Finite Group Databasebeta

← C2×#21433700 #29455819

Subgroups — C2×#21433700 #29455819

Order 15104.

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×#14273748C211yesmaximal, characteristic, complemented
2C22×M16×D59C211yesmaximal, characteristic, complemented
3C2×#16837915C211yesmaximal, characteristic, complemented
4C2×#16837912C211yesmaximal, characteristic, complemented
5#21433700C2116yesmaximal, direct product factor
6C2×#16837659C211yesmaximal, characteristic, complemented
7C2×#16837658C211yesmaximal, characteristic, complemented
8C2×#16837654C211yesmaximal, characteristic, complemented
9C2×#16837653C211yesmaximal, characteristic, complemented
10C2×#16837649C211yesmaximal, characteristic, complemented
11C2×#16837648C211yesmaximal, characteristic, complemented
12C2×#16837645C211yesmaximal, characteristic, complemented
13C2×#16837439C211yesmaximal, characteristic, complemented
14C2×#16837397C211yesmaximal, characteristic, complemented
15C2×#16837395C211yesmaximal, characteristic, complemented
16C2×C59×#468C211yesmaximal, characteristic, complemented
17C22×#11745689C2211yescharacteristic
18C22×#11745687C2211yescharacteristic
19C23×C4×D59C2211yescharacteristic
20C2×#14273748—28no—
21C2×#14273748C2218yescomplemented
22C22×#11745672C2211yescharacteristic, complemented
23C22×#11745660C2211yescharacteristic, complemented
24C22×#11745669C2211yescharacteristic, complemented
25C22×#11745664C2211yescharacteristic
26C22×#11745659C2211yescharacteristic
27C22×#11745659C2211yescharacteristic
28C2×M16×D59—28no—
29C2×M16×D59C2218yescomplemented
30C22×C8×D59C2211yescharacteristic
31C22×C8×D59C2211yescharacteristic
32#16837915—24no—
33#16837915C2218yescomplemented
34#16837912—24no—
35#16837912C2218yescomplemented
36C2×#14273712—21no—
37C2×#14273709—21no—
38C2×#14273707C2211yescharacteristic
39C2×#14273706C2211yescharacteristic
40C2×#14273703C2211yescharacteristic
41C2×#14273702C2211yescharacteristic
42C2×#14273701C2211yescharacteristic
43C2×#14273698C2211yescharacteristic
44C2×#14273697—21no—
45C2×#14273695—21no—
46C2×D4×Dic59—21no—
47C2×#14273689—21no—
48C2×(C22⋊D59)⋊C4—21no—
49C2×(C22⋊D59)⋊C4—21no—
50C2×#14273685C2211yescharacteristic
51C2×#14273685C2211yescharacteristic
52#16837659C2218yescomplemented
53#16837658C2218yescomplemented
54#16837654C2218yescomplemented
55#16837653C2218yescomplemented
56#16837649C2218yescomplemented
57#16837648C2218yescomplemented
58#16837645C2218yescomplemented
59#16837439C2218yescomplemented
60C2×#14273661C2211yescharacteristic, complemented
61C2×#14273658C2211yescharacteristic, complemented
62C2×#14273658C2211yescharacteristic, complemented
63#16837397C2218yescomplemented
64#16837395C2218yescomplemented
65C2×#14273652C2211yescharacteristic, complemented
66C2×#14273651C2211yescharacteristic, complemented
67C2×#14273650C2211yescharacteristic, complemented
68C2×#14273649C2211yescharacteristic, complemented
69C2×#14273648C2211yescharacteristic, complemented
70C2×#14273647C2211yescharacteristic, complemented
71C22×SD16×C59C2211yescharacteristic, complemented
72C22×M16×C59C2211yescharacteristic
73C2×C22⋊Q8×C59C2211yescharacteristic
74C2×#121×C59C2211yescharacteristic
75C59×#468C2218yescomplemented
76C2×#107×C59C2211yescharacteristic, complemented
77C2×#103×C59C2211yescharacteristic, complemented
78C2×#102×C59C2211yescharacteristic, complemented
79C24×D59D411yescharacteristic
80C2×#11745689—22no—
81C2×#11745689—24no—
82C2×#11745689—24no—
83C2×#11745689C2314yes—
84C2×#11745687—24no—
85C2×#11745687—22no—
86C2×#11745687—24no—
87C2×#11745687C2314yes—
88C22×Dic118C2311yescharacteristic
89C22×D236—21no—
90C22×D236—21no—
91C22×D236C2311yescharacteristic
92C22×C22⋊D59—21no—
93C22×C22⋊D59—21no—
94C22×C22⋊D59—21no—
95C23×Dic59—21no—
96C23×Dic59D411yescharacteristic
97C22×C4×D59—24no—
98C22×C4×D59—24no—
99C22×C4×D59—21no—
100C22×C4×D59D411yescharacteristic
101C22×C4×D59D414yes—
102C22×C4×D59D411yescharacteristic
103C22×C4×D59C2311yescharacteristic
104C22×C4×D59C2314yes—
105C22×C4×D59C2311yescharacteristic
106#14273748—232no—
107C2×#11745672—24no—
108C2×#11745672C2314yescomplemented
109C2×#11745660—24no—
110C2×#11745660C2314yescomplemented
111C2×#11745669—24no—
112C2×#11745669C2314yescomplemented
113C2×#11745664—24no—
114C2×#11745664C2314yes—
115C2×#11745659—24no—
116C2×#11745659—24no—
117C2×#11745659C2314yes—
118C2×#11745659C2314yes—
119M16×D59—232no—
120C22×C59⋊C8C2311yescharacteristic
121C22×C59⋊C8C2311yescharacteristic
122C2×C8×D59—24no—
123C2×C8×D59D418yescomplemented
124C2×C8×D59C2314yes—
125C2×C8×D59C2314yes—
126#14273712—28no—
127#14273709—28no—
128#14273707—22no—
129#14273707C2314yes—
130#14273706—22no—
131#14273706C2314yes—
132#14273703—22no—
133#14273703C2314yes—
134#14273702—22no—
135#14273702C2314yes—
136#14273701—22no—
137#14273701C2314yes—
138#14273698—22no—
139#14273698C2314yes—
140#14273697—28no—
141#14273695—28no—
142D4×Dic59—28no—
143#14273689—28no—
144(C22⋊D59)⋊C4—28no—
145(C22⋊D59)⋊C4—28no—
146#14273685—22no—
147#14273685—22no—
148#14273685C2314yes—
149#14273685C2314yes—
150C2×C4⋊Dic59—21no—
151C2×C4⋊Dic59C2311yescharacteristic
152C2×C4⋊Dic59C2311yescharacteristic
153C2×Dic59⋊C4—21no—
154C2×Dic59⋊C4—21no—
155C2×C22⋊Dic59—21no—
156C2×C22⋊Dic59—21no—
157C2×(C2×D59)⋊C4—21no—
158C2×(C2×D59)⋊C4—21no—
159C2×(C2×D59)⋊C4—21no—
160C2×(C2×D59)⋊C4—21no—
161C2×(C2×D59)⋊C4—21no—
162C2×(C2×D59)⋊C4—21no—
163C2×C4×Dic59—21no—
164C2×C4×Dic59—21no—
165#14273661C2314yescomplemented
166#14273658C2314yescomplemented
167#14273658C2314yescomplemented
168#14273652C2314yescomplemented
169#14273651C2314yescomplemented
170#14273650C2314yescomplemented
171#14273649C2314yescomplemented
172#14273648C2314yescomplemented
173#14273647C2314yescomplemented
174C22×Q8×C59C2311yescharacteristic
175C22×D4×C59—21no—
176C22×D4×C59C2311yescharacteristic
177C23×C4×C59C2311yescharacteristic
178C2×SD16×C59—24no—
179C2×SD16×C59C2314yescomplemented
180C2×M16×C59—24no—
181C2×M16×C59C2314yes—
182C22×C8×C59C2311yescharacteristic
183C22×C8×C59C2311yescharacteristic
184C22⋊Q8×C59—22no—
185C22⋊Q8×C59C2314yes—
186#121×C59—22no—
187#121×C59C2314yes—
188C2×C4⋊C4×C59—21no—
189C2×C4⋊C4×C59C2311yescharacteristic
190C2×C4⋊C4×C59C2311yescharacteristic
191C2×C22⋊C4×C59—21no—
192C2×C22⋊C4×C59—21no—
193#107×C59C2314yescomplemented
194#103×C59C2314yescomplemented
195#102×C59C2314yescomplemented
196C24×C59—21no—
197C24×C59C2×D411yescharacteristic
198C23×D59—24no—
199C23×D59—21no—
200C23×D59—42no—
201C23×D59—42no—
202C23×D59C2×D411yescharacteristic
203C23×D59C2×D411yescharacteristic
204C23×D59C2×D414yes—
205C2×Q8×C59—21no—
206C2×Q8×C59—22no—
207C2×Q8×C59—22no—
208C2×Q8×C59C2412yes—
209C2×D4×C59—24no—
210C2×D4×C59—22no—
211C2×D4×C59—21no—
212C2×D4×C59—22no—
213C2×D4×C59—44no—
214C2×D4×C59C2412yes—
215C22×C4×C59—22no—
216C22×C4×C59—22no—
217C22×C4×C59—21no—
218C22×C4×C59—21no—
219C22×C4×C59—21no—
220C22×C4×C59C2×D411yescharacteristic
221C22×C4×C59C2×D412yes—
222C22×C4×C59C2412yes—
223C22×C4×C59C2411yescharacteristic
224C2×C22⋊D59—24no—
225C2×C22⋊D59—24no—
226C2×C22⋊D59—24no—
227C2×C22⋊D59—44no—
228C2×C22⋊D59—44no—
229C2×C22⋊D59—44no—
230C22×Dic59—24no—
231C22×Dic59—21no—
232C22×Dic59—21no—
233C22×Dic59—21no—
234C22×Dic59—24no—
235C22×Dic59—44no—
236C22×Dic59C2×D411yescharacteristic
237C22×Dic59C2×D414yes—
238C22×Dic59C2×D411yescharacteristic
239#11745689—28no—
240#11745689—28no—
241#11745689—48no—
242#11745687—28no—
243#11745687—28no—
244#11745687—48no—
245C2×D236—22no—
246C2×D236—22no—
247C2×D236—24no—
248C2×D236—24no—
249C2×D236—21no—
250C2×D236—44no—
251C2×D236—44no—
252C2×D236C2412yes—
253C2×C4×D59—24no—
254C2×C4×D59—22no—
255C2×C4×D59—22no—
256C2×C4×D59—24no—
257C2×C4×D59—216no—
258C2×C4×D59—28no—
259C2×C4×D59—28no—
260C2×C4×D59—24no—
261C2×C4×D59—44no—
262C2×C4×D59C2×D414yes—
263C2×C4×D59C2×D412yes—
264C2×C4×D59C2×D414yes—
265C2×C4×D59C2×D412yes—
266C2×C4×D59C2×D414yes—
267C2×C4×D59#4114yes—
268C2×C4×D59C2412yes—
269C2×C4×D59C2412yes—
270C2×Dic118—22no—
271C2×Dic118—22no—
272C2×Dic118—21no—
273C2×Dic118C2412yes—
274SD16×C59—28no—
275M16×C59—28no—
276C2×C8×C59—22no—
277C2×C8×C59C2×D414yes—
278C2×C8×C59C2412yes—
279C2×C8×C59C2412yes—
280C4⋊C4×C59—24no—
281C4⋊C4×C59—21no—
282C4⋊C4×C59—21no—
283C4⋊C4×C59C2412yes—
284C4⋊C4×C59C2412yes—
285C22⋊C4×C59—24no—
286C22⋊C4×C59—24no—
287C22⋊Dic59—24no—
288C22⋊Dic59—24no—
289#11745672—28no—
290#11745669—28no—
291(C2×D59)⋊C4—24no—
292(C2×D59)⋊C4—24no—
293(C2×D59)⋊C4—24no—
294(C2×D59)⋊C4—24no—
295(C2×D59)⋊C4—24no—
296(C2×D59)⋊C4—24no—
297C4⋊Dic59—21no—
298C4⋊Dic59—21no—
299C4⋊Dic59—24no—
300C4⋊Dic59C2412yes—
301C4⋊Dic59C2412yes—
302Dic59⋊C4—24no—
303Dic59⋊C4—24no—
304C4×Dic59—24no—
305C4×Dic59—24no—
306#11745664—28no—
307C2×C59⋊C8—22no—
308C2×C59⋊C8C2×D414yes—
309C2×C59⋊C8C2412yes—
310C2×C59⋊C8C2412yes—
311#11745660—28no—
312#11745659—28no—
313#11745659—28no—
314C8×D59—28no—
315C8×D59C2×D4116yescomplemented
316C23×C59—22no—
317C23×C59—22no—
318C23×C59—22no—
319C23×C59—22no—
320C23×C59—42no—
321C23×C59—42no—
322C23×C59—42no—
323C23×C59C22×D412yes—
324C23×C59C22×D411yescharacteristic
325C22×D59—22no—
326C22×D59—22no—
327C22×D59—22no—
328C22×D59—22no—
329C22×D59—22no—
330C22×D59—28no—
331C22×D59—22no—
332C22×D59—44no—
333C22×D59—44no—
334C22×D59—416no—
335C22×D59—42no—
336C22×D59—42no—
337C22×D59—42no—
338C22×D59#12114yes—
339C22×D59C22×D412yes—
340C22×D59C22×D412yes—
341Q8×C59—22no—
342Q8×C59—22no—
343Q8×C59—42no—
344D4×C59—22no—
345D4×C59—22no—
346D4×C59—48no—
347D4×C59—42no—
348C2×C4×C59—22no—
349C2×C4×C59—24no—
350C2×C4×C59—22no—
351C2×C4×C59—22no—
352C2×C4×C59—22no—
353C2×C4×C59—22no—
354C2×C4×C59—22no—
355C2×C4×C59—42no—
356C2×C4×C59—42no—
357C2×C4×C59—42no—
358C2×C4×C59C22×D412yes—
359C2×C4×C59C22×D411yescharacteristic
360C2×C4×C59C22×D412yes—
361C2×C4×C59C2×#4112yes—
362C2×C4×C59C2511yescharacteristic
363C22⋊D59—48no—
364C22⋊D59—48no—
365C22⋊D59—48no—
366C2×Dic59—22no—
367C2×Dic59—28no—
368C2×Dic59—22no—
369C2×Dic59—22no—
370C2×Dic59—22no—
371C2×Dic59—42no—
372C2×Dic59—42no—
373C2×Dic59—42no—
374C2×Dic59—48no—
375C2×Dic59#12114yes—
376C2×Dic59C22×D412yes—
377C2×Dic59C22×D412yes—
378D236—22no—
379D236—22no—
380D236—48no—
381D236—48no—
382D236—42no—
383C4×D59—28no—
384C4×D59—24no—
385C4×D59—22no—
386C4×D59—22no—
387C4×D59—28no—
388C4×D59—48no—
389C4×D59#12118yes—
390C4×D59C22×D414yes—
391C4×D59C2×#4114yes—
392Dic118—22no—
393Dic118—22no—
394Dic118—42no—
395C8×C59—22no—
396C8×C59C22×D414yes—
397C59⋊C8—22no—
398C59⋊C8C22×D414yes—
399C2×#3054—591nomaximal, Sylow
400C22×C59—22no—
401C22×C59—22no—
402C22×C59—22no—
403C22×C59—44no—
404C22×C59—42no—
405C22×C59—42no—
406C22×C59—42no—
407C22×C59—84no—
408C22×C59C2×#12112yes—
409C22×C59#57512yes—
410C22×C59#57512yes—
411C22×C59C23×D411yescharacteristic
412C2×D59—28no—
413C2×D59—22no—
414C2×D59—22no—
415C2×D59—22no—
416C2×D59—22no—
417C2×D59—22no—
418C2×D59—416no—
419C2×D59—44no—
420C2×D59—42no—
421C2×D59—42no—
422C2×D59—42no—
423C2×D59—84no—
424C2×D59C2×#12114yes—
425C4×C59—22no—
426C4×C59—42no—
427C4×C59—42no—
428C4×C59—42no—
429C4×C59C2×#12112yes—
430C4×C59C23×D411yescharacteristic
431C4×C59C22×#4111yescharacteristic
432Dic59—22no—
433Dic59—42no—
434Dic59—42no—
435Dic59—42no—
436Dic59C2×#12114yes—
437C22×#135—591no—
438C23×M16—591no—
439C2×#525—591no—
440C2×#525—591no—
441#3054—5916no—
442C2×#470—591no—
443C2×#470—591no—
444C2×#469—591no—
445C2×#469—591no—
446C2×#468—591no—
447C2×#468—591no—
448C2×#468—591no—
449C2×#468D5911yescharacteristic, complemented
450C2×#427—591no—
451C2×#416—591no—
452C2×#416—591no—
453C2×C59—42no—
454C2×C59—82no—
455C2×C59#305414yescomplemented
456C2×C59C22×#12111yescharacteristic
457C2×C59C2×#57511yescharacteristic
458C2×C59C2×#57511yescharacteristic
459D59—24no—
460D59—42no—
461D59—82no—
462C22×#41—591no—
463C22×#41—591no—
464C24×C4—591no—
465C2×#135—598no—
466C2×#135—1188no—
467C22×Q16—591no—
468C22×SD16—591no—
469C22×SD16C2×D5911yescharacteristic, complemented
470C22×D8—591no—
471C22×M16—591no—
472C22×M16—598no—
473C22×M16—591no—
474C22×M16—591no—
475C22×M16—1188no—
476C22×M16C2×D5911yescharacteristic
477C23×C8—591no—
478C23×C8—591no—
479#525—598no—
480#525—598no—
481#525—1184no—
482#525—1184no—
483C2×#123—1181no—
484C2×#123—1181no—
485C2×C22⋊Q8—591no—
486C2×C22⋊Q8—591no—
487C2×C22⋊Q8—591no—
488C2×C22⋊Q8C2×D5911yescharacteristic
489C2×#121—591no—
490C2×#121—591no—
491C2×#121—591no—
492C2×#121C2×D5911yescharacteristic
493C2×#120—1181no—
494C2×#120—1181no—
495C2×C4×D4—1181no—
496C2×C4×D4—1181no—
497C2×C4×D4—1181no—
498C2×C4×D4—1181no—
499C2×#117—591no—
500C2×#117—591no—
501#470—598no—
502#470—598no—
503#469—598no—
504#469—598no—
505#468—598no—
506#468—598no—
507#468—598no—
508#468C2×D5918yescomplemented
509#427—598no—
510C2×#107—591no—
511C2×#107C2×D5911yescharacteristic, complemented
512C2×#106—591no—
513C2×#106—591no—
514#416—598no—
515#416—598no—
516C2×#103—591no—
517C2×#103—591no—
518C2×#103—591no—
519C2×#103C2×D5911yescharacteristic, complemented
520C2×#102—591no—
521C2×#102—591no—
522C2×#102—591no—
523C2×#102C2×D5911yescharacteristic, complemented
524C59C2×#305411yescharacteristic, complemented, Sylow
525C25—591no—
526C2×#41—594no—
527C2×#41—594no—
528C2×#41—1182no—
529C2×#41—1182no—
530C2×#41—1184no—
531C2×#41—1184no—
532C2×#41—1184no—
533C2×#41—1184no—
534C22×Q8—591no—
535C22×Q8C22×D5911yescharacteristic
536C22×D4—21no—
537C22×D4—591no—
538C22×D4—1181no—
539C22×D4—1181no—
540C22×D4—1181no—
541C22×D4—1181no—
542C22×D4—1181no—
543C22×D4C22×D5911yescharacteristic
544C23×C4—591no—
545C23×C4—591no—
546C23×C4—591no—
547C23×C4—591no—
548C23×C4—594no—
549C23×C4—591no—
550C23×C4—594no—
551C23×C4—1184no—
552C23×C4—1184no—
553C23×C4—1181no—
554C23×C4—1181no—
555C23×C4C22×D5911yescharacteristic
556#135—11832no—
557C2×Q16—594no—
558C2×Q16—1184no—
559C2×SD16—24no—
560C2×SD16—594no—
561C2×SD16—1184no—
562C2×SD16C22×D5914yescomplemented
563C2×D8—594no—
564C2×D8—1184no—
565C2×M16—24no—
566C2×M16—594no—
567C2×M16—594no—
568C2×M16—594no—
569C2×M16—1184no—
570C2×M16—11832no—
571C2×M16—1184no—
572C2×M16—1184no—
573C2×M16C22×D5914yes—
574C22×C8—591no—
575C22×C8—598no—
576C22×C8—594no—
577C22×C8—591no—
578C22×C8—594no—
579C22×C8—1184no—
580C22×C8C22×D5911yescharacteristic
581C22×C8C22×D5911yescharacteristic
582#123—1188no—
583#123—1188no—
584C22⋊Q8—22no—
585C22⋊Q8—594no—
586C22⋊Q8—594no—
587C22⋊Q8—594no—
588C22⋊Q8—1182no—
589C22⋊Q8—1182no—
590C22⋊Q8—1182no—
591C22⋊Q8C22×D5914yes—
592#121—22no—
593#121—594no—
594#121—594no—
595#121—594no—
596#121—1182no—
597#121—1182no—
598#121—1182no—
599#121C22×D5914yes—
600#120—1188no—
601#120—1188no—
602C4×D4—1188no—
603C4×D4—1188no—
604C4×D4—1188no—
605C4×D4—1188no—
606#117—594no—
607#117—594no—
608#117—1182no—
609#117—1182no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—591no—
612C2×C4⋊C4—591no—
613C2×C4⋊C4—1181no—
614C2×C4⋊C4—1181no—
615C2×C4⋊C4—1181no—
616C2×C4⋊C4C22×D5911yescharacteristic
617C2×C4⋊C4C22×D5911yescharacteristic
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—1181no—
621C2×C22⋊C4—1181no—
622C2×C22⋊C4—1181no—
623C2×C22⋊C4—1181no—
624C2×C22⋊C4—1181no—
625C2×C22⋊C4—1181no—
626C2×C22⋊C4—1181no—
627C2×C22⋊C4—1181no—
628C2×C42—1181no—
629C2×C42—1181no—
630#107—594no—
631#107C22×D5914yescomplemented
632#106—594no—
633#106—594no—
634#103—594no—
635#103—594no—
636#103—594no—
637#103C22×D5914yescomplemented
638#102—594no—
639#102—594no—
640#102—594no—
641#102C22×D5914yescomplemented
642C24—21no—
643C24—591no—
644C24—591no—
645C24—594no—
646C24—1184no—
647C24—1181no—
648C24—2362no—
649C24—2362no—
650C24D4×D5911yescharacteristic
651#41—1188no—
652#41—1188no—
653#41—1188no—
654#41—1188no—
655#41—2368no—
656#41—2368no—
657C2×Q8—21no—
658C2×Q8—22no—
659C2×Q8—22no—
660C2×Q8—592no—
661C2×Q8—1181no—
662C2×Q8—1182no—
663C2×Q8—1182no—
664C2×Q8C23×D5912yes—
665C2×D4—24no—
666C2×D4—22no—
667C2×D4—21no—
668C2×D4—22no—
669C2×D4—44no—
670C2×D4—592no—
671C2×D4—1184no—
672C2×D4—1184no—
673C2×D4—1184no—
674C2×D4—1184no—
675C2×D4—1184no—
676C2×D4—1182no—
677C2×D4—1181no—
678C2×D4—1182no—
679C2×D4—2364no—
680C2×D4—2364no—
681C2×D4—2364no—
682C2×D4—2364no—
683C2×D4—2364no—
684C2×D4C23×D5912yes—
685C22×C4—22no—
686C22×C4—22no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—591no—
691C22×C4—592no—
692C22×C4—594no—
693C22×C4—594no—
694C22×C4—592no—
695C22×C4—594no—
696C22×C4—591no—
697C22×C4—594no—
698C22×C4—592no—
699C22×C4—594no—
700C22×C4—592no—
701C22×C4—1188no—
702C22×C4—1184no—
703C22×C4—11816no—
704C22×C4—1188no—
705C22×C4—1184no—
706C22×C4—1184no—
707C22×C4—1184no—
708C22×C4—1184no—
709C22×C4—1182no—
710C22×C4—1182no—
711C22×C4—1181no—
712C22×C4—1181no—
713C22×C4—1181no—
714C22×C4—2364no—
715C22×C4—2364no—
716C22×C4D4×D5912yes—
717C22×C4D4×D5911yescharacteristic
718C22×C4C23×D5912yes—
719C22×C4C23×D5911yescharacteristic
720Q16—1188no—
721SD16—28no—
722SD16—1188no—
723D8—1188no—
724M16—28no—
725M16—1188no—
726M16—1188no—
727M16—1188no—
728C2×C8—22no—
729C2×C8—594no—
730C2×C8—592no—
731C2×C8—5916no—
732C2×C8—592no—
733C2×C8—1188no—
734C2×C8—1182no—
735C2×C8D4×D5914yes—
736C2×C8C23×D5912yes—
737C2×C8C23×D5912yes—
738C4⋊C4—24no—
739C4⋊C4—21no—
740C4⋊C4—21no—
741C4⋊C4—592no—
742C4⋊C4—592no—
743C4⋊C4—1184no—
744C4⋊C4—1184no—
745C4⋊C4—1181no—
746C4⋊C4—1181no—
747C4⋊C4—1184no—
748C4⋊C4C23×D5912yes—
749C4⋊C4C23×D5912yes—
750C22⋊C4—24no—
751C22⋊C4—24no—
752C22⋊C4—1184no—
753C22⋊C4—1184no—
754C22⋊C4—1184no—
755C22⋊C4—1184no—
756C22⋊C4—1184no—
757C22⋊C4—1184no—
758C22⋊C4—1184no—
759C22⋊C4—1184no—
760C42—1184no—
761C42—1184no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—42no—
767C23—42no—
768C23—42no—
769C23—594no—
770C23—592no—
771C23—592no—
772C23—1188no—
773C23—1182no—
774C23—1182no—
775C23—1182no—
776C23—1182no—
777C23—1182no—
778C23—1182no—
779C23—2364no—
780C23—2364no—
781C23—23616no—
782C23—2362no—
783C23—2362no—
784C23—2362no—
785C23C2×D4×D5912yes—
786C23C2×D4×D5911yescharacteristic
787Q8—22no—
788Q8—22no—
789Q8—42no—
790Q8—1182no—
791Q8—1182no—
792Q8—2362no—
793D4—22no—
794D4—22no—
795D4—48no—
796D4—42no—
797D4—1182no—
798D4—1182no—
799D4—2368no—
800D4—2368no—
801D4—2368no—
802D4—2368no—
803D4—2368no—
804D4—2362no—
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—594no—
816C2×C4—592no—
817C2×C4—598no—
818C2×C4—594no—
819C2×C4—594no—
820C2×C4—592no—
821C2×C4—1188no—
822C2×C4—1188no—
823C2×C4—1188no—
824C2×C4—1182no—
825C2×C4—1184no—
826C2×C4—1182no—
827C2×C4—1182no—
828C2×C4—1182no—
829C2×C4—1182no—
830C2×C4—1182no—
831C2×C4—2368no—
832C2×C4—2368no—
833C2×C4—2362no—
834C2×C4—2362no—
835C2×C4—2362no—
836C2×C4C2×D4×D5912yes—
837C2×C4C2×D4×D5911yescharacteristic
838C2×C4C2×D4×D5912yes—
839C2×C4#41×D5912yes—
840C2×C4C24×D5911yescharacteristic
841C8—22no—
842C8—594no—
843C8—1182no—
844C8C2×D4×D5914yes—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—44no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—84no—
853C22—594no—
854C22—1188no—
855C22—1182no—
856C22—1182no—
857C22—1182no—
858C22—1182no—
859C22—1182no—
860C22—4724no—
861C22—23616no—
862C22—2362no—
863C22—2362no—
864C22—2362no—
865C22—2364no—
866C22#121×D5912yes—
867C22#1683819812yes—
868C22#1683820112yes—
869C22C22×D4×D5911yescharacteristic
870C4—22no—
871C4—42no—
872C4—42no—
873C4—42no—
874C4—594no—
875C4—1182no—
876C4—2362no—
877C4—2362no—
878C4—2362no—
879C4#121×D5912yes—
880C4C22×D4×D5911yescharacteristic
881C4C2×#41×D5911yescharacteristic
882C2—42no—
883C2—82no—
884C2—1184no—
885C2—4722no—
886C2—2362no—
887C2#2143370014yesdirect product factor
888C2C2×#121×D5911yescharacteristic
889C2C2×#1683819811yescharacteristic
890C2C2×#1683820111yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#468C2
socleC23×C59C22×D4
hypercenterC2×#468D59
hypocenterC59C2×#3054
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#468

Complements

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

NH ≅ G/Ntype
1. C22×#14273748C2semidirect
2. C22×M16×D59C2semidirect
3. C2×#16837915C2semidirect
4. C2×#16837912C2semidirect
5. #21433700C2direct (N × H)
6. C2×#16837659C2semidirect
7. C2×#16837658C2semidirect
8. C2×#16837654C2semidirect
9. C2×#16837653C2semidirect
10. C2×#16837649C2semidirect
11. C2×#16837648C2semidirect
12. C2×#16837645C2semidirect
13. C2×#16837439C2semidirect
14. C2×#16837397C2semidirect
15. C2×#16837395C2semidirect
16. C2×C59×#468C2semidirect
21. C2×#14273748C22semidirect
22. C22×#11745672C22semidirect
23. C22×#11745660C22semidirect
24. C22×#11745669C22semidirect
29. C2×M16×D59C22semidirect
33. #16837915C22semidirect
35. #16837912C22semidirect
52. #16837659C22semidirect
53. #16837658C22semidirect
54. #16837654C22semidirect
55. #16837653C22semidirect
56. #16837649C22semidirect
57. #16837648C22semidirect
58. #16837645C22semidirect
59. #16837439C22semidirect
60. C2×#14273661C22semidirect
61. C2×#14273658C22semidirect
62. C2×#14273658C22semidirect
63. #16837397C22semidirect
64. #16837395C22semidirect
65. C2×#14273652C22semidirect
66. C2×#14273651C22semidirect
67. C2×#14273650C22semidirect
68. C2×#14273649C22semidirect
69. C2×#14273648C22semidirect
70. C2×#14273647C22semidirect
71. C22×SD16×C59C22semidirect
75. C59×#468C22semidirect
76. C2×#107×C59C22semidirect
77. C2×#103×C59C22semidirect
78. C2×#102×C59C22semidirect
108. C2×#11745672C23semidirect
110. C2×#11745660C23semidirect
112. C2×#11745669C23semidirect
123. C2×C8×D59D4semidirect
165. #14273661C23semidirect
166. #14273658C23semidirect
167. #14273658C23semidirect
168. #14273652C23semidirect
169. #14273651C23semidirect
170. #14273650C23semidirect
171. #14273649C23semidirect
172. #14273648C23semidirect
173. #14273647C23semidirect
179. C2×SD16×C59C23semidirect
193. #107×C59C23semidirect
194. #103×C59C23semidirect
195. #102×C59C23semidirect
315. C8×D59C2×D4semidirect
449. C2×#468D59semidirect
455. C2×C59#3054semidirect
469. C22×SD16C2×D59semidirect
508. #468C2×D59semidirect
511. C2×#107C2×D59semidirect
519. C2×#103C2×D59semidirect
523. C2×#102C2×D59semidirect
524. C59C2×#3054semidirect
562. C2×SD16C22×D59semidirect
631. #107C22×D59semidirect
637. #103C22×D59semidirect
641. #102C22×D59semidirect
887. C2#21433700direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#142737482
C22×M16×D592
C2×#168379152
C2×#168379122
#214337002
C2×#168376592
C2×#168376582
C2×#168376542
C2×#168376532
C2×#168376492
C2×#168376482
C2×#168376452
C2×#168374392
C2×#168373972
C2×#168373952
C2×C59×#4682
C2×#305459