Finite Group Databasebeta

← C2×#21434175 #29456771

Subgroups — C2×#21434175 #29456771

Order 15104.

2170 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837931C211yesmaximal, characteristic
2C2×C4×Q8×D59C211yesmaximal, characteristic, complemented
3#21434175C2116yesmaximal, direct product factor
4C2×#16837731C211yesmaximal, characteristic, complemented
5C2×#16837714C211yesmaximal, characteristic
6C2×#16837710C211yesmaximal, characteristic, complemented
7C2×#16837709C211yesmaximal, characteristic, complemented
8C2×#16837621C211yesmaximal, characteristic, complemented
9C2×#16837556C211yesmaximal, characteristic, complemented
10C2×#16837539C211yesmaximal, characteristic
11C2×Q16×Dic59C211yesmaximal, characteristic, complemented
12C2×#16837494C211yesmaximal, characteristic, complemented
13C2×#16837493C211yesmaximal, characteristic, complemented
14C2×SD16×Dic59C211yesmaximal, characteristic, complemented
15C2×#16837454C211yesmaximal, characteristic, complemented
16C2×C59×#464C211yesmaximal, characteristic, complemented
17C22×Q8×D59C2211yescharacteristic
18C22×#11745672C2211yescharacteristic
19C22×#11745670C2211yescharacteristic
20#16837931—24no—
21#16837931C2218yes—
22C2×#14273720—21no—
23C2×#14273719C2211yescharacteristic
24C2×#14273709—21no—
25C2×#14273703C2211yescharacteristic
26C2×#14273698C2211yescharacteristic
27C2×Q8×Dic59C2211yescharacteristic
28C2×Q8×Dic59C2211yescharacteristic
29C2×C4×Dic118—21no—
30C2×C4×Dic118C2211yescharacteristic
31C2×#14273692—21no—
32C2×#14273692C2211yescharacteristic
33C4×Q8×D59—24no—
34C4×Q8×D59C2218yescomplemented
35C2×D4×Dic59C2211yescharacteristic
36C2×(C22⋊D59)⋊C4—21no—
37C2×#14273683—21no—
38C2×C4⋊C4×D59—21no—
39C2×C4⋊C4×D59C2211yescharacteristic
40C2×C42×D59—21no—
41C2×C42×D59C2211yescharacteristic
42#16837731C2218yescomplemented
43#16837714C2218yes—
44#16837710C2218yescomplemented
45#16837709C2218yescomplemented
46#16837621C2218yescomplemented
47#16837556C2218yescomplemented
48#16837539C2218yes—
49Q16×Dic59C2218yescomplemented
50#16837494C2218yescomplemented
51#16837493C2218yescomplemented
52SD16×Dic59C2218yescomplemented
53#16837454C2218yescomplemented
54C2×#14273661C2211yescharacteristic
55C2×#14273660C2211yescharacteristic
56C2×#14273659C2211yescharacteristic
57C2×#14273658C2211yescharacteristic
58C2×C4⋊(C59⋊C8)C2211yescharacteristic
59C2×#14273652C2211yescharacteristic
60C2×#14273652C2211yescharacteristic
61C2×#14273651C2211yescharacteristic
62C2×#14273651C2211yescharacteristic
63C2×#14273651C2211yescharacteristic
64C2×#14273648C2211yescharacteristic
65C2×(C2×D59)⋊C8C2211yescharacteristic
66C2×(C2×D59)⋊C8C2211yescharacteristic
67C2×C8×Dic59C2211yescharacteristic
68C2×C8×Dic59C2211yescharacteristic
69C22×Q16×C59C2211yescharacteristic
70C22×SD16×C59C2211yescharacteristic
71C2×#124×C59C2211yescharacteristic
72C2×C4×Q8×C59C2211yescharacteristic
73C59×#464C2218yescomplemented
74C2×C4⋊C8×C59C2211yescharacteristic
75C2×#103×C59C2211yescharacteristic
76C2×#102×C59C2211yescharacteristic
77C22×Dic118—21no—
78C22×Dic118C2311yescharacteristic
79C2×Q8×D59—24no—
80C2×Q8×D59—22no—
81C2×Q8×D59—24no—
82C2×Q8×D59C2314yes—
83C22×C22⋊D59—21no—
84C23×Dic59—21no—
85C22×C4×D59—21no—
86C22×C4×D59—21no—
87C22×C4×D59D411yescharacteristic
88C22×C4×D59D411yescharacteristic
89C22×C4×D59C2311yescharacteristic
90C2×#11745672—24no—
91C2×#11745672C2314yes—
92C2×#11745670—24no—
93C2×#11745670C2314yes—
94C22×C59⋊C8C2311yescharacteristic
95C22×C59⋊C8C2311yescharacteristic
96#14273720—28no—
97#14273719—22no—
98#14273719C2314yes—
99#14273709—28no—
100#14273703—22no—
101#14273703C2314yes—
102#14273698—22no—
103#14273698C2314yes—
104Q8×Dic59—22no—
105Q8×Dic59—22no—
106Q8×Dic59C2314yes—
107Q8×Dic59C2314yes—
108C4×Dic118—22no—
109C4×Dic118—28no—
110C4×Dic118C2314yes—
111#14273692—22no—
112#14273692—28no—
113#14273692C2314yes—
114D4×Dic59—22no—
115D4×Dic59C2314yes—
116(C22⋊D59)⋊C4—28no—
117#14273683—28no—
118C2×C4⋊Dic59—21no—
119C2×C4⋊Dic59—21no—
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×Dic59⋊C4—21no—
129C4⋊C4×D59—28no—
130C4⋊C4×D59—22no—
131C4⋊C4×D59C2314yes—
132C2×C22⋊Dic59—21no—
133C2×C22⋊Dic59—21no—
134C2×(C2×D59)⋊C4—21no—
135C2×C4×Dic59—21no—
136C2×C4×Dic59—21no—
137C2×C4×Dic59—21no—
138C2×C4×Dic59—21no—
139C2×C4×Dic59D411yescharacteristic
140C2×C4×Dic59D411yescharacteristic
141C2×C4×Dic59C2311yescharacteristic
142C42×D59—28no—
143C42×D59D414yes—
144C42×D59C2314yes—
145#14273661C2314yes—
146#14273660C2314yes—
147#14273659C2314yes—
148#14273658C2314yes—
149C4⋊(C59⋊C8)C2314yes—
150#14273652C2314yes—
151#14273652C2314yes—
152#14273651C2314yes—
153#14273651C2314yes—
154#14273651C2314yes—
155#14273648C2314yes—
156(C2×D59)⋊C8C2314yes—
157(C2×D59)⋊C8C2314yes—
158C8×Dic59C2314yes—
159C8×Dic59C2314yes—
160C22×Q8×C59C2311yescharacteristic
161C22×Q8×C59C2311yescharacteristic
162C22×D4×C59C2311yescharacteristic
163C2×Q16×C59—24no—
164C2×Q16×C59C2314yes—
165C2×SD16×C59—24no—
166C2×SD16×C59C2314yes—
167C22×C8×C59C2311yescharacteristic
168C22×C8×C59C2311yescharacteristic
169#124×C59—22no—
170#124×C59C2314yes—
171C4×Q8×C59—22no—
172C4×Q8×C59C2314yes—
173C2×C4⋊C4×C59—21no—
174C2×C4⋊C4×C59C2311yescharacteristic
175C2×C22⋊C4×C59—21no—
176C2×C22⋊C4×C59—21no—
177C2×C42×C59—21no—
178C2×C42×C59C2311yescharacteristic
179C4⋊C8×C59C2314yes—
180#103×C59C2314yes—
181#102×C59C2314yes—
182C24×C59—21no—
183C23×D59C2×D411yescharacteristic
184C2×Q8×C59—21no—
185C2×Q8×C59—21no—
186C2×Q8×C59—22no—
187C2×Q8×C59—22no—
188C2×Q8×C59—22no—
189C2×Q8×C59#4114yes—
190C2×Q8×C59C2412yes—
191C2×Q8×C59C2412yes—
192C2×D4×C59—21no—
193C2×D4×C59—22no—
194C2×D4×C59—22no—
195C2×D4×C59C2412yes—
196C22×C4×C59—21no—
197C22×C4×C59—21no—
198C22×C4×C59—21no—
199C22×C4×C59C2×D411yescharacteristic
200C22×C4×C59C2×D411yescharacteristic
201C22×C4×C59C2411yescharacteristic
202C2×C22⋊D59—24no—
203C2×C22⋊D59—44no—
204C22×Dic59—21no—
205C22×Dic59—21no—
206C22×Dic59—21no—
207C22×Dic59—21no—
208C22×Dic59—24no—
209C22×Dic59—44no—
210C22×Dic59C2×D411yescharacteristic
211C22×Dic59C2×D411yescharacteristic
212C22×Dic59C2×D411yescharacteristic
213Q8×D59—216no—
214Q8×D59—28no—
215Q8×D59—28no—
216C2×C4×D59—28no—
217C2×C4×D59—24no—
218C2×C4×D59—24no—
219C2×C4×D59—22no—
220C2×C4×D59—22no—
221C2×C4×D59—24no—
222C2×C4×D59—24no—
223C2×C4×D59—44no—
224C2×C4×D59C2×D414yes—
225C2×C4×D59C2×D412yes—
226C2×C4×D59C2×D414yes—
227C2×C4×D59C2412yes—
228C2×Dic118—28no—
229C2×Dic118—21no—
230C2×Dic118—22no—
231C2×Dic118—24no—
232C2×Dic118#4114yes—
233C2×Dic118C2412yes—
234Q16×C59—28no—
235SD16×C59—28no—
236C2×C8×C59—22no—
237C2×C8×C59—22no—
238C2×C8×C59C2412yes—
239C2×C8×C59C2412yes—
240C4⋊C4×C59—24no—
241C4⋊C4×C59—21no—
242C4⋊C4×C59C2412yes—
243C22⋊C4×C59—24no—
244C22⋊C4×C59—24no—
245C42×C59—24no—
246C42×C59C2×D412yes—
247C42×C59C2412yes—
248C22⋊Dic59—24no—
249C22⋊Dic59—24no—
250#11745672—28no—
251#11745670—28no—
252(C2×D59)⋊C4—24no—
253C4⋊Dic59—21no—
254C4⋊Dic59—21no—
255C4⋊Dic59—21no—
256C4⋊Dic59—24no—
257C4⋊Dic59—24no—
258C4⋊Dic59C2412yes—
259C4⋊Dic59C2412yes—
260C4⋊Dic59C2412yes—
261Dic59⋊C4—24no—
262Dic59⋊C4—24no—
263Dic59⋊C4—24no—
264Dic59⋊C4—24no—
265Dic59⋊C4—24no—
266Dic59⋊C4—24no—
267C4×Dic59—24no—
268C4×Dic59—24no—
269C4×Dic59—24no—
270C4×Dic59—24no—
271C4×Dic59C2×D412yes—
272C4×Dic59C2×D414yes—
273C4×Dic59C2×D414yes—
274C4×Dic59C2412yes—
275C2×C59⋊C8—22no—
276C2×C59⋊C8—22no—
277C2×C59⋊C8C2412yes—
278C2×C59⋊C8C2412yes—
279C23×C59—22no—
280C23×C59—42no—
281C23×C59—42no—
282C23×C59—42no—
283C23×C59C22×D411yescharacteristic
284C22×D59—22no—
285C22×D59—22no—
286C22×D59#13514yes—
287C22×D59C22×D412yes—
288Q8×C59—24no—
289Q8×C59—22no—
290Q8×C59—22no—
291Q8×C59—22no—
292Q8×C59—42no—
293Q8×C59C2×#4114yes—
294D4×C59—22no—
295D4×C59—22no—
296D4×C59—42no—
297C2×C4×C59—24no—
298C2×C4×C59—22no—
299C2×C4×C59—22no—
300C2×C4×C59—22no—
301C2×C4×C59—22no—
302C2×C4×C59—22no—
303C2×C4×C59—42no—
304C2×C4×C59—42no—
305C2×C4×C59C22×D412yes—
306C2×C4×C59C22×D412yes—
307C2×C4×C59C22×D411yescharacteristic
308C2×C4×C59C2×#4112yes—
309C2×C4×C59C2×#4112yes—
310C2×C4×C59C2511yescharacteristic
311C22⋊D59—48no—
312C2×Dic59—22no—
313C2×Dic59—24no—
314C2×Dic59—22no—
315C2×Dic59—22no—
316C2×Dic59—22no—
317C2×Dic59—22no—
318C2×Dic59—22no—
319C2×Dic59—42no—
320C2×Dic59—42no—
321C2×Dic59—42no—
322C2×Dic59—48no—
323C2×Dic59#13714yes—
324C2×Dic59C22×D412yes—
325C2×Dic59C22×D412yes—
326C2×Dic59C22×D412yes—
327C4×D59—216no—
328C4×D59—28no—
329C4×D59—24no—
330C4×D59—22no—
331C4×D59—22no—
332C4×D59—28no—
333C4×D59—48no—
334Dic118—216no—
335Dic118—24no—
336Dic118—22no—
337Dic118C2×#4114yes—
338C8×C59—22no—
339C8×C59—22no—
340C59⋊C8—22no—
341C59⋊C8—22no—
342C2×#3108—591nomaximal, Sylow
343C22×C59—42no—
344C22×C59—42no—
345C22×C59—42no—
346C22×C59—84no—
347C22×C59#52512yes—
348C22×C59C2×#13512yes—
349C22×C59C2×#13712yes—
350C22×C59C23×D411yescharacteristic
351C2×D59—28no—
352C2×D59—22no—
353C2×D59—22no—
354C2×D59C2×#13514yes—
355C4×C59—24no—
356C4×C59—22no—
357C4×C59—22no—
358C4×C59—42no—
359C4×C59—42no—
360C4×C59#52512yes—
361C4×C59C22×#4111yescharacteristic
362C4×C59C22×#4111yescharacteristic
363Dic59—22no—
364Dic59—24no—
365Dic59—22no—
366Dic59—42no—
367Dic59—42no—
368Dic59—42no—
369Dic59C2×#13714yes—
370C2×#529—591no—
371C22×C4×Q8—591no—
372#3108—5916no—
373C2×#483—591no—
374C2×#480—591no—
375C2×#479—591no—
376C2×#479—591no—
377C2×#464—591no—
378C2×#464D5911yescharacteristic, complemented
379C2×#451—591no—
380C2×#448—591no—
381C2×C4×Q16—591no—
382C2×C4×Q16—591no—
383C2×C4×SD16—591no—
384C2×C4×SD16—591no—
385C2×#431—591no—
386C2×C59—82no—
387C2×C59#310814yescomplemented
388C2×C59C2×#52511yescharacteristic
389C2×C59C22×#13511yescharacteristic
390C2×C59C22×#13711yescharacteristic
391D59—24no—
392C23×Q8—591no—
393C22×Q16—591no—
394C22×Q16C2×D5911yescharacteristic
395C22×SD16—591no—
396C22×SD16C2×D5911yescharacteristic
397#529—598no—
398#529—1184no—
399C2×#126—1181no—
400C2×#125—591no—
401C2×#124C2×D5911yescharacteristic
402C2×#123—1181no—
403C2×C22⋊Q8—591no—
404C2×#121—591no—
405C2×C4×Q8—591no—
406C2×C4×Q8—591no—
407C2×C4×Q8—598no—
408C2×C4×Q8—591no—
409C2×C4×Q8—591no—
410C2×C4×Q8—1181no—
411C2×C4×Q8—1181no—
412C2×C4×Q8—1184no—
413C2×C4×Q8C2×D5911yescharacteristic
414C2×C4×D4—591no—
415C2×C4×D4—1181no—
416C2×#117—1181no—
417C22×C4⋊C4—591no—
418C22×C4⋊C4—1181no—
419C22×C42—591no—
420C22×C42—1181no—
421#483—598no—
422#480—598no—
423#479—598no—
424#479—598no—
425#464—598no—
426#464C2×D5918yescomplemented
427#451—598no—
428#448—598no—
429C4×Q16—598no—
430C4×Q16—598no—
431C4×SD16—598no—
432C4×SD16—598no—
433#431—598no—
434C2×#107—591no—
435C2×#107—591no—
436C2×#106—591no—
437C2×#106—591no—
438C2×C4⋊C8—591no—
439C2×C4⋊C8C2×D5911yescharacteristic
440C2×#103—591no—
441C2×#103—591no—
442C2×#103—591no—
443C2×#103—591no—
444C2×#103—591no—
445C2×#103C2×D5911yescharacteristic
446C2×#102—591no—
447C2×#102C2×D5911yescharacteristic
448C2×C22⋊C8—591no—
449C2×C22⋊C8—591no—
450C2×C4×C8—591no—
451C2×C4×C8—591no—
452C59C2×#310811yescharacteristic, complemented, Sylow
453C22×Q8—594no—
454C22×Q8—591no—
455C22×Q8—1181no—
456C22×Q8—1182no—
457C22×Q8—1184no—
458C22×Q8—1184no—
459C22×Q8C22×D5911yescharacteristic
460C22×Q8C22×D5911yescharacteristic
461C22×D4—1181no—
462C22×D4C22×D5911yescharacteristic
463C23×C4—591no—
464C23×C4—591no—
465C23×C4—591no—
466C23×C4—1181no—
467C23×C4—1181no—
468C23×C4—1181no—
469C2×Q16—24no—
470C2×Q16—594no—
471C2×Q16—1184no—
472C2×Q16C22×D5914yes—
473C2×SD16—24no—
474C2×SD16—594no—
475C2×SD16—1184no—
476C2×SD16C22×D5914yes—
477C22×C8—591no—
478C22×C8—591no—
479C22×C8C22×D5911yescharacteristic
480C22×C8C22×D5911yescharacteristic
481#126—1188no—
482#125—594no—
483#125—1182no—
484#124—22no—
485#124C22×D5914yes—
486#123—1188no—
487C22⋊Q8—594no—
488C22⋊Q8—1182no—
489#121—594no—
490#121—1182no—
491C4×Q8—22no—
492C4×Q8—594no—
493C4×Q8—594no—
494C4×Q8—594no—
495C4×Q8—594no—
496C4×Q8—1188no—
497C4×Q8—1188no—
498C4×Q8—1182no—
499C4×Q8—1182no—
500C4×Q8—1182no—
501C4×Q8—1182no—
502C4×Q8C22×D5914yes—
503C4×D4—594no—
504C4×D4—1182no—
505C4×D4—1188no—
506#117—1188no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—591no—
509C2×C4⋊C4—591no—
510C2×C4⋊C4—591no—
511C2×C4⋊C4—594no—
512C2×C4⋊C4—1182no—
513C2×C4⋊C4—1188no—
514C2×C4⋊C4—1181no—
515C2×C4⋊C4—1181no—
516C2×C4⋊C4—1181no—
517C2×C4⋊C4—1181no—
518C2×C4⋊C4—1181no—
519C2×C4⋊C4—1181no—
520C2×C4⋊C4—1181no—
521C2×C4⋊C4—1181no—
522C2×C4⋊C4C22×D5911yescharacteristic
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—1181no—
526C2×C22⋊C4—1181no—
527C2×C22⋊C4—1181no—
528C2×C42—21no—
529C2×C42—591no—
530C2×C42—591no—
531C2×C42—591no—
532C2×C42—594no—
533C2×C42—594no—
534C2×C42—1188no—
535C2×C42—1181no—
536C2×C42—1181no—
537C2×C42—1181no—
538C2×C42—1181no—
539C2×C42C22×D5911yescharacteristic
540#107—594no—
541#107—594no—
542#106—594no—
543#106—594no—
544C4⋊C8—594no—
545C4⋊C8C22×D5914yes—
546#103—594no—
547#103—594no—
548#103—594no—
549#103—594no—
550#103—594no—
551#103C22×D5914yes—
552#102—594no—
553#102C22×D5914yes—
554C22⋊C8—594no—
555C22⋊C8—594no—
556C4×C8—594no—
557C4×C8—594no—
558C24—21no—
559C24—591no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—22no—
563C2×Q8—22no—
564C2×Q8—22no—
565C2×Q8—594no—
566C2×Q8—592no—
567C2×Q8—1184no—
568C2×Q8—1188no—
569C2×Q8—1188no—
570C2×Q8—11816no—
571C2×Q8—1188no—
572C2×Q8—1181no—
573C2×Q8—1182no—
574C2×Q8#1174568714yes—
575C2×Q8C23×D5912yes—
576C2×Q8C23×D5912yes—
577C2×D4—21no—
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—1184no—
581C2×D4—2364no—
582C2×D4C23×D5912yes—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—591no—
587C22×C4—591no—
588C22×C4—591no—
589C22×C4—594no—
590C22×C4—594no—
591C22×C4—592no—
592C22×C4—592no—
593C22×C4—1184no—
594C22×C4—1184no—
595C22×C4—1184no—
596C22×C4—1188no—
597C22×C4—1184no—
598C22×C4—1184no—
599C22×C4—1181no—
600C22×C4—1182no—
601C22×C4—1182no—
602C22×C4—1181no—
603C22×C4—1181no—
604C22×C4—1181no—
605C22×C4—2364no—
606C22×C4—2364no—
607C22×C4D4×D5911yescharacteristic
608C22×C4D4×D5911yescharacteristic
609C22×C4C23×D5911yescharacteristic
610Q16—28no—
611Q16—1188no—
612SD16—28no—
613SD16—1188no—
614C2×C8—22no—
615C2×C8—22no—
616C2×C8—592no—
617C2×C8—592no—
618C2×C8—1182no—
619C2×C8—1182no—
620C2×C8C23×D5912yes—
621C2×C8C23×D5912yes—
622C4⋊C4—24no—
623C4⋊C4—21no—
624C4⋊C4—592no—
625C4⋊C4—592no—
626C4⋊C4—592no—
627C4⋊C4—1184no—
628C4⋊C4—1184no—
629C4⋊C4—1184no—
630C4⋊C4—1184no—
631C4⋊C4—1184no—
632C4⋊C4—1181no—
633C4⋊C4—1181no—
634C4⋊C4—1181no—
635C4⋊C4—1184no—
636C4⋊C4—1184no—
637C4⋊C4—1184no—
638C4⋊C4C23×D5912yes—
639C22⋊C4—24no—
640C22⋊C4—24no—
641C22⋊C4—1184no—
642C22⋊C4—1184no—
643C22⋊C4—1184no—
644C42—24no—
645C42—594no—
646C42—592no—
647C42—594no—
648C42—592no—
649C42—1184no—
650C42—1184no—
651C42—1184no—
652C42—1184no—
653C42D4×D5912yes—
654C42C23×D5912yes—
655C23—22no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—594no—
660C23—592no—
661C23—1182no—
662C23—1182no—
663C23C2×D4×D5911yescharacteristic
664Q8—24no—
665Q8—22no—
666Q8—22no—
667Q8—22no—
668Q8—42no—
669Q8—594no—
670Q8—11816no—
671Q8—1184no—
672Q8—1182no—
673Q8C2×#1174568714yes—
674D4—22no—
675D4—22no—
676D4—42no—
677D4—2368no—
678C2×C4—24no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—594no—
687C2×C4—592no—
688C2×C4—592no—
689C2×C4—592no—
690C2×C4—1188no—
691C2×C4—1188no—
692C2×C4—11816no—
693C2×C4—1182no—
694C2×C4—1184no—
695C2×C4—1182no—
696C2×C4—1182no—
697C2×C4—1184no—
698C2×C4—1182no—
699C2×C4—1182no—
700C2×C4—1182no—
701C2×C4—1182no—
702C2×C4—1182no—
703C2×C4—2368no—
704C2×C4—2368no—
705C2×C4—2362no—
706C2×C4—2362no—
707C2×C4—2362no—
708C2×C4C2×D4×D5912yes—
709C2×C4C2×D4×D5912yes—
710C2×C4C2×D4×D5911yescharacteristic
711C2×C4#41×D5912yes—
712C2×C4C2×#1174568712yes—
713C2×C4C24×D5911yescharacteristic
714C8—22no—
715C8—22no—
716C8—1182no—
717C8—1182no—
718C22—42no—
719C22—42no—
720C22—42no—
721C22—84no—
722C22—594no—
723C22—1188no—
724C22—1182no—
725C22—1182no—
726C22#1683791212yes—
727C22#135×D5912yes—
728C22#137×D5912yes—
729C22C22×D4×D5911yescharacteristic
730C4—22no—
731C4—22no—
732C4—24no—
733C4—42no—
734C4—42no—
735C4—594no—
736C4—1182no—
737C4—1182no—
738C4—1184no—
739C4—2362no—
740C4—2362no—
741C4—2362no—
742C4#1683791212yes—
743C4C2×#41×D5911yescharacteristic
744C4C22×#1174568711yescharacteristic
745C2—82no—
746C2—1184no—
747C2#2143417514yesdirect product factor
748C2C2×#1683791211yescharacteristic
749C2C2×#135×D5911yescharacteristic
750C2C2×#137×D5911yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#464C2
socleC23×C59C22×D4
prime radicalC2×#14273698C22
hypercenterC2×#464D59
hypocenterC59C2×#3108
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#464

Complements

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

NH ≅ G/Ntype
2. C2×C4×Q8×D59C2semidirect
3. #21434175C2direct (N × H)
4. C2×#16837731C2semidirect
6. C2×#16837710C2semidirect
7. C2×#16837709C2semidirect
8. C2×#16837621C2semidirect
9. C2×#16837556C2semidirect
11. C2×Q16×Dic59C2semidirect
12. C2×#16837494C2semidirect
13. C2×#16837493C2semidirect
14. C2×SD16×Dic59C2semidirect
15. C2×#16837454C2semidirect
16. C2×C59×#464C2semidirect
34. C4×Q8×D59C22semidirect
42. #16837731C22semidirect
44. #16837710C22semidirect
45. #16837709C22semidirect
46. #16837621C22semidirect
47. #16837556C22semidirect
49. Q16×Dic59C22semidirect
50. #16837494C22semidirect
51. #16837493C22semidirect
52. SD16×Dic59C22semidirect
53. #16837454C22semidirect
73. C59×#464C22semidirect
378. C2×#464D59semidirect
387. C2×C59#3108semidirect
426. #464C2×D59semidirect
452. C59C2×#3108semidirect
747. C2#21434175direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168379312
C2×C4×Q8×D592
#214341752
C2×#168377312
C2×#168377142
C2×#168377102
C2×#168377092
C2×#168376212
C2×#168375562
C2×#168375392
C2×Q16×Dic592
C2×#168374942
C2×#168374932
C2×SD16×Dic592
C2×#168374542
C2×C59×#4642
C2×#310859