Finite Group Databasebeta

← C2×#21435231 #29460746

Subgroups — C2×#21435231 #29460746

Order 15104.

2058 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837958C211yesmaximal, characteristic, complemented
2C2×#16837949C211yesmaximal, characteristic
3#21435231C2116yesmaximal, direct product factor
4C2×#16837806C211yesmaximal, characteristic, complemented
5C2×#16837799C211yesmaximal, characteristic, complemented
6C2×#16837747C211yesmaximal, characteristic, complemented
7C2×#16837747C211yesmaximal, characteristic, complemented
8C2×#16837729C211yesmaximal, characteristic, complemented
9C2×#16837728C211yesmaximal, characteristic, complemented
10C2×#16837725C211yesmaximal, characteristic, complemented
11C2×#16837724C211yesmaximal, characteristic, complemented
12C2×#16837703C211yesmaximal, characteristic, complemented
13C2×#16837702C211yesmaximal, characteristic, complemented
14C2×#16837699C211yesmaximal, characteristic, complemented
15C2×#16837454C211yesmaximal, characteristic, complemented
16C2×C59×#478C211yesmaximal, characteristic, complemented
17C22×#11745685—21no—
18#16837958—24no—
19#16837958C2218yescomplemented
20#16837949—24no—
21#16837949C2218yes—
22C2×#14273726C2211yescharacteristic
23C2×#14273726C2211yescharacteristic
24C2×#14273726C2211yescharacteristic
25C2×#14273723C2211yescharacteristic
26C2×#14273719C2211yescharacteristic
27C2×#14273713—21no—
28C2×#14273705—21no—
29C2×#14273705—21no—
30C2×#14273702C2211yescharacteristic
31C2×#14273700—21no—
32C2×#14273698C2211yescharacteristic
33C2×#14273692—21no—
34C2×#14273692—21no—
35C2×C4×D236C2211yescharacteristic
36C2×C4×C22⋊D59—21no—
37C2×#14273685C2211yescharacteristic
38C2×#14273685C2211yescharacteristic
39C2×C42×D59C2211yescharacteristic
40#16837806C2218yescomplemented
41#16837799C2218yescomplemented
42#16837747C2218yescomplemented
43#16837747C2218yescomplemented
44#16837729C2218yescomplemented
45#16837728C2218yescomplemented
46#16837725C2218yescomplemented
47#16837724C2218yescomplemented
48#16837703C2218yescomplemented
49#16837702C2218yescomplemented
50#16837699C2218yescomplemented
51#16837454C2218yescomplemented
52C2×#14273661C2211yescharacteristic
53C2×#14273660C2211yescharacteristic
54C2×#14273660C2211yescharacteristic
55C2×#14273659C2211yescharacteristic
56C2×#14273658C2211yescharacteristic
57C2×#14273658C2211yescharacteristic
58C2×C4⋊(C59⋊C8)C2211yescharacteristic
59C2×#14273649C2211yescharacteristic
60C2×#14273649C2211yescharacteristic
61C2×#14273648C2211yescharacteristic
62C2×#14273648C2211yescharacteristic
63C2×#14273647C2211yescharacteristic
64C2×#14273647C2211yescharacteristic
65C2×(C2×D59)⋊C8C2211yescharacteristic
66C2×(C2×D59)⋊C8C2211yescharacteristic
67C2×C8×Dic59C2211yescharacteristic
68C2×C8×Dic59C2211yescharacteristic
69C2×#125×C59C2211yescharacteristic
70C2×C4×D4×C59C2211yescharacteristic
71C59×#478C2218yescomplemented
72C2×#107×C59C2211yescharacteristic
73C2×#106×C59C2211yescharacteristic
74C2×C4⋊C8×C59C2211yescharacteristic
75C2×#102×C59C2211yescharacteristic
76C2×#102×C59C2211yescharacteristic
77C2×#11745685—28no—
78C2×#11745685—48no—
79C22×Dic118—21no—
80C22×Dic118—21no—
81C22×Dic118—21no—
82C22×D236—21no—
83C22×D236C2311yescharacteristic
84C22×C22⋊D59—21no—
85C22×C22⋊D59—21no—
86C22×C22⋊D59—21no—
87C22×C4×D59—21no—
88C22×C4×D59D411yescharacteristic
89C22×C4×D59D411yescharacteristic
90C22×C4×D59C2311yescharacteristic
91C22×C59⋊C8C2311yescharacteristic
92C22×C59⋊C8C2311yescharacteristic
93#14273726—22no—
94#14273726—22no—
95#14273726—22no—
96#14273726C2314yes—
97#14273726C2314yes—
98#14273726C2314yes—
99#14273723—22no—
100#14273723C2314yes—
101#14273719—22no—
102#14273719C2314yes—
103#14273713—28no—
104#14273705—28no—
105#14273705—28no—
106#14273702—22no—
107#14273702C2314yes—
108#14273700—28no—
109#14273698—22no—
110#14273698C2314yes—
111#14273692—28no—
112#14273692—28no—
113C4×D236—22no—
114C4×D236C2314yes—
115C4×C22⋊D59—28no—
116#14273685—22no—
117#14273685—22no—
118#14273685C2314yes—
119#14273685C2314yes—
120C2×C4⋊Dic59C2311yescharacteristic
121C2×C4⋊Dic59C2311yescharacteristic
122C2×C4⋊Dic59C2311yescharacteristic
123C2×Dic59⋊C4—21no—
124C2×Dic59⋊C4—21no—
125C2×Dic59⋊C4—21no—
126C2×Dic59⋊C4—21no—
127C2×Dic59⋊C4—21no—
128C2×C22⋊Dic59—21no—
129C2×(C2×D59)⋊C4—21no—
130C2×(C2×D59)⋊C4—21no—
131C2×(C2×D59)⋊C4—21no—
132C2×(C2×D59)⋊C4—21no—
133C2×C4×Dic59—21no—
134C2×C4×Dic59—21no—
135C2×C4×Dic59D411yescharacteristic
136C2×C4×Dic59D411yescharacteristic
137C2×C4×Dic59C2311yescharacteristic
138C42×D59D414yes—
139C42×D59C2314yes—
140#14273661C2314yes—
141#14273660C2314yes—
142#14273660C2314yes—
143#14273659C2314yes—
144#14273658C2314yes—
145#14273658C2314yes—
146C4⋊(C59⋊C8)C2314yes—
147#14273649C2314yes—
148#14273649C2314yes—
149#14273648C2314yes—
150#14273648C2314yes—
151#14273647C2314yes—
152#14273647C2314yes—
153(C2×D59)⋊C8C2314yes—
154(C2×D59)⋊C8C2314yes—
155C8×Dic59C2314yes—
156C8×Dic59C2314yes—
157C22×D4×C59C2311yescharacteristic
158C23×C4×C59—21no—
159C22×C8×C59C2311yescharacteristic
160C22×C8×C59C2311yescharacteristic
161#125×C59—22no—
162#125×C59C2314yes—
163C4×D4×C59—22no—
164C4×D4×C59C2314yes—
165C2×C4⋊C4×C59—21no—
166C2×C4⋊C4×C59—21no—
167C2×C4⋊C4×C59C2311yescharacteristic
168C2×C4⋊C4×C59C2311yescharacteristic
169C2×C4⋊C4×C59C2311yescharacteristic
170C2×C22⋊C4×C59—21no—
171C2×C42×C59C2311yescharacteristic
172#107×C59C2314yes—
173#106×C59C2314yes—
174C4⋊C8×C59C2314yes—
175#102×C59C2314yes—
176#102×C59C2314yes—
177C24×C59—21no—
178C23×D59—21no—
179C23×D59C2×D411yescharacteristic
180C2×D4×C59—21no—
181C2×D4×C59—22no—
182C2×D4×C59—22no—
183C2×D4×C59C2412yes—
184C22×C4×C59—21no—
185C22×C4×C59—21no—
186C22×C4×C59—21no—
187C22×C4×C59—24no—
188C22×C4×C59—44no—
189C22×C4×C59C2×D411yescharacteristic
190C22×C4×C59C2×D411yescharacteristic
191C22×C4×C59C2411yescharacteristic
192C2×C22⋊D59—24no—
193C2×C22⋊D59—24no—
194C2×C22⋊D59—24no—
195C2×C22⋊D59—44no—
196C2×C22⋊D59—44no—
197C2×C22⋊D59—44no—
198C22×Dic59—21no—
199C22×Dic59—21no—
200C22×Dic59—21no—
201C22×Dic59C2×D411yescharacteristic
202C22×Dic59C2×D411yescharacteristic
203C22×Dic59C2×D411yescharacteristic
204#11745685—432no—
205C2×D236—22no—
206C2×D236—22no—
207C2×D236—24no—
208C2×D236—21no—
209C2×D236—44no—
210C2×D236C2412yes—
211C2×C4×D59—22no—
212C2×C4×D59—22no—
213C2×C4×D59—24no—
214C2×C4×D59—24no—
215C2×C4×D59—24no—
216C2×C4×D59—44no—
217C2×C4×D59C2×D412yes—
218C2×C4×D59C2×D414yes—
219C2×C4×D59C2×D414yes—
220C2×C4×D59C2412yes—
221C2×Dic118—24no—
222C2×Dic118—24no—
223C2×Dic118—24no—
224C2×Dic118—44no—
225C2×Dic118—44no—
226C2×Dic118—44no—
227C2×C8×C59—22no—
228C2×C8×C59—22no—
229C2×C8×C59C2412yes—
230C2×C8×C59C2412yes—
231C4⋊C4×C59—24no—
232C4⋊C4×C59—24no—
233C4⋊C4×C59—21no—
234C4⋊C4×C59—21no—
235C4⋊C4×C59—21no—
236C4⋊C4×C59C2412yes—
237C4⋊C4×C59C2412yes—
238C4⋊C4×C59C2412yes—
239C22⋊C4×C59—24no—
240C42×C59C2×D412yes—
241C42×C59C2412yes—
242C22⋊Dic59—24no—
243(C2×D59)⋊C4—24no—
244(C2×D59)⋊C4—24no—
245(C2×D59)⋊C4—24no—
246(C2×D59)⋊C4—24no—
247C4⋊Dic59—21no—
248C4⋊Dic59—21no—
249C4⋊Dic59—21no—
250C4⋊Dic59C2412yes—
251C4⋊Dic59C2412yes—
252C4⋊Dic59C2412yes—
253Dic59⋊C4—24no—
254Dic59⋊C4—24no—
255Dic59⋊C4—24no—
256Dic59⋊C4—24no—
257Dic59⋊C4—24no—
258C4×Dic59—24no—
259C4×Dic59—24no—
260C4×Dic59C2×D412yes—
261C4×Dic59C2×D414yes—
262C4×Dic59C2×D414yes—
263C4×Dic59C2412yes—
264C2×C59⋊C8—22no—
265C2×C59⋊C8—22no—
266C2×C59⋊C8C2412yes—
267C2×C59⋊C8C2412yes—
268C23×C59—22no—
269C23×C59—42no—
270C23×C59—42no—
271C23×C59—42no—
272C23×C59C22×D411yescharacteristic
273C22×D59—22no—
274C22×D59—22no—
275C22×D59—22no—
276C22×D59—22no—
277C22×D59—42no—
278C22×D59—42no—
279C22×D59—42no—
280C22×D59C22×D412yes—
281D4×C59—22no—
282D4×C59—22no—
283D4×C59—42no—
284C2×C4×C59—22no—
285C2×C4×C59—22no—
286C2×C4×C59—22no—
287C2×C4×C59—22no—
288C2×C4×C59—22no—
289C2×C4×C59—48no—
290C2×C4×C59—42no—
291C2×C4×C59—42no—
292C2×C4×C59—42no—
293C2×C4×C59C22×D412yes—
294C2×C4×C59C22×D412yes—
295C2×C4×C59C22×D411yescharacteristic
296C2×C4×C592−1+412yes—
297C2×C4×C592−1+412yes—
298C2×C4×C59C2511yescharacteristic
299C22⋊D59—48no—
300C22⋊D59—48no—
301C22⋊D59—48no—
302C2×Dic59—22no—
303C2×Dic59—22no—
304C2×Dic59—22no—
305C2×Dic59—22no—
306C2×Dic59—42no—
307C2×Dic59—42no—
308C2×Dic59—42no—
309C2×Dic59#13514yes—
310C2×Dic59AGL(1,ℤ/8)14yes—
311C2×Dic59C22×D412yes—
312C2×Dic59C22×D412yes—
313C2×Dic59C22×D412yes—
314D236—22no—
315D236—22no—
316D236—48no—
317D236—42no—
318C4×D59—24no—
319C4×D59—22no—
320C4×D59—22no—
321C4×D59—28no—
322C4×D59—28no—
323C4×D59—48no—
324Dic118—48no—
325Dic118—48no—
326Dic118—48no—
327C8×C59—22no—
328C8×C59—22no—
329C59⋊C8—22no—
330C59⋊C8—22no—
331C2×#3228—591nomaximal, Sylow
332C22×C59—42no—
333C22×C59—42no—
334C22×C59—42no—
335C22×C59—84no—
336C22×C59#53612yes—
337C22×C59C2×#13512yes—
338C22×C59C2×AGL(1,ℤ/8)12yes—
339C22×C59C23×D411yescharacteristic
340C2×D59—22no—
341C2×D59—22no—
342C2×D59—22no—
343C2×D59—44no—
344C2×D59—42no—
345C2×D59—42no—
346C2×D59—42no—
347C2×D59—84no—
348C4×C59—22no—
349C4×C59—22no—
350C4×C59—42no—
351C4×C59—42no—
352C4×C59—42no—
353C4×C59#53612yes—
354C4×C59C2×2−1+411yescharacteristic
355C4×C59C2×2−1+411yescharacteristic
356Dic59—22no—
357Dic59—42no—
358Dic59—42no—
359Dic59—42no—
360Dic59C2×#13514yes—
361Dic59C2×AGL(1,ℤ/8)14yes—
362C2×#533—591no—
363C2×#532—591no—
364#3228—5916no—
365C2×#500—591no—
366C2×#498—591no—
367C2×#486—591no—
368C2×#486—591no—
369C2×#482—591no—
370C2×#482—591no—
371C2×#482—591no—
372C2×#482—591no—
373C2×#478—591no—
374C2×#478—591no—
375C2×#478—591no—
376C2×#478D5911yescharacteristic, complemented
377C2×#431—591no—
378C2×C59—82no—
379C2×C59#322814yescomplemented
380C2×C59C2×#53611yescharacteristic
381C2×C59C22×#13511yescharacteristic
382C2×C59C22×AGL(1,ℤ/8)11yescharacteristic
383D59—42no—
384D59—82no—
385C22×#41—1181no—
386#533—598no—
387#533—1184no—
388#532—598no—
389#532—1184no—
390C2×C4⋊Q8—591no—
391C2×C4⋊Q8—591no—
392C2×C4⋊Q8—591no—
393C2×#127—591no—
394C2×#125—591no—
395C2×#125C2×D5911yescharacteristic
396C2×#124—1181no—
397C2×C22⋊Q8—1181no—
398C2×C22⋊Q8—1181no—
399C2×#121—591no—
400C2×#121—591no—
401C2×#121—1181no—
402C2×C4×Q8—1181no—
403C2×C4×Q8—1181no—
404C2×C4×D4—591no—
405C2×C4×D4—1181no—
406C2×C4×D4C2×D5911yescharacteristic
407C2×#117—591no—
408C2×#117—591no—
409C22×C42—591no—
410#500—598no—
411#498—598no—
412#486—598no—
413#486—598no—
414#482—598no—
415#482—598no—
416#482—598no—
417#482—598no—
418#478—598no—
419#478—598no—
420#478—598no—
421#478C2×D5918yescomplemented
422#431—598no—
423C2×#107—591no—
424C2×#107—591no—
425C2×#107—591no—
426C2×#107C2×D5911yescharacteristic
427C2×#106—591no—
428C2×#106—591no—
429C2×#106—591no—
430C2×#106C2×D5911yescharacteristic
431C2×C4⋊C8—591no—
432C2×C4⋊C8C2×D5911yescharacteristic
433C2×#102—591no—
434C2×#102—591no—
435C2×#102—591no—
436C2×#102—591no—
437C2×#102—591no—
438C2×#102—591no—
439C2×#102C2×D5911yescharacteristic
440C2×#102C2×D5911yescharacteristic
441C2×C22⋊C8—591no—
442C2×C22⋊C8—591no—
443C2×C4×C8—591no—
444C2×C4×C8—591no—
445C59C2×#322811yescharacteristic, complemented, Sylow
446C2×#41—1188no—
447C2×#41—2368no—
448C22×Q8—1181no—
449C22×Q8—1181no—
450C22×Q8—1181no—
451C22×D4—591no—
452C22×D4—1181no—
453C22×D4—1181no—
454C22×D4—1181no—
455C22×D4—1181no—
456C22×D4C22×D5911yescharacteristic
457C23×C4—21no—
458C23×C4—591no—
459C23×C4—591no—
460C23×C4—591no—
461C23×C4—1181no—
462C22×C8—591no—
463C22×C8—591no—
464C22×C8C22×D5911yescharacteristic
465C22×C8C22×D5911yescharacteristic
466C4⋊Q8—594no—
467C4⋊Q8—594no—
468C4⋊Q8—594no—
469C4⋊Q8—1182no—
470C4⋊Q8—1182no—
471C4⋊Q8—1182no—
472#127—594no—
473#127—1182no—
474#125—22no—
475#125—594no—
476#125—1182no—
477#125C22×D5914yes—
478#124—1188no—
479C22⋊Q8—1188no—
480C22⋊Q8—1188no—
481#121—594no—
482#121—594no—
483#121—1188no—
484#121—1182no—
485#121—1182no—
486C4×Q8—1188no—
487C4×Q8—1188no—
488C4×D4—22no—
489C4×D4—594no—
490C4×D4—1188no—
491C4×D4—1182no—
492C4×D4C22×D5914yes—
493#117—594no—
494#117—594no—
495#117—1182no—
496#117—1182no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—591no—
500C2×C4⋊C4—591no—
501C2×C4⋊C4—591no—
502C2×C4⋊C4—1181no—
503C2×C4⋊C4—1181no—
504C2×C4⋊C4—1181no—
505C2×C4⋊C4—1181no—
506C2×C4⋊C4—1181no—
507C2×C4⋊C4C22×D5911yescharacteristic
508C2×C4⋊C4C22×D5911yescharacteristic
509C2×C4⋊C4C22×D5911yescharacteristic
510C2×C22⋊C4—21no—
511C2×C22⋊C4—1181no—
512C2×C22⋊C4—1181no—
513C2×C22⋊C4—1181no—
514C2×C22⋊C4—1181no—
515C2×C22⋊C4—1181no—
516C2×C42—591no—
517C2×C42—591no—
518C2×C42—591no—
519C2×C42—594no—
520C2×C42—594no—
521C2×C42—1181no—
522C2×C42—1181no—
523C2×C42C22×D5911yescharacteristic
524#107—594no—
525#107—594no—
526#107—594no—
527#107C22×D5914yes—
528#106—594no—
529#106—594no—
530#106—594no—
531#106C22×D5914yes—
532C4⋊C8—594no—
533C4⋊C8C22×D5914yes—
534#102—594no—
535#102—594no—
536#102—594no—
537#102—594no—
538#102—594no—
539#102—594no—
540#102C22×D5914yes—
541#102C22×D5914yes—
542C22⋊C8—594no—
543C22⋊C8—594no—
544C4×C8—594no—
545C4×C8—594no—
546C24—21no—
547C24—591no—
548C24—1181no—
549#41—23632no—
550C2×Q8—1184no—
551C2×Q8—1184no—
552C2×Q8—1184no—
553C2×Q8—2364no—
554C2×Q8—2364no—
555C2×Q8—2364no—
556C2×D4—21no—
557C2×D4—22no—
558C2×D4—22no—
559C2×D4—592no—
560C2×D4—1184no—
561C2×D4—1184no—
562C2×D4—1184no—
563C2×D4—1184no—
564C2×D4—1181no—
565C2×D4—1182no—
566C2×D4—1182no—
567C2×D4—2364no—
568C2×D4—2364no—
569C2×D4—2364no—
570C2×D4—2364no—
571C2×D4C23×D5912yes—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—24no—
576C22×C4—44no—
577C22×C4—591no—
578C22×C4—591no—
579C22×C4—591no—
580C22×C4—592no—
581C22×C4—594no—
582C22×C4—594no—
583C22×C4—592no—
584C22×C4—1184no—
585C22×C4—1184no—
586C22×C4—1182no—
587C22×C4—1182no—
588C22×C4—1181no—
589C22×C4—1181no—
590C22×C4—1181no—
591C22×C4—1184no—
592C22×C4—2364no—
593C22×C4D4×D5911yescharacteristic
594C22×C4D4×D5911yescharacteristic
595C22×C4C23×D5911yescharacteristic
596C2×C8—22no—
597C2×C8—22no—
598C2×C8—592no—
599C2×C8—592no—
600C2×C8—1182no—
601C2×C8—1182no—
602C2×C8C23×D5912yes—
603C2×C8C23×D5912yes—
604C4⋊C4—24no—
605C4⋊C4—24no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—592no—
610C4⋊C4—592no—
611C4⋊C4—592no—
612C4⋊C4—1184no—
613C4⋊C4—1184no—
614C4⋊C4—1184no—
615C4⋊C4—1181no—
616C4⋊C4—1181no—
617C4⋊C4—1181no—
618C4⋊C4—1184no—
619C4⋊C4—1184no—
620C4⋊C4C23×D5912yes—
621C4⋊C4C23×D5912yes—
622C4⋊C4C23×D5912yes—
623C22⋊C4—24no—
624C22⋊C4—1184no—
625C22⋊C4—1184no—
626C22⋊C4—1184no—
627C22⋊C4—1184no—
628C22⋊C4—1184no—
629C42—594no—
630C42—594no—
631C42—592no—
632C42—592no—
633C42—1184no—
634C42—1184no—
635C42D4×D5912yes—
636C42C23×D5912yes—
637C23—22no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—592no—
642C23—1182no—
643C23—1182no—
644C23—1182no—
645C23—1182no—
646C23—2362no—
647C23—2362no—
648C23—2362no—
649C23C2×D4×D5911yescharacteristic
650Q8—2368no—
651Q8—2368no—
652Q8—2368no—
653D4—22no—
654D4—22no—
655D4—42no—
656D4—1182no—
657D4—1182no—
658D4—2368no—
659D4—2368no—
660D4—2368no—
661D4—2368no—
662D4—2362no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—48no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—594no—
673C2×C4—594no—
674C2×C4—592no—
675C2×C4—592no—
676C2×C4—592no—
677C2×C4—1188no—
678C2×C4—1188no—
679C2×C4—1182no—
680C2×C4—1184no—
681C2×C4—1182no—
682C2×C4—1182no—
683C2×C4—1182no—
684C2×C4—1182no—
685C2×C4—1182no—
686C2×C4—2368no—
687C2×C4—2362no—
688C2×C4—2362no—
689C2×C4—2362no—
690C2×C4C2×D4×D5912yes—
691C2×C4C2×D4×D5912yes—
692C2×C4C2×D4×D5911yescharacteristic
693C2×C4#1427377412yes—
694C2×C4#1427377512yes—
695C2×C4C24×D5911yescharacteristic
696C8—22no—
697C8—22no—
698C8—1182no—
699C8—1182no—
700C22—42no—
701C22—42no—
702C22—42no—
703C22—84no—
704C22—1182no—
705C22—1182no—
706C22—1182no—
707C22—4724no—
708C22—2362no—
709C22—2362no—
710C22—2362no—
711C22—2364no—
712C22#1683797512yes—
713C22#135×D5912yes—
714C22AGL(1,ℤ/8)×D5912yes—
715C22C22×D4×D5911yescharacteristic
716C4—22no—
717C4—22no—
718C4—42no—
719C4—42no—
720C4—42no—
721C4—594no—
722C4—594no—
723C4—1182no—
724C4—2362no—
725C4—2362no—
726C4—2362no—
727C4#1683797512yes—
728C4C2×#1427377411yescharacteristic
729C4C2×#1427377511yescharacteristic
730C2—82no—
731C2—4722no—
732C2—2362no—
733C2#2143523114yesdirect product factor
734C2C2×#1683797511yescharacteristic
735C2C2×#135×D5911yescharacteristic
736C2C2×AGL(1,ℤ/8)×D5911yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#478C2
socleC23×C59C22×D4
prime radicalC2×#16837949C2
hypercenterC2×#478D59
hypocenterC59C2×#3228
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#478

Complements

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

NH ≅ G/Ntype
1. C2×#16837958C2semidirect
3. #21435231C2direct (N × H)
4. C2×#16837806C2semidirect
5. C2×#16837799C2semidirect
6. C2×#16837747C2semidirect
7. C2×#16837747C2semidirect
8. C2×#16837729C2semidirect
9. C2×#16837728C2semidirect
10. C2×#16837725C2semidirect
11. C2×#16837724C2semidirect
12. C2×#16837703C2semidirect
13. C2×#16837702C2semidirect
14. C2×#16837699C2semidirect
15. C2×#16837454C2semidirect
16. C2×C59×#478C2semidirect
19. #16837958C22semidirect
40. #16837806C22semidirect
41. #16837799C22semidirect
42. #16837747C22semidirect
43. #16837747C22semidirect
44. #16837729C22semidirect
45. #16837728C22semidirect
46. #16837725C22semidirect
47. #16837724C22semidirect
48. #16837703C22semidirect
49. #16837702C22semidirect
50. #16837699C22semidirect
51. #16837454C22semidirect
71. C59×#478C22semidirect
376. C2×#478D59semidirect
379. C2×C59#3228semidirect
421. #478C2×D59semidirect
445. C59C2×#3228semidirect
733. C2#21435231direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168379582
C2×#168379492
#214352312
C2×#168378062
C2×#168377992
C2×#168377472
C2×#168377292
C2×#168377282
C2×#168377252
C2×#168377242
C2×#168377032
C2×#168377022
C2×#168376992
C2×#168374542
C2×C59×#4782
C2×#322859