C23×C61—41no—
344C23×C61—41no—
345C23×C61—41no—
346C23×C61—41no—
347C23×C61—41no—
348C23×C61C23×C411yescharacteristic
349C23×C61C22×D411yescharacteristic
350C23×C61C22×D411yescharacteristic
351C23×C61C22×D411yescharacteristic
352C23×C61C2×#4111yescharacteristic
353C23×C61C2×#4111yescharacteristic
354C23×C61C2×#4111yescharacteristic
355C23×C61C2×#4111yescharacteristic
356C23×C61C2×#4111yescharacteristic
357C23×C61C2×#4111yescharacteristic
358C23×C61C2×#4111yescharacteristic
359C23×C61H(5,𝔽2)11yescharacteristic
360C23×C61H(5,𝔽2)11yescharacteristic
361C23×C61H(5,𝔽2)11yescharacteristic
362C23×C612−1+411yescharacteristic
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—22no—
374C22×D61—22no—
375C22×D61—22no—
376C22×D61—22no—
377C22×D61—22no—
378C22×D61—22no—
379C22×D61—22no—
380C22×D61—22no—
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×D61C4×D414yes—
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—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—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×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×C61C4×D414yes—
439C2×C4×C61#12114yes—
440C22⋊D61—416no—
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—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—22no—
464C2×Dic61—22no—
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—41no—
487C2×Dic61—41no—
488C2×Dic61#11714yes—
489C2×Dic61C4×D414yes—
490C4×D61—416no—
491#14012—611nomaximal, Sylow
492C22×C61—42no—
493C22×C61—42no—
494C22×C61—42no—
495C22×C61—42no—
496C22×C61—42no—
497C22×C61—42no—
498C22×C61—42no—
499C22×C61—81no—
500C22×C61—81no—
501C22×C61—81no—
502C22×C61—81no—
503C22×C61—81no—
504C22×C61—81no—
505C22×C61—81no—
506C22×C61—81no—
507C22×C61C2×#11711yescharacteristic
508C22×C61C2×C4×D411yescharacteristic
509C22×C61C2×C4×D411yescharacteristic
510C22×C61C2×C4×D411yescharacteristic
511C22×C61C4×#4111yescharacteristic
512C22×C61#51811yescharacteristic
513C22×C61#52011yescharacteristic
514C22×C61C2×#12111yescharacteristic
515C22×C61#52511yescharacteristic
516C22×C61#52911yescharacteristic
517C22×C61#52911yescharacteristic
518C22×C61#52911yescharacteristic
519C22×C61#53211yescharacteristic
520C22×C61#53211yescharacteristic
521C22×C61#53211yescharacteristic
522C22×C61#53811yescharacteristic
523C22×C61#53911yescharacteristic
524C22×C61#54011yescharacteristic
525C22×C61#54211yescharacteristic
526C22×C61D4211yescharacteristic
527C22×C61D4211yescharacteristic
528C22×C61#54611yescharacteristic
529C22×C61#54611yescharacteristic
530C22×C61#54611yescharacteristic
531C22×C61#54611yescharacteristic
532C22×C61#54711yescharacteristic
533C22×C61#54711yescharacteristic
534C22×C61#54811yescharacteristic
535C22×C61#55011yescharacteristic
536C22×C61#55111yescharacteristic
537C22×C61#55111yescharacteristic
538C22×C61#55111yescharacteristic
539C22×C61#55311yescharacteristic
540C22×C61#55511yescharacteristic
541C22×C61#55611yescharacteristic
542C2×D61—24no—
543C2×D61—24no—
544C2×D61—24no—
545C2×D61—42no—
546C2×D61—42no—
547C2×D61—42no—
548C2×D61—42no—
549C2×D61—42no—
550C2×D61—42no—
551C2×D61—42no—
552C2×D61—42no—
553C2×D61—42no—
554C2×D61—42no—
555C2×D61—42no—
556C2×D61—42no—
557C4×C61—24no—
558C4×C61—24no—
559C4×C61—42no—
560C4×C61—42no—
561C4×C61—42no—
562C4×C61—81no—
563Dic61—24no—
564Dic61—24no—
565Dic61—42no—
566Dic61—42no—
567Dic61—42no—
568Dic61—42no—
569Dic61—81no—
570C2×#390—611no—
571C2×#388—611no—
572C2×#388—611no—
573C2×#388D6111yescharacteristic, complemented
574C2×#386—611no—
575C2×#380—611no—
576C2×C4×C22⋊C4—611no—
577#1444—611no—
578#1440—611no—
579#1439—611no—
580#1438—611no—
581#1437—611no—
582#1436—611no—
583#1436—611no—
584C4×#95—611no—
585C2×C61—82no—
586C2×C61#229311yescharacteristic
587C2×C61C4×#12111yescharacteristic
588C2×C61#233511yescharacteristic
589C2×C61#234211yescharacteristic
590C2×C61#235411yescharacteristic
591C2×C61#235811yescharacteristic
592C2×C61#236111yescharacteristic
593C2×C61#242511yescharacteristic
594C2×C61#242811yescharacteristic
595C2×C61#246111yescharacteristic
596C2×C61#246711yescharacteristic
597C2×C61#252111yescharacteristic
598C2×C61#253111yescharacteristic
599C2×C61#255511yescharacteristic
600C2×C61#256011yescharacteristic
601D61—44no—
602C23×D4—611no—
603C24×C4—611no—
604C22×C4⋊C4—611no—
605C22×C4⋊C4—611no—
606C22×C4⋊C4—611no—
607C22×C4⋊C4C2×D6111yescharacteristic
608C22×C22⋊C4—611no—
609C22×C22⋊C4—611no—
610C22×C22⋊C4—611no—
611C22×C22⋊C4—611no—
612C22×C22⋊C4—611no—
613C22×C22⋊C4—611no—
614C22×C22⋊C4—611no—
615C22×C22⋊C4—611no—
616C22×C22⋊C4C2×D6111yescharacteristic
617C22×C22⋊C4C2×D6111yescharacteristic
618C22×C22⋊C4C2×D6111yescharacteristic
619C22×C42—611no—
620C22×C42—611no—
621C22×C42—611no—
622C22×C42C2×D6111yescharacteristic
623#390—1224no—
624#388—24no—
625#388—1224no—
626#388—1224no—
627#386—618no—
628#380—1224no—
629C4×C22⋊C4—1224no—
630C2×#95—611no—
631C2×#95—611no—
632C2×#95—611no—
633C2×#95—611no—
634C2×#95—611no—
635C2×#95—611no—
636C2×#95—611no—
637C2×#95—611no—
638C2×#95—611no—
639C2×#95—611no—
640C2×#95—611no—
641C2×#95—611no—
642C2×#95C2×D6111yescharacteristic
643C2×#95C2×D6111yescharacteristic
644C61#1401211yescharacteristic, complemented, Sylow
645C25—611no—
646C25C22×D6111yescharacteristic
647C22×D4—614no—
648C22×D4—1222no—
649C22×D4—1222no—
650C22×D4—1222no—
651C22×D4—1222no—
652C22×D4—2441no—
653C22×D4—2441no—
654C23×C4—611no—
655C23×C4—611no—
656C23×C4—611no—
657C23×C4—611no—
658C23×C4—611no—
659C23×C4—611no—
660C23×C4—614no—
661C23×C4—611no—
662C23×C4—1222no—
663C23×C4—1222no—
664C23×C4—1222no—
665C23×C4—1222no—
666C23×C4—2441no—
667C23×C4—2441no—
668C23×C4C22×D6111yescharacteristic
669C23×C4C22×D6111yescharacteristic
670C23×C4C22×D6111yescharacteristic
671C23×C4C22×D6111yescharacteristic
672C23×C4C22×D6111yescharacteristic
673C23×C4C22×D6111yescharacteristic
674C2×C4⋊C4—22no—
675C2×C4⋊C4—22no—
676C2×C4⋊C4—41no—
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—2441no—
684C2×C4⋊C4—2441no—
685C2×C4⋊C4—2441no—
686C2×C22⋊C4—22no—
687C2×C22⋊C4—22no—
688C2×C22⋊C4—22no—
689C2×C22⋊C4—22no—
690C2×C22⋊C4—22no—
691C2×C22⋊C4—22no—
692C2×C22⋊C4—22no—
693C2×C22⋊C4—41no—
694C2×C22⋊C4—614no—
695C2×C22⋊C4—614no—
696C2×C22⋊C4—614no—
697C2×C22⋊C4—1222no—
698C2×C22⋊C4—1222no—
699C2×C22⋊C4—1222no—
700C2×C22⋊C4—1222no—
701C2×C22⋊C4—1222no—
702C2×C22⋊C4—1222no—
703C2×C22⋊C4—1222no—
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—2441no—
714C2×C22⋊C4—2441no—
715C2×C22⋊C4—2441no—
716C2×C22⋊C4—2441no—
717C2×C22⋊C4—2441no—
718C2×C22⋊C4C4×D6114yes—
719C2×C42—22no—
720C2×C42—22no—
721C2×C42—22no—
722C2×C42—1222no—
723C2×C42—1222no—
724C2×C42—1222no—
725C2×C42—1222no—
726C2×C42—1222no—
727C2×C42—1222no—
728C2×C42—2441no—
729C2×C42—2441no—
730C2×C42—2441no—
731#95—22no—
732#95—614no—
733#95—614no—
734#95—614no—
735#95—1222no—
736#95—1222no—
737#95—1222no—
738#95—1222no—
739#95—1222no—
740#95—1222no—
741#95—1222no—
742#95—1222no—
743#95—2441no—
744#95C22⋊D6114yescomplemented
745C24—21no—
746C24—21no—
747C24—21no—
748C24—21no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—612no—
760C24—612no—
761C24—612no—
762C24—1221no—
763C24—1221no—
764C24—1221no—
765C24—1221no—
766C24—1221no—
767C24—1221no—
768C24—1221no—
769C24—1221no—
770C24—1221no—
771C24—1221no—
772C24—1221no—
773C24—1221no—
774C24C2×C4×D6112yes—
775C24C23×D6111yescharacteristic
776C2×D4—1228no—
777C2×D4—1228no—
778C2×D4—2444no—
779C2×D4—2444no—
780C2×D4—2444no—
781C2×D4—2444no—
782C2×D4—2444no—
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—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—612no—
817C22×C4—612no—
818C22×C4—612no—
819C22×C4—612no—
820C22×C4—612no—
821C22×C4—612no—
822C22×C4—612no—
823C22×C4—612no—
824C22×C4—612no—
825C22×C4—612no—
826C22×C4—1228no—
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—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—1228no—
860C22×C4—1221no—
861C22×C4—1221no—
862C22×C4—1221no—
863C22×C4—1221no—
864C22×C4—1221no—
865C22×C4—1221no—
866C22×C4—1221no—
867C22×C4—2444no—
868C22×C4—2444no—
869C22×C4—2444no—
870C22×C4—2444no—
871C22×C4—2444no—
872C22×C4C2×C4×D6112yes—
873C22×C4C2×C4×D6112yes—
874C22×C4#1175822212yes—
875C22×C4D4×D6112yes—
876C22×C4D4×D6112yes—
877C22×C4#1175822412yes—
878C22×C4C2×C22⋊D6112yes—
879C22×C4C2×C22⋊D6112yes—
880C22×C4C2×C22⋊D6112yes—
881C4⋊C4—44no—
882C4⋊C4—2444no—
883C4⋊C4—2444no—
884C4⋊C4—2444no—
885C22⋊C4—28no—
886C22⋊C4—44no—
887C22⋊C4—44no—
888C22⋊C4—1228no—
889C22⋊C4—1228no—
890C22⋊C4—1228no—
891C22⋊C4—1228no—
892C22⋊C4—2444no—
893C22⋊C4—2444no—
894C22⋊C4—2444no—
895C22⋊C4—2444no—
896C42—44no—
897C42—2444no—
898C42—2444no—
899C42—2444no—
900C23—22no—
901C23—22no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
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—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—614no—
936C23—1222no—
937C23—1222no—
938C23—1222no—
939C23—1222no—
940C23—1222no—
941C23—1222no—
942C23—1222no—
943C23—1222no—
944C23—1222no—
945C23—1222no—
946C23—1222no—
947C23—1222no—
948C23—1222no—
949C23—1222no—
950C23—1222no—
951C23—1222no—
952C23—1222no—
953C23—1222no—
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—
970C23C22×C4×D6111yescharacteristic
971C23C2×D4×D6111yescharacteristic
972C23C2×D4×D6111yescharacteristic
973C23C22×C22⋊D6111yescharacteristic
974C23#41×D6111yescharacteristic
975C23#41×D6111yescharacteristic
976C23#41×D6111yescharacteristic
977C23#41×D6111yescharacteristic
978C23#41×D6111yescharacteristic
979C23C2×#1175822411yescharacteristic
980C23C2×#1175822211yescharacteristic
981C23#1451982211yescharacteristic
982C23#1451982311yescharacteristic
983C23#1451982311yescharacteristic
984C23#1451982411yescharacteristic
985D4—24416no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
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—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
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—614no—
1027C2×C4—614no—
1028C2×C4—1222no—
1029C2×C4—1222no—
1030C2×C4—1222no—
1031C2×C4—1222no—
1032C2×C4—1222no—
1033C2×C4—1222no—
1034C2×C4—1222no—
1035C2×C4—1222no—
1036C2×C4—1222no—
1037C2×C4—1222no—
1038C2×C4—1222no—
1039C2×C4—1222no—
1040C2×C4—1222no—
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—24416no—
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×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×C4C4×C22⋊D6114yes—
1077C2×C4#1451974814yes—
1078C22—42no—
1079C22—42no—
1080C22—42no—
1081C22—42no—
1082C22—42no—
1083C22—42no—
1084C22—42no—
1085C22—81no—
1086C22—81no—
1087C22—81no—
1088C22—81no—
1089C22—81no—
1090C22—81no—
1091C22—81no—
1092C22—81no—
1093C22—1224no—
1094C22—1224no—
1095C22—1224no—
1096C22—2442no—
1097C22—2442no—
1098C22—2442no—
1099C22—2442no—
1100C22—2442no—
1101C22—2442no—
1102C22—2442no—
1103C22—2442no—
1104C22—2442no—
1105C22—2442no—
1106C22—2442no—
1107C22—2442no—
1108C22#117×D6111yescharacteristic
1109C22C4×D4×D6111yescharacteristic
1110C22C4×D4×D6111yescharacteristic
1111C22C2×C4×C22⋊D6111yescharacteristic
1112C22C4×#1175822411yescharacteristic
1113C22#1684023411yescharacteristic
1114C22#1684024211yescharacteristic
1115C22C2×#1451974811yescharacteristic
1116C22#1684026911yescharacteristic
1117C22#1684028911yescharacteristic
1118C22#1684029411yescharacteristic
1119C22#1684029511yescharacteristic
1120C22#1684030711yescharacteristic
1121C22#1684030911yescharacteristic
1122C22#1684031111yescharacteristic
1123C22#1684035111yescharacteristic
1124C22#1684035611yescharacteristic
1125C22#1684036511yescharacteristic
1126C22#1684037611yescharacteristic
1127C22D4×C22⋊D6111yescharacteristic
1128C22#1684039611yescharacteristic
1129C22#1684040011yescharacteristic
1130C22#1684040411yescharacteristic
1131C22#1684040811yescharacteristic
1132C22#1684040911yescharacteristic
1133C22#1684041011yescharacteristic
1134C22#1684041111yescharacteristic
1135C22#1684042011yescharacteristic
1136C22#1684043111yescharacteristic
1137C22#1684043711yescharacteristic
1138C22#1684044111yescharacteristic
1139C22#1684044211yescharacteristic
1140C22#1684046311yescharacteristic
1141C22#1684047511yescharacteristic
1142C22#1684048011yescharacteristic
1143C4—24no—
1144C4—24no—
1145C4—42no—
1146C4—42no—
1147C4—42no—
1148C4—81no—
1149C4—1224no—
1150C4—1224no—
1151C4—4881no—
1152C4—2442no—
1153C4—2442no—
1154C4—2442no—
1155C4—2442no—
1156C2—82no—
1157C2—2444no—
1158C2#2144827911yescharacteristic
1159C2C4×#1451974811yescharacteristic
1160C2#2144861611yescharacteristic
1161C2#2144866311yescharacteristic
1162C2#2144876911yescharacteristic
1163C2#2144879611yescharacteristic
1164C2#2144883211yescharacteristic
1165C2#2144936611yescharacteristic
1166C2#2144940311yescharacteristic
1167C2#2144978211yescharacteristic
1168C2#2144986611yescharacteristic
1169C2#2145052911yescharacteristic
1170C2#2145066511yescharacteristic
1171C2#2145089511yescharacteristic
1172C2#2145096211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC2×C61×#388C2
socle, cosocleC24×C61C24
prime radicalC23×C22⋊D61C22
hypercenterC2×#388D61
hypocenterC61#14012
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C2×#16839653C2semidirect
3. C2×#16839650C2semidirect
5. C2×#16839619C2semidirect
6. C2×#16839609C2semidirect
7. #21444082C2semidirect
8. #21444067C2semidirect
9. #21444064C2semidirect
11. #21444056C2semidirect
12. #21444053C2semidirect
13. #21444050C2semidirect
14. C4×#14519684C2semidirect
15. C2×C61×#388C2semidirect
35. #16839638C4semidirect
133. #14519684D4semidirect
157. #95×C61D4semidirect
573. C2×#388D61semidirect
644. C61#14012semidirect
744. #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×#168396532
C2×#168396502
C2×#168396382
C2×#168396192
C2×#168396092
#214440822
#214440672
#214440642
#214440582
#214440562
#214440532
#214440502
C4×#145196842
C2×C61×#3882
#1401261