Finite Group Databasebeta

← C2×#21435553 #29461650

Subgroups — C2×#21435553 #29461650

Order 15104.

1882 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838025C211yesmaximal, characteristic, complemented
2C2×#16838019C211yesmaximal, characteristic, complemented
3#21435553C2116yesmaximal, direct product factor
4C2×#16837696C211yesmaximal, characteristic, complemented
5C2×#16837695C211yesmaximal, characteristic, complemented
6C2×#16837681C211yesmaximal, characteristic, complemented
7C2×#16837680C211yesmaximal, characteristic, complemented
8C2×#16837648C211yesmaximal, characteristic, complemented
9C2×#16837641C211yesmaximal, characteristic, complemented
10C2×#16837636C211yesmaximal, characteristic
11C2×#16837627C211yesmaximal, characteristic, complemented
12C2×#16837622C211yesmaximal, characteristic, complemented
13C2×#16837619C211yesmaximal, characteristic, complemented
14C2×#16837616C211yesmaximal, characteristic, complemented
15C2×#16837430C211yesmaximal, characteristic, complemented
16C2×C59×#468C211yesmaximal, characteristic, complemented
17C22×#11745672C2211yescharacteristic
18C22×#11745660C2211yescharacteristic
19C22×#11745669C2211yescharacteristic
20C23×C59⋊C8C2211yescharacteristic
21#16838025—24no—
22#16838025C2218yescomplemented
23#16838019—24no—
24#16838019C2218yescomplemented
25C2×#14273726C2211yescharacteristic
26C2×#14273726C2211yescharacteristic
27C2×#14273722—21no—
28C2×#14273720—21no—
29C2×#14273716C2211yescharacteristic
30C2×#14273714—21no—
31C2×#14273714C2211yescharacteristic
32C2×#14273713—21no—
33C2×#14273709—21no—
34C2×#14273708—21no—
35C2×#14273707—21no—
36C2×#14273706C2211yescharacteristic
37C2×#14273704—21no—
38C2×#14273701C2211yescharacteristic
39C2×Q8×Dic59C2211yescharacteristic
40C2×#14273692C2211yescharacteristic
41C2×D4×Dic59C2211yescharacteristic
42C2×#14273689C2211yescharacteristic
43C2×#14273686C2211yescharacteristic
44#16837696C2218yescomplemented
45#16837695C2218yescomplemented
46#16837681C2218yescomplemented
47#16837680C2218yescomplemented
48#16837648C2218yescomplemented
49#16837641C2218yescomplemented
50#16837636C2218yes—
51#16837627C2218yescomplemented
52#16837622C2218yescomplemented
53#16837619C2218yescomplemented
54#16837616C2218yescomplemented
55C2×#14273661C2211yescharacteristic
56C2×#14273660C2211yescharacteristic
57C2×#14273660C2211yescharacteristic
58#16837430C2218yescomplemented
59C2×Dic59⋊C8C2211yescharacteristic
60C2×Dic59⋊C8C2211yescharacteristic
61C2×Dic59⋊C8C2211yescharacteristic
62C2×Dic59⋊C8C2211yescharacteristic
63C2×#14273652C2211yescharacteristic
64C2×#14273651C2211yescharacteristic
65C2×#14273650C2211yescharacteristic
66C2×#14273649C2211yescharacteristic
67C2×#14273648C2211yescharacteristic
68C2×#14273647C2211yescharacteristic
69C22×SD16×C59C2211yescharacteristic
70C22×M16×C59C2211yescharacteristic
71C2×C22⋊Q8×C59C2211yescharacteristic
72C2×#121×C59C2211yescharacteristic
73C59×#468C2218yescomplemented
74C2×#107×C59C2211yescharacteristic
75C2×#103×C59C2211yescharacteristic
76C2×#102×C59C2211yescharacteristic
77C22×Dic118—21no—
78C22×Dic118—21no—
79C22×Dic118C2311yescharacteristic
80C22×D236C2311yescharacteristic
81C22×C22⋊D59—21no—
82C23×Dic59—21no—
83C22×C4×D59—21no—
84C2×#11745672—42no—
85C2×#11745672C2314yes—
86C2×#11745660—42no—
87C2×#11745660C2314yes—
88C2×#11745669—42no—
89C2×#11745669C2314yes—
90C22×C59⋊C8—42no—
91C22×C59⋊C8C2311yescharacteristic
92C22×C59⋊C8C2311yescharacteristic
93C22×C59⋊C8C2314yes—
94#14273726—22no—
95#14273726—22no—
96#14273726C2314yes—
97#14273726C2314yes—
98#14273722—28no—
99#14273720—28no—
100#14273716—22no—
101#14273716C2314yes—
102#14273714—28no—
103#14273714—22no—
104#14273714C2314yes—
105#14273713—28no—
106#14273709—28no—
107#14273708—28no—
108#14273707—28no—
109#14273706—22no—
110#14273706C2314yes—
111#14273704—28no—
112#14273701—22no—
113#14273701C2314yes—
114Q8×Dic59—22no—
115Q8×Dic59C2314yes—
116#14273692—22no—
117#14273692C2314yes—
118D4×Dic59—22no—
119D4×Dic59C2314yes—
120#14273689—22no—
121#14273689C2314yes—
122#14273686D414yes—
123#14273686C2314yes—
124C2×C4⋊Dic59—21no—
125C2×C4⋊Dic59D411yescharacteristic
126C2×C4⋊Dic59D411yescharacteristic
127C2×C4⋊Dic59C2311yescharacteristic
128C2×C4⋊Dic59C2311yescharacteristic
129C2×Dic59⋊C4—21no—
130C2×Dic59⋊C4—21no—
131C2×Dic59⋊C4—21no—
132C2×Dic59⋊C4—21no—
133C2×C22⋊Dic59—21no—
134C2×C22⋊Dic59—21no—
135C2×C22⋊Dic59—21no—
136C2×C22⋊Dic59—21no—
137C2×C22⋊Dic59D411yescharacteristic
138C2×C22⋊Dic59D411yescharacteristic
139C2×(C2×D59)⋊C4—21no—
140C2×(C2×D59)⋊C4—21no—
141C2×(C2×D59)⋊C4—21no—
142C2×(C2×D59)⋊C4—21no—
143C2×C4×Dic59—21no—
144C2×C4×Dic59—21no—
145C2×C4×Dic59C2311yescharacteristic
146C2×C4×Dic59C2311yescharacteristic
147#14273661C2314yes—
148#14273660C2314yes—
149#14273660C2314yes—
150Dic59⋊C8C2314yes—
151Dic59⋊C8C2314yes—
152Dic59⋊C8C2314yes—
153Dic59⋊C8C2314yes—
154#14273652C2314yes—
155#14273651C2314yes—
156#14273650C2314yes—
157#14273649C2314yes—
158#14273648C2314yes—
159#14273647C2314yes—
160C22×Q8×C59C2311yescharacteristic
161C22×D4×C59—21no—
162C22×D4×C59C2311yescharacteristic
163C23×C4×C59C2311yescharacteristic
164C2×SD16×C59—42no—
165C2×SD16×C59C2314yes—
166C2×M16×C59—42no—
167C2×M16×C59C2314yes—
168C22×C8×C59C2311yescharacteristic
169C22×C8×C59C2311yescharacteristic
170C22⋊Q8×C59—22no—
171C22⋊Q8×C59C2314yes—
172#121×C59—22no—
173#121×C59C2314yes—
174C2×C4⋊C4×C59—21no—
175C2×C4⋊C4×C59C2311yescharacteristic
176C2×C4⋊C4×C59C2311yescharacteristic
177C2×C22⋊C4×C59—21no—
178C2×C22⋊C4×C59—21no—
179#107×C59C2314yes—
180#103×C59C2314yes—
181#102×C59C2314yes—
182C24×C59—21no—
183C24×C59C2×D411yescharacteristic
184C23×D59—21no—
185C2×Q8×C59—21no—
186C2×Q8×C59—22no—
187C2×Q8×C59—22no—
188C2×Q8×C59C2412yes—
189C2×D4×C59—24no—
190C2×D4×C59—21no—
191C2×D4×C59—22no—
192C2×D4×C59—22no—
193C2×D4×C59—82no—
194C2×D4×C59C2412yes—
195C22×C4×C59—22no—
196C22×C4×C59—22no—
197C22×C4×C59—21no—
198C22×C4×C59—21no—
199C22×C4×C59—21no—
200C22×C4×C59C2×D411yescharacteristic
201C22×C4×C59C2×D412yes—
202C22×C4×C59C2412yes—
203C22×C4×C59C2411yescharacteristic
204C2×C22⋊D59—24no—
205C2×C22⋊D59—82no—
206C22×Dic59—21no—
207C22×Dic59—21no—
208C22×Dic59—21no—
209C22×Dic59—24no—
210C22×Dic59—82no—
211C22×Dic59C2×D411yescharacteristic
212C22×Dic59C2×D411yescharacteristic
213C22×Dic59C2×D411yescharacteristic
214C22×Dic59C2×D411yescharacteristic
215C2×D236—22no—
216C2×D236—22no—
217C2×D236—21no—
218C2×D236C2412yes—
219C2×C4×D59—24no—
220C2×C4×D59—82no—
221C2×Dic118—22no—
222C2×Dic118—22no—
223C2×Dic118—21no—
224C2×Dic118—24no—
225C2×Dic118—24no—
226C2×Dic118—82no—
227C2×Dic118—82no—
228C2×Dic118C2412yes—
229SD16×C59—44no—
230M16×C59—44no—
231C2×C8×C59—22no—
232C2×C8×C59—22no—
233C2×C8×C59C2412yes—
234C2×C8×C59C2412yes—
235C4⋊C4×C59—24no—
236C4⋊C4×C59—21no—
237C4⋊C4×C59—21no—
238C4⋊C4×C59C2412yes—
239C4⋊C4×C59C2412yes—
240C22⋊C4×C59—24no—
241C22⋊C4×C59—24no—
242C22⋊Dic59—24no—
243C22⋊Dic59—24no—
244C22⋊Dic59—24no—
245C22⋊Dic59—24no—
246C22⋊Dic59C2×D414yes—
247C22⋊Dic59C2×D414yes—
248#11745672—44no—
249#11745669—44no—
250(C2×D59)⋊C4—24no—
251(C2×D59)⋊C4—24no—
252(C2×D59)⋊C4—24no—
253(C2×D59)⋊C4—24no—
254C4⋊Dic59—21no—
255C4⋊Dic59—21no—
256C4⋊Dic59—24no—
257C4⋊Dic59C2×D414yes—
258C4⋊Dic59C2×D414yes—
259C4⋊Dic59C2412yes—
260C4⋊Dic59C2412yes—
261Dic59⋊C4—24no—
262Dic59⋊C4—24no—
263Dic59⋊C4—24no—
264Dic59⋊C4—24no—
265C4×Dic59—24no—
266C4×Dic59—24no—
267C4×Dic59C2×D412yes—
268C4×Dic59C2×D412yes—
269C4×Dic59C2412yes—
270C4×Dic59C2412yes—
271C2×C59⋊C8—22no—
272C2×C59⋊C8—22no—
273C2×C59⋊C8—44no—
274C2×C59⋊C8C2412yes—
275C2×C59⋊C8C2412yes—
276#11745660—44no—
277C23×C59—22no—
278C23×C59—22no—
279C23×C59—22no—
280C23×C59—22no—
281C23×C59—42no—
282C23×C59—42no—
283C23×C59—42no—
284C23×C59C22×D412yes—
285C23×C59C22×D411yescharacteristic
286C22×D59—22no—
287C22×D59—42no—
288C22×D59—42no—
289C22×D59—42no—
290Q8×C59—22no—
291Q8×C59—22no—
292Q8×C59—42no—
293D4×C59—22no—
294D4×C59—22no—
295D4×C59—42no—
296D4×C59—84no—
297C2×C4×C59—22no—
298C2×C4×C59—24no—
299C2×C4×C59—22no—
300C2×C4×C59—22no—
301C2×C4×C59—22no—
302C2×C4×C59—22no—
303C2×C4×C59—22no—
304C2×C4×C59—42no—
305C2×C4×C59—42no—
306C2×C4×C59—42no—
307C2×C4×C59C22×D412yes—
308C2×C4×C59C22×D411yescharacteristic
309C2×C4×C59H(5,𝔽2)12yes—
310C2×C4×C592−1+412yes—
311C2×C4×C59C2511yescharacteristic
312C22⋊D59—84no—
313C2×Dic59—22no—
314C2×Dic59—22no—
315C2×Dic59—22no—
316C2×Dic59—22no—
317C2×Dic59—22no—
318C2×Dic59—22no—
319C2×Dic59—22no—
320C2×Dic59—42no—
321C2×Dic59—42no—
322C2×Dic59—42no—
323C2×Dic59—84no—
324C2×Dic59C22×D412yes—
325C2×Dic59C22×D412yes—
326C2×Dic59C22×D412yes—
327C2×Dic59C22×D412yes—
328D236—22no—
329D236—22no—
330D236—42no—
331C4×D59—84no—
332Dic118—22no—
333Dic118—22no—
334Dic118—42no—
335Dic118—84no—
336Dic118—84no—
337C8×C59—22no—
338C8×C59—22no—
339C59⋊C8—22no—
340C59⋊C8—22no—
341C2×#3262—591nomaximal, Sylow
342C22×C59—22no—
343C22×C59—22no—
344C22×C59—22no—
345C22×C59—44no—
346C22×C59—42no—
347C22×C59—42no—
348C22×C59—42no—
349C22×C59—84no—
350C22×C59#53712yes—
351C22×C59#57612yes—
352C22×C59#57812yes—
353C22×C59C23×D411yescharacteristic
354C2×D59—42no—
355C2×D59—42no—
356C2×D59—42no—
357C2×D59—84no—
358C4×C59—22no—
359C4×C59—42no—
360C4×C59—42no—
361C4×C59—42no—
362C4×C59#53712yes—
363C4×C59C2×H(5,𝔽2)11yescharacteristic
364C4×C59C2×2−1+411yescharacteristic
365Dic59—22no—
366Dic59—22no—
367Dic59—22no—
368Dic59—22no—
369Dic59—42no—
370Dic59—42no—
371Dic59—42no—
372C2×#542—591no—
373C2×#542—591no—
374#3262—5916no—
375C2×#477—591no—
376C2×#477—591no—
377C2×#474—591no—
378C2×#474—591no—
379C2×#468—591no—
380C2×#468D5911yescharacteristic, complemented
381C2×#467—591no—
382C2×#466—591no—
383C2×#464—591no—
384C2×#464—591no—
385C2×#463—591no—
386C2×#463—591no—
387C2×#424—591no—
388C2×C59—42no—
389C2×C59—82no—
390C2×C59#326214yescomplemented
391C2×C59C2×#53711yescharacteristic
392C2×C59C2×#57611yescharacteristic
393C2×C59C2×#57811yescharacteristic
394D59—82no—
395C22×Q16—591no—
396C22×SD16—591no—
397C22×SD16C2×D5911yescharacteristic
398C22×D8—591no—
399C22×M16C2×D5911yescharacteristic
400C23×C8—591no—
401#542—598no—
402#542—598no—
403#542—1184no—
404#542—1184no—
405C2×C4⋊Q8—591no—
406C2×C4⋊Q8—591no—
407C2×#126—1181no—
408C2×#126—1181no—
409C2×#124—591no—
410C2×#124—591no—
411C2×#124—1181no—
412C2×#124—1181no—
413C2×#123—1181no—
414C2×#123—1181no—
415C2×C22⋊Q8—591no—
416C2×C22⋊Q8—1181no—
417C2×C22⋊Q8—1181no—
418C2×C22⋊Q8C2×D5911yescharacteristic
419C2×#121—591no—
420C2×#121C2×D5911yescharacteristic
421C2×C4×Q8—591no—
422C2×C4×Q8—591no—
423C2×C4×D4—591no—
424C2×C4×D4—591no—
425C2×#117—591no—
426#477—598no—
427#477—598no—
428#474—598no—
429#474—598no—
430#468—598no—
431#468C2×D5918yescomplemented
432#467—598no—
433#466—598no—
434#464—598no—
435#464—598no—
436#463—598no—
437#463—598no—
438C2×#107—591no—
439C2×#107—591no—
440C2×#107—591no—
441C2×#107C2×D5911yescharacteristic
442#424—598no—
443C2×C4⋊C8—591no—
444C2×C4⋊C8—591no—
445C2×C4⋊C8—591no—
446C2×C4⋊C8—591no—
447C2×#103—591no—
448C2×#103—591no—
449C2×#103—591no—
450C2×#103C2×D5911yescharacteristic
451C2×#102—591no—
452C2×#102—591no—
453C2×#102—591no—
454C2×#102C2×D5911yescharacteristic
455C59C2×#326211yescharacteristic, complemented, Sylow
456C22×Q8—591no—
457C22×Q8—1181no—
458C22×Q8—1181no—
459C22×Q8C22×D5911yescharacteristic
460C22×D4—21no—
461C22×D4—591no—
462C22×D4—1181no—
463C22×D4C22×D5911yescharacteristic
464C23×C4—1181no—
465C23×C4—1181no—
466C23×C4C22×D5911yescharacteristic
467C2×Q16—594no—
468C2×Q16—2362no—
469C2×SD16—42no—
470C2×SD16—594no—
471C2×SD16—2362no—
472C2×SD16C22×D5914yes—
473C2×D8—594no—
474C2×D8—2362no—
475C2×M16—42no—
476C2×M16C22×D5914yes—
477C22×C8—591no—
478C22×C8—591no—
479C22×C8—594no—
480C22×C8—2362no—
481C22×C8C22×D5911yescharacteristic
482C22×C8C22×D5911yescharacteristic
483C4⋊Q8—594no—
484C4⋊Q8—594no—
485C4⋊Q8—1182no—
486C4⋊Q8—1182no—
487#126—1188no—
488#126—1188no—
489#124—594no—
490#124—594no—
491#124—1182no—
492#124—1182no—
493#124—1188no—
494#124—1188no—
495#123—1188no—
496#123—1188no—
497C22⋊Q8—22no—
498C22⋊Q8—594no—
499C22⋊Q8—1188no—
500C22⋊Q8—1188no—
501C22⋊Q8—1182no—
502C22⋊Q8C22×D5914yes—
503#121—22no—
504#121—594no—
505#121—1182no—
506#121C22×D5914yes—
507C4×Q8—594no—
508C4×Q8—594no—
509C4×Q8—1182no—
510C4×Q8—1182no—
511C4×D4—594no—
512C4×D4—594no—
513C4×D4—1182no—
514C4×D4—1182no—
515#117—594no—
516#117—594no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—591no—
519C2×C4⋊C4—591no—
520C2×C4⋊C4—591no—
521C2×C4⋊C4—591no—
522C2×C4⋊C4—1181no—
523C2×C4⋊C4—1181no—
524C2×C4⋊C4—1181no—
525C2×C4⋊C4—1181no—
526C2×C4⋊C4—1181no—
527C2×C4⋊C4C22×D5911yescharacteristic
528C2×C4⋊C4C22×D5911yescharacteristic
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—591no—
532C2×C22⋊C4—591no—
533C2×C22⋊C4—1181no—
534C2×C22⋊C4—1181no—
535C2×C22⋊C4—1181no—
536C2×C22⋊C4—1181no—
537C2×C22⋊C4—1181no—
538C2×C22⋊C4—1181no—
539C2×C22⋊C4—1181no—
540C2×C22⋊C4—1181no—
541C2×C42—591no—
542C2×C42—591no—
543C2×C42—1181no—
544C2×C42—1181no—
545#107—594no—
546#107—594no—
547#107—594no—
548#107C22×D5914yes—
549C4⋊C8—594no—
550C4⋊C8—594no—
551C4⋊C8—594no—
552C4⋊C8—594no—
553#103—594no—
554#103—594no—
555#103—594no—
556#103C22×D5914yes—
557#102—594no—
558#102—594no—
559#102—594no—
560#102C22×D5914yes—
561C24—21no—
562C24—1181no—
563C24D4×D5911yescharacteristic
564C2×Q8—21no—
565C2×Q8—22no—
566C2×Q8—22no—
567C2×Q8—592no—
568C2×Q8—1184no—
569C2×Q8—1184no—
570C2×Q8—1181no—
571C2×Q8—1182no—
572C2×Q8—1182no—
573C2×Q8—4722no—
574C2×Q8—4722no—
575C2×Q8C23×D5912yes—
576C2×D4—24no—
577C2×D4—21no—
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—82no—
581C2×D4—592no—
582C2×D4—1184no—
583C2×D4—1181no—
584C2×D4—1182no—
585C2×D4—1182no—
586C2×D4—4722no—
587C2×D4C23×D5912yes—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—591no—
594C22×C4—591no—
595C22×C4—591no—
596C22×C4—591no—
597C22×C4—1184no—
598C22×C4—1184no—
599C22×C4—1181no—
600C22×C4—1181no—
601C22×C4—1181no—
602C22×C4—4722no—
603C22×C4—4722no—
604C22×C4D4×D5912yes—
605C22×C4D4×D5911yescharacteristic
606C22×C4C23×D5912yes—
607C22×C4C23×D5911yescharacteristic
608Q16—2364no—
609SD16—44no—
610SD16—2364no—
611D8—2364no—
612M16—44no—
613C2×C8—22no—
614C2×C8—22no—
615C2×C8—592no—
616C2×C8—592no—
617C2×C8—1182no—
618C2×C8—1182no—
619C2×C8—2364no—
620C2×C8C23×D5912yes—
621C2×C8C23×D5912yes—
622C4⋊C4—24no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—594no—
626C4⋊C4—594no—
627C4⋊C4—592no—
628C4⋊C4—592no—
629C4⋊C4—1184no—
630C4⋊C4—1184no—
631C4⋊C4—1184no—
632C4⋊C4—1184no—
633C4⋊C4—1181no—
634C4⋊C4—1181no—
635C4⋊C4—1184no—
636C4⋊C4C23×D5912yes—
637C4⋊C4C23×D5912yes—
638C22⋊C4—24no—
639C22⋊C4—24no—
640C22⋊C4—594no—
641C22⋊C4—594no—
642C22⋊C4—1184no—
643C22⋊C4—1184no—
644C22⋊C4—1184no—
645C22⋊C4—1184no—
646C22⋊C4—1184no—
647C22⋊C4—1184no—
648C22⋊C4—1184no—
649C22⋊C4—1184no—
650C42—592no—
651C42—592no—
652C42—592no—
653C42—592no—
654C42—1184no—
655C42—1184no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—1182no—
664C23—2362no—
665C23—2362no—
666C23—2362no—
667C23C2×D4×D5912yes—
668C23C2×D4×D5911yescharacteristic
669Q8—22no—
670Q8—22no—
671Q8—42no—
672Q8—1182no—
673Q8—1182no—
674Q8—4724no—
675Q8—4724no—
676Q8—2362no—
677D4—22no—
678D4—22no—
679D4—42no—
680D4—84no—
681D4—1182no—
682D4—1182no—
683D4—4724no—
684D4—2362no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—24no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—592no—
696C2×C4—592no—
697C2×C4—592no—
698C2×C4—592no—
699C2×C4—1182no—
700C2×C4—1182no—
701C2×C4—1182no—
702C2×C4—1182no—
703C2×C4—1182no—
704C2×C4—1182no—
705C2×C4—1182no—
706C2×C4—4724no—
707C2×C4—4724no—
708C2×C4—2362no—
709C2×C4—2362no—
710C2×C4—2362no—
711C2×C4C2×D4×D5912yes—
712C2×C4C2×D4×D5911yescharacteristic
713C2×C4#1427377212yes—
714C2×C4#1427377412yes—
715C2×C4C24×D5911yescharacteristic
716C8—22no—
717C8—22no—
718C8—1182no—
719C8—1182no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—44no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—84no—
728C22—4724no—
729C22—2362no—
730C22—2362no—
731C22—2362no—
732C22#1683797912yes—
733C22#1683820612yes—
734C22#1683821812yes—
735C22C22×D4×D5911yescharacteristic
736C4—22no—
737C4—42no—
738C4—42no—
739C4—42no—
740C4—1182no—
741C4—1182no—
742C4—1182no—
743C4—1182no—
744C4—2362no—
745C4—2362no—
746C4—2362no—
747C4#1683797912yes—
748C4C2×#1427377211yescharacteristic
749C4C2×#1427377411yescharacteristic
750C2—42no—
751C2—82no—
752C2—4722no—
753C2#2143555314yesdirect product factor
754C2C2×#1683797911yescharacteristic
755C2C2×#1683820611yescharacteristic
756C2C2×#1683821811yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#468C2
socleC23×C59C22×D4
prime radicalC2×#16837636C2
hypercenterC2×#468D59
hypocenterC59C2×#3262
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#468

Complements

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

NH ≅ G/Ntype
1. C2×#16838025C2semidirect
2. C2×#16838019C2semidirect
3. #21435553C2direct (N × H)
4. C2×#16837696C2semidirect
5. C2×#16837695C2semidirect
6. C2×#16837681C2semidirect
7. C2×#16837680C2semidirect
8. C2×#16837648C2semidirect
9. C2×#16837641C2semidirect
11. C2×#16837627C2semidirect
12. C2×#16837622C2semidirect
13. C2×#16837619C2semidirect
14. C2×#16837616C2semidirect
15. C2×#16837430C2semidirect
16. C2×C59×#468C2semidirect
22. #16838025C22semidirect
24. #16838019C22semidirect
44. #16837696C22semidirect
45. #16837695C22semidirect
46. #16837681C22semidirect
47. #16837680C22semidirect
48. #16837648C22semidirect
49. #16837641C22semidirect
51. #16837627C22semidirect
52. #16837622C22semidirect
53. #16837619C22semidirect
54. #16837616C22semidirect
58. #16837430C22semidirect
73. C59×#468C22semidirect
380. C2×#468D59semidirect
390. C2×C59#3262semidirect
431. #468C2×D59semidirect
455. C59C2×#3262semidirect
753. C2#21435553direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168380252
C2×#168380192
#214355532
C2×#168376962
C2×#168376952
C2×#168376812
C2×#168376802
C2×#168376482
C2×#168376412
C2×#168376362
C2×#168376272
C2×#168376222
C2×#168376192
C2×#168376162
C2×#168374302
C2×C59×#4682
C2×#326259