Finite Group Databasebeta

← #29727575

Subgroups — #29727575

Order 15616.

1052 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839970C211yesmaximal, characteristic, complemented
2C2×#16839919C211yesmaximal, characteristic
3C2×#16839916C211yesmaximal, characteristic
4#21449412C211yesmaximal, characteristic
5Q8×#11758198C211yesmaximal, characteristic
6#21447209C211yesmaximal, characteristic, complemented
7#21447024C211yesmaximal, characteristic
8#21447021C211yesmaximal, characteristic
9#21446920C211yesmaximal, characteristic, complemented
10#21446680C211yesmaximal, characteristic, complemented
11#21446425C211yesmaximal, characteristic
12#21446160C211yesmaximal, characteristic, complemented
13#21446160C211yesmaximal, characteristic, complemented
14#21446075C211yesmaximal, characteristic, complemented
15C2×C4×Q16×C61C211yesmaximal, characteristic, complemented
16C22×Q8×D61C2211yescharacteristic
17C22×Dic244C2211yescharacteristic
18C22×#11758202C2211yescharacteristic
19C22×#11758202C2211yescharacteristic
20C2×#14519775C2211yescharacteristic
21C2×#14519757C2211yescharacteristic
22C2×#14519753C2211yescharacteristic
23C2×Q8×Dic61C2211yescharacteristic
24#16839970—24no—
25#16839919—24no—
26#16839916—24no—
27C2×#14519711C2211yescharacteristic
28C2×#14519706C2211yescharacteristic
29C2×#14519702C2211yescharacteristic
30C2×#14519702C2211yescharacteristic
31C2×#14519701C2211yescharacteristic
32C2×#14519701C2211yescharacteristic
33C2×#14519700C2211yescharacteristic
34C2×#14519700C2211yescharacteristic
35C2×#14519689C2211yescharacteristic
36C2×#14519689C2211yescharacteristic
37#16839692—21no—
38#16839684—21no—
39#16839668—21no—
40#16839668C2211yescharacteristic
41#16839668C2211yescharacteristic
42#16839667—21no—
43#16839667C2211yescharacteristic
44#16839661C2211yescharacteristic
45#16839660—21no—
46#16839653—21no—
47#16839619—21no—
48#16839619C2211yescharacteristic
49C4×#11758198—21no—
50C4×#11758198C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839524C2211yescharacteristic
53#16839517C2211yescharacteristic
54#16839516C2211yescharacteristic
55C22×Q16×C61C2211yescharacteristic
56C2×C4×Q8×C61C2211yescharacteristic
57C2×C4×Q8×C61C2211yescharacteristic
58C4×Q16×C61—24no—
59C2×#107×C61C2211yescharacteristic
60C2×#103×C61C2211yescharacteristic
61C2×#103×C61C2211yescharacteristic
62C2×C4×C8×C61C2211yescharacteristic
63C22×Dic122—21no—
64C22×Dic122C2311yescharacteristic
65C22×Dic122C2311yescharacteristic
66C2×Q8×D61—22no—
67C2×Q8×D61—22no—
68C2×Q8×D61—22no—
69C2×Q8×D61—22no—
70C2×Q8×D61—41no—
71C2×Q8×D61—41no—
72C22×C4×D61—21no—
73C22×C4×D61C2311yescharacteristic
74C2×Dic244—22no—
75C2×Dic244—22no—
76C2×Dic244—41no—
77C2×#11758202—22no—
78C2×#11758202—22no—
79C2×#11758202—22no—
80C2×#11758202—22no—
81C2×#11758202—22no—
82C2×#11758202—41no—
83C22×#92418C2311yescharacteristic
84C22×#92418C2311yescharacteristic
85#14519775—22no—
86#14519775—41no—
87#14519757—22no—
88#14519757—41no—
89#14519753—22no—
90#14519753—41no—
91Q8×Dic61—22no—
92Q8×Dic61—41no—
93C2×C4⋊Dic61—21no—
94C2×C4⋊Dic61—21no—
95C2×C4⋊Dic61—21no—
96C2×C4⋊Dic61C2311yescharacteristic
97C2×C4⋊Dic61C2311yescharacteristic
98C2×#11758196—21no—
99C2×#11758196—21no—
100C2×#11758196—21no—
101C2×#11758198—21no—
102C2×#11758198—21no—
103C2×#11758198—21no—
104C2×#11758198D411yescharacteristic
105C2×#11758198D411yescharacteristic
106C2×C4×Dic61—21no—
107C2×C4×Dic61C2311yescharacteristic
108#14519711—41no—
109#14519706—22no—
110#14519702—22no—
111#14519702—22no—
112#14519701—22no—
113#14519701—22no—
114#14519700—22no—
115#14519700—41no—
116#14519689—22no—
117#14519689—22no—
118#14519684—21no—
119#14519684—21no—
120#14519684—21no—
121#14519684—21no—
122#14519684—21no—
123#14519684—21no—
124#14519684—21no—
125#14519684—21no—
126#14519684D411yescharacteristic
127#14519684D411yescharacteristic
128C22×Q8×C61C2311yescharacteristic
129C22×Q8×C61C2311yescharacteristic
130C2×Q16×C61—22no—
131C2×Q16×C61—22no—
132C2×Q16×C61D414yes—
133C22×C8×C61C2311yescharacteristic
134C22×C8×C61C2311yescharacteristic
135C4×Q8×C61—22no—
136C4×Q8×C61—22no—
137C4×Q8×C61—41no—
138C4×Q8×C61—41no—
139C2×C4⋊C4×C61—21no—
140C2×C4⋊C4×C61—21no—
141C2×C4⋊C4×C61C2311yescharacteristic
142C2×C4⋊C4×C61C2311yescharacteristic
143C2×C42×C61—21no—
144C2×C42×C61—21no—
145C2×C42×C61C2311yescharacteristic
146#107×C61—22no—
147#103×C61—22no—
148#103×C61D414yes—
149C4×C8×C61—22no—
150C23×D61C2×D411yescharacteristic
151C2×Q8×C61—21no—
152C2×Q8×C61—21no—
153C2×Q8×C61—21no—
154C2×Q8×C61—21no—
155C2×Q8×C61—21no—
156C2×Q8×C61—21no—
157C2×Q8×C61—21no—
158C2×Q8×C61—21no—
159C2×Q8×C61C2×D412yes—
160C2×Q8×C61C2×D412yes—
161C2×Q8×C61C2×D412yes—
162C2×Q8×C61#4112yes—
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61—21no—
166C22×C4×C61—21no—
167C22×C4×C61C2×D411yescharacteristic
168C22×C4×C61C2×D411yescharacteristic
169C22×C4×C61C2411yescharacteristic
170C22×Dic61—21no—
171C22×Dic61—21no—
172C22×Dic61—21no—
173C22×Dic61—21no—
174C22×Dic61C2×D411yescharacteristic
175C22×Dic61C2×D411yescharacteristic
176C22×Dic61C2×D411yescharacteristic
177Q8×D61—44no—
178Q8×D61—44no—
179Q8×D61—44no—
180Q8×D61—44no—
181C2×C4×D61—24no—
182C2×C4×D61—21no—
183C2×C4×D61—21no—
184C2×C4×D61—21no—
185C2×C4×D61—21no—
186C2×C4×D61—21no—
187C2×C4×D61—21no—
188C2×C4×D61—42no—
189C2×C4×D61—42no—
190C2×Dic122—21no—
191C2×Dic122—21no—
192C2×Dic122—21no—
193C2×Dic122—21no—
194C2×Dic122—24no—
195C2×Dic122—21no—
196C2×Dic122—21no—
197C2×Dic122—21no—
198C2×Dic122—21no—
199C2×Dic122—21no—
200C2×Dic122—21no—
201C2×Dic122—21no—
202C2×Dic122—42no—
203C2×Dic122—42no—
204C2×Dic122#4112yes—
205Q16×C61—28no—
206C2×C8×C61—21no—
207C2×C8×C61—21no—
208C2×C8×C61—21no—
209C2×C8×C61—21no—
210C2×C8×C61C2×D412yes—
211C2×C8×C61C2×D412yes—
212C4⋊C4×C61—21no—
213C4⋊C4×C61—21no—
214C4⋊C4×C61—21no—
215C4⋊C4×C61—42no—
216C4⋊C4×C61—42no—
217C4⋊C4×C61C2×D412yes—
218C42×C61—21no—
219C42×C61—21no—
220C42×C61—42no—
221C42×C61—42no—
222#11758202—44no—
223#11758202—44no—
224#11758198—41no—
225#11758198—42no—
226#11758198—42no—
227#11758198—42no—
228#11758198Q1614yescomplemented
229C4⋊Dic61—21no—
230C4⋊Dic61—21no—
231C4⋊Dic61—21no—
232C4⋊Dic61—21no—
233C4⋊Dic61—42no—
234C4⋊Dic61—42no—
235C4⋊Dic61—42no—
236#11758196—42no—
237#11758196—42no—
238#11758196—42no—
239C4×Dic61—21no—
240C4×Dic61—21no—
241C4×Dic61—42no—
242C2×#92418—21no—
243C2×#92418—21no—
244C2×#92418—21no—
245C2×#92418—21no—
246C2×#92418—21no—
247C2×#92418—21no—
248Dic244—44no—
249C23×C61C22×D411yescharacteristic
250C22×D61—21no—
251C22×D61—21no—
252C22×D61—21no—
253C22×D61—21no—
254C22×D61—21no—
255C22×D61—21no—
256C22×D61C2×Q1612yes—
257Q8×C61—22no—
258Q8×C61—22no—
259Q8×C61—22no—
260Q8×C61—22no—
261Q8×C61—22no—
262Q8×C61—41no—
263Q8×C61—41no—
264Q8×C61#12114yes—
265C2×C4×C61—22no—
266C2×C4×C61—22no—
267C2×C4×C61—21no—
268C2×C4×C61—22no—
269C2×C4×C61—21no—
270C2×C4×C61—22no—
271C2×C4×C61—22no—
272C2×C4×C61—21no—
273C2×C4×C61—21no—
274C2×C4×C61—21no—
275C2×C4×C61—41no—
276C2×C4×C61—41no—
277C2×C4×C61—41no—
278C2×C4×C61—41no—
279C2×C4×C61—41no—
280C2×C4×C61—41no—
281C2×C4×C61—41no—
282C2×C4×C61C2×Q1612yes—
283C2×C4×C61C22×D411yescharacteristic
284C2×C4×C61C22×D411yescharacteristic
285C2×C4×C61C2×#4111yescharacteristic
286C2×C4×C61C2×#4111yescharacteristic
287C2×C4×C61H(5,𝔽2)11yescharacteristic
288C2×C4×C61H(5,𝔽2)11yescharacteristic
289C2×Dic61—21no—
290C2×Dic61—21no—
291C2×Dic61—21no—
292C2×Dic61—22no—
293C2×Dic61—21no—
294C2×Dic61—21no—
295C2×Dic61—21no—
296C2×Dic61—21no—
297C2×Dic61—21no—
298C2×Dic61—41no—
299C2×Dic61—41no—
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—41no—
309C2×Dic61C2×Q1612yes—
310C4×D61—48no—
311C4×D61—41no—
312C4×D61—41no—
313C4×D61—41no—
314C4×D61—41no—
315Dic122—22no—
316Dic122—22no—
317Dic122—48no—
318Dic122—41no—
319Dic122—41no—
320Dic122—41no—
321Dic122—41no—
322Dic122—41no—
323Dic122—41no—
324C8×C61—22no—
325C8×C61—22no—
326#92418—41no—
327#92418—41no—
328#25161—611nomaximal, Sylow
329C22×C61#52511yescharacteristic
330C22×C61D4211yescharacteristic
331C22×C61D4211yescharacteristic
332C22×C61C22×Q1611yescharacteristic
333C22×C61#57511yescharacteristic
334C22×C61#57811yescharacteristic
335C22×C61#57811yescharacteristic
336C2×D61—22no—
337C2×D61—22no—
338C2×D61—22no—
339C2×D61—41no—
340C2×D61—41no—
341C2×D61—41no—
342C2×D61—41no—
343C4×C61—24no—
344C4×C61—22no—
345C4×C61—42no—
346C4×C61—41no—
347C4×C61—42no—
348C4×C61—81no—
349C4×C61C2×#12111yescharacteristic
350C4×C61#53811yescharacteristic
351C4×C61#54611yescharacteristic
352C4×C61#54611yescharacteristic
353Dic61—22no—
354Dic61—42no—
355Dic61—41no—
356Dic61—41no—
357Dic61—81no—
358Dic61—81no—
359Dic61—81no—
360C2×#462—611no—
361C2×#451—611no—
362C2×#451—611no—
363C2×C4×Q16D6111yescharacteristic, complemented
364#2429—611no—
365Q8×C22⋊C4—611no—
366#2068—611no—
367#2036—611no—
368#2036—611no—
369#2016—611no—
370#1969—611no—
371#1923—611no—
372#1878—611no—
373#1878—611no—
374#1863—611no—
375C2×C61#242411yescharacteristic
376C2×C61#310411yescharacteristic
377C2×C61#312711yescharacteristic
378C2×C61#326911yescharacteristic
379C2×C61#327711yescharacteristic
380C2×C61D4×Q1611yescharacteristic
381C2×C61D4×Q1611yescharacteristic
382D61—42no—
383C23×Q8—611no—
384C22×Q16—611no—
385C22×Q16—611no—
386C22×Q16—611no—
387C22×Q16C2×D6111yescharacteristic
388C2×C4⋊Q8—611no—
389C2×C22⋊Q8—611no—
390C2×C22⋊Q8—611no—
391C2×C4×Q8—611no—
392C2×C4×Q8C2×D6111yescharacteristic
393C2×C4×Q8C2×D6111yescharacteristic
394#462—1224no—
395#451—1224no—
396#451—1224no—
397C4×Q16—24no—
398C2×#107—611no—
399C2×#107C2×D6111yescharacteristic
400C2×C4⋊C8—611no—
401C2×#103—611no—
402C2×#103—611no—
403C2×#103—611no—
404C2×#103—611no—
405C2×#103—611no—
406C2×#103—611no—
407C2×#103C2×D6111yescharacteristic
408C2×#103C2×D6111yescharacteristic
409C2×C22⋊C8—611no—
410C2×C22⋊C8—611no—
411C2×C4×C8C2×D6111yescharacteristic
412#398—1221no—
413#396—1221no—
414#391—611no—
415#391—611no—
416#391—611no—
417#391—1221no—
418#391—1221no—
419#389—611no—
420#389—1221no—
421#388—1221no—
422#380—611no—
423#380—1221no—
424C4×C22⋊C4—611no—
425C4×C22⋊C4—1221no—
426#340—611no—
427#340—611no—
428#336—611no—
429#336—611no—
430C61#2516111yescharacteristic, complemented, Sylow
431C22×Q8—611no—
432C22×Q8—611no—
433C22×Q8—1221no—
434C22×Q8—1222no—
435C22×Q8—1222no—
436C22×Q8—1222no—
437C22×Q8—1222no—
438C22×Q8—2441no—
439C22×Q8—2441no—
440C22×Q8C22×D6111yescharacteristic
441C22×Q8C22×D6111yescharacteristic
442C23×C4—611no—
443C23×C4—1221no—
444C2×Q16—22no—
445C2×Q16—22no—
446C2×Q16—1222no—
447C2×Q16—1222no—
448C2×Q16—1222no—
449C2×Q16—1222no—
450C2×Q16—1222no—
451C2×Q16—1222no—
452C2×Q16—1222no—
453C2×Q16—2441no—
454C2×Q16—2441no—
455C2×Q16D24414yes—
456C22×C8—611no—
457C22×C8—611no—
458C22×C8C22×D6111yescharacteristic
459C22×C8C22×D6111yescharacteristic
460C4⋊Q8—1222no—
461C4⋊Q8—2441no—
462C22⋊Q8—1222no—
463C22⋊Q8—1222no—
464C22⋊Q8—2441no—
465C22⋊Q8—2441no—
466C4×Q8—22no—
467C4×Q8—22no—
468C4×Q8—41no—
469C4×Q8—41no—
470C4×Q8—1222no—
471C4×Q8—2441no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—611no—
475C2×C4⋊C4—611no—
476C2×C4⋊C4—1221no—
477C2×C4⋊C4—1221no—
478C2×C4⋊C4—1221no—
479C2×C4⋊C4—1221no—
480C2×C4⋊C4—1221no—
481C2×C4⋊C4—1221no—
482C2×C4⋊C4C22×D6111yescharacteristic
483C2×C4⋊C4C22×D6111yescharacteristic
484C2×C22⋊C4—611no—
485C2×C22⋊C4—611no—
486C2×C22⋊C4—1221no—
487C2×C22⋊C4—1221no—
488C2×C22⋊C4—1221no—
489C2×C42—21no—
490C2×C42—21no—
491C2×C42—611no—
492C2×C42—1221no—
493C2×C42C22×D6111yescharacteristic
494#107—22no—
495#107—2441no—
496C4⋊C8—1222no—
497#103—22no—
498#103—1222no—
499#103—1222no—
500#103—1222no—
501#103—1222no—
502#103—1222no—
503#103—2441no—
504#103C22⋊D6114yes—
505C22⋊C8—1222no—
506C22⋊C8—1222no—
507C4×C8—22no—
508#95—611no—
509#95—611no—
510#95—1221no—
511#95—1221no—
512#95—1221no—
513#95—1221no—
514#95—1221no—
515#95—1221no—
516#95—1221no—
517#95—1221no—
518C24—611no—
519C2×Q8—21no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—612no—
528C2×Q8—1224no—
529C2×Q8—1221no—
530C2×Q8—1221no—
531C2×Q8—1221no—
532C2×Q8—1221no—
533C2×Q8—1221no—
534C2×Q8—1221no—
535C2×Q8—1221no—
536C2×Q8—1221no—
537C2×Q8—1221no—
538C2×Q8—1221no—
539C2×Q8—1221no—
540C2×Q8—2442no—
541C2×Q8—2442no—
542C2×Q8—2444no—
543C2×Q8—2444no—
544C2×Q8—2444no—
545C2×Q8—2444no—
546C2×Q8C2×D24412yes—
547C2×Q8C2×D24412yes—
548C2×Q8#1175822212yes—
549C2×Q8C2×C22⋊D6112yes—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—611no—
555C22×C4—611no—
556C22×C4—611no—
557C22×C4—1224no—
558C22×C4—1221no—
559C22×C4—1221no—
560C22×C4—1221no—
561C22×C4—1221no—
562C22×C4—1221no—
563C22×C4—1221no—
564C22×C4—1221no—
565C22×C4—1221no—
566C22×C4—1221no—
567C22×C4—1221no—
568C22×C4—2442no—
569C22×C4—2442no—
570C22×C4D4×D6111yescharacteristic
571C22×C4D4×D6111yescharacteristic
572C22×C4C23×D6111yescharacteristic
573Q16—28no—
574Q16—2444no—
575Q16—2444no—
576Q16—2444no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—1221no—
582C2×C8—1221no—
583C2×C8—1221no—
584C2×C8—1221no—
585C2×C8—1221no—
586C2×C8—1221no—
587C2×C8C2×D24412yes—
588C2×C8C2×C22⋊D6112yes—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—42no—
593C4⋊C4—42no—
594C4⋊C4—1221no—
595C4⋊C4—1221no—
596C4⋊C4—1221no—
597C4⋊C4—1221no—
598C4⋊C4—2442no—
599C4⋊C4—2442no—
600C4⋊C4—2442no—
601C4⋊C4—2442no—
602C4⋊C4—2442no—
603C4⋊C4—2442no—
604C4⋊C4C2×C22⋊D6112yes—
605C22⋊C4—614no—
606C22⋊C4—2441no—
607C22⋊C4—2442no—
608C22⋊C4—2442no—
609C22⋊C4—2442no—
610C42—21no—
611C42—21no—
612C42—42no—
613C42—42no—
614C42—1221no—
615C42—1221no—
616C42—2442no—
617C23—612no—
618C23—1221no—
619C23—1221no—
620C23—1221no—
621C23—1221no—
622C23—1221no—
623C23—1221no—
624C23C2×D4×D6111yescharacteristic
625Q8—22no—
626Q8—22no—
627Q8—22no—
628Q8—22no—
629Q8—22no—
630Q8—41no—
631Q8—41no—
632Q8—1222no—
633Q8—1222no—
634Q8—2448no—
635Q8—2441no—
636Q8—2441no—
637Q8—2441no—
638Q8—2441no—
639Q8—2441no—
640Q8—2441no—
641Q8#1451975114yes—
642C2×C4—22no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—612no—
660C2×C4—1221no—
661C2×C4—1221no—
662C2×C4—1221no—
663C2×C4—1222no—
664C2×C4—1221no—
665C2×C4—1221no—
666C2×C4—1221no—
667C2×C4—1221no—
668C2×C4—1221no—
669C2×C4—2448no—
670C2×C4—2441no—
671C2×C4—2441no—
672C2×C4—2441no—
673C2×C4—2441no—
674C2×C4—2441no—
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—2441no—
684C2×C4—2441no—
685C2×C4Q16×D6112yes—
686C2×C4C22×C22⋊D6111yescharacteristic
687C2×C4C22×D24411yescharacteristic
688C2×C4#41×D6111yescharacteristic
689C2×C4C2×#1175822211yescharacteristic
690C2×C4#1451982211yescharacteristic
691C2×C4#1451982311yescharacteristic
692C8—22no—
693C8—22no—
694C8—2441no—
695C8—2441no—
696C22—1222no—
697C22—1222no—
698C22—1222no—
699C22—2441no—
700C22—2441no—
701C22—2441no—
702C22—2441no—
703C22#1684027111yescharacteristic
704C22D4×C22⋊D6111yescharacteristic
705C22D4×D24411yescharacteristic
706C22C2×Q16×D6111yescharacteristic
707C22#1684055911yescharacteristic
708C22#1684057511yescharacteristic
709C22#1684057611yescharacteristic
710C4—24no—
711C4—22no—
712C4—42no—
713C4—41no—
714C4—42no—
715C4—81no—
716C4—1222no—
717C4—4881no—
718C4—4881no—
719C4—4881no—
720C4—2441no—
721C4—2441no—
722C4—2442no—
723C4C2×#1451975111yescharacteristic
724C4#1684034511yescharacteristic
725C4#1684040011yescharacteristic
726C4#1684040711yescharacteristic
727C2—2442no—
728C2#2144934911yescharacteristic
729C2#2145585611yescharacteristic
730C2#2145611611yescharacteristic
731C2#2145737411yescharacteristic
732C2#2145747511yescharacteristic
733C2Q16×C22⋊D6111yescharacteristic
734C2Q16×D24411yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C4×Q16×C61C2
socleC23×C61C22×D4
prime radicalC23×D61C2×D4
hypercenterC2×C4×Q16D61
hypocenterC61#25161
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×Q16

Complements

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

NH ≅ G/Ntype
1. C2×#16839970C2semidirect
6. #21447209C2semidirect
9. #21446920C2semidirect
10. #21446680C2semidirect
12. #21446160C2semidirect
13. #21446160C2semidirect
14. #21446075C2semidirect
15. C2×C4×Q16×C61C2semidirect
228. #11758198Q16semidirect
363. C2×C4×Q16D61semidirect
430. C61#25161semidirect

Maximal subgroups

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

subgroupindex
C2×#168399702
C2×#168399192
C2×#168399162
#214494122
Q8×#117581982
#214472092
#214470242
#214470212
#214469202
#214466802
#214464252
#214461602
#214460752
C2×C4×Q16×C612
#2516161