Finite Group Databasebeta

← #29685765

Subgroups — #29685765

Order 15616.

1476 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840241C211yesmaximal, characteristic, complemented
2C2×#16839904C211yesmaximal, characteristic
3C2×#16839859C211yesmaximal, characteristic, complemented
4C2×D8×Dic61C211yesmaximal, characteristic, complemented
5#21448515C211yesmaximal, characteristic, complemented
6#21446177C211yesmaximal, characteristic, complemented
7#21446133C211yesmaximal, characteristic, complemented
8#21446076C211yesmaximal, characteristic, complemented
9#21446066C211yesmaximal, characteristic, complemented
10#21446008C211yesmaximal, characteristic, complemented
11#21445756C211yesmaximal, characteristic, complemented
12#21445646C211yesmaximal, characteristic, complemented
13#21445638C211yesmaximal, characteristic, complemented
14#21445584C211yesmaximal, characteristic, complemented
15C61×#1879C211yesmaximal, characteristic, complemented
16C22×#11758224C2211yescharacteristic
17C22×#11758200C2211yescharacteristic
18C2×#14519748C2211yescharacteristic
19#16840241—24no—
20#16840241—24no—
21C2×C4×Dic122C2211yescharacteristic
22C2×#14519742C2211yescharacteristic
23C2×D4×Dic61C2211yescharacteristic
24C2×D4×Dic61C2211yescharacteristic
25C2×C4×C22⋊D61—21no—
26C2×#14519737—21no—
27C2×#14519734C2211yescharacteristic
28C2×#14519733—21no—
29C22×#11758196—21no—
30C2×C4⋊C4×D61C2211yescharacteristic
31#16839904C418yescomplemented
32#16839859—24no—
33D8×Dic61—24no—
34C2×#14519711C2211yescharacteristic
35C2×#14519710C2211yescharacteristic
36C2×#14519702C2211yescharacteristic
37C2×#14519702C2211yescharacteristic
38C2×#14519700C2211yescharacteristic
39C2×#14519698C2211yescharacteristic
40C2×#14519698C2211yescharacteristic
41C2×#14519698C2211yescharacteristic
42C2×#14519689C2211yescharacteristic
43C2×#14519689C2211yescharacteristic
44C2×#14519687C2211yescharacteristic
45C2×C8×Dic61C2211yescharacteristic
46#16839662—21no—
47#16839660C2211yescharacteristic
48#16839650—21no—
49#16839639—21no—
50#16839634—21no—
51#16839619C2211yescharacteristic
52C4⋊C4×Dic61C2211yescharacteristic
53#16839525C2211yescharacteristic
54#16839524C2211yescharacteristic
55#16839524C2211yescharacteristic
56#16839517C2211yescharacteristic
57C22×D8×C61C2211yescharacteristic
58C2×C4×D4×C61C2211yescharacteristic
59C2×#102×C61C2211yescharacteristic
60C2×#102×C61C2211yescharacteristic
61C61×#390C2211yescharacteristic
62C61×#340C2211yescharacteristic
63C61×#336C2211yescharacteristic
64C2×#11758224—22no—
65C2×#11758224—22no—
66C2×#11758224—22no—
67C2×#11758224—22no—
68C2×#11758224—22no—
69C2×#11758224C2×C414yescomplemented
70C22×Dic122C2311yescharacteristic
71C22×C22⋊D61—21no—
72C22×C22⋊D61—21no—
73C23×Dic61—21no—
74C23×Dic61—21no—
75C23×Dic61—21no—
76C22×C4×D61—21no—
77C22×C4×D61C2311yescharacteristic
78C2×#11758200—22no—
79C2×#11758200—22no—
80C2×#11758200C2×C414yescomplemented
81C22×#92418C2311yescharacteristic
82C22×#92418C2311yescharacteristic
83#14519748—22no—
84#14519748C2×C414yescomplemented
85C4×Dic122—22no—
86C4×Dic122—22no—
87#14519742—22no—
88#14519742D414yescomplemented
89D4×Dic61—22no—
90D4×Dic61—22no—
91D4×Dic61—22no—
92D4×Dic61D414yescomplemented
93C4×C22⋊D61—28no—
94#14519737—28no—
95#14519734—22no—
96#14519734—22no—
97#14519733—28no—
98C2×C4⋊Dic61C2311yescharacteristic
99C2×C4⋊Dic61C2311yescharacteristic
100C2×C4⋊Dic61C2311yescharacteristic
101C2×#11758196—28no—
102C2×#11758196—21no—
103C2×#11758196—21no—
104C2×#11758196—21no—
105C2×#11758196—21no—
106C2×#11758196D411yescharacteristic
107C2×#11758196D411yescharacteristic
108C4⋊C4×D61—22no—
109C4⋊C4×D61—22no—
110C2×C22⋊Dic61—21no—
111C2×C22⋊Dic61—21no—
112C2×C22⋊Dic61—21no—
113C2×#11758198—21no—
114C2×#11758198D411yescharacteristic
115C2×#11758198D411yescharacteristic
116C2×C4×Dic61—21no—
117C2×C4×Dic61—21no—
118C2×C4×Dic61—21no—
119C2×C4×Dic61C2311yescharacteristic
120#14519711—22no—
121#14519710—22no—
122#14519702—22no—
123#14519702C2×C414yescomplemented
124#14519700—22no—
125#14519698—22no—
126#14519698—22no—
127#14519698C2×C414yescomplemented
128#14519689—22no—
129#14519689C2×C414yescomplemented
130#14519687—22no—
131C8×Dic61—22no—
132#14519684—21no—
133#14519684—21no—
134#14519684—21no—
135C22×D4×C61C2311yescharacteristic
136C22×D4×C61C2311yescharacteristic
137C23×C4×C61—21no—
138C2×D8×C61—22no—
139C2×D8×C61—22no—
140C2×D8×C61C2×C414yescomplemented
141C22×C8×C61C2311yescharacteristic
142C22×C8×C61C2311yescharacteristic
143C4×D4×C61—22no—
144C4×D4×C61—22no—
145C2×C4⋊C4×C61C2311yescharacteristic
146C2×C4⋊C4×C61C2311yescharacteristic
147C2×C22⋊C4×C61—21no—
148C2×C22⋊C4×C61—21no—
149C2×C22⋊C4×C61—21no—
150C2×C42×C61C2311yescharacteristic
151#102×C61—22no—
152#102×C61—22no—
153C24×C61—21no—
154C24×C61—21no—
155C23×D61C2×D411yescharacteristic
156C2×D4×C61—21no—
157C2×D4×C61—21no—
158C2×D4×C61—21no—
159C2×D4×C61—21no—
160C2×D4×C61—21no—
161C2×D4×C61—21no—
162C2×D4×C61—21no—
163C2×D4×C61—21no—
164C2×D4×C61C22×C412yes—
165C2×D4×C61C22×C412yes—
166C2×D4×C61C2×D412yes—
167C2×D4×C61#4112yes—
168C22×C4×C61—21no—
169C22×C4×C61—24no—
170C22×C4×C61—21no—
171C22×C4×C61—81no—
172C22×C4×C61—81no—
173C22×C4×C61C2×D411yescharacteristic
174C22×C4×C61C2×D411yescharacteristic
175C22×C4×C61C2411yescharacteristic
176C2×C22⋊D61—24no—
177C2×C22⋊D61—24no—
178C2×C22⋊D61—24no—
179C2×C22⋊D61—24no—
180C2×C22⋊D61—81no—
181C2×C22⋊D61—81no—
182C22×Dic61—24no—
183C22×Dic61—24no—
184C22×Dic61—21no—
185C22×Dic61—24no—
186C22×Dic61—21no—
187C22×Dic61—21no—
188C22×Dic61—24no—
189C22×Dic61—21no—
190C22×Dic61—42no—
191C22×Dic61—81no—
192C22×Dic61—81no—
193C22×Dic61—81no—
194C22×Dic61—81no—
195C22×Dic61C2×D411yescharacteristic
196C22×Dic61C2×D411yescharacteristic
197C22×Dic61C2×D411yescharacteristic
198#11758224—28no—
199#11758224—28no—
200#11758224—28no—
201#11758224—28no—
202C2×C4×D61—21no—
203C2×C4×D61—21no—
204C2×C4×D61—21no—
205C2×C4×D61—21no—
206C2×C4×D61—24no—
207C2×C4×D61—81no—
208C2×C4×D61—81no—
209C2×C4×D61C22×C412yes—
210C2×C4×D61#4112yes—
211C2×Dic122—21no—
212C2×Dic122—21no—
213C2×Dic122—21no—
214C2×Dic122C22×C412yes—
215C2×Dic122C2×D412yes—
216C2×Dic122#4112yes—
217D8×C61—28no—
218C2×C8×C61—21no—
219C2×C8×C61—21no—
220C2×C8×C61—21no—
221C2×C8×C61—21no—
222C2×C8×C61—21no—
223C2×C8×C61C22×C412yes—
224C4⋊C4×C61—21no—
225C4⋊C4×C61—21no—
226C4⋊C4×C61—21no—
227C4⋊C4×C61C2×D412yes—
228C22⋊C4×C61—24no—
229C22⋊C4×C61—81no—
230C22⋊C4×C61—81no—
231C42×C61—21no—
232C42×C61—21no—
233C22⋊Dic61—24no—
234C22⋊Dic61—24no—
235C22⋊Dic61—42no—
236#11758200—28no—
237#11758198—22no—
238#11758198—22no—
239#11758198—81no—
240C4⋊Dic61—21no—
241C4⋊Dic61—21no—
242C4⋊Dic61—21no—
243C4⋊Dic61—21no—
244C4⋊Dic61C22×C412yes—
245C4⋊Dic61C2×D412yes—
246#11758196—24no—
247#11758196—24no—
248#11758196—22no—
249#11758196—24no—
250#11758196—22no—
251#11758196—81no—
252C4×Dic61—24no—
253C4×Dic61—24no—
254C4×Dic61—81no—
255C4×Dic61C2×D412yes—
256C4×Dic61C2×D412yes—
257C2×#92418—21no—
258C2×#92418—21no—
259C2×#92418—21no—
260C2×#92418—21no—
261C2×#92418—21no—
262C2×#92418C22×C412yes—
263C23×C61—22no—
264C23×C61—22no—
265C23×C61—22no—
266C23×C61—22no—
267C23×C61—41no—
268C23×C61—41no—
269C23×C61—41no—
270C23×C61—41no—
271C23×C61—41no—
272C23×C61—41no—
273C23×C61—41no—
274C23×C61—41no—
275C23×C61—41no—
276C23×C61—41no—
277C23×C61C22×D411yescharacteristic
278C22×D61—21no—
279C22×D61—21no—
280C22×D61—21no—
281C22×D61—21no—
282C22×D61—21no—
283C22×D61—21no—
284C22×D61C4×D412yes—
285D4×C61—22no—
286D4×C61—22no—
287D4×C61—22no—
288D4×C61—22no—
289D4×C61—22no—
290D4×C61—41no—
291D4×C61—41no—
292D4×C61C4×D414yes—
293C2×C4×C61—21no—
294C2×C4×C61—22no—
295C2×C4×C61—21no—
296C2×C4×C61—21no—
297C2×C4×C61—21no—
298C2×C4×C61—21no—
299C2×C4×C61—21no—
300C2×C4×C61—41no—
301C2×C4×C61—41no—
302C2×C4×C61—41no—
303C2×C4×C61—41no—
304C2×C4×C61—41no—
305C2×C4×C61—84no—
306C2×C4×C61C23×C411yescharacteristic
307C2×C4×C61C22×D411yescharacteristic
308C2×C4×C61C22×D411yescharacteristic
309C2×C4×C61C2×#4111yescharacteristic
310C2×C4×C61C2×#4111yescharacteristic
311C2×C4×C61C2×#4111yescharacteristic
312C22⋊D61—216no—
313C22⋊D61—84no—
314C2×Dic61—216no—
315C2×Dic61—22no—
316C2×Dic61—22no—
317C2×Dic61—21no—
318C2×Dic61—22no—
319C2×Dic61—21no—
320C2×Dic61—21no—
321C2×Dic61—21no—
322C2×Dic61—21no—
323C2×Dic61—21no—
324C2×Dic61—22no—
325C2×Dic61—22no—
326C2×Dic61—41no—
327C2×Dic61—41no—
328C2×Dic61—41no—
329C2×Dic61—41no—
330C2×Dic61—41no—
331C2×Dic61—41no—
332C2×Dic61—41no—
333C2×Dic61—84no—
334C2×Dic61—84no—
335C2×Dic61C4×D412yes—
336C2×Dic61#12012yes—
337C2×Dic61#12012yes—
338C4×D61—22no—
339C4×D61—22no—
340C4×D61—22no—
341C4×D61—22no—
342C4×D61—84no—
343Dic122—22no—
344Dic122—22no—
345Dic122—22no—
346Dic122C4×D414yes—
347C8×C61—22no—
348C8×C61—41no—
349#92418—22no—
350#92418—41no—
351#21460—611nomaximal, Sylow
352C22×C61—24no—
353C22×C61—42no—
354C22×C61—42no—
355C22×C61—42no—
356C22×C61—42no—
357C22×C61—42no—
358C22×C61—42no—
359C22×C61—42no—
360C22×C61—42no—
361C22×C61—42no—
362C22×C61—81no—
363C22×C61—81no—
364C22×C61—81no—
365C22×C61—81no—
366C22×C61C2×C4×D411yescharacteristic
367C22×C61C2×#12011yescharacteristic
368C22×C61#52511yescharacteristic
369C22×C61#57611yescharacteristic
370C22×C61#57611yescharacteristic
371C22×C61#57711yescharacteristic
372C22×C61#57811yescharacteristic
373C2×D61—22no—
374C2×D61—22no—
375C2×D61—22no—
376C2×D61—41no—
377C2×D61—41no—
378C2×D61—41no—
379C2×D61—41no—
380C4×C61—42no—
381C4×C61—41no—
382C4×C61—41no—
383C4×C61—81no—
384C4×C61C2×C4×D411yescharacteristic
385C4×C61C2×C4×D411yescharacteristic
386C4×C61#52511yescharacteristic
387C4×C61#52511yescharacteristic
388Dic61—22no—
389Dic61—22no—
390Dic61—24no—
391Dic61—22no—
392Dic61—42no—
393Dic61—42no—
394Dic61—81no—
395C2×#520—611no—
396C2×#449—611no—
397C2×#440—611no—
398C2×C4×D8—611no—
399#2324—611no—
400#1880—611no—
401#1879D6111yescharacteristic, complemented
402#1874—611no—
403#1863—611no—
404#1862—611no—
405#1852—611no—
406#1788—611no—
407#1762—611no—
408C4×#103—611no—
409#1750—611no—
410C2×C61—44no—
411C2×C61—82no—
412C2×C61C4×#12011yescharacteristic
413C2×C61#294611yescharacteristic
414C2×C61#295111yescharacteristic
415C2×C61#300811yescharacteristic
416C2×C61#301311yescharacteristic
417C2×C61#311911yescharacteristic
418C2×C61#312411yescharacteristic
419D61—42no—
420C22×#41—611no—
421C22×SD16—611no—
422C22×D8C2×D6111yescharacteristic
423C2×#121—611no—
424#520—1224no—
425#520—1224no—
426C2×C4×Q8—611no—
427C2×C4×Q8—611no—
428C2×C4×D4—611no—
429C2×C4×D4—611no—
430C2×C4×D4—1221no—
431C2×C4×D4—1221no—
432C2×C4×D4C2×D6111yescharacteristic
433C2×#117—611no—
434C2×#117—1221no—
435C22×C4⋊C4—611no—
436C22×C4⋊C4—1221no—
437#449—618no—
438#440—1224no—
439C4×D8—1224no—
440C2×#107—611no—
441C2×#107—611no—
442C2×#103—611no—
443C2×#103—611no—
444C2×#103—611no—
445C2×#102—611no—
446C2×#102—611no—
447C2×#102—611no—
448C2×#102C2×D6111yescharacteristic
449C2×#102C2×D6111yescharacteristic
450C2×C22⋊C8—611no—
451C2×C22⋊C8—611no—
452C2×#97—611no—
453C2×C4×C8—611no—
454#390—1221no—
455#390C2×D6111yescharacteristic
456#389—611no—
457#388—1221no—
458#386—1221no—
459#385—1221no—
460#380—611no—
461C4×C4⋊C4—611no—
462#340—611no—
463#340—611no—
464#340—611no—
465#340C2×D6111yescharacteristic
466#336—611no—
467#336C2×D6111yescharacteristic
468C61#2146011yescharacteristic, complemented, Sylow
469C2×#41—614no—
470C2×#41—1222no—
471C2×#41—1222no—
472C2×#41—1222no—
473C2×#41—1222no—
474C2×#41—1222no—
475C22×Q8—611no—
476C22×D4—1221no—
477C22×D4—1221no—
478C22×D4C22×D6111yescharacteristic
479C22×D4C22×D6111yescharacteristic
480C23×C4—21no—
481C23×C4—611no—
482C23×C4—1221no—
483C23×C4—1221no—
484C23×C4—1221no—
485C23×C4—1221no—
486C2×SD16—614no—
487C2×SD16—1222no—
488C2×SD16—1222no—
489C2×D8—22no—
490C2×D8—22no—
491C2×D8C4×D6114yescomplemented
492C22×C8—611no—
493C22×C8—611no—
494C22×C8C22×D6111yescharacteristic
495C22×C8C22×D6111yescharacteristic
496#121—614no—
497#121—1222no—
498C4×Q8—614no—
499C4×Q8—1222no—
500C4×Q8—1222no—
501C4×Q8—1222no—
502C4×D4—22no—
503C4×D4—22no—
504C4×D4—614no—
505C4×D4—1222no—
506C4×D4—1222no—
507C4×D4—1222no—
508C4×D4—1228no—
509C4×D4—1228no—
510#117—1222no—
511#117—1222no—
512#117—1228no—
513C2×C4⋊C4—611no—
514C2×C4⋊C4—611no—
515C2×C4⋊C4—611no—
516C2×C4⋊C4—611no—
517C2×C4⋊C4—611no—
518C2×C4⋊C4—1222no—
519C2×C4⋊C4—1221no—
520C2×C4⋊C4—1221no—
521C2×C4⋊C4—1228no—
522C2×C4⋊C4—1221no—
523C2×C4⋊C4—1222no—
524C2×C4⋊C4—1221no—
525C2×C4⋊C4C22×D6111yescharacteristic
526C2×C4⋊C4C22×D6111yescharacteristic
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—611no—
531C2×C22⋊C4—611no—
532C2×C22⋊C4—1221no—
533C2×C22⋊C4—1221no—
534C2×C22⋊C4—1221no—
535C2×C22⋊C4—1221no—
536C2×C42—611no—
537C2×C42—1221no—
538C2×C42—1221no—
539C2×C42—1221no—
540C2×C42C22×D6111yescharacteristic
541#107—1222no—
542#107—1222no—
543#103—614no—
544#103—1222no—
545#103—1222no—
546#102—22no—
547#102—22no—
548#102—614no—
549#102—1222no—
550#102—1222no—
551C22⋊C8—614no—
552C22⋊C8—1222no—
553#97—1222no—
554C4×C8—1222no—
555#95—1221no—
556#95—1221no—
557#95—1221no—
558C24—21no—
559C24—21no—
560C24—611no—
561#41—1228no—
562#41—1228no—
563#41—1228no—
564#41—1228no—
565C2×Q8—612no—
566C2×Q8—612no—
567C2×Q8—612no—
568C2×Q8—1221no—
569C2×Q8—1221no—
570C2×Q8—1221no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—1224no—
580C2×D4—1224no—
581C2×D4—1224no—
582C2×D4—1224no—
583C2×D4—4881no—
584C2×D4—4881no—
585C2×D4C2×C4×D6112yes—
586C2×D4C2×C4×D6112yes—
587C2×D4D4×D6112yes—
588C2×D4#1175822412yes—
589C22×C4—21no—
590C22×C4—24no—
591C22×C4—21no—
592C22×C4—81no—
593C22×C4—81no—
594C22×C4—611no—
595C22×C4—611no—
596C22×C4—611no—
597C22×C4—612no—
598C22×C4—612no—
599C22×C4—1224no—
600C22×C4—1224no—
601C22×C4—1224no—
602C22×C4—1224no—
603C22×C4—1224no—
604C22×C4—1221no—
605C22×C4—1221no—
606C22×C4—1221no—
607C22×C4—1221no—
608C22×C4—1221no—
609C22×C4—1221no—
610C22×C4—1221no—
611C22×C4—1221no—
612C22×C4—4881no—
613C22×C4—4881no—
614C22×C4—4881no—
615C22×C4—4881no—
616C22×C4—4881no—
617C22×C4—4881no—
618C22×C4—2442no—
619C22×C4D4×D6111yescharacteristic
620C22×C4D4×D6111yescharacteristic
621C22×C4C23×D6111yescharacteristic
622SD16—1228no—
623D8—28no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—612no—
630C2×C8—1221no—
631C2×C8—1221no—
632C2×C8—1221no—
633C2×C8—1221no—
634C2×C8—1221no—
635C2×C8C2×C4×D6112yes—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—612no—
640C4⋊C4—612no—
641C4⋊C4—1222no—
642C4⋊C4—1222no—
643C4⋊C4—1224no—
644C4⋊C4—1224no—
645C4⋊C4—1224no—
646C4⋊C4—1221no—
647C4⋊C4—1221no—
648C4⋊C4—1221no—
649C4⋊C4—1221no—
650C4⋊C4—4881no—
651C4⋊C4D4×D6112yes—
652C22⋊C4—24no—
653C22⋊C4—81no—
654C22⋊C4—81no—
655C22⋊C4—1222no—
656C22⋊C4—1222no—
657C22⋊C4—1224no—
658C22⋊C4—1224no—
659C22⋊C4—4881no—
660C22⋊C4—2442no—
661C42—21no—
662C42—21no—
663C42—612no—
664C42—612no—
665C42—1224no—
666C42—1224no—
667C42—4881no—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—22no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—612no—
683C23—1221no—
684C23—1221no—
685C23—1221no—
686C23—1221no—
687C23—1221no—
688C23—1221no—
689C23C2×D4×D6111yescharacteristic
690Q8—614no—
691Q8—1222no—
692Q8—1222no—
693Q8—1222no—
694D4—22no—
695D4—22no—
696D4—22no—
697D4—22no—
698D4—22no—
699D4—41no—
700D4—41no—
701D4—12216no—
702D4—4884no—
703D4#1451973714yes—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—22no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—84no—
717C2×C4—612no—
718C2×C4—612no—
719C2×C4—612no—
720C2×C4—12216no—
721C2×C4—1222no—
722C2×C4—1222no—
723C2×C4—1221no—
724C2×C4—1221no—
725C2×C4—1222no—
726C2×C4—1221no—
727C2×C4—1221no—
728C2×C4—1221no—
729C2×C4—1221no—
730C2×C4—1222no—
731C2×C4—1222no—
732C2×C4—1222no—
733C2×C4—1222no—
734C2×C4—1222no—
735C2×C4—1222no—
736C2×C4—4884no—
737C2×C4—4884no—
738C2×C4—4884no—
739C2×C4—2441no—
740C2×C4—2441no—
741C2×C4—2441no—
742C2×C4—2441no—
743C2×C4—2441no—
744C2×C4—2441no—
745C2×C4—2441no—
746C2×C4C22×C4×D6111yescharacteristic
747C2×C4C2×D4×D6111yescharacteristic
748C2×C4C2×D4×D6111yescharacteristic
749C2×C4#41×D6111yescharacteristic
750C2×C4#41×D6111yescharacteristic
751C2×C4C2×#1175822411yescharacteristic
752C8—22no—
753C8—41no—
754C8—1222no—
755C8—2441no—
756C22—24no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—42no—
762C22—42no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—81no—
767C22—81no—
768C22—81no—
769C22—81no—
770C22—1222no—
771C22—1222no—
772C22—1222no—
773C22—2441no—
774C22—2441no—
775C22—2441no—
776C22—2441no—
777C22C4×D4×D6111yescharacteristic
778C22#120×D6111yescharacteristic
779C22#1684027211yescharacteristic
780C22#1684056311yescharacteristic
781C22#1684056611yescharacteristic
782C22#1684057211yescharacteristic
783C22#1684057611yescharacteristic
784C4—41no—
785C4—41no—
786C4—42no—
787C4—81no—
788C4—1222no—
789C4—1222no—
790C4—1224no—
791C4—1222no—
792C4—4881no—
793C4—2442no—
794C4—2442no—
795C4C4×D4×D6111yescharacteristic
796C4C2×#1451973711yescharacteristic
797C4#1684027011yescharacteristic
798C4#1684027211yescharacteristic
799C2—44no—
800C2—82no—
801C2—2442no—
802C2#2144832411yescharacteristic
803C2#2145464811yescharacteristic
804C2#2145468911yescharacteristic
805C2#2145508211yescharacteristic
806C2#2145513211yescharacteristic
807C2#2145601511yescharacteristic
808C2#2145607811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1879C2
socleC23×C61C22×D4
prime radicalC2×#16839904C2
cosocleC22×C4×C61C24
hypercenter#1879D61
hypocenterC61#21460
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
1. C2×#16840241C2semidirect
3. C2×#16839859C2semidirect
4. C2×D8×Dic61C2semidirect
5. #21448515C2semidirect
6. #21446177C2semidirect
7. #21446133C2semidirect
8. #21446076C2semidirect
9. #21446066C2semidirect
10. #21446008C2semidirect
11. #21445756C2semidirect
12. #21445646C2semidirect
13. #21445638C2semidirect
14. #21445584C2semidirect
15. C61×#1879C2semidirect
31. #16839904C4semidirect
69. C2×#11758224C2×C4semidirect
80. C2×#11758200C2×C4semidirect
84. #14519748C2×C4semidirect
88. #14519742D4semidirect
92. D4×Dic61D4semidirect
123. #14519702C2×C4semidirect
127. #14519698C2×C4semidirect
129. #14519689C2×C4semidirect
140. C2×D8×C61C2×C4semidirect
401. #1879D61semidirect
468. C61#21460semidirect
491. C2×D8C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168402412
C2×#168399042
C2×#168398592
C2×D8×Dic612
#214485152
#214461772
#214461332
#214460762
#214460662
#214460082
#214457562
#214456462
#214456382
#214455842
C61×#18792
#2146061