Finite Group Databasebeta

← C2×#21449599 #29848165

Subgroups — C2×#21449599 #29848165

Order 15616.

3070 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519763C211yesmaximal, characteristic
2C22×#14519737C211yesmaximal, characteristic
3#21449599C2116yesmaximal, direct product factor
4C2×#16839691C211yesmaximal, characteristic, complemented
5C2×#16839691C211yesmaximal, characteristic, complemented
6C2×#16839690C211yesmaximal, characteristic, complemented
7C2×#16839666C211yesmaximal, characteristic, complemented
8C2×#16839666C211yesmaximal, characteristic, complemented
9C2×#16839662C211yesmaximal, characteristic
10C2×#16839657C211yesmaximal, characteristic, complemented
11C2×#16839634C211yesmaximal, characteristic, complemented
12C2×#16839633C211yesmaximal, characteristic, complemented
13C2×#16839624C211yesmaximal, characteristic, complemented
14C2×#16839623C211yesmaximal, characteristic, complemented
15C2×#16839613C211yesmaximal, characteristic, complemented
16C2×C61×#397C211yesmaximal, characteristic, complemented
17C23×Dic122C2211yescharacteristic
18C23×C22⋊D61C2211yescharacteristic
19C24×Dic61C2211yescharacteristic
20C23×C4×D61C2211yescharacteristic
21C2×#14519763—28no—
22C2×#14519763C2218yes—
23C2×#14519737—28no—
24C2×#14519737C2218yes—
25C22×#11758196C2211yescharacteristic
26C22×#11758196C2211yescharacteristic
27C22×#11758196C2211yescharacteristic
28C22×#11758196C2211yescharacteristic
29C22×#11758196C2211yescharacteristic
30C22×C22⋊Dic61C2211yescharacteristic
31C22×C22⋊Dic61C2211yescharacteristic
32C22×#11758198C2211yescharacteristic
33C22×#11758198C2211yescharacteristic
34C22×#11758198C2211yescharacteristic
35C22×#11758198C2211yescharacteristic
36C22×#11758198C2211yescharacteristic
37C22×C4×Dic61C2211yescharacteristic
38C22×C4×Dic61C2211yescharacteristic
39C22×C4×Dic61C2211yescharacteristic
40#16839691C2218yescomplemented
41#16839691C2218yescomplemented
42#16839690C2218yescomplemented
43#16839666C2218yescomplemented
44#16839666C2218yescomplemented
45#16839662C2218yes—
46#16839657C2218yescomplemented
47#16839634C2218yescomplemented
48#16839633C2218yescomplemented
49#16839624C2218yescomplemented
50#16839623C2218yescomplemented
51#16839613C2218yescomplemented
52C2×#14519684C2211yescharacteristic
53C2×#14519684C2211yescharacteristic
54C2×#14519684C2211yescharacteristic
55C2×#14519684C2211yescharacteristic
56C2×#14519684C2211yescharacteristic
57C2×#14519684C2211yescharacteristic
58C2×#14519684C2211yescharacteristic
59C2×#14519684C2211yescharacteristic
60C2×#14519684C2211yescharacteristic
61C22×C4⋊C4×C61C2211yescharacteristic
62C22×C22⋊C4×C61C2211yescharacteristic
63C22×C22⋊C4×C61C2211yescharacteristic
64C22×C22⋊C4×C61C2211yescharacteristic
65C61×#397C2218yescomplemented
66C2×#95×C61C2211yescharacteristic
67C2×#95×C61C2211yescharacteristic
68C2×#95×C61C2211yescharacteristic
69C24×D61C2311yescharacteristic
70C22×Dic122—24no—
71C22×Dic122—24no—
72C22×Dic122—24no—
73C22×Dic122C2314yes—
74C22×C22⋊D61—24no—
75C22×C22⋊D61—24no—
76C22×C22⋊D61D418yes—
77C22×C22⋊D61C2314yes—
78C23×Dic61—24no—
79C23×Dic61—24no—
80C23×Dic61—42no—
81C23×Dic61C2311yescharacteristic
82C23×Dic61C2311yescharacteristic
83C23×Dic61C2311yescharacteristic
84C23×Dic61C2311yescharacteristic
85C23×Dic61C2314yes—
86C23×Dic61C2311yescharacteristic
87C23×Dic61C2311yescharacteristic
88C23×Dic61C2311yescharacteristic
89C22×C4×D61—24no—
90C22×C4×D61—24no—
91C22×C4×D61—42no—
92C22×C4×D61C2314yes—
93#14519763—232no—
94#14519737—232no—
95C2×#11758196—24no—
96C2×#11758196—24no—
97C2×#11758196—24no—
98C2×#11758196—24no—
99C2×#11758196—42no—
100C2×#11758196C2314yes—
101C2×#11758196C2314yes—
102C2×#11758196C2314yes—
103C2×#11758196C2314yes—
104C2×#11758196C2314yes—
105C2×C22⋊Dic61—24no—
106C2×C22⋊Dic61—24no—
107C2×C22⋊Dic61C2314yes—
108C2×C22⋊Dic61C2314yes—
109C2×#11758198—24no—
110C2×#11758198—24no—
111C2×#11758198—24no—
112C2×#11758198—24no—
113C2×#11758198—42no—
114C2×#11758198C2314yes—
115C2×#11758198C2314yes—
116C2×#11758198C2314yes—
117C2×#11758198C2314yes—
118C2×#11758198C2314yes—
119C2×C4×Dic61—24no—
120C2×C4×Dic61—24no—
121C2×C4×Dic61—24no—
122C2×C4×Dic61C2314yes—
123C2×C4×Dic61C2314yes—
124C2×C4×Dic61C2314yes—
125#14519684C2314yes—
126#14519684C2314yes—
127#14519684C2314yes—
128#14519684C2314yes—
129#14519684C2314yes—
130#14519684C2314yes—
131#14519684C2314yes—
132#14519684C2314yes—
133#14519684C2314yes—
134C25×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×C61C2314yes—
143C2×C22⋊C4×C61—24no—
144C2×C22⋊C4×C61—24no—
145C2×C22⋊C4×C61—42no—
146C2×C22⋊C4×C61C2314yes—
147C2×C22⋊C4×C61C2314yes—
148C2×C22⋊C4×C61C2314yes—
149#95×C61C2314yes—
150#95×C61C2314yes—
151#95×C61C2314yes—
152C24×C61—22no—
153C24×C61—22no—
154C24×C61—22no—
155C24×C61—22no—
156C24×C61—22no—
157C24×C61—22no—
158C24×C61C2×D414yes—
159C24×C61C2412yes—
160C24×C61C2411yescharacteristic
161C23×D61—22no—
162C23×D61—22no—
163C23×D61—22no—
164C23×D61—22no—
165C23×D61—22no—
166C23×D61—22no—
167C23×D61C2×D414yes—
168C23×D61C2412yes—
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—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×C61C2412yes—
188C22×C4×C61C2412yes—
189C22×C4×C61C2412yes—
190C22×C4×C61C2412yes—
191C22×C4×C61C2412yes—
192C22×C4×C61C2412yes—
193C2×C22⋊D61—232no—
194C2×C22⋊D61—28no—
195C2×C22⋊D61—28no—
196C2×C22⋊D61C2×D4116yes—
197C22×Dic61—22no—
198C22×Dic61—22no—
199C22×Dic61—22no—
200C22×Dic61—22no—
201C22×Dic61—22no—
202C22×Dic61—28no—
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—28no—
215C22×Dic61—44no—
216C22×Dic61—416no—
217C22×Dic61C2×D414yes—
218C22×Dic61#4114yes—
219C22×Dic61#4114yes—
220C22×Dic61#4114yes—
221C22×Dic61#4114yes—
222C22×Dic61C2412yes—
223C22×Dic61C2412yes—
224C22×Dic61C2412yes—
225C22×Dic61C2412yes—
226C22×Dic61C2412yes—
227C22×Dic61C2412yes—
228C22×Dic61C2412yes—
229C2×C4×D61—28no—
230C2×C4×D61—28no—
231C2×C4×D61—44no—
232C2×C4×D61—416no—
233C2×Dic122—28no—
234C2×Dic122—28no—
235C2×Dic122—28no—
236C2×Dic122—416no—
237C4⋊C4×C61—44no—
238C22⋊C4×C61—28no—
239C22⋊C4×C61—28no—
240C22⋊C4×C61—44no—
241C22⋊Dic61—28no—
242C22⋊Dic61—28no—
243#11758198—28no—
244#11758198—28no—
245#11758198—28no—
246#11758198—28no—
247#11758198—44no—
248#11758196—28no—
249#11758196—28no—
250#11758196—28no—
251#11758196—28no—
252#11758196—44no—
253C4×Dic61—28no—
254C4×Dic61—28no—
255C4×Dic61—28no—
256C23×C61—28no—
257C23×C61—28no—
258C23×C61—28no—
259C23×C61—22no—
260C23×C61—22no—
261C23×C61—22no—
262C23×C61—22no—
263C23×C61—22no—
264C23×C61—22no—
265C23×C61—44no—
266C23×C61—44no—
267C23×C61—44no—
268C23×C61—44no—
269C23×C61C22×D414yes—
270C23×C61C22×D412yes—
271C23×C61C2×#4112yes—
272C23×C61C2×#4112yes—
273C23×C61C2×#4112yes—
274C23×C61C2×#4112yes—
275C23×C61H(5,𝔽2)12yes—
276C23×C612−1+412yes—
277C23×C61C2511yescharacteristic
278C22×D61—28no—
279C22×D61—28no—
280C22×D61—28no—
281C22×D61—22no—
282C22×D61—22no—
283C22×D61—22no—
284C22×D61—22no—
285C22×D61—22no—
286C22×D61—22no—
287C22×D61—44no—
288C22×D61—44no—
289C22×D61—44no—
290C22×D61—44no—
291C22×D61C22×D414yes—
292C2×C4×C61—22no—
293C2×C4×C61—22no—
294C2×C4×C61—22no—
295C2×C4×C61—22no—
296C2×C4×C61—22no—
297C2×C4×C61—22no—
298C2×C4×C61—22no—
299C2×C4×C61—22no—
300C2×C4×C61—22no—
301C2×C4×C61—22no—
302C2×C4×C61—22no—
303C2×C4×C61—22no—
304C2×C4×C61—22no—
305C2×C4×C61—22no—
306C2×C4×C61—22no—
307C2×C4×C61—22no—
308C2×C4×C61—22no—
309C2×C4×C61—22no—
310C2×C4×C61—44no—
311C2×C4×C61—44no—
312C2×C4×C61—44no—
313C2×C4×C61—44no—
314C2×C4×C61—44no—
315C2×C4×C61—44no—
316C22⋊D61—232no—
317C2×Dic61—28no—
318C2×Dic61—28no—
319C2×Dic61—22no—
320C2×Dic61—22no—
321C2×Dic61—22no—
322C2×Dic61—22no—
323C2×Dic61—22no—
324C2×Dic61—22no—
325C2×Dic61—22no—
326C2×Dic61—22no—
327C2×Dic61—22no—
328C2×Dic61—22no—
329C2×Dic61—22no—
330C2×Dic61—22no—
331C2×Dic61—22no—
332C2×Dic61—22no—
333C2×Dic61—22no—
334C2×Dic61—22no—
335C2×Dic61—416no—
336C2×Dic61—44no—
337C2×Dic61—44no—
338C2×Dic61—44no—
339C2×Dic61—44no—
340C2×Dic61#123116yes—
341C2×Dic61C22×D414yes—
342C2×Dic61C2×#4114yes—
343C2×Dic61C2×#4114yes—
344C2×Dic61C2×#4114yes—
345C2×Dic61C2×#4114yes—
346C4×D61—416no—
347Dic122—416no—
348C2×#2447—611nomaximal, Sylow
349C22×C61—24no—
350C22×C61—24no—
351C22×C61—24no—
352C22×C61—42no—
353C22×C61—42no—
354C22×C61—416no—
355C22×C61—42no—
356C22×C61—42no—
357C22×C61C2×#12314yes—
358C22×C61#52914yes—
359C22×C61#54214yes—
360C22×C61#54614yes—
361C22×C61#54714yes—
362C22×C61#55614yes—
363C22×C61#55914yes—
364C22×C61C23×D411yescharacteristic
365C22×C61C22×#4111yescharacteristic
366C22×C61C22×#4111yescharacteristic
367C22×C61C22×#4111yescharacteristic
368C22×C61C22×#4111yescharacteristic
369C22×C61C2×H(5,𝔽2)11yescharacteristic
370C22×C61C2×2−1+411yescharacteristic
371C2×D61—24no—
372C2×D61—24no—
373C2×D61—24no—
374C2×D61—42no—
375C2×D61—42no—
376C2×D61—416no—
377C2×D61—42no—
378C2×D61—42no—
379C4×C61—42no—
380C4×C61—42no—
381C4×C61—42no—
382C4×C61—42no—
383C4×C61—42no—
384C4×C61—42no—
385Dic61—24no—
386Dic61—24no—
387Dic61—42no—
388Dic61—42no—
389Dic61—42no—
390Dic61—42no—
391Dic61C2×#12318yes—
392C22×#124—611no—
393C22×C4×D4—611no—
394#2447—6116no—
395C2×#397—611no—
396C2×#397—611no—
397C2×#397—611no—
398C2×#397D6111yescharacteristic, complemented
399C2×#391—611no—
400C2×#391—611no—
401C2×#390—611no—
402C2×#389—611no—
403C2×#385—611no—
404C2×#385—611no—
405C2×#381—611no—
406C2×#381—611no—
407C2×C4×C4⋊C4—611no—
408C2×C61—44no—
409C2×C61#244718yescomplemented
410C2×C61C22×#12311yescharacteristic
411C2×C61C2×#52911yescharacteristic
412C2×C61C2×#54211yescharacteristic
413C2×C61C2×#54611yescharacteristic
414C2×C61C2×#54711yescharacteristic
415C2×C61C2×#55611yescharacteristic
416C2×C61C2×#55911yescharacteristic
417D61—44no—
418C23×Q8—611no—
419C23×D4—611no—
420C24×C4—611no—
421C24×C4—611no—
422C2×#124—618no—
423C2×#124—1228no—
424C2×C4×D4—618no—
425C2×C4×D4—1228no—
426C22×C4⋊C4—611no—
427C22×C4⋊C4—611no—
428C22×C4⋊C4—611no—
429C22×C4⋊C4—611no—
430C22×C4⋊C4—611no—
431C22×C4⋊C4C2×D6111yescharacteristic
432C22×C22⋊C4—611no—
433C22×C22⋊C4—611no—
434C22×C22⋊C4—611no—
435C22×C22⋊C4—611no—
436C22×C22⋊C4—611no—
437C22×C22⋊C4—611no—
438C22×C22⋊C4—611no—
439C22×C22⋊C4C2×D6111yescharacteristic
440C22×C22⋊C4C2×D6111yescharacteristic
441C22×C22⋊C4C2×D6111yescharacteristic
442C22×C42—611no—
443C22×C42—611no—
444C22×C42—611no—
445#397—618no—
446#397—618no—
447#397—618no—
448#397C2×D6118yescomplemented
449#391—618no—
450#391—618no—
451#390—618no—
452#389—618no—
453#385—618no—
454#385—618no—
455#381—618no—
456#381—618no—
457C4×C4⋊C4—618no—
458C2×#95—611no—
459C2×#95—611no—
460C2×#95—611no—
461C2×#95—611no—
462C2×#95—611no—
463C2×#95—611no—
464C2×#95—611no—
465C2×#95—611no—
466C2×#95—611no—
467C2×#95C2×D6111yescharacteristic
468C2×#95C2×D6111yescharacteristic
469C2×#95C2×D6111yescharacteristic
470C61C2×#244711yescharacteristic, complemented, Sylow
471C25—611no—
472C25C22×D6111yescharacteristic
473C22×Q8—614no—
474C22×Q8—1224no—
475C22×Q8—1224no—
476C22×Q8—1224no—
477C22×D4—618no—
478C22×D4—614no—
479C22×D4—1224no—
480C22×D4—1224no—
481C23×C4—611no—
482C23×C4—611no—
483C23×C4—611no—
484C23×C4—611no—
485C23×C4—611no—
486C23×C4—611no—
487C23×C4—611no—
488C23×C4—614no—
489C23×C4—614no—
490C23×C4—1224no—
491C23×C4—1224no—
492C23×C4—1224no—
493C23×C4—1224no—
494C23×C4—2442no—
495C23×C4—2442no—
496C23×C4C22×D6111yescharacteristic
497C23×C4C22×D6111yescharacteristic
498C23×C4C22×D6111yescharacteristic
499C23×C4C22×D6111yescharacteristic
500C23×C4C22×D6111yescharacteristic
501C23×C4C22×D6111yescharacteristic
502#124—12232no—
503C4×D4—12232no—
504C2×C4⋊C4—42no—
505C2×C4⋊C4—614no—
506C2×C4⋊C4—614no—
507C2×C4⋊C4—614no—
508C2×C4⋊C4—614no—
509C2×C4⋊C4—614no—
510C2×C4⋊C4—1224no—
511C2×C4⋊C4—1224no—
512C2×C4⋊C4—1224no—
513C2×C4⋊C4—1224no—
514C2×C4⋊C4—2442no—
515C2×C4⋊C4C22×D6114yes—
516C2×C22⋊C4—24no—
517C2×C22⋊C4—24no—
518C2×C22⋊C4—42no—
519C2×C22⋊C4—614no—
520C2×C22⋊C4—614no—
521C2×C22⋊C4—614no—
522C2×C22⋊C4—614no—
523C2×C22⋊C4—614no—
524C2×C22⋊C4—614no—
525C2×C22⋊C4—614no—
526C2×C22⋊C4—1224no—
527C2×C22⋊C4—1224no—
528C2×C22⋊C4—1224no—
529C2×C22⋊C4—1224no—
530C2×C22⋊C4—1224no—
531C2×C22⋊C4—1224no—
532C2×C22⋊C4—2442no—
533C2×C22⋊C4C22×D6114yes—
534C2×C22⋊C4C22×D6114yes—
535C2×C22⋊C4C22×D6114yes—
536C2×C42—614no—
537C2×C42—614no—
538C2×C42—614no—
539C2×C42—1224no—
540C2×C42—1224no—
541C2×C42—1224no—
542#95—614no—
543#95—614no—
544#95—614no—
545#95—614no—
546#95—614no—
547#95—614no—
548#95—614no—
549#95—614no—
550#95—614no—
551#95C22×D6114yes—
552#95C22×D6114yes—
553#95C22×D6114yes—
554C24—22no—
555C24—22no—
556C24—22no—
557C24—22no—
558C24—22no—
559C24—22no—
560C24—614no—
561C24—612no—
562C24—1222no—
563C24—1222no—
564C24—1222no—
565C24—1222no—
566C24—1222no—
567C24—1222no—
568C24D4×D6114yes—
569C24C23×D6112yes—
570C24C23×D6111yescharacteristic
571C2×Q8—1228no—
572C2×Q8—1228no—
573C2×Q8—1228no—
574C2×Q8—24416no—
575C2×D4—6116no—
576C2×D4—12232no—
577C2×D4—1228no—
578C2×D4—1228no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—614no—
598C22×C4—614no—
599C22×C4—614no—
600C22×C4—612no—
601C22×C4—614no—
602C22×C4—614no—
603C22×C4—612no—
604C22×C4—612no—
605C22×C4—612no—
606C22×C4—612no—
607C22×C4—612no—
608C22×C4—612no—
609C22×C4—1228no—
610C22×C4—1228no—
611C22×C4—1228no—
612C22×C4—1222no—
613C22×C4—1222no—
614C22×C4—1222no—
615C22×C4—1222no—
616C22×C4—1222no—
617C22×C4—1222no—
618C22×C4—1222no—
619C22×C4—1228no—
620C22×C4—1222no—
621C22×C4—1222no—
622C22×C4—1222no—
623C22×C4—1222no—
624C22×C4—1222no—
625C22×C4—1222no—
626C22×C4—1222no—
627C22×C4—1222no—
628C22×C4—1222no—
629C22×C4—2444no—
630C22×C4—24416no—
631C22×C4—2444no—
632C22×C4—24416no—
633C22×C4C23×D6112yes—
634C22×C4C23×D6112yes—
635C22×C4C23×D6112yes—
636C22×C4C23×D6112yes—
637C22×C4C23×D6112yes—
638C22×C4C23×D6112yes—
639C4⋊C4—44no—
640C4⋊C4—1228no—
641C4⋊C4—1228no—
642C4⋊C4—1228no—
643C4⋊C4—1228no—
644C4⋊C4—2444no—
645C22⋊C4—28no—
646C22⋊C4—28no—
647C22⋊C4—44no—
648C22⋊C4—1228no—
649C22⋊C4—1228no—
650C22⋊C4—1228no—
651C22⋊C4—1228no—
652C22⋊C4—1228no—
653C22⋊C4—1228no—
654C22⋊C4—2444no—
655C42—1228no—
656C42—1228no—
657C42—1228no—
658C23—28no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—28no—
666C23—28no—
667C23—44no—
668C23—44no—
669C23—44no—
670C23—44no—
671C23—614no—
672C23—1228no—
673C23—1222no—
674C23—1222no—
675C23—1222no—
676C23—1222no—
677C23—1222no—
678C23—1222no—
679C23—1228no—
680C23—1228no—
681C23—2444no—
682C23—2444no—
683C23—2444no—
684C23—2444no—
685C23C2×D4×D6114yes—
686C23C2×D4×D6112yes—
687C23#41×D6112yes—
688C23#41×D6112yes—
689C23#41×D6112yes—
690C23#41×D6112yes—
691C23#1451982212yes—
692C23#1451982412yes—
693C23C24×D6111yescharacteristic
694Q8—24416no—
695D4—12232no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—44no—
715C2×C4—44no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—44no—
719C2×C4—44no—
720C2×C4—6116no—
721C2×C4—614no—
722C2×C4—614no—
723C2×C4—614no—
724C2×C4—614no—
725C2×C4—614no—
726C2×C4—1228no—
727C2×C4—1222no—
728C2×C4—1222no—
729C2×C4—1222no—
730C2×C4—1222no—
731C2×C4—1228no—
732C2×C4—1222no—
733C2×C4—1222no—
734C2×C4—1222no—
735C2×C4—1222no—
736C2×C4—1222no—
737C2×C4—1222no—
738C2×C4—1222no—
739C2×C4—1222no—
740C2×C4—1222no—
741C2×C4—1222no—
742C2×C4—1222no—
743C2×C4—1222no—
744C2×C4—24416no—
745C2×C4—24416no—
746C2×C4—2444no—
747C2×C4—2444no—
748C2×C4—2444no—
749C2×C4—2444no—
750C22—24no—
751C22—24no—
752C22—24no—
753C22—416no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—1224no—
759C22—1224no—
760C22—1224no—
761C22—24416no—
762C22—2442no—
763C22—2442no—
764C22—2442no—
765C22—2442no—
766C22#123×D6114yes—
767C22#1684029514yes—
768C22#1684037614yes—
769C22#1684040114yes—
770C22#1684041014yes—
771C22#1684047914yes—
772C22#1684049614yes—
773C22C22×D4×D6111yescharacteristic
774C22C2×#41×D6111yescharacteristic
775C22C2×#41×D6111yescharacteristic
776C22C2×#41×D6111yescharacteristic
777C22C2×#41×D6111yescharacteristic
778C22C2×#1451982211yescharacteristic
779C22C2×#1451982411yescharacteristic
780C4—42no—
781C4—42no—
782C4—42no—
783C4—42no—
784C4—42no—
785C4—42no—
786C4—618no—
787C4—1224no—
788C4—1224no—
789C4—2442no—
790C4—2442no—
791C4—2442no—
792C4—2442no—
793C2—44no—
794C2—2444no—
795C2#2144959918yesdirect product factor
796C2C2×#123×D6111yescharacteristic
797C2C2×#1684029511yescharacteristic
798C2C2×#1684037611yescharacteristic
799C2C2×#1684040111yescharacteristic
800C2C2×#1684041011yescharacteristic
801C2C2×#1684047911yescharacteristic
802C2C2×#1684049611yescharacteristic
subgroupG/H
centerC24C23×D61
commutator, cosocleC23×C61C25
FrattiniC23C24×D61
FittingC2×C61×#397C2
socleC24×C61C24
prime radicalC23×C22⋊D61C22
hypercenterC2×#397D61
hypocenterC61C2×#2447
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#397

Complements

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

NH ≅ G/Ntype
3. #21449599C2direct (N × H)
4. C2×#16839691C2semidirect
5. C2×#16839691C2semidirect
6. C2×#16839690C2semidirect
7. C2×#16839666C2semidirect
8. C2×#16839666C2semidirect
10. C2×#16839657C2semidirect
11. C2×#16839634C2semidirect
12. C2×#16839633C2semidirect
13. C2×#16839624C2semidirect
14. C2×#16839623C2semidirect
15. C2×#16839613C2semidirect
16. C2×C61×#397C2semidirect
40. #16839691C22semidirect
41. #16839691C22semidirect
42. #16839690C22semidirect
43. #16839666C22semidirect
44. #16839666C22semidirect
46. #16839657C22semidirect
47. #16839634C22semidirect
48. #16839633C22semidirect
49. #16839624C22semidirect
50. #16839623C22semidirect
51. #16839613C22semidirect
65. C61×#397C22semidirect
398. C2×#397D61semidirect
409. C2×C61#2447semidirect
448. #397C2×D61semidirect
470. C61C2×#2447semidirect
795. C2#21449599direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197632
C22×#145197372
#214495992
C2×#168396912
C2×#168396902
C2×#168396662
C2×#168396622
C2×#168396572
C2×#168396342
C2×#168396332
C2×#168396242
C2×#168396232
C2×#168396132
C2×C61×#3972
C2×#244761