Finite Group Databasebeta

← #29695773

Subgroups — #29695773

Order 15616.

1650 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519801C211yesmaximal, characteristic
2C2×#16839871C211yesmaximal, characteristic, complemented
3C2×C4×#11758199C211yesmaximal, characteristic, complemented
4#21448644C211yesmaximal, characteristic, complemented
5#21448640C211yesmaximal, characteristic, complemented
6#21446701C211yesmaximal, characteristic, complemented
7#21446672C211yesmaximal, characteristic, complemented
8#21446169C211yesmaximal, characteristic, complemented
9#21446154C211yesmaximal, characteristic, complemented
10#21446152C211yesmaximal, characteristic, complemented
11#21445851C211yesmaximal, characteristic, complemented
12#21445756C211yesmaximal, characteristic, complemented
13#21445748C211yesmaximal, characteristic, complemented
14#21445599C211yesmaximal, characteristic, complemented
15C61×#1879C211yesmaximal, characteristic, complemented
16C22×#11758224C2211yescharacteristic
17C22×D4×D61C2211yescharacteristic
18C2×#14519801—24no—
19C2×#14519801—24no—
20C2×#14519801C418yescomplemented
21C22×#11758190C2211yescharacteristic
22C22×#11758200C2211yescharacteristic
23C22×#11758199C2211yescharacteristic
24C22×#11758189C2211yescharacteristic
25C2×C4×D244C2211yescharacteristic
26C2×D4×Dic61C2211yescharacteristic, complemented
27C2×#14519739C2211yescharacteristic
28C2×C22⋊C4×D61—21no—
29#16839871—24no—
30C4×#11758199—24no—
31C2×#14519710C2211yescharacteristic, complemented
32C2×#14519708C2211yescharacteristic, complemented
33C2×#14519702C2211yescharacteristic, complemented
34C2×#14519700C2211yescharacteristic, complemented
35C2×#14519699C2211yescharacteristic
36C2×#14519698C2211yescharacteristic
37C2×#14519698C2211yescharacteristic, complemented
38C2×#14519697C2211yescharacteristic
39C2×#14519689C2211yescharacteristic
40C2×#14519687C2211yescharacteristic, complemented
41C2×C4×#92418C2211yescharacteristic, complemented
42#16839668C2211yescharacteristic, complemented
43#16839667C2211yescharacteristic, complemented
44#16839665C2211yescharacteristic
45#16839641—21no—
46#16839639—21no—
47#16839638—21no—
48#16839638—21no—
49#16839623—21no—
50#16839619C2211yescharacteristic
51#16839619C2211yescharacteristic
52#16839617—21no—
53C4×#11758198C2211yescharacteristic
54C2×#14519684—21no—
55#16839525C2211yescharacteristic, complemented
56#16839516C2211yescharacteristic, complemented
57C22×D8×C61C2211yescharacteristic
58C2×C4×D4×C61C2211yescharacteristic, complemented
59C2×#102×C61C2211yescharacteristic
60C2×#102×C61C2211yescharacteristic, complemented
61C61×#390C2211yescharacteristic
62C61×#340C2211yescharacteristic, complemented
63C61×#336C2211yescharacteristic, complemented
64C24×D61—21no—
65C2×#11758224—22no—
66C2×#11758224—22no—
67C2×#11758224—22no—
68C2×#11758224—41no—
69C2×#11758224—41no—
70C2×#11758224C2×C414yescomplemented
71C22×Dic122C2311yescharacteristic
72C22×D244C2311yescharacteristic
73C22×C22⋊D61—21no—
74C22×C22⋊D61—21no—
75C2×D4×D61—22no—
76C2×D4×D61—22no—
77C2×D4×D61—22no—
78C2×D4×D61—41no—
79C2×D4×D61—41no—
80C2×D4×D61C2×C414yescomplemented
81C23×Dic61—21no—
82C23×Dic61—21no—
83C22×C4×D61—21no—
84C22×C4×D61—21no—
85C22×C4×D61C2311yescharacteristic
86#14519801—232no—
87C2×#11758190—22no—
88C2×#11758190—22no—
89C2×#11758190C2×C414yescomplemented
90C2×#11758200—22no—
91C2×#11758200—22no—
92C2×#11758200C2×C414yescomplemented
93C2×#11758199C2×C414yes—
94C2×#11758199D414yes—
95C2×#11758199D414yes—
96C2×#11758189—22no—
97C2×#11758189—22no—
98C2×#11758189C2×C414yescomplemented
99C22×#92418C2311yescharacteristic
100C22×#92418C2311yescharacteristic
101C4×D244—22no—
102C4×D244—41no—
103D4×Dic61—22no—
104D4×Dic61—41no—
105#14519739—22no—
106#14519739—41no—
107C2×C4⋊Dic61C2311yescharacteristic
108C2×C4⋊Dic61C2311yescharacteristic
109C2×C22⋊Dic61—21no—
110C2×C22⋊Dic61—21no—
111C2×C22⋊Dic61—21no—
112C2×#11758198—21no—
113C2×#11758198—21no—
114C2×#11758198—21no—
115C2×#11758198—21no—
116C2×#11758198D411yescharacteristic
117C2×#11758198D411yescharacteristic
118C22⋊C4×D61—44no—
119C2×C4×Dic61C2311yescharacteristic
120#14519710—22no—
121#14519708—22no—
122#14519702—41no—
123#14519700—41no—
124#14519699—22no—
125#14519698—22no—
126#14519698—41no—
127#14519697—22no—
128#14519689—22no—
129#14519687—22no—
130C4×#92418—22no—
131#14519684—21no—
132#14519684—21no—
133#14519684—21no—
134#14519684—21no—
135#14519684—21no—
136#14519684—21no—
137#14519684D411yescharacteristic
138#14519684D411yescharacteristic
139C22×D4×C61C2311yescharacteristic
140C22×D4×C61C2311yescharacteristic
141C23×C4×C61—21no—
142C2×D8×C61—22no—
143C2×D8×C61—22no—
144C2×D8×C61C2×C414yescomplemented
145C22×C8×C61C2311yescharacteristic
146C22×C8×C61C2311yescharacteristic
147C4×D4×C61—22no—
148C4×D4×C61—41no—
149C2×C4⋊C4×C61C2311yescharacteristic
150C2×C4⋊C4×C61C2311yescharacteristic
151C2×C22⋊C4×C61—21no—
152C2×C22⋊C4×C61—21no—
153C2×C22⋊C4×C61—21no—
154C2×C42×C61C2311yescharacteristic
155#102×C61—22no—
156#102×C61—41no—
157C24×C61—21no—
158C24×C61—21no—
159C23×D61—21no—
160C23×D61—24no—
161C23×D61—42no—
162C23×D61—42no—
163C23×D61—42no—
164C23×D61—42no—
165C23×D61—81no—
166C23×D61—81no—
167C23×D61C2×D411yescharacteristic
168C2×D4×C61—21no—
169C2×D4×C61—21no—
170C2×D4×C61—21no—
171C2×D4×C61—21no—
172C2×D4×C61—21no—
173C2×D4×C61—21no—
174C2×D4×C61—21no—
175C2×D4×C61—21no—
176C2×D4×C61C22×C412yes—
177C2×D4×C61C22×C412yes—
178C2×D4×C61C2×D412yes—
179C2×D4×C61C2×D412yes—
180C22×C4×C61—21no—
181C22×C4×C61—21no—
182C22×C4×C61—42no—
183C22×C4×C61—42no—
184C22×C4×C61—81no—
185C22×C4×C61C2×D411yescharacteristic
186C22×C4×C61C2×D411yescharacteristic
187C22×C4×C61C2411yescharacteristic
188C2×C22⋊D61—24no—
189C2×C22⋊D61—24no—
190C2×C22⋊D61—42no—
191C2×C22⋊D61—42no—
192C2×C22⋊D61—42no—
193C2×C22⋊D61—42no—
194C22×Dic61—21no—
195C22×Dic61—24no—
196C22×Dic61—21no—
197C22×Dic61—21no—
198C22×Dic61—42no—
199C22×Dic61—42no—
200C22×Dic61—42no—
201C22×Dic61—42no—
202C22×Dic61—81no—
203C22×Dic61C2×D411yescharacteristic
204C22×Dic61C2×D411yescharacteristic
205C22×Dic61C2×D411yescharacteristic
206#11758224—28no—
207#11758224—44no—
208#11758224—44no—
209#11758224—44no—
210D4×D61—28no—
211D4×D61—44no—
212D4×D61—44no—
213D4×D61—44no—
214C2×D244—21no—
215C2×D244—21no—
216C2×D244—21no—
217C2×D244C22×C412yes—
218C2×D244C2×D412yes—
219C2×D244C2×D412yes—
220C2×C4×D61—21no—
221C2×C4×D61—21no—
222C2×C4×D61—21no—
223C2×C4×D61—21no—
224C2×C4×D61—42no—
225C2×C4×D61—42no—
226C2×C4×D61—42no—
227C2×C4×D61—42no—
228C2×C4×D61—81no—
229C2×C4×D61—81no—
230C2×C4×D61C22×C412yes—
231C2×C4×D61#4112yes—
232C2×Dic122—21no—
233C2×Dic122—21no—
234C2×Dic122—21no—
235C2×Dic122—21no—
236C2×Dic122—21no—
237C2×Dic122C22×C412yes—
238D8×C61—28no—
239C2×C8×C61—21no—
240C2×C8×C61—21no—
241C2×C8×C61—21no—
242C2×C8×C61—21no—
243C2×C8×C61—21no—
244C2×C8×C61C22×C412yes—
245C4⋊C4×C61—21no—
246C4⋊C4×C61—21no—
247C4⋊C4×C61—21no—
248C4⋊C4×C61—21no—
249C22⋊C4×C61—42no—
250C22⋊C4×C61—42no—
251C22⋊C4×C61—81no—
252C42×C61—21no—
253C42×C61—21no—
254C22⋊Dic61—42no—
255C22⋊Dic61—42no—
256C22⋊Dic61—81no—
257#11758200—28no—
258#11758199C22⋊C4116yescomplemented
259#11758198—22no—
260#11758198—41no—
261#11758198—42no—
262#11758198—42no—
263#11758198—42no—
264#11758198—81no—
265C4⋊Dic61—21no—
266C4⋊Dic61—21no—
267C4⋊Dic61—21no—
268C4⋊Dic61—21no—
269C4×Dic61—21no—
270C4×Dic61—21no—
271C2×#92418—21no—
272C2×#92418—21no—
273C2×#92418—21no—
274C2×#92418C22×C412yes—
275C2×#92418C2×D412yes—
276C2×#92418C2×D412yes—
277#11758190—28no—
278#11758189—28no—
279C23×C61—22no—
280C23×C61—22no—
281C23×C61—22no—
282C23×C61—22no—
283C23×C61—41no—
284C23×C61—41no—
285C23×C61—41no—
286C23×C61—41no—
287C23×C61—41no—
288C23×C61—41no—
289C23×C61—41no—
290C23×C61—41no—
291C23×C61—41no—
292C23×C61—41no—
293C23×C61C22×D411yescharacteristic
294C22×D61—22no—
295C22×D61—22no—
296C22×D61—22no—
297C22×D61—21no—
298C22×D61—21no—
299C22×D61—21no—
300C22×D61—21no—
301C22×D61—21no—
302C22×D61—21no—
303C22×D61—48no—
304C22×D61—48no—
305C22×D61—41no—
306C22×D61—41no—
307C22×D61—41no—
308C22×D61—41no—
309C22×D61—84no—
310C22×D61—84no—
311C22×D61—84no—
312C22×D61—84no—
313C22×D61—84no—
314C22×D61C4×D412yes—
315D4×C61—22no—
316D4×C61—22no—
317D4×C61—22no—
318D4×C61—22no—
319D4×C61—22no—
320D4×C61—41no—
321D4×C61—41no—
322D4×C61C2×C22⋊C414yescomplemented
323C2×C4×C61—21no—
324C2×C4×C61—21no—
325C2×C4×C61—21no—
326C2×C4×C61—21no—
327C2×C4×C61—21no—
328C2×C4×C61—41no—
329C2×C4×C61—41no—
330C2×C4×C61—41no—
331C2×C4×C61—41no—
332C2×C4×C61—41no—
333C2×C4×C61—41no—
334C2×C4×C61—84no—
335C2×C4×C61AGL(1,ℤ/8)12yescomplemented
336C2×C4×C61C23×C411yescharacteristic
337C2×C4×C61C22×D411yescharacteristic
338C2×C4×C61C22×D411yescharacteristic
339C2×C4×C61C2×#4111yescharacteristic
340C2×C4×C61H(5,𝔽2)11yescharacteristic
341C2×C4×C61H(5,𝔽2)11yescharacteristic
342C22⋊D61—48no—
343C22⋊D61—48no—
344C2×Dic61—21no—
345C2×Dic61—21no—
346C2×Dic61—22no—
347C2×Dic61—21no—
348C2×Dic61—21no—
349C2×Dic61—21no—
350C2×Dic61—21no—
351C2×Dic61—21no—
352C2×Dic61—21no—
353C2×Dic61—48no—
354C2×Dic61—41no—
355C2×Dic61—41no—
356C2×Dic61—41no—
357C2×Dic61—41no—
358C2×Dic61—41no—
359C2×Dic61—41no—
360C2×Dic61—41no—
361C2×Dic61—41no—
362C2×Dic61—84no—
363C2×Dic61C4×D412yes—
364D244—22no—
365D244—22no—
366D244—22no—
367D244C2×C22⋊C414yes—
368C4×D61—22no—
369C4×D61—22no—
370C4×D61—22no—
371C4×D61—22no—
372C4×D61—84no—
373C4×D61—84no—
374Dic122—22no—
375Dic122—22no—
376Dic122—41no—
377Dic122—41no—
378C8×C61—22no—
379C8×C61—41no—
380#92418—41no—
381#92418C2×C22⋊C414yescomplemented
382#22442—611nomaximal, Sylow
383C22×C61—24no—
384C22×C61—42no—
385C22×C61—42no—
386C22×C61—42no—
387C22×C61—42no—
388C22×C61—42no—
389C22×C61—42no—
390C22×C61—42no—
391C22×C61—42no—
392C22×C61—42no—
393C22×C61—81no—
394C22×C61—81no—
395C22×C61—81no—
396C22×C61—81no—
397C22×C61C2×C4×D411yescharacteristic
398C22×C61D4211yescharacteristic
399C22×C61D4211yescharacteristic
400C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
401C22×C61#57511yescharacteristic
402C22×C61#57611yescharacteristic
403C22×C61#57711yescharacteristic
404C2×D61—22no—
405C2×D61—24no—
406C2×D61—22no—
407C2×D61—22no—
408C2×D61—42no—
409C2×D61—42no—
410C2×D61—42no—
411C2×D61—41no—
412C2×D61—41no—
413C2×D61—42no—
414C2×D61—42no—
415C2×D61—41no—
416C2×D61—41no—
417C2×D61—42no—
418C2×D61—816no—
419C4×C61—22no—
420C4×C61—41no—
421C4×C61—81no—
422C4×C61—81no—
423C4×C61C22×C22⋊C411yescharacteristic
424C4×C61#51811yescharacteristic
425C4×C61#54611yescharacteristic
426C4×C61#54611yescharacteristic
427Dic61—22no—
428Dic61—42no—
429Dic61—41no—
430Dic61—41no—
431Dic61—81no—
432Dic61—81no—
433C22×AGL(1,ℤ/8)—611no—
434C2×#442—611no—
435C2×C4×D8—611no—
436#2339—611no—
437D4×C22⋊C4—611no—
438#1973—611no—
439#1968—611no—
440#1879—611no—
441#1879D6111yescharacteristic, complemented
442#1877—611no—
443#1877—611no—
444#1809—611no—
445#1788—611no—
446#1786—611no—
447#1753—611no—
448C2×C61—44no—
449C2×C61—82no—
450C2×C61D4×C22⋊C411yescharacteristic
451C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
452C2×C61#294611yescharacteristic
453C2×C61#326411yescharacteristic
454C2×C61#326711yescharacteristic
455C2×C61#327211yescharacteristic
456C2×C61#327311yescharacteristic
457D61—42no—
458D61—44no—
459C22×#41—611no—
460C23×D4—611no—
461C2×AGL(1,ℤ/8)—618no—
462C2×AGL(1,ℤ/8)—1224no—
463C2×AGL(1,ℤ/8)—1224no—
464C22×SD16—611no—
465C22×SD16—611no—
466C22×D8—611no—
467C22×D8C2×D6111yescharacteristic
468C22×M16—611no—
469C2×C4×D4—611no—
470C2×C4×D4—611no—
471C2×C4×D4—611no—
472C2×C4×D4C2×D6111yescharacteristic, complemented
473C22×C22⋊C4—1221no—
474#442—1224no—
475C4×D8—1224no—
476C2×#107—611no—
477C2×#106—611no—
478C2×#103—611no—
479C2×#103—611no—
480C2×#102—611no—
481C2×#102—611no—
482C2×#102—611no—
483C2×#102—611no—
484C2×#102C2×D6111yescharacteristic
485C2×#102C2×D6111yescharacteristic, complemented
486C2×C22⋊C8—611no—
487C2×#97—611no—
488C2×C4×C8—611no—
489#391—611no—
490#391—611no—
491#390—611no—
492#390C2×D6111yescharacteristic
493#386—1221no—
494#386—1221no—
495#386—1221no—
496#386—1221no—
497#381—1221no—
498#380—611no—
499#380—611no—
500#379—1221no—
501C4×C22⋊C4—611no—
502C2×#95—1221no—
503#340—611no—
504#340C2×D6111yescharacteristic, complemented
505#336—611no—
506#336C2×D6111yescharacteristic, complemented
507C61#2244211yescharacteristic, complemented, Sylow
508C25—1221no—
509C2×#41—614no—
510C2×#41—1222no—
511C2×#41—1222no—
512C2×#41—1222no—
513C2×#41—2441no—
514C2×#41—2441no—
515C22×Q8—611no—
516C22×D4—614no—
517C22×D4—611no—
518C22×D4—1222no—
519C22×D4—1221no—
520C22×D4—1222no—
521C22×D4—1222no—
522C22×D4—1221no—
523C22×D4—2441no—
524C22×D4—2441no—
525C22×D4C22×D6111yescharacteristic
526C22×D4C22×D6111yescharacteristic
527C23×C4—21no—
528C23×C4—611no—
529C23×C4—1221no—
530C23×C4—1221no—
531C23×C4—1221no—
532C23×C4—1221no—
533AGL(1,ℤ/8)—12232no—
534C2×SD16—614no—
535C2×SD16—614no—
536C2×SD16—1222no—
537C2×SD16—1222no—
538C2×SD16—1222no—
539C2×SD16—1222no—
540C2×D8—22no—
541C2×D8—22no—
542C2×D8—614no—
543C2×D8—614no—
544C2×D8—614no—
545C2×D8C4×D6114yescomplemented
546C2×M16—614no—
547C2×M16—1222no—
548C2×M16—1222no—
549C22×C8—611no—
550C22×C8—611no—
551C22×C8C22×D6111yescharacteristic
552C22×C8C22×D6111yescharacteristic
553C4×D4—22no—
554C4×D4—41no—
555C4×D4—1222no—
556C4×D4—1222no—
557C4×D4—1222no—
558C4×D4—2441no—
559C4×D4—2441no—
560C4×D4—2441no—
561C2×C4⋊C4—611no—
562C2×C4⋊C4—611no—
563C2×C4⋊C4C22×D6111yescharacteristic
564C2×C4⋊C4C22×D6111yescharacteristic
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—611no—
569C2×C22⋊C4—611no—
570C2×C22⋊C4—1221no—
571C2×C22⋊C4—1221no—
572C2×C22⋊C4—1221no—
573C2×C22⋊C4—1221no—
574C2×C22⋊C4—1221no—
575C2×C22⋊C4—1221no—
576C2×C22⋊C4—1221no—
577C2×C22⋊C4—2444no—
578C2×C42—611no—
579C2×C42C22×D6111yescharacteristic
580#107—1222no—
581#106—1222no—
582#103—2441no—
583#103—2441no—
584#102—22no—
585#102—41no—
586#102—1222no—
587#102—1222no—
588#102—1222no—
589#102—2441no—
590C22⋊C8—1222no—
591#97—1222no—
592C4×C8—1222no—
593#95—611no—
594#95—611no—
595#95—1221no—
596#95—1221no—
597#95—1221no—
598#95—1221no—
599#95—1221no—
600#95—1221no—
601C24—21no—
602C24—21no—
603C24—611no—
604C24—1224no—
605C24—1221no—
606C24—4881no—
607C24—4881no—
608C24—2442no—
609C24—2442no—
610C24—2442no—
611C24—2442no—
612#41—1228no—
613#41—2444no—
614#41—2444no—
615#41—2444no—
616C2×Q8—612no—
617C2×Q8—1221no—
618C2×Q8—1221no—
619C2×Q8—1221no—
620C2×Q8—1221no—
621C2×Q8—1221no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—612no—
631C2×D4—612no—
632C2×D4—612no—
633C2×D4—1224no—
634C2×D4—1228no—
635C2×D4—1224no—
636C2×D4—1221no—
637C2×D4—1221no—
638C2×D4—1221no—
639C2×D4—2444no—
640C2×D4—2444no—
641C2×D4—2444no—
642C2×D4—2442no—
643C2×D4—2442no—
644C2×D4—2442no—
645C2×D4—2442no—
646C2×D4C2×C4×D6112yes—
647C2×D4C2×C4×D6112yes—
648C2×D4D4×D6112yes—
649C2×D4D4×D6112yes—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—42no—
653C22×C4—42no—
654C22×C4—81no—
655C22×C4—611no—
656C22×C4—612no—
657C22×C4—612no—
658C22×C4—611no—
659C22×C4—611no—
660C22×C4—1224no—
661C22×C4—1221no—
662C22×C4—1221no—
663C22×C4—1221no—
664C22×C4—1221no—
665C22×C4—1221no—
666C22×C4—1221no—
667C22×C4—1221no—
668C22×C4—4881no—
669C22×C4—4881no—
670C22×C4—4881no—
671C22×C4—2442no—
672C22×C4—2442no—
673C22×C4—2442no—
674C22×C4—2442no—
675C22×C4—2442no—
676C22×C4—2442no—
677C22×C4—2442no—
678C22×C4—2442no—
679C22×C4D4×D6111yescharacteristic
680C22×C4D4×D6111yescharacteristic
681C22×C4C23×D6111yescharacteristic
682SD16—1228no—
683SD16—1228no—
684D8—28no—
685D8—6116no—
686M16—1228no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—612no—
693C2×C8—612no—
694C2×C8—612no—
695C2×C8—1221no—
696C2×C8—1221no—
697C2×C8—1221no—
698C2×C8C2×C4×D6112yes—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—1221no—
704C4⋊C4—1221no—
705C4⋊C4—1221no—
706C4⋊C4—1221no—
707C22⋊C4—42no—
708C22⋊C4—42no—
709C22⋊C4—81no—
710C22⋊C4—1222no—
711C22⋊C4—4881no—
712C22⋊C4—4881no—
713C22⋊C4—2441no—
714C22⋊C4—2442no—
715C22⋊C4—2442no—
716C22⋊C4—2442no—
717C22⋊C4—2442no—
718C22⋊C4—2442no—
719C42—21no—
720C42—21no—
721C42—1221no—
722C42—1221no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—612no—
738C23—1222no—
739C23—1221no—
740C23—1221no—
741C23—1221no—
742C23—1221no—
743C23—1222no—
744C23—1221no—
745C23—1222no—
746C23—1221no—
747C23—4884no—
748C23—4884no—
749C23—4884no—
750C23—4884no—
751C23—4884no—
752C23—2448no—
753C23—2448no—
754C23—2441no—
755C23—2441no—
756C23—2441no—
757C23—2441no—
758C23C2×D4×D6111yescharacteristic
759Q8—1222no—
760Q8—1222no—
761Q8—2441no—
762Q8—2441no—
763D4—22no—
764D4—22no—
765D4—22no—
766D4—22no—
767D4—22no—
768D4—41no—
769D4—41no—
770D4—614no—
771D4—1222no—
772D4—1222no—
773D4—1222no—
774D4—2448no—
775D4—2448no—
776D4C22⋊C4×D6114yescomplemented
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—84no—
789C2×C4—612no—
790C2×C4—1221no—
791C2×C4—1221no—
792C2×C4—1222no—
793C2×C4—1222no—
794C2×C4—1222no—
795C2×C4—1222no—
796C2×C4—1222no—
797C2×C4—1221no—
798C2×C4—1221no—
799C2×C4—1221no—
800C2×C4—1221no—
801C2×C4—1221no—
802C2×C4—1221no—
803C2×C4—4884no—
804C2×C4—4884no—
805C2×C4—4884no—
806C2×C4—2448no—
807C2×C4—2441no—
808C2×C4—2441no—
809C2×C4—2441no—
810C2×C4—2441no—
811C2×C4—2441no—
812C2×C4—2441no—
813C2×C4—2441no—
814C2×C4—2441no—
815C2×C4#1451980112yescomplemented
816C2×C4C22×C4×D6111yescharacteristic
817C2×C4C2×D4×D6111yescharacteristic
818C2×C4C2×D4×D6111yescharacteristic
819C2×C4#41×D6111yescharacteristic
820C2×C4#1451982211yescharacteristic
821C2×C4#1451982311yescharacteristic
822C8—22no—
823C8—41no—
824C8—614no—
825C8—2441no—
826C22—24no—
827C22—42no—
828C22—42no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—42no—
836C22—81no—
837C22—81no—
838C22—81no—
839C22—81no—
840C22—1222no—
841C22—1222no—
842C22—1222no—
843C22—1224no—
844C22—48816no—
845C22—2442no—
846C22—2441no—
847C22—2441no—
848C22—2442no—
849C22—2442no—
850C22—2442no—
851C22—2442no—
852C22—2441no—
853C22—2441no—
854C22—2442no—
855C22C4×D4×D6111yescharacteristic
856C22#1684039411yescharacteristic
857C22#1684039611yescharacteristic
858C22C2×#1451980111yescharacteristic
859C22#1684055911yescharacteristic
860C22#1684056611yescharacteristic
861C22#1684057211yescharacteristic
862C4—22no—
863C4—41no—
864C4—81no—
865C4—81no—
866C4—1222no—
867C4—4881no—
868C4—4881no—
869C4—2441no—
870C4—2441no—
871C4—2442no—
872C4C2×C22⋊C4×D6111yescharacteristic
873C4#1684023411yescharacteristic
874C4#1684040111yescharacteristic
875C4#1684040411yescharacteristic
876C2—44no—
877C2—82no—
878C2—2442no—
879C2—2444no—
880C2#2144863711yescharacteristic
881C2C4×#1451980111yescharacteristic
882C2#2145464811yescharacteristic
883C2#2145729211yescharacteristic
884C2#2145733711yescharacteristic
885C2#2145741411yescharacteristic
886C2#2145742511yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1879C2
socleC23×C61C22×D4
prime radicalC22×#14519801C2
cosocleC22×C4×C61C24
hypercenter#1879D61
hypocenterC61#22442
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1879

Complements

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

NH ≅ G/Ntype
2. C2×#16839871C2semidirect
3. C2×C4×#11758199C2semidirect
4. #21448644C2semidirect
5. #21448640C2semidirect
6. #21446701C2semidirect
7. #21446672C2semidirect
8. #21446169C2semidirect
9. #21446154C2semidirect
10. #21446152C2semidirect
11. #21445851C2semidirect
12. #21445756C2semidirect
13. #21445748C2semidirect
14. #21445599C2semidirect
15. C61×#1879C2semidirect
20. C2×#14519801C4semidirect
26. C2×D4×Dic61C22semidirect
31. C2×#14519710C22semidirect
32. C2×#14519708C22semidirect
33. C2×#14519702C22semidirect
34. C2×#14519700C22semidirect
37. C2×#14519698C22semidirect
40. C2×#14519687C22semidirect
41. C2×C4×#92418C22semidirect
42. #16839668C22semidirect
43. #16839667C22semidirect
55. #16839525C22semidirect
56. #16839516C22semidirect
58. C2×C4×D4×C61C22semidirect
60. C2×#102×C61C22semidirect
62. C61×#340C22semidirect
63. C61×#336C22semidirect
70. C2×#11758224C2×C4semidirect
80. C2×D4×D61C2×C4semidirect
89. C2×#11758190C2×C4semidirect
92. C2×#11758200C2×C4semidirect
98. C2×#11758189C2×C4semidirect
144. C2×D8×C61C2×C4semidirect
258. #11758199C22⋊C4semidirect
322. D4×C61C2×C22⋊C4semidirect
335. C2×C4×C61AGL(1,ℤ/8)semidirect
381. #92418C2×C22⋊C4semidirect
441. #1879D61semidirect
472. C2×C4×D4C2×D61semidirect
485. C2×#102C2×D61semidirect
504. #340C2×D61semidirect
506. #336C2×D61semidirect
507. C61#22442semidirect
545. C2×D8C4×D61semidirect
776. D4C22⋊C4×D61semidirect
815. C2×C4#14519801semidirect

Maximal subgroups

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

subgroupindex
C22×#145198012
C2×#168398712
C2×C4×#117581992
#214486442
#214486402
#214467012
#214466722
#214461692
#214461542
#214461522
#214458512
#214457562
#214457482
#214455992
C61×#18792
#2244261