Finite Group Databasebeta

← #29685373

Subgroups — #29685373

Order 15616.

1162 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840354C211yesmaximal, characteristic
2#21448419C211yesmaximal, characteristic, complemented
3#21448174C211yesmaximal, characteristic, complemented
4#21446802C212yesmaximal, complemented
5#21446653C212yesmaximal
6#21446276C212yesmaximal, complemented
7#21446274C212yesmaximal, complemented
8C4×#14519691C211yesmaximal, characteristic, complemented
9C4×#14519691C211yesmaximal, characteristic, complemented
10C4×#14519692C211yesmaximal, characteristic, complemented
11C4×#99×C61C211yesmaximal, characteristic, complemented
12#16840354—22no—
13#16840354—22no—
14#16840354—22no—
15#16840354—22no—
16C2×#14519771C411yescharacteristic, complemented
17C2×#14519770C411yescharacteristic, complemented
18C2×#14519769C411yescharacteristic, complemented
19C2×#14519767C411yescharacteristic, complemented
20C2×#14519761C2211yescharacteristic
21C2×#14519760C411yescharacteristic, complemented
22C2×#14519759C411yescharacteristic, complemented
23C2×#14519758C2211yescharacteristic
24C2×#14519756C411yescharacteristic, complemented
25C2×#14519755C411yescharacteristic, complemented
26C2×#14519754C2211yescharacteristic
27C2×#14519749C2211yescharacteristic
28C2×C4×C22⋊D61C2211yescharacteristic
29C2×#14519733C2212yes—
30C22×#11758196C2211yescharacteristic
31C2×#14519692C2212yes—
32C2×#14519691C2212yes—
33C2×#14519691C2212yes—
34#16839646—22no—
35#16839644—22no—
36#16839623C2212yes—
37#16839620C2212yes—
38C4×#11758196—22no—
39#16839613—22no—
40C22⋊C4×Dic61C2212yes—
41C4×C22⋊Dic61C2211yescharacteristic
42C4×C22⋊Dic61C2211yescharacteristic
43#16839529C2212yes—
44#16839528C2212yes—
45#16839528C2212yes—
46C2×C4×D4×C61C2211yescharacteristic
47C2×#99×C61C2212yes—
48C4×C22⋊C4×C61C2211yescharacteristic
49C4×C22⋊C4×C61C2211yescharacteristic
50C61×#342C2212yes—
51C22×Dic122C2×C411yescharacteristic
52C22×C22⋊D61C2×C411yescharacteristic
53C22×C22⋊D61C2311yescharacteristic
54C23×Dic61C2311yescharacteristic
55C23×Dic61C2311yescharacteristic
56C22×C4×D61C2×C411yescharacteristic
57#14519771—22no—
58#14519771—22no—
59#14519770—22no—
60#14519770—22no—
61#14519769—22no—
62#14519769—22no—
63#14519767—22no—
64#14519767—22no—
65#14519761—22no—
66#14519761—22no—
67#14519760—22no—
68#14519760—22no—
69#14519759—22no—
70#14519759—22no—
71#14519758—22no—
72#14519758—22no—
73#14519756—22no—
74#14519756—22no—
75#14519755—22no—
76#14519755—22no—
77#14519754—22no—
78#14519754—22no—
79#14519749—22no—
80#14519749—22no—
81C4×C22⋊D61—21no—
82C4×C22⋊D61—21no—
83C4×C22⋊D61—21no—
84C4×C22⋊D61—21no—
85#14519733—24no—
86#14519733—24no—
87C2×C4⋊Dic61C2×C411yescharacteristic
88C2×C4⋊Dic61C2×C411yescharacteristic
89C2×C4⋊Dic61C2×C411yescharacteristic
90C2×#11758196—22no—
91C2×#11758196—22no—
92C2×#11758196C2×C411yescharacteristic
93C2×#11758196C2×C411yescharacteristic
94C2×#11758196C2×C411yescharacteristic
95C2×#11758196C2×C411yescharacteristic
96C2×#11758196C2×C411yescharacteristic
97C2×#11758196C2×C411yescharacteristic
98C2×#11758196C2×C411yescharacteristic
99C2×#11758196C2×C411yescharacteristic
100C2×#11758196C2×C411yescharacteristic
101C2×#11758196C2×C411yescharacteristic
102C2×#11758196D412yes—
103C2×#11758196D412yes—
104C2×#11758196D412yes—
105C2×#11758196D412yes—
106C2×C22⋊Dic61C2×C411yescharacteristic
107C2×C22⋊Dic61C2×C411yescharacteristic
108C2×C22⋊Dic61C2×C411yescharacteristic
109C2×C22⋊Dic61C2312yes—
110C2×C22⋊Dic61C2311yescharacteristic
111C2×C22⋊Dic61C2312yes—
112C2×#11758198C2×C411yescharacteristic
113C2×#11758198C2×C411yescharacteristic
114C2×#11758198C2×C411yescharacteristic
115C2×#11758198C2×C411yescharacteristic
116C2×C4×Dic61—22no—
117C2×C4×Dic61—21no—
118C2×C4×Dic61—21no—
119C2×C4×Dic61—22no—
120C2×C4×Dic61C2×C411yescharacteristic
121#14519692—24no—
122#14519691—24no—
123#14519691—24no—
124#14519684—21no—
125#14519684—21no—
126#14519684—22no—
127#14519684—22no—
128#14519684—24no—
129C22×D4×C61C2311yescharacteristic
130C23×C4×C61C2×C411yescharacteristic
131C23×C4×C61C2311yescharacteristic
132C4×D4×C61—21no—
133C4×D4×C61—21no—
134C4×D4×C61—21no—
135C4×D4×C61—21no—
136C2×C4⋊C4×C61C2×C411yescharacteristic
137C2×C22⋊C4×C61C2×C411yescharacteristic
138C2×C22⋊C4×C61C2312yes—
139C2×C22⋊C4×C61C2311yescharacteristic
140C2×C22⋊C4×C61C2312yes—
141C2×C42×C61—21no—
142C2×C42×C61—21no—
143C2×C42×C61C2×C411yescharacteristic
144#99×C61—24no—
145#95×C61—21no—
146#95×C61—21no—
147C24×C61C22×C411yescharacteristic
148C24×C61C2411yescharacteristic
149C23×D61C22×C411yescharacteristic
150C2×D4×C61—21no—
151C2×D4×C61—21no—
152C2×D4×C61—22no—
153C2×D4×C61—22no—
154C22×C4×C61—22no—
155C22×C4×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61—22no—
158C22×C4×C61—81no—
159C22×C4×C61—81no—
160C22×C4×C61C22×C411yescharacteristic
161C22×C4×C61C22×C411yescharacteristic
162C22×C4×C61C22×C411yescharacteristic
163C22×C4×C61C22×C411yescharacteristic
164C22×C4×C61C22×C411yescharacteristic
165C22×C4×C61C2×D411yescharacteristic
166C22×C4×C61C2×D411yescharacteristic
167C22×C4×C61C2×D411yescharacteristic
168C22×C4×C61C2×D411yescharacteristic
169C2×C22⋊D61—21no—
170C2×C22⋊D61—21no—
171C2×C22⋊D61—22no—
172C2×C22⋊D61—22no—
173C2×C22⋊D61—22no—
174C2×C22⋊D61—81no—
175C22×Dic61—22no—
176C22×Dic61—22no—
177C22×Dic61—22no—
178C22×Dic61—22no—
179C22×Dic61—81no—
180C22×Dic61C22×C411yescharacteristic
181C22×Dic61C22×C411yescharacteristic
182C22×Dic61C22×C411yescharacteristic
183C22×Dic61C22×C411yescharacteristic
184C22×Dic61C22×C411yescharacteristic
185C22×Dic61C22×C411yescharacteristic
186C22×Dic61C22×C411yescharacteristic
187C22×Dic61C2×D412yes—
188C22×Dic61C2×D412yes—
189C22×Dic61C2×D412yes—
190C22×Dic61C2×D412yes—
191C2×C4×D61—21no—
192C2×C4×D61—21no—
193C2×C4×D61—81no—
194C2×Dic122—22no—
195C2×Dic122—81no—
196C4⋊C4×C61—21no—
197C4⋊C4×C61—21no—
198C22⋊C4×C61—21no—
199C22⋊C4×C61—21no—
200C22⋊C4×C61—22no—
201C22⋊C4×C61—21no—
202C22⋊C4×C61—21no—
203C22⋊C4×C61—22no—
204C22⋊C4×C61—22no—
205C22⋊C4×C61#4114yes—
206C42×C61—21no—
207C42×C61—21no—
208C42×C61—81no—
209C42×C61—81no—
210C22⋊Dic61—21no—
211C22⋊Dic61—21no—
212C22⋊Dic61—22no—
213C22⋊Dic61—22no—
214C22⋊Dic61—22no—
215C22⋊Dic61—22no—
216C22⋊Dic61—22no—
217C22⋊Dic61—22no—
218C22⋊Dic61#4114yes—
219#11758198—21no—
220#11758198—21no—
221#11758198—22no—
222#11758198—22no—
223#11758198—22no—
224C4⋊Dic61—22no—
225C4⋊Dic61—22no—
226C4⋊Dic61—22no—
227#11758196—28no—
228#11758196—21no—
229#11758196—21no—
230#11758196—22no—
231#11758196—22no—
232#11758196—22no—
233#11758196—22no—
234#11758196—22no—
235#11758196—82no—
236#11758196C22⋊C412yes—
237#11758196C22⋊C412yes—
238#11758196C22⋊C412yes—
239#11758196C22⋊C412yes—
240#11758196C22⋊C412yes—
241#11758196C22⋊C412yes—
242#11758196C22⋊C412yes—
243#11758196C22⋊C412yes—
244C4×Dic61—28no—
245C4×Dic61—21no—
246C4×Dic61—21no—
247C4×Dic61—82no—
248C4×Dic61—81no—
249C4×Dic61—81no—
250C23×C61—21no—
251C23×C61—21no—
252C23×C61—21no—
253C23×C61—41no—
254C23×C61—41no—
255C23×C61—41no—
256C23×C61—41no—
257C23×C61C23×C411yescharacteristic
258C23×C61C22×D411yescharacteristic
259C23×C61C22×D411yescharacteristic
260C23×C61C2×#4112yes—
261C23×C61C2×#4112yes—
262C22×D61—21no—
263C22×D61—21no—
264C22×D61—21no—
265C22×D61—41no—
266C22×D61—41no—
267D4×C61—42no—
268D4×C61—42no—
269C2×C4×C61—21no—
270C2×C4×C61—21no—
271C2×C4×C61—21no—
272C2×C4×C61—21no—
273C2×C4×C61—21no—
274C2×C4×C61—24no—
275C2×C4×C61—41no—
276C2×C4×C61—41no—
277C2×C4×C61—41no—
278C2×C4×C61—41no—
279C2×C4×C61—41no—
280C2×C4×C61—41no—
281C2×C4×C61—42no—
282C2×C4×C61—42no—
283C2×C4×C61—41no—
284C2×C4×C61—41no—
285C2×C4×C61—42no—
286C2×C4×C61—42no—
287C2×C4×C61—42no—
288C2×C4×C61—81no—
289C2×C4×C61—81no—
290C2×C4×C61C2×C22⋊C411yescharacteristic
291C2×C4×C61C2×C22⋊C411yescharacteristic
292C2×C4×C61C2×C22⋊C411yescharacteristic
293C2×C4×C61C2×C22⋊C411yescharacteristic
294C22⋊D61—42no—
295C22⋊D61—42no—
296C22⋊D61—82no—
297C2×Dic61—21no—
298C2×Dic61—21no—
299C2×Dic61—21no—
300C2×Dic61—21no—
301C2×Dic61—22no—
302C2×Dic61—22no—
303C2×Dic61—24no—
304C2×Dic61—21no—
305C2×Dic61—21no—
306C2×Dic61—21no—
307C2×Dic61—21no—
308C2×Dic61—21no—
309C2×Dic61—24no—
310C2×Dic61—42no—
311C2×Dic61—42no—
312C2×Dic61—41no—
313C2×Dic61—41no—
314C2×Dic61—42no—
315C2×Dic61—42no—
316C2×Dic61—41no—
317C2×Dic61—41no—
318C2×Dic61—42no—
319C2×Dic61—42no—
320C2×Dic61—42no—
321C2×Dic61C2×C22⋊C412yes—
322C2×Dic61C2×C22⋊C412yes—
323C2×Dic61C2×C22⋊C412yes—
324C2×Dic61C2×C22⋊C412yes—
325C4×D61—81no—
326C4×D61—81no—
327Dic122—82no—
328#21423—611nomaximal, Sylow
329C22×C61—21no—
330C22×C61—21no—
331C22×C61—21no—
332C22×C61—21no—
333C22×C61—21no—
334C22×C61—21no—
335C22×C61—42no—
336C22×C61—42no—
337C22×C61—41no—
338C22×C61—41no—
339C22×C61—41no—
340C22×C61—81no—
341C22×C61—81no—
342C22×C61C22×C22⋊C411yescharacteristic
343C22×C61C4×#4111yescharacteristic
344C22×C61C4×#4111yescharacteristic
345C22×C61#52512yes—
346C22×C61#53212yes—
347C2×D61—41no—
348C2×D61—41no—
349C2×D61—41no—
350C2×D61—81no—
351C2×D61—81no—
352C4×C61—21no—
353C4×C61—21no—
354C4×C61—21no—
355C4×C61—21no—
356C4×C61—44no—
357C4×C61—41no—
358C4×C61—41no—
359C4×C61—41no—
360C4×C61—82no—
361Dic61—22no—
362Dic61—22no—
363Dic61—22no—
364Dic61—22no—
365Dic61—44no—
366Dic61—41no—
367Dic61—41no—
368Dic61—41no—
369Dic61—82no—
370C2×#539—611no—
371#2313—611no—
372#2274—611no—
373#1996—612no—
374#1964—612no—
375#1899—612no—
376#1899—612no—
377C4×#99—611no—
378C4×#99—611no—
379C4×#99—611no—
380C4×#99D6111yescharacteristic, complemented
381C2×C61—22no—
382C2×C61—22no—
383C2×C61—21no—
384C2×C61—21no—
385C2×C61—81no—
386C2×C61#229711yescharacteristic
387C2×C61#288311yescharacteristic
388C2×C61#288411yescharacteristic
389D61—81no—
390#539—1222no—
391#539—1222no—
392#539—1222no—
393#539—1222no—
394C2×#126—611no—
395C2×#126—611no—
396C2×#125—611no—
397C2×#125—611no—
398C2×#123—611no—
399C2×#123—611no—
400C2×#123—611no—
401C2×#123—611no—
402C2×C22⋊Q8—611no—
403C2×C22⋊Q8—611no—
404C2×C22⋊Q8—611no—
405C2×#121—611no—
406C2×C4×D4—611no—
407C2×C4×D4C2×D6111yescharacteristic
408C2×#117—612no—
409C22×C4⋊C4—611no—
410C2×#99—612no—
411C2×#99—612no—
412C2×#99—612no—
413C2×#99C2×D6112yes—
414#387—1222no—
415#387—1222no—
416#381—612no—
417#380—612no—
418C4×C4⋊C4—1222no—
419C4×C4⋊C4—1222no—
420C4×C22⋊C4—611no—
421C4×C22⋊C4—611no—
422C4×C22⋊C4—612no—
423C4×C22⋊C4C2×D6111yescharacteristic
424C4×C22⋊C4C2×D6111yescharacteristic
425#342—612no—
426#342—612no—
427#342—612no—
428#342C2×D6112yes—
429C61#2142311yescharacteristic, complemented, Sylow
430C22×Q8—611no—
431C22×D4—611no—
432C22×D4—611no—
433C22×D4C22×D6111yescharacteristic
434C23×C4—611no—
435C23×C4—611no—
436C23×C4—611no—
437C23×C4C4×D6111yescharacteristic
438C23×C4C22×D6111yescharacteristic
439#126—1222no—
440#126—1222no—
441#126—1222no—
442#126—1222no—
443#125—1222no—
444#125—1222no—
445#125—1222no—
446#125—1222no—
447#123—1222no—
448#123—1222no—
449#123—1222no—
450#123—1222no—
451#123—1222no—
452#123—1222no—
453#123—1222no—
454#123—1222no—
455C22⋊Q8—1222no—
456C22⋊Q8—1222no—
457C22⋊Q8—1222no—
458C22⋊Q8—1222no—
459C22⋊Q8—1222no—
460C22⋊Q8—1222no—
461#121—1222no—
462#121—1222no—
463C4×D4—21no—
464C4×D4—21no—
465C4×D4—21no—
466C4×D4—21no—
467C4×D4—1221no—
468C4×D4—1221no—
469C4×D4—1221no—
470C4×D4—1221no—
471#117—1224no—
472#117—1224no—
473C2×C4⋊C4—611no—
474C2×C4⋊C4—611no—
475C2×C4⋊C4—611no—
476C2×C4⋊C4—611no—
477C2×C4⋊C4—612no—
478C2×C4⋊C4—612no—
479C2×C4⋊C4—612no—
480C2×C4⋊C4—612no—
481C2×C4⋊C4—611no—
482C2×C4⋊C4—611no—
483C2×C4⋊C4—611no—
484C2×C4⋊C4—611no—
485C2×C4⋊C4—611no—
486C2×C4⋊C4—611no—
487C2×C4⋊C4—611no—
488C2×C4⋊C4—611no—
489C2×C4⋊C4—611no—
490C2×C4⋊C4—1222no—
491C2×C4⋊C4—1222no—
492C2×C4⋊C4C4×D6111yescharacteristic
493C2×C22⋊C4—612no—
494C2×C22⋊C4—611no—
495C2×C22⋊C4—611no—
496C2×C22⋊C4—611no—
497C2×C22⋊C4—611no—
498C2×C22⋊C4—611no—
499C2×C22⋊C4—611no—
500C2×C22⋊C4—611no—
501C2×C22⋊C4—611no—
502C2×C22⋊C4—612no—
503C2×C22⋊C4C4×D6111yescharacteristic
504C2×C22⋊C4C22×D6112yes—
505C2×C22⋊C4C22×D6111yescharacteristic
506C2×C22⋊C4C22×D6112yes—
507C2×C42—21no—
508C2×C42—21no—
509C2×C42—611no—
510C2×C42—1222no—
511C2×C42—1222no—
512C2×C42—1221no—
513C2×C42—1221no—
514C2×C42C4×D6111yescharacteristic
515#99—24no—
516#99—1224no—
517#99—1224no—
518#99—1224no—
519#95—21no—
520#95—21no—
521#95—1222no—
522#95—1222no—
523#95—1224no—
524#95—1221no—
525#95—1221no—
526C24—611no—
527C24C2×C4×D6111yescharacteristic
528C24C23×D6111yescharacteristic
529C2×Q8—1222no—
530C2×Q8—4881no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—22no—
534C2×D4—22no—
535C2×D4—1222no—
536C2×D4—1221no—
537C2×D4—1221no—
538C2×D4—1222no—
539C2×D4—1222no—
540C2×D4—4881no—
541C22×C4—22no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—22no—
545C22×C4—81no—
546C22×C4—81no—
547C22×C4—611no—
548C22×C4—611no—
549C22×C4—612no—
550C22×C4—612no—
551C22×C4—611no—
552C22×C4—611no—
553C22×C4—612no—
554C22×C4—612no—
555C22×C4—611no—
556C22×C4—611no—
557C22×C4—611no—
558C22×C4—1222no—
559C22×C4—1222no—
560C22×C4—1222no—
561C22×C4—1221no—
562C22×C4—1221no—
563C22×C4—1222no—
564C22×C4—4881no—
565C22×C4—4881no—
566C22×C4C2×C4×D6111yescharacteristic
567C22×C4C2×C4×D6111yescharacteristic
568C22×C4C2×C4×D6111yescharacteristic
569C22×C4C2×C4×D6111yescharacteristic
570C22×C4C2×C4×D6111yescharacteristic
571C22×C4D4×D6111yescharacteristic
572C22×C4D4×D6111yescharacteristic
573C22×C4D4×D6111yescharacteristic
574C22×C4D4×D6111yescharacteristic
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—612no—
578C4⋊C4—612no—
579C4⋊C4—612no—
580C4⋊C4—612no—
581C4⋊C4—612no—
582C4⋊C4—612no—
583C4⋊C4—612no—
584C4⋊C4—612no—
585C4⋊C4—1222no—
586C4⋊C4—1222no—
587C4⋊C4—1222no—
588C4⋊C4—1222no—
589C4⋊C4—1222no—
590C4⋊C4—1222no—
591C4⋊C4—1222no—
592C4⋊C4—1222no—
593C4⋊C4—1228no—
594C4⋊C4—1221no—
595C4⋊C4—1221no—
596C4⋊C4—4882no—
597C22⋊C4—21no—
598C22⋊C4—21no—
599C22⋊C4—22no—
600C22⋊C4—21no—
601C22⋊C4—21no—
602C22⋊C4—22no—
603C22⋊C4—22no—
604C22⋊C4—614no—
605C22⋊C4—1222no—
606C22⋊C4—1222no—
607C22⋊C4—1222no—
608C22⋊C4—1222no—
609C22⋊C4—1222no—
610C22⋊C4—1222no—
611C22⋊C4—1221no—
612C22⋊C4—1221no—
613C22⋊C4—1222no—
614C22⋊C4—1221no—
615C22⋊C4—1221no—
616C22⋊C4—1222no—
617C22⋊C4—1222no—
618C22⋊C4#1175822214yes—
619C42—21no—
620C42—21no—
621C42—81no—
622C42—81no—
623C42—1228no—
624C42—1221no—
625C42—1221no—
626C42—4881no—
627C42—4881no—
628C42—4882no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—1221no—
637C23—1221no—
638C23—1221no—
639C23—2441no—
640C23—2441no—
641C23C22×C4×D6111yescharacteristic
642C23C2×D4×D6111yescharacteristic
643C23C2×D4×D6111yescharacteristic
644C23#41×D6112yes—
645C23C2×#1175822212yes—
646Q8—4882no—
647D4—42no—
648D4—42no—
649D4—4882no—
650D4—2442no—
651D4—2442no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—24no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—81no—
672C2×C4—81no—
673C2×C4—612no—
674C2×C4—612no—
675C2×C4—612no—
676C2×C4—612no—
677C2×C4—1221no—
678C2×C4—1221no—
679C2×C4—1221no—
680C2×C4—1221no—
681C2×C4—1222no—
682C2×C4—1222no—
683C2×C4—1224no—
684C2×C4—1221no—
685C2×C4—1221no—
686C2×C4—1221no—
687C2×C4—1221no—
688C2×C4—1221no—
689C2×C4—1224no—
690C2×C4—4881no—
691C2×C4—4881no—
692C2×C4—2442no—
693C2×C4—2442no—
694C2×C4—2441no—
695C2×C4—2441no—
696C2×C4—2442no—
697C2×C4—2442no—
698C2×C4—2442no—
699C2×C4—2442no—
700C2×C4—2442no—
701C2×C4—2441no—
702C2×C4—2441no—
703C2×C4C22⋊C4×D6111yescharacteristic
704C2×C4C22⋊C4×D6111yescharacteristic
705C2×C4C22⋊C4×D6111yescharacteristic
706C2×C4C22⋊C4×D6111yescharacteristic
707C22—21no—
708C22—21no—
709C22—21no—
710C22—21no—
711C22—21no—
712C22—21no—
713C22—42no—
714C22—42no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—81no—
719C22—81no—
720C22—4881no—
721C22—4881no—
722C22—2441no—
723C22—2441no—
724C22—2441no—
725C22C2×C22⋊C4×D6111yescharacteristic
726C22#1684023011yescharacteristic
727C22C4×#1175822211yescharacteristic
728C22#1684027112yes—
729C22#1684030912yes—
730C4—21no—
731C4—21no—
732C4—21no—
733C4—21no—
734C4—44no—
735C4—41no—
736C4—41no—
737C4—41no—
738C4—82no—
739C4—1222no—
740C4—1222no—
741C4—1222no—
742C4—1222no—
743C4—4882no—
744C4—2444no—
745C4—2441no—
746C4—2441no—
747C4—2441no—
748C2—22no—
749C2—22no—
750C2—21no—
751C2—21no—
752C2—81no—
753C2—4881no—
754C2#2144830511yescharacteristic
755C2#2145427711yescharacteristic
756C2#2145428111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC24C23×D61
FittingC4×#99×C61C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#14519749C22
cosocleC24×C61C24
hypercenterC4×#99D61
hypocenterC61#21423
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
2. #21448419C2semidirect
3. #21448174C2semidirect
4. #21446802C2semidirect
6. #21446276C2semidirect
7. #21446274C2semidirect
8. C4×#14519691C2semidirect
9. C4×#14519691C2semidirect
10. C4×#14519692C2semidirect
11. C4×#99×C61C2semidirect
16. C2×#14519771C4semidirect
17. C2×#14519770C4semidirect
18. C2×#14519769C4semidirect
19. C2×#14519767C4semidirect
21. C2×#14519760C4semidirect
22. C2×#14519759C4semidirect
24. C2×#14519756C4semidirect
25. C2×#14519755C4semidirect
380. C4×#99D61semidirect
429. C61#21423semidirect

Maximal subgroups

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

subgroupindex
C2×#168403542
#214484192
#214481742
#214468022
#214466532
#214462762
#214462742
C4×#145196912
C4×#145196922
C4×#99×C612
#2142361