Finite Group Databasebeta

← C2×#21436845 #29468434

Subgroups — C2×#21436845 #29468434

Order 15104.

1950 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838135C211yesmaximal, characteristic, complemented
2C2×#16838111C211yesmaximal, characteristic, complemented
3#21436845C2116yesmaximal, direct product factor
4C2×#16837765C211yesmaximal, characteristic, complemented
5C2×#16837760C211yesmaximal, characteristic, complemented
6C2×#16837757C211yesmaximal, characteristic, complemented
7C2×#16837708C211yesmaximal, characteristic, complemented
8C2×#16837702C211yesmaximal, characteristic, complemented
9C2×#16837681C211yesmaximal, characteristic, complemented
10C2×#16837617C211yesmaximal, characteristic, complemented
11C2×#16837615C211yesmaximal, characteristic, complemented
12C2×#16837595C211yesmaximal, characteristic
13C2×#16837532C211yesmaximal, characteristic, complemented
14C2×#16837511C211yesmaximal, characteristic, complemented
15C2×#16837499C211yesmaximal, characteristic, complemented
16C2×C4×D8×C59C211yesmaximal, characteristic, complemented
17C22×#11745670C2211yescharacteristic
18C22×#11745669C2211yescharacteristic
19#16838135—24no—
20#16838135C2218yescomplemented
21#16838111—24no—
22#16838111C2218yescomplemented
23C2×#14273726C2211yescharacteristic
24C2×#14273723C2211yescharacteristic
25C2×#14273719C2211yescharacteristic
26C2×#14273718C2211yescharacteristic
27C2×#14273715C2211yescharacteristic
28C2×#14273714C2211yescharacteristic
29C2×#14273713—21no—
30C2×#14273710—21no—
31C2×#14273709—21no—
32C2×#14273706—21no—
33C2×#14273704—21no—
34C2×#14273704—21no—
35C2×C4×Dic118C2211yescharacteristic
36C2×#14273692C2211yescharacteristic
37C2×D4×Dic59C2211yescharacteristic
38C2×D4×Dic59C2211yescharacteristic
39C2×#14273689C2211yescharacteristic
40C2×C4×C22⋊D59—21no—
41C22×Dic59⋊C4—21no—
42#16837765C2218yescomplemented
43#16837760C2218yescomplemented
44#16837757C2218yescomplemented
45#16837708C2218yescomplemented
46#16837702C2218yescomplemented
47#16837681C2218yescomplemented
48#16837617C2218yescomplemented
49#16837615C2218yescomplemented
50#16837595C2218yes—
51#16837532C2218yescomplemented
52#16837511C2218yescomplemented
53#16837499C2218yescomplemented
54C2×#14273660C2211yescharacteristic
55C2×#14273658C2211yescharacteristic
56C2×C4⋊(C59⋊C8)C2211yescharacteristic
57C2×Dic59⋊C8C2211yescharacteristic
58C2×Dic59⋊C8C2211yescharacteristic
59C2×#14273652C2211yescharacteristic
60C2×#14273652C2211yescharacteristic
61C2×#14273650C2211yescharacteristic
62C2×#14273649C2211yescharacteristic
63C2×#14273649C2211yescharacteristic
64C2×#14273648C2211yescharacteristic
65C2×#14273648C2211yescharacteristic
66C2×#14273647C2211yescharacteristic
67C2×#14273637C2211yescharacteristic
68C2×#14273637C2211yescharacteristic
69C22×D8×C59C2211yescharacteristic
70C2×C4×D4×C59C2211yescharacteristic
71C2×C4×D4×C59C2211yescharacteristic
72C4×D8×C59C2218yescomplemented
73C2×#107×C59C2211yescharacteristic
74C2×#102×C59C2211yescharacteristic
75C2×#102×C59C2211yescharacteristic
76C2×C4×C8×C59C2211yescharacteristic
77C22×Dic118—21no—
78C22×Dic118D411yescharacteristic
79C22×Dic118C2311yescharacteristic
80C22×D236C2311yescharacteristic
81C22×C22⋊D59—21no—
82C22×C22⋊D59—21no—
83C23×Dic59—21no—
84C23×Dic59—21no—
85C22×C4×D59—21no—
86C2×#11745670—24no—
87C2×#11745670C2314yes—
88C2×#11745669—24no—
89C2×#11745669C2314yes—
90C22×C59⋊C8C2311yescharacteristic
91C22×C59⋊C8C2311yescharacteristic
92#14273726—22no—
93#14273726C2314yes—
94#14273723—22no—
95#14273723C2314yes—
96#14273719—22no—
97#14273719C2314yes—
98#14273718—22no—
99#14273718C2314yes—
100#14273715—22no—
101#14273715C2314yes—
102#14273714—22no—
103#14273714C2314yes—
104#14273713—28no—
105#14273710—28no—
106#14273709—28no—
107#14273706—28no—
108#14273704—28no—
109#14273704—28no—
110C4×Dic118D414yes—
111C4×Dic118C2314yes—
112#14273692—22no—
113#14273692C2314yes—
114D4×Dic59—22no—
115D4×Dic59—22no—
116D4×Dic59C2314yes—
117D4×Dic59C2314yes—
118#14273689—22no—
119#14273689C2314yes—
120C4×C22⋊D59—28no—
121C2×C4⋊Dic59—21no—
122C2×C4⋊Dic59D411yescharacteristic
123C2×C4⋊Dic59C2311yescharacteristic
124C2×C4⋊Dic59C2311yescharacteristic
125C2×Dic59⋊C4—21no—
126C2×Dic59⋊C4—21no—
127C2×Dic59⋊C4—21no—
128C2×Dic59⋊C4—21no—
129C2×Dic59⋊C4—21no—
130C2×Dic59⋊C4—28no—
131C2×Dic59⋊C4D411yescharacteristic
132C2×Dic59⋊C4D411yescharacteristic
133C2×C22⋊Dic59—21no—
134C2×C22⋊Dic59—21no—
135C2×C22⋊Dic59—21no—
136C2×C22⋊Dic59—21no—
137C2×(C2×D59)⋊C4—21no—
138C2×(C2×D59)⋊C4—21no—
139C2×(C2×D59)⋊C4—21no—
140C2×C4×Dic59—21no—
141C2×C4×Dic59C2311yescharacteristic
142C2×C4×Dic59C2311yescharacteristic
143#14273660C2314yes—
144#14273658C2314yes—
145C4⋊(C59⋊C8)C2314yes—
146Dic59⋊C8C2314yes—
147Dic59⋊C8C2314yes—
148#14273652C2314yes—
149#14273652C2314yes—
150#14273650C2314yes—
151#14273649C2314yes—
152#14273649C2314yes—
153#14273648C2314yes—
154#14273648C2314yes—
155#14273647C2314yes—
156#14273637C2314yes—
157#14273637C2314yes—
158C22×D4×C59C2311yescharacteristic
159C22×D4×C59C2311yescharacteristic
160C23×C4×C59—21no—
161C23×C4×C59—21no—
162C2×D8×C59—24no—
163C2×D8×C59C2314yes—
164C22×C8×C59C2311yescharacteristic
165C22×C8×C59C2311yescharacteristic
166C4×D4×C59—22no—
167C4×D4×C59—22no—
168C4×D4×C59C2314yes—
169C4×D4×C59C2314yes—
170C2×C4⋊C4×C59C2311yescharacteristic
171C2×C4⋊C4×C59C2311yescharacteristic
172C2×C22⋊C4×C59—21no—
173C2×C22⋊C4×C59—21no—
174C2×C42×C59C2311yescharacteristic
175#107×C59C2314yes—
176#102×C59C2314yes—
177#102×C59C2314yes—
178C4×C8×C59C2314yes—
179C24×C59—21no—
180C24×C59—21no—
181C23×D59—21no—
182C2×D4×C59—21no—
183C2×D4×C59—21no—
184C2×D4×C59—22no—
185C2×D4×C59—22no—
186C2×D4×C59—22no—
187C2×D4×C59#4114yes—
188C2×D4×C59C2412yes—
189C2×D4×C59C2412yes—
190C22×C4×C59—21no—
191C22×C4×C59—21no—
192C22×C4×C59—24no—
193C22×C4×C59—24no—
194C22×C4×C59—82no—
195C22×C4×C59—82no—
196C22×C4×C59C2×D411yescharacteristic
197C22×C4×C59C2×D411yescharacteristic
198C22×C4×C59C2411yescharacteristic
199C2×C22⋊D59—24no—
200C2×C22⋊D59—24no—
201C2×C22⋊D59—44no—
202C2×C22⋊D59—82no—
203C22×Dic59—21no—
204C22×Dic59—21no—
205C22×Dic59—21no—
206C22×Dic59—24no—
207C22×Dic59—24no—
208C22×Dic59—44no—
209C22×Dic59—82no—
210C22×Dic59C2×D411yescharacteristic
211C22×Dic59C2×D411yescharacteristic
212C22×Dic59C2×D411yescharacteristic
213C22×Dic59C2×D411yescharacteristic
214C2×D236—22no—
215C2×D236—22no—
216C2×D236—21no—
217C2×D236C2412yes—
218C2×C4×D59—24no—
219C2×C4×D59—82no—
220C2×Dic118—22no—
221C2×Dic118—22no—
222C2×Dic118—21no—
223C2×Dic118—24no—
224C2×Dic118—42no—
225C2×Dic118—82no—
226C2×Dic118C2×D414yes—
227C2×Dic118C2412yes—
228D8×C59—28no—
229C2×C8×C59—22no—
230C2×C8×C59—22no—
231C2×C8×C59C2412yes—
232C2×C8×C59C2412yes—
233C4⋊C4×C59—21no—
234C4⋊C4×C59—21no—
235C4⋊C4×C59C2412yes—
236C4⋊C4×C59C2412yes—
237C22⋊C4×C59—24no—
238C22⋊C4×C59—24no—
239C42×C59C2×D412yes—
240C42×C59C2412yes—
241C22⋊Dic59—24no—
242C22⋊Dic59—24no—
243C22⋊Dic59—24no—
244C22⋊Dic59—24no—
245#11745670—28no—
246#11745669—28no—
247(C2×D59)⋊C4—24no—
248(C2×D59)⋊C4—24no—
249(C2×D59)⋊C4—24no—
250C4⋊Dic59—21no—
251C4⋊Dic59—21no—
252C4⋊Dic59—24no—
253C4⋊Dic59C2×D414yes—
254C4⋊Dic59C2412yes—
255C4⋊Dic59C2412yes—
256Dic59⋊C4—24no—
257Dic59⋊C4—24no—
258Dic59⋊C4—24no—
259Dic59⋊C4—24no—
260Dic59⋊C4—24no—
261Dic59⋊C4C2×D414yes—
262Dic59⋊C4C2×D414yes—
263C4×Dic59—24no—
264C4×Dic59C2×D412yes—
265C4×Dic59C2×D412yes—
266C4×Dic59C2412yes—
267C4×Dic59C2412yes—
268C2×C59⋊C8—22no—
269C2×C59⋊C8—22no—
270C2×C59⋊C8C2412yes—
271C2×C59⋊C8C2412yes—
272C23×C59—24no—
273C23×C59—22no—
274C23×C59—22no—
275C23×C59—42no—
276C23×C59—42no—
277C23×C59—42no—
278C23×C59—42no—
279C23×C59—42no—
280C23×C59C22×D411yescharacteristic
281C22×D59—22no—
282C22×D59—42no—
283C22×D59—42no—
284C22×D59—42no—
285D4×C59—24no—
286D4×C59—22no—
287D4×C59—22no—
288D4×C59—22no—
289D4×C59—42no—
290D4×C59C2×#4114yes—
291C2×C4×C59—22no—
292C2×C4×C59—22no—
293C2×C4×C59—22no—
294C2×C4×C59—22no—
295C2×C4×C59—42no—
296C2×C4×C59—42no—
297C2×C4×C59—84no—
298C2×C4×C59—84no—
299C2×C4×C59C22×D412yes—
300C2×C4×C59C22×D412yes—
301C2×C4×C59C22×D411yescharacteristic
302C2×C4×C59C2×#4112yes—
303C2×C4×C592−1+412yes—
304C2×C4×C59C2511yescharacteristic
305C22⋊D59—48no—
306C22⋊D59—84no—
307C2×Dic59—22no—
308C2×Dic59—22no—
309C2×Dic59—22no—
310C2×Dic59—22no—
311C2×Dic59—22no—
312C2×Dic59—22no—
313C2×Dic59—22no—
314C2×Dic59—48no—
315C2×Dic59—42no—
316C2×Dic59—42no—
317C2×Dic59—42no—
318C2×Dic59—84no—
319C2×Dic59C22×D412yes—
320C2×Dic59C22×D412yes—
321C2×Dic59C22×D412yes—
322C2×Dic59C22×D412yes—
323D236—22no—
324D236—22no—
325D236—42no—
326C4×D59—84no—
327Dic118—22no—
328Dic118—22no—
329Dic118—44no—
330Dic118—42no—
331Dic118—84no—
332C8×C59—22no—
333C8×C59—22no—
334C59⋊C8—22no—
335C59⋊C8—22no—
336C2×#3370—591nomaximal, Sylow
337C22×C59—24no—
338C22×C59—48no—
339C22×C59—42no—
340C22×C59—42no—
341C22×C59—42no—
342C22×C59—42no—
343C22×C59—42no—
344C22×C59—84no—
345C22×C59#54812yes—
346C22×C59#57512yes—
347C22×C59#57612yes—
348C22×C59C23×D411yescharacteristic
349C2×D59—42no—
350C2×D59—42no—
351C2×D59—42no—
352C2×D59—84no—
353C4×C59—22no—
354C4×C59—22no—
355C4×C59—42no—
356C4×C59—42no—
357C4×C59#54812yes—
358C4×C59C22×#4111yescharacteristic
359C4×C59C2×2−1+411yescharacteristic
360Dic59—22no—
361Dic59—22no—
362Dic59—22no—
363Dic59—22no—
364Dic59—42no—
365Dic59—42no—
366Dic59—42no—
367C2×#559—591no—
368C2×#554—591no—
369#3370—5916no—
370C2×#490—591no—
371C2×#489—591no—
372C2×#488—591no—
373C2×#479—591no—
374C2×#478—591no—
375C2×#474—591no—
376C2×#463—591no—
377C2×#463—591no—
378C2×#459—591no—
379C2×#446—591no—
380C2×#442—591no—
381C2×#440—591no—
382C2×C4×D8D5911yescharacteristic, complemented
383C2×C59—44no—
384C2×C59—82no—
385C2×C59#337014yescomplemented
386C2×C59C2×#54811yescharacteristic
387C2×C59C2×#57511yescharacteristic
388C2×C59C2×#57611yescharacteristic
389D59—82no—
390C22×SD16—591no—
391C22×D8—591no—
392C22×D8C2×D5911yescharacteristic
393#559—598no—
394#559—1184no—
395#554—598no—
396#554—1184no—
397C2×C4⋊Q8—591no—
398C2×#127—591no—
399C2×#125—591no—
400C2×#125—591no—
401C2×#124—591no—
402C2×#124—591no—
403C2×#124—1181no—
404C2×#123—1181no—
405C2×#123—1181no—
406C2×C22⋊Q8—1181no—
407C2×C22⋊Q8—1181no—
408C2×C22⋊Q8—1181no—
409C2×C4×Q8—591no—
410C2×C4×Q8—591no—
411C2×C4×D4—591no—
412C2×C4×D4—591no—
413C2×C4×D4—591no—
414C2×C4×D4—1181no—
415C2×C4×D4C2×D5911yescharacteristic
416C2×C4×D4C2×D5911yescharacteristic
417C22×C4⋊C4—1181no—
418#490—598no—
419#489—598no—
420#488—598no—
421#479—598no—
422#478—598no—
423#474—598no—
424#463—598no—
425#463—598no—
426#459—598no—
427#446—598no—
428#442—598no—
429#440—598no—
430C4×D8C2×D5918yescomplemented
431C2×#107—591no—
432C2×#107C2×D5911yescharacteristic
433C2×#106—591no—
434C2×C4⋊C8—591no—
435C2×C4⋊C8—591no—
436C2×C4⋊C8—591no—
437C2×#103—591no—
438C2×#103—591no—
439C2×#103—591no—
440C2×#102—591no—
441C2×#102—591no—
442C2×#102—591no—
443C2×#102—591no—
444C2×#102—591no—
445C2×#102C2×D5911yescharacteristic
446C2×#102C2×D5911yescharacteristic
447C2×#97—591no—
448C2×#97—591no—
449C2×C4×C8C2×D5911yescharacteristic
450C59C2×#337011yescharacteristic, complemented, Sylow
451C22×Q8—591no—
452C22×Q8—591no—
453C22×Q8—1181no—
454C22×D4—591no—
455C22×D4—1181no—
456C22×D4—1181no—
457C22×D4C22×D5911yescharacteristic
458C22×D4C22×D5911yescharacteristic
459C23×C4—21no—
460C23×C4—21no—
461C23×C4—1181no—
462C23×C4—1181no—
463C23×C4—1181no—
464C2×SD16—594no—
465C2×SD16—1184no—
466C2×D8—24no—
467C2×D8—594no—
468C2×D8—1184no—
469C2×D8C22×D5914yes—
470C22×C8—591no—
471C22×C8—591no—
472C22×C8C22×D5911yescharacteristic
473C22×C8C22×D5911yescharacteristic
474C4⋊Q8—594no—
475C4⋊Q8—1182no—
476#127—594no—
477#127—1182no—
478#125—594no—
479#125—594no—
480#125—1182no—
481#125—1182no—
482#124—594no—
483#124—594no—
484#124—1182no—
485#124—1188no—
486#124—1182no—
487#123—1188no—
488#123—1188no—
489C22⋊Q8—1188no—
490C22⋊Q8—1188no—
491C22⋊Q8—1188no—
492C4×Q8—594no—
493C4×Q8—594no—
494C4×Q8—594no—
495C4×Q8—1182no—
496C4×D4—22no—
497C4×D4—22no—
498C4×D4—594no—
499C4×D4—594no—
500C4×D4—594no—
501C4×D4—1182no—
502C4×D4—1182no—
503C4×D4—1182no—
504C4×D4—1188no—
505C4×D4C22×D5914yes—
506C4×D4C22×D5914yes—
507C2×C4⋊C4—591no—
508C2×C4⋊C4—591no—
509C2×C4⋊C4—591no—
510C2×C4⋊C4—591no—
511C2×C4⋊C4—591no—
512C2×C4⋊C4—1188no—
513C2×C4⋊C4—1181no—
514C2×C4⋊C4—1181no—
515C2×C4⋊C4—1181no—
516C2×C4⋊C4—1181no—
517C2×C4⋊C4—1181no—
518C2×C4⋊C4—1181no—
519C2×C4⋊C4C22×D5911yescharacteristic
520C2×C4⋊C4C22×D5911yescharacteristic
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—1181no—
524C2×C22⋊C4—1181no—
525C2×C22⋊C4—1181no—
526C2×C22⋊C4—1181no—
527C2×C22⋊C4—1181no—
528C2×C22⋊C4—1181no—
529C2×C22⋊C4—1181no—
530C2×C42—591no—
531C2×C42—591no—
532C2×C42—1181no—
533C2×C42C22×D5911yescharacteristic
534#107—594no—
535#107C22×D5914yes—
536#106—594no—
537C4⋊C8—594no—
538C4⋊C8—594no—
539C4⋊C8—594no—
540#103—594no—
541#103—594no—
542#103—594no—
543#102—594no—
544#102—594no—
545#102—594no—
546#102—594no—
547#102—594no—
548#102C22×D5914yes—
549#102C22×D5914yes—
550#97—594no—
551#97—594no—
552C4×C8C22×D5914yes—
553C24—21no—
554C24—21no—
555C24—1181no—
556C2×Q8—594no—
557C2×Q8—592no—
558C2×Q8—1184no—
559C2×Q8—1181no—
560C2×Q8—1182no—
561C2×Q8—1182no—
562C2×Q8—4722no—
563C2×Q8—2362no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—22no—
567C2×D4—22no—
568C2×D4—22no—
569C2×D4—592no—
570C2×D4—1184no—
571C2×D4—1184no—
572C2×D4—1181no—
573C2×D4—1182no—
574C2×D4—1182no—
575C2×D4—4722no—
576C2×D4—2364no—
577C2×D4#1174568514yes—
578C2×D4C23×D5912yes—
579C2×D4C23×D5912yes—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—24no—
583C22×C4—24no—
584C22×C4—82no—
585C22×C4—82no—
586C22×C4—591no—
587C22×C4—591no—
588C22×C4—591no—
589C22×C4—591no—
590C22×C4—1184no—
591C22×C4—1184no—
592C22×C4—1184no—
593C22×C4—1181no—
594C22×C4—1181no—
595C22×C4—1181no—
596C22×C4—4722no—
597C22×C4—4722no—
598C22×C4—2364no—
599C22×C4D4×D5911yescharacteristic
600C22×C4D4×D5911yescharacteristic
601C22×C4C23×D5911yescharacteristic
602SD16—1188no—
603D8—28no—
604D8—1188no—
605C2×C8—22no—
606C2×C8—22no—
607C2×C8—592no—
608C2×C8—592no—
609C2×C8—1182no—
610C2×C8—1182no—
611C2×C8C23×D5912yes—
612C2×C8C23×D5912yes—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—594no—
616C4⋊C4—594no—
617C4⋊C4—594no—
618C4⋊C4—592no—
619C4⋊C4—592no—
620C4⋊C4—1184no—
621C4⋊C4—1184no—
622C4⋊C4—1184no—
623C4⋊C4—1184no—
624C4⋊C4—1181no—
625C4⋊C4—1181no—
626C4⋊C4—1184no—
627C4⋊C4—1184no—
628C4⋊C4C23×D5912yes—
629C4⋊C4C23×D5912yes—
630C22⋊C4—24no—
631C22⋊C4—24no—
632C22⋊C4—1184no—
633C22⋊C4—1184no—
634C22⋊C4—1184no—
635C22⋊C4—1184no—
636C22⋊C4—1184no—
637C22⋊C4—1184no—
638C22⋊C4—1184no—
639C42—592no—
640C42—592no—
641C42—592no—
642C42—592no—
643C42—1184no—
644C42D4×D5912yes—
645C42C23×D5912yes—
646C23—22no—
647C23—24no—
648C23—22no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—1182no—
655C23—2362no—
656C23—2362no—
657C23—2362no—
658C23C2×D4×D5911yescharacteristic
659Q8—1182no—
660Q8—1182no—
661Q8—4724no—
662Q8—2364no—
663Q8—2362no—
664D4—22no—
665D4—22no—
666D4—22no—
667D4—24no—
668D4—42no—
669D4—1182no—
670D4—1182no—
671D4—4724no—
672D4—2368no—
673D4—2362no—
674D4C2×#1174568514yes—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—84no—
682C2×C4—84no—
683C2×C4—592no—
684C2×C4—592no—
685C2×C4—592no—
686C2×C4—592no—
687C2×C4—1182no—
688C2×C4—1182no—
689C2×C4—1182no—
690C2×C4—1182no—
691C2×C4—1182no—
692C2×C4—1182no—
693C2×C4—1182no—
694C2×C4—4724no—
695C2×C4—4724no—
696C2×C4—2368no—
697C2×C4—2362no—
698C2×C4—2362no—
699C2×C4—2362no—
700C2×C4C2×D4×D5912yes—
701C2×C4C2×D4×D5912yes—
702C2×C4C2×D4×D5911yescharacteristic
703C2×C4C2×#1174568512yes—
704C2×C4#1427377412yes—
705C2×C4C24×D5911yescharacteristic
706C8—22no—
707C8—22no—
708C8—1182no—
709C8—1182no—
710C22—24no—
711C22—42no—
712C22—42no—
713C22—48no—
714C22—42no—
715C22—42no—
716C22—42no—
717C22—84no—
718C22—4724no—
719C22—2362no—
720C22—2362no—
721C22—2362no—
722C22#1683806112yes—
723C22#1683819912yes—
724C22#1683820312yes—
725C22C22×D4×D5911yescharacteristic
726C4—22no—
727C4—22no—
728C4—42no—
729C4—42no—
730C4—1182no—
731C4—1182no—
732C4—1182no—
733C4—1182no—
734C4—2362no—
735C4—2362no—
736C4—2362no—
737C4#1683806112yes—
738C4C22×#1174568511yescharacteristic
739C4C2×#1427377411yescharacteristic
740C2—44no—
741C2—82no—
742C2—4722no—
743C2#2143684514yesdirect product factor
744C2C2×#1683806111yescharacteristic
745C2C2×#1683819911yescharacteristic
746C2C2×#1683820311yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C4×D8×C59C2
socleC23×C59C22×D4
prime radicalC2×#16837595C2
hypercenterC2×C4×D8D59
hypocenterC59C2×#3370
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×D8

Complements

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

NH ≅ G/Ntype
1. C2×#16838135C2semidirect
2. C2×#16838111C2semidirect
3. #21436845C2direct (N × H)
4. C2×#16837765C2semidirect
5. C2×#16837760C2semidirect
6. C2×#16837757C2semidirect
7. C2×#16837708C2semidirect
8. C2×#16837702C2semidirect
9. C2×#16837681C2semidirect
10. C2×#16837617C2semidirect
11. C2×#16837615C2semidirect
13. C2×#16837532C2semidirect
14. C2×#16837511C2semidirect
15. C2×#16837499C2semidirect
16. C2×C4×D8×C59C2semidirect
20. #16838135C22semidirect
22. #16838111C22semidirect
42. #16837765C22semidirect
43. #16837760C22semidirect
44. #16837757C22semidirect
45. #16837708C22semidirect
46. #16837702C22semidirect
47. #16837681C22semidirect
48. #16837617C22semidirect
49. #16837615C22semidirect
51. #16837532C22semidirect
52. #16837511C22semidirect
53. #16837499C22semidirect
72. C4×D8×C59C22semidirect
382. C2×C4×D8D59semidirect
385. C2×C59#3370semidirect
430. C4×D8C2×D59semidirect
450. C59C2×#3370semidirect
743. C2#21436845direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168381352
C2×#168381112
#214368452
C2×#168377652
C2×#168377602
C2×#168377572
C2×#168377082
C2×#168377022
C2×#168376812
C2×#168376172
C2×#168376152
C2×#168375952
C2×#168375322
C2×#168375112
C2×#168374992
C2×C4×D8×C592
C2×#337059