Finite Group Databasebeta

← #29700425

Subgroups — #29700425

Order 15616.

1274 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839915C211yesmaximal, characteristic
2C2×#16839864C211yesmaximal, characteristic, complemented
3C2×#16839768C211yesmaximal, characteristic
4#21448844C211yesmaximal, characteristic, complemented
5C22⋊C4×D244C211yesmaximal, characteristic
6#21446673C211yesmaximal, characteristic, complemented
7#21446516C211yesmaximal, characteristic, complemented
8#21446440C211yesmaximal, characteristic, complemented
9#21446252C211yesmaximal, characteristic, complemented
10#21446173C211yesmaximal, characteristic, complemented
11#21446152C211yesmaximal, characteristic, complemented
12#21446083C211yesmaximal, characteristic, complemented
13#21446020C211yesmaximal, characteristic, complemented
14C4×#14519699C211yesmaximal, characteristic, complemented
15C61×#1753C211yesmaximal, characteristic, complemented
16C23×D244C2211yescharacteristic
17C22×#11758190C2211yescharacteristic
18C22×#11758190C2211yescharacteristic
19C2×#14519756C2211yescharacteristic
20C2×C4×Dic122C2211yescharacteristic, complemented
21C2×C4×D244C2211yescharacteristic
22C2×C4×D244C2211yescharacteristic
23C2×#14519736C2211yescharacteristic
24C2×C22⋊C4×D61—21no—
25#16839915C418yescomplemented
26#16839864—24no—
27C2×#14519711C2211yescharacteristic, complemented
28C2×#14519709C2211yescharacteristic, complemented
29#16839768—24no—
30C2×#14519702C2211yescharacteristic, complemented
31C2×#14519702C2211yescharacteristic, complemented
32C2×#14519699C2211yescharacteristic
33C2×#14519699C2211yescharacteristic
34C2×#14519699C2211yescharacteristic
35C2×#14519699C2211yescharacteristic
36C2×#14519699C2211yescharacteristic
37C2×#14519699C2211yescharacteristic
38#16839668C2211yescharacteristic, complemented
39#16839664C2211yescharacteristic
40#16839664C2211yescharacteristic
41#16839660C2211yescharacteristic, complemented
42#16839656—21no—
43#16839650—21no—
44#16839644—21no—
45#16839640—21no—
46#16839640—21no—
47#16839622C2211yescharacteristic
48#16839617—21no—
49C4×C4⋊Dic61C2211yescharacteristic, complemented
50#16839613—21no—
51#16839525C2211yescharacteristic, complemented
52#16839525C2211yescharacteristic, complemented
53#16839525C2211yescharacteristic, complemented
54#16839525C2211yescharacteristic, complemented
55C22×M16×C61C2211yescharacteristic
56C2×C22⋊C8×C61C2211yescharacteristic
57C2×#97×C61C2211yescharacteristic, complemented
58C2×C4×C8×C61C2211yescharacteristic, complemented
59C4×C22⋊C4×C61C2211yescharacteristic
60C61×#336C2211yescharacteristic, complemented
61C61×#336C2211yescharacteristic, complemented
62C24×D61—21no—
63C22×Dic122C2311yescharacteristic
64C22×D244—22no—
65C22×D244—22no—
66C22×D244—21no—
67C22×D244—22no—
68C22×D244—41no—
69C22×D244—41no—
70C22×D244C2×C414yes—
71C22×D244C2311yescharacteristic
72C22×D244C2311yescharacteristic
73C22×C4×D61—21no—
74C22×C4×D61—21no—
75C2×#11758190—22no—
76C2×#11758190—22no—
77C2×#11758190—41no—
78C2×#11758190—41no—
79C2×#11758190C2×C414yes—
80C2×#11758190C2×C414yescomplemented
81#14519756—22no—
82#14519756C2×C414yescomplemented
83C4×Dic122—22no—
84C4×Dic122—41no—
85C4×D244—22no—
86C4×D244—22no—
87C4×D244—41no—
88C4×D244—41no—
89#14519736—22no—
90#14519736—41no—
91C2×C4⋊Dic61C2311yescharacteristic
92C2×C4⋊Dic61C2311yescharacteristic
93C2×C4⋊Dic61C2311yescharacteristic
94C2×C4⋊Dic61C2311yescharacteristic
95C2×C4⋊Dic61C2311yescharacteristic
96C2×#11758196—21no—
97C2×#11758196—21no—
98C2×#11758196—21no—
99C2×C22⋊Dic61—21no—
100C2×C22⋊Dic61—21no—
101C2×C22⋊Dic61—21no—
102C2×#11758198—21no—
103C2×#11758198—21no—
104C2×#11758198—21no—
105C2×#11758198—21no—
106C2×#11758198—21no—
107C2×#11758198—21no—
108C22⋊C4×D61—44no—
109C2×C4×Dic61—21no—
110C2×C4×Dic61—21no—
111C2×C4×Dic61—21no—
112#14519711—22no—
113#14519709—41no—
114#14519702—22no—
115#14519702—41no—
116#14519699—22no—
117#14519699—22no—
118#14519699—22no—
119#14519699C2×C414yes—
120#14519699C2×C414yescomplemented
121#14519699D414yes—
122#14519684—21no—
123#14519684—21no—
124#14519684—21no—
125#14519684—21no—
126#14519684—21no—
127C23×C4×C61C2311yescharacteristic
128C2×M16×C61—22no—
129C2×M16×C61—22no—
130C2×M16×C61—41no—
131C22×C8×C61C2311yescharacteristic
132C22×C8×C61C2311yescharacteristic
133C22×C8×C61C2311yescharacteristic
134C22×C8×C61C2311yescharacteristic
135C2×C22⋊C4×C61D411yescharacteristic
136C2×C22⋊C4×C61D411yescharacteristic
137C2×C42×C61C2311yescharacteristic
138C2×C42×C61C2311yescharacteristic
139C22⋊C8×C61C2×C414yescomplemented
140#97×C61—22no—
141C4×C8×C61—41no—
142#95×C61D411yescharacteristic
143#95×C61D411yescharacteristic
144C24×C61C2×D411yescharacteristic
145C23×D61—21no—
146C23×D61—21no—
147C23×D61—24no—
148C23×D61—42no—
149C23×D61—42no—
150C23×D61—42no—
151C23×D61—42no—
152C23×D61—81no—
153C23×D61—81no—
154C22×C4×C61—21no—
155C22×C4×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61C22×C412yes—
159C22×C4×C61C2×D411yescharacteristic
160C22×C4×C61C2×D411yescharacteristic
161C22×C4×C61C2×D411yescharacteristic
162C22×C4×C61C2×D411yescharacteristic
163C22×C4×C61C2×D411yescharacteristic
164C22×C4×C61#4112yes—
165C22×C4×C61C2411yescharacteristic
166C22×Dic61—21no—
167C22×Dic61—21no—
168C22×Dic61—21no—
169C22×Dic61—21no—
170C22×Dic61—21no—
171C22×Dic61—21no—
172C2×D244—21no—
173C2×D244—21no—
174C2×D244—21no—
175C2×D244—21no—
176C2×D244—21no—
177C2×D244—21no—
178C2×D244—21no—
179C2×D244—28no—
180C2×D244—24no—
181C2×D244—21no—
182C2×D244—44no—
183C2×D244—44no—
184C2×D244—44no—
185C2×D244—42no—
186C2×D244—42no—
187C2×D244C22×C412yes—
188C2×D244C22×C412yes—
189C2×D244C2×D412yes—
190C2×D244#4112yes—
191C2×C4×D61—42no—
192C2×C4×D61—42no—
193C2×C4×D61—42no—
194C2×C4×D61—42no—
195C2×C4×D61—81no—
196C2×C4×D61—81no—
197C2×Dic122—21no—
198C2×Dic122—21no—
199C2×Dic122—21no—
200C2×Dic122—21no—
201C2×Dic122—21no—
202C2×Dic122C22×C412yes—
203M16×C61—44no—
204C2×C8×C61—21no—
205C2×C8×C61—21no—
206C2×C8×C61—21no—
207C2×C8×C61—21no—
208C2×C8×C61—21no—
209C2×C8×C61—21no—
210C2×C8×C61—21no—
211C2×C8×C61—21no—
212C2×C8×C61—21no—
213C2×C8×C61C22×C412yes—
214C2×C8×C61C22×C412yes—
215C2×C8×C61C2×D412yes—
216C22⋊C4×C61—22no—
217C22⋊C4×C61—41no—
218C42×C61—21no—
219C42×C61—21no—
220C42×C61—21no—
221C42×C61—21no—
222C22⋊Dic61—24no—
223C22⋊Dic61—42no—
224C22⋊Dic61—42no—
225#11758198—42no—
226#11758198—42no—
227#11758198—42no—
228#11758198—42no—
229#11758198—81no—
230#11758198—81no—
231C4⋊Dic61—21no—
232C4⋊Dic61—21no—
233C4⋊Dic61—21no—
234C4⋊Dic61—21no—
235C4⋊Dic61—21no—
236C4⋊Dic61—21no—
237C4⋊Dic61—21no—
238C4⋊Dic61—21no—
239C4⋊Dic61C22×C412yes—
240C4⋊Dic61C2×D412yes—
241#11758196—24no—
242#11758196—42no—
243#11758196—42no—
244C4×Dic61—42no—
245C4×Dic61—42no—
246C4×Dic61—42no—
247#11758190—28no—
248#11758190—44no—
249C23×C61—21no—
250C23×C61—21no—
251C23×C61—21no—
252C23×C61—21no—
253C23×C61—21no—
254C23×C61—21no—
255C23×C61C4×D412yes—
256C23×C61C22×D411yescharacteristic
257C22×D61—22no—
258C22×D61—22no—
259C22×D61—22no—
260C22×D61—22no—
261C22×D61—48no—
262C22×D61—41no—
263C22×D61—41no—
264C22×D61—41no—
265C22×D61—41no—
266C22×D61—48no—
267C22×D61—41no—
268C22×D61—41no—
269C22×D61—41no—
270C22×D61—41no—
271C22×D61—41no—
272C22×D61—41no—
273C22×D61—84no—
274C22×D61—84no—
275C22×D61—84no—
276C22×D61—84no—
277C22×D61—84no—
278C2×C4×C61—21no—
279C2×C4×C61—21no—
280C2×C4×C61—21no—
281C2×C4×C61—21no—
282C2×C4×C61—22no—
283C2×C4×C61—22no—
284C2×C4×C61—22no—
285C2×C4×C61—22no—
286C2×C4×C61—21no—
287C2×C4×C61—21no—
288C2×C4×C61—21no—
289C2×C4×C61—21no—
290C2×C4×C61—21no—
291C2×C4×C61—21no—
292C2×C4×C61—21no—
293C2×C4×C61—21no—
294C2×C4×C61—21no—
295C2×C4×C61C4×D412yes—
296C2×C4×C61AGL(1,ℤ/8)12yes—
297C2×C4×C61C23×C411yescharacteristic
298C2×C4×C61C22×D411yescharacteristic
299C2×C4×C61C2×#4111yescharacteristic
300C2×C4×C61C2×#4111yescharacteristic
301C2×C4×C61H(5,𝔽2)11yescharacteristic
302C2×C4×C61H(5,𝔽2)11yescharacteristic
303C2×Dic61—22no—
304C2×Dic61—22no—
305C2×Dic61—22no—
306C2×Dic61—41no—
307C2×Dic61—41no—
308C2×Dic61—41no—
309C2×Dic61—41no—
310C2×Dic61—41no—
311C2×Dic61—41no—
312C2×Dic61—41no—
313C2×Dic61—41no—
314C2×Dic61—41no—
315C2×Dic61—41no—
316C2×Dic61—41no—
317C2×Dic61—41no—
318C2×Dic61—41no—
319C2×Dic61—41no—
320C2×Dic61—41no—
321D244—22no—
322D244—22no—
323D244—22no—
324D244—22no—
325D244—22no—
326D244—48no—
327D244—41no—
328D244—41no—
329D244C4×D414yes—
330C4×D61—84no—
331C4×D61—84no—
332Dic122—22no—
333Dic122—22no—
334Dic122—41no—
335Dic122—41no—
336C8×C61—22no—
337C8×C61—22no—
338C8×C61—22no—
339C8×C61—41no—
340#22864—611nomaximal, Sylow
341C22×C61—22no—
342C22×C61—22no—
343C22×C61—22no—
344C22×C61—41no—
345C22×C61—41no—
346C22×C61—41no—
347C22×C61—41no—
348C22×C61C2×C4×D411yescharacteristic
349C22×C61D4211yescharacteristic
350C22×C61#54611yescharacteristic
351C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
352C22×C61#57511yescharacteristic
353C22×C61#57711yescharacteristic
354C22×C61#57711yescharacteristic
355C2×D61—24no—
356C2×D61—42no—
357C2×D61—42no—
358C2×D61—42no—
359C2×D61—42no—
360C2×D61—42no—
361C2×D61—42no—
362C2×D61—42no—
363C2×D61—42no—
364C2×D61—42no—
365C2×D61—816no—
366C2×D61—81no—
367C2×D61—81no—
368C2×D61—81no—
369C2×D61—81no—
370C4×C61—22no—
371C4×C61—22no—
372C4×C61—41no—
373C4×C61—41no—
374C4×C61—41no—
375C4×C61C2×C4×D411yescharacteristic
376C4×C61#51811yescharacteristic
377C4×C61#54611yescharacteristic
378C4×C61#55111yescharacteristic
379Dic61—42no—
380Dic61—42no—
381Dic61—42no—
382Dic61—81no—
383Dic61—81no—
384Dic61—81no—
385C2×#450—611no—
386C2×#440—611no—
387C2×#418—611no—
388#2362—611no—
389D4×C22⋊C4—611no—
390#1968—611no—
391#1936—611no—
392#1925—611no—
393#1894—611no—
394#1880—611no—
395#1877—611no—
396#1864—611no—
397#1854—611no—
398C4×#102—611no—
399#1753D6111yescharacteristic, complemented
400C2×C61—42no—
401C2×C61#235811yescharacteristic
402C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
403C2×C61#294911yescharacteristic
404C2×C61#327211yescharacteristic
405C2×C61#327511yescharacteristic
406C2×C61#331011yescharacteristic
407C2×C61#331111yescharacteristic
408D61—44no—
409D61—82no—
410C23×D4—611no—
411C22×SD16—611no—
412C22×SD16—611no—
413C22×M16C2×D6111yescharacteristic
414C2×C22⋊Q8—611no—
415C2×C4×Q8—611no—
416C2×C4×D4—611no—
417C2×C4×D4—611no—
418C2×#117—611no—
419C22×C22⋊C4—1221no—
420#450—618no—
421#440—1224no—
422C2×#107—611no—
423C2×#106—611no—
424#418—1224no—
425C2×#103—611no—
426C2×#103—611no—
427C2×#102—611no—
428C2×#102—611no—
429C2×#102—611no—
430C2×#102—611no—
431C2×#102—611no—
432C2×#102—611no—
433C2×C22⋊C8C2×D6111yescharacteristic
434C2×#97C2×D6111yescharacteristic, complemented
435C2×C4×C8C2×D6111yescharacteristic, complemented
436#391—611no—
437#390—611no—
438#390—611no—
439#389—611no—
440#388—1221no—
441#388—1221no—
442#387—1221no—
443#386—1221no—
444#386—1221no—
445#380—611no—
446#379—1221no—
447C4×C4⋊C4—611no—
448C4×C4⋊C4—1221no—
449C4×C22⋊C4C2×D6111yescharacteristic
450#340—611no—
451#340—611no—
452#340—611no—
453#340—611no—
454#336C2×D6111yescharacteristic, complemented
455#336C2×D6111yescharacteristic, complemented
456C61#2286411yescharacteristic, complemented, Sylow
457C25—1221no—
458C22×Q8—611no—
459C22×D4—614no—
460C22×D4—611no—
461C22×D4—611no—
462C22×D4—1222no—
463C22×D4—1222no—
464C22×D4—1221no—
465C22×D4—1222no—
466C22×D4—2441no—
467C22×D4—2441no—
468C23×C4—1221no—
469C23×C4—1221no—
470C23×C4C22×D6111yescharacteristic
471C2×SD16—614no—
472C2×SD16—614no—
473C2×SD16—1222no—
474C2×SD16—1222no—
475C2×SD16—2441no—
476C2×SD16—2441no—
477C2×M16—22no—
478C2×M16—22no—
479C2×M16—41no—
480C22×C8C22×D6111yescharacteristic
481C22×C8C22×D6111yescharacteristic
482C22×C8C22×D6111yescharacteristic
483C22×C8C22×D6111yescharacteristic
484C22⋊Q8—614no—
485C22⋊Q8—1222no—
486C4×Q8—1222no—
487C4×Q8—2441no—
488C4×D4—1222no—
489C4×D4—1222no—
490C4×D4—2441no—
491C4×D4—2441no—
492#117—1222no—
493#117—2441no—
494C2×C4⋊C4—611no—
495C2×C4⋊C4—611no—
496C2×C4⋊C4—611no—
497C2×C4⋊C4—611no—
498C2×C4⋊C4—611no—
499C2×C4⋊C4—1221no—
500C2×C4⋊C4—1221no—
501C2×C4⋊C4—1221no—
502C2×C22⋊C4—1221no—
503C2×C22⋊C4—1221no—
504C2×C22⋊C4—1221no—
505C2×C22⋊C4—1221no—
506C2×C22⋊C4—1221no—
507C2×C22⋊C4—1221no—
508C2×C22⋊C4—1221no—
509C2×C22⋊C4—1221no—
510C2×C22⋊C4—1221no—
511C2×C22⋊C4—2444no—
512C2×C22⋊C4D24411yescharacteristic
513C2×C22⋊C4D24411yescharacteristic
514C2×C42—1221no—
515C2×C42—1221no—
516C2×C42—1221no—
517C2×C42C22×D6111yescharacteristic
518C2×C42C22×D6111yescharacteristic
519#107—1222no—
520#106—2441no—
521#103—1222no—
522#103—2441no—
523#102—614no—
524#102—614no—
525#102—614no—
526#102—1222no—
527#102—1222no—
528#102—1222no—
529C22⋊C8C4×D6114yescomplemented
530#97—22no—
531C4×C8—41no—
532#95—1221no—
533#95—1221no—
534#95—1221no—
535#95—1221no—
536#95—1221no—
537#95D24411yescharacteristic
538#95D24411yescharacteristic
539C24—1221no—
540C24—1224no—
541C24—1221no—
542C24—4881no—
543C24—4881no—
544C24—2442no—
545C24—2442no—
546C24—2442no—
547C24—2442no—
548C24C2×D24411yescharacteristic
549C2×Q8—612no—
550C2×Q8—1221no—
551C2×Q8—1221no—
552C2×Q8—1221no—
553C2×Q8—1221no—
554C2×Q8—1221no—
555C2×D4—612no—
556C2×D4—612no—
557C2×D4—612no—
558C2×D4—612no—
559C2×D4—1228no—
560C2×D4—1221no—
561C2×D4—1221no—
562C2×D4—1221no—
563C2×D4—1221no—
564C2×D4—1221no—
565C2×D4—1221no—
566C2×D4—1221no—
567C2×D4—1221no—
568C2×D4—1224no—
569C2×D4—2444no—
570C2×D4—2444no—
571C2×D4—2444no—
572C2×D4—2442no—
573C2×D4—2442no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—1221no—
579C22×C4—1221no—
580C22×C4—1221no—
581C22×C4—1221no—
582C22×C4—1221no—
583C22×C4—1221no—
584C22×C4—4881no—
585C22×C4—4881no—
586C22×C4—2442no—
587C22×C4—2442no—
588C22×C4—2442no—
589C22×C4—2442no—
590C22×C4C2×C4×D6112yes—
591C22×C4C2×D24411yescharacteristic
592C22×C4C2×D24411yescharacteristic
593C22×C4C2×D24411yescharacteristic
594C22×C4C2×D24411yescharacteristic
595C22×C4C2×D24411yescharacteristic
596C22×C4#1175822212yes—
597C22×C4C23×D6111yescharacteristic
598SD16—1228no—
599SD16—2444no—
600M16—44no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8C2×C4×D6112yes—
611C2×C8C2×C4×D6112yes—
612C2×C8D4×D6112yes—
613C4⋊C4—612no—
614C4⋊C4—612no—
615C4⋊C4—1221no—
616C4⋊C4—1221no—
617C4⋊C4—1224no—
618C4⋊C4—1221no—
619C4⋊C4—1221no—
620C4⋊C4—1221no—
621C4⋊C4—1221no—
622C4⋊C4—1221no—
623C4⋊C4—1221no—
624C4⋊C4—2442no—
625C4⋊C4—2442no—
626C22⋊C4—22no—
627C22⋊C4—41no—
628C22⋊C4—1224no—
629C22⋊C4—4881no—
630C22⋊C4—4881no—
631C22⋊C4—2442no—
632C22⋊C4—2442no—
633C22⋊C4—2442no—
634C22⋊C4—2442no—
635C22⋊C4—2442no—
636C22⋊C4—2442no—
637C42—21no—
638C42—21no—
639C42—21no—
640C42—21no—
641C42—2442no—
642C42—2442no—
643C42—2442no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—1222no—
651C23—1222no—
652C23—1222no—
653C23—1222no—
654C23—4884no—
655C23—4884no—
656C23—4884no—
657C23—4884no—
658C23—4884no—
659C23—2448no—
660C23—2448no—
661C23—2441no—
662C23—2441no—
663C23—2441no—
664C23—2441no—
665C23—2441no—
666C23—2441no—
667C23—2441no—
668C23—2441no—
669C23—2441no—
670C23—2441no—
671C23C4×D24412yes—
672C23C22×D24411yescharacteristic
673Q8—1222no—
674Q8—1222no—
675Q8—2441no—
676Q8—2441no—
677D4—614no—
678D4—1222no—
679D4—1222no—
680D4—1222no—
681D4—1222no—
682D4—1222no—
683D4—2448no—
684D4—2441no—
685D4—2441no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—1222no—
704C2×C4—1222no—
705C2×C4—1222no—
706C2×C4—4884no—
707C2×C4—4884no—
708C2×C4—2441no—
709C2×C4—2441no—
710C2×C4—2441no—
711C2×C4—2441no—
712C2×C4—2441no—
713C2×C4—2441no—
714C2×C4—2441no—
715C2×C4—2441no—
716C2×C4—2441no—
717C2×C4—2441no—
718C2×C4—2441no—
719C2×C4—2441no—
720C2×C4—2441no—
721C2×C4—2441no—
722C2×C4—2441no—
723C2×C4C4×D24412yes—
724C2×C4#1451980512yes—
725C2×C4C22×C4×D6111yescharacteristic
726C2×C4C2×D4×D6111yescharacteristic
727C2×C4#41×D6111yescharacteristic
728C2×C4C2×#1175822211yescharacteristic
729C2×C4#1451982211yescharacteristic
730C2×C4#1451982311yescharacteristic
731C8—22no—
732C8—22no—
733C8—22no—
734C8—41no—
735C22—22no—
736C22—22no—
737C22—22no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—41no—
742C22—1224no—
743C22—48816no—
744C22—4881no—
745C22—4881no—
746C22—4881no—
747C22—4881no—
748C22—2442no—
749C22—2442no—
750C22—2442no—
751C22—2442no—
752C22—2442no—
753C22—2442no—
754C22—2442no—
755C22—2442no—
756C22—2442no—
757C22C2×C4×D24411yescharacteristic
758C22D4×D24411yescharacteristic
759C22#1684040711yescharacteristic
760C22C2×#1451980511yescharacteristic
761C22#1684056211yescharacteristic
762C22#1684057411yescharacteristic
763C22#1684057411yescharacteristic
764C4—22no—
765C4—22no—
766C4—41no—
767C4—41no—
768C4—41no—
769C4—4881no—
770C4—4881no—
771C4—4881no—
772C4—2442no—
773C4—2442no—
774C4—2442no—
775C4C4×D4×D6111yescharacteristic
776C4#1684023411yescharacteristic
777C4#1684040211yescharacteristic
778C4#1684043611yescharacteristic
779C2—42no—
780C2—4882no—
781C2—2444no—
782C2#2144880111yescharacteristic
783C2C4×#1451980511yescharacteristic
784C2#2145468011yescharacteristic
785C2#2145742111yescharacteristic
786C2#2145745511yescharacteristic
787C2#2145784211yescharacteristic
788C2#2145785711yescharacteristic
subgroupG/H
centerC23C22×D244
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1753C2
socleC23×C61C22×D4
prime radicalC23×D244C22
cosocleC22×C4×C61C24
hypercenter#1753D61
hypocenterC61#22864
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1753

Complements

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

NH ≅ G/Ntype
2. C2×#16839864C2semidirect
4. #21448844C2semidirect
6. #21446673C2semidirect
7. #21446516C2semidirect
8. #21446440C2semidirect
9. #21446252C2semidirect
10. #21446173C2semidirect
11. #21446152C2semidirect
12. #21446083C2semidirect
13. #21446020C2semidirect
14. C4×#14519699C2semidirect
15. C61×#1753C2semidirect
20. C2×C4×Dic122C22semidirect
25. #16839915C4semidirect
27. C2×#14519711C22semidirect
28. C2×#14519709C22semidirect
30. C2×#14519702C22semidirect
31. C2×#14519702C22semidirect
38. #16839668C22semidirect
41. #16839660C22semidirect
49. C4×C4⋊Dic61C22semidirect
51. #16839525C22semidirect
52. #16839525C22semidirect
53. #16839525C22semidirect
54. #16839525C22semidirect
57. C2×#97×C61C22semidirect
58. C2×C4×C8×C61C22semidirect
60. C61×#336C22semidirect
61. C61×#336C22semidirect
80. C2×#11758190C2×C4semidirect
82. #14519756C2×C4semidirect
120. #14519699C2×C4semidirect
139. C22⋊C8×C61C2×C4semidirect
399. #1753D61semidirect
434. C2×#97C2×D61semidirect
435. C2×C4×C8C2×D61semidirect
454. #336C2×D61semidirect
455. #336C2×D61semidirect
456. C61#22864semidirect
529. C22⋊C8C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168399152
C2×#168398642
C2×#168397682
#214488442
C22⋊C4×D2442
#214466732
#214465162
#214464402
#214462522
#214461732
#214461522
#214460832
#214460202
C4×#145196992
C61×#17532
#2286461