Finite Group Databasebeta

← C2×#21434282 #29456922

Subgroups — C2×#21434282 #29456922

Order 15104.

2274 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838023C211yesmaximal, characteristic, complemented
2C2×#16837876C211yesmaximal, characteristic, complemented
3#21434282C2116yesmaximal, direct product factor
4C2×#16837744C211yesmaximal, characteristic, complemented
5C2×#16837727C211yesmaximal, characteristic, complemented
6C2×#16837693C211yesmaximal, characteristic, complemented
7C2×#16837683C211yesmaximal, characteristic, complemented
8C2×#16837618C211yesmaximal, characteristic, complemented
9C2×#16837618C211yesmaximal, characteristic, complemented
10C2×#16837555C211yesmaximal, characteristic, complemented
11C2×#16837538C211yesmaximal, characteristic
12C2×#16837515C211yesmaximal, characteristic, complemented
13C2×#16837504C211yesmaximal, characteristic, complemented
14C2×C4×#11745660C211yesmaximal, characteristic, complemented
15C2×C4×D472C211yesmaximal, characteristic, complemented
16C2×C59×#433C211yesmaximal, characteristic, complemented
17C23×D236C2211yescharacteristic
18C22×#11745660C2211yescharacteristic
19C22×#11745660C2211yescharacteristic
20C22×D472C2211yescharacteristic
21C22×D472C2211yescharacteristic
22#16838023—24no—
23#16838023C2218yescomplemented
24C2×#14273727C2211yescharacteristic, complemented
25C2×#14273722—21no—
26C2×#14273715C2211yescharacteristic, complemented
27C2×#14273713—21no—
28C2×#14273709—21no—
29C2×#14273706C2211yescharacteristic
30C2×#14273705—21no—
31C2×#14273701C2211yescharacteristic
32#16837876—24no—
33#16837876C2218yescomplemented
34C2×C4×Dic118C2211yescharacteristic, complemented
35C2×C4×D236C2211yescharacteristic
36C2×C4×D236C2211yescharacteristic
37C2×C4×D236C2211yescharacteristic
38C2×C4×D236C2211yescharacteristic
39C2×C4×D236C2211yescharacteristic, complemented
40C2×#14273689—21no—
41C2×#14273689—21no—
42C2×#14273686C2211yescharacteristic
43C2×C22⋊C4×D59—21no—
44C2×C22⋊C4×D59—21no—
45#16837744C2218yescomplemented
46#16837727C2218yescomplemented
47#16837693C2218yescomplemented
48#16837683C2218yescomplemented
49#16837618C2218yescomplemented
50#16837618C2218yescomplemented
51#16837555C2218yescomplemented
52#16837538C2218yes—
53#16837515C2218yescomplemented
54#16837504C2218yescomplemented
55C4×#11745660C2218yescomplemented
56C4×D472C2218yescomplemented
57C2×#14273661C2211yescharacteristic, complemented
58C2×#14273661C2211yescharacteristic, complemented
59C2×#14273659C2211yescharacteristic, complemented
60C2×#14273659C2211yescharacteristic, complemented
61C2×#14273652C2211yescharacteristic, complemented
62C2×#14273652C2211yescharacteristic, complemented
63C2×#14273649C2211yescharacteristic
64C2×#14273649C2211yescharacteristic
65C2×#14273649C2211yescharacteristic
66C2×#14273649C2211yescharacteristic
67C2×#14273649C2211yescharacteristic, complemented
68C2×#14273649C2211yescharacteristic, complemented
69C2×#117×C59C2211yescharacteristic
70C59×#433C2218yescomplemented
71C2×C4⋊C8×C59C2211yescharacteristic, complemented
72C2×C4⋊C8×C59C2211yescharacteristic, complemented
73C2×C22⋊C8×C59C2211yescharacteristic
74C2×C22⋊C8×C59C2211yescharacteristic
75C2×#97×C59C2211yescharacteristic, complemented
76C2×C4×C8×C59C2211yescharacteristic, complemented
77C24×D59—21no—
78C22×Dic118—21no—
79C22×Dic118C2311yescharacteristic
80C22×D236—21no—
81C22×D236—22no—
82C22×D236—24no—
83C22×D236—24no—
84C22×D236C2311yescharacteristic
85C22×D236C2314yes—
86C22×D236C2311yescharacteristic
87C22×D236C2311yescharacteristic
88C22×C22⋊D59—21no—
89C22×C4×D59—21no—
90C22×C4×D59—21no—
91C22×C4×D59—21no—
92C22×C4×D59—21no—
93C22×C4×D59—21no—
94C2×#11745660—24no—
95C2×#11745660—24no—
96C2×#11745660C2314yes—
97C2×#11745660C2314yes—
98C2×D472—24no—
99C2×D472—24no—
100C2×D472C2314yes—
101C2×D472C2314yes—
102#14273727—22no—
103#14273727C2314yescomplemented
104#14273722—28no—
105#14273715—22no—
106#14273715C2314yescomplemented
107#14273713—28no—
108#14273709—28no—
109#14273706—22no—
110#14273706C2314yes—
111#14273705—28no—
112#14273701—22no—
113#14273701C2314yes—
114C4×Dic118—22no—
115C4×Dic118C2314yescomplemented
116C4×D236—22no—
117C4×D236—22no—
118C4×D236—22no—
119C4×D236—22no—
120C4×D236—22no—
121C4×D236C2314yes—
122C4×D236C2314yes—
123C4×D236C2314yes—
124C4×D236C2314yes—
125C4×D236C2314yescomplemented
126#14273689—28no—
127#14273689—28no—
128#14273686—22no—
129#14273686C2314yes—
130C2×C4⋊Dic59—21no—
131C2×C4⋊Dic59C2311yescharacteristic
132C2×C4⋊Dic59C2311yescharacteristic
133C2×C4⋊Dic59C2311yescharacteristic
134C2×C4⋊Dic59C2311yescharacteristic
135C2×Dic59⋊C4—21no—
136C2×Dic59⋊C4—21no—
137C2×C22⋊Dic59—21no—
138C2×C22⋊Dic59—21no—
139C2×(C2×D59)⋊C4—21no—
140C2×(C2×D59)⋊C4—21no—
141C2×(C2×D59)⋊C4—21no—
142C2×(C2×D59)⋊C4—21no—
143C2×(C2×D59)⋊C4—21no—
144C2×(C2×D59)⋊C4—21no—
145C2×(C2×D59)⋊C4—21no—
146C2×(C2×D59)⋊C4—21no—
147C22⋊C4×D59—28no—
148C22⋊C4×D59—28no—
149C2×C4×Dic59—21no—
150C2×C4×Dic59—21no—
151#14273661C2314yescomplemented
152#14273661C2314yescomplemented
153#14273659C2314yescomplemented
154#14273659C2314yescomplemented
155#14273652C2314yescomplemented
156#14273652C2314yescomplemented
157#14273649C2314yes—
158#14273649C2314yes—
159#14273649C2314yes—
160#14273649C2314yes—
161#14273649C2314yescomplemented
162#14273649C2314yescomplemented
163C23×C4×C59C2311yescharacteristic
164C22×C8×C59C2311yescharacteristic
165C22×C8×C59C2311yescharacteristic
166C22×C8×C59C2311yescharacteristic
167C22×C8×C59C2311yescharacteristic
168#117×C59D414yes—
169#117×C59C2314yes—
170C2×C4⋊C4×C59D411yescharacteristic
171C2×C4⋊C4×C59D411yescharacteristic
172C2×C22⋊C4×C59D411yescharacteristic
173C2×C22⋊C4×C59D411yescharacteristic
174C2×C42×C59C2311yescharacteristic
175C2×C42×C59C2311yescharacteristic
176C4⋊C8×C59C2314yescomplemented
177C4⋊C8×C59C2314yescomplemented
178C22⋊C8×C59C2314yes—
179C22⋊C8×C59C2314yes—
180#97×C59C2314yescomplemented
181C4×C8×C59C2314yescomplemented
182C24×C59C2×D411yescharacteristic
183C23×D59—21no—
184C23×D59—21no—
185C23×D59—28no—
186C23×D59—24no—
187C23×D59—21no—
188C23×D59—82no—
189C23×D59—82no—
190C22×C4×C59—22no—
191C22×C4×C59—22no—
192C22×C4×C59C2×D411yescharacteristic
193C22×C4×C59C2×D411yescharacteristic
194C22×C4×C59C2×D411yescharacteristic
195C22×C4×C59C2×D411yescharacteristic
196C22×C4×C59C2×D411yescharacteristic
197C22×C4×C59C2×D412yes—
198C22×C4×C59C2412yes—
199C22×C4×C59C2411yescharacteristic
200C2×C22⋊D59—24no—
201C2×C22⋊D59—82no—
202C22×Dic59—21no—
203C22×Dic59—21no—
204C22×Dic59—21no—
205C22×Dic59—21no—
206C22×Dic59—21no—
207C2×D236—28no—
208C2×D236—216no—
209C2×D236—24no—
210C2×D236—21no—
211C2×D236—21no—
212C2×D236—22no—
213C2×D236—22no—
214C2×D236—28no—
215C2×D236—28no—
216C2×D236—22no—
217C2×D236—22no—
218C2×D236—21no—
219C2×D236#4114yes—
220C2×D236#4114yes—
221C2×D236C2412yes—
222C2×D236C2412yes—
223C2×D236C2412yes—
224C2×C4×D59—24no—
225C2×C4×D59—24no—
226C2×C4×D59—24no—
227C2×C4×D59—24no—
228C2×C4×D59—24no—
229C2×C4×D59—82no—
230C2×C4×D59—82no—
231C2×C4×D59—82no—
232C2×C4×D59—82no—
233C2×C4×D59—82no—
234C2×Dic118—22no—
235C2×Dic118—22no—
236C2×Dic118—21no—
237C2×Dic118—24no—
238C2×Dic118—82no—
239C2×Dic118C2412yes—
240C2×C8×C59—22no—
241C2×C8×C59—22no—
242C2×C8×C59—22no—
243C2×C8×C59—22no—
244C2×C8×C59C2412yes—
245C2×C8×C59C2412yes—
246C2×C8×C59C2412yes—
247C2×C8×C59C2412yes—
248C4⋊C4×C59C2×D414yes—
249C4⋊C4×C59C2×D414yes—
250C22⋊C4×C59C2×D414yes—
251C22⋊C4×C59C2×D414yes—
252C42×C59C2×D412yes—
253C42×C59C2×D412yes—
254C42×C59C2412yes—
255C42×C59C2412yes—
256C22⋊Dic59—24no—
257C22⋊Dic59—24no—
258(C2×D59)⋊C4—24no—
259(C2×D59)⋊C4—24no—
260(C2×D59)⋊C4—24no—
261(C2×D59)⋊C4—24no—
262(C2×D59)⋊C4—24no—
263(C2×D59)⋊C4—24no—
264(C2×D59)⋊C4—24no—
265(C2×D59)⋊C4—24no—
266C4⋊Dic59—24no—
267C4⋊Dic59—21no—
268C4⋊Dic59—21no—
269C4⋊Dic59—21no—
270C4⋊Dic59—21no—
271C4⋊Dic59C2412yes—
272C4⋊Dic59C2412yes—
273C4⋊Dic59C2412yes—
274C4⋊Dic59C2412yes—
275Dic59⋊C4—24no—
276Dic59⋊C4—24no—
277C4×Dic59—24no—
278C4×Dic59—24no—
279D472—28no—
280D472—28no—
281#11745660—28no—
282#11745660—28no—
283C23×C59—22no—
284C23×C59—22no—
285C23×C59—22no—
286C23×C59C22×D412yes—
287C23×C59C22×D411yescharacteristic
288C22×D59—24no—
289C22×D59—24no—
290C22×D59—22no—
291C22×D59—22no—
292C22×D59—216no—
293C22×D59—22no—
294C22×D59—42no—
295C22×D59—42no—
296C22×D59—42no—
297C22×D59—42no—
298C22×D59—42no—
299C22×D59—42no—
300C22×D59—42no—
301C22×D59—84no—
302C22×D59—84no—
303C22×D59—816no—
304C2×C4×C59—22no—
305C2×C4×C59—22no—
306C2×C4×C59—22no—
307C2×C4×C59—22no—
308C2×C4×C59—22no—
309C2×C4×C59—24no—
310C2×C4×C59—22no—
311C2×C4×C59—22no—
312C2×C4×C59C22×D412yes—
313C2×C4×C59C22×D412yes—
314C2×C4×C59C22×D412yes—
315C2×C4×C59C22×D412yes—
316C2×C4×C59C22×D412yes—
317C2×C4×C59C22×D411yescharacteristic
318C2×C4×C59C2×#4112yes—
319C2×C4×C59C2×#4112yes—
320C2×C4×C59C2511yescharacteristic
321C22⋊D59—84no—
322C2×Dic59—22no—
323C2×Dic59—22no—
324C2×Dic59—22no—
325C2×Dic59—22no—
326C2×Dic59—22no—
327C2×Dic59—42no—
328C2×Dic59—42no—
329C2×Dic59—42no—
330C2×Dic59—42no—
331C2×Dic59—42no—
332D236—216no—
333D236—24no—
334D236—24no—
335D236—22no—
336D236—22no—
337D236—22no—
338D236—22no—
339D236—42no—
340D236C2×#4114yes—
341D236C2×#4114yes—
342C4×D59—84no—
343C4×D59—84no—
344C4×D59—84no—
345C4×D59—84no—
346C4×D59—84no—
347Dic118—22no—
348Dic118—22no—
349Dic118—42no—
350Dic118—84no—
351C8×C59—22no—
352C8×C59—22no—
353C8×C59—22no—
354C8×C59—22no—
355C2×#3118—591nomaximal, Sylow
356C22×C59—22no—
357C22×C59—22no—
358C22×C59—22no—
359C22×C59—44no—
360C22×C59#52512yes—
361C22×C59#57612yes—
362C22×C59#57712yes—
363C22×C59C23×D411yescharacteristic
364C2×D59—24no—
365C2×D59—24no—
366C2×D59—48no—
367C2×D59—48no—
368C2×D59—42no—
369C2×D59—42no—
370C2×D59—42no—
371C2×D59—42no—
372C2×D59—42no—
373C2×D59—42no—
374C2×D59—42no—
375C2×D59—816no—
376C2×D59—84no—
377C4×C59—22no—
378C4×C59—22no—
379C4×C59—22no—
380C4×C59—22no—
381C4×C59—22no—
382C4×C59#52512yes—
383C4×C59C22×#4111yescharacteristic
384C4×C59C22×#4111yescharacteristic
385Dic59—42no—
386Dic59—42no—
387Dic59—42no—
388Dic59—42no—
389Dic59—42no—
390C2×#542—591no—
391C2×#518—591no—
392#3118—5916no—
393C2×#485—591no—
394C2×#482—591no—
395C2×#476—591no—
396C2×#474—591no—
397C2×#463—591no—
398C2×#463—591no—
399C2×#450—591no—
400C2×#447—591no—
401C2×#442—591no—
402C2×#440—591no—
403C2×C4×SD16—591no—
404C2×C4×D8—591no—
405C2×#433D5911yescharacteristic, complemented
406C2×C59—42no—
407C2×C59#311814yescomplemented
408C2×C59C2×#52511yescharacteristic
409C2×C59C2×#57611yescharacteristic
410C2×C59C2×#57711yescharacteristic
411D59—44no—
412D59—44no—
413D59—82no—
414C23×D4—591no—
415C22×SD16—591no—
416C22×SD16—591no—
417C22×D8—591no—
418C22×D8—591no—
419#542—598no—
420#542—1184no—
421C2×C4⋊Q8—591no—
422C2×#126—1181no—
423C2×#124—591no—
424C2×#124—1181no—
425C2×#123—1181no—
426C2×C22⋊Q8—591no—
427C2×C22⋊Q8—1181no—
428C2×#121—591no—
429#518—598no—
430#518—1184no—
431C2×C4×Q8—591no—
432C2×C4×D4—591no—
433C2×C4×D4—591no—
434C2×C4×D4—591no—
435C2×C4×D4—591no—
436C2×C4×D4—591no—
437C2×C4×D4—1181no—
438C2×C4×D4—1181no—
439C2×#117—591no—
440C2×#117C2×D5911yescharacteristic
441C22×C22⋊C4—1181no—
442C22×C22⋊C4—1181no—
443#485—598no—
444#482—598no—
445#476—598no—
446#474—598no—
447#463—598no—
448#463—598no—
449#450—598no—
450#447—598no—
451#442—598no—
452#440—598no—
453C4×SD16—598no—
454C4×D8—598no—
455#433C2×D5918yescomplemented
456C2×#107—591no—
457C2×#107—591no—
458C2×#106—591no—
459C2×#106—591no—
460C2×C4⋊C8C2×D5911yescharacteristic, complemented
461C2×C4⋊C8C2×D5911yescharacteristic, complemented
462C2×#103—591no—
463C2×#103—591no—
464C2×#102—591no—
465C2×#102—591no—
466C2×#102—591no—
467C2×#102—591no—
468C2×#102—591no—
469C2×#102—591no—
470C2×C22⋊C8C2×D5911yescharacteristic
471C2×C22⋊C8C2×D5911yescharacteristic
472C2×#97C2×D5911yescharacteristic, complemented
473C2×C4×C8C2×D5911yescharacteristic, complemented
474C59C2×#311811yescharacteristic, complemented, Sylow
475C25—1181no—
476C22×Q8—591no—
477C22×Q8—1181no—
478C22×D4—591no—
479C22×D4—591no—
480C22×D4—591no—
481C22×D4—594no—
482C22×D4—1184no—
483C22×D4—1184no—
484C22×D4—1181no—
485C22×D4—1181no—
486C22×D4—1182no—
487C23×C4—1181no—
488C23×C4—1181no—
489C23×C4—1181no—
490C23×C4—1181no—
491C23×C4—1181no—
492C23×C4C22×D5911yescharacteristic
493C2×SD16—594no—
494C2×SD16—594no—
495C2×SD16—1184no—
496C2×SD16—1184no—
497C2×D8—594no—
498C2×D8—594no—
499C2×D8—1184no—
500C2×D8—1184no—
501C22×C8C22×D5911yescharacteristic
502C22×C8C22×D5911yescharacteristic
503C22×C8C22×D5911yescharacteristic
504C22×C8C22×D5911yescharacteristic
505C4⋊Q8—594no—
506C4⋊Q8—1182no—
507#126—1188no—
508#124—594no—
509#124—1188no—
510#124—1182no—
511#123—1188no—
512C22⋊Q8—594no—
513C22⋊Q8—1182no—
514C22⋊Q8—1188no—
515#121—594no—
516#121—1182no—
517C4×Q8—594no—
518C4×Q8—1182no—
519C4×D4—594no—
520C4×D4—594no—
521C4×D4—594no—
522C4×D4—594no—
523C4×D4—594no—
524C4×D4—1188no—
525C4×D4—1188no—
526C4×D4—1182no—
527C4×D4—1182no—
528C4×D4—1182no—
529C4×D4—1182no—
530C4×D4—1182no—
531#117—594no—
532#117—1182no—
533#117D23614yes—
534#117C22×D5914yes—
535C2×C4⋊C4—591no—
536C2×C4⋊C4—591no—
537C2×C4⋊C4—591no—
538C2×C4⋊C4—591no—
539C2×C4⋊C4—1181no—
540C2×C4⋊C4—1181no—
541C2×C4⋊C4—1181no—
542C2×C4⋊C4D23611yescharacteristic
543C2×C4⋊C4D23611yescharacteristic
544C2×C22⋊C4—1181no—
545C2×C22⋊C4—1181no—
546C2×C22⋊C4—1181no—
547C2×C22⋊C4—1181no—
548C2×C22⋊C4—1181no—
549C2×C22⋊C4—1181no—
550C2×C22⋊C4—1181no—
551C2×C22⋊C4—1181no—
552C2×C22⋊C4—1181no—
553C2×C22⋊C4—1181no—
554C2×C22⋊C4—1188no—
555C2×C22⋊C4—1188no—
556C2×C22⋊C4D23611yescharacteristic
557C2×C22⋊C4D23611yescharacteristic
558C2×C42—1181no—
559C2×C42—1181no—
560C2×C42C22×D5911yescharacteristic
561C2×C42C22×D5911yescharacteristic
562#107—594no—
563#107—594no—
564#106—594no—
565#106—594no—
566C4⋊C8C22×D5914yescomplemented
567C4⋊C8C22×D5914yescomplemented
568#103—594no—
569#103—594no—
570#102—594no—
571#102—594no—
572#102—594no—
573#102—594no—
574#102—594no—
575#102—594no—
576C22⋊C8C22×D5914yes—
577C22⋊C8C22×D5914yes—
578#97C22×D5914yescomplemented
579C4×C8C22×D5914yescomplemented
580C24—1188no—
581C24—1184no—
582C24—1181no—
583C24—1181no—
584C24—1181no—
585C24—4722no—
586C24—4722no—
587C24C2×D23611yescharacteristic
588C2×Q8—592no—
589C2×Q8—1184no—
590C2×Q8—1181no—
591C2×Q8—1182no—
592C2×Q8—1182no—
593C2×Q8—4722no—
594C2×D4—594no—
595C2×D4—594no—
596C2×D4—592no—
597C2×D4—592no—
598C2×D4—592no—
599C2×D4—1188no—
600C2×D4—1188no—
601C2×D4—1188no—
602C2×D4—11816no—
603C2×D4—1184no—
604C2×D4—1184no—
605C2×D4—1181no—
606C2×D4—1181no—
607C2×D4—1181no—
608C2×D4—1182no—
609C2×D4—1182no—
610C2×D4—1182no—
611C2×D4—1182no—
612C2×D4—4722no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—1181no—
616C22×C4—1181no—
617C22×C4—1181no—
618C22×C4—1181no—
619C22×C4—1181no—
620C22×C4—1184no—
621C22×C4—1184no—
622C22×C4—1184no—
623C22×C4—1184no—
624C22×C4—1184no—
625C22×C4—4722no—
626C22×C4—4722no—
627C22×C4—4722no—
628C22×C4—4722no—
629C22×C4—4722no—
630C22×C4C2×D23612yes—
631C22×C4C2×D23611yescharacteristic
632C22×C4C2×D23611yescharacteristic
633C22×C4C2×D23611yescharacteristic
634C22×C4C2×D23611yescharacteristic
635C22×C4C2×D23611yescharacteristic
636C22×C4C23×D5912yes—
637C22×C4C23×D5911yescharacteristic
638SD16—1188no—
639SD16—1188no—
640D8—1188no—
641D8—1188no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—22no—
645C2×C8—22no—
646C2×C8C23×D5912yes—
647C2×C8C23×D5912yes—
648C2×C8C23×D5912yes—
649C2×C8C23×D5912yes—
650C4⋊C4—592no—
651C4⋊C4—592no—
652C4⋊C4—592no—
653C4⋊C4—592no—
654C4⋊C4—1181no—
655C4⋊C4—1181no—
656C4⋊C4—1181no—
657C4⋊C4—1181no—
658C4⋊C4—1184no—
659C4⋊C4—1184no—
660C4⋊C4—1184no—
661C4⋊C4C2×D23614yes—
662C4⋊C4C2×D23614yes—
663C22⋊C4—1184no—
664C22⋊C4—1184no—
665C22⋊C4—1184no—
666C22⋊C4—1184no—
667C22⋊C4—1184no—
668C22⋊C4—1184no—
669C22⋊C4—1184no—
670C22⋊C4—1184no—
671C22⋊C4—1184no—
672C22⋊C4—1184no—
673C22⋊C4C2×D23614yes—
674C22⋊C4C2×D23614yes—
675C42—1184no—
676C42—1184no—
677C42C2×D23612yes—
678C42C2×D23612yes—
679C42C23×D5912yes—
680C42C23×D5912yes—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—11816no—
685C23—1184no—
686C23—1184no—
687C23—1182no—
688C23—1182no—
689C23—1182no—
690C23—4724no—
691C23—4724no—
692C23—47216no—
693C23—2362no—
694C23—2362no—
695C23—2362no—
696C23—2362no—
697C23—2362no—
698C23—2362no—
699C23—2362no—
700C23C22×D23612yes—
701C23C22×D23611yescharacteristic
702Q8—1182no—
703Q8—1182no—
704Q8—4724no—
705Q8—2362no—
706D4—594no—
707D4—594no—
708D4—11816no—
709D4—1184no—
710D4—1184no—
711D4—1182no—
712D4—1182no—
713D4—1182no—
714D4—1182no—
715D4—4724no—
716D4—2362no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—24no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—1182no—
726C2×C4—1182no—
727C2×C4—1182no—
728C2×C4—1182no—
729C2×C4—1182no—
730C2×C4—4724no—
731C2×C4—4724no—
732C2×C4—4724no—
733C2×C4—4724no—
734C2×C4—4724no—
735C2×C4—2362no—
736C2×C4—2362no—
737C2×C4—2362no—
738C2×C4—2362no—
739C2×C4—2362no—
740C2×C4C22×D23612yes—
741C2×C4C22×D23612yes—
742C2×C4C22×D23612yes—
743C2×C4C22×D23612yes—
744C2×C4C22×D23612yes—
745C2×C4C22×D23611yescharacteristic
746C2×C4#41×D5912yes—
747C2×C4#41×D5912yes—
748C2×C4C24×D5911yescharacteristic
749C8—22no—
750C8—22no—
751C8—22no—
752C8—22no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—44no—
757C22—1184no—
758C22—1184no—
759C22—47216no—
760C22—4724no—
761C22—2362no—
762C22—2362no—
763C22—2362no—
764C22—2362no—
765C22—2362no—
766C22—2362no—
767C22—2362no—
768C22—2368no—
769C22—2368no—
770C22#1683791412yes—
771C22#1683820712yes—
772C22#1683821412yes—
773C22C23×D23611yescharacteristic
774C4—22no—
775C4—22no—
776C4—22no—
777C4—22no—
778C4—22no—
779C4—2362no—
780C4—2362no—
781C4—2362no—
782C4—2362no—
783C4—2362no—
784C4#1683791412yes—
785C4C2×#41×D5911yescharacteristic
786C4C2×#41×D5911yescharacteristic
787C2—42no—
788C2—4722no—
789C2—2364no—
790C2—2364no—
791C2#2143428214yesdirect product factor
792C2C2×#1683791411yescharacteristic
793C2C2×#1683820711yescharacteristic
794C2C2×#1683821411yescharacteristic
subgroupG/H
centerC23C22×D236
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#433C2
socleC23×C59C22×D4
prime radicalC2×#16837538C2
hypercenterC2×#433D59
hypocenterC59C2×#3118
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
1. C2×#16838023C2semidirect
2. C2×#16837876C2semidirect
3. #21434282C2direct (N × H)
4. C2×#16837744C2semidirect
5. C2×#16837727C2semidirect
6. C2×#16837693C2semidirect
7. C2×#16837683C2semidirect
8. C2×#16837618C2semidirect
9. C2×#16837618C2semidirect
10. C2×#16837555C2semidirect
12. C2×#16837515C2semidirect
13. C2×#16837504C2semidirect
14. C2×C4×#11745660C2semidirect
15. C2×C4×D472C2semidirect
16. C2×C59×#433C2semidirect
23. #16838023C22semidirect
24. C2×#14273727C22semidirect
26. C2×#14273715C22semidirect
33. #16837876C22semidirect
34. C2×C4×Dic118C22semidirect
39. C2×C4×D236C22semidirect
45. #16837744C22semidirect
46. #16837727C22semidirect
47. #16837693C22semidirect
48. #16837683C22semidirect
49. #16837618C22semidirect
50. #16837618C22semidirect
51. #16837555C22semidirect
53. #16837515C22semidirect
54. #16837504C22semidirect
55. C4×#11745660C22semidirect
56. C4×D472C22semidirect
57. C2×#14273661C22semidirect
58. C2×#14273661C22semidirect
59. C2×#14273659C22semidirect
60. C2×#14273659C22semidirect
61. C2×#14273652C22semidirect
62. C2×#14273652C22semidirect
67. C2×#14273649C22semidirect
68. C2×#14273649C22semidirect
70. C59×#433C22semidirect
71. C2×C4⋊C8×C59C22semidirect
72. C2×C4⋊C8×C59C22semidirect
75. C2×#97×C59C22semidirect
76. C2×C4×C8×C59C22semidirect
103. #14273727C23semidirect
106. #14273715C23semidirect
115. C4×Dic118C23semidirect
125. C4×D236C23semidirect
151. #14273661C23semidirect
152. #14273661C23semidirect
153. #14273659C23semidirect
154. #14273659C23semidirect
155. #14273652C23semidirect
156. #14273652C23semidirect
161. #14273649C23semidirect
162. #14273649C23semidirect
176. C4⋊C8×C59C23semidirect
177. C4⋊C8×C59C23semidirect
180. #97×C59C23semidirect
181. C4×C8×C59C23semidirect
405. C2×#433D59semidirect
407. C2×C59#3118semidirect
455. #433C2×D59semidirect
460. C2×C4⋊C8C2×D59semidirect
461. C2×C4⋊C8C2×D59semidirect
472. C2×#97C2×D59semidirect
473. C2×C4×C8C2×D59semidirect
474. C59C2×#3118semidirect
566. C4⋊C8C22×D59semidirect
567. C4⋊C8C22×D59semidirect
578. #97C22×D59semidirect
579. C4×C8C22×D59semidirect
791. C2#21434282direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168380232
C2×#168378762
#214342822
C2×#168377442
C2×#168377272
C2×#168376932
C2×#168376832
C2×#168376182
C2×#168375552
C2×#168375382
C2×#168375152
C2×#168375042
C2×C4×#117456602
C2×C4×D4722
C2×C59×#4332
C2×#311859