Finite Group Databasebeta

← C2×#21451668 #29846402

Subgroups — C2×#21451668 #29846402

Order 15616.

3218 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519762C211yesmaximal, characteristic, complemented
2C22×C4×D244C211yesmaximal, characteristic, complemented
3#21451668C2116yesmaximal, direct product factor
4C2×#16839696C211yesmaximal, characteristic, complemented
5C2×#16839691C211yesmaximal, characteristic, complemented
6C2×#16839686C211yesmaximal, characteristic, complemented
7C2×#16839684C211yesmaximal, characteristic, complemented
8C2×#16839680C211yesmaximal, characteristic, complemented
9C2×#16839680C211yesmaximal, characteristic, complemented
10C2×#16839679C211yesmaximal, characteristic, complemented
11C2×#16839672C211yesmaximal, characteristic
12C2×#16839653C211yesmaximal, characteristic, complemented
13C2×#16839640C211yesmaximal, characteristic, complemented
14C2×#16839633C211yesmaximal, characteristic, complemented
15C2×#16839621C211yesmaximal, characteristic, complemented
16C2×C61×#387C211yesmaximal, characteristic, complemented
17C23×D244C2211yescharacteristic
18C23×D244C2211yescharacteristic
19C23×D244C2211yescharacteristic
20C23×C4×D61C2211yescharacteristic
21C23×C4×D61C2211yescharacteristic
22C2×#14519762—28no—
23C2×#14519762C2218yescomplemented
24C2×C4×D244—28no—
25C2×C4×D244C2218yescomplemented
26C22×C4⋊Dic61C2211yescharacteristic
27C22×#11758196C2211yescharacteristic
28C22×#11758196C2211yescharacteristic
29C22×#11758196C2211yescharacteristic
30C22×#11758196C2211yescharacteristic
31C22×#11758196C2211yescharacteristic
32C22×#11758198C2211yescharacteristic
33C22×#11758198C2211yescharacteristic
34C22×#11758198C2211yescharacteristic
35C22×#11758198C2211yescharacteristic
36C22×#11758198C2211yescharacteristic
37C22×#11758198C2211yescharacteristic
38C22×#11758198C2211yescharacteristic
39C22×#11758198C2211yescharacteristic
40C22×#11758198C2211yescharacteristic
41C22×#11758198C2211yescharacteristic
42C22×#11758198C2211yescharacteristic
43C22×#11758198C2211yescharacteristic
44C22×#11758198C2211yescharacteristic
45#16839696C2218yescomplemented
46#16839691C2218yescomplemented
47#16839686C2218yescomplemented
48#16839684C2218yescomplemented
49#16839680C2218yescomplemented
50#16839680C2218yescomplemented
51#16839679C2218yescomplemented
52#16839672C2218yes—
53#16839653C2218yescomplemented
54#16839640C2218yescomplemented
55#16839633C2218yescomplemented
56#16839621C2218yescomplemented
57C2×#14519684C2211yescharacteristic
58C2×#14519684C2211yescharacteristic
59C2×#14519684C2211yescharacteristic
60C2×#14519684C2211yescharacteristic
61C22×C4⋊C4×C61C2211yescharacteristic
62C22×C4⋊C4×C61C2211yescharacteristic
63C22×C42×C61C2211yescharacteristic
64C61×#387C2218yescomplemented
65C2×#95×C61C2211yescharacteristic
66C2×#95×C61C2211yescharacteristic
67C2×#95×C61C2211yescharacteristic
68C2×#95×C61C2211yescharacteristic
69C24×D61C2311yescharacteristic
70C24×D61C2311yescharacteristic
71C24×D61C2311yescharacteristic
72C22×D244—24no—
73C22×D244—24no—
74C22×D244—24no—
75C22×D244—24no—
76C22×D244—24no—
77C22×D244—42no—
78C22×D244—42no—
79C22×D244—42no—
80C22×D244—42no—
81C22×D244C2314yes—
82C22×D244C2314yes—
83C22×D244C2314yes—
84C23×Dic61C2311yescharacteristic
85C23×Dic61C2311yescharacteristic
86C23×Dic61C2311yescharacteristic
87C23×Dic61C2311yescharacteristic
88C23×Dic61C2311yescharacteristic
89C22×C4×D61—24no—
90C22×C4×D61—42no—
91C22×C4×D61—42no—
92C22×C4×D61—42no—
93C22×C4×D61—42no—
94C22×C4×D61D418yescomplemented
95C22×C4×D61C2314yes—
96C22×C4×D61C2314yes—
97#14519762—232no—
98C4×D244—232no—
99C2×C4⋊Dic61—24no—
100C2×C4⋊Dic61C2314yes—
101C2×#11758196—24no—
102C2×#11758196—42no—
103C2×#11758196—42no—
104C2×#11758196—42no—
105C2×#11758196—42no—
106C2×#11758196C2314yes—
107C2×#11758196C2314yes—
108C2×#11758196C2314yes—
109C2×#11758196C2314yes—
110C2×#11758196C2314yes—
111C2×#11758198—24no—
112C2×#11758198—24no—
113C2×#11758198—24no—
114C2×#11758198—24no—
115C2×#11758198—24no—
116C2×#11758198—24no—
117C2×#11758198—24no—
118C2×#11758198—42no—
119C2×#11758198—42no—
120C2×#11758198—42no—
121C2×#11758198—42no—
122C2×#11758198—42no—
123C2×#11758198—42no—
124C2×#11758198C2314yes—
125C2×#11758198C2314yes—
126C2×#11758198C2314yes—
127C2×#11758198C2314yes—
128C2×#11758198C2314yes—
129C2×#11758198C2314yes—
130C2×#11758198C2314yes—
131C2×#11758198C2314yes—
132C2×#11758198C2314yes—
133C2×#11758198C2314yes—
134C2×#11758198C2314yes—
135C2×#11758198C2314yes—
136C2×#11758198C2314yes—
137#14519684C2314yes—
138#14519684C2314yes—
139#14519684C2314yes—
140#14519684C2314yes—
141C23×C4×C61C2311yescharacteristic
142C23×C4×C61C2311yescharacteristic
143C23×C4×C61C2311yescharacteristic
144C23×C4×C61C2311yescharacteristic
145C23×C4×C61C2311yescharacteristic
146C23×C4×C61C2311yescharacteristic
147C23×C4×C61C2311yescharacteristic
148C2×C4⋊C4×C61—24no—
149C2×C4⋊C4×C61—24no—
150C2×C4⋊C4×C61C2314yes—
151C2×C4⋊C4×C61C2314yes—
152C2×C42×C61—24no—
153C2×C42×C61C2314yes—
154#95×C61C2314yes—
155#95×C61C2314yes—
156#95×C61C2314yes—
157#95×C61C2314yes—
158C24×C61C2411yescharacteristic
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—22no—
172C23×D61—22no—
173C23×D61—22no—
174C23×D61—22no—
175C23×D61—22no—
176C23×D61—22no—
177C23×D61—22no—
178C23×D61C2×D414yes—
179C23×D61#4114yes—
180C23×D61C2412yes—
181C23×D61C2412yes—
182C23×D61C2412yes—
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×C61—22no—
197C22×C4×C61—22no—
198C22×C4×C61—22no—
199C22×C4×C61—22no—
200C22×C4×C61—22no—
201C22×C4×C61—22no—
202C22×C4×C61C2×D414yes—
203C22×C4×C61#4114yes—
204C22×C4×C61C2412yes—
205C22×C4×C61C2412yes—
206C22×C4×C61C2412yes—
207C22×C4×C61C2412yes—
208C22×C4×C61C2412yes—
209C22×C4×C61C2412yes—
210C22×C4×C61C2412yes—
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×Dic61C2×D414yes—
226C22×Dic61C2412yes—
227C22×Dic61C2412yes—
228C22×Dic61C2412yes—
229C22×Dic61C2412yes—
230C22×Dic61C2412yes—
231C2×D244—232no—
232C2×D244—28no—
233C2×D244—28no—
234C2×D244—28no—
235C2×D244—28no—
236C2×D244—28no—
237C2×D244—44no—
238C2×D244—44no—
239C2×D244—44no—
240C2×D244—44no—
241C2×D244—416no—
242C2×D244—416no—
243C2×C4×D61—28no—
244C2×C4×D61—416no—
245C2×C4×D61—44no—
246C2×C4×D61—44no—
247C2×C4×D61—44no—
248C2×C4×D61—44no—
249C2×C4×D61—416no—
250C2×C4×D61C2×D4116yescomplemented
251C4⋊C4×C61—28no—
252C4⋊C4×C61—28no—
253C42×C61—28no—
254#11758198—28no—
255#11758198—28no—
256#11758198—28no—
257#11758198—28no—
258#11758198—28no—
259#11758198—28no—
260#11758198—28no—
261#11758198—44no—
262#11758198—44no—
263#11758198—44no—
264#11758198—44no—
265#11758198—44no—
266#11758198—44no—
267C4⋊Dic61—28no—
268#11758196—28no—
269#11758196—44no—
270#11758196—44no—
271#11758196—44no—
272#11758196—44no—
273C23×C61C22×D412yes—
274C23×C61C2×#4112yes—
275C23×C61C2×#4112yes—
276C23×C61H(5,𝔽2)12yes—
277C23×C61H(5,𝔽2)12yes—
278C23×C61H(5,𝔽2)12yes—
279C23×C612−1+412yes—
280C23×C61C2511yescharacteristic
281C22×D61—28no—
282C22×D61—28no—
283C22×D61—28no—
284C22×D61—28no—
285C22×D61—28no—
286C22×D61—28no—
287C22×D61—22no—
288C22×D61—22no—
289C22×D61—22no—
290C22×D61—22no—
291C22×D61—22no—
292C22×D61—22no—
293C22×D61—22no—
294C22×D61—22no—
295C22×D61—22no—
296C22×D61—22no—
297C22×D61—22no—
298C22×D61—22no—
299C22×D61—22no—
300C22×D61—22no—
301C22×D61—22no—
302C22×D61—22no—
303C22×D61—22no—
304C22×D61—22no—
305C22×D61—22no—
306C22×D61—44no—
307C22×D61—44no—
308C22×D61—44no—
309C22×D61—44no—
310C22×D61—44no—
311C22×D61—44no—
312C22×D61—44no—
313C22×D61—44no—
314C22×D61—44no—
315C22×D61—44no—
316C22×D61—44no—
317C22×D61—44no—
318C22×D61—44no—
319C22×D61—44no—
320C22×D61—44no—
321C22×D61C22×D414yes—
322C22×D61C2×#4114yes—
323C2×C4×C61—28no—
324C2×C4×C61—28no—
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—22no—
338C2×C4×C61—22no—
339C2×C4×C61—22no—
340C2×C4×C61—22no—
341C2×C4×C61—22no—
342C2×C4×C61—22no—
343C2×C4×C61—22no—
344C2×C4×C61—44no—
345C2×C4×C61—44no—
346C2×C4×C61—44no—
347C2×C4×C61—44no—
348C2×C4×C61—44no—
349C2×C4×C61C22×D414yes—
350C2×C4×C61C2×#4114yes—
351C2×Dic61—28no—
352C2×Dic61—22no—
353C2×Dic61—22no—
354C2×Dic61—22no—
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—44no—
367C2×Dic61—44no—
368C2×Dic61—44no—
369C2×Dic61—44no—
370C2×Dic61C22×D414yes—
371D244—232no—
372D244—416no—
373D244—416no—
374C4×D61—416no—
375C4×D61—416no—
376C2×#2630—611nomaximal, Sylow
377C22×C61#52514yes—
378C22×C61#53414yes—
379C22×C61#53714yes—
380C22×C61#53814yes—
381C22×C61#53914yes—
382C22×C61#54014yes—
383C22×C61#54214yes—
384C22×C61C23×D411yescharacteristic
385C22×C61C22×#4111yescharacteristic
386C22×C61C22×#4111yescharacteristic
387C22×C61C2×H(5,𝔽2)11yescharacteristic
388C22×C61C2×H(5,𝔽2)11yescharacteristic
389C22×C61C2×H(5,𝔽2)11yescharacteristic
390C22×C61C2×2−1+411yescharacteristic
391C2×D61—24no—
392C2×D61—24no—
393C2×D61—24no—
394C2×D61—24no—
395C2×D61—24no—
396C2×D61—24no—
397C2×D61—416no—
398C2×D61—416no—
399C2×D61—42no—
400C2×D61—42no—
401C2×D61—42no—
402C2×D61—42no—
403C2×D61—42no—
404C2×D61—42no—
405C2×D61—42no—
406C2×D61—42no—
407C2×D61—42no—
408C2×D61—42no—
409C2×D61—42no—
410C2×D61—42no—
411C2×D61—42no—
412C2×D61—42no—
413C2×D61—42no—
414C2×D61—88no—
415C4×C61—24no—
416C4×C61—24no—
417C4×C61—42no—
418C4×C61—42no—
419C4×C61—42no—
420C4×C61—42no—
421C4×C61—42no—
422Dic61—24no—
423Dic61—42no—
424Dic61—42no—
425Dic61—42no—
426Dic61—42no—
427C22×#123—611no—
428C22×C4×D4—611no—
429#2630—6116no—
430C2×#398—611no—
431C2×#397—611no—
432C2×#396—611no—
433C2×#396—611no—
434C2×#394—611no—
435C2×#394—611no—
436C2×#394—611no—
437C2×#392—611no—
438C2×#388—611no—
439C2×#387D6111yescharacteristic, complemented
440C2×#386—611no—
441C2×#385—611no—
442C2×#380—611no—
443C2×C61#263018yescomplemented
444C2×C61C2×#52511yescharacteristic
445C2×C61C2×#53411yescharacteristic
446C2×C61C2×#53711yescharacteristic
447C2×C61C2×#53811yescharacteristic
448C2×C61C2×#53911yescharacteristic
449C2×C61C2×#54011yescharacteristic
450C2×C61C2×#54211yescharacteristic
451D61—44no—
452D61—44no—
453D61—82no—
454C23×D4—611no—
455C23×D4—611no—
456C23×D4—611no—
457C24×C4—611no—
458C24×C4—611no—
459C2×#123—618no—
460C2×#123—1228no—
461C2×C4×D4—618no—
462C2×C4×D4—1228no—
463C22×C4⋊C4—611no—
464C22×C4⋊C4—611no—
465C22×C4⋊C4—611no—
466C22×C4⋊C4—611no—
467C22×C4⋊C4—611no—
468C22×C4⋊C4—611no—
469C22×C4⋊C4C2×D6111yescharacteristic
470C22×C4⋊C4C2×D6111yescharacteristic
471C22×C22⋊C4—611no—
472C22×C22⋊C4—611no—
473C22×C22⋊C4—611no—
474C22×C22⋊C4—611no—
475C22×C22⋊C4—611no—
476C22×C22⋊C4—611no—
477C22×C22⋊C4—611no—
478C22×C22⋊C4—611no—
479C22×C22⋊C4—611no—
480C22×C22⋊C4—611no—
481C22×C22⋊C4—611no—
482C22×C22⋊C4—611no—
483C22×C22⋊C4—611no—
484C22×C42C2×D6111yescharacteristic
485#398—618no—
486#397—618no—
487#396—618no—
488#396—618no—
489#394—618no—
490#394—618no—
491#394—618no—
492#392—618no—
493#388—618no—
494#387C2×D6118yescomplemented
495#386—618no—
496#385—618no—
497#380—618no—
498C2×#95—611no—
499C2×#95—611no—
500C2×#95—611no—
501C2×#95—611no—
502C2×#95C2×D6111yescharacteristic
503C2×#95C2×D6111yescharacteristic
504C2×#95C2×D6111yescharacteristic
505C2×#95C2×D6111yescharacteristic
506C61C2×#263011yescharacteristic, complemented, Sylow
507C25—611no—
508C25—611no—
509C25—611no—
510C22×D4—614no—
511C22×D4—614no—
512C22×D4—614no—
513C22×D4—1224no—
514C22×D4—1224no—
515C22×D4—1224no—
516C22×D4—1224no—
517C22×D4—1224no—
518C22×D4—2442no—
519C22×D4—2442no—
520C22×D4—2442no—
521C22×D4—2442no—
522C23×C4—611no—
523C23×C4—618no—
524C23×C4—614no—
525C23×C4—611no—
526C23×C4—611no—
527C23×C4—611no—
528C23×C4—611no—
529C23×C4—614no—
530C23×C4—1224no—
531C23×C4—2442no—
532C23×C4—2442no—
533C23×C4—2442no—
534C23×C4—2442no—
535C23×C4C22×D6111yescharacteristic
536C23×C4C22×D6111yescharacteristic
537C23×C4C22×D6111yescharacteristic
538C23×C4C22×D6111yescharacteristic
539C23×C4C22×D6111yescharacteristic
540C23×C4C22×D6111yescharacteristic
541C23×C4C22×D6111yescharacteristic
542#123—12232no—
543C4×D4—12232no—
544C2×C4⋊C4—24no—
545C2×C4⋊C4—24no—
546C2×C4⋊C4—614no—
547C2×C4⋊C4—614no—
548C2×C4⋊C4—614no—
549C2×C4⋊C4—614no—
550C2×C4⋊C4—614no—
551C2×C4⋊C4—614no—
552C2×C4⋊C4—1224no—
553C2×C4⋊C4—1224no—
554C2×C4⋊C4—2442no—
555C2×C4⋊C4—2442no—
556C2×C4⋊C4—2442no—
557C2×C4⋊C4—2442no—
558C2×C4⋊C4C22×D6114yes—
559C2×C4⋊C4C22×D6114yes—
560C2×C22⋊C4—614no—
561C2×C22⋊C4—614no—
562C2×C22⋊C4—614no—
563C2×C22⋊C4—614no—
564C2×C22⋊C4—614no—
565C2×C22⋊C4—614no—
566C2×C22⋊C4—614no—
567C2×C22⋊C4—614no—
568C2×C22⋊C4—614no—
569C2×C22⋊C4—614no—
570C2×C22⋊C4—614no—
571C2×C22⋊C4—614no—
572C2×C22⋊C4—614no—
573C2×C22⋊C4—1224no—
574C2×C22⋊C4—1224no—
575C2×C22⋊C4—1224no—
576C2×C22⋊C4—1224no—
577C2×C22⋊C4—1224no—
578C2×C22⋊C4—1224no—
579C2×C22⋊C4—1224no—
580C2×C22⋊C4—2442no—
581C2×C22⋊C4—2442no—
582C2×C22⋊C4—2442no—
583C2×C22⋊C4—2442no—
584C2×C22⋊C4—2442no—
585C2×C22⋊C4—2442no—
586C2×C42—24no—
587C2×C42C22×D6114yes—
588#95—614no—
589#95—614no—
590#95—614no—
591#95—614no—
592#95C22×D6114yes—
593#95C22×D6114yes—
594#95C22×D6114yes—
595#95C22×D6114yes—
596C24—614no—
597C24—614no—
598C24—612no—
599C24—612no—
600C24—612no—
601C24—1222no—
602C24—1222no—
603C24—1222no—
604C24—1222no—
605C24—1222no—
606C24—1222no—
607C24—1222no—
608C24—1222no—
609C24—1222no—
610C24—1222no—
611C24—1222no—
612C24—1222no—
613C24—1222no—
614C24—1222no—
615C24—1222no—
616C24—1222no—
617C24—1222no—
618C24—1222no—
619C24—1222no—
620C24C23×D6111yescharacteristic
621C2×D4—1228no—
622C2×D4—1228no—
623C2×D4—12232no—
624C2×D4—1228no—
625C2×D4—1228no—
626C2×D4—1228no—
627C2×D4—2444no—
628C2×D4—2444no—
629C2×D4—2444no—
630C2×D4—2444no—
631C2×D4—24416no—
632C2×D4—24416no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—614no—
653C22×C4—612no—
654C22×C4—6116no—
655C22×C4—612no—
656C22×C4—612no—
657C22×C4—612no—
658C22×C4—612no—
659C22×C4—1222no—
660C22×C4—1222no—
661C22×C4—1222no—
662C22×C4—1222no—
663C22×C4—1222no—
664C22×C4—1222no—
665C22×C4—1222no—
666C22×C4—1222no—
667C22×C4—1222no—
668C22×C4—1222no—
669C22×C4—1222no—
670C22×C4—1222no—
671C22×C4—1222no—
672C22×C4—1222no—
673C22×C4—1228no—
674C22×C4—24416no—
675C22×C4—2444no—
676C22×C4—2444no—
677C22×C4—2444no—
678C22×C4—2444no—
679C22×C4—24416no—
680C22×C4#1175822214yes—
681C22×C4D4×D6114yes—
682C22×C4C23×D6112yes—
683C22×C4C23×D6112yes—
684C22×C4C23×D6112yes—
685C22×C4C23×D6112yes—
686C22×C4C23×D6112yes—
687C22×C4C23×D6112yes—
688C22×C4C23×D6112yes—
689C4⋊C4—28no—
690C4⋊C4—28no—
691C4⋊C4—1228no—
692C4⋊C4—1228no—
693C4⋊C4—2444no—
694C4⋊C4—2444no—
695C4⋊C4—2444no—
696C4⋊C4—2444no—
697C22⋊C4—1228no—
698C22⋊C4—1228no—
699C22⋊C4—1228no—
700C22⋊C4—1228no—
701C22⋊C4—1228no—
702C22⋊C4—1228no—
703C22⋊C4—1228no—
704C22⋊C4—2444no—
705C22⋊C4—2444no—
706C22⋊C4—2444no—
707C22⋊C4—2444no—
708C22⋊C4—2444no—
709C22⋊C4—2444no—
710C42—28no—
711C23—614no—
712C23—614no—
713C23—1228no—
714C23—1228no—
715C23—1228no—
716C23—1222no—
717C23—1222no—
718C23—1222no—
719C23—1222no—
720C23—1222no—
721C23—1222no—
722C23—1222no—
723C23—1222no—
724C23—1222no—
725C23—1222no—
726C23—1222no—
727C23—1222no—
728C23—1228no—
729C23—1228no—
730C23—1228no—
731C23—1222no—
732C23—1222no—
733C23—1222no—
734C23—1222no—
735C23—1222no—
736C23—1222no—
737C23—1222no—
738C23—2444no—
739C23—2444no—
740C23—2444no—
741C23—2444no—
742C23—2444no—
743C23—2444no—
744C23—2444no—
745C23—2444no—
746C23—2444no—
747C23—2444no—
748C23—2444no—
749C23—2444no—
750C23—2444no—
751C23—2444no—
752C23—2444no—
753C23C2×D4×D6112yes—
754C23#41×D6112yes—
755C23C2×#1175822212yes—
756C23#1451982312yes—
757C23#1451982312yes—
758C23#1451982312yes—
759C23#1451982512yes—
760C23C24×D6111yescharacteristic
761D4—12232no—
762D4—24416no—
763D4—24416no—
764C2×C4—28no—
765C2×C4—28no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—44no—
786C2×C4—44no—
787C2×C4—44no—
788C2×C4—44no—
789C2×C4—44no—
790C2×C4—614no—
791C2×C4—1228no—
792C2×C4—1222no—
793C2×C4—1222no—
794C2×C4—1222no—
795C2×C4—1222no—
796C2×C4—1222no—
797C2×C4—1222no—
798C2×C4—1222no—
799C2×C4—1222no—
800C2×C4—1222no—
801C2×C4—1222no—
802C2×C4—1222no—
803C2×C4—1222no—
804C2×C4—1222no—
805C2×C4—1222no—
806C2×C4—24416no—
807C2×C4—24416no—
808C2×C4—2444no—
809C2×C4—2444no—
810C2×C4—2444no—
811C2×C4—2444no—
812C2×C4C2×D4×D6114yes—
813C2×C4C2×#1175822214yes—
814C22—1224no—
815C22—1224no—
816C22—1224no—
817C22—1224no—
818C22—1224no—
819C22—1224no—
820C22—4888no—
821C22—2442no—
822C22—2442no—
823C22—2442no—
824C22—2442no—
825C22—2442no—
826C22—2442no—
827C22—2442no—
828C22—24416no—
829C22—24416no—
830C22—2442no—
831C22—2442no—
832C22—2442no—
833C22—2442no—
834C22—2442no—
835C22—2442no—
836C22—2442no—
837C22—2442no—
838C22#1684027114yes—
839C22#1684032314yes—
840C22#1684034214yes—
841C22#1684035114yes—
842C22#1684036014yes—
843C22#1684036714yes—
844C22#1684038414yes—
845C22C22×D4×D6111yescharacteristic
846C22C2×#41×D6111yescharacteristic
847C22C22×#1175822211yescharacteristic
848C22C2×#1451982311yescharacteristic
849C22C2×#1451982311yescharacteristic
850C22C2×#1451982311yescharacteristic
851C22C2×#1451982511yescharacteristic
852C4—24no—
853C4—24no—
854C4—42no—
855C4—42no—
856C4—42no—
857C4—42no—
858C4—42no—
859C4—1224no—
860C4—2442no—
861C4—2442no—
862C4—2442no—
863C4—2442no—
864C2—4882no—
865C2—2444no—
866C2—2444no—
867C2#2145166818yesdirect product factor
868C2C2×#1684027111yescharacteristic
869C2C2×#1684032311yescharacteristic
870C2C2×#1684034211yescharacteristic
871C2C2×#1684035111yescharacteristic
872C2C2×#1684036011yescharacteristic
873C2C2×#1684036711yescharacteristic
874C2C2×#1684038411yescharacteristic
subgroupG/H
centerC24C23×D61
commutator, cosocleC23×C61C25
FrattiniC23C24×D61
FittingC2×C61×#387C2
socleC24×C61C24
prime radicalC2×#16839672C2
hypercenterC2×#387D61
hypocenterC61C2×#2630
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
1. C22×#14519762C2semidirect
2. C22×C4×D244C2semidirect
3. #21451668C2direct (N × H)
4. C2×#16839696C2semidirect
5. C2×#16839691C2semidirect
6. C2×#16839686C2semidirect
7. C2×#16839684C2semidirect
8. C2×#16839680C2semidirect
9. C2×#16839680C2semidirect
10. C2×#16839679C2semidirect
12. C2×#16839653C2semidirect
13. C2×#16839640C2semidirect
14. C2×#16839633C2semidirect
15. C2×#16839621C2semidirect
16. C2×C61×#387C2semidirect
23. C2×#14519762C22semidirect
25. C2×C4×D244C22semidirect
45. #16839696C22semidirect
46. #16839691C22semidirect
47. #16839686C22semidirect
48. #16839684C22semidirect
49. #16839680C22semidirect
50. #16839680C22semidirect
51. #16839679C22semidirect
53. #16839653C22semidirect
54. #16839640C22semidirect
55. #16839633C22semidirect
56. #16839621C22semidirect
64. C61×#387C22semidirect
94. C22×C4×D61D4semidirect
250. C2×C4×D61C2×D4semidirect
439. C2×#387D61semidirect
443. C2×C61#2630semidirect
494. #387C2×D61semidirect
506. C61C2×#2630semidirect
867. C2#21451668direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197622
C22×C4×D2442
#214516682
C2×#168396962
C2×#168396912
C2×#168396862
C2×#168396842
C2×#168396802
C2×#168396792
C2×#168396722
C2×#168396532
C2×#168396402
C2×#168396332
C2×#168396212
C2×C61×#3872
C2×#263061