Finite Group Databasebeta

← #29603596

Subgroups — #29603596

Order 15616.

1946 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×#16839662C211yesmaximal, characteristic
2C2×#16839643C211yesmaximal, characteristic, complemented
3C2×#16839638C211yesmaximal, characteristic
4C2×#16839609C211yesmaximal, characteristic, complemented
5#21444085C211yesmaximal, characteristic, complemented
6#21444066C211yesmaximal, characteristic, complemented
7#21444061C211yesmaximal, characteristic, complemented
8#21444058C211yesmaximal, characteristic
9#21444057C211yesmaximal, characteristic, complemented
10#21444056C211yesmaximal, characteristic, complemented
11#21444056C211yesmaximal, characteristic, complemented
12#21444044C211yesmaximal, characteristic, complemented
13#21444040C211yesmaximal, characteristic, complemented
14C4×#14519684C211yesmaximal, characteristic, complemented
15C2×C61×#388C211yesmaximal, characteristic, complemented
16C23×C22⋊D61C2211yescharacteristic
17C23×C4×D61C2211yescharacteristic
18C22×#11758196C2211yescharacteristic
19C22×C22⋊Dic61C2211yescharacteristic
20C22×C22⋊Dic61C2211yescharacteristic
21C22×C22⋊Dic61C2211yescharacteristic
22C22×#11758198C2211yescharacteristic
23C22×#11758198C2211yescharacteristic
24C22×#11758198C2211yescharacteristic
25C22×#11758198C2211yescharacteristic
26C22×#11758198C2211yescharacteristic
27C22×C4×Dic61C2211yescharacteristic
28C22×C4×Dic61C2211yescharacteristic
29C22×C4×Dic61C2211yescharacteristic
30#16839662C418yescomplemented
31#16839643—24no—
32#16839638—24no—
33#16839609—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—22no—
60C22×C22⋊D61—22no—
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—22no—
76C22×C4×D61—41no—
77C22×C4×D61—41no—
78C2×#11758196—22no—
79C2×#11758196—22no—
80C2×#11758196C2×C414yescomplemented
81C2×C22⋊Dic61—22no—
82C2×C22⋊Dic61—22no—
83C2×C22⋊Dic61—22no—
84C2×C22⋊Dic61—22no—
85C2×C22⋊Dic61—41no—
86C2×C22⋊Dic61—41no—
87C2×C22⋊Dic61—41no—
88C2×C22⋊Dic61—41no—
89C2×C22⋊Dic61C2×C414yescomplemented
90C2×#11758198—22no—
91C2×#11758198—22no—
92C2×#11758198—22no—
93C2×#11758198—22no—
94C2×#11758198—22no—
95C2×#11758198—22no—
96C2×#11758198—22no—
97C2×#11758198—22no—
98C2×#11758198—22no—
99C2×#11758198—41no—
100C2×#11758198—41no—
101C2×#11758198—41no—
102C2×#11758198—41no—
103C2×#11758198C2×C414yes—
104C2×#11758198C2×C414yes—
105C2×C4×Dic61—22no—
106C2×C4×Dic61—22no—
107C2×C4×Dic61—22no—
108C2×C4×Dic61—22no—
109C2×C4×Dic61—41no—
110C2×C4×Dic61—41no—
111C2×C4×Dic61—41no—
112C2×C4×Dic61—41no—
113C2×C4×Dic61C2×C414yescomplemented
114#14519684—22no—
115#14519684—22no—
116#14519684—22no—
117#14519684—22no—
118#14519684—22no—
119#14519684—22no—
120#14519684—22no—
121#14519684—22no—
122#14519684—22no—
123#14519684—41no—
124#14519684—41no—
125#14519684—41no—
126#14519684—41no—
127#14519684D414yes—
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—22no—
144C2×C22⋊C4×C61—41no—
145C2×C22⋊C4×C61—41no—
146C2×C22⋊C4×C61C2×C414yescomplemented
147C2×C42×C61—22no—
148C2×C42×C61—22no—
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×C61C22×C412yes—
218C22×C4×C61C22×C412yes—
219C22×C4×C61C2×D412yes—
220C22×C4×C61C2×D412yes—
221C22×C4×C61C2×D412yes—
222C22×C4×C61C2×D412yes—
223C22×C4×C61#4112yes—
224C22×C4×C61#4112yes—
225C2×C22⋊D61—28no—
226C2×C22⋊D61—28no—
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×Dic61C22×C412yes—
273C22×Dic61C22×C412yes—
274C22×Dic61C22×C412yes—
275C22×Dic61C2×D412yes—
276C22×Dic61C2×D412yes—
277C22×Dic61#4112yes—
278C22×Dic61#4112yes—
279C22×Dic61#4112yes—
280C22×Dic61#4112yes—
281C2×C4×D61—28no—
282C2×C4×D61—44no—
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—44no—
294C22⋊Dic61—44no—
295C22⋊Dic61—44no—
296#11758198—28no—
297#11758198—28no—
298#11758198—44no—
299#11758198—44no—
300#11758198—44no—
301#11758196—28no—
302C4×Dic61—44no—
303C4×Dic61—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×C61C2×#4111yescharacteristic
348C23×C61C2×#4111yescharacteristic
349C23×C61C2×#4111yescharacteristic
350C23×C61C2×#4111yescharacteristic
351C23×C61H(5,𝔽2)11yescharacteristic
352C23×C61H(5,𝔽2)11yescharacteristic
353C23×C61H(5,𝔽2)11yescharacteristic
354C23×C61H(5,𝔽2)11yescharacteristic
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—22no—
409C2×C4×C61—22no—
410C2×C4×C61—22no—
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—22no—
449C2×Dic61—22no—
450C2×Dic61—22no—
451C2×Dic61—22no—
452C2×Dic61—22no—
453C2×Dic61—22no—
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×Dic61C4×D414yes—
481C2×Dic61#12414yes—
482C4×D61—416no—
483#14034—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×C61C4×#4111yescharacteristic
503C22×C61C4×#4111yescharacteristic
504C22×C61#51811yescharacteristic
505C22×C61#51811yescharacteristic
506C22×C61#52511yescharacteristic
507C22×C61#52511yescharacteristic
508C22×C61C2×#12411yescharacteristic
509C22×C61#52911yescharacteristic
510C22×C61#52911yescharacteristic
511C22×C61#52911yescharacteristic
512C22×C61#52911yescharacteristic
513C22×C61#53211yescharacteristic
514C22×C61#53811yescharacteristic
515C22×C61#53811yescharacteristic
516C22×C61#54011yescharacteristic
517C22×C61#54011yescharacteristic
518C22×C61D4211yescharacteristic
519C22×C61#54611yescharacteristic
520C22×C61#54611yescharacteristic
521C22×C61#54611yescharacteristic
522C22×C61#54611yescharacteristic
523C22×C61#55011yescharacteristic
524C22×C61#55011yescharacteristic
525C22×C61#55111yescharacteristic
526C22×C61#55111yescharacteristic
527C22×C61#55111yescharacteristic
528C22×C61#55111yescharacteristic
529C22×C61#55311yescharacteristic
530C22×C61#55311yescharacteristic
531C22×C61#55311yescharacteristic
532C22×C61#55311yescharacteristic
533C22×C61#55911yescharacteristic
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—42no—
555Dic61—24no—
556Dic61—24no—
557Dic61—42no—
558Dic61—42no—
559Dic61—42no—
560Dic61—81no—
561Dic61—81no—
562C2×#390—611no—
563C2×#388D6111yescharacteristic, complemented
564C2×#387—611no—
565C2×#386—611no—
566C2×C4×C22⋊C4—611no—
567#1445—611no—
568#1440—611no—
569#1439—611no—
570#1438—611no—
571#1437—611no—
572#1437—611no—
573#1437—611no—
574#1434—611no—
575C22⋊#95—611no—
576C4×#95—611no—
577C2×C61—82no—
578C2×C61#229011yescharacteristic
579C2×C61C4×#12411yescharacteristic
580C2×C61#233311yescharacteristic
581C2×C61#234211yescharacteristic
582C2×C61#235311yescharacteristic
583C2×C61#236411yescharacteristic
584C2×C61#236611yescharacteristic
585C2×C61#246411yescharacteristic
586C2×C61#246711yescharacteristic
587C2×C61#247111yescharacteristic
588C2×C61#247211yescharacteristic
589C2×C61#249011yescharacteristic
590C2×C61#251611yescharacteristic
591C2×C61#255411yescharacteristic
592C2×C61#259511yescharacteristic
593D61—44no—
594C23×D4—611no—
595C24×C4—611no—
596C22×C4⋊C4—611no—
597C22×C4⋊C4C2×D6111yescharacteristic
598C22×C22⋊C4—611no—
599C22×C22⋊C4—611no—
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⋊C4C2×D6111yescharacteristic
607C22×C22⋊C4C2×D6111yescharacteristic
608C22×C22⋊C4C2×D6111yescharacteristic
609C22×C42—611no—
610C22×C42—611no—
611C22×C42—611no—
612C22×C42C2×D6111yescharacteristic
613#390—618no—
614#388—24no—
615#387—1224no—
616#386—1224no—
617C4×C22⋊C4—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#1403411yescharacteristic, complemented, Sylow
635C25—611no—
636C25C22×D6111yescharacteristic
637C22×D4—614no—
638C22×D4—1222no—
639C22×D4—1222no—
640C22×D4—1222no—
641C22×D4—1222no—
642C22×D4—2441no—
643C22×D4—2441no—
644C23×C4—611no—
645C23×C4—611no—
646C23×C4—611no—
647C23×C4—611no—
648C23×C4—611no—
649C23×C4—611no—
650C23×C4—611no—
651C23×C4—1222no—
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—614no—
668C2×C4⋊C4—1222no—
669C2×C4⋊C4—1222no—
670C2×C22⋊C4—22no—
671C2×C22⋊C4—22no—
672C2×C22⋊C4—22no—
673C2×C22⋊C4—22no—
674C2×C22⋊C4—22no—
675C2×C22⋊C4—22no—
676C2×C22⋊C4—41no—
677C2×C22⋊C4—41no—
678C2×C22⋊C4—614no—
679C2×C22⋊C4—614no—
680C2×C22⋊C4—614no—
681C2×C22⋊C4—1222no—
682C2×C22⋊C4—1222no—
683C2×C22⋊C4—1222no—
684C2×C22⋊C4—1222no—
685C2×C22⋊C4—1222no—
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—2441no—
695C2×C22⋊C4—2441no—
696C2×C22⋊C4—2441no—
697C2×C22⋊C4—2441no—
698C2×C22⋊C4—2441no—
699C2×C22⋊C4—2441no—
700C2×C22⋊C4—2441no—
701C2×C22⋊C4—2441no—
702C2×C22⋊C4C4×D6114yescomplemented
703C2×C42—22no—
704C2×C42—22no—
705C2×C42—41no—
706C2×C42—614no—
707C2×C42—1222no—
708C2×C42—1222no—
709C2×C42—1222no—
710C2×C42—1222no—
711C2×C42—2441no—
712C2×C42—2441no—
713C2×C42—2441no—
714C2×C42—2441no—
715#95—22no—
716#95—614no—
717#95—1222no—
718#95—1222no—
719#95—1222no—
720#95—1222no—
721#95—1222no—
722#95—1222no—
723#95—1222no—
724#95—1222no—
725#95—1222no—
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—1228no—
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—612no—
804C22×C4—612no—
805C22×C4—612no—
806C22×C4—612no—
807C22×C4—612no—
808C22×C4—612no—
809C22×C4—612no—
810C22×C4—612no—
811C22×C4—612no—
812C22×C4—1228no—
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—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—2444no—
854C22×C4—2444no—
855C22×C4—2444no—
856C22×C4—2444no—
857C22×C4—2444no—
858C22×C4—2444no—
859C22×C4C2×C4×D6112yes—
860C22×C4C2×C4×D6112yes—
861C22×C4#1175822212yes—
862C22×C4D4×D6112yes—
863C22×C4#1175822412yes—
864C22×C4C2×C22⋊D6112yes—
865C22×C4C2×C22⋊D6112yes—
866C22×C4C2×C22⋊D6112yes—
867C4⋊C4—44no—
868C4⋊C4—1228no—
869C22⋊C4—28no—
870C22⋊C4—44no—
871C22⋊C4—44no—
872C22⋊C4—1228no—
873C22⋊C4—1228no—
874C22⋊C4—2444no—
875C22⋊C4—2444no—
876C22⋊C4—2444no—
877C22⋊C4—2444no—
878C22⋊C4—2444no—
879C22⋊C4—2444no—
880C42—44no—
881C42—2444no—
882C42—2444no—
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
960C23#41×D6111yescharacteristic
961C23#41×D6111yescharacteristic
962C23#41×D6111yescharacteristic
963C23C2×#1175822411yescharacteristic
964C23C2×#1175822211yescharacteristic
965C23#1451982211yescharacteristic
966C23#1451982211yescharacteristic
967C23#1451982311yescharacteristic
968C23#1451982311yescharacteristic
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—22no—
989C2×C4—22no—
990C2×C4—22no—
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—614no—
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—1222no—
1028C2×C4—1222no—
1029C2×C4—1222no—
1030C2×C4—1222no—
1031C2×C4—1222no—
1032C2×C4—1222no—
1033C2×C4—1222no—
1034C2×C4—24416no—
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
1095C22C4×#1175822411yescharacteristic
1096C22#1684023011yescharacteristic
1097C22#1684023411yescharacteristic
1098C22#1684023411yescharacteristic
1099C22#1684026911yescharacteristic
1100C22#1684026911yescharacteristic
1101C22#124×D6111yescharacteristic
1102C22#1684028911yescharacteristic
1103C22#1684029011yescharacteristic
1104C22#1684029011yescharacteristic
1105C22#1684029511yescharacteristic
1106C22#1684030711yescharacteristic
1107C22#1684034611yescharacteristic
1108C22#1684035111yescharacteristic
1109C22#1684036211yescharacteristic
1110C22#1684036411yescharacteristic
1111C22D4×C22⋊D6111yescharacteristic
1112C22#1684040011yescharacteristic
1113C22#1684040111yescharacteristic
1114C22#1684040511yescharacteristic
1115C22#1684040611yescharacteristic
1116C22#1684043111yescharacteristic
1117C22#1684043311yescharacteristic
1118C22#1684043511yescharacteristic
1119C22#1684043711yescharacteristic
1120C22#1684044011yescharacteristic
1121C22#1684044211yescharacteristic
1122C22#1684045811yescharacteristic
1123C22#1684045911yescharacteristic
1124C22#1684046111yescharacteristic
1125C22#1684046311yescharacteristic
1126C22#1684049511yescharacteristic
1127C4—24no—
1128C4—42no—
1129C4—42no—
1130C4—42no—
1131C4—42no—
1132C4—42no—
1133C4—1224no—
1134C4—1224no—
1135C4—4881no—
1136C4—4881no—
1137C4—2442no—
1138C4—2442no—
1139C4—2442no—
1140C2—82no—
1141C2—2444no—
1142C2#2144825611yescharacteristic
1143C2#2144836011yescharacteristic
1144C2#2144858211yescharacteristic
1145C2#2144866711yescharacteristic
1146C2#2144875411yescharacteristic
1147C2#2144886411yescharacteristic
1148C2#2144888111yescharacteristic
1149C2#2144982111yescharacteristic
1150C2#2144986611yescharacteristic
1151C2#2144992611yescharacteristic
1152C2#2144994111yescharacteristic
1153C2#2145017011yescharacteristic
1154C2#2145046011yescharacteristic
1155C2#2145087811yescharacteristic
1156C2#2145133611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC2×C61×#388C2
socle, cosocleC24×C61C24
prime radicalC23×C22⋊D61C22
hypercenterC2×#388D61
hypocenterC61#14034
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C2×#16839643C2semidirect
4. C2×#16839609C2semidirect
5. #21444085C2semidirect
6. #21444066C2semidirect
7. #21444061C2semidirect
9. #21444057C2semidirect
10. #21444056C2semidirect
11. #21444056C2semidirect
12. #21444044C2semidirect
13. #21444040C2semidirect
14. C4×#14519684C2semidirect
15. C2×C61×#388C2semidirect
30. #16839662C4semidirect
80. C2×#11758196C2×C4semidirect
89. C2×C22⋊Dic61C2×C4semidirect
113. C2×C4×Dic61C2×C4semidirect
146. C2×C22⋊C4×C61C2×C4semidirect
151. #95×C61D4semidirect
563. C2×#388D61semidirect
634. C61#14034semidirect
702. C2×C22⋊C4C4×D61semidirect
730. #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×#168396432
C2×#168396382
C2×#168396092
#214440852
#214440662
#214440612
#214440582
#214440572
#214440562
#214440442
#214440402
C4×#145196842
C2×C61×#3882
#1403461