Finite Group Databasebeta

← #29696563

Subgroups — #29696563

Order 15616.

1114 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×#16840471C211yesmaximal, characteristic
2#21448691C212yesmaximal, complemented
3#21446803C212yesmaximal, complemented
4#21446802C212yesmaximal, complemented
5#21446802C212yesmaximal, complemented
6#21445805C211yesmaximal, characteristic
7#21445805C211yesmaximal, characteristic
8#99×Dic61C211yesmaximal, characteristic
9#99×Dic61C211yesmaximal, characteristic
10C4×#14519692C211yesmaximal, characteristic
11C61×#1799C211yesmaximal, characteristic
12#16840471—22no—
13#16840471—22no—
14#16840471—22no—
15#16840471—22no—
16C2×#14519776C411yescharacteristic, complemented
17C2×#14519769C411yescharacteristic, complemented
18C2×#14519768C411yescharacteristic, complemented
19C2×#14519756C411yescharacteristic, complemented
20C2×#14519756C2211yescharacteristic
21C2×#14519754C411yescharacteristic, complemented
22C2×#14519754C411yescharacteristic, complemented
23C2×#14519754C2211yescharacteristic
24C2×#14519754C2211yescharacteristic
25C2×C4×Dic122C411yescharacteristic, complemented
26C2×D4×Dic61C2211yescharacteristic
27C2×D4×Dic61C2211yescharacteristic
28C22×#11758196C411yescharacteristic, complemented
29C22×#11758196C2211yescharacteristic
30C2×#14519692C2211yescharacteristic
31C2×#14519692C2211yescharacteristic
32#16839657—22no—
33#16839644—22no—
34#16839643—22no—
35#16839620C2212yes—
36#16839620C2212yes—
37#16839613—22no—
38C22⋊C4×Dic61C2212yes—
39C22⋊C4×Dic61C2212yes—
40C4×C22⋊Dic61C2212yes—
41#16839529C2212yes—
42#16839528C2212yes—
43#16839528C2212yes—
44#16839528C2212yes—
45#16839528C2212yes—
46C2×C4×D4×C61C2211yescharacteristic
47C2×#99×C61C2211yescharacteristic
48C2×#99×C61C2211yescharacteristic
49C61×#380C2212yes—
50C61×#342C2212yes—
51C22×Dic122C2×C411yescharacteristic
52C22×Dic122C2×C411yescharacteristic
53C22×Dic122C2×C411yescharacteristic
54C23×Dic61C2×C411yescharacteristic
55C23×Dic61C2×C411yescharacteristic
56C23×Dic61C2311yescharacteristic
57C23×Dic61C2311yescharacteristic
58#14519776—22no—
59#14519776—22no—
60#14519769—22no—
61#14519769—22no—
62#14519768—22no—
63#14519768—22no—
64#14519756—22no—
65#14519756—22no—
66#14519756—22no—
67#14519756—22no—
68#14519754—22no—
69#14519754—22no—
70#14519754—22no—
71#14519754—22no—
72#14519754—22no—
73#14519754—22no—
74#14519754—22no—
75#14519754—22no—
76C4×Dic122—21no—
77C4×Dic122—21no—
78C4×Dic122—21no—
79C4×Dic122—21no—
80D4×Dic61—22no—
81D4×Dic61—22no—
82D4×Dic61—22no—
83D4×Dic61—22no—
84C2×C4⋊Dic61C2×C411yescharacteristic
85C2×C4⋊Dic61C2×C411yescharacteristic
86C2×C4⋊Dic61C2×C411yescharacteristic
87C2×C4⋊Dic61C2×C411yescharacteristic
88C2×C4⋊Dic61C2×C411yescharacteristic
89C2×#11758196—21no—
90C2×#11758196—21no—
91C2×#11758196—21no—
92C2×#11758196—21no—
93C2×#11758196—22no—
94C2×#11758196—22no—
95C2×#11758196C2×C411yescharacteristic
96C2×#11758196C2×C411yescharacteristic
97C2×#11758196C2×C411yescharacteristic
98C2×#11758196C2×C411yescharacteristic
99C2×#11758196C2×C411yescharacteristic
100C2×#11758196C2×C411yescharacteristic
101C2×#11758196C2×C411yescharacteristic
102C2×#11758196C2×C411yescharacteristic
103C2×#11758196C2×C411yescharacteristic
104C2×#11758196C2×C411yescharacteristic
105C2×#11758196D412yes—
106C2×#11758196D412yes—
107C2×#11758196D412yes—
108C2×#11758196D412yes—
109C2×C22⋊Dic61C2×C411yescharacteristic
110C2×C22⋊Dic61C2×C411yescharacteristic
111C2×C22⋊Dic61C2312yes—
112C2×C22⋊Dic61C2311yescharacteristic
113C2×C22⋊Dic61C2311yescharacteristic
114C2×C22⋊Dic61C2312yes—
115C2×C4×Dic61—22no—
116C2×C4×Dic61—22no—
117C2×C4×Dic61—22no—
118C2×C4×Dic61C2×C411yescharacteristic
119C2×C4×Dic61C2×C411yescharacteristic
120#14519692—22no—
121#14519692Q814yescomplemented
122#14519684—22no—
123#14519684—22no—
124#14519684—22no—
125#14519684—22no—
126#14519684—22no—
127C22×D4×C61C2311yescharacteristic
128C23×C4×C61C2×C411yescharacteristic
129C23×C4×C61C2311yescharacteristic
130C4×D4×C61—22no—
131C4×D4×C61—22no—
132C2×C4⋊C4×C61—22no—
133C2×C4⋊C4×C61C2×C411yescharacteristic
134C2×C22⋊C4×C61C2×C411yescharacteristic
135C2×C22⋊C4×C61C2312yes—
136C2×C22⋊C4×C61C2312yes—
137C2×C22⋊C4×C61C2311yescharacteristic
138C2×C42×C61C2×C411yescharacteristic
139#99×C61—22no—
140#99×C61—22no—
141#95×C61—22no—
142C24×C61C22×C411yescharacteristic
143C24×C61C2411yescharacteristic
144C2×D4×C61—22no—
145C2×D4×C61—22no—
146C2×D4×C61C2×Q812yes—
147C2×D4×C61#4112yes—
148C22×C4×C61—21no—
149C22×C4×C61—21no—
150C22×C4×C61—22no—
151C22×C4×C61—22no—
152C22×C4×C61—81no—
153C22×C4×C61—81no—
154C22×C4×C61C22×C411yescharacteristic
155C22×C4×C61C22×C411yescharacteristic
156C22×C4×C61C22×C411yescharacteristic
157C22×C4×C61C22×C411yescharacteristic
158C22×C4×C61C22×C411yescharacteristic
159C22×C4×C61C2×D412yes—
160C22×C4×C61C2×D412yes—
161C22×Dic61—22no—
162C22×Dic61—21no—
163C22×Dic61—21no—
164C22×Dic61—21no—
165C22×Dic61—21no—
166C22×Dic61—22no—
167C22×Dic61—42no—
168C22×Dic61—42no—
169C22×Dic61—81no—
170C22×Dic61—81no—
171C22×Dic61C22×C411yescharacteristic
172C22×Dic61C22×C411yescharacteristic
173C22×Dic61C22×C411yescharacteristic
174C22×Dic61C22×C411yescharacteristic
175C22×Dic61C22×C411yescharacteristic
176C22×Dic61C22×C411yescharacteristic
177C22×Dic61C22×C411yescharacteristic
178C22×Dic61C22×C411yescharacteristic
179C22×Dic61C2×D412yes—
180C22×Dic61C2×D412yes—
181C22×Dic61C2×D412yes—
182C22×Dic61C2×D412yes—
183C2×Dic122—21no—
184C2×Dic122—21no—
185C2×Dic122—22no—
186C2×Dic122—22no—
187C2×Dic122—42no—
188C2×Dic122—81no—
189C2×Dic122—81no—
190C4⋊C4×C61—22no—
191C4⋊C4×C61—82no—
192C22⋊C4×C61—22no—
193C22⋊C4×C61—22no—
194C22⋊C4×C61—22no—
195C22⋊C4×C61—22no—
196C22⋊C4×C61—22no—
197C22⋊C4×C61—22no—
198C42×C61—21no—
199C42×C61—21no—
200C22⋊Dic61—22no—
201C22⋊Dic61—22no—
202C22⋊Dic61—22no—
203C22⋊Dic61—22no—
204C22⋊Dic61—22no—
205C22⋊Dic61—22no—
206C22⋊Dic61—22no—
207C22⋊Dic61C2×Q814yes—
208C4⋊Dic61—22no—
209C4⋊Dic61—22no—
210C4⋊Dic61—22no—
211C4⋊Dic61—21no—
212C4⋊Dic61—21no—
213C4⋊Dic61—22no—
214#11758196—21no—
215#11758196—21no—
216#11758196—21no—
217#11758196—21no—
218#11758196—21no—
219#11758196—21no—
220#11758196—21no—
221#11758196—21no—
222#11758196—22no—
223#11758196—22no—
224#11758196—44no—
225#11758196—82no—
226#11758196C22⋊C411yescharacteristic
227#11758196C22⋊C411yescharacteristic
228#11758196C22⋊C411yescharacteristic
229#11758196C22⋊C411yescharacteristic
230#11758196C22⋊C412yes—
231#11758196C22⋊C412yes—
232#11758196C22⋊C412yes—
233#11758196C22⋊C412yes—
234#11758196C22⋊C412yes—
235#11758196C22⋊C412yes—
236C4×Dic61—21no—
237C4×Dic61—21no—
238C4×Dic61—21no—
239C4×Dic61—21no—
240C4×Dic61—44no—
241C4×Dic61—82no—
242C4×Dic61—82no—
243C23×C61—21no—
244C23×C61—21no—
245C23×C61—41no—
246C23×C61—41no—
247C23×C61—41no—
248C23×C61—41no—
249C23×C61C4×Q812yes—
250C23×C61C23×C411yescharacteristic
251C23×C61C22×D412yes—
252C23×C61C22×Q811yescharacteristic
253C23×C61C2×#4111yescharacteristic
254C23×C612−1+412yes—
255D4×C61—24no—
256D4×C61—24no—
257C2×C4×C61—21no—
258C2×C4×C61—21no—
259C2×C4×C61—21no—
260C2×C4×C61—21no—
261C2×C4×C61—42no—
262C2×C4×C61—42no—
263C2×C4×C61—41no—
264C2×C4×C61—41no—
265C2×C4×C61—41no—
266C2×C4×C61—41no—
267C2×C4×C61—42no—
268C2×C4×C61—42no—
269C2×C4×C61—42no—
270C2×C4×C61—42no—
271C2×C4×C61—42no—
272C2×C4×C61—42no—
273C2×C4×C61—81no—
274C2×C4×C61—81no—
275C2×C4×C61C2×C22⋊C411yescharacteristic
276C2×C4×C61C2×C22⋊C411yescharacteristic
277C2×C4×C61C2×C22⋊C412yes—
278C2×C4×C61C4×Q812yes—
279C2×Dic61—24no—
280C2×Dic61—22no—
281C2×Dic61—21no—
282C2×Dic61—21no—
283C2×Dic61—21no—
284C2×Dic61—21no—
285C2×Dic61—24no—
286C2×Dic61—42no—
287C2×Dic61—42no—
288C2×Dic61—41no—
289C2×Dic61—41no—
290C2×Dic61—42no—
291C2×Dic61—41no—
292C2×Dic61—42no—
293C2×Dic61—42no—
294C2×Dic61—42no—
295C2×Dic61—42no—
296C2×Dic61—41no—
297C2×Dic61—41no—
298C2×Dic61—41no—
299C2×Dic61—41no—
300C2×Dic61—42no—
301C2×Dic61—42no—
302C2×Dic61—42no—
303C2×Dic61—81no—
304C2×Dic61—81no—
305C2×Dic61C2×C22⋊C411yescharacteristic
306C2×Dic61C2×C22⋊C411yescharacteristic
307C2×Dic61C2×C22⋊C411yescharacteristic
308C2×Dic61C2×C22⋊C412yes—
309C2×Dic61C2×C22⋊C412yes—
310C2×Dic61C2×C22⋊C411yescharacteristic
311Dic122—42no—
312Dic122—42no—
313Dic122—82no—
314Dic122—82no—
315#22513—611nomaximal, Sylow
316C22×C61—22no—
317C22×C61—21no—
318C22×C61—22no—
319C22×C61—21no—
320C22×C61—22no—
321C22×C61—41no—
322C22×C61—41no—
323C22×C61—42no—
324C22×C61—42no—
325C22×C61—42no—
326C22×C61—41no—
327C22×C61—41no—
328C22×C61C22×C22⋊C411yescharacteristic
329C22×C61C2×C4×Q811yescharacteristic
330C22×C61#51911yescharacteristic
331C22×C61#54812yes—
332C22×C61D4×Q812yes—
333C4×C61—22no—
334C4×C61—22no—
335C4×C61—21no—
336C4×C61—21no—
337C4×C61—41no—
338C4×C61—41no—
339C4×C61—82no—
340C4×C61—82no—
341Dic61—21no—
342Dic61—22no—
343Dic61—22no—
344Dic61—21no—
345Dic61—21no—
346Dic61—44no—
347Dic61—41no—
348Dic61—41no—
349Dic61—41no—
350Dic61—41no—
351Dic61—82no—
352Dic61#41012yes—
353C2×#554—611no—
354#2345—612no—
355#1996—612no—
356#1996—612no—
357#1996—612no—
358#1799—611no—
359#1799—611no—
360#1799D6111yescharacteristic
361C4×#99—611no—
362C4×#99—611no—
363C4×#99—611no—
364C2×C61—22no—
365C2×C61—22no—
366C2×C61—21no—
367C2×C61—21no—
368C2×C61—42no—
369C2×C61Q8×C22⋊C411yescharacteristic
370C2×C61C2×#41011yescharacteristic
371C2×C61#288311yescharacteristic
372#554—1222no—
373#554—1222no—
374#554—1222no—
375#554—1222no—
376C2×C4⋊Q8—611no—
377C2×#125—611no—
378C2×#125—611no—
379C2×C22⋊Q8—611no—
380C2×C22⋊Q8—611no—
381C2×C22⋊Q8—611no—
382C2×C22⋊Q8—611no—
383C2×C22⋊Q8—611no—
384C2×C22⋊Q8—611no—
385C2×C4×Q8—611no—
386C2×C4×D4—611no—
387C2×C4×D4—611no—
388C2×C4×D4C2×D6111yescharacteristic
389C22×C4⋊C4—611no—
390C22×C4⋊C4—611no—
391C2×#99—611no—
392C2×#99—611no—
393C2×#99C2×D6111yescharacteristic
394C2×#99C2×D6111yescharacteristic
395#389—1222no—
396#387—1222no—
397#387—1222no—
398#380—612no—
399#380—612no—
400#380C2×D6112yes—
401C4×C4⋊C4—1222no—
402C4×C22⋊C4—612no—
403C4×C22⋊C4—612no—
404C4×C22⋊C4—612no—
405#342—612no—
406#342—612no—
407#342—612no—
408#342—612no—
409#342—612no—
410#342C2×D6112yes—
411C61#2251311yescharacteristic, complemented, Sylow
412C22×Q8—611no—
413C22×Q8—611no—
414C22×Q8—611no—
415C22×D4C22×D6111yescharacteristic
416C23×C4—611no—
417C23×C4—611no—
418C23×C4—611no—
419C23×C4—611no—
420C23×C4C4×D6111yescharacteristic
421C23×C4C22×D6111yescharacteristic
422C4⋊Q8—1222no—
423C4⋊Q8—1222no—
424#125—1222no—
425#125—1222no—
426#125—1222no—
427#125—1222no—
428C22⋊Q8—1222no—
429C22⋊Q8—1222no—
430C22⋊Q8—1222no—
431C22⋊Q8—1222no—
432C22⋊Q8—1222no—
433C22⋊Q8—1222no—
434C22⋊Q8—1222no—
435C22⋊Q8—1222no—
436C22⋊Q8—1222no—
437C22⋊Q8—1222no—
438C22⋊Q8—1222no—
439C22⋊Q8—1222no—
440C4×Q8—1221no—
441C4×Q8—1221no—
442C4×Q8—1221no—
443C4×Q8—1221no—
444C4×D4—22no—
445C4×D4—22no—
446C4×D4—1222no—
447C4×D4—1222no—
448C4×D4—1222no—
449C4×D4—1222no—
450C2×C4⋊C4—22no—
451C2×C4⋊C4—611no—
452C2×C4⋊C4—611no—
453C2×C4⋊C4—611no—
454C2×C4⋊C4—611no—
455C2×C4⋊C4—612no—
456C2×C4⋊C4—612no—
457C2×C4⋊C4—612no—
458C2×C4⋊C4—612no—
459C2×C4⋊C4—611no—
460C2×C4⋊C4—611no—
461C2×C4⋊C4—611no—
462C2×C4⋊C4—611no—
463C2×C4⋊C4—611no—
464C2×C4⋊C4—611no—
465C2×C4⋊C4—611no—
466C2×C4⋊C4—611no—
467C2×C4⋊C4—611no—
468C2×C4⋊C4—611no—
469C2×C4⋊C4—611no—
470C2×C4⋊C4—1221no—
471C2×C4⋊C4—1221no—
472C2×C4⋊C4—1221no—
473C2×C4⋊C4—1221no—
474C2×C4⋊C4—1222no—
475C2×C4⋊C4—1222no—
476C2×C4⋊C4C4×D6111yescharacteristic
477C2×C22⋊C4—612no—
478C2×C22⋊C4—611no—
479C2×C22⋊C4—611no—
480C2×C22⋊C4—611no—
481C2×C22⋊C4—611no—
482C2×C22⋊C4—612no—
483C2×C22⋊C4C4×D6111yescharacteristic
484C2×C22⋊C4C22×D6112yes—
485C2×C22⋊C4C22×D6112yes—
486C2×C22⋊C4C22×D6111yescharacteristic
487C2×C42—611no—
488C2×C42—611no—
489C2×C42—1222no—
490C2×C42—1222no—
491C2×C42—1222no—
492C2×C42C4×D6111yescharacteristic
493#99—22no—
494#99—22no—
495#99—614no—
496#99—1222no—
497#95—22no—
498#95—1222no—
499#95—1222no—
500#95—1222no—
501#95—1222no—
502#95—1222no—
503C24C2×C4×D6111yescharacteristic
504C24C23×D6111yescharacteristic
505C2×Q8—1222no—
506C2×Q8—1221no—
507C2×Q8—1221no—
508C2×Q8—1222no—
509C2×Q8—4881no—
510C2×Q8—4881no—
511C2×Q8—2442no—
512C2×D4—22no—
513C2×D4—22no—
514C2×D4#1175822412yes—
515C2×D4Q8×D6112yes—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—81no—
521C22×C4—81no—
522C22×C4—611no—
523C22×C4—612no—
524C22×C4—611no—
525C22×C4—611no—
526C22×C4—611no—
527C22×C4—612no—
528C22×C4—612no—
529C22×C4—612no—
530C22×C4—611no—
531C22×C4—611no—
532C22×C4—611no—
533C22×C4—611no—
534C22×C4—1221no—
535C22×C4—1221no—
536C22×C4—1221no—
537C22×C4—1221no—
538C22×C4—1222no—
539C22×C4—1222no—
540C22×C4—4881no—
541C22×C4—4881no—
542C22×C4—2442no—
543C22×C4—2442no—
544C22×C4C2×C4×D6111yescharacteristic
545C22×C4C2×C4×D6111yescharacteristic
546C22×C4C2×C4×D6111yescharacteristic
547C22×C4C2×C4×D6111yescharacteristic
548C22×C4C2×C4×D6111yescharacteristic
549C22×C4D4×D6112yes—
550C22×C4D4×D6112yes—
551C4⋊C4—22no—
552C4⋊C4—82no—
553C4⋊C4—611no—
554C4⋊C4—611no—
555C4⋊C4—611no—
556C4⋊C4—611no—
557C4⋊C4—612no—
558C4⋊C4—612no—
559C4⋊C4—612no—
560C4⋊C4—612no—
561C4⋊C4—612no—
562C4⋊C4—612no—
563C4⋊C4—1221no—
564C4⋊C4—1221no—
565C4⋊C4—1221no—
566C4⋊C4—1221no—
567C4⋊C4—1222no—
568C4⋊C4—1222no—
569C4⋊C4—1222no—
570C4⋊C4—1222no—
571C4⋊C4—1221no—
572C4⋊C4—1221no—
573C4⋊C4—1222no—
574C4⋊C4—1221no—
575C4⋊C4—1221no—
576C4⋊C4—1221no—
577C4⋊C4—1221no—
578C4⋊C4—1222no—
579C4⋊C4—4882no—
580C4⋊C4—2444no—
581C22⋊C4—22no—
582C22⋊C4—22no—
583C22⋊C4—22no—
584C22⋊C4—22no—
585C22⋊C4—22no—
586C22⋊C4—22no—
587C22⋊C4—614no—
588C22⋊C4—1222no—
589C22⋊C4—1222no—
590C22⋊C4—1222no—
591C22⋊C4—1222no—
592C22⋊C4—1222no—
593C22⋊C4—1222no—
594C22⋊C4—1222no—
595C42—21no—
596C42—21no—
597C42—1221no—
598C42—1221no—
599C42—1221no—
600C42—1221no—
601C42—4882no—
602C42—4882no—
603C42—2444no—
604C23—21no—
605C23—21no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23#1451974212yes—
611C23C22×C4×D6111yescharacteristic
612C23C2×D4×D6112yes—
613C23C2×Q8×D6111yescharacteristic
614C23C2×#1175822411yescharacteristic
615C23#1451982412yes—
616Q8—4882no—
617Q8—4882no—
618Q8—2442no—
619Q8—2442no—
620D4—24no—
621D4—24no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—42no—
627C2×C4—42no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4—81no—
639C2×C4—81no—
640C2×C4—611no—
641C2×C4—611no—
642C2×C4—611no—
643C2×C4—611no—
644C2×C4—612no—
645C2×C4—612no—
646C2×C4—1224no—
647C2×C4—1222no—
648C2×C4—1221no—
649C2×C4—1221no—
650C2×C4—1221no—
651C2×C4—1221no—
652C2×C4—1224no—
653C2×C4—4881no—
654C2×C4—4881no—
655C2×C4—2442no—
656C2×C4—2442no—
657C2×C4—2442no—
658C2×C4—2441no—
659C2×C4—2441no—
660C2×C4—2441no—
661C2×C4—2442no—
662C2×C4—2442no—
663C2×C4—2442no—
664C2×C4—2442no—
665C2×C4—2442no—
666C2×C4—2442no—
667C2×C4—2442no—
668C2×C4—2441no—
669C2×C4—2441no—
670C2×C4—2441no—
671C2×C4—2441no—
672C2×C4C22⋊C4×D6111yescharacteristic
673C2×C4C22⋊C4×D6111yescharacteristic
674C2×C4C22⋊C4×D6112yes—
675C2×C4#1451974212yes—
676C22—22no—
677C22—21no—
678C22—22no—
679C22—21no—
680C22—22no—
681C22—41no—
682C22—41no—
683C22—42no—
684C22—42no—
685C22—42no—
686C22—41no—
687C22—41no—
688C22C2×C22⋊C4×D6111yescharacteristic
689C22C2×#1451974211yescharacteristic
690C22#1684023911yescharacteristic
691C22#1684041812yes—
692C22#1684042512yes—
693C4—21no—
694C4—21no—
695C4—22no—
696C4—22no—
697C4—41no—
698C4—41no—
699C4—82no—
700C4—82no—
701C4—612no—
702C4—1222no—
703C4—1221no—
704C4—1221no—
705C4—1221no—
706C4—1222no—
707C4—4882no—
708C4—2444no—
709C4—2441no—
710C4—2441no—
711C4—2441no—
712C4—2441no—
713C2—22no—
714C2—22no—
715C2—21no—
716C2—21no—
717C2—42no—
718C2#2144865111yescharacteristic
719C2#410×D6111yescharacteristic
720C2#2145427711yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC24C23×D61
FittingC61×#1799C2
socleC22×C61C22×C22⋊C4
prime radicalC22×D4×C61C23
cosocleC24×C61C24
hypercenter#1799D61
hypocenterC61#22513
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1799

Complements

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

NH ≅ G/Ntype
2. #21448691C2semidirect
3. #21446803C2semidirect
4. #21446802C2semidirect
5. #21446802C2semidirect
16. C2×#14519776C4semidirect
17. C2×#14519769C4semidirect
18. C2×#14519768C4semidirect
19. C2×#14519756C4semidirect
21. C2×#14519754C4semidirect
22. C2×#14519754C4semidirect
25. C2×C4×Dic122C4semidirect
28. C22×#11758196C4semidirect
121. #14519692Q8semidirect
411. C61#22513semidirect

Maximal subgroups

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

subgroupindex
C2×#168404712
#214486912
#214468032
#214468022
#214458052
#99×Dic612
C4×#145196922
C61×#17992
#2251361