Finite Group Databasebeta

← C2×#21434945 #29459339

Subgroups — C2×#21434945 #29459339

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×#16837980C211yesmaximal, characteristic, complemented
2C2×#16837968C211yesmaximal, characteristic, complemented
3#21434945C2116yesmaximal, direct product factor
4C2×#16837718C211yesmaximal, characteristic, complemented
5C2×#16837742C211yesmaximal, characteristic, complemented
6C2×#16837724C211yesmaximal, characteristic, complemented
7C2×#16837716C211yesmaximal, characteristic, complemented
8C2×#16837654C211yesmaximal, characteristic, complemented
9C2×#16837645C211yesmaximal, characteristic, complemented
10C2×#16837635C211yesmaximal, characteristic, complemented
11C2×#16837634C211yesmaximal, characteristic, complemented
12C2×#16837547C211yesmaximal, characteristic, complemented
13C2×#16837551C211yesmaximal, characteristic, complemented
14C2×#16837534C211yesmaximal, characteristic, complemented
15C2×#16837367C211yesmaximal, characteristic, complemented
16C2×C59×#449C211yesmaximal, characteristic, complemented
17C22×#11745685C2211yescharacteristic
18C22×D4×D59C2211yescharacteristic
19C22×#11745671C2211yescharacteristic
20C22×#11745669C2211yescharacteristic
21C22×#11745659C2211yescharacteristic, complemented
22C22×C8×D59C2211yescharacteristic, complemented
23#16837980—24no—
24#16837980C2218yescomplemented
25#16837968—24no—
26#16837968C2218yescomplemented
27C2×#14273723—21no—
28C2×#14273713—21no—
29C2×#14273706—21no—
30C2×#14273703C2211yescharacteristic
31C2×#14273703C2211yescharacteristic, complemented
32C2×#14273702C2211yescharacteristic
33C2×#14273701—21no—
34C2×#14273701C2211yescharacteristic
35C2×#14273699—21no—
36C2×#14273699—21no—
37C2×#14273698C2211yescharacteristic
38C2×#14273698C2211yescharacteristic
39C2×#14273698C2211yescharacteristic, complemented
40C2×#14273697—21no—
41C2×#14273695—21no—
42C2×#14273685C2211yescharacteristic
43C22×C4⋊Dic59C2211yescharacteristic, complemented
44#16837742C2218yescomplemented
45#16837724C2218yescomplemented
46#16837718C2218yescomplemented
47#16837716C2218yescomplemented
48#16837654C2218yescomplemented
49#16837645C2218yescomplemented
50#16837635C2218yescomplemented
51#16837634C2218yescomplemented
52#16837551C2218yescomplemented
53#16837547C2218yescomplemented
54#16837534C2218yescomplemented
55C2×#14273661C2211yescharacteristic, complemented
56C2×#14273661C2211yescharacteristic, complemented
57C2×#14273658C2211yescharacteristic, complemented
58C2×#14273658C2211yescharacteristic, complemented
59C2×#14273651C2211yescharacteristic, complemented
60C2×#14273649C2211yescharacteristic
61C2×#14273649C2211yescharacteristic
62C2×#14273648C2211yescharacteristic
63C2×#14273648C2211yescharacteristic
64C2×#14273648C2211yescharacteristic, complemented
65#16837367C2218yescomplemented
66C2×C22⋊(C59⋊C8)C2211yescharacteristic, complemented
67C2×(C2×D59)⋊C8C2211yescharacteristic
68C2×(C2×D59)⋊C8C2211yescharacteristic
69C22×#41×C59C2211yescharacteristic, complemented
70C22×SD16×C59C2211yescharacteristic
71C22×D8×C59C2211yescharacteristic
72C2×#121×C59C2211yescharacteristic
73C59×#449C2218yescomplemented
74C2×#103×C59C2211yescharacteristic, complemented
75C2×#102×C59C2211yescharacteristic, complemented
76C2×C22⋊C8×C59C2211yescharacteristic, complemented
77C24×D59—21no—
78C2×#11745685—42no—
79C2×#11745685—42no—
80C2×#11745685D414yes—
81C2×#11745685C2314yes—
82C22×Dic118D411yescharacteristic
83C22×D236—21no—
84C22×D236D411yescharacteristic
85C22×D236C2311yescharacteristic
86C22×C22⋊D59—21no—
87C22×C22⋊D59—21no—
88C22×C22⋊D59—21no—
89C22×C22⋊D59—21no—
90C22×C22⋊D59—21no—
91C22×C22⋊D59D411yescharacteristic
92C22×C22⋊D59D411yescharacteristic
93C2×D4×D59—22no—
94C2×D4×D59—42no—
95C2×D4×D59—42no—
96C2×D4×D59C2314yes—
97C23×Dic59—21no—
98C22×C4×D59C2311yescharacteristic
99C22×C4×D59C2311yescharacteristic
100C2×#11745671—42no—
101C2×#11745671C2314yes—
102C2×#11745669—42no—
103C2×#11745669C2314yes—
104C2×#11745659—42no—
105C2×#11745659C2314yescomplemented
106C22×C59⋊C8C2311yescharacteristic
107C22×C59⋊C8C2311yescharacteristic
108C2×C8×D59—42no—
109C2×C8×D59C2314yescomplemented
110#14273723—28no—
111#14273713—28no—
112#14273706—28no—
113#14273703—22no—
114#14273703—22no—
115#14273703C2314yes—
116#14273703C2314yescomplemented
117#14273702—22no—
118#14273702C2314yes—
119#14273701—22no—
120#14273701—28no—
121#14273701C2314yes—
122#14273699—28no—
123#14273699—28no—
124#14273698—22no—
125#14273698—22no—
126#14273698—22no—
127#14273698C2314yes—
128#14273698C2314yes—
129#14273698C2314yescomplemented
130#14273697—28no—
131#14273695—28no—
132#14273685—22no—
133#14273685C2314yes—
134C2×C4⋊Dic59—21no—
135C2×C4⋊Dic59—22no—
136C2×C4⋊Dic59C2311yescharacteristic
137C2×C4⋊Dic59C2311yescharacteristic
138C2×C4⋊Dic59C2311yescharacteristic
139C2×C4⋊Dic59C2314yescomplemented
140C2×Dic59⋊C4—21no—
141C2×Dic59⋊C4—21no—
142C2×C22⋊Dic59—21no—
143C2×C22⋊Dic59—21no—
144C2×C22⋊Dic59—21no—
145C2×(C2×D59)⋊C4—21no—
146C2×(C2×D59)⋊C4—21no—
147C2×(C2×D59)⋊C4—21no—
148C2×(C2×D59)⋊C4—21no—
149C2×(C2×D59)⋊C4—21no—
150C2×C4×Dic59—21no—
151#14273661C2314yescomplemented
152#14273661C2314yescomplemented
153#14273658C2314yescomplemented
154#14273658C2314yescomplemented
155#14273651C2314yescomplemented
156#14273649C2314yes—
157#14273649C2314yes—
158#14273648C2314yes—
159#14273648C2314yes—
160#14273648C2314yescomplemented
161C22⋊(C59⋊C8)C2314yescomplemented
162(C2×D59)⋊C8C2314yes—
163(C2×D59)⋊C8C2314yes—
164C2×#41×C59—22no—
165C2×#41×C59—42no—
166C2×#41×C59—42no—
167C2×#41×C59C2314yescomplemented
168C22×Q8×C59C2311yescharacteristic
169C22×D4×C59—21no—
170C22×D4×C59—21no—
171C22×D4×C59C2311yescharacteristic
172C22×D4×C59C2311yescharacteristic
173C23×C4×C59—21no—
174C23×C4×C59C2311yescharacteristic
175C2×SD16×C59—42no—
176C2×SD16×C59C2314yes—
177C2×D8×C59—42no—
178C2×D8×C59C2314yes—
179C22×C8×C59C2311yescharacteristic
180C22×C8×C59C2311yescharacteristic
181#121×C59—22no—
182#121×C59C2314yes—
183C2×C4⋊C4×C59C2311yescharacteristic
184C2×C22⋊C4×C59—21no—
185#103×C59C2314yescomplemented
186#102×C59C2314yescomplemented
187C22⋊C8×C59C2314yescomplemented
188C24×C59—21no—
189C24×C59—21no—
190C24×C59C2×D411yescharacteristic
191C23×D59—21no—
192C23×D59—24no—
193C23×D59—44no—
194C23×D59—82no—
195C23×D59—82no—
196C23×D59C2×D411yescharacteristic
197C23×D59C2×D411yescharacteristic
198#41×C59—44no—
199#41×C59—44no—
200#41×C59—48no—
201C2×Q8×C59—21no—
202C2×Q8×C59—22no—
203C2×Q8×C59—22no—
204C2×Q8×C59C2412yes—
205C2×D4×C59—24no—
206C2×D4×C59—24no—
207C2×D4×C59—21no—
208C2×D4×C59—21no—
209C2×D4×C59—22no—
210C2×D4×C59—22no—
211C2×D4×C59—22no—
212C2×D4×C59—22no—
213C2×D4×C59—44no—
214C2×D4×C59—82no—
215C2×D4×C59C2412yes—
216C2×D4×C59C2412yes—
217C22×C4×C59—22no—
218C22×C4×C59—22no—
219C22×C4×C59—21no—
220C22×C4×C59—21no—
221C22×C4×C59—24no—
222C22×C4×C59—44no—
223C22×C4×C59C2×D411yescharacteristic
224C22×C4×C59C2×D412yes—
225C22×C4×C59C2412yes—
226C22×C4×C59C2411yescharacteristic
227C2×C22⋊D59—24no—
228C2×C22⋊D59—24no—
229C2×C22⋊D59—24no—
230C2×C22⋊D59—24no—
231C2×C22⋊D59—24no—
232C2×C22⋊D59—42no—
233C2×C22⋊D59—42no—
234C2×C22⋊D59—44no—
235C2×C22⋊D59—82no—
236C2×C22⋊D59—82no—
237C2×C22⋊D59—82no—
238C2×C22⋊D59—82no—
239C2×C22⋊D59C2×D414yes—
240C2×C22⋊D59C2×D414yes—
241C22×Dic59—21no—
242C22×Dic59—21no—
243C22×Dic59—21no—
244C22×Dic59—24no—
245C22×Dic59—82no—
246C22×Dic59C2×D411yescharacteristic
247C22×Dic59C2×D411yescharacteristic
248D4×D59—44no—
249D4×D59—44no—
250D4×D59—48no—
251#11745685—48no—
252#11745685—44no—
253#11745685—44no—
254C2×D236—22no—
255C2×D236—22no—
256C2×D236—21no—
257C2×D236—24no—
258C2×D236—42no—
259C2×D236—82no—
260C2×D236C2×D414yes—
261C2×D236C2412yes—
262C2×C4×D59—22no—
263C2×C4×D59—22no—
264C2×C4×D59—22no—
265C2×C4×D59—22no—
266C2×C4×D59C2×D412yes—
267C2×C4×D59C2×D412yes—
268C2×C4×D59C2412yes—
269C2×C4×D59C2412yes—
270C2×Dic118—42no—
271C2×Dic118C2×D414yes—
272SD16×C59—44no—
273D8×C59—44no—
274C2×C8×C59—22no—
275C2×C8×C59—22no—
276C2×C8×C59C2412yes—
277C2×C8×C59C2412yes—
278C4⋊C4×C59—21no—
279C4⋊C4×C59C2412yes—
280C22⋊C4×C59—24no—
281C22⋊Dic59—24no—
282C22⋊Dic59—24no—
283C22⋊Dic59—24no—
284#11745671—44no—
285#11745669—44no—
286(C2×D59)⋊C4—24no—
287(C2×D59)⋊C4—24no—
288(C2×D59)⋊C4—24no—
289(C2×D59)⋊C4—24no—
290(C2×D59)⋊C4—24no—
291C4⋊Dic59—21no—
292C4⋊Dic59—21no—
293C4⋊Dic59—24no—
294C4⋊Dic59—21no—
295C4⋊Dic59C2412yes—
296C4⋊Dic59C2412yes—
297C4⋊Dic59C2412yes—
298Dic59⋊C4—24no—
299Dic59⋊C4—24no—
300C4×Dic59—24no—
301C2×C59⋊C8—22no—
302C2×C59⋊C8—22no—
303C2×C59⋊C8C2412yes—
304C2×C59⋊C8C2412yes—
305#11745659—44no—
306C8×D59—44no—
307C23×C59—22no—
308C23×C59—22no—
309C23×C59—22no—
310C23×C59—22no—
311C23×C59—22no—
312C23×C59—42no—
313C23×C59—42no—
314C23×C59—42no—
315C23×C59—42no—
316C23×C59—42no—
317C23×C59—42no—
318C23×C59C22×D412yes—
319C23×C59C22×D411yescharacteristic
320C22×D59—22no—
321C22×D59—22no—
322C22×D59—22no—
323C22×D59—22no—
324C22×D59—22no—
325C22×D59—22no—
326C22×D59—22no—
327C22×D59—48no—
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—22no—
342D4×C59—22no—
343D4×C59—48no—
344D4×C59—42no—
345D4×C59—42no—
346D4×C59—84no—
347C2×C4×C59—22no—
348C2×C4×C59—24no—
349C2×C4×C59—22no—
350C2×C4×C59—22no—
351C2×C4×C59—22no—
352C2×C4×C59—22no—
353C2×C4×C59—48no—
354C2×C4×C59—42no—
355C2×C4×C59—42no—
356C2×C4×C59C22×D412yes—
357C2×C4×C59C22×D411yescharacteristic
358C2×C4×C59H(5,𝔽2)12yes—
359C2×C4×C59H(5,𝔽2)12yes—
360C2×C4×C59C2511yescharacteristic
361C22⋊D59—44no—
362C22⋊D59—44no—
363C22⋊D59—48no—
364C22⋊D59—84no—
365C22⋊D59—84no—
366C22⋊D59—84no—
367C22⋊D59—84no—
368C2×Dic59—22no—
369C2×Dic59—22no—
370C2×Dic59—22no—
371C2×Dic59—22no—
372C2×Dic59—22no—
373C2×Dic59—42no—
374C2×Dic59—42no—
375C2×Dic59—42no—
376C2×Dic59—84no—
377C2×Dic59C22×D412yes—
378C2×Dic59C22×D412yes—
379D236—22no—
380D236—22no—
381D236—44no—
382D236—42no—
383D236—84no—
384C4×D59—24no—
385C4×D59—24no—
386C4×D59—22no—
387C4×D59—22no—
388C4×D59—22no—
389C4×D59—22no—
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—42no—
404C22×C59—42no—
405C22×C59—42no—
406C22×C59—84no—
407C22×C59—84no—
408C22×C59#53412yes—
409C22×C59#57612yes—
410C22×C59#57712yes—
411C22×C59C23×D411yescharacteristic
412C2×D59—22no—
413C2×D59—22no—
414C2×D59—22no—
415C2×D59—22no—
416C2×D59—22no—
417C2×D59—22no—
418C2×D59—44no—
419C2×D59—44no—
420C2×D59—42no—
421C2×D59—42no—
422C2×D59—42no—
423C2×D59—816no—
424C2×D59—84no—
425C4×C59—22no—
426C4×C59—42no—
427C4×C59—42no—
428C4×C59#53412yes—
429C4×C59C2×H(5,𝔽2)11yescharacteristic
430C4×C59C2×H(5,𝔽2)11yescharacteristic
431Dic59—22no—
432Dic59—22no—
433Dic59—42no—
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×#468—591no—
445C2×#466—591no—
446C2×#465—591no—
447C2×#449—591no—
448C2×#449D5911yescharacteristic, complemented
449C2×#450—591no—
450C2×#447—591no—
451C2×#408—591no—
452C2×C59—42no—
453C2×C59—82no—
454C2×C59—82no—
455C2×C59#319814yescomplemented
456C2×C59C2×#53411yescharacteristic
457C2×C59C2×#57611yescharacteristic
458C2×C59C2×#57711yescharacteristic
459D59—42no—
460D59—42no—
461D59—82no—
462C22×#41—591no—
463C22×#41C2×D5911yescharacteristic, complemented
464C23×D4—591no—
465C22×SD16—591no—
466C22×SD16C2×D5911yescharacteristic
467C22×D8—591no—
468C22×D8C2×D5911yescharacteristic
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⋊C4—591no—
493#485—598no—
494#482—598no—
495#481—598no—
496#480—598no—
497#469—598no—
498#468—598no—
499#466—598no—
500#465—598no—
501#450—598no—
502#449—598no—
503#449C2×D5918yescomplemented
504#447—598no—
505C2×#107—591no—
506C2×#107—591no—
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, complemented
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—22no—
525C2×#41—42no—
526C2×#41—42no—
527C2×#41—594no—
528C2×#41—594no—
529C2×#41—2362no—
530C2×#41—2362no—
531C2×#41C22×D5914yescomplemented
532C22×Q8—591no—
533C22×Q8C22×D5911yescharacteristic
534C22×D4—21no—
535C22×D4—21no—
536C22×D4—591no—
537C22×D4—591no—
538C22×D4—594no—
539C22×D4—591no—
540C22×D4—591no—
541C22×D4—1181no—
542C22×D4—1182no—
543C22×D4—1181no—
544C22×D4—1181no—
545C22×D4—1181no—
546C22×D4—1181no—
547C22×D4—1181no—
548C22×D4—2362no—
549C22×D4—2362no—
550C22×D4C22×D5911yescharacteristic
551C22×D4C22×D5911yescharacteristic
552C23×C4—21no—
553C23×C4—591no—
554C23×C4—591no—
555C23×C4—1181no—
556C23×C4C22×D5911yescharacteristic
557C2×SD16—42no—
558C2×SD16—594no—
559C2×SD16—2362no—
560C2×SD16C22×D5914yes—
561C2×D8—42no—
562C2×D8—594no—
563C2×D8—2362no—
564C2×D8C22×D5914yes—
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—1188no—
578C22⋊Q8—1182no—
579C22⋊Q8—1182no—
580#121—22no—
581#121—594no—
582#121—594no—
583#121—594no—
584#121—594no—
585#121—594no—
586#121—1182no—
587#121—1188no—
588#121—1182no—
589#121—1182no—
590#121—1182no—
591#121—1188no—
592#121—1188no—
593#121—1182no—
594#121C22×D5914yes—
595#120—1188no—
596#120—1188no—
597#117—594no—
598#117—1182no—
599C2×C4⋊C4—591no—
600C2×C4⋊C4—591no—
601C2×C4⋊C4—594no—
602C2×C4⋊C4—591no—
603C2×C4⋊C4—1181no—
604C2×C4⋊C4—1181no—
605C2×C4⋊C4—1181no—
606C2×C4⋊C4—1182no—
607C2×C4⋊C4C22×D5911yescharacteristic
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#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×D5914yescomplemented
630C22⋊C8—594no—
631C22⋊C8—594no—
632C22⋊C8—594no—
633C22⋊C8C22×D5914yescomplemented
634C24—21no—
635C24—21no—
636C24—591no—
637C24—591no—
638C24—1184no—
639C24—1181no—
640C24—4722no—
641C24—4722no—
642C24—2364no—
643C24D4×D5911yescharacteristic
644#41—44no—
645#41—44no—
646#41—48no—
647#41—2368no—
648#41—2364no—
649#41—2364no—
650C2×Q8—21no—
651C2×Q8—22no—
652C2×Q8—22no—
653C2×Q8—594no—
654C2×Q8—2362no—
655C2×Q8C23×D5912yes—
656C2×D4—24no—
657C2×D4—24no—
658C2×D4—21no—
659C2×D4—21no—
660C2×D4—22no—
661C2×D4—22no—
662C2×D4—22no—
663C2×D4—22no—
664C2×D4—44no—
665C2×D4—82no—
666C2×D4—594no—
667C2×D4—594no—
668C2×D4—594no—
669C2×D4—592no—
670C2×D4—1184no—
671C2×D4—1184no—
672C2×D4—1184no—
673C2×D4—1184no—
674C2×D4—1184no—
675C2×D4—1184no—
676C2×D4—1181no—
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×D4C23×D5912yes—
692C2×D4C23×D5912yes—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—24no—
698C22×C4—44no—
699C22×C4—591no—
700C22×C4—591no—
701C22×C4—592no—
702C22×C4—592no—
703C22×C4—592no—
704C22×C4—592no—
705C22×C4—1182no—
706C22×C4—1182no—
707C22×C4—1182no—
708C22×C4—1182no—
709C22×C4—1184no—
710C22×C4—1181no—
711C22×C4—1181no—
712C22×C4—1181no—
713C22×C4—4722no—
714C22×C4D4×D5912yes—
715C22×C4D4×D5911yescharacteristic
716C22×C4C23×D5912yes—
717C22×C4C23×D5911yescharacteristic
718SD16—44no—
719SD16—2364no—
720D8—44no—
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—592no—
734C4⋊C4—592no—
735C4⋊C4—592no—
736C4⋊C4—1184no—
737C4⋊C4—1184no—
738C4⋊C4—1184no—
739C4⋊C4—1181no—
740C4⋊C4—1181no—
741C4⋊C4—1181no—
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—22no—
758C23—42no—
759C23—42no—
760C23—42no—
761C23—42no—
762C23—42no—
763C23—42no—
764C23—592no—
765C23—592no—
766C23—1182no—
767C23—1182no—
768C23—1182no—
769C23—1182no—
770C23—1182no—
771C23—1182no—
772C23—1182no—
773C23—4724no—
774C23—4724no—
775C23—47216no—
776C23—2368no—
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—22no—
789D4—22no—
790D4—48no—
791D4—42no—
792D4—42no—
793D4—84no—
794D4—1182no—
795D4—1182no—
796D4—4724no—
797D4—4724no—
798D4—4724no—
799D4—4724no—
800D4—4724no—
801D4—2364no—
802D4—2364no—
803D4—2364no—
804D4—2368no—
805D4—2362no—
806C2×C4—22no—
807C2×C4—24no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—48no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—592no—
816C2×C4—592no—
817C2×C4—1182no—
818C2×C4—1182no—
819C2×C4—1184no—
820C2×C4—1184no—
821C2×C4—1182no—
822C2×C4—1182no—
823C2×C4—1182no—
824C2×C4—1182no—
825C2×C4—1182no—
826C2×C4—1182no—
827C2×C4—1182no—
828C2×C4—4724no—
829C2×C4—2362no—
830C2×C4—2362no—
831C2×C4—2362no—
832C2×C4C2×D4×D5912yes—
833C2×C4C2×D4×D5911yescharacteristic
834C2×C4#1427377212yes—
835C2×C4#1427377212yes—
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—42no—
849C22—42no—
850C22—42no—
851C22—84no—
852C22—84no—
853C22—1182no—
854C22—1182no—
855C22—1182no—
856C22—1182no—
857C22—1182no—
858C22—1182no—
859C22—47216no—
860C22—4724no—
861C22—2362no—
862C22—2362no—
863C22—2362no—
864C22—2364no—
865C22—2364no—
866C22#1683796212yes—
867C22#1683820412yes—
868C22#1683821212yes—
869C22C22×D4×D5911yescharacteristic
870C4—22no—
871C4—42no—
872C4—42no—
873C4—1182no—
874C4—1182no—
875C4—2362no—
876C4—2362no—
877C4—2362no—
878C4#1683796212yes—
879C4C2×#1427377211yescharacteristic
880C4C2×#1427377211yescharacteristic
881C2—42no—
882C2—82no—
883C2—82no—
884C2—4722no—
885C2—2362no—
886C2—2362no—
887C2#2143494514yesdirect product factor
888C2C2×#1683796211yescharacteristic
889C2C2×#1683820411yescharacteristic
890C2C2×#1683821211yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#449C2
socleC23×C59C22×D4
hypercenterC2×#449D59
hypocenterC59C2×#3198
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#449

Complements

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

NH ≅ G/Ntype
1. C2×#16837980C2semidirect
2. C2×#16837968C2semidirect
3. #21434945C2direct (N × H)
4. C2×#16837718C2semidirect
5. C2×#16837742C2semidirect
6. C2×#16837724C2semidirect
7. C2×#16837716C2semidirect
8. C2×#16837654C2semidirect
9. C2×#16837645C2semidirect
10. C2×#16837635C2semidirect
11. C2×#16837634C2semidirect
12. C2×#16837547C2semidirect
13. C2×#16837551C2semidirect
14. C2×#16837534C2semidirect
15. C2×#16837367C2semidirect
16. C2×C59×#449C2semidirect
21. C22×#11745659C22semidirect
22. C22×C8×D59C22semidirect
24. #16837980C22semidirect
26. #16837968C22semidirect
31. C2×#14273703C22semidirect
39. C2×#14273698C22semidirect
43. C22×C4⋊Dic59C22semidirect
44. #16837742C22semidirect
45. #16837724C22semidirect
46. #16837718C22semidirect
47. #16837716C22semidirect
48. #16837654C22semidirect
49. #16837645C22semidirect
50. #16837635C22semidirect
51. #16837634C22semidirect
52. #16837551C22semidirect
53. #16837547C22semidirect
54. #16837534C22semidirect
55. C2×#14273661C22semidirect
56. C2×#14273661C22semidirect
57. C2×#14273658C22semidirect
58. C2×#14273658C22semidirect
59. C2×#14273651C22semidirect
64. C2×#14273648C22semidirect
65. #16837367C22semidirect
66. C2×C22⋊(C59⋊C8)C22semidirect
69. C22×#41×C59C22semidirect
73. C59×#449C22semidirect
74. C2×#103×C59C22semidirect
75. C2×#102×C59C22semidirect
76. C2×C22⋊C8×C59C22semidirect
105. C2×#11745659C23semidirect
109. C2×C8×D59C23semidirect
116. #14273703C23semidirect
129. #14273698C23semidirect
139. C2×C4⋊Dic59C23semidirect
151. #14273661C23semidirect
152. #14273661C23semidirect
153. #14273658C23semidirect
154. #14273658C23semidirect
155. #14273651C23semidirect
160. #14273648C23semidirect
161. C22⋊(C59⋊C8)C23semidirect
167. C2×#41×C59C23semidirect
185. #103×C59C23semidirect
186. #102×C59C23semidirect
187. C22⋊C8×C59C23semidirect
448. C2×#449D59semidirect
455. C2×C59#3198semidirect
463. C22×#41C2×D59semidirect
503. #449C2×D59semidirect
510. C2×#103C2×D59semidirect
516. C2×#102C2×D59semidirect
521. C2×C22⋊C8C2×D59semidirect
522. C59C2×#3198semidirect
531. C2×#41C22×D59semidirect
623. #103C22×D59semidirect
629. #102C22×D59semidirect
633. C22⋊C8C22×D59semidirect
887. C2#21434945direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168379802
C2×#168379682
#214349452
C2×#168377182
C2×#168377422
C2×#168377242
C2×#168377162
C2×#168376542
C2×#168376452
C2×#168376352
C2×#168376342
C2×#168375472
C2×#168375512
C2×#168375342
C2×#168373672
C2×C59×#4492
C2×#319859