Finite Group Databasebeta

← #29700279

Subgroups — #29700279

Order 15616.

1170 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839899C211yesmaximal, characteristic
2C2×#103×D61C211yesmaximal, characteristic, complemented
3#21448831C211yesmaximal, characteristic
4Q8×#11758198C211yesmaximal, characteristic, complemented
5#21446701C211yesmaximal, characteristic, complemented
6#21446509C211yesmaximal, characteristic, complemented
7#21446459C211yesmaximal, characteristic, complemented
8#21446244C211yesmaximal, characteristic
9#21446176C211yesmaximal, characteristic, complemented
10#21446153C211yesmaximal, characteristic, complemented
11#21446073C211yesmaximal, characteristic, complemented
12#21446005C211yesmaximal, characteristic, complemented
13#21445651C211yesmaximal, characteristic, complemented
14#21445596C211yesmaximal, characteristic, complemented
15C2×C61×#440C211yesmaximal, characteristic, complemented
16C22×Q8×D61C2211yescharacteristic
17C22×#11758200C2211yescharacteristic
18C22×C8×D61C2211yescharacteristic
19C2×#14519748C2211yescharacteristic
20C2×Q8×Dic61C2211yescharacteristic
21C2×C4×C22⋊D61—21no—
22C2×C4⋊C4×D61C2211yescharacteristic
23#16839899C418yescomplemented
24C2×#14519710C2211yescharacteristic
25C2×#14519702C2211yescharacteristic
26C2×#14519702C2211yescharacteristic
27C2×#14519701C2211yescharacteristic
28C2×#14519701C2211yescharacteristic
29C2×#14519700C2211yescharacteristic
30#103×D61—24no—
31C2×#14519698C2211yescharacteristic
32C2×#14519689C2211yescharacteristic
33C2×#14519687C2211yescharacteristic
34#16839668—21no—
35#16839668C2211yescharacteristic
36#16839667—21no—
37#16839667C2211yescharacteristic
38#16839665C2211yescharacteristic
39#16839660C2211yescharacteristic
40#16839656—21no—
41#16839638—21no—
42#16839635—21no—
43#16839619—21no—
44#16839619C2211yescharacteristic
45C4⋊C4×Dic61C2211yescharacteristic
46C4×#11758198—21no—
47C4×#11758198C2211yescharacteristic
48#16839525C2211yescharacteristic
49#16839525C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839517C2211yescharacteristic
53#16839516C2211yescharacteristic
54C22×SD16×C61C2211yescharacteristic
55C2×C4×Q8×C61C2211yescharacteristic
56C2×C4×D4×C61C2211yescharacteristic
57C61×#440—24no—
58C2×#107×C61C2211yescharacteristic
59C2×#103×C61C2211yescharacteristic
60C2×#102×C61C2211yescharacteristic
61C2×#97×C61C2211yescharacteristic
62C22×Dic122—21no—
63C22×Dic122C2311yescharacteristic
64C2×Q8×D61—22no—
65C2×Q8×D61—22no—
66C2×Q8×D61—22no—
67C2×Q8×D61—41no—
68C2×Q8×D61—41no—
69C2×Q8×D61C2×C414yescomplemented
70C22×C22⋊D61—21no—
71C22×C4×D61—21no—
72C22×C4×D61—21no—
73C22×C4×D61C2311yescharacteristic
74C2×#11758200—41no—
75C2×#11758200—41no—
76C2×#11758200C2×C414yescomplemented
77C22×#92418C2311yescharacteristic
78C22×#92418C2311yescharacteristic
79C2×C8×D61—22no—
80C2×C8×D61—22no—
81C2×C8×D61—41no—
82#14519748—22no—
83#14519748C2×C414yes—
84Q8×Dic61—22no—
85Q8×Dic61—41no—
86C4×C22⋊D61—44no—
87C2×C4⋊Dic61—21no—
88C2×C4⋊Dic61C2311yescharacteristic
89C2×C4⋊Dic61C2311yescharacteristic
90C2×C4⋊Dic61C2311yescharacteristic
91C2×#11758196—21no—
92C2×#11758196—21no—
93C4⋊C4×D61—22no—
94C4⋊C4×D61—41no—
95C2×C22⋊Dic61—21no—
96C2×C22⋊Dic61—21no—
97C2×C22⋊Dic61—21no—
98C2×#11758198—21no—
99C2×#11758198D411yescharacteristic
100C2×#11758198D411yescharacteristic
101C2×C4×Dic61—21no—
102C2×C4×Dic61—21no—
103C2×C4×Dic61C2311yescharacteristic
104#14519710—41no—
105#14519702—22no—
106#14519702C2×C414yescomplemented
107#14519701—22no—
108#14519701C2×C414yescomplemented
109#14519700—22no—
110#14519698—41no—
111#14519689C2×C414yescomplemented
112#14519687—41no—
113#14519684—21no—
114#14519684—21no—
115#14519684—21no—
116#14519684—21no—
117#14519684—21no—
118#14519684—21no—
119#14519684—21no—
120#14519684D411yescharacteristic
121#14519684D411yescharacteristic
122C22×Q8×C61C2311yescharacteristic
123C22×D4×C61C2311yescharacteristic
124C23×C4×C61—21no—
125C2×SD16×C61—22no—
126C2×SD16×C61—22no—
127C2×SD16×C61C2×C414yescomplemented
128C22×C8×C61C2311yescharacteristic
129C22×C8×C61C2311yescharacteristic
130C4×Q8×C61—22no—
131C4×Q8×C61—41no—
132C4×D4×C61—22no—
133C4×D4×C61—41no—
134C2×C4⋊C4×C61—21no—
135C2×C4⋊C4×C61C2311yescharacteristic
136C2×C4⋊C4×C61C2311yescharacteristic
137C2×C22⋊C4×C61—21no—
138C2×C42×C61—21no—
139C2×C42×C61C2311yescharacteristic
140#107×C61—22no—
141#103×C61D414yescomplemented
142#102×C61—22no—
143#97×C61—22no—
144C24×C61—21no—
145C23×D61C2×D411yescharacteristic
146C2×Q8×C61—21no—
147C2×Q8×C61—21no—
148C2×Q8×C61—21no—
149C2×Q8×C61C22×C412yes—
150C2×Q8×C61C2×D412yes—
151C2×Q8×C61#4112yes—
152C2×D4×C61—21no—
153C2×D4×C61—21no—
154C2×D4×C61—21no—
155C2×D4×C61—21no—
156C2×D4×C61—21no—
157C2×D4×C61C22×C412yes—
158C22×C4×C61—21no—
159C22×C4×C61—21no—
160C22×C4×C61—21no—
161C22×C4×C61—42no—
162C22×C4×C61—42no—
163C22×C4×C61—81no—
164C22×C4×C61C2×D411yescharacteristic
165C22×C4×C61C2×D411yescharacteristic
166C22×C4×C61C2411yescharacteristic
167C2×C22⋊D61—24no—
168C2×C22⋊D61—42no—
169C2×C22⋊D61—42no—
170C22×Dic61—21no—
171C22×Dic61—21no—
172C22×Dic61—21no—
173C22×Dic61—21no—
174C22×Dic61C2×D411yescharacteristic
175C22×Dic61C2×D411yescharacteristic
176C22×Dic61C2×D411yescharacteristic
177Q8×D61—28no—
178Q8×D61—44no—
179Q8×D61—44no—
180Q8×D61—44no—
181C2×C4×D61—21no—
182C2×C4×D61—21no—
183C2×C4×D61—21no—
184C2×C4×D61—21no—
185C2×C4×D61—24no—
186C2×C4×D61—42no—
187C2×C4×D61—42no—
188C2×C4×D61—42no—
189C2×C4×D61—42no—
190C2×C4×D61—81no—
191C2×C4×D61C22×C412yes—
192C2×C4×D61#4112yes—
193C2×Dic122—21no—
194C2×Dic122—21no—
195C2×Dic122—21no—
196C2×Dic122—21no—
197C2×Dic122—21no—
198C2×Dic122—24no—
199C2×Dic122—42no—
200C2×Dic122—42no—
201C2×Dic122C22×C412yes—
202SD16×C61—28no—
203C2×C8×C61—21no—
204C2×C8×C61—21no—
205C2×C8×C61—21no—
206C2×C8×C61—21no—
207C2×C8×C61C22×C412yes—
208C2×C8×C61C2×D412yes—
209C4⋊C4×C61—21no—
210C4⋊C4×C61—21no—
211C4⋊C4×C61—21no—
212C4⋊C4×C61—42no—
213C4⋊C4×C61C2×D412yes—
214C22⋊C4×C61—42no—
215C42×C61—21no—
216C42×C61—21no—
217C42×C61—42no—
218C22⋊Dic61—24no—
219C22⋊Dic61—42no—
220C22⋊Dic61—81no—
221#11758200—44no—
222#11758198—22no—
223#11758198—22no—
224#11758198—42no—
225C4⋊Dic61—21no—
226C4⋊Dic61—21no—
227C4⋊Dic61—21no—
228C4⋊Dic61—21no—
229C4⋊Dic61—21no—
230C4⋊Dic61—42no—
231C4⋊Dic61C22×C412yes—
232#11758196—42no—
233#11758196—42no—
234C4×Dic61—21no—
235C4×Dic61—21no—
236C4×Dic61—42no—
237C4×Dic61—42no—
238C2×#92418—21no—
239C2×#92418—21no—
240C2×#92418—21no—
241C2×#92418—21no—
242C2×#92418—21no—
243C2×#92418C22×C412yes—
244C8×D61—44no—
245C23×C61—22no—
246C23×C61—41no—
247C23×C61—41no—
248C23×C61—41no—
249C23×C61—41no—
250C23×C61—41no—
251C23×C61—41no—
252C23×C61C22×D411yescharacteristic
253C22×D61—21no—
254C22×D61—21no—
255C22×D61—21no—
256C22×D61—21no—
257C22×D61C4×D412yes—
258C22×D61AGL(1,ℤ/8)12yes—
259C22×D61#13712yes—
260Q8×C61—22no—
261Q8×C61—22no—
262Q8×C61—22no—
263Q8×C61C4×D414yescomplemented
264D4×C61—22no—
265D4×C61—22no—
266D4×C61—41no—
267D4×C61—41no—
268C2×C4×C61—22no—
269C2×C4×C61—22no—
270C2×C4×C61—22no—
271C2×C4×C61—22no—
272C2×C4×C61—21no—
273C2×C4×C61—21no—
274C2×C4×C61—21no—
275C2×C4×C61—21no—
276C2×C4×C61—21no—
277C2×C4×C61—21no—
278C2×C4×C61—41no—
279C2×C4×C61—41no—
280C2×C4×C61—41no—
281C2×C4×C61—41no—
282C2×C4×C61—41no—
283C2×C4×C61—84no—
284C2×C4×C61C23×C411yescharacteristic
285C2×C4×C61C22×D411yescharacteristic
286C2×C4×C61C2×#4111yescharacteristic
287C2×C4×C61C2×#4111yescharacteristic
288C2×C4×C61H(5,𝔽2)11yescharacteristic
289C2×C4×C61H(5,𝔽2)11yescharacteristic
290C22⋊D61—48no—
291C2×Dic61—21no—
292C2×Dic61—21no—
293C2×Dic61—22no—
294C2×Dic61—22no—
295C2×Dic61—21no—
296C2×Dic61—21no—
297C2×Dic61—21no—
298C2×Dic61—21no—
299C2×Dic61—21no—
300C2×Dic61—21no—
301C2×Dic61—41no—
302C2×Dic61—41no—
303C2×Dic61—41no—
304C2×Dic61—41no—
305C2×Dic61—41no—
306C2×Dic61—41no—
307C2×Dic61—41no—
308C2×Dic61—41no—
309C2×Dic61—41no—
310C2×Dic61—41no—
311C2×Dic61C4×D412yes—
312C4×D61—22no—
313C4×D61—22no—
314C4×D61—22no—
315C4×D61—22no—
316C4×D61—48no—
317C4×D61—84no—
318Dic122—22no—
319Dic122—22no—
320Dic122—48no—
321Dic122—41no—
322Dic122—41no—
323C8×C61—22no—
324C8×C61—22no—
325#92418—22no—
326#92418—41no—
327#22855—611nomaximal, Sylow
328C22×C61—42no—
329C22×C61—42no—
330C22×C61—42no—
331C22×C61—81no—
332C22×C61—81no—
333C22×C61—81no—
334C22×C61—81no—
335C22×C61C2×C4×D411yescharacteristic
336C22×C61D4211yescharacteristic
337C22×C61#54611yescharacteristic
338C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
339C22×C61C2×#13711yescharacteristic
340C22×C61#57711yescharacteristic
341C22×C61#57811yescharacteristic
342C2×D61—22no—
343C2×D61—22no—
344C2×D61—22no—
345C2×D61—22no—
346C2×D61—22no—
347C2×D61—22no—
348C2×D61#44014yescomplemented
349C4×C61—24no—
350C4×C61—42no—
351C4×C61—41no—
352C4×C61—41no—
353C4×C61—81no—
354C4×C61C2×C4×D411yescharacteristic
355C4×C61#51811yescharacteristic
356C4×C61#54611yescharacteristic
357C4×C61#55111yescharacteristic
358Dic61—22no—
359Dic61—42no—
360Dic61—42no—
361Dic61—41no—
362Dic61—41no—
363Dic61—81no—
364Dic61—81no—
365C2×#448—611no—
366C2×#440D6111yescharacteristic, complemented
367C22×#103—611no—
368#2361—611no—
369Q8×C22⋊C4—611no—
370#1973—611no—
371#1935—611no—
372#1928—611no—
373#1893—611no—
374#1880—611no—
375#1877—611no—
376#1863—611no—
377#1852—611no—
378#1763—611no—
379#1752—611no—
380C2×C61—82no—
381C2×C61#235811yescharacteristic
382C2×C61C2×#44011yescharacteristic
383C2×C61#294711yescharacteristic
384C2×C61#326511yescharacteristic
385C2×C61#327011yescharacteristic
386C2×C61#330811yescharacteristic
387C2×C61#332011yescharacteristic
388D61—24no—
389C23×Q8—611no—
390C22×SD16—611no—
391C22×SD16C2×D6111yescharacteristic
392C23×C8—611no—
393C2×#121—611no—
394C2×C4×Q8—611no—
395C2×C4×Q8C2×D6111yescharacteristic
396C2×C4×D4—1221no—
397C2×C4×D4C2×D6111yescharacteristic
398C22×C4⋊C4—611no—
399#448—618no—
400#440—24no—
401C2×#107—611no—
402C2×#107C2×D6111yescharacteristic
403C2×#103—611no—
404C2×#103—611no—
405C2×#103—611no—
406C2×#103—611no—
407C2×#103—611no—
408C2×#103—1224no—
409C2×#103C2×D6111yescharacteristic
410C2×#102—611no—
411C2×#102C2×D6111yescharacteristic
412C2×C22⋊C8—611no—
413C2×#97—611no—
414C2×#97C2×D6111yescharacteristic
415#391—611no—
416#391—611no—
417#391—1221no—
418#391—1221no—
419#390—611no—
420#389—611no—
421#388—1221no—
422#386—1221no—
423#385—1221no—
424#380—611no—
425#380—1221no—
426C4×C4⋊C4—611no—
427C4×C22⋊C4—611no—
428C4×C22⋊C4—1221no—
429#340—611no—
430#340—611no—
431#340—611no—
432#340—611no—
433#336—611no—
434#336—611no—
435C61#2285511yescharacteristic, complemented, Sylow
436C22×Q8—614no—
437C22×Q8—611no—
438C22×Q8—1221no—
439C22×Q8—1222no—
440C22×Q8—1222no—
441C22×Q8—1222no—
442C22×Q8—2441no—
443C22×Q8—2441no—
444C22×Q8C22×D6111yescharacteristic
445C22×D4—1221no—
446C22×D4C22×D6111yescharacteristic
447C23×C4—21no—
448C23×C4—611no—
449C23×C4—1221no—
450C23×C4—1221no—
451C2×SD16—22no—
452C2×SD16—22no—
453C2×SD16—614no—
454C2×SD16—2441no—
455C2×SD16—2441no—
456C2×SD16C4×D6114yescomplemented
457C22×C8—611no—
458C22×C8—611no—
459C22×C8—1222no—
460C22×C8—1222no—
461C22×C8—2441no—
462C22×C8C22×D6111yescharacteristic
463C22×C8C22×D6111yescharacteristic
464#121—614no—
465#121—1222no—
466C4×Q8—22no—
467C4×Q8—41no—
468C4×Q8—1222no—
469C4×Q8—2441no—
470C4×D4—22no—
471C4×D4—41no—
472C4×D4—2444no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—611no—
475C2×C4⋊C4—611no—
476C2×C4⋊C4—611no—
477C2×C4⋊C4—1222no—
478C2×C4⋊C4—1221no—
479C2×C4⋊C4—1221no—
480C2×C4⋊C4—1221no—
481C2×C4⋊C4—2441no—
482C2×C4⋊C4C22×D6111yescharacteristic
483C2×C4⋊C4C22×D6111yescharacteristic
484C2×C22⋊C4—21no—
485C2×C22⋊C4—611no—
486C2×C22⋊C4—611no—
487C2×C22⋊C4—1221no—
488C2×C22⋊C4—1221no—
489C2×C22⋊C4—1221no—
490C2×C22⋊C4—1221no—
491C2×C42—21no—
492C2×C42—611no—
493C2×C42—1221no—
494C2×C42—1221no—
495C2×C42C22×D6111yescharacteristic
496#107—22no—
497#107—2441no—
498#103—614no—
499#103—614no—
500#103—1222no—
501#103—1222no—
502#103—1222no—
503#103C22⋊D6114yescomplemented
504#102—22no—
505#102—2441no—
506C22⋊C8—614no—
507#97—22no—
508#97—2441no—
509#95—611no—
510#95—611no—
511#95—1221no—
512#95—1221no—
513#95—1221no—
514#95—1221no—
515#95—1221no—
516#95—1221no—
517#95—1221no—
518C24—21no—
519C24—611no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—612no—
524C2×Q8—1224no—
525C2×Q8—1221no—
526C2×Q8—1228no—
527C2×Q8—1221no—
528C2×Q8—1221no—
529C2×Q8—1221no—
530C2×Q8—1221no—
531C2×Q8—2442no—
532C2×Q8—2442no—
533C2×Q8—2444no—
534C2×Q8—2444no—
535C2×Q8—2444no—
536C2×Q8C2×C4×D6112yes—
537C2×Q8#1175822212yes—
538C2×Q8C2×C22⋊D6112yes—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—1224no—
545C2×D4—2442no—
546C2×D4—2442no—
547C2×D4C2×C4×D6112yes—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—42no—
552C22×C4—42no—
553C22×C4—81no—
554C22×C4—611no—
555C22×C4—612no—
556C22×C4—612no—
557C22×C4—611no—
558C22×C4—611no—
559C22×C4—1224no—
560C22×C4—1221no—
561C22×C4—1221no—
562C22×C4—1221no—
563C22×C4—1221no—
564C22×C4—1221no—
565C22×C4—1221no—
566C22×C4—1221no—
567C22×C4—1221no—
568C22×C4—4881no—
569C22×C4—2442no—
570C22×C4—2442no—
571C22×C4—2442no—
572C22×C4—2442no—
573C22×C4D4×D6111yescharacteristic
574C22×C4D4×D6111yescharacteristic
575C22×C4C23×D6111yescharacteristic
576SD16—28no—
577SD16—2444no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—612no—
583C2×C8—1221no—
584C2×C8—1221no—
585C2×C8—1221no—
586C2×C8—1221no—
587C2×C8—1221no—
588C2×C8—2444no—
589C2×C8C2×C4×D6112yes—
590C2×C8C2×C22⋊D6112yes—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—42no—
595C4⋊C4—612no—
596C4⋊C4—1221no—
597C4⋊C4—1221no—
598C4⋊C4—1221no—
599C4⋊C4—1221no—
600C4⋊C4—1221no—
601C4⋊C4—2442no—
602C4⋊C4—2442no—
603C4⋊C4—2442no—
604C4⋊C4C2×C22⋊D6112yes—
605C22⋊C4—42no—
606C22⋊C4—1222no—
607C22⋊C4—1222no—
608C22⋊C4—1224no—
609C22⋊C4—4881no—
610C22⋊C4—2442no—
611C22⋊C4—2442no—
612C42—21no—
613C42—21no—
614C42—42no—
615C42—1221no—
616C42—1221no—
617C42—2442no—
618C42—2442no—
619C23—22no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—612no—
627C23—612no—
628C23—612no—
629C23—1221no—
630C23—1221no—
631C23—1221no—
632C23—1221no—
633C23C2×D4×D6111yescharacteristic
634Q8—22no—
635Q8—22no—
636Q8—22no—
637Q8—1222no—
638Q8—1222no—
639Q8—2448no—
640Q8—2441no—
641Q8—2441no—
642Q8C4×C22⋊D6114yescomplemented
643D4—22no—
644D4—22no—
645D4—41no—
646D4—41no—
647D4—2448no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—22no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—84no—
664C2×C4—612no—
665C2×C4—1221no—
666C2×C4—1221no—
667C2×C4—1222no—
668C2×C4—1222no—
669C2×C4—1222no—
670C2×C4—1222no—
671C2×C4—1222no—
672C2×C4—1222no—
673C2×C4—1221no—
674C2×C4—1221no—
675C2×C4—1221no—
676C2×C4—1221no—
677C2×C4—1221no—
678C2×C4—1221no—
679C2×C4—4884no—
680C2×C4—2448no—
681C2×C4—2441no—
682C2×C4—2441no—
683C2×C4—2441no—
684C2×C4—2441no—
685C2×C4—2441no—
686C2×C4—2441no—
687C2×C4—2441no—
688C2×C4—2441no—
689C2×C4—2441no—
690C2×C4—2441no—
691C2×C4C22×C4×D6111yescharacteristic
692C2×C4C22×C22⋊D6111yescharacteristic
693C2×C4#41×D6111yescharacteristic
694C2×C4C2×#1175822211yescharacteristic
695C2×C4#1451982211yescharacteristic
696C2×C4#1451982311yescharacteristic
697C8—22no—
698C8—22no—
699C8—1222no—
700C8—2441no—
701C22—42no—
702C22—42no—
703C22—42no—
704C22—81no—
705C22—81no—
706C22—81no—
707C22—81no—
708C22—614no—
709C22—1222no—
710C22—1222no—
711C22—1222no—
712C22—1222no—
713C22—1222no—
714C22—1222no—
715C22C4×D4×D6111yescharacteristic
716C22D4×C22⋊D6111yescharacteristic
717C22#1684040811yescharacteristic
718C22AGL(1,ℤ/8)×D6111yescharacteristic
719C22#137×D6111yescharacteristic
720C22#1684057211yescharacteristic
721C22#1684057811yescharacteristic
722C4—24no—
723C4—41no—
724C4—42no—
725C4—41no—
726C4—81no—
727C4—1222no—
728C4—4881no—
729C4—4881no—
730C4—2442no—
731C4—2441no—
732C4—2442no—
733C4—2441no—
734C4C2×C4×C22⋊D6111yescharacteristic
735C4#1684023411yescharacteristic
736C4#1684040011yescharacteristic
737C4#1684044111yescharacteristic
738C2—82no—
739C2—1224no—
740C2#2144879611yescharacteristic
741C2#440×D6111yescharacteristic
742C2#2145465911yescharacteristic
743C2#2145730811yescharacteristic
744C2#2145738311yescharacteristic
745C2#2145781511yescharacteristic
746C2#2145799511yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#440C2
socleC23×C61C22×D4
prime radicalC2×#14519748C22
cosocleC22×C4×C61C24
hypercenterC2×#440D61
hypocenterC61#22855
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
2. C2×#103×D61C2semidirect
4. Q8×#11758198C2semidirect
5. #21446701C2semidirect
6. #21446509C2semidirect
7. #21446459C2semidirect
9. #21446176C2semidirect
10. #21446153C2semidirect
11. #21446073C2semidirect
12. #21446005C2semidirect
13. #21445651C2semidirect
14. #21445596C2semidirect
15. C2×C61×#440C2semidirect
23. #16839899C4semidirect
69. C2×Q8×D61C2×C4semidirect
76. C2×#11758200C2×C4semidirect
106. #14519702C2×C4semidirect
108. #14519701C2×C4semidirect
111. #14519689C2×C4semidirect
127. C2×SD16×C61C2×C4semidirect
141. #103×C61D4semidirect
263. Q8×C61C4×D4semidirect
348. C2×D61#440semidirect
366. C2×#440D61semidirect
435. C61#22855semidirect
456. C2×SD16C4×D61semidirect
503. #103C22⋊D61semidirect
642. Q8C4×C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168398992
C2×#103×D612
#214488312
Q8×#117581982
#214467012
#214465092
#214464592
#214462442
#214461762
#214461532
#214460732
#214460052
#214456512
#214455962
C2×C61×#4402
#2285561