Finite Group Databasebeta

← C2×#21436295 #29465484

Subgroups — C2×#21436295 #29465484

Order 15104.

2318 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838096C211yesmaximal, characteristic, complemented
2C2×#16838043C211yesmaximal, characteristic, complemented
3#21436295C2116yesmaximal, direct product factor
4C2×#16837758C211yesmaximal, characteristic, complemented
5C2×#16837717C211yesmaximal, characteristic, complemented
6C2×#16837701C211yesmaximal, characteristic, complemented
7C2×#16837656C211yesmaximal, characteristic, complemented
8C2×#16837650C211yesmaximal, characteristic, complemented
9C2×#16837620C211yesmaximal, characteristic, complemented
10C2×#16837550C211yesmaximal, characteristic, complemented
11C2×#16837538C211yesmaximal, characteristic, complemented
12C2×#16837484C211yesmaximal, characteristic, complemented
13C2×#16837477C211yesmaximal, characteristic, complemented
14C2×#16837402C211yesmaximal, characteristic, complemented
15C2×#16837406C211yesmaximal, characteristic, complemented
16C2×C59×#485C211yesmaximal, characteristic, complemented
17C22×#11745689C2211yescharacteristic
18C23×D236C2211yescharacteristic
19C22×#11745671C2211yescharacteristic, complemented
20C22×D472C2211yescharacteristic
21C22×D472C2211yescharacteristic
22C22×#11745664C2211yescharacteristic
23C22×#11745659C2211yescharacteristic, complemented
24#16838096—24no—
25#16838096C2218yescomplemented
26#16838043—24no—
27#16838043C2218yescomplemented
28C2×#14273721—21no—
29C2×#14273718C2211yescharacteristic, complemented
30C2×#14273716C2211yescharacteristic
31C2×#14273712—21no—
32C2×#14273709—21no—
33C2×#14273702—21no—
34C2×#14273702C2211yescharacteristic
35C2×#14273702C2211yescharacteristic, complemented
36C2×#14273701C2211yescharacteristic
37C2×#14273700—21no—
38C2×#14273697—21no—
39C2×C4×D236—21no—
40C2×#14273689C2211yescharacteristic
41C2×#14273689C2211yescharacteristic, complemented
42C2×C4×C22⋊D59C2211yescharacteristic
43C2×C4⋊C4×D59C2211yescharacteristic, complemented
44C2×C22⋊C4×D59—21no—
45#16837758C2218yescomplemented
46#16837717C2218yescomplemented
47#16837701C2218yescomplemented
48#16837656C2218yescomplemented
49#16837650C2218yescomplemented
50#16837620C2218yescomplemented
51#16837550C2218yescomplemented
52#16837538C2218yescomplemented
53#16837484C2218yescomplemented
54#16837477C2218yescomplemented
55C2×#14273660C2211yescharacteristic, complemented
56C2×Dic59⋊C8C2211yescharacteristic, complemented
57#16837406C2218yescomplemented
58#16837402C2218yescomplemented
59C2×#14273651C2211yescharacteristic, complemented
60C2×#14273649C2211yescharacteristic
61C2×#14273649C2211yescharacteristic
62C2×#14273647C2211yescharacteristic
63C2×#14273647C2211yescharacteristic
64C2×#14273647C2211yescharacteristic
65C2×#14273647C2211yescharacteristic
66C2×#14273647C2211yescharacteristic, complemented
67C2×(C2×D59)⋊C8C2211yescharacteristic, complemented
68C2×C8×Dic59C2211yescharacteristic, complemented
69C2×C22⋊Q8×C59C2211yescharacteristic
70C2×#117×C59C2211yescharacteristic
71C59×#485C2218yescomplemented
72C2×#107×C59C2211yescharacteristic, complemented
73C2×#106×C59C2211yescharacteristic, complemented
74C2×#103×C59C2211yescharacteristic, complemented
75C2×#103×C59C2211yescharacteristic, complemented
76C2×C22⋊C8×C59C2211yescharacteristic
77C24×D59—21no—
78C2×#11745689—22no—
79C2×#11745689—24no—
80C2×#11745689—42no—
81C2×#11745689C2314yes—
82C22×D236—24no—
83C22×D236—21no—
84C22×D236—21no—
85C22×D236—21no—
86C22×D236—22no—
87C22×D236—21no—
88C22×D236—42no—
89C22×D236C2311yescharacteristic
90C22×D236C2311yescharacteristic
91C22×D236C2314yes—
92C22×D236C2311yescharacteristic
93C22×C22⋊D59—21no—
94C22×C22⋊D59D411yescharacteristic
95C22×C4×D59—21no—
96C22×C4×D59—21no—
97C22×C4×D59—21no—
98C22×C4×D59—21no—
99C22×C4×D59C2311yescharacteristic
100C2×#11745671—42no—
101C2×#11745671C2314yescomplemented
102C2×D472—24no—
103C2×D472—42no—
104C2×D472C2314yes—
105C2×D472C2314yes—
106C2×#11745664—42no—
107C2×#11745664C2314yes—
108C2×#11745659—42no—
109C2×#11745659C2314yescomplemented
110C22×C59⋊C8C2311yescharacteristic
111C22×C59⋊C8C2311yescharacteristic
112#14273721—28no—
113#14273718—22no—
114#14273718C2314yescomplemented
115#14273716—22no—
116#14273716C2314yes—
117#14273712—28no—
118#14273709—28no—
119#14273702—22no—
120#14273702—22no—
121#14273702—28no—
122#14273702C2314yes—
123#14273702C2314yescomplemented
124#14273701—22no—
125#14273701C2314yes—
126#14273700—28no—
127#14273697—28no—
128C4×D236—28no—
129#14273689—22no—
130#14273689—22no—
131#14273689C2314yes—
132#14273689C2314yescomplemented
133C4×C22⋊D59D414yes—
134C4×C22⋊D59C2314yes—
135C2×C4⋊Dic59—21no—
136C2×C4⋊Dic59C2311yescharacteristic
137C2×Dic59⋊C4—21no—
138C2×Dic59⋊C4—21no—
139C2×Dic59⋊C4D411yescharacteristic
140C4⋊C4×D59—22no—
141C4⋊C4×D59C2314yescomplemented
142C2×C22⋊Dic59D411yescharacteristic
143C2×(C2×D59)⋊C4—21no—
144C2×(C2×D59)⋊C4—21no—
145C2×(C2×D59)⋊C4—21no—
146C2×(C2×D59)⋊C4—21no—
147C2×(C2×D59)⋊C4—21no—
148C2×(C2×D59)⋊C4—21no—
149C2×(C2×D59)⋊C4—21no—
150C2×(C2×D59)⋊C4D411yescharacteristic
151C22⋊C4×D59—28no—
152C2×C4×Dic59C2311yescharacteristic
153#14273660C2314yescomplemented
154Dic59⋊C8C2314yescomplemented
155#14273651C2314yescomplemented
156#14273649C2314yes—
157#14273649C2314yes—
158#14273647C2314yes—
159#14273647C2314yes—
160#14273647C2314yes—
161#14273647C2314yes—
162#14273647C2314yescomplemented
163(C2×D59)⋊C8C2314yescomplemented
164C8×Dic59C2314yescomplemented
165C22×Q8×C59C2311yescharacteristic
166C23×C4×C59C2311yescharacteristic
167C22×C8×C59C2311yescharacteristic
168C22×C8×C59C2311yescharacteristic
169C22⋊Q8×C59—22no—
170C22⋊Q8×C59C2314yes—
171#117×C59—22no—
172#117×C59C2314yes—
173C2×C4⋊C4×C59—21no—
174C2×C4⋊C4×C59C2311yescharacteristic
175C2×C4⋊C4×C59C2311yescharacteristic
176C2×C4⋊C4×C59C2311yescharacteristic
177C2×C22⋊C4×C59—21no—
178C2×C22⋊C4×C59—21no—
179C2×C42×C59—21no—
180#107×C59C2314yescomplemented
181#106×C59C2314yescomplemented
182#103×C59C2314yescomplemented
183#103×C59C2314yescomplemented
184C22⋊C8×C59C2314yes—
185C24×C59C2×D411yescharacteristic
186C23×D59—21no—
187C23×D59—21no—
188C23×D59—21no—
189C23×D59—24no—
190C23×D59—44no—
191C23×D59—44no—
192C23×D59—82no—
193C23×D59C2×D411yescharacteristic
194C2×Q8×C59—21no—
195C2×Q8×C59—22no—
196C2×Q8×C59—22no—
197C2×Q8×C59C2412yes—
198C22×C4×C59—22no—
199C22×C4×C59—22no—
200C22×C4×C59—21no—
201C22×C4×C59—21no—
202C22×C4×C59—21no—
203C22×C4×C59—21no—
204C22×C4×C59C2×D411yescharacteristic
205C22×C4×C59C2×D412yes—
206C22×C4×C59C2412yes—
207C22×C4×C59C2411yescharacteristic
208C2×C22⋊D59—24no—
209C2×C22⋊D59—42no—
210C2×C22⋊D59—82no—
211C2×C22⋊D59C2×D414yes—
212C22×Dic59—21no—
213C22×Dic59C2×D411yescharacteristic
214C22×Dic59C2×D411yescharacteristic
215C22×Dic59C2×D411yescharacteristic
216#11745689—28no—
217#11745689—44no—
218#11745689—48no—
219C2×D236—21no—
220C2×D236—22no—
221C2×D236—22no—
222C2×D236—22no—
223C2×D236—22no—
224C2×D236—22no—
225C2×D236—28no—
226C2×D236—24no—
227C2×D236—24no—
228C2×D236—21no—
229C2×D236—24no—
230C2×D236—21no—
231C2×D236—24no—
232C2×D236—44no—
233C2×D236—48no—
234C2×D236—44no—
235C2×D236—44no—
236C2×D236—44no—
237C2×D236—82no—
238C2×D236#4114yes—
239C2×D236C2412yes—
240C2×D236C2412yes—
241C2×D236C2412yes—
242C2×C4×D59—22no—
243C2×C4×D59—22no—
244C2×C4×D59—24no—
245C2×C4×D59—24no—
246C2×C4×D59—24no—
247C2×C4×D59—24no—
248C2×C4×D59—44no—
249C2×C4×D59—82no—
250C2×C4×D59—82no—
251C2×C4×D59—82no—
252C2×C4×D59C2×D412yes—
253C2×C4×D59C2412yes—
254C2×C8×C59—22no—
255C2×C8×C59—22no—
256C2×C8×C59C2412yes—
257C2×C8×C59C2412yes—
258C4⋊C4×C59—24no—
259C4⋊C4×C59—21no—
260C4⋊C4×C59—21no—
261C4⋊C4×C59—21no—
262C4⋊C4×C59C2412yes—
263C4⋊C4×C59C2412yes—
264C4⋊C4×C59C2412yes—
265C22⋊C4×C59—24no—
266C22⋊C4×C59—24no—
267C42×C59—24no—
268C22⋊Dic59C2×D414yes—
269#11745671—44no—
270(C2×D59)⋊C4—24no—
271(C2×D59)⋊C4—24no—
272(C2×D59)⋊C4—24no—
273(C2×D59)⋊C4—24no—
274(C2×D59)⋊C4—24no—
275(C2×D59)⋊C4—24no—
276(C2×D59)⋊C4—24no—
277(C2×D59)⋊C4C2×D414yes—
278C4⋊Dic59—21no—
279C4⋊Dic59—24no—
280C4⋊Dic59C2412yes—
281Dic59⋊C4—24no—
282Dic59⋊C4—24no—
283Dic59⋊C4C2×D414yes—
284C4×Dic59C2×D412yes—
285C4×Dic59C2412yes—
286#11745664—44no—
287C2×C59⋊C8—22no—
288C2×C59⋊C8—22no—
289C2×C59⋊C8C2412yes—
290C2×C59⋊C8C2412yes—
291D472—28no—
292D472—44no—
293#11745659—44no—
294C23×C59—22no—
295C23×C59—22no—
296C23×C59—22no—
297C23×C59C22×D412yes—
298C23×C59C22×D411yescharacteristic
299C22×D59—22no—
300C22×D59—24no—
301C22×D59—22no—
302C22×D59—22no—
303C22×D59—22no—
304C22×D59—22no—
305C22×D59—22no—
306C22×D59—48no—
307C22×D59—42no—
308C22×D59—42no—
309C22×D59—48no—
310C22×D59—42no—
311C22×D59—42no—
312C22×D59—42no—
313C22×D59—42no—
314C22×D59—42no—
315C22×D59—42no—
316C22×D59—84no—
317C22×D59—816no—
318C22×D59C22×D412yes—
319Q8×C59—22no—
320Q8×C59—22no—
321Q8×C59—42no—
322C2×C4×C59—22no—
323C2×C4×C59—24no—
324C2×C4×C59—22no—
325C2×C4×C59—22no—
326C2×C4×C59—22no—
327C2×C4×C59—22no—
328C2×C4×C59—22no—
329C2×C4×C59—22no—
330C2×C4×C59—42no—
331C2×C4×C59—42no—
332C2×C4×C59—42no—
333C2×C4×C59—42no—
334C2×C4×C59C22×D412yes—
335C2×C4×C59C22×D411yescharacteristic
336C2×C4×C59C2×#4112yes—
337C2×C4×C59H(5,𝔽2)12yes—
338C2×C4×C59C2511yescharacteristic
339C22⋊D59—44no—
340C22⋊D59—84no—
341C2×Dic59—22no—
342C2×Dic59—22no—
343C2×Dic59—22no—
344C2×Dic59—22no—
345C2×Dic59—42no—
346C2×Dic59C22×D412yes—
347C2×Dic59C22×D412yes—
348C2×Dic59C22×D412yes—
349D236—24no—
350D236—22no—
351D236—22no—
352D236—22no—
353D236—22no—
354D236—22no—
355D236—48no—
356D236—48no—
357D236—48no—
358D236—42no—
359D236—42no—
360D236—84no—
361D236C2×#4114yes—
362C4×D59—24no—
363C4×D59—22no—
364C4×D59—22no—
365C4×D59—48no—
366C4×D59—84no—
367C4×D59—84no—
368C4×D59—84no—
369C8×C59—22no—
370C8×C59—22no—
371C59⋊C8—22no—
372C59⋊C8—22no—
373C2×#3322—591nomaximal, Sylow
374C22×C59—22no—
375C22×C59—22no—
376C22×C59—22no—
377C22×C59—44no—
378C22×C59#54612yes—
379C22×C59#57512yes—
380C22×C59#57612yes—
381C22×C59C23×D411yescharacteristic
382C2×D59—22no—
383C2×D59—24no—
384C2×D59—22no—
385C2×D59—22no—
386C2×D59—44no—
387C2×D59—48no—
388C2×D59—42no—
389C2×D59—42no—
390C2×D59—42no—
391C2×D59—42no—
392C2×D59—42no—
393C2×D59—42no—
394C2×D59—42no—
395C2×D59—42no—
396C2×D59—816no—
397C2×D59—84no—
398C2×D59—84no—
399C4×C59—22no—
400C4×C59—42no—
401C4×C59—42no—
402C4×C59—42no—
403C4×C59—42no—
404C4×C59#54612yes—
405C4×C59C22×#4111yescharacteristic
406C4×C59C2×H(5,𝔽2)11yescharacteristic
407Dic59—22no—
408Dic59—22no—
409Dic59—22no—
410Dic59—42no—
411C2×#553—591no—
412C2×#546—591no—
413#3322—5916no—
414C2×#488—591no—
415C2×#485D5911yescharacteristic, complemented
416C2×#480—591no—
417C2×#478—591no—
418C2×#469—591no—
419C2×#468—591no—
420C2×#463—591no—
421C2×#449—591no—
422C2×#447—591no—
423C2×C4×D8—591no—
424C2×#436—591no—
425C2×#417—591no—
426C2×#418—591no—
427C2×C59—42no—
428C2×C59#332214yescomplemented
429C2×C59C2×#54611yescharacteristic
430C2×C59C2×#57511yescharacteristic
431C2×C59C2×#57611yescharacteristic
432D59—42no—
433D59—44no—
434D59—82no—
435D59—82no—
436C22×#41—591no—
437C23×D4—591no—
438C22×SD16—591no—
439C22×D8—591no—
440C22×D8—591no—
441C22×M16—591no—
442C22×M16—591no—
443#553—598no—
444#553—1184no—
445#546—598no—
446#546—1184no—
447C2×#126—1181no—
448C2×#125—591no—
449C2×#124—591no—
450C2×#123—1181no—
451C2×#123—1181no—
452C2×C22⋊Q8C2×D5911yescharacteristic
453C2×#121—591no—
454C2×#121—591no—
455C2×#121—591no—
456C2×#121—1181no—
457C2×#121—1181no—
458C2×#120—1181no—
459C2×C4×D4—591no—
460C2×C4×D4—591no—
461C2×C4×D4—591no—
462C2×C4×D4—1181no—
463C2×#117C2×D5911yescharacteristic
464C22×C4⋊C4—591no—
465C22×C22⋊C4—1181no—
466#488—598no—
467#485C2×D5918yescomplemented
468#480—598no—
469#478—598no—
470#469—598no—
471#468—598no—
472#463—598no—
473#449—598no—
474#447—598no—
475C4×D8—598no—
476#436—598no—
477C2×#107—591no—
478C2×#107C2×D5911yescharacteristic, complemented
479C2×#106C2×D5911yescharacteristic, complemented
480C2×C4⋊C8—591no—
481#418—598no—
482#417—598no—
483C2×#103—591no—
484C2×#103C2×D5911yescharacteristic, complemented
485C2×#103C2×D5911yescharacteristic, complemented
486C2×#102—591no—
487C2×#102—591no—
488C2×#102—591no—
489C2×#102—591no—
490C2×#102—591no—
491C2×#102—591no—
492C2×#102—591no—
493C2×C22⋊C8—591no—
494C2×C22⋊C8C2×D5911yescharacteristic
495C2×C4×C8—591no—
496C59C2×#332211yescharacteristic, complemented, Sylow
497C25—1181no—
498C2×#41—594no—
499C2×#41—1182no—
500C2×#41—1184no—
501C2×#41—2362no—
502C22×Q8C22×D5911yescharacteristic
503C22×D4—591no—
504C22×D4—591no—
505C22×D4—591no—
506C22×D4—591no—
507C22×D4—594no—
508C22×D4—1184no—
509C22×D4—1181no—
510C22×D4—1181no—
511C22×D4—1181no—
512C22×D4—1181no—
513C22×D4—1181no—
514C22×D4—1182no—
515C22×D4—2362no—
516C23×C4—591no—
517C23×C4—1181no—
518C23×C4—1181no—
519C23×C4—1181no—
520C23×C4—1181no—
521C23×C4C22×D5911yescharacteristic
522C2×SD16—594no—
523C2×SD16—2362no—
524C2×D8—594no—
525C2×D8—594no—
526C2×D8—1184no—
527C2×D8—2362no—
528C2×M16—594no—
529C2×M16—594no—
530C2×M16—2362no—
531C2×M16—2362no—
532C22×C8—591no—
533C22×C8—591no—
534C22×C8C22×D5911yescharacteristic
535C22×C8C22×D5911yescharacteristic
536#126—1188no—
537#125—594no—
538#125—1182no—
539#124—594no—
540#124—1182no—
541#123—1188no—
542#123—1188no—
543C22⋊Q8—22no—
544C22⋊Q8C22×D5914yes—
545#121—594no—
546#121—594no—
547#121—594no—
548#121—1188no—
549#121—1188no—
550#121—1182no—
551#121—1182no—
552#121—1182no—
553#120—1188no—
554C4×D4—594no—
555C4×D4—594no—
556C4×D4—594no—
557C4×D4—594no—
558C4×D4—1188no—
559C4×D4—1182no—
560C4×D4—1182no—
561#117—22no—
562#117C22×D5914yes—
563C2×C4⋊C4—21no—
564C2×C4⋊C4—591no—
565C2×C4⋊C4—591no—
566C2×C4⋊C4—594no—
567C2×C4⋊C4—1182no—
568C2×C4⋊C4—1181no—
569C2×C4⋊C4—1181no—
570C2×C4⋊C4—1181no—
571C2×C4⋊C4C22×D5911yescharacteristic
572C2×C4⋊C4C22×D5911yescharacteristic
573C2×C4⋊C4C22×D5911yescharacteristic
574C2×C22⋊C4—21no—
575C2×C22⋊C4—21no—
576C2×C22⋊C4—591no—
577C2×C22⋊C4—591no—
578C2×C22⋊C4—1188no—
579C2×C22⋊C4—1181no—
580C2×C22⋊C4—1181no—
581C2×C22⋊C4—1181no—
582C2×C22⋊C4—1181no—
583C2×C22⋊C4—1181no—
584C2×C22⋊C4—1181no—
585C2×C22⋊C4—1181no—
586C2×C42—21no—
587C2×C42—591no—
588#107—594no—
589#107C22×D5914yescomplemented
590#106C22×D5914yescomplemented
591C4⋊C8—594no—
592#103—594no—
593#103C22×D5914yescomplemented
594#103C22×D5914yescomplemented
595#102—594no—
596#102—594no—
597#102—594no—
598#102—594no—
599#102—594no—
600#102—594no—
601#102—594no—
602C22⋊C8—594no—
603C22⋊C8C22×D5914yes—
604C4×C8—594no—
605C24—591no—
606C24—1181no—
607C24—1184no—
608C24—1181no—
609C24—1181no—
610C24—4722no—
611C24—2364no—
612C24—2364no—
613C24D4×D5911yescharacteristic
614#41—1188no—
615#41—2364no—
616#41—2368no—
617C2×Q8—21no—
618C2×Q8—22no—
619C2×Q8—22no—
620C2×Q8C23×D5912yes—
621C2×D4—594no—
622C2×D4—594no—
623C2×D4—592no—
624C2×D4—592no—
625C2×D4—592no—
626C2×D4—1188no—
627C2×D4—1184no—
628C2×D4—1184no—
629C2×D4—1184no—
630C2×D4—1184no—
631C2×D4—1181no—
632C2×D4—1181no—
633C2×D4—1184no—
634C2×D4—1181no—
635C2×D4—1182no—
636C2×D4—1182no—
637C2×D4—1182no—
638C2×D4—1182no—
639C2×D4—1182no—
640C2×D4—4722no—
641C2×D4—4722no—
642C2×D4—2364no—
643C2×D4—2368no—
644C2×D4—2364no—
645C2×D4—2364no—
646C2×D4—2364no—
647C2×D4—2362no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—591no—
655C22×C4—591no—
656C22×C4—591no—
657C22×C4—592no—
658C22×C4—592no—
659C22×C4—1184no—
660C22×C4—1184no—
661C22×C4—1184no—
662C22×C4—1184no—
663C22×C4—1182no—
664C22×C4—1182no—
665C22×C4—1181no—
666C22×C4—4722no—
667C22×C4—4722no—
668C22×C4—4722no—
669C22×C4—2364no—
670C22×C4D4×D5912yes—
671C22×C4D4×D5911yescharacteristic
672C22×C4C23×D5912yes—
673C22×C4C23×D5911yescharacteristic
674SD16—2364no—
675D8—1188no—
676D8—2364no—
677M16—2364no—
678M16—2364no—
679C2×C8—22no—
680C2×C8—22no—
681C2×C8—592no—
682C2×C8—592no—
683C2×C8—1182no—
684C2×C8—1182no—
685C2×C8C23×D5912yes—
686C2×C8C23×D5912yes—
687C4⋊C4—24no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—594no—
692C4⋊C4—592no—
693C4⋊C4—1184no—
694C4⋊C4—1184no—
695C4⋊C4—1184no—
696C4⋊C4—1181no—
697C4⋊C4C23×D5912yes—
698C4⋊C4C23×D5912yes—
699C4⋊C4C23×D5912yes—
700C22⋊C4—24no—
701C22⋊C4—24no—
702C22⋊C4—594no—
703C22⋊C4—594no—
704C22⋊C4—1184no—
705C22⋊C4—1184no—
706C22⋊C4—1184no—
707C22⋊C4—1184no—
708C22⋊C4—1184no—
709C22⋊C4—1184no—
710C22⋊C4—1184no—
711C42—24no—
712C42—592no—
713C42—592no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—592no—
718C23—1182no—
719C23—1182no—
720C23—1182no—
721C23—1182no—
722C23—1184no—
723C23—1182no—
724C23—1182no—
725C23—4724no—
726C23—47216no—
727C23—2368no—
728C23—2368no—
729C23—2362no—
730C23—2362no—
731C23—2362no—
732C23—2362no—
733C23—2362no—
734C23—2362no—
735C23—2362no—
736C23—2362no—
737C23C2×D4×D5912yes—
738C23C2×D4×D5911yescharacteristic
739Q8—22no—
740Q8—22no—
741Q8—42no—
742D4—594no—
743D4—1182no—
744D4—1182no—
745D4—1182no—
746D4—1182no—
747D4—1182no—
748D4—1184no—
749D4—4724no—
750D4—4724no—
751D4—2368no—
752D4—2368no—
753D4—2368no—
754D4—2364no—
755D4—2362no—
756D4—2362no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—24no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—592no—
770C2×C4—592no—
771C2×C4—592no—
772C2×C4—1182no—
773C2×C4—1182no—
774C2×C4—1182no—
775C2×C4—1182no—
776C2×C4—1182no—
777C2×C4—1184no—
778C2×C4—1182no—
779C2×C4—4724no—
780C2×C4—4724no—
781C2×C4—4724no—
782C2×C4—2368no—
783C2×C4—2362no—
784C2×C4C2×D4×D5912yes—
785C2×C4C2×D4×D5911yescharacteristic
786C2×C4#41×D5912yes—
787C2×C4#1427377312yes—
788C2×C4C24×D5911yescharacteristic
789C8—22no—
790C8—22no—
791C8—1182no—
792C8—1182no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—44no—
797C22—1182no—
798C22—1184no—
799C22—1182no—
800C22—1182no—
801C22—47216no—
802C22—4724no—
803C22—4724no—
804C22—2362no—
805C22—2362no—
806C22—2362no—
807C22—2362no—
808C22—2362no—
809C22—2362no—
810C22—2362no—
811C22—2362no—
812C22—2364no—
813C22—2368no—
814C22#1683804412yes—
815C22#1683820112yes—
816C22#1683820412yes—
817C22C22×D4×D5911yescharacteristic
818C4—22no—
819C4—42no—
820C4—42no—
821C4—42no—
822C4—42no—
823C4—1182no—
824C4—1182no—
825C4—1182no—
826C4—2362no—
827C4#1683804412yes—
828C4C2×#41×D5911yescharacteristic
829C4C2×#1427377311yescharacteristic
830C2—42no—
831C2—4722no—
832C2—4722no—
833C2—2362no—
834C2—2364no—
835C2#2143629514yesdirect product factor
836C2C2×#1683804411yescharacteristic
837C2C2×#1683820111yescharacteristic
838C2C2×#1683820411yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#485C2
socleC23×C59C22×D4
hypercenterC2×#485D59
hypocenterC59C2×#3322
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#485

Complements

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

NH ≅ G/Ntype
1. C2×#16838096C2semidirect
2. C2×#16838043C2semidirect
3. #21436295C2direct (N × H)
4. C2×#16837758C2semidirect
5. C2×#16837717C2semidirect
6. C2×#16837701C2semidirect
7. C2×#16837656C2semidirect
8. C2×#16837650C2semidirect
9. C2×#16837620C2semidirect
10. C2×#16837550C2semidirect
11. C2×#16837538C2semidirect
12. C2×#16837484C2semidirect
13. C2×#16837477C2semidirect
14. C2×#16837402C2semidirect
15. C2×#16837406C2semidirect
16. C2×C59×#485C2semidirect
19. C22×#11745671C22semidirect
23. C22×#11745659C22semidirect
25. #16838096C22semidirect
27. #16838043C22semidirect
29. C2×#14273718C22semidirect
35. C2×#14273702C22semidirect
41. C2×#14273689C22semidirect
43. C2×C4⋊C4×D59C22semidirect
45. #16837758C22semidirect
46. #16837717C22semidirect
47. #16837701C22semidirect
48. #16837656C22semidirect
49. #16837650C22semidirect
50. #16837620C22semidirect
51. #16837550C22semidirect
52. #16837538C22semidirect
53. #16837484C22semidirect
54. #16837477C22semidirect
55. C2×#14273660C22semidirect
56. C2×Dic59⋊C8C22semidirect
57. #16837406C22semidirect
58. #16837402C22semidirect
59. C2×#14273651C22semidirect
66. C2×#14273647C22semidirect
67. C2×(C2×D59)⋊C8C22semidirect
68. C2×C8×Dic59C22semidirect
71. C59×#485C22semidirect
72. C2×#107×C59C22semidirect
73. C2×#106×C59C22semidirect
74. C2×#103×C59C22semidirect
75. C2×#103×C59C22semidirect
101. C2×#11745671C23semidirect
109. C2×#11745659C23semidirect
114. #14273718C23semidirect
123. #14273702C23semidirect
132. #14273689C23semidirect
141. C4⋊C4×D59C23semidirect
153. #14273660C23semidirect
154. Dic59⋊C8C23semidirect
155. #14273651C23semidirect
162. #14273647C23semidirect
163. (C2×D59)⋊C8C23semidirect
164. C8×Dic59C23semidirect
180. #107×C59C23semidirect
181. #106×C59C23semidirect
182. #103×C59C23semidirect
183. #103×C59C23semidirect
415. C2×#485D59semidirect
428. C2×C59#3322semidirect
467. #485C2×D59semidirect
478. C2×#107C2×D59semidirect
479. C2×#106C2×D59semidirect
484. C2×#103C2×D59semidirect
485. C2×#103C2×D59semidirect
496. C59C2×#3322semidirect
589. #107C22×D59semidirect
590. #106C22×D59semidirect
593. #103C22×D59semidirect
594. #103C22×D59semidirect
835. C2#21436295direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168380962
C2×#168380432
#214362952
C2×#168377582
C2×#168377172
C2×#168377012
C2×#168376562
C2×#168376502
C2×#168376202
C2×#168375502
C2×#168375382
C2×#168374842
C2×#168374772
C2×#168374022
C2×#168374062
C2×C59×#4852
C2×#332259