Finite Group Databasebeta

← D61×#2405 #29847562

Subgroups — D61×#2405 #29847562

Order 15616.

7822 conjugacy classes of subgroups.

The subgroup lattice has 1148 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×D4×D61C211yesmaximal, characteristic
2C2×#123×D61C212yesmaximal, complemented
3C22×C22⋊C4×D61C211yesmaximal, characteristic, complemented
4#21449148C212yesmaximal, complemented
5#21449147C211yesmaximal, characteristic, complemented
6#21449146C211yesmaximal, characteristic, complemented
7#21449145C212yesmaximal, complemented
8#21449144C212yesmaximal, complemented
9#21449143C212yesmaximal, complemented
10#21449142C211yesmaximal, characteristic, complemented
11#21449141C214yesmaximal, complemented
12#394×D61C214yesmaximal, complemented
13#386×D61C212yesmaximal, complemented
14#385×D61C212yesmaximal, complemented
15#379×D61C212yesmaximal, complemented
16#379×D61C211yesmaximal, characteristic, complemented
17C61×#2405C211yesmaximal, characteristic, complemented
18C25×D61C2211yescharacteristic
19C25×D61C2211yescharacteristic
20C23×D244C2211yescharacteristic
21C23×C22⋊D61C2211yescharacteristic
22C23×C22⋊D61C2211yescharacteristic
23C22×D4×D61—28no—
24C22×D4×D61—216no—
25C22×D4×D61C2212yes—
26C22×D4×D61C2212yes—
27C22×D4×D61C2212yes—
28C22×D4×D61C2212yes—
29C23×C4×D61C2211yescharacteristic
30C23×C4×D61C2211yescharacteristic, complemented
31C23×C4×D61C2211yescharacteristic, complemented
32C2×#14519762C2214yescomplemented
33C2×#14519761C2212yescomplemented
34C2×#14519760C2212yescomplemented
35C2×#14519759C2214yescomplemented
36C2×#14519758C2212yescomplemented
37#123×D61—216no—
38C2×C4⋊C4×D61C2214yescomplemented
39C22×C22⋊Dic61C2211yescharacteristic, complemented
40C22×#11758198C2211yescharacteristic, complemented
41C22×#11758198C2211yescharacteristic, complemented
42C2×C22⋊C4×D61—28no—
43C2×C22⋊C4×D61C2212yes—
44C2×C22⋊C4×D61C2212yes—
45C2×C22⋊C4×D61C2212yescomplemented
46C2×C22⋊C4×D61C2212yescomplemented
47C2×C22⋊C4×D61C2214yescomplemented
48C2×C22⋊C4×D61C2214yescomplemented
49C2×C22⋊C4×D61C2212yescomplemented
50C2×C22⋊C4×D61C2212yescomplemented
51C2×C22⋊C4×D61C2212yescomplemented
52#16839680C2214yescomplemented
53#16839679C2214yescomplemented
54#16839678C2214yescomplemented
55#16839678C2214yescomplemented
56#16839677C2214yescomplemented
57#16839677C2214yescomplemented
58#16839676C2214yescomplemented
59#16839642C2212yescomplemented
60#16839641C2212yescomplemented
61#16839640C2214yescomplemented
62#16839639C2212yescomplemented
63#16839638C2214yescomplemented
64#16839637C2212yescomplemented
65#16839636C2214yescomplemented
66#16839635C2212yescomplemented
67#16839634C2212yescomplemented
68#16839633C2214yescomplemented
69#16839618C2212yescomplemented
70#16839618C2211yescharacteristic, complemented
71#16839617C2212yescomplemented
72#16839617C2212yescomplemented
73#16839617C2212yescomplemented
74#16839617C2212yescomplemented
75#16839617C2214yescomplemented
76#16839617C2214yescomplemented
77#16839617C2212yescomplemented
78#95×D61C2214yescomplemented
79C23×D4×C61C2211yescharacteristic
80C2×#123×C61C2212yescomplemented
81C22×C22⋊C4×C61C2211yescharacteristic, complemented
82C61×#394C2214yescomplemented
83C61×#386C2212yescomplemented
84C61×#385C2212yescomplemented
85C61×#379C2212yescomplemented
86C61×#379C2211yescharacteristic, complemented
87C24×D61—28no—
88C24×D61—28no—
89C24×D61—24no—
90C24×D61—28no—
91C24×D61—28no—
92C24×D61—44no—
93C24×D61—44no—
94C24×D61D418yes—
95C24×D61C2311yescharacteristic
96C24×D61C2312yes—
97C24×D61C2312yes—
98C24×D61C2311yescharacteristic
99C24×D61C2311yescharacteristic
100C24×D61C2311yescharacteristic
101C24×D61C2311yescharacteristic
102C24×D61C2311yescharacteristic
103C24×D61C2311yescharacteristic
104C22×D244—24no—
105C22×D244—28no—
106C22×D244C2312yes—
107C22×D244C2312yes—
108C22×C22⋊D61—24no—
109C22×C22⋊D61—24no—
110C22×C22⋊D61—28no—
111C22×C22⋊D61—28no—
112C22×C22⋊D61C2312yes—
113C22×C22⋊D61C2312yes—
114C22×C22⋊D61C2312yes—
115C22×C22⋊D61C2312yes—
116C2×D4×D61—2128no—
117C2×D4×D61—28no—
118C2×D4×D61—28no—
119C2×D4×D61—28no—
120C2×D4×D61—28no—
121C2×D4×D61—28no—
122C2×D4×D61—28no—
123C2×D4×D61—28no—
124C2×D4×D61—28no—
125C2×D4×D61—28no—
126C2×D4×D61—28no—
127C2×D4×D61—28no—
128C2×D4×D61D4116yes—
129C23×Dic61C2311yescharacteristic
130C23×Dic61C2311yescharacteristic, complemented
131C23×Dic61C2311yescharacteristic, complemented
132C22×C4×D61—24no—
133C22×C4×D61—28no—
134C22×C4×D61—24no—
135C22×C4×D61—24no—
136C22×C4×D61—28no—
137C22×C4×D61—44no—
138C22×C4×D61C2314yes—
139C22×C4×D61C2312yes—
140C22×C4×D61C2312yes—
141C22×C4×D61C2312yes—
142C22×C4×D61C2312yes—
143C22×C4×D61C2312yescomplemented
144C22×C4×D61C2312yescomplemented
145#14519762—216no—
146#14519761—28no—
147#14519760—28no—
148#14519759—216no—
149#14519758—28no—
150C2×C4⋊Dic61C2314yescomplemented
151C2×#11758196C2314yescomplemented
152C2×#11758196C2314yescomplemented
153C4⋊C4×D61—216no—
154C2×C22⋊Dic61—24no—
155C2×C22⋊Dic61C2312yes—
156C2×C22⋊Dic61C2312yes—
157C2×C22⋊Dic61C2312yescomplemented
158C2×C22⋊Dic61C2314yescomplemented
159C2×C22⋊Dic61C2312yescomplemented
160C2×C22⋊Dic61C2314yescomplemented
161C2×C22⋊Dic61C2312yescomplemented
162C2×#11758198—24no—
163C2×#11758198—24no—
164C2×#11758198C2312yes—
165C2×#11758198C2312yes—
166C2×#11758198C2314yes—
167C2×#11758198C2312yescomplemented
168C2×#11758198C2314yescomplemented
169C2×#11758198C2312yescomplemented
170C2×#11758198C2314yescomplemented
171C2×#11758198C2314yescomplemented
172C2×#11758198C2314yescomplemented
173C2×#11758198C2314yescomplemented
174C2×#11758198C2314yescomplemented
175C22⋊C4×D61—28no—
176C22⋊C4×D61—28no—
177C22⋊C4×D61—28no—
178C22⋊C4×D61—28no—
179C22⋊C4×D61—28no—
180C22⋊C4×D61—216no—
181C22⋊C4×D61—28no—
182C22⋊C4×D61—48no—
183C22⋊C4×D61—44no—
184#14519684C2314yescomplemented
185#14519684C2314yescomplemented
186#14519684C2314yescomplemented
187C25×C61C2311yescharacteristic
188C25×C61C2311yescharacteristic
189C22×D4×C61—24no—
190C22×D4×C61—28no—
191C22×D4×C61C2312yes—
192C22×D4×C61C2312yes—
193C23×C4×C61C2311yescharacteristic
194C23×C4×C61C2311yescharacteristic, complemented
195C23×C4×C61C2311yescharacteristic, complemented
196#123×C61—28no—
197C2×C4⋊C4×C61C2314yescomplemented
198C2×C22⋊C4×C61—24no—
199C2×C22⋊C4×C61C2312yes—
200C2×C22⋊C4×C61C2312yes—
201C2×C22⋊C4×C61C2312yescomplemented
202C2×C22⋊C4×C61C2314yescomplemented
203C2×C22⋊C4×C61C2312yescomplemented
204C2×C22⋊C4×C61C2314yescomplemented
205C2×C22⋊C4×C61C2312yescomplemented
206#95×C61C2314yescomplemented
207C24×C61—24no—
208C24×C61—24no—
209C24×C61—22no—
210C24×C61—24no—
211C24×C61—24no—
212C24×C61—42no—
213C24×C61—42no—
214C24×C61C2×D414yes—
215C24×C61C2411yescharacteristic
216C24×C61C2412yes—
217C24×C61C2411yescharacteristic
218C24×C61C2411yescharacteristic
219C23×D61—24no—
220C23×D61—24no—
221C23×D61—24no—
222C23×D61—24no—
223C23×D61—232no—
224C23×D61—24no—
225C23×D61—24no—
226C23×D61—22no—
227C23×D61—24no—
228C23×D61—232no—
229C23×D61—232no—
230C23×D61—24no—
231C23×D61—24no—
232C23×D61—24no—
233C23×D61—24no—
234C23×D61—24no—
235C23×D61—24no—
236C23×D61—24no—
237C23×D61—24no—
238C23×D61—24no—
239C23×D61—24no—
240C23×D61—24no—
241C23×D61—28no—
242C23×D61—24no—
243C23×D61—28no—
244C23×D61—24no—
245C23×D61—28no—
246C23×D61—416no—
247C23×D61—42no—
248C23×D61—42no—
249C23×D61—42no—
250C23×D61—44no—
251C23×D61—42no—
252C23×D61—464no—
253C23×D61—464no—
254C23×D61—416no—
255C23×D61—416no—
256C23×D61C2×D414yes—
257C23×D61C2×D418yes—
258C23×D61C2×D414yes—
259C23×D61C2×D414yes—
260C23×D61C2×D414yes—
261C23×D61C2×D414yes—
262C23×D61C2×D418yes—
263C23×D61C2×D414yes—
264C23×D61#4118yes—
265C23×D61C2411yescharacteristic
266C23×D61C2412yes—
267C23×D61C2411yescharacteristic
268C23×D61C2411yescharacteristic
269C23×D61C2411yescharacteristic
270C2×D4×C61—232no—
271C2×D4×C61—24no—
272C2×D4×C61—24no—
273C2×D4×C61—24no—
274C2×D4×C61—24no—
275C2×D4×C61—24no—
276C2×D4×C61C2×D418yes—
277C22×C4×C61—22no—
278C22×C4×C61—24no—
279C22×C4×C61—22no—
280C22×C4×C61—22no—
281C22×C4×C61—24no—
282C22×C4×C61—42no—
283C22×C4×C61C2412yes—
284C22×C4×C61C2412yes—
285C22×C4×C61C2414yes—
286C22×C4×C61C2412yes—
287C2×C22⋊D61—232no—
288C2×C22⋊D61—232no—
289C2×C22⋊D61—24no—
290C2×C22⋊D61—24no—
291C2×C22⋊D61—24no—
292C2×C22⋊D61—24no—
293C2×C22⋊D61—24no—
294C2×C22⋊D61—24no—
295C2×C22⋊D61—24no—
296C2×C22⋊D61—24no—
297C2×C22⋊D61—24no—
298C2×C22⋊D61—24no—
299C2×C22⋊D61C2×D418yes—
300C2×C22⋊D61C2×D418yes—
301C22×Dic61—22no—
302C22×Dic61—24no—
303C22×Dic61—22no—
304C22×Dic61—22no—
305C22×Dic61—24no—
306C22×Dic61—42no—
307C22×Dic61C2412yes—
308C22×Dic61C2412yes—
309C22×Dic61C2414yes—
310C22×Dic61C2412yes—
311D4×D61—264no—
312D4×D61—264no—
313D4×D61—264no—
314D4×D61—264no—
315C2×D244—232no—
316C2×D244—24no—
317C2×D244—24no—
318C2×D244—24no—
319C2×D244—24no—
320C2×D244—24no—
321C2×D244C2×D418yes—
322C2×C4×D61—232no—
323C2×C4×D61—24no—
324C2×C4×D61—24no—
325C2×C4×D61—24no—
326C2×C4×D61—24no—
327C2×C4×D61—24no—
328C2×C4×D61—24no—
329C2×C4×D61—24no—
330C2×C4×D61—28no—
331C2×C4×D61—24no—
332C2×C4×D61—24no—
333C2×C4×D61—28no—
334C2×C4×D61—28no—
335C2×C4×D61—28no—
336C2×C4×D61—28no—
337C2×C4×D61—28no—
338C2×C4×D61—44no—
339C2×C4×D61—416no—
340C2×C4×D61—416no—
341C2×C4×D61C2×D418yes—
342C4⋊C4×C61—28no—
343C22⋊C4×C61—24no—
344C22⋊C4×C61—24no—
345C22⋊C4×C61—28no—
346C22⋊C4×C61—24no—
347C22⋊C4×C61—24no—
348C22⋊C4×C61—42no—
349C22⋊C4×C61—44no—
350C22⋊Dic61—24no—
351C22⋊Dic61—24no—
352C22⋊Dic61—28no—
353C22⋊Dic61—24no—
354C22⋊Dic61—24no—
355C22⋊Dic61—42no—
356C22⋊Dic61—44no—
357#11758198—24no—
358#11758198—24no—
359#11758198—24no—
360#11758198—24no—
361#11758198—28no—
362#11758198—28no—
363#11758198—28no—
364#11758198—28no—
365#11758198—44no—
366#11758198—44no—
367#11758198—44no—
368C4⋊Dic61—28no—
369#11758196—28no—
370#11758196—28no—
371C23×C61—22no—
372C23×C61—22no—
373C23×C61—22no—
374C23×C61—22no—
375C23×C61—28no—
376C23×C61—28no—
377C23×C61—28no—
378C23×C61—22no—
379C23×C61—22no—
380C23×C61—22no—
381C23×C61—22no—
382C23×C61—24no—
383C23×C61—22no—
384C23×C61—24no—
385C23×C61—44no—
386C23×C61—416no—
387C23×C61—416no—
388C23×C61—44no—
389C23×C61—44no—
390C23×C61C22×D412yes—
391C23×C61C22×D414yes—
392C23×C61C22×D414yes—
393C23×C61C22×D412yes—
394C23×C61C22×D412yes—
395C23×C61C2×#4114yes—
396C23×C61C2511yescharacteristic
397C22×D61—22no—
398C22×D61—22no—
399C22×D61—22no—
400C22×D61—22no—
401C22×D61—28no—
402C22×D61—28no—
403C22×D61—28no—
404C22×D61—28no—
405C22×D61—232no—
406C22×D61—232no—
407C22×D61—28no—
408C22×D61—216no—
409C22×D61—28no—
410C22×D61—28no—
411C22×D61—22no—
412C22×D61—22no—
413C22×D61—22no—
414C22×D61—22no—
415C22×D61—24no—
416C22×D61—22no—
417C22×D61—24no—
418C22×D61—28no—
419C22×D61—28no—
420C22×D61—28no—
421C22×D61—216no—
422C22×D61—28no—
423C22×D61—28no—
424C22×D61—28no—
425C22×D61—28no—
426C22×D61—232no—
427C22×D61—44no—
428C22×D61—44no—
429C22×D61—44no—
430C22×D61—416no—
431C22×D61—416no—
432C22×D61—4128no—
433C22×D61—416no—
434C22×D61—416no—
435C22×D61—416no—
436C22×D61—416no—
437C22×D61—48no—
438C22×D61—4128no—
439C22×D61—44no—
440C22×D61—44no—
441C22×D61—48no—
442C22×D61—48no—
443C22×D61—48no—
444C22×D61—416no—
445C22×D61—416no—
446C22×D61#120116yes—
447C22×D61#123116yescomplemented
448C22×D61C22×D412yes—
449C22×D61C22×D414yes—
450C22×D61C22×D414yes—
451C22×D61C22×D412yes—
452C22×D61C22×D412yes—
453C22×D61C22×D412yes—
454C22×D61C22×D414yes—
455C22×D61C2×#4114yes—
456C22×D61C2×#4114yes—
457C22×D61H(5,𝔽2)14yes—
458D4×C61—216no—
459D4×C61—216no—
460C2×C4×C61—28no—
461C2×C4×C61—22no—
462C2×C4×C61—22no—
463C2×C4×C61—24no—
464C2×C4×C61—24no—
465C2×C4×C61—22no—
466C2×C4×C61—22no—
467C2×C4×C61—24no—
468C2×C4×C61—24no—
469C2×C4×C61—24no—
470C2×C4×C61—44no—
471C2×C4×C61—44no—
472C2×C4×C61C22×D414yes—
473C22⋊D61—216no—
474C22⋊D61—216no—
475C22⋊D61—216no—
476C22⋊D61—216no—
477C2×Dic61—28no—
478C2×Dic61—22no—
479C2×Dic61—22no—
480C2×Dic61—24no—
481C2×Dic61—24no—
482C2×Dic61—22no—
483C2×Dic61—22no—
484C2×Dic61—24no—
485C2×Dic61—24no—
486C2×Dic61—24no—
487C2×Dic61—44no—
488C2×Dic61—44no—
489C2×Dic61C22×D414yes—
490D244—216no—
491D244—216no—
492C4×D61—216no—
493C4×D61—216no—
494C4×D61—48no—
495C4×D61—48no—
496C4×D61—48no—
497C4×D61—48no—
498C4×D61—416no—
499C2×#2405—611nomaximal, Sylow
500C22×C61—22no—
501C22×C61—22no—
502C22×C61—22no—
503C22×C61—22no—
504C22×C61—28no—
505C22×C61—28no—
506C22×C61—22no—
507C22×C61—24no—
508C22×C61—22no—
509C22×C61—22no—
510C22×C61—28no—
511C22×C61—416no—
512C22×C61—416no—
513C22×C61—42no—
514C22×C61—42no—
515C22×C61—44no—
516C22×C61—44no—
517C22×C61C2×#12014yes—
518C22×C61C2×#12314yescomplemented
519C22×C61C23×D411yescharacteristic
520C22×C61C23×D412yes—
521C22×C61C22×#4112yes—
522C22×C61C2×H(5,𝔽2)12yes—
523C2×D61—22no—
524C2×D61—22no—
525C2×D61—22no—
526C2×D61—22no—
527C2×D61—28no—
528C2×D61—28no—
529C2×D61—232no—
530C2×D61—232no—
531C2×D61—22no—
532C2×D61—24no—
533C2×D61—22no—
534C2×D61—22no—
535C2×D61—28no—
536C2×D61—416no—
537C2×D61—416no—
538C2×D61—416no—
539C2×D61—432no—
540C2×D61—416no—
541C2×D61—42no—
542C2×D61—42no—
543C2×D61—44no—
544C2×D61—44no—
545C2×D61—416no—
546C2×D61—432no—
547C2×D61C2×#12014yes—
548C2×D61C2×#12014yes—
549C2×D61C2×#12314yes—
550C2×D61C2×#12314yescomplemented
551C2×D61#53414yes—
552C2×D61#546116yes—
553C4×C61—24no—
554C4×C61—42no—
555C4×C61—42no—
556C4×C61—44no—
557Dic61—24no—
558Dic61—42no—
559Dic61—42no—
560Dic61—44no—
561C24×D4—611no—
562C22×#123—612no—
563C23×C22⋊C4—611no—
564#2405—614no—
565#2405—612no—
566#2405—612no—
567#2405—612no—
568#2405—611no—
569#2405—611no—
570#2405—612no—
571#2405—611no—
572#2405D6111yescharacteristic, direct product factor
573C2×#394—614no—
574C2×#386—612no—
575C2×#385—612no—
576C2×#379—612no—
577C2×#379—611no—
578C2×C61—24no—
579C2×C61—24no—
580C2×C61—42no—
581C2×C61—44no—
582C2×C61C22×#12011yescharacteristic
583C2×C61C22×#12311yescharacteristic
584C2×C61C2×#53411yescharacteristic
585C2×C61C2×#54614yes—
586D61—24no—
587D61—24no—
588D61—42no—
589D61—44no—
590D61#240518yesdirect product factor
591C26—611no—
592C26—611no—
593C23×D4—612no—
594C23×D4—611no—
595C23×D4—611no—
596C23×D4—612no—
597C23×D4—612no—
598C23×D4—612no—
599C23×D4—611no—
600C23×D4—12216no—
601C23×D4—1228no—
602C23×D4C2×D6111yescharacteristic
603C24×C4—611no—
604C24×C4—611no—
605C24×C4—611no—
606C2×#123—612no—
607C2×#123—612no—
608C2×#123—614no—
609C2×#123—614no—
610C2×#123—612no—
611C2×#123—12216no—
612C2×#123C2×D6112yescomplemented
613C22×C4⋊C4—614no—
614C22×C22⋊C4—611no—
615C22×C22⋊C4—611no—
616C22×C22⋊C4—611no—
617C22×C22⋊C4—612no—
618C22×C22⋊C4—612no—
619C22×C22⋊C4—612no—
620C22×C22⋊C4—612no—
621C22×C22⋊C4—614no—
622C22×C22⋊C4—612no—
623C22×C22⋊C4—612no—
624C22×C22⋊C4—612no—
625C22×C22⋊C4—614no—
626C22×C22⋊C4—1228no—
627C22×C22⋊C4C2×D6111yescharacteristic, complemented
628#394—614no—
629#394—614no—
630#394—614no—
631#394—614no—
632#394—614no—
633#394—614no—
634#394—614no—
635#394C2×D6114yescomplemented
636#386—612no—
637#386—612no—
638#386—614no—
639#386—612no—
640#386—614no—
641#386C2×D6112yescomplemented
642#385—612no—
643#385—614no—
644#385—612no—
645#385—612no—
646#385—614no—
647#385C2×D6112yescomplemented
648#379—612no—
649#379—611no—
650#379—612no—
651#379—612no—
652#379—612no—
653#379—612no—
654#379—614no—
655#379—614no—
656#379—612no—
657#379C2×D6112yescomplemented
658#379C2×D6111yescharacteristic, complemented
659C2×#95—614no—
660C61C2×#240511yescharacteristic, complemented, Sylow
661C25—611no—
662C25—611no—
663C25—612no—
664C25—611no—
665C25—618no—
666C25—611no—
667C25—611no—
668C25—611no—
669C25—612no—
670C25—611no—
671C25—1224no—
672C25—1228no—
673C25—1228no—
674C25—1228no—
675C25—1228no—
676C25—2444no—
677C25—2444no—
678C25C22×D6111yescharacteristic
679C25C22×D6111yescharacteristic
680C22×D4—24no—
681C22×D4—28no—
682C22×D4—612no—
683C22×D4—612no—
684C22×D4—6116no—
685C22×D4—612no—
686C22×D4—612no—
687C22×D4—612no—
688C22×D4—612no—
689C22×D4—1228no—
690C22×D4—1224no—
691C22×D4—1228no—
692C22×D4—1228no—
693C22×D4—1228no—
694C22×D4—1228no—
695C22×D4—1228no—
696C22×D4—1228no—
697C22×D4—1228no—
698C22×D4—1228no—
699C22×D4—1228no—
700C22×D4—1228no—
701C22×D4—122128no—
702C22×D4—1228no—
703C22×D4—1228no—
704C22×D4—1224no—
705C22×D4—1224no—
706C22×D4—1228no—
707C22×D4C22×D6112yes—
708C22×D4C22×D6112yes—
709C23×C4—612no—
710C23×C4—611no—
711C23×C4—611no—
712C23×C4—611no—
713C23×C4—614no—
714C23×C4—612no—
715C23×C4—612no—
716C23×C4—612no—
717C23×C4—612no—
718C23×C4—612no—
719C23×C4—1228no—
720C23×C4—1224no—
721C23×C4—1224no—
722C23×C4—1224no—
723C23×C4—1228no—
724C23×C4—2444no—
725C23×C4C22×D6111yescharacteristic
726C23×C4C22×D6111yescharacteristic, complemented
727C23×C4C22×D6111yescharacteristic, complemented
728#123—28no—
729#123—12216no—
730#123—1228no—
731#123—12216no—
732#123—1228no—
733#123—1228no—
734C2×C4⋊C4—614no—
735C2×C4⋊C4—614no—
736C2×C4⋊C4—614no—
737C2×C4⋊C4—12216no—
738C2×C4⋊C4C22×D6114yescomplemented
739C2×C22⋊C4—24no—
740C2×C22⋊C4—612no—
741C2×C22⋊C4—612no—
742C2×C22⋊C4—612no—
743C2×C22⋊C4—614no—
744C2×C22⋊C4—612no—
745C2×C22⋊C4—612no—
746C2×C22⋊C4—612no—
747C2×C22⋊C4—612no—
748C2×C22⋊C4—612no—
749C2×C22⋊C4—614no—
750C2×C22⋊C4—614no—
751C2×C22⋊C4—614no—
752C2×C22⋊C4—614no—
753C2×C22⋊C4—614no—
754C2×C22⋊C4—612no—
755C2×C22⋊C4—614no—
756C2×C22⋊C4—614no—
757C2×C22⋊C4—614no—
758C2×C22⋊C4—1228no—
759C2×C22⋊C4—1228no—
760C2×C22⋊C4—1228no—
761C2×C22⋊C4—1228no—
762C2×C22⋊C4—1228no—
763C2×C22⋊C4—12216no—
764C2×C22⋊C4—1228no—
765C2×C22⋊C4—1224no—
766C2×C22⋊C4—1224no—
767C2×C22⋊C4—1224no—
768C2×C22⋊C4—2444no—
769C2×C22⋊C4—2448no—
770C2×C22⋊C4C22×D6112yes—
771C2×C22⋊C4C22×D6112yes—
772C2×C22⋊C4C22×D6112yescomplemented
773C2×C22⋊C4C22×D6112yescomplemented
774C2×C22⋊C4C22×D6114yescomplemented
775C2×C22⋊C4C22×D6114yescomplemented
776C2×C22⋊C4C22×D6112yescomplemented
777#95—614no—
778#95—614no—
779#95—614no—
780#95C22×D6114yescomplemented
781C24—24no—
782C24—24no—
783C24—22no—
784C24—24no—
785C24—24no—
786C24—42no—
787C24—42no—
788C24—611no—
789C24—614no—
790C24—618no—
791C24—614no—
792C24—618no—
793C24—611no—
794C24—611no—
795C24—618no—
796C24—614no—
797C24—612no—
798C24—611no—
799C24—614no—
800C24—614no—
801C24—614no—
802C24—1224no—
803C24—1224no—
804C24—1224no—
805C24—1224no—
806C24—1228no—
807C24—1224no—
808C24—1224no—
809C24—1224no—
810C24—12232no—
811C24—1224no—
812C24—1224no—
813C24—1224no—
814C24—1224no—
815C24—1224no—
816C24—1224no—
817C24—1224no—
818C24—12232no—
819C24—1224no—
820C24—1228no—
821C24—1224no—
822C24—1228no—
823C24—12232no—
824C24—1224no—
825C24—1222no—
826C24—1224no—
827C24—1224no—
828C24—1224no—
829C24—2442no—
830C24—2442no—
831C24—2442no—
832C24—2442no—
833C24—2444no—
834C24—24416no—
835C24—24416no—
836C24—24464no—
837C24—24464no—
838C24—24416no—
839C24D4×D6114yes—
840C24C23×D6111yescharacteristic
841C24C23×D6112yes—
842C24C23×D6111yescharacteristic
843C24C23×D6111yescharacteristic
844C2×D4—232no—
845C2×D4—24no—
846C2×D4—24no—
847C2×D4—24no—
848C2×D4—24no—
849C2×D4—24no—
850C2×D4—618no—
851C2×D4—618no—
852C2×D4—618no—
853C2×D4—1224no—
854C2×D4—1224no—
855C2×D4—1224no—
856C2×D4—1224no—
857C2×D4—12232no—
858C2×D4—1224no—
859C2×D4—1224no—
860C2×D4—12264no—
861C2×D4—12264no—
862C2×D4—12264no—
863C2×D4—12264no—
864C2×D4—1224no—
865C2×D4—1224no—
866C2×D4—1224no—
867C2×D4—1224no—
868C2×D4—12232no—
869C2×D4—12232no—
870C2×D4—1224no—
871C2×D4—1224no—
872C2×D4—1224no—
873C2×D4—1224no—
874C2×D4—1224no—
875C2×D4D4×D6118yes—
876C22×C4—22no—
877C22×C4—24no—
878C22×C4—22no—
879C22×C4—22no—
880C22×C4—24no—
881C22×C4—42no—
882C22×C4—612no—
883C22×C4—618no—
884C22×C4—612no—
885C22×C4—614no—
886C22×C4—612no—
887C22×C4—1224no—
888C22×C4—1224no—
889C22×C4—1224no—
890C22×C4—1224no—
891C22×C4—12232no—
892C22×C4—1228no—
893C22×C4—1224no—
894C22×C4—1224no—
895C22×C4—1224no—
896C22×C4—1224no—
897C22×C4—1228no—
898C22×C4—1228no—
899C22×C4—1228no—
900C22×C4—1228no—
901C22×C4—1228no—
902C22×C4—1224no—
903C22×C4—1222no—
904C22×C4—1224no—
905C22×C4—1222no—
906C22×C4—1222no—
907C22×C4—1224no—
908C22×C4—2444no—
909C22×C4—24416no—
910C22×C4—24416no—
911C22×C4—2442no—
912C22×C4C23×D6112yes—
913C22×C4C23×D6114yes—
914C22×C4C23×D6112yes—
915C22×C4C23×D6112yes—
916C4⋊C4—28no—
917C4⋊C4—1228no—
918C4⋊C4—1228no—
919C4⋊C4—1228no—
920C22⋊C4—24no—
921C22⋊C4—24no—
922C22⋊C4—24no—
923C22⋊C4—28no—
924C22⋊C4—24no—
925C22⋊C4—42no—
926C22⋊C4—44no—
927C22⋊C4—1224no—
928C22⋊C4—1224no—
929C22⋊C4—1224no—
930C22⋊C4—1224no—
931C22⋊C4—1228no—
932C22⋊C4—1228no—
933C22⋊C4—1228no—
934C22⋊C4—1228no—
935C22⋊C4—1224no—
936C22⋊C4—1224no—
937C22⋊C4—1224no—
938C22⋊C4—1228no—
939C22⋊C4—1224no—
940C22⋊C4—2444no—
941C22⋊C4—2444no—
942C22⋊C4—2444no—
943C22⋊C4—2442no—
944C22⋊C4—2444no—
945C23—22no—
946C23—22no—
947C23—22no—
948C23—22no—
949C23—28no—
950C23—28no—
951C23—28no—
952C23—22no—
953C23—22no—
954C23—22no—
955C23—24no—
956C23—22no—
957C23—24no—
958C23—22no—
959C23—44no—
960C23—416no—
961C23—416no—
962C23—44no—
963C23—44no—
964C23—614no—
965C23—612no—
966C23—614no—
967C23—614no—
968C23—6116no—
969C23—6116no—
970C23—612no—
971C23—614no—
972C23—612no—
973C23—614no—
974C23—614no—
975C23—612no—
976C23—1228no—
977C23—1228no—
978C23—1228no—
979C23—12232no—
980C23—12232no—
981C23—1228no—
982C23—1228no—
983C23—12216no—
984C23—1228no—
985C23—1228no—
986C23—1228no—
987C23—1228no—
988C23—1228no—
989C23—12232no—
990C23—1228no—
991C23—1228no—
992C23—12216no—
993C23—1222no—
994C23—1222no—
995C23—1222no—
996C23—1222no—
997C23—1228no—
998C23—1228no—
999C23—1222no—
1000C23—1222no—
1001C23—1222no—
1002C23—1224no—
1003C23—1222no—
1004C23—1224no—
1005C23—1222no—
1006C23—2444no—
1007C23—2444no—
1008C23—2444no—
1009C23—24416no—
1010C23—24416no—
1011C23—24416no—
1012C23—24416no—
1013C23—2444no—
1014C23—24416no—
1015C23—24416no—
1016C23—2448no—
1017C23—2448no—
1018C23—2448no—
1019C23—244128no—
1020C23—24416no—
1021C23—24416no—
1022C23—244128no—
1023C23—2448no—
1024C23—2444no—
1025C23C2×D4×D6112yes—
1026C23C2×D4×D6114yes—
1027C23C2×D4×D6114yes—
1028C23C2×D4×D6112yes—
1029C23C2×D4×D6112yes—
1030C23#41×D6114yes—
1031C23C24×D6111yescharacteristic
1032D4—216no—
1033D4—216no—
1034D4—12216no—
1035D4—12216no—
1036D4—12216no—
1037D4—12216no—
1038D4—12216no—
1039D4—12216no—
1040C2×C4—28no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—24no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—24no—
1047C2×C4—24no—
1048C2×C4—24no—
1049C2×C4—24no—
1050C2×C4—44no—
1051C2×C4—44no—
1052C2×C4—614no—
1053C2×C4—12216no—
1054C2×C4—12216no—
1055C2×C4—1228no—
1056C2×C4—1222no—
1057C2×C4—1222no—
1058C2×C4—1224no—
1059C2×C4—1222no—
1060C2×C4—1222no—
1061C2×C4—1224no—
1062C2×C4—1224no—
1063C2×C4—1224no—
1064C2×C4—1224no—
1065C2×C4—24416no—
1066C2×C4—2448no—
1067C2×C4—2448no—
1068C2×C4—2448no—
1069C2×C4—2448no—
1070C2×C4—2444no—
1071C2×C4—2444no—
1072C2×C4C2×D4×D6114yes—
1073C22—28no—
1074C22—28no—
1075C22—22no—
1076C22—22no—
1077C22—22no—
1078C22—22no—
1079C22—28no—
1080C22—22no—
1081C22—24no—
1082C22—22no—
1083C22—22no—
1084C22—416no—
1085C22—416no—
1086C22—44no—
1087C22—44no—
1088C22—42no—
1089C22—42no—
1090C22—6116no—
1091C22—614no—
1092C22—614no—
1093C22—614no—
1094C22—614no—
1095C22—614no—
1096C22—12232no—
1097C22—12232no—
1098C22—1228no—
1099C22—1228no—
1100C22—1222no—
1101C22—1222no—
1102C22—1222no—
1103C22—1222no—
1104C22—1228no—
1105C22—1224no—
1106C22—1222no—
1107C22—1222no—
1108C22—1222no—
1109C22—24416no—
1110C22—24416no—
1111C22—24416no—
1112C22—24416no—
1113C22—24432no—
1114C22—24416no—
1115C22—24432no—
1116C22—2444no—
1117C22—2444no—
1118C22—2442no—
1119C22—2442no—
1120C22#120×D6114yes—
1121C22#123×D6114yescomplemented
1122C22C22×D4×D6112yes—
1123C22C22×D4×D6111yescharacteristic
1124C22C2×#41×D6112yes—
1125C22H(5,𝔽2)×D6112yes—
1126C4—24no—
1127C4—44no—
1128C4—42no—
1129C4—42no—
1130C4—1224no—
1131C4—2444no—
1132C4—2442no—
1133C4—2442no—
1134C2—24no—
1135C2—24no—
1136C2—44no—
1137C2—42no—
1138C2—618no—
1139C2—1224no—
1140C2—1224no—
1141C2—2444no—
1142C2—2442no—
1143C2C2×#120×D6111yescharacteristic
1144C2C2×#123×D6111yescharacteristic
1145C2#534×D6111yescharacteristic
1146C2#546×D6114yes—
subgroupG/H
center, FrattiniC23C24×D61
commutator, socle, cosocleC23×C61C25
FittingC61×#2405C2
prime radicalC23×D4×D61C2
hypercenter#2405D61
hypocenterC61C2×#2405
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #2405

Complements

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

NH ≅ G/Ntype
2. C2×#123×D61C2semidirect
3. C22×C22⋊C4×D61C2semidirect
4. #21449148C2semidirect
5. #21449147C2semidirect
6. #21449146C2semidirect
7. #21449145C2semidirect
8. #21449144C2semidirect
9. #21449143C2semidirect
10. #21449142C2semidirect
11. #21449141C2semidirect
12. #394×D61C2semidirect
13. #386×D61C2semidirect
14. #385×D61C2semidirect
15. #379×D61C2semidirect
16. #379×D61C2semidirect
17. C61×#2405C2semidirect
30. C23×C4×D61C22semidirect
31. C23×C4×D61C22semidirect
32. C2×#14519762C22semidirect
33. C2×#14519761C22semidirect
34. C2×#14519760C22semidirect
35. C2×#14519759C22semidirect
36. C2×#14519758C22semidirect
38. C2×C4⋊C4×D61C22semidirect
39. C22×C22⋊Dic61C22semidirect
40. C22×#11758198C22semidirect
41. C22×#11758198C22semidirect
45. C2×C22⋊C4×D61C22semidirect
46. C2×C22⋊C4×D61C22semidirect
47. C2×C22⋊C4×D61C22semidirect
48. C2×C22⋊C4×D61C22semidirect
49. C2×C22⋊C4×D61C22semidirect
50. C2×C22⋊C4×D61C22semidirect
51. C2×C22⋊C4×D61C22semidirect
52. #16839680C22semidirect
53. #16839679C22semidirect
54. #16839678C22semidirect
55. #16839678C22semidirect
56. #16839677C22semidirect
57. #16839677C22semidirect
58. #16839676C22semidirect
59. #16839642C22semidirect
60. #16839641C22semidirect
61. #16839640C22semidirect
62. #16839639C22semidirect
63. #16839638C22semidirect
64. #16839637C22semidirect
65. #16839636C22semidirect
66. #16839635C22semidirect
67. #16839634C22semidirect
68. #16839633C22semidirect
69. #16839618C22semidirect
70. #16839618C22semidirect
71. #16839617C22semidirect
72. #16839617C22semidirect
73. #16839617C22semidirect
74. #16839617C22semidirect
75. #16839617C22semidirect
76. #16839617C22semidirect
77. #16839617C22semidirect
78. #95×D61C22semidirect
80. C2×#123×C61C22semidirect
81. C22×C22⋊C4×C61C22semidirect
82. C61×#394C22semidirect
83. C61×#386C22semidirect
84. C61×#385C22semidirect
85. C61×#379C22semidirect
86. C61×#379C22semidirect
130. C23×Dic61C23semidirect
131. C23×Dic61C23semidirect
143. C22×C4×D61C23semidirect
144. C22×C4×D61C23semidirect
150. C2×C4⋊Dic61C23semidirect
151. C2×#11758196C23semidirect
152. C2×#11758196C23semidirect
157. C2×C22⋊Dic61C23semidirect
158. C2×C22⋊Dic61C23semidirect
159. C2×C22⋊Dic61C23semidirect
160. C2×C22⋊Dic61C23semidirect
161. C2×C22⋊Dic61C23semidirect
167. C2×#11758198C23semidirect
168. C2×#11758198C23semidirect
169. C2×#11758198C23semidirect
170. C2×#11758198C23semidirect
171. C2×#11758198C23semidirect
172. C2×#11758198C23semidirect
173. C2×#11758198C23semidirect
174. C2×#11758198C23semidirect
184. #14519684C23semidirect
185. #14519684C23semidirect
186. #14519684C23semidirect
194. C23×C4×C61C23semidirect
195. C23×C4×C61C23semidirect
197. C2×C4⋊C4×C61C23semidirect
201. C2×C22⋊C4×C61C23semidirect
202. C2×C22⋊C4×C61C23semidirect
203. C2×C22⋊C4×C61C23semidirect
204. C2×C22⋊C4×C61C23semidirect
205. C2×C22⋊C4×C61C23semidirect
206. #95×C61C23semidirect
447. C22×D61#123semidirect
518. C22×C61C2×#123semidirect
550. C2×D61C2×#123semidirect
572. #2405D61direct (N × H)
590. D61#2405direct (N × H)
612. C2×#123C2×D61semidirect
627. C22×C22⋊C4C2×D61semidirect
635. #394C2×D61semidirect
641. #386C2×D61semidirect
647. #385C2×D61semidirect
657. #379C2×D61semidirect
658. #379C2×D61semidirect
660. C61C2×#2405semidirect
726. C23×C4C22×D61semidirect
727. C23×C4C22×D61semidirect
738. C2×C4⋊C4C22×D61semidirect
772. C2×C22⋊C4C22×D61semidirect
773. C2×C22⋊C4C22×D61semidirect
774. C2×C22⋊C4C22×D61semidirect
775. C2×C22⋊C4C22×D61semidirect
776. C2×C22⋊C4C22×D61semidirect
780. #95C22×D61semidirect
1121. C22#123×D61semidirect

Maximal subgroups

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

subgroupindex
C23×D4×D612
C2×#123×D612
C22×C22⋊C4×D612
#214491482
#214491472
#214491462
#214491452
#214491442
#214491432
#214491422
#214491412
#394×D612
#386×D612
#385×D612
#379×D612
C61×#24052
C2×#240561