Finite Group Databasebeta

← #29608495

Subgroups — #29608495

Order 15616.

1398 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839655C211yesmaximal, characteristic
2C2×#16839648C211yesmaximal, characteristic, complemented
3#21444081C211yesmaximal, characteristic, complemented
4#21444072C211yesmaximal, characteristic, complemented
5#21444068C211yesmaximal, characteristic
6#21444064C211yesmaximal, characteristic
7#21444064C211yesmaximal, characteristic
8#21444064C211yesmaximal, characteristic
9#21444056C211yesmaximal, characteristic
10#21444053C211yesmaximal, characteristic, complemented
11#21444053C211yesmaximal, characteristic, complemented
12#21444049C211yesmaximal, characteristic, complemented
13#21444049C211yesmaximal, characteristic, complemented
14#21444044C211yesmaximal, characteristic, complemented
15C2×C61×#388C211yesmaximal, characteristic
16C22×C4⋊Dic61C2211yescharacteristic
17C22×C4⋊Dic61C2211yescharacteristic
18C22×C4⋊Dic61C2211yescharacteristic
19C22×C4⋊Dic61C2211yescharacteristic
20C22×C22⋊Dic61C2211yescharacteristic
21C22×C22⋊Dic61C2211yescharacteristic
22C22×C22⋊Dic61C2211yescharacteristic
23C22×C22⋊Dic61C2211yescharacteristic
24C22×C4×Dic61C2211yescharacteristic
25C22×C4×Dic61C2211yescharacteristic
26#16839655—24no—
27#16839648—24no—
28C2×#14519684C2211yescharacteristic
29C2×#14519684C2211yescharacteristic
30C2×#14519684C2211yescharacteristic
31C2×#14519684C2211yescharacteristic
32C2×#14519684C2211yescharacteristic
33C2×#14519684C2211yescharacteristic
34C2×#14519684C2211yescharacteristic
35C2×#14519684C2211yescharacteristic
36C2×#14519684C2211yescharacteristic
37C2×#14519684C2211yescharacteristic
38C2×#14519684C2211yescharacteristic
39C2×#14519684C2211yescharacteristic
40C2×#14519684C2211yescharacteristic
41C2×#14519684C2211yescharacteristic
42C2×#14519684C2211yescharacteristic
43C2×#14519684C2211yescharacteristic
44C2×#14519684C2211yescharacteristic
45C2×#14519684C2211yescharacteristic
46C22×C4⋊C4×C61C2211yescharacteristic
47C22×C22⋊C4×C61C2211yescharacteristic
48C22×C22⋊C4×C61C2211yescharacteristic
49C22×C22⋊C4×C61C2211yescharacteristic
50C22×C42×C61C2211yescharacteristic
51C61×#388C418yescomplemented
52C2×#95×C61C2211yescharacteristic
53C2×#95×C61C2211yescharacteristic
54C23×Dic61C2311yescharacteristic
55C23×Dic61C2311yescharacteristic
56C23×Dic61C2311yescharacteristic
57C23×Dic61C2311yescharacteristic
58C23×Dic61C2311yescharacteristic
59C23×Dic61C2311yescharacteristic
60C23×Dic61C2311yescharacteristic
61C23×Dic61C2311yescharacteristic
62C2×C4⋊Dic61—22no—
63C2×C4⋊Dic61—22no—
64C2×C4⋊Dic61—22no—
65C2×C4⋊Dic61—22no—
66C2×C4⋊Dic61—22no—
67C2×C4⋊Dic61—41no—
68C2×C4⋊Dic61—41no—
69C2×C4⋊Dic61—41no—
70C2×C4⋊Dic61—41no—
71C2×C4⋊Dic61—41no—
72C2×C4⋊Dic61—41no—
73C2×C4⋊Dic61D414yes—
74C2×C22⋊Dic61—22no—
75C2×C22⋊Dic61—22no—
76C2×C22⋊Dic61—22no—
77C2×C22⋊Dic61—22no—
78C2×C22⋊Dic61—41no—
79C2×C22⋊Dic61—41no—
80C2×C22⋊Dic61—41no—
81C2×C22⋊Dic61—41no—
82C2×C22⋊Dic61—41no—
83C2×C22⋊Dic61—41no—
84C2×C22⋊Dic61—41no—
85C2×C22⋊Dic61—41no—
86C2×C4×Dic61—22no—
87C2×C4×Dic61—22no—
88C2×C4×Dic61—22no—
89C2×C4×Dic61—41no—
90C2×C4×Dic61—41no—
91C2×C4×Dic61—41no—
92#14519684—22no—
93#14519684—22no—
94#14519684—22no—
95#14519684—22no—
96#14519684—22no—
97#14519684—22no—
98#14519684—22no—
99#14519684—22no—
100#14519684—22no—
101#14519684—41no—
102#14519684—41no—
103#14519684—41no—
104#14519684—41no—
105#14519684—41no—
106#14519684—41no—
107#14519684—41no—
108#14519684—41no—
109#14519684—41no—
110C25×C61C2311yescharacteristic
111C23×C4×C61C2311yescharacteristic
112C23×C4×C61C2311yescharacteristic
113C23×C4×C61C2311yescharacteristic
114C23×C4×C61C2311yescharacteristic
115C23×C4×C61C2311yescharacteristic
116C23×C4×C61C2311yescharacteristic
117C2×C4⋊C4×C61—22no—
118C2×C4⋊C4×C61—22no—
119C2×C4⋊C4×C61C2×C414yes—
120C2×C22⋊C4×C61—22no—
121C2×C22⋊C4×C61—22no—
122C2×C22⋊C4×C61—22no—
123C2×C22⋊C4×C61—22no—
124C2×C22⋊C4×C61—41no—
125C2×C22⋊C4×C61—41no—
126C2×C22⋊C4×C61C2×C414yes—
127C2×C22⋊C4×C61C2×C414yes—
128C2×C22⋊C4×C61C2×C414yes—
129C2×C42×C61—41no—
130C2×C42×C61—41no—
131C2×C42×C61C2×C414yes—
132#95×C61C2×C414yes—
133#95×C61C2×C414yes—
134C24×C61—21no—
135C24×C61—21no—
136C24×C61—21no—
137C24×C61—21no—
138C24×C61—21no—
139C24×C61—21no—
140C24×C61—21no—
141C24×C61—21no—
142C24×C61—21no—
143C24×C61—21no—
144C24×C61—21no—
145C24×C61—21no—
146C24×C61—21no—
147C24×C61—21no—
148C24×C61C22×C412yes—
149C24×C61C2411yescharacteristic
150C22×C4×C61—21no—
151C22×C4×C61—21no—
152C22×C4×C61—21no—
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61—21no—
159C22×C4×C61—21no—
160C22×C4×C61—21no—
161C22×C4×C61—21no—
162C22×C4×C61—21no—
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61—21no—
166C22×C4×C61—21no—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61—21no—
172C22×C4×C61—21no—
173C22×C4×C61—21no—
174C22×C4×C61—21no—
175C22×C4×C61—21no—
176C22×C4×C61—21no—
177C22×C4×C61—21no—
178C22×C4×C61—21no—
179C22×C4×C61—21no—
180C22×C4×C61—21no—
181C22×C4×C61—21no—
182C22×C4×C61C22×C412yes—
183C22×C4×C61C22×C412yes—
184C22×C4×C61C22×C412yes—
185C22×C4×C61C22×C412yes—
186C22×C4×C61C22×C412yes—
187C22×C4×C61C22×C412yes—
188C22×C4×C61C2×D412yes—
189C22×C4×C61#4112yes—
190C22×C4×C61#4112yes—
191C22×C4×C61#4112yes—
192C22×Dic61—21no—
193C22×Dic61—21no—
194C22×Dic61—21no—
195C22×Dic61—21no—
196C22×Dic61—21no—
197C22×Dic61—21no—
198C22×Dic61—21no—
199C22×Dic61—21no—
200C22×Dic61—21no—
201C22×Dic61—21no—
202C22×Dic61—21no—
203C22×Dic61—21no—
204C22×Dic61—21no—
205C22×Dic61—21no—
206C22×Dic61—21no—
207C22×Dic61—21no—
208C22×Dic61—21no—
209C22×Dic61—21no—
210C22×Dic61—21no—
211C22×Dic61—21no—
212C22×Dic61—21no—
213C22×Dic61—21no—
214C22×Dic61—21no—
215C22×Dic61—21no—
216C22×Dic61—21no—
217C22×Dic61—21no—
218C22×Dic61—21no—
219C22×Dic61—21no—
220C22×Dic61—21no—
221C22×Dic61—21no—
222C22×Dic61—21no—
223C22×Dic61—21no—
224C22×Dic61—21no—
225C22×Dic61—21no—
226C22×Dic61—21no—
227C22×Dic61—21no—
228C22×Dic61—21no—
229C22×Dic61—21no—
230C22×Dic61—21no—
231C22×Dic61—21no—
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×Dic61C2×D412yes—
245C22×Dic61C2×D412yes—
246C22×Dic61#4112yes—
247C22×Dic61#4112yes—
248C4⋊C4×C61—28no—
249C22⋊C4×C61—28no—
250C22⋊C4×C61—28no—
251C22⋊C4×C61—44no—
252C42×C61—44no—
253C22⋊Dic61—44no—
254C22⋊Dic61—44no—
255C22⋊Dic61—44no—
256C22⋊Dic61—44no—
257C4⋊Dic61—44no—
258C4⋊Dic61—44no—
259C4⋊Dic61—44no—
260C4⋊Dic61—44no—
261C4×Dic61—44no—
262C4×Dic61—44no—
263C23×C61—22no—
264C23×C61—22no—
265C23×C61—22no—
266C23×C61—22no—
267C23×C61—22no—
268C23×C61—22no—
269C23×C61—22no—
270C23×C61—41no—
271C23×C61—41no—
272C23×C61—41no—
273C23×C61—41no—
274C23×C61—41no—
275C23×C61—41no—
276C23×C61—41no—
277C23×C61—41no—
278C23×C61—41no—
279C23×C61—41no—
280C23×C61—41no—
281C23×C61—41no—
282C23×C61—41no—
283C23×C61—41no—
284C23×C61—41no—
285C23×C61—41no—
286C23×C61—41no—
287C23×C61—41no—
288C23×C61—41no—
289C23×C61—41no—
290C23×C61—41no—
291C23×C61—41no—
292C23×C61—41no—
293C23×C61—41no—
294C23×C61—41no—
295C23×C61—41no—
296C23×C61—41no—
297C23×C61—41no—
298C23×C61C23×C411yescharacteristic
299C23×C61C22×D411yescharacteristic
300C23×C61C2×#4111yescharacteristic
301C23×C61C2×#4111yescharacteristic
302C23×C61C2×#4111yescharacteristic
303C23×C61C2×#4111yescharacteristic
304C23×C61C2×#4111yescharacteristic
305C23×C61H(5,𝔽2)11yescharacteristic
306C23×C61H(5,𝔽2)11yescharacteristic
307C23×C61H(5,𝔽2)11yescharacteristic
308C23×C61H(5,𝔽2)11yescharacteristic
309C23×C61H(5,𝔽2)11yescharacteristic
310C23×C612−1+411yescharacteristic
311C23×C612−1+411yescharacteristic
312C23×C612−1+411yescharacteristic
313C2×C4×C61—22no—
314C2×C4×C61—22no—
315C2×C4×C61—22no—
316C2×C4×C61—22no—
317C2×C4×C61—22no—
318C2×C4×C61—22no—
319C2×C4×C61—22no—
320C2×C4×C61—22no—
321C2×C4×C61—22no—
322C2×C4×C61—22no—
323C2×C4×C61—22no—
324C2×C4×C61—22no—
325C2×C4×C61—22no—
326C2×C4×C61—22no—
327C2×C4×C61—22no—
328C2×C4×C61—22no—
329C2×C4×C61—22no—
330C2×C4×C61—22no—
331C2×C4×C61—22no—
332C2×C4×C61—22no—
333C2×C4×C61—22no—
334C2×C4×C61—22no—
335C2×C4×C61—22no—
336C2×C4×C61—22no—
337C2×C4×C61—41no—
338C2×C4×C61—41no—
339C2×C4×C61—41no—
340C2×C4×C61—41no—
341C2×C4×C61—41no—
342C2×C4×C61—41no—
343C2×C4×C61—41no—
344C2×C4×C61—41no—
345C2×C4×C61—41no—
346C2×C4×C61—41no—
347C2×C4×C61—41no—
348C2×C4×C61—41no—
349C2×C4×C61—41no—
350C2×C4×C61—41no—
351C2×C4×C61—41no—
352C2×C4×C61—41no—
353C2×C4×C61#11714yes—
354C2×C4×C61C4×D414yes—
355C2×Dic61—22no—
356C2×Dic61—22no—
357C2×Dic61—22no—
358C2×Dic61—22no—
359C2×Dic61—22no—
360C2×Dic61—22no—
361C2×Dic61—22no—
362C2×Dic61—22no—
363C2×Dic61—22no—
364C2×Dic61—22no—
365C2×Dic61—22no—
366C2×Dic61—22no—
367C2×Dic61—41no—
368C2×Dic61—41no—
369C2×Dic61—41no—
370C2×Dic61—41no—
371C2×Dic61—41no—
372C2×Dic61—41no—
373C2×Dic61—41no—
374C2×Dic61—41no—
375C2×Dic61—41no—
376C2×Dic61—41no—
377C2×Dic61—41no—
378C2×Dic61—41no—
379C2×Dic61—41no—
380C2×Dic61—41no—
381C2×Dic61—41no—
382C2×Dic61—41no—
383C2×Dic61—41no—
384C2×Dic61—41no—
385C2×Dic61—41no—
386C2×Dic61—41no—
387C2×Dic61—41no—
388C2×Dic61—41no—
389C2×Dic61—41no—
390C2×Dic61—41no—
391C2×Dic61—41no—
392C2×Dic61—41no—
393C2×Dic61—41no—
394C2×Dic61—41no—
395C2×Dic61—41no—
396C2×Dic61—41no—
397C2×Dic61—41no—
398C2×Dic61—41no—
399C2×Dic61—41no—
400C2×Dic61—41no—
401C2×Dic61—41no—
402C2×Dic61—41no—
403C2×Dic61—41no—
404C2×Dic61—41no—
405C2×Dic61—41no—
406C2×Dic61—41no—
407C2×Dic61—41no—
408C2×Dic61—41no—
409C2×Dic61—41no—
410C2×Dic61—41no—
411#14447—611nomaximal, Sylow
412C22×C61—42no—
413C22×C61—42no—
414C22×C61—42no—
415C22×C61—42no—
416C22×C61—42no—
417C22×C61—42no—
418C22×C61—42no—
419C22×C61—81no—
420C22×C61—81no—
421C22×C61—81no—
422C22×C61—81no—
423C22×C61—81no—
424C22×C61—81no—
425C22×C61—81no—
426C22×C61—81no—
427C22×C61C2×#11711yescharacteristic
428C22×C61C2×C4×D411yescharacteristic
429C22×C61C4×#4111yescharacteristic
430C22×C61#51811yescharacteristic
431C22×C61#52011yescharacteristic
432C22×C61#52011yescharacteristic
433C22×C61#52011yescharacteristic
434C22×C61#53411yescharacteristic
435C22×C61#53711yescharacteristic
436C22×C61#53811yescharacteristic
437C22×C61#53811yescharacteristic
438C22×C61#53911yescharacteristic
439C22×C61#53911yescharacteristic
440C22×C61#54011yescharacteristic
441C22×C61#54111yescharacteristic
442C22×C61#54111yescharacteristic
443C22×C61#54211yescharacteristic
444C22×C61#54211yescharacteristic
445C22×C61#54211yescharacteristic
446C22×C61#54611yescharacteristic
447C22×C61#54711yescharacteristic
448C22×C61#54811yescharacteristic
449C22×C61#55011yescharacteristic
450C22×C61#55111yescharacteristic
451C22×C61#55111yescharacteristic
452C22×C61#55311yescharacteristic
453C22×C61#55311yescharacteristic
454C22×C61#55511yescharacteristic
455C22×C61#55611yescharacteristic
456C22×C61#55611yescharacteristic
457C22×C61#55911yescharacteristic
458C22×C61#56011yescharacteristic
459C22×C61#56211yescharacteristic
460C22×C61#56211yescharacteristic
461C22×C61#56311yescharacteristic
462C4×C61—24no—
463C4×C61—24no—
464C4×C61—42no—
465C4×C61—42no—
466C4×C61—42no—
467C4×C61—42no—
468Dic61—42no—
469Dic61—42no—
470Dic61—42no—
471Dic61—42no—
472Dic61—81no—
473Dic61—81no—
474Dic61—81no—
475Dic61—81no—
476C2×#388—611no—
477C2×#388D6111yescharacteristic
478C2×#387—611no—
479#1443—611no—
480#1441—611no—
481#1440—611no—
482#1439—611no—
483#1439—611no—
484#1439—611no—
485#1437—611no—
486#1436—611no—
487#1436—611no—
488C4⋊#95—611no—
489C4⋊#95—611no—
490#1434—611no—
491C2×C61—82no—
492C2×C61#231411yescharacteristic
493C2×C61#232511yescharacteristic
494C2×C61#233411yescharacteristic
495C2×C61#235311yescharacteristic
496C2×C61#235411yescharacteristic
497C2×C61#236711yescharacteristic
498C2×C61#237611yescharacteristic
499C2×C61#270111yescharacteristic
500C2×C61#270511yescharacteristic
501C2×C61#272511yescharacteristic
502C2×C61#273011yescharacteristic
503C2×C61#275911yescharacteristic
504C2×C61#278311yescharacteristic
505C2×C61#279811yescharacteristic
506C2×C61#280311yescharacteristic
507C22×C4⋊C4—611no—
508C22×C4⋊C4—611no—
509C22×C4⋊C4—611no—
510C22×C4⋊C4—611no—
511C22×C4⋊C4C2×D6111yescharacteristic
512C22×C22⋊C4—611no—
513C22×C22⋊C4—611no—
514C22×C22⋊C4—611no—
515C22×C22⋊C4—611no—
516C22×C22⋊C4C2×D6111yescharacteristic
517C22×C22⋊C4C2×D6111yescharacteristic
518C22×C22⋊C4C2×D6111yescharacteristic
519C22×C42—611no—
520C22×C42—611no—
521C22×C42C2×D6111yescharacteristic
522#388—1224no—
523#388Dic6118yescomplemented
524#387—1224no—
525C2×#95—611no—
526C2×#95—611no—
527C2×#95—611no—
528C2×#95—611no—
529C2×#95—611no—
530C2×#95—611no—
531C2×#95—611no—
532C2×#95—611no—
533C2×#95—611no—
534C2×#95—611no—
535C2×#95—611no—
536C2×#95—611no—
537C2×#95—611no—
538C2×#95—611no—
539C2×#95—611no—
540C2×#95—611no—
541C2×#95—611no—
542C2×#95—611no—
543C2×#95C2×D6111yescharacteristic
544C2×#95C2×D6111yescharacteristic
545C61#1444711yescharacteristic, complemented, Sylow
546C25C22×D6111yescharacteristic
547C23×C4—611no—
548C23×C4—611no—
549C23×C4—611no—
550C23×C4—611no—
551C23×C4—611no—
552C23×C4—611no—
553C23×C4—611no—
554C23×C4—611no—
555C23×C4C22×D6111yescharacteristic
556C23×C4C22×D6111yescharacteristic
557C23×C4C22×D6111yescharacteristic
558C23×C4C22×D6111yescharacteristic
559C23×C4C22×D6111yescharacteristic
560C23×C4C22×D6111yescharacteristic
561C2×C4⋊C4—22no—
562C2×C4⋊C4—22no—
563C2×C4⋊C4—614no—
564C2×C4⋊C4—1222no—
565C2×C4⋊C4—1222no—
566C2×C4⋊C4—1222no—
567C2×C4⋊C4—1222no—
568C2×C4⋊C4—1222no—
569C2×C4⋊C4—2441no—
570C2×C4⋊C4—2441no—
571C2×C4⋊C4—2441no—
572C2×C4⋊C4—2441no—
573C2×C4⋊C4—2441no—
574C2×C4⋊C4—2441no—
575C2×C4⋊C4C2×Dic6114yes—
576C2×C22⋊C4—22no—
577C2×C22⋊C4—22no—
578C2×C22⋊C4—22no—
579C2×C22⋊C4—22no—
580C2×C22⋊C4—41no—
581C2×C22⋊C4—41no—
582C2×C22⋊C4—1222no—
583C2×C22⋊C4—1222no—
584C2×C22⋊C4—1222no—
585C2×C22⋊C4—1222no—
586C2×C22⋊C4—2441no—
587C2×C22⋊C4—2441no—
588C2×C22⋊C4—2441no—
589C2×C22⋊C4—2441no—
590C2×C22⋊C4—2441no—
591C2×C22⋊C4—2441no—
592C2×C22⋊C4—2441no—
593C2×C22⋊C4—2441no—
594C2×C22⋊C4C2×Dic6114yes—
595C2×C22⋊C4C2×Dic6114yes—
596C2×C22⋊C4C2×Dic6114yes—
597C2×C42—41no—
598C2×C42—41no—
599C2×C42—1222no—
600C2×C42—1222no—
601C2×C42—1222no—
602C2×C42—2441no—
603C2×C42—2441no—
604C2×C42—2441no—
605C2×C42C2×Dic6114yes—
606#95—1222no—
607#95—1222no—
608#95—1222no—
609#95—1222no—
610#95—1222no—
611#95—1222no—
612#95—1222no—
613#95—1222no—
614#95—1222no—
615#95—2441no—
616#95—2441no—
617#95—2441no—
618#95—2441no—
619#95—2441no—
620#95—2441no—
621#95—2441no—
622#95—2441no—
623#95—2441no—
624#95C2×Dic6114yes—
625#95C2×Dic6114yes—
626C24—21no—
627C24—21no—
628C24—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24C22×Dic6112yes—
641C24C23×D6111yescharacteristic
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—612no—
675C22×C4—612no—
676C22×C4—612no—
677C22×C4—612no—
678C22×C4—1221no—
679C22×C4—1221no—
680C22×C4—1221no—
681C22×C4—1221no—
682C22×C4—1221no—
683C22×C4—1221no—
684C22×C4—1221no—
685C22×C4—1221no—
686C22×C4—1221no—
687C22×C4—1221no—
688C22×C4—1221no—
689C22×C4—1221no—
690C22×C4—1221no—
691C22×C4—1221no—
692C22×C4—1221no—
693C22×C4—1221no—
694C22×C4—1221no—
695C22×C4—1221no—
696C22×C4—1221no—
697C22×C4—1221no—
698C22×C4—1221no—
699C22×C4—1221no—
700C22×C4—1221no—
701C22×C4—1221no—
702C22×C4—1221no—
703C22×C4—1221no—
704C22×C4—1221no—
705C22×C4—1221no—
706C22×C4—1221no—
707C22×C4—1221no—
708C22×C4—1221no—
709C22×C4—1221no—
710C22×C4—1221no—
711C22×C4—1221no—
712C22×C4—1221no—
713C22×C4—1221no—
714C22×C4—1221no—
715C22×C4—1221no—
716C22×C4—1221no—
717C22×C4—1221no—
718C22×C4—1221no—
719C22×C4—1221no—
720C22×C4—1221no—
721C22×C4—1221no—
722C22×C4—1221no—
723C22×C4—1221no—
724C22×C4—1221no—
725C22×C4—1221no—
726C22×C4—1221no—
727C22×C4—1221no—
728C22×C4—1221no—
729C22×C4—1221no—
730C22×C4#1175822212yes—
731C22×C4#1175822212yes—
732C22×C4D4×D6112yes—
733C22×C4#1175822412yes—
734C22×C4C22×Dic6112yes—
735C22×C4C22×Dic6112yes—
736C22×C4C22×Dic6112yes—
737C22×C4C22×Dic6112yes—
738C22×C4C22×Dic6112yes—
739C22×C4C22×Dic6112yes—
740C4⋊C4—28no—
741C4⋊C4—2444no—
742C4⋊C4—2444no—
743C4⋊C4—2444no—
744C4⋊C4—2444no—
745C22⋊C4—28no—
746C22⋊C4—28no—
747C22⋊C4—44no—
748C22⋊C4—2444no—
749C22⋊C4—2444no—
750C22⋊C4—2444no—
751C22⋊C4—2444no—
752C42—44no—
753C42—2444no—
754C42—2444no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23C23×Dic6111yescharacteristic
791C23C2×D4×D6111yescharacteristic
792C23#41×D6111yescharacteristic
793C23#41×D6111yescharacteristic
794C23C2×#1175822411yescharacteristic
795C23C2×#1175822211yescharacteristic
796C23C2×#1175822211yescharacteristic
797C23#1451982211yescharacteristic
798C23#1451982211yescharacteristic
799C23#1451982311yescharacteristic
800C23#1451982311yescharacteristic
801C23#1451982311yescharacteristic
802C23#1451982411yescharacteristic
803C23#1451982411yescharacteristic
804C23#1451982411yescharacteristic
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—1222no—
846C2×C4—1222no—
847C2×C4—1222no—
848C2×C4—1222no—
849C2×C4—1222no—
850C2×C4—1222no—
851C2×C4—1222no—
852C2×C4—1222no—
853C2×C4—1222no—
854C2×C4—1222no—
855C2×C4—1222no—
856C2×C4—1222no—
857C2×C4—2441no—
858C2×C4—2441no—
859C2×C4—2441no—
860C2×C4—2441no—
861C2×C4—2441no—
862C2×C4—2441no—
863C2×C4—2441no—
864C2×C4—2441no—
865C2×C4—2441no—
866C2×C4—2441no—
867C2×C4—2441no—
868C2×C4—2441no—
869C2×C4—2441no—
870C2×C4—2441no—
871C2×C4—2441no—
872C2×C4—2441no—
873C2×C4—2441no—
874C2×C4—2441no—
875C2×C4—2441no—
876C2×C4—2441no—
877C2×C4—2441no—
878C2×C4—2441no—
879C2×C4—2441no—
880C2×C4—2441no—
881C2×C4—2441no—
882C2×C4—2441no—
883C2×C4—2441no—
884C2×C4—2441no—
885C2×C4—2441no—
886C2×C4—2441no—
887C2×C4—2441no—
888C2×C4—2441no—
889C2×C4—2441no—
890C2×C4—2441no—
891C2×C4—2441no—
892C2×C4—2441no—
893C2×C4—2441no—
894C2×C4—2441no—
895C2×C4—2441no—
896C2×C4—2441no—
897C2×C4—2441no—
898C2×C4—2441no—
899C2×C4—2441no—
900C2×C4—2441no—
901C2×C4#1451973614yes—
902C2×C4D4×Dic6114yes—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—42no—
907C22—42no—
908C22—42no—
909C22—42no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22C2×#1451973611yescharacteristic
919C22C2×D4×Dic6111yescharacteristic
920C22#41×Dic6111yescharacteristic
921C22#1684023711yescharacteristic
922C22#1684024511yescharacteristic
923C22#1684024511yescharacteristic
924C22#1684024511yescharacteristic
925C22#1684032011yescharacteristic
926C22#1684033911yescharacteristic
927C22#1684034911yescharacteristic
928C22#1684035111yescharacteristic
929C22#1684035311yescharacteristic
930C22#1684035711yescharacteristic
931C22#1684036711yescharacteristic
932C22#1684036911yescharacteristic
933C22#1684037411yescharacteristic
934C22#1684037811yescharacteristic
935C22#1684038311yescharacteristic
936C22#1684038311yescharacteristic
937C22#1684040511yescharacteristic
938C22#1684041711yescharacteristic
939C22#1684042011yescharacteristic
940C22#1684043311yescharacteristic
941C22#1684044111yescharacteristic
942C22#1684044111yescharacteristic
943C22#1684046111yescharacteristic
944C22#1684046111yescharacteristic
945C22#1684047711yescharacteristic
946C22#1684048111yescharacteristic
947C22#1684048211yescharacteristic
948C22#1684049411yescharacteristic
949C22#1684050211yescharacteristic
950C22#1684050911yescharacteristic
951C22#1684050911yescharacteristic
952C22#1684051511yescharacteristic
953C4—24no—
954C4—24no—
955C4—42no—
956C4—42no—
957C4—42no—
958C4—42no—
959C4—4881no—
960C4—4881no—
961C4—4881no—
962C4—4881no—
963C4—2442no—
964C4—2442no—
965C4—2442no—
966C4—2442no—
967C2—82no—
968C2#2144842811yescharacteristic
969C2#2144852411yescharacteristic
970C2#2144859811yescharacteristic
971C2#2144875911yescharacteristic
972C2#2144876811yescharacteristic
973C2#2144889411yescharacteristic
974C2#2144896711yescharacteristic
975C2#2145242911yescharacteristic
976C2#2145248911yescharacteristic
977C2#2145275411yescharacteristic
978C2#2145281311yescharacteristic
979C2#2145318911yescharacteristic
980C2#2145350911yescharacteristic
981C2#2145368711yescharacteristic
982C2#2145375511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC2×C61×#388C2
socle, cosocleC24×C61C24
prime radicalC25×C61C23
hypercenterC2×#388D61
hypocenterC61#14447
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C2×#16839648C2semidirect
3. #21444081C2semidirect
4. #21444072C2semidirect
10. #21444053C2semidirect
11. #21444053C2semidirect
12. #21444049C2semidirect
13. #21444049C2semidirect
14. #21444044C2semidirect
51. C61×#388C4semidirect
523. #388Dic61semidirect
545. C61#14447semidirect

Maximal subgroups

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

subgroupindex
C2×#168396552
C2×#168396482
#214440812
#214440722
#214440682
#214440642
#214440562
#214440532
#214440492
#214440442
C2×C61×#3882
#1444761