Finite Group Databasebeta

← C2×#21434253 #29456822

Subgroups — C2×#21434253 #29456822

Order 15104.

2150 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×#16837954C211yesmaximal, characteristic, complemented
2C2×#16837870C211yesmaximal, characteristic
3#21434253C2116yesmaximal, direct product factor
4C2×#16837743C211yesmaximal, characteristic, complemented
5C2×#16837696C211yesmaximal, characteristic, complemented
6C2×#16837691C211yesmaximal, characteristic, complemented
7C2×#16837611C211yesmaximal, characteristic, complemented
8C2×#16837606C211yesmaximal, characteristic, complemented
9C2×#16837566C211yesmaximal, characteristic
10C2×#16837562C211yesmaximal, characteristic
11C2×#16837508C211yesmaximal, characteristic, complemented
12C2×#16837506C211yesmaximal, characteristic, complemented
13C2×#16837505C211yesmaximal, characteristic, complemented
14C2×#16837501C211yesmaximal, characteristic, complemented
15C2×#16837456C211yesmaximal, characteristic, complemented
16C2×C59×#485C211yesmaximal, characteristic, complemented
17C22×#11745685C2211yescharacteristic
18C22×Dic236C2211yescharacteristic
19C22×#11745672C2211yescharacteristic
20C22×#11745660C2211yescharacteristic
21C22×#11745671C2211yescharacteristic
22#16837954—24no—
23#16837954C2218yescomplemented
24C2×#14273726C2211yescharacteristic
25C2×#14273725C2211yescharacteristic
26C2×#14273717—21no—
27C2×#14273706C2211yescharacteristic
28C2×#14273704—21no—
29#16837870—24no—
30#16837870C2218yes—
31C2×Q8×Dic59C2211yescharacteristic
32C2×#14273692—21no—
33C2×#14273692C2211yescharacteristic
34C2×#14273692C2211yescharacteristic
35C2×#14273692C2211yescharacteristic
36C2×#14273689C2211yescharacteristic
37C2×#14273689C2211yescharacteristic
38C2×(C22⋊D59)⋊C4—21no—
39C2×(C22⋊D59)⋊C4—21no—
40C2×#14273684—21no—
41C2×#14273683—21no—
42C22×C4×Dic59C2211yescharacteristic
43C2×C42×D59—21no—
44#16837743C2218yescomplemented
45#16837696C2218yescomplemented
46#16837691C2218yescomplemented
47#16837611C2218yescomplemented
48#16837606C2218yescomplemented
49#16837566C2218yes—
50#16837562C2218yes—
51#16837508C2218yescomplemented
52#16837506C2218yescomplemented
53#16837505C2218yescomplemented
54#16837501C2218yescomplemented
55#16837456C2218yescomplemented
56C2×#14273660C2211yescharacteristic
57C2×#14273658C2211yescharacteristic
58C2×Dic59⋊C8C2211yescharacteristic
59C2×Dic59⋊C8C2211yescharacteristic
60C2×#14273652C2211yescharacteristic
61C2×#14273650C2211yescharacteristic
62C2×#14273650C2211yescharacteristic
63C2×#14273650C2211yescharacteristic
64C2×#14273649C2211yescharacteristic
65C2×#14273647C2211yescharacteristic
66C2×C22⋊(C59⋊C8)C2211yescharacteristic
67C2×#14273637C2211yescharacteristic
68C2×#14273637C2211yescharacteristic
69C2×C22⋊Q8×C59C2211yescharacteristic
70C2×#117×C59C2211yescharacteristic
71C59×#485C2218yescomplemented
72C2×#107×C59C2211yescharacteristic
73C2×#106×C59C2211yescharacteristic
74C2×#103×C59C2211yescharacteristic
75C2×#103×C59C2211yescharacteristic
76C2×C22⋊C8×C59C2211yescharacteristic
77C2×#11745685—22no—
78C2×#11745685—24no—
79C2×#11745685—24no—
80C2×#11745685C2314yes—
81C22×Dic118—21no—
82C22×Dic118C2311yescharacteristic
83C22×Dic118C2311yescharacteristic
84C22×D236C2311yescharacteristic
85C22×C22⋊D59—21no—
86C23×Dic59D411yescharacteristic
87C23×Dic59D411yescharacteristic
88C22×C4×D59—21no—
89C22×C4×D59—21no—
90C22×C4×D59—21no—
91C2×Dic236—24no—
92C2×Dic236C2314yes—
93C2×#11745672—24no—
94C2×#11745672C2314yes—
95C2×#11745660—24no—
96C2×#11745660C2314yes—
97C2×#11745671—24no—
98C2×#11745671C2314yes—
99C22×C59⋊C8C2311yescharacteristic
100C22×C59⋊C8C2311yescharacteristic
101#14273726—22no—
102#14273726C2314yes—
103#14273725—22no—
104#14273725C2314yes—
105#14273717—28no—
106#14273706—22no—
107#14273706C2314yes—
108#14273704—28no—
109Q8×Dic59—22no—
110Q8×Dic59C2314yes—
111#14273692—22no—
112#14273692—28no—
113#14273692—22no—
114#14273692—22no—
115#14273692C2314yes—
116#14273692C2314yes—
117#14273692C2314yes—
118#14273689—22no—
119#14273689—22no—
120#14273689C2314yes—
121#14273689C2314yes—
122(C22⋊D59)⋊C4—28no—
123(C22⋊D59)⋊C4—28no—
124#14273684—28no—
125#14273683—28no—
126C2×C4⋊Dic59—21no—
127C2×C4⋊Dic59C2311yescharacteristic
128C2×Dic59⋊C4—21no—
129C2×Dic59⋊C4—21no—
130C2×Dic59⋊C4—21no—
131C2×Dic59⋊C4—21no—
132C2×Dic59⋊C4—21no—
133C2×Dic59⋊C4—21no—
134C2×Dic59⋊C4—21no—
135C2×C22⋊Dic59—21no—
136C2×(C2×D59)⋊C4—21no—
137C2×(C2×D59)⋊C4—21no—
138C2×C4×Dic59—21no—
139C2×C4×Dic59—21no—
140C2×C4×Dic59—21no—
141C2×C4×Dic59—21no—
142C2×C4×Dic59D411yescharacteristic
143C2×C4×Dic59D414yes—
144C2×C4×Dic59D411yescharacteristic
145C2×C4×Dic59C2311yescharacteristic
146C2×C4×Dic59C2314yes—
147C2×C4×Dic59C2311yescharacteristic
148C42×D59—28no—
149#14273660C2314yes—
150#14273658C2314yes—
151Dic59⋊C8C2314yes—
152Dic59⋊C8C2314yes—
153#14273652C2314yes—
154#14273650C2314yes—
155#14273650C2314yes—
156#14273650C2314yes—
157#14273649C2314yes—
158#14273647C2314yes—
159C22⋊(C59⋊C8)C2314yes—
160#14273637C2314yes—
161#14273637C2314yes—
162C22×Q8×C59C2311yescharacteristic
163C23×C4×C59C2311yescharacteristic
164C22×C8×C59C2311yescharacteristic
165C22×C8×C59C2311yescharacteristic
166C22⋊Q8×C59—22no—
167C22⋊Q8×C59C2314yes—
168#117×C59—22no—
169#117×C59C2314yes—
170C2×C4⋊C4×C59—21no—
171C2×C4⋊C4×C59C2311yescharacteristic
172C2×C4⋊C4×C59C2311yescharacteristic
173C2×C4⋊C4×C59C2311yescharacteristic
174C2×C22⋊C4×C59—21no—
175C2×C22⋊C4×C59—21no—
176C2×C42×C59—21no—
177#107×C59C2314yes—
178#106×C59C2314yes—
179#103×C59C2314yes—
180#103×C59C2314yes—
181C22⋊C8×C59C2314yes—
182C24×C59C2×D411yescharacteristic
183C23×D59—21no—
184C2×Q8×C59—21no—
185C2×Q8×C59—22no—
186C2×Q8×C59—22no—
187C2×Q8×C59C2412yes—
188C22×C4×C59—22no—
189C22×C4×C59—22no—
190C22×C4×C59—21no—
191C22×C4×C59—21no—
192C22×C4×C59—21no—
193C22×C4×C59—21no—
194C22×C4×C59C2×D411yescharacteristic
195C22×C4×C59C2×D412yes—
196C22×C4×C59C2412yes—
197C22×C4×C59C2411yescharacteristic
198C2×C22⋊D59—28no—
199C2×C22⋊D59—24no—
200C22×Dic59—21no—
201C22×Dic59—24no—
202C22×Dic59—21no—
203C22×Dic59—21no—
204C22×Dic59—42no—
205C22×Dic59C2×D411yescharacteristic
206C22×Dic59C2×D411yescharacteristic
207C22×Dic59C2×D411yescharacteristic
208C22×Dic59C2×D414yes—
209C22×Dic59C2×D414yes—
210C22×Dic59C2×D411yescharacteristic
211#11745685—216no—
212#11745685—28no—
213#11745685—28no—
214C2×D236—21no—
215C2×D236—22no—
216C2×D236#4114yes—
217C2×D236C2412yes—
218C2×C4×D59—28no—
219C2×C4×D59—24no—
220C2×C4×D59—24no—
221C2×C4×D59—24no—
222C2×C4×D59—44no—
223C2×C4×D59—44no—
224C2×Dic118—21no—
225C2×Dic118—22no—
226C2×Dic118—22no—
227C2×Dic118—22no—
228C2×Dic118—21no—
229C2×Dic118—24no—
230C2×Dic118—44no—
231C2×Dic118#4114yes—
232C2×Dic118C2412yes—
233C2×Dic118C2412yes—
234C2×C8×C59—22no—
235C2×C8×C59—22no—
236C2×C8×C59C2412yes—
237C2×C8×C59C2412yes—
238C4⋊C4×C59—24no—
239C4⋊C4×C59—21no—
240C4⋊C4×C59—21no—
241C4⋊C4×C59—21no—
242C4⋊C4×C59C2412yes—
243C4⋊C4×C59C2412yes—
244C4⋊C4×C59C2412yes—
245C22⋊C4×C59—24no—
246C22⋊C4×C59—24no—
247C42×C59—24no—
248C22⋊Dic59—24no—
249#11745672—28no—
250#11745671—28no—
251(C2×D59)⋊C4—24no—
252(C2×D59)⋊C4—24no—
253C4⋊Dic59—21no—
254C4⋊Dic59—24no—
255C4⋊Dic59C2412yes—
256Dic59⋊C4—24no—
257Dic59⋊C4—24no—
258Dic59⋊C4—24no—
259Dic59⋊C4—24no—
260Dic59⋊C4—24no—
261Dic59⋊C4—24no—
262Dic59⋊C4—24no—
263C4×Dic59—24no—
264C4×Dic59—24no—
265C4×Dic59—24no—
266C4×Dic59—24no—
267C4×Dic59C2×D414yes—
268C4×Dic59C2×D414yes—
269C4×Dic59C2×D412yes—
270C4×Dic59C2×D412yes—
271C4×Dic59C2412yes—
272C4×Dic59C2412yes—
273C2×C59⋊C8—22no—
274C2×C59⋊C8—22no—
275C2×C59⋊C8C2412yes—
276C2×C59⋊C8C2412yes—
277Dic236—28no—
278#11745660—28no—
279C23×C59—22no—
280C23×C59—22no—
281C23×C59—22no—
282C23×C59C22×D412yes—
283C23×C59C22×D411yescharacteristic
284C22×D59—24no—
285C22×D59—22no—
286C22×D59—42no—
287C22×D59—42no—
288Q8×C59—22no—
289Q8×C59—22no—
290Q8×C59—42no—
291C2×C4×C59—22no—
292C2×C4×C59—24no—
293C2×C4×C59—22no—
294C2×C4×C59—22no—
295C2×C4×C59—22no—
296C2×C4×C59—22no—
297C2×C4×C59—22no—
298C2×C4×C59—22no—
299C2×C4×C59—42no—
300C2×C4×C59—42no—
301C2×C4×C59—42no—
302C2×C4×C59—42no—
303C2×C4×C59C22×D412yes—
304C2×C4×C59C22×D411yescharacteristic
305C2×C4×C59C2×#4112yes—
306C2×C4×C59C2×#4112yes—
307C2×C4×C59C2511yescharacteristic
308C22⋊D59—216no—
309C2×Dic59—24no—
310C2×Dic59—22no—
311C2×Dic59—22no—
312C2×Dic59—22no—
313C2×Dic59—22no—
314C2×Dic59—28no—
315C2×Dic59—22no—
316C2×Dic59—22no—
317C2×Dic59—44no—
318C2×Dic59—42no—
319C2×Dic59—42no—
320C2×Dic59#13714yes—
321C2×Dic59C22×D412yes—
322C2×Dic59C22×D412yes—
323C2×Dic59C22×D412yes—
324C2×Dic59C22×D412yes—
325D236—24no—
326D236—22no—
327D236C2×#4114yes—
328C4×D59—216no—
329C4×D59—48no—
330C4×D59—48no—
331Dic118—24no—
332Dic118—22no—
333Dic118—22no—
334Dic118—22no—
335Dic118—48no—
336Dic118—42no—
337Dic118C2×#4114yes—
338C8×C59—22no—
339C8×C59—22no—
340C59⋊C8—22no—
341C59⋊C8—22no—
342C2×#3116—591nomaximal, Sylow
343C22×C59—22no—
344C22×C59—22no—
345C22×C59—22no—
346C22×C59—44no—
347C22×C59#52512yes—
348C22×C59C2×#13712yes—
349C22×C59#57512yes—
350C22×C59C23×D411yescharacteristic
351C2×D59—24no—
352C2×D59—48no—
353C2×D59—42no—
354C2×D59—42no—
355C4×C59—22no—
356C4×C59—42no—
357C4×C59—42no—
358C4×C59—42no—
359C4×C59—42no—
360C4×C59#52512yes—
361C4×C59C22×#4111yescharacteristic
362C4×C59C22×#4111yescharacteristic
363Dic59—24no—
364Dic59—22no—
365Dic59—22no—
366Dic59—22no—
367Dic59—42no—
368Dic59—42no—
369Dic59C2×#13714yes—
370C2×#533—591no—
371C2×C4×#41—591no—
372#3116—5916no—
373C2×#485—591no—
374C2×#485D5911yescharacteristic, complemented
375C2×#477—591no—
376C2×#476—591no—
377C2×#462—591no—
378C2×#461—591no—
379C2×#452—591no—
380C2×#452—591no—
381C2×#441—591no—
382C2×#441—591no—
383C2×#440—591no—
384C2×#440—591no—
385C2×#432—591no—
386C2×C59—42no—
387C2×C59#311614yescomplemented
388C2×C59C2×#52511yescharacteristic
389C2×C59C22×#13711yescharacteristic
390C2×C59C2×#57511yescharacteristic
391D59—44no—
392C22×#41—591no—
393C22×Q16—591no—
394C22×Q16—591no—
395C22×SD16—591no—
396C22×SD16—591no—
397#533—598no—
398#533—1184no—
399C2×C4⋊Q8—591no—
400C2×C4⋊Q8—591no—
401C2×#125—1181no—
402C2×C22⋊Q8—591no—
403C2×C22⋊Q8—1181no—
404C2×C22⋊Q8C2×D5911yescharacteristic
405C4×#41—598no—
406C4×#41—1184no—
407C2×C4×Q8—591no—
408C2×C4×Q8—591no—
409C2×C4×Q8—591no—
410C2×C4×Q8—591no—
411C2×C4×Q8—1181no—
412C2×C4×D4—591no—
413C2×C4×D4—591no—
414C2×C4×D4—1181no—
415C2×C4×D4—1181no—
416C2×#117—1181no—
417C2×#117—1181no—
418C2×#117C2×D5911yescharacteristic
419C22×C42—591no—
420C22×C42—1181no—
421#485—598no—
422#485C2×D5918yescomplemented
423#477—598no—
424#476—598no—
425#462—598no—
426#461—598no—
427#452—598no—
428#452—598no—
429#441—598no—
430#441—598no—
431#440—598no—
432#440—598no—
433#432—598no—
434C2×#107—591no—
435C2×#107C2×D5911yescharacteristic
436C2×#106—591no—
437C2×#106C2×D5911yescharacteristic
438C2×C4⋊C8—591no—
439C2×C4⋊C8—591no—
440C2×#103—591no—
441C2×#103—591no—
442C2×#103—591no—
443C2×#103—591no—
444C2×#103C2×D5911yescharacteristic
445C2×#103C2×D5911yescharacteristic
446C2×#102—591no—
447C2×#102—591no—
448C2×C22⋊C8—591no—
449C2×C22⋊C8C2×D5911yescharacteristic
450C2×#97—591no—
451C2×#97—591no—
452C59C2×#311611yescharacteristic, complemented, Sylow
453C2×#41—594no—
454C2×#41—1184no—
455C2×#41—1184no—
456C2×#41—1182no—
457C22×Q8—591no—
458C22×Q8—591no—
459C22×Q8—1181no—
460C22×Q8C22×D5911yescharacteristic
461C22×D4—591no—
462C22×D4—1181no—
463C23×C4—591no—
464C23×C4—591no—
465C23×C4—1181no—
466C23×C4—1181no—
467C23×C4—1181no—
468C23×C4C22×D5911yescharacteristic
469C2×Q16—594no—
470C2×Q16—594no—
471C2×Q16—1184no—
472C2×Q16—1184no—
473C2×SD16—594no—
474C2×SD16—594no—
475C2×SD16—1184no—
476C2×SD16—1184no—
477C22×C8—591no—
478C22×C8—591no—
479C22×C8C22×D5911yescharacteristic
480C22×C8C22×D5911yescharacteristic
481C4⋊Q8—594no—
482C4⋊Q8—594no—
483C4⋊Q8—1182no—
484C4⋊Q8—1182no—
485#125—1188no—
486C22⋊Q8—22no—
487C22⋊Q8—594no—
488C22⋊Q8—1188no—
489C22⋊Q8—1182no—
490C22⋊Q8C22×D5914yes—
491C4×Q8—594no—
492C4×Q8—594no—
493C4×Q8—594no—
494C4×Q8—594no—
495C4×Q8—1182no—
496C4×Q8—1182no—
497C4×Q8—1182no—
498C4×Q8—1188no—
499C4×Q8—1182no—
500C4×D4—594no—
501C4×D4—594no—
502C4×D4—1182no—
503C4×D4—1182no—
504C4×D4—1188no—
505C4×D4—1188no—
506#117—22no—
507#117—1188no—
508#117—1188no—
509#117C22×D5914yes—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—591no—
512C2×C4⋊C4—1181no—
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⋊C4—1181no—
520C2×C4⋊C4C22×D5911yescharacteristic
521C2×C4⋊C4C22×D5911yescharacteristic
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—594no—
531C2×C42—591no—
532C2×C42—591no—
533C2×C42—591no—
534C2×C42—594no—
535C2×C42—1188no—
536C2×C42—1181no—
537C2×C42—1181no—
538C2×C42—1181no—
539C2×C42—1181no—
540#107—594no—
541#107C22×D5914yes—
542#106—594no—
543#106C22×D5914yes—
544C4⋊C8—594no—
545C4⋊C8—594no—
546#103—594no—
547#103—594no—
548#103—594no—
549#103—594no—
550#103C22×D5914yes—
551#103C22×D5914yes—
552#102—594no—
553#102—594no—
554C22⋊C8—594no—
555C22⋊C8C22×D5914yes—
556#97—594no—
557#97—594no—
558C24—1181no—
559C24D4×D5911yescharacteristic
560#41—1188no—
561#41—1188no—
562#41—11816no—
563C2×Q8—21no—
564C2×Q8—22no—
565C2×Q8—22no—
566C2×Q8—594no—
567C2×Q8—592no—
568C2×Q8—592no—
569C2×Q8—1184no—
570C2×Q8—1181no—
571C2×Q8—1181no—
572C2×Q8—1182no—
573C2×Q8—1182no—
574C2×Q8—1182no—
575C2×Q8—2364no—
576C2×Q8C23×D5912yes—
577C2×D4—594no—
578C2×D4—592no—
579C2×D4—1188no—
580C2×D4—1184no—
581C2×D4—1181no—
582C2×D4—1182no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—591no—
590C22×C4—594no—
591C22×C4—591no—
592C22×C4—591no—
593C22×C4—591no—
594C22×C4—594no—
595C22×C4—1184no—
596C22×C4—1184no—
597C22×C4—1188no—
598C22×C4—1184no—
599C22×C4—1181no—
600C22×C4—1184no—
601C22×C4—1181no—
602C22×C4—1181no—
603C22×C4—2364no—
604C22×C4—2364no—
605C22×C4—2362no—
606C22×C4D4×D5912yes—
607C22×C4D4×D5911yescharacteristic
608C22×C4C23×D5912yes—
609C22×C4C23×D5911yescharacteristic
610Q16—1188no—
611Q16—1188no—
612SD16—1188no—
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—21no—
625C4⋊C4—21no—
626C4⋊C4—592no—
627C4⋊C4—1184no—
628C4⋊C4—1184no—
629C4⋊C4—1184no—
630C4⋊C4—1184no—
631C4⋊C4—1184no—
632C4⋊C4—1184no—
633C4⋊C4—1184no—
634C4⋊C4—1181no—
635C4⋊C4—1184no—
636C4⋊C4C23×D5912yes—
637C4⋊C4C23×D5912yes—
638C4⋊C4C23×D5912yes—
639C22⋊C4—24no—
640C22⋊C4—24no—
641C22⋊C4—1184no—
642C22⋊C4—1184no—
643C22⋊C4—1184no—
644C42—24no—
645C42—594no—
646C42—594no—
647C42—592no—
648C42—592no—
649C42—592no—
650C42—592no—
651C42—1184no—
652C42—1184no—
653C42—1184no—
654C42—1184no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—1184no—
659C23—1182no—
660C23—2362no—
661C23—2362no—
662C23C2×D4×D5912yes—
663C23C2×D4×D5911yescharacteristic
664Q8—22no—
665Q8—22no—
666Q8—42no—
667Q8—594no—
668Q8—1184no—
669Q8—1182no—
670Q8—1182no—
671Q8—1182no—
672Q8—2368no—
673Q8—2362no—
674D4—594no—
675D4—11816no—
676D4—1184no—
677D4—1182no—
678C2×C4—22no—
679C2×C4—24no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—594no—
691C2×C4—592no—
692C2×C4—592no—
693C2×C4—592no—
694C2×C4—592no—
695C2×C4—11816no—
696C2×C4—1188no—
697C2×C4—1184no—
698C2×C4—1182no—
699C2×C4—1182no—
700C2×C4—1182no—
701C2×C4—1182no—
702C2×C4—1182no—
703C2×C4—1182no—
704C2×C4—2368no—
705C2×C4—2368no—
706C2×C4—2364no—
707C2×C4—2362no—
708C2×C4—2362no—
709C2×C4C2×D4×D5912yes—
710C2×C4C2×D4×D5911yescharacteristic
711C2×C4#41×D5912yes—
712C2×C4#41×D5912yes—
713C2×C4C24×D5911yescharacteristic
714C8—22no—
715C8—22no—
716C8—1182no—
717C8—1182no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—44no—
722C22—1184no—
723C22—2362no—
724C22—2362no—
725C22—2368no—
726C22#1683791012yes—
727C22#137×D5912yes—
728C22#1683819912yes—
729C22C22×D4×D5911yescharacteristic
730C4—22no—
731C4—42no—
732C4—42no—
733C4—42no—
734C4—42no—
735C4—594no—
736C4—1182no—
737C4—1182no—
738C4—1182no—
739C4—1184no—
740C4—2362no—
741C4—2362no—
742C4#1683791012yes—
743C4C2×#41×D5911yescharacteristic
744C4C2×#41×D5911yescharacteristic
745C2—42no—
746C2—2364no—
747C2#2143425314yesdirect product factor
748C2C2×#1683791011yescharacteristic
749C2C2×#137×D5911yescharacteristic
750C2C2×#1683819911yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#485C2
socleC23×C59C22×D4
prime radicalC22×#11745685C22
hypercenterC2×#485D59
hypocenterC59C2×#3116
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#485

Complements

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

NH ≅ G/Ntype
1. C2×#16837954C2semidirect
3. #21434253C2direct (N × H)
4. C2×#16837743C2semidirect
5. C2×#16837696C2semidirect
6. C2×#16837691C2semidirect
7. C2×#16837611C2semidirect
8. C2×#16837606C2semidirect
11. C2×#16837508C2semidirect
12. C2×#16837506C2semidirect
13. C2×#16837505C2semidirect
14. C2×#16837501C2semidirect
15. C2×#16837456C2semidirect
16. C2×C59×#485C2semidirect
23. #16837954C22semidirect
44. #16837743C22semidirect
45. #16837696C22semidirect
46. #16837691C22semidirect
47. #16837611C22semidirect
48. #16837606C22semidirect
51. #16837508C22semidirect
52. #16837506C22semidirect
53. #16837505C22semidirect
54. #16837501C22semidirect
55. #16837456C22semidirect
71. C59×#485C22semidirect
374. C2×#485D59semidirect
387. C2×C59#3116semidirect
422. #485C2×D59semidirect
452. C59C2×#3116semidirect
747. C2#21434253direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168379542
C2×#168378702
#214342532
C2×#168377432
C2×#168376962
C2×#168376912
C2×#168376112
C2×#168376062
C2×#168375662
C2×#168375622
C2×#168375082
C2×#168375062
C2×#168375052
C2×#168375012
C2×#168374562
C2×C59×#4852
C2×#311659