Finite Group Databasebeta

← C2×#21435284 #29460792

Subgroups — C2×#21435284 #29460792

Order 15104.

2050 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×#16837949C211yesmaximal, characteristic
2C2×#125×D59C211yesmaximal, characteristic, complemented
3#21435284C2116yesmaximal, direct product factor
4C2×#16837810C211yesmaximal, characteristic, complemented
5C2×#16837809C211yesmaximal, characteristic, complemented
6C2×#16837765C211yesmaximal, characteristic, complemented
7C2×#16837765C211yesmaximal, characteristic, complemented
8C2×#16837722C211yesmaximal, characteristic, complemented
9C2×#16837719C211yesmaximal, characteristic, complemented
10C2×#16837717C211yesmaximal, characteristic, complemented
11C2×#16837714C211yesmaximal, characteristic, complemented
12C2×#16837703C211yesmaximal, characteristic, complemented
13C2×#16837702C211yesmaximal, characteristic, complemented
14C2×#16837699C211yesmaximal, characteristic, complemented
15C2×#16837458C211yesmaximal, characteristic, complemented
16C2×C59×#478C211yesmaximal, characteristic, complemented
17C22×#11745685—21no—
18#16837949—24no—
19#16837949C2218yes—
20C2×#14273726C2211yescharacteristic
21C2×#14273723C2211yescharacteristic
22C2×#14273719C2211yescharacteristic
23C2×#14273718C2211yescharacteristic
24C2×#14273718C2211yescharacteristic
25C2×#14273717—21no—
26C2×#14273717—21no—
27#125×D59—24no—
28#125×D59C2218yescomplemented
29C2×#14273713—21no—
30C2×#14273702C2211yescharacteristic
31C2×#14273700—21no—
32C2×#14273698C2211yescharacteristic
33C2×C4×D236C2211yescharacteristic
34C2×C4×C22⋊D59—21no—
35C2×C4⋊C4×D59—21no—
36C2×C4⋊C4×D59—21no—
37C2×C4⋊C4×D59C2211yescharacteristic
38C2×C4⋊C4×D59C2211yescharacteristic
39C2×C42×D59C2211yescharacteristic
40#16837810C2218yescomplemented
41#16837809C2218yescomplemented
42#16837765C2218yescomplemented
43#16837765C2218yescomplemented
44#16837722C2218yescomplemented
45#16837719C2218yescomplemented
46#16837717C2218yescomplemented
47#16837714C2218yescomplemented
48#16837703C2218yescomplemented
49#16837702C2218yescomplemented
50#16837699C2218yescomplemented
51#16837458C2218yescomplemented
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×#14273637C2211yescharacteristic
68C2×#14273637C2211yescharacteristic
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×D236—21no—
81C22×D236C2311yescharacteristic
82C22×C22⋊D59—21no—
83C22×C22⋊D59—21no—
84C22×C22⋊D59—21no—
85C22×C4×D59—21no—
86C22×C4×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#14273726C2314yes—
95#14273723—22no—
96#14273723C2314yes—
97#14273719—22no—
98#14273719C2314yes—
99#14273718—22no—
100#14273718—22no—
101#14273718C2314yes—
102#14273718C2314yes—
103#14273717—28no—
104#14273717—28no—
105#14273713—28no—
106#14273702—22no—
107#14273702C2314yes—
108#14273700—28no—
109#14273698—22no—
110#14273698C2314yes—
111C4×D236—22no—
112C4×D236C2314yes—
113C4×C22⋊D59—28no—
114C2×C4⋊Dic59—21no—
115C2×C4⋊Dic59—21no—
116C2×C4⋊Dic59C2311yescharacteristic
117C2×C4⋊Dic59C2311yescharacteristic
118C2×C4⋊Dic59C2311yescharacteristic
119C2×Dic59⋊C4—21no—
120C2×Dic59⋊C4—21no—
121C2×Dic59⋊C4—21no—
122C2×Dic59⋊C4—21no—
123C2×Dic59⋊C4—21no—
124C2×Dic59⋊C4—21no—
125C2×Dic59⋊C4—21no—
126C4⋊C4×D59—22no—
127C4⋊C4×D59—22no—
128C4⋊C4×D59—28no—
129C4⋊C4×D59—28no—
130C4⋊C4×D59C2314yes—
131C4⋊C4×D59C2314yes—
132C2×C22⋊Dic59—21no—
133C2×(C2×D59)⋊C4—21no—
134C2×(C2×D59)⋊C4—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—
155#14273637C2314yes—
156#14273637C2314yes—
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—24no—
212C2×C4×D59—22no—
213C2×C4×D59—22no—
214C2×C4×D59—24no—
215C2×C4×D59—24no—
216C2×C4×D59—24no—
217C2×C4×D59—42no—
218C2×C4×D59—44no—
219C2×C4×D59—44no—
220C2×C4×D59—44no—
221C2×C4×D59C2×D412yes—
222C2×C4×D59C2×D414yes—
223C2×C4×D59C2×D414yes—
224C2×C4×D59C2412yes—
225C2×Dic118—24no—
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—
245C4⋊Dic59—21no—
246C4⋊Dic59—21no—
247C4⋊Dic59—21no—
248C4⋊Dic59—24no—
249C4⋊Dic59—24no—
250C4⋊Dic59C2412yes—
251C4⋊Dic59C2412yes—
252C4⋊Dic59C2412yes—
253Dic59⋊C4—24no—
254Dic59⋊C4—24no—
255Dic59⋊C4—24no—
256Dic59⋊C4—24no—
257Dic59⋊C4—24no—
258Dic59⋊C4—24no—
259Dic59⋊C4—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—42no—
277C22×D59—42no—
278C22×D59—42no—
279C22×D59AGL(1,ℤ/8)14yes—
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—22no—
307C2×Dic59—22no—
308C2×Dic59—42no—
309C2×Dic59—42no—
310C2×Dic59—42no—
311C2×Dic59C22×D412yes—
312C2×Dic59C22×D412yes—
313C2×Dic59C22×D412yes—
314D236—22no—
315D236—22no—
316D236—48no—
317D236—42no—
318C4×D59—28no—
319C4×D59—24no—
320C4×D59—22no—
321C4×D59—22no—
322C4×D59—44no—
323C4×D59—48no—
324C4×D59—48no—
325C4×D59—48no—
326Dic118—48no—
327C8×C59—22no—
328C8×C59—22no—
329C59⋊C8—22no—
330C59⋊C8—22no—
331C2×#3234—591nomaximal, Sylow
332C22×C59—42no—
333C22×C59—42no—
334C22×C59—42no—
335C22×C59—84no—
336C22×C59#53612yes—
337C22×C59C2×AGL(1,ℤ/8)12yes—
338C22×C59#57512yes—
339C22×C59C23×D411yescharacteristic
340C2×D59—22no—
341C2×D59—28no—
342C2×D59—22no—
343C2×D59—42no—
344C2×D59—42no—
345C2×D59—42no—
346C2×D59—84no—
347C2×D59C2×AGL(1,ℤ/8)14yes—
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—22no—
358Dic59—22no—
359Dic59—42no—
360Dic59—42no—
361Dic59—42no—
362C2×#532—591no—
363C22×#125—591no—
364#3234—5916no—
365C2×#501—591no—
366C2×#501—591no—
367C2×#490—591no—
368C2×#490—591no—
369C2×#481—591no—
370C2×#481—591no—
371C2×#480—591no—
372C2×#480—591no—
373C2×#478—591no—
374C2×#478—591no—
375C2×#478—591no—
376C2×#478D5911yescharacteristic, complemented
377C2×#432—591no—
378C2×C59—82no—
379C2×C59#323414yescomplemented
380C2×C59C2×#53611yescharacteristic
381C2×C59C22×AGL(1,ℤ/8)11yescharacteristic
382C2×C59C2×#57511yescharacteristic
383D59—24no—
384D59—82no—
385C22×#41—1181no—
386#532—598no—
387#532—1184no—
388C2×C4⋊Q8—591no—
389C2×#127—591no—
390C2×#125—598no—
391C2×#125—591no—
392C2×#125—591no—
393C2×#125—591no—
394C2×#125—1181no—
395C2×#125—1181no—
396C2×#125—1184no—
397C2×#125C2×D5911yescharacteristic
398C2×#124—1181no—
399C2×#121—591no—
400C2×#121—591no—
401C2×#121—1181no—
402C2×C4×D4—591no—
403C2×C4×D4—1181no—
404C2×C4×D4C2×D5911yescharacteristic
405C22×C4⋊C4—591no—
406C22×C4⋊C4—591no—
407C22×C4⋊C4—1181no—
408C22×C4⋊C4—1181no—
409C22×C42—591no—
410#501—598no—
411#501—598no—
412#490—598no—
413#490—598no—
414#481—598no—
415#481—598no—
416#480—598no—
417#480—598no—
418#478—598no—
419#478—598no—
420#478—598no—
421#478C2×D5918yescomplemented
422#432—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×#97—591no—
444C2×#97—591no—
445C59C2×#323411yescharacteristic, complemented, Sylow
446C2×#41—1188no—
447C2×#41—2368no—
448C22×Q8—1181no—
449C22×D4—591no—
450C22×D4—1181no—
451C22×D4—1181no—
452C22×D4—1181no—
453C22×D4—1181no—
454C22×D4C22×D5911yescharacteristic
455C23×C4—21no—
456C23×C4—591no—
457C23×C4—591no—
458C23×C4—591no—
459C23×C4—1181no—
460C23×C4—1181no—
461C23×C4—1181no—
462C22×C8—591no—
463C22×C8—591no—
464C22×C8C22×D5911yescharacteristic
465C22×C8C22×D5911yescharacteristic
466C4⋊Q8—594no—
467C4⋊Q8—1182no—
468#127—594no—
469#127—1182no—
470#125—22no—
471#125—594no—
472#125—594no—
473#125—594no—
474#125—1188no—
475#125—1188no—
476#125—1182no—
477#125—1182no—
478#125—1182no—
479#125C22×D5914yes—
480#124—1188no—
481#121—594no—
482#121—594no—
483#121—1188no—
484#121—1182no—
485#121—1182no—
486C4×D4—22no—
487C4×D4—594no—
488C4×D4—1188no—
489C4×D4—1182no—
490C4×D4C22×D5914yes—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—591no—
494C2×C4⋊C4—591no—
495C2×C4⋊C4—591no—
496C2×C4⋊C4—594no—
497C2×C4⋊C4—594no—
498C2×C4⋊C4—1182no—
499C2×C4⋊C4—1182no—
500C2×C4⋊C4—1188no—
501C2×C4⋊C4—1188no—
502C2×C4⋊C4—1181no—
503C2×C4⋊C4—1181no—
504C2×C4⋊C4—1181no—
505C2×C4⋊C4—1181no—
506C2×C4⋊C4—1181no—
507C2×C4⋊C4—1181no—
508C2×C4⋊C4—1181no—
509C2×C4⋊C4—1181no—
510C2×C4⋊C4—1181no—
511C2×C4⋊C4C22×D5911yescharacteristic
512C2×C4⋊C4C22×D5911yescharacteristic
513C2×C4⋊C4C22×D5911yescharacteristic
514C2×C22⋊C4—21no—
515C2×C22⋊C4—1181no—
516C2×C22⋊C4—1181no—
517C2×C22⋊C4—1181no—
518C2×C42—591no—
519C2×C42—591no—
520C2×C42—591no—
521C2×C42—594no—
522C2×C42—594no—
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—
544#97—594no—
545#97—594no—
546C24—21no—
547C24—591no—
548C24—1181no—
549#41—23632no—
550C2×Q8—1184no—
551C2×Q8—2364no—
552C2×D4—21no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—592no—
556C2×D4—1184no—
557C2×D4—1184no—
558C2×D4—1184no—
559C2×D4—1184no—
560C2×D4—1181no—
561C2×D4—1182no—
562C2×D4—1182no—
563C2×D4—2364no—
564C2×D4—2364no—
565C2×D4—2364no—
566C2×D4—2364no—
567C2×D4C23×D5912yes—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—24no—
572C22×C4—44no—
573C22×C4—591no—
574C22×C4—591no—
575C22×C4—591no—
576C22×C4—592no—
577C22×C4—594no—
578C22×C4—592no—
579C22×C4—594no—
580C22×C4—1184no—
581C22×C4—1184no—
582C22×C4—1184no—
583C22×C4—1182no—
584C22×C4—1182no—
585C22×C4—1181no—
586C22×C4—1181no—
587C22×C4—1181no—
588C22×C4—1184no—
589C22×C4—2362no—
590C22×C4—2364no—
591C22×C4—2364no—
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—1184no—
616C4⋊C4—1184no—
617C4⋊C4—1184no—
618C4⋊C4—1184no—
619C4⋊C4—1181no—
620C4⋊C4—1181no—
621C4⋊C4—1181no—
622C4⋊C4—1184no—
623C4⋊C4—1184no—
624C4⋊C4C23×D5912yes—
625C4⋊C4C23×D5912yes—
626C4⋊C4C23×D5912yes—
627C22⋊C4—24no—
628C22⋊C4—1184no—
629C22⋊C4—1184no—
630C22⋊C4—1184no—
631C42—594no—
632C42—594no—
633C42—592no—
634C42—592no—
635C42D4×D5912yes—
636C42C23×D5912yes—
637C23—22no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—594no—
642C23—592no—
643C23—1182no—
644C23—1182no—
645C23—1182no—
646C23—2362no—
647C23—2362no—
648C23—2362no—
649C23C2×D4×D5911yescharacteristic
650Q8—2368no—
651D4—22no—
652D4—22no—
653D4—42no—
654D4—1182no—
655D4—1182no—
656D4—2368no—
657D4—2368no—
658D4—2368no—
659D4—2368no—
660D4—2362no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—48no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—592no—
671C2×C4—592no—
672C2×C4—592no—
673C2×C4—1188no—
674C2×C4—1182no—
675C2×C4—1182no—
676C2×C4—1182no—
677C2×C4—1184no—
678C2×C4—1182no—
679C2×C4—1182no—
680C2×C4—1182no—
681C2×C4—1182no—
682C2×C4—1182no—
683C2×C4—2364no—
684C2×C4—2368no—
685C2×C4—2368no—
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—594no—
705C22—1182no—
706C22—1188no—
707C22—1182no—
708C22—4724no—
709C22—2362no—
710C22—2362no—
711C22—2362no—
712C22#1683797512yes—
713C22AGL(1,ℤ/8)×D5912yes—
714C22#1683819912yes—
715C22C22×D4×D5911yescharacteristic
716C4—22no—
717C4—22no—
718C4—42no—
719C4—42no—
720C4—42no—
721C4—1182no—
722C4—1182no—
723C4—1182no—
724C4—2362no—
725C4—2362no—
726C4—2362no—
727C4#1683797512yes—
728C4C2×#1427377411yescharacteristic
729C4C2×#1427377511yescharacteristic
730C2—82no—
731C2—1184no—
732C2—4722no—
733C2#2143528414yesdirect product factor
734C2C2×#1683797511yescharacteristic
735C2C2×AGL(1,ℤ/8)×D5911yescharacteristic
736C2C2×#1683819911yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#478C2
socleC23×C59C22×D4
prime radicalC2×#16837949C2
hypercenterC2×#478D59
hypocenterC59C2×#3234
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
2. C2×#125×D59C2semidirect
3. #21435284C2direct (N × H)
4. C2×#16837810C2semidirect
5. C2×#16837809C2semidirect
6. C2×#16837765C2semidirect
7. C2×#16837765C2semidirect
8. C2×#16837722C2semidirect
9. C2×#16837719C2semidirect
10. C2×#16837717C2semidirect
11. C2×#16837714C2semidirect
12. C2×#16837703C2semidirect
13. C2×#16837702C2semidirect
14. C2×#16837699C2semidirect
15. C2×#16837458C2semidirect
16. C2×C59×#478C2semidirect
28. #125×D59C22semidirect
40. #16837810C22semidirect
41. #16837809C22semidirect
42. #16837765C22semidirect
43. #16837765C22semidirect
44. #16837722C22semidirect
45. #16837719C22semidirect
46. #16837717C22semidirect
47. #16837714C22semidirect
48. #16837703C22semidirect
49. #16837702C22semidirect
50. #16837699C22semidirect
51. #16837458C22semidirect
71. C59×#478C22semidirect
376. C2×#478D59semidirect
379. C2×C59#3234semidirect
421. #478C2×D59semidirect
445. C59C2×#3234semidirect
733. C2#21435284direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168379492
C2×#125×D592
#214352842
C2×#168378102
C2×#168378092
C2×#168377652
C2×#168377222
C2×#168377192
C2×#168377172
C2×#168377142
C2×#168377032
C2×#168377022
C2×#168376992
C2×#168374582
C2×C59×#4782
C2×#323459