Finite Group Databasebeta

← C2×#21436249 #29465372

Subgroups — C2×#21436249 #29465372

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×#16838118C211yesmaximal, characteristic, complemented
2C2×#16838047C211yesmaximal, characteristic, complemented
3#21436249C2116yesmaximal, direct product factor
4C2×#16837764C211yesmaximal, characteristic, complemented
5C2×#16837745C211yesmaximal, characteristic, complemented
6C2×#16837729C211yesmaximal, characteristic, complemented
7C2×#16837649C211yesmaximal, characteristic, complemented
8C2×#16837639C211yesmaximal, characteristic, complemented
9C2×#16837618C211yesmaximal, characteristic, complemented
10C2×#16837548C211yesmaximal, characteristic, complemented
11C2×#16837537C211yesmaximal, characteristic, complemented
12C2×#16837512C211yesmaximal, characteristic, complemented
13C2×#16837472C211yesmaximal, characteristic, complemented
14C2×#16837405C211yesmaximal, characteristic, complemented
15C2×#16837395C211yesmaximal, characteristic, complemented
16C2×C59×#474C211yesmaximal, characteristic, complemented
17C22×#11745687C2211yescharacteristic
18C22×D4×D59C2211yescharacteristic
19C22×#11745660C2211yescharacteristic, complemented
20C22×D472C2211yescharacteristic
21C22×#11745669C2211yescharacteristic
22C22×#11745659C2211yescharacteristic
23C22×C8×D59C2211yescharacteristic, complemented
24#16838118—24no—
25#16838118C2218yescomplemented
26#16838047—24no—
27#16838047C2218yescomplemented
28C2×#14273716—21no—
29C2×#14273716—21no—
30C2×#14273715C2211yescharacteristic
31C2×#14273711—21no—
32C2×#14273707C2211yescharacteristic
33C2×#14273702—21no—
34C2×#14273702C2211yescharacteristic
35C2×#14273702C2211yescharacteristic
36C2×#14273702C2211yescharacteristic, complemented
37C2×#14273701—21no—
38C2×#14273697—21no—
39C2×C4×D236C2211yescharacteristic
40C2×C4×D236C2211yescharacteristic, complemented
41C2×#14273685—21no—
42C2×#14273685C2211yescharacteristic
43C2×#14273685C2211yescharacteristic, complemented
44C22×(C2×D59)⋊C4—21no—
45#16837764C2218yescomplemented
46#16837745C2218yescomplemented
47#16837729C2218yescomplemented
48#16837649C2218yescomplemented
49#16837639C2218yescomplemented
50#16837618C2218yescomplemented
51#16837548C2218yescomplemented
52#16837537C2218yescomplemented
53#16837512C2218yescomplemented
54#16837472C2218yescomplemented
55C2×#14273658C2211yescharacteristic, complemented
56#16837405C2218yescomplemented
57#16837395C2218yescomplemented
58C2×#14273652C2211yescharacteristic, complemented
59C2×#14273650C2211yescharacteristic, complemented
60C2×#14273650C2211yescharacteristic, complemented
61C2×#14273649C2211yescharacteristic
62C2×#14273648C2211yescharacteristic
63C2×#14273647C2211yescharacteristic
64C2×#14273647C2211yescharacteristic
65C2×#14273647C2211yescharacteristic, complemented
66C2×(C2×D59)⋊C8C2211yescharacteristic
67C2×(C2×D59)⋊C8C2211yescharacteristic, complemented
68C2×#14273638C2211yescharacteristic, complemented
69C2×C4⋊Q8×C59C2211yescharacteristic, complemented
70C2×C4×D4×C59C2211yescharacteristic
71C59×#474C2218yescomplemented
72C2×#107×C59C2211yescharacteristic, complemented
73C2×#107×C59C2211yescharacteristic, complemented
74C2×C4⋊C8×C59C2211yescharacteristic, complemented
75C2×#102×C59C2211yescharacteristic
76C2×#102×C59C2211yescharacteristic
77C24×D59—21no—
78C2×#11745687—24no—
79C2×#11745687—22no—
80C2×#11745687—42no—
81C2×#11745687C2314yes—
82C22×Dic118C2311yescharacteristic
83C22×D236—21no—
84C22×D236—21no—
85C22×D236—21no—
86C22×D236D411yescharacteristic
87C22×D236C2311yescharacteristic
88C22×D236C2311yescharacteristic
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×D59—21no—
97C22×C4×D59C2311yescharacteristic
98C22×C4×D59C2311yescharacteristic
99C2×#11745660—42no—
100C2×#11745660C2314yescomplemented
101C2×D472—42no—
102C2×D472C2314yes—
103C2×#11745669—24no—
104C2×#11745669C2314yes—
105C2×#11745659—42no—
106C2×#11745659C2314yes—
107C22×C59⋊C8C2311yescharacteristic
108C22×C59⋊C8C2311yescharacteristic
109C2×C8×D59—42no—
110C2×C8×D59C2314yescomplemented
111#14273716—28no—
112#14273716—28no—
113#14273715—22no—
114#14273715C2314yes—
115#14273711—28no—
116#14273707—22no—
117#14273707C2314yes—
118#14273702—28no—
119#14273702—22no—
120#14273702—22no—
121#14273702—22no—
122#14273702C2314yes—
123#14273702C2314yes—
124#14273702C2314yescomplemented
125#14273701—28no—
126#14273697—28no—
127C4×D236—22no—
128C4×D236D414yes—
129C4×D236C2314yes—
130C4×D236C2314yescomplemented
131#14273685—22no—
132#14273685—22no—
133#14273685—28no—
134#14273685C2314yes—
135#14273685C2314yescomplemented
136C2×C4⋊Dic59—21no—
137C2×C4⋊Dic59D411yescharacteristic
138C2×C4⋊Dic59C2311yescharacteristic
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—21no—
147C2×(C2×D59)⋊C4—21no—
148C2×(C2×D59)⋊C4—28no—
149C2×(C2×D59)⋊C4D411yescharacteristic
150C2×(C2×D59)⋊C4D411yescharacteristic
151C2×C4×Dic59—21no—
152C2×C4×Dic59—21no—
153#14273658C2314yescomplemented
154#14273652C2314yescomplemented
155#14273650C2314yescomplemented
156#14273650C2314yescomplemented
157#14273649C2314yes—
158#14273648C2314yes—
159#14273647C2314yes—
160#14273647C2314yes—
161#14273647C2314yescomplemented
162(C2×D59)⋊C8C2314yes—
163(C2×D59)⋊C8C2314yescomplemented
164#14273638C2314yescomplemented
165C22×Q8×C59—21no—
166C22×D4×C59C2311yescharacteristic
167C23×C4×C59—21no—
168C22×C8×C59C2311yescharacteristic
169C22×C8×C59C2311yescharacteristic
170C4⋊Q8×C59—22no—
171C4⋊Q8×C59C2314yescomplemented
172C4×D4×C59—22no—
173C4×D4×C59C2314yes—
174C2×C4⋊C4×C59—21no—
175C2×C4⋊C4×C59C2311yescharacteristic
176C2×C4⋊C4×C59C2311yescharacteristic
177C2×C4⋊C4×C59C2311yescharacteristic
178C2×C22⋊C4×C59—21no—
179C2×C42×C59C2311yescharacteristic
180#107×C59C2314yescomplemented
181#107×C59C2314yescomplemented
182C4⋊C8×C59C2314yescomplemented
183#102×C59C2314yes—
184#102×C59C2314yes—
185C24×C59—21no—
186C23×D59—21no—
187C23×D59—21no—
188C23×D59—24no—
189C23×D59—44no—
190C23×D59—44no—
191C23×D59—82no—
192C23×D59C2×D411yescharacteristic
193C23×D59C2×D411yescharacteristic
194C2×Q8×C59—24no—
195C2×Q8×C59—82no—
196C2×D4×C59—21no—
197C2×D4×C59—22no—
198C2×D4×C59#4114yes—
199C2×D4×C59C2412yes—
200C22×C4×C59—21no—
201C22×C4×C59—21no—
202C22×C4×C59—21no—
203C22×C4×C59—24no—
204C22×C4×C59—82no—
205C22×C4×C59C2×D411yescharacteristic
206C22×C4×C59C2×D411yescharacteristic
207C22×C4×C59C2411yescharacteristic
208C2×C22⋊D59—24no—
209C2×C22⋊D59—24no—
210C2×C22⋊D59—44no—
211C2×C22⋊D59—44no—
212C22×Dic59—21no—
213C22×Dic59—21no—
214C22×Dic59—24no—
215C22×Dic59—44no—
216C22×Dic59C2×D411yescharacteristic
217C22×Dic59C2×D411yescharacteristic
218#11745687—28no—
219#11745687—44no—
220#11745687—48no—
221D4×D59—28no—
222D4×D59—44no—
223D4×D59—48no—
224C2×D236—22no—
225C2×D236—22no—
226C2×D236—22no—
227C2×D236—22no—
228C2×D236—21no—
229C2×D236—21no—
230C2×D236—24no—
231C2×D236—24no—
232C2×D236—24no—
233C2×D236—42no—
234C2×D236—82no—
235C2×D236—82no—
236C2×D236—82no—
237C2×D236C2×D414yes—
238C2×D236C2412yes—
239C2×D236C2412yes—
240C2×C4×D59—22no—
241C2×C4×D59—22no—
242C2×C4×D59—22no—
243C2×C4×D59—22no—
244C2×C4×D59—24no—
245C2×C4×D59—44no—
246C2×C4×D59C2×D412yes—
247C2×C4×D59C2×D412yes—
248C2×C4×D59C2412yes—
249C2×C4×D59C2412yes—
250C2×Dic118—22no—
251C2×Dic118—22no—
252C2×Dic118—21no—
253C2×Dic118C2412yes—
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—
266C42×C59C2×D412yes—
267C42×C59C2412yes—
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)⋊C4—24no—
277(C2×D59)⋊C4—24no—
278(C2×D59)⋊C4C2×D414yes—
279(C2×D59)⋊C4C2×D414yes—
280C4⋊Dic59—21no—
281C4⋊Dic59—24no—
282C4⋊Dic59C2×D414yes—
283C4⋊Dic59C2412yes—
284C4×Dic59—24no—
285C4×Dic59—24no—
286C2×C59⋊C8—22no—
287C2×C59⋊C8—22no—
288C2×C59⋊C8C2412yes—
289C2×C59⋊C8C2412yes—
290D472—44no—
291#11745660—44no—
292#11745659—44no—
293C8×D59—44no—
294C23×C59—24no—
295C23×C59—22no—
296C23×C59—42no—
297C23×C59—42no—
298C23×C59C22×D411yescharacteristic
299C22×D59—22no—
300C22×D59—22no—
301C22×D59—22no—
302C22×D59—22no—
303C22×D59—22no—
304C22×D59—22no—
305C22×D59—22no—
306C22×D59—22no—
307C22×D59—48no—
308C22×D59—48no—
309C22×D59—42no—
310C22×D59—42no—
311C22×D59—42no—
312C22×D59—42no—
313C22×D59—42no—
314C22×D59—42no—
315C22×D59—84no—
316C22×D59—816no—
317C22×D59C22×D412yes—
318C22×D59C22×D412yes—
319Q8×C59—84no—
320D4×C59—24no—
321D4×C59—22no—
322D4×C59C2×#4114yes—
323C2×C4×C59—22no—
324C2×C4×C59—22no—
325C2×C4×C59—22no—
326C2×C4×C59—22no—
327C2×C4×C59—22no—
328C2×C4×C59—42no—
329C2×C4×C59—42no—
330C2×C4×C59—42no—
331C2×C4×C59—84no—
332C2×C4×C59C22×D412yes—
333C2×C4×C59C22×D412yes—
334C2×C4×C59C22×D411yescharacteristic
335C2×C4×C59C2×#4112yes—
336C2×C4×C59H(5,𝔽2)12yes—
337C2×C4×C59C2511yescharacteristic
338C22⋊D59—48no—
339C22⋊D59—48no—
340C2×Dic59—22no—
341C2×Dic59—22no—
342C2×Dic59—22no—
343C2×Dic59—22no—
344C2×Dic59—48no—
345C2×Dic59—42no—
346C2×Dic59—42no—
347C2×Dic59C22×D412yes—
348C2×Dic59C22×D412yes—
349D236—22no—
350D236—22no—
351D236—22no—
352D236—22no—
353D236—44no—
354D236—42no—
355D236—42no—
356D236—84no—
357D236—84no—
358D236—84no—
359C4×D59—24no—
360C4×D59—24no—
361C4×D59—22no—
362C4×D59—22no—
363C4×D59—22no—
364C4×D59—22no—
365C4×D59—48no—
366Dic118—22no—
367Dic118—22no—
368Dic118—42no—
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#54612yes—
379C22×C59#57512yes—
380C22×C59#57612yes—
381C22×C59C23×D411yescharacteristic
382C2×D59—22no—
383C2×D59—22no—
384C2×D59—22no—
385C2×D59—22no—
386C2×D59—22no—
387C2×D59—22no—
388C2×D59—44no—
389C2×D59—44no—
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—22no—
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—42no—
410Dic59—42no—
411C2×#555—591no—
412C2×#546—591no—
413#3319—5916no—
414C2×#489—591no—
415C2×#485—591no—
416C2×#482—591no—
417C2×#474D5911yescharacteristic, complemented
418C2×#468—591no—
419C2×#466—591no—
420C2×#463—591no—
421C2×#449—591no—
422C2×#447—591no—
423C2×#442—591no—
424C2×#435—591no—
425C2×#418—591no—
426C2×#416—591no—
427C2×C59—44no—
428C2×C59#331914yescomplemented
429C2×C59C2×#54611yescharacteristic
430C2×C59C2×#57511yescharacteristic
431C2×C59C2×#57611yescharacteristic
432D59—42no—
433D59—42no—
434D59—82no—
435D59—82no—
436C22×#41—591no—
437C23×D4—591no—
438C22×SD16—591no—
439C22×D8—591no—
440C22×D8—591no—
441C22×M16—591no—
442C23×C8—591no—
443#555—598no—
444#555—1184no—
445#546—598no—
446#546—1184no—
447C2×C4⋊Q8C2×D5911yescharacteristic, complemented
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×D4—591no—
461C2×C4×D4C2×D5911yescharacteristic
462C2×#117—591no—
463C2×#117—591no—
464C2×#117—1181no—
465C22×C22⋊C4—1181no—
466#489—598no—
467#485—598no—
468#482—598no—
469#474C2×D5918yescomplemented
470#468—598no—
471#466—598no—
472#463—598no—
473#449—598no—
474#447—598no—
475#442—598no—
476#435—598no—
477C2×#107C2×D5911yescharacteristic, complemented
478C2×#107C2×D5911yescharacteristic, complemented
479C2×#106—591no—
480C2×C4⋊C8C2×D5911yescharacteristic, complemented
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
493C2×C22⋊C8—591no—
494C2×C22⋊C8—591no—
495C2×#97—591no—
496C59C2×#331911yescharacteristic, complemented, Sylow
497C25—1181no—
498C2×#41—594no—
499C2×#41—1182no—
500C2×#41—1184no—
501C2×#41—2362no—
502C22×Q8—21no—
503C22×Q8—591no—
504C22×D4—594no—
505C22×D4—591no—
506C22×D4—591no—
507C22×D4—591no—
508C22×D4—1181no—
509C22×D4—1181no—
510C22×D4—1181no—
511C22×D4—1182no—
512C22×D4—1181no—
513C22×D4—1184no—
514C22×D4—1181no—
515C22×D4—2362no—
516C22×D4C22×D5911yescharacteristic
517C23×C4—21no—
518C23×C4—591no—
519C23×C4—591no—
520C23×C4—1181no—
521C23×C4—1181no—
522C2×SD16—594no—
523C2×SD16—2362no—
524C2×D8—594no—
525C2×D8—594no—
526C2×D8—1184no—
527C2×D8—2362no—
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—22no—
537C4⋊Q8C22×D5914yescomplemented
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—1182no—
551#121—1182no—
552#121—1188no—
553#120—1188no—
554C4×D4—22no—
555C4×D4—594no—
556C4×D4—594no—
557C4×D4—594no—
558C4×D4—1182no—
559C4×D4C22×D5914yes—
560#117—594no—
561#117—594no—
562#117—1188no—
563#117—1182no—
564#117—1182no—
565C2×C4⋊C4—21no—
566C2×C4⋊C4—591no—
567C2×C4⋊C4—591no—
568C2×C4⋊C4—1181no—
569C2×C4⋊C4C22×D5911yescharacteristic
570C2×C4⋊C4C22×D5911yescharacteristic
571C2×C4⋊C4C22×D5911yescharacteristic
572C2×C22⋊C4—21no—
573C2×C22⋊C4—591no—
574C2×C22⋊C4—591no—
575C2×C22⋊C4—1188no—
576C2×C22⋊C4—1181no—
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#107C22×D5914yescomplemented
589#107C22×D5914yescomplemented
590#106—594no—
591C4⋊C8C22×D5914yescomplemented
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×D5914yes—
602C22⋊C8—594no—
603C22⋊C8—594no—
604#97—594no—
605C24—21no—
606C24—591no—
607C24—591no—
608C24—1184no—
609C24—1181no—
610C24—1181no—
611C24—4722no—
612C24—2364no—
613C24—2364no—
614#41—1188no—
615#41—2364no—
616#41—2368no—
617C2×Q8—24no—
618C2×Q8—82no—
619C2×Q8—592no—
620C2×Q8—1181no—
621C2×Q8—1182no—
622C2×Q8—1182no—
623C2×D4—21no—
624C2×D4—22no—
625C2×D4—594no—
626C2×D4—592no—
627C2×D4—592no—
628C2×D4—1184no—
629C2×D4—1184no—
630C2×D4—1184no—
631C2×D4—1184no—
632C2×D4—1188no—
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—4722no—
643C2×D4—2362no—
644C2×D4—2364no—
645C2×D4—2368no—
646C2×D4—2364no—
647C2×D4—2364no—
648C2×D4#1174568914yes—
649C2×D4C23×D5912yes—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—24no—
654C22×C4—82no—
655C22×C4—591no—
656C22×C4—591no—
657C22×C4—592no—
658C22×C4—592no—
659C22×C4—592no—
660C22×C4—592no—
661C22×C4—1184no—
662C22×C4—1182no—
663C22×C4—1182no—
664C22×C4—1182no—
665C22×C4—1182no—
666C22×C4—1181no—
667C22×C4—1181no—
668C22×C4—1184no—
669C22×C4—2364no—
670C22×C4—2364no—
671C22×C4D4×D5911yescharacteristic
672C22×C4D4×D5911yescharacteristic
673C22×C4C23×D5911yescharacteristic
674SD16—2364no—
675D8—1188no—
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—24no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—594no—
692C4⋊C4—592no—
693C4⋊C4—1184no—
694C4⋊C4—1181no—
695C4⋊C4C23×D5912yes—
696C4⋊C4C23×D5912yes—
697C4⋊C4C23×D5912yes—
698C22⋊C4—24no—
699C22⋊C4—594no—
700C22⋊C4—594no—
701C22⋊C4—1184no—
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—42no—
717C23—42no—
718C23—592no—
719C23—592no—
720C23—1182no—
721C23—1182no—
722C23—1182no—
723C23—1182no—
724C23—1182no—
725C23—1182no—
726C23—1182no—
727C23—1182no—
728C23—4724no—
729C23—47216no—
730C23—2368no—
731C23—2368no—
732C23—2362no—
733C23—2362no—
734C23—2362no—
735C23—2362no—
736C23—2362no—
737C23—2362no—
738C23C2×D4×D5911yescharacteristic
739Q8—84no—
740Q8—1182no—
741Q8—1182no—
742Q8—2362no—
743D4—22no—
744D4—24no—
745D4—1182no—
746D4—1182no—
747D4—1182no—
748D4—1182no—
749D4—4724no—
750D4—4724no—
751D4—4724no—
752D4—2364no—
753D4—2368no—
754D4—2368no—
755D4—2362no—
756D4—2362no—
757D4C2×#1174568914yes—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—84no—
767C2×C4—592no—
768C2×C4—592no—
769C2×C4—1182no—
770C2×C4—1182no—
771C2×C4—1182no—
772C2×C4—1182no—
773C2×C4—1182no—
774C2×C4—1182no—
775C2×C4—1184no—
776C2×C4—1184no—
777C2×C4—1182no—
778C2×C4—1182no—
779C2×C4—2368no—
780C2×C4—2368no—
781C2×C4—2362no—
782C2×C4—2362no—
783C2×C4C2×D4×D5912yes—
784C2×C4C2×D4×D5912yes—
785C2×C4C2×D4×D5911yescharacteristic
786C2×C4C2×#1174568912yes—
787C2×C4#1427377312yes—
788C2×C4C24×D5911yescharacteristic
789C8—22no—
790C8—22no—
791C8—1182no—
792C8—1182no—
793C22—24no—
794C22—48no—
795C22—42no—
796C22—42no—
797C22—1182no—
798C22—1182no—
799C22—1182no—
800C22—1182no—
801C22—1182no—
802C22—1182no—
803C22—47216no—
804C22—4724no—
805C22—4724no—
806C22—2362no—
807C22—2362no—
808C22—2362no—
809C22—2362no—
810C22—2362no—
811C22—2362no—
812C22—2364no—
813C22—2364no—
814C22#1683804312yes—
815C22#1683820112yes—
816C22#1683820312yes—
817C22C22×D4×D5911yescharacteristic
818C4—22no—
819C4—22no—
820C4—42no—
821C4—42no—
822C4—42no—
823C4—1182no—
824C4—1182no—
825C4—2362no—
826C4—2362no—
827C4#1683804312yes—
828C4C22×#1174568911yescharacteristic
829C4C2×#1427377311yescharacteristic
830C2—44no—
831C2—4722no—
832C2—4722no—
833C2—2362no—
834C2—2362no—
835C2#2143624914yesdirect product factor
836C2C2×#1683804311yescharacteristic
837C2C2×#1683820111yescharacteristic
838C2C2×#1683820311yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#474C2
socleC23×C59C22×D4
hypercenterC2×#474D59
hypocenterC59C2×#3319
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#474

Complements

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

NH ≅ G/Ntype
1. C2×#16838118C2semidirect
2. C2×#16838047C2semidirect
3. #21436249C2direct (N × H)
4. C2×#16837764C2semidirect
5. C2×#16837745C2semidirect
6. C2×#16837729C2semidirect
7. C2×#16837649C2semidirect
8. C2×#16837639C2semidirect
9. C2×#16837618C2semidirect
10. C2×#16837548C2semidirect
11. C2×#16837537C2semidirect
12. C2×#16837512C2semidirect
13. C2×#16837472C2semidirect
14. C2×#16837405C2semidirect
15. C2×#16837395C2semidirect
16. C2×C59×#474C2semidirect
19. C22×#11745660C22semidirect
23. C22×C8×D59C22semidirect
25. #16838118C22semidirect
27. #16838047C22semidirect
36. C2×#14273702C22semidirect
40. C2×C4×D236C22semidirect
43. C2×#14273685C22semidirect
45. #16837764C22semidirect
46. #16837745C22semidirect
47. #16837729C22semidirect
48. #16837649C22semidirect
49. #16837639C22semidirect
50. #16837618C22semidirect
51. #16837548C22semidirect
52. #16837537C22semidirect
53. #16837512C22semidirect
54. #16837472C22semidirect
55. C2×#14273658C22semidirect
56. #16837405C22semidirect
57. #16837395C22semidirect
58. C2×#14273652C22semidirect
59. C2×#14273650C22semidirect
60. C2×#14273650C22semidirect
65. C2×#14273647C22semidirect
67. C2×(C2×D59)⋊C8C22semidirect
68. C2×#14273638C22semidirect
69. C2×C4⋊Q8×C59C22semidirect
71. C59×#474C22semidirect
72. C2×#107×C59C22semidirect
73. C2×#107×C59C22semidirect
74. C2×C4⋊C8×C59C22semidirect
100. C2×#11745660C23semidirect
110. C2×C8×D59C23semidirect
124. #14273702C23semidirect
130. C4×D236C23semidirect
135. #14273685C23semidirect
153. #14273658C23semidirect
154. #14273652C23semidirect
155. #14273650C23semidirect
156. #14273650C23semidirect
161. #14273647C23semidirect
163. (C2×D59)⋊C8C23semidirect
164. #14273638C23semidirect
171. C4⋊Q8×C59C23semidirect
180. #107×C59C23semidirect
181. #107×C59C23semidirect
182. C4⋊C8×C59C23semidirect
417. C2×#474D59semidirect
428. C2×C59#3319semidirect
447. C2×C4⋊Q8C2×D59semidirect
469. #474C2×D59semidirect
477. C2×#107C2×D59semidirect
478. C2×#107C2×D59semidirect
480. C2×C4⋊C8C2×D59semidirect
496. C59C2×#3319semidirect
537. C4⋊Q8C22×D59semidirect
588. #107C22×D59semidirect
589. #107C22×D59semidirect
591. C4⋊C8C22×D59semidirect
835. C2#21436249direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168381182
C2×#168380472
#214362492
C2×#168377642
C2×#168377452
C2×#168377292
C2×#168376492
C2×#168376392
C2×#168376182
C2×#168375482
C2×#168375372
C2×#168375122
C2×#168374722
C2×#168374052
C2×#168373952
C2×C59×#4742
C2×#331959