Finite Group Databasebeta

← #29722307

Subgroups — #29722307

Order 15616.

990 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840007C211yesmaximal, characteristic, complemented
2C2×#16839989C211yesmaximal, characteristic, complemented
3C2×#16839830C211yesmaximal, characteristic, complemented
4C2×#16839798C211yesmaximal, characteristic, complemented
5#21449242C211yesmaximal, characteristic, complemented
6#21449238C211yesmaximal, characteristic
7#21447201C211yesmaximal, characteristic, complemented
8#21447189C211yesmaximal, characteristic, complemented
9#21447018C211yesmaximal, characteristic, complemented
10#21447006C211yesmaximal, characteristic, complemented
11#21446701C211yesmaximal, characteristic, complemented
12#21446556C211yesmaximal, characteristic, complemented
13#21446129C211yesmaximal, characteristic, complemented
14#21445851C211yesmaximal, characteristic, complemented
15C61×#1875C211yesmaximal, characteristic, complemented
16C22×#11758200C2211yescharacteristic
17C22×#11758189C2211yescharacteristic
18C23×#92418C2211yescharacteristic
19C2×#14519757C2211yescharacteristic
20C2×#14519756C2211yescharacteristic
21C2×#14519748C2211yescharacteristic
22C2×C4×C22⋊D61C2211yescharacteristic
23C2×#14519736C2211yescharacteristic
24#16840007—24no—
25#16839989—24no—
26#16839830—24no—
27#16839798—24no—
28C2×#14519710C2211yescharacteristic
29C2×#14519710C2211yescharacteristic
30C2×#14519708C2211yescharacteristic
31C2×#14519708C2211yescharacteristic
32C2×#14519708C2211yescharacteristic
33C2×#14519706C2211yescharacteristic
34C2×#14519702C2211yescharacteristic
35C2×#14519702C2211yescharacteristic
36C2×#14519700C2211yescharacteristic
37C2×#14519698C2211yescharacteristic
38C2×#14519689C2211yescharacteristic
39C2×#14519687C2211yescharacteristic
40#16839687—21no—
41#16839678—21no—
42#16839676—21no—
43#16839670—21no—
44#16839667C2211yescharacteristic
45#16839665C2211yescharacteristic
46#16839662—21no—
47#16839661C2211yescharacteristic
48#16839660—21no—
49#16839658C2211yescharacteristic
50#16839656—21no—
51#16839653—21no—
52#16839619C2211yescharacteristic
53#16839619C2211yescharacteristic
54#16839525C2211yescharacteristic
55#16839525C2211yescharacteristic
56C2×#121×C61C2211yescharacteristic
57C2×#117×C61C2211yescharacteristic
58C2×#102×C61C2211yescharacteristic
59C2×#102×C61C2211yescharacteristic
60C2×C22⋊C8×C61C2211yescharacteristic
61C61×#340C2211yescharacteristic
62C61×#340C2211yescharacteristic
63C22×Dic122C2311yescharacteristic
64C22×C22⋊D61—21no—
65C22×C22⋊D61D411yescharacteristic
66C22×C4×D61C2311yescharacteristic
67C2×#11758200—22no—
68C2×#11758200—22no—
69C2×#11758200—22no—
70C2×#11758189—22no—
71C2×#11758189—22no—
72C2×#11758189—22no—
73C22×#92418—22no—
74C22×#92418—22no—
75C22×#92418D414yescomplemented
76C22×#92418C2311yescharacteristic
77C22×#92418C2311yescharacteristic
78#14519757—22no—
79#14519757—41no—
80#14519756—22no—
81#14519756—22no—
82#14519748—22no—
83#14519748—41no—
84C4×C22⋊D61—22no—
85C4×C22⋊D61—22no—
86#14519736—22no—
87#14519736—41no—
88C2×C4⋊Dic61—21no—
89C2×C4⋊Dic61—21no—
90C2×C4⋊Dic61C2311yescharacteristic
91C2×C4⋊Dic61C2311yescharacteristic
92C2×C4⋊Dic61C2311yescharacteristic
93C2×#11758196—21no—
94C2×#11758196—21no—
95C2×#11758196D411yescharacteristic
96C2×C22⋊Dic61—21no—
97C2×C22⋊Dic61—21no—
98C2×C22⋊Dic61—21no—
99C2×C22⋊Dic61—21no—
100C2×C22⋊Dic61—21no—
101C2×C22⋊Dic61D411yescharacteristic
102C2×#11758198—21no—
103C2×#11758198—21no—
104C2×#11758198—21no—
105C2×#11758198D411yescharacteristic
106C2×C4×Dic61—21no—
107C2×C4×Dic61C2311yescharacteristic
108#14519710—22no—
109#14519710D414yescomplemented
110#14519708—22no—
111#14519708—22no—
112#14519708—22no—
113#14519706—22no—
114#14519702—22no—
115#14519702—41no—
116#14519700—22no—
117#14519698—22no—
118#14519689—22no—
119#14519687—22no—
120#14519684—21no—
121#14519684—21no—
122#14519684—21no—
123#14519684—21no—
124#14519684—21no—
125#14519684—21no—
126C22×D4×C61—21no—
127C22×D4×C61C2311yescharacteristic
128C23×C4×C61C2311yescharacteristic
129C22×C8×C61C2311yescharacteristic
130C22×C8×C61C2311yescharacteristic
131#121×C61—22no—
132#121×C61—22no—
133#117×C61—22no—
134#117×C61—41no—
135C2×C4⋊C4×C61C2311yescharacteristic
136C2×C4⋊C4×C61C2311yescharacteristic
137C2×C4⋊C4×C61C2311yescharacteristic
138C2×C22⋊C4×C61—21no—
139C2×C22⋊C4×C61—21no—
140C2×C42×C61—21no—
141#102×C61—22no—
142#102×C61—41no—
143C22⋊C8×C61—22no—
144C24×C61—21no—
145C24×C61C2×D411yescharacteristic
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×C61—21no—
153C2×D4×C61—42no—
154C2×D4×C61—81no—
155C2×D4×C61—81no—
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61—21no—
159C22×C4×C61—21no—
160C22×C4×C61—21no—
161C22×C4×C61—21no—
162C22×C4×C61—21no—
163C22×C4×C61C2×D411yescharacteristic
164C22×C4×C61C2×D412yes—
165C22×C4×C61#4112yes—
166C22×C4×C61C2411yescharacteristic
167C2×C22⋊D61—22no—
168C2×C22⋊D61—41no—
169C2×C22⋊D61—41no—
170C2×C22⋊D61—42no—
171C2×C22⋊D61—42no—
172C2×C22⋊D61—81no—
173C22×Dic61—21no—
174C22×Dic61—21no—
175C22×Dic61—21no—
176C22×Dic61—21no—
177C22×Dic61C2×D411yescharacteristic
178C22×Dic61C2×D411yescharacteristic
179C22×Dic61C2×D411yescharacteristic
180C2×C4×D61—21no—
181C2×C4×D61—21no—
182C2×C4×D61—21no—
183C2×C4×D61—21no—
184C2×C4×D61—21no—
185C2×C4×D61—21no—
186C2×Dic122—21no—
187C2×Dic122—21no—
188C2×Dic122—21no—
189C2×Dic122—21no—
190C2×Dic122—21no—
191C2×Dic122—21no—
192C2×C8×C61—21no—
193C2×C8×C61—21no—
194C2×C8×C61—21no—
195C2×C8×C61—21no—
196C2×C8×C61—21no—
197C2×C8×C61—21no—
198C4⋊C4×C61—21no—
199C4⋊C4×C61—21no—
200C4⋊C4×C61—21no—
201C4⋊C4×C61—21no—
202C4⋊C4×C61—21no—
203C4⋊C4×C61C2×D412yes—
204C22⋊C4×C61—42no—
205C22⋊C4×C61—42no—
206C42×C61—42no—
207C22⋊Dic61—22no—
208C22⋊Dic61—42no—
209C22⋊Dic61—42no—
210C22⋊Dic61—42no—
211C22⋊Dic61—42no—
212C22⋊Dic61—81no—
213#11758200—44no—
214#11758198—22no—
215#11758198—42no—
216#11758198—42no—
217#11758198—81no—
218C4⋊Dic61—21no—
219C4⋊Dic61—21no—
220C4⋊Dic61—21no—
221C4⋊Dic61—21no—
222C4⋊Dic61—21no—
223C4⋊Dic61—42no—
224C4⋊Dic61—42no—
225C4⋊Dic61C2×D412yes—
226#11758196—22no—
227#11758196—42no—
228#11758196—81no—
229C4×Dic61—21no—
230C4×Dic61—21no—
231C4×Dic61—42no—
232C2×#92418—21no—
233C2×#92418—21no—
234C2×#92418—28no—
235C2×#92418C2×D412yes—
236C2×#92418C2×D412yes—
237C2×#92418C2×D412yes—
238C2×#92418#4112yes—
239#11758189—44no—
240C23×C61—21no—
241C23×C61—21no—
242C23×C61—21no—
243C23×C61—21no—
244C23×C61—21no—
245C23×C61—21no—
246C23×C61—41no—
247C23×C61—41no—
248C23×C61—41no—
249C23×C61—41no—
250C23×C61—41no—
251C23×C61—41no—
252C23×C61—41no—
253C23×C61#12112yes—
254C23×C61C22×D411yescharacteristic
255C22×D61—21no—
256C22×D61—21no—
257C22×D61—21no—
258C22×D61—21no—
259C22×D61—21no—
260C22×D61—21no—
261C22×D61—21no—
262D4×C61—41no—
263D4×C61—41no—
264D4×C61—41no—
265D4×C61—41no—
266D4×C61—84no—
267C2×C4×C61—21no—
268C2×C4×C61—21no—
269C2×C4×C61—22no—
270C2×C4×C61—22no—
271C2×C4×C61—22no—
272C2×C4×C61—22no—
273C2×C4×C61—22no—
274C2×C4×C61—41no—
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#12112yes—
283C2×C4×C61C22×D411yescharacteristic
284C2×C4×C61C22×D411yescharacteristic
285C2×C4×C61C2×#4111yescharacteristic
286C2×C4×C61C2×#4111yescharacteristic
287C2×C4×C61H(5,𝔽2)11yescharacteristic
288C2×C4×C612−1+411yescharacteristic
289C22⋊D61—44no—
290C22⋊D61—84no—
291C2×Dic61—21no—
292C2×Dic61—21no—
293C2×Dic61—21no—
294C2×Dic61—22no—
295C2×Dic61—21no—
296C2×Dic61—21no—
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×Dic61—41no—
310C2×Dic61—41no—
311C2×Dic61—41no—
312C4×D61—41no—
313C4×D61—41no—
314C4×D61—41no—
315C4×D61—41no—
316Dic122—41no—
317Dic122—41no—
318Dic122—41no—
319Dic122—41no—
320C8×C61—41no—
321C8×C61—41no—
322#92418—22no—
323#92418#12114yes—
324#24786—611nomaximal, Sylow
325C22×C61—22no—
326C22×C61—22no—
327C22×C61—22no—
328C22×C61—41no—
329C22×C61—41no—
330C22×C61—41no—
331C22×C61—41no—
332C22×C61—81no—
333C22×C61—81no—
334C22×C61—81no—
335C22×C61—81no—
336C22×C61—81no—
337C22×C61—81no—
338C22×C61—81no—
339C22×C61C2×#12111yescharacteristic
340C22×C61D4211yescharacteristic
341C22×C61#54711yescharacteristic
342C22×C61#57511yescharacteristic
343C22×C61#57511yescharacteristic
344C22×C61#57711yescharacteristic
345C22×C61#57711yescharacteristic
346C2×D61—41no—
347C2×D61—41no—
348C2×D61—41no—
349C2×D61—41no—
350C2×D61—41no—
351C2×D61—41no—
352C2×D61—41no—
353C4×C61—22no—
354C4×C61—42no—
355C4×C61—81no—
356C4×C61—81no—
357C4×C61C2×#12111yescharacteristic
358C4×C61#53711yescharacteristic
359C4×C61#54811yescharacteristic
360C4×C61#55311yescharacteristic
361Dic61—41no—
362Dic61—42no—
363Dic61—41no—
364Dic61—41no—
365Dic61—81no—
366Dic61—81no—
367Dic61—81no—
368C2×#468—611no—
369C2×#465—611no—
370C2×#435—611no—
371C2×#427—611no—
372#2415—611no—
373#2414—611no—
374#2066—611no—
375#2065—611no—
376#2035—611no—
377#2034—611no—
378#1973—611no—
379#1943—611no—
380#1875D6111yescharacteristic, complemented
381#1873—611no—
382#1809—611no—
383C2×C61—42no—
384C2×C61—161no—
385C2×C61#241611yescharacteristic
386C2×C61#305411yescharacteristic
387C2×C61#305711yescharacteristic
388C2×C61#326711yescharacteristic
389C2×C61#327111yescharacteristic
390C2×C61#334811yescharacteristic
391C2×C61#335011yescharacteristic
392D61—81no—
393C22×SD16—611no—
394C22×M16—611no—
395C23×C8—611no—
396C2×C22⋊Q8—611no—
397C2×C22⋊Q8—611no—
398C2×#121—611no—
399C2×#121C2×D6111yescharacteristic
400C2×C4×D4—611no—
401C2×#117—611no—
402C2×#117C2×D6111yescharacteristic
403#468—1224no—
404#465—1224no—
405#435—1224no—
406#427—1224no—
407C2×#107—611no—
408C2×#107—611no—
409C2×#106—611no—
410C2×#106—611no—
411C2×#106—611no—
412C2×C4⋊C8—611no—
413C2×#103—611no—
414C2×#103—611no—
415C2×#103—611no—
416C2×#102—611no—
417C2×#102C2×D6111yescharacteristic
418C2×#102C2×D6111yescharacteristic
419C2×C22⋊C8—611no—
420C2×C22⋊C8C2×D6111yescharacteristic
421C2×#97—611no—
422#397—1221no—
423#394—1221no—
424#394—1221no—
425#392—1221no—
426#391—611no—
427#390—611no—
428#390—1221no—
429#389—611no—
430#389—611no—
431#389—1221no—
432#388—1221no—
433#388—1221no—
434#380—611no—
435#380—611no—
436#340—611no—
437#340—611no—
438#340C2×D6111yescharacteristic
439#340C2×D6111yescharacteristic
440C61#2478611yescharacteristic, complemented, Sylow
441C22×Q8—611no—
442C22×D4—21no—
443C22×D4—611no—
444C22×D4—1221no—
445C22×D4C22×D6111yescharacteristic
446C23×C4—611no—
447C23×C4C22×D6111yescharacteristic
448C2×SD16—1222no—
449C2×SD16—1222no—
450C2×SD16—1222no—
451C2×M16—1222no—
452C2×M16—1222no—
453C2×M16—1222no—
454C22×C8—611no—
455C22×C8—614no—
456C22×C8—611no—
457C22×C8—1222no—
458C22×C8—1222no—
459C22×C8C22×D6111yescharacteristic
460C22×C8C22×D6111yescharacteristic
461C22⋊Q8—1222no—
462C22⋊Q8—1222no—
463C22⋊Q8—1222no—
464C22⋊Q8—2441no—
465#121—22no—
466#121—22no—
467#121—1222no—
468#121—2441no—
469C4×D4—1222no—
470C4×D4—1222no—
471#117—22no—
472#117—41no—
473#117—1222no—
474#117—2441no—
475C2×C4⋊C4—611no—
476C2×C4⋊C4—611no—
477C2×C4⋊C4—611no—
478C2×C4⋊C4—611no—
479C2×C4⋊C4—1221no—
480C2×C4⋊C4—1221no—
481C2×C4⋊C4—1221no—
482C2×C4⋊C4—1221no—
483C2×C4⋊C4C22×D6111yescharacteristic
484C2×C4⋊C4C22×D6111yescharacteristic
485C2×C4⋊C4C22×D6111yescharacteristic
486C2×C22⋊C4—21no—
487C2×C22⋊C4—21no—
488C2×C22⋊C4—611no—
489C2×C22⋊C4—611no—
490C2×C22⋊C4—1221no—
491C2×C22⋊C4—1221no—
492C2×C22⋊C4—1221no—
493C2×C22⋊C4—1221no—
494C2×C22⋊C4—1221no—
495C2×C22⋊C4—1221no—
496C2×C22⋊C4—1221no—
497C2×C22⋊C4—1221no—
498C2×C42—21no—
499C2×C42—611no—
500C2×C42—1221no—
501#107—614no—
502#107—1222no—
503#106—1222no—
504#106—1222no—
505#106—1222no—
506C4⋊C8—1222no—
507#103—1222no—
508#103—1222no—
509#103—2441no—
510#102—22no—
511#102—41no—
512#102—1222no—
513C22⋊C8—22no—
514C22⋊C8—1222no—
515#97—1222no—
516#95—1221no—
517#95—1221no—
518#95—1221no—
519#95—1221no—
520#95—1221no—
521#95—1221no—
522C24—21no—
523C24—611no—
524C24D4×D6111yescharacteristic
525C2×Q8—1221no—
526C2×Q8—1221no—
527C2×Q8—1221no—
528C2×Q8—1221no—
529C2×Q8—1221no—
530C2×Q8—1221no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—42no—
538C2×D4—81no—
539C2×D4—81no—
540C2×D4—1222no—
541C2×D4—4881no—
542C2×D4—2442no—
543C2×D4—2441no—
544C2×D4—2441no—
545C2×D4—2442no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—611no—
554C22×C4—611no—
555C22×C4—611no—
556C22×C4—1221no—
557C22×C4—1221no—
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#1175822212yes—
567C22×C4D4×D6112yes—
568C22×C4D4×D6111yescharacteristic
569C22×C4C23×D6111yescharacteristic
570SD16—2444no—
571M16—2444no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—612no—
579C2×C8—612no—
580C2×C8—612no—
581C2×C8—612no—
582C2×C8—1228no—
583C2×C8—1221no—
584C2×C8—1221no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—612no—
591C4⋊C4—1221no—
592C4⋊C4—1222no—
593C4⋊C4—1221no—
594C4⋊C4—1221no—
595C4⋊C4—1221no—
596C4⋊C4—1221no—
597C4⋊C4—4881no—
598C4⋊C4—2442no—
599C4⋊C4—2442no—
600C4⋊C4—2442no—
601C4⋊C4D4×D6112yes—
602C22⋊C4—42no—
603C22⋊C4—42no—
604C22⋊C4—1222no—
605C22⋊C4—1222no—
606C22⋊C4—4881no—
607C22⋊C4—4881no—
608C22⋊C4—2442no—
609C22⋊C4—2442no—
610C22⋊C4—2442no—
611C22⋊C4—2442no—
612C22⋊C4—2442no—
613C22⋊C4—2442no—
614C42—42no—
615C42—1221no—
616C42—1221no—
617C42—2442no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—1221no—
632C23—1221no—
633C23—1221no—
634C23—1221no—
635C23—1221no—
636C23—1221no—
637C23—1221no—
638C23#1451975012yes—
639C23C2×D4×D6111yescharacteristic
640Q8—2441no—
641Q8—2441no—
642Q8—2441no—
643Q8—2441no—
644D4—41no—
645D4—41no—
646D4—41no—
647D4—41no—
648D4—84no—
649D4—4884no—
650D4—2444no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—1221no—
667C2×C4—1221no—
668C2×C4—1221no—
669C2×C4—1221no—
670C2×C4—1221no—
671C2×C4—1221no—
672C2×C4—1221no—
673C2×C4—1222no—
674C2×C4—1221no—
675C2×C4—1221no—
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×C4—2441no—
686C2×C4—2441no—
687C2×C4—2441no—
688C2×C4—2441no—
689C2×C4—2441no—
690C2×C4—2441no—
691C2×C4#1451975012yes—
692C2×C4C2×D4×D6111yescharacteristic
693C2×C4C2×D4×D6111yescharacteristic
694C2×C4#41×D6111yescharacteristic
695C2×C4C2×#1175822211yescharacteristic
696C2×C4#1451982211yescharacteristic
697C2×C4#1451982411yescharacteristic
698C8—41no—
699C8—41no—
700C8—614no—
701C8—1222no—
702C22—22no—
703C22—22no—
704C22—22no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—81no—
710C22—81no—
711C22—81no—
712C22—81no—
713C22—81no—
714C22—81no—
715C22—81no—
716C22—2441no—
717C22—2441no—
718C22—2441no—
719C22—2441no—
720C22—2441no—
721C22—2441no—
722C22—2441no—
723C22C2×#1451975011yescharacteristic
724C22#1684039411yescharacteristic
725C22#1684041011yescharacteristic
726C22#1684055911yescharacteristic
727C22#1684055911yescharacteristic
728C22#1684057211yescharacteristic
729C22#1684057211yescharacteristic
730C4—22no—
731C4—42no—
732C4—81no—
733C4—81no—
734C4—4881no—
735C4—4881no—
736C4—4881no—
737C4—2441no—
738C4—2441no—
739C4—2441no—
740C4—2442no—
741C4#121×D6111yescharacteristic
742C4#1684033911yescharacteristic
743C4#1684042111yescharacteristic
744C4#1684046111yescharacteristic
745C2—42no—
746C2—161no—
747C2—4881no—
748C2#2144925811yescharacteristic
749C2#2145542711yescharacteristic
750C2#2145545711yescharacteristic
751C2#2145733711yescharacteristic
752C2#2145739711yescharacteristic
753C2#2145833211yescharacteristic
754C2#2145836811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1875C2
socleC23×C61C22×D4
prime radical#21449238C2
hypercenter#1875D61
hypocenterC61#24786
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1875

Complements

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

NH ≅ G/Ntype
1. C2×#16840007C2semidirect
2. C2×#16839989C2semidirect
3. C2×#16839830C2semidirect
4. C2×#16839798C2semidirect
5. #21449242C2semidirect
7. #21447201C2semidirect
8. #21447189C2semidirect
9. #21447018C2semidirect
10. #21447006C2semidirect
11. #21446701C2semidirect
12. #21446556C2semidirect
13. #21446129C2semidirect
14. #21445851C2semidirect
15. C61×#1875C2semidirect
75. C22×#92418D4semidirect
109. #14519710D4semidirect
380. #1875D61semidirect
440. C61#24786semidirect

Maximal subgroups

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

subgroupindex
C2×#168400072
C2×#168399892
C2×#168398302
C2×#168397982
#214492422
#214492382
#214472012
#214471892
#214470182
#214470062
#214467012
#214465562
#214461292
#214458512
C61×#18752
#2478661