Finite Group Databasebeta

← #29717721

Subgroups — #29717721

Order 15616.

1674 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840408C211yesmaximal, characteristic, complemented
2C2×#16839989C211yesmaximal, characteristic, complemented
3C2×#16839905C211yesmaximal, characteristic, complemented
4C2×#16839895C211yesmaximal, characteristic, complemented
5C22×#14519697C211yesmaximal, characteristic, complemented
6#21447060C211yesmaximal, characteristic, complemented
7#21447008C211yesmaximal, characteristic, complemented
8#21446895C211yesmaximal, characteristic, complemented
9#21446815C211yesmaximal, characteristic, complemented
10#21446170C211yesmaximal, characteristic, complemented
11#21446126C211yesmaximal, characteristic, complemented
12#21446112C211yesmaximal, characteristic, complemented
13#21446079C211yesmaximal, characteristic, complemented
14#21445757C211yesmaximal, characteristic, complemented
15C61×#2416C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C23×D244C2211yescharacteristic
18C22×#11758200C2211yescharacteristic, complemented
19C22×#11758199C2211yescharacteristic
20C22×#11758199C2211yescharacteristic
21C23×#92418C2211yescharacteristic
22#16840408—24no—
23#16840408—24no—
24C2×#14519765C2211yescharacteristic
25C2×#14519762—21no—
26C2×#14519756C2211yescharacteristic
27C2×#14519751C2211yescharacteristic
28C2×#14519750—21no—
29C2×#14519745—21no—
30C2×C4×D244C2211yescharacteristic
31C2×C22⋊C4×D61—21no—
32#16839989—24no—
33#16839905—24no—
34#16839895—24no—
35C2×#14519708C2211yescharacteristic, complemented
36C2×#14519700C2211yescharacteristic, complemented
37C2×#14519700C2211yescharacteristic, complemented
38C2×#14519700C2211yescharacteristic, complemented
39C2×#14519698C2211yescharacteristic, complemented
40C2×#14519697—24no—
41C2×#14519697C2211yescharacteristic
42C2×#14519697C2211yescharacteristic
43C2×#14519697C2211yescharacteristic
44C2×#14519697C2211yescharacteristic
45C2×#14519697C2211yescharacteristic
46C2×#14519697C2211yescharacteristic
47C2×C22⋊#92418C2211yescharacteristic
48C2×C22⋊#92418C2211yescharacteristic, complemented
49C2×C22⋊#92418C2211yescharacteristic, complemented
50#16839524C2211yescharacteristic, complemented
51#16839524C2211yescharacteristic, complemented
52#16839517C2211yescharacteristic, complemented
53#16839517C2211yescharacteristic, complemented
54C2×#121×C61—21no—
55C2×#121×C61C2211yescharacteristic
56C2×#121×C61C2211yescharacteristic, complemented
57C2×C4×D4×C61C2211yescharacteristic
58C22×C4⋊C4×C61C2211yescharacteristic
59C61×#396—21no—
60C61×#394—21no—
61C61×#390C2211yescharacteristic, complemented
62C61×#389C2211yescharacteristic, complemented
63C61×#386—21no—
64C61×#380C2211yescharacteristic, complemented
65C24×D61—21no—
66C2×#11758222—22no—
67C2×#11758222—22no—
68C2×#11758222—22no—
69C2×#11758222—22no—
70C2×#11758222—41no—
71C2×#11758222—41no—
72C22×Dic122C2311yescharacteristic
73C22×D244—22no—
74C22×D244—22no—
75C22×D244—21no—
76C22×D244—22no—
77C22×D244—41no—
78C22×D244—41no—
79C22×D244D414yescomplemented
80C22×D244C2311yescharacteristic
81C22×D244C2311yescharacteristic
82C22×C22⋊D61—21no—
83C22×C22⋊D61—21no—
84C22×C4×D61—21no—
85C22×C4×D61—21no—
86C2×#11758200—22no—
87C2×#11758200—22no—
88C2×#11758200—41no—
89C2×#11758199—22no—
90C2×#11758199—22no—
91C2×#11758199—22no—
92C2×#11758199—22no—
93C2×#11758199—41no—
94C2×#11758199—41no—
95C22×#92418—22no—
96C22×#92418—22no—
97C22×#92418—41no—
98C22×#92418C2311yescharacteristic
99C22×#92418C2311yescharacteristic
100C22×#92418C2311yescharacteristic
101C22×#92418C2311yescharacteristic
102#14519765—22no—
103#14519765—22no—
104#14519762—28no—
105#14519756—22no—
106#14519756D414yescomplemented
107#14519751—22no—
108#14519751—22no—
109#14519750—28no—
110#14519745—28no—
111C4×D244—22no—
112C4×D244—22no—
113C2×C4⋊Dic61C2311yescharacteristic
114C2×#11758196—21no—
115C2×C22⋊Dic61—21no—
116C2×#11758198—21no—
117C2×#11758198—21no—
118C2×#11758198—21no—
119C2×#11758198—21no—
120C22⋊C4×D61—28no—
121#14519708—22no—
122#14519700—22no—
123#14519700—22no—
124#14519700—41no—
125#14519698—22no—
126#14519697—22no—
127#14519697—22no—
128#14519697—22no—
129#14519697—22no—
130#14519697—22no—
131#14519697D414yescomplemented
132C22⋊#92418—22no—
133C22⋊#92418—22no—
134C22⋊#92418—41no—
135C22×D4×C61—21no—
136C22×D4×C61—21no—
137C22×D4×C61D411yescharacteristic
138C22×D4×C61C2311yescharacteristic
139C23×C4×C61—21no—
140C23×C4×C61C2311yescharacteristic
141C23×C4×C61C2311yescharacteristic
142#121×C61—22no—
143#121×C61—22no—
144#121×C61—22no—
145#121×C61—41no—
146#121×C61—44no—
147C4×D4×C61—22no—
148C4×D4×C61—22no—
149C2×C4⋊C4×C61—22no—
150C2×C4⋊C4×C61—21no—
151C2×C4⋊C4×C61—21no—
152C2×C4⋊C4×C61—41no—
153C2×C4⋊C4×C61D411yescharacteristic
154C2×C4⋊C4×C61C2311yescharacteristic
155C2×C4⋊C4×C61C2311yescharacteristic
156C2×C4⋊C4×C61C2311yescharacteristic
157C2×C22⋊C4×C61—21no—
158C2×C22⋊C4×C61—21no—
159C2×C22⋊C4×C61—21no—
160C2×C22⋊C4×C61—21no—
161C2×C22⋊C4×C61—21no—
162C2×C22⋊C4×C61D411yescharacteristic
163C2×C22⋊C4×C61D411yescharacteristic
164C2×C42×C61C2311yescharacteristic
165#95×C61—21no—
166#95×C61—21no—
167C24×C61—21no—
168C24×C61C2×D411yescharacteristic
169C24×C61C2×D411yescharacteristic
170C23×D61—21no—
171C23×D61—21no—
172C23×D61—24no—
173C23×D61—42no—
174C23×D61—42no—
175C23×D61—42no—
176C23×D61—42no—
177C23×D61—81no—
178C23×D61—81no—
179C2×D4×C61—22no—
180C2×D4×C61—22no—
181C2×D4×C61—22no—
182C2×D4×C61—21no—
183C2×D4×C61—21no—
184C2×D4×C61—21no—
185C2×D4×C61—21no—
186C2×D4×C61—21no—
187C2×D4×C61—21no—
188C2×D4×C61—42no—
189C2×D4×C61—42no—
190C2×D4×C61—42no—
191C2×D4×C61—42no—
192C2×D4×C61—42no—
193C2×D4×C61—81no—
194C22×C4×C61—21no—
195C22×C4×C61—21no—
196C22×C4×C61—21no—
197C22×C4×C61—21no—
198C22×C4×C61—21no—
199C22×C4×C61—21no—
200C22×C4×C61—21no—
201C22×C4×C61—21no—
202C22×C4×C61—21no—
203C22×C4×C61—21no—
204C22×C4×C61—21no—
205C22×C4×C61—21no—
206C22×C4×C61—21no—
207C22×C4×C61—42no—
208C22×C4×C61—42no—
209C22×C4×C61—81no—
210C22×C4×C61C2×D411yescharacteristic
211C22×C4×C61C2×D411yescharacteristic
212C22×C4×C61C2×D411yescharacteristic
213C22×C4×C61C2×D411yescharacteristic
214C22×C4×C61C2×D412yes—
215C22×C4×C61C2×D412yes—
216C22×C4×C61C2411yescharacteristic
217C2×C22⋊D61—24no—
218C2×C22⋊D61—24no—
219C2×C22⋊D61—42no—
220C2×C22⋊D61—42no—
221C2×C22⋊D61—81no—
222C2×C22⋊D61—81no—
223C22×Dic61—21no—
224C22×Dic61—21no—
225#11758222—44no—
226#11758222—44no—
227#11758222—44no—
228#11758222—44no—
229C2×D244—21no—
230C2×D244—21no—
231C2×D244—21no—
232C2×D244—21no—
233C2×D244—21no—
234C2×D244—21no—
235C2×D244—21no—
236C2×D244—28no—
237C2×D244—24no—
238C2×D244—21no—
239C2×D244—44no—
240C2×D244—44no—
241C2×D244—44no—
242C2×D244—42no—
243C2×D244—42no—
244C2×D244C2×D412yes—
245C2×D244C2×D412yes—
246C2×D244C2×D412yes—
247C2×D244#4112yes—
248C2×C4×D61—24no—
249C2×C4×D61—24no—
250C2×C4×D61—42no—
251C2×C4×D61—42no—
252C2×C4×D61—81no—
253C2×C4×D61—81no—
254C2×Dic122—21no—
255C2×Dic122—21no—
256C2×Dic122—21no—
257C2×Dic122—21no—
258C2×Dic122—21no—
259C2×Dic122C2×D412yes—
260C4⋊C4×C61—22no—
261C4⋊C4×C61—21no—
262C4⋊C4×C61—21no—
263C4⋊C4×C61—21no—
264C4⋊C4×C61—21no—
265C4⋊C4×C61—21no—
266C4⋊C4×C61—42no—
267C4⋊C4×C61—42no—
268C4⋊C4×C61C2×D412yes—
269C22⋊C4×C61—22no—
270C22⋊C4×C61—22no—
271C22⋊C4×C61—42no—
272C22⋊C4×C61—42no—
273C22⋊C4×C61—42no—
274C22⋊C4×C61—42no—
275C22⋊C4×C61—81no—
276C42×C61—21no—
277C42×C61—21no—
278C22⋊Dic61—24no—
279#11758200—44no—
280#11758199—44no—
281#11758199—44no—
282#11758198—24no—
283#11758198—24no—
284#11758198—24no—
285#11758198—24no—
286C4⋊Dic61—21no—
287C4⋊Dic61C2×D412yes—
288#11758196—24no—
289C2×#92418—21no—
290C2×#92418—21no—
291C2×#92418—21no—
292C2×#92418—21no—
293C2×#92418—21no—
294C2×#92418—21no—
295C2×#92418—21no—
296C2×#92418—21no—
297C2×#92418—21no—
298C2×#92418—21no—
299C2×#92418—21no—
300C2×#92418—44no—
301C2×#92418C2×D412yes—
302C23×C61—21no—
303C23×C61—21no—
304C23×C61—21no—
305C23×C61—21no—
306C23×C61—21no—
307C23×C61—21no—
308C23×C61—21no—
309C23×C61—21no—
310C23×C61—21no—
311C23×C61—21no—
312C23×C61—21no—
313C23×C61—41no—
314C23×C61—41no—
315C23×C61—41no—
316C23×C61—41no—
317C23×C61—41no—
318C23×C61—41no—
319C23×C61—41no—
320C23×C61#12012yes—
321C23×C61#13512yes—
322C23×C61AGL(1,ℤ/8)12yes—
323C23×C61C22×D411yescharacteristic
324C22×D61—22no—
325C22×D61—22no—
326C22×D61—22no—
327C22×D61—22no—
328C22×D61—48no—
329C22×D61—41no—
330C22×D61—41no—
331C22×D61—41no—
332C22×D61—41no—
333C22×D61—41no—
334C22×D61—41no—
335C22×D61—41no—
336C22×D61—41no—
337C22×D61—41no—
338C22×D61—41no—
339C22×D61—48no—
340C22×D61—84no—
341C22×D61—84no—
342C22×D61—84no—
343C22×D61—84no—
344C22×D61—84no—
345D4×C61—44no—
346D4×C61—41no—
347D4×C61—41no—
348D4×C61—41no—
349D4×C61—41no—
350D4×C61—84no—
351D4×C61—84no—
352C2×C4×C61—21no—
353C2×C4×C61—21no—
354C2×C4×C61—22no—
355C2×C4×C61—22no—
356C2×C4×C61—22no—
357C2×C4×C61—22no—
358C2×C4×C61—21no—
359C2×C4×C61—21no—
360C2×C4×C61—21no—
361C2×C4×C61—21no—
362C2×C4×C61—22no—
363C2×C4×C61—21no—
364C2×C4×C61—21no—
365C2×C4×C61—21no—
366C2×C4×C61—21no—
367C2×C4×C61—21no—
368C2×C4×C61—41no—
369C2×C4×C61—41no—
370C2×C4×C61—41no—
371C2×C4×C61—41no—
372C2×C4×C61—41no—
373C2×C4×C61—41no—
374C2×C4×C61—41no—
375C2×C4×C61—41no—
376C2×C4×C61—41no—
377C2×C4×C61—41no—
378C2×C4×C61—41no—
379C2×C4×C61—41no—
380C2×C4×C61—84no—
381C2×C4×C61#12012yes—
382C2×C4×C61C22×D411yescharacteristic
383C2×C4×C61C22×D411yescharacteristic
384C2×C4×C61C22×D411yescharacteristic
385C2×C4×C61C2×#4111yescharacteristic
386C2×C4×C61H(5,𝔽2)11yescharacteristic
387C2×C4×C61H(5,𝔽2)11yescharacteristic
388C22⋊D61—48no—
389C22⋊D61—84no—
390C2×Dic61—22no—
391C2×Dic61—22no—
392C2×Dic61—41no—
393C2×Dic61—41no—
394C2×Dic61—41no—
395C2×Dic61—41no—
396D244—22no—
397D244—22no—
398D244—22no—
399D244—22no—
400D244—22no—
401D244—48no—
402D244—41no—
403D244—41no—
404D244#12114yescomplemented
405C4×D61—48no—
406C4×D61—84no—
407Dic122—22no—
408Dic122—22no—
409Dic122—41no—
410Dic122—41no—
411#92418—22no—
412#92418—41no—
413#92418—41no—
414#92418—41no—
415#24434—611nomaximal, Sylow
416C22×C61—22no—
417C22×C61—22no—
418C22×C61—22no—
419C22×C61—22no—
420C22×C61—22no—
421C22×C61—22no—
422C22×C61—41no—
423C22×C61—41no—
424C22×C61—41no—
425C22×C61—41no—
426C22×C61—41no—
427C22×C61—41no—
428C22×C61—41no—
429C22×C61—81no—
430C22×C61—81no—
431C22×C61—81no—
432C22×C61—81no—
433C22×C61—81no—
434C22×C61—81no—
435C22×C61—81no—
436C22×C61#44914yescomplemented
437C22×C61C2×#12011yescharacteristic
438C22×C61D4211yescharacteristic
439C22×C61#54611yescharacteristic
440C22×C61C2×#13511yescharacteristic
441C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
442C22×C61#57611yescharacteristic
443C22×C61#57711yescharacteristic
444C2×D61—24no—
445C2×D61—42no—
446C2×D61—42no—
447C2×D61—42no—
448C2×D61—42no—
449C2×D61—42no—
450C2×D61—42no—
451C2×D61—42no—
452C2×D61—42no—
453C2×D61—42no—
454C2×D61—816no—
455C2×D61—81no—
456C2×D61—81no—
457C2×D61—81no—
458C2×D61—81no—
459C4×C61—22no—
460C4×C61—41no—
461C4×C61—41no—
462C4×C61—42no—
463C4×C61—41no—
464C4×C61—81no—
465C4×C61—81no—
466C4×C61C2×#12111yescharacteristic
467C4×C61#53411yescharacteristic
468C4×C61D4211yescharacteristic
469C4×C61#54611yescharacteristic
470Dic61—42no—
471Dic61—42no—
472C2×#546—611no—
473C2×#465—611no—
474C2×#449—611no—
475C2×#447—611no—
476C22×#102—611no—
477#2416D6111yescharacteristic, complemented
478#2042—611no—
479#2034—611no—
480#2012—611no—
481#1999—611no—
482#1879—611no—
483#1872—611no—
484#1869—611no—
485#1864—611no—
486#1788—611no—
487C2×C61—24no—
488C2×C61—81no—
489C2×C61—161no—
490C2×C61#241011yescharacteristic
491C2×C61C2×#44911yescharacteristic
492C2×C61#301211yescharacteristic
493C2×C61#326411yescharacteristic
494C2×C61#328211yescharacteristic
495C2×C61#329711yescharacteristic
496C2×C61#330611yescharacteristic
497D61—44no—
498D61—82no—
499C22×#41—611no—
500C23×D4—611no—
501C22×SD16—611no—
502C22×D8—611no—
503C22×D8—611no—
504C23×C8—611no—
505#546—1224no—
506#546—1224no—
507C2×#124—611no—
508C2×#123—1221no—
509C2×C22⋊Q8—611no—
510C2×#121—21no—
511C2×#121—611no—
512C2×#121—1221no—
513C2×#121C2×D6111yescharacteristic
514C2×#121C2×D6111yescharacteristic, complemented
515C2×#120—1221no—
516C2×C4×D4—611no—
517C2×C4×D4C2×D6111yescharacteristic
518C22×C4⋊C4C2×D6111yescharacteristic
519C22×C22⋊C4—1221no—
520#465—1224no—
521#449—1224no—
522#447—1224no—
523C2×#106—611no—
524C2×#103—611no—
525C2×#103—611no—
526C2×#103—611no—
527C2×#102—611no—
528C2×#102—611no—
529C2×#102—611no—
530C2×#102—611no—
531C2×#102—611no—
532C2×#102—611no—
533C2×#102—611no—
534C2×#102—1224no—
535C2×C22⋊C8—611no—
536C2×C22⋊C8—611no—
537C2×C22⋊C8—611no—
538#396—21no—
539#394—21no—
540#390C2×D6111yescharacteristic, complemented
541#389C2×D6111yescharacteristic, complemented
542#386—21no—
543#380C2×D6111yescharacteristic, complemented
544#340—611no—
545#340—611no—
546#336—611no—
547#336—611no—
548C61#2443411yescharacteristic, complemented, Sylow
549C25—1221no—
550C2×#41—1222no—
551C2×#41—1222no—
552C2×#41—1222no—
553C2×#41—1222no—
554C2×#41—2441no—
555C2×#41—2441no—
556C22×Q8—611no—
557C22×D4—21no—
558C22×D4—21no—
559C22×D4—614no—
560C22×D4—611no—
561C22×D4—611no—
562C22×D4—1222no—
563C22×D4—1222no—
564C22×D4—1221no—
565C22×D4—1221no—
566C22×D4—1222no—
567C22×D4—1221no—
568C22×D4—2441no—
569C22×D4—2441no—
570C22×D4C22⋊D6111yescharacteristic
571C22×D4C22×D6111yescharacteristic
572C23×C4—21no—
573C23×C4—1221no—
574C23×C4—1221no—
575C23×C4C22×D6111yescharacteristic
576C23×C4C22×D6111yescharacteristic
577C2×SD16—1222no—
578C2×SD16—1222no—
579C2×SD16—2441no—
580C2×D8—1222no—
581C2×D8—1222no—
582C2×D8—1222no—
583C2×D8—1222no—
584C2×D8—2441no—
585C2×D8—2441no—
586C22×C8—611no—
587C22×C8—611no—
588C22×C8—611no—
589C22×C8—611no—
590C22×C8—1222no—
591C22×C8—1222no—
592C22×C8—2441no—
593#124—1222no—
594#124—1222no—
595#123—1228no—
596C22⋊Q8—614no—
597C22⋊Q8—1222no—
598#121—22no—
599#121—22no—
600#121—22no—
601#121—41no—
602#121—44no—
603#121—1228no—
604#121—1222no—
605#121—1222no—
606#120—1228no—
607C4×D4—22no—
608C4×D4—22no—
609C4×D4—1222no—
610C4×D4—1222no—
611C2×C4⋊C4—22no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—41no—
615C2×C4⋊C4—611no—
616C2×C4⋊C4—1221no—
617C2×C4⋊C4C22⋊D6111yescharacteristic
618C2×C4⋊C4C22×D6111yescharacteristic
619C2×C4⋊C4C22×D6111yescharacteristic
620C2×C4⋊C4C22×D6111yescharacteristic
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—1228no—
627C2×C22⋊C4—1221no—
628C2×C22⋊C4—1221no—
629C2×C22⋊C4—1221no—
630C2×C22⋊C4—1221no—
631C2×C22⋊C4—1221no—
632C2×C22⋊C4C22⋊D6111yescharacteristic
633C2×C22⋊C4C22⋊D6111yescharacteristic
634C2×C42C22×D6111yescharacteristic
635#106—1222no—
636#103—1222no—
637#103—1222no—
638#103—2441no—
639#102—614no—
640#102—1222no—
641#102—1222no—
642#102—1222no—
643#102—1222no—
644#102—1222no—
645#102—1222no—
646C22⋊C8—1222no—
647C22⋊C8—1222no—
648C22⋊C8—2441no—
649#95—21no—
650#95—21no—
651C24—21no—
652C24—1221no—
653C24—1224no—
654C24—1221no—
655C24—4881no—
656C24—4881no—
657C24—2442no—
658C24—2442no—
659C24—2442no—
660C24—2442no—
661C24C2×C22⋊D6111yescharacteristic
662C24C2×C22⋊D6111yescharacteristic
663#41—2444no—
664#41—2444no—
665#41—2444no—
666#41—2444no—
667C2×Q8—612no—
668C2×Q8—1221no—
669C2×Q8—1221no—
670C2×Q8—1221no—
671C2×Q8—1221no—
672C2×Q8—1221no—
673C2×D4—22no—
674C2×D4—22no—
675C2×D4—22no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—42no—
683C2×D4—42no—
684C2×D4—42no—
685C2×D4—42no—
686C2×D4—42no—
687C2×D4—81no—
688C2×D4—612no—
689C2×D4—612no—
690C2×D4—612no—
691C2×D4—612no—
692C2×D4—1228no—
693C2×D4—1224no—
694C2×D4—1224no—
695C2×D4—1221no—
696C2×D4—1221no—
697C2×D4—1221no—
698C2×D4—1221no—
699C2×D4—1221no—
700C2×D4—1221no—
701C2×D4—1221no—
702C2×D4—1221no—
703C2×D4—1224no—
704C2×D4—4881no—
705C2×D4—4881no—
706C2×D4—2444no—
707C2×D4—2444no—
708C2×D4—2444no—
709C2×D4—2442no—
710C2×D4—2442no—
711C2×D4—2442no—
712C2×D4—2442no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—42no—
727C22×C4—42no—
728C22×C4—81no—
729C22×C4—1224no—
730C22×C4—1224no—
731C22×C4—1221no—
732C22×C4—1221no—
733C22×C4—4881no—
734C22×C4—4881no—
735C22×C4—2442no—
736C22×C4—2442no—
737C22×C4D4×D6112yes—
738C22×C4D4×D6112yes—
739C22×C4C2×C22⋊D6111yescharacteristic
740C22×C4C2×C22⋊D6111yescharacteristic
741C22×C4C2×C22⋊D6111yescharacteristic
742C22×C4C2×C22⋊D6111yescharacteristic
743C22×C4C23×D6111yescharacteristic
744SD16—2444no—
745D8—2444no—
746D8—2444no—
747C2×C8—612no—
748C2×C8—1221no—
749C2×C8—1221no—
750C2×C8—1221no—
751C2×C8—1221no—
752C2×C8—1221no—
753C2×C8—1221no—
754C2×C8—1221no—
755C2×C8—1221no—
756C2×C8—1221no—
757C2×C8—1221no—
758C2×C8—1221no—
759C2×C8—2444no—
760C4⋊C4—21no—
761C4⋊C4—22no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—42no—
767C4⋊C4—42no—
768C4⋊C4—612no—
769C4⋊C4—1221no—
770C4⋊C4—1224no—
771C4⋊C4D4×D6112yes—
772C22⋊C4—22no—
773C22⋊C4—22no—
774C22⋊C4—42no—
775C22⋊C4—42no—
776C22⋊C4—42no—
777C22⋊C4—42no—
778C22⋊C4—81no—
779C22⋊C4—1224no—
780C22⋊C4—1224no—
781C22⋊C4—1224no—
782C22⋊C4—1224no—
783C22⋊C4—1224no—
784C42—21no—
785C42—21no—
786C23—21no—
787C23—21no—
788C23—21no—
789C23—21no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—21no—
795C23—21no—
796C23—21no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—1222no—
805C23—1222no—
806C23—1222no—
807C23—1222no—
808C23—4884no—
809C23—4884no—
810C23—4884no—
811C23—4884no—
812C23—4884no—
813C23—2448no—
814C23—2441no—
815C23—2441no—
816C23—2441no—
817C23—2441no—
818C23—2441no—
819C23—2441no—
820C23—2448no—
821C23—2441no—
822C23—2441no—
823C23—2441no—
824C23—2441no—
825C23#1451974512yes—
826C23#1451979712yes—
827C23#1451980312yes—
828C23C22×C22⋊D6111yescharacteristic
829Q8—1222no—
830Q8—1222no—
831Q8—2441no—
832Q8—2441no—
833D4—44no—
834D4—41no—
835D4—41no—
836D4—41no—
837D4—41no—
838D4—84no—
839D4—84no—
840D4—614no—
841D4—1222no—
842D4—1222no—
843D4—1222no—
844D4—1222no—
845D4—1222no—
846D4—4884no—
847D4—2448no—
848D4—2448no—
849D4—2441no—
850D4—2441no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—22no—
866C2×C4—21no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—84no—
880C2×C4—1222no—
881C2×C4—1222no—
882C2×C4—4884no—
883C2×C4—2448no—
884C2×C4—2441no—
885C2×C4—2441no—
886C2×C4—2441no—
887C2×C4—2441no—
888C2×C4#1451974512yes—
889C2×C4C2×D4×D6111yescharacteristic
890C2×C4C2×D4×D6111yescharacteristic
891C2×C4C2×D4×D6111yescharacteristic
892C2×C4#41×D6111yescharacteristic
893C2×C4#1451982211yescharacteristic
894C2×C4#1451982311yescharacteristic
895C8—1222no—
896C8—2441no—
897C8—2441no—
898C8—2441no—
899C22—22no—
900C22—22no—
901C22—22no—
902C22—22no—
903C22—22no—
904C22—22no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—41no—
909C22—41no—
910C22—41no—
911C22—41no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22—1224no—
920C22—48816no—
921C22—4881no—
922C22—4881no—
923C22—4881no—
924C22—4881no—
925C22—2442no—
926C22—2442no—
927C22—2442no—
928C22—2442no—
929C22—2442no—
930C22—2442no—
931C22—2442no—
932C22—2442no—
933C22—2442no—
934C22#1683990514yescomplemented
935C22C2×#1451974511yescharacteristic
936C22D4×C22⋊D6111yescharacteristic
937C22#1684040011yescharacteristic
938C22C2×#1451979711yescharacteristic
939C22C2×#1451980311yescharacteristic
940C22#1684056511yescharacteristic
941C22#1684057011yescharacteristic
942C4—22no—
943C4—41no—
944C4—42no—
945C4—41no—
946C4—41no—
947C4—81no—
948C4—81no—
949C4—2442no—
950C4—2442no—
951C4#121×D6111yescharacteristic
952C4#1684032011yescharacteristic
953C4#1684039611yescharacteristic
954C4#1684040111yescharacteristic
955C2—24no—
956C2—81no—
957C2—161no—
958C2—4882no—
959C2—2444no—
960C2#2144919011yescharacteristic
961C2C2×#1683990511yescharacteristic
962C2#2145512011yescharacteristic
963C2#2145729511yescharacteristic
964C2#2145752711yescharacteristic
965C2#2145766311yescharacteristic
966C2#2145777411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2416C2
socleC23×C61C22×D4
hypercenter#2416D61
hypocenterC61#24434
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2416

Complements

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

NH ≅ G/Ntype
1. C2×#16840408C2semidirect
2. C2×#16839989C2semidirect
3. C2×#16839905C2semidirect
4. C2×#16839895C2semidirect
5. C22×#14519697C2semidirect
6. #21447060C2semidirect
7. #21447008C2semidirect
8. #21446895C2semidirect
9. #21446815C2semidirect
10. #21446170C2semidirect
11. #21446126C2semidirect
12. #21446112C2semidirect
13. #21446079C2semidirect
14. #21445757C2semidirect
15. C61×#2416C2semidirect
18. C22×#11758200C22semidirect
35. C2×#14519708C22semidirect
36. C2×#14519700C22semidirect
37. C2×#14519700C22semidirect
38. C2×#14519700C22semidirect
39. C2×#14519698C22semidirect
48. C2×C22⋊#92418C22semidirect
49. C2×C22⋊#92418C22semidirect
50. #16839524C22semidirect
51. #16839524C22semidirect
52. #16839517C22semidirect
53. #16839517C22semidirect
56. C2×#121×C61C22semidirect
61. C61×#390C22semidirect
62. C61×#389C22semidirect
64. C61×#380C22semidirect
79. C22×D244D4semidirect
106. #14519756D4semidirect
131. #14519697D4semidirect
404. D244#121semidirect
436. C22×C61#449semidirect
477. #2416D61semidirect
514. C2×#121C2×D61semidirect
540. #390C2×D61semidirect
541. #389C2×D61semidirect
543. #380C2×D61semidirect
548. C61#24434semidirect
934. C22#16839905semidirect

Maximal subgroups

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

subgroupindex
C2×#168404082
C2×#168399892
C2×#168399052
C2×#168398952
C22×#145196972
#214470602
#214470082
#214468952
#214468152
#214461702
#214461262
#214461122
#214460792
#214457572
C61×#24162
#2443461