Finite Group Databasebeta

← #29603395

Subgroups — #29603395

Order 15616.

1810 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519742C211yesmaximal, characteristic
2C2×#16839668C211yesmaximal, characteristic
3C2×#16839667C211yesmaximal, characteristic
4C2×#16839658C211yesmaximal, characteristic
5C2×C4×C4⋊Dic61C211yesmaximal, characteristic
6#21444083C212yesmaximal
7#21444074C212yesmaximal
8#21444054C212yesmaximal
9#21444053C212yesmaximal
10#21444048C211yesmaximal, characteristic
11C61×C4⋊#95C211yesmaximal, characteristic
12C23×Dic122C2211yescharacteristic
13C2×#14519742—24no—
14C2×#14519742—24no—
15C2×#14519742—24no—
16C22×C4⋊Dic61C2211yescharacteristic
17C22×C4⋊Dic61C2211yescharacteristic
18C22×C4⋊Dic61C2211yescharacteristic
19C22×#11758196C2212yes—
20C22×#11758196C2212yes—
21C22×C4×Dic61C2212yes—
22C22×C4×Dic61C2211yescharacteristic
23C22×C4×Dic61C2211yescharacteristic
24#16839668C418yescomplemented
25#16839667—24no—
26#16839658—24no—
27C4×C4⋊Dic61—24no—
28C2×#14519684C2212yes—
29C2×#14519684C2212yes—
30C2×#14519684C2212yes—
31C2×#14519684C2212yes—
32C2×#14519684C2211yescharacteristic
33C2×#14519684C2211yescharacteristic
34C2×#14519684C2212yes—
35C2×#14519684C2212yes—
36C2×#14519684C2212yes—
37C22×C4⋊C4×C61C2211yescharacteristic
38C22×C4⋊C4×C61C2211yescharacteristic
39C22×C42×C61C2211yescharacteristic
40C2×#95×C61C2212yes—
41C2×#95×C61C2212yes—
42C22×Dic122—22no—
43C22×Dic122—22no—
44C22×Dic122—22no—
45C22×Dic122—22no—
46C22×Dic122C2×C414yes—
47C22×Dic122D414yes—
48C22×Dic122Q814yes—
49C23×Dic61C2312yes—
50C23×Dic61C2311yescharacteristic
51C23×Dic61C2311yescharacteristic
52C23×Dic61C2311yescharacteristic
53C23×Dic61C2312yes—
54C23×Dic61C2311yescharacteristic
55#14519742—232no—
56C2×C4⋊Dic61—22no—
57C2×C4⋊Dic61—22no—
58C2×C4⋊Dic61—22no—
59C2×C4⋊Dic61—22no—
60C2×C4⋊Dic61—22no—
61C2×C4⋊Dic61—22no—
62C2×C4⋊Dic61—22no—
63C2×C4⋊Dic61C2×C414yes—
64C2×C4⋊Dic61Q814yescomplemented
65C2×#11758196—24no—
66C2×#11758196—24no—
67C2×#11758196—24no—
68C2×#11758196—24no—
69C2×#11758196—24no—
70C2×#11758196—42no—
71C2×C4×Dic61—24no—
72C2×C4×Dic61—22no—
73C2×C4×Dic61—22no—
74C2×C4×Dic61—24no—
75C2×C4×Dic61—24no—
76C2×C4×Dic61—22no—
77C2×C4×Dic61—22no—
78C2×C4×Dic61—22no—
79C2×C4×Dic61D414yes—
80#14519684—24no—
81#14519684—22no—
82#14519684—22no—
83#14519684—24no—
84#14519684—24no—
85#14519684—24no—
86#14519684—42no—
87#14519684C2×C418yes—
88#14519684C2×C418yes—
89C23×C4×C61C2312yes—
90C23×C4×C61C2311yescharacteristic
91C23×C4×C61C2312yes—
92C23×C4×C61C2311yescharacteristic
93C23×C4×C61C2311yescharacteristic
94C2×C4⋊C4×C61—22no—
95C2×C4⋊C4×C61—22no—
96C2×C4⋊C4×C61—22no—
97C2×C4⋊C4×C61—22no—
98C2×C4⋊C4×C61—22no—
99C2×C4⋊C4×C61D414yes—
100C2×C42×C61—22no—
101C2×C42×C61—22no—
102C2×C42×C61C2×C414yes—
103#95×C61—24no—
104#95×C61—42no—
105C24×C61C2411yescharacteristic
106C22×C4×C61—21no—
107C22×C4×C61—21no—
108C22×C4×C61—21no—
109C22×C4×C61—21no—
110C22×C4×C61—21no—
111C22×C4×C61—22no—
112C22×C4×C61—22no—
113C22×C4×C61—22no—
114C22×C4×C61—21no—
115C22×C4×C61—22no—
116C22×C4×C61—21no—
117C22×C4×C61—22no—
118C22×C4×C61—21no—
119C22×C4×C61—21no—
120C22×C4×C61—21no—
121C22×C4×C61—22no—
122C22×C4×C61—22no—
123C22×C4×C61—22no—
124C22×C4×C61—22no—
125C22×C4×C61—22no—
126C22×C4×C61—22no—
127C22×C4×C61—22no—
128C22×C4×C61—22no—
129C22×C4×C61C22×C412yes—
130C22×C4×C61C22×C412yes—
131C22×C4×C61C22×C412yes—
132C22×C4×C61C2×D414yes—
133C22×C4×C61C2×D412yes—
134C22×C4×C61C2×D412yes—
135C22×C4×C61C2×D412yes—
136C22×C4×C61C2×Q812yes—
137C22×C4×C61C2×Q812yes—
138C22×C4×C61#4112yes—
139C22×C4×C61#4112yes—
140C22×C4×C61#4112yes—
141C22×Dic61—22no—
142C22×Dic61—22no—
143C22×Dic61—21no—
144C22×Dic61—21no—
145C22×Dic61—22no—
146C22×Dic61—22no—
147C22×Dic61—21no—
148C22×Dic61—21no—
149C22×Dic61—21no—
150C22×Dic61—21no—
151C22×Dic61—21no—
152C22×Dic61—21no—
153C22×Dic61—21no—
154C22×Dic61—22no—
155C22×Dic61—21no—
156C22×Dic61—21no—
157C22×Dic61—21no—
158C22×Dic61—22no—
159C22×Dic61—22no—
160C22×Dic61—22no—
161C22×Dic61—21no—
162C22×Dic61—21no—
163C22×Dic61—21no—
164C22×Dic61—21no—
165C22×Dic61—21no—
166C22×Dic61—22no—
167C22×Dic61—21no—
168C22×Dic61—22no—
169C22×Dic61—21no—
170C22×Dic61—21no—
171C22×Dic61—21no—
172C22×Dic61—21no—
173C22×Dic61C22×C414yes—
174C22×Dic61C22×C414yes—
175C22×Dic61C2×D412yes—
176C22×Dic61C2×D414yes—
177C22×Dic61C2×D412yes—
178C22×Dic61C2×Q812yes—
179C22×Dic61C2×Q814yes—
180C22×Dic61C2×Q812yes—
181C22×Dic61#4112yes—
182C22×Dic61#4112yes—
183C2×Dic122—28no—
184C2×Dic122—28no—
185C2×Dic122—28no—
186C2×Dic122—28no—
187C2×Dic122—28no—
188C2×Dic122—28no—
189C2×Dic122C4⋊C4116yescomplemented
190C4⋊C4×C61—28no—
191C4⋊C4×C61—44no—
192C42×C61—28no—
193C4⋊Dic61—28no—
194C4⋊Dic61—28no—
195C4⋊Dic61—28no—
196#11758196—216no—
197#11758196—48no—
198C4×Dic61—216no—
199C4×Dic61—28no—
200C4×Dic61—44no—
201C23×C61C23×C411yescharacteristic
202C23×C61C22×D411yescharacteristic
203C23×C61C22×D411yescharacteristic
204C23×C61C22×D411yescharacteristic
205C23×C61C22×Q811yescharacteristic
206C23×C61C22×Q811yescharacteristic
207C23×C61C2×#4111yescharacteristic
208C23×C61C2×#4111yescharacteristic
209C23×C61C2×#4111yescharacteristic
210C23×C61C2×#4111yescharacteristic
211C23×C61C2×#4111yescharacteristic
212C23×C61H(5,𝔽2)11yescharacteristic
213C23×C612−1+411yescharacteristic
214C23×C612−1+411yescharacteristic
215C23×C612−1+411yescharacteristic
216C2×C4×C61—22no—
217C2×C4×C61—22no—
218C2×C4×C61—22no—
219C2×C4×C61—22no—
220C2×C4×C61—22no—
221C2×C4×C61—22no—
222C2×C4×C61—22no—
223C2×C4×C61—22no—
224C2×C4×C61—22no—
225C2×C4×C61—24no—
226C2×C4×C61—24no—
227C2×C4×C61—24no—
228C2×C4×C61—42no—
229C2×C4×C61—41no—
230C2×C4×C61—41no—
231C2×C4×C61—42no—
232C2×C4×C61—41no—
233C2×C4×C61—41no—
234C2×C4×C61—42no—
235C2×C4×C61—42no—
236C2×C4×C61—42no—
237C2×C4×C61—42no—
238C2×C4×C61—42no—
239C2×C4×C61—42no—
240C2×C4×C61—42no—
241C2×C4×C61—42no—
242C2×C4×C61—42no—
243C2×C4×C61C2×C4⋊C414yes—
244C2×C4×C61C4×D414yes—
245C2×C4×C61C4×D414yes—
246C2×C4×C61C4×Q814yescomplemented
247C2×C4×C61#12014yes—
248C2×C4×C61C22⋊Q814yes—
249C2×C4×C61C22⋊Q814yes—
250C2×C4×C61#12314yes—
251C2×Dic61—24no—
252C2×Dic61—24no—
253C2×Dic61—22no—
254C2×Dic61—24no—
255C2×Dic61—24no—
256C2×Dic61—24no—
257C2×Dic61—24no—
258C2×Dic61—22no—
259C2×Dic61—22no—
260C2×Dic61—22no—
261C2×Dic61—22no—
262C2×Dic61—22no—
263C2×Dic61—24no—
264C2×Dic61—24no—
265C2×Dic61—24no—
266C2×Dic61—22no—
267C2×Dic61—22no—
268C2×Dic61—22no—
269C2×Dic61—22no—
270C2×Dic61—22no—
271C2×Dic61—22no—
272C2×Dic61—22no—
273C2×Dic61—22no—
274C2×Dic61—22no—
275C2×Dic61—41no—
276C2×Dic61—41no—
277C2×Dic61—41no—
278C2×Dic61—41no—
279C2×Dic61—42no—
280C2×Dic61—41no—
281C2×Dic61—41no—
282C2×Dic61—41no—
283C2×Dic61—42no—
284C2×Dic61—41no—
285C2×Dic61—41no—
286C2×Dic61—41no—
287C2×Dic61—41no—
288C2×Dic61—41no—
289C2×Dic61—42no—
290C2×Dic61—42no—
291C2×Dic61C2×C4⋊C418yes—
292C2×Dic61C22⋊Q814yes—
293Dic122—232no—
294#14017—611nomaximal, Sylow
295C22×C61C22×C4⋊C411yescharacteristic
296C22×C61C2×C4×D411yescharacteristic
297C22×C61C2×C4×D411yescharacteristic
298C22×C61C2×C4×Q811yescharacteristic
299C22×C61C4×#4111yescharacteristic
300C22×C61#51911yescharacteristic
301C22×C61#52011yescharacteristic
302C22×C61C2×#12011yescharacteristic
303C22×C61C2×C22⋊Q811yescharacteristic
304C22×C61C2×C22⋊Q811yescharacteristic
305C22×C61C2×C22⋊Q811yescharacteristic
306C22×C61C2×#12311yescharacteristic
307C22×C61#52511yescharacteristic
308C22×C61#52911yescharacteristic
309C22×C61#53311yescharacteristic
310C22×C61#53611yescharacteristic
311C22×C61#53711yescharacteristic
312C22×C61#54111yescharacteristic
313C22×C61#54211yescharacteristic
314C22×C61#54611yescharacteristic
315C22×C61#54711yescharacteristic
316C22×C61#54811yescharacteristic
317C22×C61#54811yescharacteristic
318C22×C61#54811yescharacteristic
319C22×C61D4×Q811yescharacteristic
320C22×C61D4×Q811yescharacteristic
321C22×C61#55011yescharacteristic
322C22×C61#55611yescharacteristic
323C22×C61#55611yescharacteristic
324C22×C61#55711yescharacteristic
325C22×C61#55711yescharacteristic
326C22×C61#55711yescharacteristic
327C22×C61#55711yescharacteristic
328C22×C61Q8211yescharacteristic
329C22×C61#55911yescharacteristic
330C4×C61—24no—
331C4×C61—42no—
332C4×C61—44no—
333C4×C61—82no—
334C4×C61#38518yes—
335Dic61—24no—
336Dic61—28no—
337Dic61—44no—
338Dic61—42no—
339Dic61—42no—
340Dic61—42no—
341C22×C4×Q8—611no—
342C2×#391—611no—
343C2×#391—611no—
344C2×#389—611no—
345C2×C4×C4⋊C4—611no—
346#1444—612no—
347#1442—612no—
348#1436—612no—
349#1436—612no—
350C4⋊#95—611no—
351C4⋊#95D6111yescharacteristic
352C2×C61C2×#38511yescharacteristic
353C2×C61C4×C22⋊Q811yescharacteristic
354C2×C61#232311yescharacteristic
355C2×C61Q8×C4⋊C411yescharacteristic
356C2×C61#235111yescharacteristic
357C2×C61#236511yescharacteristic
358C2×C61#236711yescharacteristic
359C2×C61#240711yescharacteristic
360C2×C61#240911yescharacteristic
361C2×C61#244611yescharacteristic
362C2×C61#244811yescharacteristic
363C2×C61#245111yescharacteristic
364C2×C61#245311yescharacteristic
365C2×C61#258111yescharacteristic
366C2×C61#258211yescharacteristic
367C23×Q8—611no—
368C2×C4×Q8—1224no—
369C2×C4×Q8—1224no—
370C2×C4×Q8—1224no—
371C22×C4⋊C4—611no—
372C22×C4⋊C4—611no—
373C22×C4⋊C4—612no—
374C22×C4⋊C4—611no—
375C22×C4⋊C4—612no—
376C22×C4⋊C4C2×D6111yescharacteristic
377C22×C4⋊C4C2×D6111yescharacteristic
378C22×C42—611no—
379C22×C42—612no—
380C22×C42—611no—
381C22×C42C2×D6111yescharacteristic
382#391—618no—
383#391—1224no—
384#389—1224no—
385C4×C4⋊C4—1224no—
386C2×#95—612no—
387C2×#95—612no—
388C2×#95—612no—
389C2×#95—611no—
390C2×#95—612no—
391C2×#95—612no—
392C2×#95—612no—
393C2×#95—611no—
394C2×#95—612no—
395C2×#95C2×D6112yes—
396C2×#95C2×D6112yes—
397C61#1401711yescharacteristic, complemented, Sylow
398C22×Q8—614no—
399C22×Q8—614no—
400C22×Q8—614no—
401C22×Q8—1222no—
402C22×Q8—1222no—
403C22×Q8—1222no—
404C22×Q8—1222no—
405C23×C4—612no—
406C23×C4—611no—
407C23×C4—611no—
408C23×C4—611no—
409C23×C4—612no—
410C23×C4—611no—
411C23×C4C22×D6112yes—
412C23×C4C22×D6111yescharacteristic
413C23×C4C22×D6112yes—
414C23×C4C22×D6111yescharacteristic
415C23×C4C22×D6111yescharacteristic
416C4×Q8—12232no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—614no—
423C2×C4⋊C4—614no—
424C2×C4⋊C4—1224no—
425C2×C4⋊C4—1224no—
426C2×C4⋊C4—1222no—
427C2×C4⋊C4—1222no—
428C2×C4⋊C4—1222no—
429C2×C4⋊C4—1222no—
430C2×C4⋊C4—1224no—
431C2×C4⋊C4—1222no—
432C2×C4⋊C4—1222no—
433C2×C4⋊C4—1222no—
434C2×C4⋊C4—1224no—
435C2×C4⋊C4—1224no—
436C2×C4⋊C4—2442no—
437C2×C4⋊C4D24414yes—
438C2×C42—22no—
439C2×C42—22no—
440C2×C42—614no—
441C2×C42—1224no—
442C2×C42—1224no—
443C2×C42—1224no—
444C2×C42—1222no—
445C2×C42—1222no—
446C2×C42—1222no—
447C2×C42—1222no—
448C2×C42—1222no—
449C2×C42C4×D6114yes—
450#95—24no—
451#95—42no—
452#95—618no—
453#95—618no—
454#95—1222no—
455#95—1222no—
456#95—1224no—
457#95—1224no—
458#95—1224no—
459#95—1224no—
460#95—2442no—
461C24C23×D6111yescharacteristic
462C2×Q8—6116no—
463C2×Q8—1228no—
464C2×Q8—1228no—
465C2×Q8—1228no—
466C2×Q8—1228no—
467C2×Q8—1228no—
468C2×Q8—1228no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—22no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—22no—
484C22×C4—21no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—614no—
493C22×C4—614no—
494C22×C4—612no—
495C22×C4—612no—
496C22×C4—614no—
497C22×C4—612no—
498C22×C4—614no—
499C22×C4—612no—
500C22×C4—612no—
501C22×C4—612no—
502C22×C4—1221no—
503C22×C4—1222no—
504C22×C4—1221no—
505C22×C4—1222no—
506C22×C4—1222no—
507C22×C4—1222no—
508C22×C4—1221no—
509C22×C4—1221no—
510C22×C4—1221no—
511C22×C4—1221no—
512C22×C4—1221no—
513C22×C4—1221no—
514C22×C4—1221no—
515C22×C4—1221no—
516C22×C4—1222no—
517C22×C4—1221no—
518C22×C4—1221no—
519C22×C4—1222no—
520C22×C4—1222no—
521C22×C4—1221no—
522C22×C4—1221no—
523C22×C4—1221no—
524C22×C4—1221no—
525C22×C4—1222no—
526C22×C4—1221no—
527C22×C4—1222no—
528C22×C4—1221no—
529C22×C4—1221no—
530C22×C4—1221no—
531C22×C4—1221no—
532C22×C4—1222no—
533C22×C4—1221no—
534C22×C4C2×C4×D6112yes—
535C22×C4C2×C4×D6112yes—
536C22×C4C2×C4×D6112yes—
537C22×C4C2×D24414yes—
538C22×C4C2×D24412yes—
539C22×C4#1175822212yes—
540C22×C4D4×D6112yes—
541C22×C4D4×D6112yes—
542C22×C4#1175822412yes—
543C22×C4#1175822412yes—
544C22×C4Q8×D6112yes—
545C22×C4Q8×D6112yes—
546C4⋊C4—28no—
547C4⋊C4—44no—
548C4⋊C4—1228no—
549C4⋊C4—12216no—
550C4⋊C4—1228no—
551C4⋊C4—1228no—
552C4⋊C4—2448no—
553C42—28no—
554C42—12216no—
555C42—1228no—
556C42—2444no—
557C23C22×C4×D6111yescharacteristic
558C23C2×D4×D6111yescharacteristic
559C23C2×D4×D6111yescharacteristic
560C23C22×D24411yescharacteristic
561C23C2×Q8×D6111yescharacteristic
562C23C2×Q8×D6111yescharacteristic
563C23#41×D6111yescharacteristic
564C23#41×D6111yescharacteristic
565C23C2×#1175822411yescharacteristic
566C23C2×#1175822411yescharacteristic
567C23C2×#1175822211yescharacteristic
568C23#1451982211yescharacteristic
569C23#1451982411yescharacteristic
570C23#1451982411yescharacteristic
571C23#1451982511yescharacteristic
572Q8—12232no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—24no—
583C2×C4—24no—
584C2×C4—24no—
585C2×C4—42no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—42no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—618no—
601C2×C4—614no—
602C2×C4—1224no—
603C2×C4—1224no—
604C2×C4—1222no—
605C2×C4—1224no—
606C2×C4—1224no—
607C2×C4—1224no—
608C2×C4—1224no—
609C2×C4—1222no—
610C2×C4—1222no—
611C2×C4—1222no—
612C2×C4—1222no—
613C2×C4—1222no—
614C2×C4—1224no—
615C2×C4—1224no—
616C2×C4—1224no—
617C2×C4—1222no—
618C2×C4—1222no—
619C2×C4—1222no—
620C2×C4—1222no—
621C2×C4—1222no—
622C2×C4—1222no—
623C2×C4—1222no—
624C2×C4—1222no—
625C2×C4—1222no—
626C2×C4—2442no—
627C2×C4—2442no—
628C2×C4—2441no—
629C2×C4—2441no—
630C2×C4—2441no—
631C2×C4—2441no—
632C2×C4—2442no—
633C2×C4—2441no—
634C2×C4—2441no—
635C2×C4—2441no—
636C2×C4—2441no—
637C2×C4—2441no—
638C2×C4—2442no—
639C2×C4—2441no—
640C2×C4—2441no—
641C2×C4—2441no—
642C2×C4C4⋊C4×D6114yes—
643C2×C4#1451973714yes—
644C2×C4C4×D24414yes—
645C2×C4#1451974214yescomplemented
646C2×C4#1451974714yes—
647C2×C4#1451975514yes—
648C2×C4#1451975714yes—
649C2×C4#1451975914yes—
650C22C2×C4⋊C4×D6111yescharacteristic
651C22C2×#1451973711yescharacteristic
652C22C2×C4×D24411yescharacteristic
653C22C2×#1451974211yescharacteristic
654C22#1684023011yescharacteristic
655C22#1684023911yescharacteristic
656C22#1684024311yescharacteristic
657C22C2×#1451974711yescharacteristic
658C22C22⋊Q8×D6111yescharacteristic
659C22C2×#1451975511yescharacteristic
660C22C2×#1451975711yescharacteristic
661C22C2×#1451975911yescharacteristic
662C22#1684027211yescharacteristic
663C22#1684029311yescharacteristic
664C22#1684031411yescharacteristic
665C22#1684033511yescharacteristic
666C22#1684034111yescharacteristic
667C22#1684037211yescharacteristic
668C22#1684037911yescharacteristic
669C22#1684040711yescharacteristic
670C22#1684041611yescharacteristic
671C22#1684042011yescharacteristic
672C22#1684042011yescharacteristic
673C22#1684042411yescharacteristic
674C22#1684042711yescharacteristic
675C22Q8×D24411yescharacteristic
676C22#1684043211yescharacteristic
677C22#1684048211yescharacteristic
678C22#1684048411yescharacteristic
679C22#1684048711yescharacteristic
680C22#1684048911yescharacteristic
681C22#1684048911yescharacteristic
682C22#1684049011yescharacteristic
683C22#1684049211yescharacteristic
684C22#1684049511yescharacteristic
685C4—24no—
686C4—42no—
687C4—44no—
688C4—82no—
689C4—1228no—
690C4—1224no—
691C4—2444no—
692C4—2442no—
693C4—2442no—
694C4—2442no—
695C4#1683963618yes—
696C2C2×#1683963611yescharacteristic
697C2#2144834711yescharacteristic
698C2#2144849711yescharacteristic
699C2#2144873111yescharacteristic
700C2#2144873611yescharacteristic
701C2#2144887711yescharacteristic
702C2#2144889011yescharacteristic
703C2#2144916211yescharacteristic
704C2#2144918211yescharacteristic
705C2#2144959811yescharacteristic
706C2#2144962011yescharacteristic
707C2#2144965611yescharacteristic
708C2#2144967811yescharacteristic
709C2#2145118711yescharacteristic
710C2#2145119111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×C4⋊#95C2
socle, prime radical, cosocleC24×C61C24
hypercenterC4⋊#95D61
hypocenterC61#14017
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
24. #16839668C4semidirect
64. C2×C4⋊Dic61Q8semidirect
189. C2×Dic122C4⋊C4semidirect
246. C2×C4×C61C4×Q8semidirect
397. C61#14017semidirect
645. C2×C4#14519742semidirect

Maximal subgroups

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

subgroupindex
C22×#145197422
C2×#168396682
C2×#168396672
C2×#168396582
C2×C4×C4⋊Dic612
#214440832
#214440742
#214440542
#214440532
#214440482
C61×C4⋊#952
#1401761