Finite Group Databasebeta

← #29737463

Subgroups — #29737463

Order 15616.

1136 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840061C211yesmaximal, characteristic, complemented
2C2×#16839765C211yesmaximal, characteristic
3#21449535C211yesmaximal, characteristic, complemented
4#21448640C211yesmaximal, characteristic
5#21447207C211yesmaximal, characteristic, complemented
6#21447205C211yesmaximal, characteristic, complemented
7#21446963C211yesmaximal, characteristic, complemented
8#21446077C211yesmaximal, characteristic, complemented
9#21446069C211yesmaximal, characteristic, complemented
10#21446017C211yesmaximal, characteristic, complemented
11#21446003C211yesmaximal, characteristic, complemented
12#21445849C211yesmaximal, characteristic, complemented
13#21445816C211yesmaximal, characteristic, complemented
14#21445748C211yesmaximal, characteristic
15C61×#2094C211yesmaximal, characteristic, complemented
16C22×D4×D61C2211yescharacteristic
17C22×#11758189C2211yescharacteristic
18C2×#14519768C2211yescharacteristic, complemented
19C2×C4×D244C2211yescharacteristic
20C2×#14519739C2211yescharacteristic
21C2×#14519735C2211yescharacteristic
22C2×C22⋊C4×D61—21no—
23#16840061—24no—
24C2×#14519711C2211yescharacteristic, complemented
25C2×#14519710C2211yescharacteristic, complemented
26C2×C4⋊#92418C2211yescharacteristic, complemented
27C2×#14519706C2211yescharacteristic, complemented
28#16839765—24no—
29C2×#14519699C2211yescharacteristic
30C2×#14519699C2211yescharacteristic
31C2×#14519698C2211yescharacteristic
32C2×#14519698C2211yescharacteristic
33C2×#14519697C2211yescharacteristic
34C2×#14519697C2211yescharacteristic
35C2×#14519689C2211yescharacteristic
36#16839697—21no—
37#16839684—21no—
38#16839665C2211yescharacteristic
39#16839660C2211yescharacteristic, complemented
40#16839658C2211yescharacteristic, complemented
41#16839657—21no—
42#16839648—21no—
43#16839638—21no—
44#16839638—21no—
45#16839619C2211yescharacteristic
46#16839619C2211yescharacteristic
47#16839617—21no—
48C4×#11758198C2211yescharacteristic
49#16839525C2211yescharacteristic, complemented
50#16839524C2211yescharacteristic, complemented
51#16839524C2211yescharacteristic, complemented
52#16839524C2211yescharacteristic, complemented
53#16839516C2211yescharacteristic, complemented
54C2×#106×C61C2211yescharacteristic, complemented
55C2×#106×C61C2211yescharacteristic, complemented
56C2×#102×C61C2211yescharacteristic
57C2×#102×C61C2211yescharacteristic
58C61×#390C2211yescharacteristic
59C61×#384C2211yescharacteristic, complemented
60C61×#336C2211yescharacteristic, complemented
61C24×D61—21no—
62C22×D244C2311yescharacteristic
63C22×C22⋊D61—21no—
64C2×D4×D61—22no—
65C2×D4×D61—22no—
66C2×D4×D61—22no—
67C2×D4×D61—41no—
68C2×D4×D61—41no—
69C2×D4×D61Q814yes—
70C22×C4×D61—21no—
71C22×C4×D61—21no—
72C22×C4×D61C2311yescharacteristic
73C2×#11758189—22no—
74C2×#11758189—22no—
75C2×#11758189—41no—
76C22×#92418C2311yescharacteristic
77C22×#92418C2311yescharacteristic
78#14519768—22no—
79#14519768—41no—
80C4×D244—22no—
81C4×D244—41no—
82#14519739—22no—
83#14519739—41no—
84#14519735—22no—
85#14519735—41no—
86C2×C4⋊Dic61—21no—
87C2×C4⋊Dic61C2311yescharacteristic
88C2×C4⋊Dic61C2311yescharacteristic
89C2×C4⋊Dic61C2311yescharacteristic
90C2×#11758196—21no—
91C2×#11758196—21no—
92C2×#11758196—21no—
93C2×C22⋊Dic61—21no—
94C2×C22⋊Dic61—21no—
95C2×#11758198—21no—
96C2×#11758198—21no—
97C2×#11758198—21no—
98C2×#11758198—21no—
99C2×#11758198—21no—
100C2×#11758198D411yescharacteristic
101C2×#11758198D411yescharacteristic
102C22⋊C4×D61—44no—
103C2×C4×Dic61—21no—
104C2×C4×Dic61C2311yescharacteristic
105#14519711—41no—
106#14519710—22no—
107C4⋊#92418—41no—
108#14519706—22no—
109#14519699—22no—
110#14519699D414yes—
111#14519698—22no—
112#14519698—41no—
113#14519697—22no—
114#14519697—22no—
115#14519689—22no—
116#14519684—21no—
117#14519684—21no—
118#14519684—21no—
119#14519684—21no—
120#14519684D411yescharacteristic
121#14519684D411yescharacteristic
122C22×D4×C61C2311yescharacteristic
123C22×C8×C61C2311yescharacteristic
124C22×C8×C61C2311yescharacteristic
125C2×C4⋊C4×C61—21no—
126C2×C4⋊C4×C61—21no—
127C2×C4⋊C4×C61C2311yescharacteristic
128C2×C4⋊C4×C61C2311yescharacteristic
129C2×C4⋊C4×C61C2311yescharacteristic
130C2×C22⋊C4×C61—21no—
131C2×C22⋊C4×C61—21no—
132C2×C42×C61C2311yescharacteristic
133#106×C61—22no—
134#106×C61—41no—
135#102×C61—22no—
136#102×C61—41no—
137C24×C61—21no—
138C23×D61—21no—
139C23×D61—24no—
140C23×D61—42no—
141C23×D61—42no—
142C23×D61—42no—
143C23×D61—42no—
144C23×D61—81no—
145C23×D61—81no—
146C23×D61C2×D411yescharacteristic
147C2×D4×C61—21no—
148C2×D4×C61—21no—
149C2×D4×C61—21no—
150C2×D4×C61—21no—
151C2×D4×C61—21no—
152C2×D4×C61C2×Q812yes—
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61—21no—
156C22×C4×C61C2×D411yescharacteristic
157C22×C4×C61C2×D411yescharacteristic
158C22×C4×C61C2411yescharacteristic
159C2×C22⋊D61—24no—
160C2×C22⋊D61—42no—
161C2×C22⋊D61—42no—
162C22×Dic61—21no—
163C22×Dic61—21no—
164C22×Dic61—21no—
165C22×Dic61C2×D411yescharacteristic
166C22×Dic61C2×D411yescharacteristic
167C22×Dic61C2×D411yescharacteristic
168D4×D61—28no—
169D4×D61—44no—
170D4×D61—44no—
171D4×D61—44no—
172C2×D244—21no—
173C2×D244—21no—
174C2×D244—21no—
175C2×D244C2×D412yes—
176C2×D244C2×Q812yes—
177C2×D244#4112yes—
178C2×C4×D61—21no—
179C2×C4×D61—21no—
180C2×C4×D61—21no—
181C2×C4×D61—21no—
182C2×C4×D61—42no—
183C2×C4×D61—42no—
184C2×C4×D61—42no—
185C2×C4×D61—42no—
186C2×C4×D61—81no—
187C2×C4×D61—81no—
188C2×C4×D61C2×Q812yes—
189C2×C4×D61#4112yes—
190C2×C8×C61—21no—
191C2×C8×C61—21no—
192C2×C8×C61—21no—
193C2×C8×C61—21no—
194C2×C8×C61—21no—
195C2×C8×C61C2×D412yes—
196C4⋊C4×C61—21no—
197C4⋊C4×C61—21no—
198C4⋊C4×C61—21no—
199C4⋊C4×C61—21no—
200C4⋊C4×C61—21no—
201C4⋊C4×C61—21no—
202C4⋊C4×C61—42no—
203C4⋊C4×C61—81no—
204C22⋊C4×C61—42no—
205C22⋊C4×C61—81no—
206C42×C61—21no—
207C42×C61—21no—
208C22⋊Dic61—42no—
209C22⋊Dic61—81no—
210#11758198—22no—
211#11758198—41no—
212#11758198—42no—
213#11758198—42no—
214#11758198—42no—
215#11758198—42no—
216#11758198—81no—
217C4⋊Dic61—21no—
218C4⋊Dic61—21no—
219C4⋊Dic61—21no—
220C4⋊Dic61—21no—
221C4⋊Dic61—21no—
222C4⋊Dic61—42no—
223C4⋊Dic61C2×D412yes—
224#11758196—42no—
225#11758196—42no—
226#11758196—81no—
227C4×Dic61—21no—
228C4×Dic61—21no—
229C4×Dic61—42no—
230C2×#92418—21no—
231C2×#92418—21no—
232C2×#92418—21no—
233C2×#92418—21no—
234C2×#92418—21no—
235C2×#92418—21no—
236#11758189—44no—
237C23×C61—22no—
238C23×C61—41no—
239C23×C61—41no—
240C23×C61—41no—
241C23×C61—41no—
242C23×C61—41no—
243C23×C61—41no—
244C23×C61C22×D411yescharacteristic
245C22×D61—22no—
246C22×D61—21no—
247C22×D61—22no—
248C22×D61—22no—
249C22×D61—21no—
250C22×D61—21no—
251C22×D61—21no—
252C22×D61—21no—
253C22×D61—21no—
254C22×D61—48no—
255C22×D61—48no—
256C22×D61—41no—
257C22×D61—41no—
258C22×D61—41no—
259C22×D61—41no—
260C22×D61—84no—
261C22×D61—84no—
262C22×D61—84no—
263C22×D61—84no—
264C22×D61—84no—
265C22×D61C22⋊Q812yes—
266D4×C61—22no—
267D4×C61—22no—
268D4×C61—41no—
269D4×C61—41no—
270C2×C4×C61—21no—
271C2×C4×C61—21no—
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×C61—41no—
283C2×C4×C61—41no—
284C2×C4×C61AGL(1,ℤ/8)12yes—
285C2×C4×C61C22×D411yescharacteristic
286C2×C4×C61C22×Q811yescharacteristic
287C2×C4×C61C2×#4111yescharacteristic
288C2×C4×C61C2×#4111yescharacteristic
289C2×C4×C61H(5,𝔽2)11yescharacteristic
290C2×C4×C61H(5,𝔽2)11yescharacteristic
291C22⋊D61—48no—
292C2×Dic61—21no—
293C2×Dic61—21no—
294C2×Dic61—21no—
295C2×Dic61—21no—
296C2×Dic61—22no—
297C2×Dic61—21no—
298C2×Dic61—21no—
299C2×Dic61—21no—
300C2×Dic61—21no—
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×Dic61C22⋊Q812yes—
310D244—22no—
311D244—22no—
312D244—22no—
313D244C22⋊Q814yes—
314C4×D61—22no—
315C4×D61—22no—
316C4×D61—22no—
317C4×D61—22no—
318C4×D61—84no—
319C4×D61—84no—
320C8×C61—22no—
321C8×C61—41no—
322#92418—41no—
323#92418—41no—
324#25976—611nomaximal, Sylow
325C22×C61—42no—
326C22×C61—42no—
327C22×C61—42no—
328C22×C61—81no—
329C22×C61—81no—
330C22×C61—81no—
331C22×C61—81no—
332C22×C61C2×C22⋊Q811yescharacteristic
333C22×C61D4211yescharacteristic
334C22×C61#54611yescharacteristic
335C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
336C22×C61#57511yescharacteristic
337C22×C61#57611yescharacteristic
338C22×C61#57711yescharacteristic
339C2×D61—22no—
340C2×D61—22no—
341C2×D61—22no—
342C2×D61—24no—
343C2×D61—42no—
344C2×D61—42no—
345C2×D61—41no—
346C2×D61—42no—
347C2×D61—42no—
348C2×D61—41no—
349C2×D61—42no—
350C2×D61—41no—
351C2×D61—41no—
352C2×D61—42no—
353C2×D61—816no—
354C4×C61—22no—
355C4×C61—41no—
356C4×C61—81no—
357C4×C61—81no—
358C4×C61—81no—
359C4×C61C2×C22⋊Q811yescharacteristic
360C4×C61#54311yescharacteristic
361C4×C61#54611yescharacteristic
362C4×C61#55111yescharacteristic
363Dic61—22no—
364Dic61—41no—
365Dic61—41no—
366Dic61—42no—
367Dic61—81no—
368Dic61—81no—
369C2×#478—611no—
370C2×#418—611no—
371#2441—611no—
372D4×C22⋊C4—611no—
373#2094D6111yescharacteristic, complemented
374#2067—611no—
375#2067—611no—
376#2025—611no—
377#1864—611no—
378#1862—611no—
379#1854—611no—
380#1851—611no—
381#1809—611no—
382#1802—611no—
383#1786—611no—
384C2×C61—82no—
385C2×C61#243711yescharacteristic
386C2×C61#307711yescharacteristic
387C2×C61#308111yescharacteristic
388C2×C61#326811yescharacteristic
389C2×C61#327211yescharacteristic
390C2×C61#331811yescharacteristic
391C2×C61#332311yescharacteristic
392D61—42no—
393D61—44no—
394C23×D4—611no—
395C22×M16—611no—
396C2×#125—611no—
397C2×C4×D4—611no—
398C2×C4×D4—611no—
399C2×#117—611no—
400C22×C22⋊C4—1221no—
401#478—1224no—
402C2×#107—611no—
403C2×#107—611no—
404C2×#106C2×D6111yescharacteristic, complemented
405C2×#106C2×D6111yescharacteristic, complemented
406C2×C4⋊C8—611no—
407C2×C4⋊C8—611no—
408#418—1224no—
409C2×#102—611no—
410C2×#102—611no—
411C2×#102—611no—
412C2×#102—611no—
413C2×#102—611no—
414C2×#102—611no—
415C2×#102C2×D6111yescharacteristic
416C2×#102C2×D6111yescharacteristic
417C2×C22⋊C8—611no—
418#399—1221no—
419#396—1221no—
420#390—611no—
421#390C2×D6111yescharacteristic
422#389—611no—
423#389—611no—
424#389—1221no—
425#387—1221no—
426#386—1221no—
427#386—1221no—
428#384C2×D6111yescharacteristic, complemented
429#380—611no—
430#380—611no—
431#379—1221no—
432C4×C22⋊C4—611no—
433#340—611no—
434#340—611no—
435#340—611no—
436#340—611no—
437#336—611no—
438#336C2×D6111yescharacteristic, complemented
439C61#2597611yescharacteristic, complemented, Sylow
440C25—1221no—
441C22×D4—614no—
442C22×D4—611no—
443C22×D4—1222no—
444C22×D4—1221no—
445C22×D4—1222no—
446C22×D4—1222no—
447C22×D4—2441no—
448C22×D4—2441no—
449C22×D4C22×D6111yescharacteristic
450C23×C4—611no—
451C23×C4—1221no—
452C23×C4—1221no—
453C2×M16—1222no—
454C2×M16—1222no—
455C2×M16—2441no—
456C22×C8—611no—
457C22×C8—611no—
458C22×C8C22×D6111yescharacteristic
459C22×C8C22×D6111yescharacteristic
460#125—1222no—
461#125—2441no—
462C4×D4—1222no—
463C4×D4—1222no—
464C4×D4—2441no—
465C4×D4—2441no—
466#117—1222no—
467#117—2441no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—611no—
471C2×C4⋊C4—611no—
472C2×C4⋊C4—611no—
473C2×C4⋊C4—1221no—
474C2×C4⋊C4—1221no—
475C2×C4⋊C4—1221no—
476C2×C4⋊C4—1221no—
477C2×C4⋊C4C22×D6111yescharacteristic
478C2×C4⋊C4C22×D6111yescharacteristic
479C2×C4⋊C4C22×D6111yescharacteristic
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—611no—
483C2×C22⋊C4—611no—
484C2×C22⋊C4—1221no—
485C2×C22⋊C4—1221no—
486C2×C22⋊C4—1221no—
487C2×C22⋊C4—1221no—
488C2×C22⋊C4—1221no—
489C2×C22⋊C4—1221no—
490C2×C22⋊C4—1221no—
491C2×C22⋊C4—2444no—
492C2×C42—611no—
493C2×C42—1221no—
494C2×C42C22×D6111yescharacteristic
495#107—1222no—
496#107—2441no—
497#106—22no—
498#106—41no—
499C4⋊C8—1222no—
500C4⋊C8—2441no—
501#102—22no—
502#102—41no—
503#102—614no—
504#102—1222no—
505#102—1222no—
506#102—1222no—
507#102—1222no—
508#102—2441no—
509C22⋊C8—1222no—
510#95—611no—
511#95—611no—
512#95—1221no—
513#95—1221no—
514#95—1221no—
515#95—1221no—
516C24—21no—
517C24—611no—
518C24—1224no—
519C24—1221no—
520C24—4881no—
521C24—4881no—
522C24—2442no—
523C24—2442no—
524C24—2442no—
525C24—2442no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—612no—
532C2×D4—612no—
533C2×D4—612no—
534C2×D4—1224no—
535C2×D4—1228no—
536C2×D4—1221no—
537C2×D4—1221no—
538C2×D4—1221no—
539C2×D4—2444no—
540C2×D4—2444no—
541C2×D4—2444no—
542C2×D4—2442no—
543C2×D4—2442no—
544C2×D4Q8×D6112yes—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—611no—
549C22×C4—612no—
550C22×C4—612no—
551C22×C4—611no—
552C22×C4—611no—
553C22×C4—1221no—
554C22×C4—1221no—
555C22×C4—1221no—
556C22×C4—1221no—
557C22×C4—1221no—
558C22×C4—1221no—
559C22×C4—1221no—
560C22×C4—4881no—
561C22×C4—4881no—
562C22×C4—2442no—
563C22×C4—2442no—
564C22×C4—2442no—
565C22×C4—2442no—
566C22×C4D4×D6111yescharacteristic
567C22×C4D4×D6111yescharacteristic
568C22×C4C23×D6111yescharacteristic
569M16—2444no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—1221no—
576C2×C8—1221no—
577C2×C8—1221no—
578C2×C8—1221no—
579C2×C8—1221no—
580C2×C8—1221no—
581C2×C8D4×D6112yes—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—42no—
589C4⋊C4—81no—
590C4⋊C4—612no—
591C4⋊C4—1221no—
592C4⋊C4—1221no—
593C4⋊C4—1221no—
594C4⋊C4—1221no—
595C4⋊C4—1221no—
596C4⋊C4—4881no—
597C4⋊C4—2442no—
598C4⋊C4—2442no—
599C4⋊C4—2442no—
600C22⋊C4—42no—
601C22⋊C4—81no—
602C22⋊C4—1222no—
603C22⋊C4—4881no—
604C22⋊C4—4881no—
605C22⋊C4—2441no—
606C22⋊C4—2442no—
607C22⋊C4—2442no—
608C22⋊C4—2442no—
609C22⋊C4—2442no—
610C22⋊C4—2442no—
611C42—21no—
612C42—21no—
613C42—1221no—
614C42—1221no—
615C42—2442no—
616C23—22no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—612no—
624C23—1222no—
625C23—1221no—
626C23—1221no—
627C23—1221no—
628C23—1221no—
629C23—1221no—
630C23—1222no—
631C23—1222no—
632C23—1221no—
633C23—4884no—
634C23—4884no—
635C23—4884no—
636C23—4884no—
637C23—4884no—
638C23—2448no—
639C23—2448no—
640C23—2441no—
641C23—2441no—
642C23—2441no—
643C23—2441no—
644C23C2×D4×D6111yescharacteristic
645D4—22no—
646D4—22no—
647D4—41no—
648D4—41no—
649D4—614no—
650D4—1222no—
651D4—1222no—
652D4—1222no—
653D4—2448no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—612no—
669C2×C4—1221no—
670C2×C4—1221no—
671C2×C4—1222no—
672C2×C4—1222no—
673C2×C4—1222no—
674C2×C4—1222no—
675C2×C4—1221no—
676C2×C4—1221no—
677C2×C4—1221no—
678C2×C4—1221no—
679C2×C4—1221no—
680C2×C4—1221no—
681C2×C4—1222no—
682C2×C4—4884no—
683C2×C4—4884no—
684C2×C4—2441no—
685C2×C4—2441no—
686C2×C4—2441no—
687C2×C4—2441no—
688C2×C4—2441no—
689C2×C4—2441no—
690C2×C4—2441no—
691C2×C4—2441no—
692C2×C4#1451980412yes—
693C2×C4C2×D4×D6111yescharacteristic
694C2×C4C2×Q8×D6111yescharacteristic
695C2×C4#41×D6111yescharacteristic
696C2×C4#41×D6111yescharacteristic
697C2×C4#1451982211yescharacteristic
698C2×C4#1451982311yescharacteristic
699C8—22no—
700C8—41no—
701C8—2441no—
702C8—2441no—
703C22—42no—
704C22—42no—
705C22—42no—
706C22—81no—
707C22—81no—
708C22—81no—
709C22—81no—
710C22—1222no—
711C22—1222no—
712C22—1224no—
713C22—1222no—
714C22—48816no—
715C22—2442no—
716C22—2442no—
717C22—2441no—
718C22—2442no—
719C22—2442no—
720C22—2441no—
721C22—2441no—
722C22—2442no—
723C22—2441no—
724C22—2442no—
725C22C22⋊Q8×D6111yescharacteristic
726C22#1684039711yescharacteristic
727C22#1684040411yescharacteristic
728C22C2×#1451980411yescharacteristic
729C22#1684055811yescharacteristic
730C22#1684056611yescharacteristic
731C22#1684056811yescharacteristic
732C4—22no—
733C4—41no—
734C4—81no—
735C4—81no—
736C4—81no—
737C4—1222no—
738C4—4881no—
739C4—4881no—
740C4—2441no—
741C4—2442no—
742C4—2441no—
743C4C22⋊Q8×D6111yescharacteristic
744C4#1684038711yescharacteristic
745C4#1684040411yescharacteristic
746C4#1684044011yescharacteristic
747C2—82no—
748C2—2442no—
749C2—2444no—
750C2#2144948611yescharacteristic
751C2#2145561711yescharacteristic
752C2#2145564511yescharacteristic
753C2#2145735811yescharacteristic
754C2#2145741811yescharacteristic
755C2#2145795811yescharacteristic
756C2#2145803811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2094C2
socleC23×C61C22×D4
prime radicalC22×D4×D61C22
hypercenter#2094D61
hypocenterC61#25976
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2094

Complements

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

NH ≅ G/Ntype
1. C2×#16840061C2semidirect
3. #21449535C2semidirect
5. #21447207C2semidirect
6. #21447205C2semidirect
7. #21446963C2semidirect
8. #21446077C2semidirect
9. #21446069C2semidirect
10. #21446017C2semidirect
11. #21446003C2semidirect
12. #21445849C2semidirect
13. #21445816C2semidirect
15. C61×#2094C2semidirect
18. C2×#14519768C22semidirect
24. C2×#14519711C22semidirect
25. C2×#14519710C22semidirect
26. C2×C4⋊#92418C22semidirect
27. C2×#14519706C22semidirect
39. #16839660C22semidirect
40. #16839658C22semidirect
49. #16839525C22semidirect
50. #16839524C22semidirect
51. #16839524C22semidirect
52. #16839524C22semidirect
53. #16839516C22semidirect
54. C2×#106×C61C22semidirect
55. C2×#106×C61C22semidirect
59. C61×#384C22semidirect
60. C61×#336C22semidirect
373. #2094D61semidirect
404. C2×#106C2×D61semidirect
405. C2×#106C2×D61semidirect
428. #384C2×D61semidirect
438. #336C2×D61semidirect
439. C61#25976semidirect

Maximal subgroups

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

subgroupindex
C2×#168400612
C2×#168397652
#214495352
#214486402
#214472072
#214472052
#214469632
#214460772
#214460692
#214460172
#214460032
#214458492
#214458162
#214457482
C61×#20942
#2597661