Finite Group Databasebeta

← C2×#21451802 #29846477

Subgroups — C2×#21451802 #29846477

Order 15616.

2654 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21451802C2116yesmaximal, direct product factor
2C2×#16839703C211yesmaximal, characteristic, complemented
3C2×#16839688C211yesmaximal, characteristic, complemented
4C2×#16839687C211yesmaximal, characteristic, complemented
5C2×#16839685C211yesmaximal, characteristic, complemented
6C2×#16839677C211yesmaximal, characteristic, complemented
7C2×#16839677C211yesmaximal, characteristic, complemented
8C2×#16839670C211yesmaximal, characteristic
9C2×#16839662C211yesmaximal, characteristic, complemented
10C2×#16839656C211yesmaximal, characteristic, complemented
11C2×#16839654C211yesmaximal, characteristic, complemented
12C2×#16839643C211yesmaximal, characteristic, complemented
13C2×#16839642C211yesmaximal, characteristic, complemented
14C2×#16839639C211yesmaximal, characteristic, complemented
15C2×C22⋊C4×Dic61C211yesmaximal, characteristic, complemented
16C2×C61×#394C211yesmaximal, characteristic, complemented
17C23×C22⋊D61C2211yescharacteristic
18C23×C22⋊D61C2211yescharacteristic
19C24×Dic61C2211yescharacteristic
20C22×C4⋊Dic61C2211yescharacteristic
21C22×#11758196C2211yescharacteristic
22C22×#11758196C2211yescharacteristic
23C22×#11758196C2211yescharacteristic
24C22×C22⋊Dic61C2211yescharacteristic
25C22×C22⋊Dic61C2211yescharacteristic
26C22×C22⋊Dic61C2211yescharacteristic
27C22×C22⋊Dic61C2211yescharacteristic
28C22×C22⋊Dic61C2211yescharacteristic
29C22×#11758198C2211yescharacteristic
30C22×#11758198C2211yescharacteristic
31C22×#11758198C2211yescharacteristic
32C22×#11758198C2211yescharacteristic
33C22×#11758198C2211yescharacteristic
34C22×C4×Dic61C2211yescharacteristic
35C22×C4×Dic61C2211yescharacteristic
36#16839703C2218yescomplemented
37#16839688C2218yescomplemented
38#16839687C2218yescomplemented
39#16839685C2218yescomplemented
40#16839677C2218yescomplemented
41#16839677C2218yescomplemented
42#16839670C2218yes—
43#16839662C2218yescomplemented
44#16839656C2218yescomplemented
45#16839654C2218yescomplemented
46#16839643C2218yescomplemented
47#16839642C2218yescomplemented
48#16839639C2218yescomplemented
49C22⋊C4×Dic61C2218yescomplemented
50C2×#14519684C2211yescharacteristic
51C2×#14519684C2211yescharacteristic
52C2×#14519684C2211yescharacteristic
53C2×#14519684C2211yescharacteristic
54C2×#14519684C2211yescharacteristic
55C2×#14519684C2211yescharacteristic
56C2×#14519684C2211yescharacteristic
57C2×#14519684C2211yescharacteristic
58C2×#14519684C2211yescharacteristic
59C23×D4×C61C2211yescharacteristic
60C22×C4⋊C4×C61C2211yescharacteristic
61C22×C22⋊C4×C61C2211yescharacteristic
62C22×C22⋊C4×C61C2211yescharacteristic
63C22×C22⋊C4×C61C2211yescharacteristic
64C22×C22⋊C4×C61C2211yescharacteristic
65C61×#394C2218yescomplemented
66C2×#95×C61C2211yescharacteristic
67C24×D61C2311yescharacteristic
68C22×C22⋊D61—24no—
69C22×C22⋊D61—24no—
70C22×C22⋊D61—42no—
71C22×C22⋊D61—42no—
72C22×C22⋊D61—42no—
73C22×C22⋊D61—42no—
74C22×C22⋊D61C2314yes—
75C22×C22⋊D61C2314yes—
76C23×Dic61—24no—
77C23×Dic61—42no—
78C23×Dic61—42no—
79C23×Dic61C2311yescharacteristic
80C23×Dic61C2311yescharacteristic
81C23×Dic61C2311yescharacteristic
82C23×Dic61C2311yescharacteristic
83C23×Dic61C2311yescharacteristic
84C23×Dic61C2311yescharacteristic
85C23×Dic61C2311yescharacteristic
86C23×Dic61C2314yes—
87C2×C4⋊Dic61—42no—
88C2×C4⋊Dic61C2314yes—
89C2×#11758196—24no—
90C2×#11758196—42no—
91C2×#11758196—42no—
92C2×#11758196C2314yes—
93C2×#11758196C2314yes—
94C2×#11758196C2314yes—
95C2×C22⋊Dic61—24no—
96C2×C22⋊Dic61—24no—
97C2×C22⋊Dic61—42no—
98C2×C22⋊Dic61—42no—
99C2×C22⋊Dic61—42no—
100C2×C22⋊Dic61C2314yes—
101C2×C22⋊Dic61C2314yes—
102C2×C22⋊Dic61C2314yes—
103C2×C22⋊Dic61C2314yes—
104C2×C22⋊Dic61C2314yes—
105C2×#11758198—24no—
106C2×#11758198—42no—
107C2×#11758198—42no—
108C2×#11758198—42no—
109C2×#11758198—42no—
110C2×#11758198C2314yes—
111C2×#11758198C2314yes—
112C2×#11758198C2314yes—
113C2×#11758198C2314yes—
114C2×#11758198C2314yes—
115C2×C4×Dic61—42no—
116C2×C4×Dic61—42no—
117C2×C4×Dic61C2314yes—
118C2×C4×Dic61C2314yes—
119#14519684C2314yes—
120#14519684C2314yes—
121#14519684C2314yes—
122#14519684C2314yes—
123#14519684C2314yes—
124#14519684C2314yes—
125#14519684C2314yes—
126#14519684C2314yes—
127#14519684C2314yes—
128C25×C61C2311yescharacteristic
129C25×C61C2311yescharacteristic
130C22×D4×C61—24no—
131C22×D4×C61—42no—
132C22×D4×C61—42no—
133C22×D4×C61C2314yes—
134C23×C4×C61C2311yescharacteristic
135C23×C4×C61C2311yescharacteristic
136C23×C4×C61C2311yescharacteristic
137C23×C4×C61C2311yescharacteristic
138C23×C4×C61C2311yescharacteristic
139C2×C4⋊C4×C61—42no—
140C2×C4⋊C4×C61C2314yes—
141C2×C22⋊C4×C61—24no—
142C2×C22⋊C4×C61—42no—
143C2×C22⋊C4×C61—42no—
144C2×C22⋊C4×C61—42no—
145C2×C22⋊C4×C61C2314yes—
146C2×C22⋊C4×C61C2314yes—
147C2×C22⋊C4×C61C2314yes—
148C2×C22⋊C4×C61C2314yes—
149#95×C61C2314yes—
150C24×C61—22no—
151C24×C61—22no—
152C24×C61—22no—
153C24×C61—22no—
154C24×C61—22no—
155C24×C61—22no—
156C24×C61—22no—
157C24×C61—22no—
158C24×C61—22no—
159C24×C61—22no—
160C24×C61—22no—
161C24×C61—22no—
162C24×C61—22no—
163C24×C61#4114yes—
164C24×C61C2412yes—
165C24×C61C2412yes—
166C24×C61C2411yescharacteristic
167C23×D61—22no—
168C23×D61—22no—
169C23×D61—22no—
170C23×D61—22no—
171C23×D61—22no—
172C23×D61—22no—
173C23×D61—22no—
174C23×D61C2412yes—
175C2×D4×C61—28no—
176C2×D4×C61—44no—
177C2×D4×C61—44no—
178C2×D4×C61—416no—
179C22×C4×C61—22no—
180C22×C4×C61—22no—
181C22×C4×C61—22no—
182C22×C4×C61—22no—
183C22×C4×C61—22no—
184C22×C4×C61—22no—
185C22×C4×C61—22no—
186C22×C4×C61—22no—
187C22×C4×C61—22no—
188C22×C4×C61—22no—
189C22×C4×C61—22no—
190C22×C4×C61—22no—
191C22×C4×C61—22no—
192C22×C4×C61—22no—
193C22×C4×C61—22no—
194C22×C4×C61C2412yes—
195C22×C4×C61C2412yes—
196C22×C4×C61C2412yes—
197C22×C4×C61C2412yes—
198C22×C4×C61C2412yes—
199C2×C22⋊D61—28no—
200C2×C22⋊D61—28no—
201C2×C22⋊D61—44no—
202C2×C22⋊D61—44no—
203C2×C22⋊D61—44no—
204C2×C22⋊D61—44no—
205C2×C22⋊D61—416no—
206C2×C22⋊D61—416no—
207C22×Dic61—22no—
208C22×Dic61—22no—
209C22×Dic61—22no—
210C22×Dic61—22no—
211C22×Dic61—22no—
212C22×Dic61—22no—
213C22×Dic61—22no—
214C22×Dic61—22no—
215C22×Dic61—22no—
216C22×Dic61—22no—
217C22×Dic61—22no—
218C22×Dic61—22no—
219C22×Dic61—22no—
220C22×Dic61—22no—
221C22×Dic61—22no—
222C22×Dic61—22no—
223C22×Dic61—22no—
224C22×Dic61—22no—
225C22×Dic61—22no—
226C22×Dic61—28no—
227C22×Dic61—44no—
228C22×Dic61—44no—
229C22×Dic61—416no—
230C22×Dic61#4114yes—
231C22×Dic61#4114yes—
232C22×Dic61C2412yes—
233C22×Dic61C2412yes—
234C22×Dic61C2412yes—
235C22×Dic61C2412yes—
236C22×Dic61C2412yes—
237C22×Dic61C2412yes—
238C22×Dic61C2412yes—
239C4⋊C4×C61—44no—
240C22⋊C4×C61—28no—
241C22⋊C4×C61—44no—
242C22⋊C4×C61—44no—
243C22⋊C4×C61—44no—
244C22⋊Dic61—28no—
245C22⋊Dic61—28no—
246C22⋊Dic61—44no—
247C22⋊Dic61—44no—
248C22⋊Dic61—44no—
249#11758198—28no—
250#11758198—44no—
251#11758198—44no—
252#11758198—44no—
253#11758198—44no—
254C4⋊Dic61—44no—
255#11758196—28no—
256#11758196—44no—
257#11758196—44no—
258C4×Dic61—44no—
259C4×Dic61—44no—
260C23×C61—28no—
261C23×C61—28no—
262C23×C61—28no—
263C23×C61—22no—
264C23×C61—22no—
265C23×C61—22no—
266C23×C61—22no—
267C23×C61—22no—
268C23×C61—22no—
269C23×C61—22no—
270C23×C61—22no—
271C23×C61—22no—
272C23×C61—22no—
273C23×C61—22no—
274C23×C61—22no—
275C23×C61—22no—
276C23×C61—44no—
277C23×C61—44no—
278C23×C61—44no—
279C23×C61—44no—
280C23×C61—44no—
281C23×C61—44no—
282C23×C61—44no—
283C23×C61—44no—
284C23×C61—44no—
285C23×C61—44no—
286C23×C61—44no—
287C23×C61C2×#4114yes—
288C23×C61C2×#4112yes—
289C23×C61C2×#4112yes—
290C23×C61C2×#4112yes—
291C23×C61H(5,𝔽2)12yes—
292C23×C61H(5,𝔽2)12yes—
293C23×C61H(5,𝔽2)12yes—
294C23×C61H(5,𝔽2)12yes—
295C23×C61C2511yescharacteristic
296C22×D61—22no—
297C22×D61—22no—
298C22×D61—22no—
299C22×D61—22no—
300C22×D61—22no—
301C22×D61—22no—
302C22×D61—22no—
303C22×D61—44no—
304C22×D61—44no—
305C22×D61—44no—
306C22×D61—44no—
307C22×D61—44no—
308C22×D61—44no—
309C22×D61—44no—
310D4×C61—416no—
311C2×C4×C61—22no—
312C2×C4×C61—22no—
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—44no—
327C2×C4×C61—44no—
328C2×C4×C61—44no—
329C2×C4×C61—44no—
330C2×C4×C61—44no—
331C22⋊D61—416no—
332C22⋊D61—416no—
333C2×Dic61—28no—
334C2×Dic61—28no—
335C2×Dic61—22no—
336C2×Dic61—22no—
337C2×Dic61—22no—
338C2×Dic61—22no—
339C2×Dic61—22no—
340C2×Dic61—22no—
341C2×Dic61—22no—
342C2×Dic61—22no—
343C2×Dic61—22no—
344C2×Dic61—22no—
345C2×Dic61—22no—
346C2×Dic61—22no—
347C2×Dic61—22no—
348C2×Dic61—22no—
349C2×Dic61—22no—
350C2×Dic61—22no—
351C2×Dic61—22no—
352C2×Dic61—22no—
353C2×Dic61—22no—
354C2×Dic61—416no—
355C2×Dic61—44no—
356C2×Dic61—44no—
357C2×Dic61—44no—
358C2×Dic61—44no—
359C2×Dic61—44no—
360C2×Dic61C2×#4114yes—
361C2×Dic61C2×#4114yes—
362C2×#2648—611nomaximal, Sylow
363C22×C61—24no—
364C22×C61—24no—
365C22×C61—24no—
366C22×C61—416no—
367C22×C61—42no—
368C22×C61—42no—
369C22×C61—42no—
370C22×C61—42no—
371C22×C61—42no—
372C22×C61—42no—
373C22×C61—42no—
374C22×C61—42no—
375C22×C61—42no—
376C22×C61—42no—
377C22×C61—42no—
378C22×C61—88no—
379C22×C61#52914yes—
380C22×C61#53814yes—
381C22×C61#53814yes—
382C22×C61#53814yes—
383C22×C61#53814yes—
384C22×C61#54014yes—
385C22×C61#54014yes—
386C22×C61C22×#4111yescharacteristic
387C22×C61C22×#4111yescharacteristic
388C22×C61C22×#4111yescharacteristic
389C22×C61C2×H(5,𝔽2)11yescharacteristic
390C22×C61C2×H(5,𝔽2)11yescharacteristic
391C22×C61C2×H(5,𝔽2)11yescharacteristic
392C22×C61C2×H(5,𝔽2)11yescharacteristic
393C2×D61—42no—
394C2×D61—42no—
395C2×D61—42no—
396C2×D61—42no—
397C2×D61—42no—
398C2×D61—42no—
399C2×D61—42no—
400C2×D61—88no—
401C4×C61—42no—
402C4×C61—42no—
403C4×C61—42no—
404C4×C61—42no—
405C4×C61—42no—
406Dic61—24no—
407Dic61—24no—
408Dic61—42no—
409Dic61—42no—
410Dic61—42no—
411Dic61—42no—
412Dic61—42no—
413#2648—6116no—
414C2×#400—611no—
415C2×#397—611no—
416C2×#397—611no—
417C2×#396—611no—
418C2×#394—611no—
419C2×#394—611no—
420C2×#394D6111yescharacteristic, complemented
421C2×#392—611no—
422C2×#390—611no—
423C2×#388—611no—
424C2×#388—611no—
425C2×#387—611no—
426C2×#386—611no—
427C2×#386—611no—
428C2×C4×C22⋊C4—611no—
429C2×C61—44no—
430C2×C61—82no—
431C2×C61#264818yescomplemented
432C2×C61C2×#52911yescharacteristic
433C2×C61C2×#53811yescharacteristic
434C2×C61C2×#53811yescharacteristic
435C2×C61C2×#53811yescharacteristic
436C2×C61C2×#53811yescharacteristic
437C2×C61C2×#54011yescharacteristic
438C2×C61C2×#54011yescharacteristic
439D61—82no—
440C23×D4—611no—
441C23×D4—611no—
442C23×D4C2×D6111yescharacteristic
443C24×C4—611no—
444C22×C4⋊C4—611no—
445C22×C4⋊C4—611no—
446C22×C4⋊C4—611no—
447C22×C4⋊C4—611no—
448C22×C4⋊C4C2×D6111yescharacteristic
449C22×C22⋊C4—611no—
450C22×C22⋊C4—611no—
451C22×C22⋊C4—611no—
452C22×C22⋊C4—611no—
453C22×C22⋊C4—611no—
454C22×C22⋊C4—611no—
455C22×C22⋊C4—611no—
456C22×C22⋊C4—611no—
457C22×C22⋊C4—611no—
458C22×C22⋊C4—611no—
459C22×C22⋊C4C2×D6111yescharacteristic
460C22×C22⋊C4C2×D6111yescharacteristic
461C22×C22⋊C4C2×D6111yescharacteristic
462C22×C22⋊C4C2×D6111yescharacteristic
463C22×C42—611no—
464C22×C42—611no—
465#400—618no—
466#397—618no—
467#397—618no—
468#396—618no—
469#394—618no—
470#394—618no—
471#394C2×D6118yescomplemented
472#392—618no—
473#390—618no—
474#388—618no—
475#388—618no—
476#387—618no—
477#386—618no—
478#386—618no—
479C4×C22⋊C4—618no—
480C2×#95—611no—
481C2×#95—611no—
482C2×#95—611no—
483C2×#95—611no—
484C2×#95—611no—
485C2×#95—611no—
486C2×#95—611no—
487C2×#95—611no—
488C2×#95—611no—
489C2×#95C2×D6111yescharacteristic
490C61C2×#264811yescharacteristic, complemented, Sylow
491C25—611no—
492C25C22×D6111yescharacteristic
493C25C22×D6111yescharacteristic
494C22×D4—24no—
495C22×D4—42no—
496C22×D4—42no—
497C22×D4—614no—
498C22×D4—614no—
499C22×D4—1224no—
500C22×D4—1224no—
501C22×D4—2442no—
502C22×D4—2442no—
503C22×D4—2442no—
504C22×D4—2442no—
505C22×D4C22×D6114yes—
506C23×C4—611no—
507C23×C4—611no—
508C23×C4—611no—
509C23×C4—611no—
510C23×C4—611no—
511C23×C4—611no—
512C23×C4—611no—
513C23×C4—614no—
514C23×C4—1224no—
515C23×C4—2442no—
516C23×C4—2442no—
517C23×C4C22×D6111yescharacteristic
518C23×C4C22×D6111yescharacteristic
519C23×C4C22×D6111yescharacteristic
520C23×C4C22×D6111yescharacteristic
521C23×C4C22×D6111yescharacteristic
522C2×C4⋊C4—42no—
523C2×C4⋊C4—614no—
524C2×C4⋊C4—614no—
525C2×C4⋊C4—614no—
526C2×C4⋊C4—614no—
527C2×C4⋊C4—1224no—
528C2×C4⋊C4—2442no—
529C2×C4⋊C4—2442no—
530C2×C4⋊C4—2442no—
531C2×C4⋊C4C22×D6114yes—
532C2×C22⋊C4—24no—
533C2×C22⋊C4—42no—
534C2×C22⋊C4—42no—
535C2×C22⋊C4—42no—
536C2×C22⋊C4—614no—
537C2×C22⋊C4—614no—
538C2×C22⋊C4—614no—
539C2×C22⋊C4—614no—
540C2×C22⋊C4—614no—
541C2×C22⋊C4—614no—
542C2×C22⋊C4—614no—
543C2×C22⋊C4—614no—
544C2×C22⋊C4—614no—
545C2×C22⋊C4—614no—
546C2×C22⋊C4—1224no—
547C2×C22⋊C4—1224no—
548C2×C22⋊C4—1224no—
549C2×C22⋊C4—2442no—
550C2×C22⋊C4—2442no—
551C2×C22⋊C4—2442no—
552C2×C22⋊C4—2442no—
553C2×C22⋊C4—2442no—
554C2×C22⋊C4—2442no—
555C2×C22⋊C4—2442no—
556C2×C22⋊C4C22×D6114yes—
557C2×C22⋊C4C22×D6114yes—
558C2×C22⋊C4C22×D6114yes—
559C2×C22⋊C4C22×D6114yes—
560C2×C42—614no—
561C2×C42—614no—
562C2×C42—2442no—
563C2×C42—2442no—
564#95—614no—
565#95—614no—
566#95—614no—
567#95—614no—
568#95—614no—
569#95—614no—
570#95—614no—
571#95—614no—
572#95—614no—
573#95C22×D6114yes—
574C24—22no—
575C24—22no—
576C24—22no—
577C24—22no—
578C24—22no—
579C24—22no—
580C24—22no—
581C24—22no—
582C24—22no—
583C24—22no—
584C24—22no—
585C24—22no—
586C24—22no—
587C24—612no—
588C24—1222no—
589C24—1222no—
590C24—1222no—
591C24—1222no—
592C24—1222no—
593C24—1222no—
594C24—1222no—
595C24#1175822414yes—
596C24C23×D6112yes—
597C24C23×D6112yes—
598C24C23×D6111yescharacteristic
599C2×D4—28no—
600C2×D4—44no—
601C2×D4—44no—
602C2×D4—416no—
603C2×D4—1228no—
604C2×D4—1228no—
605C2×D4—2444no—
606C2×D4—2444no—
607C2×D4—2444no—
608C2×D4—2444no—
609C2×D4—24416no—
610C2×D4—24416no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—614no—
627C22×C4—614no—
628C22×C4—612no—
629C22×C4—612no—
630C22×C4—612no—
631C22×C4—612no—
632C22×C4—612no—
633C22×C4—612no—
634C22×C4—612no—
635C22×C4—1228no—
636C22×C4—1222no—
637C22×C4—1222no—
638C22×C4—1222no—
639C22×C4—1222no—
640C22×C4—1222no—
641C22×C4—1222no—
642C22×C4—1222no—
643C22×C4—1222no—
644C22×C4—1222no—
645C22×C4—1222no—
646C22×C4—1222no—
647C22×C4—1222no—
648C22×C4—1222no—
649C22×C4—1222no—
650C22×C4—1222no—
651C22×C4—1222no—
652C22×C4—1222no—
653C22×C4—1222no—
654C22×C4—1222no—
655C22×C4—2444no—
656C22×C4—2444no—
657C22×C4—24416no—
658C22×C4C23×D6112yes—
659C22×C4C23×D6112yes—
660C22×C4C23×D6112yes—
661C22×C4C23×D6112yes—
662C22×C4C23×D6112yes—
663C4⋊C4—44no—
664C4⋊C4—1228no—
665C4⋊C4—2444no—
666C4⋊C4—2444no—
667C4⋊C4—2444no—
668C22⋊C4—28no—
669C22⋊C4—44no—
670C22⋊C4—44no—
671C22⋊C4—44no—
672C22⋊C4—1228no—
673C22⋊C4—1228no—
674C22⋊C4—1228no—
675C22⋊C4—2444no—
676C22⋊C4—2444no—
677C22⋊C4—2444no—
678C22⋊C4—2444no—
679C22⋊C4—2444no—
680C22⋊C4—2444no—
681C22⋊C4—2444no—
682C42—2444no—
683C42—2444no—
684C23—28no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—28no—
692C23—28no—
693C23—22no—
694C23—22no—
695C23—22no—
696C23—22no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—44no—
701C23—44no—
702C23—44no—
703C23—44no—
704C23—44no—
705C23—44no—
706C23—44no—
707C23—44no—
708C23—44no—
709C23—44no—
710C23—44no—
711C23—1222no—
712C23—1222no—
713C23—1222no—
714C23—1222no—
715C23—1222no—
716C23—1222no—
717C23—1222no—
718C23—2444no—
719C23—2444no—
720C23—2444no—
721C23—2444no—
722C23—2444no—
723C23—2444no—
724C23—2444no—
725C23#41×D6112yes—
726C23#41×D6112yes—
727C23C2×#1175822414yes—
728C23C2×#1175822412yes—
729C23#1451982212yes—
730C23#1451982212yes—
731C23#1451982212yes—
732C23#1451982312yes—
733C23C24×D6111yescharacteristic
734D4—416no—
735D4—24416no—
736D4—24416no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—44no—
753C2×C4—44no—
754C2×C4—44no—
755C2×C4—44no—
756C2×C4—44no—
757C2×C4—614no—
758C2×C4—614no—
759C2×C4—1222no—
760C2×C4—1222no—
761C2×C4—1222no—
762C2×C4—1222no—
763C2×C4—1228no—
764C2×C4—1228no—
765C2×C4—1222no—
766C2×C4—1222no—
767C2×C4—1222no—
768C2×C4—1222no—
769C2×C4—1222no—
770C2×C4—1222no—
771C2×C4—1222no—
772C2×C4—1222no—
773C2×C4—1222no—
774C2×C4—1222no—
775C2×C4—1222no—
776C2×C4—1222no—
777C2×C4—1222no—
778C2×C4—1222no—
779C2×C4—1222no—
780C2×C4—24416no—
781C2×C4—2444no—
782C2×C4—2444no—
783C2×C4—2444no—
784C2×C4—2444no—
785C2×C4—2444no—
786C22—24no—
787C22—24no—
788C22—24no—
789C22—416no—
790C22—42no—
791C22—42no—
792C22—42no—
793C22—42no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—42no—
801C22—88no—
802C22—4888no—
803C22—2442no—
804C22—2442no—
805C22—2442no—
806C22—2442no—
807C22—2442no—
808C22—2442no—
809C22—2442no—
810C22#1684028914yes—
811C22#1684034414yes—
812C22#1684034614yes—
813C22#1684034714yes—
814C22#1684034914yes—
815C22#1684036214yes—
816C22#1684036414yes—
817C22C2×#41×D6111yescharacteristic
818C22C2×#41×D6111yescharacteristic
819C22C22×#1175822411yescharacteristic
820C22C2×#1451982211yescharacteristic
821C22C2×#1451982211yescharacteristic
822C22C2×#1451982211yescharacteristic
823C22C2×#1451982311yescharacteristic
824C4—42no—
825C4—42no—
826C4—42no—
827C4—42no—
828C4—42no—
829C4—1224no—
830C4—1224no—
831C4—2442no—
832C4—2442no—
833C4—2442no—
834C4—2442no—
835C4—2442no—
836C2—44no—
837C2—82no—
838C2—4882no—
839C2#2145180218yesdirect product factor
840C2C2×#1684028911yescharacteristic
841C2C2×#1684034411yescharacteristic
842C2C2×#1684034611yescharacteristic
843C2C2×#1684034711yescharacteristic
844C2C2×#1684034911yescharacteristic
845C2C2×#1684036211yescharacteristic
846C2C2×#1684036411yescharacteristic
subgroupG/H
centerC24C23×D61
commutator, cosocleC23×C61C25
FrattiniC23C24×D61
FittingC2×C61×#394C2
socleC24×C61C24
prime radicalC2×#16839670C2
hypercenterC2×#394D61
hypocenterC61C2×#2648
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
1. #21451802C2direct (N × H)
2. C2×#16839703C2semidirect
3. C2×#16839688C2semidirect
4. C2×#16839687C2semidirect
5. C2×#16839685C2semidirect
6. C2×#16839677C2semidirect
7. C2×#16839677C2semidirect
9. C2×#16839662C2semidirect
10. C2×#16839656C2semidirect
11. C2×#16839654C2semidirect
12. C2×#16839643C2semidirect
13. C2×#16839642C2semidirect
14. C2×#16839639C2semidirect
15. C2×C22⋊C4×Dic61C2semidirect
16. C2×C61×#394C2semidirect
36. #16839703C22semidirect
37. #16839688C22semidirect
38. #16839687C22semidirect
39. #16839685C22semidirect
40. #16839677C22semidirect
41. #16839677C22semidirect
43. #16839662C22semidirect
44. #16839656C22semidirect
45. #16839654C22semidirect
46. #16839643C22semidirect
47. #16839642C22semidirect
48. #16839639C22semidirect
49. C22⋊C4×Dic61C22semidirect
65. C61×#394C22semidirect
420. C2×#394D61semidirect
431. C2×C61#2648semidirect
471. #394C2×D61semidirect
490. C61C2×#2648semidirect
839. C2#21451802direct (N × H)

Maximal subgroups

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

subgroupindex
#214518022
C2×#168397032
C2×#168396882
C2×#168396872
C2×#168396852
C2×#168396772
C2×#168396702
C2×#168396622
C2×#168396562
C2×#168396542
C2×#168396432
C2×#168396422
C2×#168396392
C2×C22⋊C4×Dic612
C2×C61×#3942
C2×#264861