Finite Group Databasebeta

← #29602849

Subgroups — #29602849

Order 15616.

1746 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839661C211yesmaximal, characteristic, complemented
2C2×#16839619C211yesmaximal, characteristic
3C2×#16839619C211yesmaximal, characteristic
4C2×C4⋊C4×Dic61C211yesmaximal, characteristic, complemented
5C2×C4×#11758198C211yesmaximal, characteristic
6#21444075C212yesmaximal, complemented
7#21444065C212yesmaximal
8#21444055C212yesmaximal
9#21444049C211yesmaximal, characteristic, complemented
10#21444043C212yesmaximal, complemented
11C61×C4⋊#95C211yesmaximal, characteristic, complemented
12C23×C4×D61C2211yescharacteristic
13C22×C4⋊Dic61C2211yescharacteristic
14C22×C4⋊Dic61C2211yescharacteristic
15C22×C4⋊Dic61C2212yes—
16C22×#11758198C2211yescharacteristic
17C22×#11758198C2212yes—
18C22×#11758198C2211yescharacteristic
19C22×#11758198C2212yes—
20C22×C4×Dic61C2212yes—
21C22×C4×Dic61C2211yescharacteristic
22#16839661—24no—
23#16839619—24no—
24#16839619C418yescomplemented
25C4⋊C4×Dic61—24no—
26C4×#11758198—24no—
27C2×#14519684C2212yes—
28C2×#14519684C2211yescharacteristic
29C2×#14519684C2212yes—
30C2×#14519684C2212yes—
31C2×#14519684C2211yescharacteristic
32C2×#14519684C2212yes—
33C2×#14519684C2212yes—
34C2×#14519684C2212yes—
35C22×C4⋊C4×C61C2211yescharacteristic
36C22×C4⋊C4×C61C2211yescharacteristic
37C22×C42×C61C2211yescharacteristic
38C2×#95×C61C2212yes—
39C2×#95×C61C2212yes—
40C24×D61C2311yescharacteristic
41C23×Dic61C2312yes—
42C23×Dic61C2312yes—
43C23×Dic61C2311yescharacteristic
44C23×Dic61C2311yescharacteristic
45C23×Dic61C2311yescharacteristic
46C22×C4×D61—22no—
47C22×C4×D61—22no—
48C22×C4×D61—22no—
49C22×C4×D61—22no—
50C22×C4×D61—22no—
51C22×C4×D61—22no—
52C22×C4×D61C2×C414yes—
53C2×C4⋊Dic61—22no—
54C2×C4⋊Dic61—22no—
55C2×C4⋊Dic61—22no—
56C2×C4⋊Dic61—22no—
57C2×C4⋊Dic61—22no—
58C2×C4⋊Dic61—24no—
59C2×C4⋊Dic61—42no—
60C2×C4⋊Dic61—42no—
61C2×C4⋊Dic61C2×C414yes—
62C2×#11758198—22no—
63C2×#11758198—22no—
64C2×#11758198—22no—
65C2×#11758198—22no—
66C2×#11758198—22no—
67C2×#11758198—24no—
68C2×#11758198—24no—
69C2×#11758198—42no—
70C2×#11758198—42no—
71C2×#11758198—42no—
72C2×#11758198C2×C418yes—
73C2×#11758198Q814yes—
74C2×C4×Dic61—22no—
75C2×C4×Dic61—22no—
76C2×C4×Dic61—24no—
77C2×C4×Dic61—24no—
78C2×C4×Dic61—42no—
79C2×C4×Dic61D414yes—
80#14519684—24no—
81#14519684—24no—
82#14519684—24no—
83#14519684—22no—
84#14519684—22no—
85#14519684—24no—
86#14519684—42no—
87#14519684C2×C418yes—
88C23×C4×C61C2312yes—
89C23×C4×C61C2312yes—
90C23×C4×C61C2311yescharacteristic
91C23×C4×C61C2311yescharacteristic
92C23×C4×C61C2311yescharacteristic
93C2×C4⋊C4×C61—22no—
94C2×C4⋊C4×C61—22no—
95C2×C4⋊C4×C61—22no—
96C2×C4⋊C4×C61—22no—
97C2×C4⋊C4×C61C2×C414yes—
98C2×C4⋊C4×C61D414yes—
99C2×C42×C61—22no—
100C2×C42×C61—22no—
101C2×C42×C61—22no—
102#95×C61—42no—
103#95×C61—42no—
104C24×C61C2411yescharacteristic
105C23×D61—21no—
106C23×D61—21no—
107C23×D61—21no—
108C23×D61—21no—
109C23×D61—21no—
110C23×D61—21no—
111C23×D61—21no—
112C23×D61—21no—
113C23×D61—21no—
114C23×D61—21no—
115C23×D61—21no—
116C23×D61—21no—
117C23×D61C22×C412yes—
118C23×D61C2×Q812yes—
119C23×D61#4112yes—
120C22×C4×C61—21no—
121C22×C4×C61—21no—
122C22×C4×C61—22no—
123C22×C4×C61—21no—
124C22×C4×C61—21no—
125C22×C4×C61—21no—
126C22×C4×C61—21no—
127C22×C4×C61—22no—
128C22×C4×C61—22no—
129C22×C4×C61—22no—
130C22×C4×C61—22no—
131C22×C4×C61—21no—
132C22×C4×C61—21no—
133C22×C4×C61—22no—
134C22×C4×C61—21no—
135C22×C4×C61—21no—
136C22×C4×C61—22no—
137C22×C4×C61—22no—
138C22×C4×C61—22no—
139C22×C4×C61—22no—
140C22×C4×C61—21no—
141C22×C4×C61—22no—
142C22×C4×C61—22no—
143C22×C4×C61—21no—
144C22×C4×C61C22×C414yes—
145C22×C4×C61C22×C412yes—
146C22×C4×C61C2×D414yes—
147C22×C4×C61C2×D412yes—
148C22×C4×C61C2×D412yes—
149C22×C4×C61C2×Q812yes—
150C22×C4×C61#4112yes—
151C22×C4×C61#4112yes—
152C22×C4×C61#4112yes—
153C22×C4×C61#4112yes—
154C22×C4×C61#4112yes—
155C22×Dic61—21no—
156C22×Dic61—21no—
157C22×Dic61—21no—
158C22×Dic61—21no—
159C22×Dic61—21no—
160C22×Dic61—21no—
161C22×Dic61—21no—
162C22×Dic61—22no—
163C22×Dic61—21no—
164C22×Dic61—21no—
165C22×Dic61—21no—
166C22×Dic61—21no—
167C22×Dic61—22no—
168C22×Dic61—22no—
169C22×Dic61—21no—
170C22×Dic61—21no—
171C22×Dic61—21no—
172C22×Dic61—22no—
173C22×Dic61—22no—
174C22×Dic61—22no—
175C22×Dic61—21no—
176C22×Dic61—21no—
177C22×Dic61—22no—
178C22×Dic61—22no—
179C22×Dic61—22no—
180C22×Dic61—22no—
181C22×Dic61—22no—
182C22×Dic61—22no—
183C22×Dic61—22no—
184C22×Dic61C22×C412yes—
185C22×Dic61C22×C414yes—
186C22×Dic61C2×D412yes—
187C22×Dic61C2×D412yes—
188C22×Dic61C2×Q812yes—
189C22×Dic61#4112yes—
190C2×C4×D61—28no—
191C2×C4×D61—28no—
192C2×C4×D61—28no—
193C2×C4×D61—44no—
194C2×C4×D61—44no—
195C2×C4×D61—44no—
196C2×C4×D61—44no—
197C4⋊C4×C61—28no—
198C4⋊C4×C61—28no—
199C42×C61—44no—
200#11758198—28no—
201#11758198—28no—
202#11758198—48no—
203#11758198—48no—
204C4⋊Dic61—28no—
205C4⋊Dic61—48no—
206C4⋊Dic61—44no—
207C4×Dic61—28no—
208C4×Dic61—48no—
209C23×C61C23×C411yescharacteristic
210C23×C61C22×D411yescharacteristic
211C23×C61C22×D411yescharacteristic
212C23×C61C22×Q811yescharacteristic
213C23×C61C2×#4111yescharacteristic
214C23×C61C2×#4111yescharacteristic
215C23×C61C2×#4111yescharacteristic
216C23×C61C2×#4111yescharacteristic
217C23×C61C2×#4111yescharacteristic
218C23×C61C2×#4111yescharacteristic
219C23×C61C2×#4111yescharacteristic
220C23×C61H(5,𝔽2)11yescharacteristic
221C23×C61H(5,𝔽2)11yescharacteristic
222C23×C61H(5,𝔽2)11yescharacteristic
223C23×C612−1+411yescharacteristic
224C22×D61—22no—
225C22×D61—22no—
226C22×D61—22no—
227C22×D61—22no—
228C22×D61—22no—
229C22×D61—22no—
230C22×D61—22no—
231C22×D61—22no—
232C22×D61—22no—
233C22×D61—22no—
234C22×D61—22no—
235C22×D61—22no—
236C22×D61—22no—
237C22×D61—22no—
238C22×D61—22no—
239C22×D61—22no—
240C22×D61—22no—
241C22×D61—22no—
242C22×D61—41no—
243C22×D61—41no—
244C22×D61—41no—
245C22×D61—41no—
246C22×D61—41no—
247C22×D61—41no—
248C22×D61—41no—
249C22×D61—41no—
250C22×D61—41no—
251C22×D61—41no—
252C22×D61—41no—
253C22×D61—41no—
254C22×D61—41no—
255C22×D61—41no—
256C22×D61—41no—
257C22×D61—41no—
258C22×D61C4×Q814yes—
259C2×C4×C61—24no—
260C2×C4×C61—24no—
261C2×C4×C61—24no—
262C2×C4×C61—22no—
263C2×C4×C61—24no—
264C2×C4×C61—22no—
265C2×C4×C61—24no—
266C2×C4×C61—24no—
267C2×C4×C61—22no—
268C2×C4×C61—22no—
269C2×C4×C61—22no—
270C2×C4×C61—22no—
271C2×C4×C61—41no—
272C2×C4×C61—41no—
273C2×C4×C61—42no—
274C2×C4×C61—42no—
275C2×C4×C61—41no—
276C2×C4×C61—41no—
277C2×C4×C61—42no—
278C2×C4×C61—42no—
279C2×C4×C61—42no—
280C2×C4×C61—42no—
281C2×C4×C61—41no—
282C2×C4×C61—41no—
283C2×C4×C61—42no—
284C2×C4×C61—41no—
285C2×C4×C61—41no—
286C2×C4×C61—42no—
287C2×C4×C61#11714yes—
288C2×C4×C61C4×D414yes—
289C2×C4×C61C4×D414yes—
290C2×C4×C61#12114yes—
291C2×C4×C61#12314yes—
292C2×C4×C61#12414yes—
293C2×C4×C61#12614yes—
294C2×Dic61—22no—
295C2×Dic61—22no—
296C2×Dic61—22no—
297C2×Dic61—22no—
298C2×Dic61—22no—
299C2×Dic61—22no—
300C2×Dic61—22no—
301C2×Dic61—24no—
302C2×Dic61—22no—
303C2×Dic61—22no—
304C2×Dic61—24no—
305C2×Dic61—24no—
306C2×Dic61—22no—
307C2×Dic61—22no—
308C2×Dic61—22no—
309C2×Dic61—41no—
310C2×Dic61—41no—
311C2×Dic61—41no—
312C2×Dic61—41no—
313C2×Dic61—42no—
314C2×Dic61—41no—
315C2×Dic61—42no—
316C2×Dic61—41no—
317C2×Dic61—42no—
318C2×Dic61—41no—
319C2×Dic61—42no—
320C2×Dic61—41no—
321C2×Dic61—42no—
322C2×Dic61—42no—
323C2×Dic61—42no—
324C2×Dic61—42no—
325C2×Dic61—42no—
326C2×Dic61—42no—
327C2×Dic61—42no—
328C2×Dic61C22⋊Q814yes—
329C4×D61—416no—
330#13973—611nomaximal, Sylow
331C22×C61C2×#11711yescharacteristic
332C22×C61C2×C4×D411yescharacteristic
333C22×C61C2×C4×D411yescharacteristic
334C22×C61C2×C4×Q811yescharacteristic
335C22×C61C4×#4111yescharacteristic
336C22×C61#51811yescharacteristic
337C22×C61#52011yescharacteristic
338C22×C61C2×#12111yescharacteristic
339C22×C61C2×C22⋊Q811yescharacteristic
340C22×C61C2×#12311yescharacteristic
341C22×C61#52511yescharacteristic
342C22×C61C2×#12411yescharacteristic
343C22×C61C2×#12611yescharacteristic
344C22×C61#52911yescharacteristic
345C22×C61#53311yescharacteristic
346C22×C61#53511yescharacteristic
347C22×C61#53711yescharacteristic
348C22×C61#54011yescharacteristic
349C22×C61#54211yescharacteristic
350C22×C61#54611yescharacteristic
351C22×C61#54611yescharacteristic
352C22×C61D4×Q811yescharacteristic
353C22×C61#55011yescharacteristic
354C22×C61#55211yescharacteristic
355C22×C61#55211yescharacteristic
356C22×C61#55211yescharacteristic
357C22×C61#55311yescharacteristic
358C22×C61#55311yescharacteristic
359C22×C61#55311yescharacteristic
360C22×C61#55411yescharacteristic
361C22×C61#55411yescharacteristic
362C22×C61#55411yescharacteristic
363C22×C61#55511yescharacteristic
364C22×C61#55511yescharacteristic
365C22×C61#55511yescharacteristic
366C2×D61—24no—
367C2×D61—24no—
368C2×D61—24no—
369C2×D61—42no—
370C2×D61—42no—
371C2×D61—42no—
372C2×D61—42no—
373C2×D61—42no—
374C2×D61—42no—
375C2×D61—42no—
376C2×D61—42no—
377C2×D61—42no—
378C2×D61—42no—
379C2×D61—42no—
380C2×D61—42no—
381C4×C61—42no—
382C4×C61—42no—
383C4×C61—44no—
384C4×C61—44no—
385C4×C61#38818yes—
386Dic61—24no—
387Dic61—44no—
388Dic61—42no—
389Dic61—42no—
390Dic61—82no—
391C2×#389—611no—
392C2×#380—611no—
393C2×#380—611no—
394C2×C4×C4⋊C4—611no—
395C2×C4×C22⋊C4—611no—
396#1442—612no—
397#1439—612no—
398#1437—612no—
399C4⋊#95—611no—
400C4⋊#95D6111yescharacteristic, complemented
401#1434—612no—
402C2×C61C2×#38811yescharacteristic
403C2×C61C4×C22⋊Q811yescharacteristic
404C2×C61#232411yescharacteristic
405C2×C61#234511yescharacteristic
406C2×C61#234611yescharacteristic
407C2×C61#236011yescharacteristic
408C2×C61#236311yescharacteristic
409C2×C61#241411yescharacteristic
410C2×C61#241711yescharacteristic
411C2×C61#242011yescharacteristic
412C2×C61#242311yescharacteristic
413C2×C61#249511yescharacteristic
414C2×C61#249711yescharacteristic
415C2×C61#256211yescharacteristic
416C2×C61#256311yescharacteristic
417D61—44no—
418C24×C4—611no—
419C22×C4⋊C4—611no—
420C22×C4⋊C4—611no—
421C22×C4⋊C4—612no—
422C22×C4⋊C4C2×D6111yescharacteristic
423C22×C4⋊C4C2×D6111yescharacteristic
424C22×C22⋊C4—611no—
425C22×C22⋊C4—612no—
426C22×C22⋊C4—611no—
427C22×C22⋊C4—612no—
428C22×C42—611no—
429C22×C42—612no—
430C22×C42C2×D6111yescharacteristic
431#389—1224no—
432#380—618no—
433#380—1224no—
434C4×C4⋊C4—1224no—
435C4×C22⋊C4—1224no—
436C2×#95—612no—
437C2×#95—611no—
438C2×#95—612no—
439C2×#95—612no—
440C2×#95—612no—
441C2×#95—612no—
442C2×#95—611no—
443C2×#95—612no—
444C2×#95C2×D6112yes—
445C2×#95C2×D6112yes—
446C61#1397311yescharacteristic, complemented, Sylow
447C25—611no—
448C23×C4—611no—
449C23×C4—611no—
450C23×C4—612no—
451C23×C4—611no—
452C23×C4—614no—
453C23×C4—612no—
454C23×C4—1222no—
455C23×C4—1222no—
456C23×C4—1222no—
457C23×C4—1222no—
458C23×C4—1222no—
459C23×C4—1222no—
460C23×C4C22×D6112yes—
461C23×C4C22×D6112yes—
462C23×C4C22×D6111yescharacteristic
463C23×C4C22×D6111yescharacteristic
464C23×C4C22×D6111yescharacteristic
465C2×C4⋊C4—22no—
466C2×C4⋊C4—22no—
467C2×C4⋊C4—22no—
468C2×C4⋊C4—22no—
469C2×C4⋊C4—614no—
470C2×C4⋊C4—1222no—
471C2×C4⋊C4—1222no—
472C2×C4⋊C4—1224no—
473C2×C4⋊C4—1222no—
474C2×C4⋊C4—1222no—
475C2×C4⋊C4—1222no—
476C2×C4⋊C4—2442no—
477C2×C4⋊C4—2442no—
478C2×C4⋊C4C4×D6114yes—
479C2×C4⋊C4D24414yes—
480C2×C22⋊C4—614no—
481C2×C22⋊C4—618no—
482C2×C22⋊C4—1222no—
483C2×C22⋊C4—1222no—
484C2×C22⋊C4—1222no—
485C2×C22⋊C4—1222no—
486C2×C22⋊C4—1222no—
487C2×C22⋊C4—1224no—
488C2×C22⋊C4—1224no—
489C2×C22⋊C4—2442no—
490C2×C22⋊C4—2442no—
491C2×C22⋊C4—2442no—
492C2×C42—22no—
493C2×C42—22no—
494C2×C42—22no—
495C2×C42—614no—
496C2×C42—1222no—
497C2×C42—1222no—
498C2×C42—1224no—
499C2×C42—1224no—
500C2×C42—2442no—
501#95—42no—
502#95—42no—
503#95—618no—
504#95—1222no—
505#95—1222no—
506#95—1224no—
507#95—1224no—
508#95—1224no—
509#95—1224no—
510#95—2442no—
511C24—612no—
512C24—612no—
513C24—612no—
514C24—1221no—
515C24—1221no—
516C24—1221no—
517C24—1221no—
518C24—1221no—
519C24—1221no—
520C24—1221no—
521C24—1221no—
522C24—1221no—
523C24—1221no—
524C24—1221no—
525C24—1221no—
526C24C23×D6111yescharacteristic
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—22no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—21no—
548C22×C4—22no—
549C22×C4—21no—
550C22×C4—22no—
551C22×C4—612no—
552C22×C4—612no—
553C22×C4—612no—
554C22×C4—612no—
555C22×C4—614no—
556C22×C4—612no—
557C22×C4—1221no—
558C22×C4—1221no—
559C22×C4—1221no—
560C22×C4—1221no—
561C22×C4—1221no—
562C22×C4—1221no—
563C22×C4—1221no—
564C22×C4—1222no—
565C22×C4—1222no—
566C22×C4—1221no—
567C22×C4—1221no—
568C22×C4—1221no—
569C22×C4—1222no—
570C22×C4—1221no—
571C22×C4—1222no—
572C22×C4—1221no—
573C22×C4—1221no—
574C22×C4—1221no—
575C22×C4—1222no—
576C22×C4—1221no—
577C22×C4—1222no—
578C22×C4—1221no—
579C22×C4—1228no—
580C22×C4—1228no—
581C22×C4—1228no—
582C22×C4—1222no—
583C22×C4—1222no—
584C22×C4—1222no—
585C22×C4—1222no—
586C22×C4—1222no—
587C22×C4—1222no—
588C22×C4—1222no—
589C22×C4—2444no—
590C22×C4—2444no—
591C22×C4—2444no—
592C22×C4—2444no—
593C22×C4C2×C4×D6114yes—
594C22×C4C2×C4×D6112yes—
595C22×C4C2×D24414yes—
596C22×C4C2×D24412yes—
597C22×C4#1175822212yes—
598C22×C4D4×D6112yes—
599C22×C4#1175822412yes—
600C22×C4#1175822412yes—
601C22×C4Q8×D6112yes—
602C22×C4#1175822612yes—
603C22×C4#1175822612yes—
604C4⋊C4—28no—
605C4⋊C4—28no—
606C4⋊C4—1228no—
607C4⋊C4—2448no—
608C4⋊C4—2444no—
609C22⋊C4—1228no—
610C22⋊C4—1228no—
611C22⋊C4—2448no—
612C22⋊C4—2448no—
613C42—44no—
614C42—1228no—
615C42—2448no—
616C23—614no—
617C23—1222no—
618C23—1222no—
619C23—1222no—
620C23—1222no—
621C23—1222no—
622C23—1222no—
623C23—1222no—
624C23—1222no—
625C23—1222no—
626C23—1222no—
627C23—1222no—
628C23—1222no—
629C23—1222no—
630C23—1222no—
631C23—1222no—
632C23—1222no—
633C23—1222no—
634C23—1222no—
635C23—2441no—
636C23—2441no—
637C23—2441no—
638C23—2441no—
639C23—2441no—
640C23—2441no—
641C23—2441no—
642C23—2441no—
643C23—2441no—
644C23—2441no—
645C23—2441no—
646C23—2441no—
647C23—2441no—
648C23—2441no—
649C23—2441no—
650C23—2441no—
651C23C22×C4×D6111yescharacteristic
652C23C2×D4×D6111yescharacteristic
653C23C22×D24411yescharacteristic
654C23C2×Q8×D6111yescharacteristic
655C23#41×D6111yescharacteristic
656C23#41×D6111yescharacteristic
657C23C2×#1175822411yescharacteristic
658C23C2×#1175822411yescharacteristic
659C23C2×#1175822211yescharacteristic
660C23C2×#1175822611yescharacteristic
661C23C2×#1175822611yescharacteristic
662C23#1451982211yescharacteristic
663C23#1451982211yescharacteristic
664C23#1451982311yescharacteristic
665C23#1451982411yescharacteristic
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—22no—
674C2×C4—24no—
675C2×C4—22no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—41no—
679C2×C4—42no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—42no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—41no—
689C2×C4—42no—
690C2×C4—41no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—614no—
695C2×C4—1222no—
696C2×C4—1222no—
697C2×C4—1222no—
698C2×C4—1222no—
699C2×C4—1222no—
700C2×C4—1222no—
701C2×C4—1222no—
702C2×C4—1222no—
703C2×C4—1224no—
704C2×C4—1222no—
705C2×C4—1224no—
706C2×C4—1224no—
707C2×C4—1222no—
708C2×C4—1222no—
709C2×C4—1222no—
710C2×C4—2442no—
711C2×C4—2442no—
712C2×C4—2442no—
713C2×C4—2442no—
714C2×C4—2442no—
715C2×C4—2442no—
716C2×C4—2442no—
717C2×C4—2442no—
718C2×C4—2441no—
719C2×C4—2442no—
720C2×C4—2441no—
721C2×C4—2441no—
722C2×C4—2441no—
723C2×C4—2441no—
724C2×C4—2441no—
725C2×C4—2442no—
726C2×C4—2441no—
727C2×C4—2441no—
728C2×C4—2442no—
729C2×C4—24416no—
730C2×C4#1451973514yes—
731C2×C4#1451973714yes—
732C2×C4C4×D24414yes—
733C2×C4#1451975214yes—
734C2×C4#1451976114yes—
735C2×C4#1451976314yes—
736C2×C4#1451977214yes—
737C22—1224no—
738C22—1224no—
739C22—1224no—
740C22—2442no—
741C22—2442no—
742C22—2442no—
743C22—2442no—
744C22—2442no—
745C22—2442no—
746C22—2442no—
747C22—2442no—
748C22—2442no—
749C22—2442no—
750C22—2442no—
751C22—2442no—
752C22C2×#1451973511yescharacteristic
753C22C2×#1451973711yescharacteristic
754C22C2×C4×D24411yescharacteristic
755C22C4×Q8×D6111yescharacteristic
756C22C4×#1175822611yescharacteristic
757C22#1684023411yescharacteristic
758C22#1684024111yescharacteristic
759C22C2×#1451975211yescharacteristic
760C22C22⋊Q8×D6111yescharacteristic
761C22C2×#1451976111yescharacteristic
762C22#1684027511yescharacteristic
763C22C2×#1451976311yescharacteristic
764C22C2×#1451977211yescharacteristic
765C22#1684029111yescharacteristic
766C22#1684031711yescharacteristic
767C22#1684032811yescharacteristic
768C22#1684034111yescharacteristic
769C22#1684036611yescharacteristic
770C22#1684038111yescharacteristic
771C22#1684040711yescharacteristic
772C22#1684040711yescharacteristic
773C22Q8×D24411yescharacteristic
774C22#1684043411yescharacteristic
775C22#1684045011yescharacteristic
776C22#1684045111yescharacteristic
777C22#1684045411yescharacteristic
778C22#1684045911yescharacteristic
779C22#1684046011yescharacteristic
780C22#1684046511yescharacteristic
781C22#1684046711yescharacteristic
782C22#1684047011yescharacteristic
783C22#1684047311yescharacteristic
784C22#1684047511yescharacteristic
785C22#1684047611yescharacteristic
786C22#1684047811yescharacteristic
787C4—44no—
788C4—44no—
789C4—42no—
790C4—42no—
791C4—1224no—
792C4—4882no—
793C4—2442no—
794C4—2442no—
795C4—2444no—
796C4#1683965418yes—
797C2—2444no—
798C2C2×#1683965411yescharacteristic
799C2#2144835711yescharacteristic
800C2#2144851511yescharacteristic
801C2#2144869511yescharacteristic
802C2#2144870311yescharacteristic
803C2#2144882611yescharacteristic
804C2#2144885911yescharacteristic
805C2#2144923511yescharacteristic
806C2#2144926811yescharacteristic
807C2#2144930911yescharacteristic
808C2#2144934211yescharacteristic
809C2#2145023311yescharacteristic
810C2#2145025511yescharacteristic
811C2#2145098411yescharacteristic
812C2#2145098911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×C4⋊#95C2
socle, cosocleC24×C61C24
prime radicalC24×D61C23
hypercenterC4⋊#95D61
hypocenterC61#13973
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
1. C2×#16839661C2semidirect
4. C2×C4⋊C4×Dic61C2semidirect
6. #21444075C2semidirect
9. #21444049C2semidirect
10. #21444043C2semidirect
11. C61×C4⋊#95C2semidirect
24. #16839619C4semidirect
400. C4⋊#95D61semidirect
446. C61#13973semidirect

Maximal subgroups

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

subgroupindex
C2×#168396612
C2×#168396192
C2×C4⋊C4×Dic612
C2×C4×#117581982
#214440752
#214440652
#214440552
#214440492
#214440432
C61×C4⋊#952
#1397361