Finite Group Databasebeta

← #29708171

Subgroups — #29708171

Order 15616.

1240 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840316C211yesmaximal, characteristic, complemented
2C2×C4×#11758200C211yesmaximal, characteristic, complemented
3C4×#14519748C211yesmaximal, characteristic
4#21447150C211yesmaximal, characteristic, complemented
5#21447063C211yesmaximal, characteristic, complemented
6#21447017C211yesmaximal, characteristic, complemented
7#21447013C211yesmaximal, characteristic, complemented
8#21446953C211yesmaximal, characteristic, complemented
9#21446900C211yesmaximal, characteristic, complemented
10#21446823C211yesmaximal, characteristic
11#21446819C211yesmaximal, characteristic
12C4×#14519702C211yesmaximal, characteristic, complemented
13C4×#14519701C211yesmaximal, characteristic, complemented
14C4×#14519689C211yesmaximal, characteristic, complemented
15C2×C4×SD16×C61C211yesmaximal, characteristic, complemented
16C22×#11758200C2211yescharacteristic
17#16840316—24no—
18#16840316—24no—
19C2×#14519776C2211yescharacteristic
20C2×#14519775C2211yescharacteristic
21C2×#14519767—21no—
22C2×#14519757C2211yescharacteristic
23C2×#14519755—21no—
24C2×#14519753C2211yescharacteristic
25C2×#14519748C2211yescharacteristic
26C2×C4×Dic122—21no—
27C2×C4×Dic122C2211yescharacteristic
28C2×C4×C22⋊D61—21no—
29C2×#14519734—21no—
30C2×C42×D61C2211yescharacteristic
31C4×#11758200—24no—
32C2×#14519708C2211yescharacteristic
33C2×#14519702C2211yescharacteristic
34C2×#14519702C2211yescharacteristic
35C2×#14519701C2211yescharacteristic
36C2×#14519701C2211yescharacteristic
37C2×#14519700C2211yescharacteristic
38C2×#14519698C2211yescharacteristic
39C2×#14519689C2211yescharacteristic
40C2×#14519689C2211yescharacteristic
41C2×C4×#92418C2211yescharacteristic
42#16839665C2211yescharacteristic
43#16839658C2211yescharacteristic
44#16839650—21no—
45#16839638—21no—
46#16839619C2211yescharacteristic
47C4×C4⋊Dic61C2211yescharacteristic
48C4×C22⋊Dic61—21no—
49#16839525C2211yescharacteristic
50#16839525C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839524C2211yescharacteristic
53#16839516C2211yescharacteristic
54#16839516C2211yescharacteristic
55C22×SD16×C61C2211yescharacteristic
56C2×C4×Q8×C61C2211yescharacteristic
57C2×C4×D4×C61C2211yescharacteristic
58C4×SD16×C61—24no—
59C2×#106×C61C2211yescharacteristic
60C2×#103×C61C2211yescharacteristic
61C2×#102×C61C2211yescharacteristic
62C2×C4×C8×C61C2211yescharacteristic
63C22×Dic122—21no—
64C22×Dic122C2311yescharacteristic
65C22×C22⋊D61—21no—
66C22×C4×D61D411yescharacteristic
67C22×C4×D61D411yescharacteristic
68C22×C4×D61C2311yescharacteristic
69C2×#11758200—22no—
70C2×#11758200—22no—
71C2×#11758200—22no—
72C22×#92418C2311yescharacteristic
73C22×#92418C2311yescharacteristic
74#14519776—22no—
75#14519776—22no—
76#14519775—22no—
77#14519775—22no—
78#14519767—28no—
79#14519757—22no—
80#14519757—22no—
81#14519755—28no—
82#14519753—22no—
83#14519753—22no—
84#14519748—22no—
85#14519748—22no—
86C4×Dic122—28no—
87C4×Dic122—22no—
88C4×Dic122D414yescomplemented
89C4×C22⋊D61—44no—
90#14519734—28no—
91C2×C4⋊Dic61—21no—
92C2×C4⋊Dic61C2311yescharacteristic
93C2×C4⋊Dic61C2311yescharacteristic
94C2×C4⋊Dic61C2311yescharacteristic
95C2×#11758196—21no—
96C2×#11758196—21no—
97C2×#11758196—21no—
98C2×#11758196—21no—
99C2×#11758196—21no—
100C2×#11758196—21no—
101C2×C22⋊Dic61—21no—
102C2×C22⋊Dic61—21no—
103C2×C22⋊Dic61—21no—
104C2×#11758198—21no—
105C2×#11758198—21no—
106C2×#11758198—21no—
107C2×C4×Dic61—21no—
108C2×C4×Dic61—21no—
109C2×C4×Dic61D411yescharacteristic
110C2×C4×Dic61D411yescharacteristic
111C2×C4×Dic61C2311yescharacteristic
112C42×D61—22no—
113C42×D61—22no—
114#14519708—22no—
115#14519702—22no—
116#14519702—22no—
117#14519701—22no—
118#14519701—22no—
119#14519700—22no—
120#14519698—22no—
121#14519689—22no—
122#14519689—22no—
123C4×#92418—22no—
124#14519684—21no—
125#14519684—21no—
126#14519684—21no—
127C22×Q8×C61C2311yescharacteristic
128C22×D4×C61C2311yescharacteristic
129C23×C4×C61—21no—
130C2×SD16×C61—22no—
131C2×SD16×C61—22no—
132C2×SD16×C61—22no—
133C22×C8×C61C2311yescharacteristic
134C22×C8×C61C2311yescharacteristic
135C4×Q8×C61—22no—
136C4×Q8×C61D414yescomplemented
137C4×D4×C61—22no—
138C4×D4×C61—22no—
139C2×C4⋊C4×C61—21no—
140C2×C4⋊C4×C61C2311yescharacteristic
141C2×C4⋊C4×C61C2311yescharacteristic
142C2×C22⋊C4×C61—21no—
143C2×C42×C61—21no—
144C2×C42×C61C2311yescharacteristic
145#106×C61—22no—
146#103×C61—22no—
147#102×C61—22no—
148C4×C8×C61—22no—
149C24×C61—21no—
150C23×D61C2×D411yescharacteristic
151C2×Q8×C61—21no—
152C2×Q8×C61—21no—
153C2×Q8×C61—21no—
154C2×Q8×C61—21no—
155C2×Q8×C61—21no—
156C2×Q8×C61C2×D412yes—
157C2×D4×C61—21no—
158C2×D4×C61—21no—
159C2×D4×C61—21no—
160C2×D4×C61—21no—
161C2×D4×C61—21no—
162C2×D4×C61#4112yes—
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61—21no—
166C22×C4×C61—42no—
167C22×C4×C61—42no—
168C22×C4×C61—42no—
169C22×C4×C61C2×D411yescharacteristic
170C22×C4×C61C2×D411yescharacteristic
171C22×C4×C61C2411yescharacteristic
172C2×C22⋊D61—24no—
173C2×C22⋊D61—42no—
174C2×C22⋊D61—42no—
175C22×Dic61—21no—
176C22×Dic61—21no—
177C22×Dic61—21no—
178C22×Dic61—21no—
179C22×Dic61C2×D411yescharacteristic
180C22×Dic61C2×D411yescharacteristic
181C22×Dic61C2×D411yescharacteristic
182C2×C4×D61—22no—
183C2×C4×D61—22no—
184C2×C4×D61—22no—
185C2×C4×D61—21no—
186C2×C4×D61—21no—
187C2×C4×D61—21no—
188C2×C4×D61—21no—
189C2×C4×D61—21no—
190C2×C4×D61—21no—
191C2×C4×D61—22no—
192C2×C4×D61—41no—
193C2×C4×D61SD1614yescomplemented
194C2×Dic122—21no—
195C2×Dic122—21no—
196C2×Dic122—21no—
197C2×Dic122—21no—
198C2×Dic122—24no—
199C2×Dic122—21no—
200C2×Dic122—42no—
201C2×Dic122—42no—
202C2×Dic122C2×D412yes—
203SD16×C61—28no—
204C2×C8×C61—21no—
205C2×C8×C61—21no—
206C2×C8×C61—21no—
207C2×C8×C61—21no—
208C2×C8×C61—21no—
209C2×C8×C61#4112yes—
210C4⋊C4×C61—24no—
211C4⋊C4×C61—21no—
212C4⋊C4×C61—21no—
213C4⋊C4×C61—21no—
214C4⋊C4×C61C2×D412yes—
215C22⋊C4×C61—42no—
216C42×C61—24no—
217C42×C61C2×D412yes—
218C42×C61C2×D412yes—
219C22⋊Dic61—24no—
220C22⋊Dic61—42no—
221C22⋊Dic61—42no—
222#11758200—28no—
223#11758198—24no—
224#11758198—24no—
225#11758198—42no—
226C4⋊Dic61—24no—
227C4⋊Dic61—21no—
228C4⋊Dic61—21no—
229C4⋊Dic61—21no—
230C4⋊Dic61—21no—
231C4⋊Dic61C2×D412yes—
232C4⋊Dic61#4112yes—
233#11758196—24no—
234#11758196—24no—
235#11758196—24no—
236#11758196—24no—
237#11758196—24no—
238#11758196—42no—
239C4×Dic61—22no—
240C4×Dic61—22no—
241C4×Dic61—24no—
242C4×Dic61—21no—
243C4×Dic61—21no—
244C4×Dic61—42no—
245C2×#92418—21no—
246C2×#92418—21no—
247C2×#92418—21no—
248C2×#92418—21no—
249C2×#92418—21no—
250C2×#92418#4112yes—
251C23×C61—22no—
252C23×C61—41no—
253C23×C61—41no—
254C23×C61—41no—
255C23×C61—41no—
256C23×C61—41no—
257C23×C61—41no—
258C23×C61C22×D411yescharacteristic
259C22×D61—21no—
260C22×D61—21no—
261C22×D61—21no—
262C22×D61—21no—
263C22×D61—21no—
264C22×D61—21no—
265C22×D61C2×SD1612yes—
266Q8×C61—22no—
267Q8×C61—22no—
268Q8×C61—41no—
269Q8×C61—41no—
270D4×C61—22no—
271D4×C61—22no—
272D4×C61—41no—
273D4×C61—41no—
274C2×C4×C61—21no—
275C2×C4×C61—21no—
276C2×C4×C61—22no—
277C2×C4×C61—22no—
278C2×C4×C61—41no—
279C2×C4×C61—41no—
280C2×C4×C61—41no—
281C2×C4×C61—41no—
282C2×C4×C61—41no—
283C2×C4×C61—41no—
284C2×C4×C61—41no—
285C2×C4×C61—84no—
286C2×C4×C61#12012yes—
287C2×C4×C61#12012yes—
288C2×C4×C61C2×SD1612yes—
289C2×C4×C61#13712yes—
290C2×C4×C61C22×D411yescharacteristic
291C2×C4×C61C22×D411yescharacteristic
292C2×C4×C61C2×#4111yescharacteristic
293C2×C4×C61C2×#4111yescharacteristic
294C2×C4×C61C2×#4111yescharacteristic
295C2×C4×C61C2×#4111yescharacteristic
296C22⋊D61—48no—
297C2×Dic61—21no—
298C2×Dic61—21no—
299C2×Dic61—21no—
300C2×Dic61—21no—
301C2×Dic61—21no—
302C2×Dic61—22no—
303C2×Dic61—22no—
304C2×Dic61—22no—
305C2×Dic61—21no—
306C2×Dic61—21no—
307C2×Dic61—41no—
308C2×Dic61—41no—
309C2×Dic61—41no—
310C2×Dic61—41no—
311C2×Dic61—41no—
312C2×Dic61—41no—
313C2×Dic61—41no—
314C2×Dic61—41no—
315C2×Dic61—41no—
316C2×Dic61C2×SD1612yes—
317C2×Dic61#13512yes—
318C4×D61—28no—
319C4×D61—44no—
320C4×D61—41no—
321C4×D61—41no—
322C4×D61—41no—
323C4×D61—41no—
324Dic122—22no—
325Dic122—22no—
326Dic122—48no—
327Dic122—41no—
328Dic122—41no—
329C8×C61—22no—
330C8×C61—41no—
331#92418—22no—
332#92418—41no—
333#23568—611nomaximal, Sylow
334C22×C61—42no—
335C22×C61—42no—
336C22×C61—42no—
337C22×C61—81no—
338C22×C61—81no—
339C22×C61—81no—
340C22×C61—81no—
341C22×C61C2×#12011yescharacteristic
342C22×C61#52511yescharacteristic
343C22×C61#53211yescharacteristic
344C22×C61C22×SD1611yescharacteristic
345C22×C61C2×#13511yescharacteristic
346C22×C61C2×#13711yescharacteristic
347C22×C61#57511yescharacteristic
348C2×D61—22no—
349C2×D61—22no—
350C2×D61—22no—
351C2×D61—41no—
352C2×D61—41no—
353C2×D61—41no—
354C2×D61—41no—
355C4×C61—22no—
356C4×C61—42no—
357C4×C61—42no—
358C4×C61—81no—
359C4×C61#44814yes—
360C4×C61#52511yescharacteristic
361C4×C61#52511yescharacteristic
362C4×C61#53211yescharacteristic
363C4×C61#53211yescharacteristic
364Dic61—22no—
365Dic61—22no—
366Dic61—42no—
367Dic61—42no—
368Dic61—41no—
369Dic61—42no—
370Dic61—81no—
371C2×#533—611no—
372C2×C4×SD16—611no—
373C2×C4×SD16D6111yescharacteristic, complemented
374C4×#121—611no—
375#2058—611no—
376#2043—611no—
377#2035—611no—
378#2035—611no—
379#2023—611no—
380#2013—611no—
381#2000—611no—
382#2000—611no—
383C4×#103—611no—
384C4×#103—611no—
385C4×C22⋊C8—611no—
386C2×C61—82no—
387C2×C61#238811yescharacteristic
388C2×C61C2×#44811yescharacteristic
389C2×C61#300211yescharacteristic
390C2×C61#310111yescharacteristic
391C2×C61#310711yescharacteristic
392C2×C61#316711yescharacteristic
393C2×C61#317211yescharacteristic
394D61—42no—
395C22×SD16—611no—
396C22×SD16C2×D6111yescharacteristic
397#533—1224no—
398#533—1224no—
399C2×C4⋊Q8—611no—
400C2×C4⋊Q8—611no—
401C2×#125—1221no—
402C2×C22⋊Q8—611no—
403C2×C22⋊Q8—611no—
404C2×C22⋊Q8—1221no—
405C2×#121—611no—
406C2×C4×Q8—611no—
407C2×C4×Q8—1221no—
408C2×C4×Q8C2×D6111yescharacteristic
409C2×C4×D4—1221no—
410C2×C4×D4C2×D6111yescharacteristic
411C2×#117—1221no—
412C22×C42—611no—
413C4×SD16—24no—
414C4×SD16—1224no—
415C2×#106—611no—
416C2×#106C2×D6111yescharacteristic
417C2×#103—611no—
418C2×#103—611no—
419C2×#103—611no—
420C2×#103—611no—
421C2×#103—611no—
422C2×#103C2×D6111yescharacteristic
423C2×#102—611no—
424C2×#102C2×D6111yescharacteristic
425C2×C22⋊C8—611no—
426C2×C22⋊C8—611no—
427C2×C4×C8—611no—
428C2×C4×C8C2×D6111yescharacteristic
429#390—611no—
430#389—611no—
431#388—1221no—
432#386—1221no—
433#380—611no—
434C4×C4⋊C4—611no—
435C4×C22⋊C4—1221no—
436#340—611no—
437#340—611no—
438#340—611no—
439#340—611no—
440#336—611no—
441#336—611no—
442C61#2356811yescharacteristic, complemented, Sylow
443C22×Q8—611no—
444C22×Q8—1221no—
445C22×Q8C22×D6111yescharacteristic
446C22×D4—1221no—
447C22×D4C22×D6111yescharacteristic
448C23×C4—21no—
449C23×C4—611no—
450C23×C4—611no—
451C23×C4—611no—
452C2×SD16—22no—
453C2×SD16—22no—
454C2×SD16—22no—
455C2×SD16—1222no—
456C2×SD16—1222no—
457C2×SD16—1222no—
458C22×C8—611no—
459C22×C8—611no—
460C22×C8C22×D6111yescharacteristic
461C22×C8C22×D6111yescharacteristic
462C4⋊Q8—1222no—
463C4⋊Q8—1222no—
464C4⋊Q8—1222no—
465C4⋊Q8—1222no—
466#125—1228no—
467C22⋊Q8—1222no—
468C22⋊Q8—1228no—
469C22⋊Q8—1222no—
470C22⋊Q8—1222no—
471C22⋊Q8—1222no—
472#121—1222no—
473#121—1222no—
474C4×Q8—22no—
475C4×Q8—614no—
476C4×Q8—1228no—
477C4×Q8—1222no—
478C4×Q8C22⋊D6114yescomplemented
479C4×D4—22no—
480C4×D4—22no—
481C4×D4—2444no—
482#117—1228no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—611no—
485C2×C4⋊C4—611no—
486C2×C4⋊C4—611no—
487C2×C4⋊C4—1221no—
488C2×C4⋊C4—1221no—
489C2×C4⋊C4—1221no—
490C2×C4⋊C4—1221no—
491C2×C4⋊C4—1221no—
492C2×C4⋊C4—1221no—
493C2×C4⋊C4—1221no—
494C2×C4⋊C4C22×D6111yescharacteristic
495C2×C4⋊C4C22×D6111yescharacteristic
496C2×C22⋊C4—21no—
497C2×C22⋊C4—1221no—
498C2×C22⋊C4—1221no—
499C2×C22⋊C4—1221no—
500C2×C22⋊C4—1221no—
501C2×C22⋊C4—1221no—
502C2×C22⋊C4—1221no—
503C2×C42—21no—
504C2×C42—611no—
505C2×C42—611no—
506C2×C42—611no—
507C2×C42—1221no—
508C2×C42—1222no—
509C2×C42—1222no—
510C2×C42—1221no—
511C2×C42C22×D6111yescharacteristic
512#106—22no—
513#106—1222no—
514#103—22no—
515#103—1222no—
516#103—1222no—
517#103—1222no—
518#103—1222no—
519#103—1222no—
520#102—22no—
521#102—1222no—
522C22⋊C8—1222no—
523C22⋊C8—1222no—
524C4×C8—22no—
525C4×C8—1222no—
526#95—1221no—
527#95—1221no—
528#95—1221no—
529C24—21no—
530C24—611no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8—612no—
537C2×Q8—1224no—
538C2×Q8—1221no—
539C2×Q8—1221no—
540C2×Q8—1221no—
541C2×Q8—1221no—
542C2×Q8—1221no—
543C2×Q8—2442no—
544C2×Q8—2442no—
545C2×Q8C2×C22⋊D6112yes—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—1224no—
552C2×D4—2442no—
553C2×D4—2442no—
554C2×D4#1175822212yes—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—611no—
562C22×C4—611no—
563C22×C4—614no—
564C22×C4—611no—
565C22×C4—1222no—
566C22×C4—1222no—
567C22×C4—1222no—
568C22×C4—1221no—
569C22×C4—1221no—
570C22×C4—1221no—
571C22×C4—1221no—
572C22×C4—1221no—
573C22×C4—1221no—
574C22×C4—1221no—
575C22×C4—1221no—
576C22×C4—1221no—
577C22×C4—1222no—
578C22×C4—1221no—
579C22×C4—2441no—
580C22×C4D4×D6111yescharacteristic
581C22×C4D4×D6111yescharacteristic
582C22×C4C23×D6111yescharacteristic
583SD16—28no—
584SD16—1228no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—612no—
591C2×C8—1221no—
592C2×C8—1221no—
593C2×C8—1221no—
594C2×C8—1221no—
595C2×C8—1221no—
596C2×C8#1175822212yes—
597C4⋊C4—21no—
598C4⋊C4—24no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—612no—
602C4⋊C4—612no—
603C4⋊C4—1224no—
604C4⋊C4—1224no—
605C4⋊C4—1224no—
606C4⋊C4—1224no—
607C4⋊C4—1224no—
608C4⋊C4—1221no—
609C4⋊C4—1221no—
610C4⋊C4—1224no—
611C4⋊C4—1221no—
612C4⋊C4—1221no—
613C4⋊C4—2442no—
614C4⋊C4C2×C22⋊D6112yes—
615C22⋊C4—42no—
616C22⋊C4—1224no—
617C22⋊C4—1224no—
618C22⋊C4—1224no—
619C22⋊C4—2442no—
620C22⋊C4—2442no—
621C22⋊C4—2442no—
622C42—24no—
623C42—1221no—
624C42—1221no—
625C42—1222no—
626C42—1222no—
627C42—1224no—
628C42—2442no—
629C42D4×D6112yes—
630C42C2×C22⋊D6112yes—
631C23—22no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—612no—
639C23—1221no—
640C23—1221no—
641C23—1221no—
642C23—1221no—
643C23—1221no—
644C23—1221no—
645C23C2×D4×D6111yescharacteristic
646Q8—22no—
647Q8—22no—
648Q8—41no—
649Q8—41no—
650Q8—1222no—
651Q8—1222no—
652Q8—2448no—
653Q8—2441no—
654Q8—2441no—
655D4—22no—
656D4—22no—
657D4—41no—
658D4—41no—
659D4—2448no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—84no—
672C2×C4—612no—
673C2×C4—612no—
674C2×C4—1221no—
675C2×C4—1221no—
676C2×C4—1221no—
677C2×C4—1221no—
678C2×C4—1228no—
679C2×C4—1221no—
680C2×C4—1222no—
681C2×C4—1222no—
682C2×C4—1221no—
683C2×C4—1222no—
684C2×C4—1221no—
685C2×C4—2444no—
686C2×C4—2441no—
687C2×C4—2441no—
688C2×C4—2441no—
689C2×C4—2441no—
690C2×C4—2441no—
691C2×C4—2441no—
692C2×C4—2441no—
693C2×C4—2441no—
694C2×C4—2441no—
695C2×C4—2441no—
696C2×C4—2441no—
697C2×C4—2441no—
698C2×C4—2441no—
699C2×C4#1451974512yes—
700C2×C4#1451974512yes—
701C2×C4SD16×D6112yes—
702C2×C4#1451980612yes—
703C2×C4C2×D4×D6111yescharacteristic
704C2×C4C22×C22⋊D6111yescharacteristic
705C2×C4#41×D6111yescharacteristic
706C2×C4#41×D6111yescharacteristic
707C2×C4C2×#1175822211yescharacteristic
708C2×C4C2×#1175822211yescharacteristic
709C8—22no—
710C8—41no—
711C8—1222no—
712C8—2441no—
713C22—42no—
714C22—42no—
715C22—42no—
716C22—81no—
717C22—81no—
718C22—81no—
719C22—81no—
720C22—1222no—
721C22—1222no—
722C22—1222no—
723C22—2441no—
724C22—2441no—
725C22—2441no—
726C22—2441no—
727C22C2×#1451974511yescharacteristic
728C22#1684027111yescharacteristic
729C22#1684030911yescharacteristic
730C22C2×SD16×D6111yescharacteristic
731C22#135×D6111yescharacteristic
732C22C2×#1451980611yescharacteristic
733C22#1684055911yescharacteristic
734C4—22no—
735C4—42no—
736C4—42no—
737C4—81no—
738C4—1222no—
739C4—1222no—
740C4—4881no—
741C4—2441no—
742C4—2442no—
743C4—2442no—
744C4—2442no—
745C4#1683989914yes—
746C4#1684027111yescharacteristic
747C4#1684027311yescharacteristic
748C4#1684030811yescharacteristic
749C4#1684030911yescharacteristic
750C2—82no—
751C2—2442no—
752C2#2144903411yescharacteristic
753C2C2×#1683989911yescharacteristic
754C2#2145503311yescharacteristic
755C2#2145582511yescharacteristic
756C2#2145588611yescharacteristic
757C2#2145637511yescharacteristic
758C2#2145642111yescharacteristic
subgroupG/H
centerC22×C4D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C4×SD16×C61C2
socleC23×C61C22×D4
prime radicalC2×#14519748C22
hypercenterC2×C4×SD16D61
hypocenterC61#23568
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#16840316C2semidirect
2. C2×C4×#11758200C2semidirect
4. #21447150C2semidirect
5. #21447063C2semidirect
6. #21447017C2semidirect
7. #21447013C2semidirect
8. #21446953C2semidirect
9. #21446900C2semidirect
12. C4×#14519702C2semidirect
13. C4×#14519701C2semidirect
14. C4×#14519689C2semidirect
15. C2×C4×SD16×C61C2semidirect
88. C4×Dic122D4semidirect
136. C4×Q8×C61D4semidirect
193. C2×C4×D61SD16semidirect
373. C2×C4×SD16D61semidirect
442. C61#23568semidirect
478. C4×Q8C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168403162
C2×C4×#117582002
C4×#145197482
#214471502
#214470632
#214470172
#214470132
#214469532
#214469002
#214468232
#214468192
C4×#145197022
C4×#145197012
C4×#145196892
C2×C4×SD16×C612
#2356861