Finite Group Databasebeta

← C2×#21436063 #29465205

Subgroups — C2×#21436063 #29465205

Order 15104.

2514 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838052C211yesmaximal, characteristic, complemented
2C2×#16838043C211yesmaximal, characteristic, complemented
3#21436063C2116yesmaximal, direct product factor
4C2×#16837763C211yesmaximal, characteristic, complemented
5C2×#16837722C211yesmaximal, characteristic, complemented
6C2×#16837730C211yesmaximal, characteristic, complemented
7C2×#16837691C211yesmaximal, characteristic, complemented
8C2×#16837654C211yesmaximal, characteristic, complemented
9C2×#16837619C211yesmaximal, characteristic, complemented
10C2×#16837546C211yesmaximal, characteristic, complemented
11C2×#16837535C211yesmaximal, characteristic, complemented
12C2×#16837511C211yesmaximal, characteristic, complemented
13C2×#16837473C211yesmaximal, characteristic, complemented
14C2×#16837402C211yesmaximal, characteristic, complemented
15C22×#14273649C211yesmaximal, characteristic, complemented
16C2×C59×#465C211yesmaximal, characteristic, complemented
17C22×#11745689C2211yescharacteristic
18C22×#11745687—21no—
19C23×D236C2211yescharacteristic
20C22×#11745669C2211yescharacteristic
21C22×#11745669C2211yescharacteristic
22C22×#11745659C2211yescharacteristic, complemented
23#16838052—24no—
24#16838052C2218yescomplemented
25#16838043—24no—
26#16838043C2218yescomplemented
27C2×#14273726C2211yescharacteristic, complemented
28C2×#14273716C2211yescharacteristic
29C2×#14273712—21no—
30C2×#14273709—21no—
31C2×#14273708—21no—
32C2×#14273704—21no—
33C2×#14273702—21no—
34C2×#14273702C2211yescharacteristic
35C2×#14273698C2211yescharacteristic, complemented
36C2×#14273697—21no—
37C2×D4×Dic59C2211yescharacteristic, complemented
38C2×#14273689C2211yescharacteristic
39C2×C4×C22⋊D59C2211yescharacteristic
40C22×C4⋊Dic59C2211yescharacteristic
41C2×C4⋊C4×D59C2211yescharacteristic, complemented
42C2×C22⋊C4×D59—21no—
43#16837763C2218yescomplemented
44#16837730C2218yescomplemented
45#16837722C2218yescomplemented
46#16837691C2218yescomplemented
47#16837654C2218yescomplemented
48#16837619C2218yescomplemented
49#16837546C2218yescomplemented
50#16837535C2218yescomplemented
51#16837511C2218yescomplemented
52#16837473C2218yescomplemented
53C2×#14273658C2211yescharacteristic, complemented
54C2×#14273658C2211yescharacteristic, complemented
55C2×Dic59⋊C8C2211yescharacteristic, complemented
56#16837402C2218yescomplemented
57C2×#14273651C2211yescharacteristic, complemented
58C2×#14273651C2211yescharacteristic, complemented
59C2×#14273649C2211yescharacteristic
60C2×#14273649C2211yescharacteristic
61C2×#14273649C2211yescharacteristic
62C2×#14273649C2211yescharacteristic
63C2×#14273649C2218yescomplemented
64C2×#14273647C2211yescharacteristic
65C2×#14273647C2211yescharacteristic
66C2×C22⋊(C59⋊C8)C2211yescharacteristic
67C2×(C2×D59)⋊C8C2211yescharacteristic, complemented
68C2×#14273637C2211yescharacteristic, complemented
69C22×SD16×C59C2211yescharacteristic, complemented
70C23×C8×C59C2211yescharacteristic
71C2×C22⋊Q8×C59C2211yescharacteristic
72C2×#121×C59C2211yescharacteristic
73C59×#465C2218yescomplemented
74C2×#106×C59C2211yescharacteristic, complemented
75C2×#103×C59C2211yescharacteristic, complemented
76C2×#102×C59C2211yescharacteristic, complemented
77C24×D59—21no—
78C2×#11745689—22no—
79C2×#11745689—24no—
80C2×#11745689—42no—
81C2×#11745689C2314yes—
82C2×#11745687—28no—
83C2×#11745687—48no—
84C22×Dic118—21no—
85C22×D236—24no—
86C22×D236—21no—
87C22×D236—21no—
88C22×D236—22no—
89C22×D236—21no—
90C22×D236—42no—
91C22×D236C2311yescharacteristic
92C22×D236C2314yes—
93C22×D236C2311yescharacteristic
94C22×C22⋊D59—21no—
95C22×C22⋊D59D411yescharacteristic
96C23×Dic59—21no—
97C23×Dic59—21no—
98C22×C4×D59—21no—
99C22×C4×D59—21no—
100C22×C4×D59—21no—
101C22×C4×D59C2311yescharacteristic
102C2×#11745669—24no—
103C2×#11745669—42no—
104C2×#11745669C2314yes—
105C2×#11745669C2314yes—
106C2×#11745659—42no—
107C2×#11745659C2314yescomplemented
108C22×C59⋊C8C2311yescharacteristic
109C22×C59⋊C8C2311yescharacteristic
110#14273726—22no—
111#14273726C2314yescomplemented
112#14273716—22no—
113#14273716C2314yes—
114#14273712—28no—
115#14273709—28no—
116#14273708—28no—
117#14273704—28no—
118#14273702—22no—
119#14273702—28no—
120#14273702C2314yes—
121#14273698—22no—
122#14273698C2314yescomplemented
123#14273697—28no—
124D4×Dic59—22no—
125D4×Dic59C2314yescomplemented
126#14273689—22no—
127#14273689C2314yes—
128C4×C22⋊D59D414yes—
129C4×C22⋊D59C2314yes—
130C2×C4⋊Dic59—21no—
131C2×C4⋊Dic59—22no—
132C2×C4⋊Dic59C2311yescharacteristic
133C2×C4⋊Dic59C2311yescharacteristic
134C2×C4⋊Dic59C2314yes—
135C2×Dic59⋊C4—21no—
136C2×Dic59⋊C4—21no—
137C2×Dic59⋊C4D411yescharacteristic
138C4⋊C4×D59—22no—
139C4⋊C4×D59C2314yescomplemented
140C2×C22⋊Dic59—21no—
141C2×C22⋊Dic59—21no—
142C2×C22⋊Dic59D411yescharacteristic
143C2×(C2×D59)⋊C4—21no—
144C2×(C2×D59)⋊C4—21no—
145C2×(C2×D59)⋊C4—21no—
146C2×(C2×D59)⋊C4—21no—
147C2×(C2×D59)⋊C4D411yescharacteristic
148C22⋊C4×D59—28no—
149C2×C4×Dic59C2311yescharacteristic
150#14273658C2314yescomplemented
151#14273658C2314yescomplemented
152Dic59⋊C8C2314yescomplemented
153#14273651C2314yescomplemented
154#14273651C2314yescomplemented
155#14273649C2314yes—
156#14273649C2314yes—
157#14273649C2314yes—
158#14273649C2314yes—
159#14273647C2314yes—
160#14273647C2314yes—
161C22⋊(C59⋊C8)C2314yes—
162(C2×D59)⋊C8C2314yescomplemented
163#14273637C2314yescomplemented
164C22×Q8×C59C2311yescharacteristic
165C22×D4×C59—21no—
166C22×D4×C59C2311yescharacteristic
167C23×C4×C59C2311yescharacteristic
168C2×SD16×C59—42no—
169C2×SD16×C59C2314yescomplemented
170C22×C8×C59—42no—
171C22×C8×C59C2311yescharacteristic
172C22×C8×C59C2311yescharacteristic
173C22×C8×C59C2314yes—
174C22⋊Q8×C59—22no—
175C22⋊Q8×C59C2314yes—
176#121×C59—22no—
177#121×C59C2314yes—
178C2×C4⋊C4×C59—21no—
179C2×C4⋊C4×C59C2311yescharacteristic
180C2×C4⋊C4×C59C2311yescharacteristic
181C2×C22⋊C4×C59—21no—
182C2×C22⋊C4×C59—21no—
183#106×C59C2314yescomplemented
184#103×C59C2314yescomplemented
185#102×C59C2314yescomplemented
186C24×C59—21no—
187C24×C59C2×D411yescharacteristic
188C23×D59—21no—
189C23×D59—21no—
190C23×D59—24no—
191C23×D59—44no—
192C23×D59—44no—
193C23×D59—82no—
194C23×D59C2×D411yescharacteristic
195C2×Q8×C59—21no—
196C2×Q8×C59—22no—
197C2×Q8×C59—22no—
198C2×Q8×C59C2412yes—
199C2×D4×C59—24no—
200C2×D4×C59—21no—
201C2×D4×C59—22no—
202C2×D4×C59—22no—
203C2×D4×C59—44no—
204C2×D4×C59C2412yes—
205C22×C4×C59—22no—
206C22×C4×C59—22no—
207C22×C4×C59—21no—
208C22×C4×C59—21no—
209C22×C4×C59—21no—
210C22×C4×C59C2×D411yescharacteristic
211C22×C4×C59C2×D412yes—
212C22×C4×C59C2412yes—
213C22×C4×C59C2411yescharacteristic
214C2×C22⋊D59—24no—
215C2×C22⋊D59—24no—
216C2×C22⋊D59—44no—
217C2×C22⋊D59C2×D414yes—
218C22×Dic59—21no—
219C22×Dic59—21no—
220C22×Dic59—24no—
221C22×Dic59—24no—
222C22×Dic59—44no—
223C22×Dic59—44no—
224C22×Dic59C2×D411yescharacteristic
225C22×Dic59C2×D411yescharacteristic
226C22×Dic59C2×D411yescharacteristic
227#11745689—28no—
228#11745689—44no—
229#11745689—48no—
230#11745687—432no—
231C2×D236—21no—
232C2×D236—22no—
233C2×D236—22no—
234C2×D236—22no—
235C2×D236—28no—
236C2×D236—24no—
237C2×D236—24no—
238C2×D236—21no—
239C2×D236—24no—
240C2×D236—44no—
241C2×D236—48no—
242C2×D236—44no—
243C2×D236—44no—
244C2×D236—82no—
245C2×D236#4114yescomplemented
246C2×D236C2412yes—
247C2×D236C2412yes—
248C2×C4×D59—22no—
249C2×C4×D59—22no—
250C2×C4×D59—24no—
251C2×C4×D59—24no—
252C2×C4×D59—24no—
253C2×C4×D59—44no—
254C2×C4×D59—44no—
255C2×C4×D59—82no—
256C2×C4×D59C2×D412yes—
257C2×C4×D59C2412yes—
258C2×Dic118—24no—
259C2×Dic118—44no—
260SD16×C59—44no—
261C2×C8×C59—22no—
262C2×C8×C59—22no—
263C2×C8×C59—44no—
264C2×C8×C59C2412yes—
265C2×C8×C59C2412yes—
266C4⋊C4×C59—24no—
267C4⋊C4×C59—21no—
268C4⋊C4×C59—21no—
269C4⋊C4×C59C2412yes—
270C4⋊C4×C59C2412yes—
271C22⋊C4×C59—24no—
272C22⋊C4×C59—24no—
273C22⋊Dic59—24no—
274C22⋊Dic59—24no—
275C22⋊Dic59C2×D414yes—
276#11745669—28no—
277#11745669—44no—
278(C2×D59)⋊C4—24no—
279(C2×D59)⋊C4—24no—
280(C2×D59)⋊C4—24no—
281(C2×D59)⋊C4—24no—
282(C2×D59)⋊C4C2×D414yes—
283C4⋊Dic59—21no—
284C4⋊Dic59—21no—
285C4⋊Dic59—24no—
286C4⋊Dic59C2412yes—
287C4⋊Dic59C2412yes—
288Dic59⋊C4—24no—
289Dic59⋊C4—24no—
290Dic59⋊C4C2×D414yes—
291C4×Dic59C2×D412yes—
292C4×Dic59C2412yes—
293C2×C59⋊C8—22no—
294C2×C59⋊C8—22no—
295C2×C59⋊C8C2412yes—
296C2×C59⋊C8C2412yes—
297#11745659—44no—
298C23×C59—22no—
299C23×C59—22no—
300C23×C59—22no—
301C23×C59—42no—
302C23×C59—42no—
303C23×C59—42no—
304C23×C59AGL(1,ℤ/8)14yes—
305C23×C59C22×D412yes—
306C23×C59C22×D411yescharacteristic
307C22×D59—22no—
308C22×D59—24no—
309C22×D59—22no—
310C22×D59—22no—
311C22×D59—22no—
312C22×D59—22no—
313C22×D59—48no—
314C22×D59—42no—
315C22×D59—42no—
316C22×D59—42no—
317C22×D59—48no—
318C22×D59—42no—
319C22×D59—42no—
320C22×D59—84no—
321C22×D59—816no—
322C22×D59C22×D412yes—
323Q8×C59—22no—
324Q8×C59—22no—
325Q8×C59—42no—
326D4×C59—22no—
327D4×C59—22no—
328D4×C59—48no—
329D4×C59—42no—
330C2×C4×C59—22no—
331C2×C4×C59—24no—
332C2×C4×C59—22no—
333C2×C4×C59—22no—
334C2×C4×C59—22no—
335C2×C4×C59—22no—
336C2×C4×C59—22no—
337C2×C4×C59—42no—
338C2×C4×C59—42no—
339C2×C4×C59—42no—
340C2×C4×C59C22×D412yes—
341C2×C4×C59C22×D411yescharacteristic
342C2×C4×C59C2×#4112yes—
343C2×C4×C59H(5,𝔽2)12yes—
344C2×C4×C59C2511yescharacteristic
345C22⋊D59—28no—
346C22⋊D59—48no—
347C2×Dic59—22no—
348C2×Dic59—22no—
349C2×Dic59—22no—
350C2×Dic59—22no—
351C2×Dic59—22no—
352C2×Dic59—48no—
353C2×Dic59—42no—
354C2×Dic59—42no—
355C2×Dic59—48no—
356C2×Dic59C22×D412yes—
357C2×Dic59C22×D412yes—
358C2×Dic59C22×D412yes—
359D236—24no—
360D236—22no—
361D236—22no—
362D236—22no—
363D236—48no—
364D236—48no—
365D236—42no—
366D236—84no—
367D236C2×#4114yescomplemented
368C4×D59—24no—
369C4×D59—22no—
370C4×D59—22no—
371C4×D59—48no—
372C4×D59—48no—
373C4×D59—84no—
374Dic118—48no—
375C8×C59—22no—
376C8×C59—22no—
377C59⋊C8—22no—
378C59⋊C8—22no—
379C2×#3306—591nomaximal, Sylow
380C22×C59—22no—
381C22×C59—28no—
382C22×C59—22no—
383C22×C59—42no—
384C22×C59—42no—
385C22×C59—42no—
386C22×C59—84no—
387C22×C59#54612yes—
388C22×C59C2×AGL(1,ℤ/8)14yes—
389C22×C59C2×AGL(1,ℤ/8)12yes—
390C22×C59#57712yes—
391C22×C59C23×D411yescharacteristic
392C2×D59—22no—
393C2×D59—24no—
394C2×D59—22no—
395C2×D59—22no—
396C2×D59—44no—
397C2×D59—48no—
398C2×D59—42no—
399C2×D59—42no—
400C2×D59—42no—
401C2×D59—42no—
402C2×D59—42no—
403C2×D59—816no—
404C2×D59—84no—
405C4×C59—22no—
406C4×C59—42no—
407C4×C59—42no—
408C4×C59—42no—
409C4×C59#54612yes—
410C4×C59C22×#4111yescharacteristic
411C4×C59C2×H(5,𝔽2)11yescharacteristic
412Dic59—22no—
413Dic59—22no—
414Dic59—22no—
415Dic59—42no—
416Dic59—42no—
417C2×#547—591no—
418C2×#546—591no—
419#3306—5916no—
420C2×#489—591no—
421C2×#481—591no—
422C2×#483—591no—
423C2×#476—591no—
424C2×#469—591no—
425C2×#465D5911yescharacteristic, complemented
426C2×#463—591no—
427C2×#449—591no—
428C2×#447—591no—
429C2×#442—591no—
430C2×#435—591no—
431C2×#417—591no—
432C22×#102—591no—
433C2×C59—24no—
434C2×C59—82no—
435C2×C59#330614yescomplemented
436C2×C59C2×#54611yescharacteristic
437C2×C59C22×AGL(1,ℤ/8)11yescharacteristic
438C2×C59C2×#57711yescharacteristic
439D59—42no—
440D59—44no—
441D59—82no—
442C22×#41—591no—
443C22×#41—1181no—
444C23×D4—591no—
445C22×SD16C2×D5911yescharacteristic, complemented
446C22×D8—591no—
447C22×D8—591no—
448C22×M16—591no—
449C23×C8C2×D5911yescharacteristic
450#547—598no—
451#547—1184no—
452#546—598no—
453#546—1184no—
454C2×C4⋊Q8—591no—
455C2×#124—591no—
456C2×#123—1181no—
457C2×#123—1181no—
458C2×#123—1181no—
459C2×C22⋊Q8—1181no—
460C2×C22⋊Q8C2×D5911yescharacteristic
461C2×#121—591no—
462C2×#121—591no—
463C2×#121—1181no—
464C2×#121C2×D5911yescharacteristic
465C2×#120—1181no—
466C2×C4×D4—591no—
467C2×C4×D4—591no—
468C2×C4×D4—591no—
469C22×C4⋊C4—591no—
470C22×C4⋊C4—591no—
471C22×C22⋊C4—1181no—
472#489—598no—
473#483—598no—
474#481—598no—
475#476—598no—
476#469—598no—
477#465C2×D5918yescomplemented
478#463—598no—
479#449—598no—
480#447—598no—
481#442—598no—
482#435—598no—
483C2×#106—591no—
484C2×#106—591no—
485C2×#106C2×D5911yescharacteristic, complemented
486C2×C4⋊C8—591no—
487#417—598no—
488C2×#103—591no—
489C2×#103—591no—
490C2×#103C2×D5911yescharacteristic, complemented
491C2×#102—591no—
492C2×#102—591no—
493C2×#102—591no—
494C2×#102—591no—
495C2×#102—598no—
496C2×#102—591no—
497C2×#102—591no—
498C2×#102C2×D5911yescharacteristic, complemented
499C2×C22⋊C8—591no—
500C2×C22⋊C8—591no—
501C2×#97—591no—
502C59C2×#330611yescharacteristic, complemented, Sylow
503C25—1181no—
504C2×#41—594no—
505C2×#41—1182no—
506C2×#41—1188no—
507C2×#41—1184no—
508C2×#41—2362no—
509C2×#41—2368no—
510C22×Q8—1181no—
511C22×Q8C22×D5911yescharacteristic
512C22×D4—21no—
513C22×D4—591no—
514C22×D4—591no—
515C22×D4—591no—
516C22×D4—594no—
517C22×D4—1184no—
518C22×D4—1181no—
519C22×D4—1181no—
520C22×D4—1181no—
521C22×D4—1181no—
522C22×D4—1182no—
523C22×D4—2362no—
524C22×D4C22×D5911yescharacteristic
525C23×C4—591no—
526C23×C4—1181no—
527C23×C4—1181no—
528C23×C4—1181no—
529C23×C4—1181no—
530C23×C4—1181no—
531C23×C4C22×D5911yescharacteristic
532C2×SD16—42no—
533C2×SD16C22×D5914yescomplemented
534C2×D8—594no—
535C2×D8—594no—
536C2×D8—1184no—
537C2×D8—2362no—
538C2×M16—594no—
539C2×M16—2362no—
540C22×C8—42no—
541C22×C8—591no—
542C22×C8—591no—
543C22×C8C22×D5911yescharacteristic
544C22×C8C22×D5911yescharacteristic
545C22×C8C22×D5914yes—
546C4⋊Q8—594no—
547C4⋊Q8—1182no—
548#124—594no—
549#124—1182no—
550#123—1188no—
551#123—1188no—
552#123—1188no—
553C22⋊Q8—22no—
554C22⋊Q8—1188no—
555C22⋊Q8C22×D5914yes—
556#121—22no—
557#121—594no—
558#121—594no—
559#121—1188no—
560#121—1182no—
561#121—1182no—
562#121C22×D5914yes—
563#120—1188no—
564C4×D4—594no—
565C4×D4—594no—
566C4×D4—594no—
567C4×D4—594no—
568C4×D4—1182no—
569C4×D4—1182no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—591no—
572C2×C4⋊C4—591no—
573C2×C4⋊C4—591no—
574C2×C4⋊C4—594no—
575C2×C4⋊C4—594no—
576C2×C4⋊C4—1182no—
577C2×C4⋊C4—1181no—
578C2×C4⋊C4—1181no—
579C2×C4⋊C4—1181no—
580C2×C4⋊C4—1182no—
581C2×C4⋊C4C22×D5911yescharacteristic
582C2×C4⋊C4C22×D5911yescharacteristic
583C2×C22⋊C4—21no—
584C2×C22⋊C4—21no—
585C2×C22⋊C4—591no—
586C2×C22⋊C4—591no—
587C2×C22⋊C4—1188no—
588C2×C22⋊C4—1181no—
589C2×C22⋊C4—1181no—
590C2×C22⋊C4—1181no—
591C2×C22⋊C4—1181no—
592C2×C22⋊C4—1181no—
593C2×C22⋊C4—1181no—
594C2×C42—591no—
595#106—594no—
596#106—594no—
597#106C22×D5914yescomplemented
598C4⋊C8—594no—
599#103—594no—
600#103—594no—
601#103C22×D5914yescomplemented
602#102—594no—
603#102—594no—
604#102—594no—
605#102—594no—
606#102—594no—
607#102—594no—
608#102C22×D5914yescomplemented
609C22⋊C8—594no—
610C22⋊C8—594no—
611#97—594no—
612C24—21no—
613C24—591no—
614C24—1181no—
615C24—1184no—
616C24—1181no—
617C24—4722no—
618C24—2364no—
619C24—2364no—
620C24D4×D5911yescharacteristic
621#41—1188no—
622#41—2364no—
623#41—2368no—
624#41—23632no—
625C2×Q8—21no—
626C2×Q8—22no—
627C2×Q8—22no—
628C2×Q8—1184no—
629C2×Q8—2364no—
630C2×Q8C23×D5912yes—
631C2×D4—24no—
632C2×D4—21no—
633C2×D4—22no—
634C2×D4—22no—
635C2×D4—44no—
636C2×D4—594no—
637C2×D4—594no—
638C2×D4—592no—
639C2×D4—592no—
640C2×D4—1188no—
641C2×D4—1184no—
642C2×D4—1184no—
643C2×D4—1184no—
644C2×D4—1184no—
645C2×D4—1181no—
646C2×D4—1184no—
647C2×D4—1181no—
648C2×D4—1182no—
649C2×D4—1182no—
650C2×D4—1182no—
651C2×D4—4722no—
652C2×D4—2364no—
653C2×D4—2368no—
654C2×D4—2364no—
655C2×D4—2364no—
656C2×D4—2364no—
657C2×D4C23×D5912yes—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—591no—
664C22×C4—591no—
665C22×C4—591no—
666C22×C4—592no—
667C22×C4—592no—
668C22×C4—1184no—
669C22×C4—1184no—
670C22×C4—1184no—
671C22×C4—1184no—
672C22×C4—1182no—
673C22×C4—1182no—
674C22×C4—1184no—
675C22×C4—1181no—
676C22×C4—1181no—
677C22×C4—4722no—
678C22×C4—2364no—
679C22×C4—2364no—
680C22×C4—2364no—
681C22×C4—2364no—
682C22×C4D4×D5912yes—
683C22×C4D4×D5911yescharacteristic
684C22×C4C23×D5912yes—
685C22×C4C23×D5911yescharacteristic
686SD16—44no—
687D8—1188no—
688D8—2364no—
689M16—2364no—
690C2×C8—22no—
691C2×C8—22no—
692C2×C8—44no—
693C2×C8—592no—
694C2×C8—592no—
695C2×C8—1182no—
696C2×C8—1182no—
697C2×C8C23×D5912yes—
698C2×C8C23×D5912yes—
699C4⋊C4—24no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—594no—
703C4⋊C4—592no—
704C4⋊C4—592no—
705C4⋊C4—1184no—
706C4⋊C4—1184no—
707C4⋊C4—1181no—
708C4⋊C4—1181no—
709C4⋊C4—1184no—
710C4⋊C4C23×D5912yes—
711C4⋊C4C23×D5912yes—
712C22⋊C4—24no—
713C22⋊C4—24no—
714C22⋊C4—594no—
715C22⋊C4—594no—
716C22⋊C4—1184no—
717C22⋊C4—1184no—
718C22⋊C4—1184no—
719C22⋊C4—1184no—
720C22⋊C4—1184no—
721C22⋊C4—1184no—
722C42—592no—
723C42—592no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—42no—
728C23—42no—
729C23—42no—
730C23—592no—
731C23—1182no—
732C23—1182no—
733C23—1182no—
734C23—1182no—
735C23—1184no—
736C23—1182no—
737C23—47216no—
738C23—4724no—
739C23—2368no—
740C23—2368no—
741C23—2362no—
742C23—2362no—
743C23—2362no—
744C23—2362no—
745C23—2362no—
746C23#1427375414yes—
747C23C2×D4×D5912yes—
748C23C2×D4×D5911yescharacteristic
749Q8—22no—
750Q8—22no—
751Q8—42no—
752Q8—2368no—
753D4—22no—
754D4—22no—
755D4—48no—
756D4—42no—
757D4—594no—
758D4—1188no—
759D4—1182no—
760D4—1182no—
761D4—1182no—
762D4—1184no—
763D4—4724no—
764D4—2368no—
765D4—2368no—
766D4—2368no—
767D4—2362no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—24no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—592no—
779C2×C4—592no—
780C2×C4—592no—
781C2×C4—1182no—
782C2×C4—1182no—
783C2×C4—1182no—
784C2×C4—1182no—
785C2×C4—1182no—
786C2×C4—1184no—
787C2×C4—1182no—
788C2×C4—1182no—
789C2×C4—4724no—
790C2×C4—2368no—
791C2×C4—2368no—
792C2×C4—2368no—
793C2×C4—2362no—
794C2×C4—2362no—
795C2×C4—2368no—
796C2×C4C2×D4×D5912yes—
797C2×C4C2×D4×D5911yescharacteristic
798C2×C4#41×D5912yes—
799C2×C4#1427377212yes—
800C2×C4C24×D5911yescharacteristic
801C8—22no—
802C8—22no—
803C8—1182no—
804C8—1182no—
805C22—22no—
806C22—22no—
807C22—28no—
808C22—42no—
809C22—42no—
810C22—42no—
811C22—84no—
812C22—1182no—
813C22—1184no—
814C22—1182no—
815C22—1182no—
816C22—47216no—
817C22—4724no—
818C22—2362no—
819C22—2362no—
820C22—2362no—
821C22—2362no—
822C22—2362no—
823C22—2364no—
824C22—2368no—
825C22#1683804112yes—
826C22C2×#1427375414yes—
827C22C2×#1427375412yes—
828C22#1683820912yes—
829C22C22×D4×D5911yescharacteristic
830C4—22no—
831C4—42no—
832C4—42no—
833C4—42no—
834C4—1182no—
835C4—1182no—
836C4—1182no—
837C4—2362no—
838C4—2362no—
839C4#1683804112yes—
840C4C2×#41×D5911yescharacteristic
841C4C2×#1427377211yescharacteristic
842C2—24no—
843C2—82no—
844C2—4722no—
845C2—2362no—
846C2—2364no—
847C2#2143606314yesdirect product factor
848C2C2×#1683804111yescharacteristic
849C2C22×#1427375411yescharacteristic
850C2C2×#1683820911yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#465C2
socleC23×C59C22×D4
hypercenterC2×#465D59
hypocenterC59C2×#3306
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#465

Complements

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

NH ≅ G/Ntype
1. C2×#16838052C2semidirect
2. C2×#16838043C2semidirect
3. #21436063C2direct (N × H)
4. C2×#16837763C2semidirect
5. C2×#16837722C2semidirect
6. C2×#16837730C2semidirect
7. C2×#16837691C2semidirect
8. C2×#16837654C2semidirect
9. C2×#16837619C2semidirect
10. C2×#16837546C2semidirect
11. C2×#16837535C2semidirect
12. C2×#16837511C2semidirect
13. C2×#16837473C2semidirect
14. C2×#16837402C2semidirect
15. C22×#14273649C2semidirect
16. C2×C59×#465C2semidirect
22. C22×#11745659C22semidirect
24. #16838052C22semidirect
26. #16838043C22semidirect
27. C2×#14273726C22semidirect
35. C2×#14273698C22semidirect
37. C2×D4×Dic59C22semidirect
41. C2×C4⋊C4×D59C22semidirect
43. #16837763C22semidirect
44. #16837730C22semidirect
45. #16837722C22semidirect
46. #16837691C22semidirect
47. #16837654C22semidirect
48. #16837619C22semidirect
49. #16837546C22semidirect
50. #16837535C22semidirect
51. #16837511C22semidirect
52. #16837473C22semidirect
53. C2×#14273658C22semidirect
54. C2×#14273658C22semidirect
55. C2×Dic59⋊C8C22semidirect
56. #16837402C22semidirect
57. C2×#14273651C22semidirect
58. C2×#14273651C22semidirect
63. C2×#14273649C22semidirect
67. C2×(C2×D59)⋊C8C22semidirect
68. C2×#14273637C22semidirect
69. C22×SD16×C59C22semidirect
73. C59×#465C22semidirect
74. C2×#106×C59C22semidirect
75. C2×#103×C59C22semidirect
76. C2×#102×C59C22semidirect
107. C2×#11745659C23semidirect
111. #14273726C23semidirect
122. #14273698C23semidirect
125. D4×Dic59C23semidirect
139. C4⋊C4×D59C23semidirect
150. #14273658C23semidirect
151. #14273658C23semidirect
152. Dic59⋊C8C23semidirect
153. #14273651C23semidirect
154. #14273651C23semidirect
162. (C2×D59)⋊C8C23semidirect
163. #14273637C23semidirect
169. C2×SD16×C59C23semidirect
183. #106×C59C23semidirect
184. #103×C59C23semidirect
185. #102×C59C23semidirect
245. C2×D236#41semidirect
367. D236C2×#41semidirect
425. C2×#465D59semidirect
435. C2×C59#3306semidirect
445. C22×SD16C2×D59semidirect
477. #465C2×D59semidirect
485. C2×#106C2×D59semidirect
490. C2×#103C2×D59semidirect
498. C2×#102C2×D59semidirect
502. C59C2×#3306semidirect
533. C2×SD16C22×D59semidirect
597. #106C22×D59semidirect
601. #103C22×D59semidirect
608. #102C22×D59semidirect
847. C2#21436063direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168380522
C2×#168380432
#214360632
C2×#168377632
C2×#168377222
C2×#168377302
C2×#168376912
C2×#168376542
C2×#168376192
C2×#168375462
C2×#168375352
C2×#168375112
C2×#168374732
C2×#168374022
C22×#142736492
C2×C59×#4652
C2×#330659