Finite Group Databasebeta

← #29611432

Subgroups — #29611432

Order 15616.

2494 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519754C211yesmaximal, characteristic
2C23×C4⋊Dic61C211yesmaximal, characteristic
3C2×#16839683C212yesmaximal, complemented
4C2×#16839637C211yesmaximal, characteristic
5C2×#16839634C211yesmaximal, characteristic
6#21444084C212yesmaximal, complemented
7#21444083C212yesmaximal, complemented
8#21444071C212yesmaximal, complemented
9#21444042C211yesmaximal, characteristic
10#21444041C211yesmaximal, characteristic
11C61×C22⋊#95C211yesmaximal, characteristic
12C23×Dic122C2211yescharacteristic
13C24×Dic61C2211yescharacteristic
14C24×Dic61C2211yescharacteristic
15C2×#14519754—24no—
16C2×#14519754—24no—
17C2×#14519754—24no—
18C22×C4⋊Dic61—28no—
19C22×C4⋊Dic61—24no—
20C22×C4⋊Dic61C2212yes—
21C22×C4⋊Dic61C2211yescharacteristic
22C22×C4⋊Dic61C2212yes—
23C22×C4⋊Dic61C2212yes—
24C22×#11758196C2211yescharacteristic
25C22×#11758196C2211yescharacteristic
26C22×#11758196C2212yes—
27C22×C22⋊Dic61C2211yescharacteristic
28C22×C22⋊Dic61C2211yescharacteristic
29#16839683—28no—
30#16839637—24no—
31#16839634—24no—
32C2×#14519684C2212yes—
33C2×#14519684C2212yes—
34C2×#14519684C2212yes—
35C2×#14519684C2212yes—
36C2×#14519684C2212yes—
37C2×#14519684C2212yes—
38C24×C4×C61C2211yescharacteristic
39C22×C22⋊C4×C61C2211yescharacteristic
40C22×C22⋊C4×C61C2211yescharacteristic
41C2×#95×C61C2212yes—
42C2×#95×C61C2212yes—
43C22×Dic122—22no—
44C22×Dic122—22no—
45C22×Dic122—22no—
46C22×Dic122—24no—
47C22×Dic122—42no—
48C23×Dic61—22no—
49C23×Dic61—22no—
50C23×Dic61—22no—
51C23×Dic61—24no—
52C23×Dic61—24no—
53C23×Dic61—22no—
54C23×Dic61—22no—
55C23×Dic61—42no—
56C23×Dic61—42no—
57C23×Dic61D414yes—
58C23×Dic61C2311yescharacteristic
59C23×Dic61C2311yescharacteristic
60C23×Dic61C2312yes—
61C23×Dic61C2311yescharacteristic
62C23×Dic61C2312yes—
63C23×Dic61C2311yescharacteristic
64#14519754—232no—
65C2×C4⋊Dic61—232no—
66C2×C4⋊Dic61—24no—
67C2×C4⋊Dic61—22no—
68C2×C4⋊Dic61—24no—
69C2×C4⋊Dic61—24no—
70C2×C4⋊Dic61—24no—
71C2×C4⋊Dic61—24no—
72C2×C4⋊Dic61—22no—
73C2×C4⋊Dic61—22no—
74C2×C4⋊Dic61—24no—
75C2×C4⋊Dic61—24no—
76C2×C4⋊Dic61—42no—
77C2×C4⋊Dic61D418yes—
78C2×#11758196—22no—
79C2×#11758196—22no—
80C2×#11758196—22no—
81C2×#11758196—22no—
82C2×#11758196—22no—
83C2×#11758196—22no—
84C2×#11758196—24no—
85C2×#11758196—24no—
86C2×#11758196—42no—
87C2×C22⋊Dic61—22no—
88C2×C22⋊Dic61—22no—
89C2×C22⋊Dic61—22no—
90C2×C22⋊Dic61—22no—
91C2×C22⋊Dic61D414yes—
92C2×C22⋊Dic61Q814yescomplemented
93#14519684—24no—
94#14519684—24no—
95#14519684—24no—
96#14519684—24no—
97#14519684—24no—
98#14519684—42no—
99C25×C61C2311yescharacteristic
100C23×C4×C61—22no—
101C23×C4×C61—22no—
102C23×C4×C61—24no—
103C23×C4×C61—24no—
104C23×C4×C61Q814yescomplemented
105C23×C4×C61C2311yescharacteristic
106C23×C4×C61C2311yescharacteristic
107C23×C4×C61C2312yes—
108C23×C4×C61C2312yes—
109C2×C22⋊C4×C61—22no—
110C2×C22⋊C4×C61—22no—
111C2×C22⋊C4×C61—22no—
112C2×C22⋊C4×C61—22no—
113C2×C22⋊C4×C61D414yes—
114C2×C22⋊C4×C61Q814yescomplemented
115#95×C61—24no—
116#95×C61—24no—
117C24×C61—22no—
118C24×C61—22no—
119C24×C61—22no—
120C24×C61—22no—
121C24×C61C2×D412yes—
122C24×C61C2×D412yes—
123C24×C61C2×D412yes—
124C24×C61C2×Q812yes—
125C24×C61C2×Q812yes—
126C24×C61C2×Q812yes—
127C24×C61#4112yes—
128C24×C61C2411yescharacteristic
129C22×C4×C61—216no—
130C22×C4×C61—28no—
131C22×C4×C61—28no—
132C22×C4×C61—28no—
133C22×C4×C61—22no—
134C22×C4×C61—22no—
135C22×C4×C61—22no—
136C22×C4×C61—22no—
137C22×C4×C61—216no—
138C22×C4×C61—22no—
139C22×C4×C61—21no—
140C22×C4×C61—21no—
141C22×C4×C61—22no—
142C22×C4×C61—22no—
143C22×C4×C61—21no—
144C22×C4×C61—21no—
145C22×C4×C61—22no—
146C22×C4×C61—22no—
147C22×C4×C61—22no—
148C22×C4×C61—22no—
149C22×C4×C61—22no—
150C22×C4×C61—22no—
151C22×C4×C61—22no—
152C22×C4×C61C2×D412yes—
153C22×C4×C61C2×D412yes—
154C22×C4×C61C2×D414yes—
155C22×C4×C61C2×Q814yes—
156C22×C4×C61C2×Q814yes—
157C22×C4×C61#4114yes—
158C22×Dic61—21no—
159C22×Dic61—21no—
160C22×Dic61—22no—
161C22×Dic61—28no—
162C22×Dic61—28no—
163C22×Dic61—22no—
164C22×Dic61—22no—
165C22×Dic61—21no—
166C22×Dic61—21no—
167C22×Dic61—22no—
168C22×Dic61—22no—
169C22×Dic61—22no—
170C22×Dic61—22no—
171C22×Dic61—21no—
172C22×Dic61—21no—
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×Dic61—22no—
185C22×Dic61—22no—
186C22×Dic61—22no—
187C22×Dic61—28no—
188C22×Dic61—44no—
189C22×Dic61—48no—
190C22×Dic61—48no—
191C22×Dic61—48no—
192C22×Dic61—48no—
193C22×Dic61—44no—
194C22×Dic61—44no—
195C22×Dic61C2×D414yes—
196C22×Dic61C2×D412yes—
197C22×Dic61C2×D412yes—
198C22×Dic61C2×D412yes—
199C22×Dic61C2×D414yes—
200C22×Dic61C2×D412yes—
201C22×Dic61C2×Q814yes—
202C2×Dic122—28no—
203C2×Dic122—48no—
204C2×Dic122—48no—
205C2×Dic122—44no—
206C2×Dic122—44no—
207C22⋊C4×C61—28no—
208C22⋊C4×C61—28no—
209C22⋊Dic61—28no—
210C22⋊Dic61—28no—
211C4⋊Dic61—216no—
212C4⋊Dic61—28no—
213C4⋊Dic61—216no—
214C4⋊Dic61—48no—
215#11758196—28no—
216#11758196—28no—
217#11758196—48no—
218C23×C61—22no—
219C23×C61—24no—
220C23×C61—22no—
221C23×C61—24no—
222C23×C61—22no—
223C23×C61—22no—
224C23×C61—24no—
225C23×C61—24no—
226C23×C61—24no—
227C23×C61—24no—
228C23×C61—24no—
229C23×C61—24no—
230C23×C61—24no—
231C23×C61—24no—
232C23×C61—24no—
233C23×C61—24no—
234C23×C61#12014yes—
235C23×C61C22⋊Q814yes—
236C23×C61C22⋊Q814yes—
237C23×C61C22⋊Q814yes—
238C23×C61C4⋊Q814yes—
239C23×C61C4⋊Q814yes—
240C23×C61C4⋊Q814yes—
241C23×C61C22×D411yescharacteristic
242C23×C61C22×D412yes—
243C23×C61C22×D411yescharacteristic
244C23×C61C22×D411yescharacteristic
245C23×C61C22×Q811yescharacteristic
246C23×C61C22×Q811yescharacteristic
247C23×C61C22×Q811yescharacteristic
248C23×C61C2×#4111yescharacteristic
249C23×C61C2×#4112yes—
250C23×C61H(5,𝔽2)12yes—
251C23×C612−1+412yes—
252C2×C4×C61—232no—
253C2×C4×C61—24no—
254C2×C4×C61—24no—
255C2×C4×C61—24no—
256C2×C4×C61—24no—
257C2×C4×C61—24no—
258C2×C4×C61—24no—
259C2×C4×C61—22no—
260C2×C4×C61—22no—
261C2×C4×C61—24no—
262C2×C4×C61—24no—
263C2×C4×C61—24no—
264C2×C4×C61—24no—
265C2×C4×C61—24no—
266C2×C4×C61—41no—
267C2×C4×C61—41no—
268C2×C4×C61—42no—
269C2×C4×C61—41no—
270C2×C4×C61—41no—
271C2×C4×C61—42no—
272C2×C4×C61—42no—
273C2×C4×C61—42no—
274C2×C4×C61—42no—
275C2×C4×C61—42no—
276C2×C4×C61C22⋊Q818yescomplemented
277C2×Dic61—22no—
278C2×Dic61—22no—
279C2×Dic61—24no—
280C2×Dic61—24no—
281C2×Dic61—22no—
282C2×Dic61—22no—
283C2×Dic61—22no—
284C2×Dic61—24no—
285C2×Dic61—22no—
286C2×Dic61—24no—
287C2×Dic61—22no—
288C2×Dic61—24no—
289C2×Dic61—24no—
290C2×Dic61—24no—
291C2×Dic61—24no—
292C2×Dic61—24no—
293C2×Dic61—24no—
294C2×Dic61—416no—
295C2×Dic61—416no—
296C2×Dic61—41no—
297C2×Dic61—42no—
298C2×Dic61—41no—
299C2×Dic61—42no—
300C2×Dic61—41no—
301C2×Dic61—42no—
302C2×Dic61—41no—
303C2×Dic61—42no—
304C2×Dic61—42no—
305C2×Dic61—42no—
306C2×Dic61—42no—
307C2×Dic61—42no—
308C2×Dic61—42no—
309C2×Dic61—42no—
310C2×Dic61—42no—
311C2×Dic61—42no—
312C2×Dic61#12014yes—
313Dic122—416no—
314#14720—611nomaximal, Sylow
315C22×C61—24no—
316C22×C61—24no—
317C22×C61—24no—
318C22×C61—24no—
319C22×C61—24no—
320C22×C61—24no—
321C22×C61—28no—
322C22×C61—28no—
323C22×C61—28no—
324C22×C61—28no—
325C22×C61#39518yescomplemented
326C22×C61C2×#12011yescharacteristic
327C22×C61C2×#12011yescharacteristic
328C22×C61C2×C22⋊Q811yescharacteristic
329C22×C61C2×C22⋊Q812yes—
330C22×C61C2×C22⋊Q811yescharacteristic
331C22×C61C2×C22⋊Q811yescharacteristic
332C22×C61#52511yescharacteristic
333C22×C61#52512yes—
334C22×C61C2×C4⋊Q811yescharacteristic
335C22×C61C2×C4⋊Q811yescharacteristic
336C22×C61C2×C4⋊Q811yescharacteristic
337C22×C61#53411yescharacteristic
338C22×C61#53611yescharacteristic
339C22×C61#53912yes—
340C22×C61#54412yes—
341C22×C61D4212yes—
342C22×C61D4212yes—
343C22×C61#54712yes—
344C22×C61#54712yes—
345C22×C61D4×Q812yes—
346C22×C61D4×Q812yes—
347C22×C61#55412yes—
348C22×C61#55412yes—
349C4×C61—28no—
350C4×C61—42no—
351C4×C61—42no—
352C4×C61—44no—
353Dic61—24no—
354Dic61—42no—
355Dic61—42no—
356Dic61—44no—
357Dic61—42no—
358Dic61—44no—
359C22×C22⋊Q8—611no—
360C23×C4⋊C4—611no—
361C2×#395—612no—
362C2×#385—611no—
363C2×#385—611no—
364#1444—612no—
365#1444—612no—
366#1441—612no—
367C22⋊#95—611no—
368C22⋊#95—611no—
369C22⋊#95D6111yescharacteristic
370C2×C61—28no—
371C2×C61C2×#39511yescharacteristic
372C2×C61#240311yescharacteristic
373C2×C61#240611yescharacteristic
374C2×C61#243411yescharacteristic
375C2×C61#244012yes—
376C2×C61#244012yes—
377C2×C61#244912yes—
378C2×C61#244912yes—
379C2×C61#258311yescharacteristic
380C2×C61#262711yescharacteristic
381C2×C61#284811yescharacteristic
382C23×Q8—611no—
383C24×C4—611no—
384C24×C4—611no—
385C24×C4C2×D6111yescharacteristic
386C2×C22⋊Q8—1224no—
387C2×C22⋊Q8—1224no—
388C2×C22⋊Q8—1224no—
389C22×C4⋊C4—612no—
390C22×C4⋊C4—611no—
391C22×C4⋊C4—611no—
392C22×C4⋊C4—612no—
393C22×C4⋊C4—611no—
394C22×C4⋊C4—612no—
395C22×C4⋊C4—612no—
396C22×C4⋊C4—1228no—
397C22×C4⋊C4—1224no—
398C22×C22⋊C4—611no—
399C22×C22⋊C4—611no—
400C22×C22⋊C4C2×D6111yescharacteristic
401C22×C22⋊C4C2×D6111yescharacteristic
402#395—1228no—
403#385—1224no—
404#385—1224no—
405C2×#95—612no—
406C2×#95—612no—
407C2×#95—612no—
408C2×#95—612no—
409C2×#95—612no—
410C2×#95—612no—
411C2×#95C2×D6112yes—
412C2×#95C2×D6112yes—
413C61#1472011yescharacteristic, complemented, Sylow
414C25C22×D6111yescharacteristic
415C22×Q8—1222no—
416C22×Q8—1222no—
417C22×Q8—1224no—
418C22×Q8—1222no—
419C22×Q8—2442no—
420C23×C4—22no—
421C23×C4—22no—
422C23×C4—24no—
423C23×C4—24no—
424C23×C4—611no—
425C23×C4—611no—
426C23×C4—611no—
427C23×C4—612no—
428C23×C4—612no—
429C23×C4—611no—
430C23×C4—614no—
431C23×C4—1224no—
432C23×C4—1224no—
433C23×C4—1222no—
434C23×C4—1222no—
435C23×C4—1222no—
436C23×C4—1222no—
437C23×C4—1222no—
438C23×C4—2442no—
439C23×C4—2442no—
440C23×C4Dic12214yescomplemented
441C23×C4C22×D6112yes—
442C23×C4C22×D6111yescharacteristic
443C23×C4C22×D6111yescharacteristic
444C23×C4C22×D6112yes—
445C22⋊Q8—12232no—
446C2×C4⋊C4—618no—
447C2×C4⋊C4—1224no—
448C2×C4⋊C4—1224no—
449C2×C4⋊C4—1224no—
450C2×C4⋊C4—1224no—
451C2×C4⋊C4—1222no—
452C2×C4⋊C4—1222no—
453C2×C4⋊C4—1222no—
454C2×C4⋊C4—1222no—
455C2×C4⋊C4—1222no—
456C2×C4⋊C4—1222no—
457C2×C4⋊C4—12232no—
458C2×C4⋊C4—1222no—
459C2×C4⋊C4—1222no—
460C2×C4⋊C4—1222no—
461C2×C4⋊C4—1224no—
462C2×C4⋊C4—1224no—
463C2×C4⋊C4—1224no—
464C2×C4⋊C4—1224no—
465C2×C4⋊C4—1224no—
466C2×C4⋊C4—2442no—
467C2×C4⋊C4—2442no—
468C2×C22⋊C4—22no—
469C2×C22⋊C4—22no—
470C2×C22⋊C4—22no—
471C2×C22⋊C4—22no—
472C2×C22⋊C4—614no—
473C2×C22⋊C4—614no—
474C2×C22⋊C4—1222no—
475C2×C22⋊C4—1222no—
476C2×C22⋊C4—1222no—
477C2×C22⋊C4—1222no—
478C2×C22⋊C4Dic12214yescomplemented
479C2×C22⋊C4D24414yes—
480#95—24no—
481#95—24no—
482#95—1224no—
483#95—1224no—
484#95—1224no—
485#95—1224no—
486#95—1224no—
487#95—2442no—
488C24—22no—
489C24—22no—
490C24—22no—
491C24—22no—
492C24C2×Dic12212yes—
493C24C2×Dic12212yes—
494C24C2×D24412yes—
495C24D4×D6112yes—
496C24D4×D6112yes—
497C24#1175822412yes—
498C24Q8×D6112yes—
499C24C23×D6111yescharacteristic
500C2×Q8—1228no—
501C2×Q8—2448no—
502C2×Q8—2444no—
503C2×Q8—2448no—
504C2×Q8—2444no—
505C22×C4—28no—
506C22×C4—216no—
507C22×C4—28no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—28no—
513C22×C4—216no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—614no—
529C22×C4—612no—
530C22×C4—612no—
531C22×C4—612no—
532C22×C4—614no—
533C22×C4—612no—
534C22×C4—614no—
535C22×C4—1228no—
536C22×C4—1221no—
537C22×C4—1221no—
538C22×C4—1222no—
539C22×C4—1228no—
540C22×C4—1222no—
541C22×C4—1222no—
542C22×C4—1222no—
543C22×C4—1221no—
544C22×C4—1221no—
545C22×C4—1222no—
546C22×C4—1222no—
547C22×C4—1222no—
548C22×C4—1221no—
549C22×C4—1222no—
550C22×C4—1222no—
551C22×C4—1221no—
552C22×C4—1221no—
553C22×C4—1221no—
554C22×C4—1222no—
555C22×C4—1222no—
556C22×C4—1222no—
557C22×C4—1222no—
558C22×C4—1222no—
559C22×C4—1222no—
560C22×C4—1222no—
561C22×C4—1222no—
562C22×C4—1222no—
563C22×C4—1222no—
564C22×C4—1228no—
565C22×C4—2444no—
566C22×C4—2448no—
567C22×C4—2448no—
568C22×C4—2448no—
569C22×C4—2448no—
570C22×C4—2444no—
571C22×C4—2444no—
572C22×C4C2×Dic12214yes—
573C22×C4C2×Dic12214yes—
574C22×C4C2×D24412yes—
575C22×C4C2×D24412yes—
576C22×C4D4×D6114yes—
577C22×C4#1175822414yes—
578C4⋊C4—12216no—
579C4⋊C4—12216no—
580C4⋊C4—1228no—
581C4⋊C4—1228no—
582C4⋊C4—1228no—
583C4⋊C4—2448no—
584C4⋊C4—2448no—
585C22⋊C4—28no—
586C22⋊C4—28no—
587C22⋊C4—1228no—
588C22⋊C4—1228no—
589C23—24no—
590C23—24no—
591C23—22no—
592C23—24no—
593C23—22no—
594C23—24no—
595C23—22no—
596C23—22no—
597C23—24no—
598C23—24no—
599C23—24no—
600C23—24no—
601C23—24no—
602C23—24no—
603C23—24no—
604C23—24no—
605C23#1451974714yes—
606C23#1451975414yes—
607C23#1451975414yes—
608C23#1451975714yes—
609C23#1451977614yes—
610C23#1451977614yes—
611C23#1451977714yes—
612C23C2×D4×D6111yescharacteristic
613C23C2×D4×D6112yes—
614C23C2×D4×D6111yescharacteristic
615C23C22×D24411yescharacteristic
616C23C2×Q8×D6111yescharacteristic
617C23C22×Dic12211yescharacteristic
618C23C22×Dic12211yescharacteristic
619C23C2×#1175822412yes—
620C23C2×#1175822411yescharacteristic
621C23#1451982312yes—
622C23#1451982412yes—
623Q8—24416no—
624C2×C4—232no—
625C2×C4—24no—
626C2×C4—24no—
627C2×C4—24no—
628C2×C4—24no—
629C2×C4—24no—
630C2×C4—24no—
631C2×C4—24no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—24no—
635C2×C4—24no—
636C2×C4—24no—
637C2×C4—24no—
638C2×C4—41no—
639C2×C4—42no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—42no—
644C2×C4—42no—
645C2×C4—42no—
646C2×C4—42no—
647C2×C4—42no—
648C2×C4—614no—
649C2×C4—1222no—
650C2×C4—1222no—
651C2×C4—1224no—
652C2×C4—1224no—
653C2×C4—1224no—
654C2×C4—1224no—
655C2×C4—1222no—
656C2×C4—1222no—
657C2×C4—1222no—
658C2×C4—1222no—
659C2×C4—1224no—
660C2×C4—1222no—
661C2×C4—1224no—
662C2×C4—1224no—
663C2×C4—1224no—
664C2×C4—1224no—
665C2×C4—1224no—
666C2×C4—24416no—
667C2×C4—24416no—
668C2×C4—2441no—
669C2×C4—2442no—
670C2×C4—2442no—
671C2×C4—2441no—
672C2×C4—2442no—
673C2×C4—2441no—
674C2×C4—2441no—
675C2×C4—2442no—
676C2×C4—2442no—
677C2×C4—2442no—
678C2×C4—2442no—
679C2×C4—2442no—
680C2×C4—2442no—
681C2×C4—2442no—
682C2×C4—2442no—
683C2×C4—2442no—
684C2×C4#1451975418yescomplemented
685C22—24no—
686C22—28no—
687C22—28no—
688C22—24no—
689C22—28no—
690C22—28no—
691C22—24no—
692C22—24no—
693C22—24no—
694C22—24no—
695C22#1683968318yescomplemented
696C22#120×D6111yescharacteristic
697C22C2×#1451974711yescharacteristic
698C22C2×#1451975412yes—
699C22C2×#1451975411yescharacteristic
700C22C2×#1451975411yescharacteristic
701C22C2×#1451975711yescharacteristic
702C22#1684026812yes—
703C22#1684026811yescharacteristic
704C22C2×#1451977611yescharacteristic
705C22C2×#1451977611yescharacteristic
706C22C2×#1451977711yescharacteristic
707C22#1684032311yescharacteristic
708C22#1684033411yescharacteristic
709C22#1684035612yes—
710C22#1684039012yes—
711C22#1684039612yes—
712C22D4×D24412yes—
713C22#1684041212yes—
714C22#1684041612yes—
715C22#1684042512yes—
716C22D4×Dic12212yes—
717C22#1684046912yes—
718C22#1684047012yes—
719C4—28no—
720C4—44no—
721C4—42no—
722C4—42no—
723C4—1224no—
724C4—2444no—
725C4—2442no—
726C4—2444no—
727C4—2442no—
728C4—2442no—
729C2—28no—
730C2C2×#1683968311yescharacteristic
731C2#2144913111yescharacteristic
732C2#2144915311yescharacteristic
733C2#2144946111yescharacteristic
734C2#2144952112yes—
735C2#2144952212yes—
736C2#2144962612yes—
737C2#2144963412yes—
738C2#2145119611yescharacteristic
739C2#2145163611yescharacteristic
740C2#2145410411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutator, socle, cosocleC24×C61C24
FittingC61×C22⋊#95C2
prime radicalC25×C61C23
hypercenterC22⋊#95D61
hypocenterC61#14720
LCSG ▷ C24×C61 ▷ C61
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
3. C2×#16839683C2semidirect
6. #21444084C2semidirect
7. #21444083C2semidirect
8. #21444071C2semidirect
92. C2×C22⋊Dic61Q8semidirect
104. C23×C4×C61Q8semidirect
114. C2×C22⋊C4×C61Q8semidirect
276. C2×C4×C61C22⋊Q8semidirect
325. C22×C61#395semidirect
413. C61#14720semidirect
440. C23×C4Dic122semidirect
478. C2×C22⋊C4Dic122semidirect
684. C2×C4#14519754semidirect
695. C22#16839683semidirect

Maximal subgroups

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

subgroupindex
C22×#145197542
C23×C4⋊Dic612
C2×#168396832
C2×#168396372
C2×#168396342
#214440842
#214440832
#214440712
#214440422
#214440412
C61×C22⋊#952
#1472061