Finite Group Databasebeta

← C2×#21436257 #29465380

Subgroups — C2×#21436257 #29465380

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×#16838117C211yesmaximal, characteristic, complemented
2C2×#16838047C211yesmaximal, characteristic, complemented
3#21436257C2116yesmaximal, direct product factor
4C2×#16837762C211yesmaximal, characteristic, complemented
5C2×#16837746C211yesmaximal, characteristic, complemented
6C2×#16837728C211yesmaximal, characteristic, complemented
7C2×#16837682C211yesmaximal, characteristic, complemented
8C2×#16837647C211yesmaximal, characteristic, complemented
9C2×#16837637C211yesmaximal, characteristic, complemented
10C2×#16837617C211yesmaximal, characteristic, complemented
11C2×#16837544C211yesmaximal, characteristic, complemented
12C2×#16837534C211yesmaximal, characteristic, complemented
13C2×#16837475C211yesmaximal, characteristic, complemented
14C2×#16837405C211yesmaximal, characteristic, complemented
15C2×#16837395C211yesmaximal, characteristic, complemented
16C2×C59×#442C211yesmaximal, characteristic, complemented
17C22×#11745687C2211yescharacteristic
18C22×D4×D59C2211yescharacteristic
19C22×#11745670C2211yescharacteristic, complemented
20C22×#11745669C2211yescharacteristic
21C22×#11745659C2211yescharacteristic
22C22×C8×D59C2211yescharacteristic, complemented
23#16838117—24no—
24#16838117C2218yescomplemented
25#16838047—24no—
26#16838047C2218yescomplemented
27C2×#14273727C2211yescharacteristic, complemented
28C2×#14273715C2211yescharacteristic
29C2×#14273713—21no—
30C2×#14273713—21no—
31C2×#14273711—21no—
32C2×#14273707C2211yescharacteristic
33C2×#14273702C2211yescharacteristic
34C2×#14273701—21no—
35C2×#14273701—21no—
36C2×#14273698C2211yescharacteristic
37C2×#14273698C2211yescharacteristic, complemented
38C2×#14273697—21no—
39C2×C4×D236C2211yescharacteristic
40C2×#14273686—21no—
41C2×#14273685C2211yescharacteristic
42C2×#14273685C2211yescharacteristic, complemented
43C22×(C2×D59)⋊C4—21no—
44#16837762C2218yescomplemented
45#16837746C2218yescomplemented
46#16837728C2218yescomplemented
47#16837682C2218yescomplemented
48#16837647C2218yescomplemented
49#16837637C2218yescomplemented
50#16837617C2218yescomplemented
51#16837544C2218yescomplemented
52#16837534C2218yescomplemented
53#16837475C2218yescomplemented
54C2×#14273660C2211yescharacteristic, complemented
55C2×#14273660C2211yescharacteristic, complemented
56C2×C4⋊(C59⋊C8)C2211yescharacteristic, complemented
57#16837405C2218yescomplemented
58#16837395C2218yescomplemented
59C2×#14273652C2211yescharacteristic, complemented
60C2×#14273652C2211yescharacteristic, complemented
61C2×#14273650C2211yescharacteristic, complemented
62C2×#14273649C2211yescharacteristic
63C2×#14273649C2211yescharacteristic
64C2×#14273648C2211yescharacteristic
65C2×#14273648C2211yescharacteristic
66C2×#14273647C2211yescharacteristic
67C2×(C2×D59)⋊C8C2211yescharacteristic
68C2×(C2×D59)⋊C8C2211yescharacteristic, complemented
69C22×D8×C59C2211yescharacteristic
70C2×C4×D4×C59C2211yescharacteristic
71C2×C4×D4×C59C2211yescharacteristic, complemented
72C59×#442C2218yescomplemented
73C2×#106×C59C2211yescharacteristic, complemented
74C2×#102×C59C2211yescharacteristic
75C2×#102×C59C2211yescharacteristic, complemented
76C2×#97×C59C2211yescharacteristic, complemented
77C24×D59—21no—
78C2×#11745687—24no—
79C2×#11745687—22no—
80C2×#11745687—42no—
81C2×#11745687C2314yes—
82C22×Dic118—21no—
83C22×Dic118C2311yescharacteristic
84C22×D236—21no—
85C22×D236D411yescharacteristic
86C22×D236C2311yescharacteristic
87C22×C22⋊D59—21no—
88C22×C22⋊D59—21no—
89C22×C22⋊D59—21no—
90C22×C22⋊D59—21no—
91C2×D4×D59—24no—
92C2×D4×D59—22no—
93C2×D4×D59—42no—
94C2×D4×D59C2314yes—
95C23×Dic59—21no—
96C22×C4×D59C2311yescharacteristic
97C22×C4×D59C2311yescharacteristic
98C2×#11745670—42no—
99C2×#11745670C2314yescomplemented
100C2×#11745669—42no—
101C2×#11745669C2314yes—
102C2×#11745659—42no—
103C2×#11745659C2314yes—
104C22×C59⋊C8C2311yescharacteristic
105C22×C59⋊C8C2311yescharacteristic
106C2×C8×D59—42no—
107C2×C8×D59C2314yescomplemented
108#14273727—22no—
109#14273727C2314yescomplemented
110#14273715—22no—
111#14273715C2314yes—
112#14273713—28no—
113#14273713—28no—
114#14273711—28no—
115#14273707—22no—
116#14273707C2314yes—
117#14273702—22no—
118#14273702C2314yes—
119#14273701—28no—
120#14273701—28no—
121#14273698—22no—
122#14273698—22no—
123#14273698C2314yes—
124#14273698C2314yescomplemented
125#14273697—28no—
126C4×D236D414yes—
127C4×D236C2314yes—
128#14273686—28no—
129#14273685—22no—
130#14273685—22no—
131#14273685C2314yes—
132#14273685C2314yescomplemented
133C2×C4⋊Dic59—21no—
134C2×C4⋊Dic59—21no—
135C2×C4⋊Dic59D411yescharacteristic
136C2×C4⋊Dic59C2311yescharacteristic
137C2×C4⋊Dic59C2311yescharacteristic
138C2×C22⋊Dic59—21no—
139C2×C22⋊Dic59—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×(C2×D59)⋊C4D411yescharacteristic
149C2×C4×Dic59—21no—
150C2×C4×Dic59—21no—
151#14273660C2314yescomplemented
152#14273660C2314yescomplemented
153C4⋊(C59⋊C8)C2314yescomplemented
154#14273652C2314yescomplemented
155#14273652C2314yescomplemented
156#14273650C2314yescomplemented
157#14273649C2314yes—
158#14273649C2314yes—
159#14273648C2314yes—
160#14273648C2314yes—
161#14273647C2314yes—
162(C2×D59)⋊C8C2314yes—
163(C2×D59)⋊C8C2314yescomplemented
164C22×D4×C59C2311yescharacteristic
165C22×D4×C59C2311yescharacteristic
166C23×C4×C59—21no—
167C23×C4×C59—21no—
168C2×D8×C59—24no—
169C2×D8×C59C2314yes—
170C22×C8×C59C2311yescharacteristic
171C22×C8×C59C2311yescharacteristic
172C4×D4×C59—22no—
173C4×D4×C59—22no—
174C4×D4×C59C2314yes—
175C4×D4×C59C2314yescomplemented
176C2×C4⋊C4×C59C2311yescharacteristic
177C2×C4⋊C4×C59C2311yescharacteristic
178C2×C22⋊C4×C59—21no—
179C2×C22⋊C4×C59—21no—
180C2×C42×C59C2311yescharacteristic
181#106×C59C2314yescomplemented
182#102×C59C2314yes—
183#102×C59C2314yescomplemented
184#97×C59C2314yescomplemented
185C24×C59—21no—
186C24×C59—21no—
187C23×D59—21no—
188C23×D59—24no—
189C23×D59—44no—
190C23×D59—44no—
191C23×D59—82no—
192C23×D59C2×D411yescharacteristic
193C23×D59C2×D411yescharacteristic
194C2×D4×C59—21no—
195C2×D4×C59—21no—
196C2×D4×C59—22no—
197C2×D4×C59—22no—
198C2×D4×C59—22no—
199C2×D4×C59#4114yes—
200C2×D4×C59C2412yes—
201C2×D4×C59C2412yes—
202C22×C4×C59—21no—
203C22×C4×C59—21no—
204C22×C4×C59—24no—
205C22×C4×C59—24no—
206C22×C4×C59—44no—
207C22×C4×C59—82no—
208C22×C4×C59C2×D411yescharacteristic
209C22×C4×C59C2×D411yescharacteristic
210C22×C4×C59C2411yescharacteristic
211C2×C22⋊D59—24no—
212C2×C22⋊D59—24no—
213C2×C22⋊D59—24no—
214C2×C22⋊D59—24no—
215C2×C22⋊D59—44no—
216C2×C22⋊D59—44no—
217C2×C22⋊D59—82no—
218C2×C22⋊D59—82no—
219C22×Dic59—21no—
220C22×Dic59—21no—
221C22×Dic59—21no—
222C22×Dic59—24no—
223C22×Dic59—44no—
224C22×Dic59C2×D411yescharacteristic
225C22×Dic59C2×D411yescharacteristic
226#11745687—28no—
227#11745687—44no—
228#11745687—48no—
229D4×D59—28no—
230D4×D59—44no—
231D4×D59—48no—
232C2×D236—22no—
233C2×D236—22no—
234C2×D236—21no—
235C2×D236—24no—
236C2×D236—42no—
237C2×D236—82no—
238C2×D236C2×D414yes—
239C2×D236C2412yes—
240C2×C4×D59—22no—
241C2×C4×D59—22no—
242C2×C4×D59—22no—
243C2×C4×D59—22no—
244C2×C4×D59C2×D412yes—
245C2×C4×D59C2×D412yes—
246C2×C4×D59C2412yes—
247C2×C4×D59C2412yes—
248C2×Dic118—22no—
249C2×Dic118—22no—
250C2×Dic118—21no—
251C2×Dic118—24no—
252C2×Dic118—82no—
253C2×Dic118C2412yes—
254D8×C59—28no—
255C2×C8×C59—22no—
256C2×C8×C59—22no—
257C2×C8×C59C2412yes—
258C2×C8×C59C2412yes—
259C4⋊C4×C59—21no—
260C4⋊C4×C59—21no—
261C4⋊C4×C59C2412yes—
262C4⋊C4×C59C2412yes—
263C22⋊C4×C59—24no—
264C22⋊C4×C59—24no—
265C42×C59C2×D412yes—
266C42×C59C2412yes—
267C22⋊Dic59—24no—
268C22⋊Dic59—24no—
269#11745670—44no—
270#11745669—44no—
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—
278(C2×D59)⋊C4C2×D414yes—
279C4⋊Dic59—24no—
280C4⋊Dic59—21no—
281C4⋊Dic59—21no—
282C4⋊Dic59—24no—
283C4⋊Dic59C2×D414yes—
284C4⋊Dic59C2412yes—
285C4⋊Dic59C2412yes—
286C4×Dic59—24no—
287C4×Dic59—24no—
288C2×C59⋊C8—22no—
289C2×C59⋊C8—22no—
290C2×C59⋊C8C2412yes—
291C2×C59⋊C8C2412yes—
292#11745659—44no—
293C8×D59—44no—
294C23×C59—24no—
295C23×C59—22no—
296C23×C59—22no—
297C23×C59—42no—
298C23×C59—42no—
299C23×C59—42no—
300C23×C59—42no—
301C23×C59—42no—
302C23×C59C22×D411yescharacteristic
303C22×D59—22no—
304C22×D59—22no—
305C22×D59—22no—
306C22×D59—22no—
307C22×D59—22no—
308C22×D59—22no—
309C22×D59—22no—
310C22×D59—48no—
311C22×D59—48no—
312C22×D59—42no—
313C22×D59—42no—
314C22×D59—42no—
315C22×D59—84no—
316C22×D59—816no—
317C22×D59C22×D412yes—
318C22×D59C22×D412yes—
319D4×C59—24no—
320D4×C59—22no—
321D4×C59—22no—
322D4×C59—22no—
323D4×C59—42no—
324D4×C59C2×#4114yes—
325C2×C4×C59—22no—
326C2×C4×C59—22no—
327C2×C4×C59—22no—
328C2×C4×C59—22no—
329C2×C4×C59—48no—
330C2×C4×C59—42no—
331C2×C4×C59—42no—
332C2×C4×C59—84no—
333C2×C4×C59C22×D412yes—
334C2×C4×C59C22×D412yes—
335C2×C4×C59C22×D411yescharacteristic
336C2×C4×C59C2×#4112yes—
337C2×C4×C59H(5,𝔽2)12yes—
338C2×C4×C59C2511yescharacteristic
339C22⋊D59—48no—
340C22⋊D59—48no—
341C22⋊D59—84no—
342C22⋊D59—84no—
343C2×Dic59—22no—
344C2×Dic59—22no—
345C2×Dic59—22no—
346C2×Dic59—22no—
347C2×Dic59—22no—
348C2×Dic59—48no—
349C2×Dic59—42no—
350C2×Dic59—42no—
351C2×Dic59—42no—
352C2×Dic59C22×D412yes—
353C2×Dic59C22×D412yes—
354D236—22no—
355D236—22no—
356D236—44no—
357D236—42no—
358D236—84no—
359C4×D59—24no—
360C4×D59—24no—
361C4×D59—22no—
362C4×D59—22no—
363C4×D59—22no—
364C4×D59—22no—
365Dic118—22no—
366Dic118—22no—
367Dic118—42no—
368Dic118—84no—
369C8×C59—22no—
370C8×C59—22no—
371C59⋊C8—22no—
372C59⋊C8—22no—
373C2×#3319—591nomaximal, Sylow
374C22×C59—24no—
375C22×C59—48no—
376C22×C59—42no—
377C22×C59—42no—
378C22×C59—42no—
379C22×C59—42no—
380C22×C59—42no—
381C22×C59—84no—
382C22×C59#54612yes—
383C22×C59#57512yes—
384C22×C59#57612yes—
385C22×C59C23×D411yescharacteristic
386C2×D59—22no—
387C2×D59—22no—
388C2×D59—22no—
389C2×D59—22no—
390C2×D59—22no—
391C2×D59—22no—
392C2×D59—44no—
393C2×D59—44no—
394C2×D59—42no—
395C2×D59—42no—
396C2×D59—42no—
397C2×D59—816no—
398C2×D59—84no—
399C4×C59—22no—
400C4×C59—22no—
401C4×C59—42no—
402C4×C59—42no—
403C4×C59#54612yes—
404C4×C59C22×#4111yescharacteristic
405C4×C59C2×H(5,𝔽2)11yescharacteristic
406Dic59—22no—
407Dic59—22no—
408Dic59—42no—
409Dic59—42no—
410Dic59—42no—
411C2×#555—591no—
412C2×#546—591no—
413#3319—5916no—
414C2×#489—591no—
415C2×#485—591no—
416C2×#482—591no—
417C2×#474—591no—
418C2×#468—591no—
419C2×#466—591no—
420C2×#463—591no—
421C2×#449—591no—
422C2×#447—591no—
423C2×#442D5911yescharacteristic, complemented
424C2×#435—591no—
425C2×#418—591no—
426C2×#416—591no—
427C2×C59—44no—
428C2×C59—82no—
429C2×C59#331914yescomplemented
430C2×C59C2×#54611yescharacteristic
431C2×C59C2×#57511yescharacteristic
432C2×C59C2×#57611yescharacteristic
433D59—42no—
434D59—42no—
435D59—82no—
436C22×#41—591no—
437C23×D4—591no—
438C22×SD16—591no—
439C22×D8—591no—
440C22×D8C2×D5911yescharacteristic
441C22×M16—591no—
442C23×C8—591no—
443#555—598no—
444#555—1184no—
445#546—598no—
446#546—1184no—
447C2×C4⋊Q8—591no—
448C2×#124—591no—
449C2×#124—1181no—
450C2×#124—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×D4C2×D5911yescharacteristic
461C2×C4×D4C2×D5911yescharacteristic, complemented
462C2×#117—591no—
463C2×#117—591no—
464C2×#117—1181no—
465C22×C22⋊C4—1181no—
466#489—598no—
467#485—598no—
468#482—598no—
469#474—598no—
470#468—598no—
471#466—598no—
472#463—598no—
473#449—598no—
474#447—598no—
475#442C2×D5918yescomplemented
476#435—598no—
477C2×#107—591no—
478C2×#107—591no—
479C2×#106C2×D5911yescharacteristic, complemented
480C2×C4⋊C8—591no—
481#418—598no—
482#416—598no—
483C2×#103—591no—
484C2×#103—591no—
485C2×#103—591no—
486C2×#102—591no—
487C2×#102—591no—
488C2×#102—591no—
489C2×#102—591no—
490C2×#102—591no—
491C2×#102C2×D5911yescharacteristic
492C2×#102C2×D5911yescharacteristic, complemented
493C2×C22⋊C8—591no—
494C2×C22⋊C8—591no—
495C2×#97C2×D5911yescharacteristic, complemented
496C59C2×#331911yescharacteristic, complemented, Sylow
497C25—1181no—
498C2×#41—594no—
499C2×#41—1182no—
500C2×#41—1184no—
501C2×#41—2362no—
502C22×Q8—591no—
503C22×Q8—1181no—
504C22×D4—594no—
505C22×D4—591no—
506C22×D4—591no—
507C22×D4—1181no—
508C22×D4—1182no—
509C22×D4—1181no—
510C22×D4—1184no—
511C22×D4—1181no—
512C22×D4—1181no—
513C22×D4—1181no—
514C22×D4—2362no—
515C22×D4C22×D5911yescharacteristic
516C22×D4C22×D5911yescharacteristic
517C23×C4—21no—
518C23×C4—21no—
519C23×C4—591no—
520C23×C4—591no—
521C23×C4—1181no—
522C2×SD16—594no—
523C2×SD16—2362no—
524C2×D8—24no—
525C2×D8—594no—
526C2×D8—2362no—
527C2×D8C22×D5914yes—
528C2×M16—594no—
529C2×M16—2362no—
530C22×C8—591no—
531C22×C8—591no—
532C22×C8—594no—
533C22×C8—2362no—
534C22×C8C22×D5911yescharacteristic
535C22×C8C22×D5911yescharacteristic
536C4⋊Q8—594no—
537C4⋊Q8—1182no—
538#124—594no—
539#124—1188no—
540#124—1188no—
541#124—1182no—
542#123—1188no—
543C22⋊Q8—594no—
544C22⋊Q8—1182no—
545#121—594no—
546#121—594no—
547#121—594no—
548#121—1188no—
549#121—1182no—
550#121—1188no—
551#121—1182no—
552#121—1182no—
553#120—1188no—
554C4×D4—22no—
555C4×D4—22no—
556C4×D4—594no—
557C4×D4—594no—
558C4×D4C22×D5914yes—
559C4×D4C22×D5914yescomplemented
560#117—594no—
561#117—594no—
562#117—1182no—
563#117—1182no—
564#117—1188no—
565C2×C4⋊C4—591no—
566C2×C4⋊C4—591no—
567C2×C4⋊C4—591no—
568C2×C4⋊C4—1181no—
569C2×C4⋊C4—1181no—
570C2×C4⋊C4C22×D5911yescharacteristic
571C2×C4⋊C4C22×D5911yescharacteristic
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—591no—
575C2×C22⋊C4—591no—
576C2×C22⋊C4—1188no—
577C2×C22⋊C4—1181no—
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×C42—1181no—
586C2×C42—1181no—
587C2×C42C22×D5911yescharacteristic
588#107—594no—
589#107—594no—
590#106C22×D5914yescomplemented
591C4⋊C8—594no—
592#103—594no—
593#103—594no—
594#103—594no—
595#102—594no—
596#102—594no—
597#102—594no—
598#102—594no—
599#102—594no—
600#102C22×D5914yes—
601#102C22×D5914yescomplemented
602C22⋊C8—594no—
603C22⋊C8—594no—
604#97C22×D5914yescomplemented
605C24—21no—
606C24—21no—
607C24—591no—
608C24—591no—
609C24—1184no—
610C24—1181no—
611C24—4722no—
612C24—2364no—
613C24—2364no—
614#41—1188no—
615#41—2364no—
616#41—2368no—
617C2×Q8—592no—
618C2×Q8—1184no—
619C2×Q8—1181no—
620C2×Q8—1182no—
621C2×Q8—1182no—
622C2×Q8—4722no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—22no—
626C2×D4—22no—
627C2×D4—22no—
628C2×D4—594no—
629C2×D4—592no—
630C2×D4—1184no—
631C2×D4—1184no—
632C2×D4—1188no—
633C2×D4—1184no—
634C2×D4—1184no—
635C2×D4—1184no—
636C2×D4—1181no—
637C2×D4—1182no—
638C2×D4—1182no—
639C2×D4—4722no—
640C2×D4—4722no—
641C2×D4—4722no—
642C2×D4—2362no—
643C2×D4—2364no—
644C2×D4—2368no—
645C2×D4—2364no—
646C2×D4—2364no—
647C2×D4#1174568514yes—
648C2×D4C23×D5912yes—
649C2×D4C23×D5912yes—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—24no—
653C22×C4—24no—
654C22×C4—44no—
655C22×C4—82no—
656C22×C4—591no—
657C22×C4—591no—
658C22×C4—592no—
659C22×C4—592no—
660C22×C4—592no—
661C22×C4—592no—
662C22×C4—1184no—
663C22×C4—1182no—
664C22×C4—1182no—
665C22×C4—1182no—
666C22×C4—1182no—
667C22×C4—1181no—
668C22×C4—1181no—
669C22×C4—1181no—
670C22×C4—2364no—
671C22×C4D4×D5911yescharacteristic
672C22×C4D4×D5911yescharacteristic
673C22×C4C23×D5911yescharacteristic
674SD16—2364no—
675D8—28no—
676D8—2364no—
677M16—2364no—
678C2×C8—22no—
679C2×C8—22no—
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—1181no—
694C4⋊C4—1181no—
695C4⋊C4—1184no—
696C4⋊C4C23×D5912yes—
697C4⋊C4C23×D5912yes—
698C22⋊C4—24no—
699C22⋊C4—24no—
700C22⋊C4—594no—
701C22⋊C4—594no—
702C22⋊C4—1184no—
703C22⋊C4—1184no—
704C22⋊C4—1184no—
705C22⋊C4—1184no—
706C22⋊C4—1184no—
707C22⋊C4—1184no—
708C22⋊C4—1184no—
709C22⋊C4—1184no—
710C42—1184no—
711C42—1184no—
712C42D4×D5912yes—
713C42C23×D5912yes—
714C23—22no—
715C23—24no—
716C23—22no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—592no—
723C23—592no—
724C23—1182no—
725C23—1182no—
726C23—1182no—
727C23—1182no—
728C23—1182no—
729C23—1182no—
730C23—1182no—
731C23—4724no—
732C23—47216no—
733C23—2368no—
734C23—2368no—
735C23—2362no—
736C23—2362no—
737C23—2362no—
738C23C2×D4×D5911yescharacteristic
739Q8—1182no—
740Q8—1182no—
741Q8—4724no—
742Q8—2362no—
743D4—22no—
744D4—22no—
745D4—22no—
746D4—24no—
747D4—42no—
748D4—1182no—
749D4—1182no—
750D4—4724no—
751D4—4724no—
752D4—4724no—
753D4—2364no—
754D4—2368no—
755D4—2368no—
756D4—2362no—
757D4C2×#1174568514yes—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—48no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—84no—
766C2×C4—592no—
767C2×C4—592no—
768C2×C4—1182no—
769C2×C4—1182no—
770C2×C4—1182no—
771C2×C4—1182no—
772C2×C4—1182no—
773C2×C4—1182no—
774C2×C4—1184no—
775C2×C4—1184no—
776C2×C4—1182no—
777C2×C4—1182no—
778C2×C4—1182no—
779C2×C4—2368no—
780C2×C4—2362no—
781C2×C4—2362no—
782C2×C4—2362no—
783C2×C4C2×D4×D5912yes—
784C2×C4C2×D4×D5912yes—
785C2×C4C2×D4×D5911yescharacteristic
786C2×C4C2×#1174568512yes—
787C2×C4#1427377312yes—
788C2×C4C24×D5911yescharacteristic
789C8—22no—
790C8—22no—
791C8—1182no—
792C8—1182no—
793C22—24no—
794C22—48no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—84no—
801C22—1182no—
802C22—1182no—
803C22—1182no—
804C22—1182no—
805C22—1182no—
806C22—1182no—
807C22—47216no—
808C22—4724no—
809C22—2362no—
810C22—2362no—
811C22—2362no—
812C22—2364no—
813C22—2364no—
814C22#1683804812yes—
815C22#1683819812yes—
816C22#1683820612yes—
817C22C22×D4×D5911yescharacteristic
818C4—22no—
819C4—22no—
820C4—42no—
821C4—42no—
822C4—1182no—
823C4—1182no—
824C4—2362no—
825C4—2362no—
826C4—2362no—
827C4#1683804812yes—
828C4C22×#1174568511yescharacteristic
829C4C2×#1427377311yescharacteristic
830C2—44no—
831C2—82no—
832C2—4722no—
833C2—2362no—
834C2—2362no—
835C2#2143625714yesdirect product factor
836C2C2×#1683804811yescharacteristic
837C2C2×#1683819811yescharacteristic
838C2C2×#1683820611yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#442C2
socleC23×C59C22×D4
hypercenterC2×#442D59
hypocenterC59C2×#3319
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#442

Complements

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

NH ≅ G/Ntype
1. C2×#16838117C2semidirect
2. C2×#16838047C2semidirect
3. #21436257C2direct (N × H)
4. C2×#16837762C2semidirect
5. C2×#16837746C2semidirect
6. C2×#16837728C2semidirect
7. C2×#16837682C2semidirect
8. C2×#16837647C2semidirect
9. C2×#16837637C2semidirect
10. C2×#16837617C2semidirect
11. C2×#16837544C2semidirect
12. C2×#16837534C2semidirect
13. C2×#16837475C2semidirect
14. C2×#16837405C2semidirect
15. C2×#16837395C2semidirect
16. C2×C59×#442C2semidirect
19. C22×#11745670C22semidirect
22. C22×C8×D59C22semidirect
24. #16838117C22semidirect
26. #16838047C22semidirect
27. C2×#14273727C22semidirect
37. C2×#14273698C22semidirect
42. C2×#14273685C22semidirect
44. #16837762C22semidirect
45. #16837746C22semidirect
46. #16837728C22semidirect
47. #16837682C22semidirect
48. #16837647C22semidirect
49. #16837637C22semidirect
50. #16837617C22semidirect
51. #16837544C22semidirect
52. #16837534C22semidirect
53. #16837475C22semidirect
54. C2×#14273660C22semidirect
55. C2×#14273660C22semidirect
56. C2×C4⋊(C59⋊C8)C22semidirect
57. #16837405C22semidirect
58. #16837395C22semidirect
59. C2×#14273652C22semidirect
60. C2×#14273652C22semidirect
61. C2×#14273650C22semidirect
68. C2×(C2×D59)⋊C8C22semidirect
71. C2×C4×D4×C59C22semidirect
72. C59×#442C22semidirect
73. C2×#106×C59C22semidirect
75. C2×#102×C59C22semidirect
76. C2×#97×C59C22semidirect
99. C2×#11745670C23semidirect
107. C2×C8×D59C23semidirect
109. #14273727C23semidirect
124. #14273698C23semidirect
132. #14273685C23semidirect
151. #14273660C23semidirect
152. #14273660C23semidirect
153. C4⋊(C59⋊C8)C23semidirect
154. #14273652C23semidirect
155. #14273652C23semidirect
156. #14273650C23semidirect
163. (C2×D59)⋊C8C23semidirect
175. C4×D4×C59C23semidirect
181. #106×C59C23semidirect
183. #102×C59C23semidirect
184. #97×C59C23semidirect
423. C2×#442D59semidirect
429. C2×C59#3319semidirect
461. C2×C4×D4C2×D59semidirect
475. #442C2×D59semidirect
479. C2×#106C2×D59semidirect
492. C2×#102C2×D59semidirect
495. C2×#97C2×D59semidirect
496. C59C2×#3319semidirect
559. C4×D4C22×D59semidirect
590. #106C22×D59semidirect
601. #102C22×D59semidirect
604. #97C22×D59semidirect
835. C2#21436257direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168381172
C2×#168380472
#214362572
C2×#168377622
C2×#168377462
C2×#168377282
C2×#168376822
C2×#168376472
C2×#168376372
C2×#168376172
C2×#168375442
C2×#168375342
C2×#168374752
C2×#168374052
C2×#168373952
C2×C59×#4422
C2×#331959