Finite Group Databasebeta

← #29702248

Subgroups — #29702248

Order 15616.

1170 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839956C211yesmaximal, characteristic
2C2×C4×D488C211yesmaximal, characteristic, complemented
3C2×#16839842C211yesmaximal, characteristic, complemented
4#21448880C211yesmaximal, characteristic, complemented
5#21448720C211yesmaximal, characteristic, complemented
6#21446623C211yesmaximal, characteristic, complemented
7#21446576C211yesmaximal, characteristic, complemented
8#21446503C211yesmaximal, characteristic, complemented
9#21446170C211yesmaximal, characteristic, complemented
10#21446168C211yesmaximal, characteristic, complemented
11#21446068C211yesmaximal, characteristic, complemented
12#21446065C211yesmaximal, characteristic, complemented
13C8×#11758196C211yesmaximal, characteristic, complemented
14#21445633C211yesmaximal, characteristic, complemented
15C61×#1934C211yesmaximal, characteristic, complemented
16C22×D488C2211yescharacteristic
17C22×#11758199C2211yescharacteristic
18C2×#14519773C2211yescharacteristic
19C2×C4×D244C2211yescharacteristic
20C2×C4×D244C2211yescharacteristic
21C2×D4×Dic61C2211yescharacteristic
22C2×#14519739C2211yescharacteristic
23C2×#14519739C2211yescharacteristic
24C2×#14519737—21no—
25C2×C4⋊C4×D61—21no—
26#16839956C418yescomplemented
27C4×D488—24no—
28#16839842—24no—
29C2×#14519711C2211yescharacteristic
30C2×#14519710C2211yescharacteristic
31C2×#14519706C2211yescharacteristic
32C2×#14519699C2211yescharacteristic
33C2×#14519699C2211yescharacteristic
34C2×#14519698C2211yescharacteristic
35C2×#14519697C2211yescharacteristic
36C2×#14519697C2211yescharacteristic
37C2×#14519697C2211yescharacteristic
38C2×C8×Dic61C2211yescharacteristic
39C2×C8×Dic61C2211yescharacteristic
40#16839663C2211yescharacteristic
41#16839662—21no—
42#16839661C2211yescharacteristic
43#16839639—21no—
44#16839638—21no—
45#16839636—21no—
46#16839633—21no—
47#16839631C2211yescharacteristic
48#16839621—21no—
49C4⋊C4×Dic61C2211yescharacteristic
50C4×#11758196C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839524C2211yescharacteristic
53#16839517C2211yescharacteristic
54#16839516C2211yescharacteristic
55C2×#102×C61C2211yescharacteristic
56C2×#102×C61C2211yescharacteristic
57C2×C4×C8×C61C2211yescharacteristic
58C61×#390C2211yescharacteristic
59C61×#389C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C61×#340C2211yescharacteristic
62C22×D244C2311yescharacteristic
63C22×D244C2311yescharacteristic
64C22×C22⋊D61—21no—
65C22×C22⋊D61—21no—
66C23×Dic61—21no—
67C22×C4×D61—21no—
68C22×C4×D61—21no—
69C22×C4×D61—21no—
70C22×C4×D61—21no—
71C2×D488—22no—
72C2×D488—22no—
73C2×D488C2×C414yescomplemented
74C2×#11758199—22no—
75C2×#11758199—22no—
76C2×#11758199C2×C414yescomplemented
77C22×#92418C2311yescharacteristic
78C22×#92418C2311yescharacteristic
79#14519773—22no—
80#14519773C2×C414yescomplemented
81C4×D244—22no—
82C4×D244—22no—
83C4×D244—41no—
84C4×D244—41no—
85D4×Dic61—22no—
86D4×Dic61—41no—
87#14519739—22no—
88#14519739—22no—
89#14519739—41no—
90#14519739C2×C414yescomplemented
91#14519737—44no—
92C2×C4⋊Dic61—21no—
93C2×C4⋊Dic61C2311yescharacteristic
94C2×C4⋊Dic61C2311yescharacteristic
95C2×#11758196—21no—
96C2×#11758196—21no—
97C2×#11758196D411yescharacteristic
98C2×#11758196D411yescharacteristic
99C4⋊C4×D61—44no—
100C2×C22⋊Dic61—21no—
101C2×#11758198—21no—
102C2×#11758198—21no—
103C2×#11758198—21no—
104C2×#11758198—21no—
105C2×#11758198—21no—
106C2×#11758198—21no—
107C2×C4×Dic61—21no—
108C2×C4×Dic61C2311yescharacteristic
109C2×C4×Dic61C2311yescharacteristic
110#14519711—22no—
111#14519710—22no—
112#14519706C2×C414yescomplemented
113#14519699—22no—
114#14519699D414yescomplemented
115#14519698—41no—
116#14519697—22no—
117#14519697—41no—
118#14519697C2×C414yescomplemented
119C8×Dic61—22no—
120C8×Dic61—22no—
121#14519684—21no—
122#14519684—21no—
123#14519684D411yescharacteristic
124#14519684D411yescharacteristic
125C22×D4×C61C2311yescharacteristic
126C22×C8×C61C2311yescharacteristic
127C22×C8×C61C2311yescharacteristic
128C2×C4⋊C4×C61—21no—
129C2×C4⋊C4×C61C2311yescharacteristic
130C2×C4⋊C4×C61C2311yescharacteristic
131C2×C4⋊C4×C61C2311yescharacteristic
132C2×C22⋊C4×C61—21no—
133C2×C22⋊C4×C61—21no—
134C2×C42×C61C2311yescharacteristic
135#102×C61—22no—
136#102×C61C2×C414yescomplemented
137C4×C8×C61—22no—
138#95×C61—21no—
139C24×C61—21no—
140C23×D61—21no—
141C23×D61—21no—
142C2×D4×C61—21no—
143C2×D4×C61—21no—
144C2×D4×C61—21no—
145C2×D4×C61—21no—
146C2×D4×C61—21no—
147C2×D4×C61C22×C412yes—
148C22×C4×C61—21no—
149C22×C4×C61—21no—
150C22×C4×C61—21no—
151C22×C4×C61C2×D411yescharacteristic
152C22×C4×C61C2×D411yescharacteristic
153C22×C4×C61C2411yescharacteristic
154C2×C22⋊D61—24no—
155C2×C22⋊D61—24no—
156C2×C22⋊D61—42no—
157C2×C22⋊D61—42no—
158C2×C22⋊D61—81no—
159C2×C22⋊D61—81no—
160C22×Dic61—21no—
161C22×Dic61—21no—
162C22×Dic61—42no—
163C22×Dic61—42no—
164C22×Dic61—81no—
165C22×Dic61C2×D411yescharacteristic
166C22×Dic61C2×D411yescharacteristic
167C22×Dic61C2×D411yescharacteristic
168C22×Dic61C2×D411yescharacteristic
169C2×D244—21no—
170C2×D244—21no—
171C2×D244—21no—
172C2×D244—21no—
173C2×D244—21no—
174C2×D244—21no—
175C2×D244—21no—
176C2×D244—21no—
177C2×D244C22×C412yes—
178C2×D244C22×C412yes—
179C2×D244C2×D412yes—
180C2×D244#4112yes—
181C2×C4×D61—24no—
182C2×C4×D61—42no—
183C2×C4×D61—42no—
184C2×C4×D61—42no—
185C2×C4×D61—42no—
186C2×C4×D61—42no—
187C2×C4×D61—42no—
188C2×C4×D61—42no—
189C2×C4×D61—42no—
190C2×C4×D61—81no—
191C2×C4×D61—81no—
192C2×C4×D61—81no—
193C2×C8×C61—21no—
194C2×C8×C61—21no—
195C2×C8×C61—21no—
196C2×C8×C61—21no—
197C2×C8×C61C22×C412yes—
198C2×C8×C61C2×D412yes—
199C4⋊C4×C61—21no—
200C4⋊C4×C61—21no—
201C4⋊C4×C61—21no—
202C4⋊C4×C61—21no—
203C4⋊C4×C61—21no—
204C4⋊C4×C61—42no—
205C4⋊C4×C61C22×C412yes—
206C22⋊C4×C61—42no—
207C22⋊C4×C61—81no—
208C42×C61—21no—
209C42×C61—21no—
210C22⋊Dic61—42no—
211#11758199—28no—
212#11758198—24no—
213#11758198—42no—
214#11758198—42no—
215#11758198—42no—
216#11758198—42no—
217#11758198—81no—
218C4⋊Dic61—21no—
219C4⋊Dic61—21no—
220C4⋊Dic61—21no—
221C4⋊Dic61—42no—
222C4⋊Dic61C2×D412yes—
223#11758196—22no—
224#11758196—42no—
225#11758196—81no—
226#11758196D814yescomplemented
227C4×Dic61—21no—
228C4×Dic61—21no—
229C4×Dic61—42no—
230C4×Dic61C22×C412yes—
231C4×Dic61#4112yes—
232C2×#92418—21no—
233C2×#92418—21no—
234C2×#92418—21no—
235C2×#92418—21no—
236C2×#92418—21no—
237C2×#92418C22×C412yes—
238D488—28no—
239C23×C61—22no—
240C23×C61—41no—
241C23×C61—41no—
242C23×C61—41no—
243C23×C61—41no—
244C23×C61—41no—
245C23×C61—41no—
246C23×C61C22×D411yescharacteristic
247C22×D61—22no—
248C22×D61—22no—
249C22×D61—22no—
250C22×D61—22no—
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—
261D4×C61—22no—
262D4×C61—22no—
263D4×C61—41no—
264D4×C61—41no—
265C2×C4×C61—21no—
266C2×C4×C61—21no—
267C2×C4×C61—22no—
268C2×C4×C61—21no—
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×C61—41no—
279C2×C4×C61C2×D812yes—
280C2×C4×C61C23×C411yescharacteristic
281C2×C4×C61C22×D411yescharacteristic
282C2×C4×C61C2×#4111yescharacteristic
283C2×C4×C61C2×#4111yescharacteristic
284C2×C4×C61H(5,𝔽2)11yescharacteristic
285C2×C4×C612−1+411yescharacteristic
286C22⋊D61—48no—
287C22⋊D61—84no—
288C2×Dic61—21no—
289C2×Dic61—21no—
290C2×Dic61—21no—
291C2×Dic61—21no—
292C2×Dic61—21no—
293C2×Dic61—22no—
294C2×Dic61—21no—
295C2×Dic61—21no—
296C2×Dic61—41no—
297C2×Dic61—41no—
298C2×Dic61—41no—
299C2×Dic61—41no—
300C2×Dic61—41no—
301C2×Dic61—84no—
302C2×Dic61C4×D412yes—
303C2×Dic61C4×D412yes—
304C2×Dic61C2×D812yes—
305C2×Dic61C2×D812yes—
306C2×Dic61#13512yes—
307D244—22no—
308D244—22no—
309D244—22no—
310D244—22no—
311D244—22no—
312D244—41no—
313D244—41no—
314D244C4×D414yescomplemented
315C4×D61—48no—
316C4×D61—84no—
317C4×D61—84no—
318C4×D61—84no—
319C8×C61—22no—
320C8×C61—22no—
321#92418—22no—
322#92418—41no—
323#22995—611nomaximal, Sylow
324C22×C61—42no—
325C22×C61—42no—
326C22×C61—42no—
327C22×C61—81no—
328C22×C61—81no—
329C22×C61—81no—
330C22×C61—81no—
331C22×C61C2×C4×D411yescharacteristic
332C22×C61D4211yescharacteristic
333C22×C61#54811yescharacteristic
334C22×C61C22×D811yescharacteristic
335C22×C61C2×#13511yescharacteristic
336C22×C61#57611yescharacteristic
337C22×C61#57711yescharacteristic
338C2×D61—24no—
339C2×D61—42no—
340C2×D61—42no—
341C2×D61—42no—
342C2×D61—42no—
343C2×D61—42no—
344C2×D61—42no—
345C2×D61—42no—
346C2×D61—42no—
347C2×D61—42no—
348C2×D61—81no—
349C2×D61—81no—
350C2×D61—81no—
351C2×D61—81no—
352C4×C61—22no—
353C4×C61—42no—
354C4×C61—41no—
355C4×C61—81no—
356C4×C61—81no—
357C4×C61C2×C4×D411yescharacteristic
358C4×C61#52011yescharacteristic
359C4×C61#54711yescharacteristic
360C4×C61#55311yescharacteristic
361Dic61—22no—
362Dic61—22no—
363Dic61—42no—
364Dic61—41no—
365Dic61—81no—
366Dic61C4×D814yescomplemented
367C2×#459—611no—
368C2×C4×D8—611no—
369C2×C4×D8—611no—
370#2366—611no—
371D4×C4⋊C4—611no—
372#1957—611no—
373#1947—611no—
374#1934—611no—
375#1934D6111yescharacteristic, complemented
376#1879—611no—
377#1879—611no—
378#1862—611no—
379#1862—611no—
380C8×C4⋊C4—611no—
381C4×#102—611no—
382C2×C61—82no—
383C2×C61#236111yescharacteristic
384C2×C61C2×C4×D811yescharacteristic
385C2×C61#294611yescharacteristic
386C2×C61D4×D811yescharacteristic
387C2×C61#328411yescharacteristic
388C2×C61#335811yescharacteristic
389C2×C61#336111yescharacteristic
390D61—44no—
391D61—82no—
392C22×D8—611no—
393C22×D8—611no—
394C2×#127—611no—
395C2×C4×D4—611no—
396C2×C4×D4—611no—
397C2×C4×D4—611no—
398C2×C4×D4—611no—
399C2×C4×D4—611no—
400C2×C4×D4—1221no—
401C22×C4⋊C4—1221no—
402#459—618no—
403C4×D8—1224no—
404C4×D8—1224no—
405C2×#107—611no—
406C2×#107—611no—
407C2×C4⋊C8—611no—
408C2×#102—611no—
409C2×#102—611no—
410C2×#102—611no—
411C2×#102—611no—
412C2×#102—611no—
413C2×#102—611no—
414C2×#102C2×D6111yescharacteristic
415C2×#102C2×D6111yescharacteristic
416C2×C4×C8—611no—
417C2×C4×C8—611no—
418C2×C4×C8C2×D6111yescharacteristic
419#390—611no—
420#390—1221no—
421#390C2×D6111yescharacteristic
422#389—611no—
423#389C2×D6111yescharacteristic
424#386—1221no—
425#386—1221no—
426#385—1221no—
427#385—1221no—
428#384—611no—
429#380—1221no—
430C4×C4⋊C4—611no—
431C4×C4⋊C4—611no—
432#340—611no—
433#340—611no—
434#340C2×D6111yescharacteristic
435#340C2×D6111yescharacteristic
436#336—611no—
437#336—611no—
438C61#2299511yescharacteristic, complemented, Sylow
439C22×D4—611no—
440C22×D4—611no—
441C22×D4—1221no—
442C22×D4—1221no—
443C22×D4C22×D6111yescharacteristic
444C23×C4—1221no—
445C23×C4—1221no—
446C23×C4—1221no—
447C23×C4—1221no—
448C23×C4—1221no—
449C2×D8—614no—
450C2×D8—614no—
451C2×D8—1222no—
452C2×D8—1222no—
453C2×D8—1222no—
454C2×D8—1222no—
455C22×C8—611no—
456C22×C8—611no—
457C22×C8C22×D6111yescharacteristic
458C22×C8C22×D6111yescharacteristic
459#127—614no—
460#127—1222no—
461C4×D4—614no—
462C4×D4—1222no—
463C4×D4—1222no—
464C4×D4—1222no—
465C4×D4—1222no—
466C4×D4—1222no—
467C4×D4—2441no—
468C4×D4—2441no—
469C4×D4—2441no—
470C4×D4—2441no—
471C4×D4—2444no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—611no—
474C2×C4⋊C4—611no—
475C2×C4⋊C4—611no—
476C2×C4⋊C4—611no—
477C2×C4⋊C4—1221no—
478C2×C4⋊C4—1221no—
479C2×C4⋊C4—1221no—
480C2×C4⋊C4—2444no—
481C2×C4⋊C4C22×D6111yescharacteristic
482C2×C4⋊C4C22×D6111yescharacteristic
483C2×C4⋊C4C22×D6111yescharacteristic
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
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⋊C4—1221no—
493C2×C42—611no—
494C2×C42—611no—
495C2×C42—1221no—
496C2×C42C22×D6111yescharacteristic
497#107—1222no—
498#107—1222no—
499C4⋊C8—614no—
500#102—22no—
501#102—614no—
502#102—614no—
503#102—1222no—
504#102—1222no—
505#102—2441no—
506#102—2441no—
507#102C4×D6114yescomplemented
508C4×C8—22no—
509C4×C8—1222no—
510C4×C8—1222no—
511#95—21no—
512#95—611no—
513#95—611no—
514#95—1221no—
515#95—1221no—
516C24—21no—
517C24—1221no—
518C24—1221no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—612no—
525C2×D4—612no—
526C2×D4—612no—
527C2×D4—612no—
528C2×D4—1224no—
529C2×D4—1224no—
530C2×D4—1221no—
531C2×D4—1221no—
532C2×D4—1221no—
533C2×D4—1221no—
534C2×D4—1221no—
535C2×D4—1221no—
536C2×D4—1221no—
537C2×D4—1221no—
538C2×D4—4881no—
539C2×D4—4881no—
540C2×D4—2442no—
541C2×D4—2442no—
542C2×D4C2×C4×D6112yes—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—611no—
547C22×C4—611no—
548C22×C4—611no—
549C22×C4—611no—
550C22×C4—1224no—
551C22×C4—1221no—
552C22×C4—1221no—
553C22×C4—4881no—
554C22×C4—4881no—
555C22×C4—4881no—
556C22×C4—4881no—
557C22×C4—2442no—
558C22×C4—2442no—
559C22×C4—2442no—
560C22×C4—2442no—
561C22×C4—2442no—
562C22×C4—2442no—
563C22×C4—2442no—
564C22×C4—2442no—
565C22×C4—2442no—
566C22×C4—2442no—
567C22×C4D4×D6111yescharacteristic
568C22×C4D4×D6111yescharacteristic
569C22×C4C23×D6111yescharacteristic
570D8—1228no—
571D8—1228no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—612no—
577C2×C8—1221no—
578C2×C8—1221no—
579C2×C8—1221no—
580C2×C8—1221no—
581C2×C8—1221no—
582C2×C8C2×C4×D6112yes—
583C2×C8D4×D6112yes—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—42no—
590C4⋊C4—614no—
591C4⋊C4—612no—
592C4⋊C4—1222no—
593C4⋊C4—1221no—
594C4⋊C4—1221no—
595C4⋊C4—1221no—
596C4⋊C4—4881no—
597C4⋊C4—2442no—
598C4⋊C4—2442no—
599C4⋊C4C2×C4×D6112yes—
600C22⋊C4—42no—
601C22⋊C4—81no—
602C22⋊C4—1224no—
603C22⋊C4—4881no—
604C22⋊C4—2442no—
605C22⋊C4—2442no—
606C22⋊C4—2442no—
607C22⋊C4—2442no—
608C22⋊C4—2442no—
609C42—21no—
610C42—21no—
611C42—612no—
612C42—612no—
613C42—1221no—
614C42—1221no—
615C42—2442no—
616C23—22no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—1222no—
624C23—1222no—
625C23—1222no—
626C23—1222no—
627C23—2441no—
628C23—2441no—
629C23—2441no—
630C23—2441no—
631C23—2441no—
632C23—2441no—
633C23—2441no—
634C23—2441no—
635C23—2441no—
636C23—2441no—
637C23C2×D4×D6111yescharacteristic
638D4—22no—
639D4—22no—
640D4—41no—
641D4—41no—
642D4—614no—
643D4—1222no—
644D4—1222no—
645D4—1222no—
646D4—1222no—
647D4—1222no—
648D4—4884no—
649D4—2448no—
650D4—2441no—
651D4—2441no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—22no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
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—612no—
667C2×C4—612no—
668C2×C4—612no—
669C2×C4—612no—
670C2×C4—612no—
671C2×C4—1221no—
672C2×C4—1221no—
673C2×C4—1221no—
674C2×C4—1221no—
675C2×C4—1221no—
676C2×C4—1221no—
677C2×C4—1221no—
678C2×C4—1222no—
679C2×C4—4884no—
680C2×C4—4884no—
681C2×C4—4884no—
682C2×C4—4884no—
683C2×C4—2448no—
684C2×C4—2441no—
685C2×C4—2441no—
686C2×C4—2441no—
687C2×C4—2441no—
688C2×C4—2441no—
689C2×C4D8×D6112yes—
690C2×C4C22×C4×D6111yescharacteristic
691C2×C4C2×D4×D6111yescharacteristic
692C2×C4#41×D6111yescharacteristic
693C2×C4#41×D6111yescharacteristic
694C2×C4#1451982311yescharacteristic
695C2×C4#1451982411yescharacteristic
696C8—22no—
697C8—22no—
698C8—1222no—
699C8—2441no—
700C22—42no—
701C22—42no—
702C22—42no—
703C22—81no—
704C22—81no—
705C22—81no—
706C22—81no—
707C22—1224no—
708C22—4881no—
709C22—4881no—
710C22—4881no—
711C22—4881no—
712C22—2442no—
713C22—2442no—
714C22—2442no—
715C22—2442no—
716C22—2442no—
717C22—2442no—
718C22—2442no—
719C22—2442no—
720C22—2442no—
721C22C4×D4×D6111yescharacteristic
722C22#1684039611yescharacteristic
723C22#1684042011yescharacteristic
724C22C2×D8×D6111yescharacteristic
725C22#135×D6111yescharacteristic
726C22#1684056411yescharacteristic
727C22#1684056811yescharacteristic
728C4—22no—
729C4—41no—
730C4—42no—
731C4—81no—
732C4—81no—
733C4—614no—
734C4—1222no—
735C4—1222no—
736C4—4881no—
737C4—2442no—
738C4—2441no—
739C4C4×D4×D6111yescharacteristic
740C4#1684024211yescharacteristic
741C4#1684041011yescharacteristic
742C4#1684046311yescharacteristic
743C2—82no—
744C2—4882no—
745C2—2444no—
746C2#2144883211yescharacteristic
747C2C4×D8×D6111yescharacteristic
748C2#2145464611yescharacteristic
749C2#2145749311yescharacteristic
750C2#2145754611yescharacteristic
751C2#2145845111yescharacteristic
752C2#2145847611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1934C2
socleC23×C61C22×D4
prime radicalC2×#16839956C2
cosocleC22×C4×C61C24
hypercenter#1934D61
hypocenterC61#22995
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1934

Complements

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

NH ≅ G/Ntype
2. C2×C4×D488C2semidirect
3. C2×#16839842C2semidirect
4. #21448880C2semidirect
5. #21448720C2semidirect
6. #21446623C2semidirect
7. #21446576C2semidirect
8. #21446503C2semidirect
9. #21446170C2semidirect
10. #21446168C2semidirect
11. #21446068C2semidirect
12. #21446065C2semidirect
13. C8×#11758196C2semidirect
14. #21445633C2semidirect
15. C61×#1934C2semidirect
26. #16839956C4semidirect
73. C2×D488C2×C4semidirect
76. C2×#11758199C2×C4semidirect
80. #14519773C2×C4semidirect
90. #14519739C2×C4semidirect
112. #14519706C2×C4semidirect
114. #14519699D4semidirect
118. #14519697C2×C4semidirect
136. #102×C61C2×C4semidirect
226. #11758196D8semidirect
314. D244C4×D4semidirect
366. Dic61C4×D8semidirect
375. #1934D61semidirect
438. C61#22995semidirect
507. #102C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168399562
C2×C4×D4882
C2×#168398422
#214488802
#214487202
#214466232
#214465762
#214465032
#214461702
#214461682
#214460682
#214460652
C8×#117581962
#214456332
C61×#19342
#2299561