Finite Group Databasebeta

← #29681476

Subgroups — #29681476

Order 15616.

1814 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519796C211yesmaximal, characteristic
2C2×#16840241C211yesmaximal, characteristic, complemented
3C2×#16839760C211yesmaximal, characteristic, complemented
4C2×#16839760C211yesmaximal, characteristic, complemented
5#21448409C211yesmaximal, characteristic, complemented
6#21446177C211yesmaximal, characteristic, complemented
7#21446171C211yesmaximal, characteristic, complemented
8#21446169C211yesmaximal, characteristic, complemented
9#21446161C211yesmaximal, characteristic, complemented
10#21446159C211yesmaximal, characteristic, complemented
11#21446153C211yesmaximal, characteristic, complemented
12#21446151C211yesmaximal, characteristic, complemented
13#340×D61C211yesmaximal, characteristic, complemented
14#21445514C211yesmaximal, characteristic, complemented
15C61×#1879C211yesmaximal, characteristic, complemented
16C22×#11758224C2211yescharacteristic
17C22×#11758224C2211yescharacteristic
18C2×#14519796—24no—
19C2×#14519796—24no—
20C2×#14519796C418yescomplemented
21C22×Dic244C2211yescharacteristic
22C22×#11758200C2211yescharacteristic
23C22×#11758200C2211yescharacteristic
24C22×#11758189C2211yescharacteristic
25C22×C8×D61C2211yescharacteristic
26#16840241—24no—
27#16840241—24no—
28C2×C4×Dic122C2211yescharacteristic
29C2×#14519742C2211yescharacteristic
30C2×D4×Dic61C2211yescharacteristic
31C2×C4×C22⋊D61—21no—
32C2×#14519737—21no—
33C2×#14519734C2211yescharacteristic
34C2×#14519733—21no—
35C22×#11758196—21no—
36C2×C4⋊C4×D61C2211yescharacteristic
37C2×C4⋊C4×D61C2211yescharacteristic
38#16839760—24no—
39#16839760—24no—
40C2×#14519702C2211yescharacteristic
41C2×#14519702C2211yescharacteristic
42C2×#14519700C2211yescharacteristic
43C2×#14519700C2211yescharacteristic
44C2×#14519698C2211yescharacteristic
45C2×#14519698C2211yescharacteristic
46#16839668C2211yescharacteristic
47#16839667C2211yescharacteristic
48#16839665C2211yescharacteristic
49#16839638—21no—
50#16839638—21no—
51#16839620—21no—
52#16839620—21no—
53#16839525C2211yescharacteristic
54#16839524C2211yescharacteristic
55#16839524C2211yescharacteristic
56#16839517C2211yescharacteristic
57#16839516C2211yescharacteristic
58#16839516C2211yescharacteristic
59C22×D8×C61C2211yescharacteristic
60C2×C4×D4×C61C2211yescharacteristic
61C2×#102×C61C2211yescharacteristic
62C2×#102×C61C2211yescharacteristic
63C61×#390C2211yescharacteristic
64C61×#340C2211yescharacteristic
65C61×#336C2211yescharacteristic
66C2×#11758224—22no—
67C2×#11758224—22no—
68C2×#11758224—22no—
69C2×#11758224—22no—
70C2×#11758224—22no—
71C2×#11758224—22no—
72C2×#11758224—22no—
73C2×#11758224—22no—
74C2×#11758224C2×C414yes—
75C2×#11758224C2×C414yescomplemented
76C2×#11758224D414yes—
77C2×#11758224D414yes—
78C22×Dic122C2311yescharacteristic
79C22×Dic122C2311yescharacteristic
80C22×C22⋊D61—21no—
81C22×C22⋊D61—21no—
82C23×Dic61—21no—
83C23×Dic61—21no—
84C23×Dic61—21no—
85C22×C4×D61—21no—
86C22×C4×D61—21no—
87C22×C4×D61C2311yescharacteristic
88#14519796—232no—
89C2×Dic244—22no—
90C2×Dic244—22no—
91C2×Dic244C2×C414yescomplemented
92C2×#11758200—22no—
93C2×#11758200—22no—
94C2×#11758200—22no—
95C2×#11758200—22no—
96C2×#11758200C2×C414yescomplemented
97C2×#11758200C2×C414yescomplemented
98C2×#11758189—22no—
99C2×#11758189—22no—
100C2×#11758189—22no—
101C22×#92418C2311yescharacteristic
102C22×#92418C2311yescharacteristic
103C2×C8×D61—22no—
104C2×C8×D61—22no—
105C2×C8×D61C2×C414yescomplemented
106C4×Dic122—22no—
107C4×Dic122—22no—
108#14519742—22no—
109#14519742—22no—
110D4×Dic61—22no—
111D4×Dic61—22no—
112C4×C22⋊D61—28no—
113#14519737—28no—
114#14519734—22no—
115#14519734—22no—
116#14519733—28no—
117C2×C4⋊Dic61C2311yescharacteristic
118C2×C4⋊Dic61C2311yescharacteristic
119C2×#11758196—28no—
120C2×#11758196—21no—
121C2×#11758196—21no—
122C2×#11758196—21no—
123C2×#11758196—21no—
124C2×#11758196D411yescharacteristic
125C2×#11758196D411yescharacteristic
126C4⋊C4×D61—22no—
127C4⋊C4×D61—22no—
128C4⋊C4×D61—22no—
129C4⋊C4×D61D414yes—
130C2×C22⋊Dic61—21no—
131C2×C22⋊Dic61—21no—
132C2×C22⋊Dic61—21no—
133C2×#11758198D411yescharacteristic
134C2×#11758198D411yescharacteristic
135C2×C4×Dic61—21no—
136C2×C4×Dic61—21no—
137C2×C4×Dic61C2311yescharacteristic
138#14519702—22no—
139#14519702—22no—
140#14519700—22no—
141#14519700—22no—
142#14519698—22no—
143#14519698—22no—
144#14519684—21no—
145#14519684—21no—
146#14519684—21no—
147#14519684—21no—
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×D61C2×D411yescharacteristic
169C2×D4×C61—21no—
170C2×D4×C61—21no—
171C2×D4×C61—21no—
172C2×D4×C61—21no—
173C2×D4×C61—21no—
174C2×D4×C61—21no—
175C2×D4×C61—21no—
176C2×D4×C61—21no—
177C2×D4×C61C22×C412yes—
178C2×D4×C61C22×C412yes—
179C2×D4×C61C2×D412yes—
180C2×D4×C61C2×D412yes—
181C22×C4×C61—21no—
182C22×C4×C61—24no—
183C22×C4×C61—21no—
184C22×C4×C61—81no—
185C22×C4×C61—81no—
186C22×C4×C61C2×D411yescharacteristic
187C22×C4×C61C2×D411yescharacteristic
188C22×C4×C61C2411yescharacteristic
189C2×C22⋊D61—24no—
190C2×C22⋊D61—24no—
191C2×C22⋊D61—24no—
192C2×C22⋊D61—24no—
193C2×C22⋊D61—42no—
194C2×C22⋊D61—42no—
195C22×Dic61—21no—
196C22×Dic61—24no—
197C22×Dic61—24no—
198C22×Dic61—24no—
199C22×Dic61—21no—
200C22×Dic61—21no—
201C22×Dic61—24no—
202C22×Dic61—24no—
203C22×Dic61—21no—
204C22×Dic61—42no—
205C22×Dic61—42no—
206C22×Dic61—81no—
207C22×Dic61—81no—
208C22×Dic61C2×D411yescharacteristic
209C22×Dic61C2×D411yescharacteristic
210C22×Dic61C2×D411yescharacteristic
211#11758224—28no—
212#11758224—28no—
213#11758224—28no—
214#11758224—28no—
215#11758224—28no—
216#11758224—44no—
217#11758224—44no—
218#11758224C22⋊C4116yescomplemented
219C2×C4×D61—24no—
220C2×C4×D61—42no—
221C2×C4×D61—81no—
222C2×C4×D61—81no—
223C2×C4×D61—81no—
224C2×C4×D61—81no—
225C2×C4×D61C22×C412yes—
226C2×C4×D61C2×D412yes—
227C2×C4×D61C2×D412yes—
228C2×C4×D61C2×D412yes—
229C2×C4×D61#4112yes—
230C2×C4×D61#4112yes—
231C2×Dic122—21no—
232C2×Dic122—21no—
233C2×Dic122—21no—
234C2×Dic122—21no—
235C2×Dic122—21no—
236C2×Dic122—21no—
237C2×Dic122—21no—
238C2×Dic122—21no—
239C2×Dic122C22×C412yes—
240C2×Dic122C22×C412yes—
241C2×Dic122C2×D412yes—
242C2×Dic122C2×D412yes—
243D8×C61—28no—
244C2×C8×C61—21no—
245C2×C8×C61—21no—
246C2×C8×C61—21no—
247C2×C8×C61—21no—
248C2×C8×C61—21no—
249C2×C8×C61C22×C412yes—
250C4⋊C4×C61—21no—
251C4⋊C4×C61—21no—
252C4⋊C4×C61—21no—
253C4⋊C4×C61C2×D412yes—
254C22⋊C4×C61—24no—
255C22⋊C4×C61—81no—
256C22⋊C4×C61—81no—
257C42×C61—21no—
258C42×C61—21no—
259C22⋊Dic61—24no—
260C22⋊Dic61—81no—
261C22⋊Dic61—81no—
262#11758200—28no—
263#11758200—28no—
264#11758198—22no—
265#11758198—22no—
266C4⋊Dic61—21no—
267C4⋊Dic61—21no—
268C4⋊Dic61—21no—
269C4⋊Dic61C2×D412yes—
270#11758196—24no—
271#11758196—24no—
272#11758196—24no—
273#11758196—22no—
274#11758196—22no—
275#11758196—42no—
276C4×Dic61—24no—
277C4×Dic61—24no—
278C4×Dic61—21no—
279C4×Dic61—21no—
280C2×#92418—21no—
281C2×#92418—21no—
282C2×#92418—21no—
283C2×#92418—21no—
284C2×#92418—21no—
285C2×#92418C22×C412yes—
286Dic244—28no—
287#11758189—44no—
288C8×D61—28no—
289C23×C61—22no—
290C23×C61—22no—
291C23×C61—22no—
292C23×C61—22no—
293C23×C61—41no—
294C23×C61—41no—
295C23×C61—41no—
296C23×C61—41no—
297C23×C61—41no—
298C23×C61—41no—
299C23×C61—41no—
300C23×C61—41no—
301C23×C61—41no—
302C23×C61—41no—
303C23×C61C22×D411yescharacteristic
304C22×D61—21no—
305C22×D61—21no—
306C22×D61—21no—
307C22×D61—21no—
308C22×D61C4×D412yes—
309C22×D61#12012yes—
310C22×D61#12112yes—
311D4×C61—22no—
312D4×C61—22no—
313D4×C61—22no—
314D4×C61—22no—
315D4×C61—22no—
316D4×C61—41no—
317D4×C61—41no—
318D4×C61C2×C22⋊C414yes—
319C2×C4×C61—21no—
320C2×C4×C61—22no—
321C2×C4×C61—21no—
322C2×C4×C61—21no—
323C2×C4×C61—21no—
324C2×C4×C61—21no—
325C2×C4×C61—21no—
326C2×C4×C61—41no—
327C2×C4×C61—41no—
328C2×C4×C61—41no—
329C2×C4×C61—41no—
330C2×C4×C61—41no—
331C2×C4×C61—84no—
332C2×C4×C61C23×C411yescharacteristic
333C2×C4×C61C22×D411yescharacteristic
334C2×C4×C61C22×D411yescharacteristic
335C2×C4×C61C22×D411yescharacteristic
336C2×C4×C61C2×#4111yescharacteristic
337C2×C4×C61C2×#4111yescharacteristic
338C22⋊D61—216no—
339C22⋊D61—48no—
340C2×Dic61—22no—
341C2×Dic61—22no—
342C2×Dic61—22no—
343C2×Dic61—216no—
344C2×Dic61—22no—
345C2×Dic61—21no—
346C2×Dic61—21no—
347C2×Dic61—22no—
348C2×Dic61—21no—
349C2×Dic61—21no—
350C2×Dic61—21no—
351C2×Dic61—21no—
352C2×Dic61—41no—
353C2×Dic61—41no—
354C2×Dic61—41no—
355C2×Dic61—41no—
356C2×Dic61—48no—
357C2×Dic61—41no—
358C2×Dic61—41no—
359C2×Dic61—41no—
360C2×Dic61—84no—
361C2×Dic61C4×D412yes—
362C2×Dic61#12012yes—
363C2×Dic61#12112yes—
364C4×D61—84no—
365C4×D61—84no—
366C4×D61C2×C22⋊C414yes—
367C4×D61C4×D414yes—
368C4×D61#12114yes—
369C4×D61#12314yes—
370Dic122—22no—
371Dic122—22no—
372Dic122—22no—
373Dic122—22no—
374Dic122—22no—
375Dic122—41no—
376Dic122—41no—
377Dic122C2×C22⋊C414yes—
378C8×C61—22no—
379C8×C61—41no—
380#92418—22no—
381#92418—41no—
382#20937—611nomaximal, Sylow
383C22×C61—24no—
384C22×C61—42no—
385C22×C61—42no—
386C22×C61—42no—
387C22×C61—42no—
388C22×C61—42no—
389C22×C61—42no—
390C22×C61—42no—
391C22×C61—42no—
392C22×C61—42no—
393C22×C61—81no—
394C22×C61—81no—
395C22×C61—81no—
396C22×C61—81no—
397C22×C61C2×C4×D411yescharacteristic
398C22×C61C2×#12011yescharacteristic
399C22×C61C2×#12111yescharacteristic
400C22×C61#57611yescharacteristic
401C22×C61#57711yescharacteristic
402C22×C61#57711yescharacteristic
403C22×C61#57811yescharacteristic
404C2×D61—22no—
405C2×D61—22no—
406C2×D61—22no—
407C2×D61—22no—
408C2×D61—22no—
409C2×D61—22no—
410C2×D61#38614yes—
411C4×C61—42no—
412C4×C61—41no—
413C4×C61—41no—
414C4×C61—81no—
415C4×C61C22×C22⋊C411yescharacteristic
416C4×C61C2×C4×D411yescharacteristic
417C4×C61C2×#12111yescharacteristic
418C4×C61C2×#12311yescharacteristic
419Dic61—24no—
420Dic61—42no—
421Dic61—41no—
422Dic61—41no—
423Dic61—42no—
424Dic61—81no—
425Dic61#38614yes—
426C22×#135—611no—
427C2×#520—611no—
428C2×#417—611no—
429C2×#417—611no—
430#2311—611no—
431#1880—611no—
432#1880—611no—
433#1879—611no—
434#1879D6111yescharacteristic, complemented
435#1878—611no—
436#1878—611no—
437#1877—611no—
438#1877—611no—
439C2×#340—611no—
440#1729—611no—
441C2×C61—44no—
442C2×C61—82no—
443C2×C61C2×#38611yescharacteristic
444C2×C61#295111yescharacteristic
445C2×C61#295211yescharacteristic
446C2×C61#301211yescharacteristic
447C2×C61#301311yescharacteristic
448C2×C61#304511yescharacteristic
449C2×C61#304611yescharacteristic
450D61—24no—
451C22×#41—611no—
452C22×#41—611no—
453C2×#135—618no—
454C2×#135—1224no—
455C2×#135—1224no—
456C22×Q16—611no—
457C22×SD16—611no—
458C22×SD16—611no—
459C22×D8C2×D6111yescharacteristic
460C22×M16—611no—
461C23×C8—611no—
462#520—1224no—
463#520—1224no—
464C2×C4×Q8—611no—
465C2×C4×Q8—611no—
466C2×C4×D4—611no—
467C2×C4×D4—1221no—
468C2×C4×D4—1221no—
469C2×C4×D4C2×D6111yescharacteristic
470C2×#117—611no—
471C2×#117—1221no—
472C22×C4⋊C4—611no—
473C22×C4⋊C4—611no—
474C22×C4⋊C4—1221no—
475#417—1224no—
476#417—1224no—
477C2×#103—611no—
478C2×#103—611no—
479C2×#103—611no—
480C2×#103—611no—
481C2×#102—611no—
482C2×#102—611no—
483C2×#102C2×D6111yescharacteristic
484C2×#102C2×D6111yescharacteristic
485#391—611no—
486#391—611no—
487#390—611no—
488#390C2×D6111yescharacteristic
489#386—1221no—
490#386—1221no—
491#380—1221no—
492#380—1221no—
493#340—611no—
494#340—611no—
495#340—611no—
496#340C2×D6111yescharacteristic
497#336—611no—
498#336—611no—
499#336—611no—
500#336C2×D6111yescharacteristic
501C61#2093711yescharacteristic, complemented, Sylow
502C2×#41—614no—
503C2×#41—614no—
504C2×#41—614no—
505C2×#41—614no—
506C2×#41—1222no—
507C2×#41—1222no—
508C2×#41—1222no—
509C2×#41—1222no—
510C2×#41—1222no—
511C2×#41—1222no—
512C2×#41—1222no—
513C2×#41—1222no—
514C22×Q8—611no—
515C22×Q8—611no—
516C22×D4—1221no—
517C22×D4—1221no—
518C22×D4C22×D6111yescharacteristic
519C22×D4C22×D6111yescharacteristic
520C23×C4—21no—
521C23×C4—611no—
522C23×C4—1221no—
523C23×C4—1221no—
524C23×C4—1221no—
525C23×C4—1221no—
526C23×C4—1221no—
527#135—12232no—
528C2×Q16—614no—
529C2×Q16—1222no—
530C2×Q16—1222no—
531C2×SD16—614no—
532C2×SD16—614no—
533C2×SD16—1222no—
534C2×SD16—1222no—
535C2×SD16—1222no—
536C2×SD16—1222no—
537C2×D8—22no—
538C2×D8—22no—
539C2×D8C4×D6114yescomplemented
540C2×M16—1222no—
541C2×M16—1222no—
542C2×M16—1222no—
543C22×C8—611no—
544C22×C8—614no—
545C22×C8—611no—
546C22×C8—1222no—
547C22×C8—1222no—
548C22×C8C22×D6111yescharacteristic
549C22×C8C22×D6111yescharacteristic
550C4×Q8—1222no—
551C4×Q8—1222no—
552C4×Q8—1222no—
553C4×Q8—1222no—
554C4×D4—22no—
555C4×D4—22no—
556C4×D4—1228no—
557C4×D4—1222no—
558C4×D4—1228no—
559C4×D4—1222no—
560#117—1222no—
561#117—1222no—
562#117—1228no—
563C2×C4⋊C4—611no—
564C2×C4⋊C4—614no—
565C2×C4⋊C4—611no—
566C2×C4⋊C4—611no—
567C2×C4⋊C4—611no—
568C2×C4⋊C4—1222no—
569C2×C4⋊C4—1222no—
570C2×C4⋊C4—1222no—
571C2×C4⋊C4—1221no—
572C2×C4⋊C4—1221no—
573C2×C4⋊C4—1228no—
574C2×C4⋊C4—1221no—
575C2×C4⋊C4—1221no—
576C2×C4⋊C4C22×D6111yescharacteristic
577C2×C4⋊C4C22×D6111yescharacteristic
578C2×C22⋊C4—21no—
579C2×C22⋊C4—21no—
580C2×C22⋊C4—21no—
581C2×C22⋊C4—611no—
582C2×C22⋊C4—611no—
583C2×C22⋊C4—1221no—
584C2×C22⋊C4—1221no—
585C2×C22⋊C4—1221no—
586C2×C42—611no—
587C2×C42—1221no—
588C2×C42—1221no—
589C2×C42C22×D6111yescharacteristic
590#103—1222no—
591#103—1222no—
592#103—1222no—
593#103—1222no—
594#102—22no—
595#102—22no—
596#102—1222no—
597#102—1222no—
598#95—1221no—
599#95—1221no—
600#95—1221no—
601#95—1221no—
602C24—21no—
603C24—21no—
604C24—611no—
605#41—6116no—
606#41—1228no—
607#41—1228no—
608#41—1228no—
609#41—1228no—
610#41—1228no—
611#41—2444no—
612#41—2444no—
613C2×Q8—612no—
614C2×Q8—612no—
615C2×Q8—612no—
616C2×Q8—612no—
617C2×Q8—1221no—
618C2×Q8—1221no—
619C2×Q8—1221no—
620C2×Q8—1221no—
621C2×Q8—1221no—
622C2×Q8—1221no—
623C2×Q8—1221no—
624C2×Q8—1221no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—1224no—
634C2×D4—1224no—
635C2×D4—1224no—
636C2×D4—1224no—
637C2×D4—2442no—
638C2×D4—2442no—
639C2×D4C2×C4×D6112yes—
640C2×D4C2×C4×D6112yes—
641C2×D4D4×D6112yes—
642C2×D4D4×D6112yes—
643C22×C4—21no—
644C22×C4—24no—
645C22×C4—21no—
646C22×C4—81no—
647C22×C4—81no—
648C22×C4—611no—
649C22×C4—612no—
650C22×C4—612no—
651C22×C4—612no—
652C22×C4—612no—
653C22×C4—612no—
654C22×C4—612no—
655C22×C4—611no—
656C22×C4—611no—
657C22×C4—1224no—
658C22×C4—1224no—
659C22×C4—1224no—
660C22×C4—1224no—
661C22×C4—1224no—
662C22×C4—1221no—
663C22×C4—1224no—
664C22×C4—1221no—
665C22×C4—1221no—
666C22×C4—1221no—
667C22×C4—4881no—
668C22×C4—4881no—
669C22×C4—4881no—
670C22×C4—4881no—
671C22×C4—4881no—
672C22×C4—4881no—
673C22×C4—2442no—
674C22×C4—2442no—
675C22×C4—2442no—
676C22×C4D4×D6111yescharacteristic
677C22×C4D4×D6111yescharacteristic
678C22×C4C23×D6111yescharacteristic
679Q16—1228no—
680SD16—1228no—
681SD16—1228no—
682D8—28no—
683M16—2444no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—612no—
690C2×C8—1228no—
691C2×C8—1221no—
692C2×C8—1221no—
693C2×C8—1221no—
694C2×C8—1221no—
695C2×C8—1221no—
696C2×C8C2×C4×D6112yes—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—612no—
701C4⋊C4—1222no—
702C4⋊C4—1224no—
703C4⋊C4—1222no—
704C4⋊C4—1224no—
705C4⋊C4—1224no—
706C4⋊C4—1221no—
707C4⋊C4—1221no—
708C4⋊C4—1221no—
709C4⋊C4—2442no—
710C4⋊C4D4×D6112yes—
711C22⋊C4—24no—
712C22⋊C4—81no—
713C22⋊C4—81no—
714C22⋊C4—1222no—
715C22⋊C4—1222no—
716C22⋊C4—1224no—
717C22⋊C4—4881no—
718C22⋊C4—4881no—
719C42—21no—
720C42—21no—
721C42—1224no—
722C42—1224no—
723C42—1221no—
724C42—1221no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—612no—
740C23—612no—
741C23—612no—
742C23—1221no—
743C23—1221no—
744C23—1221no—
745C23—1221no—
746C23C2×D4×D6111yescharacteristic
747Q8—614no—
748Q8—1222no—
749Q8—1222no—
750Q8—1222no—
751Q8—1222no—
752Q8—1222no—
753Q8—2441no—
754Q8—2441no—
755D4—22no—
756D4—22no—
757D4—22no—
758D4—22no—
759D4—22no—
760D4—41no—
761D4—41no—
762D4—12216no—
763D4—2448no—
764D4C22⋊C4×D6114yes—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—22no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—84no—
778C2×C4—612no—
779C2×C4—612no—
780C2×C4—612no—
781C2×C4—614no—
782C2×C4—614no—
783C2×C4—614no—
784C2×C4—614no—
785C2×C4—12216no—
786C2×C4—1222no—
787C2×C4—1222no—
788C2×C4—1222no—
789C2×C4—1222no—
790C2×C4—1221no—
791C2×C4—1222no—
792C2×C4—1221no—
793C2×C4—1221no—
794C2×C4—1221no—
795C2×C4—1221no—
796C2×C4—1221no—
797C2×C4—4884no—
798C2×C4—4884no—
799C2×C4—4884no—
800C2×C4—2448no—
801C2×C4—2441no—
802C2×C4—2441no—
803C2×C4—2441no—
804C2×C4—2441no—
805C2×C4—2441no—
806C2×C4—2441no—
807C2×C4—2441no—
808C2×C4C22×C4×D6111yescharacteristic
809C2×C4C2×D4×D6111yescharacteristic
810C2×C4C2×D4×D6111yescharacteristic
811C2×C4C2×D4×D6111yescharacteristic
812C2×C4#41×D6111yescharacteristic
813C2×C4#41×D6111yescharacteristic
814C8—22no—
815C8—41no—
816C8—1222no—
817C8—2441no—
818C22—24no—
819C22—42no—
820C22—42no—
821C22—42no—
822C22—42no—
823C22—42no—
824C22—42no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—81no—
829C22—81no—
830C22—81no—
831C22—81no—
832C22—614no—
833C22—1222no—
834C22—1222no—
835C22—1222no—
836C22—1222no—
837C22—1222no—
838C22—1222no—
839C22C4×D4×D6111yescharacteristic
840C22#120×D6111yescharacteristic
841C22#121×D6111yescharacteristic
842C22#1684056311yescharacteristic
843C22#1684057211yescharacteristic
844C22#1684057211yescharacteristic
845C22#1684057611yescharacteristic
846C4—41no—
847C4—42no—
848C4—41no—
849C4—81no—
850C4—614no—
851C4—1224no—
852C4—4881no—
853C4—2441no—
854C4—2442no—
855C4—2441no—
856C4—2442no—
857C4C2×C22⋊C4×D6111yescharacteristic
858C4C4×D4×D6111yescharacteristic
859C4#121×D6111yescharacteristic
860C4#123×D6111yescharacteristic
861C2—44no—
862C2—82no—
863C2—1224no—
864C2#386×D6111yescharacteristic
865C2#2145468911yescharacteristic
866C2#2145470111yescharacteristic
867C2#2145511811yescharacteristic
868C2#2145513211yescharacteristic
869C2#2145535311yescharacteristic
870C2#2145537011yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1879C2
socleC23×C61C22×D4
prime radicalC22×#14519796C2
cosocleC22×C4×C61C24
hypercenter#1879D61
hypocenterC61#20937
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×#16839760C2semidirect
4. C2×#16839760C2semidirect
5. #21448409C2semidirect
6. #21446177C2semidirect
7. #21446171C2semidirect
8. #21446169C2semidirect
9. #21446161C2semidirect
10. #21446159C2semidirect
11. #21446153C2semidirect
12. #21446151C2semidirect
13. #340×D61C2semidirect
14. #21445514C2semidirect
15. C61×#1879C2semidirect
20. C2×#14519796C4semidirect
75. C2×#11758224C2×C4semidirect
91. C2×Dic244C2×C4semidirect
96. C2×#11758200C2×C4semidirect
97. C2×#11758200C2×C4semidirect
105. C2×C8×D61C2×C4semidirect
153. C2×D8×C61C2×C4semidirect
218. #11758224C22⋊C4semidirect
434. #1879D61semidirect
501. C61#20937semidirect
539. C2×D8C4×D61semidirect

Maximal subgroups

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

subgroupindex
C22×#145197962
C2×#168402412
C2×#168397602
#214484092
#214461772
#214461712
#214461692
#214461612
#214461592
#214461532
#214461512
#340×D612
#214455142
C61×#18792
#2093761