Finite Group Databasebeta

← C2×#21436299 #29465488

Subgroups — C2×#21436299 #29465488

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×#16838098C211yesmaximal, characteristic, complemented
2C2×#16838048C211yesmaximal, characteristic, complemented
3#21436299C2116yesmaximal, direct product factor
4C2×#16837757C211yesmaximal, characteristic, complemented
5C2×#16837744C211yesmaximal, characteristic, complemented
6C2×#16837716C211yesmaximal, characteristic, complemented
7C2×#16837703C211yesmaximal, characteristic, complemented
8C2×#16837655C211yesmaximal, characteristic, complemented
9C2×#16837648C211yesmaximal, characteristic, complemented
10C2×#16837618C211yesmaximal, characteristic, complemented
11C2×#16837549C211yesmaximal, characteristic, complemented
12C2×#16837538C211yesmaximal, characteristic, complemented
13C2×C4×D472C211yesmaximal, characteristic, complemented
14C2×#16837404C211yesmaximal, characteristic, complemented
15C2×#16837408C211yesmaximal, characteristic, complemented
16C2×C59×#436C211yesmaximal, characteristic, complemented
17C22×#11745685C2211yescharacteristic
18C23×D236C2211yescharacteristic
19C22×#11745660C2211yescharacteristic, complemented
20C22×D472C2211yescharacteristic
21C22×D472C2211yescharacteristic
22#16838098—24no—
23#16838098C2218yescomplemented
24#16838048—24no—
25#16838048C2218yescomplemented
26C2×#14273722—21no—
27C2×#14273719C2211yescharacteristic, complemented
28C2×#14273715C2211yescharacteristic
29C2×#14273712—21no—
30C2×#14273709—21no—
31C2×#14273706C2211yescharacteristic
32C2×#14273701C2211yescharacteristic
33C2×#14273701C2211yescharacteristic
34C2×#14273701C2211yescharacteristic, complemented
35C2×#14273700—21no—
36C2×#14273699—21no—
37C2×#14273695—21no—
38C2×C4×D236C2211yescharacteristic
39C2×C4×D236C2211yescharacteristic, complemented
40C2×(C22⋊D59)⋊C4—21no—
41C2×#14273686C2211yescharacteristic
42C22×C4⋊Dic59C2211yescharacteristic, complemented
43C2×C22⋊C4×D59—21no—
44#16837757C2218yescomplemented
45#16837744C2218yescomplemented
46#16837716C2218yescomplemented
47#16837703C2218yescomplemented
48#16837655C2218yescomplemented
49#16837648C2218yescomplemented
50#16837618C2218yescomplemented
51#16837549C2218yescomplemented
52#16837538C2218yescomplemented
53C4×D472C2218yescomplemented
54C2×#14273661C2211yescharacteristic, complemented
55C2×#14273661C2211yescharacteristic, complemented
56C2×#14273659C2211yescharacteristic, complemented
57#16837408C2218yescomplemented
58#16837404C2218yescomplemented
59C2×#14273652C2211yescharacteristic, complemented
60C2×#14273652C2211yescharacteristic, complemented
61C2×#14273652C2211yescharacteristic, complemented
62C2×#14273649C2211yescharacteristic
63C2×#14273649C2211yescharacteristic
64C2×#14273649C2211yescharacteristic
65C2×#14273649C2211yescharacteristic
66C2×#14273649C2211yescharacteristic
67C2×#14273649C2211yescharacteristic
68C2×#14273649C2211yescharacteristic, complemented
69C22×M16×C59C2211yescharacteristic
70C22×M16×C59C2211yescharacteristic, complemented
71C2×C4×D4×C59C2211yescharacteristic
72C59×#436C2218yescomplemented
73C2×C4⋊C8×C59C2211yescharacteristic, complemented
74C2×C22⋊C8×C59C2211yescharacteristic
75C2×C22⋊C8×C59C2211yescharacteristic, complemented
76C2×C4×C8×C59C2211yescharacteristic, complemented
77C24×D59—21no—
78C2×#11745685—22no—
79C2×#11745685—24no—
80C2×#11745685—42no—
81C2×#11745685C2314yes—
82C22×Dic118C2311yescharacteristic
83C22×D236—24no—
84C22×D236—21no—
85C22×D236—22no—
86C22×D236—42no—
87C22×D236C2311yescharacteristic
88C22×D236C2311yescharacteristic
89C22×D236C2314yes—
90C22×D236C2311yescharacteristic
91C22×C22⋊D59—21no—
92C22×C22⋊D59—21no—
93C22×C22⋊D59—21no—
94C22×C22⋊D59—21no—
95C23×Dic59—21no—
96C22×C4×D59—21no—
97C22×C4×D59—21no—
98C22×C4×D59—21no—
99C2×#11745660—42no—
100C2×#11745660C2314yescomplemented
101C2×D472—24no—
102C2×D472—42no—
103C2×D472C2314yes—
104C2×D472C2314yes—
105#14273722—28no—
106#14273719—22no—
107#14273719C2314yescomplemented
108#14273715—22no—
109#14273715C2314yes—
110#14273712—28no—
111#14273709—28no—
112#14273706—22no—
113#14273706C2314yes—
114#14273701—22no—
115#14273701—22no—
116#14273701—22no—
117#14273701C2314yes—
118#14273701C2314yes—
119#14273701C2314yescomplemented
120#14273700—28no—
121#14273699—28no—
122#14273695—28no—
123C4×D236—22no—
124C4×D236—22no—
125C4×D236C2314yes—
126C4×D236C2314yescomplemented
127(C22⋊D59)⋊C4—28no—
128#14273686—22no—
129#14273686C2314yes—
130C2×C4⋊Dic59—21no—
131C2×C4⋊Dic59—22no—
132C2×C4⋊Dic59C2311yescharacteristic
133C2×C4⋊Dic59C2311yescharacteristic
134C2×C4⋊Dic59C2311yescharacteristic
135C2×C4⋊Dic59C2311yescharacteristic
136C2×C4⋊Dic59C2314yescomplemented
137C2×Dic59⋊C4—21no—
138C2×Dic59⋊C4—21no—
139C2×Dic59⋊C4—21no—
140C2×C22⋊Dic59—21no—
141C2×C22⋊Dic59—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—21no—
149C22⋊C4×D59—28no—
150C2×C4×Dic59—21no—
151#14273661C2314yescomplemented
152#14273661C2314yescomplemented
153#14273659C2314yescomplemented
154#14273652C2314yescomplemented
155#14273652C2314yescomplemented
156#14273652C2314yescomplemented
157#14273649C2314yes—
158#14273649C2314yes—
159#14273649C2314yes—
160#14273649C2314yes—
161#14273649C2314yes—
162#14273649C2314yes—
163#14273649C2314yescomplemented
164C22×D4×C59D411yescharacteristic
165C23×C4×C59C2311yescharacteristic
166C23×C4×C59C2311yescharacteristic
167C2×M16×C59—42no—
168C2×M16×C59—42no—
169C2×M16×C59C2314yes—
170C2×M16×C59C2314yescomplemented
171C22×C8×C59C2311yescharacteristic
172C22×C8×C59C2311yescharacteristic
173C22×C8×C59C2311yescharacteristic
174C22×C8×C59C2311yescharacteristic
175C4×D4×C59D414yes—
176C4×D4×C59C2314yes—
177C2×C4⋊C4×C59D411yescharacteristic
178C2×C22⋊C4×C59D411yescharacteristic
179C2×C22⋊C4×C59D411yescharacteristic
180C2×C42×C59C2311yescharacteristic
181C4⋊C8×C59C2314yescomplemented
182C22⋊C8×C59C2314yes—
183C22⋊C8×C59C2314yescomplemented
184C4×C8×C59C2314yescomplemented
185C24×C59C2×D411yescharacteristic
186C24×C59C2×D411yescharacteristic
187C23×D59—21no—
188C23×D59—21no—
189C23×D59—21no—
190C23×D59—24no—
191C23×D59—44no—
192C23×D59—44no—
193C23×D59—82no—
194C2×D4×C59—42no—
195C2×D4×C59C2×D414yes—
196C22×C4×C59—22no—
197C22×C4×C59—22no—
198C22×C4×C59—22no—
199C22×C4×C59—22no—
200C22×C4×C59C2×D411yescharacteristic
201C22×C4×C59C2×D411yescharacteristic
202C22×C4×C59C2×D411yescharacteristic
203C22×C4×C59C2×D411yescharacteristic
204C22×C4×C59C2×D412yes—
205C22×C4×C59C2×D412yes—
206C22×C4×C59C2412yes—
207C22×C4×C59C2412yes—
208C22×C4×C59C2411yescharacteristic
209C2×C22⋊D59—24no—
210C2×C22⋊D59—24no—
211C2×C22⋊D59—24no—
212C2×C22⋊D59—24no—
213C2×C22⋊D59—44no—
214C2×C22⋊D59—44no—
215C2×C22⋊D59—82no—
216C2×C22⋊D59—82no—
217C22×Dic59—21no—
218C22×Dic59—21no—
219C22×Dic59—21no—
220C22×Dic59—21no—
221C22×Dic59—21no—
222C22×Dic59—24no—
223C22×Dic59—82no—
224#11745685—28no—
225#11745685—44no—
226#11745685—48no—
227C2×D236—21no—
228C2×D236—22no—
229C2×D236—22no—
230C2×D236—22no—
231C2×D236—22no—
232C2×D236—22no—
233C2×D236—28no—
234C2×D236—21no—
235C2×D236—24no—
236C2×D236—21no—
237C2×D236—44no—
238C2×D236—48no—
239C2×D236—44no—
240C2×D236#4114yes—
241C2×D236C2412yes—
242C2×D236C2412yes—
243C2×D236C2412yes—
244C2×C4×D59—24no—
245C2×C4×D59—24no—
246C2×C4×D59—24no—
247C2×C4×D59—44no—
248C2×C4×D59—82no—
249C2×C4×D59—82no—
250C2×Dic118—22no—
251C2×Dic118—22no—
252C2×Dic118—21no—
253C2×Dic118C2412yes—
254M16×C59—44no—
255M16×C59—44no—
256C2×C8×C59—22no—
257C2×C8×C59—22no—
258C2×C8×C59—22no—
259C2×C8×C59—22no—
260C2×C8×C59C2412yes—
261C2×C8×C59C2412yes—
262C2×C8×C59C2412yes—
263C2×C8×C59C2412yes—
264C4⋊C4×C59C2×D414yes—
265C22⋊C4×C59C2×D414yes—
266C22⋊C4×C59C2×D414yes—
267C42×C59C2×D412yes—
268C42×C59C2412yes—
269C22⋊Dic59—24no—
270C22⋊Dic59—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—
278C4⋊Dic59—21no—
279C4⋊Dic59—21no—
280C4⋊Dic59—24no—
281C4⋊Dic59—21no—
282C4⋊Dic59—21no—
283C4⋊Dic59C2412yes—
284C4⋊Dic59C2412yes—
285C4⋊Dic59C2412yes—
286C4⋊Dic59C2412yes—
287Dic59⋊C4—24no—
288Dic59⋊C4—24no—
289Dic59⋊C4—24no—
290C4×Dic59—24no—
291D472—28no—
292D472—44no—
293#11745660—44no—
294C23×C59—22no—
295C23×C59—22no—
296C23×C59—22no—
297C23×C59—22no—
298C23×C59—22no—
299C23×C59—22no—
300C23×C59C22×D412yes—
301C23×C59C22×D412yes—
302C23×C59C22×D411yescharacteristic
303C22×D59—24no—
304C22×D59—22no—
305C22×D59—22no—
306C22×D59—22no—
307C22×D59—48no—
308C22×D59—42no—
309C22×D59—42no—
310C22×D59—48no—
311C22×D59—42no—
312C22×D59—42no—
313C22×D59—42no—
314C22×D59—42no—
315C22×D59—42no—
316C22×D59—42no—
317C22×D59—84no—
318C22×D59—816no—
319D4×C59—44no—
320C2×C4×C59—22no—
321C2×C4×C59—22no—
322C2×C4×C59—22no—
323C2×C4×C59—22no—
324C2×C4×C59—24no—
325C2×C4×C59—24no—
326C2×C4×C59—22no—
327C2×C4×C59—22no—
328C2×C4×C59—22no—
329C2×C4×C59—22no—
330C2×C4×C59C22×D412yes—
331C2×C4×C59C22×D412yes—
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—
340C22⋊D59—84no—
341C22⋊D59—84no—
342C2×Dic59—22no—
343C2×Dic59—22no—
344C2×Dic59—22no—
345C2×Dic59—22no—
346C2×Dic59—22no—
347C2×Dic59—42no—
348C2×Dic59—42no—
349C2×Dic59—42no—
350C2×Dic59—42no—
351C2×Dic59—42no—
352C2×Dic59—84no—
353D236—24no—
354D236—22no—
355D236—22no—
356D236—22no—
357D236—22no—
358D236—22no—
359D236—48no—
360D236—42no—
361D236—42no—
362D236C2×#4114yes—
363C4×D59—48no—
364C4×D59—84no—
365C4×D59—84no—
366Dic118—22no—
367Dic118—22no—
368Dic118—42no—
369C8×C59—22no—
370C8×C59—22no—
371C8×C59—22no—
372C8×C59—22no—
373C2×#3322—591nomaximal, Sylow
374C22×C59—22no—
375C22×C59—22no—
376C22×C59—22no—
377C22×C59—22no—
378C22×C59—22no—
379C22×C59—22no—
380C22×C59—44no—
381C22×C59—44no—
382C22×C59#54612yes—
383C22×C59#57512yes—
384C22×C59#57612yes—
385C22×C59C23×D411yescharacteristic
386C2×D59—24no—
387C2×D59—48no—
388C2×D59—42no—
389C2×D59—42no—
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—22no—
402C4×C59—22no—
403C4×C59#54612yes—
404C4×C59C22×#4111yescharacteristic
405C4×C59C2×H(5,𝔽2)11yescharacteristic
406Dic59—42no—
407Dic59—42no—
408Dic59—42no—
409Dic59—42no—
410Dic59—42no—
411C2×#553—591no—
412C2×#546—591no—
413#3322—5916no—
414C2×#488—591no—
415C2×#485—591no—
416C2×#480—591no—
417C2×#478—591no—
418C2×#469—591no—
419C2×#468—591no—
420C2×#463—591no—
421C2×#449—591no—
422C2×#447—591no—
423C2×C4×D8—591no—
424C2×#436D5911yescharacteristic, complemented
425C2×#417—591no—
426C2×#418—591no—
427C2×C59—42no—
428C2×C59—42no—
429C2×C59#332214yescomplemented
430C2×C59C2×#54611yescharacteristic
431C2×C59C2×#57511yescharacteristic
432C2×C59C2×#57611yescharacteristic
433D59—44no—
434D59—82no—
435D59—82no—
436C22×#41—591no—
437C23×D4—591no—
438C22×SD16—591no—
439C22×D8—591no—
440C22×D8—591no—
441C22×M16C2×D5911yescharacteristic
442C22×M16C2×D5911yescharacteristic, complemented
443#553—598no—
444#553—1184no—
445#546—598no—
446#546—1184no—
447C2×#126—1181no—
448C2×#125—591no—
449C2×#124—591no—
450C2×#123—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×D4—1181no—
462C2×C4×D4C2×D5911yescharacteristic
463C2×#117—591no—
464C22×C4⋊C4—591no—
465C22×C22⋊C4—1181no—
466#488—598no—
467#485—598no—
468#480—598no—
469#478—598no—
470#469—598no—
471#468—598no—
472#463—598no—
473#449—598no—
474#447—598no—
475C4×D8—598no—
476#436C2×D5918yescomplemented
477C2×#107—591no—
478C2×#107—591no—
479C2×#106—591no—
480C2×C4⋊C8C2×D5911yescharacteristic, complemented
481#418—598no—
482#417—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×#102—591no—
492C2×#102—591no—
493C2×C22⋊C8C2×D5911yescharacteristic
494C2×C22⋊C8C2×D5911yescharacteristic, complemented
495C2×C4×C8C2×D5911yescharacteristic, complemented
496C59C2×#332211yescharacteristic, complemented, Sylow
497C25—1181no—
498C2×#41—594no—
499C2×#41—1184no—
500C2×#41—1182no—
501C2×#41—2362no—
502C22×Q8—591no—
503C22×D4—591no—
504C22×D4—591no—
505C22×D4—591no—
506C22×D4—594no—
507C22×D4—1184no—
508C22×D4—1181no—
509C22×D4—1181no—
510C22×D4—1181no—
511C22×D4—1181no—
512C22×D4—1181no—
513C22×D4—1182no—
514C22×D4—2362no—
515C22×D4D23611yescharacteristic
516C23×C4—1181no—
517C23×C4—1181no—
518C23×C4—1181no—
519C23×C4—1181no—
520C23×C4C22×D5911yescharacteristic
521C23×C4C22×D5911yescharacteristic
522C2×SD16—594no—
523C2×SD16—2362no—
524C2×D8—594no—
525C2×D8—594no—
526C2×D8—1184no—
527C2×D8—2362no—
528C2×M16—42no—
529C2×M16—42no—
530C2×M16C22×D5914yes—
531C2×M16C22×D5914yescomplemented
532C22×C8C22×D5911yescharacteristic
533C22×C8C22×D5911yescharacteristic
534C22×C8C22×D5911yescharacteristic
535C22×C8C22×D5911yescharacteristic
536#126—1188no—
537#125—594no—
538#125—1182no—
539#124—594no—
540#124—1182no—
541#123—1188no—
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—594no—
555C4×D4—594no—
556C4×D4—1188no—
557C4×D4—1182no—
558C4×D4—1182no—
559C4×D4D23614yes—
560C4×D4C22×D5914yes—
561#117—594no—
562#117—1182no—
563C2×C4⋊C4—591no—
564C2×C4⋊C4—591no—
565C2×C4⋊C4—594no—
566C2×C4⋊C4—591no—
567C2×C4⋊C4—591no—
568C2×C4⋊C4—1181no—
569C2×C4⋊C4—1182no—
570C2×C4⋊C4—1181no—
571C2×C4⋊C4—1181no—
572C2×C4⋊C4—1181no—
573C2×C4⋊C4D23611yescharacteristic
574C2×C22⋊C4—1181no—
575C2×C22⋊C4—1181no—
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—1188no—
584C2×C22⋊C4D23611yescharacteristic
585C2×C22⋊C4D23611yescharacteristic
586C2×C42—1181no—
587C2×C42C22×D5911yescharacteristic
588#107—594no—
589#107—594no—
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#102—594no—
601#102—594no—
602C22⋊C8C22×D5914yes—
603C22⋊C8C22×D5914yescomplemented
604C4×C8C22×D5914yescomplemented
605C24—1181no—
606C24—1184no—
607C24—1181no—
608C24—1181no—
609C24—4722no—
610C24—2364no—
611C24—2364no—
612C24C2×D23611yescharacteristic
613C24C2×D23611yescharacteristic
614#41—1188no—
615#41—2364no—
616#41—2368no—
617C2×Q8—592no—
618C2×Q8—1181no—
619C2×Q8—1182no—
620C2×Q8—1182no—
621C2×D4—42no—
622C2×D4—594no—
623C2×D4—592no—
624C2×D4—592no—
625C2×D4—592no—
626C2×D4—1188no—
627C2×D4—1184no—
628C2×D4—1184no—
629C2×D4—1184no—
630C2×D4—1184no—
631C2×D4—1181no—
632C2×D4—1181no—
633C2×D4—1184no—
634C2×D4—1181no—
635C2×D4—1182no—
636C2×D4—1182no—
637C2×D4—1182no—
638C2×D4—1182no—
639C2×D4—1182no—
640C2×D4—4722no—
641C2×D4—4722no—
642C2×D4—2364no—
643C2×D4—2368no—
644C2×D4—2364no—
645C2×D4—2364no—
646C2×D4—2364no—
647C2×D4C2×D23614yes—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—1184no—
653C22×C4—1181no—
654C22×C4—1181no—
655C22×C4—1181no—
656C22×C4—1181no—
657C22×C4—1181no—
658C22×C4—1184no—
659C22×C4—1184no—
660C22×C4—1184no—
661C22×C4—4722no—
662C22×C4—4722no—
663C22×C4—4722no—
664C22×C4—2364no—
665C22×C4C2×D23612yes—
666C22×C4C2×D23612yes—
667C22×C4C2×D23611yescharacteristic
668C22×C4C2×D23611yescharacteristic
669C22×C4C2×D23611yescharacteristic
670C22×C4C2×D23611yescharacteristic
671C22×C4C23×D5912yes—
672C22×C4C23×D5912yes—
673C22×C4C23×D5911yescharacteristic
674SD16—2364no—
675D8—1188no—
676D8—2364no—
677M16—44no—
678M16—44no—
679C2×C8—22no—
680C2×C8—22no—
681C2×C8—22no—
682C2×C8—22no—
683C2×C8C23×D5912yes—
684C2×C8C23×D5912yes—
685C2×C8C23×D5912yes—
686C2×C8C23×D5912yes—
687C4⋊C4—592no—
688C4⋊C4—592no—
689C4⋊C4—592no—
690C4⋊C4—592no—
691C4⋊C4—1181no—
692C4⋊C4—1181no—
693C4⋊C4—1184no—
694C4⋊C4—1181no—
695C4⋊C4—1181no—
696C4⋊C4—1184no—
697C4⋊C4—1184no—
698C4⋊C4—1184no—
699C4⋊C4C2×D23614yes—
700C22⋊C4—1184no—
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⋊C4C2×D23614yes—
710C22⋊C4C2×D23614yes—
711C42—1184no—
712C42C2×D23612yes—
713C42C23×D5912yes—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—1182no—
721C23—1184no—
722C23—1182no—
723C23—1182no—
724C23—4724no—
725C23—47216no—
726C23—2368no—
727C23—2368no—
728C23—2362no—
729C23—2362no—
730C23—2362no—
731C23—2362no—
732C23—2362no—
733C23—2362no—
734C23—2362no—
735C23—2362no—
736C23C22×D23612yes—
737C23C22×D23612yes—
738C23C22×D23611yescharacteristic
739Q8—1182no—
740Q8—1182no—
741Q8—2362no—
742D4—44no—
743D4—594no—
744D4—1182no—
745D4—1182no—
746D4—1182no—
747D4—1182no—
748D4—1182no—
749D4—1184no—
750D4—4724no—
751D4—4724no—
752D4—2368no—
753D4—2368no—
754D4—2368no—
755D4—2362no—
756D4—2362no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—24no—
766C2×C4—24no—
767C2×C4—1182no—
768C2×C4—1182no—
769C2×C4—1182no—
770C2×C4—1182no—
771C2×C4—1182no—
772C2×C4—4724no—
773C2×C4—4724no—
774C2×C4—4724no—
775C2×C4—2368no—
776C2×C4—2362no—
777C2×C4—2362no—
778C2×C4—2362no—
779C2×C4—2362no—
780C2×C4—2362no—
781C2×C4C22×D23612yes—
782C2×C4C22×D23612yes—
783C2×C4C22×D23612yes—
784C2×C4C22×D23612yes—
785C2×C4C22×D23611yescharacteristic
786C2×C4#41×D5912yes—
787C2×C4#1427377212yes—
788C2×C4C24×D5911yescharacteristic
789C8—22no—
790C8—22no—
791C8—22no—
792C8—22no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—44no—
800C22—44no—
801C22—1184no—
802C22—47216no—
803C22—4724no—
804C22—4724no—
805C22—2362no—
806C22—2362no—
807C22—2362no—
808C22—2362no—
809C22—2362no—
810C22—2362no—
811C22—2362no—
812C22—2362no—
813C22—2368no—
814C22#1683804712yes—
815C22#1683820212yes—
816C22#1683820712yes—
817C22C23×D23611yescharacteristic
818C4—22no—
819C4—22no—
820C4—22no—
821C4—22no—
822C4—2362no—
823C4—2362no—
824C4—2362no—
825C4—2362no—
826C4—2362no—
827C4#1683804712yes—
828C4C2×#41×D5911yescharacteristic
829C4C2×#1427377211yescharacteristic
830C2—42no—
831C2—42no—
832C2—4722no—
833C2—4722no—
834C2—2364no—
835C2#2143629914yesdirect product factor
836C2C2×#1683804711yescharacteristic
837C2C2×#1683820211yescharacteristic
838C2C2×#1683820711yescharacteristic
subgroupG/H
centerC23C22×D236
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#436C2
socleC23×C59C22×D4
hypercenterC2×#436D59
hypocenterC59C2×#3322
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#436

Complements

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

NH ≅ G/Ntype
1. C2×#16838098C2semidirect
2. C2×#16838048C2semidirect
3. #21436299C2direct (N × H)
4. C2×#16837757C2semidirect
5. C2×#16837744C2semidirect
6. C2×#16837716C2semidirect
7. C2×#16837703C2semidirect
8. C2×#16837655C2semidirect
9. C2×#16837648C2semidirect
10. C2×#16837618C2semidirect
11. C2×#16837549C2semidirect
12. C2×#16837538C2semidirect
13. C2×C4×D472C2semidirect
14. C2×#16837404C2semidirect
15. C2×#16837408C2semidirect
16. C2×C59×#436C2semidirect
19. C22×#11745660C22semidirect
23. #16838098C22semidirect
25. #16838048C22semidirect
27. C2×#14273719C22semidirect
34. C2×#14273701C22semidirect
39. C2×C4×D236C22semidirect
42. C22×C4⋊Dic59C22semidirect
44. #16837757C22semidirect
45. #16837744C22semidirect
46. #16837716C22semidirect
47. #16837703C22semidirect
48. #16837655C22semidirect
49. #16837648C22semidirect
50. #16837618C22semidirect
51. #16837549C22semidirect
52. #16837538C22semidirect
53. C4×D472C22semidirect
54. C2×#14273661C22semidirect
55. C2×#14273661C22semidirect
56. C2×#14273659C22semidirect
57. #16837408C22semidirect
58. #16837404C22semidirect
59. C2×#14273652C22semidirect
60. C2×#14273652C22semidirect
61. C2×#14273652C22semidirect
68. C2×#14273649C22semidirect
70. C22×M16×C59C22semidirect
72. C59×#436C22semidirect
73. C2×C4⋊C8×C59C22semidirect
75. C2×C22⋊C8×C59C22semidirect
76. C2×C4×C8×C59C22semidirect
100. C2×#11745660C23semidirect
107. #14273719C23semidirect
119. #14273701C23semidirect
126. C4×D236C23semidirect
136. C2×C4⋊Dic59C23semidirect
151. #14273661C23semidirect
152. #14273661C23semidirect
153. #14273659C23semidirect
154. #14273652C23semidirect
155. #14273652C23semidirect
156. #14273652C23semidirect
163. #14273649C23semidirect
170. C2×M16×C59C23semidirect
181. C4⋊C8×C59C23semidirect
183. C22⋊C8×C59C23semidirect
184. C4×C8×C59C23semidirect
424. C2×#436D59semidirect
429. C2×C59#3322semidirect
442. C22×M16C2×D59semidirect
476. #436C2×D59semidirect
480. C2×C4⋊C8C2×D59semidirect
494. C2×C22⋊C8C2×D59semidirect
495. C2×C4×C8C2×D59semidirect
496. C59C2×#3322semidirect
531. C2×M16C22×D59semidirect
591. C4⋊C8C22×D59semidirect
603. C22⋊C8C22×D59semidirect
604. C4×C8C22×D59semidirect
835. C2#21436299direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168380982
C2×#168380482
#214362992
C2×#168377572
C2×#168377442
C2×#168377162
C2×#168377032
C2×#168376552
C2×#168376482
C2×#168376182
C2×#168375492
C2×#168375382
C2×C4×D4722
C2×#168374042
C2×#168374082
C2×C59×#4362
C2×#332259