Finite Group Databasebeta

← #29718852

Subgroups — #29718852

Order 15616.

1056 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839915C211yesmaximal, characteristic
2#21451616C211yesmaximal, characteristic, complemented
3#21448399C211yesmaximal, characteristic
4#21447206C211yesmaximal, characteristic, complemented
5#21447192C211yesmaximal, characteristic, complemented
6#21447137C211yesmaximal, characteristic, complemented
7#21447137C211yesmaximal, characteristic, complemented
8#21446700C211yesmaximal, characteristic, complemented
9#21446673C211yesmaximal, characteristic, complemented
10#21446516C211yesmaximal, characteristic, complemented
11#21446502C211yesmaximal, characteristic, complemented
12#21446129C211yesmaximal, characteristic, complemented
13#21446020C211yesmaximal, characteristic, complemented
14#21445751C211yesmaximal, characteristic
15C2×C61×#433C211yesmaximal, characteristic, complemented
16C23×D244C2211yescharacteristic
17C22×#11758190C2211yescharacteristic
18C22×#11758190C2211yescharacteristic
19C2×#14519756C2211yescharacteristic
20C2×#14519736C2211yescharacteristic
21#16839915—24no—
22C2×#14519711C2211yescharacteristic, complemented
23C2×#14519709C2211yescharacteristic, complemented
24C2×#14519702C2211yescharacteristic, complemented
25C2×#14519702C2211yescharacteristic, complemented
26C2×#14519699C2211yescharacteristic
27C2×#14519699C2211yescharacteristic
28C2×#14519699C2211yescharacteristic
29C2×#14519699C2211yescharacteristic
30C2×#14519699C2211yescharacteristic
31C2×#14519699C2211yescharacteristic
32#16839700—21no—
33#16839693—21no—
34#16839690—21no—
35#16839690—21no—
36#16839668C2211yescharacteristic, complemented
37#16839668C2211yescharacteristic, complemented
38#16839664C2211yescharacteristic
39#16839664C2211yescharacteristic
40#16839664C2211yescharacteristic
41#16839664C2211yescharacteristic
42#16839663—21no—
43#16839663—21no—
44#16839660C2211yescharacteristic, complemented
45#16839660C2211yescharacteristic, complemented
46#16839622C2211yescharacteristic
47#16839617—21no—
48#16839617—21no—
49#16839525C2211yescharacteristic, complemented
50#16839525C2211yescharacteristic, complemented
51#16839525C2211yescharacteristic, complemented
52#16839525C2211yescharacteristic, complemented
53C2×#117×C61C2211yescharacteristic
54C61×#433—24no—
55C2×C4⋊C8×C61C2211yescharacteristic, complemented
56C2×C4⋊C8×C61C2211yescharacteristic, complemented
57C2×C22⋊C8×C61C2211yescharacteristic
58C2×C22⋊C8×C61C2211yescharacteristic
59C2×#97×C61C2211yescharacteristic, complemented
60C2×C4×C8×C61C2211yescharacteristic, complemented
61C24×D61—21no—
62C22×Dic122C2311yescharacteristic
63C22×D244—21no—
64C22×D244—22no—
65C22×D244—22no—
66C22×D244—22no—
67C22×D244—22no—
68C22×D244—41no—
69C22×D244—41no—
70C22×D244C2311yescharacteristic
71C22×D244C2311yescharacteristic
72C2×#11758190—22no—
73C2×#11758190—22no—
74C2×#11758190—22no—
75C2×#11758190—22no—
76C2×#11758190—41no—
77C2×#11758190—41no—
78#14519756—22no—
79#14519756—22no—
80#14519736—41no—
81#14519736—41no—
82C2×C4⋊Dic61C2311yescharacteristic
83C2×C4⋊Dic61C2311yescharacteristic
84C2×C4⋊Dic61C2311yescharacteristic
85C2×C4⋊Dic61C2311yescharacteristic
86C2×C4⋊Dic61C2311yescharacteristic
87C2×#11758196—21no—
88C2×#11758196—21no—
89C2×#11758196—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×#11758198—21no—
98C2×#11758198—21no—
99C2×#11758198—21no—
100C2×#11758198—21no—
101C2×C4×Dic61—21no—
102#14519711—41no—
103#14519709—41no—
104#14519702—41no—
105#14519702—41no—
106#14519699—22no—
107#14519699—22no—
108#14519699—22no—
109#14519699—22no—
110#14519699—41no—
111#14519699—41no—
112#14519684—21no—
113#14519684—21no—
114#14519684—21no—
115#14519684—21no—
116#14519684—21no—
117#14519684—21no—
118#14519684—21no—
119C23×C4×C61C2311yescharacteristic
120C22×C8×C61C2311yescharacteristic
121C22×C8×C61C2311yescharacteristic
122C22×C8×C61C2311yescharacteristic
123C22×C8×C61C2311yescharacteristic
124#117×C61—22no—
125#117×C61—22no—
126C2×C4⋊C4×C61D411yescharacteristic
127C2×C4⋊C4×C61D411yescharacteristic
128C2×C22⋊C4×C61D411yescharacteristic
129C2×C22⋊C4×C61D411yescharacteristic
130C2×C42×C61C2311yescharacteristic
131C2×C42×C61C2311yescharacteristic
132C4⋊C8×C61—22no—
133C4⋊C8×C61—22no—
134C22⋊C8×C61—22no—
135C22⋊C8×C61D414yes—
136#97×C61—22no—
137C4×C8×C61—22no—
138C24×C61C2×D411yescharacteristic
139C23×D61—21no—
140C23×D61—21no—
141C23×D61—24no—
142C23×D61—42no—
143C23×D61—42no—
144C23×D61—81no—
145C23×D61—81no—
146C23×D61—81no—
147C23×D61—81no—
148C22×C4×C61—21no—
149C22×C4×C61—21no—
150C22×C4×C61—21no—
151C22×C4×C61—21no—
152C22×C4×C61C2×D411yescharacteristic
153C22×C4×C61C2×D411yescharacteristic
154C22×C4×C61C2×D411yescharacteristic
155C22×C4×C61C2×D411yescharacteristic
156C22×C4×C61C2×D411yescharacteristic
157C22×C4×C61C2×D412yes—
158C22×C4×C61#4112yes—
159C22×C4×C61C2411yescharacteristic
160C22×Dic61—21no—
161C22×Dic61—21no—
162C22×Dic61—21no—
163C22×Dic61—21no—
164C22×Dic61—21no—
165C22×Dic61—21no—
166C2×D244—21no—
167C2×D244—21no—
168C2×D244—21no—
169C2×D244—21no—
170C2×D244—21no—
171C2×D244—21no—
172C2×D244—21no—
173C2×D244—21no—
174C2×D244—24no—
175C2×D244—21no—
176C2×D244—21no—
177C2×D244—44no—
178C2×D244—44no—
179C2×D244—44no—
180C2×D244—44no—
181C2×D244—42no—
182C2×D244—42no—
183C2×D244#4112yes—
184C2×D244#4112yes—
185C2×Dic122—21no—
186C2×Dic122—21no—
187C2×Dic122—21no—
188C2×Dic122—21no—
189C2×Dic122—21no—
190C2×Dic122—21no—
191C2×C8×C61—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—
198C2×C8×C61—21no—
199C2×C8×C61—21no—
200C2×C8×C61—21no—
201C2×C8×C61C2×D412yes—
202C2×C8×C61C2×D412yes—
203C4⋊C4×C61—22no—
204C4⋊C4×C61—22no—
205C22⋊C4×C61—22no—
206C22⋊C4×C61—22no—
207C42×C61—21no—
208C42×C61—21no—
209C42×C61—21no—
210C42×C61—21no—
211C22⋊Dic61—42no—
212C22⋊Dic61—42no—
213C22⋊Dic61—81no—
214#11758198—81no—
215#11758198—81no—
216#11758198—81no—
217#11758198—81no—
218#11758198—81no—
219#11758198—81no—
220#11758198—81no—
221#11758198—81no—
222C4⋊Dic61—21no—
223C4⋊Dic61—21no—
224C4⋊Dic61—21no—
225C4⋊Dic61—21no—
226C4⋊Dic61—21no—
227C4⋊Dic61—21no—
228C4⋊Dic61—21no—
229C4⋊Dic61—21no—
230C4⋊Dic61—21no—
231C4⋊Dic61—21no—
232#11758196—42no—
233#11758196—81no—
234#11758196—81no—
235C4×Dic61—42no—
236#11758190—44no—
237#11758190—44no—
238C23×C61—21no—
239C23×C61—21no—
240C23×C61—21no—
241C23×C61—21no—
242C23×C61—21no—
243C23×C61—21no—
244C23×C61#12112yes—
245C23×C61C22×D411yescharacteristic
246C22×D61—22no—
247C22×D61—22no—
248C22×D61—48no—
249C22×D61—41no—
250C22×D61—41no—
251C22×D61—41no—
252C22×D61—41no—
253C22×D61—41no—
254C22×D61—41no—
255C22×D61—41no—
256C22×D61—41no—
257C22×D61—41no—
258C22×D61—41no—
259C22×D61—41no—
260C22×D61—41no—
261C22×D61—84no—
262C22×D61—84no—
263C22×D61—84no—
264C22×D61—84no—
265C22×D61—84no—
266C22×D61—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—21no—
274C2×C4×C61—21no—
275C2×C4×C61—21no—
276C2×C4×C61—21no—
277C2×C4×C61—21no—
278C2×C4×C61—21no—
279C2×C4×C61—21no—
280C2×C4×C61—21no—
281C2×C4×C61—21no—
282C2×C4×C61—21no—
283C2×C4×C61—21no—
284C2×C4×C61—21no—
285C2×C4×C61#12112yes—
286C2×C4×C61C22×D411yescharacteristic
287C2×C4×C61C2×#4111yescharacteristic
288C2×C4×C61C2×#4111yescharacteristic
289C2×C4×C61C2×#4111yescharacteristic
290C2×C4×C61H(5,𝔽2)11yescharacteristic
291C2×C4×C61H(5,𝔽2)11yescharacteristic
292C2×Dic61—41no—
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—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—
310D244—22no—
311D244—22no—
312D244—22no—
313D244—22no—
314D244—48no—
315D244—41no—
316D244—41no—
317D244—41no—
318D244—41no—
319Dic122—41no—
320Dic122—41no—
321Dic122—41no—
322Dic122—41no—
323C8×C61—22no—
324C8×C61—22no—
325C8×C61—41no—
326C8×C61—41no—
327#24516—611nomaximal, Sylow
328C22×C61—22no—
329C22×C61—22no—
330C22×C61—22no—
331C22×C61—41no—
332C22×C61—41no—
333C22×C61—41no—
334C22×C61—41no—
335C22×C61C2×#12111yescharacteristic
336C22×C61#52511yescharacteristic
337C22×C61#53511yescharacteristic
338C22×C61#57611yescharacteristic
339C22×C61#57711yescharacteristic
340C22×C61#57711yescharacteristic
341C22×C61#57711yescharacteristic
342C2×D61—42no—
343C2×D61—42no—
344C2×D61—42no—
345C2×D61—42no—
346C2×D61—42no—
347C2×D61—42no—
348C2×D61—816no—
349C2×D61—81no—
350C2×D61—81no—
351C2×D61—81no—
352C2×D61—81no—
353C2×D61—81no—
354C2×D61—81no—
355C2×D61—81no—
356C2×D61—81no—
357C4×C61—22no—
358C4×C61—41no—
359C4×C61—41no—
360C4×C61—41no—
361C4×C61—41no—
362C4×C61#54611yescharacteristic
363C4×C61#54611yescharacteristic
364C4×C61#55111yescharacteristic
365C4×C61#55111yescharacteristic
366Dic61—81no—
367Dic61—81no—
368Dic61—81no—
369Dic61—81no—
370Dic61—81no—
371Dic61—81no—
372C2×#450—611no—
373C2×#433D6111yescharacteristic, complemented
374#2625—611no—
375#2309—611no—
376#2067—611no—
377#2065—611no—
378#2055—611no—
379#2055—611no—
380#1973—611no—
381#1968—611no—
382#1936—611no—
383#1934—611no—
384#1873—611no—
385#1854—611no—
386#1786—611no—
387C2×C61—42no—
388C2×C61#241111yescharacteristic
389C2×C61#305711yescharacteristic
390C2×C61#306211yescharacteristic
391C2×C61#311811yescharacteristic
392C2×C61#312311yescharacteristic
393C2×C61#322211yescharacteristic
394C2×C61#322411yescharacteristic
395D61—82no—
396D61—82no—
397C23×D4—611no—
398C22×SD16—611no—
399C22×SD16—611no—
400C2×C22⋊Q8—611no—
401C2×#117—611no—
402C2×#117C2×D6111yescharacteristic
403#450—1224no—
404#433—24no—
405C2×#107—611no—
406C2×#106—611no—
407C2×C4⋊C8C2×D6111yescharacteristic, complemented
408C2×C4⋊C8C2×D6111yescharacteristic, complemented
409C2×#103—611no—
410C2×#103—611no—
411C2×#102—611no—
412C2×#102—611no—
413C2×#102—611no—
414C2×#102—611no—
415C2×#102—611no—
416C2×#102—611no—
417C2×C22⋊C8C2×D6111yescharacteristic
418C2×C22⋊C8C2×D6111yescharacteristic
419C2×#97C2×D6111yescharacteristic, complemented
420C2×C4×C8C2×D6111yescharacteristic, complemented
421#400—1221no—
422#398—1221no—
423#397—1221no—
424#397—1221no—
425#391—611no—
426#391—611no—
427#390—611no—
428#390—611no—
429#390—611no—
430#390—611no—
431#390—1221no—
432#390—1221no—
433#389—611no—
434#389—611no—
435#380—611no—
436#379—1221no—
437#379—1221no—
438#340—611no—
439#340—611no—
440#340—611no—
441#340—611no—
442C61#2451611yescharacteristic, complemented, Sylow
443C25—1221no—
444C22×Q8—611no—
445C22×D4—611no—
446C22×D4—611no—
447C22×D4—1222no—
448C22×D4—1222no—
449C22×D4—1221no—
450C22×D4—1222no—
451C22×D4—1222no—
452C22×D4—2441no—
453C22×D4—2441no—
454C23×C4C22×D6111yescharacteristic
455C2×SD16—1222no—
456C2×SD16—1222no—
457C2×SD16—1222no—
458C2×SD16—1222no—
459C2×SD16—2441no—
460C2×SD16—2441no—
461C22×C8C22×D6111yescharacteristic
462C22×C8C22×D6111yescharacteristic
463C22×C8C22×D6111yescharacteristic
464C22×C8C22×D6111yescharacteristic
465C22⋊Q8—1222no—
466C22⋊Q8—1222no—
467#117—22no—
468#117—22no—
469#117—2441no—
470#117—2441no—
471C2×C4⋊C4—611no—
472C2×C4⋊C4—611no—
473C2×C4⋊C4—611no—
474C2×C4⋊C4—611no—
475C2×C4⋊C4—611no—
476C2×C4⋊C4—1221no—
477C2×C4⋊C4—1221no—
478C2×C4⋊C4—1221no—
479C2×C4⋊C4D24411yescharacteristic
480C2×C4⋊C4D24411yescharacteristic
481C2×C22⋊C4—1221no—
482C2×C22⋊C4—1221no—
483C2×C22⋊C4—1221no—
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—1221no—
492C2×C22⋊C4D24411yescharacteristic
493C2×C22⋊C4D24411yescharacteristic
494C2×C42—1221no—
495C2×C42C22×D6111yescharacteristic
496C2×C42C22×D6111yescharacteristic
497#107—2441no—
498#106—2441no—
499C4⋊C8—22no—
500C4⋊C8—22no—
501#103—2441no—
502#103—2441no—
503#102—1222no—
504#102—1222no—
505#102—1222no—
506#102—1222no—
507#102—2441no—
508#102—2441no—
509C22⋊C8—22no—
510C22⋊C8C22⋊D6114yes—
511#97—22no—
512C4×C8—22no—
513#95—1221no—
514#95—1221no—
515#95—1221no—
516#95—1221no—
517#95—1221no—
518#95—1221no—
519#95—1221no—
520C24—1224no—
521C24—1221no—
522C24—1221no—
523C24—4881no—
524C24—4881no—
525C24—4881no—
526C24—4881no—
527C24—2442no—
528C24—2442no—
529C24C2×D24411yescharacteristic
530C2×Q8—1221no—
531C2×Q8—1221no—
532C2×Q8—1221no—
533C2×Q8—1221no—
534C2×Q8—1221no—
535C2×Q8—1221no—
536C2×D4—612no—
537C2×D4—612no—
538C2×D4—1224no—
539C2×D4—1221no—
540C2×D4—1221no—
541C2×D4—1221no—
542C2×D4—1221no—
543C2×D4—1221no—
544C2×D4—1221no—
545C2×D4—1221no—
546C2×D4—1221no—
547C2×D4—1221no—
548C2×D4—1221no—
549C2×D4—2444no—
550C2×D4—2444no—
551C2×D4—2444no—
552C2×D4—2444no—
553C2×D4—2442no—
554C2×D4—2442no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—1221no—
560C22×C4—1221no—
561C22×C4—1221no—
562C22×C4—1221no—
563C22×C4—1221no—
564C22×C4—1221no—
565C22×C4C2×D24411yescharacteristic
566C22×C4C2×D24411yescharacteristic
567C22×C4C2×D24411yescharacteristic
568C22×C4C2×D24411yescharacteristic
569C22×C4C2×D24411yescharacteristic
570C22×C4#1175822212yes—
571C22×C4C2×C22⋊D6112yes—
572C22×C4C23×D6111yescharacteristic
573SD16—2444no—
574SD16—2444no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8C2×C22⋊D6112yes—
586C2×C8C2×C22⋊D6112yes—
587C4⋊C4—22no—
588C4⋊C4—22no—
589C4⋊C4—1221no—
590C4⋊C4—1221no—
591C4⋊C4—1221no—
592C4⋊C4—1221no—
593C4⋊C4—1221no—
594C4⋊C4—1221no—
595C4⋊C4—1221no—
596C4⋊C4—1221no—
597C4⋊C4—1221no—
598C4⋊C4—1221no—
599C4⋊C4—4881no—
600C4⋊C4—4881no—
601C4⋊C4—2442no—
602C22⋊C4—22no—
603C22⋊C4—22no—
604C22⋊C4—4881no—
605C22⋊C4—4881no—
606C22⋊C4—4881no—
607C22⋊C4—4881no—
608C22⋊C4—4881no—
609C22⋊C4—4881no—
610C22⋊C4—4881no—
611C22⋊C4—4881no—
612C22⋊C4—4881no—
613C22⋊C4—2442no—
614C22⋊C4—2442no—
615C42—21no—
616C42—21no—
617C42—21no—
618C42—21no—
619C42—2442no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—1222no—
627C23—1222no—
628C23—4884no—
629C23—4884no—
630C23—4884no—
631C23—4884no—
632C23—4884no—
633C23—4884no—
634C23—2448no—
635C23—2441no—
636C23—2441no—
637C23—2441no—
638C23—2441no—
639C23—2441no—
640C23—2441no—
641C23—2441no—
642C23—2441no—
643C23—2441no—
644C23—2441no—
645C23—2441no—
646C23—2441no—
647C23#1451975112yes—
648C23C22×D24411yescharacteristic
649Q8—2441no—
650Q8—2441no—
651Q8—2441no—
652Q8—2441no—
653D4—1222no—
654D4—1222no—
655D4—1222no—
656D4—1222no—
657D4—2448no—
658D4—2441no—
659D4—2441no—
660D4—2441no—
661D4—2441no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
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—2441no—
692C2×C4—2441no—
693C2×C4—2441no—
694C2×C4—2441no—
695C2×C4—2441no—
696C2×C4—2441no—
697C2×C4—2441no—
698C2×C4#1451975112yes—
699C2×C4C22×C22⋊D6111yescharacteristic
700C2×C4#41×D6111yescharacteristic
701C2×C4#41×D6111yescharacteristic
702C2×C4C2×#1175822211yescharacteristic
703C2×C4#1451982311yescharacteristic
704C2×C4#1451982311yescharacteristic
705C8—22no—
706C8—22no—
707C8—41no—
708C8—41no—
709C22—22no—
710C22—22no—
711C22—22no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—48816no—
717C22—4881no—
718C22—4881no—
719C22—4881no—
720C22—4881no—
721C22—4881no—
722C22—4881no—
723C22—4881no—
724C22—4881no—
725C22—2442no—
726C22—2442no—
727C22—2442no—
728C22—2442no—
729C22—2442no—
730C22—2442no—
731C22C2×#1451975111yescharacteristic
732C22#1684027411yescharacteristic
733C22#1684033111yescharacteristic
734C22#1684056711yescharacteristic
735C22#1684057411yescharacteristic
736C22#1684057411yescharacteristic
737C22#1684057411yescharacteristic
738C4—22no—
739C4—41no—
740C4—41no—
741C4—41no—
742C4—41no—
743C4—4881no—
744C4—4881no—
745C4—4881no—
746C4—4881no—
747C4—4881no—
748C4—4881no—
749C4#1684040011yescharacteristic
750C4#1684040011yescharacteristic
751C4#1684043611yescharacteristic
752C4#1684043611yescharacteristic
753C2—42no—
754C2—4882no—
755C2—4882no—
756C2#2144919811yescharacteristic
757C2#2145545811yescharacteristic
758C2#2145549911yescharacteristic
759C2#2145600511yescharacteristic
760C2#2145607211yescharacteristic
761C2#2145689311yescharacteristic
762C2#2145691511yescharacteristic
subgroupG/H
centerC23C22×D244
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#433C2
socleC23×C61C22×D4
prime radicalC23×D244C22
hypercenterC2×#433D61
hypocenterC61#24516
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
2. #21451616C2semidirect
4. #21447206C2semidirect
5. #21447192C2semidirect
6. #21447137C2semidirect
7. #21447137C2semidirect
8. #21446700C2semidirect
9. #21446673C2semidirect
10. #21446516C2semidirect
11. #21446502C2semidirect
12. #21446129C2semidirect
13. #21446020C2semidirect
15. C2×C61×#433C2semidirect
22. C2×#14519711C22semidirect
23. C2×#14519709C22semidirect
24. C2×#14519702C22semidirect
25. C2×#14519702C22semidirect
36. #16839668C22semidirect
37. #16839668C22semidirect
44. #16839660C22semidirect
45. #16839660C22semidirect
49. #16839525C22semidirect
50. #16839525C22semidirect
51. #16839525C22semidirect
52. #16839525C22semidirect
55. C2×C4⋊C8×C61C22semidirect
56. C2×C4⋊C8×C61C22semidirect
59. C2×#97×C61C22semidirect
60. C2×C4×C8×C61C22semidirect
373. C2×#433D61semidirect
407. C2×C4⋊C8C2×D61semidirect
408. C2×C4⋊C8C2×D61semidirect
419. C2×#97C2×D61semidirect
420. C2×C4×C8C2×D61semidirect
442. C61#24516semidirect

Maximal subgroups

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

subgroupindex
C2×#168399152
#214516162
#214483992
#214472062
#214471922
#214471372
#214467002
#214466732
#214465162
#214465022
#214461292
#214460202
#214457512
C2×C61×#4332
#2451661