Finite Group Databasebeta

← C2×#21451097 #29850253

Subgroups — C2×#21451097 #29850253

Order 15616.

2334 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21451097C2116yesmaximal, direct product factor
2C2×#16839696C211yesmaximal, characteristic, complemented
3C2×#16839684C211yesmaximal, characteristic
4C2×#16839683C211yesmaximal, characteristic, complemented
5C2×#16839675C211yesmaximal, characteristic
6C2×#16839666C211yesmaximal, characteristic, complemented
7C2×#16839654C211yesmaximal, characteristic
8C2×#16839654C211yesmaximal, characteristic
9C2×#16839644C211yesmaximal, characteristic, complemented
10C2×#16839643C211yesmaximal, characteristic, complemented
11C2×#16839633C211yesmaximal, characteristic
12C2×#16839628C211yesmaximal, characteristic, complemented
13C2×#16839621C211yesmaximal, characteristic
14C2×C4⋊C4×Dic61C211yesmaximal, characteristic, complemented
15C2×C4×#11758198C211yesmaximal, characteristic
16C2×C61×#387C211yesmaximal, characteristic, complemented
17C23×Dic122C2211yescharacteristic
18C23×C4×D61C2211yescharacteristic
19C22×C4⋊Dic61C2211yescharacteristic
20C22×C4⋊Dic61C2211yescharacteristic
21C22×C4⋊Dic61C2211yescharacteristic
22C22×#11758196C2211yescharacteristic
23C22×#11758196C2211yescharacteristic
24C22×#11758196C2211yescharacteristic
25C22×#11758196C2211yescharacteristic
26C22×#11758198C2211yescharacteristic
27C22×#11758198C2211yescharacteristic
28C22×#11758198C2211yescharacteristic
29C22×#11758198C2211yescharacteristic
30C22×#11758198C2211yescharacteristic
31C22×#11758198C2211yescharacteristic
32C22×C4×Dic61C2211yescharacteristic
33C22×C4×Dic61C2211yescharacteristic
34C22×C4×Dic61C2211yescharacteristic
35#16839696C2218yescomplemented
36#16839684C2218yes—
37#16839683C2218yescomplemented
38#16839675C2218yes—
39#16839666C2218yescomplemented
40#16839654C2218yes—
41#16839654C2218yes—
42#16839644C2218yescomplemented
43#16839643C2218yescomplemented
44#16839633C2218yes—
45#16839628C2218yescomplemented
46#16839621C2218yes—
47C4⋊C4×Dic61C2218yescomplemented
48C4×#11758198C2218yes—
49C2×#14519684C2211yescharacteristic
50C2×#14519684C2211yescharacteristic
51C2×#14519684C2211yescharacteristic
52C2×#14519684C2211yescharacteristic
53C2×#14519684C2211yescharacteristic
54C2×#14519684C2211yescharacteristic
55C2×#14519684C2211yescharacteristic
56C2×#14519684C2211yescharacteristic
57C2×#14519684C2211yescharacteristic
58C2×#14519684C2211yescharacteristic
59C22×C4⋊C4×C61C2211yescharacteristic
60C22×C4⋊C4×C61C2211yescharacteristic
61C22×C42×C61C2211yescharacteristic
62C61×#387C2218yescomplemented
63C2×#95×C61C2211yescharacteristic
64C2×#95×C61C2211yescharacteristic
65C2×#95×C61C2211yescharacteristic
66C2×#95×C61C2211yescharacteristic
67C24×D61C2311yescharacteristic
68C22×Dic122—24no—
69C22×Dic122—42no—
70C22×Dic122—42no—
71C22×Dic122C2314yes—
72C23×Dic61C2311yescharacteristic
73C23×Dic61C2311yescharacteristic
74C23×Dic61C2311yescharacteristic
75C23×Dic61C2311yescharacteristic
76C23×Dic61C2311yescharacteristic
77C23×Dic61C2311yescharacteristic
78C23×Dic61C2311yescharacteristic
79C22×C4×D61—24no—
80C22×C4×D61—24no—
81C22×C4×D61—42no—
82C22×C4×D61C2314yes—
83C2×C4⋊Dic61—24no—
84C2×C4⋊Dic61—42no—
85C2×C4⋊Dic61—42no—
86C2×C4⋊Dic61C2314yes—
87C2×C4⋊Dic61C2314yes—
88C2×C4⋊Dic61C2314yes—
89C2×#11758196—24no—
90C2×#11758196—24no—
91C2×#11758196—42no—
92C2×#11758196—42no—
93C2×#11758196C2314yes—
94C2×#11758196C2314yes—
95C2×#11758196C2314yes—
96C2×#11758196C2314yes—
97C2×#11758198—24no—
98C2×#11758198—24no—
99C2×#11758198—42no—
100C2×#11758198—42no—
101C2×#11758198—42no—
102C2×#11758198Q818yescomplemented
103C2×#11758198C2314yes—
104C2×#11758198C2314yes—
105C2×#11758198C2314yes—
106C2×#11758198C2314yes—
107C2×#11758198C2314yes—
108C2×#11758198C2314yes—
109C2×C4×Dic61—24no—
110C2×C4×Dic61—42no—
111C2×C4×Dic61—42no—
112C2×C4×Dic61C2314yes—
113C2×C4×Dic61C2314yes—
114C2×C4×Dic61C2314yes—
115#14519684C2314yes—
116#14519684C2314yes—
117#14519684C2314yes—
118#14519684C2314yes—
119#14519684C2314yes—
120#14519684C2314yes—
121#14519684C2314yes—
122#14519684C2314yes—
123#14519684C2314yes—
124#14519684C2314yes—
125C23×C4×C61C2311yescharacteristic
126C23×C4×C61C2311yescharacteristic
127C23×C4×C61C2311yescharacteristic
128C23×C4×C61C2311yescharacteristic
129C23×C4×C61C2311yescharacteristic
130C23×C4×C61C2311yescharacteristic
131C23×C4×C61C2311yescharacteristic
132C2×C4⋊C4×C61—24no—
133C2×C4⋊C4×C61—24no—
134C2×C4⋊C4×C61C2314yes—
135C2×C4⋊C4×C61C2314yes—
136C2×C42×C61—24no—
137C2×C42×C61C2314yes—
138#95×C61C2314yes—
139#95×C61C2314yes—
140#95×C61C2314yes—
141#95×C61C2314yes—
142C24×C61C2411yescharacteristic
143C23×D61—22no—
144C23×D61—22no—
145C23×D61—22no—
146C23×D61—22no—
147C23×D61—22no—
148C23×D61—22no—
149C23×D61C2×Q814yes—
150C23×D61C2412yes—
151C22×C4×C61—22no—
152C22×C4×C61—22no—
153C22×C4×C61—22no—
154C22×C4×C61—22no—
155C22×C4×C61—22no—
156C22×C4×C61—22no—
157C22×C4×C61—22no—
158C22×C4×C61—22no—
159C22×C4×C61—22no—
160C22×C4×C61—22no—
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×C61C2×Q814yes—
170C22×C4×C61#4114yes—
171C22×C4×C61#4114yes—
172C22×C4×C61C2412yes—
173C22×C4×C61C2412yes—
174C22×C4×C61C2412yes—
175C22×C4×C61C2412yes—
176C22×C4×C61C2412yes—
177C22×C4×C61C2412yes—
178C22×C4×C61C2412yes—
179C22×Dic61—22no—
180C22×Dic61—22no—
181C22×Dic61—22no—
182C22×Dic61—22no—
183C22×Dic61—22no—
184C22×Dic61—22no—
185C22×Dic61—22no—
186C22×Dic61—22no—
187C22×Dic61—22no—
188C22×Dic61—22no—
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×Dic61C2×Q814yes—
198C22×Dic61#4114yes—
199C22×Dic61#4114yes—
200C22×Dic61C2412yes—
201C22×Dic61C2412yes—
202C22×Dic61C2412yes—
203C22×Dic61C2412yes—
204C22×Dic61C2412yes—
205C22×Dic61C2412yes—
206C22×Dic61C2412yes—
207C2×C4×D61—28no—
208C2×C4×D61—28no—
209C2×C4×D61—44no—
210C2×C4×D61—416no—
211C2×Dic122—28no—
212C2×Dic122—44no—
213C2×Dic122—44no—
214C2×Dic122—416no—
215C4⋊C4×C61—28no—
216C4⋊C4×C61—28no—
217C42×C61—28no—
218#11758198—28no—
219#11758198—28no—
220#11758198—44no—
221#11758198—44no—
222#11758198—44no—
223#11758198C2×Q8116yescomplemented
224C4⋊Dic61—28no—
225C4⋊Dic61—44no—
226C4⋊Dic61—44no—
227#11758196—28no—
228#11758196—28no—
229#11758196—44no—
230#11758196—44no—
231C4×Dic61—28no—
232C4×Dic61—44no—
233C4×Dic61—44no—
234C23×C61C22×Q812yes—
235C23×C61C2×#4112yes—
236C23×C61C2×#4112yes—
237C23×C61C2×#4112yes—
238C23×C61C2×#4112yes—
239C23×C61H(5,𝔽2)12yes—
240C23×C61H(5,𝔽2)12yes—
241C23×C61C2511yescharacteristic
242C22×D61—28no—
243C22×D61—28no—
244C22×D61—28no—
245C22×D61—22no—
246C22×D61—22no—
247C22×D61—22no—
248C22×D61—22no—
249C22×D61—22no—
250C22×D61—22no—
251C22×D61—44no—
252C22×D61—44no—
253C22×D61—44no—
254C22×D61—44no—
255C22×D61C22×Q814yes—
256C2×C4×C61—28no—
257C2×C4×C61—28no—
258C2×C4×C61—28no—
259C2×C4×C61—22no—
260C2×C4×C61—22no—
261C2×C4×C61—22no—
262C2×C4×C61—22no—
263C2×C4×C61—22no—
264C2×C4×C61—22no—
265C2×C4×C61—22no—
266C2×C4×C61—22no—
267C2×C4×C61—22no—
268C2×C4×C61—22no—
269C2×C4×C61—22no—
270C2×C4×C61—22no—
271C2×C4×C61—22no—
272C2×C4×C61—22no—
273C2×C4×C61—22no—
274C2×C4×C61—22no—
275C2×C4×C61—22no—
276C2×C4×C61—22no—
277C2×C4×C61—44no—
278C2×C4×C61—44no—
279C2×C4×C61—44no—
280C2×C4×C61—44no—
281C2×C4×C61C22×Q814yes—
282C2×C4×C61C2×#4114yes—
283C2×C4×C61C2×#4114yes—
284C2×Dic61—28no—
285C2×Dic61—28no—
286C2×Dic61—28no—
287C2×Dic61—22no—
288C2×Dic61—22no—
289C2×Dic61—22no—
290C2×Dic61—22no—
291C2×Dic61—22no—
292C2×Dic61—22no—
293C2×Dic61—22no—
294C2×Dic61—22no—
295C2×Dic61—22no—
296C2×Dic61—22no—
297C2×Dic61—22no—
298C2×Dic61—22no—
299C2×Dic61—22no—
300C2×Dic61—22no—
301C2×Dic61—22no—
302C2×Dic61—22no—
303C2×Dic61—22no—
304C2×Dic61—22no—
305C2×Dic61—44no—
306C2×Dic61—44no—
307C2×Dic61—44no—
308C2×Dic61—44no—
309C2×Dic61C22×Q814yes—
310C2×Dic61C2×#4114yes—
311C2×Dic61C2×#4114yes—
312C4×D61—416no—
313Dic122—416no—
314C2×#2574—611nomaximal, Sylow
315C22×C61#52914yes—
316C22×C61#53314yes—
317C22×C61#53814yes—
318C22×C61#55114yes—
319C22×C61#55414yes—
320C22×C61#55414yes—
321C22×C61#55514yes—
322C22×C61C23×Q811yescharacteristic
323C22×C61C22×#4111yescharacteristic
324C22×C61C22×#4111yescharacteristic
325C22×C61C22×#4111yescharacteristic
326C22×C61C22×#4111yescharacteristic
327C22×C61C2×H(5,𝔽2)11yescharacteristic
328C22×C61C2×H(5,𝔽2)11yescharacteristic
329C2×D61—24no—
330C2×D61—24no—
331C2×D61—24no—
332C2×D61—416no—
333C2×D61—42no—
334C2×D61—42no—
335C2×D61—42no—
336C2×D61—42no—
337C4×C61—24no—
338C4×C61—24no—
339C4×C61—24no—
340C4×C61—42no—
341C4×C61—42no—
342C4×C61—42no—
343C4×C61—42no—
344Dic61—24no—
345Dic61—24no—
346Dic61—24no—
347Dic61—42no—
348Dic61—42no—
349Dic61—42no—
350Dic61—42no—
351#2574—6116no—
352C2×#398—611no—
353C2×#396—611no—
354C2×#395—611no—
355C2×#393—611no—
356C2×#391—611no—
357C2×#388—611no—
358C2×#388—611no—
359C2×#387—611no—
360C2×#387—611no—
361C2×#387D6111yescharacteristic, complemented
362C2×#385—611no—
363C2×#382—611no—
364C2×#380—611no—
365C2×C4×C4⋊C4—611no—
366C2×C4×C22⋊C4—611no—
367C2×C61#257418yescomplemented
368C2×C61C2×#52911yescharacteristic
369C2×C61C2×#53311yescharacteristic
370C2×C61C2×#53811yescharacteristic
371C2×C61C2×#55111yescharacteristic
372C2×C61C2×#55411yescharacteristic
373C2×C61C2×#55411yescharacteristic
374C2×C61C2×#55511yescharacteristic
375D61—44no—
376C23×Q8—611no—
377C24×C4—611no—
378C22×C4⋊C4—611no—
379C22×C4⋊C4—611no—
380C22×C4⋊C4—611no—
381C22×C4⋊C4—611no—
382C22×C4⋊C4—611no—
383C22×C4⋊C4—611no—
384C22×C4⋊C4—611no—
385C22×C4⋊C4C2×D6111yescharacteristic
386C22×C4⋊C4C2×D6111yescharacteristic
387C22×C22⋊C4—611no—
388C22×C22⋊C4—611no—
389C22×C22⋊C4—611no—
390C22×C22⋊C4—611no—
391C22×C22⋊C4—611no—
392C22×C22⋊C4—611no—
393C22×C42—611no—
394C22×C42—611no—
395C22×C42—611no—
396C22×C42C2×D6111yescharacteristic
397#398—618no—
398#396—618no—
399#395—618no—
400#393—618no—
401#391—618no—
402#388—618no—
403#388—618no—
404#387—618no—
405#387—618no—
406#387C2×D6118yescomplemented
407#385—618no—
408#382—618no—
409#380—618no—
410C4×C4⋊C4—618no—
411C4×C22⋊C4—618no—
412C2×#95—611no—
413C2×#95—611no—
414C2×#95—611no—
415C2×#95—611no—
416C2×#95—611no—
417C2×#95—611no—
418C2×#95—611no—
419C2×#95—611no—
420C2×#95—611no—
421C2×#95—611no—
422C2×#95C2×D6111yescharacteristic
423C2×#95C2×D6111yescharacteristic
424C2×#95C2×D6111yescharacteristic
425C2×#95C2×D6111yescharacteristic
426C61C2×#257411yescharacteristic, complemented, Sylow
427C25—611no—
428C22×Q8—614no—
429C22×Q8—1224no—
430C22×Q8—2442no—
431C22×Q8—2442no—
432C23×C4—611no—
433C23×C4—611no—
434C23×C4—611no—
435C23×C4—611no—
436C23×C4—611no—
437C23×C4—611no—
438C23×C4—611no—
439C23×C4—614no—
440C23×C4—1224no—
441C23×C4—1224no—
442C23×C4—2442no—
443C23×C4C22×D6111yescharacteristic
444C23×C4C22×D6111yescharacteristic
445C23×C4C22×D6111yescharacteristic
446C23×C4C22×D6111yescharacteristic
447C23×C4C22×D6111yescharacteristic
448C23×C4C22×D6111yescharacteristic
449C23×C4C22×D6111yescharacteristic
450C2×C4⋊C4—24no—
451C2×C4⋊C4—24no—
452C2×C4⋊C4—614no—
453C2×C4⋊C4—614no—
454C2×C4⋊C4—614no—
455C2×C4⋊C4—614no—
456C2×C4⋊C4—614no—
457C2×C4⋊C4—614no—
458C2×C4⋊C4—614no—
459C2×C4⋊C4—1224no—
460C2×C4⋊C4—1224no—
461C2×C4⋊C4—1224no—
462C2×C4⋊C4—2442no—
463C2×C4⋊C4—2442no—
464C2×C4⋊C4—2442no—
465C2×C4⋊C4—2442no—
466C2×C4⋊C4C22×D6114yes—
467C2×C4⋊C4C22×D6114yes—
468C2×C22⋊C4—618no—
469C2×C22⋊C4—614no—
470C2×C22⋊C4—614no—
471C2×C22⋊C4—614no—
472C2×C22⋊C4—614no—
473C2×C22⋊C4—614no—
474C2×C22⋊C4—614no—
475C2×C22⋊C4—1224no—
476C2×C22⋊C4—1224no—
477C2×C22⋊C4—2442no—
478C2×C22⋊C4—2442no—
479C2×C22⋊C4—2442no—
480C2×C42—24no—
481C2×C42—614no—
482C2×C42—614no—
483C2×C42—614no—
484C2×C42—1224no—
485C2×C42—2442no—
486C2×C42—2442no—
487C2×C42C22×D6114yes—
488#95—614no—
489#95—614no—
490#95—614no—
491#95—614no—
492#95—614no—
493#95—614no—
494#95—614no—
495#95—614no—
496#95—614no—
497#95—614no—
498#95C22×D6114yes—
499#95C22×D6114yes—
500#95C22×D6114yes—
501#95C22×D6114yes—
502C24—614no—
503C24—612no—
504C24—1222no—
505C24—1222no—
506C24—1222no—
507C24—1222no—
508C24—1222no—
509C24—1222no—
510C24C23×D6111yescharacteristic
511C2×Q8—1228no—
512C2×Q8—2444no—
513C2×Q8—2444no—
514C2×Q8—24416no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—614no—
534C22×C4—614no—
535C22×C4—614no—
536C22×C4—612no—
537C22×C4—612no—
538C22×C4—612no—
539C22×C4—612no—
540C22×C4—612no—
541C22×C4—612no—
542C22×C4—612no—
543C22×C4—1228no—
544C22×C4—1222no—
545C22×C4—1222no—
546C22×C4—1222no—
547C22×C4—1222no—
548C22×C4—1222no—
549C22×C4—1222no—
550C22×C4—1222no—
551C22×C4—1222no—
552C22×C4—1222no—
553C22×C4—1222no—
554C22×C4—1222no—
555C22×C4—1222no—
556C22×C4—1222no—
557C22×C4—1222no—
558C22×C4—1222no—
559C22×C4—1222no—
560C22×C4—1222no—
561C22×C4—1222no—
562C22×C4—1228no—
563C22×C4—2444no—
564C22×C4—24416no—
565C22×C4#1175822214yes—
566C22×C4#1175822414yes—
567C22×C4Q8×D6114yes—
568C22×C4C23×D6112yes—
569C22×C4C23×D6112yes—
570C22×C4C23×D6112yes—
571C22×C4C23×D6112yes—
572C22×C4C23×D6112yes—
573C22×C4C23×D6112yes—
574C22×C4C23×D6112yes—
575C4⋊C4—28no—
576C4⋊C4—28no—
577C4⋊C4—1228no—
578C4⋊C4—1228no—
579C4⋊C4—1228no—
580C4⋊C4—2444no—
581C4⋊C4—2444no—
582C4⋊C4—2444no—
583C4⋊C4—2444no—
584C22⋊C4—6116no—
585C22⋊C4—1228no—
586C22⋊C4—1228no—
587C22⋊C4—2444no—
588C22⋊C4—2444no—
589C22⋊C4—2444no—
590C42—28no—
591C42—1228no—
592C42—2444no—
593C42—2444no—
594C23—614no—
595C23—1228no—
596C23—1228no—
597C23—1228no—
598C23—1222no—
599C23—1222no—
600C23—1222no—
601C23—1222no—
602C23—1222no—
603C23—1222no—
604C23—2444no—
605C23—2444no—
606C23—2444no—
607C23—2444no—
608C23C2×Q8×D6112yes—
609C23#41×D6112yes—
610C23#41×D6112yes—
611C23C2×#1175822412yes—
612C23C2×#1175822212yes—
613C23#1451982312yes—
614C23#1451982312yes—
615C23C24×D6111yescharacteristic
616Q8—24416no—
617C2×C4—28no—
618C2×C4—28no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—28no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—44no—
639C2×C4—44no—
640C2×C4—44no—
641C2×C4—44no—
642C2×C4—614no—
643C2×C4—614no—
644C2×C4—614no—
645C2×C4—1228no—
646C2×C4—1222no—
647C2×C4—1222no—
648C2×C4—1222no—
649C2×C4—1222no—
650C2×C4—1222no—
651C2×C4—1222no—
652C2×C4—1228no—
653C2×C4—1228no—
654C2×C4—1222no—
655C2×C4—1222no—
656C2×C4—1222no—
657C2×C4—1222no—
658C2×C4—1222no—
659C2×C4—1222no—
660C2×C4—1222no—
661C2×C4—1222no—
662C2×C4—1222no—
663C2×C4—1222no—
664C2×C4—1222no—
665C2×C4—1222no—
666C2×C4—24416no—
667C2×C4—2444no—
668C2×C4—2444no—
669C2×C4—2444no—
670C2×C4—2444no—
671C2×C4C2×Q8×D6114yes—
672C2×C4C2×#1175822414yes—
673C2×C4C2×#1175822214yes—
674C22—1224no—
675C22—1224no—
676C22—1224no—
677C22—24416no—
678C22—2442no—
679C22—2442no—
680C22—2442no—
681C22—2442no—
682C22#1684029214yes—
683C22#1684031814yes—
684C22#1684035114yes—
685C22#1684043514yes—
686C22#1684047014yes—
687C22#1684047214yes—
688C22#1684047514yes—
689C22C22×Q8×D6111yescharacteristic
690C22C2×#41×D6111yescharacteristic
691C22C2×#41×D6111yescharacteristic
692C22C22×#1175822411yescharacteristic
693C22C22×#1175822211yescharacteristic
694C22C2×#1451982311yescharacteristic
695C22C2×#1451982311yescharacteristic
696C4—24no—
697C4—24no—
698C4—24no—
699C4—42no—
700C4—42no—
701C4—42no—
702C4—42no—
703C4—1224no—
704C4—1224no—
705C4—1224no—
706C4—2442no—
707C4—2442no—
708C4—2442no—
709C4—2442no—
710C2—2444no—
711C2#2145109718yesdirect product factor
712C2C2×#1684029211yescharacteristic
713C2C2×#1684031811yescharacteristic
714C2C2×#1684035111yescharacteristic
715C2C2×#1684043511yescharacteristic
716C2C2×#1684047011yescharacteristic
717C2C2×#1684047211yescharacteristic
718C2C2×#1684047511yescharacteristic
subgroupG/H
centerC24C23×D61
commutator, cosocleC23×C61C25
FrattiniC23C24×D61
FittingC2×C61×#387C2
socleC24×C61C24
prime radicalC24×D61C23
hypercenterC2×#387D61
hypocenterC61C2×#2574
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
1. #21451097C2direct (N × H)
2. C2×#16839696C2semidirect
4. C2×#16839683C2semidirect
6. C2×#16839666C2semidirect
9. C2×#16839644C2semidirect
10. C2×#16839643C2semidirect
12. C2×#16839628C2semidirect
14. C2×C4⋊C4×Dic61C2semidirect
16. C2×C61×#387C2semidirect
35. #16839696C22semidirect
37. #16839683C22semidirect
39. #16839666C22semidirect
42. #16839644C22semidirect
43. #16839643C22semidirect
45. #16839628C22semidirect
47. C4⋊C4×Dic61C22semidirect
62. C61×#387C22semidirect
102. C2×#11758198Q8semidirect
223. #11758198C2×Q8semidirect
361. C2×#387D61semidirect
367. C2×C61#2574semidirect
406. #387C2×D61semidirect
426. C61C2×#2574semidirect
711. C2#21451097direct (N × H)

Maximal subgroups

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

subgroupindex
#214510972
C2×#168396962
C2×#168396842
C2×#168396832
C2×#168396752
C2×#168396662
C2×#168396542
C2×#168396442
C2×#168396432
C2×#168396332
C2×#168396282
C2×#168396212
C2×C4⋊C4×Dic612
C2×C4×#117581982
C2×C61×#3872
C2×#257461