Finite Group Databasebeta

← #29716377

Subgroups — #29716377

Order 15616.

1330 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×#16840427C211yesmaximal, characteristic, complemented
2C2×#16840040C211yesmaximal, characteristic, complemented
3C2×#16839842C211yesmaximal, characteristic
4#21450739C211yesmaximal, characteristic, complemented
5#21447146C211yesmaximal, characteristic, complemented
6#21447144C211yesmaximal, characteristic, complemented
7#21446953C211yesmaximal, characteristic, complemented
8#21446778C211yesmaximal, characteristic, complemented
9#21446753C211yesmaximal, characteristic, complemented
10#21446170C211yesmaximal, characteristic
11#21446164C211yesmaximal, characteristic
12#21446069C211yesmaximal, characteristic, complemented
13#21446067C211yesmaximal, characteristic, complemented
14#21445818C211yesmaximal, characteristic, complemented
15C61×#2023C211yesmaximal, characteristic, complemented
16C22×Q8×D61—21no—
17C22×#11758199C2211yescharacteristic
18#16840427—24no—
19#16840427—24no—
20C2×#14519776C2211yescharacteristic
21C2×#14519776C2211yescharacteristic
22C2×#14519755—21no—
23C2×#14519755—21no—
24C2×#14519754—21no—
25C2×#14519753—21no—
26C2×C4×Dic122C2211yescharacteristic
27C2×C4×D244C2211yescharacteristic
28C2×D4×Dic61C2211yescharacteristic
29C2×#14519739C2211yescharacteristic
30C2×#14519739C2211yescharacteristic
31#16840040—24no—
32#16839842—24no—
33C2×#14519711C2211yescharacteristic
34C2×#14519710C2211yescharacteristic
35C2×#14519710C2211yescharacteristic
36C2×#14519706C2211yescharacteristic
37C2×#14519699C2211yescharacteristic
38C2×#14519699C2211yescharacteristic
39C2×#14519698C2211yescharacteristic
40C2×#14519697C2211yescharacteristic
41C2×C8×Dic61C2211yescharacteristic
42#16839685—21no—
43#16839685—21no—
44#16839665C2211yescharacteristic
45#16839661C2211yescharacteristic
46#16839660C2211yescharacteristic
47#16839631C2211yescharacteristic
48#16839620—21no—
49#16839525C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839524C2211yescharacteristic
53#16839517C2211yescharacteristic
54#16839516C2211yescharacteristic
55#16839516C2211yescharacteristic
56C2×C4⋊Q8×C61C2211yescharacteristic
57C2×#102×C61C2211yescharacteristic
58C2×#102×C61C2211yescharacteristic
59C61×#390C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C61×#340C2211yescharacteristic
62C61×#336C2211yescharacteristic
63C22×Dic122—21no—
64C22×Dic122—21no—
65C22×Dic122D411yescharacteristic
66C2×Q8×D61—28no—
67C2×Q8×D61—44no—
68C2×Q8×D61—44no—
69C22×D244C2311yescharacteristic
70C23×Dic61—21no—
71C22×C4×D61—21no—
72C22×C4×D61—21no—
73C22×C4×D61—21no—
74C2×#11758199—22no—
75C2×#11758199—22no—
76C2×#11758199Q814yescomplemented
77C22×#92418C2311yescharacteristic
78C22×#92418C2311yescharacteristic
79#14519776—22no—
80#14519776—22no—
81#14519776—22no—
82#14519776D414yes—
83#14519755—28no—
84#14519755—28no—
85#14519754—44no—
86#14519753—28no—
87C4×Dic122—22no—
88C4×Dic122—22no—
89C4×D244—22no—
90C4×D244—22no—
91D4×Dic61—22no—
92D4×Dic61—22no—
93#14519739—22no—
94#14519739—22no—
95#14519739—22no—
96#14519739D414yes—
97C2×C4⋊Dic61—21no—
98C2×C4⋊Dic61D411yescharacteristic
99C2×C4⋊Dic61C2311yescharacteristic
100C2×C4⋊Dic61C2311yescharacteristic
101C2×C4⋊Dic61C2311yescharacteristic
102C2×#11758196—21no—
103C2×#11758196—21no—
104C2×#11758196—21no—
105C2×#11758196—21no—
106C2×#11758196—21no—
107C2×#11758196D411yescharacteristic
108C2×#11758196D411yescharacteristic
109C2×C22⋊Dic61—21no—
110C2×C22⋊Dic61—21no—
111C2×C22⋊Dic61—21no—
112C2×#11758198—21no—
113C2×#11758198—21no—
114C2×#11758198—21no—
115C2×C4×Dic61C2311yescharacteristic
116C2×C4×Dic61C2311yescharacteristic
117#14519711—22no—
118#14519710—22no—
119#14519710—22no—
120#14519706—22no—
121#14519699—22no—
122#14519699—22no—
123#14519698—22no—
124#14519697—22no—
125C8×Dic61—22no—
126#14519684—21no—
127#14519684—21no—
128C22×Q8×C61—21no—
129C22×D4×C61C2311yescharacteristic
130C22×C8×C61C2311yescharacteristic
131C22×C8×C61C2311yescharacteristic
132C4⋊Q8×C61—22no—
133C4⋊Q8×C61—22no—
134C2×C4⋊C4×C61—21no—
135C2×C4⋊C4×C61C2311yescharacteristic
136C2×C4⋊C4×C61C2311yescharacteristic
137C2×C4⋊C4×C61C2311yescharacteristic
138C2×C22⋊C4×C61—21no—
139C2×C22⋊C4×C61—21no—
140C2×C42×C61C2311yescharacteristic
141#102×C61—22no—
142#102×C61—22no—
143C24×C61—21no—
144C23×D61—21no—
145C2×Q8×C61—24no—
146C2×Q8×C61—42no—
147C2×Q8×C61—42no—
148C2×D4×C61—21no—
149C2×D4×C61—21no—
150C2×D4×C61—21no—
151C2×D4×C61—21no—
152C2×D4×C61—21no—
153C2×D4×C61C2×Q812yescomplemented
154C22×C4×C61—21no—
155C22×C4×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61C2×D411yescharacteristic
158C22×C4×C61C2×D411yescharacteristic
159C22×C4×C61C2411yescharacteristic
160C22×Dic61—21no—
161C22×Dic61—21no—
162C22×Dic61—21no—
163C22×Dic61—42no—
164C22×Dic61—42no—
165C22×Dic61—42no—
166C22×Dic61C2×D411yescharacteristic
167C22×Dic61C2×D411yescharacteristic
168C22×Dic61C2×D411yescharacteristic
169C22×Dic61C2×D411yescharacteristic
170Q8×D61—432no—
171C2×D244—21no—
172C2×D244—21no—
173C2×D244—21no—
174C2×D244C2×D412yes—
175C2×D244C2×Q812yes—
176C2×D244#4112yes—
177C2×C4×D61—24no—
178C2×C4×D61—24no—
179C2×C4×D61—24no—
180C2×C4×D61—42no—
181C2×C4×D61—42no—
182C2×C4×D61—42no—
183C2×C4×D61—42no—
184C2×C4×D61—42no—
185C2×C4×D61—42no—
186C2×Dic122—22no—
187C2×Dic122—22no—
188C2×Dic122—24no—
189C2×Dic122—24no—
190C2×Dic122—42no—
191C2×Dic122—42no—
192C2×Dic122—42no—
193C2×Dic122—42no—
194C2×Dic122D814yescomplemented
195C2×C8×C61—21no—
196C2×C8×C61—21no—
197C2×C8×C61—21no—
198C2×C8×C61—21no—
199C2×C8×C61—21no—
200C2×C8×C61—21no—
201C4⋊C4×C61—24no—
202C4⋊C4×C61—21no—
203C4⋊C4×C61—21no—
204C4⋊C4×C61—21no—
205C4⋊C4×C61—21no—
206C4⋊C4×C61C2×D412yes—
207C4⋊C4×C61C2×D412yes—
208C22⋊C4×C61—42no—
209C22⋊C4×C61—81no—
210C42×C61—21no—
211C42×C61—21no—
212C22⋊Dic61—42no—
213C22⋊Dic61—42no—
214C22⋊Dic61—81no—
215#11758199—28no—
216#11758198—24no—
217#11758198—24no—
218#11758198—24no—
219C4⋊Dic61—21no—
220C4⋊Dic61—22no—
221C4⋊Dic61—21no—
222C4⋊Dic61—21no—
223C4⋊Dic61—21no—
224C4⋊Dic61—21no—
225C4⋊Dic61—42no—
226C4⋊Dic61C2×D412yes—
227#11758196—24no—
228#11758196—24no—
229#11758196—22no—
230#11758196—22no—
231#11758196—42no—
232#11758196—42no—
233#11758196—81no—
234C4×Dic61—21no—
235C4×Dic61—21no—
236C4×Dic61C2×D412yes—
237C4×Dic61C2×D412yes—
238C2×#92418—21no—
239C2×#92418—21no—
240C2×#92418—21no—
241C2×#92418—21no—
242C2×#92418—21no—
243C2×#92418C2×Q812yescomplemented
244C23×C61—22no—
245C23×C61—41no—
246C23×C61—41no—
247C23×C61—41no—
248C23×C61—41no—
249C23×C61—41no—
250C23×C61—41no—
251C23×C61C22×D411yescharacteristic
252C22×D61—22no—
253C22×D61—22no—
254C22×D61—22no—
255C22×D61—41no—
256C22×D61—41no—
257C22×D61—41no—
258C22×D61—41no—
259Q8×C61—48no—
260D4×C61—22no—
261D4×C61—22no—
262D4×C61—41no—
263D4×C61—41no—
264C2×C4×C61—21no—
265C2×C4×C61—21no—
266C2×C4×C61—21no—
267C2×C4×C61—22no—
268C2×C4×C61—22no—
269C2×C4×C61—21no—
270C2×C4×C61—21no—
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×C61C2×D812yes—
279C2×C4×C61C22×D411yescharacteristic
280C2×C4×C61C22×D411yescharacteristic
281C2×C4×C61C22×Q811yescharacteristic
282C2×C4×C61C2×#4111yescharacteristic
283C2×C4×C612−1+411yescharacteristic
284C2×C4×C612−1+411yescharacteristic
285C2×Dic61—21no—
286C2×Dic61—21no—
287C2×Dic61—21no—
288C2×Dic61—21no—
289C2×Dic61—21no—
290C2×Dic61—22no—
291C2×Dic61—21no—
292C2×Dic61—21no—
293C2×Dic61—41no—
294C2×Dic61—41no—
295C2×Dic61—41no—
296C2×Dic61—41no—
297C2×Dic61—41no—
298C2×Dic61—41no—
299C2×Dic61—41no—
300C2×Dic61—41no—
301C2×Dic61—84no—
302C2×Dic61#12012yes—
303C2×Dic61#12012yes—
304C2×Dic61C2×D812yes—
305C2×Dic61C2×D812yes—
306C2×Dic61AGL(1,ℤ/8)12yes—
307D244—22no—
308D244—22no—
309D244—22no—
310D244C22⋊Q814yescomplemented
311C4×D61—48no—
312C4×D61—48no—
313C4×D61—48no—
314Dic122—28no—
315Dic122—48no—
316Dic122—48no—
317C8×C61—41no—
318C8×C61—41no—
319#92418—22no—
320#92418—41no—
321#24326—611nomaximal, Sylow
322C22×C61—42no—
323C22×C61—42no—
324C22×C61—42no—
325C22×C61—81no—
326C22×C61—81no—
327C22×C61—81no—
328C22×C61—81no—
329C22×C61C2×#12011yescharacteristic
330C22×C61#54811yescharacteristic
331C22×C61D4×Q811yescharacteristic
332C22×C61C22×D811yescharacteristic
333C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
334C22×C61#57711yescharacteristic
335C22×C61#57811yescharacteristic
336C2×D61—24no—
337C2×D61—42no—
338C2×D61—42no—
339C2×D61—42no—
340C2×D61—42no—
341C2×D61—42no—
342C2×D61—42no—
343C4×C61—22no—
344C4×C61—42no—
345C4×C61—42no—
346C4×C61—41no—
347C4×C61—81no—
348C4×C61C2×C22⋊Q811yescharacteristic
349C4×C61#53611yescharacteristic
350C4×C61#54811yescharacteristic
351C4×C61D4×Q811yescharacteristic
352Dic61—22no—
353Dic61—22no—
354Dic61—42no—
355Dic61—41no—
356Dic61—81no—
357Dic61—81no—
358Dic61#44714yes—
359C2×D4×Q8—611no—
360C2×#474—611no—
361C2×C4×D8—611no—
362#2538—611no—
363#2057—611no—
364#2057—611no—
365#2023—611no—
366#2023D6111yescharacteristic, complemented
367#1990—611no—
368#1984—611no—
369#1879—611no—
370#1879—611no—
371#1862—611no—
372#1862—611no—
373#1802—611no—
374C2×C61—82no—
375C2×C61#240911yescharacteristic
376C2×C61C2×#44711yescharacteristic
377C2×C61#301311yescharacteristic
378C2×C61#335811yescharacteristic
379C2×C61#336711yescharacteristic
380C2×C61Q8×D811yescharacteristic
381C2×C61#338411yescharacteristic
382D61—44no—
383C23×Q8—1221no—
384C22×D8—611no—
385D4×Q8—1224no—
386D4×Q8—1224no—
387C2×C4⋊Q8—611no—
388C2×C4⋊Q8—611no—
389C2×C4⋊Q8C2×D6111yescharacteristic
390C2×C22⋊Q8—1221no—
391C2×C22⋊Q8—1221no—
392C2×C22⋊Q8—1221no—
393C2×C22⋊Q8—1221no—
394C2×C4×Q8—611no—
395C2×C4×D4—611no—
396C2×C4×D4—611no—
397C2×C4×D4—611no—
398C2×C4×D4—611no—
399#474—1224no—
400C4×D8—1224no—
401C2×#107—611no—
402C2×#107—611no—
403C2×#107—611no—
404C2×C4⋊C8—611no—
405C2×#102—611no—
406C2×#102—611no—
407C2×#102—611no—
408C2×#102—611no—
409C2×#102C2×D6111yescharacteristic
410C2×#102C2×D6111yescharacteristic
411C2×C4×C8—611no—
412#396—1221no—
413#396—1221no—
414#390—611no—
415#390C2×D6111yescharacteristic
416#389—611no—
417#389—611no—
418#384—611no—
419#380—1221no—
420#340—611no—
421#340—611no—
422#340—611no—
423#340—611no—
424#340C2×D6111yescharacteristic
425#340C2×D6111yescharacteristic
426#336—611no—
427#336—611no—
428#336—611no—
429#336C2×D6111yescharacteristic
430C61#2432611yescharacteristic, complemented, Sylow
431C22×Q8—21no—
432C22×Q8—611no—
433C22×Q8—1221no—
434C22×Q8—1221no—
435C22×Q8—1228no—
436C22×Q8—2444no—
437C22×Q8—2444no—
438C22×D4—611no—
439C22×D4C22×D6111yescharacteristic
440C23×C4—1221no—
441C23×C4—1221no—
442C23×C4—1221no—
443C23×C4—1221no—
444C2×D8—614no—
445C2×D8—1222no—
446C2×D8—1222no—
447C22×C8—611no—
448C22×C8—611no—
449C22×C8C22×D6111yescharacteristic
450C22×C8C22×D6111yescharacteristic
451C4⋊Q8—22no—
452C4⋊Q8—22no—
453C4⋊Q8—614no—
454C4⋊Q8—1222no—
455C4⋊Q8—1222no—
456C4⋊Q8—1222no—
457C22⋊Q8—1228no—
458C22⋊Q8—1228no—
459C22⋊Q8—1228no—
460C22⋊Q8—2444no—
461C4×Q8—1222no—
462C4×Q8—1222no—
463C4×D4—614no—
464C4×D4—1222no—
465C4×D4—1222no—
466C4×D4—1222no—
467C4×D4—1222no—
468C4×D4—1222no—
469C4×D4—1222no—
470C4×D4—1222no—
471C2×C4⋊C4—21no—
472C2×C4⋊C4—611no—
473C2×C4⋊C4—611no—
474C2×C4⋊C4—611no—
475C2×C4⋊C4—611no—
476C2×C4⋊C4—611no—
477C2×C4⋊C4—611no—
478C2×C4⋊C4—1221no—
479C2×C4⋊C4—1221no—
480C2×C4⋊C4—1221no—
481C2×C4⋊C4—1221no—
482C2×C4⋊C4—1221no—
483C2×C4⋊C4—1221no—
484C2×C4⋊C4C22×D6111yescharacteristic
485C2×C4⋊C4C22×D6111yescharacteristic
486C2×C4⋊C4C22×D6111yescharacteristic
487C2×C22⋊C4—21no—
488C2×C22⋊C4—21no—
489C2×C22⋊C4—1221no—
490C2×C22⋊C4—1221no—
491C2×C22⋊C4—1221no—
492C2×C22⋊C4—1221no—
493C2×C22⋊C4—1221no—
494C2×C22⋊C4—1221no—
495C2×C42—611no—
496C2×C42—611no—
497C2×C42C22×D6111yescharacteristic
498#107—1222no—
499#107—1222no—
500#107—1222no—
501C4⋊C8—1222no—
502#102—22no—
503#102—22no—
504#102—1222no—
505#102—1222no—
506#102—1222no—
507#102—1222no—
508C4×C8—1222no—
509#95—1221no—
510#95—1221no—
511C24—21no—
512C24—1221no—
513C2×Q8—24no—
514C2×Q8—42no—
515C2×Q8—42no—
516C2×Q8—614no—
517C2×Q8—1222no—
518C2×Q8—1222no—
519C2×Q8—1224no—
520C2×Q8—1224no—
521C2×Q8—2442no—
522C2×Q8—2442no—
523C2×Q8—2442no—
524C2×Q8—2442no—
525C2×Q8—24432no—
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—1221no—
535C2×D4—1221no—
536C2×D4—1221no—
537C2×D4Q8×D6112yescomplemented
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—611no—
542C22×C4—611no—
543C22×C4—611no—
544C22×C4—611no—
545C22×C4—1224no—
546C22×C4—1224no—
547C22×C4—1224no—
548C22×C4—1221no—
549C22×C4—1221no—
550C22×C4—1221no—
551C22×C4—2442no—
552C22×C4—2442no—
553C22×C4—2442no—
554C22×C4—2442no—
555C22×C4—2442no—
556C22×C4—2442no—
557C22×C4—2442no—
558C22×C4—2442no—
559C22×C4—2442no—
560C22×C4D4×D6111yescharacteristic
561C22×C4D4×D6111yescharacteristic
562C22×C4C23×D6111yescharacteristic
563D8—1228no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—612no—
571C2×C8—1221no—
572C2×C8—1221no—
573C2×C8—1221no—
574C2×C8—1221no—
575C2×C8—1221no—
576C4⋊C4—24no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—612no—
582C4⋊C4—1222no—
583C4⋊C4—1222no—
584C4⋊C4—1222no—
585C4⋊C4—1224no—
586C4⋊C4—1224no—
587C4⋊C4—1221no—
588C4⋊C4—1221no—
589C4⋊C4—1221no—
590C4⋊C4—1221no—
591C4⋊C4—1221no—
592C4⋊C4—4881no—
593C4⋊C4—2442no—
594C4⋊C4—2442no—
595C4⋊C4—2442no—
596C4⋊C4D4×D6112yes—
597C4⋊C4D4×D6112yes—
598C22⋊C4—42no—
599C22⋊C4—81no—
600C22⋊C4—1224no—
601C22⋊C4—1224no—
602C22⋊C4—1224no—
603C22⋊C4—4881no—
604C22⋊C4—2442no—
605C22⋊C4—2442no—
606C42—21no—
607C42—21no—
608C42—612no—
609C42—612no—
610C42—1221no—
611C42—1221no—
612C23—22no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—1222no—
620C23—1222no—
621C23—1222no—
622C23—2441no—
623C23—2441no—
624C23—2441no—
625C23—2441no—
626C23C2×D4×D6111yescharacteristic
627Q8—48no—
628Q8—1228no—
629Q8—2448no—
630Q8—2448no—
631D4—22no—
632D4—22no—
633D4—41no—
634D4—41no—
635D4—614no—
636D4—1222no—
637D4—1222no—
638D4—1222no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—612no—
654C2×C4—612no—
655C2×C4—612no—
656C2×C4—612no—
657C2×C4—612no—
658C2×C4—1221no—
659C2×C4—1221no—
660C2×C4—1221no—
661C2×C4—1221no—
662C2×C4—1221no—
663C2×C4—1222no—
664C2×C4—1221no—
665C2×C4—1221no—
666C2×C4—4884no—
667C2×C4—2448no—
668C2×C4—2448no—
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×C4D8×D6112yes—
679C2×C4C2×D4×D6111yescharacteristic
680C2×C4C2×D4×D6111yescharacteristic
681C2×C4C2×Q8×D6111yescharacteristic
682C2×C4#41×D6111yescharacteristic
683C2×C4#1451982411yescharacteristic
684C2×C4#1451982411yescharacteristic
685C8—41no—
686C8—41no—
687C8—1222no—
688C8—2441no—
689C22—42no—
690C22—42no—
691C22—42no—
692C22—81no—
693C22—81no—
694C22—81no—
695C22—81no—
696C22—1224no—
697C22—2442no—
698C22—2442no—
699C22—2442no—
700C22—2442no—
701C22—2442no—
702C22—2442no—
703C22#120×D6111yescharacteristic
704C22#1684042011yescharacteristic
705C22#1684042511yescharacteristic
706C22C2×D8×D6111yescharacteristic
707C22AGL(1,ℤ/8)×D6111yescharacteristic
708C22#1684056811yescharacteristic
709C22#1684057811yescharacteristic
710C4—22no—
711C4—41no—
712C4—42no—
713C4—42no—
714C4—81no—
715C4—614no—
716C4—1222no—
717C4—1222no—
718C4—4881no—
719C4—4881no—
720C4—2441no—
721C4—2442no—
722C4C22⋊Q8×D6111yescharacteristic
723C4#1684033211yescharacteristic
724C4#1684042011yescharacteristic
725C4#1684042511yescharacteristic
726C2—82no—
727C2—2444no—
728C2#2144917711yescharacteristic
729C2#447×D6111yescharacteristic
730C2#2145512911yescharacteristic
731C2#2145845111yescharacteristic
732C2#2145853411yescharacteristic
733C2#2145866911yescharacteristic
734C2#2145871311yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2023C2
socleC23×C61C22×D4
prime radicalC22×#11758199C22
hypercenter#2023D61
hypocenterC61#24326
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2023

Complements

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

NH ≅ G/Ntype
1. C2×#16840427C2semidirect
2. C2×#16840040C2semidirect
4. #21450739C2semidirect
5. #21447146C2semidirect
6. #21447144C2semidirect
7. #21446953C2semidirect
8. #21446778C2semidirect
9. #21446753C2semidirect
12. #21446069C2semidirect
13. #21446067C2semidirect
14. #21445818C2semidirect
15. C61×#2023C2semidirect
76. C2×#11758199Q8semidirect
153. C2×D4×C61C2×Q8semidirect
194. C2×Dic122D8semidirect
243. C2×#92418C2×Q8semidirect
310. D244C22⋊Q8semidirect
366. #2023D61semidirect
430. C61#24326semidirect
537. C2×D4Q8×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168404272
C2×#168400402
C2×#168398422
#214507392
#214471462
#214471442
#214469532
#214467782
#214467532
#214461702
#214461642
#214460692
#214460672
#214458182
C61×#20232
#2432661