Finite Group Databasebeta

← C2×#21449241 #29848420

Subgroups — C2×#21449241 #29848420

Order 15616.

3526 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519754C211yesmaximal, characteristic, complemented
2C22×#14519754C211yesmaximal, characteristic, complemented
3C22×D4×Dic61C211yesmaximal, characteristic
4C22×#14519733C211yesmaximal, characteristic, complemented
5#21449241C2116yesmaximal, direct product factor
6C2×#16839690C211yesmaximal, characteristic, complemented
7C2×#16839687C211yesmaximal, characteristic, complemented
8C2×#16839676C211yesmaximal, characteristic
9C2×#16839666C211yesmaximal, characteristic, complemented
10C2×#16839661C211yesmaximal, characteristic, complemented
11C2×#16839659C211yesmaximal, characteristic, complemented
12C2×#16839657C211yesmaximal, characteristic, complemented
13C2×#16839655C211yesmaximal, characteristic, complemented
14C2×#16839650C211yesmaximal, characteristic, complemented
15C2×#16839620C211yesmaximal, characteristic, complemented
16C2×C61×#394C211yesmaximal, characteristic
17C23×Dic122C2211yescharacteristic
18C24×Dic61C2211yescharacteristic
19C24×Dic61C2211yescharacteristic
20C2×#14519754—28no—
21C2×#14519754—28no—
22C2×#14519754C2218yescomplemented
23C2×#14519754C2218yescomplemented
24C2×D4×Dic61—28no—
25C2×D4×Dic61C2218yes—
26C2×#14519733—28no—
27C2×#14519733C2218yescomplemented
28C22×C4⋊Dic61C2211yescharacteristic
29C22×C4⋊Dic61C2211yescharacteristic
30C22×C4⋊Dic61C2211yescharacteristic
31C22×#11758196C2211yescharacteristic
32C22×#11758196C2211yescharacteristic
33C22×#11758196C2211yescharacteristic
34C22×#11758196C2211yescharacteristic
35C22×#11758196C2211yescharacteristic
36C22×#11758196C2211yescharacteristic
37C22×C22⋊Dic61C2211yescharacteristic
38C22×C22⋊Dic61C2211yescharacteristic
39C22×C22⋊Dic61C2211yescharacteristic
40C22×C22⋊Dic61C2211yescharacteristic
41C22×C22⋊Dic61C2211yescharacteristic
42C22×C22⋊Dic61C2211yescharacteristic
43C22×C4×Dic61C2211yescharacteristic
44C22×C4×Dic61C2211yescharacteristic
45C22×C4×Dic61C2211yescharacteristic
46#16839690C2218yescomplemented
47#16839687C2218yescomplemented
48#16839676C2218yes—
49#16839666C2218yescomplemented
50#16839661C2218yescomplemented
51#16839659C2218yescomplemented
52#16839657C2218yescomplemented
53#16839655C2218yescomplemented
54#16839650C2218yescomplemented
55#16839620C2218yescomplemented
56C2×#14519684C2211yescharacteristic
57C2×#14519684C2211yescharacteristic
58C2×#14519684C2211yescharacteristic
59C2×#14519684C2211yescharacteristic
60C2×#14519684C2211yescharacteristic
61C2×#14519684C2211yescharacteristic
62C2×#14519684C2211yescharacteristic
63C23×D4×C61C2211yescharacteristic
64C22×C4⋊C4×C61C2211yescharacteristic
65C22×C22⋊C4×C61C2211yescharacteristic
66C22×C22⋊C4×C61C2211yescharacteristic
67C22×C22⋊C4×C61C2211yescharacteristic
68C22×C22⋊C4×C61C2211yescharacteristic
69C61×#394C2218yes—
70C2×#95×C61C2211yescharacteristic
71C22×Dic122—24no—
72C22×Dic122—24no—
73C22×Dic122—24no—
74C22×Dic122C2314yes—
75C23×Dic61—24no—
76C23×Dic61—24no—
77C23×Dic61—24no—
78C23×Dic61—24no—
79C23×Dic61—24no—
80C23×Dic61D418yes—
81C23×Dic61C2311yescharacteristic
82C23×Dic61C2311yescharacteristic
83C23×Dic61C2311yescharacteristic
84C23×Dic61C2311yescharacteristic
85C23×Dic61C2311yescharacteristic
86C23×Dic61C2314yes—
87C23×Dic61C2311yescharacteristic
88C23×Dic61C2311yescharacteristic
89C23×Dic61C2314yes—
90C23×Dic61C2311yescharacteristic
91#14519754—232no—
92#14519754—232no—
93D4×Dic61—232no—
94#14519733—232no—
95C2×C4⋊Dic61—24no—
96C2×C4⋊Dic61—24no—
97C2×C4⋊Dic61—24no—
98C2×C4⋊Dic61C2314yes—
99C2×C4⋊Dic61C2314yes—
100C2×C4⋊Dic61C2314yes—
101C2×#11758196—24no—
102C2×#11758196—24no—
103C2×#11758196—24no—
104C2×#11758196—24no—
105C2×#11758196—24no—
106C2×#11758196D418yescomplemented
107C2×#11758196C2314yes—
108C2×#11758196C2314yes—
109C2×#11758196C2314yes—
110C2×#11758196C2314yes—
111C2×#11758196C2314yes—
112C2×#11758196C2314yes—
113C2×C22⋊Dic61—24no—
114C2×C22⋊Dic61—24no—
115C2×C22⋊Dic61—24no—
116C2×C22⋊Dic61—24no—
117C2×C22⋊Dic61—24no—
118C2×C22⋊Dic61—24no—
119C2×C22⋊Dic61C2314yes—
120C2×C22⋊Dic61C2314yes—
121C2×C22⋊Dic61C2314yes—
122C2×C22⋊Dic61C2314yes—
123C2×C22⋊Dic61C2314yes—
124C2×C22⋊Dic61C2314yes—
125C2×C4×Dic61—24no—
126C2×C4×Dic61—24no—
127C2×C4×Dic61—24no—
128C2×C4×Dic61C2314yes—
129C2×C4×Dic61C2314yes—
130C2×C4×Dic61C2314yes—
131#14519684C2314yes—
132#14519684C2314yes—
133#14519684C2314yes—
134#14519684C2314yes—
135#14519684C2314yes—
136#14519684C2314yes—
137#14519684C2314yes—
138C25×C61C2311yescharacteristic
139C25×C61C2311yescharacteristic
140C22×D4×C61—24no—
141C22×D4×C61—24no—
142C22×D4×C61—24no—
143C22×D4×C61C2314yes—
144C23×C4×C61C2311yescharacteristic
145C23×C4×C61C2311yescharacteristic
146C23×C4×C61C2311yescharacteristic
147C23×C4×C61C2311yescharacteristic
148C23×C4×C61C2311yescharacteristic
149C2×C4⋊C4×C61—24no—
150C2×C4⋊C4×C61C2314yes—
151C2×C22⋊C4×C61—24no—
152C2×C22⋊C4×C61—24no—
153C2×C22⋊C4×C61—24no—
154C2×C22⋊C4×C61—24no—
155C2×C22⋊C4×C61C2314yes—
156C2×C22⋊C4×C61C2314yes—
157C2×C22⋊C4×C61C2314yes—
158C2×C22⋊C4×C61C2314yes—
159#95×C61C2314yes—
160C24×C61—22no—
161C24×C61—22no—
162C24×C61—22no—
163C24×C61—22no—
164C24×C61—22no—
165C24×C61—22no—
166C24×C61—22no—
167C24×C61—22no—
168C24×C61—22no—
169C24×C61—22no—
170C24×C61—22no—
171C24×C61—22no—
172C24×C61C2×D414yes—
173C24×C61#4114yes—
174C24×C61C2412yes—
175C24×C61C2412yes—
176C24×C61C2411yescharacteristic
177C2×D4×C61—232no—
178C2×D4×C61—28no—
179C2×D4×C61—28no—
180C2×D4×C61—28no—
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×C61C2×D414yes—
195C22×C4×C61#4114yes—
196C22×C4×C61C2412yes—
197C22×C4×C61C2412yes—
198C22×C4×C61C2412yes—
199C22×C4×C61C2412yes—
200C22×C4×C61C2412yes—
201C22×Dic61—22no—
202C22×Dic61—22no—
203C22×Dic61—22no—
204C22×Dic61—22no—
205C22×Dic61—232no—
206C22×Dic61—28no—
207C22×Dic61—28no—
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—28no—
224C22×Dic61—28no—
225C22×Dic61—28no—
226C22×Dic61—416no—
227C22×Dic61C2×D414yes—
228C22×Dic61C2×D4116yes—
229C22×Dic61C2×D414yes—
230C22×Dic61C2×D414yes—
231C22×Dic61C2×D414yes—
232C22×Dic61#4114yes—
233C22×Dic61C2412yes—
234C22×Dic61C2412yes—
235C22×Dic61C2412yes—
236C22×Dic61C2412yes—
237C22×Dic61C2412yes—
238C22×Dic61C2412yes—
239C22×Dic61C2412yes—
240C22×Dic61C2412yes—
241C2×Dic122—28no—
242C2×Dic122—28no—
243C2×Dic122—28no—
244C2×Dic122—416no—
245C4⋊C4×C61—28no—
246C22⋊C4×C61—28no—
247C22⋊C4×C61—28no—
248C22⋊C4×C61—28no—
249C22⋊C4×C61—28no—
250C22⋊Dic61—28no—
251C22⋊Dic61—28no—
252C22⋊Dic61—28no—
253C22⋊Dic61—28no—
254C22⋊Dic61—28no—
255C22⋊Dic61—28no—
256C4⋊Dic61—28no—
257C4⋊Dic61—28no—
258C4⋊Dic61—28no—
259#11758196—28no—
260#11758196—28no—
261#11758196—28no—
262#11758196—28no—
263#11758196—28no—
264#11758196C2×D4116yescomplemented
265C4×Dic61—28no—
266C4×Dic61—28no—
267C4×Dic61—28no—
268C23×C61—28no—
269C23×C61—28no—
270C23×C61—28no—
271C23×C61—28no—
272C23×C61—28no—
273C23×C61—28no—
274C23×C61—22no—
275C23×C61—22no—
276C23×C61—22no—
277C23×C61—22no—
278C23×C61—22no—
279C23×C61—22no—
280C23×C61—22no—
281C23×C61—22no—
282C23×C61—22no—
283C23×C61—22no—
284C23×C61—22no—
285C23×C61—22no—
286C23×C61—44no—
287C23×C61—44no—
288C23×C61—44no—
289C23×C61—44no—
290C23×C61—44no—
291C23×C61—44no—
292C23×C61—44no—
293C23×C61—44no—
294C23×C61C22×D414yes—
295C23×C61C22×D412yes—
296C23×C61C22×D412yes—
297C23×C61C2×#4114yes—
298C23×C61C2×#4112yes—
299C23×C61C2×#4112yes—
300C23×C61C2×#4112yes—
301C23×C612−1+412yes—
302C23×C612−1+412yes—
303C23×C61C2511yescharacteristic
304D4×C61—232no—
305C2×C4×C61—28no—
306C2×C4×C61—28no—
307C2×C4×C61—22no—
308C2×C4×C61—22no—
309C2×C4×C61—22no—
310C2×C4×C61—22no—
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—44no—
321C2×C4×C61—44no—
322C2×C4×C61—44no—
323C2×C4×C61C22×D414yes—
324C2×C4×C61C2×#4114yes—
325C2×Dic61—28no—
326C2×Dic61—28no—
327C2×Dic61—22no—
328C2×Dic61—22no—
329C2×Dic61—22no—
330C2×Dic61—22no—
331C2×Dic61—232no—
332C2×Dic61—22no—
333C2×Dic61—22no—
334C2×Dic61—22no—
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—44no—
348C2×Dic61—44no—
349C2×Dic61—44no—
350C2×Dic61—44no—
351C2×Dic61—44no—
352C2×Dic61—416no—
353C2×Dic61#121116yes—
354C2×Dic61C22×D414yes—
355C2×Dic61C22×D414yes—
356C2×Dic61C22×D414yes—
357C2×Dic61C22×D414yes—
358C2×Dic61C2×#4114yes—
359Dic122—416no—
360C2×#2415—611nomaximal, Sylow
361C22×C61—24no—
362C22×C61—24no—
363C22×C61—24no—
364C22×C61—24no—
365C22×C61—24no—
366C22×C61—24no—
367C22×C61—42no—
368C22×C61—416no—
369C22×C61—416no—
370C22×C61—42no—
371C22×C61—42no—
372C22×C61—42no—
373C22×C61—42no—
374C22×C61—42no—
375C22×C61—42no—
376C22×C61—42no—
377C22×C61C2×#12114yes—
378C22×C61#52514yes—
379C22×C61#53614yes—
380C22×C61#54714yes—
381C22×C61#54814yes—
382C22×C61#55214yes—
383C22×C61#55614yes—
384C22×C61C23×D411yescharacteristic
385C22×C61C23×D411yescharacteristic
386C22×C61C22×#4111yescharacteristic
387C22×C61C22×#4111yescharacteristic
388C22×C61C22×#4111yescharacteristic
389C22×C61C2×2−1+411yescharacteristic
390C22×C61C2×2−1+411yescharacteristic
391C4×C61—24no—
392C4×C61—24no—
393C4×C61—42no—
394C4×C61—42no—
395C4×C61—42no—
396Dic61—24no—
397Dic61—24no—
398Dic61—42no—
399Dic61—42no—
400Dic61—42no—
401Dic61—42no—
402Dic61—42no—
403Dic61C2×#12118yes—
404C22×C22⋊Q8—611no—
405C22×C22⋊Q8—611no—
406C22×C4×D4—611no—
407C22×#117—611no—
408#2415—6116no—
409C2×#397—611no—
410C2×#397—611no—
411C2×#394—611no—
412C2×#394D6111yescharacteristic
413C2×#391—611no—
414C2×#389—611no—
415C2×#389—611no—
416C2×#389—611no—
417C2×#388—611no—
418C2×#388—611no—
419C2×#380—611no—
420C2×C61—44no—
421C2×C61—44no—
422C2×C61#241518yescomplemented
423C2×C61C22×#12111yescharacteristic
424C2×C61C2×#52511yescharacteristic
425C2×C61C2×#53611yescharacteristic
426C2×C61C2×#54711yescharacteristic
427C2×C61C2×#54811yescharacteristic
428C2×C61C2×#55211yescharacteristic
429C2×C61C2×#55611yescharacteristic
430C23×Q8—611no—
431C23×D4C2×D6111yescharacteristic
432C24×C4—611no—
433C24×C4—611no—
434C2×C22⋊Q8—618no—
435C2×C22⋊Q8—618no—
436C2×C22⋊Q8—1228no—
437C2×C22⋊Q8—1228no—
438C2×C4×D4—618no—
439C2×C4×D4—1228no—
440C2×#117—618no—
441C2×#117—1228no—
442C22×C4⋊C4—611no—
443C22×C4⋊C4—611no—
444C22×C4⋊C4—611no—
445C22×C4⋊C4—611no—
446C22×C4⋊C4—611no—
447C22×C4⋊C4—611no—
448C22×C4⋊C4—611no—
449C22×C4⋊C4—611no—
450C22×C4⋊C4—611no—
451C22×C4⋊C4C2×D6111yescharacteristic
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⋊C4C2×D6111yescharacteristic
459C22×C22⋊C4C2×D6111yescharacteristic
460C22×C22⋊C4C2×D6111yescharacteristic
461C22×C22⋊C4C2×D6111yescharacteristic
462C22×C42—611no—
463C22×C42—611no—
464C22×C42—611no—
465#397—618no—
466#397—618no—
467#394—618no—
468#394C2×D6118yes—
469#391—618no—
470#389—618no—
471#389—618no—
472#389—618no—
473#388—618no—
474#388—618no—
475#380—618no—
476C2×#95—611no—
477C2×#95—611no—
478C2×#95—611no—
479C2×#95—611no—
480C2×#95—611no—
481C2×#95—611no—
482C2×#95—611no—
483C2×#95C2×D6111yescharacteristic
484C61C2×#241511yescharacteristic, complemented, Sylow
485C25C22×D6111yescharacteristic
486C25C22×D6111yescharacteristic
487C22×Q8—614no—
488C22×Q8—1224no—
489C22×Q8—1224no—
490C22×Q8—1224no—
491C22×D4—24no—
492C22×D4—24no—
493C22×D4—24no—
494C22×D4C22×D6114yes—
495C23×C4—611no—
496C23×C4—618no—
497C23×C4—614no—
498C23×C4—611no—
499C23×C4—611no—
500C23×C4—614no—
501C23×C4—611no—
502C23×C4—611no—
503C23×C4—611no—
504C23×C4—611no—
505C23×C4—611no—
506C23×C4—1224no—
507C23×C4—1224no—
508C23×C4—1224no—
509C23×C4—1224no—
510C23×C4—1224no—
511C23×C4C22×D6111yescharacteristic
512C23×C4C22×D6111yescharacteristic
513C23×C4C22×D6111yescharacteristic
514C23×C4C22×D6111yescharacteristic
515C23×C4C22×D6111yescharacteristic
516C22⋊Q8—12232no—
517C22⋊Q8—12232no—
518C4×D4—12232no—
519#117—12232no—
520C2×C4⋊C4—24no—
521C2×C4⋊C4—618no—
522C2×C4⋊C4—614no—
523C2×C4⋊C4—614no—
524C2×C4⋊C4—614no—
525C2×C4⋊C4—614no—
526C2×C4⋊C4—614no—
527C2×C4⋊C4—614no—
528C2×C4⋊C4—614no—
529C2×C4⋊C4—614no—
530C2×C4⋊C4—614no—
531C2×C4⋊C4—1224no—
532C2×C4⋊C4—1224no—
533C2×C4⋊C4—1224no—
534C2×C4⋊C4—1224no—
535C2×C4⋊C4—1224no—
536C2×C4⋊C4—1224no—
537C2×C4⋊C4—1224no—
538C2×C4⋊C4—1224no—
539C2×C4⋊C4C22×D6114yes—
540C2×C22⋊C4—24no—
541C2×C22⋊C4—24no—
542C2×C22⋊C4—24no—
543C2×C22⋊C4—24no—
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—1224no—
552C2×C22⋊C4—1224no—
553C2×C22⋊C4—1224no—
554C2×C22⋊C4—1224no—
555C2×C22⋊C4—1224no—
556C2×C22⋊C4C22×D6114yes—
557C2×C22⋊C4C22×D6114yes—
558C2×C22⋊C4C22×D6114yes—
559C2×C22⋊C4C22×D6114yes—
560C2×C42—614no—
561C2×C42—614no—
562C2×C42—614no—
563C2×C42—1224no—
564C2×C42—1224no—
565C2×C42—1224no—
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—
586C24D4×D6114yes—
587C24#1175822414yes—
588C24C23×D6112yes—
589C24C23×D6112yes—
590C24C23×D6111yescharacteristic
591C2×Q8—1228no—
592C2×Q8—1228no—
593C2×Q8—1228no—
594C2×Q8—24416no—
595C2×D4—232no—
596C2×D4—28no—
597C2×D4—28no—
598C2×D4—28no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—614no—
613C22×C4—614no—
614C22×C4—614no—
615C22×C4—612no—
616C22×C4—614no—
617C22×C4—614no—
618C22×C4—6116no—
619C22×C4—612no—
620C22×C4—612no—
621C22×C4—612no—
622C22×C4—612no—
623C22×C4—612no—
624C22×C4—612no—
625C22×C4—612no—
626C22×C4—1228no—
627C22×C4—12232no—
628C22×C4—1228no—
629C22×C4—1228no—
630C22×C4—1228no—
631C22×C4—1228no—
632C22×C4—1222no—
633C22×C4—1222no—
634C22×C4—1222no—
635C22×C4—1222no—
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—24416no—
652C22×C4D4×D6114yes—
653C22×C4#1175822414yes—
654C22×C4C23×D6112yes—
655C22×C4C23×D6112yes—
656C22×C4C23×D6112yes—
657C22×C4C23×D6112yes—
658C22×C4C23×D6112yes—
659C4⋊C4—28no—
660C4⋊C4—6116no—
661C4⋊C4—1228no—
662C4⋊C4—1228no—
663C4⋊C4—1228no—
664C4⋊C4—1228no—
665C4⋊C4—1228no—
666C4⋊C4—1228no—
667C4⋊C4—1228no—
668C4⋊C4—1228no—
669C22⋊C4—28no—
670C22⋊C4—28no—
671C22⋊C4—28no—
672C22⋊C4—28no—
673C22⋊C4—1228no—
674C22⋊C4—1228no—
675C22⋊C4—1228no—
676C22⋊C4—1228no—
677C22⋊C4—1228no—
678C22⋊C4—1228no—
679C42—1228no—
680C42—1228no—
681C42—1228no—
682C23—28no—
683C23—28no—
684C23—28no—
685C23—28no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—22no—
694C23—28no—
695C23—22no—
696C23—22no—
697C23—22no—
698C23—22no—
699C23—28no—
700C23—44no—
701C23—44no—
702C23—44no—
703C23—44no—
704C23—44no—
705C23—44no—
706C23—44no—
707C23—44no—
708C23C2×D4×D6114yes—
709C23C2×D4×D6112yes—
710C23C2×D4×D6112yes—
711C23#41×D6112yes—
712C23C2×#1175822414yes—
713C23C2×#1175822412yes—
714C23C2×#1175822412yes—
715C23#1451982412yes—
716C23#1451982412yes—
717C23C24×D6111yescharacteristic
718Q8—24416no—
719D4—232no—
720C2×C4—28no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—28no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—44no—
738C2×C4—6116no—
739C2×C4—614no—
740C2×C4—614no—
741C2×C4—614no—
742C2×C4—614no—
743C2×C4—614no—
744C2×C4—12232no—
745C2×C4—1228no—
746C2×C4—1222no—
747C2×C4—1222no—
748C2×C4—1222no—
749C2×C4—1222no—
750C2×C4—1228no—
751C2×C4—1222no—
752C2×C4—1222no—
753C2×C4—1222no—
754C2×C4—1222no—
755C2×C4—1222no—
756C2×C4—1222no—
757C2×C4—1222no—
758C2×C4—1222no—
759C2×C4—1222no—
760C2×C4—1222no—
761C2×C4—1222no—
762C2×C4—1222no—
763C2×C4—1222no—
764C2×C4—1222no—
765C2×C4—1222no—
766C2×C4—24416no—
767C2×C4—2444no—
768C2×C4—2444no—
769C2×C4—2444no—
770C2×C4—2444no—
771C2×C4—2444no—
772C2×C4C2×D4×D6114yes—
773C2×C4C2×#1175822414yes—
774C22—24no—
775C22—24no—
776C22—24no—
777C22—24no—
778C22—24no—
779C22—24no—
780C22—416no—
781C22—416no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22#121×D6114yes—
791C22#1684026814yes—
792C22#1684033414yes—
793C22#1684041214yes—
794C22#1684041814yes—
795C22#1684044914yes—
796C22#1684048114yes—
797C22C22×D4×D6111yescharacteristic
798C22C22×D4×D6111yescharacteristic
799C22C2×#41×D6111yescharacteristic
800C22C22×#1175822411yescharacteristic
801C22C22×#1175822411yescharacteristic
802C22C2×#1451982411yescharacteristic
803C22C2×#1451982411yescharacteristic
804C4—24no—
805C4—24no—
806C4—42no—
807C4—42no—
808C4—42no—
809C4—618no—
810C4—1224no—
811C4—1224no—
812C4—2442no—
813C4—2442no—
814C4—2442no—
815C4—2442no—
816C4—2442no—
817C2—44no—
818C2—44no—
819C2#2144924118yesdirect product factor
820C2C2×#121×D6111yescharacteristic
821C2C2×#1684026811yescharacteristic
822C2C2×#1684033411yescharacteristic
823C2C2×#1684041211yescharacteristic
824C2C2×#1684041811yescharacteristic
825C2C2×#1684044911yescharacteristic
826C2C2×#1684048111yescharacteristic
subgroupG/H
centerC24C23×D61
commutator, cosocleC23×C61C25
FrattiniC23C24×D61
FittingC2×C61×#394C2
socleC24×C61C24
prime radicalC23×D4×C61C22
hypercenterC2×#394D61
hypocenterC61C2×#2415
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
1. C22×#14519754C2semidirect
2. C22×#14519754C2semidirect
4. C22×#14519733C2semidirect
5. #21449241C2direct (N × H)
6. C2×#16839690C2semidirect
7. C2×#16839687C2semidirect
9. C2×#16839666C2semidirect
10. C2×#16839661C2semidirect
11. C2×#16839659C2semidirect
12. C2×#16839657C2semidirect
13. C2×#16839655C2semidirect
14. C2×#16839650C2semidirect
15. C2×#16839620C2semidirect
22. C2×#14519754C22semidirect
23. C2×#14519754C22semidirect
27. C2×#14519733C22semidirect
46. #16839690C22semidirect
47. #16839687C22semidirect
49. #16839666C22semidirect
50. #16839661C22semidirect
51. #16839659C22semidirect
52. #16839657C22semidirect
53. #16839655C22semidirect
54. #16839650C22semidirect
55. #16839620C22semidirect
106. C2×#11758196D4semidirect
264. #11758196C2×D4semidirect
422. C2×C61#2415semidirect
484. C61C2×#2415semidirect
819. C2#21449241direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197542
C22×D4×Dic612
C22×#145197332
#214492412
C2×#168396902
C2×#168396872
C2×#168396762
C2×#168396662
C2×#168396612
C2×#168396592
C2×#168396572
C2×#168396552
C2×#168396502
C2×#168396202
C2×C61×#3942
C2×#241561