Finite Group Databasebeta

← #29691281

Subgroups — #29691281

Order 15616.

1084 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839909C211yesmaximal, characteristic
2C4×#14519751C211yesmaximal, characteristic, complemented
3#21448309C211yesmaximal, characteristic, complemented
4#21446700C211yesmaximal, characteristic, complemented
5#21446695C211yesmaximal, characteristic, complemented
6#21446516C211yesmaximal, characteristic, complemented
7#21446509C211yesmaximal, characteristic, complemented
8#21446454C211yesmaximal, characteristic, complemented
9#21446440C211yesmaximal, characteristic, complemented
10#21446166C211yesmaximal, characteristic, complemented
11#21446152C211yesmaximal, characteristic, complemented
12#21446139C211yesmaximal, characteristic, complemented
13#21446020C211yesmaximal, characteristic, complemented
14#21445760C211yesmaximal, characteristic, complemented
15C61×#1749C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C22×#11758190C2211yescharacteristic
18C22×D488C2211yescharacteristic
19C2×#14519751C2211yescharacteristic
20C2×C4×D244C2211yescharacteristic
21C2×C4×C22⋊D61—21no—
22C2×#14519736C2211yescharacteristic
23#16839909C418yescomplemented
24C2×#14519711C2211yescharacteristic
25C2×#14519709C2211yescharacteristic
26C2×#14519702C2211yescharacteristic
27C2×#14519702C2211yescharacteristic
28C2×#14519702C2211yescharacteristic
29C2×#14519699C2211yescharacteristic
30C2×#14519699C2211yescharacteristic
31C2×#14519699C2211yescharacteristic
32C2×#14519699C2211yescharacteristic
33C2×#14519699C2211yescharacteristic
34#16839668C2211yescharacteristic
35#16839668C2211yescharacteristic
36#16839664C2211yescharacteristic
37#16839664C2211yescharacteristic
38#16839664C2211yescharacteristic
39#16839660C2211yescharacteristic
40#16839653—21no—
41#16839641—21no—
42#16839641—21no—
43#16839641—21no—
44#16839622C2211yescharacteristic
45C4×C4⋊Dic61C2211yescharacteristic
46C4×#11758198—21no—
47C4×#11758198—21no—
48C4×#11758198—21no—
49#16839525C2211yescharacteristic
50#16839525C2211yescharacteristic
51#16839525C2211yescharacteristic
52#16839525C2211yescharacteristic
53C22×C42×C61C2211yescharacteristic
54C2×C22⋊C8×C61C2211yescharacteristic
55C2×C22⋊C8×C61C2211yescharacteristic
56C2×#97×C61C2211yescharacteristic
57C2×#97×C61C2211yescharacteristic
58C61×#336C2211yescharacteristic
59C61×#336C2211yescharacteristic
60C2×#11758222—22no—
61C2×#11758222—41no—
62C2×#11758222—41no—
63C2×#11758222—41no—
64C2×#11758222—41no—
65C2×#11758222C2×C414yescomplemented
66C22×Dic122C2311yescharacteristic
67C22×D244C2311yescharacteristic
68C22×D244C2311yescharacteristic
69C22×C22⋊D61—21no—
70C22×C22⋊D61—21no—
71C22×C4×D61—21no—
72C22×C4×D61—21no—
73C2×#11758190—41no—
74C2×#11758190—41no—
75C2×#11758190C2×C414yescomplemented
76C2×D488—41no—
77C2×D488—41no—
78C2×D488C2×C414yescomplemented
79#14519751—22no—
80#14519751C2×C414yes—
81C4×D244—41no—
82C4×D244—41no—
83C4×C22⋊D61—44no—
84#14519736—41no—
85#14519736—41no—
86C2×C4⋊Dic61C2311yescharacteristic
87C2×C4⋊Dic61C2311yescharacteristic
88C2×C4⋊Dic61C2311yescharacteristic
89C2×C4⋊Dic61C2311yescharacteristic
90C2×C4⋊Dic61C2311yescharacteristic
91C2×#11758196—21no—
92C2×C22⋊Dic61—21no—
93C2×C22⋊Dic61—21no—
94C2×#11758198—21no—
95C2×#11758198—21no—
96C2×#11758198—21no—
97C2×#11758198—21no—
98C2×#11758198—21no—
99C2×#11758198—21no—
100C2×#11758198—21no—
101C2×#11758198—21no—
102C2×C4×Dic61—21no—
103C2×C4×Dic61—21no—
104#14519711—41no—
105#14519709—41no—
106#14519702—41no—
107#14519702—41no—
108#14519702C2×C414yescomplemented
109#14519699—41no—
110#14519699—41no—
111#14519699—41no—
112#14519699—41no—
113#14519699C2×C414yescomplemented
114#14519684—21no—
115#14519684—21no—
116#14519684—21no—
117#14519684—21no—
118#14519684—21no—
119#14519684—21no—
120#14519684—21no—
121C23×C4×C61D411yescharacteristic
122C23×C4×C61D411yescharacteristic
123C23×C4×C61C2311yescharacteristic
124C22×C8×C61C2311yescharacteristic
125C22×C8×C61C2311yescharacteristic
126C22×C8×C61C2311yescharacteristic
127C22×C8×C61C2311yescharacteristic
128C2×C42×C61—41no—
129C2×C42×C61—41no—
130C2×C42×C61D411yescharacteristic
131C2×C42×C61D411yescharacteristic
132C2×C42×C61C2311yescharacteristic
133C2×C42×C61C2311yescharacteristic
134C22⋊C8×C61—22no—
135C22⋊C8×C61C2×C414yescomplemented
136#97×C61—41no—
137#97×C61—41no—
138C24×C61C2×D411yescharacteristic
139C23×D61—21no—
140C23×D61—21no—
141C22×C4×C61—21no—
142C22×C4×C61—21no—
143C22×C4×C61—21no—
144C22×C4×C61—21no—
145C22×C4×C61—22no—
146C22×C4×C61—41no—
147C22×C4×C61—41no—
148C22×C4×C61—41no—
149C22×C4×C61—41no—
150C22×C4×C61—41no—
151C22×C4×C61C22×C412yes—
152C22×C4×C61C2×D411yescharacteristic
153C22×C4×C61C2×D411yescharacteristic
154C22×C4×C61C2×D411yescharacteristic
155C22×C4×C61C2×D411yescharacteristic
156C22×C4×C61C2×D411yescharacteristic
157C22×C4×C61#4112yes—
158C22×C4×C61C2411yescharacteristic
159C2×C22⋊D61—24no—
160C2×C22⋊D61—24no—
161C2×C22⋊D61—42no—
162C2×C22⋊D61—42no—
163C2×C22⋊D61—42no—
164C2×C22⋊D61—42no—
165C22×Dic61—21no—
166C22×Dic61—21no—
167C22×Dic61—21no—
168C22×Dic61—21no—
169C22×Dic61—21no—
170C22×Dic61—21no—
171#11758222—44no—
172#11758222—44no—
173#11758222—44no—
174#11758222—44no—
175C2×D244—21no—
176C2×D244—21no—
177C2×D244—21no—
178C2×D244—21no—
179C2×D244—21no—
180C2×D244—21no—
181C2×D244—21no—
182C2×D244—21no—
183C2×D244—21no—
184C2×D244—21no—
185C2×D244C22×C412yes—
186C2×D244C22×C412yes—
187C2×C4×D61—24no—
188C2×C4×D61—42no—
189C2×C4×D61—42no—
190C2×C4×D61—42no—
191C2×C4×D61—42no—
192C2×C4×D61—42no—
193C2×Dic122—21no—
194C2×Dic122—21no—
195C2×Dic122—21no—
196C2×Dic122—21no—
197C2×Dic122—21no—
198C2×Dic122C22×C412yes—
199C2×C8×C61—21no—
200C2×C8×C61—21no—
201C2×C8×C61—21no—
202C2×C8×C61—21no—
203C2×C8×C61—21no—
204C2×C8×C61—21no—
205C2×C8×C61—21no—
206C2×C8×C61—21no—
207C2×C8×C61—21no—
208C2×C8×C61—21no—
209C2×C8×C61C22×C412yes—
210C2×C8×C61C22×C412yes—
211C42×C61—21no—
212C42×C61—21no—
213C42×C61—21no—
214C42×C61—21no—
215C42×C61—41no—
216C42×C61—41no—
217C22⋊Dic61—42no—
218C22⋊Dic61—42no—
219#11758198—24no—
220#11758198—42no—
221#11758198—42no—
222#11758198—42no—
223#11758198—42no—
224#11758198—42no—
225#11758198—42no—
226#11758198—42no—
227C4⋊Dic61—21no—
228C4⋊Dic61—21no—
229C4⋊Dic61—21no—
230C4⋊Dic61—21no—
231C4⋊Dic61—21no—
232C4⋊Dic61—21no—
233C4⋊Dic61—21no—
234C4⋊Dic61—21no—
235C4⋊Dic61—21no—
236C4⋊Dic61C22×C412yes—
237#11758196—42no—
238C4×Dic61—42no—
239C4×Dic61—42no—
240D488—44no—
241#11758190—44no—
242C23×C61—21no—
243C23×C61—21no—
244C23×C61—21no—
245C23×C61—21no—
246C23×C61—21no—
247C23×C61—21no—
248C23×C61C4×D412yes—
249C23×C61C22×D411yescharacteristic
250C22×D61—22no—
251C22×D61—22no—
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—41no—
262C22×D61—41no—
263C22×D61—41no—
264C2×C4×C61—21no—
265C2×C4×C61—21no—
266C2×C4×C61—21no—
267C2×C4×C61—21no—
268C2×C4×C61—22no—
269C2×C4×C61—22no—
270C2×C4×C61—22no—
271C2×C4×C61—22no—
272C2×C4×C61—21no—
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—44no—
282C2×C4×C61—44no—
283C2×C4×C61C4×D412yes—
284C2×C4×C61AGL(1,ℤ/8)12yes—
285C2×C4×C61C23×C411yescharacteristic
286C2×C4×C61C2×#4111yescharacteristic
287C2×C4×C61H(5,𝔽2)11yescharacteristic
288C2×C4×C61H(5,𝔽2)11yescharacteristic
289C2×C4×C61H(5,𝔽2)11yescharacteristic
290C2×C4×C61H(5,𝔽2)11yescharacteristic
291C22⋊D61—48no—
292C22⋊D61—48no—
293C2×Dic61—22no—
294C2×Dic61—22no—
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—
310C2×Dic61—41no—
311D244—22no—
312D244—22no—
313D244—22no—
314D244—22no—
315D244—41no—
316D244—41no—
317D244—41no—
318D244—41no—
319C4×D61—48no—
320C4×D61—84no—
321Dic122—22no—
322Dic122—22no—
323Dic122—41no—
324Dic122—41no—
325C8×C61—22no—
326C8×C61—22no—
327C8×C61—41no—
328C8×C61—41no—
329#22051—611nomaximal, Sylow
330C22×C61—22no—
331C22×C61—22no—
332C22×C61—22no—
333C22×C61—41no—
334C22×C61—41no—
335C22×C61—41no—
336C22×C61—41no—
337C22×C61C2×C4×D411yescharacteristic
338C22×C61#53411yescharacteristic
339C22×C61#53511yescharacteristic
340C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
341C22×C61#57511yescharacteristic
342C22×C61#57511yescharacteristic
343C22×C61#57511yescharacteristic
344C2×D61—42no—
345C2×D61—42no—
346C2×D61—42no—
347C2×D61—42no—
348C2×D61—42no—
349C2×D61—42no—
350C2×D61—81no—
351C2×D61—81no—
352C2×D61—81no—
353C2×D61—81no—
354C2×D61—81no—
355C2×D61—81no—
356C2×D61—81no—
357C2×D61—81no—
358C4×C61—22no—
359C4×C61—22no—
360C4×C61—41no—
361C4×C61—41no—
362C4×C61—41no—
363C4×C61#51811yescharacteristic
364C4×C61#51811yescharacteristic
365C4×C61#53811yescharacteristic
366C4×C61#53811yescharacteristic
367Dic61—42no—
368Dic61—42no—
369Dic61—81no—
370Dic61—81no—
371Dic61—81no—
372Dic61—81no—
373C2×#449—611no—
374C4×#121—611no—
375#2297—611no—
376#1973—611no—
377#1972—611no—
378#1936—611no—
379#1935—611no—
380#1927—611no—
381#1925—611no—
382#1879—611no—
383#1877—611no—
384#1875—611no—
385#1854—611no—
386#1788—611no—
387#1749D6111yescharacteristic, complemented
388C2×C61—42no—
389C2×C61#232111yescharacteristic
390C2×C61#294311yescharacteristic
391C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
392C2×C61#319411yescharacteristic
393C2×C61#319711yescharacteristic
394C2×C61#321411yescharacteristic
395C2×C61#321911yescharacteristic
396D61—82no—
397D61—82no—
398C22×#41—611no—
399C22×SD16—611no—
400C22×D8—611no—
401C2×#121—611no—
402C2×C4×D4—611no—
403C2×C4×D4—1221no—
404C2×#117—611no—
405C22×C42C2×D6111yescharacteristic
406#449—618no—
407C2×#107—611no—
408C2×#106—611no—
409C2×#103—611no—
410C2×#103—611no—
411C2×#103—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
420C2×#97C2×D6111yescharacteristic
421#391—611no—
422#391—611no—
423#390—611no—
424#390—611no—
425#390—611no—
426#389—611no—
427#388—1221no—
428#386—1221no—
429#386—1221no—
430#386—1221no—
431#380—611no—
432C4×C4⋊C4—611no—
433C4×C22⋊C4—1221no—
434C4×C22⋊C4—1221no—
435C4×C22⋊C4—1221no—
436#340—611no—
437#340—611no—
438#340—611no—
439#340—611no—
440#336C2×D6111yescharacteristic
441#336C2×D6111yescharacteristic
442C61#2205111yescharacteristic, complemented, Sylow
443C2×#41—614no—
444C2×#41—1222no—
445C2×#41—2441no—
446C2×#41—2441no—
447C2×#41—2441no—
448C2×#41—2441no—
449C22×Q8—611no—
450C22×D4—611no—
451C22×D4—611no—
452C22×D4—1221no—
453C22×D4—1221no—
454C23×C4—1221no—
455C23×C4—1221no—
456C23×C4D24411yescharacteristic
457C23×C4D24411yescharacteristic
458C23×C4C22×D6111yescharacteristic
459C2×SD16—614no—
460C2×SD16—2441no—
461C2×SD16—2441no—
462C2×D8—614no—
463C2×D8—2441no—
464C2×D8—2441no—
465C22×C8C22×D6111yescharacteristic
466C22×C8C22×D6111yescharacteristic
467C22×C8C22×D6111yescharacteristic
468C22×C8C22×D6111yescharacteristic
469#121—614no—
470#121—1222no—
471C4×D4—2441no—
472C4×D4—2441no—
473C4×D4—2444no—
474#117—2441no—
475#117—2441no—
476C2×C4⋊C4—611no—
477C2×C4⋊C4—611no—
478C2×C4⋊C4—611no—
479C2×C4⋊C4—611no—
480C2×C4⋊C4—611no—
481C2×C4⋊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×C42—41no—
493C2×C42—41no—
494C2×C42—1221no—
495C2×C42—1221no—
496C2×C42D24411yescharacteristic
497C2×C42D24411yescharacteristic
498C2×C42C22×D6111yescharacteristic
499C2×C42C22×D6111yescharacteristic
500#107—2441no—
501#106—2441no—
502#103—614no—
503#103—2441no—
504#103—2441no—
505#102—614no—
506#102—2441no—
507#102—2441no—
508#102—2441no—
509#102—2441no—
510C22⋊C8—22no—
511C22⋊C8C4×D6114yescomplemented
512#97—41no—
513#97—41no—
514#95—1221no—
515#95—1221no—
516#95—1221no—
517#95—1221no—
518#95—1221no—
519#95—1221no—
520#95—1221no—
521C24—1221no—
522C24—1221no—
523C24C2×D24411yescharacteristic
524#41—2444no—
525#41—2444no—
526#41—2444no—
527#41—2444no—
528C2×Q8—612no—
529C2×Q8—1221no—
530C2×Q8—1221no—
531C2×Q8—1221no—
532C2×Q8—1221no—
533C2×Q8—1221no—
534C2×D4—612no—
535C2×D4—612no—
536C2×D4—1224no—
537C2×D4—1224no—
538C2×D4—1221no—
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—2442no—
549C2×D4—2442no—
550C2×D4—2442no—
551C2×D4—2442no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—22no—
557C22×C4—41no—
558C22×C4—41no—
559C22×C4—41no—
560C22×C4—41no—
561C22×C4—41no—
562C22×C4—1221no—
563C22×C4—1221no—
564C22×C4—1224no—
565C22×C4—1221no—
566C22×C4—1221no—
567C22×C4—1221no—
568C22×C4—1221no—
569C22×C4—2442no—
570C22×C4—2442no—
571C22×C4—2442no—
572C22×C4—2442no—
573C22×C4—2442no—
574C22×C4C2×C4×D6112yes—
575C22×C4C2×D24411yescharacteristic
576C22×C4C2×D24411yescharacteristic
577C22×C4C2×D24411yescharacteristic
578C22×C4C2×D24411yescharacteristic
579C22×C4C2×D24411yescharacteristic
580C22×C4#1175822212yes—
581C22×C4C23×D6111yescharacteristic
582SD16—2444no—
583D8—2444no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8C2×C4×D6112yes—
595C2×C8C2×C4×D6112yes—
596C4⋊C4—612no—
597C4⋊C4—1221no—
598C4⋊C4—1221no—
599C4⋊C4—1221no—
600C4⋊C4—1221no—
601C4⋊C4—1221no—
602C4⋊C4—1221no—
603C4⋊C4—1221no—
604C4⋊C4—1221no—
605C4⋊C4—1221no—
606C4⋊C4—2442no—
607C22⋊C4—1224no—
608C22⋊C4—2442no—
609C22⋊C4—2442no—
610C22⋊C4—2442no—
611C22⋊C4—2442no—
612C22⋊C4—2442no—
613C22⋊C4—2442no—
614C22⋊C4—2442no—
615C22⋊C4—2442no—
616C22⋊C4—2442no—
617C42—21no—
618C42—21no—
619C42—21no—
620C42—21no—
621C42—41no—
622C42—41no—
623C42—2442no—
624C42—2442no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—1222no—
632C23—1222no—
633C23—2441no—
634C23—2441no—
635C23—2441no—
636C23—2441no—
637C23—2441no—
638C23—2441no—
639C23—2441no—
640C23—2441no—
641C23—2441no—
642C23—2441no—
643C23—2441no—
644C23—2441no—
645C23C4×D24412yes—
646C23C22×D24411yescharacteristic
647Q8—1222no—
648Q8—1222no—
649Q8—2441no—
650Q8—2441no—
651D4—1222no—
652D4—1222no—
653D4—1222no—
654D4—1222no—
655D4—2448no—
656D4—2448no—
657D4—2441no—
658D4—2441no—
659D4—2441no—
660D4—2441no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
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—44no—
679C2×C4—44no—
680C2×C4—1222no—
681C2×C4—1222no—
682C2×C4—4884no—
683C2×C4—2448no—
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—2441no—
699C2×C4—2441no—
700C2×C4C4×D24412yes—
701C2×C4#1451980512yes—
702C2×C4C22×C4×D6111yescharacteristic
703C2×C4C2×#1175822211yescharacteristic
704C2×C4#1451982211yescharacteristic
705C2×C4#1451982211yescharacteristic
706C2×C4#1451982311yescharacteristic
707C2×C4#1451982311yescharacteristic
708C8—22no—
709C8—22no—
710C8—41no—
711C8—41no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—4881no—
720C22—4881no—
721C22—4881no—
722C22—4881no—
723C22—4881no—
724C22—4881no—
725C22—4881no—
726C22—4881no—
727C22—2442no—
728C22—2442no—
729C22—2442no—
730C22—2442no—
731C22—2442no—
732C22—2442no—
733C22C2×C4×D24411yescharacteristic
734C22#1684032411yescharacteristic
735C22#1684033111yescharacteristic
736C22C2×#1451980511yescharacteristic
737C22#1684056211yescharacteristic
738C22#1684056211yescharacteristic
739C22#1684056211yescharacteristic
740C4—22no—
741C4—22no—
742C4—41no—
743C4—41no—
744C4—41no—
745C4—4881no—
746C4—4881no—
747C4—4881no—
748C4—4881no—
749C4—2442no—
750C4—2442no—
751C4#1684023411yescharacteristic
752C4#1684023411yescharacteristic
753C4#1684034511yescharacteristic
754C4#1684034511yescharacteristic
755C2—42no—
756C2—4882no—
757C2—4882no—
758C2#2144847911yescharacteristic
759C2#2145462111yescharacteristic
760C2C4×#1451980511yescharacteristic
761C2#2145663511yescharacteristic
762C2#2145666111yescharacteristic
763C2#2145681611yescharacteristic
764C2#2145685811yescharacteristic
subgroupG/H
centerC23C22×D244
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1749C2
socleC23×C61C22×D4
prime radicalC2×#16839909C2
cosocleC22×C4×C61C24
hypercenter#1749D61
hypocenterC61#22051
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1749

Complements

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

NH ≅ G/Ntype
2. C4×#14519751C2semidirect
3. #21448309C2semidirect
4. #21446700C2semidirect
5. #21446695C2semidirect
6. #21446516C2semidirect
7. #21446509C2semidirect
8. #21446454C2semidirect
9. #21446440C2semidirect
10. #21446166C2semidirect
11. #21446152C2semidirect
12. #21446139C2semidirect
13. #21446020C2semidirect
14. #21445760C2semidirect
15. C61×#1749C2semidirect
23. #16839909C4semidirect
65. C2×#11758222C2×C4semidirect
75. C2×#11758190C2×C4semidirect
78. C2×D488C2×C4semidirect
108. #14519702C2×C4semidirect
113. #14519699C2×C4semidirect
135. C22⋊C8×C61C2×C4semidirect
387. #1749D61semidirect
442. C61#22051semidirect
511. C22⋊C8C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168399092
C4×#145197512
#214483092
#214467002
#214466952
#214465162
#214465092
#214464542
#214464402
#214461662
#214461522
#214461392
#214460202
#214457602
C61×#17492
#2205161