Finite Group Databasebeta

← D61⋊#1870 #30615553

Subgroups — D61⋊#1870 #30615553

Order 15616.

2286 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D61⋊M16C211yesmaximal, characteristic, complemented
2C2×D61⋊(C22⋊C8)C212yesmaximal, complemented
3C2×D61⋊(C22⋊C8)C211yesmaximal, characteristic, complemented
4#21461799C212yesmaximal, complemented
5#21461798C212yesmaximal, complemented
6#21461797C212yesmaximal, complemented
7#21461796C212yesmaximal, complemented
8#21461480C212yesmaximal, complemented
9C2×C4×D4×D61C211yesmaximal, characteristic
10C22×#11758213C2212yescomplemented
11C2×D61⋊M16—28no—
12C2×D61⋊M16—24no—
13C22×#11758217C2212yescomplemented
14C22×D61⋊C8C2212yes—
15C22×D61⋊C8C2212yes—
16C2×#14519834C2212yescomplemented
17C2×#14519834C2214yescomplemented
18D61⋊(C22⋊C8)—28no—
19D61⋊(C22⋊C8)—24no—
20C2×C22⋊#92420C2214yescomplemented
21C2×C22⋊#92420C2212yescomplemented
22#16840628C2214yescomplemented
23#16840628C2214yescomplemented
24C22×D4×D61C411yescharacteristic
25C23×C4×D61C2211yescharacteristic
26C23×C4×D61C2211yescharacteristic
27C2×C4×D244C411yescharacteristic
28C2×D4×Dic61C2211yescharacteristic
29C2×#14519739C2211yescharacteristic
30C2×C4×C22⋊D61C411yescharacteristic
31C2×C4×C22⋊D61C411yescharacteristic
32C2×#14519737C2211yescharacteristic
33C2×#14519737C2211yescharacteristic
34C4×D4×D61—24no—
35C4×D4×D61—24no—
36C2×C4⋊C4×D61C411yescharacteristic
37C2×C22⋊C4×D61C411yescharacteristic
38C2×C22⋊C4×D61C411yescharacteristic
39C2×C42×D61C2211yescharacteristic
40C2×C4×D4×C61C411yescharacteristic
41C2×#11758213—24no—
42C2×#11758213—28no—
43D61⋊M16—232no—
44C2×#11758217—24no—
45C2×#11758217—28no—
46C2×D61⋊C8—24no—
47C2×D61⋊C8—24no—
48C2×D61⋊C8—24no—
49C2×D61⋊C8—24no—
50C2×D61⋊C8—24no—
51C2×D61⋊C8D418yescomplemented
52C22×#92420C2314yes—
53C22×#92420C2314yes—
54#14519834—24no—
55#14519834—28no—
56C22⋊#92420—24no—
57C22⋊#92420—28no—
58C24×D61C2×C411yescharacteristic
59C24×D61C2×C411yescharacteristic
60C22×D244C2×C411yescharacteristic
61C22×C22⋊D61C2×C411yescharacteristic
62C22×C22⋊D61C2×C411yescharacteristic
63C2×D4×D61—24no—
64C2×D4×D61—24no—
65C2×D4×D61—24no—
66C23×Dic61C2311yescharacteristic
67C23×Dic61C2311yescharacteristic
68C22×C4×D61—24no—
69C22×C4×D61—24no—
70C22×C4×D61—24no—
71C22×C4×D61—22no—
72C22×C4×D61—22no—
73C22×C4×D61—24no—
74C22×C4×D61C2×C411yescharacteristic
75C22×C4×D61C2×C411yescharacteristic
76C22×C4×D61C2×C411yescharacteristic
77C22×C4×D61C2×C411yescharacteristic
78C22×C4×D61C2×C411yescharacteristic
79C22×C4×D61C2×C411yescharacteristic
80C22×C4×D61D414yes—
81C22×C4×D61D414yes—
82C22×C4×D61C2311yescharacteristic
83C22×C4×D61C2311yescharacteristic
84C22×C4×D61C2311yescharacteristic
85C4×D244—24no—
86D4×Dic61—22no—
87D4×Dic61—22no—
88#14519739—22no—
89#14519739—22no—
90C4×C22⋊D61—24no—
91C4×C22⋊D61—24no—
92#14519737—22no—
93#14519737—22no—
94#14519737—22no—
95#14519737—22no—
96C2×C4⋊Dic61C2×C411yescharacteristic
97C2×#11758196C2×C411yescharacteristic
98C2×#11758196C2×C411yescharacteristic
99C4⋊C4×D61—24no—
100C2×C22⋊Dic61C2×C411yescharacteristic
101C2×C22⋊Dic61C2×C411yescharacteristic
102C2×#11758198C2×C411yescharacteristic
103C2×#11758198C2×C411yescharacteristic
104C2×#11758198C2×C411yescharacteristic
105C2×#11758198C2×C411yescharacteristic
106C22⋊C4×D61—24no—
107C22⋊C4×D61—24no—
108C2×C4×Dic61C2×C411yescharacteristic
109C2×C4×Dic61C2311yescharacteristic
110C2×C4×Dic61C2311yescharacteristic
111C42×D61—22no—
112C42×D61—22no—
113C22×D4×C61C2×C411yescharacteristic
114C23×C4×C61C2×C411yescharacteristic
115C23×C4×C61C2×C411yescharacteristic
116C4×D4×C61—24no—
117C2×C4⋊C4×C61C2×C411yescharacteristic
118C2×C22⋊C4×C61C2×C411yescharacteristic
119C2×C22⋊C4×C61C2×C411yescharacteristic
120C2×C42×C61C2×C411yescharacteristic
121C24×C61C22×C411yescharacteristic
122C24×C61C22×C411yescharacteristic
123C23×D61—22no—
124C23×D61—24no—
125C23×D61—24no—
126C23×D61—22no—
127C23×D61—22no—
128C23×D61—22no—
129C23×D61—24no—
130C23×D61—24no—
131C23×D61C22⋊C414yes—
132C23×D61M1614yescomplemented
133C23×D61C22×C411yescharacteristic
134C23×D61C22×C411yescharacteristic
135C23×D61C22×C411yescharacteristic
136C2×D4×C61—22no—
137C2×D4×C61—22no—
138C2×D4×C61—22no—
139C22×C4×C61—24no—
140C22×C4×C61—22no—
141C22×C4×C61—24no—
142C22×C4×C61C22⋊C414yes—
143C22×C4×C61C22×C411yescharacteristic
144C22×C4×C61C22×C411yescharacteristic
145C22×C4×C61C22×C411yescharacteristic
146C22×C4×C61C22×C411yescharacteristic
147C22×C4×C61C22×C411yescharacteristic
148C2×C22⋊D61—22no—
149C2×C22⋊D61—22no—
150C2×C22⋊D61—22no—
151C2×C22⋊D61—22no—
152C2×C22⋊D61—22no—
153C2×C22⋊D61—22no—
154C22×Dic61—22no—
155C22×Dic61—22no—
156C22×Dic61—22no—
157C22×Dic61—21no—
158C22×Dic61—21no—
159C22×Dic61—22no—
160C22×Dic61C22×C411yescharacteristic
161C22×Dic61C22×C411yescharacteristic
162C22×Dic61C22×C411yescharacteristic
163C22×Dic61C22×C411yescharacteristic
164C22×Dic61C2×D412yes—
165C22×Dic61C2×D412yes—
166C22×Dic61C2411yescharacteristic
167D4×D61—232no—
168C2×D244—22no—
169C2×D244—22no—
170C2×D244—22no—
171C2×C4×D61—22no—
172C2×C4×D61—24no—
173C2×C4×D61—22no—
174C2×C4×D61—24no—
175C2×C4×D61—22no—
176C2×C4×D61—22no—
177C2×C4×D61—28no—
178C2×C4×D61—216no—
179C2×C4×D61—28no—
180C2×C4×D61—22no—
181C2×C4×D61—22no—
182C2×C4×D61—24no—
183C2×C4×D61—24no—
184C2×C4×D61—22no—
185C2×C4×D61—24no—
186C2×C4×D61—22no—
187C2×C4×D61—21no—
188C2×C4×D61—21no—
189C2×C4×D61—22no—
190C2×C4×D61—44no—
191C2×C4×D61—48no—
192C2×C4×D61—44no—
193C2×C4×D61C22⋊C414yes—
194C2×C4×D61C22⋊C414yes—
195C2×C4×D61M1614yescomplemented
196C2×C4×D61C2×D412yes—
197C2×C4×D61C2×D412yes—
198C2×C4×D61C2×D414yes—
199C2×C4×D61C2×D412yes—
200C2×C4×D61C2×D412yes—
201C2×C4×D61#4114yes—
202#11758217—216no—
203C2×#92420—24no—
204C2×#92420—24no—
205C2×#92420—24no—
206C2×#92420—24no—
207C2×#92420—24no—
208C2×#92420C2×D418yescomplemented
209#11758213—216no—
210D61⋊C8—216no—
211D61⋊C8—48no—
212C4⋊C4×C61—22no—
213C22⋊C4×C61—22no—
214C22⋊C4×C61—22no—
215C42×C61—22no—
216C22⋊Dic61—22no—
217C22⋊Dic61—22no—
218#11758198—22no—
219#11758198—22no—
220#11758198—22no—
221#11758198—22no—
222C4⋊Dic61—22no—
223#11758196—22no—
224#11758196—22no—
225C4×Dic61—22no—
226C4×Dic61—21no—
227C4×Dic61—21no—
228C4×Dic61—21no—
229C4×Dic61—21no—
230C23×C61—21no—
231C23×C61—22no—
232C23×C61—22no—
233C23×C61—21no—
234C23×C61—21no—
235C23×C61—21no—
236C23×C61—22no—
237C23×C61—22no—
238C23×C61C2×C22⋊C412yes—
239C23×C61C2×M1612yescomplemented
240C23×C61C23×C411yescharacteristic
241C22×D61—21no—
242C22×D61—22no—
243C22×D61—22no—
244C22×D61—21no—
245C22×D61—21no—
246C22×D61—21no—
247C22×D61—22no—
248C22×D61—22no—
249C22×D61—28no—
250C22×D61—28no—
251C22×D61—28no—
252C22×D61—28no—
253C22×D61—216no—
254C22×D61—44no—
255C22×D61—44no—
256C22×D61—48no—
257C22×D61—48no—
258C22×D61—48no—
259C22×D61C2×C22⋊C412yes—
260C22×D61C2×C22⋊C412yes—
261C22×D61C4×D414yes—
262C22×D61C2×M1612yes—
263C22×D61C2×M1612yes—
264C22×D61C2×M1612yescomplemented
265C22×D61#13114yes—
266D4×C61—28no—
267C2×C4×C61—21no—
268C2×C4×C61—22no—
269C2×C4×C61—21no—
270C2×C4×C61—28no—
271C2×C4×C61—21no—
272C2×C4×C61—21no—
273C2×C4×C61—22no—
274C2×C4×C61—22no—
275C2×C4×C61—44no—
276C2×C4×C61C2×C22⋊C412yes—
277C2×C4×C61C2×C22⋊C412yes—
278C2×C4×C61C4×D414yes—
279C2×C4×C61C2×M1612yescomplemented
280C22⋊D61—28no—
281C22⋊D61—28no—
282C2×Dic61—21no—
283C2×Dic61—22no—
284C2×Dic61—21no—
285C2×Dic61—22no—
286C2×Dic61—24no—
287C2×Dic61—22no—
288C2×Dic61—21no—
289C2×Dic61—21no—
290C2×Dic61—22no—
291C2×Dic61—22no—
292C2×Dic61—41no—
293C2×Dic61—42no—
294C2×Dic61—41no—
295C2×Dic61C2×C22⋊C412yes—
296C2×Dic61C2×M1612yescomplemented
297C2×Dic61C22×D412yes—
298C2×Dic61C22×D411yescharacteristic
299C2×Dic61C22×D411yescharacteristic
300C2×Dic61C2×#4112yes—
301D244—28no—
302C4×D61—28no—
303C4×D61—28no—
304C4×D61—28no—
305C4×D61—22no—
306C4×D61—24no—
307C4×D61—22no—
308C4×D61—44no—
309C4×D61—44no—
310C4×D61—44no—
311C4×D61—41no—
312C4×D61—42no—
313C4×D61—41no—
314C4×D61#12014yes—
315C4×D61#12118yes—
316C4×D61#12314yes—
317#92420—28no—
318#92420—44no—
319C2×#1870—611nomaximal, Sylow
320C22×C61—22no—
321C22×C61—22no—
322C22×C61—22no—
323C22×C61—24no—
324C22×C61—22no—
325C22×C61—41no—
326C22×C61—42no—
327C22×C61—42no—
328C22×C61—42no—
329C22×C61—41no—
330C22×C61C22×C22⋊C411yescharacteristic
331C22×C61C2×C4×D412yes—
332C22×C61C22×M1611yescharacteristic
333C22×C61C22×M1611yescharacteristic
334C22×C61C2×#13112yes—
335C2×D61—22no—
336C2×D61—22no—
337C2×D61—22no—
338C2×D61—24no—
339C2×D61—22no—
340C2×D61—41no—
341C2×D61—42no—
342C2×D61—42no—
343C2×D61—42no—
344C2×D61—41no—
345C2×D61—416no—
346C2×D61—416no—
347C2×D61#38614yes—
348C2×D61#40714yes—
349C2×D61#40814yes—
350C2×D61#43518yes—
351C2×D61#43618yes—
352C4×C61—22no—
353C4×C61—22no—
354C4×C61—41no—
355C4×C61—41no—
356C4×C61#38614yes—
357Dic61—22no—
358Dic61—22no—
359Dic61—41no—
360Dic61—41no—
361Dic61C2×#12011yescharacteristic
362Dic61C2×#12112yes—
363Dic61C2×#12311yescharacteristic
364C23×M16—611no—
365C22×C4×D4—611no—
366C22×C22⋊C8—612no—
367C22×C22⋊C8—611no—
368#1870—612no—
369#1870—612no—
370#1870—612no—
371#1870—612no—
372C2×#336—612no—
373C2×C61—42no—
374C2×C61—42no—
375C2×C61C2×#38611yescharacteristic
376C2×C61C2×#40711yescharacteristic
377C2×C61C2×#40811yescharacteristic
378C2×C61C2×#43512yes—
379C2×C61C2×#43612yes—
380D61—42no—
381D61—42no—
382D61#187018yescomplemented
383C23×D4—611no—
384C24×C4—611no—
385C24×C4—611no—
386C22×M16—612no—
387C22×M16—612no—
388C22×M16—1228no—
389C22×M16—1224no—
390C23×C8—612no—
391C23×C8—612no—
392C2×C4×D4—611no—
393C2×C4×D4—611no—
394C2×C4×D4—611no—
395C2×C4×D4—611no—
396C2×C4×D4—611no—
397C2×C4×D4—611no—
398C2×C4×D4—611no—
399C2×C4×D4—1224no—
400C2×C4×D4—1224no—
401C2×C4×D4#692311yescharacteristic
402C22×C4⋊C4—611no—
403C22×C22⋊C4—611no—
404C22×C22⋊C4—611no—
405C22×C42—611no—
406C2×C22⋊C8—614no—
407C2×C22⋊C8—612no—
408C2×C22⋊C8—614no—
409C2×C22⋊C8—612no—
410C2×C22⋊C8—1228no—
411C2×C22⋊C8—1224no—
412#336—614no—
413#336—614no—
414C61C2×#187011yescharacteristic, complemented, Sylow
415C25—611no—
416C25—611no—
417C22×D4—611no—
418C22×D4—611no—
419C22×D4—611no—
420C22×D4—1224no—
421C22×D4—1224no—
422C22×D4—1224no—
423C22×D4C2×#692311yescharacteristic
424C23×C4—611no—
425C23×C4—611no—
426C23×C4—614no—
427C23×C4—614no—
428C23×C4—611no—
429C23×C4—611no—
430C23×C4—611no—
431C23×C4—611no—
432C23×C4—611no—
433C23×C4—611no—
434C23×C4—611no—
435C23×C4—611no—
436C23×C4—611no—
437C23×C4—1224no—
438C23×C4—1224no—
439C23×C4—1222no—
440C23×C4—1222no—
441C23×C4—1224no—
442C23×C4—1224no—
443C23×C4C2×#692311yescharacteristic
444C23×C4C2×#692311yescharacteristic
445C2×M16—1228no—
446C2×M16—1228no—
447C2×M16—1224no—
448C2×M16—1224no—
449C2×M16—12232no—
450C22×C8—614no—
451C22×C8—618no—
452C22×C8—614no—
453C22×C8—1224no—
454C22×C8—1224no—
455C22×C8—1224no—
456C22×C8—1224no—
457C22×C8—1224no—
458C4×D4—24no—
459C4×D4—1224no—
460C4×D4—1222no—
461C4×D4—1222no—
462C4×D4—1222no—
463C4×D4—1222no—
464C4×D4—1222no—
465C4×D4—1222no—
466C4×D4—1224no—
467C4×D4—1222no—
468C4×D4—1222no—
469C4×D4—1224no—
470C2×C4⋊C4—611no—
471C2×C4⋊C4—611no—
472C2×C4⋊C4—611no—
473C2×C4⋊C4—1224no—
474C2×C4⋊C4C2×#692311yescharacteristic
475C2×C22⋊C4—611no—
476C2×C22⋊C4—611no—
477C2×C22⋊C4—611no—
478C2×C22⋊C4—611no—
479C2×C22⋊C4—611no—
480C2×C22⋊C4—611no—
481C2×C22⋊C4—1224no—
482C2×C22⋊C4—1224no—
483C2×C22⋊C4C2×#692311yescharacteristic
484C2×C22⋊C4C2×#692311yescharacteristic
485C2×C42—611no—
486C2×C42—611no—
487C2×C42—611no—
488C2×C42—1222no—
489C2×C42—1222no—
490C2×C42C2×#692311yescharacteristic
491C22⋊C8—1228no—
492C22⋊C8—1228no—
493C22⋊C8—1224no—
494C22⋊C8—1224no—
495C24—611no—
496C24—614no—
497C24—614no—
498C24—611no—
499C24—611no—
500C24—1222no—
501C24—1224no—
502C24—1224no—
503C24—1222no—
504C24—1222no—
505C24—1222no—
506C24—1224no—
507C24—1224no—
508C24C22×#692311yescharacteristic
509C24C22×#692311yescharacteristic
510C2×D4—22no—
511C2×D4—22no—
512C2×D4—22no—
513C2×D4—1222no—
514C2×D4—1222no—
515C2×D4—1222no—
516C2×D4—1222no—
517C2×D4—12232no—
518C2×D4—1222no—
519C2×D4—1222no—
520C2×D4—1222no—
521C2×D4—1222no—
522C2×D4—1222no—
523C22×C4—24no—
524C22×C4—22no—
525C22×C4—24no—
526C22×C4—611no—
527C22×C4—612no—
528C22×C4—612no—
529C22×C4—614no—
530C22×C4—614no—
531C22×C4—612no—
532C22×C4—612no—
533C22×C4—611no—
534C22×C4—611no—
535C22×C4—612no—
536C22×C4—614no—
537C22×C4—612no—
538C22×C4—614no—
539C22×C4—614no—
540C22×C4—611no—
541C22×C4—611no—
542C22×C4—1222no—
543C22×C4—1228no—
544C22×C4—1222no—
545C22×C4—12216no—
546C22×C4—1228no—
547C22×C4—1222no—
548C22×C4—1221no—
549C22×C4—1221no—
550C22×C4—1222no—
551C22×C4—1222no—
552C22×C4—1224no—
553C22×C4—1222no—
554C22×C4—1222no—
555C22×C4—1222no—
556C22×C4—1224no—
557C22×C4—1224no—
558C22×C4—1222no—
559C22×C4—1222no—
560C22×C4—1222no—
561C22×C4—1221no—
562C22×C4—1221no—
563C22×C4—1222no—
564C22×C4—1224no—
565C22×C4—1222no—
566C22×C4—1224no—
567C22×C4—2444no—
568C22×C4—2448no—
569C22×C4—2444no—
570C22×C4C22⋊#692314yes—
571C22×C4C22×#692311yescharacteristic
572C22×C4C22×#692311yescharacteristic
573C22×C4C22×#692311yescharacteristic
574C22×C4C22×#692311yescharacteristic
575C22×C4C22×#692311yescharacteristic
576M16—12216no—
577M16—12216no—
578C2×C8—618no—
579C2×C8—12216no—
580C2×C8—1224no—
581C2×C8—1224no—
582C2×C8—1224no—
583C2×C8—1224no—
584C2×C8—1224no—
585C2×C8—2448no—
586C4⋊C4—22no—
587C4⋊C4—1222no—
588C4⋊C4—1222no—
589C4⋊C4—1222no—
590C22⋊C4—22no—
591C22⋊C4—22no—
592C22⋊C4—1222no—
593C22⋊C4—1222no—
594C22⋊C4—1222no—
595C22⋊C4—1222no—
596C22⋊C4—1222no—
597C22⋊C4—1222no—
598C42—22no—
599C42—1221no—
600C42—1221no—
601C42—1221no—
602C42—1221no—
603C42—1222no—
604C23—21no—
605C23—22no—
606C23—22no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—22no—
611C23—22no—
612C23—612no—
613C23—614no—
614C23—612no—
615C23—612no—
616C23—614no—
617C23—612no—
618C23—612no—
619C23—1228no—
620C23—1228no—
621C23—1228no—
622C23—1228no—
623C23—12216no—
624C23—1221no—
625C23—1222no—
626C23—1222no—
627C23—1221no—
628C23—1221no—
629C23—1221no—
630C23—1222no—
631C23—1222no—
632C23—2444no—
633C23—2448no—
634C23—2448no—
635C23—2444no—
636C23—2448no—
637C23C2×C22⋊#692312yes—
638C23D61⋊M1612yescomplemented
639C23C23×#692311yescharacteristic
640D4—28no—
641D4—1228no—
642D4—1228no—
643D4—1228no—
644C2×C4—21no—
645C2×C4—22no—
646C2×C4—21no—
647C2×C4—28no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—44no—
653C2×C4—611no—
654C2×C4—611no—
655C2×C4—612no—
656C2×C4—612no—
657C2×C4—614no—
658C2×C4—618no—
659C2×C4—614no—
660C2×C4—612no—
661C2×C4—612no—
662C2×C4—1222no—
663C2×C4—1224no—
664C2×C4—1222no—
665C2×C4—1228no—
666C2×C4—1228no—
667C2×C4—1222no—
668C2×C4—1224no—
669C2×C4—1222no—
670C2×C4—1221no—
671C2×C4—1222no—
672C2×C4—1221no—
673C2×C4—1228no—
674C2×C4—1221no—
675C2×C4—1221no—
676C2×C4—1222no—
677C2×C4—1222no—
678C2×C4—2441no—
679C2×C4—2442no—
680C2×C4—2441no—
681C2×C4—2444no—
682C2×C4—2444no—
683C2×C4—2441no—
684C2×C4—2442no—
685C2×C4—2441no—
686C2×C4—2444no—
687C2×C4C2×C22⋊#692312yes—
688C2×C4C2×C22⋊#692312yes—
689C2×C4D4×#692314yes—
690C2×C4D61⋊M1612yescomplemented
691C8—1228no—
692C8—2444no—
693C22—22no—
694C22—22no—
695C22—22no—
696C22—22no—
697C22—24no—
698C22—42no—
699C22—42no—
700C22—41no—
701C22—41no—
702C22—42no—
703C22—618no—
704C22—614no—
705C22—614no—
706C22—614no—
707C22—618no—
708C22—1222no—
709C22—1222no—
710C22—1222no—
711C22—1222no—
712C22—1224no—
713C22—24416no—
714C22—24416no—
715C22—2442no—
716C22—2442no—
717C22—2441no—
718C22—2441no—
719C22—2442no—
720C22C22×C22⋊#692311yescharacteristic
721C22C2×D4×#692312yes—
722C22C2×D61⋊M1611yescharacteristic
723C22C2×D61⋊M1611yescharacteristic
724C22D61⋊#13112yes—
725C4—22no—
726C4—22no—
727C4—41no—
728C4—41no—
729C4—611no—
730C4—612no—
731C4—611no—
732C4—1222no—
733C4—1222no—
734C4—2441no—
735C4—2441no—
736C4#1684071014yes—
737C2—42no—
738C2—42no—
739C2—618no—
740C2—2442no—
741C2—2442no—
742C2C2×#1684071011yescharacteristic
743C2D61⋊#40711yescharacteristic
744C2D61⋊#40811yescharacteristic
745C2D61⋊#43512yes—
746C2D61⋊#43612yes—
subgroupG/H
centerC22×C4C22×#6923
commutator, socleC23×C61C23×C4
FrattiniC23C23×#6923
FittingC2×C4×D4×C61C4
prime radicalC22×D4×D61C4
cosocleC22×Dic61C24
hypercenterC2×C4×D4#6923
hypocenterC61C2×#1870
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. C22×D61⋊M16C2semidirect
2. C2×D61⋊(C22⋊C8)C2semidirect
3. C2×D61⋊(C22⋊C8)C2semidirect
4. #21461799C2semidirect
5. #21461798C2semidirect
6. #21461797C2semidirect
7. #21461796C2semidirect
8. #21461480C2semidirect
10. C22×#11758213C22semidirect
13. C22×#11758217C22semidirect
16. C2×#14519834C22semidirect
17. C2×#14519834C22semidirect
20. C2×C22⋊#92420C22semidirect
21. C2×C22⋊#92420C22semidirect
22. #16840628C22semidirect
23. #16840628C22semidirect
51. C2×D61⋊C8D4semidirect
132. C23×D61M16semidirect
195. C2×C4×D61M16semidirect
208. C2×#92420C2×D4semidirect
239. C23×C61C2×M16semidirect
264. C22×D61C2×M16semidirect
279. C2×C4×C61C2×M16semidirect
296. C2×Dic61C2×M16semidirect
382. D61#1870semidirect
414. C61C2×#1870semidirect
638. C23D61⋊M16semidirect
690. C2×C4D61⋊M16semidirect

Maximal subgroups

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

subgroupindex
C22×D61⋊M162
C2×D61⋊(C22⋊C8)2
#214617992
#214617982
#214617972
#214617962
#214614802
C2×C4×D4×D612
C2×#187061