Finite Group Databasebeta

← D61×#1826 #29679837

Subgroups — D61×#1826 #29679837

Order 15616.

1606 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#117×D61C211yesmaximal, characteristic
2#407×D61C211yesmaximal, characteristic
3C4×C22⋊C4×D61C211yesmaximal, characteristic
4#21445919C211yesmaximal, characteristic, complemented
5#21445918C211yesmaximal, characteristic, complemented
6#21445917C214yesmaximal, complemented
7#21445916C211yesmaximal, characteristic, complemented
8#339×D61C214yesmaximal, complemented
9C61×#1826C211yesmaximal, characteristic, complemented
10C23×C4×D61C2211yescharacteristic
11C2×M16×D61C2212yes—
12C2×#14519736C2211yescharacteristic
13C2×#14519735C411yescharacteristic, complemented
14C2×#14519735C411yescharacteristic, complemented
15C2×#14519734—21no—
16C2×#14519733—21no—
17#117×D61—21no—
18#117×D61—21no—
19#117×D61—21no—
20#117×D61—21no—
21#117×D61C412yescomplemented
22#117×D61C412yescomplemented
23#117×D61C2212yes—
24#117×D61C2212yes—
25C2×C4⋊C4×D61C411yescharacteristic, complemented
26C2×C4⋊C4×D61C411yescharacteristic, complemented
27C2×C22⋊C4×D61—21no—
28C2×C22⋊C4×D61—21no—
29C2×C42×D61—21no—
30C2×C42×D61C2212yes—
31#16839726C2211yescharacteristic
32#16839725C2212yes—
33#16839724—21no—
34#16839724—21no—
35C22⋊C8×D61—21no—
36C22⋊C8×D61—21no—
37C22⋊C4×Dic61—21no—
38C4×#11758198C2212yes—
39C4×C22⋊Dic61C2211yescharacteristic
40#16839609—21no—
41#95×D61—21no—
42#16839523C2214yescomplemented
43#16839522C2214yescomplemented
44#16839521C2214yescomplemented
45C2×#117×C61C2211yescharacteristic
46C61×#407C2211yescharacteristic
47C4×C22⋊C4×C61C2211yescharacteristic
48C61×#339C2214yescomplemented
49C24×D61D411yescharacteristic
50C23×Dic61D411yescharacteristic
51C22×C4×D61—28no—
52C22×C4×D61—21no—
53C22×C4×D61—21no—
54C22×C4×D61—22no—
55C22×C4×D61C2×C411yescharacteristic
56C22×C4×D61C2×C411yescharacteristic
57C22×C4×D61C2×C411yescharacteristic
58C22×C4×D61C2×C411yescharacteristic
59C22×C4×D61D411yescharacteristic
60C22×C4×D61D411yescharacteristic
61C22×C4×D61D411yescharacteristic
62C22×C4×D61D411yescharacteristic
63C22×C4×D61D411yescharacteristic
64C22×C4×D61D411yescharacteristic
65C22×C4×D61C2311yescharacteristic
66C22×C4×D61C2311yescharacteristic
67C2×#11758194C2312yes—
68C2×#11758189—22no—
69M16×D61—28no—
70C2×C8×D61—22no—
71#14519736—21no—
72#14519736—21no—
73#14519736C2×C412yescomplemented
74#14519736C2312yes—
75#14519735—21no—
76#14519735—21no—
77#14519735—21no—
78#14519735—21no—
79#14519735C2×C412yes—
80#14519735C2×C412yes—
81#14519735C2×C412yescomplemented
82#14519735C2×C412yescomplemented
83#14519734—22no—
84#14519734—22no—
85#14519734—22no—
86#14519734—22no—
87#14519733—22no—
88#14519733—22no—
89#14519733—22no—
90#14519733—22no—
91C2×C4⋊Dic61C2×C411yescharacteristic, complemented
92C2×C4⋊Dic61C2×C411yescharacteristic, complemented
93C2×#11758196—21no—
94C2×#11758196—21no—
95C4⋊C4×D61—21no—
96C4⋊C4×D61—21no—
97C4⋊C4×D61—21no—
98C4⋊C4×D61—21no—
99C4⋊C4×D61C2×C412yes—
100C4⋊C4×D61C2×C412yes—
101C4⋊C4×D61C2×C412yescomplemented
102C4⋊C4×D61C2×C412yescomplemented
103C2×C22⋊Dic61—21no—
104C2×C22⋊Dic61—21no—
105C2×#11758198—21no—
106C2×#11758198—21no—
107C2×#11758198—22no—
108C22⋊C4×D61—28no—
109C22⋊C4×D61—22no—
110C22⋊C4×D61—22no—
111C22⋊C4×D61—22no—
112C22⋊C4×D61—22no—
113C2×C4×Dic61—21no—
114C2×C4×Dic61—21no—
115C2×C4×Dic61—21no—
116C2×C4×Dic61—22no—
117C2×C4×Dic61C2312yes—
118C42×D61—22no—
119C42×D61—22no—
120C42×D61—22no—
121C42×D61—22no—
122C42×D61—28no—
123C22⋊#92418—21no—
124C22⋊#92418—21no—
125#14519689—22no—
126#14519689—22no—
127#14519684—21no—
128#14519684—22no—
129C23×C4×C61C2311yescharacteristic
130C2×M16×C61C2312yes—
131#117×C61—21no—
132#117×C61—21no—
133#117×C61C2×C412yescomplemented
134#117×C61C2312yes—
135C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
136C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
137C2×C22⋊C4×C61—21no—
138C2×C22⋊C4×C61—21no—
139C2×C42×C61—21no—
140C2×C42×C61C2312yes—
141C22⋊C8×C61—21no—
142C22⋊C8×C61—21no—
143#95×C61—21no—
144C24×C61C2×D411yescharacteristic
145C23×D61—24no—
146C23×D61—24no—
147C23×D61—42no—
148C23×D61C22⋊C411yescharacteristic
149C23×D61C22⋊C411yescharacteristic
150C23×D61C22⋊C411yescharacteristic
151C23×D61C22⋊C411yescharacteristic
152C23×D61C2×D411yescharacteristic
153C23×D61C2×D411yescharacteristic
154C22×C4×C61—24no—
155C22×C4×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61—22no—
158C22×C4×C61C22×C411yescharacteristic
159C22×C4×C61C22×C411yescharacteristic
160C22×C4×C61C2×D411yescharacteristic
161C22×C4×C61C2×D411yescharacteristic
162C22×C4×C61C2×D411yescharacteristic
163C22×C4×C61C2411yescharacteristic
164C22×Dic61—24no—
165C22×Dic61—21no—
166C22×Dic61—21no—
167C22×Dic61—22no—
168C22×Dic61C22⋊C411yescharacteristic
169C22×Dic61C22⋊C411yescharacteristic
170C22×Dic61C22⋊C411yescharacteristic
171C22×Dic61C22⋊C411yescharacteristic
172C22×Dic61C2×D411yescharacteristic
173C22×Dic61C2×D411yescharacteristic
174C2×C4×D61—24no—
175C2×C4×D61—24no—
176C2×C4×D61—24no—
177C2×C4×D61—24no—
178C2×C4×D61—24no—
179C2×C4×D61—24no—
180C2×C4×D61—24no—
181C2×C4×D61—24no—
182C2×C4×D61—24no—
183C2×C4×D61—24no—
184C2×C4×D61—24no—
185C2×C4×D61—28no—
186C2×C4×D61—22no—
187C2×C4×D61—22no—
188C2×C4×D61—22no—
189C2×C4×D61—22no—
190C2×C4×D61—44no—
191C2×C4×D61—44no—
192C2×C4×D61—44no—
193C2×C4×D61—44no—
194C2×C4×D61C22⋊C411yescharacteristic
195C2×C4×D61C22⋊C411yescharacteristic
196C2×C4×D61C22⋊C411yescharacteristic
197C2×C4×D61C22⋊C411yescharacteristic
198C2×C4×D61C22⋊C411yescharacteristic
199C2×C4×D61C22⋊C411yescharacteristic
200C2×C4×D61C22⋊C411yescharacteristic
201C2×C4×D61C22⋊C411yescharacteristic
202C2×C4×D61C22×C411yescharacteristic
203C2×C4×D61C22×C411yescharacteristic
204C2×C4×D61C22×C411yescharacteristic
205C2×C4×D61C22×C411yescharacteristic
206C2×C4×D61C2×D411yescharacteristic
207C2×C4×D61C2×D411yescharacteristic
208C2×C4×D61C2×D411yescharacteristic
209C2×C4×D61C2×D411yescharacteristic
210C2×C4×D61#4118yes—
211M16×C61—24no—
212C2×C8×C61—22no—
213C4⋊C4×C61—21no—
214C4⋊C4×C61—21no—
215C4⋊C4×C61C22×C412yes—
216C4⋊C4×C61C22×C412yes—
217C22⋊C4×C61—24no—
218C22⋊C4×C61—22no—
219C22⋊C4×C61—22no—
220C42×C61—22no—
221C42×C61—22no—
222C42×C61—24no—
223C22⋊Dic61—24no—
224C22⋊Dic61—22no—
225C22⋊Dic61—22no—
226#11758198—28no—
227#11758198—22no—
228#11758198—22no—
229#11758198—22no—
230#11758198—22no—
231C4⋊Dic61—21no—
232C4⋊Dic61—21no—
233C4⋊Dic61C22×C412yes—
234C4⋊Dic61C22×C412yes—
235#11758196—22no—
236#11758196—22no—
237#11758196—22no—
238#11758196—22no—
239C4×Dic61—22no—
240C4×Dic61—22no—
241C4×Dic61—22no—
242C4×Dic61—22no—
243C4×Dic61—22no—
244C4×Dic61—22no—
245C4×Dic61—24no—
246C4×Dic61—44no—
247#11758194—24no—
248C2×#92418—22no—
249#11758189—44no—
250C8×D61—44no—
251C23×C61—22no—
252C23×C61—22no—
253C23×C61—41no—
254C23×C61C2×C22⋊C411yescharacteristic
255C23×C61C2×C22⋊C411yescharacteristic
256C23×C61C22×D411yescharacteristic
257C22×D61—22no—
258C22×D61—22no—
259C22×D61—22no—
260C22×D61—22no—
261C22×D61—22no—
262C22×D61—22no—
263C22×D61—22no—
264C22×D61—22no—
265C22×D61—22no—
266C22×D61—22no—
267C22×D61—22no—
268C22×D61—22no—
269C22×D61—22no—
270C22×D61—41no—
271C22×D61—41no—
272C22×D61—41no—
273C22×D61—416no—
274C22×D61#10414yes—
275C22×D61C2×C22⋊C411yescharacteristic
276C22×D61C2×C22⋊C411yescharacteristic
277C22×D61C2×C22⋊C411yescharacteristic
278C22×D61C2×C22⋊C411yescharacteristic
279C22×D61#12314yes—
280C2×C4×C61—22no—
281C2×C4×C61—22no—
282C2×C4×C61—22no—
283C2×C4×C61—22no—
284C2×C4×C61—22no—
285C2×C4×C61—24no—
286C2×C4×C61—22no—
287C2×C4×C61—22no—
288C2×C4×C61—42no—
289C2×C4×C61—42no—
290C2×C4×C61—42no—
291C2×C4×C61—42no—
292C2×C4×C61C2×C22⋊C411yescharacteristic
293C2×C4×C61C2×C22⋊C411yescharacteristic
294C2×C4×C61C23×C411yescharacteristic
295C2×C4×C61C22×D411yescharacteristic
296C2×C4×C61C2×#4114yes—
297C2×Dic61—22no—
298C2×Dic61—22no—
299C2×Dic61—22no—
300C2×Dic61—22no—
301C2×Dic61—22no—
302C2×Dic61—24no—
303C2×Dic61—22no—
304C2×Dic61—22no—
305C2×Dic61—42no—
306C2×Dic61—42no—
307C2×Dic61—42no—
308C2×Dic61—42no—
309C2×Dic61C2×C22⋊C411yescharacteristic
310C2×Dic61C2×C22⋊C411yescharacteristic
311C2×Dic61C2×C22⋊C411yescharacteristic
312C2×Dic61C2×C22⋊C411yescharacteristic
313C2×Dic61#12314yes—
314C4×D61—22no—
315C4×D61—22no—
316C4×D61—22no—
317C4×D61—22no—
318C4×D61—22no—
319C4×D61—22no—
320C4×D61—22no—
321C4×D61—22no—
322C4×D61—22no—
323C4×D61—22no—
324C4×D61—22no—
325C4×D61—22no—
326C4×D61—416no—
327C4×D61—44no—
328C4×D61—44no—
329C4×D61—44no—
330C4×D61—44no—
331C4×D61#11714yes—
332C4×D61#11714yes—
333C4×D61#12314yes—
334C4×D61#12314yes—
335C8×C61—42no—
336#92418—42no—
337C2×#1826—611nomaximal, Sylow
338C22×C61—21no—
339C22×C61—21no—
340C22×C61—21no—
341C22×C61—21no—
342C22×C61—21no—
343C22×C61—21no—
344C22×C61—21no—
345C22×C61—44no—
346C22×C61C2×#10412yes—
347C22×C61C22×C22⋊C411yescharacteristic
348C22×C61C2×#12312yes—
349C2×D61—21no—
350C2×D61—21no—
351C2×D61—21no—
352C2×D61—21no—
353C2×D61—28no—
354C2×D61—28no—
355C2×D61—21no—
356C2×D61—21no—
357C2×D61—21no—
358C2×D61—44no—
359C2×D61—44no—
360C2×D61—44no—
361C2×D61—44no—
362C2×D61#38112yes—
363C2×D61#38112yes—
364C2×D61C2×#10412yes—
365C2×D61C2×#10412yes—
366C2×D61#42112yes—
367C4×C61—21no—
368C4×C61—21no—
369C4×C61—44no—
370C4×C61—42no—
371C4×C61—42no—
372C4×C61C2×#11712yes—
373C4×C61C2×#12312yes—
374Dic61—21no—
375Dic61—21no—
376Dic61—44no—
377Dic61—42no—
378Dic61—42no—
379Dic61#38112yes—
380Dic61#38112yes—
381C22×#117—611no—
382C2×#407—611no—
383C2×C4×C22⋊C4—611no—
384#1826—611no—
385#1826—611no—
386#1826—614no—
387#1826—611no—
388#1826D6111yescharacteristic, direct product factor
389C2×#339—614no—
390C2×C61—22no—
391C2×C61—22no—
392C2×C61—41no—
393C2×C61C2×#38111yescharacteristic
394C2×C61C22×#10411yescharacteristic
395C2×C61C2×#42111yescharacteristic
396D61—22no—
397D61—22no—
398D61—41no—
399D61#182614yesdirect product factor
400C24×C4—611no—
401C22×M16—612no—
402C2×#117—611no—
403C2×#117—612no—
404C2×#117—612no—
405C2×#117—612no—
406C2×#117—612no—
407C2×#117—611no—
408C2×#117—611no—
409C2×#117—1221no—
410C2×#117—1221no—
411C2×#117—1221no—
412C2×#117—1221no—
413C2×#117—1221no—
414C2×#117—1221no—
415C2×#117C2×D6111yescharacteristic
416C22×C4⋊C4—611no—
417C22×C4⋊C4—611no—
418C22×C22⋊C4—1221no—
419C22×C22⋊C4—1221no—
420C22×C42—612no—
421C22×C42—1221no—
422#407—611no—
423#407—612no—
424#407—1221no—
425#407—1221no—
426#407C2×D6111yescharacteristic
427C2×C22⋊C8—1221no—
428C2×C22⋊C8—1221no—
429C4×C22⋊C4—611no—
430C4×C22⋊C4—612no—
431C4×C22⋊C4—1221no—
432C4×C22⋊C4—1221no—
433C4×C22⋊C4C2×D6111yescharacteristic
434C2×#95—1221no—
435#339—614no—
436#339—614no—
437#339—614no—
438#339C2×D6114yescomplemented
439C61C2×#182611yescharacteristic, complemented, Sylow
440C25—611no—
441C23×C4—611no—
442C23×C4—611no—
443C23×C4—611no—
444C23×C4—611no—
445C23×C4—611no—
446C23×C4—611no—
447C23×C4—611no—
448C23×C4—611no—
449C23×C4—611no—
450C23×C4—611no—
451C23×C4—611no—
452C23×C4—611no—
453C23×C4—611no—
454C23×C4—1228no—
455C23×C4—1221no—
456C23×C4—1221no—
457C23×C4—1222no—
458C23×C4C22×D6111yescharacteristic
459C2×M16—612no—
460C2×M16—1222no—
461C2×M16—1228no—
462C2×M16C22×D6112yes—
463C22×C8—1222no—
464#117—21no—
465#117—21no—
466#117—612no—
467#117—612no—
468#117—612no—
469#117—612no—
470#117—612no—
471#117—612no—
472#117—1222no—
473#117—1222no—
474#117—1222no—
475#117—1222no—
476#117—1222no—
477#117—1222no—
478#117—1222no—
479#117—1222no—
480#117—1221no—
481#117—1221no—
482#117—1221no—
483#117—1221no—
484#117—1221no—
485#117—1221no—
486#117C4×D6112yescomplemented
487#117C22×D6112yes—
488C2×C4⋊C4—611no—
489C2×C4⋊C4—611no—
490C2×C4⋊C4—612no—
491C2×C4⋊C4—612no—
492C2×C4⋊C4—612no—
493C2×C4⋊C4—612no—
494C2×C4⋊C4—1221no—
495C2×C4⋊C4—1221no—
496C2×C4⋊C4—1221no—
497C2×C4⋊C4—1221no—
498C2×C4⋊C4—1221no—
499C2×C4⋊C4—1221no—
500C2×C4⋊C4C4×D6111yescharacteristic, complemented
501C2×C4⋊C4C4×D6111yescharacteristic, complemented
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—1222no—
505C2×C22⋊C4—1222no—
506C2×C22⋊C4—1222no—
507C2×C22⋊C4—1222no—
508C2×C22⋊C4—1228no—
509C2×C22⋊C4—1221no—
510C2×C22⋊C4—1221no—
511C2×C22⋊C4—1222no—
512C2×C22⋊C4—1221no—
513C2×C22⋊C4—1221no—
514C2×C42—21no—
515C2×C42—612no—
516C2×C42—1222no—
517C2×C42—1222no—
518C2×C42—1222no—
519C2×C42—1222no—
520C2×C42—1228no—
521C2×C42—1221no—
522C2×C42—1221no—
523C2×C42—1221no—
524C2×C42—1222no—
525C2×C42C22×D6112yes—
526C22⋊C8—21no—
527C22⋊C8—21no—
528C22⋊C8—1222no—
529C22⋊C8—1222no—
530C22⋊C8—1221no—
531C22⋊C8—1221no—
532#95—21no—
533#95—1222no—
534#95—1221no—
535C24—611no—
536C24—611no—
537C24—611no—
538C24—611no—
539C24—611no—
540C24—611no—
541C24—1224no—
542C24—1224no—
543C24—2442no—
544C24D4×D6111yescharacteristic
545C22×C4—24no—
546C22×C4—22no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—611no—
550C22×C4—611no—
551C22×C4—611no—
552C22×C4—611no—
553C22×C4—611no—
554C22×C4—618no—
555C22×C4—611no—
556C22×C4—611no—
557C22×C4—611no—
558C22×C4—611no—
559C22×C4—611no—
560C22×C4—611no—
561C22×C4—611no—
562C22×C4—611no—
563C22×C4—611no—
564C22×C4—611no—
565C22×C4—611no—
566C22×C4—611no—
567C22×C4—611no—
568C22×C4—611no—
569C22×C4—611no—
570C22×C4—611no—
571C22×C4—611no—
572C22×C4—1224no—
573C22×C4—1224no—
574C22×C4—1224no—
575C22×C4—1224no—
576C22×C4—1224no—
577C22×C4—1224no—
578C22×C4—1224no—
579C22×C4—1224no—
580C22×C4—1224no—
581C22×C4—1224no—
582C22×C4—1222no—
583C22×C4—1222no—
584C22×C4—1222no—
585C22×C4—1222no—
586C22×C4—1228no—
587C22×C4—1224no—
588C22×C4—1224no—
589C22×C4—1222no—
590C22×C4—1221no—
591C22×C4—1221no—
592C22×C4—2444no—
593C22×C4—2444no—
594C22×C4—2444no—
595C22×C4—2444no—
596C22×C4C2×C4×D6111yescharacteristic
597C22×C4C2×C4×D6111yescharacteristic
598C22×C4D4×D6111yescharacteristic
599C22×C4D4×D6111yescharacteristic
600C22×C4D4×D6111yescharacteristic
601C22×C4C23×D6111yescharacteristic
602M16—24no—
603M16—1224no—
604M16—2444no—
605C2×C8—22no—
606C2×C8—1222no—
607C2×C8—2444no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—612no—
611C4⋊C4—612no—
612C4⋊C4—1222no—
613C4⋊C4—1222no—
614C4⋊C4—1222no—
615C4⋊C4—1222no—
616C4⋊C4—1221no—
617C4⋊C4—1221no—
618C4⋊C4C2×C4×D6112yes—
619C4⋊C4C2×C4×D6112yes—
620C22⋊C4—24no—
621C22⋊C4—22no—
622C22⋊C4—22no—
623C22⋊C4—1222no—
624C22⋊C4—1222no—
625C22⋊C4—1222no—
626C22⋊C4—1222no—
627C22⋊C4—1228no—
628C22⋊C4—1224no—
629C22⋊C4—1222no—
630C22⋊C4—1222no—
631C42—22no—
632C42—22no—
633C42—24no—
634C42—1222no—
635C42—1222no—
636C42—1222no—
637C42—1222no—
638C42—1222no—
639C42—1222no—
640C42—1224no—
641C42—2444no—
642C23—22no—
643C23—22no—
644C23—41no—
645C23—611no—
646C23—611no—
647C23—611no—
648C23—614no—
649C23—614no—
650C23—611no—
651C23—1222no—
652C23—1222no—
653C23—1222no—
654C23—1222no—
655C23—1222no—
656C23—1222no—
657C23—1222no—
658C23—1222no—
659C23—1222no—
660C23—1222no—
661C23—1222no—
662C23—1222no—
663C23—1222no—
664C23—2441no—
665C23—2441no—
666C23—2441no—
667C23—24416no—
668C23C22⋊C4×D6111yescharacteristic
669C23C22⋊C4×D6111yescharacteristic
670C23C2×D4×D6111yescharacteristic
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—24no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—611no—
684C2×C4—611no—
685C2×C4—614no—
686C2×C4—614no—
687C2×C4—614no—
688C2×C4—614no—
689C2×C4—614no—
690C2×C4—611no—
691C2×C4—611no—
692C2×C4—1222no—
693C2×C4—1222no—
694C2×C4—1222no—
695C2×C4—1222no—
696C2×C4—1222no—
697C2×C4—1222no—
698C2×C4—1222no—
699C2×C4—1222no—
700C2×C4—1222no—
701C2×C4—1222no—
702C2×C4—1222no—
703C2×C4—1222no—
704C2×C4—1222no—
705C2×C4—1222no—
706C2×C4—1222no—
707C2×C4—1222no—
708C2×C4—1222no—
709C2×C4—1224no—
710C2×C4—1222no—
711C2×C4—1222no—
712C2×C4—2444no—
713C2×C4—2444no—
714C2×C4—2444no—
715C2×C4—24416no—
716C2×C4—2444no—
717C2×C4—2442no—
718C2×C4—2442no—
719C2×C4—2442no—
720C2×C4—2442no—
721C2×C4C22⋊C4×D6111yescharacteristic
722C2×C4C22⋊C4×D6111yescharacteristic
723C2×C4C22×C4×D6111yescharacteristic
724C2×C4C2×D4×D6111yescharacteristic
725C2×C4#41×D6114yes—
726C8—42no—
727C8—2442no—
728C22—21no—
729C22—21no—
730C22—21no—
731C22—21no—
732C22—21no—
733C22—21no—
734C22—21no—
735C22—44no—
736C22—612no—
737C22—612no—
738C22—612no—
739C22—612no—
740C22—612no—
741C22—1228no—
742C22—1228no—
743C22—1221no—
744C22—1221no—
745C22—1221no—
746C22—1221no—
747C22—1221no—
748C22—1221no—
749C22—1221no—
750C22—2444no—
751C22—2444no—
752C22—2444no—
753C22—2444no—
754C22#104×D6112yes—
755C22C2×C22⋊C4×D6111yescharacteristic
756C22#123×D6112yes—
757C4—21no—
758C4—21no—
759C4—44no—
760C4—42no—
761C4—42no—
762C4—612no—
763C4—612no—
764C4—1221no—
765C4—1221no—
766C4—2444no—
767C4—2442no—
768C4—2442no—
769C4#117×D6112yes—
770C4#123×D6112yes—
771C2—22no—
772C2—22no—
773C2—41no—
774C2—614no—
775C2—1222no—
776C2—1222no—
777C2—2441no—
778C2#381×D6111yescharacteristic
779C2C2×#104×D6111yescharacteristic
780C2#421×D6111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1826C2
socleC22×C61C22×C22⋊C4
prime radicalC24×D61D4
cosocleC22×C4×C61C24
hypercenter#1826D61
hypocenterC61C2×#1826
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1826

Complements

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

NH ≅ G/Ntype
4. #21445919C2semidirect
5. #21445918C2semidirect
6. #21445917C2semidirect
7. #21445916C2semidirect
8. #339×D61C2semidirect
9. C61×#1826C2semidirect
13. C2×#14519735C4semidirect
14. C2×#14519735C4semidirect
21. #117×D61C4semidirect
22. #117×D61C4semidirect
25. C2×C4⋊C4×D61C4semidirect
26. C2×C4⋊C4×D61C4semidirect
42. #16839523C22semidirect
43. #16839522C22semidirect
44. #16839521C22semidirect
48. C61×#339C22semidirect
73. #14519736C2×C4semidirect
81. #14519735C2×C4semidirect
82. #14519735C2×C4semidirect
91. C2×C4⋊Dic61C2×C4semidirect
92. C2×C4⋊Dic61C2×C4semidirect
101. C4⋊C4×D61C2×C4semidirect
102. C4⋊C4×D61C2×C4semidirect
133. #117×C61C2×C4semidirect
135. C2×C4⋊C4×C61C2×C4semidirect
136. C2×C4⋊C4×C61C2×C4semidirect
388. #1826D61direct (N × H)
399. D61#1826direct (N × H)
438. #339C2×D61semidirect
439. C61C2×#1826semidirect
486. #117C4×D61semidirect
500. C2×C4⋊C4C4×D61semidirect
501. C2×C4⋊C4C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#117×D612
#407×D612
C4×C22⋊C4×D612
#214459192
#214459182
#214459172
#214459162
#339×D612
C61×#18262
C2×#182661