Finite Group Databasebeta

← D61⋊#1826 #30615107

Subgroups — D61⋊#1826 #30615107

Order 15616.

1606 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D61⋊#407C211yesmaximal, characteristic
2C2×C4×C22⋊#6923C211yesmaximal, characteristic
3#21461727C214yesmaximal, complemented
4#21461726C212yesmaximal, complemented
5#21461725C212yesmaximal, complemented
6#21461495C214yesmaximal, complemented
7C2×#117×D61C211yesmaximal, characteristic
8C2×D61⋊M16C2212yes—
9C22×C22⋊#6923—21no—
10C22×C4×#6923C2212yes—
11#16840734—21no—
12#16840733C2212yes—
13#16840733C2212yes—
14#16840732—21no—
15D61⋊(C22⋊C8)—21no—
16D61⋊(C22⋊C8)—21no—
17C4×C22⋊#6923—21no—
18C4×C22⋊#6923—21no—
19C4×C22⋊#6923C2212yes—
20C4×C22⋊#6923C2212yes—
21C2×(C2×#6923)⋊C4—21no—
22#16840632C2218yescomplemented
23#16840632C2218yescomplemented
24C23×C4×D61C2211yescharacteristic
25C2×#14519736C411yescharacteristic, complemented
26C2×#14519735C2211yescharacteristic
27C2×#14519735C2211yescharacteristic
28C2×#14519734—21no—
29C2×#14519733—21no—
30#117×D61—21no—
31#117×D61—21no—
32#117×D61—21no—
33#117×D61—21no—
34#117×D61C412yescomplemented
35#117×D61C412yescomplemented
36#117×D61C2212yes—
37#117×D61C2212yes—
38C2×C4⋊C4×D61C411yescharacteristic, complemented
39C2×C4⋊C4×D61C411yescharacteristic, complemented
40C2×C22⋊C4×D61—21no—
41C2×C42×D61—21no—
42C2×#117×C61C411yescharacteristic, complemented
43C23×#6923—22no—
44C2×#11758213C2314yes—
45D61⋊M16—28no—
46C2×#11758217—22no—
47C2×D61⋊C8—22no—
48C2×C22⋊#6923—28no—
49C2×C22⋊#6923—22no—
50C2×C22⋊#6923—22no—
51C2×C4×#6923—28no—
52C2×C4×#6923—22no—
53C2×C4×#6923C2314yes—
54#14519834—22no—
55#14519834—22no—
56C22⋊#92420—22no—
57C22⋊#92420—22no—
58(C2×#6923)⋊C4—22no—
59(C2×#6923)⋊C4—22no—
60C24×D61D411yescharacteristic
61C23×Dic61D411yescharacteristic
62C22×C4×D61—28no—
63C22×C4×D61—21no—
64C22×C4×D61—21no—
65C22×C4×D61C2×C411yescharacteristic
66C22×C4×D61C2×C411yescharacteristic
67C22×C4×D61C2×C411yescharacteristic
68C22×C4×D61D411yescharacteristic
69C22×C4×D61D411yescharacteristic
70C22×C4×D61D411yescharacteristic
71C22×C4×D61D411yescharacteristic
72C22×C4×D61D411yescharacteristic
73C22×C4×D61D411yescharacteristic
74C22×C4×D61C2311yescharacteristic
75C22×C4×D61C2311yescharacteristic
76C22×C4×D61C2311yescharacteristic
77#14519736—21no—
78#14519736—21no—
79#14519736C2×C412yes—
80#14519736C2×C412yescomplemented
81#14519735—21no—
82#14519735—21no—
83#14519735—21no—
84#14519735—21no—
85#14519735C2×C412yescomplemented
86#14519735C2×C412yescomplemented
87#14519735C2312yes—
88#14519735C2312yes—
89#14519734—22no—
90#14519734—22no—
91#14519734—22no—
92#14519734—22no—
93#14519733—22no—
94#14519733—22no—
95#14519733—22no—
96#14519733—22no—
97C2×C4⋊Dic61C2×C411yescharacteristic, complemented
98C2×C4⋊Dic61C2×C411yescharacteristic, complemented
99C2×#11758196—21no—
100C2×#11758196—21no—
101C4⋊C4×D61—21no—
102C4⋊C4×D61—21no—
103C4⋊C4×D61—21no—
104C4⋊C4×D61—21no—
105C4⋊C4×D61C2×C412yes—
106C4⋊C4×D61C2×C412yes—
107C4⋊C4×D61C2×C412yescomplemented
108C4⋊C4×D61C2×C412yescomplemented
109C2×C22⋊Dic61—21no—
110C2×#11758198—21no—
111C2×#11758198—21no—
112C22⋊C4×D61—22no—
113C22⋊C4×D61—22no—
114C22⋊C4×D61—22no—
115C22⋊C4×D61—22no—
116C2×C4×Dic61—21no—
117C2×C4×Dic61—21no—
118C2×C4×Dic61—21no—
119C42×D61—22no—
120C42×D61—22no—
121C42×D61—22no—
122C42×D61—22no—
123C23×C4×C61C2×C411yescharacteristic
124#117×C61—21no—
125#117×C61—21no—
126#117×C61C2×C412yes—
127#117×C61C2×C412yescomplemented
128C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
129C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
130C2×C22⋊C4×C61—21no—
131C2×C42×C61—21no—
132C24×C61C22⋊C411yescharacteristic
133C23×D61—24no—
134C23×D61—24no—
135C23×D61—42no—
136C23×D61C22⋊C411yescharacteristic
137C23×D61C22⋊C411yescharacteristic
138C23×D61C22⋊C411yescharacteristic
139C23×D61C2×D411yescharacteristic
140C23×D61C2×D411yescharacteristic
141C23×D61C2×D411yescharacteristic
142C22×#6923—28no—
143C22×#6923—24no—
144C22×#6923—44no—
145C22×#6923—44no—
146C22×C4×C61—24no—
147C22×C4×C61—21no—
148C22×C4×C61—21no—
149C22×C4×C61C22⋊C411yescharacteristic
150C22×C4×C61C22⋊C411yescharacteristic
151C22×C4×C61C22⋊C411yescharacteristic
152C22×C4×C61C22×C411yescharacteristic
153C22×C4×C61C22×C411yescharacteristic
154C22×C4×C61C22×C411yescharacteristic
155C22×Dic61—24no—
156C22×Dic61—21no—
157C22×Dic61—21no—
158C22×Dic61C22⋊C411yescharacteristic
159C22×Dic61C22⋊C411yescharacteristic
160C22×Dic61C22⋊C411yescharacteristic
161C22×Dic61C2×D411yescharacteristic
162C22×Dic61C2×D411yescharacteristic
163C22×Dic61C2×D411yescharacteristic
164C2×C4×D61—24no—
165C2×C4×D61—24no—
166C2×C4×D61—24no—
167C2×C4×D61—24no—
168C2×C4×D61—24no—
169C2×C4×D61—24no—
170C2×C4×D61—24no—
171C2×C4×D61—24no—
172C2×C4×D61—24no—
173C2×C4×D61—24no—
174C2×C4×D61—24no—
175C2×C4×D61—22no—
176C2×C4×D61—22no—
177C2×C4×D61—22no—
178C2×C4×D61—22no—
179C2×C4×D61—44no—
180C2×C4×D61—44no—
181C2×C4×D61C22⋊C411yescharacteristic
182C2×C4×D61C22⋊C411yescharacteristic
183C2×C4×D61C22⋊C411yescharacteristic
184C2×C4×D61C22⋊C411yescharacteristic
185C2×C4×D61C22⋊C411yescharacteristic
186C2×C4×D61C22⋊C411yescharacteristic
187C2×C4×D61C22×C411yescharacteristic
188C2×C4×D61C22×C411yescharacteristic
189C2×C4×D61C22×C411yescharacteristic
190C2×C4×D61C2×D411yescharacteristic
191C2×C4×D61C2×D411yescharacteristic
192C2×C4×D61C2×D411yescharacteristic
193C2×C4×D61C2×D411yescharacteristic
194C2×C4×D61C2×D411yescharacteristic
195C2×C4×D61C2×D411yescharacteristic
196C2×C4×D61#4118yes—
197C2×C4×D61C2411yescharacteristic
198C22⋊#6923—28no—
199C22⋊#6923—28no—
200#11758217—44no—
201C2×#92420—24no—
202C4×#6923—28no—
203C4×#6923—44no—
204#11758213—28no—
205D61⋊C8—44no—
206C4⋊C4×C61—21no—
207C4⋊C4×C61—21no—
208C4⋊C4×C61C22×C412yes—
209C4⋊C4×C61C22×C412yes—
210C22⋊C4×C61—22no—
211C22⋊C4×C61—22no—
212C42×C61—22no—
213C42×C61—22no—
214C22⋊Dic61—22no—
215C22⋊Dic61—22no—
216#11758198—22no—
217#11758198—22no—
218#11758198—22no—
219#11758198—22no—
220C4⋊Dic61—21no—
221C4⋊Dic61—21no—
222C4⋊Dic61C22×C412yes—
223C4⋊Dic61C22×C412yes—
224#11758196—22no—
225#11758196—22no—
226#11758196—22no—
227#11758196—22no—
228C4×Dic61—22no—
229C4×Dic61—22no—
230C4×Dic61—22no—
231C4×Dic61—22no—
232C4×Dic61—22no—
233C4×Dic61—22no—
234C23×C61—22no—
235C23×C61—22no—
236C23×C61—41no—
237C23×C61C2×C22⋊C411yescharacteristic
238C23×C61C2×C22⋊C411yescharacteristic
239C23×C61C2×C22⋊C411yescharacteristic
240C22×D61—22no—
241C22×D61—22no—
242C22×D61—22no—
243C22×D61—22no—
244C22×D61—22no—
245C22×D61—22no—
246C22×D61—22no—
247C22×D61—22no—
248C22×D61—22no—
249C22×D61—22no—
250C22×D61—22no—
251C22×D61—22no—
252C22×D61—22no—
253C22×D61—41no—
254C22×D61—41no—
255C22×D61—41no—
256C22×D61—416no—
257C22×D61#10414yes—
258C22×D61C2×C22⋊C411yescharacteristic
259C22×D61C2×C22⋊C411yescharacteristic
260C22×D61C2×C22⋊C411yescharacteristic
261C22×D61#12314yes—
262C22×D61C22×D411yescharacteristic
263C2×#6923—28no—
264C2×#6923—44no—
265C2×#6923—416no—
266C2×#6923—44no—
267C2×C4×C61—22no—
268C2×C4×C61—22no—
269C2×C4×C61—22no—
270C2×C4×C61—22no—
271C2×C4×C61—22no—
272C2×C4×C61—22no—
273C2×C4×C61—22no—
274C2×C4×C61—42no—
275C2×C4×C61—42no—
276C2×C4×C61C2×C22⋊C411yescharacteristic
277C2×C4×C61C2×C22⋊C411yescharacteristic
278C2×C4×C61C2×C22⋊C411yescharacteristic
279C2×C4×C61#11714yes—
280C2×C4×C61C23×C411yescharacteristic
281C2×Dic61—22no—
282C2×Dic61—22no—
283C2×Dic61—22no—
284C2×Dic61—22no—
285C2×Dic61—22no—
286C2×Dic61—22no—
287C2×Dic61—22no—
288C2×Dic61—42no—
289C2×Dic61—42no—
290C2×Dic61C2×C22⋊C411yescharacteristic
291C2×Dic61C2×C22⋊C411yescharacteristic
292C2×Dic61C2×C22⋊C411yescharacteristic
293C2×Dic61#12314yes—
294C2×Dic61C22×D411yescharacteristic
295C4×D61—22no—
296C4×D61—22no—
297C4×D61—22no—
298C4×D61—22no—
299C4×D61—22no—
300C4×D61—22no—
301C4×D61—22no—
302C4×D61—22no—
303C4×D61—22no—
304C4×D61—22no—
305C4×D61—22no—
306C4×D61—22no—
307C4×D61—44no—
308C4×D61—44no—
309C4×D61—44no—
310C4×D61—44no—
311C4×D61#11714yes—
312C4×D61#12314yes—
313C4×D61#12314yes—
314C4×D61C2×#4114yes—
315#92420—44no—
316C2×#1826—611nomaximal, Sylow
317C22×C61—21no—
318C22×C61—21no—
319C22×C61—21no—
320C22×C61—21no—
321C22×C61—21no—
322C22×C61—21no—
323C22×C61—21no—
324C22×C61—44no—
325C22×C61#38112yes—
326C22×C61C2×#10412yes—
327C22×C61C22×C22⋊C411yescharacteristic
328C2×D61—21no—
329C2×D61—21no—
330C2×D61—21no—
331C2×D61—21no—
332C2×D61—28no—
333C2×D61—28no—
334C2×D61—21no—
335C2×D61—21no—
336C2×D61—21no—
337C2×D61—44no—
338C2×D61—44no—
339C2×D61—44no—
340C2×D61—44no—
341C2×D61#38112yes—
342C2×D61C2×#10412yes—
343C2×D61C2×#10412yes—
344C2×D61#42112yes—
345C2×D61C2×#12312yes—
346#6923—48no—
347C4×C61—21no—
348C4×C61—21no—
349C4×C61—42no—
350C4×C61—42no—
351C4×C61#38112yes—
352C4×C61C2×#11712yes—
353Dic61—21no—
354Dic61—21no—
355Dic61—42no—
356Dic61—42no—
357Dic61#38112yes—
358Dic61C2×#12312yes—
359C22×#117—611no—
360C2×#407—611no—
361C2×C4×C22⋊C4—611no—
362#1826—612no—
363#1826—612no—
364#1826—614no—
365C2×#339—614no—
366C2×C61—22no—
367C2×C61—22no—
368C2×C61—41no—
369C2×C61C2×#38111yescharacteristic
370C2×C61C22×#10411yescharacteristic
371C2×C61C2×#42111yescharacteristic
372D61—22no—
373D61—22no—
374D61—41no—
375D61#182614yescomplemented
376C24×C4—611no—
377C22×M16—612no—
378C2×#117—611no—
379C2×#117—612no—
380C2×#117—612no—
381C2×#117—612no—
382C2×#117—612no—
383C2×#117—611no—
384C2×#117—611no—
385C2×#117—1221no—
386C2×#117—1221no—
387C2×#117—1221no—
388C2×#117—1221no—
389C2×#117—1221no—
390C2×#117—1221no—
391C2×#117#692311yescharacteristic, complemented
392C22×C4⋊C4—611no—
393C22×C4⋊C4—611no—
394C22×C22⋊C4—1221no—
395C22×C22⋊C4—1221no—
396C22×C42—612no—
397C22×C42—1221no—
398#407—612no—
399#407—612no—
400#407—1221no—
401#407—1221no—
402C2×C22⋊C8—1221no—
403C2×C22⋊C8—1221no—
404C4×C22⋊C4—612no—
405C4×C22⋊C4—612no—
406C4×C22⋊C4—1221no—
407C4×C22⋊C4—1221no—
408C2×#95—1221no—
409#339—618no—
410#339—618no—
411C61C2×#182611yescharacteristic, complemented, Sylow
412C25—611no—
413C23×C4—611no—
414C23×C4—611no—
415C23×C4—611no—
416C23×C4—611no—
417C23×C4—611no—
418C23×C4—611no—
419C23×C4—611no—
420C23×C4—611no—
421C23×C4—611no—
422C23×C4—611no—
423C23×C4—611no—
424C23×C4—611no—
425C23×C4—611no—
426C23×C4—1228no—
427C23×C4—1221no—
428C23×C4—1221no—
429C23×C4—1222no—
430C23×C4C2×#692311yescharacteristic
431C2×M16—614no—
432C2×M16—1222no—
433C2×M16—1228no—
434C22×C8—1222no—
435#117—21no—
436#117—21no—
437#117—612no—
438#117—612no—
439#117—612no—
440#117—612no—
441#117—612no—
442#117—612no—
443#117—1222no—
444#117—1222no—
445#117—1222no—
446#117—1222no—
447#117—1222no—
448#117—1222no—
449#117—1222no—
450#117—1222no—
451#117—1221no—
452#117—1221no—
453#117—1221no—
454#117—1221no—
455#117—1221no—
456#117—1221no—
457#117C2×#692312yes—
458#117C2×#692312yescomplemented
459C2×C4⋊C4—611no—
460C2×C4⋊C4—611no—
461C2×C4⋊C4—612no—
462C2×C4⋊C4—612no—
463C2×C4⋊C4—612no—
464C2×C4⋊C4—612no—
465C2×C4⋊C4—1221no—
466C2×C4⋊C4—1221no—
467C2×C4⋊C4—1221no—
468C2×C4⋊C4—1221no—
469C2×C4⋊C4—1221no—
470C2×C4⋊C4—1221no—
471C2×C4⋊C4C2×#692311yescharacteristic, complemented
472C2×C4⋊C4C2×#692311yescharacteristic, complemented
473C2×C22⋊C4—21no—
474C2×C22⋊C4—1222no—
475C2×C22⋊C4—1222no—
476C2×C22⋊C4—1222no—
477C2×C22⋊C4—1222no—
478C2×C22⋊C4—1221no—
479C2×C22⋊C4—1221no—
480C2×C22⋊C4—1222no—
481C2×C22⋊C4—1222no—
482C2×C22⋊C4—1228no—
483C2×C22⋊C4—1221no—
484C2×C42—21no—
485C2×C42—614no—
486C2×C42—1222no—
487C2×C42—1222no—
488C2×C42—1222no—
489C2×C42—1222no—
490C2×C42—1221no—
491C2×C42—1221no—
492C2×C42—1221no—
493C2×C42—1228no—
494C2×C42—1222no—
495C22⋊C8—1222no—
496C22⋊C8—1222no—
497C22⋊C8—1222no—
498C22⋊C8—1222no—
499#95—1222no—
500#95—1222no—
501C24—611no—
502C24—611no—
503C24—611no—
504C24—611no—
505C24—611no—
506C24—611no—
507C24—1224no—
508C24—1224no—
509C24—2442no—
510C24C22⋊#692311yescharacteristic
511C22×C4—24no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—611no—
515C22×C4—611no—
516C22×C4—611no—
517C22×C4—618no—
518C22×C4—611no—
519C22×C4—611no—
520C22×C4—611no—
521C22×C4—611no—
522C22×C4—611no—
523C22×C4—611no—
524C22×C4—611no—
525C22×C4—611no—
526C22×C4—611no—
527C22×C4—611no—
528C22×C4—611no—
529C22×C4—611no—
530C22×C4—611no—
531C22×C4—611no—
532C22×C4—611no—
533C22×C4—611no—
534C22×C4—611no—
535C22×C4—611no—
536C22×C4—611no—
537C22×C4—1224no—
538C22×C4—1224no—
539C22×C4—1224no—
540C22×C4—1224no—
541C22×C4—1224no—
542C22×C4—1224no—
543C22×C4—1224no—
544C22×C4—1224no—
545C22×C4—1224no—
546C22×C4—1224no—
547C22×C4—1222no—
548C22×C4—1222no—
549C22×C4—1222no—
550C22×C4—1222no—
551C22×C4—1224no—
552C22×C4—1224no—
553C22×C4—1224no—
554C22×C4—1228no—
555C22×C4—1221no—
556C22×C4—1221no—
557C22×C4—2444no—
558C22×C4—2444no—
559C22×C4—2444no—
560C22×C4—2444no—
561C22×C4C22⋊#692311yescharacteristic
562C22×C4C22⋊#692311yescharacteristic
563C22×C4C22⋊#692311yescharacteristic
564C22×C4C22×#692311yescharacteristic
565C22×C4C22×#692311yescharacteristic
566C22×C4C22×#692311yescharacteristic
567M16—1228no—
568M16—2444no—
569C2×C8—1224no—
570C2×C8—2444no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—612no—
574C4⋊C4—612no—
575C4⋊C4—1222no—
576C4⋊C4—1222no—
577C4⋊C4—1222no—
578C4⋊C4—1222no—
579C4⋊C4—1221no—
580C4⋊C4—1221no—
581C4⋊C4C22×#692312yes—
582C4⋊C4C22×#692312yes—
583C22⋊C4—22no—
584C22⋊C4—22no—
585C22⋊C4—1222no—
586C22⋊C4—1222no—
587C22⋊C4—1222no—
588C22⋊C4—1222no—
589C22⋊C4—1228no—
590C22⋊C4—1228no—
591C22⋊C4—1222no—
592C22⋊C4—1222no—
593C42—22no—
594C42—22no—
595C42—1222no—
596C42—1222no—
597C42—1222no—
598C42—1222no—
599C42—1228no—
600C42—1222no—
601C42—1222no—
602C42—2444no—
603C23—22no—
604C23—22no—
605C23—41no—
606C23—611no—
607C23—614no—
608C23—614no—
609C23—611no—
610C23—611no—
611C23—611no—
612C23—1222no—
613C23—1222no—
614C23—1222no—
615C23—1222no—
616C23—1222no—
617C23—1222no—
618C23—1222no—
619C23—1222no—
620C23—1222no—
621C23—1222no—
622C23—1222no—
623C23—1222no—
624C23—1222no—
625C23—2441no—
626C23—2441no—
627C23—2441no—
628C23—24416no—
629C23C2×C22⋊#692311yescharacteristic
630C23C2×C22⋊#692311yescharacteristic
631C23C2×C22⋊#692311yescharacteristic
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—42no—
640C2×C4—42no—
641C2×C4—614no—
642C2×C4—611no—
643C2×C4—611no—
644C2×C4—614no—
645C2×C4—614no—
646C2×C4—614no—
647C2×C4—614no—
648C2×C4—611no—
649C2×C4—611no—
650C2×C4—1222no—
651C2×C4—1222no—
652C2×C4—1222no—
653C2×C4—1222no—
654C2×C4—1222no—
655C2×C4—1222no—
656C2×C4—1222no—
657C2×C4—1222no—
658C2×C4—1222no—
659C2×C4—1222no—
660C2×C4—1222no—
661C2×C4—1222no—
662C2×C4—1222no—
663C2×C4—1222no—
664C2×C4—1222no—
665C2×C4—1222no—
666C2×C4—1222no—
667C2×C4—1228no—
668C2×C4—1222no—
669C2×C4—1222no—
670C2×C4—2444no—
671C2×C4—2444no—
672C2×C4—2444no—
673C2×C4—2444no—
674C2×C4—2442no—
675C2×C4—2444no—
676C2×C4—24416no—
677C2×C4—2444no—
678C2×C4—2442no—
679C2×C4C2×C22⋊#692311yescharacteristic
680C2×C4C2×C22⋊#692311yescharacteristic
681C2×C4C2×C22⋊#692311yescharacteristic
682C2×C4#1451985614yes—
683C2×C4C23×#692311yescharacteristic
684C8—2444no—
685C22—21no—
686C22—21no—
687C22—21no—
688C22—21no—
689C22—21no—
690C22—21no—
691C22—21no—
692C22—44no—
693C22—612no—
694C22—612no—
695C22—612no—
696C22—612no—
697C22—612no—
698C22—1228no—
699C22—1228no—
700C22—1221no—
701C22—1221no—
702C22—1221no—
703C22—1221no—
704C22—1221no—
705C22—1221no—
706C22—1221no—
707C22—2444no—
708C22—2444no—
709C22—2444no—
710C22—2444no—
711C22#1684070512yes—
712C22D61⋊#10412yes—
713C22C22×C22⋊#692311yescharacteristic
714C4—21no—
715C4—21no—
716C4—42no—
717C4—42no—
718C4—612no—
719C4—612no—
720C4—1221no—
721C4—1221no—
722C4—2448no—
723C4—2442no—
724C4—2442no—
725C4#1684070512yes—
726C4C2×#1451985612yes—
727C2—22no—
728C2—22no—
729C2—41no—
730C2—614no—
731C2—1222no—
732C2—1222no—
733C2—2441no—
734C2C2×#1684070511yescharacteristic
735C2C2×D61⋊#10411yescharacteristic
736C2D61⋊#42111yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC2×#117×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC24×D61D4
cosocleC2×C4×D61C24
hypercenterC2×#117#6923
hypocenterC61C2×#1826
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
3. #21461727C2semidirect
4. #21461726C2semidirect
5. #21461725C2semidirect
6. #21461495C2semidirect
22. #16840632C22semidirect
23. #16840632C22semidirect
25. C2×#14519736C4semidirect
34. #117×D61C4semidirect
35. #117×D61C4semidirect
38. C2×C4⋊C4×D61C4semidirect
39. C2×C4⋊C4×D61C4semidirect
42. C2×#117×C61C4semidirect
80. #14519736C2×C4semidirect
85. #14519735C2×C4semidirect
86. #14519735C2×C4semidirect
97. C2×C4⋊Dic61C2×C4semidirect
98. C2×C4⋊Dic61C2×C4semidirect
107. C4⋊C4×D61C2×C4semidirect
108. C4⋊C4×D61C2×C4semidirect
127. #117×C61C2×C4semidirect
128. C2×C4⋊C4×C61C2×C4semidirect
129. C2×C4⋊C4×C61C2×C4semidirect
375. D61#1826semidirect
391. C2×#117#6923semidirect
411. C61C2×#1826semidirect
458. #117C2×#6923semidirect
471. C2×C4⋊C4C2×#6923semidirect
472. C2×C4⋊C4C2×#6923semidirect

Maximal subgroups

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

subgroupindex
D61⋊#4072
C2×C4×C22⋊#69232
#214617272
#214617262
#214617252
#214614952
C2×#117×D612
C2×#182661