Finite Group Databasebeta

← D61×#2344 #29839243

Subgroups — D61×#2344 #29839243

Order 15616.

3526 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#117×D61C212yesmaximal
2C22×C4⋊C4×D61C211yesmaximal, characteristic
3#21448690C211yesmaximal, characteristic, complemented
4#21448689C212yesmaximal, complemented
5#21448688C211yesmaximal, characteristic, complemented
6#21448687C212yesmaximal, complemented
7#21448686C211yesmaximal, characteristic, complemented
8#21448685C214yesmaximal, complemented
9#21448684C212yesmaximal, complemented
10#21448683C212yesmaximal, complemented
11#389×D61C212yesmaximal, complemented
12#387×D61C214yesmaximal, complemented
13#381×D61C212yesmaximal
14#380×D61C211yesmaximal, characteristic
15C4×C4⋊C4×D61C212yesmaximal, complemented
16C4×C22⋊C4×D61C211yesmaximal, characteristic
17C61×#2344C211yesmaximal, characteristic, complemented
18C23×C4×D61C2212yes—
19C23×C4×D61C2211yescharacteristic
20C2×#14519736C2212yes—
21C2×#14519735C2214yes—
22C2×#14519734C2214yes—
23C2×#14519733C2212yes—
24C2×#14519733C2212yes—
25#117×D61—216no—
26C22×C4⋊Dic61C2211yescharacteristic
27C22×#11758196C2212yes—
28C2×C4⋊C4×D61C4116yescomplemented
29C2×C4⋊C4×D61C2214yes—
30C2×C4⋊C4×D61C2212yes—
31C2×C4⋊C4×D61C2212yes—
32C2×C4⋊C4×D61C2211yescharacteristic
33C2×C4⋊C4×D61C2211yescharacteristic
34C2×C4⋊C4×D61C2211yescharacteristic
35C2×C4⋊C4×D61C2212yes—
36C2×C4⋊C4×D61C2211yescharacteristic
37C2×C22⋊C4×D61C2211yescharacteristic
38C2×C22⋊C4×D61C2212yes—
39C2×C22⋊C4×D61C2211yescharacteristic
40C2×C42×D61C2214yes—
41C2×C42×D61C2212yes—
42#16839661C2212yescomplemented
43#16839660C2212yescomplemented
44#16839659C2214yescomplemented
45#16839658C2212yescomplemented
46#16839657C2214yescomplemented
47#16839649C2214yescomplemented
48#16839648C2214yescomplemented
49#16839647C2214yescomplemented
50#16839646C2214yescomplemented
51#16839645C2214yescomplemented
52#16839644C2214yescomplemented
53#16839643C2214yescomplemented
54#16839625C2212yes—
55#16839624C2214yes—
56#16839624C2214yes—
57#16839623C2212yes—
58#16839623C2212yes—
59#16839622C2211yescharacteristic
60#16839621C2212yes—
61#16839620C2212yes—
62#16839619C2212yes—
63C4⋊C4×Dic61C2212yescomplemented
64C4⋊C4×Dic61C2212yescomplemented
65C4×#11758196C2214yescomplemented
66C4×C4⋊Dic61C2212yescomplemented
67#16839613C2214yescomplemented
68C22⋊C4×Dic61C2211yescharacteristic
69C22⋊C4×Dic61C2211yescharacteristic
70C4×#11758198C2212yes—
71C4×C22⋊Dic61C2211yescharacteristic
72#16839609C2212yes—
73#95×D61C2214yes—
74#95×D61C2214yes—
75#95×D61C2212yes—
76#95×D61C2212yes—
77C2×#117×C61C2212yes—
78C22×C4⋊C4×C61C2211yescharacteristic
79C61×#389C2212yescomplemented
80C61×#387C2214yescomplemented
81C61×#381C2212yes—
82C61×#380C2211yescharacteristic
83C4×C4⋊C4×C61C2212yescomplemented
84C4×C22⋊C4×C61C2211yescharacteristic
85C24×D61C2311yescharacteristic
86C23×Dic61C2311yescharacteristic
87C23×Dic61C2312yes—
88C22×C4×D61—28no—
89C22×C4×D61—28no—
90C22×C4×D61—28no—
91C22×C4×D61C2×C4116yes—
92C22×C4×D61C2×C418yes—
93C22×C4×D61C2314yes—
94C22×C4×D61C2312yes—
95C22×C4×D61C2312yes—
96C22×C4×D61C2312yes—
97C22×C4×D61C2312yes—
98C22×C4×D61C2312yes—
99C22×C4×D61C2311yescharacteristic
100C22×C4×D61C2311yescharacteristic
101C22×C4×D61C2311yescharacteristic
102C22×C4×D61C2312yes—
103C22×C4×D61C2311yescharacteristic
104#14519736—28no—
105#14519735—216no—
106#14519734—216no—
107#14519733—28no—
108#14519733—28no—
109C2×C4⋊Dic61C2×C418yescomplemented
110C2×C4⋊Dic61C2314yes—
111C2×C4⋊Dic61C2312yes—
112C2×C4⋊Dic61C2311yescharacteristic
113C2×C4⋊Dic61C2312yes—
114C2×C4⋊Dic61C2311yescharacteristic
115C2×#11758196C2×C4116yescomplemented
116C2×#11758196C2314yes—
117C2×#11758196C2314yes—
118C2×#11758196C2314yes—
119C2×#11758196C2312yes—
120C2×#11758196C2312yes—
121C2×#11758196C2312yes—
122C2×#11758196C2312yes—
123C4⋊C4×D61—216no—
124C4⋊C4×D61—28no—
125C4⋊C4×D61C2×C4116yes—
126C4⋊C4×D61C2×C418yes—
127C4⋊C4×D61C2×C418yes—
128C4⋊C4×D61C2×C418yescomplemented
129C4⋊C4×D61C2×C4116yescomplemented
130C4⋊C4×D61C2×C418yescomplemented
131C2×C22⋊Dic61C2312yes—
132C2×C22⋊Dic61C2311yescharacteristic
133C2×C22⋊Dic61C2311yescharacteristic
134C2×#11758198C2314yes—
135C2×#11758198C2312yes—
136C2×#11758198C2312yes—
137C22⋊C4×D61—28no—
138C22⋊C4×D61—24no—
139C22⋊C4×D61D418yes—
140C2×C4×Dic61C2314yes—
141C2×C4×Dic61C2314yes—
142C2×C4×Dic61C2314yes—
143C2×C4×Dic61C2312yes—
144C2×C4×Dic61C2312yes—
145C2×C4×Dic61C2312yes—
146C42×D61—216no—
147C42×D61—28no—
148#14519684C2312yes—
149#14519684C2312yes—
150#14519684C2312yes—
151#14519684C2314yes—
152#14519684C2314yes—
153#14519684C2314yes—
154#14519684C2314yes—
155#14519684C2312yes—
156#14519684C2314yes—
157#14519684C2314yes—
158#14519684C2314yes—
159C23×C4×C61C2312yes—
160C23×C4×C61C2311yescharacteristic
161#117×C61—28no—
162C2×C4⋊C4×C61C2×C418yescomplemented
163C2×C4⋊C4×C61C2314yes—
164C2×C4⋊C4×C61C2312yes—
165C2×C4⋊C4×C61C2311yescharacteristic
166C2×C4⋊C4×C61C2312yes—
167C2×C4⋊C4×C61C2311yescharacteristic
168C2×C22⋊C4×C61C2312yes—
169C2×C22⋊C4×C61C2311yescharacteristic
170C2×C22⋊C4×C61C2311yescharacteristic
171C2×C42×C61C2314yes—
172C2×C42×C61C2312yes—
173#95×C61C2312yes—
174#95×C61C2314yes—
175#95×C61C2312yes—
176#95×C61C2314yes—
177C24×C61C2411yescharacteristic
178C23×D61—24no—
179C23×D61—24no—
180C23×D61C22×C414yes—
181C23×D61C2×D414yes—
182C23×D61#4114yes—
183C23×D61C2411yescharacteristic
184C23×D61C2411yescharacteristic
185C22×C4×C61—24no—
186C22×C4×C61—24no—
187C22×C4×C61—24no—
188C22×C4×C61C22×C418yes—
189C22×C4×C61C22×C414yes—
190C22×C4×C61C2412yes—
191C22×C4×C61C2414yes—
192C22×C4×C61C2411yescharacteristic
193C22×C4×C61C2412yes—
194C22×C4×C61C2412yes—
195C22×C4×C61C2412yes—
196C22×C4×C61C2411yescharacteristic
197C22×Dic61—24no—
198C22×Dic61—24no—
199C22×Dic61—24no—
200C22×Dic61C22×C414yes—
201C22×Dic61C22×C418yes—
202C22×Dic61C2412yes—
203C22×Dic61C2414yes—
204C22×Dic61C2411yescharacteristic
205C22×Dic61C2412yes—
206C22×Dic61C2412yes—
207C22×Dic61C2412yes—
208C22×Dic61C2411yescharacteristic
209C2×C4×D61—264no—
210C2×C4×D61—24no—
211C2×C4×D61—24no—
212C2×C4×D61—24no—
213C2×C4×D61—24no—
214C2×C4×D61—24no—
215C2×C4×D61—24no—
216C2×C4×D61—24no—
217C2×C4×D61—24no—
218C2×C4×D61—24no—
219C2×C4×D61—24no—
220C2×C4×D61—24no—
221C2×C4×D61—24no—
222C2×C4×D61—24no—
223C2×C4×D61—232no—
224C2×C4×D61—28no—
225C2×C4×D61—24no—
226C2×C4×D61—24no—
227C2×C4×D61—28no—
228C2×C4×D61—28no—
229C2×C4×D61—24no—
230C2×C4×D61C22×C414yes—
231C2×C4×D61C22×C418yes—
232C2×C4×D61C22×C418yes—
233C2×C4×D61C22×C418yes—
234C2×C4×D61C22×C418yes—
235C2×C4×D61C22×C414yes—
236C2×C4×D61C22×C414yes—
237C2×C4×D61C22×C414yes—
238C2×C4×D61C2×D418yes—
239C2×C4×D61#4118yes—
240C4⋊C4×C61—28no—
241C4⋊C4×C61—24no—
242C4⋊C4×C61C22×C418yes—
243C4⋊C4×C61C22×C414yes—
244C4⋊C4×C61C22×C414yes—
245C22⋊C4×C61—24no—
246C22⋊C4×C61—22no—
247C22⋊C4×C61C2×D414yes—
248C42×C61—28no—
249C42×C61—24no—
250C22⋊Dic61—24no—
251C22⋊Dic61—22no—
252C22⋊Dic61C2×D414yes—
253#11758198—28no—
254#11758198—24no—
255#11758198C2×D418yes—
256C4⋊Dic61—24no—
257C4⋊Dic61—28no—
258C4⋊Dic61C22×C418yes—
259C4⋊Dic61C22×C414yes—
260C4⋊Dic61C22×C414yes—
261#11758196—28no—
262#11758196—28no—
263#11758196—28no—
264#11758196C22×C418yes—
265#11758196C22×C418yes—
266#11758196C22×C418yes—
267#11758196C22×C418yes—
268C4×Dic61—28no—
269C4×Dic61—24no—
270C4×Dic61—28no—
271C4×Dic61—28no—
272C4×Dic61—24no—
273C4×Dic61—24no—
274C23×C61—22no—
275C23×C61—22no—
276C23×C61C23×C412yes—
277C23×C61C22×D412yes—
278C23×C61C2×#4112yes—
279C23×C61C2511yescharacteristic
280C22×D61—22no—
281C22×D61—22no—
282C22×D61—28no—
283C22×D61—28no—
284C22×D61—216no—
285C22×D61—216no—
286C22×D61C4×D4116yes—
287C22×D61C23×C412yes—
288C22×D61C23×C412yes—
289C22×D61C22×D412yes—
290C22×D61C22×D412yes—
291C22×D61C2×#4112yes—
292C22×D61C2×#4114yes—
293C22×D61C2×#4112yes—
294C22×D612−1+414yes—
295C2×C4×C61—216no—
296C2×C4×C61—22no—
297C2×C4×C61—22no—
298C2×C4×C61—22no—
299C2×C4×C61—22no—
300C2×C4×C61—22no—
301C2×C4×C61—22no—
302C2×C4×C61—22no—
303C2×C4×C61—28no—
304C2×C4×C61—24no—
305C2×C4×C61—22no—
306C2×C4×C61—24no—
307C2×C4×C61—22no—
308C2×C4×C61—24no—
309C2×C4×C61—22no—
310C2×C4×C61C23×C414yes—
311C2×C4×C61C23×C414yes—
312C2×C4×C61C23×C412yes—
313C2×C4×C61C23×C412yes—
314C2×C4×C61C22×D414yes—
315C2×C4×C61C2×#4114yes—
316C2×Dic61—216no—
317C2×Dic61—22no—
318C2×Dic61—22no—
319C2×Dic61—22no—
320C2×Dic61—22no—
321C2×Dic61—22no—
322C2×Dic61—22no—
323C2×Dic61—22no—
324C2×Dic61—28no—
325C2×Dic61—24no—
326C2×Dic61—22no—
327C2×Dic61—24no—
328C2×Dic61—22no—
329C2×Dic61—24no—
330C2×Dic61—22no—
331C2×Dic61C23×C412yes—
332C2×Dic61C23×C414yes—
333C2×Dic61C23×C414yes—
334C2×Dic61C23×C412yes—
335C2×Dic61C22×D414yes—
336C2×Dic61C2×#4114yes—
337C4×D61—28no—
338C4×D61—216no—
339C4×D61—216no—
340C4×D61—216no—
341C4×D61—216no—
342C4×D61—216no—
343C4×D61—28no—
344C4×D61—28no—
345C4×D61—416no—
346C4×D61—48no—
347C4×D61#117116yescomplemented
348C2×#2344—611nomaximal, Sylow
349C22×C61—22no—
350C22×C61—22no—
351C22×C61—24no—
352C22×C61—24no—
353C22×C61C2×C4×D414yes—
354C22×C61C24×C411yescharacteristic
355C22×C61C23×D411yescharacteristic
356C22×C61C22×#4112yes—
357C22×C61C22×#4111yescharacteristic
358C22×C61C2×2−1+412yes—
359C2×D61—22no—
360C2×D61—22no—
361C2×D61—24no—
362C2×D61—24no—
363C2×D61—232no—
364C2×D61C2×#11714yes—
365C2×D61C2×C4×D414yes—
366C2×D61C2×C4×D414yes—
367C2×D61#51914yes—
368C2×D61#54718yes—
369C2×D61#55218yes—
370C4×C61—22no—
371C4×C61—24no—
372C4×C61—24no—
373C4×C61—24no—
374C4×C61—44no—
375C4×C61—42no—
376C4×C61C2×#11714yescomplemented
377Dic61—22no—
378Dic61—24no—
379Dic61—24no—
380Dic61—24no—
381Dic61—44no—
382Dic61—42no—
383Dic61C2×#11714yescomplemented
384C22×#117—612no—
385C23×C4⋊C4—611no—
386#2344—612no—
387#2344—614no—
388#2344—612no—
389#2344—611no—
390#2344—612no—
391#2344—611no—
392#2344—612no—
393#2344—611no—
394#2344D6111yescharacteristic, direct product factor
395C2×#389—612no—
396C2×#387—614no—
397C2×#381—612no—
398C2×#380—611no—
399C2×C4×C4⋊C4—612no—
400C2×C4×C22⋊C4—611no—
401C2×C61—24no—
402C2×C61C22×#11711yescharacteristic
403C2×C61C22×C4×D411yescharacteristic
404C2×C61C2×#51911yescharacteristic
405C2×C61C2×#54712yes—
406C2×C61C2×#55212yes—
407D61—24no—
408D61#234418yesdirect product factor
409C24×C4—612no—
410C24×C4—611no—
411C2×#117—612no—
412C2×#117—614no—
413C2×#117—612no—
414C2×#117—612no—
415C2×#117—614no—
416C2×#117—12216no—
417C2×#117C2×D6112yes—
418C22×C4⋊C4—612no—
419C22×C4⋊C4—611no—
420C22×C4⋊C4—6116no—
421C22×C4⋊C4—612no—
422C22×C4⋊C4—611no—
423C22×C4⋊C4—611no—
424C22×C4⋊C4—611no—
425C22×C4⋊C4—612no—
426C22×C4⋊C4—611no—
427C22×C4⋊C4—614no—
428C22×C4⋊C4—612no—
429C22×C4⋊C4C2×D6111yescharacteristic
430C22×C22⋊C4—611no—
431C22×C22⋊C4—612no—
432C22×C22⋊C4—611no—
433C22×C42—614no—
434C22×C42—612no—
435#389—614no—
436#389—612no—
437#389—612no—
438#389—612no—
439#389—614no—
440#389C2×D6112yescomplemented
441#387—614no—
442#387—614no—
443#387—614no—
444#387—614no—
445#387—614no—
446#387—614no—
447#387—614no—
448#387C2×D6114yescomplemented
449#381—612no—
450#381—612no—
451#381—612no—
452#381—614no—
453#381—614no—
454#381C2×D6112yes—
455#380—611no—
456#380—612no—
457#380—612no—
458#380—612no—
459#380C2×D6111yescharacteristic
460C4×C4⋊C4—612no—
461C4×C4⋊C4—612no—
462C4×C4⋊C4—612no—
463C4×C4⋊C4—614no—
464C4×C4⋊C4—614no—
465C4×C4⋊C4C2×D6112yescomplemented
466C4×C22⋊C4—611no—
467C4×C22⋊C4—611no—
468C4×C22⋊C4—611no—
469C4×C22⋊C4—612no—
470C4×C22⋊C4—612no—
471C4×C22⋊C4C2×D6111yescharacteristic
472C2×#95—612no—
473C2×#95—614no—
474C2×#95—612no—
475C2×#95—614no—
476C61C2×#234411yescharacteristic, complemented, Sylow
477C25—611no—
478C23×C4—611no—
479C23×C4—612no—
480C23×C4—611no—
481C23×C4—618no—
482C23×C4—6116no—
483C23×C4—612no—
484C23×C4—612no—
485C23×C4—612no—
486C23×C4—612no—
487C23×C4—611no—
488C23×C4—612no—
489C23×C4—611no—
490C23×C4—611no—
491C23×C4—614no—
492C23×C4—612no—
493C23×C4—1228no—
494C23×C4—1228no—
495C23×C4—1228no—
496C23×C4C22×D6112yes—
497C23×C4C22×D6111yescharacteristic
498#117—28no—
499#117—12216no—
500#117—1228no—
501#117—12216no—
502#117—1228no—
503#117—1228no—
504C2×C4⋊C4—6116no—
505C2×C4⋊C4—618no—
506C2×C4⋊C4—612no—
507C2×C4⋊C4—611no—
508C2×C4⋊C4—612no—
509C2×C4⋊C4—612no—
510C2×C4⋊C4—612no—
511C2×C4⋊C4—612no—
512C2×C4⋊C4—611no—
513C2×C4⋊C4—618no—
514C2×C4⋊C4—618no—
515C2×C4⋊C4—6116no—
516C2×C4⋊C4—6116no—
517C2×C4⋊C4—618no—
518C2×C4⋊C4—618no—
519C2×C4⋊C4—614no—
520C2×C4⋊C4—614no—
521C2×C4⋊C4—614no—
522C2×C4⋊C4—614no—
523C2×C4⋊C4—612no—
524C2×C4⋊C4—12216no—
525C2×C4⋊C4—1228no—
526C2×C4⋊C4C4×D6118yescomplemented
527C2×C4⋊C4C22×D6114yes—
528C2×C4⋊C4C22×D6112yes—
529C2×C4⋊C4C22×D6111yescharacteristic
530C2×C4⋊C4C22×D6112yes—
531C2×C4⋊C4C22×D6111yescharacteristic
532C2×C22⋊C4—611no—
533C2×C22⋊C4—612no—
534C2×C22⋊C4—618no—
535C2×C22⋊C4—612no—
536C2×C22⋊C4—611no—
537C2×C22⋊C4—614no—
538C2×C22⋊C4—612no—
539C2×C22⋊C4—1228no—
540C2×C22⋊C4—1224no—
541C2×C22⋊C4C22×D6112yes—
542C2×C22⋊C4C22×D6111yescharacteristic
543C2×C22⋊C4C22×D6111yescharacteristic
544C2×C42—614no—
545C2×C42—614no—
546C2×C42—614no—
547C2×C42—612no—
548C2×C42—612no—
549C2×C42—612no—
550C2×C42—12216no—
551C2×C42—1228no—
552C2×C42C22×D6114yes—
553C2×C42C22×D6112yes—
554#95—612no—
555#95—612no—
556#95—612no—
557#95—614no—
558#95—614no—
559#95—614no—
560#95—614no—
561#95—612no—
562#95—614no—
563#95—614no—
564#95—614no—
565#95C22×D6112yes—
566#95C22×D6114yes—
567#95C22×D6112yes—
568#95C22×D6114yes—
569C24—611no—
570C24—614no—
571C24—614no—
572C24—614no—
573C24—611no—
574C24—1224no—
575C24—1224no—
576C24C23×D6111yescharacteristic
577C22×C4—24no—
578C22×C4—24no—
579C22×C4—24no—
580C22×C4—611no—
581C22×C4—614no—
582C22×C4—618no—
583C22×C4—614no—
584C22×C4—618no—
585C22×C4—611no—
586C22×C4—612no—
587C22×C4—612no—
588C22×C4—612no—
589C22×C4—614no—
590C22×C4—618no—
591C22×C4—614no—
592C22×C4—618no—
593C22×C4—618no—
594C22×C4—618no—
595C22×C4—614no—
596C22×C4—618no—
597C22×C4—612no—
598C22×C4—614no—
599C22×C4—1224no—
600C22×C4—12232no—
601C22×C4—1224no—
602C22×C4—1224no—
603C22×C4—1224no—
604C22×C4—1224no—
605C22×C4—1224no—
606C22×C4—12264no—
607C22×C4—1224no—
608C22×C4—1224no—
609C22×C4—1224no—
610C22×C4—1224no—
611C22×C4—1224no—
612C22×C4—1224no—
613C22×C4—1228no—
614C22×C4—1224no—
615C22×C4—1224no—
616C22×C4—1228no—
617C22×C4—1228no—
618C22×C4—1224no—
619C22×C4—1224no—
620C22×C4—1224no—
621C22×C4—1224no—
622C22×C4—1224no—
623C22×C4C2×C4×D6118yes—
624C22×C4C2×C4×D6114yes—
625C22×C4C23×D6112yes—
626C22×C4C23×D6114yes—
627C22×C4C23×D6111yescharacteristic
628C22×C4C23×D6112yes—
629C22×C4C23×D6112yes—
630C22×C4C23×D6112yes—
631C22×C4C23×D6111yescharacteristic
632C4⋊C4—28no—
633C4⋊C4—24no—
634C4⋊C4—618no—
635C4⋊C4—618no—
636C4⋊C4—618no—
637C4⋊C4—618no—
638C4⋊C4—618no—
639C4⋊C4—614no—
640C4⋊C4—614no—
641C4⋊C4—1228no—
642C4⋊C4—1228no—
643C4⋊C4—1228no—
644C4⋊C4—1228no—
645C4⋊C4—1224no—
646C4⋊C4C2×C4×D6118yes—
647C4⋊C4C2×C4×D6114yes—
648C4⋊C4C2×C4×D6114yes—
649C22⋊C4—24no—
650C22⋊C4—22no—
651C22⋊C4—614no—
652C22⋊C4—618no—
653C22⋊C4—1228no—
654C22⋊C4—1224no—
655C22⋊C4—1224no—
656C22⋊C4—1222no—
657C22⋊C4D4×D6114yes—
658C42—28no—
659C42—24no—
660C42—1224no—
661C42—1224no—
662C42—1228no—
663C42—1228no—
664C42—1228no—
665C42—1224no—
666C23—22no—
667C23—22no—
668C23—612no—
669C23—612no—
670C23—614no—
671C23—612no—
672C23—614no—
673C23—6116no—
674C23—612no—
675C23—612no—
676C23—612no—
677C23—1228no—
678C23—1228no—
679C23—12216no—
680C23—12216no—
681C23—1222no—
682C23—1222no—
683C23C22×C4×D6112yes—
684C23C2×D4×D6112yes—
685C23#41×D6112yes—
686C23C24×D6111yescharacteristic
687C2×C4—216no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—28no—
696C2×C4—24no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—22no—
702C2×C4—612no—
703C2×C4—614no—
704C2×C4—6116no—
705C2×C4—612no—
706C2×C4—614no—
707C2×C4—614no—
708C2×C4—614no—
709C2×C4—1228no—
710C2×C4—12216no—
711C2×C4—1228no—
712C2×C4—12216no—
713C2×C4—12216no—
714C2×C4—12216no—
715C2×C4—12216no—
716C2×C4—1228no—
717C2×C4—12216no—
718C2×C4—1222no—
719C2×C4—1222no—
720C2×C4—1222no—
721C2×C4—1222no—
722C2×C4—1222no—
723C2×C4—1222no—
724C2×C4—1222no—
725C2×C4—1228no—
726C2×C4—1224no—
727C2×C4—1222no—
728C2×C4—1222no—
729C2×C4—1224no—
730C2×C4—1224no—
731C2×C4—1222no—
732C2×C4—24416no—
733C2×C4—2448no—
734C2×C4C22×C4×D6112yes—
735C2×C4C22×C4×D6114yes—
736C2×C4C22×C4×D6114yes—
737C2×C4C22×C4×D6112yes—
738C2×C4C2×D4×D6114yes—
739C2×C4#41×D6114yes—
740C22—22no—
741C22—22no—
742C22—24no—
743C22—24no—
744C22—614no—
745C22—614no—
746C22—614no—
747C22—618no—
748C22—618no—
749C22—614no—
750C22—12232no—
751C22—1222no—
752C22—1222no—
753C22—1224no—
754C22—1224no—
755C22C4×D4×D6114yes—
756C22C23×C4×D6111yescharacteristic
757C22C22×D4×D6111yescharacteristic
758C22C2×#41×D6112yes—
759C22C2×#41×D6111yescharacteristic
760C222−1+4×D6112yes—
761C4—22no—
762C4—24no—
763C4—24no—
764C4—24no—
765C4—44no—
766C4—42no—
767C4—614no—
768C4—1222no—
769C4—1224no—
770C4—1224no—
771C4—1224no—
772C4—2444no—
773C4—2442no—
774C4#117×D6114yescomplemented
775C2—24no—
776C2—618no—
777C2—1224no—
778C2C2×#117×D6111yescharacteristic
779C2C2×C4×D4×D6111yescharacteristic
780C2#519×D6111yescharacteristic
781C2#547×D6112yes—
782C2#552×D6112yes—
subgroupG/H
center, FrattiniC23C24×D61
commutatorC22×C61C24×C4
FittingC61×#2344C2
socle, cosocleC23×C61C25
prime radicalC24×D61C23
hypercenter#2344D61
hypocenterC61C2×#2344
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ #2344

Complements

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

NH ≅ G/Ntype
3. #21448690C2semidirect
4. #21448689C2semidirect
5. #21448688C2semidirect
6. #21448687C2semidirect
7. #21448686C2semidirect
8. #21448685C2semidirect
9. #21448684C2semidirect
10. #21448683C2semidirect
11. #389×D61C2semidirect
12. #387×D61C2semidirect
15. C4×C4⋊C4×D61C2semidirect
17. C61×#2344C2semidirect
28. C2×C4⋊C4×D61C4semidirect
42. #16839661C22semidirect
43. #16839660C22semidirect
44. #16839659C22semidirect
45. #16839658C22semidirect
46. #16839657C22semidirect
47. #16839649C22semidirect
48. #16839648C22semidirect
49. #16839647C22semidirect
50. #16839646C22semidirect
51. #16839645C22semidirect
52. #16839644C22semidirect
53. #16839643C22semidirect
63. C4⋊C4×Dic61C22semidirect
64. C4⋊C4×Dic61C22semidirect
65. C4×#11758196C22semidirect
66. C4×C4⋊Dic61C22semidirect
67. #16839613C22semidirect
79. C61×#389C22semidirect
80. C61×#387C22semidirect
83. C4×C4⋊C4×C61C22semidirect
109. C2×C4⋊Dic61C2×C4semidirect
115. C2×#11758196C2×C4semidirect
128. C4⋊C4×D61C2×C4semidirect
129. C4⋊C4×D61C2×C4semidirect
130. C4⋊C4×D61C2×C4semidirect
162. C2×C4⋊C4×C61C2×C4semidirect
347. C4×D61#117semidirect
376. C4×C61C2×#117semidirect
383. Dic61C2×#117semidirect
394. #2344D61direct (N × H)
408. D61#2344direct (N × H)
440. #389C2×D61semidirect
448. #387C2×D61semidirect
465. C4×C4⋊C4C2×D61semidirect
476. C61C2×#2344semidirect
526. C2×C4⋊C4C4×D61semidirect
774. C4#117×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#117×D612
C22×C4⋊C4×D612
#214486902
#214486892
#214486882
#214486872
#214486862
#214486852
#214486842
#214486832
#389×D612
#387×D612
#381×D612
#380×D612
C4×C4⋊C4×D612
C4×C22⋊C4×D612
C61×#23442
C2×#234461