Finite Group Databasebeta

← C2×#21434953 #29459347

Subgroups — C2×#21434953 #29459347

Order 15104.

2378 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
1C2×#16837983C211yesmaximal, characteristic, complemented
2C2×#16837968C211yesmaximal, characteristic, complemented
3#21434953C2116yesmaximal, direct product factor
4C2×#16837746C211yesmaximal, characteristic, complemented
5C2×#16837728C211yesmaximal, characteristic, complemented
6C2×#16837715C211yesmaximal, characteristic, complemented
7C2×#16837656C211yesmaximal, characteristic, complemented
8C2×#16837647C211yesmaximal, characteristic, complemented
9C2×#16837637C211yesmaximal, characteristic, complemented
10C2×#16837632C211yesmaximal, characteristic, complemented
11C2×#16837549C211yesmaximal, characteristic, complemented
12C2×#16837545C211yesmaximal, characteristic, complemented
13C2×#16837554C211yesmaximal, characteristic, complemented
14C2×#16837537C211yesmaximal, characteristic, complemented
15C2×#16837367C211yesmaximal, characteristic, complemented
16C2×C59×#481C211yesmaximal, characteristic, complemented
17C22×#11745685C2211yescharacteristic
18C22×#11745685C2211yescharacteristic, complemented
19C22×D4×D59C2211yescharacteristic
20C22×#11745660C2211yescharacteristic
21C22×#11745670C2211yescharacteristic
22C22×D472C2211yescharacteristic
23C22×#11745669C2211yescharacteristic
24C22×#11745659C2211yescharacteristic, complemented
25C22×C8×D59C2211yescharacteristic, complemented
26#16837983—24no—
27#16837983C2218yescomplemented
28#16837968—24no—
29#16837968C2218yescomplemented
30C2×#14273723—21no—
31C2×#14273713—21no—
32C2×#14273707—21no—
33C2×#14273707C2211yescharacteristic
34C2×#14273707C2211yescharacteristic, complemented
35C2×#14273702—21no—
36C2×#14273702C2211yescharacteristic
37C2×#14273702C2211yescharacteristic
38C2×#14273702C2211yescharacteristic, complemented
39C2×#14273701—21no—
40C2×#14273701—21no—
41C2×#14273701C2211yescharacteristic
42C2×#14273698C2211yescharacteristic
43C2×#14273697—21no—
44C2×#14273695—21no—
45C2×#14273685C2211yescharacteristic
46#16837746C2218yescomplemented
47#16837728C2218yescomplemented
48#16837715C2218yescomplemented
49#16837656C2218yescomplemented
50#16837647C2218yescomplemented
51#16837637C2218yescomplemented
52#16837632C2218yescomplemented
53#16837554C2218yescomplemented
54#16837549C2218yescomplemented
55#16837545C2218yescomplemented
56#16837537C2218yescomplemented
57C2×#14273660C2211yescharacteristic, complemented
58C2×#14273660C2211yescharacteristic, complemented
59C2×#14273652C2211yescharacteristic, complemented
60C2×#14273650C2211yescharacteristic, complemented
61C2×#14273649C2211yescharacteristic, complemented
62C2×#14273647C2211yescharacteristic
63C2×#14273647C2211yescharacteristic
64C2×#14273647C2211yescharacteristic, complemented
65#16837367C2218yescomplemented
66C2×C22⋊(C59⋊C8)C2211yescharacteristic, complemented
67C2×(C2×D59)⋊C8C2211yescharacteristic
68C2×(C2×D59)⋊C8C2211yescharacteristic
69C2×#121×C59C2211yescharacteristic
70C22×C4⋊C4×C59C2211yescharacteristic, complemented
71C59×#481C2218yescomplemented
72C2×#106×C59C2211yescharacteristic, complemented
73C2×#106×C59C2211yescharacteristic, complemented
74C2×#102×C59C2211yescharacteristic
75C2×#102×C59C2211yescharacteristic
76C2×C22⋊C8×C59C2211yescharacteristic, complemented
77C24×D59—21no—
78C2×#11745685—22no—
79C2×#11745685—42no—
80C2×#11745685—42no—
81C2×#11745685—42no—
82C2×#11745685—42no—
83C2×#11745685D414yes—
84C2×#11745685C2314yes—
85C2×#11745685C2314yescomplemented
86C22×Dic118D411yescharacteristic
87C22×Dic118C2311yescharacteristic
88C22×D236—21no—
89C22×D236—21no—
90C22×D236—21no—
91C22×D236D411yescharacteristic
92C22×D236C2311yescharacteristic
93C22×D236C2311yescharacteristic
94C22×C22⋊D59—21no—
95C22×C22⋊D59—21no—
96C22×C22⋊D59—21no—
97C22×C22⋊D59—21no—
98C22×C22⋊D59D411yescharacteristic
99C22×C22⋊D59D411yescharacteristic
100C2×D4×D59—22no—
101C2×D4×D59—42no—
102C2×D4×D59—42no—
103C2×D4×D59C2314yes—
104C22×C4×D59—21no—
105C22×C4×D59C2311yescharacteristic
106C22×C4×D59C2311yescharacteristic
107C2×#11745660—42no—
108C2×#11745660C2314yes—
109C2×#11745670—42no—
110C2×#11745670C2314yes—
111C2×D472—42no—
112C2×D472C2314yes—
113C2×#11745669—42no—
114C2×#11745669C2314yes—
115C2×#11745659—42no—
116C2×#11745659C2314yescomplemented
117C22×C59⋊C8C2311yescharacteristic
118C22×C59⋊C8C2311yescharacteristic
119C2×C8×D59—42no—
120C2×C8×D59C2314yescomplemented
121#14273723—28no—
122#14273713—28no—
123#14273707—22no—
124#14273707—22no—
125#14273707—28no—
126#14273707C2314yes—
127#14273707C2314yescomplemented
128#14273702—28no—
129#14273702—22no—
130#14273702—22no—
131#14273702—22no—
132#14273702C2314yes—
133#14273702C2314yes—
134#14273702C2314yescomplemented
135#14273701—22no—
136#14273701—28no—
137#14273701—28no—
138#14273701C2314yes—
139#14273698—22no—
140#14273698C2314yes—
141#14273697—28no—
142#14273695—28no—
143#14273685—22no—
144#14273685C2314yes—
145C2×C4⋊Dic59—21no—
146C2×C4⋊Dic59—21no—
147C2×C4⋊Dic59C2311yescharacteristic
148C2×C22⋊Dic59—21no—
149C2×(C2×D59)⋊C4—21no—
150C2×(C2×D59)⋊C4—21no—
151C2×(C2×D59)⋊C4—21no—
152C2×(C2×D59)⋊C4—21no—
153C2×(C2×D59)⋊C4—21no—
154C2×(C2×D59)⋊C4—21no—
155C2×(C2×D59)⋊C4—21no—
156C2×C4×Dic59—21no—
157#14273660C2314yescomplemented
158#14273660C2314yescomplemented
159#14273652C2314yescomplemented
160#14273650C2314yescomplemented
161#14273649C2314yescomplemented
162#14273647C2314yes—
163#14273647C2314yes—
164#14273647C2314yescomplemented
165C22⋊(C59⋊C8)C2314yescomplemented
166(C2×D59)⋊C8C2314yes—
167(C2×D59)⋊C8C2314yes—
168C22×D4×C59—21no—
169C22×D4×C59C2311yescharacteristic
170C23×C4×C59—21no—
171C23×C4×C59C2311yescharacteristic
172C22×C8×C59C2311yescharacteristic
173C22×C8×C59C2311yescharacteristic
174#121×C59—22no—
175#121×C59C2314yes—
176C2×C4⋊C4×C59—21no—
177C2×C4⋊C4×C59—22no—
178C2×C4⋊C4×C59C2311yescharacteristic
179C2×C4⋊C4×C59C2311yescharacteristic
180C2×C4⋊C4×C59C2311yescharacteristic
181C2×C4⋊C4×C59C2314yescomplemented
182C2×C22⋊C4×C59—21no—
183#106×C59C2314yescomplemented
184#106×C59C2314yescomplemented
185#102×C59C2314yes—
186#102×C59C2314yes—
187C22⋊C8×C59C2314yescomplemented
188C24×C59—21no—
189C24×C59C2×D411yescharacteristic
190C23×D59—21no—
191C23×D59—21no—
192C23×D59—24no—
193C23×D59—44no—
194C23×D59—82no—
195C23×D59—82no—
196C23×D59C2×D411yescharacteristic
197C23×D59C2×D411yescharacteristic
198C2×D4×C59—24no—
199C2×D4×C59—21no—
200C2×D4×C59—22no—
201C2×D4×C59—22no—
202C2×D4×C59—82no—
203C2×D4×C59C2412yes—
204C22×C4×C59—22no—
205C22×C4×C59—22no—
206C22×C4×C59—21no—
207C22×C4×C59—21no—
208C22×C4×C59—21no—
209C22×C4×C59—24no—
210C22×C4×C59—82no—
211C22×C4×C59C2×D411yescharacteristic
212C22×C4×C59C2×D412yes—
213C22×C4×C59C2412yes—
214C22×C4×C59C2411yescharacteristic
215C2×C22⋊D59—24no—
216C2×C22⋊D59—24no—
217C2×C22⋊D59—24no—
218C2×C22⋊D59—24no—
219C2×C22⋊D59—42no—
220C2×C22⋊D59—42no—
221C2×C22⋊D59—44no—
222C2×C22⋊D59—44no—
223C2×C22⋊D59—82no—
224C2×C22⋊D59—82no—
225C2×C22⋊D59C2×D414yes—
226C2×C22⋊D59C2×D414yes—
227C22×Dic59—21no—
228C22×Dic59—21no—
229C22×Dic59C2×D411yescharacteristic
230C22×Dic59C2×D411yescharacteristic
231D4×D59—44no—
232D4×D59—44no—
233D4×D59—48no—
234#11745685—44no—
235#11745685—44no—
236#11745685—48no—
237#11745685—44no—
238#11745685—44no—
239#11745685—48no—
240C2×D236—22no—
241C2×D236—22no—
242C2×D236—22no—
243C2×D236—22no—
244C2×D236—21no—
245C2×D236—21no—
246C2×D236—24no—
247C2×D236—24no—
248C2×D236—24no—
249C2×D236—42no—
250C2×D236—82no—
251C2×D236—82no—
252C2×D236—82no—
253C2×D236C2×D414yes—
254C2×D236C2412yes—
255C2×D236C2412yes—
256C2×C4×D59—22no—
257C2×C4×D59—22no—
258C2×C4×D59—22no—
259C2×C4×D59—22no—
260C2×C4×D59—24no—
261C2×C4×D59—44no—
262C2×C4×D59C2×D412yes—
263C2×C4×D59C2×D412yes—
264C2×C4×D59C2412yes—
265C2×C4×D59C2412yes—
266C2×Dic118—22no—
267C2×Dic118—22no—
268C2×Dic118—21no—
269C2×Dic118—42no—
270C2×Dic118C2×D414yes—
271C2×Dic118C2412yes—
272C2×C8×C59—22no—
273C2×C8×C59—22no—
274C2×C8×C59C2412yes—
275C2×C8×C59C2412yes—
276C4⋊C4×C59—21no—
277C4⋊C4×C59—21no—
278C4⋊C4×C59—24no—
279C4⋊C4×C59—21no—
280C4⋊C4×C59C2412yes—
281C4⋊C4×C59C2412yes—
282C4⋊C4×C59C2412yes—
283C22⋊C4×C59—24no—
284C22⋊Dic59—24no—
285#11745670—44no—
286#11745669—44no—
287(C2×D59)⋊C4—24no—
288(C2×D59)⋊C4—24no—
289(C2×D59)⋊C4—24no—
290(C2×D59)⋊C4—24no—
291(C2×D59)⋊C4—24no—
292(C2×D59)⋊C4—24no—
293(C2×D59)⋊C4—24no—
294C4⋊Dic59—21no—
295C4⋊Dic59—24no—
296C4⋊Dic59—24no—
297C4⋊Dic59C2412yes—
298C4×Dic59—24no—
299C2×C59⋊C8—22no—
300C2×C59⋊C8—22no—
301C2×C59⋊C8C2412yes—
302C2×C59⋊C8C2412yes—
303D472—44no—
304#11745660—44no—
305#11745659—44no—
306C8×D59—44no—
307C23×C59—22no—
308C23×C59—22no—
309C23×C59—22no—
310C23×C59—22no—
311C23×C59—42no—
312C23×C59—42no—
313C23×C59—42no—
314C23×C59C22×D412yes—
315C23×C59C22×D411yescharacteristic
316C22×D59—22no—
317C22×D59—22no—
318C22×D59—22no—
319C22×D59—22no—
320C22×D59—22no—
321C22×D59—22no—
322C22×D59—22no—
323C22×D59—22no—
324C22×D59—48no—
325C22×D59—42no—
326C22×D59—42no—
327C22×D59—42no—
328C22×D59—42no—
329C22×D59—42no—
330C22×D59—42no—
331C22×D59—84no—
332C22×D59—84no—
333C22×D59—816no—
334C22×D59C22×D412yes—
335C22×D59C22×D412yes—
336D4×C59—22no—
337D4×C59—22no—
338D4×C59—42no—
339D4×C59—84no—
340C2×C4×C59—22no—
341C2×C4×C59—24no—
342C2×C4×C59—22no—
343C2×C4×C59—22no—
344C2×C4×C59—22no—
345C2×C4×C59—22no—
346C2×C4×C59—22no—
347C2×C4×C59—42no—
348C2×C4×C59—42no—
349C2×C4×C59—42no—
350C2×C4×C59—84no—
351C2×C4×C59C22×D412yes—
352C2×C4×C59C22×D411yescharacteristic
353C2×C4×C59H(5,𝔽2)12yes—
354C2×C4×C59H(5,𝔽2)12yes—
355C2×C4×C59C2511yescharacteristic
356C22⋊D59—44no—
357C22⋊D59—44no—
358C22⋊D59—48no—
359C22⋊D59—48no—
360C22⋊D59—84no—
361C22⋊D59—84no—
362C2×Dic59—22no—
363C2×Dic59—22no—
364C2×Dic59—22no—
365C2×Dic59—22no—
366C2×Dic59—42no—
367C2×Dic59—42no—
368C2×Dic59C22×D412yes—
369C2×Dic59C22×D412yes—
370D236—22no—
371D236—22no—
372D236—22no—
373D236—22no—
374D236—44no—
375D236—42no—
376D236—42no—
377D236—84no—
378D236—84no—
379D236—84no—
380C4×D59—24no—
381C4×D59—24no—
382C4×D59—22no—
383C4×D59—22no—
384C4×D59—22no—
385C4×D59—22no—
386C4×D59—48no—
387Dic118—22no—
388Dic118—22no—
389Dic118—44no—
390Dic118—42no—
391C8×C59—22no—
392C8×C59—22no—
393C59⋊C8—22no—
394C59⋊C8—22no—
395C2×#3198—591nomaximal, Sylow
396C22×C59—22no—
397C22×C59—22no—
398C22×C59—22no—
399C22×C59—44no—
400C22×C59—42no—
401C22×C59—42no—
402C22×C59—42no—
403C22×C59—84no—
404C22×C59#53412yes—
405C22×C59#57612yes—
406C22×C59#57712yes—
407C22×C59C23×D411yescharacteristic
408C2×D59—22no—
409C2×D59—22no—
410C2×D59—22no—
411C2×D59—22no—
412C2×D59—22no—
413C2×D59—22no—
414C2×D59—44no—
415C2×D59—44no—
416C2×D59—42no—
417C2×D59—42no—
418C2×D59—42no—
419C2×D59—42no—
420C2×D59—42no—
421C2×D59—42no—
422C2×D59—816no—
423C2×D59—84no—
424C2×D59—84no—
425C4×C59—22no—
426C4×C59—42no—
427C4×C59—42no—
428C4×C59—42no—
429C4×C59#53412yes—
430C4×C59C2×H(5,𝔽2)11yescharacteristic
431C4×C59C2×H(5,𝔽2)11yescharacteristic
432Dic59—22no—
433Dic59—22no—
434Dic59—42no—
435Dic59—42no—
436C2×#537—591no—
437C2×#535—591no—
438#3198—5916no—
439C2×#481D5911yescharacteristic, complemented
440C2×#485—591no—
441C2×#482—591no—
442C2×#480—591no—
443C2×#469—591no—
444C2×#468—591no—
445C2×#466—591no—
446C2×#465—591no—
447C2×#449—591no—
448C2×#449—591no—
449C2×#450—591no—
450C2×#447—591no—
451C2×#408—591no—
452C2×C59—42no—
453C2×C59—82no—
454C2×C59#319814yescomplemented
455C2×C59C2×#53411yescharacteristic
456C2×C59C2×#57611yescharacteristic
457C2×C59C2×#57711yescharacteristic
458D59—42no—
459D59—42no—
460D59—82no—
461D59—82no—
462C22×#41—591no—
463C22×#41—591no—
464C23×D4—591no—
465C22×SD16—591no—
466C22×SD16—591no—
467C22×D8—591no—
468C22×D8—591no—
469C22×M16—591no—
470C23×C8—591no—
471#537—598no—
472#537—1184no—
473#535—598no—
474#535—1184no—
475C2×#127—1181no—
476C2×#124—1181no—
477C2×C22⋊Q8—591no—
478C2×C22⋊Q8—591no—
479C2×C22⋊Q8—1181no—
480C2×#121—591no—
481C2×#121—591no—
482C2×#121—591no—
483C2×#121—591no—
484C2×#121—591no—
485C2×#121—1181no—
486C2×#121—1181no—
487C2×#121—1181no—
488C2×#121C2×D5911yescharacteristic
489C2×#120—1181no—
490C2×#120—1181no—
491C2×#117—591no—
492C22×C4⋊C4C2×D5911yescharacteristic, complemented
493#485—598no—
494#482—598no—
495#481C2×D5918yescomplemented
496#480—598no—
497#469—598no—
498#468—598no—
499#466—598no—
500#465—598no—
501#450—598no—
502#449—598no—
503#449—598no—
504#447—598no—
505C2×#107—591no—
506C2×#107—591no—
507C2×#106C2×D5911yescharacteristic, complemented
508C2×#106C2×D5911yescharacteristic, complemented
509C2×#103—591no—
510C2×#103—591no—
511C2×#102—591no—
512C2×#102—591no—
513C2×#102—591no—
514C2×#102—591no—
515C2×#102C2×D5911yescharacteristic
516C2×#102C2×D5911yescharacteristic
517#408—598no—
518C2×C22⋊C8—591no—
519C2×C22⋊C8—591no—
520C2×C22⋊C8—591no—
521C2×C22⋊C8C2×D5911yescharacteristic, complemented
522C59C2×#319811yescharacteristic, complemented, Sylow
523C25—1181no—
524C2×#41—594no—
525C2×#41—594no—
526C2×#41—594no—
527C2×#41—1182no—
528C2×#41—2362no—
529C2×#41—2362no—
530C2×#41—2362no—
531C2×#41—2362no—
532C22×Q8—591no—
533C22×Q8—591no—
534C22×D4—21no—
535C22×D4—591no—
536C22×D4—591no—
537C22×D4—594no—
538C22×D4—591no—
539C22×D4—591no—
540C22×D4—591no—
541C22×D4—1181no—
542C22×D4—1181no—
543C22×D4—1181no—
544C22×D4—1182no—
545C22×D4—1181no—
546C22×D4—1181no—
547C22×D4—1181no—
548C22×D4—1181no—
549C22×D4—2362no—
550C22×D4—2362no—
551C22×D4C22×D5911yescharacteristic
552C23×C4—21no—
553C23×C4—591no—
554C23×C4—591no—
555C23×C4—1181no—
556C23×C4C22×D5911yescharacteristic
557C2×SD16—594no—
558C2×SD16—594no—
559C2×SD16—2362no—
560C2×SD16—2362no—
561C2×D8—594no—
562C2×D8—594no—
563C2×D8—2362no—
564C2×D8—2362no—
565C2×M16—594no—
566C2×M16—2362no—
567C22×C8—591no—
568C22×C8—591no—
569C22×C8—594no—
570C22×C8—2362no—
571C22×C8C22×D5911yescharacteristic
572C22×C8C22×D5911yescharacteristic
573#127—1188no—
574#124—1188no—
575C22⋊Q8—594no—
576C22⋊Q8—594no—
577C22⋊Q8—1182no—
578C22⋊Q8—1182no—
579C22⋊Q8—1188no—
580#121—22no—
581#121—594no—
582#121—594no—
583#121—594no—
584#121—594no—
585#121—594no—
586#121—1182no—
587#121—1182no—
588#121—1182no—
589#121—1188no—
590#121—1188no—
591#121—1188no—
592#121—1182no—
593#121—1182no—
594#121C22×D5914yes—
595#120—1188no—
596#120—1188no—
597#117—594no—
598#117—1182no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—22no—
601C2×C4⋊C4—591no—
602C2×C4⋊C4—1181no—
603C2×C4⋊C4—1181no—
604C2×C4⋊C4C22×D5911yescharacteristic
605C2×C4⋊C4C22×D5911yescharacteristic
606C2×C4⋊C4C22×D5911yescharacteristic
607C2×C4⋊C4C22×D5914yescomplemented
608C2×C22⋊C4—21no—
609C2×C22⋊C4—1181no—
610C2×C22⋊C4—1181no—
611C2×C22⋊C4—1181no—
612C2×C22⋊C4—1181no—
613C2×C22⋊C4—1181no—
614C2×C22⋊C4—1181no—
615C2×C22⋊C4—1181no—
616C2×C22⋊C4—1181no—
617C2×C42—1181no—
618#107—594no—
619#107—594no—
620#106C22×D5914yescomplemented
621#106C22×D5914yescomplemented
622#103—594no—
623#103—594no—
624#102—594no—
625#102—594no—
626#102—594no—
627#102—594no—
628#102C22×D5914yes—
629#102C22×D5914yes—
630C22⋊C8—594no—
631C22⋊C8—594no—
632C22⋊C8—594no—
633C22⋊C8C22×D5914yescomplemented
634C24—21no—
635C24—591no—
636C24—591no—
637C24—1184no—
638C24—1181no—
639C24—1181no—
640C24—4722no—
641C24—4722no—
642C24—2364no—
643C24D4×D5911yescharacteristic
644#41—2368no—
645#41—2364no—
646#41—2364no—
647#41—2364no—
648#41—2364no—
649#41—2368no—
650C2×Q8—594no—
651C2×Q8—592no—
652C2×Q8—1181no—
653C2×Q8—1182no—
654C2×Q8—1182no—
655C2×Q8—2362no—
656C2×D4—24no—
657C2×D4—21no—
658C2×D4—22no—
659C2×D4—22no—
660C2×D4—82no—
661C2×D4—594no—
662C2×D4—594no—
663C2×D4—594no—
664C2×D4—592no—
665C2×D4—592no—
666C2×D4—1184no—
667C2×D4—1184no—
668C2×D4—1184no—
669C2×D4—1184no—
670C2×D4—1184no—
671C2×D4—1184no—
672C2×D4—1184no—
673C2×D4—1181no—
674C2×D4—1181no—
675C2×D4—1182no—
676C2×D4—1182no—
677C2×D4—1182no—
678C2×D4—1182no—
679C2×D4—4722no—
680C2×D4—4722no—
681C2×D4—4722no—
682C2×D4—4722no—
683C2×D4—4722no—
684C2×D4—2362no—
685C2×D4—2364no—
686C2×D4—2364no—
687C2×D4—2368no—
688C2×D4—2362no—
689C2×D4—2362no—
690C2×D4—2364no—
691C2×D4—2364no—
692C2×D4C23×D5912yes—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—24no—
699C22×C4—82no—
700C22×C4—591no—
701C22×C4—591no—
702C22×C4—592no—
703C22×C4—592no—
704C22×C4—592no—
705C22×C4—592no—
706C22×C4—1182no—
707C22×C4—1182no—
708C22×C4—1182no—
709C22×C4—1182no—
710C22×C4—1181no—
711C22×C4—1181no—
712C22×C4—1184no—
713C22×C4—2364no—
714C22×C4D4×D5912yes—
715C22×C4D4×D5911yescharacteristic
716C22×C4C23×D5912yes—
717C22×C4C23×D5911yescharacteristic
718SD16—2364no—
719SD16—2364no—
720D8—2364no—
721D8—2364no—
722M16—2364no—
723C2×C8—22no—
724C2×C8—22no—
725C2×C8—592no—
726C2×C8—592no—
727C2×C8—1182no—
728C2×C8—1182no—
729C2×C8—2364no—
730C2×C8C23×D5912yes—
731C2×C8C23×D5912yes—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—24no—
735C4⋊C4—21no—
736C4⋊C4—592no—
737C4⋊C4—1184no—
738C4⋊C4—1184no—
739C4⋊C4—1181no—
740C4⋊C4C23×D5912yes—
741C4⋊C4C23×D5912yes—
742C4⋊C4C23×D5912yes—
743C22⋊C4—24no—
744C22⋊C4—1184no—
745C22⋊C4—1184no—
746C22⋊C4—1184no—
747C22⋊C4—1184no—
748C22⋊C4—1184no—
749C22⋊C4—1184no—
750C22⋊C4—1184no—
751C22⋊C4—1184no—
752C42—1184no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—42no—
758C23—42no—
759C23—42no—
760C23—592no—
761C23—592no—
762C23—1182no—
763C23—1182no—
764C23—1182no—
765C23—1182no—
766C23—1182no—
767C23—1182no—
768C23—1182no—
769C23—1182no—
770C23—4724no—
771C23—4724no—
772C23—47216no—
773C23—2368no—
774C23—2362no—
775C23—2362no—
776C23—2362no—
777C23—2362no—
778C23—2362no—
779C23—2362no—
780C23C2×D4×D5912yes—
781C23C2×D4×D5911yescharacteristic
782Q8—1182no—
783Q8—1182no—
784Q8—2364no—
785Q8—2362no—
786D4—22no—
787D4—22no—
788D4—42no—
789D4—84no—
790D4—1182no—
791D4—1182no—
792D4—1182no—
793D4—1182no—
794D4—4724no—
795D4—4724no—
796D4—4724no—
797D4—4724no—
798D4—4724no—
799D4—2364no—
800D4—2364no—
801D4—2364no—
802D4—2368no—
803D4—2368no—
804D4—2362no—
805D4—2362no—
806C2×C4—22no—
807C2×C4—24no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—84no—
817C2×C4—592no—
818C2×C4—592no—
819C2×C4—1182no—
820C2×C4—1182no—
821C2×C4—1184no—
822C2×C4—1184no—
823C2×C4—1182no—
824C2×C4—1182no—
825C2×C4—1182no—
826C2×C4—1182no—
827C2×C4—1182no—
828C2×C4—1182no—
829C2×C4—2368no—
830C2×C4—2362no—
831C2×C4—2362no—
832C2×C4C2×D4×D5912yes—
833C2×C4C2×D4×D5911yescharacteristic
834C2×C4#1427377312yes—
835C2×C4#1427377312yes—
836C2×C4C24×D5911yescharacteristic
837C8—22no—
838C8—22no—
839C8—1182no—
840C8—1182no—
841C22—22no—
842C22—22no—
843C22—22no—
844C22—44no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—84no—
849C22—1182no—
850C22—1182no—
851C22—1182no—
852C22—1182no—
853C22—1182no—
854C22—1182no—
855C22—47216no—
856C22—4724no—
857C22—4724no—
858C22—2362no—
859C22—2362no—
860C22—2362no—
861C22—2362no—
862C22—2362no—
863C22—2362no—
864C22—2364no—
865C22—2364no—
866C22#1683796312yes—
867C22#1683820612yes—
868C22#1683820812yes—
869C22C22×D4×D5911yescharacteristic
870C4—22no—
871C4—42no—
872C4—42no—
873C4—42no—
874C4—1182no—
875C4—1182no—
876C4—2362no—
877C4—2362no—
878C4#1683796312yes—
879C4C2×#1427377311yescharacteristic
880C4C2×#1427377311yescharacteristic
881C2—42no—
882C2—82no—
883C2—4722no—
884C2—4722no—
885C2—2362no—
886C2—2362no—
887C2#2143495314yesdirect product factor
888C2C2×#1683796311yescharacteristic
889C2C2×#1683820611yescharacteristic
890C2C2×#1683820811yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#481C2
socleC23×C59C22×D4
hypercenterC2×#481D59
hypocenterC59C2×#3198
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#481

Complements

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

NH ≅ G/Ntype
1. C2×#16837983C2semidirect
2. C2×#16837968C2semidirect
3. #21434953C2direct (N × H)
4. C2×#16837746C2semidirect
5. C2×#16837728C2semidirect
6. C2×#16837715C2semidirect
7. C2×#16837656C2semidirect
8. C2×#16837647C2semidirect
9. C2×#16837637C2semidirect
10. C2×#16837632C2semidirect
11. C2×#16837549C2semidirect
12. C2×#16837545C2semidirect
13. C2×#16837554C2semidirect
14. C2×#16837537C2semidirect
15. C2×#16837367C2semidirect
16. C2×C59×#481C2semidirect
18. C22×#11745685C22semidirect
24. C22×#11745659C22semidirect
25. C22×C8×D59C22semidirect
27. #16837983C22semidirect
29. #16837968C22semidirect
34. C2×#14273707C22semidirect
38. C2×#14273702C22semidirect
46. #16837746C22semidirect
47. #16837728C22semidirect
48. #16837715C22semidirect
49. #16837656C22semidirect
50. #16837647C22semidirect
51. #16837637C22semidirect
52. #16837632C22semidirect
53. #16837554C22semidirect
54. #16837549C22semidirect
55. #16837545C22semidirect
56. #16837537C22semidirect
57. C2×#14273660C22semidirect
58. C2×#14273660C22semidirect
59. C2×#14273652C22semidirect
60. C2×#14273650C22semidirect
61. C2×#14273649C22semidirect
64. C2×#14273647C22semidirect
65. #16837367C22semidirect
66. C2×C22⋊(C59⋊C8)C22semidirect
70. C22×C4⋊C4×C59C22semidirect
71. C59×#481C22semidirect
72. C2×#106×C59C22semidirect
73. C2×#106×C59C22semidirect
76. C2×C22⋊C8×C59C22semidirect
85. C2×#11745685C23semidirect
116. C2×#11745659C23semidirect
120. C2×C8×D59C23semidirect
127. #14273707C23semidirect
134. #14273702C23semidirect
157. #14273660C23semidirect
158. #14273660C23semidirect
159. #14273652C23semidirect
160. #14273650C23semidirect
161. #14273649C23semidirect
164. #14273647C23semidirect
165. C22⋊(C59⋊C8)C23semidirect
181. C2×C4⋊C4×C59C23semidirect
183. #106×C59C23semidirect
184. #106×C59C23semidirect
187. C22⋊C8×C59C23semidirect
439. C2×#481D59semidirect
454. C2×C59#3198semidirect
492. C22×C4⋊C4C2×D59semidirect
495. #481C2×D59semidirect
507. C2×#106C2×D59semidirect
508. C2×#106C2×D59semidirect
521. C2×C22⋊C8C2×D59semidirect
522. C59C2×#3198semidirect
607. C2×C4⋊C4C22×D59semidirect
620. #106C22×D59semidirect
621. #106C22×D59semidirect
633. C22⋊C8C22×D59semidirect
887. C2#21434953direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168379832
C2×#168379682
#214349532
C2×#168377462
C2×#168377282
C2×#168377152
C2×#168376562
C2×#168376472
C2×#168376372
C2×#168376322
C2×#168375492
C2×#168375452
C2×#168375542
C2×#168375372
C2×#168373672
C2×C59×#4812
C2×#319859