Finite Group Databasebeta

← C2×#21451847 #29846643

Subgroups — C2×#21451847 #29846643

Order 15616.

2222 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21451847C2116yesmaximal, direct product factor
2C2×#16839697C211yesmaximal, characteristic, complemented
3C2×#16839696C211yesmaximal, characteristic, complemented
4C2×#16839694C211yesmaximal, characteristic, complemented
5C2×#16839689C211yesmaximal, characteristic, complemented
6C2×#16839685C211yesmaximal, characteristic, complemented
7C2×#16839678C211yesmaximal, characteristic
8C2×#16839678C211yesmaximal, characteristic
9C2×#16839662C211yesmaximal, characteristic
10C2×#16839656C211yesmaximal, characteristic, complemented
11C2×#16839655C211yesmaximal, characteristic, complemented
12C2×#16839654C211yesmaximal, characteristic, complemented
13C2×#16839651C211yesmaximal, characteristic, complemented
14C2×#16839647C211yesmaximal, characteristic, complemented
15C2×C4⋊C4×Dic61C211yesmaximal, characteristic, complemented
16C2×C61×#397C211yesmaximal, characteristic, complemented
17C23×C22⋊D61C2211yescharacteristic
18C22×C4⋊Dic61C2211yescharacteristic
19C22×C4⋊Dic61C2211yescharacteristic
20C22×C4⋊Dic61C2211yescharacteristic
21C22×C4⋊Dic61C2211yescharacteristic
22C22×#11758196C2211yescharacteristic
23C22×#11758196C2211yescharacteristic
24C22×#11758196C2211yescharacteristic
25C22×#11758196C2211yescharacteristic
26C22×C22⋊Dic61C2211yescharacteristic
27C22×C22⋊Dic61C2211yescharacteristic
28C22×C22⋊Dic61C2211yescharacteristic
29C22×#11758198C2211yescharacteristic
30C22×#11758198C2211yescharacteristic
31C22×#11758198C2211yescharacteristic
32C22×#11758198C2211yescharacteristic
33C22×#11758198C2211yescharacteristic
34C22×#11758198C2211yescharacteristic
35C22×C4×Dic61C2211yescharacteristic
36C22×C4×Dic61C2211yescharacteristic
37C22×C4×Dic61C2211yescharacteristic
38#16839697C2218yescomplemented
39#16839696C2218yescomplemented
40#16839694C2218yescomplemented
41#16839689C2218yescomplemented
42#16839685C2218yescomplemented
43#16839678C2218yes—
44#16839678C2218yes—
45#16839662C2218yes—
46#16839656C2218yescomplemented
47#16839655C2218yescomplemented
48#16839654C2218yescomplemented
49#16839651C2218yescomplemented
50#16839647C2218yescomplemented
51C4⋊C4×Dic61C2218yescomplemented
52C2×#14519684C2211yescharacteristic
53C2×#14519684C2211yescharacteristic
54C2×#14519684C2211yescharacteristic
55C2×#14519684C2211yescharacteristic
56C2×#14519684C2211yescharacteristic
57C2×#14519684C2211yescharacteristic
58C2×#14519684C2211yescharacteristic
59C22×C4⋊C4×C61C2211yescharacteristic
60C22×C22⋊C4×C61C2211yescharacteristic
61C22×C22⋊C4×C61C2211yescharacteristic
62C22×C22⋊C4×C61C2211yescharacteristic
63C61×#397C2218yescomplemented
64C2×#95×C61C2211yescharacteristic
65C2×#95×C61C2211yescharacteristic
66C2×#95×C61C2211yescharacteristic
67C24×D61C2311yescharacteristic
68C22×C22⋊D61—24no—
69C22×C22⋊D61—42no—
70C22×C22⋊D61—42no—
71C22×C22⋊D61C2314yes—
72C23×Dic61C2311yescharacteristic
73C23×Dic61C2311yescharacteristic
74C23×Dic61C2311yescharacteristic
75C23×Dic61C2311yescharacteristic
76C23×Dic61C2311yescharacteristic
77C23×Dic61C2311yescharacteristic
78C23×Dic61C2311yescharacteristic
79C2×C4⋊Dic61—24no—
80C2×C4⋊Dic61—24no—
81C2×C4⋊Dic61—42no—
82C2×C4⋊Dic61—42no—
83C2×C4⋊Dic61C2314yes—
84C2×C4⋊Dic61C2314yes—
85C2×C4⋊Dic61C2314yes—
86C2×C4⋊Dic61C2314yes—
87C2×#11758196—42no—
88C2×#11758196—42no—
89C2×#11758196—42no—
90C2×#11758196—42no—
91C2×#11758196C2314yes—
92C2×#11758196C2314yes—
93C2×#11758196C2314yes—
94C2×#11758196C2314yes—
95C2×C22⋊Dic61—24no—
96C2×C22⋊Dic61—42no—
97C2×C22⋊Dic61—42no—
98C2×C22⋊Dic61C2314yes—
99C2×C22⋊Dic61C2314yes—
100C2×C22⋊Dic61C2314yes—
101C2×#11758198—24no—
102C2×#11758198—24no—
103C2×#11758198—42no—
104C2×#11758198—42no—
105C2×#11758198—42no—
106C2×#11758198—42no—
107C2×#11758198C2314yes—
108C2×#11758198C2314yes—
109C2×#11758198C2314yes—
110C2×#11758198C2314yes—
111C2×#11758198C2314yes—
112C2×#11758198C2314yes—
113C2×C4×Dic61—24no—
114C2×C4×Dic61—42no—
115C2×C4×Dic61—42no—
116C2×C4×Dic61C2314yes—
117C2×C4×Dic61C2314yes—
118C2×C4×Dic61C2314yes—
119#14519684C2314yes—
120#14519684C2314yes—
121#14519684C2314yes—
122#14519684C2314yes—
123#14519684C2314yes—
124#14519684C2314yes—
125#14519684C2314yes—
126C25×C61C2311yescharacteristic
127C23×C4×C61C2311yescharacteristic
128C23×C4×C61C2311yescharacteristic
129C23×C4×C61C2311yescharacteristic
130C23×C4×C61C2311yescharacteristic
131C23×C4×C61C2311yescharacteristic
132C23×C4×C61C2311yescharacteristic
133C2×C4⋊C4×C61—24no—
134C2×C4⋊C4×C61C2314yes—
135C2×C22⋊C4×C61—24no—
136C2×C22⋊C4×C61—42no—
137C2×C22⋊C4×C61—42no—
138C2×C22⋊C4×C61C2314yes—
139C2×C22⋊C4×C61C2314yes—
140C2×C22⋊C4×C61C2314yes—
141#95×C61C2314yes—
142#95×C61C2314yes—
143#95×C61C2314yes—
144C24×C61—22no—
145C24×C61—22no—
146C24×C61—22no—
147C24×C61—22no—
148C24×C61—22no—
149C24×C61—22no—
150C24×C61—22no—
151C24×C61C2412yes—
152C24×C61C2411yescharacteristic
153C23×D61—22no—
154C23×D61—22no—
155C23×D61—22no—
156C23×D61—22no—
157C23×D61—22no—
158C23×D61—22no—
159C23×D61—22no—
160C23×D61C2412yes—
161C22×C4×C61—22no—
162C22×C4×C61—22no—
163C22×C4×C61—22no—
164C22×C4×C61—22no—
165C22×C4×C61—22no—
166C22×C4×C61—22no—
167C22×C4×C61—22no—
168C22×C4×C61—22no—
169C22×C4×C61—22no—
170C22×C4×C61—22no—
171C22×C4×C61—22no—
172C22×C4×C61—22no—
173C22×C4×C61—22no—
174C22×C4×C61—22no—
175C22×C4×C61—22no—
176C22×C4×C61—22no—
177C22×C4×C61—22no—
178C22×C4×C61#4114yes—
179C22×C4×C61C2412yes—
180C22×C4×C61C2412yes—
181C22×C4×C61C2412yes—
182C22×C4×C61C2412yes—
183C22×C4×C61C2412yes—
184C22×C4×C61C2412yes—
185C2×C22⋊D61—28no—
186C2×C22⋊D61—44no—
187C2×C22⋊D61—44no—
188C2×C22⋊D61—416no—
189C22×Dic61—22no—
190C22×Dic61—22no—
191C22×Dic61—22no—
192C22×Dic61—22no—
193C22×Dic61—22no—
194C22×Dic61—22no—
195C22×Dic61—22no—
196C22×Dic61—22no—
197C22×Dic61—22no—
198C22×Dic61—22no—
199C22×Dic61—22no—
200C22×Dic61—22no—
201C22×Dic61—22no—
202C22×Dic61—22no—
203C22×Dic61—22no—
204C22×Dic61—22no—
205C22×Dic61—22no—
206C22×Dic61—22no—
207C22×Dic61—22no—
208C22×Dic61#4114yes—
209C22×Dic61#4114yes—
210C22×Dic61C2412yes—
211C22×Dic61C2412yes—
212C22×Dic61C2412yes—
213C22×Dic61C2412yes—
214C22×Dic61C2412yes—
215C22×Dic61C2412yes—
216C22×Dic61C2412yes—
217C4⋊C4×C61—28no—
218C22⋊C4×C61—28no—
219C22⋊C4×C61—44no—
220C22⋊C4×C61—44no—
221C22⋊Dic61—28no—
222C22⋊Dic61—44no—
223C22⋊Dic61—44no—
224#11758198—28no—
225#11758198—28no—
226#11758198—44no—
227#11758198—44no—
228#11758198—44no—
229#11758198—44no—
230C4⋊Dic61—28no—
231C4⋊Dic61—28no—
232C4⋊Dic61—44no—
233C4⋊Dic61—44no—
234#11758196—44no—
235#11758196—44no—
236#11758196—44no—
237#11758196—44no—
238C4×Dic61—28no—
239C4×Dic61—44no—
240C4×Dic61—44no—
241C23×C61—22no—
242C23×C61—22no—
243C23×C61—22no—
244C23×C61—22no—
245C23×C61—22no—
246C23×C61—22no—
247C23×C61—22no—
248C23×C61—44no—
249C23×C61—44no—
250C23×C61—44no—
251C23×C61—44no—
252C23×C61—44no—
253C23×C61—44no—
254C23×C61—44no—
255C23×C61C2×#4112yes—
256C23×C61C2×#4112yes—
257C23×C61C2×#4112yes—
258C23×C61H(5,𝔽2)12yes—
259C23×C61H(5,𝔽2)12yes—
260C23×C61H(5,𝔽2)12yes—
261C23×C612−1+412yes—
262C23×C61C2511yescharacteristic
263C22×D61—22no—
264C22×D61—22no—
265C22×D61—22no—
266C22×D61—22no—
267C22×D61—22no—
268C22×D61—22no—
269C22×D61—22no—
270C22×D61—44no—
271C22×D61—44no—
272C22×D61—44no—
273C22×D61—44no—
274C22×D61—44no—
275C22×D61—44no—
276C22×D61—44no—
277C2×C4×C61—28no—
278C2×C4×C61—22no—
279C2×C4×C61—22no—
280C2×C4×C61—22no—
281C2×C4×C61—22no—
282C2×C4×C61—22no—
283C2×C4×C61—22no—
284C2×C4×C61—22no—
285C2×C4×C61—22no—
286C2×C4×C61—22no—
287C2×C4×C61—22no—
288C2×C4×C61—22no—
289C2×C4×C61—22no—
290C2×C4×C61—22no—
291C2×C4×C61—22no—
292C2×C4×C61—22no—
293C2×C4×C61—22no—
294C2×C4×C61—22no—
295C2×C4×C61—44no—
296C2×C4×C61—44no—
297C2×C4×C61—44no—
298C2×C4×C61—44no—
299C2×C4×C61—44no—
300C2×C4×C61C2×#4114yes—
301C22⋊D61—416no—
302C2×Dic61—28no—
303C2×Dic61—28no—
304C2×Dic61—22no—
305C2×Dic61—22no—
306C2×Dic61—22no—
307C2×Dic61—22no—
308C2×Dic61—22no—
309C2×Dic61—22no—
310C2×Dic61—22no—
311C2×Dic61—22no—
312C2×Dic61—22no—
313C2×Dic61—22no—
314C2×Dic61—22no—
315C2×Dic61—22no—
316C2×Dic61—22no—
317C2×Dic61—22no—
318C2×Dic61—22no—
319C2×Dic61—22no—
320C2×Dic61—22no—
321C2×Dic61—22no—
322C2×Dic61—22no—
323C2×Dic61—44no—
324C2×Dic61—44no—
325C2×Dic61—44no—
326C2×Dic61—44no—
327C2×Dic61—44no—
328C2×Dic61C2×#4114yes—
329C2×Dic61C2×#4114yes—
330C2×#2651—611nomaximal, Sylow
331C22×C61—42no—
332C22×C61—42no—
333C22×C61—42no—
334C22×C61—42no—
335C22×C61—42no—
336C22×C61—42no—
337C22×C61—42no—
338C22×C61—88no—
339C22×C61#52914yes—
340C22×C61#53814yes—
341C22×C61#53914yes—
342C22×C61#54014yes—
343C22×C61#54014yes—
344C22×C61#54214yes—
345C22×C61#54214yes—
346C22×C61C22×#4111yescharacteristic
347C22×C61C22×#4111yescharacteristic
348C22×C61C22×#4111yescharacteristic
349C22×C61C2×H(5,𝔽2)11yescharacteristic
350C22×C61C2×H(5,𝔽2)11yescharacteristic
351C22×C61C2×H(5,𝔽2)11yescharacteristic
352C22×C61C2×2−1+411yescharacteristic
353C2×D61—42no—
354C2×D61—42no—
355C2×D61—42no—
356C2×D61—42no—
357C2×D61—42no—
358C2×D61—42no—
359C2×D61—42no—
360C2×D61—88no—
361C4×C61—24no—
362C4×C61—42no—
363C4×C61—42no—
364C4×C61—42no—
365C4×C61—42no—
366C4×C61—42no—
367Dic61—24no—
368Dic61—24no—
369Dic61—42no—
370Dic61—42no—
371Dic61—42no—
372Dic61—42no—
373Dic61—42no—
374#2651—6116no—
375C2×#399—611no—
376C2×#398—611no—
377C2×#398—611no—
378C2×#397—611no—
379C2×#397D6111yescharacteristic, complemented
380C2×#396—611no—
381C2×#394—611no—
382C2×#394—611no—
383C2×#390—611no—
384C2×#388—611no—
385C2×#388—611no—
386C2×#388—611no—
387C2×#388—611no—
388C2×#387—611no—
389C2×C4×C4⋊C4—611no—
390C2×C61—82no—
391C2×C61#265118yescomplemented
392C2×C61C2×#52911yescharacteristic
393C2×C61C2×#53811yescharacteristic
394C2×C61C2×#53911yescharacteristic
395C2×C61C2×#54011yescharacteristic
396C2×C61C2×#54011yescharacteristic
397C2×C61C2×#54211yescharacteristic
398C2×C61C2×#54211yescharacteristic
399D61—82no—
400C23×D4—611no—
401C22×C4⋊C4—611no—
402C22×C4⋊C4—611no—
403C22×C4⋊C4—611no—
404C22×C4⋊C4—611no—
405C22×C4⋊C4—611no—
406C22×C4⋊C4—611no—
407C22×C4⋊C4—611no—
408C22×C4⋊C4—611no—
409C22×C4⋊C4C2×D6111yescharacteristic
410C22×C22⋊C4—611no—
411C22×C22⋊C4—611no—
412C22×C22⋊C4—611no—
413C22×C22⋊C4—611no—
414C22×C22⋊C4—611no—
415C22×C22⋊C4—611no—
416C22×C22⋊C4—611no—
417C22×C22⋊C4—611no—
418C22×C22⋊C4—611no—
419C22×C22⋊C4C2×D6111yescharacteristic
420C22×C22⋊C4C2×D6111yescharacteristic
421C22×C22⋊C4C2×D6111yescharacteristic
422C22×C42—611no—
423C22×C42—611no—
424C22×C42—611no—
425#399—618no—
426#398—618no—
427#398—618no—
428#397—618no—
429#397C2×D6118yescomplemented
430#396—618no—
431#394—618no—
432#394—618no—
433#390—618no—
434#388—618no—
435#388—618no—
436#388—618no—
437#388—618no—
438#387—618no—
439C4×C4⋊C4—618no—
440C2×#95—611no—
441C2×#95—611no—
442C2×#95—611no—
443C2×#95—611no—
444C2×#95—611no—
445C2×#95—611no—
446C2×#95—611no—
447C2×#95C2×D6111yescharacteristic
448C2×#95C2×D6111yescharacteristic
449C2×#95C2×D6111yescharacteristic
450C61C2×#265111yescharacteristic, complemented, Sylow
451C25—611no—
452C25C22×D6111yescharacteristic
453C22×D4—614no—
454C22×D4—1224no—
455C22×D4—2442no—
456C22×D4—2442no—
457C23×C4—611no—
458C23×C4—611no—
459C23×C4—611no—
460C23×C4—611no—
461C23×C4—611no—
462C23×C4—611no—
463C23×C4—611no—
464C23×C4C22×D6111yescharacteristic
465C23×C4C22×D6111yescharacteristic
466C23×C4C22×D6111yescharacteristic
467C23×C4C22×D6111yescharacteristic
468C23×C4C22×D6111yescharacteristic
469C23×C4C22×D6111yescharacteristic
470C2×C4⋊C4—24no—
471C2×C4⋊C4—614no—
472C2×C4⋊C4—614no—
473C2×C4⋊C4—614no—
474C2×C4⋊C4—614no—
475C2×C4⋊C4—614no—
476C2×C4⋊C4—614no—
477C2×C4⋊C4—614no—
478C2×C4⋊C4—614no—
479C2×C4⋊C4—1224no—
480C2×C4⋊C4—1224no—
481C2×C4⋊C4—2442no—
482C2×C4⋊C4—2442no—
483C2×C4⋊C4—2442no—
484C2×C4⋊C4—2442no—
485C2×C4⋊C4—2442no—
486C2×C4⋊C4—2442no—
487C2×C4⋊C4C22×D6114yes—
488C2×C22⋊C4—24no—
489C2×C22⋊C4—42no—
490C2×C22⋊C4—42no—
491C2×C22⋊C4—614no—
492C2×C22⋊C4—614no—
493C2×C22⋊C4—614no—
494C2×C22⋊C4—614no—
495C2×C22⋊C4—614no—
496C2×C22⋊C4—614no—
497C2×C22⋊C4—614no—
498C2×C22⋊C4—614no—
499C2×C22⋊C4—614no—
500C2×C22⋊C4—1224no—
501C2×C22⋊C4—1224no—
502C2×C22⋊C4—1224no—
503C2×C22⋊C4—2442no—
504C2×C22⋊C4—2442no—
505C2×C22⋊C4—2442no—
506C2×C22⋊C4—2442no—
507C2×C22⋊C4—2442no—
508C2×C22⋊C4—2442no—
509C2×C22⋊C4C22×D6114yes—
510C2×C22⋊C4C22×D6114yes—
511C2×C22⋊C4C22×D6114yes—
512C2×C42—614no—
513C2×C42—614no—
514C2×C42—614no—
515C2×C42—1224no—
516C2×C42—2442no—
517C2×C42—2442no—
518#95—614no—
519#95—614no—
520#95—614no—
521#95—614no—
522#95—614no—
523#95—614no—
524#95—614no—
525#95C22×D6114yes—
526#95C22×D6114yes—
527#95C22×D6114yes—
528C24—22no—
529C24—22no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—22no—
534C24—22no—
535C24—612no—
536C24—1222no—
537C24—1222no—
538C24—1222no—
539C24—1222no—
540C24—1222no—
541C24—1222no—
542C24—1222no—
543C24C23×D6112yes—
544C24C23×D6111yescharacteristic
545C2×D4—1228no—
546C2×D4—2444no—
547C2×D4—2444no—
548C2×D4—24416no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—614no—
567C22×C4—614no—
568C22×C4—612no—
569C22×C4—612no—
570C22×C4—612no—
571C22×C4—612no—
572C22×C4—612no—
573C22×C4—612no—
574C22×C4—612no—
575C22×C4—1222no—
576C22×C4—1222no—
577C22×C4—1222no—
578C22×C4—1222no—
579C22×C4—1222no—
580C22×C4—1222no—
581C22×C4—1222no—
582C22×C4—1222no—
583C22×C4—1222no—
584C22×C4—1222no—
585C22×C4—1222no—
586C22×C4—1222no—
587C22×C4—1222no—
588C22×C4—1222no—
589C22×C4—1222no—
590C22×C4—1222no—
591C22×C4—1222no—
592C22×C4—1222no—
593C22×C4—1222no—
594C22×C4#1175822414yes—
595C22×C4C23×D6112yes—
596C22×C4C23×D6112yes—
597C22×C4C23×D6112yes—
598C22×C4C23×D6112yes—
599C22×C4C23×D6112yes—
600C22×C4C23×D6112yes—
601C4⋊C4—28no—
602C4⋊C4—1228no—
603C4⋊C4—1228no—
604C4⋊C4—2444no—
605C4⋊C4—2444no—
606C4⋊C4—2444no—
607C4⋊C4—2444no—
608C4⋊C4—2444no—
609C4⋊C4—2444no—
610C22⋊C4—28no—
611C22⋊C4—44no—
612C22⋊C4—44no—
613C22⋊C4—1228no—
614C22⋊C4—1228no—
615C22⋊C4—1228no—
616C22⋊C4—2444no—
617C22⋊C4—2444no—
618C22⋊C4—2444no—
619C22⋊C4—2444no—
620C22⋊C4—2444no—
621C22⋊C4—2444no—
622C42—1228no—
623C42—2444no—
624C42—2444no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—44no—
633C23—44no—
634C23—44no—
635C23—44no—
636C23—44no—
637C23—44no—
638C23—44no—
639C23—1222no—
640C23—1222no—
641C23—1222no—
642C23—1222no—
643C23—1222no—
644C23—1222no—
645C23—1222no—
646C23—2444no—
647C23—2444no—
648C23—2444no—
649C23—2444no—
650C23—2444no—
651C23—2444no—
652C23—2444no—
653C23#41×D6112yes—
654C23#41×D6112yes—
655C23C2×#1175822412yes—
656C23#1451982212yes—
657C23#1451982312yes—
658C23#1451982312yes—
659C23#1451982412yes—
660C23C24×D6111yescharacteristic
661D4—24416no—
662C2×C4—28no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—44no—
681C2×C4—44no—
682C2×C4—44no—
683C2×C4—44no—
684C2×C4—44no—
685C2×C4—614no—
686C2×C4—614no—
687C2×C4—1222no—
688C2×C4—1222no—
689C2×C4—1222no—
690C2×C4—1222no—
691C2×C4—1228no—
692C2×C4—1228no—
693C2×C4—1222no—
694C2×C4—1222no—
695C2×C4—1222no—
696C2×C4—1222no—
697C2×C4—1222no—
698C2×C4—1222no—
699C2×C4—1222no—
700C2×C4—1222no—
701C2×C4—1222no—
702C2×C4—1222no—
703C2×C4—1222no—
704C2×C4—1222no—
705C2×C4—1222no—
706C2×C4—1222no—
707C2×C4—1222no—
708C2×C4—2444no—
709C2×C4—2444no—
710C2×C4—2444no—
711C2×C4—2444no—
712C2×C4—2444no—
713C2×C4C2×#1175822414yes—
714C22—42no—
715C22—42no—
716C22—42no—
717C22—42no—
718C22—42no—
719C22—42no—
720C22—42no—
721C22—88no—
722C22—4888no—
723C22—2442no—
724C22—2442no—
725C22—2442no—
726C22—2442no—
727C22—2442no—
728C22—2442no—
729C22—2442no—
730C22#1684028914yes—
731C22#1684035114yes—
732C22#1684035314yes—
733C22#1684036414yes—
734C22#1684036514yes—
735C22#1684038014yes—
736C22#1684038114yes—
737C22C2×#41×D6111yescharacteristic
738C22C2×#41×D6111yescharacteristic
739C22C22×#1175822411yescharacteristic
740C22C2×#1451982211yescharacteristic
741C22C2×#1451982311yescharacteristic
742C22C2×#1451982311yescharacteristic
743C22C2×#1451982411yescharacteristic
744C4—24no—
745C4—42no—
746C4—42no—
747C4—42no—
748C4—42no—
749C4—42no—
750C4—1224no—
751C4—1224no—
752C4—2442no—
753C4—2442no—
754C4—2442no—
755C4—2442no—
756C4—2442no—
757C2—82no—
758C2—4882no—
759C2#2145184718yesdirect product factor
760C2C2×#1684028911yescharacteristic
761C2C2×#1684035111yescharacteristic
762C2C2×#1684035311yescharacteristic
763C2C2×#1684036411yescharacteristic
764C2C2×#1684036511yescharacteristic
765C2C2×#1684038011yescharacteristic
766C2C2×#1684038111yescharacteristic
subgroupG/H
centerC24C23×D61
commutator, cosocleC23×C61C25
FrattiniC23C24×D61
FittingC2×C61×#397C2
socleC24×C61C24
prime radicalC23×C22⋊D61C22
hypercenterC2×#397D61
hypocenterC61C2×#2651
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#397

Complements

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

NH ≅ G/Ntype
1. #21451847C2direct (N × H)
2. C2×#16839697C2semidirect
3. C2×#16839696C2semidirect
4. C2×#16839694C2semidirect
5. C2×#16839689C2semidirect
6. C2×#16839685C2semidirect
10. C2×#16839656C2semidirect
11. C2×#16839655C2semidirect
12. C2×#16839654C2semidirect
13. C2×#16839651C2semidirect
14. C2×#16839647C2semidirect
15. C2×C4⋊C4×Dic61C2semidirect
16. C2×C61×#397C2semidirect
38. #16839697C22semidirect
39. #16839696C22semidirect
40. #16839694C22semidirect
41. #16839689C22semidirect
42. #16839685C22semidirect
46. #16839656C22semidirect
47. #16839655C22semidirect
48. #16839654C22semidirect
49. #16839651C22semidirect
50. #16839647C22semidirect
51. C4⋊C4×Dic61C22semidirect
63. C61×#397C22semidirect
379. C2×#397D61semidirect
391. C2×C61#2651semidirect
429. #397C2×D61semidirect
450. C61C2×#2651semidirect
759. C2#21451847direct (N × H)

Maximal subgroups

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

subgroupindex
#214518472
C2×#168396972
C2×#168396962
C2×#168396942
C2×#168396892
C2×#168396852
C2×#168396782
C2×#168396622
C2×#168396562
C2×#168396552
C2×#168396542
C2×#168396512
C2×#168396472
C2×C4⋊C4×Dic612
C2×C61×#3972
C2×#265161