Finite Group Databasebeta

← C2×#21435947 #29465057

Subgroups — C2×#21435947 #29465057

Order 15104.

2350 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×#16838040C211yesmaximal, characteristic, complemented
3#21435947C2116yesmaximal, direct product factor
4C2×#16837758C211yesmaximal, characteristic, complemented
5C2×#16837736C211yesmaximal, characteristic, complemented
6C2×#16837726C211yesmaximal, characteristic, complemented
7C2×#16837700C211yesmaximal, characteristic, complemented
8C2×#16837638C211yesmaximal, characteristic, complemented
9C2×#16837634C211yesmaximal, characteristic, complemented
10C2×#16837620C211yesmaximal, characteristic, complemented
11C2×#16837547C211yesmaximal, characteristic, complemented
12C2×#16837537C211yesmaximal, characteristic, complemented
13C2×#16837482C211yesmaximal, characteristic, complemented
14C2×C8×C22⋊D59C211yesmaximal, characteristic, complemented
15C2×#102×D59C211yesmaximal, characteristic, complemented
16C2×C59×#416C211yesmaximal, characteristic, complemented
17C22×D4×D59C2211yescharacteristic
18C22×#11745671C2211yescharacteristic, complemented
19C22×D472C2211yescharacteristic
20C22×#11745669C2211yescharacteristic
21C22×C8×D59C2211yescharacteristic
22#16838096—24no—
23#16838096C2218yescomplemented
24#16838040—24no—
25#16838040C2218yescomplemented
26C2×#14273721—21no—
27C2×#14273718C2211yescharacteristic, complemented
28C2×#14273716C2211yescharacteristic
29C2×#14273710—21no—
30C2×#14273709—21no—
31C2×#14273703C2211yescharacteristic
32C2×#14273702C2211yescharacteristic
33C2×#14273701C2211yescharacteristic
34C2×#14273701C2211yescharacteristic, complemented
35C2×#14273700—21no—
36C2×#14273699—21no—
37C2×#14273695—21no—
38C2×C4×D236—21no—
39C2×D4×Dic59C2211yescharacteristic
40C2×#14273689C2211yescharacteristic, complemented
41C2×C4×C22⋊D59C2211yescharacteristic
42C2×C4⋊C4×D59C2211yescharacteristic
43C22×(C2×D59)⋊C4—21no—
44#16837758C2218yescomplemented
45#16837736C2218yescomplemented
46#16837726C2218yescomplemented
47#16837700C2218yescomplemented
48#16837638C2218yescomplemented
49#16837634C2218yescomplemented
50#16837620C2218yescomplemented
51#16837547C2218yescomplemented
52#16837537C2218yescomplemented
53#16837482C2218yescomplemented
54C8×C22⋊D59C2218yescomplemented
55C2×#14273661C2211yescharacteristic, complemented
56C2×#14273660C2211yescharacteristic, complemented
57C2×#14273658C2211yescharacteristic, complemented
58C2×Dic59⋊C8C2211yescharacteristic, complemented
59C2×#14273651C2211yescharacteristic, complemented
60C2×#14273649C2211yescharacteristic
61C2×#14273649C2211yescharacteristic, complemented
62C2×#14273648C2211yescharacteristic
63C2×#14273647C2211yescharacteristic
64C2×#14273647C2211yescharacteristic
65#102×D59C2218yescomplemented
66C2×C22⋊(C59⋊C8)C2211yescharacteristic, complemented
67C2×(C2×D59)⋊C8C2211yescharacteristic
68C2×C8×Dic59C2211yescharacteristic, complemented
69C22×#41×C59C2211yescharacteristic
70C23×C8×C59C2211yescharacteristic, complemented
71C2×#117×C59C2211yescharacteristic, complemented
72C59×#416C2218yescomplemented
73C2×#103×C59C2211yescharacteristic, complemented
74C2×#103×C59C2211yescharacteristic, complemented
75C2×#102×C59C2211yescharacteristic
76C2×#102×C59C2211yescharacteristic
77C24×D59—21no—
78C22×D236—21no—
79C22×D236C2311yescharacteristic
80C22×D236C2311yescharacteristic
81C22×C22⋊D59—21no—
82C22×C22⋊D59—21no—
83C22×C22⋊D59—21no—
84C22×C22⋊D59D411yescharacteristic
85C2×D4×D59—24no—
86C2×D4×D59—22no—
87C2×D4×D59—42no—
88C2×D4×D59C2314yes—
89C23×Dic59—21no—
90C22×C4×D59—21no—
91C22×C4×D59—21no—
92C22×C4×D59C2311yescharacteristic
93C2×#11745671—42no—
94C2×#11745671C2314yescomplemented
95C2×D472—42no—
96C2×D472C2314yes—
97C2×#11745669—24no—
98C2×#11745669C2314yes—
99C22×C59⋊C8C2311yescharacteristic
100C22×C59⋊C8C2311yescharacteristic
101C2×C8×D59—42no—
102C2×C8×D59C2314yes—
103#14273721—28no—
104#14273718—22no—
105#14273718C2314yescomplemented
106#14273716—22no—
107#14273716C2314yes—
108#14273710—28no—
109#14273709—28no—
110#14273703—22no—
111#14273703C2314yes—
112#14273702—22no—
113#14273702C2314yes—
114#14273701—22no—
115#14273701—22no—
116#14273701C2314yes—
117#14273701C2314yescomplemented
118#14273700—28no—
119#14273699—28no—
120#14273695—28no—
121C4×D236—28no—
122D4×Dic59—22no—
123D4×Dic59C2314yes—
124#14273689—22no—
125#14273689C2314yescomplemented
126C4×C22⋊D59D414yes—
127C4×C22⋊D59C2314yes—
128C2×C4⋊Dic59—21no—
129C2×C4⋊Dic59C2311yescharacteristic
130C2×C4⋊Dic59C2311yescharacteristic
131C2×Dic59⋊C4—21no—
132C2×Dic59⋊C4—21no—
133C2×Dic59⋊C4—21no—
134C2×Dic59⋊C4D411yescharacteristic
135C4⋊C4×D59—22no—
136C4⋊C4×D59C2314yes—
137C2×C22⋊Dic59—21no—
138C2×C22⋊Dic59D411yescharacteristic
139C2×(C2×D59)⋊C4—21no—
140C2×(C2×D59)⋊C4—21no—
141C2×(C2×D59)⋊C4—21no—
142C2×(C2×D59)⋊C4—21no—
143C2×(C2×D59)⋊C4—21no—
144C2×(C2×D59)⋊C4—21no—
145C2×(C2×D59)⋊C4—21no—
146C2×(C2×D59)⋊C4—28no—
147C2×(C2×D59)⋊C4D411yescharacteristic
148C2×C4×Dic59C2311yescharacteristic
149#14273661C2314yescomplemented
150#14273660C2314yescomplemented
151#14273658C2314yescomplemented
152Dic59⋊C8C2314yescomplemented
153#14273651C2314yescomplemented
154#14273649C2314yes—
155#14273649C2314yescomplemented
156#14273648C2314yes—
157#14273647C2314yes—
158#14273647C2314yes—
159C22⋊(C59⋊C8)C2314yescomplemented
160(C2×D59)⋊C8C2314yes—
161C8×Dic59C2314yescomplemented
162C2×#41×C59—22no—
163C2×#41×C59—24no—
164C2×#41×C59—42no—
165C2×#41×C59C2314yes—
166C22×Q8×C59C2311yescharacteristic
167C22×D4×C59—21no—
168C22×D4×C59C2311yescharacteristic
169C23×C4×C59—21no—
170C23×C4×C59C2311yescharacteristic
171C22×C8×C59—42no—
172C22×C8×C59C2311yescharacteristic
173C22×C8×C59C2311yescharacteristic
174C22×C8×C59C2314yescomplemented
175#117×C59—22no—
176#117×C59C2314yescomplemented
177C2×C4⋊C4×C59C2311yescharacteristic
178C2×C4⋊C4×C59C2311yescharacteristic
179C2×C22⋊C4×C59—21no—
180C2×C42×C59—21no—
181#103×C59C2314yescomplemented
182#103×C59C2314yescomplemented
183#102×C59C2314yes—
184#102×C59C2314yes—
185C24×C59—21no—
186C24×C59C2×D411yescharacteristic
187C23×D59—21no—
188C23×D59—21no—
189C23×D59—24no—
190C23×D59—44no—
191C23×D59—44no—
192C23×D59—82no—
193C23×D59C2×D411yescharacteristic
194#41×C59—28no—
195#41×C59—44no—
196#41×C59—48no—
197C2×Q8×C59—21no—
198C2×Q8×C59—22no—
199C2×Q8×C59—22no—
200C2×Q8×C59C2412yes—
201C2×D4×C59—24no—
202C2×D4×C59—21no—
203C2×D4×C59—22no—
204C2×D4×C59—44no—
205C2×D4×C59#4114yes—
206C2×D4×C59C2412yes—
207C22×C4×C59—22no—
208C22×C4×C59—22no—
209C22×C4×C59—21no—
210C22×C4×C59—21no—
211C22×C4×C59—21no—
212C22×C4×C59—24no—
213C22×C4×C59—44no—
214C22×C4×C59C2×D411yescharacteristic
215C22×C4×C59C2×D412yes—
216C22×C4×C59C2412yes—
217C22×C4×C59C2411yescharacteristic
218C2×C22⋊D59—24no—
219C2×C22⋊D59—24no—
220C2×C22⋊D59—24no—
221C2×C22⋊D59—24no—
222C2×C22⋊D59—44no—
223C2×C22⋊D59—82no—
224C2×C22⋊D59—82no—
225C2×C22⋊D59C2×D414yes—
226C22×Dic59—21no—
227C22×Dic59—21no—
228C22×Dic59—24no—
229C22×Dic59—82no—
230C22×Dic59C2×D411yescharacteristic
231C22×Dic59C2×D411yescharacteristic
232C22×Dic59C2×D411yescharacteristic
233D4×D59—28no—
234D4×D59—44no—
235D4×D59—48no—
236C2×D236—22no—
237C2×D236—22no—
238C2×D236—22no—
239C2×D236—22no—
240C2×D236—24no—
241C2×D236—21no—
242C2×D236—21no—
243C2×D236—44no—
244C2×D236C2412yes—
245C2×D236C2412yes—
246C2×C4×D59—22no—
247C2×C4×D59—22no—
248C2×C4×D59—24no—
249C2×C4×D59—24no—
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×C59—44no—
257C2×C8×C59C2412yes—
258C2×C8×C59C2412yes—
259C4⋊C4×C59—21no—
260C4⋊C4×C59—21no—
261C4⋊C4×C59C2412yes—
262C4⋊C4×C59C2412yes—
263C22⋊C4×C59—24no—
264C42×C59—24no—
265C22⋊Dic59—24no—
266C22⋊Dic59C2×D414yes—
267#11745671—44no—
268#11745669—28no—
269(C2×D59)⋊C4—24no—
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)⋊C4C2×D414yes—
277C4⋊Dic59—21no—
278C4⋊Dic59—21no—
279C4⋊Dic59—24no—
280C4⋊Dic59C2412yes—
281C4⋊Dic59C2412yes—
282Dic59⋊C4—24no—
283Dic59⋊C4—24no—
284Dic59⋊C4—24no—
285Dic59⋊C4C2×D414yes—
286C4×Dic59C2×D412yes—
287C4×Dic59C2412yes—
288C2×C59⋊C8—22no—
289C2×C59⋊C8—22no—
290C2×C59⋊C8C2412yes—
291C2×C59⋊C8C2412yes—
292D472—44no—
293C8×D59—44no—
294C23×C59—24no—
295C23×C59—22no—
296C23×C59—22no—
297C23×C59—22no—
298C23×C59—22no—
299C23×C59—42no—
300C23×C59—42no—
301C23×C59C22×D412yes—
302C23×C59C22×D411yescharacteristic
303C22×D59—22no—
304C22×D59—22no—
305C22×D59—22no—
306C22×D59—22no—
307C22×D59—48no—
308C22×D59—42no—
309C22×D59—42no—
310C22×D59—42no—
311C22×D59—42no—
312C22×D59—42no—
313C22×D59—42no—
314C22×D59—48no—
315C22×D59—84no—
316C22×D59—816no—
317C22×D59#13514yes—
318C22×D59C22×D412yes—
319Q8×C59—22no—
320Q8×C59—22no—
321Q8×C59—42no—
322D4×C59—24no—
323D4×C59—22no—
324D4×C59—48no—
325D4×C59C2×#4114yes—
326C2×C4×C59—22no—
327C2×C4×C59—24no—
328C2×C4×C59—22no—
329C2×C4×C59—22no—
330C2×C4×C59—22no—
331C2×C4×C59—22no—
332C2×C4×C59—22no—
333C2×C4×C59—48no—
334C2×C4×C59—42no—
335C2×C4×C59—42no—
336C2×C4×C59—42no—
337C2×C4×C59C22×D412yes—
338C2×C4×C59C22×D411yescharacteristic
339C2×C4×C59C2×#4112yes—
340C2×C4×C59H(5,𝔽2)12yes—
341C2×C4×C59C2511yescharacteristic
342C22⋊D59—28no—
343C22⋊D59—48no—
344C22⋊D59—84no—
345C22⋊D59—84no—
346C2×Dic59—22no—
347C2×Dic59—22no—
348C2×Dic59—22no—
349C2×Dic59—22no—
350C2×Dic59—22no—
351C2×Dic59—42no—
352C2×Dic59—42no—
353C2×Dic59—84no—
354C2×Dic59C22×D412yes—
355C2×Dic59C22×D412yes—
356C2×Dic59C22×D412yes—
357D236—22no—
358D236—22no—
359D236—22no—
360D236—22no—
361D236—48no—
362D236—42no—
363D236—42no—
364C4×D59—24no—
365C4×D59—22no—
366C4×D59—22no—
367C4×D59—84no—
368C4×D59—84no—
369C8×C59—22no—
370C8×C59—22no—
371C59⋊C8—22no—
372C59⋊C8—22no—
373C2×#3297—591nomaximal, Sylow
374C22×C59—24no—
375C22×C59—22no—
376C22×C59—22no—
377C22×C59—22no—
378C22×C59—48no—
379C22×C59—44no—
380C22×C59—42no—
381C22×C59—42no—
382C22×C59#54612yes—
383C22×C59C2×#13512yes—
384C22×C59#57612yes—
385C22×C59C23×D411yescharacteristic
386C2×D59—22no—
387C2×D59—28no—
388C2×D59—22no—
389C2×D59—42no—
390C2×D59—42no—
391C2×D59—42no—
392C2×D59—42no—
393C2×D59—42no—
394C2×D59—42no—
395C2×D59—816no—
396C2×D59—84no—
397C2×D59—84no—
398C2×D59C2×#13514yes—
399C4×C59—22no—
400C4×C59—42no—
401C4×C59—42no—
402C4×C59—42no—
403C4×C59#54612yes—
404C4×C59C22×#4111yescharacteristic
405C4×C59C2×H(5,𝔽2)11yescharacteristic
406Dic59—22no—
407Dic59—22no—
408Dic59—22no—
409Dic59—42no—
410Dic59—42no—
411C2×#553—591no—
412C2×#546—591no—
413#3297—5916no—
414C2×#488—591no—
415C2×#484—591no—
416C2×#482—591no—
417C2×#478—591no—
418C2×#466—591no—
419C2×#465—591no—
420C2×#463—591no—
421C2×#449—591no—
422C2×#447—591no—
423C2×C4×D8—591no—
424C2×C8×D4—591no—
425C2×#416D5911yescharacteristic, complemented
426C22×#102—591no—
427C2×C59—44no—
428C2×C59—42no—
429C2×C59#329714yescomplemented
430C2×C59C2×#54611yescharacteristic
431C2×C59C22×#13511yescharacteristic
432C2×C59C2×#57611yescharacteristic
433D59—24no—
434D59—82no—
435D59—82no—
436C22×#41C2×D5911yescharacteristic
437C23×D4—591no—
438C22×SD16—591no—
439C22×D8—591no—
440C22×D8—591no—
441C23×C8—591no—
442C23×C8C2×D5911yescharacteristic, complemented
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⋊Q8—591no—
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, complemented
464C22×C4⋊C4—591no—
465C22×C22⋊C4—1181no—
466#488—598no—
467#484—598no—
468#482—598no—
469#478—598no—
470#466—598no—
471#465—598no—
472#463—598no—
473#449—598no—
474#447—598no—
475C4×D8—598no—
476C8×D4—598no—
477C2×#107—591no—
478C2×#107—591no—
479C2×#106—591no—
480C2×C4⋊C8—591no—
481#416C2×D5918yescomplemented
482C2×#103—591no—
483C2×#103C2×D5911yescharacteristic, complemented
484C2×#103C2×D5911yescharacteristic, complemented
485C2×#102—591no—
486C2×#102—591no—
487C2×#102—591no—
488C2×#102—591no—
489C2×#102—591no—
490C2×#102—598no—
491C2×#102C2×D5911yescharacteristic
492C2×#102C2×D5911yescharacteristic
493C2×C22⋊C8—591no—
494C2×C22⋊C8—591no—
495C2×C4×C8—591no—
496C59C2×#329711yescharacteristic, complemented, Sylow
497C25—1181no—
498C2×#41—22no—
499C2×#41—24no—
500C2×#41—42no—
501C2×#41C22×D5914yes—
502C22×Q8C22×D5911yescharacteristic
503C22×D4—21no—
504C22×D4—591no—
505C22×D4—594no—
506C22×D4—591no—
507C22×D4—591no—
508C22×D4—1181no—
509C22×D4—1182no—
510C22×D4—1181no—
511C22×D4—1184no—
512C22×D4—1181no—
513C22×D4—1181no—
514C22×D4—2362no—
515C22×D4C22×D5911yescharacteristic
516C23×C4—21no—
517C23×C4—591no—
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—
528C22×C8—42no—
529C22×C8—591no—
530C22×C8—591no—
531C22×C8—594no—
532C22×C8—2362no—
533C22×C8C22×D5911yescharacteristic
534C22×C8C22×D5911yescharacteristic
535C22×C8C22×D5914yescomplemented
536#126—1188no—
537#125—594no—
538#125—1182no—
539#124—594no—
540#124—1182no—
541#123—1188no—
542#123—1188no—
543C22⋊Q8—594no—
544C22⋊Q8—1182no—
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×D5914yescomplemented
563C2×C4⋊C4—591no—
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⋊C4—1181no—
572C2×C4⋊C4C22×D5911yescharacteristic
573C2×C4⋊C4C22×D5911yescharacteristic
574C2×C22⋊C4—21no—
575C2×C22⋊C4—591no—
576C2×C22⋊C4—591no—
577C2×C22⋊C4—1188no—
578C2×C22⋊C4—1181no—
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#107—594no—
590#106—594no—
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#102C22×D5914yes—
601#102C22×D5914yes—
602C22⋊C8—594no—
603C22⋊C8—594no—
604C4×C8—594no—
605C24—21no—
606C24—591no—
607C24—1184no—
608C24—1181no—
609C24—1181no—
610C24—4722no—
611C24—2364no—
612C24—2364no—
613C24D4×D5911yescharacteristic
614#41—28no—
615#41—44no—
616#41—48no—
617C2×Q8—21no—
618C2×Q8—22no—
619C2×Q8—22no—
620C2×Q8C23×D5912yes—
621C2×D4—24no—
622C2×D4—21no—
623C2×D4—22no—
624C2×D4—44no—
625C2×D4—594no—
626C2×D4—592no—
627C2×D4—592no—
628C2×D4—1184no—
629C2×D4—1184no—
630C2×D4—1184no—
631C2×D4—1188no—
632C2×D4—1184no—
633C2×D4—1184no—
634C2×D4—1181no—
635C2×D4—1181no—
636C2×D4—1182no—
637C2×D4—1182no—
638C2×D4—1182no—
639C2×D4—1182no—
640C2×D4—4722no—
641C2×D4—4722no—
642C2×D4—2364no—
643C2×D4—2364no—
644C2×D4—2368no—
645C2×D4—2364no—
646C2×D4#1174568514yes—
647C2×D4C23×D5912yes—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—24no—
654C22×C4—44no—
655C22×C4—591no—
656C22×C4—591no—
657C22×C4—591no—
658C22×C4—592no—
659C22×C4—592no—
660C22×C4—1184no—
661C22×C4—1184no—
662C22×C4—1184no—
663C22×C4—1182no—
664C22×C4—1182no—
665C22×C4—1181no—
666C22×C4—1181no—
667C22×C4—4722no—
668C22×C4—4722no—
669C22×C4—4722no—
670C22×C4D4×D5912yes—
671C22×C4D4×D5911yescharacteristic
672C22×C4C23×D5912yes—
673C22×C4C23×D5911yescharacteristic
674SD16—2364no—
675D8—1188no—
676D8—2364no—
677C2×C8—22no—
678C2×C8—22no—
679C2×C8—44no—
680C2×C8—592no—
681C2×C8—592no—
682C2×C8—1182no—
683C2×C8—1182no—
684C2×C8—2364no—
685C2×C8C23×D5912yes—
686C2×C8C23×D5912yes—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—594no—
690C4⋊C4—592no—
691C4⋊C4—592no—
692C4⋊C4—1184no—
693C4⋊C4—1184no—
694C4⋊C4—1184no—
695C4⋊C4—1184no—
696C4⋊C4—1181no—
697C4⋊C4—1181no—
698C4⋊C4C23×D5912yes—
699C4⋊C4C23×D5912yes—
700C22⋊C4—24no—
701C22⋊C4—594no—
702C22⋊C4—594no—
703C22⋊C4—1184no—
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—22no—
718C23—24no—
719C23—42no—
720C23—42no—
721C23—594no—
722C23—592no—
723C23—1182no—
724C23—1182no—
725C23—1182no—
726C23—1182no—
727C23—47216no—
728C23—4724no—
729C23—2368no—
730C23—2368no—
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—22no—
743D4—24no—
744D4—48no—
745D4—1188no—
746D4—1182no—
747D4—1182no—
748D4—1182no—
749D4—1182no—
750D4—4724no—
751D4—4724no—
752D4—2368no—
753D4—2368no—
754D4—2362no—
755D4—2362no—
756D4C2×#1174568514yes—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—24no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—48no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—592no—
769C2×C4—592no—
770C2×C4—592no—
771C2×C4—1182no—
772C2×C4—1182no—
773C2×C4—1182no—
774C2×C4—1182no—
775C2×C4—1182no—
776C2×C4—1184no—
777C2×C4—1182no—
778C2×C4—1182no—
779C2×C4—4724no—
780C2×C4—4724no—
781C2×C4—4724no—
782C2×C4—2362no—
783C2×C4—2362no—
784C2×C4C2×D4×D5912yes—
785C2×C4C2×D4×D5911yescharacteristic
786C2×C4C2×#1174568512yes—
787C2×C4#1427377212yes—
788C2×C4C24×D5911yescharacteristic
789C8—22no—
790C8—22no—
791C8—1182no—
792C8—1182no—
793C22—22no—
794C22—22no—
795C22—24no—
796C22—22no—
797C22—44no—
798C22—48no—
799C22—42no—
800C22—42no—
801C22—594no—
802C22—1188no—
803C22—1182no—
804C22—1182no—
805C22—47216no—
806C22—4724no—
807C22—4724no—
808C22—2362no—
809C22—2362no—
810C22—2362no—
811C22—2362no—
812C22—2362no—
813C22—2362no—
814C22#1683804212yes—
815C22#135×D5912yes—
816C22#1683820412yes—
817C22C22×D4×D5911yescharacteristic
818C4—22no—
819C4—42no—
820C4—42no—
821C4—42no—
822C4—1182no—
823C4—1182no—
824C4—1182no—
825C4—2362no—
826C4—2362no—
827C4#1683804212yes—
828C4C22×#1174568511yescharacteristic
829C4C2×#1427377211yescharacteristic
830C2—42no—
831C2—44no—
832C2—1184no—
833C2—4722no—
834C2—4722no—
835C2#2143594714yesdirect product factor
836C2C2×#1683804211yescharacteristic
837C2C2×#135×D5911yescharacteristic
838C2C2×#1683820411yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#416C2
socleC23×C59C22×D4
hypercenterC2×#416D59
hypocenterC59C2×#3297
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#416

Complements

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

NH ≅ G/Ntype
1. C2×#16838096C2semidirect
2. C2×#16838040C2semidirect
3. #21435947C2direct (N × H)
4. C2×#16837758C2semidirect
5. C2×#16837736C2semidirect
6. C2×#16837726C2semidirect
7. C2×#16837700C2semidirect
8. C2×#16837638C2semidirect
9. C2×#16837634C2semidirect
10. C2×#16837620C2semidirect
11. C2×#16837547C2semidirect
12. C2×#16837537C2semidirect
13. C2×#16837482C2semidirect
14. C2×C8×C22⋊D59C2semidirect
15. C2×#102×D59C2semidirect
16. C2×C59×#416C2semidirect
18. C22×#11745671C22semidirect
23. #16838096C22semidirect
25. #16838040C22semidirect
27. C2×#14273718C22semidirect
34. C2×#14273701C22semidirect
40. C2×#14273689C22semidirect
44. #16837758C22semidirect
45. #16837736C22semidirect
46. #16837726C22semidirect
47. #16837700C22semidirect
48. #16837638C22semidirect
49. #16837634C22semidirect
50. #16837620C22semidirect
51. #16837547C22semidirect
52. #16837537C22semidirect
53. #16837482C22semidirect
54. C8×C22⋊D59C22semidirect
55. C2×#14273661C22semidirect
56. C2×#14273660C22semidirect
57. C2×#14273658C22semidirect
58. C2×Dic59⋊C8C22semidirect
59. C2×#14273651C22semidirect
61. C2×#14273649C22semidirect
65. #102×D59C22semidirect
66. C2×C22⋊(C59⋊C8)C22semidirect
68. C2×C8×Dic59C22semidirect
70. C23×C8×C59C22semidirect
71. C2×#117×C59C22semidirect
72. C59×#416C22semidirect
73. C2×#103×C59C22semidirect
74. C2×#103×C59C22semidirect
94. C2×#11745671C23semidirect
105. #14273718C23semidirect
117. #14273701C23semidirect
125. #14273689C23semidirect
149. #14273661C23semidirect
150. #14273660C23semidirect
151. #14273658C23semidirect
152. Dic59⋊C8C23semidirect
153. #14273651C23semidirect
155. #14273649C23semidirect
159. C22⋊(C59⋊C8)C23semidirect
161. C8×Dic59C23semidirect
174. C22×C8×C59C23semidirect
176. #117×C59C23semidirect
181. #103×C59C23semidirect
182. #103×C59C23semidirect
425. C2×#416D59semidirect
429. C2×C59#3297semidirect
442. C23×C8C2×D59semidirect
463. C2×#117C2×D59semidirect
481. #416C2×D59semidirect
483. C2×#103C2×D59semidirect
484. C2×#103C2×D59semidirect
496. C59C2×#3297semidirect
535. C22×C8C22×D59semidirect
562. #117C22×D59semidirect
593. #103C22×D59semidirect
594. #103C22×D59semidirect
835. C2#21435947direct (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×#168380402
#214359472
C2×#168377582
C2×#168377362
C2×#168377262
C2×#168377002
C2×#168376382
C2×#168376342
C2×#168376202
C2×#168375472
C2×#168375372
C2×#168374822
C2×C8×C22⋊D592
C2×#102×D592
C2×C59×#4162
C2×#329759