Finite Group Databasebeta

← C2×#21455423 #30547143

Subgroups — C2×#21455423 #30547143

Order 15616.

2918 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519798C211yesmaximal, characteristic, complemented
2C22×M16×D61C211yesmaximal, characteristic, complemented
3C2×#16840275C211yesmaximal, characteristic, complemented
4C2×#16840272C211yesmaximal, characteristic, complemented
5#21455423C2116yesmaximal, direct product factor
6C2×#16840019C211yesmaximal, characteristic, complemented
7C2×#16840018C211yesmaximal, characteristic, complemented
8C2×#16840014C211yesmaximal, characteristic, complemented
9C2×#16840013C211yesmaximal, characteristic, complemented
10C2×#16840009C211yesmaximal, characteristic, complemented
11C2×#16840008C211yesmaximal, characteristic, complemented
12C2×#16840005C211yesmaximal, characteristic, complemented
13C2×#16839799C211yesmaximal, characteristic, complemented
14C2×#16839757C211yesmaximal, characteristic, complemented
15C2×#16839755C211yesmaximal, characteristic, complemented
16C2×C61×#468C211yesmaximal, characteristic, complemented
17C22×#11758226C2211yescharacteristic
18C22×#11758224C2211yescharacteristic
19C23×C4×D61C2211yescharacteristic
20C2×#14519798—28no—
21C2×#14519798C2218yescomplemented
22C22×#11758202C2211yescharacteristic, complemented
23C22×#11758190C2211yescharacteristic, complemented
24C22×#11758199C2211yescharacteristic, complemented
25C22×#11758194C2211yescharacteristic
26C22×#11758189C2211yescharacteristic
27C22×#11758189C2211yescharacteristic
28C2×M16×D61—28no—
29C2×M16×D61C2218yescomplemented
30C22×C8×D61C2211yescharacteristic
31C22×C8×D61C2211yescharacteristic
32#16840275—24no—
33#16840275C2218yescomplemented
34#16840272—24no—
35#16840272C2218yescomplemented
36C2×#14519762—21no—
37C2×#14519759—21no—
38C2×#14519757C2211yescharacteristic
39C2×#14519756C2211yescharacteristic
40C2×#14519753C2211yescharacteristic
41C2×#14519752C2211yescharacteristic
42C2×#14519751C2211yescharacteristic
43C2×#14519748C2211yescharacteristic
44C2×#14519747—21no—
45C2×#14519745—21no—
46C2×D4×Dic61—21no—
47C2×#14519739—21no—
48C2×#14519737—21no—
49C2×#14519737—21no—
50C2×#14519735C2211yescharacteristic
51C2×#14519735C2211yescharacteristic
52#16840019C2218yescomplemented
53#16840018C2218yescomplemented
54#16840014C2218yescomplemented
55#16840013C2218yescomplemented
56#16840009C2218yescomplemented
57#16840008C2218yescomplemented
58#16840005C2218yescomplemented
59#16839799C2218yescomplemented
60C2×#14519711C2211yescharacteristic, complemented
61C2×#14519708C2211yescharacteristic, complemented
62C2×#14519708C2211yescharacteristic, complemented
63#16839757C2218yescomplemented
64#16839755C2218yescomplemented
65C2×#14519702C2211yescharacteristic, complemented
66C2×#14519701C2211yescharacteristic, complemented
67C2×#14519700C2211yescharacteristic, complemented
68C2×#14519699C2211yescharacteristic, complemented
69C2×#14519698C2211yescharacteristic, complemented
70C2×#14519697C2211yescharacteristic, complemented
71C22×SD16×C61C2211yescharacteristic, complemented
72C22×M16×C61C2211yescharacteristic
73C2×C22⋊Q8×C61C2211yescharacteristic
74C2×#121×C61C2211yescharacteristic
75C61×#468C2218yescomplemented
76C2×#107×C61C2211yescharacteristic, complemented
77C2×#103×C61C2211yescharacteristic, complemented
78C2×#102×C61C2211yescharacteristic, complemented
79C24×D61D411yescharacteristic
80C2×#11758226—22no—
81C2×#11758226—24no—
82C2×#11758226—24no—
83C2×#11758226C2314yes—
84C2×#11758224—24no—
85C2×#11758224—22no—
86C2×#11758224—24no—
87C2×#11758224C2314yes—
88C22×Dic122C2311yescharacteristic
89C22×D244—21no—
90C22×D244—21no—
91C22×D244C2311yescharacteristic
92C22×C22⋊D61—21no—
93C22×C22⋊D61—21no—
94C22×C22⋊D61—21no—
95C23×Dic61—21no—
96C23×Dic61D411yescharacteristic
97C22×C4×D61—24no—
98C22×C4×D61—24no—
99C22×C4×D61—21no—
100C22×C4×D61D411yescharacteristic
101C22×C4×D61D411yescharacteristic
102C22×C4×D61D414yes—
103C22×C4×D61C2311yescharacteristic
104C22×C4×D61C2314yes—
105C22×C4×D61C2311yescharacteristic
106#14519798—232no—
107C2×#11758202—24no—
108C2×#11758202C2314yescomplemented
109C2×#11758190—24no—
110C2×#11758190C2314yescomplemented
111C2×#11758199—24no—
112C2×#11758199C2314yescomplemented
113C2×#11758194—24no—
114C2×#11758194C2314yes—
115C2×#11758189—24no—
116C2×#11758189—24no—
117C2×#11758189C2314yes—
118C2×#11758189C2314yes—
119M16×D61—232no—
120C22×#92418C2311yescharacteristic
121C22×#92418C2311yescharacteristic
122C2×C8×D61—24no—
123C2×C8×D61D418yescomplemented
124C2×C8×D61C2314yes—
125C2×C8×D61C2314yes—
126#14519762—28no—
127#14519759—28no—
128#14519757—22no—
129#14519757C2314yes—
130#14519756—22no—
131#14519756C2314yes—
132#14519753—22no—
133#14519753C2314yes—
134#14519752—22no—
135#14519752C2314yes—
136#14519751—22no—
137#14519751C2314yes—
138#14519748—22no—
139#14519748C2314yes—
140#14519747—28no—
141#14519745—28no—
142D4×Dic61—28no—
143#14519739—28no—
144#14519737—28no—
145#14519737—28no—
146#14519735—22no—
147#14519735—22no—
148#14519735C2314yes—
149#14519735C2314yes—
150C2×C4⋊Dic61—21no—
151C2×C4⋊Dic61C2311yescharacteristic
152C2×C4⋊Dic61C2311yescharacteristic
153C2×#11758196—21no—
154C2×#11758196—21no—
155C2×C22⋊Dic61—21no—
156C2×C22⋊Dic61—21no—
157C2×#11758198—21no—
158C2×#11758198—21no—
159C2×#11758198—21no—
160C2×#11758198—21no—
161C2×#11758198—21no—
162C2×#11758198—21no—
163C2×C4×Dic61—21no—
164C2×C4×Dic61—21no—
165#14519711C2314yescomplemented
166#14519708C2314yescomplemented
167#14519708C2314yescomplemented
168#14519702C2314yescomplemented
169#14519701C2314yescomplemented
170#14519700C2314yescomplemented
171#14519699C2314yescomplemented
172#14519698C2314yescomplemented
173#14519697C2314yescomplemented
174C22×Q8×C61C2311yescharacteristic
175C22×D4×C61—21no—
176C22×D4×C61C2311yescharacteristic
177C23×C4×C61C2311yescharacteristic
178C2×SD16×C61—24no—
179C2×SD16×C61C2314yescomplemented
180C2×M16×C61—24no—
181C2×M16×C61C2314yes—
182C22×C8×C61C2311yescharacteristic
183C22×C8×C61C2311yescharacteristic
184C22⋊Q8×C61—22no—
185C22⋊Q8×C61C2314yes—
186#121×C61—22no—
187#121×C61C2314yes—
188C2×C4⋊C4×C61—21no—
189C2×C4⋊C4×C61C2311yescharacteristic
190C2×C4⋊C4×C61C2311yescharacteristic
191C2×C22⋊C4×C61—21no—
192C2×C22⋊C4×C61—21no—
193#107×C61C2314yescomplemented
194#103×C61C2314yescomplemented
195#102×C61C2314yescomplemented
196C24×C61—21no—
197C24×C61C2×D411yescharacteristic
198C23×D61—24no—
199C23×D61—21no—
200C23×D61—42no—
201C23×D61—42no—
202C23×D61C2×D411yescharacteristic
203C23×D61C2×D411yescharacteristic
204C23×D61C2×D414yes—
205C2×Q8×C61—21no—
206C2×Q8×C61—22no—
207C2×Q8×C61—22no—
208C2×Q8×C61C2412yes—
209C2×D4×C61—24no—
210C2×D4×C61—22no—
211C2×D4×C61—21no—
212C2×D4×C61—22no—
213C2×D4×C61—44no—
214C2×D4×C61C2412yes—
215C22×C4×C61—22no—
216C22×C4×C61—22no—
217C22×C4×C61—21no—
218C22×C4×C61—21no—
219C22×C4×C61—21no—
220C22×C4×C61C2×D411yescharacteristic
221C22×C4×C61C2×D412yes—
222C22×C4×C61C2412yes—
223C22×C4×C61C2411yescharacteristic
224C2×C22⋊D61—24no—
225C2×C22⋊D61—24no—
226C2×C22⋊D61—24no—
227C2×C22⋊D61—44no—
228C2×C22⋊D61—44no—
229C2×C22⋊D61—44no—
230C22×Dic61—24no—
231C22×Dic61—21no—
232C22×Dic61—21no—
233C22×Dic61—21no—
234C22×Dic61—24no—
235C22×Dic61—44no—
236C22×Dic61C2×D411yescharacteristic
237C22×Dic61C2×D414yes—
238C22×Dic61C2×D411yescharacteristic
239#11758226—28no—
240#11758226—28no—
241#11758226—48no—
242#11758224—28no—
243#11758224—28no—
244#11758224—48no—
245C2×D244—22no—
246C2×D244—22no—
247C2×D244—24no—
248C2×D244—24no—
249C2×D244—21no—
250C2×D244—44no—
251C2×D244—44no—
252C2×D244C2412yes—
253C2×C4×D61—24no—
254C2×C4×D61—22no—
255C2×C4×D61—22no—
256C2×C4×D61—24no—
257C2×C4×D61—216no—
258C2×C4×D61—28no—
259C2×C4×D61—28no—
260C2×C4×D61—24no—
261C2×C4×D61—44no—
262C2×C4×D61C2×D414yes—
263C2×C4×D61C2×D412yes—
264C2×C4×D61C2×D414yes—
265C2×C4×D61C2×D412yes—
266C2×C4×D61C2×D414yes—
267C2×C4×D61#4114yes—
268C2×C4×D61C2412yes—
269C2×C4×D61C2412yes—
270C2×Dic122—22no—
271C2×Dic122—22no—
272C2×Dic122—21no—
273C2×Dic122C2412yes—
274SD16×C61—28no—
275M16×C61—28no—
276C2×C8×C61—22no—
277C2×C8×C61C2×D414yes—
278C2×C8×C61C2412yes—
279C2×C8×C61C2412yes—
280C4⋊C4×C61—24no—
281C4⋊C4×C61—21no—
282C4⋊C4×C61—21no—
283C4⋊C4×C61C2412yes—
284C4⋊C4×C61C2412yes—
285C22⋊C4×C61—24no—
286C22⋊C4×C61—24no—
287C22⋊Dic61—24no—
288C22⋊Dic61—24no—
289#11758202—28no—
290#11758199—28no—
291#11758198—24no—
292#11758198—24no—
293#11758198—24no—
294#11758198—24no—
295#11758198—24no—
296#11758198—24no—
297C4⋊Dic61—21no—
298C4⋊Dic61—21no—
299C4⋊Dic61—24no—
300C4⋊Dic61C2412yes—
301C4⋊Dic61C2412yes—
302#11758196—24no—
303#11758196—24no—
304C4×Dic61—24no—
305C4×Dic61—24no—
306#11758194—28no—
307C2×#92418—22no—
308C2×#92418C2×D414yes—
309C2×#92418C2412yes—
310C2×#92418C2412yes—
311#11758190—28no—
312#11758189—28no—
313#11758189—28no—
314C8×D61—28no—
315C8×D61C2×D4116yescomplemented
316C23×C61—22no—
317C23×C61—22no—
318C23×C61—22no—
319C23×C61—22no—
320C23×C61—42no—
321C23×C61—42no—
322C23×C61—42no—
323C23×C61C22×D412yes—
324C23×C61C22×D411yescharacteristic
325C22×D61—22no—
326C22×D61—22no—
327C22×D61—22no—
328C22×D61—22no—
329C22×D61—22no—
330C22×D61—28no—
331C22×D61—22no—
332C22×D61—44no—
333C22×D61—44no—
334C22×D61—416no—
335C22×D61—42no—
336C22×D61—42no—
337C22×D61—42no—
338C22×D61#12114yes—
339C22×D61C22×D412yes—
340C22×D61C22×D412yes—
341Q8×C61—22no—
342Q8×C61—22no—
343Q8×C61—42no—
344D4×C61—22no—
345D4×C61—22no—
346D4×C61—48no—
347D4×C61—42no—
348C2×C4×C61—22no—
349C2×C4×C61—24no—
350C2×C4×C61—22no—
351C2×C4×C61—22no—
352C2×C4×C61—22no—
353C2×C4×C61—22no—
354C2×C4×C61—22no—
355C2×C4×C61—42no—
356C2×C4×C61—42no—
357C2×C4×C61—42no—
358C2×C4×C61C22×D412yes—
359C2×C4×C61C22×D411yescharacteristic
360C2×C4×C61C22×D412yes—
361C2×C4×C61C2×#4112yes—
362C2×C4×C61C2511yescharacteristic
363C22⋊D61—48no—
364C22⋊D61—48no—
365C22⋊D61—48no—
366C2×Dic61—22no—
367C2×Dic61—28no—
368C2×Dic61—22no—
369C2×Dic61—22no—
370C2×Dic61—22no—
371C2×Dic61—42no—
372C2×Dic61—42no—
373C2×Dic61—42no—
374C2×Dic61—48no—
375C2×Dic61#12114yes—
376C2×Dic61C22×D412yes—
377C2×Dic61C22×D412yes—
378D244—22no—
379D244—22no—
380D244—48no—
381D244—48no—
382D244—42no—
383C4×D61—28no—
384C4×D61—24no—
385C4×D61—22no—
386C4×D61—22no—
387C4×D61—28no—
388C4×D61—48no—
389C4×D61#12118yes—
390C4×D61C22×D414yes—
391C4×D61C2×#4114yes—
392Dic122—22no—
393Dic122—22no—
394Dic122—42no—
395C8×C61—22no—
396C8×C61C22×D414yes—
397#92418—22no—
398#92418C22×D414yes—
399C2×#3054—611nomaximal, Sylow
400C22×C61—22no—
401C22×C61—22no—
402C22×C61—22no—
403C22×C61—44no—
404C22×C61—42no—
405C22×C61—42no—
406C22×C61—42no—
407C22×C61—84no—
408C22×C61C2×#12112yes—
409C22×C61#57512yes—
410C22×C61#57512yes—
411C22×C61C23×D411yescharacteristic
412C2×D61—28no—
413C2×D61—22no—
414C2×D61—22no—
415C2×D61—22no—
416C2×D61—22no—
417C2×D61—22no—
418C2×D61—416no—
419C2×D61—44no—
420C2×D61—42no—
421C2×D61—42no—
422C2×D61—42no—
423C2×D61—84no—
424C2×D61C2×#12114yes—
425C4×C61—22no—
426C4×C61—42no—
427C4×C61—42no—
428C4×C61—42no—
429C4×C61C2×#12112yes—
430C4×C61C23×D411yescharacteristic
431C4×C61C22×#4111yescharacteristic
432Dic61—22no—
433Dic61—42no—
434Dic61—42no—
435Dic61—42no—
436Dic61C2×#12114yes—
437C22×#135—611no—
438C23×M16—611no—
439C2×#525—611no—
440C2×#525—611no—
441#3054—6116no—
442C2×#470—611no—
443C2×#470—611no—
444C2×#469—611no—
445C2×#469—611no—
446C2×#468—611no—
447C2×#468—611no—
448C2×#468—611no—
449C2×#468D6111yescharacteristic, complemented
450C2×#427—611no—
451C2×#416—611no—
452C2×#416—611no—
453C2×C61—42no—
454C2×C61—82no—
455C2×C61#305414yescomplemented
456C2×C61C22×#12111yescharacteristic
457C2×C61C2×#57511yescharacteristic
458C2×C61C2×#57511yescharacteristic
459D61—24no—
460D61—42no—
461D61—82no—
462C22×#41—611no—
463C22×#41—611no—
464C24×C4—611no—
465C2×#135—618no—
466C2×#135—1228no—
467C22×Q16—611no—
468C22×SD16—611no—
469C22×SD16C2×D6111yescharacteristic, complemented
470C22×D8—611no—
471C22×M16—611no—
472C22×M16—618no—
473C22×M16—611no—
474C22×M16—611no—
475C22×M16—1228no—
476C22×M16C2×D6111yescharacteristic
477C23×C8—611no—
478C23×C8—611no—
479#525—618no—
480#525—618no—
481#525—1224no—
482#525—1224no—
483C2×#123—1221no—
484C2×#123—1221no—
485C2×C22⋊Q8—611no—
486C2×C22⋊Q8—611no—
487C2×C22⋊Q8—611no—
488C2×C22⋊Q8C2×D6111yescharacteristic
489C2×#121—611no—
490C2×#121—611no—
491C2×#121—611no—
492C2×#121C2×D6111yescharacteristic
493C2×#120—1221no—
494C2×#120—1221no—
495C2×C4×D4—1221no—
496C2×C4×D4—1221no—
497C2×C4×D4—1221no—
498C2×C4×D4—1221no—
499C2×#117—611no—
500C2×#117—611no—
501#470—618no—
502#470—618no—
503#469—618no—
504#469—618no—
505#468—618no—
506#468—618no—
507#468—618no—
508#468C2×D6118yescomplemented
509#427—618no—
510C2×#107—611no—
511C2×#107C2×D6111yescharacteristic, complemented
512C2×#106—611no—
513C2×#106—611no—
514#416—618no—
515#416—618no—
516C2×#103—611no—
517C2×#103—611no—
518C2×#103—611no—
519C2×#103C2×D6111yescharacteristic, complemented
520C2×#102—611no—
521C2×#102—611no—
522C2×#102—611no—
523C2×#102C2×D6111yescharacteristic, complemented
524C61C2×#305411yescharacteristic, complemented, Sylow
525C25—611no—
526C2×#41—614no—
527C2×#41—614no—
528C2×#41—1222no—
529C2×#41—1222no—
530C2×#41—1224no—
531C2×#41—1224no—
532C2×#41—1224no—
533C2×#41—1224no—
534C22×Q8—611no—
535C22×Q8C22×D6111yescharacteristic
536C22×D4—21no—
537C22×D4—611no—
538C22×D4—1221no—
539C22×D4—1221no—
540C22×D4—1221no—
541C22×D4—1221no—
542C22×D4—1221no—
543C22×D4C22×D6111yescharacteristic
544C23×C4—611no—
545C23×C4—611no—
546C23×C4—611no—
547C23×C4—611no—
548C23×C4—614no—
549C23×C4—611no—
550C23×C4—614no—
551C23×C4—1224no—
552C23×C4—1224no—
553C23×C4—1221no—
554C23×C4—1221no—
555C23×C4C22×D6111yescharacteristic
556#135—12232no—
557C2×Q16—614no—
558C2×Q16—1224no—
559C2×SD16—24no—
560C2×SD16—614no—
561C2×SD16—1224no—
562C2×SD16C22×D6114yescomplemented
563C2×D8—614no—
564C2×D8—1224no—
565C2×M16—24no—
566C2×M16—614no—
567C2×M16—614no—
568C2×M16—614no—
569C2×M16—1224no—
570C2×M16—12232no—
571C2×M16—1224no—
572C2×M16—1224no—
573C2×M16C22×D6114yes—
574C22×C8—611no—
575C22×C8—618no—
576C22×C8—614no—
577C22×C8—611no—
578C22×C8—614no—
579C22×C8—1224no—
580C22×C8C22×D6111yescharacteristic
581C22×C8C22×D6111yescharacteristic
582#123—1228no—
583#123—1228no—
584C22⋊Q8—22no—
585C22⋊Q8—614no—
586C22⋊Q8—614no—
587C22⋊Q8—614no—
588C22⋊Q8—1222no—
589C22⋊Q8—1222no—
590C22⋊Q8—1222no—
591C22⋊Q8C22×D6114yes—
592#121—22no—
593#121—614no—
594#121—614no—
595#121—614no—
596#121—1222no—
597#121—1222no—
598#121—1222no—
599#121C22×D6114yes—
600#120—1228no—
601#120—1228no—
602C4×D4—1228no—
603C4×D4—1228no—
604C4×D4—1228no—
605C4×D4—1228no—
606#117—614no—
607#117—614no—
608#117—1222no—
609#117—1222no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—611no—
612C2×C4⋊C4—611no—
613C2×C4⋊C4—1221no—
614C2×C4⋊C4—1221no—
615C2×C4⋊C4—1221no—
616C2×C4⋊C4C22×D6111yescharacteristic
617C2×C4⋊C4C22×D6111yescharacteristic
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—1221no—
621C2×C22⋊C4—1221no—
622C2×C22⋊C4—1221no—
623C2×C22⋊C4—1221no—
624C2×C22⋊C4—1221no—
625C2×C22⋊C4—1221no—
626C2×C22⋊C4—1221no—
627C2×C22⋊C4—1221no—
628C2×C42—1221no—
629C2×C42—1221no—
630#107—614no—
631#107C22×D6114yescomplemented
632#106—614no—
633#106—614no—
634#103—614no—
635#103—614no—
636#103—614no—
637#103C22×D6114yescomplemented
638#102—614no—
639#102—614no—
640#102—614no—
641#102C22×D6114yescomplemented
642C24—21no—
643C24—611no—
644C24—611no—
645C24—614no—
646C24—1224no—
647C24—1221no—
648C24—2442no—
649C24—2442no—
650C24D4×D6111yescharacteristic
651#41—1228no—
652#41—1228no—
653#41—1228no—
654#41—1228no—
655#41—2448no—
656#41—2448no—
657C2×Q8—21no—
658C2×Q8—22no—
659C2×Q8—22no—
660C2×Q8—612no—
661C2×Q8—1221no—
662C2×Q8—1222no—
663C2×Q8—1222no—
664C2×Q8C23×D6112yes—
665C2×D4—24no—
666C2×D4—22no—
667C2×D4—21no—
668C2×D4—22no—
669C2×D4—44no—
670C2×D4—612no—
671C2×D4—1224no—
672C2×D4—1224no—
673C2×D4—1224no—
674C2×D4—1224no—
675C2×D4—1224no—
676C2×D4—1222no—
677C2×D4—1221no—
678C2×D4—1222no—
679C2×D4—2444no—
680C2×D4—2444no—
681C2×D4—2444no—
682C2×D4—2444no—
683C2×D4—2444no—
684C2×D4C23×D6112yes—
685C22×C4—22no—
686C22×C4—22no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—611no—
691C22×C4—612no—
692C22×C4—614no—
693C22×C4—614no—
694C22×C4—612no—
695C22×C4—614no—
696C22×C4—611no—
697C22×C4—614no—
698C22×C4—612no—
699C22×C4—614no—
700C22×C4—612no—
701C22×C4—1228no—
702C22×C4—1224no—
703C22×C4—12216no—
704C22×C4—1228no—
705C22×C4—1224no—
706C22×C4—1224no—
707C22×C4—1224no—
708C22×C4—1224no—
709C22×C4—1222no—
710C22×C4—1222no—
711C22×C4—1221no—
712C22×C4—1221no—
713C22×C4—1221no—
714C22×C4—2444no—
715C22×C4—2444no—
716C22×C4D4×D6112yes—
717C22×C4D4×D6111yescharacteristic
718C22×C4C23×D6112yes—
719C22×C4C23×D6111yescharacteristic
720Q16—1228no—
721SD16—28no—
722SD16—1228no—
723D8—1228no—
724M16—28no—
725M16—1228no—
726M16—1228no—
727M16—1228no—
728C2×C8—22no—
729C2×C8—614no—
730C2×C8—612no—
731C2×C8—6116no—
732C2×C8—612no—
733C2×C8—1228no—
734C2×C8—1222no—
735C2×C8D4×D6114yes—
736C2×C8C23×D6112yes—
737C2×C8C23×D6112yes—
738C4⋊C4—24no—
739C4⋊C4—21no—
740C4⋊C4—21no—
741C4⋊C4—612no—
742C4⋊C4—612no—
743C4⋊C4—1224no—
744C4⋊C4—1224no—
745C4⋊C4—1221no—
746C4⋊C4—1221no—
747C4⋊C4—1224no—
748C4⋊C4C23×D6112yes—
749C4⋊C4C23×D6112yes—
750C22⋊C4—24no—
751C22⋊C4—24no—
752C22⋊C4—1224no—
753C22⋊C4—1224no—
754C22⋊C4—1224no—
755C22⋊C4—1224no—
756C22⋊C4—1224no—
757C22⋊C4—1224no—
758C22⋊C4—1224no—
759C22⋊C4—1224no—
760C42—1224no—
761C42—1224no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—42no—
767C23—42no—
768C23—42no—
769C23—614no—
770C23—612no—
771C23—612no—
772C23—1228no—
773C23—1222no—
774C23—1222no—
775C23—1222no—
776C23—1222no—
777C23—1222no—
778C23—1222no—
779C23—2444no—
780C23—2444no—
781C23—24416no—
782C23—2442no—
783C23—2442no—
784C23—2442no—
785C23C2×D4×D6112yes—
786C23C2×D4×D6111yescharacteristic
787Q8—22no—
788Q8—22no—
789Q8—42no—
790Q8—1222no—
791Q8—1222no—
792Q8—2442no—
793D4—22no—
794D4—22no—
795D4—48no—
796D4—42no—
797D4—1222no—
798D4—1222no—
799D4—2448no—
800D4—2448no—
801D4—2448no—
802D4—2448no—
803D4—2448no—
804D4—2442no—
805C2×C4—22no—
806C2×C4—24no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—614no—
816C2×C4—612no—
817C2×C4—618no—
818C2×C4—614no—
819C2×C4—614no—
820C2×C4—612no—
821C2×C4—1228no—
822C2×C4—1228no—
823C2×C4—1228no—
824C2×C4—1222no—
825C2×C4—1224no—
826C2×C4—1222no—
827C2×C4—1222no—
828C2×C4—1222no—
829C2×C4—1222no—
830C2×C4—1222no—
831C2×C4—2448no—
832C2×C4—2448no—
833C2×C4—2442no—
834C2×C4—2442no—
835C2×C4—2442no—
836C2×C4C2×D4×D6112yes—
837C2×C4C2×D4×D6111yescharacteristic
838C2×C4C2×D4×D6112yes—
839C2×C4#41×D6112yes—
840C2×C4C24×D6111yescharacteristic
841C8—22no—
842C8—614no—
843C8—1222no—
844C8C2×D4×D6114yes—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—44no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—84no—
853C22—614no—
854C22—1228no—
855C22—1222no—
856C22—1222no—
857C22—1222no—
858C22—1222no—
859C22—1222no—
860C22—4884no—
861C22—24416no—
862C22—2442no—
863C22—2442no—
864C22—2442no—
865C22—2444no—
866C22#121×D6112yes—
867C22#1684055812yes—
868C22#1684056112yes—
869C22C22×D4×D6111yescharacteristic
870C4—22no—
871C4—42no—
872C4—42no—
873C4—42no—
874C4—614no—
875C4—1222no—
876C4—2442no—
877C4—2442no—
878C4—2442no—
879C4#121×D6112yes—
880C4C22×D4×D6111yescharacteristic
881C4C2×#41×D6111yescharacteristic
882C2—42no—
883C2—82no—
884C2—1224no—
885C2—4882no—
886C2—2442no—
887C2#2145542314yesdirect product factor
888C2C2×#121×D6111yescharacteristic
889C2C2×#1684055811yescharacteristic
890C2C2×#1684056111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#468C2
socleC23×C61C22×D4
hypercenterC2×#468D61
hypocenterC61C2×#3054
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#468

Complements

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

NH ≅ G/Ntype
1. C22×#14519798C2semidirect
2. C22×M16×D61C2semidirect
3. C2×#16840275C2semidirect
4. C2×#16840272C2semidirect
5. #21455423C2direct (N × H)
6. C2×#16840019C2semidirect
7. C2×#16840018C2semidirect
8. C2×#16840014C2semidirect
9. C2×#16840013C2semidirect
10. C2×#16840009C2semidirect
11. C2×#16840008C2semidirect
12. C2×#16840005C2semidirect
13. C2×#16839799C2semidirect
14. C2×#16839757C2semidirect
15. C2×#16839755C2semidirect
16. C2×C61×#468C2semidirect
21. C2×#14519798C22semidirect
22. C22×#11758202C22semidirect
23. C22×#11758190C22semidirect
24. C22×#11758199C22semidirect
29. C2×M16×D61C22semidirect
33. #16840275C22semidirect
35. #16840272C22semidirect
52. #16840019C22semidirect
53. #16840018C22semidirect
54. #16840014C22semidirect
55. #16840013C22semidirect
56. #16840009C22semidirect
57. #16840008C22semidirect
58. #16840005C22semidirect
59. #16839799C22semidirect
60. C2×#14519711C22semidirect
61. C2×#14519708C22semidirect
62. C2×#14519708C22semidirect
63. #16839757C22semidirect
64. #16839755C22semidirect
65. C2×#14519702C22semidirect
66. C2×#14519701C22semidirect
67. C2×#14519700C22semidirect
68. C2×#14519699C22semidirect
69. C2×#14519698C22semidirect
70. C2×#14519697C22semidirect
71. C22×SD16×C61C22semidirect
75. C61×#468C22semidirect
76. C2×#107×C61C22semidirect
77. C2×#103×C61C22semidirect
78. C2×#102×C61C22semidirect
108. C2×#11758202C23semidirect
110. C2×#11758190C23semidirect
112. C2×#11758199C23semidirect
123. C2×C8×D61D4semidirect
165. #14519711C23semidirect
166. #14519708C23semidirect
167. #14519708C23semidirect
168. #14519702C23semidirect
169. #14519701C23semidirect
170. #14519700C23semidirect
171. #14519699C23semidirect
172. #14519698C23semidirect
173. #14519697C23semidirect
179. C2×SD16×C61C23semidirect
193. #107×C61C23semidirect
194. #103×C61C23semidirect
195. #102×C61C23semidirect
315. C8×D61C2×D4semidirect
449. C2×#468D61semidirect
455. C2×C61#3054semidirect
469. C22×SD16C2×D61semidirect
508. #468C2×D61semidirect
511. C2×#107C2×D61semidirect
519. C2×#103C2×D61semidirect
523. C2×#102C2×D61semidirect
524. C61C2×#3054semidirect
562. C2×SD16C22×D61semidirect
631. #107C22×D61semidirect
637. #103C22×D61semidirect
641. #102C22×D61semidirect
887. C2#21455423direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197982
C22×M16×D612
C2×#168402752
C2×#168402722
#214554232
C2×#168400192
C2×#168400182
C2×#168400142
C2×#168400132
C2×#168400092
C2×#168400082
C2×#168400052
C2×#168397992
C2×#168397572
C2×#168397552
C2×C61×#4682
C2×#305461