Finite Group Databasebeta

← #29686565

Subgroups — #29686565

Order 15616.

1182 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
1C2×#16839996C211yesmaximal, characteristic
2C2×#16839871C211yesmaximal, characteristic, complemented
3C22×#14519687C211yesmaximal, characteristic, complemented
4#121×Dic61C211yesmaximal, characteristic, complemented
5#21448325C211yesmaximal, characteristic, complemented
6#21446692C211yesmaximal, characteristic, complemented
7#21446556C211yesmaximal, characteristic, complemented
8#21446517C211yesmaximal, characteristic, complemented
9#21446513C211yesmaximal, characteristic, complemented
10#21446247C211yesmaximal, characteristic, complemented
11#21445842C211yesmaximal, characteristic, complemented
12#21445715C211yesmaximal, characteristic, complemented
13#21445646C211yesmaximal, characteristic, complemented
14#21445643C211yesmaximal, characteristic, complemented
15C61×#1893C211yesmaximal, characteristic, complemented
16C22×#11758199C2211yescharacteristic
17C23×#92418C2211yescharacteristic
18C2×#14519751C2211yescharacteristic
19C2×D4×Dic61—21no—
20C2×D4×Dic61C2211yescharacteristic
21C2×#14519739C2211yescharacteristic
22C2×#14519737—21no—
23C22×C4×Dic61C2211yescharacteristic
24#16839996C418yescomplemented
25#16839871—24no—
26C2×#14519710C2211yescharacteristic
27C2×#14519708C2211yescharacteristic
28C2×#14519708C2211yescharacteristic
29C2×#14519699C2211yescharacteristic
30C2×#14519699C2211yescharacteristic
31C2×#14519698C2211yescharacteristic
32C2×#14519697C2211yescharacteristic
33C2×#14519687—24no—
34C2×#14519687C2211yescharacteristic
35C2×#14519687C2211yescharacteristic
36C2×#14519687C2211yescharacteristic
37C2×#14519687C2211yescharacteristic
38#16839665C2211yescharacteristic
39#16839663C2211yescharacteristic
40#16839661C2211yescharacteristic
41#16839658C2211yescharacteristic
42#16839655—21no—
43#16839651—21no—
44#16839642—21no—
45#16839639—21no—
46#16839622C2211yescharacteristic
47C4⋊C4×Dic61C2211yescharacteristic
48C4⋊C4×Dic61C2211yescharacteristic
49C22⋊C4×Dic61—21no—
50#16839609—21no—
51#16839525C2211yescharacteristic
52#16839525C2211yescharacteristic
53#16839524C2211yescharacteristic
54#16839524C2211yescharacteristic
55C23×C8×C61C2211yescharacteristic
56C2×#121×C61C2211yescharacteristic
57C2×#102×C61C2211yescharacteristic
58C2×#102×C61C2211yescharacteristic
59C61×#380C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C61×#340C2211yescharacteristic
62C22×D244C2311yescharacteristic
63C22×C22⋊D61—21no—
64C23×Dic61—21no—
65C23×Dic61D411yescharacteristic
66C23×Dic61D411yescharacteristic
67C22×C4×D61—21no—
68C2×#11758199—22no—
69C2×#11758199—22no—
70C2×#11758199C2×C414yescomplemented
71C22×#92418—22no—
72C22×#92418—22no—
73C22×#92418C2×C414yescomplemented
74C22×#92418C2311yescharacteristic
75C22×#92418C2311yescharacteristic
76#14519751—22no—
77#14519751C2×C414yescomplemented
78D4×Dic61—22no—
79D4×Dic61—22no—
80D4×Dic61—44no—
81#14519739—22no—
82#14519739—22no—
83#14519737—44no—
84C2×C4⋊Dic61—21no—
85C2×C4⋊Dic61C2311yescharacteristic
86C2×C4⋊Dic61C2311yescharacteristic
87C2×C4⋊Dic61C2311yescharacteristic
88C2×#11758196—21no—
89C2×C22⋊Dic61—21no—
90C2×C22⋊Dic61—21no—
91C2×C22⋊Dic61—21no—
92C2×C22⋊Dic61—21no—
93C2×#11758198—21no—
94C2×#11758198—21no—
95C2×#11758198—21no—
96C2×#11758198—21no—
97C2×C4×Dic61—22no—
98C2×C4×Dic61—22no—
99C2×C4×Dic61—21no—
100C2×C4×Dic61—21no—
101C2×C4×Dic61D411yescharacteristic
102C2×C4×Dic61D411yescharacteristic
103C2×C4×Dic61C2311yescharacteristic
104C2×C4×Dic61C2311yescharacteristic
105#14519710C2×C414yescomplemented
106#14519708—22no—
107#14519708—22no—
108#14519699—22no—
109#14519699—22no—
110#14519698C2×C414yescomplemented
111#14519697C2×C414yescomplemented
112#14519687—22no—
113#14519687—22no—
114#14519687—22no—
115#14519687D414yescomplemented
116#14519684—21no—
117#14519684—21no—
118#14519684—21no—
119#14519684—21no—
120#14519684—21no—
121C22×D4×C61—21no—
122C22×D4×C61C2311yescharacteristic
123C23×C4×C61C2311yescharacteristic
124C22×C8×C61—22no—
125C22×C8×C61—22no—
126C22×C8×C61—22no—
127C22×C8×C61C2311yescharacteristic
128C22×C8×C61C2311yescharacteristic
129#121×C61—22no—
130#121×C61C2×C414yescomplemented
131C2×C4⋊C4×C61C2311yescharacteristic
132C2×C4⋊C4×C61C2311yescharacteristic
133C2×C4⋊C4×C61C2311yescharacteristic
134C2×C22⋊C4×C61—21no—
135C2×C22⋊C4×C61—21no—
136#102×C61—22no—
137#102×C61—22no—
138#95×C61—21no—
139C24×C61—21no—
140C24×C61C2×D411yescharacteristic
141C23×D61—21no—
142C2×D4×C61—24no—
143C2×D4×C61—21no—
144C2×D4×C61—21no—
145C2×D4×C61—21no—
146C2×D4×C61—21no—
147C2×D4×C61—21no—
148C2×D4×C61—42no—
149C2×D4×C61—42no—
150C2×D4×C61C22×C412yes—
151C22×C4×C61—21no—
152C22×C4×C61—21no—
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61C22×C412yes—
159C22×C4×C61C2×D411yescharacteristic
160C22×C4×C61#4112yes—
161C22×C4×C61C2411yescharacteristic
162C2×C22⋊D61—24no—
163C2×C22⋊D61—42no—
164C2×C22⋊D61—42no—
165C22×Dic61—22no—
166C22×Dic61—22no—
167C22×Dic61—21no—
168C22×Dic61—22no—
169C22×Dic61—22no—
170C22×Dic61—21no—
171C22×Dic61—21no—
172C22×Dic61—41no—
173C22×Dic61—41no—
174C22×Dic61—42no—
175C22×Dic61—42no—
176C22×Dic61—42no—
177C22×Dic61C2×D411yescharacteristic
178C22×Dic61C2×D411yescharacteristic
179C22×Dic61C2×D411yescharacteristic
180C22×Dic61C2×D411yescharacteristic
181C2×D244—21no—
182C2×D244—21no—
183C2×D244—21no—
184C2×D244—21no—
185C2×D244—21no—
186C2×D244C22×C412yes—
187C2×C4×D61—42no—
188C2×C4×D61—42no—
189C2×C4×D61—42no—
190C2×C8×C61—28no—
191C2×C8×C61—21no—
192C2×C8×C61—21no—
193C2×C8×C61—21no—
194C2×C8×C61—21no—
195C2×C8×C61C2×D412yes—
196C2×C8×C61#4112yes—
197C4⋊C4×C61—21no—
198C4⋊C4×C61—21no—
199C4⋊C4×C61—21no—
200C4⋊C4×C61—21no—
201C4⋊C4×C61—21no—
202C4⋊C4×C61C22×C412yes—
203C22⋊C4×C61—24no—
204C22⋊C4×C61—42no—
205C22⋊Dic61—42no—
206C22⋊Dic61—42no—
207C22⋊Dic61—42no—
208C22⋊Dic61—42no—
209#11758199—28no—
210#11758198—24no—
211#11758198—42no—
212#11758198—42no—
213#11758198—42no—
214C4⋊Dic61—21no—
215C4⋊Dic61—21no—
216C4⋊Dic61—21no—
217C4⋊Dic61—21no—
218C4⋊Dic61—21no—
219C4⋊Dic61—42no—
220C4⋊Dic61C22×C412yes—
221#11758196—42no—
222C4×Dic61—21no—
223C4×Dic61—21no—
224C4×Dic61—22no—
225C4×Dic61—22no—
226C4×Dic61—42no—
227C4×Dic61—42no—
228C4×Dic61C2×D412yes—
229C4×Dic61#4112yes—
230C2×#92418—21no—
231C2×#92418—21no—
232C2×#92418—28no—
233C2×#92418C22×C412yes—
234C2×#92418C22×C412yes—
235C2×#92418C2×D412yes—
236C2×#92418#4112yes—
237C23×C61—21no—
238C23×C61—21no—
239C23×C61—21no—
240C23×C61—21no—
241C23×C61—22no—
242C23×C61—41no—
243C23×C61—41no—
244C23×C61—41no—
245C23×C61—41no—
246C23×C61—41no—
247C23×C61—41no—
248C23×C61C4×D412yes—
249C23×C61AGL(1,ℤ/8)12yes—
250C23×C61AGL(1,ℤ/8)12yes—
251C23×C61C22×D411yescharacteristic
252C22×D61—22no—
253C22×D61—41no—
254C22×D61—41no—
255C22×D61—41no—
256C22×D61—41no—
257C22×D61—41no—
258C22×D61—41no—
259D4×C61—22no—
260D4×C61—22no—
261D4×C61—48no—
262D4×C61—41no—
263D4×C61—41no—
264C2×C4×C61—21no—
265C2×C4×C61—21no—
266C2×C4×C61—22no—
267C2×C4×C61—22no—
268C2×C4×C61—22no—
269C2×C4×C61—22no—
270C2×C4×C61—22no—
271C2×C4×C61—41no—
272C2×C4×C61—41no—
273C2×C4×C61—41no—
274C2×C4×C61—41no—
275C2×C4×C61—41no—
276C2×C4×C61—41no—
277C2×C4×C61—41no—
278C2×C4×C61—41no—
279C2×C4×C61C4×D412yes—
280C2×C4×C61C23×C411yescharacteristic
281C2×C4×C61C22×D411yescharacteristic
282C2×C4×C61C2×#4111yescharacteristic
283C2×C4×C61C2×#4111yescharacteristic
284C2×C4×C61C2×#4111yescharacteristic
285C2×C4×C61C2×#4111yescharacteristic
286C22⋊D61—48no—
287C2×Dic61—21no—
288C2×Dic61—21no—
289C2×Dic61—21no—
290C2×Dic61—21no—
291C2×Dic61—22no—
292C2×Dic61—21no—
293C2×Dic61—21no—
294C2×Dic61—21no—
295C2×Dic61—21no—
296C2×Dic61—21no—
297C2×Dic61—21no—
298C2×Dic61—44no—
299C2×Dic61—44no—
300C2×Dic61—41no—
301C2×Dic61—41no—
302C2×Dic61—41no—
303C2×Dic61—41no—
304C2×Dic61—41no—
305C2×Dic61—41no—
306C2×Dic61—41no—
307C2×Dic61—41no—
308C2×Dic61—84no—
309C2×Dic61#12112yes—
310C2×Dic61#12112yes—
311D244—22no—
312D244—22no—
313D244—41no—
314D244—41no—
315C4×D61—84no—
316C8×C61—22no—
317C8×C61—22no—
318#92418—22no—
319#92418C4×D414yescomplemented
320#21526—611nomaximal, Sylow
321C22×C61—22no—
322C22×C61—22no—
323C22×C61—22no—
324C22×C61—22no—
325C22×C61—22no—
326C22×C61—22no—
327C22×C61—42no—
328C22×C61—42no—
329C22×C61—42no—
330C22×C61—81no—
331C22×C61—81no—
332C22×C61—81no—
333C22×C61—81no—
334C22×C61#44214yescomplemented
335C22×C61C2×C4×D411yescharacteristic
336C22×C61C2×#12111yescharacteristic
337C22×C61#53211yescharacteristic
338C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
339C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
340C22×C61#57511yescharacteristic
341C22×C61#57511yescharacteristic
342C2×D61—42no—
343C2×D61—42no—
344C2×D61—42no—
345C2×D61—81no—
346C2×D61—81no—
347C2×D61—81no—
348C2×D61—81no—
349C4×C61—22no—
350C4×C61—42no—
351C4×C61—81no—
352C4×C61—81no—
353C4×C61C2×C4×D411yescharacteristic
354C4×C61C4×#4111yescharacteristic
355C4×C61#52511yescharacteristic
356C4×C61#52911yescharacteristic
357Dic61—22no—
358Dic61—22no—
359Dic61—42no—
360Dic61—41no—
361Dic61—41no—
362Dic61—81no—
363Dic61—81no—
364C2×#466—611no—
365C2×#442—611no—
366C22×#97—611no—
367C4×#121—611no—
368C4×#121—611no—
369#1972—611no—
370#1943—611no—
371#1936—611no—
372#1936—611no—
373#1893—611no—
374#1893D6111yescharacteristic, complemented
375#1807—611no—
376#1776—611no—
377#1762—611no—
378#1762—611no—
379C2×C61—24no—
380C2×C61—82no—
381C2×C61C4×#12111yescharacteristic
382C2×C61C2×#44211yescharacteristic
383C2×C61#294311yescharacteristic
384C2×C61#305511yescharacteristic
385C2×C61#305511yescharacteristic
386C2×C61#318011yescharacteristic
387C2×C61#318011yescharacteristic
388D61—82no—
389C22×D8—611no—
390C23×C8—611no—
391C23×C8C2×D6111yescharacteristic
392C2×#121—611no—
393C2×#121C2×D6111yescharacteristic
394C2×C4×D4—611no—
395C2×C4×D4—611no—
396C2×C4×D4—1221no—
397C2×C4×D4—1221no—
398C22×C42—611no—
399#466—618no—
400#442—1224no—
401C2×#107—611no—
402C2×#106—611no—
403C2×#106—611no—
404C2×#102—611no—
405C2×#102—611no—
406C2×#102—611no—
407C2×#102—611no—
408C2×#102C2×D6111yescharacteristic
409C2×#102C2×D6111yescharacteristic
410C2×#97—611no—
411C2×#97—611no—
412C2×#97—611no—
413C2×#97—611no—
414C2×#97—1224no—
415#390—611no—
416#390—611no—
417#389—611no—
418#389—611no—
419#388—1221no—
420#388—1221no—
421#386—1221no—
422#386—1221no—
423#380—611no—
424#380C2×D6111yescharacteristic
425C4×C4⋊C4—611no—
426C4×C4⋊C4—611no—
427C4×C22⋊C4—1221no—
428C4×C22⋊C4—1221no—
429#340—611no—
430#340—611no—
431#340—611no—
432#340—611no—
433#340C2×D6111yescharacteristic
434#340C2×D6111yescharacteristic
435C61#2152611yescharacteristic, complemented, Sylow
436C22×D4—21no—
437C22×D4—611no—
438C22×D4—1221no—
439C22×D4C22×D6111yescharacteristic
440C23×C4—611no—
441C23×C4—611no—
442C23×C4—1221no—
443C23×C4—1221no—
444C23×C4C22×D6111yescharacteristic
445C2×D8—614no—
446C2×D8—1222no—
447C2×D8—1222no—
448C22×C8—22no—
449C22×C8—22no—
450C22×C8—22no—
451C22×C8—611no—
452C22×C8—614no—
453C22×C8—611no—
454C22×C8—1222no—
455C22×C8—1222no—
456C22×C8C22×D6111yescharacteristic
457C22×C8C22×D6111yescharacteristic
458#121—22no—
459#121—614no—
460#121—1222no—
461#121C4×D6114yescomplemented
462C4×D4—1222no—
463C4×D4—1222no—
464C4×D4—1222no—
465C4×D4—1222no—
466C4×D4—2444no—
467C4×D4—2444no—
468C2×C4⋊C4—611no—
469C2×C4⋊C4—611no—
470C2×C4⋊C4—611no—
471C2×C4⋊C4—1221no—
472C2×C4⋊C4—1221no—
473C2×C4⋊C4C22×D6111yescharacteristic
474C2×C4⋊C4C22×D6111yescharacteristic
475C2×C4⋊C4C22×D6111yescharacteristic
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—1221no—
479C2×C22⋊C4—1221no—
480C2×C22⋊C4—1221no—
481C2×C22⋊C4—1221no—
482C2×C22⋊C4—1221no—
483C2×C22⋊C4—1221no—
484C2×C22⋊C4—1221no—
485C2×C22⋊C4—1221no—
486C2×C42—611no—
487C2×C42—611no—
488C2×C42—611no—
489C2×C42—611no—
490C2×C42—1222no—
491C2×C42—1222no—
492C2×C42—1221no—
493C2×C42—1221no—
494#107—614no—
495#106—1222no—
496#106—1222no—
497#102—22no—
498#102—22no—
499#102—614no—
500#102—614no—
501#102—1222no—
502#102—1222no—
503#97—614no—
504#97—1222no—
505#97—1222no—
506#97—1222no—
507#95—21no—
508#95—1221no—
509#95—1221no—
510#95—1221no—
511#95—1221no—
512#95—1221no—
513C24—21no—
514C24—1221no—
515C24D4×D6111yescharacteristic
516C2×D4—24no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—42no—
523C2×D4—42no—
524C2×D4—612no—
525C2×D4—1224no—
526C2×D4—1221no—
527C2×D4—1221no—
528C2×D4—1221no—
529C2×D4—1221no—
530C2×D4—1221no—
531C2×D4—2442no—
532C2×D4—2442no—
533C2×D4C2×C4×D6112yes—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—611no—
542C22×C4—611no—
543C22×C4—611no—
544C22×C4—611no—
545C22×C4—1222no—
546C22×C4—1222no—
547C22×C4—1221no—
548C22×C4—1222no—
549C22×C4—1222no—
550C22×C4—1221no—
551C22×C4—1221no—
552C22×C4—2442no—
553C22×C4—2442no—
554C22×C4—2442no—
555C22×C4—2442no—
556C22×C4—2441no—
557C22×C4—2441no—
558C22×C4—2442no—
559C22×C4—2442no—
560C22×C4C2×C4×D6112yes—
561C22×C4D4×D6111yescharacteristic
562C22×C4#1175822412yes—
563C22×C4C23×D6111yescharacteristic
564D8—1228no—
565C2×C8—28no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—612no—
571C2×C8—612no—
572C2×C8—612no—
573C2×C8—612no—
574C2×C8—1228no—
575C2×C8—1221no—
576C2×C8—1221no—
577C2×C8D4×D6112yes—
578C2×C8#1175822412yes—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—612no—
585C4⋊C4—1221no—
586C4⋊C4—1221no—
587C4⋊C4—1221no—
588C4⋊C4—1221no—
589C4⋊C4—1221no—
590C4⋊C4—2442no—
591C4⋊C4—2442no—
592C4⋊C4C2×C4×D6112yes—
593C22⋊C4—24no—
594C22⋊C4—42no—
595C22⋊C4—1224no—
596C22⋊C4—2442no—
597C22⋊C4—2442no—
598C22⋊C4—2442no—
599C22⋊C4—2442no—
600C22⋊C4—2442no—
601C22⋊C4—2442no—
602C22⋊C4—2442no—
603C42—612no—
604C42—612no—
605C42—1222no—
606C42—1222no—
607C42—1221no—
608C42—1221no—
609C42—2442no—
610C42—2442no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—22no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—1222no—
623C23—2441no—
624C23—2441no—
625C23—2441no—
626C23—2441no—
627C23—2441no—
628C23—2441no—
629C23#1451973712yes—
630C23#1451980112yes—
631C23#1451980412yes—
632C23C2×D4×D6111yescharacteristic
633D4—22no—
634D4—22no—
635D4—48no—
636D4—41no—
637D4—41no—
638D4—1222no—
639D4—1222no—
640D4—2448no—
641D4—2441no—
642D4—2441no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—612no—
659C2×C4—612no—
660C2×C4—1221no—
661C2×C4—1221no—
662C2×C4—1221no—
663C2×C4—1221no—
664C2×C4—1222no—
665C2×C4—1221no—
666C2×C4—1221no—
667C2×C4—1221no—
668C2×C4—1221no—
669C2×C4—1221no—
670C2×C4—1221no—
671C2×C4—4884no—
672C2×C4—4884no—
673C2×C4—2444no—
674C2×C4—2444no—
675C2×C4—2441no—
676C2×C4—2441no—
677C2×C4—2441no—
678C2×C4—2441no—
679C2×C4—2441no—
680C2×C4—2441no—
681C2×C4—2441no—
682C2×C4—2441no—
683C2×C4#1451973712yes—
684C2×C4C22×C4×D6111yescharacteristic
685C2×C4C2×D4×D6111yescharacteristic
686C2×C4#41×D6111yescharacteristic
687C2×C4#41×D6111yescharacteristic
688C2×C4C2×#1175822411yescharacteristic
689C2×C4C2×#1175822411yescharacteristic
690C8—22no—
691C8—22no—
692C8—614no—
693C8—1222no—
694C22—22no—
695C22—22no—
696C22—22no—
697C22—22no—
698C22—22no—
699C22—22no—
700C22—42no—
701C22—42no—
702C22—42no—
703C22—81no—
704C22—81no—
705C22—81no—
706C22—81no—
707C22—4881no—
708C22—4881no—
709C22—4881no—
710C22—4881no—
711C22—2442no—
712C22—2442no—
713C22—2442no—
714C22#1683987114yescomplemented
715C22C2×#1451973711yescharacteristic
716C22#121×D6111yescharacteristic
717C22#1684030711yescharacteristic
718C22C2×#1451980111yescharacteristic
719C22C2×#1451980411yescharacteristic
720C22#1684055911yescharacteristic
721C22#1684055911yescharacteristic
722C4—22no—
723C4—42no—
724C4—81no—
725C4—81no—
726C4—1222no—
727C4—1222no—
728C4—4881no—
729C4—4881no—
730C4—2442no—
731C4—2441no—
732C4—2441no—
733C4C4×D4×D6111yescharacteristic
734C4C4×#1175822411yescharacteristic
735C4#1684026811yescharacteristic
736C4#1684028911yescharacteristic
737C2—24no—
738C2—82no—
739C2—4882no—
740C2#2144832911yescharacteristic
741C2C2×#1683987111yescharacteristic
742C2#2145461511yescharacteristic
743C2#2145543111yescharacteristic
744C2#2145543511yescharacteristic
745C2#2145651011yescharacteristic
746C2#2145651211yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1893C2
socleC23×C61C22×D4
prime radicalC2×#16839996C2
cosocleC22×C4×C61C24
hypercenter#1893D61
hypocenterC61#21526
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1893

Complements

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

NH ≅ G/Ntype
2. C2×#16839871C2semidirect
3. C22×#14519687C2semidirect
4. #121×Dic61C2semidirect
5. #21448325C2semidirect
6. #21446692C2semidirect
7. #21446556C2semidirect
8. #21446517C2semidirect
9. #21446513C2semidirect
10. #21446247C2semidirect
11. #21445842C2semidirect
12. #21445715C2semidirect
13. #21445646C2semidirect
14. #21445643C2semidirect
15. C61×#1893C2semidirect
24. #16839996C4semidirect
70. C2×#11758199C2×C4semidirect
73. C22×#92418C2×C4semidirect
77. #14519751C2×C4semidirect
105. #14519710C2×C4semidirect
110. #14519698C2×C4semidirect
111. #14519697C2×C4semidirect
115. #14519687D4semidirect
130. #121×C61C2×C4semidirect
319. #92418C4×D4semidirect
334. C22×C61#442semidirect
374. #1893D61semidirect
435. C61#21526semidirect
461. #121C4×D61semidirect
714. C22#16839871semidirect

Maximal subgroups

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

subgroupindex
C2×#168399962
C2×#168398712
C22×#145196872
#121×Dic612
#214483252
#214466922
#214465562
#214465172
#214465132
#214462472
#214458422
#214457152
#214456462
#214456432
C61×#18932
#2152661