Finite Group Databasebeta

← C2×#21453900 #29886197

Subgroups — C2×#21453900 #29886197

Order 15616.

2606 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21453900C2116yesmaximal, direct product factor
2C2×#16839703C211yesmaximal, characteristic, complemented
3C2×#16839691C211yesmaximal, characteristic, complemented
4C2×#16839688C211yesmaximal, characteristic, complemented
5C2×#16839680C211yesmaximal, characteristic, complemented
6C2×#16839680C211yesmaximal, characteristic, complemented
7C2×#16839679C211yesmaximal, characteristic, complemented
8C2×#16839679C211yesmaximal, characteristic, complemented
9C2×#16839675C211yesmaximal, characteristic, complemented
10C2×#16839675C211yesmaximal, characteristic, complemented
11C2×#16839675C211yesmaximal, characteristic, complemented
12C2×#16839672C211yesmaximal, characteristic
13C2×#16839640C211yesmaximal, characteristic, complemented
14C2×#16839640C211yesmaximal, characteristic, complemented
15C2×#16839633C211yesmaximal, characteristic, complemented
16C2×C61×#400C211yesmaximal, characteristic, complemented
17C23×Dic122C2211yescharacteristic
18C23×D244C2211yescharacteristic
19C23×D244C2211yescharacteristic
20C23×D244C2211yescharacteristic
21C23×C4×D61C2211yescharacteristic
22C22×#11758196C2211yescharacteristic
23C22×#11758196C2211yescharacteristic
24C22×#11758198C2211yescharacteristic
25C22×#11758198C2211yescharacteristic
26C22×#11758198C2211yescharacteristic
27C22×#11758198C2211yescharacteristic
28C22×#11758198C2211yescharacteristic
29C22×#11758198C2211yescharacteristic
30C22×#11758198C2211yescharacteristic
31C22×#11758198C2211yescharacteristic
32C22×#11758198C2211yescharacteristic
33C22×#11758198C2211yescharacteristic
34C22×#11758198C2211yescharacteristic
35C22×#11758198C2211yescharacteristic
36C22×#11758198C2211yescharacteristic
37C22×#11758198C2211yescharacteristic
38#16839703C2218yescomplemented
39#16839691C2218yescomplemented
40#16839688C2218yescomplemented
41#16839680C2218yescomplemented
42#16839680C2218yescomplemented
43#16839679C2218yescomplemented
44#16839679C2218yescomplemented
45#16839675C2218yescomplemented
46#16839675C2218yescomplemented
47#16839675C2218yescomplemented
48#16839672C2218yes—
49#16839640C2218yescomplemented
50#16839640C2218yescomplemented
51#16839633C2218yescomplemented
52C2×#14519684C2211yescharacteristic
53C2×#14519684C2211yescharacteristic
54C2×#14519684C2211yescharacteristic
55C2×#14519684C2211yescharacteristic
56C2×#14519684C2211yescharacteristic
57C2×#14519684C2211yescharacteristic
58C2×#14519684C2211yescharacteristic
59C22×C4⋊C4×C61C2211yescharacteristic
60C22×C4⋊C4×C61C2211yescharacteristic
61C61×#400C2218yescomplemented
62C2×#95×C61C2211yescharacteristic
63C2×#95×C61C2211yescharacteristic
64C2×#95×C61C2211yescharacteristic
65C2×#95×C61C2211yescharacteristic
66C2×#95×C61C2211yescharacteristic
67C24×D61C2311yescharacteristic
68C24×D61C2311yescharacteristic
69C24×D61C2311yescharacteristic
70C22×Dic122—42no—
71C22×Dic122—42no—
72C22×Dic122—42no—
73C22×Dic122C2314yes—
74C22×D244—24no—
75C22×D244—24no—
76C22×D244—42no—
77C22×D244—42no—
78C22×D244—42no—
79C22×D244—42no—
80C22×D244—42no—
81C22×D244—42no—
82C22×D244—42no—
83C22×D244C2314yes—
84C22×D244C2314yes—
85C22×D244C2314yes—
86C23×Dic61C2311yescharacteristic
87C23×Dic61C2311yescharacteristic
88C23×Dic61C2311yescharacteristic
89C23×Dic61C2311yescharacteristic
90C23×Dic61C2311yescharacteristic
91C22×C4×D61—42no—
92C22×C4×D61—42no—
93C22×C4×D61—42no—
94C22×C4×D61C2314yes—
95C2×#11758196—42no—
96C2×#11758196—42no—
97C2×#11758196C2314yes—
98C2×#11758196C2314yes—
99C2×#11758198—24no—
100C2×#11758198—42no—
101C2×#11758198—42no—
102C2×#11758198—42no—
103C2×#11758198—42no—
104C2×#11758198—42no—
105C2×#11758198—42no—
106C2×#11758198—42no—
107C2×#11758198—42no—
108C2×#11758198—42no—
109C2×#11758198—42no—
110C2×#11758198—42no—
111C2×#11758198—42no—
112C2×#11758198—42no—
113C2×#11758198C2314yes—
114C2×#11758198C2314yes—
115C2×#11758198C2314yes—
116C2×#11758198C2314yes—
117C2×#11758198C2314yes—
118C2×#11758198C2314yes—
119C2×#11758198C2314yes—
120C2×#11758198C2314yes—
121C2×#11758198C2314yes—
122C2×#11758198C2314yes—
123C2×#11758198C2314yes—
124C2×#11758198C2314yes—
125C2×#11758198C2314yes—
126C2×#11758198C2314yes—
127#14519684C2314yes—
128#14519684C2314yes—
129#14519684C2314yes—
130#14519684C2314yes—
131#14519684C2314yes—
132#14519684C2314yes—
133#14519684C2314yes—
134C23×C4×C61C2311yescharacteristic
135C23×C4×C61C2311yescharacteristic
136C23×C4×C61C2311yescharacteristic
137C23×C4×C61C2311yescharacteristic
138C23×C4×C61C2311yescharacteristic
139C23×C4×C61C2311yescharacteristic
140C23×C4×C61C2311yescharacteristic
141C2×C4⋊C4×C61—42no—
142C2×C4⋊C4×C61—42no—
143C2×C4⋊C4×C61C2314yes—
144C2×C4⋊C4×C61C2314yes—
145#95×C61C2314yes—
146#95×C61C2314yes—
147#95×C61C2314yes—
148#95×C61C2314yes—
149#95×C61C2314yes—
150C24×C61C2411yescharacteristic
151C23×D61—22no—
152C23×D61—22no—
153C23×D61—22no—
154C23×D61—22no—
155C23×D61—22no—
156C23×D61—22no—
157C23×D61—22no—
158C23×D61—22no—
159C23×D61—22no—
160C23×D61—22no—
161C23×D61—22no—
162C23×D61—22no—
163C23×D61—22no—
164C23×D61—22no—
165C23×D61—22no—
166C23×D61—22no—
167C23×D61—22no—
168C23×D61—22no—
169C23×D61—22no—
170C23×D61—22no—
171C23×D61#4114yes—
172C23×D61C2412yes—
173C23×D61C2412yes—
174C23×D61C2412yes—
175C22×C4×C61—22no—
176C22×C4×C61—22no—
177C22×C4×C61—22no—
178C22×C4×C61—22no—
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×C61—22no—
195C22×C4×C61—22no—
196C22×C4×C61C2412yes—
197C22×C4×C61C2412yes—
198C22×C4×C61C2412yes—
199C22×C4×C61C2412yes—
200C22×C4×C61C2412yes—
201C22×C4×C61C2412yes—
202C22×C4×C61C2412yes—
203C22×Dic61—22no—
204C22×Dic61—22no—
205C22×Dic61—22no—
206C22×Dic61—22no—
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×Dic61C2412yes—
219C22×Dic61C2412yes—
220C22×Dic61C2412yes—
221C22×Dic61C2412yes—
222C22×Dic61C2412yes—
223C2×D244—28no—
224C2×D244—28no—
225C2×D244—44no—
226C2×D244—44no—
227C2×D244—44no—
228C2×D244—44no—
229C2×D244—44no—
230C2×D244—44no—
231C2×D244—44no—
232C2×D244—416no—
233C2×D244—416no—
234C2×D244—416no—
235C2×C4×D61—44no—
236C2×C4×D61—44no—
237C2×C4×D61—44no—
238C2×C4×D61—416no—
239C2×Dic122—44no—
240C2×Dic122—44no—
241C2×Dic122—44no—
242C2×Dic122—416no—
243C4⋊C4×C61—44no—
244C4⋊C4×C61—44no—
245#11758198—28no—
246#11758198—44no—
247#11758198—44no—
248#11758198—44no—
249#11758198—44no—
250#11758198—44no—
251#11758198—44no—
252#11758198—44no—
253#11758198—44no—
254#11758198—44no—
255#11758198—44no—
256#11758198—44no—
257#11758198—44no—
258#11758198—44no—
259#11758196—44no—
260#11758196—44no—
261C23×C61C2×#4112yes—
262C23×C61H(5,𝔽2)12yes—
263C23×C61H(5,𝔽2)12yes—
264C23×C61H(5,𝔽2)12yes—
265C23×C61H(5,𝔽2)12yes—
266C23×C61H(5,𝔽2)12yes—
267C23×C612−1+412yes—
268C23×C61C2511yescharacteristic
269C22×D61—28no—
270C22×D61—28no—
271C22×D61—28no—
272C22×D61—22no—
273C22×D61—22no—
274C22×D61—22no—
275C22×D61—22no—
276C22×D61—22no—
277C22×D61—22no—
278C22×D61—22no—
279C22×D61—22no—
280C22×D61—22no—
281C22×D61—22no—
282C22×D61—22no—
283C22×D61—22no—
284C22×D61—22no—
285C22×D61—22no—
286C22×D61—22no—
287C22×D61—22no—
288C22×D61—22no—
289C22×D61—22no—
290C22×D61—22no—
291C22×D61—22no—
292C22×D61—44no—
293C22×D61—44no—
294C22×D61—44no—
295C22×D61—44no—
296C22×D61—44no—
297C22×D61—44no—
298C22×D61—44no—
299C22×D61—44no—
300C22×D61—44no—
301C22×D61—44no—
302C22×D61—44no—
303C22×D61—44no—
304C22×D61—44no—
305C22×D61—44no—
306C22×D61—44no—
307C22×D61—44no—
308C22×D61—44no—
309C22×D61—44no—
310C22×D61C2×#4114yes—
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—22no—
327C2×C4×C61—22no—
328C2×C4×C61—22no—
329C2×C4×C61—22no—
330C2×C4×C61—22no—
331C2×C4×C61—22no—
332C2×C4×C61—44no—
333C2×C4×C61—44no—
334C2×C4×C61—44no—
335C2×C4×C61—44no—
336C2×C4×C61—44no—
337C2×C4×C61—44no—
338C2×C4×C61—44no—
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—44no—
355C2×Dic61—44no—
356C2×Dic61—44no—
357C2×Dic61—44no—
358C2×Dic61—44no—
359D244—416no—
360D244—416no—
361D244—416no—
362C4×D61—416no—
363Dic122—416no—
364C2×#2824—611nomaximal, Sylow
365C22×C61#53814yes—
366C22×C61#53814yes—
367C22×C61#53914yes—
368C22×C61#56014yes—
369C22×C61H(3,𝔽4)14yes—
370C22×C61#56214yes—
371C22×C61#56214yes—
372C22×C61C22×#4111yescharacteristic
373C22×C61C2×H(5,𝔽2)11yescharacteristic
374C22×C61C2×H(5,𝔽2)11yescharacteristic
375C22×C61C2×H(5,𝔽2)11yescharacteristic
376C22×C61C2×H(5,𝔽2)11yescharacteristic
377C22×C61C2×H(5,𝔽2)11yescharacteristic
378C22×C61C2×2−1+411yescharacteristic
379C2×D61—24no—
380C2×D61—24no—
381C2×D61—24no—
382C2×D61—416no—
383C2×D61—42no—
384C2×D61—42no—
385C2×D61—42no—
386C2×D61—42no—
387C2×D61—42no—
388C2×D61—42no—
389C2×D61—42no—
390C2×D61—42no—
391C2×D61—42no—
392C2×D61—42no—
393C2×D61—42no—
394C2×D61—42no—
395C2×D61—42no—
396C2×D61—42no—
397C2×D61—42no—
398C2×D61—42no—
399C2×D61—42no—
400C2×D61—42no—
401C2×D61—88no—
402C2×D61—88no—
403C4×C61—42no—
404C4×C61—42no—
405C4×C61—42no—
406C4×C61—42no—
407C4×C61—42no—
408C4×C61—42no—
409C4×C61—42no—
410Dic61—42no—
411Dic61—42no—
412Dic61—42no—
413Dic61—42no—
414Dic61—42no—
415#2824—6116no—
416C2×#400—611no—
417C2×#400D6111yescharacteristic, complemented
418C2×#397—611no—
419C2×#397—611no—
420C2×#394—611no—
421C2×#394—611no—
422C2×#394—611no—
423C2×#394—611no—
424C2×#393—611no—
425C2×#393—611no—
426C2×#393—611no—
427C2×#392—611no—
428C2×#386—611no—
429C2×#386—611no—
430C2×#385—611no—
431C2×C61#282418yescomplemented
432C2×C61C2×#53811yescharacteristic
433C2×C61C2×#53811yescharacteristic
434C2×C61C2×#53911yescharacteristic
435C2×C61C2×#56011yescharacteristic
436C2×C61C2×H(3,𝔽4)11yescharacteristic
437C2×C61C2×#56211yescharacteristic
438C2×C61C2×#56211yescharacteristic
439D61—44no—
440D61—82no—
441D61—82no—
442C23×Q8—611no—
443C23×D4—611no—
444C23×D4—611no—
445C23×D4—611no—
446C24×C4—611no—
447C22×C4⋊C4—611no—
448C22×C4⋊C4—611no—
449C22×C4⋊C4C2×D6111yescharacteristic
450C22×C4⋊C4C2×D6111yescharacteristic
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⋊C4—611no—
460C22×C22⋊C4—611no—
461C22×C22⋊C4—611no—
462C22×C22⋊C4—611no—
463C22×C22⋊C4—611no—
464C22×C22⋊C4—611no—
465#400—618no—
466#400C2×D6118yescomplemented
467#397—618no—
468#397—618no—
469#394—618no—
470#394—618no—
471#394—618no—
472#394—618no—
473#393—618no—
474#393—618no—
475#393—618no—
476#392—618no—
477#386—618no—
478#386—618no—
479#385—618no—
480C2×#95—611no—
481C2×#95—611no—
482C2×#95—611no—
483C2×#95—611no—
484C2×#95—611no—
485C2×#95—611no—
486C2×#95—611no—
487C2×#95C2×D6111yescharacteristic
488C2×#95C2×D6111yescharacteristic
489C2×#95C2×D6111yescharacteristic
490C2×#95C2×D6111yescharacteristic
491C2×#95C2×D6111yescharacteristic
492C61C2×#282411yescharacteristic, complemented, Sylow
493C25—611no—
494C25—611no—
495C25—611no—
496C22×Q8—614no—
497C22×Q8—2442no—
498C22×Q8—2442no—
499C22×Q8—2442no—
500C22×D4—614no—
501C22×D4—614no—
502C22×D4—614no—
503C22×D4—1224no—
504C22×D4—1224no—
505C22×D4—2442no—
506C22×D4—2442no—
507C22×D4—2442no—
508C22×D4—2442no—
509C22×D4—2442no—
510C22×D4—2442no—
511C22×D4—2442no—
512C23×C4—611no—
513C23×C4—611no—
514C23×C4—611no—
515C23×C4—611no—
516C23×C4—611no—
517C23×C4—614no—
518C23×C4—2442no—
519C23×C4—2442no—
520C23×C4—2442no—
521C23×C4C22×D6111yescharacteristic
522C23×C4C22×D6111yescharacteristic
523C23×C4C22×D6111yescharacteristic
524C23×C4C22×D6111yescharacteristic
525C23×C4C22×D6111yescharacteristic
526C23×C4C22×D6111yescharacteristic
527C23×C4C22×D6111yescharacteristic
528C2×C4⋊C4—42no—
529C2×C4⋊C4—42no—
530C2×C4⋊C4—614no—
531C2×C4⋊C4—614no—
532C2×C4⋊C4—2442no—
533C2×C4⋊C4—2442no—
534C2×C4⋊C4C22×D6114yes—
535C2×C4⋊C4C22×D6114yes—
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—614no—
547C2×C22⋊C4—614no—
548C2×C22⋊C4—614no—
549C2×C22⋊C4—614no—
550C2×C22⋊C4—1224no—
551C2×C22⋊C4—2442no—
552C2×C22⋊C4—2442no—
553C2×C22⋊C4—2442no—
554C2×C22⋊C4—2442no—
555C2×C22⋊C4—2442no—
556C2×C22⋊C4—2442no—
557C2×C22⋊C4—2442no—
558C2×C22⋊C4—2442no—
559C2×C22⋊C4—2442no—
560C2×C22⋊C4—2442no—
561C2×C22⋊C4—2442no—
562C2×C22⋊C4—2442no—
563C2×C22⋊C4—2442no—
564#95—614no—
565#95—614no—
566#95—614no—
567#95—614no—
568#95—614no—
569#95—614no—
570#95—614no—
571#95C22×D6114yes—
572#95C22×D6114yes—
573#95C22×D6114yes—
574#95C22×D6114yes—
575#95C22×D6114yes—
576C24—614no—
577C24—612no—
578C24—612no—
579C24—612no—
580C24—1222no—
581C24—1222no—
582C24—1222no—
583C24—1222no—
584C24—1222no—
585C24—1222no—
586C24—1222no—
587C24—1222no—
588C24—1222no—
589C24—1222no—
590C24—1222no—
591C24—1222no—
592C24—1222no—
593C24—1222no—
594C24—1222no—
595C24—1222no—
596C24—1222no—
597C24—1222no—
598C24—1222no—
599C24—1222no—
600C24C23×D6111yescharacteristic
601C2×Q8—2444no—
602C2×Q8—2444no—
603C2×Q8—2444no—
604C2×Q8—24416no—
605C2×D4—1228no—
606C2×D4—1228no—
607C2×D4—2444no—
608C2×D4—2444no—
609C2×D4—2444no—
610C2×D4—2444no—
611C2×D4—2444no—
612C2×D4—2444no—
613C2×D4—2444no—
614C2×D4—24416no—
615C2×D4—24416no—
616C2×D4—24416no—
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—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—612no—
639C22×C4—612no—
640C22×C4—612no—
641C22×C4—612no—
642C22×C4—612no—
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—1222no—
656C22×C4—1222no—
657C22×C4—1222no—
658C22×C4—2444no—
659C22×C4—2444no—
660C22×C4—2444no—
661C22×C4—24416no—
662C22×C4C23×D6112yes—
663C22×C4C23×D6112yes—
664C22×C4C23×D6112yes—
665C22×C4C23×D6112yes—
666C22×C4C23×D6112yes—
667C22×C4C23×D6112yes—
668C22×C4C23×D6112yes—
669C4⋊C4—44no—
670C4⋊C4—44no—
671C4⋊C4—2444no—
672C4⋊C4—2444no—
673C22⋊C4—1228no—
674C22⋊C4—2444no—
675C22⋊C4—2444no—
676C22⋊C4—2444no—
677C22⋊C4—2444no—
678C22⋊C4—2444no—
679C22⋊C4—2444no—
680C22⋊C4—2444no—
681C22⋊C4—2444no—
682C22⋊C4—2444no—
683C22⋊C4—2444no—
684C22⋊C4—2444no—
685C22⋊C4—2444no—
686C22⋊C4—2444no—
687C23—614no—
688C23—1222no—
689C23—1222no—
690C23—1222no—
691C23—1222no—
692C23—1222no—
693C23—1222no—
694C23—1228no—
695C23—1228no—
696C23—1228no—
697C23—1222no—
698C23—1222no—
699C23—1222no—
700C23—1222no—
701C23—1222no—
702C23—1222no—
703C23—1222no—
704C23—1222no—
705C23—1222no—
706C23—1222no—
707C23—1222no—
708C23—1222no—
709C23—1222no—
710C23—1222no—
711C23—2444no—
712C23—2444no—
713C23—2444no—
714C23—2444no—
715C23—2444no—
716C23—2444no—
717C23—2444no—
718C23—2444no—
719C23—2444no—
720C23—2444no—
721C23—2444no—
722C23—2444no—
723C23—2444no—
724C23—2444no—
725C23—2444no—
726C23—2444no—
727C23—2444no—
728C23—2444no—
729C23#41×D6112yes—
730C23#1451982212yes—
731C23#1451982312yes—
732C23#1451982312yes—
733C23#1451982312yes—
734C23#1451982312yes—
735C23#1451982512yes—
736C23C24×D6111yescharacteristic
737Q8—24416no—
738D4—24416no—
739D4—24416no—
740D4—24416no—
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—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—44no—
763C2×C4—44no—
764C2×C4—44no—
765C2×C4—44no—
766C2×C4—44no—
767C2×C4—44no—
768C2×C4—44no—
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—1222no—
781C2×C4—1222no—
782C2×C4—1222no—
783C2×C4—1222no—
784C2×C4—24416no—
785C2×C4—2444no—
786C2×C4—2444no—
787C2×C4—2444no—
788C2×C4—2444no—
789C2×C4—2444no—
790C22—1224no—
791C22—1224no—
792C22—1224no—
793C22—4888no—
794C22—4888no—
795C22—2442no—
796C22—2442no—
797C22—2442no—
798C22—2442no—
799C22—2442no—
800C22—2442no—
801C22—2442no—
802C22—2442no—
803C22—2442no—
804C22—2442no—
805C22—2442no—
806C22—2442no—
807C22—2442no—
808C22—2442no—
809C22—24416no—
810C22—2442no—
811C22—2442no—
812C22—2442no—
813C22—2442no—
814C22#1684034814yes—
815C22#1684035114yes—
816C22#1684036014yes—
817C22#1684050314yes—
818C22#1684050414yes—
819C22#1684050814yes—
820C22#1684051014yes—
821C22C2×#41×D6111yescharacteristic
822C22C2×#1451982211yescharacteristic
823C22C2×#1451982311yescharacteristic
824C22C2×#1451982311yescharacteristic
825C22C2×#1451982311yescharacteristic
826C22C2×#1451982311yescharacteristic
827C22C2×#1451982511yescharacteristic
828C4—42no—
829C4—42no—
830C4—42no—
831C4—42no—
832C4—42no—
833C4—42no—
834C4—42no—
835C4—2442no—
836C4—2442no—
837C4—2442no—
838C4—2442no—
839C4—2442no—
840C2—4882no—
841C2—4882no—
842C2—2444no—
843C2#2145390018yesdirect product factor
844C2C2×#1684034811yescharacteristic
845C2C2×#1684035111yescharacteristic
846C2C2×#1684036011yescharacteristic
847C2C2×#1684050311yescharacteristic
848C2C2×#1684050411yescharacteristic
849C2C2×#1684050811yescharacteristic
850C2C2×#1684051011yescharacteristic
subgroupG/H
centerC24C23×D61
commutator, cosocleC23×C61C25
FrattiniC23C24×D61
FittingC2×C61×#400C2
socleC24×C61C24
prime radicalC2×#16839672C2
hypercenterC2×#400D61
hypocenterC61C2×#2824
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#400

Complements

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

NH ≅ G/Ntype
1. #21453900C2direct (N × H)
2. C2×#16839703C2semidirect
3. C2×#16839691C2semidirect
4. C2×#16839688C2semidirect
5. C2×#16839680C2semidirect
6. C2×#16839680C2semidirect
7. C2×#16839679C2semidirect
8. C2×#16839679C2semidirect
9. C2×#16839675C2semidirect
10. C2×#16839675C2semidirect
11. C2×#16839675C2semidirect
13. C2×#16839640C2semidirect
14. C2×#16839640C2semidirect
15. C2×#16839633C2semidirect
16. C2×C61×#400C2semidirect
38. #16839703C22semidirect
39. #16839691C22semidirect
40. #16839688C22semidirect
41. #16839680C22semidirect
42. #16839680C22semidirect
43. #16839679C22semidirect
44. #16839679C22semidirect
45. #16839675C22semidirect
46. #16839675C22semidirect
47. #16839675C22semidirect
49. #16839640C22semidirect
50. #16839640C22semidirect
51. #16839633C22semidirect
61. C61×#400C22semidirect
417. C2×#400D61semidirect
431. C2×C61#2824semidirect
466. #400C2×D61semidirect
492. C61C2×#2824semidirect
843. C2#21453900direct (N × H)

Maximal subgroups

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

subgroupindex
#214539002
C2×#168397032
C2×#168396912
C2×#168396882
C2×#168396802
C2×#168396792
C2×#168396752
C2×#168396722
C2×#168396402
C2×#168396332
C2×C61×#4002
C2×#282461