Finite Group Databasebeta

← C2×#21434949 #29459343

Subgroups — C2×#21434949 #29459343

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×#16837982C211yesmaximal, characteristic, complemented
2C2×#16837968C211yesmaximal, characteristic, complemented
3#21434949C2116yesmaximal, direct product factor
4C2×#16837719C211yesmaximal, characteristic, complemented
5C2×#16837741C211yesmaximal, characteristic, complemented
6C2×#16837729C211yesmaximal, characteristic, complemented
7C2×#16837717C211yesmaximal, characteristic, complemented
8C2×#16837655C211yesmaximal, characteristic, complemented
9C2×#16837636C211yesmaximal, characteristic, complemented
10C2×#16837633C211yesmaximal, characteristic, complemented
11C2×#16837550C211yesmaximal, characteristic, complemented
12C2×#16837546C211yesmaximal, characteristic, complemented
13C2×#16837551C211yesmaximal, characteristic, complemented
14C2×#16837537C211yesmaximal, characteristic, complemented
15C2×#16837370C211yesmaximal, characteristic, complemented
16C2×C59×#468C211yesmaximal, characteristic, complemented
17C22×#11745689C2211yescharacteristic, complemented
18C22×#11745685C2211yescharacteristic
19C22×D4×D59C2211yescharacteristic
20C22×#11745671C2211yescharacteristic
21C22×D472C2211yescharacteristic
22C22×#11745669C2211yescharacteristic
23C23×C59⋊C8C2211yescharacteristic, complemented
24#16837982—24no—
25#16837982C2218yescomplemented
26#16837968—24no—
27#16837968C2218yescomplemented
28C2×#14273723—21no—
29C2×#14273713—21no—
30C2×#14273705—21no—
31C2×#14273703C2211yescharacteristic
32C2×#14273702—21no—
33C2×#14273702C2211yescharacteristic
34C2×#14273702C2211yescharacteristic
35C2×#14273701C2211yescharacteristic
36C2×#14273701C2211yescharacteristic, complemented
37C2×#14273700—21no—
38C2×#14273700—21no—
39C2×#14273698C2211yescharacteristic
40C2×#14273697—21no—
41C2×#14273695—21no—
42C2×#14273685C2211yescharacteristic
43C2×C4⋊C4×D59C2211yescharacteristic, complemented
44#16837741C2218yescomplemented
45#16837729C2218yescomplemented
46#16837719C2218yescomplemented
47#16837717C2218yescomplemented
48#16837655C2218yescomplemented
49#16837636C2218yescomplemented
50#16837633C2218yescomplemented
51#16837551C2218yescomplemented
52#16837550C2218yescomplemented
53#16837546C2218yescomplemented
54#16837537C2218yescomplemented
55C2×#14273660C2211yescharacteristic, complemented
56C2×#14273659C2211yescharacteristic, complemented
57C2×#14273658C2211yescharacteristic, complemented
58C2×#14273651C2211yescharacteristic, complemented
59C2×#14273649C2211yescharacteristic
60C2×#14273649C2211yescharacteristic, complemented
61C2×#14273648C2211yescharacteristic
62C2×#14273647C2211yescharacteristic
63C2×#14273647C2211yescharacteristic, complemented
64#16837370C2218yescomplemented
65C2×(C2×D59)⋊C8C2211yescharacteristic
66C2×(C2×D59)⋊C8C2211yescharacteristic
67C2×(C2×D59)⋊C8C2211yescharacteristic, complemented
68C2×(C2×D59)⋊C8C2211yescharacteristic, complemented
69C22×SD16×C59C2211yescharacteristic
70C22×M16×C59C2211yescharacteristic, complemented
71C2×C22⋊Q8×C59C2211yescharacteristic, complemented
72C2×#121×C59C2211yescharacteristic
73C59×#468C2218yescomplemented
74C2×#107×C59C2211yescharacteristic, complemented
75C2×#103×C59C2211yescharacteristic, complemented
76C2×#102×C59C2211yescharacteristic
77C24×D59—21no—
78C2×#11745689—22no—
79C2×#11745689—42no—
80C2×#11745689—42no—
81C2×#11745689C2314yescomplemented
82C2×#11745685—42no—
83C2×#11745685—42no—
84C2×#11745685D414yes—
85C2×#11745685C2314yes—
86C22×Dic118D411yescharacteristic
87C22×D236—21no—
88C22×D236—21no—
89C22×D236—21no—
90C22×D236D411yescharacteristic
91C22×D236C2311yescharacteristic
92C22×D236C2311yescharacteristic
93C22×C22⋊D59—21no—
94C22×C22⋊D59—21no—
95C22×C22⋊D59—21no—
96C22×C22⋊D59—21no—
97C22×C22⋊D59D411yescharacteristic
98C22×C22⋊D59D411yescharacteristic
99C2×D4×D59—22no—
100C2×D4×D59—42no—
101C2×D4×D59—42no—
102C2×D4×D59C2314yes—
103C22×C4×D59—21no—
104C22×C4×D59—21no—
105C22×C4×D59C2311yescharacteristic
106C22×C4×D59C2311yescharacteristic
107C2×#11745671—42no—
108C2×#11745671C2314yes—
109C2×D472—42no—
110C2×D472C2314yes—
111C2×#11745669—42no—
112C2×#11745669C2314yes—
113C22×C59⋊C8—42no—
114C22×C59⋊C8C2311yescharacteristic
115C22×C59⋊C8C2311yescharacteristic
116C22×C59⋊C8C2314yescomplemented
117#14273723—28no—
118#14273713—28no—
119#14273705—28no—
120#14273703—22no—
121#14273703C2314yes—
122#14273702—28no—
123#14273702—22no—
124#14273702—22no—
125#14273702C2314yes—
126#14273702C2314yes—
127#14273701—22no—
128#14273701—22no—
129#14273701C2314yes—
130#14273701C2314yescomplemented
131#14273700—28no—
132#14273700—28no—
133#14273698—22no—
134#14273698C2314yes—
135#14273697—28no—
136#14273695—28no—
137#14273685—22no—
138#14273685C2314yes—
139C2×C4⋊Dic59C2311yescharacteristic
140C2×C4⋊Dic59C2311yescharacteristic
141C2×Dic59⋊C4—21no—
142C2×Dic59⋊C4—21no—
143C4⋊C4×D59—22no—
144C4⋊C4×D59C2314yescomplemented
145C2×C22⋊Dic59—21no—
146C2×(C2×D59)⋊C4—21no—
147C2×(C2×D59)⋊C4—21no—
148C2×(C2×D59)⋊C4—21no—
149C2×(C2×D59)⋊C4—21no—
150C2×(C2×D59)⋊C4—21no—
151C2×(C2×D59)⋊C4—21no—
152C2×C4×Dic59—21no—
153#14273660C2314yescomplemented
154#14273659C2314yescomplemented
155#14273658C2314yescomplemented
156#14273651C2314yescomplemented
157#14273649C2314yes—
158#14273649C2314yescomplemented
159#14273648C2314yes—
160#14273647C2314yes—
161#14273647C2314yescomplemented
162(C2×D59)⋊C8C2314yes—
163(C2×D59)⋊C8C2314yes—
164(C2×D59)⋊C8C2314yescomplemented
165(C2×D59)⋊C8C2314yescomplemented
166C22×Q8×C59C2311yescharacteristic
167C22×D4×C59—21no—
168C22×D4×C59C2311yescharacteristic
169C23×C4×C59C2311yescharacteristic
170C2×SD16×C59—42no—
171C2×SD16×C59C2314yes—
172C2×M16×C59—42no—
173C2×M16×C59C2314yescomplemented
174C22×C8×C59C2311yescharacteristic
175C22×C8×C59C2311yescharacteristic
176C22⋊Q8×C59—22no—
177C22⋊Q8×C59C2314yescomplemented
178#121×C59—22no—
179#121×C59C2314yes—
180C2×C4⋊C4×C59—21no—
181C2×C4⋊C4×C59C2311yescharacteristic
182C2×C4⋊C4×C59C2311yescharacteristic
183C2×C22⋊C4×C59—21no—
184C2×C22⋊C4×C59—21no—
185#107×C59C2314yescomplemented
186#103×C59C2314yescomplemented
187#102×C59C2314yes—
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×Q8×C59—21no—
199C2×Q8×C59—22no—
200C2×Q8×C59—22no—
201C2×Q8×C59C2412yes—
202C2×D4×C59—24no—
203C2×D4×C59—21no—
204C2×D4×C59—22no—
205C2×D4×C59—22no—
206C2×D4×C59—82no—
207C2×D4×C59C2412yes—
208C22×C4×C59—22no—
209C22×C4×C59—22no—
210C22×C4×C59—21no—
211C22×C4×C59—21no—
212C22×C4×C59—21no—
213C22×C4×C59C2×D411yescharacteristic
214C22×C4×C59C2×D412yes—
215C22×C4×C59C2412yes—
216C22×C4×C59C2411yescharacteristic
217C2×C22⋊D59—24no—
218C2×C22⋊D59—24no—
219C2×C22⋊D59—24no—
220C2×C22⋊D59—24no—
221C2×C22⋊D59—42no—
222C2×C22⋊D59—42no—
223C2×C22⋊D59—44no—
224C2×C22⋊D59—82no—
225C2×C22⋊D59—82no—
226C2×C22⋊D59—82no—
227C2×C22⋊D59C2×D414yes—
228C2×C22⋊D59C2×D414yes—
229C22×Dic59—21no—
230C22×Dic59—21no—
231C22×Dic59C2×D411yescharacteristic
232C22×Dic59C2×D411yescharacteristic
233#11745689—44no—
234#11745689—44no—
235#11745689—48no—
236D4×D59—44no—
237D4×D59—44no—
238D4×D59—48no—
239#11745685—48no—
240#11745685—44no—
241#11745685—44no—
242C2×D236—22no—
243C2×D236—22no—
244C2×D236—22no—
245C2×D236—22no—
246C2×D236—24no—
247C2×D236—21no—
248C2×D236—21no—
249C2×D236—24no—
250C2×D236—24no—
251C2×D236—42no—
252C2×D236—44no—
253C2×D236—82no—
254C2×D236—82no—
255C2×D236C2×D414yes—
256C2×D236C2412yes—
257C2×D236C2412yes—
258C2×C4×D59—22no—
259C2×C4×D59—22no—
260C2×C4×D59—22no—
261C2×C4×D59—22no—
262C2×C4×D59—24no—
263C2×C4×D59—24no—
264C2×C4×D59—44no—
265C2×C4×D59—82no—
266C2×C4×D59C2×D412yes—
267C2×C4×D59C2×D412yes—
268C2×C4×D59C2412yes—
269C2×C4×D59C2412yes—
270C2×Dic118—42no—
271C2×Dic118C2×D414yes—
272SD16×C59—44no—
273M16×C59—44no—
274C2×C8×C59—22no—
275C2×C8×C59—22no—
276C2×C8×C59C2412yes—
277C2×C8×C59C2412yes—
278C4⋊C4×C59—24no—
279C4⋊C4×C59—21no—
280C4⋊C4×C59—21no—
281C4⋊C4×C59C2412yes—
282C4⋊C4×C59C2412yes—
283C22⋊C4×C59—24no—
284C22⋊C4×C59—24no—
285C22⋊Dic59—24no—
286#11745671—44no—
287#11745669—44no—
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—21no—
296C4⋊Dic59C2412yes—
297C4⋊Dic59C2412yes—
298Dic59⋊C4—24no—
299Dic59⋊C4—24no—
300C4×Dic59—24no—
301C2×C59⋊C8—22no—
302C2×C59⋊C8—22no—
303C2×C59⋊C8—44no—
304C2×C59⋊C8C2412yes—
305C2×C59⋊C8C2412yes—
306D472—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—
336Q8×C59—22no—
337Q8×C59—22no—
338Q8×C59—42no—
339D4×C59—22no—
340D4×C59—22no—
341D4×C59—42no—
342D4×C59—84no—
343C2×C4×C59—22no—
344C2×C4×C59—24no—
345C2×C4×C59—22no—
346C2×C4×C59—22no—
347C2×C4×C59—22no—
348C2×C4×C59—22no—
349C2×C4×C59—22no—
350C2×C4×C59—42no—
351C2×C4×C59—42no—
352C2×C4×C59—42no—
353C2×C4×C59C22×D412yes—
354C2×C4×C59C22×D411yescharacteristic
355C2×C4×C59H(5,𝔽2)12yes—
356C2×C4×C59H(5,𝔽2)12yes—
357C2×C4×C59C2511yescharacteristic
358C22⋊D59—44no—
359C22⋊D59—44no—
360C22⋊D59—48no—
361C22⋊D59—84no—
362C22⋊D59—84no—
363C22⋊D59—84no—
364C2×Dic59—22no—
365C2×Dic59—22no—
366C2×Dic59—22no—
367C2×Dic59—22no—
368C2×Dic59—42no—
369C2×Dic59—42no—
370C2×Dic59C22×D412yes—
371C2×Dic59C22×D412yes—
372D236—22no—
373D236—22no—
374D236—22no—
375D236—22no—
376D236—44no—
377D236—48no—
378D236—42no—
379D236—42no—
380D236—84no—
381D236—84no—
382C4×D59—24no—
383C4×D59—24no—
384C4×D59—22no—
385C4×D59—22no—
386C4×D59—22no—
387C4×D59—22no—
388C4×D59—48no—
389C4×D59—84no—
390Dic118—44no—
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×#481—591no—
440C2×#485—591no—
441C2×#482—591no—
442C2×#480—591no—
443C2×#469—591no—
444C2×#468D5911yescharacteristic, complemented
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×SD16C2×D5911yescharacteristic
467C22×D8—591no—
468C22×D8—591no—
469C22×M16C2×D5911yescharacteristic, complemented
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—1181no—
479C2×C22⋊Q8C2×D5911yescharacteristic, complemented
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⋊C4—591no—
493#485—598no—
494#482—598no—
495#481—598no—
496#480—598no—
497#469—598no—
498#468C2×D5918yescomplemented
499#466—598no—
500#465—598no—
501#450—598no—
502#449—598no—
503#449—598no—
504#447—598no—
505C2×#107—591no—
506C2×#107C2×D5911yescharacteristic, complemented
507C2×#106—591no—
508C2×#106—591no—
509C2×#103—591no—
510C2×#103C2×D5911yescharacteristic, complemented
511C2×#102—591no—
512C2×#102—591no—
513C2×#102—591no—
514C2×#102—591no—
515C2×#102—591no—
516C2×#102C2×D5911yescharacteristic
517#408—598no—
518C2×C22⋊C8—591no—
519C2×C22⋊C8—591no—
520C2×C22⋊C8—591no—
521C2×C22⋊C8—591no—
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×Q8C22×D5911yescharacteristic
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—591no—
553C23×C4—591no—
554C23×C4—1181no—
555C23×C4—1181no—
556C23×C4C22×D5911yescharacteristic
557C2×SD16—42no—
558C2×SD16—594no—
559C2×SD16—2362no—
560C2×SD16C22×D5914yes—
561C2×D8—594no—
562C2×D8—594no—
563C2×D8—2362no—
564C2×D8—2362no—
565C2×M16—42no—
566C2×M16C22×D5914yescomplemented
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—22no—
576C22⋊Q8—594no—
577C22⋊Q8—1188no—
578C22⋊Q8—1182no—
579C22⋊Q8C22×D5914yescomplemented
580#121—22no—
581#121—594no—
582#121—594no—
583#121—594no—
584#121—594no—
585#121—594no—
586#121—1188no—
587#121—1188no—
588#121—1182no—
589#121—1182no—
590#121—1188no—
591#121—1182no—
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—591no—
601C2×C4⋊C4—591no—
602C2×C4⋊C4—594no—
603C2×C4⋊C4—1182no—
604C2×C4⋊C4—1181no—
605C2×C4⋊C4—1181no—
606C2×C4⋊C4C22×D5911yescharacteristic
607C2×C4⋊C4C22×D5911yescharacteristic
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
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#107C22×D5914yescomplemented
620#106—594no—
621#106—594no—
622#103—594no—
623#103C22×D5914yescomplemented
624#102—594no—
625#102—594no—
626#102—594no—
627#102—594no—
628#102—594no—
629#102C22×D5914yes—
630C22⋊C8—594no—
631C22⋊C8—594no—
632C22⋊C8—594no—
633C22⋊C8—594no—
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—21no—
651C2×Q8—22no—
652C2×Q8—22no—
653C2×Q8—594no—
654C2×Q8—2362no—
655C2×Q8C23×D5912yes—
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—2364no—
688C2×D4—2368no—
689C2×D4—2362no—
690C2×D4—2362no—
691C2×D4—2364no—
692C2×D4C23×D5912yes—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—591no—
699C22×C4—591no—
700C22×C4—592no—
701C22×C4—592no—
702C22×C4—592no—
703C22×C4—592no—
704C22×C4—1184no—
705C22×C4—1184no—
706C22×C4—1182no—
707C22×C4—1182no—
708C22×C4—1182no—
709C22×C4—1182no—
710C22×C4—1181no—
711C22×C4—1181no—
712C22×C4—4722no—
713C22×C4—2364no—
714C22×C4D4×D5912yes—
715C22×C4D4×D5911yescharacteristic
716C22×C4C23×D5912yes—
717C22×C4C23×D5911yescharacteristic
718SD16—44no—
719SD16—2364no—
720D8—2364no—
721D8—2364no—
722M16—44no—
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—24no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—592no—
736C4⋊C4—592no—
737C4⋊C4—1184no—
738C4⋊C4—1184no—
739C4⋊C4—1181no—
740C4⋊C4—1181no—
741C4⋊C4C23×D5912yes—
742C4⋊C4C23×D5912yes—
743C22⋊C4—24no—
744C22⋊C4—24no—
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—22no—
783Q8—22no—
784Q8—42no—
785Q8—2364no—
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—2368no—
801D4—2364no—
802D4—2364no—
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—592no—
817C2×C4—592no—
818C2×C4—1182no—
819C2×C4—1182no—
820C2×C4—1184no—
821C2×C4—1184no—
822C2×C4—1182no—
823C2×C4—1182no—
824C2×C4—1182no—
825C2×C4—1182no—
826C2×C4—1182no—
827C2×C4—1182no—
828C2×C4—4724no—
829C2×C4—2368no—
830C2×C4—2362no—
831C2×C4—2362no—
832C2×C4C2×D4×D5912yes—
833C2×C4C2×D4×D5911yescharacteristic
834C2×C4#1427377212yes—
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#1683796012yes—
867C22#1683820612yes—
868C22#1683821112yes—
869C22C22×D4×D5911yescharacteristic
870C4—22no—
871C4—42no—
872C4—42no—
873C4—42no—
874C4—1182no—
875C4—1182no—
876C4—2362no—
877C4—2362no—
878C4#1683796012yes—
879C4C2×#1427377211yescharacteristic
880C4C2×#1427377311yescharacteristic
881C2—42no—
882C2—82no—
883C2—4722no—
884C2—4722no—
885C2—2362no—
886C2—2362no—
887C2#2143494914yesdirect product factor
888C2C2×#1683796011yescharacteristic
889C2C2×#1683820611yescharacteristic
890C2C2×#1683821111yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#468C2
socleC23×C59C22×D4
hypercenterC2×#468D59
hypocenterC59C2×#3198
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#468

Complements

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

NH ≅ G/Ntype
1. C2×#16837982C2semidirect
2. C2×#16837968C2semidirect
3. #21434949C2direct (N × H)
4. C2×#16837719C2semidirect
5. C2×#16837741C2semidirect
6. C2×#16837729C2semidirect
7. C2×#16837717C2semidirect
8. C2×#16837655C2semidirect
9. C2×#16837636C2semidirect
10. C2×#16837633C2semidirect
11. C2×#16837550C2semidirect
12. C2×#16837546C2semidirect
13. C2×#16837551C2semidirect
14. C2×#16837537C2semidirect
15. C2×#16837370C2semidirect
16. C2×C59×#468C2semidirect
17. C22×#11745689C22semidirect
23. C23×C59⋊C8C22semidirect
25. #16837982C22semidirect
27. #16837968C22semidirect
36. C2×#14273701C22semidirect
43. C2×C4⋊C4×D59C22semidirect
44. #16837741C22semidirect
45. #16837729C22semidirect
46. #16837719C22semidirect
47. #16837717C22semidirect
48. #16837655C22semidirect
49. #16837636C22semidirect
50. #16837633C22semidirect
51. #16837551C22semidirect
52. #16837550C22semidirect
53. #16837546C22semidirect
54. #16837537C22semidirect
55. C2×#14273660C22semidirect
56. C2×#14273659C22semidirect
57. C2×#14273658C22semidirect
58. C2×#14273651C22semidirect
60. C2×#14273649C22semidirect
63. C2×#14273647C22semidirect
64. #16837370C22semidirect
67. C2×(C2×D59)⋊C8C22semidirect
68. C2×(C2×D59)⋊C8C22semidirect
70. C22×M16×C59C22semidirect
71. C2×C22⋊Q8×C59C22semidirect
73. C59×#468C22semidirect
74. C2×#107×C59C22semidirect
75. C2×#103×C59C22semidirect
81. C2×#11745689C23semidirect
116. C22×C59⋊C8C23semidirect
130. #14273701C23semidirect
144. C4⋊C4×D59C23semidirect
153. #14273660C23semidirect
154. #14273659C23semidirect
155. #14273658C23semidirect
156. #14273651C23semidirect
158. #14273649C23semidirect
161. #14273647C23semidirect
164. (C2×D59)⋊C8C23semidirect
165. (C2×D59)⋊C8C23semidirect
173. C2×M16×C59C23semidirect
177. C22⋊Q8×C59C23semidirect
185. #107×C59C23semidirect
186. #103×C59C23semidirect
444. C2×#468D59semidirect
454. C2×C59#3198semidirect
469. C22×M16C2×D59semidirect
479. C2×C22⋊Q8C2×D59semidirect
498. #468C2×D59semidirect
506. C2×#107C2×D59semidirect
510. C2×#103C2×D59semidirect
522. C59C2×#3198semidirect
566. C2×M16C22×D59semidirect
579. C22⋊Q8C22×D59semidirect
619. #107C22×D59semidirect
623. #103C22×D59semidirect
887. C2#21434949direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168379822
C2×#168379682
#214349492
C2×#168377192
C2×#168377412
C2×#168377292
C2×#168377172
C2×#168376552
C2×#168376362
C2×#168376332
C2×#168375502
C2×#168375462
C2×#168375512
C2×#168375372
C2×#168373702
C2×C59×#4682
C2×#319859