Finite Group Databasebeta

← D61×#1802 #29679456

Subgroups — D61×#1802 #29679456

Order 15616.

2030 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D4×D61C211yesmaximal, characteristic
2C2×C4⋊C8×D61C211yesmaximal, characteristic, complemented
3C2×#102×D61C212yesmaximal
4#384×D61C211yesmaximal, characteristic, complemented
5#21445820C211yesmaximal, characteristic, complemented
6#21445819C211yesmaximal, characteristic, complemented
7#21445818C212yesmaximal, complemented
8#21445817C212yesmaximal, complemented
9#21445816C211yesmaximal, characteristic, complemented
10#340×D61C212yesmaximal, complemented
11C61×#1802C211yesmaximal, characteristic, complemented
12C22×D4×D61C2211yescharacteristic
13C23×C4×D61—21no—
14C22×C8×D61C2212yes—
15C2×C4×D244C2211yescharacteristic
16C2×D4×Dic61C2211yescharacteristic
17C2×#14519739C2211yescharacteristic
18C2×C4×C22⋊D61—21no—
19C2×#14519737—21no—
20C4×D4×D61—24no—
21C4×D4×D61C418yescomplemented
22C2×C4⋊C4×D61—21no—
23C2×C4⋊C4×D61—21no—
24C2×C4⋊C4×D61C2212yes—
25C2×C4⋊C4×D61C2211yescharacteristic
26C2×C22⋊C4×D61—21no—
27C2×C42×D61C2211yescharacteristic
28C2×C4⋊#92418C2211yescharacteristic, complemented
29C2×#14519706C2212yescomplemented
30C4⋊C8×D61—24no—
31C2×#14519699C2212yes—
32C2×#14519698C2212yes—
33C2×#14519697C2212yes—
34#102×D61—28no—
35#16839632C2211yescharacteristic, complemented
36#16839631—21no—
37#16839631—21no—
38#16839631C2212yescomplemented
39#16839525C2212yescomplemented
40#16839524C2212yescomplemented
41#16839524C2212yescomplemented
42C2×C4×D4×C61C2211yescharacteristic
43C2×C4⋊C8×C61C2211yescharacteristic, complemented
44C2×#102×C61C2212yes—
45C61×#384C2211yescharacteristic, complemented
46C61×#340C2212yescomplemented
47C24×D61—21no—
48C22×D244C2311yescharacteristic
49C22×C22⋊D61—21no—
50C2×D4×D61—22no—
51C2×D4×D61—22no—
52C2×D4×D61—22no—
53C2×D4×D61C2×C414yes—
54C2×D4×D61D414yes—
55C2×D4×D61Q814yes—
56C23×Dic61—21no—
57C22×C4×D61—21no—
58C22×C4×D61—21no—
59C22×C4×D61—21no—
60C22×C4×D61—28no—
61C22×C4×D61—22no—
62C22×C4×D61—44no—
63C22×C4×D61—44no—
64C22×C4×D61D411yescharacteristic
65C22×C4×D61D411yescharacteristic
66C22×C4×D61C2311yescharacteristic
67C22×#92418C2312yes—
68C2×C8×D61—24no—
69C2×C8×D61—24no—
70C2×C8×D61—24no—
71C4×D244—22no—
72C4×D244C2×C414yescomplemented
73D4×Dic61—22no—
74D4×Dic61C2×C414yescomplemented
75#14519739—22no—
76#14519739C2×C414yescomplemented
77C4×C22⋊D61—28no—
78#14519737—28no—
79C2×C4⋊Dic61—21no—
80C2×C4⋊Dic61—21no—
81C2×C4⋊Dic61C2312yes—
82C2×C4⋊Dic61C2311yescharacteristic
83C2×#11758196—21no—
84C2×#11758196—22no—
85C2×#11758196—22no—
86C2×#11758196—22no—
87C4⋊C4×D61—22no—
88C4⋊C4×D61—24no—
89C4⋊C4×D61—24no—
90C4⋊C4×D61—44no—
91C4⋊C4×D61—44no—
92C4⋊C4×D61C2×C414yes—
93C2×C22⋊Dic61—21no—
94C2×#11758198—21no—
95C2×#11758198—21no—
96C22⋊C4×D61—28no—
97C2×C4×Dic61D411yescharacteristic
98C2×C4×Dic61D411yescharacteristic
99C2×C4×Dic61C2311yescharacteristic
100C42×D61C2×C414yes—
101C42×D61D414yes—
102C4⋊#92418—22no—
103#14519706—24no—
104#14519699—24no—
105#14519698—24no—
106#14519697—24no—
107C22×D4×C61C2311yescharacteristic
108C23×C4×C61—21no—
109C22×C8×C61C2312yes—
110C4×D4×C61—22no—
111C4×D4×C61C2×C414yescomplemented
112C2×C4⋊C4×C61—21no—
113C2×C4⋊C4×C61—21no—
114C2×C4⋊C4×C61C2312yes—
115C2×C4⋊C4×C61C2311yescharacteristic
116C2×C22⋊C4×C61—21no—
117C2×C42×C61C2311yescharacteristic
118C4⋊C8×C61—22no—
119#102×C61—24no—
120C24×C61—21no—
121C23×D61—21no—
122C23×D61—24no—
123C23×D61—24no—
124C23×D61—24no—
125C23×D61—42no—
126C23×D61—42no—
127C23×D61—42no—
128C23×D61—42no—
129C23×D61C2×D411yescharacteristic
130C2×D4×C61—21no—
131C2×D4×C61—21no—
132C2×D4×C61—21no—
133C2×D4×C61C22×C412yes—
134C2×D4×C61C2×D412yes—
135C2×D4×C61C2×Q812yes—
136C22×C4×C61—21no—
137C22×C4×C61—24no—
138C22×C4×C61—22no—
139C22×C4×C61—42no—
140C22×C4×C61—42no—
141C22×C4×C61C2×D411yescharacteristic
142C22×C4×C61C2×D411yescharacteristic
143C22×C4×C61C2411yescharacteristic
144C2×C22⋊D61—24no—
145C2×C22⋊D61—24no—
146C2×C22⋊D61—24no—
147C22×Dic61—21no—
148C22×Dic61—24no—
149C22×Dic61—22no—
150C22×Dic61—42no—
151C22×Dic61—42no—
152C22×Dic61C2×D411yescharacteristic
153C22×Dic61C2×D411yescharacteristic
154C22×Dic61C2×D411yescharacteristic
155D4×D61—28no—
156D4×D61—28no—
157D4×D61—28no—
158D4×D61C4⋊C4116yescomplemented
159C2×D244—21no—
160C2×D244—21no—
161C2×D244—21no—
162C2×D244C22×C412yes—
163C2×D244C2×D412yes—
164C2×D244C2×Q812yes—
165C2×C4×D61—22no—
166C2×C4×D61—22no—
167C2×C4×D61—24no—
168C2×C4×D61—24no—
169C2×C4×D61—24no—
170C2×C4×D61—42no—
171C2×C4×D61—42no—
172C2×C4×D61—42no—
173C2×C4×D61—42no—
174C2×C4×D61—42no—
175C2×C4×D61—42no—
176C2×C4×D61—432no—
177C2×C4×D61—44no—
178C2×C4×D61—44no—
179C2×C4×D61—44no—
180C2×C4×D61C22⋊C414yes—
181C2×C4×D61C22⋊C414yes—
182C2×C4×D61D814yes—
183C2×C4×D61SD1614yes—
184C2×C4×D61C22×C412yes—
185C2×C4×D61C2×D412yes—
186C2×C4×D61C2×D412yes—
187C2×C4×D61C2×Q812yes—
188C2×C4×D61#4112yes—
189C2×C4×D61#4112yes—
190C2×C8×C61—22no—
191C2×C8×C61—22no—
192C2×C8×C61—22no—
193C4⋊C4×C61—21no—
194C4⋊C4×C61—22no—
195C4⋊C4×C61—22no—
196C4⋊C4×C61—42no—
197C4⋊C4×C61—42no—
198C4⋊C4×C61C22×C412yes—
199C22⋊C4×C61—24no—
200C42×C61C22×C412yes—
201C42×C61C2×D412yes—
202C22⋊Dic61—24no—
203#11758198—24no—
204#11758198—24no—
205C4⋊Dic61—21no—
206C4⋊Dic61—22no—
207C4⋊Dic61—22no—
208C4⋊Dic61—42no—
209C4⋊Dic61—42no—
210C4⋊Dic61C22×C412yes—
211#11758196—24no—
212#11758196—44no—
213#11758196—44no—
214#11758196—44no—
215C4×Dic61C22⋊C414yes—
216C4×Dic61C22⋊C414yes—
217C4×Dic61C22×C412yes—
218C4×Dic61C2×D412yes—
219C2×#92418—22no—
220C2×#92418—22no—
221C2×#92418—22no—
222C8×D61—48no—
223C23×C61—22no—
224C23×C61—22no—
225C23×C61—22no—
226C23×C61—41no—
227C23×C61—41no—
228C23×C61—41no—
229C23×C61—41no—
230C23×C61C22×D411yescharacteristic
231C22×D61—22no—
232C22×D61—22no—
233C22×D61—22no—
234C22×D61—216no—
235C22×D61—41no—
236C22×D61—41no—
237C22×D61—41no—
238C22×D61—41no—
239C22×D61—48no—
240C22×D61—48no—
241C22×D61—48no—
242C22×D61—48no—
243C22×D61—48no—
244C22×D61—48no—
245C22×D61C2×C22⋊C412yes—
246C22×D61#12112yes—
247C22×D61C22⋊Q812yes—
248C22×D61C2×D812yes—
249C22×D61C2×SD1612yes—
250C22×D61AGL(1,ℤ/8)12yes—
251C22×D61#13712yes—
252D4×C61—22no—
253D4×C61—22no—
254D4×C61—22no—
255D4×C61C2×C4⋊C414yescomplemented
256C2×C4×C61—21no—
257C2×C4×C61—21no—
258C2×C4×C61—22no—
259C2×C4×C61—41no—
260C2×C4×C61—41no—
261C2×C4×C61—48no—
262C2×C4×C61—42no—
263C2×C4×C61—42no—
264C2×C4×C61—42no—
265C2×C4×C61C2×C22⋊C412yes—
266C2×C4×C61C2×C22⋊C412yes—
267C2×C4×C61C2×D812yes—
268C2×C4×C61C2×SD1612yes—
269C2×C4×C61C23×C411yescharacteristic
270C2×C4×C61C22×D411yescharacteristic
271C2×C4×C61C22×D411yescharacteristic
272C2×C4×C61C22×Q811yescharacteristic
273C2×C4×C61C2×#4111yescharacteristic
274C2×C4×C61C2×#4111yescharacteristic
275C22⋊D61—216no—
276C2×Dic61—21no—
277C2×Dic61—21no—
278C2×Dic61—22no—
279C2×Dic61—41no—
280C2×Dic61—41no—
281C2×Dic61—48no—
282C2×Dic61—42no—
283C2×Dic61—42no—
284C2×Dic61—42no—
285C2×Dic61C2×C22⋊C412yes—
286C2×Dic61C2×C22⋊C412yes—
287C2×Dic61C2×C22⋊C412yes—
288C2×Dic61#12112yes—
289C2×Dic61C22⋊Q812yes—
290C2×Dic61C2×D812yes—
291C2×Dic61C2×SD1612yes—
292D244—22no—
293D244—22no—
294D244—22no—
295D244C2×C4⋊C414yescomplemented
296C4×D61—28no—
297C4×D61—48no—
298C4×D61—48no—
299C4×D61—48no—
300C4×D61—88no—
301C4×D61#102116yescomplemented
302C4×D61C2×C4⋊C414yes—
303C4×D61#11714yes—
304C4×D61#12114yes—
305C4×D61C22⋊Q814yes—
306C8×C61—42no—
307#92418—42no—
308C2×#1802—611nomaximal, Sylow
309C22×C61—24no—
310C22×C61—42no—
311C22×C61—42no—
312C22×C61—42no—
313C22×C61—42no—
314C22×C61—42no—
315C22×C61—42no—
316C22×C61C22×C22⋊C411yescharacteristic
317C22×C61C2×#12111yescharacteristic
318C22×C61C2×C22⋊Q811yescharacteristic
319C22×C61C22×D811yescharacteristic
320C22×C61C22×SD1611yescharacteristic
321C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
322C22×C61C2×#13711yescharacteristic
323C2×D61—24no—
324C2×D61—42no—
325C2×D61—42no—
326C2×D61—42no—
327C2×D61—42no—
328C2×D61—42no—
329C2×D61—42no—
330C2×D61—432no—
331C2×D61#38014yes—
332C2×D61C2×#10214yes—
333C2×D61#41714yes—
334C2×D61#45914yes—
335C2×D61#46114yes—
336C2×D61#47414yes—
337C2×D61#47614yes—
338C4×C61—22no—
339C4×C61—42no—
340C4×C61—82no—
341C4×C61C2×#10214yescomplemented
342C4×C61C22×C4⋊C411yescharacteristic
343C4×C61C2×#11711yescharacteristic
344C4×C61C2×#12111yescharacteristic
345C4×C61C2×C22⋊Q811yescharacteristic
346Dic61—22no—
347Dic61—42no—
348Dic61—82no—
349Dic61#38014yes—
350Dic61C2×#10214yescomplemented
351C22×C4×D4—611no—
352C22×C4⋊C8—611no—
353C22×#102—612no—
354C2×#384—611no—
355#1802—611no—
356#1802—612no—
357#1802—611no—
358#1802—612no—
359#1802—611no—
360#1802D6111yescharacteristic, direct product factor
361C2×#340—612no—
362C2×C61—44no—
363C2×C61C2×#38011yescharacteristic
364C2×C61C22×#10211yescharacteristic
365C2×C61C2×#41711yescharacteristic
366C2×C61C2×#45911yescharacteristic
367C2×C61C2×#46111yescharacteristic
368C2×C61C2×#47411yescharacteristic
369C2×C61C2×#47611yescharacteristic
370D61—44no—
371D61#180218yesdirect product factor
372C23×D4—611no—
373C24×C4—1221no—
374C23×C8—612no—
375C2×C4×D4—611no—
376C2×C4×D4—618no—
377C2×C4×D4—611no—
378C2×C4×D4—611no—
379C2×C4×D4—1221no—
380C2×C4×D4—1224no—
381C2×C4×D4—1221no—
382C2×C4×D4C2×D6111yescharacteristic
383C22×C4⋊C4—611no—
384C22×C4⋊C4—612no—
385C22×C4⋊C4—1221no—
386C22×C4⋊C4—1221no—
387C22×C22⋊C4—1221no—
388C22×C42—611no—
389C2×C4⋊C8—612no—
390C2×C4⋊C8—611no—
391C2×C4⋊C8—1224no—
392C2×C4⋊C8C2×D6111yescharacteristic, complemented
393C2×#102—612no—
394C2×#102—612no—
395C2×#102—612no—
396C2×#102—1228no—
397C2×#102C2×D6112yes—
398#384—612no—
399#384—611no—
400#384—1221no—
401#384—1221no—
402#384C2×D6111yescharacteristic, complemented
403#340—612no—
404#340—612no—
405#340—612no—
406#340C2×D6112yescomplemented
407C61C2×#180211yescharacteristic, complemented, Sylow
408C25—1221no—
409C22×D4—614no—
410C22×D4—614no—
411C22×D4—614no—
412C22×D4—611no—
413C22×D4—1222no—
414C22×D4—1222no—
415C22×D4—1222no—
416C22×D4—1221no—
417C22×D4C22×D6111yescharacteristic
418C23×C4—21no—
419C23×C4—611no—
420C23×C4—611no—
421C23×C4—611no—
422C23×C4—1221no—
423C23×C4—1228no—
424C23×C4—1221no—
425C23×C4—1222no—
426C23×C4—1221no—
427C23×C4—1221no—
428C23×C4—2444no—
429C23×C4—2444no—
430C22×C8—612no—
431C22×C8—1224no—
432C22×C8—1224no—
433C22×C8—1224no—
434C22×C8C22×D6112yes—
435C4×D4—22no—
436C4×D4—614no—
437C4×D4—614no—
438C4×D4—614no—
439C4×D4—1228no—
440C4×D4—1222no—
441C4×D4—1228no—
442C4×D4—1222no—
443C4×D4—1222no—
444C4×D4C4×D6114yescomplemented
445C2×C4⋊C4—21no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—611no—
448C2×C4⋊C4—614no—
449C2×C4⋊C4—612no—
450C2×C4⋊C4—1222no—
451C2×C4⋊C4—1224no—
452C2×C4⋊C4—1224no—
453C2×C4⋊C4—1221no—
454C2×C4⋊C4—1222no—
455C2×C4⋊C4—1222no—
456C2×C4⋊C4—1222no—
457C2×C4⋊C4—1221no—
458C2×C4⋊C4—1221no—
459C2×C4⋊C4—2444no—
460C2×C4⋊C4—2444no—
461C2×C4⋊C4C22×D6112yes—
462C2×C4⋊C4C22×D6111yescharacteristic
463C2×C22⋊C4—21no—
464C2×C22⋊C4—1228no—
465C2×C22⋊C4—1221no—
466C2×C22⋊C4—1221no—
467C2×C22⋊C4—1221no—
468C2×C42—611no—
469C2×C42—611no—
470C2×C42—611no—
471C2×C42—614no—
472C2×C42—614no—
473C2×C42C22×D6111yescharacteristic
474C4⋊C8—22no—
475C4⋊C8—1224no—
476C4⋊C8—1222no—
477#102—24no—
478#102—1224no—
479#102—1224no—
480#102—1224no—
481C24—21no—
482C24—611no—
483C24—1224no—
484C24—1224no—
485C24—1224no—
486C24—1221no—
487C24—2442no—
488C24—2442no—
489C24—2442no—
490C24—2442no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—6116no—
495C2×D4—612no—
496C2×D4—612no—
497C2×D4—612no—
498C2×D4—1228no—
499C2×D4—1228no—
500C2×D4—1228no—
501C2×D4—1224no—
502C2×D4—1224no—
503C2×D4—1224no—
504C2×D4—1221no—
505C2×D4—1221no—
506C2×D4—1221no—
507C2×D4C2×C4×D6112yes—
508C2×D4D4×D6112yes—
509C2×D4Q8×D6112yes—
510C22×C4—21no—
511C22×C4—24no—
512C22×C4—22no—
513C22×C4—42no—
514C22×C4—42no—
515C22×C4—611no—
516C22×C4—611no—
517C22×C4—612no—
518C22×C4—612no—
519C22×C4—612no—
520C22×C4—612no—
521C22×C4—612no—
522C22×C4—612no—
523C22×C4—614no—
524C22×C4—614no—
525C22×C4—614no—
526C22×C4—611no—
527C22×C4—614no—
528C22×C4—1224no—
529C22×C4—1222no—
530C22×C4—1222no—
531C22×C4—1224no—
532C22×C4—1224no—
533C22×C4—1221no—
534C22×C4—1224no—
535C22×C4—1222no—
536C22×C4—2442no—
537C22×C4—2442no—
538C22×C4—24432no—
539C22×C4—2444no—
540C22×C4—2444no—
541C22×C4—2444no—
542C22×C4—2442no—
543C22×C4—2442no—
544C22×C4—2442no—
545C22×C4—2442no—
546C22×C4—2442no—
547C22×C4—2442no—
548C22×C4D4×D6111yescharacteristic
549C22×C4D4×D6111yescharacteristic
550C22×C4C23×D6111yescharacteristic
551C2×C8—22no—
552C2×C8—22no—
553C2×C8—22no—
554C2×C8—1222no—
555C2×C8—1222no—
556C2×C8—1222no—
557C2×C8—2448no—
558C4⋊C4—21no—
559C4⋊C4—22no—
560C4⋊C4—22no—
561C4⋊C4—42no—
562C4⋊C4—42no—
563C4⋊C4—612no—
564C4⋊C4—1224no—
565C4⋊C4—1221no—
566C4⋊C4—1222no—
567C4⋊C4—1222no—
568C4⋊C4—2442no—
569C4⋊C4—2444no—
570C4⋊C4—2444no—
571C4⋊C4—2444no—
572C4⋊C4—2442no—
573C4⋊C4C2×C4×D6112yes—
574C22⋊C4—24no—
575C22⋊C4—1224no—
576C22⋊C4—1224no—
577C22⋊C4—1224no—
578C42—612no—
579C42—612no—
580C42—614no—
581C42—614no—
582C42C2×C4×D6112yes—
583C42D4×D6112yes—
584C23—22no—
585C23—22no—
586C23—22no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—612no—
592C23—612no—
593C23—612no—
594C23—612no—
595C23—612no—
596C23—612no—
597C23—612no—
598C23—12216no—
599C23—1222no—
600C23—1222no—
601C23—1222no—
602C23—2448no—
603C23—2448no—
604C23—2448no—
605C23—2448no—
606C23—2448no—
607C23—2448no—
608C23—2441no—
609C23—2441no—
610C23—2441no—
611C23—2441no—
612C23C2×D4×D6111yescharacteristic
613D4—22no—
614D4—22no—
615D4—22no—
616D4—614no—
617D4—12216no—
618D4—1222no—
619D4—1222no—
620D4—1222no—
621D4C4⋊C4×D6114yescomplemented
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—22no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—48no—
628C2×C4—42no—
629C2×C4—42no—
630C2×C4—42no—
631C2×C4—612no—
632C2×C4—612no—
633C2×C4—612no—
634C2×C4—612no—
635C2×C4—612no—
636C2×C4—612no—
637C2×C4—614no—
638C2×C4—614no—
639C2×C4—614no—
640C2×C4—614no—
641C2×C4—6116no—
642C2×C4—612no—
643C2×C4—1228no—
644C2×C4—1221no—
645C2×C4—1221no—
646C2×C4—1222no—
647C2×C4—4888no—
648C2×C4—2448no—
649C2×C4—2448no—
650C2×C4—2448no—
651C2×C4—2442no—
652C2×C4—2442no—
653C2×C4—2442no—
654C2×C4—2441no—
655C2×C4—2441no—
656C2×C4—2448no—
657C2×C4C22⋊C4×D6112yes—
658C2×C4C22⋊C4×D6112yes—
659C2×C4D8×D6112yes—
660C2×C4SD16×D6112yes—
661C2×C4C22×C4×D6111yescharacteristic
662C2×C4C2×D4×D6111yescharacteristic
663C2×C4C2×D4×D6111yescharacteristic
664C2×C4C2×Q8×D6111yescharacteristic
665C2×C4#41×D6111yescharacteristic
666C2×C4#41×D6111yescharacteristic
667C8—42no—
668C8—2442no—
669C22—24no—
670C22—42no—
671C22—42no—
672C22—42no—
673C22—42no—
674C22—42no—
675C22—42no—
676C22—614no—
677C22—614no—
678C22—614no—
679C22—614no—
680C22—614no—
681C22—614no—
682C22—614no—
683C22—1224no—
684C22—24432no—
685C22—2442no—
686C22—2442no—
687C22—2442no—
688C22—2442no—
689C22—2442no—
690C22—2442no—
691C22C2×C22⋊C4×D6111yescharacteristic
692C22#121×D6111yescharacteristic
693C22C22⋊Q8×D6111yescharacteristic
694C22C2×D8×D6111yescharacteristic
695C22C2×SD16×D6111yescharacteristic
696C22AGL(1,ℤ/8)×D6111yescharacteristic
697C22#137×D6111yescharacteristic
698C4—22no—
699C4—42no—
700C4—82no—
701C4—614no—
702C4—614no—
703C4—1222no—
704C4—4882no—
705C4—2442no—
706C4#102×D6114yescomplemented
707C4C2×C4⋊C4×D6111yescharacteristic
708C4#117×D6111yescharacteristic
709C4#121×D6111yescharacteristic
710C4C22⋊Q8×D6111yescharacteristic
711C2—44no—
712C2—618no—
713C2—2444no—
714C2#380×D6111yescharacteristic
715C2C2×#102×D6111yescharacteristic
716C2#417×D6111yescharacteristic
717C2#459×D6111yescharacteristic
718C2#461×D6111yescharacteristic
719C2#474×D6111yescharacteristic
720C2#476×D6111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1802C2
socleC23×C61C22×D4
prime radicalC22×D4×D61C22
cosocleC22×C4×C61C24
hypercenter#1802D61
hypocenterC61C2×#1802
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1802

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C8×D61C2semidirect
4. #384×D61C2semidirect
5. #21445820C2semidirect
6. #21445819C2semidirect
7. #21445818C2semidirect
8. #21445817C2semidirect
9. #21445816C2semidirect
10. #340×D61C2semidirect
11. C61×#1802C2semidirect
21. C4×D4×D61C4semidirect
28. C2×C4⋊#92418C22semidirect
29. C2×#14519706C22semidirect
35. #16839632C22semidirect
38. #16839631C22semidirect
39. #16839525C22semidirect
40. #16839524C22semidirect
41. #16839524C22semidirect
43. C2×C4⋊C8×C61C22semidirect
45. C61×#384C22semidirect
46. C61×#340C22semidirect
72. C4×D244C2×C4semidirect
74. D4×Dic61C2×C4semidirect
76. #14519739C2×C4semidirect
111. C4×D4×C61C2×C4semidirect
158. D4×D61C4⋊C4semidirect
255. D4×C61C2×C4⋊C4semidirect
295. D244C2×C4⋊C4semidirect
301. C4×D61#102semidirect
341. C4×C61C2×#102semidirect
350. Dic61C2×#102semidirect
360. #1802D61direct (N × H)
371. D61#1802direct (N × H)
392. C2×C4⋊C8C2×D61semidirect
402. #384C2×D61semidirect
406. #340C2×D61semidirect
407. C61C2×#1802semidirect
444. C4×D4C4×D61semidirect
621. D4C4⋊C4×D61semidirect
706. C4#102×D61semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D4×D612
C2×C4⋊C8×D612
C2×#102×D612
#384×D612
#214458202
#214458192
#214458182
#214458172
#214458162
#340×D612
C61×#18022
C2×#180261