Finite Group Databasebeta

← #29686473

Subgroups — #29686473

Order 15616.

902 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455268C211yesmaximal, characteristic
2C2×#16839882C211yesmaximal, characteristic, complemented
3C2×#16839877C211yesmaximal, characteristic, complemented
4#21454244C211yesmaximal, characteristic, complemented
5#21446739C211yesmaximal, characteristic, complemented
6#21446592C211yesmaximal, characteristic, complemented
7#21446464C211yesmaximal, characteristic, complemented
8#21446464C211yesmaximal, characteristic, complemented
9#21446149C211yesmaximal, characteristic, complemented
10#21446149C211yesmaximal, characteristic, complemented
11#21445836C211yesmaximal, characteristic, complemented
12#21445691C211yesmaximal, characteristic, complemented
13#21445661C211yesmaximal, characteristic, complemented
14#21445654C211yesmaximal, characteristic, complemented
15C61×#2932C211yesmaximal, characteristic, complemented
16C2×#14519797C2211yescharacteristic
17C2×#14519797C2211yescharacteristic
18C2×#14519783C2211yescharacteristic
19C2×#14519783C2211yescharacteristic
20C4×#11758222C2211yescharacteristic
21#16839981C411yescharacteristic, complemented
22#16839981C411yescharacteristic, complemented
23#16839974C411yescharacteristic, complemented
24#16839974C411yescharacteristic, complemented
25#16839969C411yescharacteristic, complemented
26#16839964C411yescharacteristic, complemented
27#16839959C411yescharacteristic, complemented
28#16839954C411yescharacteristic, complemented
29#16839882—24no—
30#16839877—24no—
31C2×#14519712C2211yescharacteristic
32C2×#14519712C2211yescharacteristic
33C2×C4⋊#92418C2211yescharacteristic
34C2×#14519704C2211yescharacteristic
35C2×#14519704C2211yescharacteristic
36C2×#14519704C2211yescharacteristic
37C2×#14519704C2211yescharacteristic
38C2×#14519703C2211yescharacteristic
39C2×#14519703C2211yescharacteristic
40#16839758C2211yescharacteristic
41#16839758C2211yescharacteristic
42#16839719—21no—
43#16839719—21no—
44#16839717C2211yescharacteristic
45#16839717C2211yescharacteristic
46C4×#11758194C2211yescharacteristic
47#16839714—21no—
48C2×#14519687C2211yescharacteristic
49#97×D61—21no—
50C2×C8×Dic61C2211yescharacteristic
51C4×C4⋊Dic61C2211yescharacteristic
52#16839526C2211yescharacteristic
53#16839526C2211yescharacteristic
54#16839523C2211yescharacteristic
55#16839523C2211yescharacteristic
56#16839516C2211yescharacteristic
57#16839516C2211yescharacteristic
58C2×#131×C61C2211yescharacteristic
59C2×#131×C61C2211yescharacteristic
60C61×#532C2211yescharacteristic
61C61×#435—21no—
62C61×#435—21no—
63C61×#435—21no—
64C61×#435—21no—
65C61×#423C2211yescharacteristic
66C61×#408C2211yescharacteristic
67C61×#408C2211yescharacteristic
68C2×#97×C61C2211yescharacteristic
69C2×#11758222C2311yescharacteristic
70#14519797—22no—
71#14519797—22no—
72#14519797—22no—
73#14519797—22no—
74C2×#11758202C2×C411yescharacteristic
75C2×#11758202C2×C411yescharacteristic
76C2×#11758200C2×C411yescharacteristic
77C2×#11758200C2×C411yescharacteristic
78C2×#11758201C2×C411yescharacteristic
79C2×#11758201C2×C411yescharacteristic
80C2×#11758199C2×C411yescharacteristic
81C2×#11758199C2×C411yescharacteristic
82#14519783—22no—
83#14519783—22no—
84#14519783—22no—
85#14519783D414yescomplemented
86C2×#11758194C2311yescharacteristic
87C2×#11758194C2311yescharacteristic
88C2×#11758189—21no—
89C2×#11758189—21no—
90C22×#92418C2311yescharacteristic
91C22×#92418C2311yescharacteristic
92C2×C8×D61—21no—
93C2×C8×D61—21no—
94C4×Dic122C2×C411yescharacteristic
95C4×Dic122C2×C411yescharacteristic
96C4×D244C2×C411yescharacteristic
97C4×D244C2×C411yescharacteristic
98C4×C22⋊D61—21no—
99C4×C22⋊D61—21no—
100#14519736C2311yescharacteristic
101#14519734—21no—
102C2×C4⋊Dic61—21no—
103C2×C4×Dic61C2311yescharacteristic
104C2×C4×Dic61C2311yescharacteristic
105C42×D61—21no—
106#14519712—22no—
107#14519712—22no—
108C4⋊#92418C2×C411yescharacteristic
109C4⋊#92418C2×C411yescharacteristic
110C4⋊#92418C2×C411yescharacteristic
111C4⋊#92418C2×C411yescharacteristic
112#14519704—22no—
113#14519704—22no—
114#14519704—22no—
115#14519704—22no—
116#14519703—22no—
117#14519703—22no—
118#14519701C2×C411yescharacteristic
119#14519701C2×C411yescharacteristic
120#14519701C2×C411yescharacteristic
121#14519701C2×C411yescharacteristic
122#14519698C2×C411yescharacteristic
123#14519698C2×C411yescharacteristic
124#14519698C2×C411yescharacteristic
125#14519698C2×C411yescharacteristic
126#14519688—21no—
127#14519687—21no—
128#14519687—21no—
129#14519687—22no—
130C4×#92418—21no—
131C8×Dic61—22no—
132C8×Dic61—21no—
133C8×Dic61—21no—
134#14519684—21no—
135C2×#41×C61C2311yescharacteristic
136C2×#41×C61C2311yescharacteristic
137#131×C61—22no—
138#131×C61—22no—
139#131×C61—22no—
140#131×C61—22no—
141C2×M16×C61—21no—
142C2×M16×C61—21no—
143C2×M16×C61C2311yescharacteristic
144C2×M16×C61C2311yescharacteristic
145C22×C8×C61—21no—
146C22×C8×C61—21no—
147C22×C8×C61C2311yescharacteristic
148C22×C8×C61C2311yescharacteristic
149C4⋊Q8×C61C2×C411yescharacteristic
150#127×C61C2×C411yescharacteristic
151#124×C61C2×C411yescharacteristic
152#124×C61C2×C411yescharacteristic
153#121×C61—21no—
154#121×C61—21no—
155C4×D4×C61—21no—
156C4×D4×C61—21no—
157C2×C42×C61C2311yescharacteristic
158C4⋊C8×C61—21no—
159C4⋊C8×C61—21no—
160C22⋊C8×C61—21no—
161C22⋊C8×C61—21no—
162C22⋊C8×C61—21no—
163C22⋊C8×C61—21no—
164#97×C61D411yescharacteristic
165#97×C61D411yescharacteristic
166#97×C61D411yescharacteristic
167#97×C61D411yescharacteristic
168#41×C61—21no—
169#41×C61—21no—
170#41×C61—21no—
171#41×C61—21no—
172#41×C61—21no—
173#41×C61—21no—
174#41×C61—21no—
175#41×C61—21no—
176C2×Q8×C61C22×C411yescharacteristic
177C2×Q8×C61C22×C411yescharacteristic
178C2×D4×C61—21no—
179C2×D4×C61—21no—
180C2×D4×C61—21no—
181C2×D4×C61—21no—
182C2×D4×C61C22×C411yescharacteristic
183C2×D4×C61C22×C411yescharacteristic
184C22×C4×C61—21no—
185C22×C4×C61—21no—
186C22×C4×C61#4111yescharacteristic
187C22×C4×C61#4111yescharacteristic
188C22×C4×C61C2411yescharacteristic
189C2×C22⋊D61—21no—
190C22×Dic61—21no—
191C22×Dic61—21no—
192#11758222—21no—
193#11758222—21no—
194#11758222C2×D412yes—
195#11758222#4112yes—
196C2×D244C22×C411yescharacteristic
197C2×C4×D61—21no—
198C2×C4×D61—21no—
199C2×C4×D61—21no—
200C2×Dic122C22×C411yescharacteristic
201M16×C61—21no—
202M16×C61—21no—
203M16×C61—21no—
204M16×C61—21no—
205M16×C61—42no—
206M16×C61—42no—
207C2×C8×C61—21no—
208C2×C8×C61—21no—
209C2×C8×C61—21no—
210C2×C8×C61—21no—
211C2×C8×C61—42no—
212C2×C8×C61—42no—
213C2×C8×C61C2×D411yescharacteristic
214C2×C8×C61C2×D411yescharacteristic
215C2×C8×C61C2×D412yes—
216C2×C8×C61C2×D411yescharacteristic
217C2×C8×C61C2×D411yescharacteristic
218C2×C8×C61#4112yes—
219C4⋊C4×C61—21no—
220C4⋊C4×C61—21no—
221C22⋊C4×C61—21no—
222C22⋊C4×C61—21no—
223C22⋊C4×C61—21no—
224C22⋊C4×C61—21no—
225C42×C61C22×C411yescharacteristic
226C42×C61C22×C411yescharacteristic
227C42×C61C2×D411yescharacteristic
228C42×C61C2×D411yescharacteristic
229C22⋊Dic61—21no—
230#11758202—22no—
231#11758202—22no—
232#11758201—22no—
233#11758201—22no—
234#11758200—22no—
235#11758200—22no—
236#11758199—22no—
237#11758199—22no—
238#11758198—21no—
239#11758198—21no—
240C4⋊Dic61—42no—
241C4⋊Dic61C22×C411yescharacteristic
242C4⋊Dic61C22×C411yescharacteristic
243#11758196—21no—
244#11758196—21no—
245C4×Dic61—21no—
246C4×Dic61—21no—
247C4×Dic61—21no—
248C4×Dic61—21no—
249C4×Dic61—21no—
250C4×Dic61—21no—
251C4×Dic61—21no—
252#11758194—21no—
253#11758194—21no—
254#11758194C2×D412yes—
255#11758194#4112yes—
256C2×#92418—21no—
257C2×#92418—21no—
258C2×#92418—21no—
259C2×#92418—21no—
260C2×#92418—21no—
261C2×#92418—21no—
262C2×#92418C22×C411yescharacteristic
263C2×#92418C22×C411yescharacteristic
264C2×#92418C22×C411yescharacteristic
265C2×#92418C22×C411yescharacteristic
266#11758189—24no—
267#11758189—24no—
268C8×D61—24no—
269C8×D61—24no—
270C23×C61—21no—
271C23×C61—21no—
272C23×C61C2×#4111yescharacteristic
273C22×D61—21no—
274Q8×C61—21no—
275Q8×C61—21no—
276Q8×C61—21no—
277Q8×C61—21no—
278D4×C61—21no—
279D4×C61—21no—
280D4×C61—21no—
281D4×C61—21no—
282D4×C61—41no—
283D4×C61—41no—
284D4×C61—41no—
285D4×C61—41no—
286D4×C61—81no—
287D4×C61—81no—
288C2×C4×C61—21no—
289C2×C4×C61—21no—
290C2×C4×C61—41no—
291C2×C4×C61—41no—
292C2×C4×C61—41no—
293C2×C4×C61—41no—
294C2×C4×C61—41no—
295C2×C4×C61—41no—
296C2×C4×C61C4×D411yescharacteristic
297C2×C4×C61C4×D411yescharacteristic
298C2×C4×C61C4×D411yescharacteristic
299C2×C4×C61C4×D411yescharacteristic
300C2×C4×C61C23×C411yescharacteristic
301C2×C4×C61C22×D411yescharacteristic
302C2×C4×C61C22×D411yescharacteristic
303C2×C4×C61C2×#4111yescharacteristic
304C2×C4×C61C2×#4111yescharacteristic
305C2×C4×C61C2×#4111yescharacteristic
306C22⋊D61—22no—
307C22⋊D61—22no—
308C2×Dic61—21no—
309C2×Dic61—22no—
310C2×Dic61—21no—
311C2×Dic61—21no—
312C2×Dic61—41no—
313C2×Dic61—41no—
314C2×Dic61—41no—
315C2×Dic61—41no—
316C2×Dic61—41no—
317D244—21no—
318D244C4×D412yes—
319C4×D61—22no—
320C4×D61—22no—
321C4×D61—81no—
322C4×D61—81no—
323Dic122—21no—
324Dic122C4×D412yes—
325C8×C61—21no—
326C8×C61—21no—
327C8×C61—41no—
328C8×C61—41no—
329C8×C61#12112yes—
330C8×C61#12112yes—
331#92418—21no—
332#92418—21no—
333#92418—21no—
334#92418—21no—
335#92418—22no—
336#92418—22no—
337#21519—611nomaximal, Sylow
338C22×C61—21no—
339C22×C61—21no—
340C22×C61—41no—
341C22×C61—41no—
342C22×C61—41no—
343C22×C61—41no—
344C22×C61—41no—
345C22×C61—41no—
346C22×C61C2×C4×D411yescharacteristic
347C22×C61#52911yescharacteristic
348C22×C61#53211yescharacteristic
349C2×D61—22no—
350C2×D61—41no—
351C2×D61—41no—
352C4×C61—21no—
353C4×C61—21no—
354C4×C61—21no—
355C4×C61—21no—
356C4×C61—41no—
357C4×C61—41no—
358C4×C61C2×C4×D411yescharacteristic
359C4×C61C4×#4111yescharacteristic
360C4×C61C2×#12111yescharacteristic
361C4×C61#52511yescharacteristic
362Dic61—22no—
363Dic61—42no—
364Dic61—41no—
365Dic61—41no—
366Dic61—81no—
367#3035—611no—
368C2×#444—611no—
369C2×#443—611no—
370#2932D6111yescharacteristic, complemented
371#2875—611no—
372#1980—611no—
373#1950—611no—
374#1929—611no—
375#1929—611no—
376#1876—611no—
377#1876—611no—
378#1806—611no—
379#1771—611no—
380#1765—611no—
381#1764—611no—
382C2×C61—21no—
383C2×C61—21no—
384C2×C61—81no—
385C2×C61—81no—
386C2×C61C4×#12111yescharacteristic
387C2×C61#295611yescharacteristic
388C2×C61#295711yescharacteristic
389D61—42no—
390C2×#135—611no—
391C2×#135—611no—
392C2×#131—611no—
393C2×#131—611no—
394C2×#131C2×D6111yescharacteristic
395C2×#131C2×D6111yescharacteristic
396#532C2×D6111yescharacteristic
397C4×#41—611no—
398#464—611no—
399#464—611no—
400#463—611no—
401#463—611no—
402#462—611no—
403#461—611no—
404#460—611no—
405#459—611no—
406#444—1224no—
407#443—1224no—
408#435—21no—
409#435—21no—
410#435—21no—
411#435—21no—
412C2×#108—611no—
413C2×#108—611no—
414#423C2×D6111yescharacteristic
415C2×C4⋊C8—611no—
416C2×#104—611no—
417C2×#104—611no—
418C2×#104—611no—
419C2×#104—611no—
420C2×#104—611no—
421C2×#104—611no—
422#416—611no—
423#416—611no—
424#408C2×D6111yescharacteristic
425#408C2×D6111yescharacteristic
426#405—611no—
427#405—611no—
428#405—1221no—
429#405—1221no—
430C4×M16—611no—
431C4×M16—1221no—
432C2×#97—611no—
433C2×#97—1221no—
434C2×#97C2×D6111yescharacteristic
435C2×C4×C8—611no—
436C4×C4⋊C4—611no—
437#341—611no—
438#341—611no—
439#339—611no—
440#339—611no—
441#336—611no—
442#336—611no—
443C61#2151911yescharacteristic, complemented, Sylow
444C2×#41—611no—
445C2×#41C22×D6111yescharacteristic
446C2×#41C22×D6111yescharacteristic
447#135—1222no—
448#135—1222no—
449#135—1222no—
450#135—1222no—
451C2×Q16—611no—
452C2×Q16—611no—
453C2×SD16—611no—
454C2×SD16—611no—
455C2×SD16—611no—
456C2×SD16—611no—
457C2×D8—611no—
458C2×D8—611no—
459#131—22no—
460#131—22no—
461#131—22no—
462#131—22no—
463#131—614no—
464#131—1222no—
465#131—1222no—
466#131—1222no—
467C2×M16—21no—
468C2×M16—21no—
469C2×M16—611no—
470C2×M16—611no—
471C2×M16—1221no—
472C2×M16—1221no—
473C2×M16C22×D6111yescharacteristic
474C2×M16C22×D6111yescharacteristic
475C22×C8—21no—
476C22×C8—21no—
477C22×C8—611no—
478C22×C8—611no—
479C22×C8—1221no—
480C22×C8—1221no—
481C22×C8C22×D6111yescharacteristic
482C22×C8C22×D6111yescharacteristic
483C4⋊Q8C4×D6111yescharacteristic
484#127C4×D6111yescharacteristic
485#124C4×D6111yescharacteristic
486#124C4×D6111yescharacteristic
487#121—21no—
488#121—21no—
489C4×Q8—611no—
490C4×Q8—611no—
491C4×D4—21no—
492C4×D4—21no—
493C4×D4—611no—
494C4×D4—611no—
495C4×D4—1221no—
496C4×D4—1221no—
497#117—611no—
498#117—1221no—
499C2×C4⋊C4—1221no—
500C2×C42—611no—
501C2×C42—611no—
502C2×C42—1221no—
503C2×C42C22×D6111yescharacteristic
504#108—1222no—
505#108—1222no—
506C4⋊C8—21no—
507C4⋊C8—21no—
508C4⋊C8—611no—
509C4⋊C8—611no—
510C4⋊C8—611no—
511C4⋊C8—611no—
512#104—1222no—
513#104—1222no—
514#104—1222no—
515#104—1222no—
516#104—1222no—
517#104—1222no—
518#103—611no—
519#103—611no—
520#103—611no—
521#103—611no—
522#102—611no—
523#102—611no—
524#102—611no—
525#102—611no—
526C22⋊C8—21no—
527C22⋊C8—21no—
528C22⋊C8—21no—
529C22⋊C8—21no—
530#97—1222no—
531#97—1221no—
532#97—1221no—
533#97—1221no—
534#97C22⋊D6111yescharacteristic
535#97C22⋊D6111yescharacteristic
536#97C22⋊D6111yescharacteristic
537#97C22⋊D6111yescharacteristic
538C4×C8—1222no—
539C4×C8—1221no—
540C4×C8—1221no—
541C4×C8—1221no—
542#95—1221no—
543#41—21no—
544#41—21no—
545#41—21no—
546#41—21no—
547#41—21no—
548#41—21no—
549#41—21no—
550#41—21no—
551#41—612no—
552#41—612no—
553#41—1221no—
554#41—1221no—
555C2×Q8—611no—
556C2×Q8C2×C4×D6111yescharacteristic
557C2×Q8C2×C4×D6111yescharacteristic
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—611no—
563C2×D4—1221no—
564C2×D4C2×C4×D6111yescharacteristic
565C2×D4C2×C4×D6111yescharacteristic
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—1221no—
569C22×C4—1221no—
570C22×C4—1221no—
571C22×C4—1221no—
572C22×C4—1221no—
573C22×C4#1175822211yescharacteristic
574C22×C4#1175822211yescharacteristic
575C22×C4C23×D6111yescharacteristic
576Q16—1222no—
577Q16—1222no—
578SD16—1222no—
579SD16—1222no—
580SD16—1222no—
581SD16—1222no—
582D8—1222no—
583D8—1222no—
584M16—21no—
585M16—21no—
586M16—21no—
587M16—21no—
588M16—42no—
589M16—42no—
590M16—612no—
591M16—612no—
592M16—1224no—
593M16—1221no—
594M16—1221no—
595M16—1224no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—42no—
601C2×C8—42no—
602C2×C8—611no—
603C2×C8—611no—
604C2×C8—611no—
605C2×C8—611no—
606C2×C8—1224no—
607C2×C8—1221no—
608C2×C8—1221no—
609C2×C8—1221no—
610C2×C8—1221no—
611C2×C8—1221no—
612C2×C8—1221no—
613C2×C8—1224no—
614C2×C8D4×D6112yes—
615C2×C8#1175822412yes—
616C2×C8C2×C22⋊D6111yescharacteristic
617C2×C8C2×C22⋊D6111yescharacteristic
618C2×C8C2×C22⋊D6111yescharacteristic
619C2×C8C2×C22⋊D6111yescharacteristic
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—611no—
623C4⋊C4—611no—
624C4⋊C4—1221no—
625C4⋊C4—1221no—
626C4⋊C4—2442no—
627C22⋊C4—21no—
628C22⋊C4—21no—
629C22⋊C4—21no—
630C22⋊C4—21no—
631C22⋊C4—1221no—
632C22⋊C4—1221no—
633C22⋊C4—1221no—
634C42—1221no—
635C42—1221no—
636C42—1221no—
637C42—1221no—
638C42—1221no—
639C42—1221no—
640C42—1221no—
641C42C2×C4×D6111yescharacteristic
642C42C2×C4×D6111yescharacteristic
643C42C2×C22⋊D6111yescharacteristic
644C42C2×C22⋊D6111yescharacteristic
645C23—21no—
646C23—21no—
647C23—1221no—
648C23C2×#1175822211yescharacteristic
649Q8—21no—
650Q8—21no—
651Q8—21no—
652Q8—21no—
653Q8—612no—
654Q8—1221no—
655D4—21no—
656D4—21no—
657D4—21no—
658D4—21no—
659D4—41no—
660D4—41no—
661D4—41no—
662D4—41no—
663D4—81no—
664D4—81no—
665D4—612no—
666D4—1222no—
667D4—1222no—
668D4—1221no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—1221no—
678C2×C4—1222no—
679C2×C4—1222no—
680C2×C4—1222no—
681C2×C4—1221no—
682C2×C4—1221no—
683C2×C4—4881no—
684C2×C4—4881no—
685C2×C4—2441no—
686C2×C4—2441no—
687C2×C4—2441no—
688C2×C4—2441no—
689C2×C4—2441no—
690C2×C4C4×C22⋊D6111yescharacteristic
691C2×C4C4×C22⋊D6111yescharacteristic
692C2×C4C4×C22⋊D6111yescharacteristic
693C2×C4C4×C22⋊D6111yescharacteristic
694C2×C4C22×C4×D6111yescharacteristic
695C2×C4C2×D4×D6111yescharacteristic
696C2×C4C22×C22⋊D6111yescharacteristic
697C2×C4#41×D6111yescharacteristic
698C2×C4#41×D6111yescharacteristic
699C2×C4C2×#1175822411yescharacteristic
700C8—21no—
701C8—21no—
702C8—41no—
703C8—41no—
704C8—1221no—
705C8—1221no—
706C8—1221no—
707C8—1221no—
708C8—1222no—
709C8—1222no—
710C8#1451974812yes—
711C8#1451974812yes—
712C22—21no—
713C22—21no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—1222no—
721C22—2441no—
722C22—2441no—
723C22C2×C4×C22⋊D6111yescharacteristic
724C22#1684029411yescharacteristic
725C22#1684030911yescharacteristic
726C4—21no—
727C4—21no—
728C4—21no—
729C4—21no—
730C4—41no—
731C4—41no—
732C4—1222no—
733C4—4881no—
734C4—2442no—
735C4—2441no—
736C4—2441no—
737C4C4×D4×D6111yescharacteristic
738C4C4×#1175822411yescharacteristic
739C4C2×#1451974811yescharacteristic
740C4#1684026911yescharacteristic
741C2—21no—
742C2—21no—
743C2—81no—
744C2—81no—
745C2—2442no—
746C2C4×#1451974811yescharacteristic
747C2#2145472611yescharacteristic
748C2#2145473411yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#2932C2
socleC22×C61C2×C4×D4
prime radical#21455268C2
cosocleC22×C4×C61C24
hypercenter#2932D61
hypocenterC61#21519
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×#97 ◁ #2932

Complements

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

NH ≅ G/Ntype
2. C2×#16839882C2semidirect
3. C2×#16839877C2semidirect
4. #21454244C2semidirect
5. #21446739C2semidirect
6. #21446592C2semidirect
7. #21446464C2semidirect
8. #21446464C2semidirect
9. #21446149C2semidirect
10. #21446149C2semidirect
11. #21445836C2semidirect
12. #21445691C2semidirect
13. #21445661C2semidirect
14. #21445654C2semidirect
15. C61×#2932C2semidirect
21. #16839981C4semidirect
22. #16839981C4semidirect
23. #16839974C4semidirect
24. #16839974C4semidirect
25. #16839969C4semidirect
26. #16839964C4semidirect
27. #16839959C4semidirect
28. #16839954C4semidirect
85. #14519783D4semidirect
370. #2932D61semidirect
443. C61#21519semidirect

Maximal subgroups

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

subgroupindex
#214552682
C2×#168398822
C2×#168398772
#214542442
#214467392
#214465922
#214464642
#214461492
#214458362
#214456912
#214456612
#214456542
C61×#29322
#2151961