Finite Group Databasebeta

← C2×#21436561 #29467247

Subgroups — C2×#21436561 #29467247

Order 15104.

2158 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838099C211yesmaximal, characteristic, complemented
2C2×#16838052C211yesmaximal, characteristic, complemented
3#21436561C2116yesmaximal, direct product factor
4C2×#16837809C211yesmaximal, characteristic, complemented
5C2×#16837719C211yesmaximal, characteristic, complemented
6C2×#16837718C211yesmaximal, characteristic, complemented
7C2×#16837723C211yesmaximal, characteristic, complemented
8C2×#16837714C211yesmaximal, characteristic, complemented
9C2×#16837700C211yesmaximal, characteristic, complemented
10C2×#16837690C211yesmaximal, characteristic, complemented
11C2×#16837635C211yesmaximal, characteristic, complemented
12C2×#16837514C211yesmaximal, characteristic, complemented
13C2×#16837471C211yesmaximal, characteristic, complemented
14C2×#16837444C211yesmaximal, characteristic, complemented
15C2×#106×D59C211yesmaximal, characteristic, complemented
16C2×C59×#469C211yesmaximal, characteristic, complemented
17C22×#11745687—21no—
18C22×C8×D59C2211yescharacteristic
19#16838099—24no—
20#16838099C2218yescomplemented
21#16838052—24no—
22#16838052C2218yescomplemented
23C2×#14273726C2211yescharacteristic
24C2×#14273720—21no—
25C2×#14273718C2211yescharacteristic
26C2×#14273709—21no—
27C2×#14273708—21no—
28C2×#14273708—21no—
29C2×#14273704—21no—
30C2×#14273698—21no—
31C2×#14273698C2211yescharacteristic
32C2×#14273698C2211yescharacteristic
33C2×D4×Dic59C2211yescharacteristic
34C2×D4×Dic59C2211yescharacteristic
35C2×C4×C22⋊D59C2211yescharacteristic
36C2×(C22⋊D59)⋊C4—21no—
37C2×#14273686C2211yescharacteristic
38C22×C4⋊Dic59C2211yescharacteristic
39C2×C4⋊C4×D59C2211yescharacteristic
40C2×C4⋊C4×D59C2211yescharacteristic
41#16837809C2218yescomplemented
42#16837723C2218yescomplemented
43#16837719C2218yescomplemented
44#16837718C2218yescomplemented
45#16837714C2218yescomplemented
46#16837700C2218yescomplemented
47#16837690C2218yescomplemented
48#16837635C2218yescomplemented
49#16837514C2218yescomplemented
50#16837471C2218yescomplemented
51#16837444C2218yescomplemented
52C2×#14273661C2211yescharacteristic
53C2×#14273661C2211yescharacteristic
54C2×#14273660C2211yescharacteristic
55C2×#14273659C2211yescharacteristic
56C2×#14273659C2211yescharacteristic
57C2×#14273658C2211yescharacteristic
58C2×#14273658C2211yescharacteristic
59C2×#14273658C2211yescharacteristic
60#106×D59C2218yescomplemented
61C2×Dic59⋊C8C2211yescharacteristic
62C2×#14273648C2211yescharacteristic
63C2×#14273648C2211yescharacteristic
64C2×#14273648C2211yescharacteristic
65C2×#14273648C2211yescharacteristic
66C2×C22⋊(C59⋊C8)C2211yescharacteristic
67C2×(C2×D59)⋊C8C2211yescharacteristic
68C2×#14273637C2211yescharacteristic
69C22×D8×C59C2211yescharacteristic
70C22×M16×C59C2211yescharacteristic
71C2×#121×C59C2211yescharacteristic
72C2×#121×C59C2211yescharacteristic
73C59×#469C2218yescomplemented
74C2×#106×C59C2211yescharacteristic
75C2×#102×C59C2211yescharacteristic
76C2×#102×C59C2211yescharacteristic
77C2×#11745687—28no—
78C2×#11745687—48no—
79C22×Dic118—21no—
80C22×C22⋊D59—21no—
81C22×C22⋊D59—21no—
82C22×C22⋊D59D411yescharacteristic
83C23×Dic59—21no—
84C23×Dic59—21no—
85C23×Dic59—21no—
86C22×C4×D59—21no—
87C22×C4×D59—21no—
88C22×C4×D59C2311yescharacteristic
89C22×C59⋊C8C2311yescharacteristic
90C22×C59⋊C8C2311yescharacteristic
91C2×C8×D59—24no—
92C2×C8×D59C2314yes—
93#14273726—22no—
94#14273726C2314yes—
95#14273720—28no—
96#14273718—22no—
97#14273718C2314yes—
98#14273709—28no—
99#14273708—28no—
100#14273708—28no—
101#14273704—28no—
102#14273698—28no—
103#14273698—22no—
104#14273698—22no—
105#14273698C2314yes—
106#14273698C2314yes—
107D4×Dic59—22no—
108D4×Dic59—22no—
109D4×Dic59C2314yes—
110D4×Dic59C2314yes—
111C4×C22⋊D59D414yes—
112C4×C22⋊D59C2314yes—
113(C22⋊D59)⋊C4—28no—
114#14273686—22no—
115#14273686C2314yes—
116C2×C4⋊Dic59—21no—
117C2×C4⋊Dic59—22no—
118C2×C4⋊Dic59—21no—
119C2×C4⋊Dic59C2311yescharacteristic
120C2×C4⋊Dic59C2311yescharacteristic
121C2×C4⋊Dic59C2311yescharacteristic
122C2×C4⋊Dic59C2311yescharacteristic
123C2×C4⋊Dic59C2314yes—
124C2×Dic59⋊C4—21no—
125C2×Dic59⋊C4—21no—
126C2×Dic59⋊C4—21no—
127C2×Dic59⋊C4—21no—
128C2×Dic59⋊C4D411yescharacteristic
129C4⋊C4×D59—22no—
130C4⋊C4×D59—22no—
131C4⋊C4×D59C2314yes—
132C4⋊C4×D59C2314yes—
133C2×C22⋊Dic59—21no—
134C2×C22⋊Dic59—21no—
135C2×C22⋊Dic59—21no—
136C2×C22⋊Dic59—21no—
137C2×C22⋊Dic59—21no—
138C2×C22⋊Dic59D411yescharacteristic
139C2×(C2×D59)⋊C4D411yescharacteristic
140C2×C4×Dic59—21no—
141C2×C4×Dic59C2311yescharacteristic
142#14273661C2314yes—
143#14273661C2314yes—
144#14273660C2314yes—
145#14273659C2314yes—
146#14273659C2314yes—
147#14273658C2314yes—
148#14273658C2314yes—
149#14273658C2314yes—
150Dic59⋊C8C2314yes—
151#14273648C2314yes—
152#14273648C2314yes—
153#14273648C2314yes—
154#14273648C2314yes—
155C22⋊(C59⋊C8)C2314yes—
156(C2×D59)⋊C8C2314yes—
157#14273637C2314yes—
158C22×D4×C59—21no—
159C22×D4×C59—21no—
160C22×D4×C59C2311yescharacteristic
161C22×D4×C59C2311yescharacteristic
162C23×C4×C59C2311yescharacteristic
163C2×D8×C59—24no—
164C2×D8×C59C2314yes—
165C2×M16×C59—24no—
166C2×M16×C59C2314yes—
167C22×C8×C59C2311yescharacteristic
168C22×C8×C59C2311yescharacteristic
169#121×C59—22no—
170#121×C59—22no—
171#121×C59C2314yes—
172#121×C59C2314yes—
173C2×C4⋊C4×C59C2311yescharacteristic
174C2×C4⋊C4×C59C2311yescharacteristic
175C2×C22⋊C4×C59—21no—
176C2×C22⋊C4×C59—21no—
177#106×C59C2314yes—
178#102×C59C2314yes—
179#102×C59C2314yes—
180C24×C59—21no—
181C24×C59—21no—
182C24×C59C2×D411yescharacteristic
183C23×D59C2×D411yescharacteristic
184C2×D4×C59—24no—
185C2×D4×C59—24no—
186C2×D4×C59—21no—
187C2×D4×C59—21no—
188C2×D4×C59—22no—
189C2×D4×C59—22no—
190C2×D4×C59—22no—
191C2×D4×C59—22no—
192C2×D4×C59—44no—
193C2×D4×C59—82no—
194C2×D4×C59C2412yes—
195C2×D4×C59C2412yes—
196C22×C4×C59—22no—
197C22×C4×C59—22no—
198C22×C4×C59—21no—
199C22×C4×C59—21no—
200C22×C4×C59C2×D411yescharacteristic
201C22×C4×C59C2×D412yes—
202C22×C4×C59C2412yes—
203C22×C4×C59C2411yescharacteristic
204C2×C22⋊D59—24no—
205C2×C22⋊D59—24no—
206C2×C22⋊D59—24no—
207C2×C22⋊D59—44no—
208C2×C22⋊D59—44no—
209C2×C22⋊D59C2×D414yes—
210C22×Dic59—21no—
211C22×Dic59—21no—
212C22×Dic59—21no—
213C22×Dic59—21no—
214C22×Dic59—24no—
215C22×Dic59—24no—
216C22×Dic59—24no—
217C22×Dic59—44no—
218C22×Dic59—44no—
219C22×Dic59—82no—
220C22×Dic59C2×D411yescharacteristic
221C22×Dic59C2×D411yescharacteristic
222C22×Dic59C2×D411yescharacteristic
223#11745687—432no—
224C2×C4×D59—22no—
225C2×C4×D59—22no—
226C2×C4×D59—24no—
227C2×C4×D59—24no—
228C2×C4×D59—44no—
229C2×C4×D59—82no—
230C2×C4×D59C2×D412yes—
231C2×C4×D59C2412yes—
232C2×Dic118—24no—
233C2×Dic118—44no—
234D8×C59—28no—
235M16×C59—28no—
236C2×C8×C59—22no—
237C2×C8×C59#4114yescomplemented
238C2×C8×C59C2412yes—
239C2×C8×C59C2412yes—
240C4⋊C4×C59—21no—
241C4⋊C4×C59—21no—
242C4⋊C4×C59C2412yes—
243C4⋊C4×C59C2412yes—
244C22⋊C4×C59—24no—
245C22⋊C4×C59—24no—
246C22⋊Dic59—24no—
247C22⋊Dic59—24no—
248C22⋊Dic59—24no—
249C22⋊Dic59—24no—
250C22⋊Dic59—24no—
251C22⋊Dic59C2×D414yes—
252(C2×D59)⋊C4C2×D414yes—
253C4⋊Dic59—21no—
254C4⋊Dic59—21no—
255C4⋊Dic59—21no—
256C4⋊Dic59—24no—
257C4⋊Dic59—21no—
258C4⋊Dic59—24no—
259C4⋊Dic59C2412yes—
260C4⋊Dic59C2412yes—
261C4⋊Dic59C2412yes—
262C4⋊Dic59C2412yes—
263Dic59⋊C4—24no—
264Dic59⋊C4—24no—
265Dic59⋊C4—24no—
266Dic59⋊C4—24no—
267Dic59⋊C4C2×D414yes—
268C4×Dic59—24no—
269C4×Dic59C2×D412yes—
270C4×Dic59C2412yes—
271C2×C59⋊C8—22no—
272C2×C59⋊C8—22no—
273C2×C59⋊C8C2412yes—
274C2×C59⋊C8C2412yes—
275C8×D59—28no—
276C23×C59—22no—
277C23×C59—22no—
278C23×C59—22no—
279C23×C59—22no—
280C23×C59—22no—
281C23×C59—42no—
282C23×C59—42no—
283C23×C59—42no—
284C23×C59—42no—
285C23×C59—42no—
286C23×C59—42no—
287C23×C59C22×D412yes—
288C23×C59C22×D411yescharacteristic
289C22×D59—22no—
290C22×D59—22no—
291C22×D59AGL(1,ℤ/8)14yes—
292C22×D59C22×D412yes—
293D4×C59—22no—
294D4×C59—22no—
295D4×C59—22no—
296D4×C59—22no—
297D4×C59—48no—
298D4×C59—42no—
299D4×C59—42no—
300D4×C59—84no—
301C2×C4×C59—22no—
302C2×C4×C59—24no—
303C2×C4×C59—22no—
304C2×C4×C59—22no—
305C2×C4×C59—22no—
306C2×C4×C59—22no—
307C2×C4×C59—42no—
308C2×C4×C59—42no—
309C2×C4×C59C22×D412yes—
310C2×C4×C59C22×D411yescharacteristic
311C2×C4×C59C2×#4112yes—
312C2×C4×C592−1+412yes—
313C2×C4×C59C2511yescharacteristic
314C22⋊D59—28no—
315C22⋊D59—48no—
316C22⋊D59—48no—
317C2×Dic59—22no—
318C2×Dic59—22no—
319C2×Dic59—22no—
320C2×Dic59—22no—
321C2×Dic59—22no—
322C2×Dic59—22no—
323C2×Dic59—22no—
324C2×Dic59—48no—
325C2×Dic59—48no—
326C2×Dic59—42no—
327C2×Dic59—42no—
328C2×Dic59—42no—
329C2×Dic59—42no—
330C2×Dic59—84no—
331C2×Dic59C22×D412yes—
332C2×Dic59C22×D412yes—
333C2×Dic59C22×D412yes—
334C4×D59—24no—
335C4×D59—22no—
336C4×D59—22no—
337C4×D59—48no—
338C4×D59—84no—
339Dic118—48no—
340C8×C59—22no—
341C8×C59C2×#4114yescomplemented
342C59⋊C8—22no—
343C59⋊C8—22no—
344C2×#3345—591nomaximal, Sylow
345C22×C59—22no—
346C22×C59—22no—
347C22×C59—22no—
348C22×C59—44no—
349C22×C59—42no—
350C22×C59—42no—
351C22×C59—42no—
352C22×C59—42no—
353C22×C59—42no—
354C22×C59—42no—
355C22×C59—84no—
356C22×C59—84no—
357C22×C59#54712yes—
358C22×C59C2×AGL(1,ℤ/8)12yes—
359C22×C59#57712yes—
360C22×C59C23×D411yescharacteristic
361C2×D59—28no—
362C2×D59—22no—
363C2×D59—22no—
364C2×D59C2×AGL(1,ℤ/8)14yes—
365C4×C59—22no—
366C4×C59—42no—
367C4×C59—42no—
368C4×C59#54712yes—
369C4×C59C22×#4111yescharacteristic
370C4×C59C2×2−1+411yescharacteristic
371Dic59—22no—
372Dic59—22no—
373Dic59—22no—
374Dic59—42no—
375Dic59—42no—
376Dic59—42no—
377Dic59—42no—
378C2×#553—591no—
379C2×#547—591no—
380#3345—5916no—
381C2×#501—591no—
382C2×#481—591no—
383C2×#481—591no—
384C2×#482—591no—
385C2×#480—591no—
386C2×#478—591no—
387C2×#476—591no—
388C2×#469D5911yescharacteristic, complemented
389C2×#466—591no—
390C2×#442—591no—
391C2×#435—591no—
392C2×#428—591no—
393C22×#106—591no—
394C2×C59—42no—
395C2×C59—82no—
396C2×C59—82no—
397C2×C59#334514yescomplemented
398C2×C59C2×#54711yescharacteristic
399C2×C59C22×AGL(1,ℤ/8)11yescharacteristic
400C2×C59C2×#57711yescharacteristic
401D59—24no—
402C22×#41—1181no—
403C22×D8C2×D5911yescharacteristic
404C22×M16C2×D5911yescharacteristic
405C23×C8—591no—
406#553—598no—
407#553—1184no—
408#547—598no—
409#547—1184no—
410C2×C4⋊Q8—591no—
411C2×#126—1181no—
412C2×#125—591no—
413C2×#123—1181no—
414C2×#123—1181no—
415C2×#123—1181no—
416C2×C22⋊Q8—1181no—
417C2×#121—591no—
418C2×#121—591no—
419C2×#121—1181no—
420C2×#121C2×D5911yescharacteristic
421C2×#121C2×D5911yescharacteristic
422C2×C4×D4—591no—
423C2×C4×D4—591no—
424C2×C4×D4—591no—
425C2×C4×D4—1181no—
426C2×#117—591no—
427C22×C4⋊C4—591no—
428C22×C4⋊C4—591no—
429C22×C4⋊C4—591no—
430#501—598no—
431#482—598no—
432#481—598no—
433#481—598no—
434#480—598no—
435#478—598no—
436#476—598no—
437#469C2×D5918yescomplemented
438#466—598no—
439#442—598no—
440#435—598no—
441#428—598no—
442C2×#107—591no—
443C2×#107—591no—
444C2×#107—591no—
445C2×#106—591no—
446C2×#106—591no—
447C2×#106—591no—
448C2×#106—591no—
449C2×#106—591no—
450C2×#106—598no—
451C2×#106C2×D5911yescharacteristic
452C2×C4⋊C8—591no—
453C2×#102—591no—
454C2×#102—591no—
455C2×#102—591no—
456C2×#102—591no—
457C2×#102C2×D5911yescharacteristic
458C2×#102C2×D5911yescharacteristic
459C2×C22⋊C8—591no—
460C2×C22⋊C8—591no—
461C2×#97—591no—
462C59C2×#334511yescharacteristic, complemented, Sylow
463C2×#41—1188no—
464C2×#41—2368no—
465C22×Q8—1181no—
466C22×D4—21no—
467C22×D4—21no—
468C22×D4—591no—
469C22×D4—1181no—
470C22×D4—1181no—
471C22×D4C22×D5911yescharacteristic
472C22×D4C22×D5911yescharacteristic
473C23×C4—591no—
474C23×C4—1181no—
475C23×C4—1181no—
476C23×C4—1181no—
477C23×C4—1181no—
478C23×C4—1181no—
479C23×C4C22×D5911yescharacteristic
480C2×D8—24no—
481C2×D8C22×D5914yes—
482C2×M16—24no—
483C2×M16C22×D5914yes—
484C22×C8—591no—
485C22×C8—591no—
486C22×C8—594no—
487C22×C8—1184no—
488C22×C8C22×D5911yescharacteristic
489C22×C8C22×D5911yescharacteristic
490C4⋊Q8—594no—
491C4⋊Q8—1182no—
492#126—1188no—
493#125—594no—
494#125—1182no—
495#123—1188no—
496#123—1188no—
497#123—1188no—
498C22⋊Q8—1188no—
499#121—22no—
500#121—22no—
501#121—594no—
502#121—594no—
503#121—1182no—
504#121—1182no—
505#121—1188no—
506#121C22×D5914yes—
507#121C22×D5914yes—
508C4×D4—594no—
509C4×D4—594no—
510C4×D4—594no—
511C4×D4—594no—
512C4×D4—1182no—
513C4×D4—1182no—
514C4×D4—1188no—
515#117—594no—
516#117—1182no—
517C2×C4⋊C4—591no—
518C2×C4⋊C4—591no—
519C2×C4⋊C4—591no—
520C2×C4⋊C4—591no—
521C2×C4⋊C4—594no—
522C2×C4⋊C4—591no—
523C2×C4⋊C4—594no—
524C2×C4⋊C4—594no—
525C2×C4⋊C4—1182no—
526C2×C4⋊C4—1182no—
527C2×C4⋊C4—1181no—
528C2×C4⋊C4—1181no—
529C2×C4⋊C4—1181no—
530C2×C4⋊C4—1181no—
531C2×C4⋊C4—1181no—
532C2×C4⋊C4—1181no—
533C2×C4⋊C4—1182no—
534C2×C4⋊C4C22×D5911yescharacteristic
535C2×C4⋊C4C22×D5911yescharacteristic
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—591no—
539C2×C22⋊C4—591no—
540C2×C22⋊C4—1181no—
541C2×C22⋊C4—1181no—
542C2×C22⋊C4—1181no—
543C2×C22⋊C4—1181no—
544C2×C22⋊C4—1181no—
545C2×C42—591no—
546C2×C42—1181no—
547#107—594no—
548#107—594no—
549#107—594no—
550#106—594no—
551#106—594no—
552#106—594no—
553#106—594no—
554#106—594no—
555#106C22×D5914yes—
556C4⋊C8—594no—
557#102—594no—
558#102—594no—
559#102—594no—
560#102—594no—
561#102C22×D5914yes—
562#102C22×D5914yes—
563C22⋊C8—594no—
564C22⋊C8—594no—
565#97—594no—
566C24—21no—
567C24—21no—
568C24—591no—
569C24D4×D5911yescharacteristic
570#41—23632no—
571C2×Q8—1184no—
572C2×Q8—2364no—
573C2×D4—24no—
574C2×D4—24no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4—44no—
582C2×D4—82no—
583C2×D4—594no—
584C2×D4—1184no—
585C2×D4—1184no—
586C2×D4—1184no—
587C2×D4—2364no—
588C2×D4—2364no—
589C2×D4C23×D5912yes—
590C2×D4C23×D5912yes—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—591no—
596C22×C4—591no—
597C22×C4—591no—
598C22×C4—592no—
599C22×C4—592no—
600C22×C4—1184no—
601C22×C4—1184no—
602C22×C4—1184no—
603C22×C4—1184no—
604C22×C4—1182no—
605C22×C4—1182no—
606C22×C4—1184no—
607C22×C4—1181no—
608C22×C4—1181no—
609C22×C4—1181no—
610C22×C4—1181no—
611C22×C4—4722no—
612C22×C4—4722no—
613C22×C4—2364no—
614C22×C4—2364no—
615C22×C4—2364no—
616C22×C4D4×D5912yes—
617C22×C4D4×D5911yescharacteristic
618C22×C4C23×D5912yes—
619C22×C4C23×D5911yescharacteristic
620D8—28no—
621M16—28no—
622C2×C8—22no—
623C2×C8—592no—
624C2×C8—592no—
625C2×C8—1182no—
626C2×C8—1182no—
627C2×C8—1188no—
628C2×C8#1174568714yescomplemented
629C2×C8C23×D5912yes—
630C2×C8C23×D5912yes—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—594no—
634C4⋊C4—592no—
635C4⋊C4—592no—
636C4⋊C4—592no—
637C4⋊C4—592no—
638C4⋊C4—1184no—
639C4⋊C4—1184no—
640C4⋊C4—1184no—
641C4⋊C4—1184no—
642C4⋊C4—1184no—
643C4⋊C4—1181no—
644C4⋊C4—1181no—
645C4⋊C4—1181no—
646C4⋊C4—1184no—
647C4⋊C4—1181no—
648C4⋊C4C23×D5912yes—
649C4⋊C4C23×D5912yes—
650C22⋊C4—24no—
651C22⋊C4—24no—
652C22⋊C4—594no—
653C22⋊C4—594no—
654C22⋊C4—1184no—
655C22⋊C4—1184no—
656C22⋊C4—1184no—
657C22⋊C4—1184no—
658C22⋊C4—1184no—
659C42—592no—
660C42—592no—
661C42—1184no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—594no—
674C23—592no—
675C23—1182no—
676C23—1182no—
677C23C2×D4×D5912yes—
678C23C2×D4×D5911yescharacteristic
679Q8—2368no—
680D4—22no—
681D4—22no—
682D4—22no—
683D4—22no—
684D4—48no—
685D4—42no—
686D4—42no—
687D4—84no—
688D4—1188no—
689D4—2368no—
690D4—2368no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—24no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—592no—
700C2×C4—592no—
701C2×C4—592no—
702C2×C4—1182no—
703C2×C4—1182no—
704C2×C4—1182no—
705C2×C4—1182no—
706C2×C4—1182no—
707C2×C4—1184no—
708C2×C4—1182no—
709C2×C4—1182no—
710C2×C4—1182no—
711C2×C4—1182no—
712C2×C4—4724no—
713C2×C4—4724no—
714C2×C4—2368no—
715C2×C4—2368no—
716C2×C4—2368no—
717C2×C4—2362no—
718C2×C4—2362no—
719C2×C4—2362no—
720C2×C4—2362no—
721C2×C4C2×D4×D5912yes—
722C2×C4C2×D4×D5911yescharacteristic
723C2×C4C2×#1174568712yes—
724C2×C4#1427377412yes—
725C2×C4C24×D5911yescharacteristic
726C8—22no—
727C8—1182no—
728C8—1182no—
729C8C2×#1174568714yescomplemented
730C22—22no—
731C22—22no—
732C22—22no—
733C22—44no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—84no—
741C22—84no—
742C22—594no—
743C22—1182no—
744C22—1182no—
745C22—1188no—
746C22#1683805212yes—
747C22AGL(1,ℤ/8)×D5912yes—
748C22#1683821212yes—
749C22C22×D4×D5911yescharacteristic
750C4—22no—
751C4—42no—
752C4—42no—
753C4—1182no—
754C4—1182no—
755C4—1182no—
756C4—2362no—
757C4—2362no—
758C4—2362no—
759C4—2362no—
760C4#1683805212yes—
761C4C22×#1174568711yescharacteristic
762C4C2×#1427377411yescharacteristic
763C2—42no—
764C2—82no—
765C2—82no—
766C2—1184no—
767C2#2143656114yesdirect product factor
768C2C2×#1683805211yescharacteristic
769C2C2×AGL(1,ℤ/8)×D5911yescharacteristic
770C2C2×#1683821211yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#469C2
socleC23×C59C22×D4
hypercenterC2×#469D59
hypocenterC59C2×#3345
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#469

Complements

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

NH ≅ G/Ntype
1. C2×#16838099C2semidirect
2. C2×#16838052C2semidirect
3. #21436561C2direct (N × H)
4. C2×#16837809C2semidirect
5. C2×#16837719C2semidirect
6. C2×#16837718C2semidirect
7. C2×#16837723C2semidirect
8. C2×#16837714C2semidirect
9. C2×#16837700C2semidirect
10. C2×#16837690C2semidirect
11. C2×#16837635C2semidirect
12. C2×#16837514C2semidirect
13. C2×#16837471C2semidirect
14. C2×#16837444C2semidirect
15. C2×#106×D59C2semidirect
16. C2×C59×#469C2semidirect
20. #16838099C22semidirect
22. #16838052C22semidirect
41. #16837809C22semidirect
42. #16837723C22semidirect
43. #16837719C22semidirect
44. #16837718C22semidirect
45. #16837714C22semidirect
46. #16837700C22semidirect
47. #16837690C22semidirect
48. #16837635C22semidirect
49. #16837514C22semidirect
50. #16837471C22semidirect
51. #16837444C22semidirect
60. #106×D59C22semidirect
73. C59×#469C22semidirect
237. C2×C8×C59#41semidirect
341. C8×C59C2×#41semidirect
388. C2×#469D59semidirect
397. C2×C59#3345semidirect
437. #469C2×D59semidirect
462. C59C2×#3345semidirect
628. C2×C8#11745687semidirect
729. C8C2×#11745687semidirect
767. C2#21436561direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168380992
C2×#168380522
#214365612
C2×#168378092
C2×#168377192
C2×#168377182
C2×#168377232
C2×#168377142
C2×#168377002
C2×#168376902
C2×#168376352
C2×#168375142
C2×#168374712
C2×#168374442
C2×#106×D592
C2×C59×#4692
C2×#334559