Finite Group Databasebeta

← #29603141

Subgroups — #29603141

Order 15616.

2106 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
1C22×#14519757C211yesmaximal, characteristic
2C2×#16839668C211yesmaximal, characteristic, complemented
3C2×#16839667C211yesmaximal, characteristic, complemented
4C2×#16839661C211yesmaximal, characteristic, complemented
5C2×#16839619C211yesmaximal, characteristic
6C2×C4×#11758198C211yesmaximal, characteristic
7#21444086C212yesmaximal, complemented
8#21444065C212yesmaximal
9#21444057C212yesmaximal
10#21444049C212yesmaximal, complemented
11C2×C4×C4⋊C4×C61C211yesmaximal, characteristic, complemented
12C23×Dic122C2211yescharacteristic
13C23×C4×D61C2211yescharacteristic
14C2×#14519757—24no—
15C2×#14519757—24no—
16C2×#14519757C418yescomplemented
17C22×C4⋊Dic61C2211yescharacteristic
18C22×C4⋊Dic61C2212yes—
19C22×C4⋊Dic61C2212yes—
20C22×#11758198C2211yescharacteristic
21C22×#11758198C2212yes—
22C22×#11758198C2212yes—
23C22×#11758198C2211yescharacteristic
24C22×C4×Dic61C2211yescharacteristic
25#16839668—24no—
26#16839667—24no—
27#16839661—24no—
28#16839619—24no—
29C4×#11758198—24no—
30C2×#14519684C2212yes—
31C2×#14519684C2212yes—
32C2×#14519684C2212yes—
33C2×#14519684C2212yes—
34C2×#14519684C2212yes—
35C2×#14519684C2211yescharacteristic
36C2×#14519684C2212yes—
37C2×#14519684C2211yescharacteristic
38C22×C4⋊C4×C61C2211yescharacteristic
39C22×C4⋊C4×C61C2211yescharacteristic
40C22×C42×C61C2212yes—
41C22×C42×C61C2211yescharacteristic
42C4×C4⋊C4×C61—24no—
43C2×#95×C61C2212yes—
44C24×D61C2311yescharacteristic
45C22×Dic122—22no—
46C22×Dic122—22no—
47C22×Dic122—22no—
48C22×Dic122—22no—
49C22×Dic122—22no—
50C22×Dic122—22no—
51C22×Dic122C2×C414yes—
52C23×Dic61C2312yes—
53C23×Dic61C2312yes—
54C23×Dic61C2311yescharacteristic
55C23×Dic61C2311yescharacteristic
56C23×Dic61C2311yescharacteristic
57C22×C4×D61—22no—
58C22×C4×D61—22no—
59C22×C4×D61—22no—
60C22×C4×D61—22no—
61C22×C4×D61—22no—
62C22×C4×D61—22no—
63C22×C4×D61C2×C414yes—
64#14519757—232no—
65C2×C4⋊Dic61—24no—
66C2×C4⋊Dic61—24no—
67C2×C4⋊Dic61—22no—
68C2×C4⋊Dic61—24no—
69C2×C4⋊Dic61—22no—
70C2×C4⋊Dic61—22no—
71C2×C4⋊Dic61—24no—
72C2×C4⋊Dic61—42no—
73C2×C4⋊Dic61C2×C418yes—
74C2×#11758198—22no—
75C2×#11758198—24no—
76C2×#11758198—24no—
77C2×#11758198—22no—
78C2×#11758198—22no—
79C2×#11758198—22no—
80C2×#11758198—22no—
81C2×#11758198—24no—
82C2×#11758198—24no—
83C2×#11758198—42no—
84C2×#11758198C2×C418yes—
85C2×#11758198Q814yescomplemented
86C2×C4×Dic61—22no—
87C2×C4×Dic61—22no—
88C2×C4×Dic61—22no—
89#14519684—22no—
90#14519684—22no—
91#14519684—24no—
92#14519684—24no—
93#14519684—24no—
94#14519684—24no—
95#14519684—24no—
96#14519684—24no—
97C23×C4×C61C2311yescharacteristic
98C23×C4×C61C2312yes—
99C23×C4×C61C2312yes—
100C23×C4×C61C2311yescharacteristic
101C23×C4×C61C2311yescharacteristic
102C2×C4⋊C4×C61—22no—
103C2×C4⋊C4×C61—22no—
104C2×C4⋊C4×C61C2×C414yes—
105C2×C4⋊C4×C61D414yes—
106C2×C4⋊C4×C61D414yes—
107C2×C4⋊C4×C61D414yes—
108C2×C42×C61—22no—
109C2×C42×C61—22no—
110C2×C42×C61—24no—
111C2×C42×C61—24no—
112C2×C42×C61—42no—
113C2×C42×C61D414yes—
114#95×C61—24no—
115C24×C61C2411yescharacteristic
116C23×D61—21no—
117C23×D61—21no—
118C23×D61—21no—
119C23×D61—21no—
120C23×D61—21no—
121C23×D61—21no—
122C23×D61—21no—
123C23×D61—21no—
124C23×D61—21no—
125C23×D61—21no—
126C23×D61—21no—
127C23×D61—21no—
128C23×D61C22×C412yes—
129C23×D61C2×Q812yes—
130C23×D61#4112yes—
131C22×C4×C61—21no—
132C22×C4×C61—22no—
133C22×C4×C61—21no—
134C22×C4×C61—22no—
135C22×C4×C61—21no—
136C22×C4×C61—22no—
137C22×C4×C61—22no—
138C22×C4×C61—21no—
139C22×C4×C61—21no—
140C22×C4×C61—22no—
141C22×C4×C61—21no—
142C22×C4×C61—22no—
143C22×C4×C61—22no—
144C22×C4×C61—21no—
145C22×C4×C61—21no—
146C22×C4×C61—22no—
147C22×C4×C61—22no—
148C22×C4×C61—21no—
149C22×C4×C61—21no—
150C22×C4×C61—22no—
151C22×C4×C61C22×C414yes—
152C22×C4×C61C22×C412yes—
153C22×C4×C61C2×D412yes—
154C22×C4×C61C2×D414yes—
155C22×C4×C61C2×D414yes—
156C22×C4×C61C2×D414yes—
157C22×C4×C61C2×D412yes—
158C22×C4×C61C2×D412yes—
159C22×C4×C61C2×D412yes—
160C22×C4×C61C2×D412yes—
161C22×C4×C61C2×D412yes—
162C22×C4×C61C2×Q812yes—
163C22×C4×C61#4112yes—
164C22×C4×C61#4112yes—
165C22×C4×C61#4112yes—
166C22×Dic61—21no—
167C22×Dic61—21no—
168C22×Dic61—21no—
169C22×Dic61—21no—
170C22×Dic61—22no—
171C22×Dic61—22no—
172C22×Dic61—22no—
173C22×Dic61—22no—
174C22×Dic61—21no—
175C22×Dic61—21no—
176C22×Dic61—21no—
177C22×Dic61—21no—
178C22×Dic61—21no—
179C22×Dic61—21no—
180C22×Dic61—21no—
181C22×Dic61—21no—
182C22×Dic61—22no—
183C22×Dic61—22no—
184C22×Dic61—21no—
185C22×Dic61—21no—
186C22×Dic61—21no—
187C22×Dic61—21no—
188C22×Dic61—21no—
189C22×Dic61—21no—
190C22×Dic61—22no—
191C22×Dic61—22no—
192C22×Dic61—22no—
193C22×Dic61—22no—
194C22×Dic61—22no—
195C22×Dic61—22no—
196C22×Dic61—22no—
197C22×Dic61C22×C412yes—
198C22×Dic61C22×C414yes—
199C22×Dic61C2×Q812yes—
200C22×Dic61#4112yes—
201C2×C4×D61—28no—
202C2×C4×D61—28no—
203C2×C4×D61—28no—
204C2×C4×D61—44no—
205C2×C4×D61—44no—
206C2×C4×D61—44no—
207C2×C4×D61—44no—
208C2×Dic122—28no—
209C2×Dic122—28no—
210C2×Dic122—28no—
211C2×Dic122—44no—
212C2×Dic122—44no—
213C2×Dic122—44no—
214C2×Dic122—44no—
215C4⋊C4×C61—28no—
216C4⋊C4×C61C22⋊C4116yescomplemented
217C42×C61—28no—
218C42×C61—48no—
219#11758198—28no—
220#11758198—216no—
221#11758198—28no—
222#11758198—48no—
223C4⋊Dic61—216no—
224C4⋊Dic61—48no—
225C4⋊Dic61—44no—
226C4×Dic61—44no—
227C23×C61C23×C411yescharacteristic
228C23×C61C22×D411yescharacteristic
229C23×C61C22×D411yescharacteristic
230C23×C61C22×D411yescharacteristic
231C23×C61C22×D411yescharacteristic
232C23×C61C22×Q811yescharacteristic
233C23×C61C2×#4111yescharacteristic
234C23×C61C2×#4111yescharacteristic
235C23×C61C2×#4111yescharacteristic
236C23×C61C2×#4111yescharacteristic
237C23×C61C2×#4111yescharacteristic
238C23×C61H(5,𝔽2)11yescharacteristic
239C23×C612−1+411yescharacteristic
240C23×C612−1+411yescharacteristic
241C23×C612−1+411yescharacteristic
242C22×D61—22no—
243C22×D61—22no—
244C22×D61—22no—
245C22×D61—22no—
246C22×D61—22no—
247C22×D61—22no—
248C22×D61—22no—
249C22×D61—22no—
250C22×D61—22no—
251C22×D61—22no—
252C22×D61—22no—
253C22×D61—22no—
254C22×D61—22no—
255C22×D61—22no—
256C22×D61—22no—
257C22×D61—22no—
258C22×D61—22no—
259C22×D61—22no—
260C22×D61—41no—
261C22×D61—41no—
262C22×D61—41no—
263C22×D61—41no—
264C22×D61—41no—
265C22×D61—41no—
266C22×D61—41no—
267C22×D61—41no—
268C22×D61—41no—
269C22×D61—41no—
270C22×D61—41no—
271C22×D61—41no—
272C22×D61—41no—
273C22×D61—41no—
274C22×D61—41no—
275C22×D61—41no—
276C22×D61C4×Q814yes—
277C2×C4×C61—24no—
278C2×C4×C61—24no—
279C2×C4×C61—22no—
280C2×C4×C61—22no—
281C2×C4×C61—24no—
282C2×C4×C61—22no—
283C2×C4×C61—24no—
284C2×C4×C61—24no—
285C2×C4×C61—24no—
286C2×C4×C61—22no—
287C2×C4×C61—22no—
288C2×C4×C61—22no—
289C2×C4×C61—22no—
290C2×C4×C61—24no—
291C2×C4×C61—22no—
292C2×C4×C61—22no—
293C2×C4×C61—24no—
294C2×C4×C61—24no—
295C2×C4×C61—42no—
296C2×C4×C61—42no—
297C2×C4×C61—42no—
298C2×C4×C61—41no—
299C2×C4×C61—41no—
300C2×C4×C61—42no—
301C2×C4×C61—41no—
302C2×C4×C61—41no—
303C2×C4×C61C2×C22⋊C418yes—
304C2×C4×C61C2×C22⋊C414yes—
305C2×C4×C61C4×D414yes—
306C2×C4×C61C4×D414yes—
307C2×C4×C61#12114yes—
308C2×C4×C61#12114yes—
309C2×C4×C61C22⋊Q814yescomplemented
310C2×C4×C61#12414yes—
311C2×C4×C61#12714yes—
312C2×Dic61—22no—
313C2×Dic61—24no—
314C2×Dic61—24no—
315C2×Dic61—24no—
316C2×Dic61—22no—
317C2×Dic61—22no—
318C2×Dic61—22no—
319C2×Dic61—22no—
320C2×Dic61—22no—
321C2×Dic61—22no—
322C2×Dic61—22no—
323C2×Dic61—22no—
324C2×Dic61—42no—
325C2×Dic61—42no—
326C2×Dic61—41no—
327C2×Dic61—41no—
328C2×Dic61—42no—
329C2×Dic61—41no—
330C2×Dic61—41no—
331C2×Dic61—41no—
332C2×Dic61—42no—
333C2×Dic61—41no—
334C2×Dic61—41no—
335C2×Dic61—41no—
336C2×Dic61—41no—
337C2×Dic61—41no—
338C2×Dic61—41no—
339C2×Dic61—41no—
340C2×Dic61—42no—
341C2×Dic61—42no—
342C2×Dic61—42no—
343C2×Dic61—42no—
344C2×Dic61—42no—
345C2×Dic61—42no—
346C2×Dic61—42no—
347C4×D61—416no—
348Dic122—416no—
349#13997—611nomaximal, Sylow
350C22×C61C22×C22⋊C411yescharacteristic
351C22×C61C2×C4×D411yescharacteristic
352C22×C61C2×C4×D411yescharacteristic
353C22×C61C2×C4×Q811yescharacteristic
354C22×C61C4×#4111yescharacteristic
355C22×C61#51911yescharacteristic
356C22×C61#52011yescharacteristic
357C22×C61C2×#12111yescharacteristic
358C22×C61C2×#12111yescharacteristic
359C22×C61C2×C22⋊Q811yescharacteristic
360C22×C61#52511yescharacteristic
361C22×C61C2×#12411yescharacteristic
362C22×C61#52911yescharacteristic
363C22×C61C2×#12711yescharacteristic
364C22×C61#53311yescharacteristic
365C22×C61#53611yescharacteristic
366C22×C61#53711yescharacteristic
367C22×C61#54111yescharacteristic
368C22×C61#54211yescharacteristic
369C22×C61#54611yescharacteristic
370C22×C61#54611yescharacteristic
371C22×C61#54611yescharacteristic
372C22×C61#54711yescharacteristic
373C22×C61#54711yescharacteristic
374C22×C61#54711yescharacteristic
375C22×C61#54811yescharacteristic
376C22×C61#54811yescharacteristic
377C22×C61#54811yescharacteristic
378C22×C61D4×Q811yescharacteristic
379C22×C61D4×Q811yescharacteristic
380C22×C61D4×Q811yescharacteristic
381C22×C61#55211yescharacteristic
382C22×C61#55211yescharacteristic
383C22×C61#55411yescharacteristic
384C22×C61#55611yescharacteristic
385C2×D61—24no—
386C2×D61—24no—
387C2×D61—24no—
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—
400C4×C61—28no—
401C4×C61—24no—
402C4×C61—42no—
403C4×C61—44no—
404C4×C61#39018yes—
405Dic61—42no—
406Dic61—42no—
407Dic61—44no—
408Dic61—42no—
409Dic61—82no—
410C22×C22⋊Q8—611no—
411C2×#391—611no—
412C2×#391—611no—
413C2×#389—611no—
414C2×#380—611no—
415C2×C4×C4⋊C4D6111yescharacteristic, complemented
416C2×C4×C22⋊C4—611no—
417#1445—612no—
418#1439—612no—
419#1437—612no—
420C4⋊#95—612no—
421C2×C61C2×#39011yescharacteristic
422C2×C61C4×C22⋊Q811yescharacteristic
423C2×C61#232311yescharacteristic
424C2×C61#233911yescharacteristic
425C2×C61Q8×C22⋊C411yescharacteristic
426C2×C61#236011yescharacteristic
427C2×C61#236211yescharacteristic
428C2×C61#241511yescharacteristic
429C2×C61#241711yescharacteristic
430C2×C61#242711yescharacteristic
431C2×C61#242911yescharacteristic
432C2×C61#248911yescharacteristic
433C2×C61#249211yescharacteristic
434C2×C61#254011yescharacteristic
435C2×C61#254211yescharacteristic
436D61—44no—
437C23×Q8—611no—
438C24×C4—611no—
439C2×C22⋊Q8—618no—
440C2×C22⋊Q8—1224no—
441C2×C22⋊Q8—1224no—
442C22×C4⋊C4—612no—
443C22×C4⋊C4—611no—
444C22×C4⋊C4—612no—
445C22×C4⋊C4C2×D6111yescharacteristic
446C22×C4⋊C4C2×D6111yescharacteristic
447C22×C22⋊C4—612no—
448C22×C22⋊C4—611no—
449C22×C22⋊C4—611no—
450C22×C22⋊C4—612no—
451C22×C42—611no—
452C22×C42C2×D6112yes—
453C22×C42C2×D6111yescharacteristic
454#391—1224no—
455#391—1224no—
456#389—1224no—
457#380—1224no—
458C4×C4⋊C4—24no—
459C4×C22⋊C4—1224no—
460C2×#95—611no—
461C2×#95—612no—
462C2×#95—612no—
463C2×#95—612no—
464C2×#95—612no—
465C2×#95—612no—
466C2×#95—612no—
467C2×#95—611no—
468C2×#95C2×D6112yes—
469C61#1399711yescharacteristic, complemented, Sylow
470C25—611no—
471C22×Q8—614no—
472C22×Q8—1222no—
473C22×Q8—1222no—
474C22×Q8—1222no—
475C22×Q8—1222no—
476C22×Q8—1222no—
477C22×Q8—1222no—
478C23×C4—611no—
479C23×C4—612no—
480C23×C4—611no—
481C23×C4—611no—
482C23×C4—614no—
483C23×C4—612no—
484C23×C4—1222no—
485C23×C4—1222no—
486C23×C4—1222no—
487C23×C4—1222no—
488C23×C4—1222no—
489C23×C4—1222no—
490C23×C4C22×D6112yes—
491C23×C4C22×D6111yescharacteristic
492C23×C4C22×D6112yes—
493C23×C4C22×D6111yescharacteristic
494C23×C4C22×D6111yescharacteristic
495C22⋊Q8—12232no—
496C2×C4⋊C4—22no—
497C2×C4⋊C4—22no—
498C2×C4⋊C4—618no—
499C2×C4⋊C4—1224no—
500C2×C4⋊C4—1224no—
501C2×C4⋊C4—1224no—
502C2×C4⋊C4—1222no—
503C2×C4⋊C4—1224no—
504C2×C4⋊C4—1222no—
505C2×C4⋊C4—1222no—
506C2×C4⋊C4—2442no—
507C2×C4⋊C4C4×D6114yes—
508C2×C4⋊C4D24414yes—
509C2×C4⋊C4D24414yes—
510C2×C4⋊C4C22⋊D6114yes—
511C2×C22⋊C4—618no—
512C2×C22⋊C4—614no—
513C2×C22⋊C4—1222no—
514C2×C22⋊C4—1222no—
515C2×C22⋊C4—1224no—
516C2×C22⋊C4—1222no—
517C2×C22⋊C4—1222no—
518C2×C22⋊C4—1222no—
519C2×C22⋊C4—1224no—
520C2×C22⋊C4—1224no—
521C2×C22⋊C4—1224no—
522C2×C22⋊C4—2442no—
523C2×C42—22no—
524C2×C42—22no—
525C2×C42—24no—
526C2×C42—24no—
527C2×C42—42no—
528C2×C42—1222no—
529C2×C42—1222no—
530C2×C42—1222no—
531C2×C42D24414yes—
532#95—24no—
533#95—1222no—
534#95—1222no—
535#95—1224no—
536#95—1224no—
537#95—1224no—
538#95—1224no—
539#95—1224no—
540#95—1224no—
541C24—612no—
542C24—612no—
543C24—612no—
544C24—1221no—
545C24—1221no—
546C24—1221no—
547C24—1221no—
548C24—1221no—
549C24—1221no—
550C24—1221no—
551C24—1221no—
552C24—1221no—
553C24—1221no—
554C24—1221no—
555C24—1221no—
556C24C23×D6111yescharacteristic
557C2×Q8—1228no—
558C2×Q8—1228no—
559C2×Q8—1228no—
560C2×Q8—2444no—
561C2×Q8—2444no—
562C2×Q8—2444no—
563C2×Q8—2444no—
564C22×C4—21no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—21no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—22no—
584C22×C4—614no—
585C22×C4—612no—
586C22×C4—612no—
587C22×C4—612no—
588C22×C4—1222no—
589C22×C4—1221no—
590C22×C4—1221no—
591C22×C4—1221no—
592C22×C4—1221no—
593C22×C4—1221no—
594C22×C4—1221no—
595C22×C4—1222no—
596C22×C4—1222no—
597C22×C4—1221no—
598C22×C4—1221no—
599C22×C4—1221no—
600C22×C4—1222no—
601C22×C4—1221no—
602C22×C4—1221no—
603C22×C4—1221no—
604C22×C4—1221no—
605C22×C4—1221no—
606C22×C4—1222no—
607C22×C4—1222no—
608C22×C4—1221no—
609C22×C4—1221no—
610C22×C4—1221no—
611C22×C4—1221no—
612C22×C4—1228no—
613C22×C4—1228no—
614C22×C4—1228no—
615C22×C4—1222no—
616C22×C4—1222no—
617C22×C4—1222no—
618C22×C4—1222no—
619C22×C4—1222no—
620C22×C4—1222no—
621C22×C4—1222no—
622C22×C4—2444no—
623C22×C4—2444no—
624C22×C4—2444no—
625C22×C4—2444no—
626C22×C4C2×C4×D6114yes—
627C22×C4C2×C4×D6112yes—
628C22×C4C2×D24412yes—
629C22×C4C2×D24414yes—
630C22×C4C2×D24414yes—
631C22×C4C2×D24412yes—
632C22×C4C2×D24412yes—
633C22×C4C2×D24412yes—
634C22×C4C2×D24412yes—
635C22×C4#1175822212yes—
636C22×C4#1175822212yes—
637C22×C4#1175822412yes—
638C22×C4Q8×D6112yes—
639C22×C4C2×C22⋊D6114yes—
640C22×C4C2×C22⋊D6112yes—
641C4⋊C4—28no—
642C4⋊C4—12216no—
643C4⋊C4—2448no—
644C4⋊C4—2444no—
645C4⋊C4#11758198116yescomplemented
646C22⋊C4—1228no—
647C22⋊C4—12216no—
648C22⋊C4—1228no—
649C22⋊C4—2448no—
650C42—28no—
651C42—48no—
652C42—2444no—
653C23—614no—
654C23—1222no—
655C23—1222no—
656C23—1222no—
657C23—1222no—
658C23—1222no—
659C23—1222no—
660C23—1222no—
661C23—1222no—
662C23—1222no—
663C23—1222no—
664C23—1222no—
665C23—1222no—
666C23—1222no—
667C23—1222no—
668C23—1222no—
669C23—1222no—
670C23—1222no—
671C23—1222no—
672C23—2441no—
673C23—2441no—
674C23—2441no—
675C23—2441no—
676C23—2441no—
677C23—2441no—
678C23—2441no—
679C23—2441no—
680C23—2441no—
681C23—2441no—
682C23—2441no—
683C23—2441no—
684C23—2441no—
685C23—2441no—
686C23—2441no—
687C23—2441no—
688C23C22×C4×D6111yescharacteristic
689C23C22×C22⋊D6111yescharacteristic
690C23C22×D24411yescharacteristic
691C23C22×D24411yescharacteristic
692C23C22×D24411yescharacteristic
693C23C2×Q8×D6111yescharacteristic
694C23#41×D6111yescharacteristic
695C23#41×D6111yescharacteristic
696C23C2×#1175822411yescharacteristic
697C23C2×#1175822211yescharacteristic
698C23C2×#1175822211yescharacteristic
699C23#1451982211yescharacteristic
700C23#1451982411yescharacteristic
701C23#1451982411yescharacteristic
702C23#1451982511yescharacteristic
703Q8—24416no—
704C2×C4—22no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—24no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—42no—
730C2×C4—1224no—
731C2×C4—1222no—
732C2×C4—1222no—
733C2×C4—1222no—
734C2×C4—1224no—
735C2×C4—1224no—
736C2×C4—1222no—
737C2×C4—1222no—
738C2×C4—1222no—
739C2×C4—1222no—
740C2×C4—1222no—
741C2×C4—1222no—
742C2×C4—2442no—
743C2×C4—2442no—
744C2×C4—2442no—
745C2×C4—2442no—
746C2×C4—2442no—
747C2×C4—2442no—
748C2×C4—2442no—
749C2×C4—2441no—
750C2×C4—2441no—
751C2×C4—2442no—
752C2×C4—2442no—
753C2×C4—2441no—
754C2×C4—2442no—
755C2×C4—2441no—
756C2×C4—2441no—
757C2×C4—2441no—
758C2×C4—2442no—
759C2×C4—2441no—
760C2×C4—2441no—
761C2×C4—2441no—
762C2×C4—2441no—
763C2×C4—2441no—
764C2×C4—2441no—
765C2×C4—24416no—
766C2×C4C2×#1175819818yes—
767C2×C4C2×#1175819814yes—
768C2×C4C4×D24414yes—
769C2×C4C4×D24414yes—
770C2×C4#1451975114yes—
771C2×C4#1451975114yes—
772C2×C4#1451975714yescomplemented
773C2×C4#1451976514yes—
774C2×C4#1451977414yes—
775C22—1224no—
776C22—1224no—
777C22—1224no—
778C22—2442no—
779C22—2442no—
780C22—2442no—
781C22—2442no—
782C22—2442no—
783C22—2442no—
784C22—2442no—
785C22—2442no—
786C22—2442no—
787C22—2442no—
788C22—2442no—
789C22—2442no—
790C22C22×#1175819811yescharacteristic
791C22C2×C4×D24411yescharacteristic
792C22C2×C4×D24411yescharacteristic
793C22C4×Q8×D6111yescharacteristic
794C22C4×#1175822411yescharacteristic
795C22#1684023811yescharacteristic
796C22#1684024111yescharacteristic
797C22C2×#1451975111yescharacteristic
798C22C2×#1451975111yescharacteristic
799C22C2×#1451975711yescharacteristic
800C22#1684027411yescharacteristic
801C22C2×#1451976511yescharacteristic
802C22#1684029411yescharacteristic
803C22C2×#1451977411yescharacteristic
804C22#1684031611yescharacteristic
805C22#1684033811yescharacteristic
806C22#1684034311yescharacteristic
807C22#1684037011yescharacteristic
808C22#1684037711yescharacteristic
809C22#1684040611yescharacteristic
810C22#1684040711yescharacteristic
811C22#1684040711yescharacteristic
812C22#1684041111yescharacteristic
813C22#1684041611yescharacteristic
814C22#1684041611yescharacteristic
815C22#1684041911yescharacteristic
816C22#1684042411yescharacteristic
817C22#1684042411yescharacteristic
818C22Q8×C22⋊D6111yescharacteristic
819C22Q8×D24411yescharacteristic
820C22Q8×D24411yescharacteristic
821C22#1684044711yescharacteristic
822C22#1684045111yescharacteristic
823C22#1684046711yescharacteristic
824C22#1684048011yescharacteristic
825C4—24no—
826C4—28no—
827C4—42no—
828C4—44no—
829C4—4882no—
830C4—2442no—
831C4—2442no—
832C4—2442no—
833C4—2444no—
834C4#1683966418yes—
835C2—2444no—
836C2C2×#1683966411yescharacteristic
837C2C4×#1451975711yescharacteristic
838C2#2144850211yescharacteristic
839C2#2144864411yescharacteristic
840C2Q8×#1175819811yescharacteristic
841C2#2144882611yescharacteristic
842C2#2144884811yescharacteristic
843C2#2144924211yescharacteristic
844C2#2144926411yescharacteristic
845C2#2144939011yescharacteristic
846C2#2144941211yescharacteristic
847C2#2145015411yescharacteristic
848C2#2145018711yescharacteristic
849C2#2145075311yescharacteristic
850C2#2145076811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC2×C4×C4⋊C4×C61C2
socle, cosocleC24×C61C24
prime radicalC24×D61C23
hypercenterC2×C4×C4⋊C4D61
hypocenterC61#13997
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#16839668C2semidirect
3. C2×#16839667C2semidirect
4. C2×#16839661C2semidirect
7. #21444086C2semidirect
10. #21444049C2semidirect
11. C2×C4×C4⋊C4×C61C2semidirect
16. C2×#14519757C4semidirect
85. C2×#11758198Q8semidirect
216. C4⋊C4×C61C22⋊C4semidirect
309. C2×C4×C61C22⋊Q8semidirect
415. C2×C4×C4⋊C4D61semidirect
469. C61#13997semidirect
645. C4⋊C4#11758198semidirect
772. C2×C4#14519757semidirect

Maximal subgroups

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

subgroupindex
C22×#145197572
C2×#168396682
C2×#168396672
C2×#168396612
C2×#168396192
C2×C4×#117581982
#214440862
#214440652
#214440572
#214440492
C2×C4×C4⋊C4×C612
#1399761