Finite Group Databasebeta

← #29681431

Subgroups — #29681431

Order 15616.

1926 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519801C211yesmaximal, characteristic
2C2×#16840241C211yesmaximal, characteristic, complemented
3C2×#16839755C211yesmaximal, characteristic, complemented
4C2×#102×D61C211yesmaximal, characteristic, complemented
5#21448398C211yesmaximal, characteristic, complemented
6#21446177C211yesmaximal, characteristic, complemented
7#21446175C211yesmaximal, characteristic, complemented
8#21446173C211yesmaximal, characteristic, complemented
9#21446171C211yesmaximal, characteristic, complemented
10#21446169C211yesmaximal, characteristic, complemented
11#21446167C211yesmaximal, characteristic, complemented
12#21446165C211yesmaximal, characteristic, complemented
13#21445537C211yesmaximal, characteristic, complemented
14#21445514C211yesmaximal, characteristic, complemented
15C61×#1879C211yesmaximal, characteristic, complemented
16C22×#11758224C2211yescharacteristic
17C22×D4×D61C2211yescharacteristic
18C2×#14519801—24no—
19C2×#14519801—24no—
20C2×#14519801C418yescomplemented
21C22×#11758190C2211yescharacteristic
22C22×#11758200C2211yescharacteristic
23C22×#11758199C2211yescharacteristic
24C22×#11758189C2211yescharacteristic
25C22×C8×D61C2211yescharacteristic
26#16840241—24no—
27#16840241—24no—
28C2×C4×Dic122C2211yescharacteristic, complemented
29C2×#14519742C2211yescharacteristic, complemented
30C2×D4×Dic61C2211yescharacteristic, complemented
31C2×C4×C22⋊D61—21no—
32C2×#14519737—21no—
33C2×#14519735C2211yescharacteristic
34C2×#14519734C2211yescharacteristic
35C2×#14519733—21no—
36C22×#11758196—21no—
37C2×C4⋊C4×D61C2211yescharacteristic
38#16839755—24no—
39C2×#14519702C2211yescharacteristic, complemented
40C2×#14519700C2211yescharacteristic, complemented
41C2×#14519699C2211yescharacteristic
42C2×#14519698C2211yescharacteristic
43C2×#14519698C2211yescharacteristic, complemented
44C2×#14519697C2211yescharacteristic
45#102×D61—24no—
46#16839665C2211yescharacteristic
47#16839664C2211yescharacteristic
48#16839663C2211yescharacteristic
49#16839662—21no—
50#16839662—21no—
51#16839617—21no—
52#16839617—21no—
53#16839525C2211yescharacteristic, complemented
54#16839524C2211yescharacteristic, complemented
55#16839524C2211yescharacteristic, complemented
56#16839517C2211yescharacteristic, complemented
57#16839516C2211yescharacteristic, complemented
58#16839516C2211yescharacteristic, complemented
59C22×D8×C61C2211yescharacteristic
60C2×C4×D4×C61C2211yescharacteristic, complemented
61C2×#102×C61C2211yescharacteristic
62C2×#102×C61C2211yescharacteristic, complemented
63C61×#390C2211yescharacteristic
64C61×#340C2211yescharacteristic, complemented
65C61×#336C2211yescharacteristic, complemented
66C24×D61—21no—
67C2×#11758224—22no—
68C2×#11758224—22no—
69C2×#11758224—22no—
70C2×#11758224C2×C414yes—
71C2×#11758224D414yes—
72C2×#11758224D414yes—
73C22×Dic122C2311yescharacteristic
74C22×D244C2311yescharacteristic
75C22×C22⋊D61—21no—
76C22×C22⋊D61—21no—
77C2×D4×D61—22no—
78C2×D4×D61—22no—
79C2×D4×D61—22no—
80C2×D4×D61—22no—
81C2×D4×D61—22no—
82C2×D4×D61C2×C414yescomplemented
83C23×Dic61—21no—
84C23×Dic61—21no—
85C22×C4×D61—21no—
86C22×C4×D61C2311yescharacteristic
87#14519801—232no—
88C2×#11758190—22no—
89C2×#11758190—22no—
90C2×#11758190C2×C414yescomplemented
91C2×#11758200—22no—
92C2×#11758200—22no—
93C2×#11758200C2×C414yescomplemented
94C2×#11758199—22no—
95C2×#11758199—22no—
96C2×#11758199C2×C414yescomplemented
97C2×#11758189—22no—
98C2×#11758189—22no—
99C2×#11758189C2×C414yescomplemented
100C22×#92418C2311yescharacteristic
101C22×#92418C2311yescharacteristic
102C2×C8×D61—22no—
103C2×C8×D61—22no—
104C2×C8×D61—22no—
105C4×Dic122—22no—
106C4×Dic122—22no—
107#14519742—22no—
108#14519742—22no—
109D4×Dic61—22no—
110D4×Dic61—22no—
111C4×C22⋊D61—28no—
112#14519737—28no—
113#14519735—22no—
114#14519735—22no—
115#14519734—22no—
116#14519734—22no—
117#14519733—28no—
118C2×C4⋊Dic61C2311yescharacteristic
119C2×C4⋊Dic61C2311yescharacteristic
120C2×#11758196—28no—
121C2×#11758196—21no—
122C2×#11758196—21no—
123C2×#11758196—21no—
124C2×#11758196D411yescharacteristic
125C2×#11758196D411yescharacteristic
126C4⋊C4×D61—22no—
127C4⋊C4×D61D414yes—
128C2×C22⋊Dic61—21no—
129C2×C22⋊Dic61—21no—
130C2×C22⋊Dic61—21no—
131C2×#11758198—21no—
132C2×#11758198—21no—
133C2×#11758198—21no—
134C2×#11758198—21no—
135C2×#11758198—21no—
136C2×#11758198D411yescharacteristic
137C2×#11758198D411yescharacteristic
138C2×C4×Dic61—21no—
139C2×C4×Dic61—21no—
140C2×C4×Dic61—21no—
141C2×C4×Dic61C2311yescharacteristic
142#14519702—22no—
143#14519700—22no—
144#14519699—22no—
145#14519698—22no—
146#14519698—22no—
147#14519697—22no—
148C22×D4×C61C2311yescharacteristic
149C22×D4×C61C2311yescharacteristic
150C23×C4×C61—21no—
151C2×D8×C61—22no—
152C2×D8×C61—22no—
153C2×D8×C61C2×C414yescomplemented
154C22×C8×C61C2311yescharacteristic
155C22×C8×C61C2311yescharacteristic
156C4×D4×C61—22no—
157C4×D4×C61—22no—
158C2×C4⋊C4×C61C2311yescharacteristic
159C2×C4⋊C4×C61C2311yescharacteristic
160C2×C22⋊C4×C61—21no—
161C2×C22⋊C4×C61—21no—
162C2×C22⋊C4×C61—21no—
163C2×C42×C61C2311yescharacteristic
164#102×C61—22no—
165#102×C61—22no—
166C24×C61—21no—
167C24×C61—21no—
168C23×D61—21no—
169C23×D61—24no—
170C23×D61—42no—
171C23×D61—42no—
172C23×D61—81no—
173C23×D61—81no—
174C23×D61—81no—
175C23×D61—81no—
176C23×D61C2×D411yescharacteristic
177C2×D4×C61—21no—
178C2×D4×C61—21no—
179C2×D4×C61—21no—
180C2×D4×C61—21no—
181C2×D4×C61—21no—
182C2×D4×C61—21no—
183C2×D4×C61—21no—
184C2×D4×C61—21no—
185C2×D4×C61C22×C412yes—
186C2×D4×C61C22×C412yes—
187C2×D4×C61C2×D412yes—
188C2×D4×C61C2×D412yes—
189C22×C4×C61—21no—
190C22×C4×C61—24no—
191C22×C4×C61—21no—
192C22×C4×C61—81no—
193C22×C4×C61—81no—
194C22×C4×C61C2×D411yescharacteristic
195C22×C4×C61C2×D411yescharacteristic
196C22×C4×C61C2411yescharacteristic
197C2×C22⋊D61—24no—
198C2×C22⋊D61—24no—
199C2×C22⋊D61—24no—
200C2×C22⋊D61—24no—
201C2×C22⋊D61—42no—
202C2×C22⋊D61—42no—
203C22×Dic61—21no—
204C22×Dic61—24no—
205C22×Dic61—24no—
206C22×Dic61—24no—
207C22×Dic61—21no—
208C22×Dic61—24no—
209C22×Dic61—21no—
210C22×Dic61—81no—
211C22×Dic61—81no—
212C22×Dic61C2×D411yescharacteristic
213C22×Dic61C2×D411yescharacteristic
214C22×Dic61C2×D411yescharacteristic
215#11758224—28no—
216#11758224—28no—
217#11758224—28no—
218#11758224C22⋊C4116yescomplemented
219D4×D61—28no—
220D4×D61—28no—
221D4×D61—44no—
222D4×D61—44no—
223C2×D244—21no—
224C2×D244—21no—
225C2×D244—21no—
226C2×D244—21no—
227C2×D244—21no—
228C2×D244C22×C412yes—
229C2×C4×D61—24no—
230C2×C4×D61—81no—
231C2×C4×D61—81no—
232C2×C4×D61C22×C412yes—
233C2×C4×D61C2×D412yes—
234C2×C4×D61C2×D412yes—
235C2×C4×D61C2×D412yes—
236C2×C4×D61#4112yes—
237C2×C4×D61#4112yes—
238C2×Dic122—21no—
239C2×Dic122—21no—
240C2×Dic122—21no—
241C2×Dic122C22×C412yes—
242C2×Dic122C2×D412yes—
243C2×Dic122C2×D412yes—
244D8×C61—28no—
245C2×C8×C61—21no—
246C2×C8×C61—21no—
247C2×C8×C61—21no—
248C2×C8×C61—21no—
249C2×C8×C61—21no—
250C2×C8×C61C22×C412yes—
251C4⋊C4×C61—21no—
252C4⋊C4×C61—21no—
253C4⋊C4×C61—21no—
254C4⋊C4×C61C2×D412yes—
255C22⋊C4×C61—24no—
256C22⋊C4×C61—81no—
257C22⋊C4×C61—81no—
258C42×C61—21no—
259C42×C61—21no—
260C22⋊Dic61—24no—
261C22⋊Dic61—81no—
262C22⋊Dic61—81no—
263#11758200—28no—
264#11758199—28no—
265#11758198—22no—
266#11758198—22no—
267#11758198—42no—
268#11758198—81no—
269#11758198—81no—
270#11758198—81no—
271#11758198—81no—
272C4⋊Dic61—21no—
273C4⋊Dic61—21no—
274C4⋊Dic61—21no—
275C4⋊Dic61C2×D412yes—
276#11758196—24no—
277#11758196—24no—
278#11758196—24no—
279#11758196—22no—
280#11758196—22no—
281C4×Dic61—24no—
282C4×Dic61—24no—
283C4×Dic61—21no—
284C4×Dic61—21no—
285C4×Dic61—42no—
286C2×#92418—21no—
287C2×#92418—21no—
288C2×#92418—21no—
289C2×#92418—21no—
290C2×#92418—21no—
291C2×#92418C22×C412yes—
292#11758190—28no—
293#11758189—28no—
294C8×D61—44no—
295C23×C61—22no—
296C23×C61—22no—
297C23×C61—22no—
298C23×C61—22no—
299C23×C61—41no—
300C23×C61—41no—
301C23×C61—41no—
302C23×C61—41no—
303C23×C61—41no—
304C23×C61—41no—
305C23×C61—41no—
306C23×C61—41no—
307C23×C61—41no—
308C23×C61—41no—
309C23×C61C22×D411yescharacteristic
310C22×D61—21no—
311C22×D61—21no—
312C22×D61—21no—
313C22×D61—21no—
314C22×D61—22no—
315C22×D61—41no—
316C22×D61—41no—
317C22×D61—41no—
318C22×D61—41no—
319C22×D61—41no—
320C22×D61—41no—
321C22×D61—48no—
322C22×D61—84no—
323C22×D61—84no—
324C22×D61—84no—
325C22×D61—84no—
326C22×D61—84no—
327C22×D61—84no—
328C22×D61C4×D412yes—
329C22×D61#12012yes—
330C22×D61#12112yes—
331D4×C61—22no—
332D4×C61—22no—
333D4×C61—22no—
334D4×C61—22no—
335D4×C61—22no—
336D4×C61—41no—
337D4×C61—41no—
338D4×C61C2×C22⋊C414yes—
339C2×C4×C61—21no—
340C2×C4×C61—22no—
341C2×C4×C61—21no—
342C2×C4×C61—21no—
343C2×C4×C61—21no—
344C2×C4×C61—21no—
345C2×C4×C61—21no—
346C2×C4×C61—41no—
347C2×C4×C61—41no—
348C2×C4×C61—41no—
349C2×C4×C61—41no—
350C2×C4×C61—41no—
351C2×C4×C61—84no—
352C2×C4×C61C23×C411yescharacteristic
353C2×C4×C61C22×D411yescharacteristic
354C2×C4×C61C22×D411yescharacteristic
355C2×C4×C61C22×D411yescharacteristic
356C2×C4×C61C2×#4111yescharacteristic
357C2×C4×C61C2×#4111yescharacteristic
358C22⋊D61—216no—
359C22⋊D61—48no—
360C2×Dic61—22no—
361C2×Dic61—22no—
362C2×Dic61—22no—
363C2×Dic61—216no—
364C2×Dic61—21no—
365C2×Dic61—21no—
366C2×Dic61—22no—
367C2×Dic61—21no—
368C2×Dic61—21no—
369C2×Dic61—21no—
370C2×Dic61—21no—
371C2×Dic61—41no—
372C2×Dic61—41no—
373C2×Dic61—41no—
374C2×Dic61—41no—
375C2×Dic61—41no—
376C2×Dic61—84no—
377C2×Dic61C4×D412yes—
378C2×Dic61#12012yes—
379C2×Dic61#12112yes—
380D244—22no—
381D244—22no—
382D244—41no—
383D244—41no—
384C4×D61—84no—
385C4×D61C2×C22⋊C414yes—
386C4×D61C4×D414yes—
387C4×D61#12114yes—
388C4×D61#12314yes—
389Dic122—22no—
390Dic122—22no—
391Dic122—22no—
392Dic122C2×C22⋊C414yes—
393C8×C61—22no—
394C8×C61—41no—
395#92418—22no—
396#92418—41no—
397#20932—611nomaximal, Sylow
398C22×C61—24no—
399C22×C61—42no—
400C22×C61—42no—
401C22×C61—42no—
402C22×C61—42no—
403C22×C61—42no—
404C22×C61—42no—
405C22×C61—42no—
406C22×C61—42no—
407C22×C61—42no—
408C22×C61—81no—
409C22×C61—81no—
410C22×C61—81no—
411C22×C61—81no—
412C22×C61C2×C4×D411yescharacteristic
413C22×C61C2×#12011yescharacteristic
414C22×C61C2×#12111yescharacteristic
415C22×C61#57611yescharacteristic
416C22×C61#57611yescharacteristic
417C22×C61#57711yescharacteristic
418C22×C61#57711yescharacteristic
419C2×D61—22no—
420C2×D61—22no—
421C2×D61—22no—
422C2×D61—22no—
423C2×D61—22no—
424C2×D61—22no—
425C2×D61—42no—
426C2×D61—42no—
427C2×D61—42no—
428C2×D61—816no—
429C2×D61—81no—
430C2×D61—81no—
431C2×D61—81no—
432C2×D61—81no—
433C2×D61#38614yes—
434C4×C61—42no—
435C4×C61—41no—
436C4×C61—41no—
437C4×C61—81no—
438C4×C61C22×C22⋊C411yescharacteristic
439C4×C61C2×C4×D411yescharacteristic
440C4×C61C2×#12111yescharacteristic
441C4×C61C2×#12311yescharacteristic
442Dic61—24no—
443Dic61—42no—
444Dic61—41no—
445Dic61—41no—
446Dic61—81no—
447Dic61#38614yes—
448C22×AGL(1,ℤ/8)—611no—
449C2×#520—611no—
450C2×#416—611no—
451C22×#102—611no—
452#2309—611no—
453#1880—611no—
454#1880—611no—
455#1880—611no—
456#1880—611no—
457#1879—611no—
458#1879—611no—
459#1879—611no—
460#1879D6111yescharacteristic, complemented
461#1736—611no—
462#1729—611no—
463C2×C61—44no—
464C2×C61—82no—
465C2×C61C2×#38611yescharacteristic
466C2×C61#294611yescharacteristic
467C2×C61#294611yescharacteristic
468C2×C61#300811yescharacteristic
469C2×C61#301011yescharacteristic
470C2×C61#304511yescharacteristic
471C2×C61#304511yescharacteristic
472D61—24no—
473D61—82no—
474C22×#41—611no—
475C23×D4—611no—
476C2×AGL(1,ℤ/8)—618no—
477C2×AGL(1,ℤ/8)—1224no—
478C2×AGL(1,ℤ/8)—1224no—
479C22×SD16—611no—
480C22×SD16—611no—
481C22×D8—611no—
482C22×D8C2×D6111yescharacteristic
483C22×M16—611no—
484C23×C8—611no—
485#520—1224no—
486#520—1224no—
487C2×C4×Q8—611no—
488C2×C4×Q8—611no—
489C2×C4×D4—611no—
490C2×C4×D4—1221no—
491C2×C4×D4—1221no—
492C2×C4×D4C2×D6111yescharacteristic, complemented
493C2×#117—611no—
494C2×#117—611no—
495C2×#117—1221no—
496C22×C4⋊C4—611no—
497C22×C4⋊C4—1221no—
498#416—1224no—
499C2×#103—611no—
500C2×#103—611no—
501C2×#102—611no—
502C2×#102—611no—
503C2×#102—611no—
504C2×#102—611no—
505C2×#102—1224no—
506C2×#102C2×D6111yescharacteristic
507C2×#102C2×D6111yescharacteristic, complemented
508#390—611no—
509#390—611no—
510#390—611no—
511#390—1221no—
512#390—1221no—
513#390C2×D6111yescharacteristic
514#379—1221no—
515#379—1221no—
516#340—611no—
517#340—611no—
518#340—611no—
519#340C2×D6111yescharacteristic, complemented
520#336—611no—
521#336—611no—
522#336—611no—
523#336C2×D6111yescharacteristic, complemented
524C61#2093211yescharacteristic, complemented, Sylow
525C25—1221no—
526C2×#41—614no—
527C2×#41—614no—
528C2×#41—614no—
529C2×#41—1222no—
530C2×#41—1222no—
531C2×#41—1222no—
532C22×Q8—611no—
533C22×D4—614no—
534C22×D4—611no—
535C22×D4—1222no—
536C22×D4—1222no—
537C22×D4—1222no—
538C22×D4—1222no—
539C22×D4—1222no—
540C22×D4—1221no—
541C22×D4—1221no—
542C22×D4C22×D6111yescharacteristic
543C22×D4C22×D6111yescharacteristic
544C23×C4—21no—
545C23×C4—611no—
546C23×C4—1221no—
547C23×C4—1221no—
548C23×C4—1221no—
549AGL(1,ℤ/8)—12232no—
550C2×SD16—614no—
551C2×SD16—614no—
552C2×SD16—1222no—
553C2×SD16—1222no—
554C2×SD16—1222no—
555C2×SD16—1222no—
556C2×D8—22no—
557C2×D8—22no—
558C2×D8—614no—
559C2×D8—1222no—
560C2×D8—1222no—
561C2×D8C4×D6114yescomplemented
562C2×M16—614no—
563C2×M16—1222no—
564C2×M16—1222no—
565C22×C8—611no—
566C22×C8—611no—
567C22×C8—1222no—
568C22×C8—1222no—
569C22×C8—1222no—
570C22×C8C22×D6111yescharacteristic
571C22×C8C22×D6111yescharacteristic
572C4×Q8—1222no—
573C4×Q8—1222no—
574C4×Q8—1222no—
575C4×Q8—1222no—
576C4×D4—22no—
577C4×D4—22no—
578C4×D4—1228no—
579C4×D4—1222no—
580C4×D4—1228no—
581C4×D4—1222no—
582#117—1222no—
583#117—1222no—
584#117—1228no—
585#117—1222no—
586#117—1222no—
587C2×C4⋊C4—611no—
588C2×C4⋊C4—614no—
589C2×C4⋊C4—611no—
590C2×C4⋊C4—611no—
591C2×C4⋊C4—611no—
592C2×C4⋊C4—1222no—
593C2×C4⋊C4—1221no—
594C2×C4⋊C4—1221no—
595C2×C4⋊C4—1228no—
596C2×C4⋊C4—1221no—
597C2×C4⋊C4C22×D6111yescharacteristic
598C2×C4⋊C4C22×D6111yescharacteristic
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—611no—
603C2×C22⋊C4—611no—
604C2×C22⋊C4—1221no—
605C2×C22⋊C4—1221no—
606C2×C22⋊C4—1221no—
607C2×C22⋊C4—1221no—
608C2×C22⋊C4—1221no—
609C2×C22⋊C4—1221no—
610C2×C22⋊C4—1221no—
611C2×C22⋊C4—1221no—
612C2×C42—611no—
613C2×C42—1221no—
614C2×C42—1221no—
615C2×C42—1221no—
616C2×C42C22×D6111yescharacteristic
617#103—1222no—
618#103—1222no—
619#102—22no—
620#102—22no—
621#102—1222no—
622#102—1222no—
623#102—1222no—
624#102—1222no—
625C24—21no—
626C24—21no—
627C24—611no—
628C24—1224no—
629C24—1221no—
630C24—4881no—
631C24—4881no—
632C24—4881no—
633C24—4881no—
634C24—2442no—
635C24—2442no—
636#41—6116no—
637#41—1228no—
638#41—1228no—
639#41—1228no—
640C2×Q8—612no—
641C2×Q8—612no—
642C2×Q8—612no—
643C2×Q8—1221no—
644C2×Q8—1221no—
645C2×Q8—1221no—
646C2×D4—21no—
647C2×D4—21no—
648C2×D4—21no—
649C2×D4—21no—
650C2×D4—21no—
651C2×D4—21no—
652C2×D4—21no—
653C2×D4—21no—
654C2×D4—612no—
655C2×D4—1228no—
656C2×D4—1228no—
657C2×D4—1224no—
658C2×D4—1224no—
659C2×D4—1224no—
660C2×D4—1224no—
661C2×D4—1221no—
662C2×D4—1221no—
663C2×D4—1221no—
664C2×D4—1221no—
665C2×D4—1221no—
666C2×D4—2444no—
667C2×D4—2444no—
668C2×D4—2442no—
669C2×D4—2442no—
670C2×D4C2×C4×D6112yes—
671C2×D4C2×C4×D6112yes—
672C2×D4D4×D6112yes—
673C2×D4D4×D6112yes—
674C22×C4—21no—
675C22×C4—24no—
676C22×C4—21no—
677C22×C4—81no—
678C22×C4—81no—
679C22×C4—611no—
680C22×C4—612no—
681C22×C4—612no—
682C22×C4—612no—
683C22×C4—612no—
684C22×C4—612no—
685C22×C4—612no—
686C22×C4—611no—
687C22×C4—611no—
688C22×C4—1224no—
689C22×C4—1224no—
690C22×C4—1224no—
691C22×C4—1224no—
692C22×C4—1221no—
693C22×C4—1224no—
694C22×C4—1221no—
695C22×C4—1221no—
696C22×C4—4881no—
697C22×C4—4881no—
698C22×C4—4881no—
699C22×C4—4881no—
700C22×C4D4×D6111yescharacteristic
701C22×C4D4×D6111yescharacteristic
702C22×C4C23×D6111yescharacteristic
703SD16—1228no—
704SD16—1228no—
705D8—28no—
706D8—1228no—
707M16—1228no—
708C2×C8—21no—
709C2×C8—21no—
710C2×C8—21no—
711C2×C8—21no—
712C2×C8—21no—
713C2×C8—612no—
714C2×C8—1221no—
715C2×C8—1221no—
716C2×C8—1221no—
717C2×C8—1221no—
718C2×C8—1221no—
719C2×C8—2444no—
720C2×C8C2×C4×D6112yes—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—21no—
724C4⋊C4—612no—
725C4⋊C4—1222no—
726C4⋊C4—1224no—
727C4⋊C4—1222no—
728C4⋊C4—1224no—
729C4⋊C4—1224no—
730C4⋊C4—1221no—
731C4⋊C4—1221no—
732C4⋊C4—1221no—
733C4⋊C4D4×D6112yes—
734C22⋊C4—24no—
735C22⋊C4—81no—
736C22⋊C4—81no—
737C22⋊C4—1222no—
738C22⋊C4—1222no—
739C22⋊C4—1224no—
740C22⋊C4—4881no—
741C22⋊C4—4881no—
742C22⋊C4—4881no—
743C22⋊C4—4881no—
744C22⋊C4—4881no—
745C22⋊C4—4881no—
746C22⋊C4—2442no—
747C42—21no—
748C42—21no—
749C42—1224no—
750C42—1224no—
751C42—1221no—
752C42—1221no—
753C42—2442no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—612no—
769C23—612no—
770C23—612no—
771C23—1221no—
772C23—1221no—
773C23—1221no—
774C23—1221no—
775C23—1222no—
776C23—4884no—
777C23—4884no—
778C23—4884no—
779C23—4884no—
780C23—4884no—
781C23—4884no—
782C23—2448no—
783C23—2441no—
784C23—2441no—
785C23—2441no—
786C23—2441no—
787C23—2441no—
788C23—2441no—
789C23C2×D4×D6111yescharacteristic
790Q8—614no—
791Q8—1222no—
792Q8—1222no—
793Q8—1222no—
794D4—22no—
795D4—22no—
796D4—22no—
797D4—22no—
798D4—22no—
799D4—41no—
800D4—41no—
801D4—12216no—
802D4—1222no—
803D4—1222no—
804D4—2448no—
805D4—2441no—
806D4—2441no—
807D4C22⋊C4×D6114yes—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—22no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—84no—
821C2×C4—612no—
822C2×C4—612no—
823C2×C4—612no—
824C2×C4—614no—
825C2×C4—614no—
826C2×C4—614no—
827C2×C4—614no—
828C2×C4—12216no—
829C2×C4—1222no—
830C2×C4—1222no—
831C2×C4—1222no—
832C2×C4—1221no—
833C2×C4—1222no—
834C2×C4—1221no—
835C2×C4—1221no—
836C2×C4—1221no—
837C2×C4—1221no—
838C2×C4—1221no—
839C2×C4—4884no—
840C2×C4—4884no—
841C2×C4—2441no—
842C2×C4—2441no—
843C2×C4—2441no—
844C2×C4—2441no—
845C2×C4—2441no—
846C2×C4C22×C4×D6111yescharacteristic
847C2×C4C2×D4×D6111yescharacteristic
848C2×C4C2×D4×D6111yescharacteristic
849C2×C4C2×D4×D6111yescharacteristic
850C2×C4#41×D6111yescharacteristic
851C2×C4#41×D6111yescharacteristic
852C8—22no—
853C8—41no—
854C8—1222no—
855C8—2441no—
856C22—24no—
857C22—42no—
858C22—42no—
859C22—42no—
860C22—42no—
861C22—42no—
862C22—42no—
863C22—42no—
864C22—42no—
865C22—42no—
866C22—81no—
867C22—81no—
868C22—81no—
869C22—81no—
870C22—614no—
871C22—1222no—
872C22—1222no—
873C22—1222no—
874C22—1222no—
875C22—1222no—
876C22—1222no—
877C22—48816no—
878C22—4881no—
879C22—4881no—
880C22—4881no—
881C22—4881no—
882C22—2442no—
883C22—2442no—
884C22—2442no—
885C22C4×D4×D6111yescharacteristic
886C22#120×D6111yescharacteristic
887C22#121×D6111yescharacteristic
888C22#1684056311yescharacteristic
889C22#1684056611yescharacteristic
890C22#1684056911yescharacteristic
891C22#1684057211yescharacteristic
892C4—41no—
893C4—42no—
894C4—41no—
895C4—81no—
896C4—614no—
897C4—1224no—
898C4—4881no—
899C4—2441no—
900C4—2442no—
901C4—2441no—
902C4C2×C22⋊C4×D6111yescharacteristic
903C4C4×D4×D6111yescharacteristic
904C4#121×D6111yescharacteristic
905C4#123×D6111yescharacteristic
906C2—44no—
907C2—82no—
908C2—1224no—
909C2—4882no—
910C2#386×D6111yescharacteristic
911C2#2145464411yescharacteristic
912C2#2145464811yescharacteristic
913C2#2145508211yescharacteristic
914C2#2145510211yescharacteristic
915C2#2145535311yescharacteristic
916C2#2145535911yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1879C2
socleC23×C61C22×D4
prime radicalC22×#14519801C2
cosocleC22×C4×C61C24
hypercenter#1879D61
hypocenterC61#20932
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1879

Complements

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

NH ≅ G/Ntype
2. C2×#16840241C2semidirect
3. C2×#16839755C2semidirect
4. C2×#102×D61C2semidirect
5. #21448398C2semidirect
6. #21446177C2semidirect
7. #21446175C2semidirect
8. #21446173C2semidirect
9. #21446171C2semidirect
10. #21446169C2semidirect
11. #21446167C2semidirect
12. #21446165C2semidirect
13. #21445537C2semidirect
14. #21445514C2semidirect
15. C61×#1879C2semidirect
20. C2×#14519801C4semidirect
28. C2×C4×Dic122C22semidirect
29. C2×#14519742C22semidirect
30. C2×D4×Dic61C22semidirect
39. C2×#14519702C22semidirect
40. C2×#14519700C22semidirect
43. C2×#14519698C22semidirect
53. #16839525C22semidirect
54. #16839524C22semidirect
55. #16839524C22semidirect
56. #16839517C22semidirect
57. #16839516C22semidirect
58. #16839516C22semidirect
60. C2×C4×D4×C61C22semidirect
62. C2×#102×C61C22semidirect
64. C61×#340C22semidirect
65. C61×#336C22semidirect
82. C2×D4×D61C2×C4semidirect
90. C2×#11758190C2×C4semidirect
93. C2×#11758200C2×C4semidirect
96. C2×#11758199C2×C4semidirect
99. C2×#11758189C2×C4semidirect
153. C2×D8×C61C2×C4semidirect
218. #11758224C22⋊C4semidirect
460. #1879D61semidirect
492. C2×C4×D4C2×D61semidirect
507. C2×#102C2×D61semidirect
519. #340C2×D61semidirect
523. #336C2×D61semidirect
524. C61#20932semidirect
561. C2×D8C4×D61semidirect

Maximal subgroups

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

subgroupindex
C22×#145198012
C2×#168402412
C2×#168397552
C2×#102×D612
#214483982
#214461772
#214461752
#214461732
#214461712
#214461692
#214461672
#214461652
#214455372
#214455142
C61×#18792
#2093261