Finite Group Databasebeta

← C2×#21435509 #29461601

Subgroups — C2×#21435509 #29461601

Order 15104.

1946 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838023C211yesmaximal, characteristic, complemented
2C2×#16838007C211yesmaximal, characteristic, complemented
3#21435509C2116yesmaximal, direct product factor
4C2×#16837710C211yesmaximal, characteristic, complemented
5C2×#16837703C211yesmaximal, characteristic, complemented
6C2×#16837693C211yesmaximal, characteristic, complemented
7C2×#16837683C211yesmaximal, characteristic, complemented
8C2×#16837655C211yesmaximal, characteristic, complemented
9C2×#16837648C211yesmaximal, characteristic, complemented
10C2×#16837638C211yesmaximal, characteristic, complemented
11C2×#16837631C211yesmaximal, characteristic, complemented
12C2×#16837603C211yesmaximal, characteristic, complemented
13C2×#16837618C211yesmaximal, characteristic, complemented
14C2×#16837618C211yesmaximal, characteristic, complemented
15C2×#16837598C211yesmaximal, characteristic, complemented
16C2×C59×#424C211yesmaximal, characteristic, complemented
17C22×#11745660C2211yescharacteristic
18C22×#11745660C2211yescharacteristic
19C22×D472C2211yescharacteristic
20C22×D472C2211yescharacteristic
21#16838023—24no—
22#16838023C2218yescomplemented
23#16838007—24no—
24#16838007C2218yescomplemented
25C2×#14273727C2211yescharacteristic
26C2×#14273724C2211yescharacteristic
27C2×#14273722—21no—
28C2×#14273719C2211yescharacteristic
29C2×#14273715C2211yescharacteristic
30C2×#14273713—21no—
31C2×#14273712—21no—
32C2×#14273712—21no—
33C2×#14273709—21no—
34C2×#14273706C2211yescharacteristic
35C2×#14273705—21no—
36C2×#14273701C2211yescharacteristic
37C2×#14273701C2211yescharacteristic
38C2×#14273701C2211yescharacteristic
39C2×#14273700—21no—
40C2×#14273700—21no—
41C2×C4×Dic118C2211yescharacteristic
42C2×C4×D236C2211yescharacteristic
43C2×C4×D236C2211yescharacteristic
44C2×C4×D236C2211yescharacteristic
45#16837710C2218yescomplemented
46#16837703C2218yescomplemented
47#16837693C2218yescomplemented
48#16837683C2218yescomplemented
49#16837655C2218yescomplemented
50#16837648C2218yescomplemented
51#16837638C2218yescomplemented
52#16837631C2218yescomplemented
53#16837618C2218yescomplemented
54#16837618C2218yescomplemented
55#16837603C2218yescomplemented
56#16837598C2218yescomplemented
57C2×#14273661C2211yescharacteristic
58C2×#14273661C2211yescharacteristic
59C2×#14273659C2211yescharacteristic
60C2×#14273659C2211yescharacteristic
61C2×#14273652C2211yescharacteristic
62C2×#14273652C2211yescharacteristic
63C2×#14273649C2211yescharacteristic
64C2×#14273649C2211yescharacteristic
65C2×#14273649C2211yescharacteristic
66C2×#14273649C2211yescharacteristic
67C2×#14273649C2211yescharacteristic
68C2×#14273649C2211yescharacteristic
69C22×M16×C59C2211yescharacteristic
70C23×C8×C59C2211yescharacteristic
71C2×#117×C59C2211yescharacteristic
72C59×#424C2218yescomplemented
73C2×C4⋊C8×C59C2211yescharacteristic
74C2×C4⋊C8×C59C2211yescharacteristic
75C2×C4⋊C8×C59C2211yescharacteristic
76C2×C4⋊C8×C59C2211yescharacteristic
77C22×Dic118—21no—
78C22×Dic118C2311yescharacteristic
79C22×D236—21no—
80C22×D236—21no—
81C22×D236C2311yescharacteristic
82C22×D236C2311yescharacteristic
83C22×D236C2311yescharacteristic
84C22×C22⋊D59—21no—
85C22×C22⋊D59—21no—
86C22×C22⋊D59—21no—
87C22×C4×D59—21no—
88C22×C4×D59—21no—
89C22×C4×D59—21no—
90C2×#11745660—42no—
91C2×#11745660—42no—
92C2×#11745660C2314yes—
93C2×#11745660C2314yes—
94C2×D472—42no—
95C2×D472—42no—
96C2×D472C2314yes—
97C2×D472C2314yes—
98#14273727—22no—
99#14273727C2314yes—
100#14273724—22no—
101#14273724C2314yes—
102#14273722—28no—
103#14273719—22no—
104#14273719C2314yes—
105#14273715—22no—
106#14273715C2314yes—
107#14273713—28no—
108#14273712—28no—
109#14273712—28no—
110#14273709—28no—
111#14273706—22no—
112#14273706C2314yes—
113#14273705—28no—
114#14273701—22no—
115#14273701—22no—
116#14273701—22no—
117#14273701C2314yes—
118#14273701C2314yes—
119#14273701C2314yes—
120#14273700—28no—
121#14273700—28no—
122C4×Dic118—22no—
123C4×Dic118C2314yes—
124C4×D236—22no—
125C4×D236—22no—
126C4×D236—22no—
127C4×D236C2314yes—
128C4×D236C2314yes—
129C4×D236C2314yes—
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×Dic59⋊C4—21no—
138C2×Dic59⋊C4—21no—
139C2×C22⋊Dic59—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—
147C2×(C2×D59)⋊C4—21no—
148C2×C4×Dic59—21no—
149#14273661C2314yes—
150#14273661C2314yes—
151#14273659C2314yes—
152#14273659C2314yes—
153#14273652C2314yes—
154#14273652C2314yes—
155#14273649C2314yes—
156#14273649C2314yes—
157#14273649C2314yes—
158#14273649C2314yes—
159#14273649C2314yes—
160#14273649C2314yes—
161C23×C4×C59C2311yescharacteristic
162C2×M16×C59—42no—
163C2×M16×C59C2314yes—
164C22×C8×C59—42no—
165C22×C8×C59C2311yescharacteristic
166C22×C8×C59C2311yescharacteristic
167C22×C8×C59C2311yescharacteristic
168C22×C8×C59C2311yescharacteristic
169C22×C8×C59C2314yes—
170#117×C59D414yes—
171#117×C59C2314yes—
172C2×C4⋊C4×C59D411yescharacteristic
173C2×C4⋊C4×C59D411yescharacteristic
174C2×C22⋊C4×C59D411yescharacteristic
175C2×C22⋊C4×C59D411yescharacteristic
176C2×C42×C59C2311yescharacteristic
177C2×C42×C59C2311yescharacteristic
178C4⋊C8×C59C2314yes—
179C4⋊C8×C59C2314yes—
180C4⋊C8×C59C2314yes—
181C4⋊C8×C59C2314yes—
182C24×C59C2×D411yescharacteristic
183C23×D59—21no—
184C23×D59—21no—
185C23×D59—21no—
186C22×C4×C59—22no—
187C22×C4×C59—22no—
188C22×C4×C59C2×D411yescharacteristic
189C22×C4×C59C2×D411yescharacteristic
190C22×C4×C59C2×D411yescharacteristic
191C22×C4×C59C2×D411yescharacteristic
192C22×C4×C59C2×D411yescharacteristic
193C22×C4×C59C2×D412yes—
194C22×C4×C59C2412yes—
195C22×C4×C59C2411yescharacteristic
196C2×C22⋊D59—24no—
197C2×C22⋊D59—24no—
198C2×C22⋊D59—24no—
199C2×C22⋊D59—82no—
200C2×C22⋊D59—82no—
201C2×C22⋊D59—82no—
202C22×Dic59—21no—
203C22×Dic59—21no—
204C22×Dic59—21no—
205C22×Dic59—21no—
206C22×Dic59—21no—
207C2×D236—22no—
208C2×D236—22no—
209C2×D236—22no—
210C2×D236—22no—
211C2×D236—22no—
212C2×D236—22no—
213C2×D236—21no—
214C2×D236—21no—
215C2×D236—21no—
216C2×D236—24no—
217C2×D236—24no—
218C2×D236—82no—
219C2×D236—82no—
220C2×D236C2412yes—
221C2×D236C2412yes—
222C2×D236C2412yes—
223C2×C4×D59—24no—
224C2×C4×D59—24no—
225C2×C4×D59—24no—
226C2×C4×D59—82no—
227C2×C4×D59—82no—
228C2×C4×D59—82no—
229C2×Dic118—22no—
230C2×Dic118—22no—
231C2×Dic118—21no—
232C2×Dic118—24no—
233C2×Dic118—82no—
234C2×Dic118C2412yes—
235M16×C59—44no—
236C2×C8×C59—22no—
237C2×C8×C59—22no—
238C2×C8×C59—22no—
239C2×C8×C59—22no—
240C2×C8×C59—44no—
241C2×C8×C59C2412yes—
242C2×C8×C59C2412yes—
243C2×C8×C59C2412yes—
244C2×C8×C59C2412yes—
245C4⋊C4×C59C2×D414yes—
246C4⋊C4×C59C2×D414yes—
247C22⋊C4×C59C2×D414yes—
248C22⋊C4×C59C2×D414yes—
249C42×C59C2×D412yes—
250C42×C59C2×D412yes—
251C42×C59C2412yes—
252C42×C59C2412yes—
253C22⋊Dic59—24no—
254(C2×D59)⋊C4—24no—
255(C2×D59)⋊C4—24no—
256(C2×D59)⋊C4—24no—
257(C2×D59)⋊C4—24no—
258(C2×D59)⋊C4—24no—
259(C2×D59)⋊C4—24no—
260(C2×D59)⋊C4—24no—
261(C2×D59)⋊C4—24no—
262C4⋊Dic59—24no—
263C4⋊Dic59—21no—
264C4⋊Dic59—21no—
265C4⋊Dic59—21no—
266C4⋊Dic59—21no—
267C4⋊Dic59C2412yes—
268C4⋊Dic59C2412yes—
269C4⋊Dic59C2412yes—
270C4⋊Dic59C2412yes—
271Dic59⋊C4—24no—
272Dic59⋊C4—24no—
273Dic59⋊C4—24no—
274Dic59⋊C4—24no—
275C4×Dic59—24no—
276D472—44no—
277D472—44no—
278#11745660—44no—
279#11745660—44no—
280C23×C59—22no—
281C23×C59—22no—
282C23×C59—22no—
283C23×C59C22×D412yes—
284C23×C59C22×D411yescharacteristic
285C22×D59—22no—
286C22×D59—22no—
287C22×D59—22no—
288C22×D59—42no—
289C22×D59—42no—
290C22×D59—42no—
291C22×D59—42no—
292C22×D59—42no—
293C22×D59—42no—
294C22×D59—42no—
295C22×D59—42no—
296C22×D59—42no—
297C2×C4×C59—22no—
298C2×C4×C59—22no—
299C2×C4×C59—22no—
300C2×C4×C59—22no—
301C2×C4×C59—22no—
302C2×C4×C59—24no—
303C2×C4×C59—22no—
304C2×C4×C59—22no—
305C2×C4×C59C22×D412yes—
306C2×C4×C59C22×D412yes—
307C2×C4×C59C22×D412yes—
308C2×C4×C59C22×D412yes—
309C2×C4×C59C22×D412yes—
310C2×C4×C59C22×D411yescharacteristic
311C2×C4×C59H(5,𝔽2)12yes—
312C2×C4×C592−1+412yes—
313C2×C4×C59C2511yescharacteristic
314C22⋊D59—84no—
315C22⋊D59—84no—
316C22⋊D59—84no—
317C2×Dic59—22no—
318C2×Dic59—22no—
319C2×Dic59—22no—
320C2×Dic59—22no—
321C2×Dic59—22no—
322C2×Dic59—42no—
323C2×Dic59—42no—
324C2×Dic59—42no—
325C2×Dic59—42no—
326C2×Dic59—42no—
327D236—22no—
328D236—22no—
329D236—22no—
330D236—22no—
331D236—22no—
332D236—22no—
333D236—42no—
334D236—42no—
335D236—42no—
336D236—84no—
337D236—84no—
338C4×D59—84no—
339C4×D59—84no—
340C4×D59—84no—
341Dic118—22no—
342Dic118—22no—
343Dic118—42no—
344Dic118—84no—
345C8×C59—22no—
346C8×C59—22no—
347C8×C59—22no—
348C8×C59—22no—
349C2×#3257—591nomaximal, Sylow
350C22×C59—22no—
351C22×C59—22no—
352C22×C59—22no—
353C22×C59—44no—
354C22×C59#53712yes—
355C22×C59#57612yes—
356C22×C59#57712yes—
357C22×C59C23×D411yescharacteristic
358C2×D59—42no—
359C2×D59—42no—
360C2×D59—42no—
361C2×D59—42no—
362C2×D59—42no—
363C2×D59—42no—
364C2×D59—42no—
365C2×D59—42no—
366C2×D59—42no—
367C2×D59—84no—
368C2×D59—84no—
369C2×D59—84no—
370C4×C59—22no—
371C4×C59—22no—
372C4×C59—22no—
373C4×C59—22no—
374C4×C59—22no—
375C4×C59#53712yes—
376C4×C59C2×H(5,𝔽2)11yescharacteristic
377C4×C59C2×2−1+411yescharacteristic
378Dic59—42no—
379Dic59—42no—
380Dic59—42no—
381Dic59—42no—
382Dic59—42no—
383C2×#542—591no—
384C2×#540—591no—
385#3257—5916no—
386C2×#479—591no—
387C2×#478—591no—
388C2×#476—591no—
389C2×#474—591no—
390C2×#469—591no—
391C2×#468—591no—
392C2×#466—591no—
393C2×#465—591no—
394C2×#460—591no—
395C2×#463—591no—
396C2×#463—591no—
397C2×#459—591no—
398C2×#424D5911yescharacteristic, complemented
399C2×C59—42no—
400C2×C59#325714yescomplemented
401C2×C59C2×#53711yescharacteristic
402C2×C59C2×#57611yescharacteristic
403C2×C59C2×#57711yescharacteristic
404D59—82no—
405D59—82no—
406D59—82no—
407C22×SD16—591no—
408C22×SD16—591no—
409C22×D8—591no—
410C22×D8—591no—
411C22×M16C2×D5911yescharacteristic
412C23×C8C2×D5911yescharacteristic
413#542—598no—
414#542—1184no—
415#540—598no—
416#540—1184no—
417C2×C4⋊Q8—591no—
418C2×#127—591no—
419C2×#126—1181no—
420C2×#125—591no—
421C2×#124—591no—
422C2×#124—1181no—
423C2×#123—1181no—
424C2×#123—1181no—
425C2×#123—1181no—
426C2×C22⋊Q8—591no—
427C2×C22⋊Q8—1181no—
428C2×#121—591no—
429C2×#121—591no—
430C2×#121—591no—
431C2×#121—1181no—
432C2×#121—1181no—
433C2×C4×Q8—591no—
434C2×C4×D4—591no—
435C2×C4×D4—591no—
436C2×C4×D4—591no—
437C2×#117C2×D5911yescharacteristic
438#479—598no—
439#478—598no—
440#476—598no—
441#474—598no—
442#469—598no—
443#468—598no—
444#466—598no—
445#465—598no—
446#463—598no—
447#463—598no—
448#460—598no—
449#459—598no—
450C2×#107—591no—
451C2×#107—591no—
452C2×#106—591no—
453C2×#106—591no—
454#424C2×D5918yescomplemented
455C2×C4⋊C8C2×D5911yescharacteristic
456C2×C4⋊C8C2×D5911yescharacteristic
457C2×C4⋊C8C2×D5911yescharacteristic
458C2×C4⋊C8C2×D5911yescharacteristic
459C2×#103—591no—
460C2×#103—591no—
461C2×#102—591no—
462C2×#102—591no—
463C2×#102—591no—
464C2×#102—591no—
465C2×#102—591no—
466C2×#102—591no—
467C59C2×#325711yescharacteristic, complemented, Sylow
468C22×Q8—591no—
469C22×Q8—1181no—
470C22×D4—591no—
471C22×D4—591no—
472C22×D4—591no—
473C22×D4—1181no—
474C22×D4—1181no—
475C22×D4—1181no—
476C22×D4—1181no—
477C22×D4—1181no—
478C23×C4—1181no—
479C23×C4—1181no—
480C23×C4—1181no—
481C23×C4C22×D5911yescharacteristic
482C2×SD16—594no—
483C2×SD16—594no—
484C2×SD16—2362no—
485C2×SD16—2362no—
486C2×D8—594no—
487C2×D8—594no—
488C2×D8—2362no—
489C2×D8—2362no—
490C2×M16—42no—
491C2×M16C22×D5914yes—
492C22×C8—42no—
493C22×C8C22×D5911yescharacteristic
494C22×C8C22×D5911yescharacteristic
495C22×C8C22×D5911yescharacteristic
496C22×C8C22×D5911yescharacteristic
497C22×C8C22×D5914yes—
498C4⋊Q8—594no—
499C4⋊Q8—1182no—
500#127—594no—
501#127—1182no—
502#126—1188no—
503#125—594no—
504#125—1182no—
505#124—594no—
506#124—1188no—
507#124—1182no—
508#123—1188no—
509#123—1188no—
510#123—1188no—
511C22⋊Q8—594no—
512C22⋊Q8—1182no—
513C22⋊Q8—1188no—
514#121—594no—
515#121—594no—
516#121—594no—
517#121—1182no—
518#121—1182no—
519#121—1182no—
520#121—1188no—
521#121—1188no—
522C4×Q8—594no—
523C4×Q8—1182no—
524C4×D4—594no—
525C4×D4—594no—
526C4×D4—594no—
527C4×D4—1182no—
528C4×D4—1182no—
529C4×D4—1182no—
530#117D23614yes—
531#117C22×D5914yes—
532C2×C4⋊C4—591no—
533C2×C4⋊C4—591no—
534C2×C4⋊C4—591no—
535C2×C4⋊C4—591no—
536C2×C4⋊C4—1181no—
537C2×C4⋊C4—1181no—
538C2×C4⋊C4—1181no—
539C2×C4⋊C4—1181no—
540C2×C4⋊C4—1181no—
541C2×C4⋊C4D23611yescharacteristic
542C2×C4⋊C4D23611yescharacteristic
543C2×C22⋊C4—1181no—
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⋊C4D23611yescharacteristic
553C2×C22⋊C4D23611yescharacteristic
554C2×C42—1181no—
555C2×C42C22×D5911yescharacteristic
556C2×C42C22×D5911yescharacteristic
557#107—594no—
558#107—594no—
559#106—594no—
560#106—594no—
561C4⋊C8C22×D5914yes—
562C4⋊C8C22×D5914yes—
563C4⋊C8C22×D5914yes—
564C4⋊C8C22×D5914yes—
565#103—594no—
566#103—594no—
567#102—594no—
568#102—594no—
569#102—594no—
570#102—594no—
571#102—594no—
572#102—594no—
573C24—1181no—
574C24—1181no—
575C24—1181no—
576C24C2×D23611yescharacteristic
577C2×Q8—592no—
578C2×Q8—1184no—
579C2×Q8—1181no—
580C2×Q8—1182no—
581C2×Q8—1182no—
582C2×Q8—4722no—
583C2×D4—592no—
584C2×D4—592no—
585C2×D4—592no—
586C2×D4—1184no—
587C2×D4—1184no—
588C2×D4—1184no—
589C2×D4—1184no—
590C2×D4—1184no—
591C2×D4—1181no—
592C2×D4—1181no—
593C2×D4—1181no—
594C2×D4—1182no—
595C2×D4—1182no—
596C2×D4—1182no—
597C2×D4—1182no—
598C2×D4—1182no—
599C2×D4—1182no—
600C2×D4—4722no—
601C2×D4—4722no—
602C2×D4—4722no—
603C2×D4—4722no—
604C2×D4—4722no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—1181no—
608C22×C4—1181no—
609C22×C4—1181no—
610C22×C4—1181no—
611C22×C4—1181no—
612C22×C4—1184no—
613C22×C4—1184no—
614C22×C4—1184no—
615C22×C4—4722no—
616C22×C4—4722no—
617C22×C4—4722no—
618C22×C4C2×D23612yes—
619C22×C4C2×D23611yescharacteristic
620C22×C4C2×D23611yescharacteristic
621C22×C4C2×D23611yescharacteristic
622C22×C4C2×D23611yescharacteristic
623C22×C4C2×D23611yescharacteristic
624C22×C4C23×D5912yes—
625C22×C4C23×D5911yescharacteristic
626SD16—2364no—
627SD16—2364no—
628D8—2364no—
629D8—2364no—
630M16—44no—
631C2×C8—22no—
632C2×C8—22no—
633C2×C8—22no—
634C2×C8—22no—
635C2×C8—44no—
636C2×C8C23×D5912yes—
637C2×C8C23×D5912yes—
638C2×C8C23×D5912yes—
639C2×C8C23×D5912yes—
640C4⋊C4—592no—
641C4⋊C4—592no—
642C4⋊C4—592no—
643C4⋊C4—592no—
644C4⋊C4—1181no—
645C4⋊C4—1181no—
646C4⋊C4—1181no—
647C4⋊C4—1181no—
648C4⋊C4—1184no—
649C4⋊C4—1184no—
650C4⋊C4—1184no—
651C4⋊C4—1184no—
652C4⋊C4—1184no—
653C4⋊C4C2×D23614yes—
654C4⋊C4C2×D23614yes—
655C22⋊C4—1184no—
656C22⋊C4—1184no—
657C22⋊C4—1184no—
658C22⋊C4—1184no—
659C22⋊C4—1184no—
660C22⋊C4—1184no—
661C22⋊C4—1184no—
662C22⋊C4—1184no—
663C22⋊C4—1184no—
664C22⋊C4C2×D23614yes—
665C22⋊C4C2×D23614yes—
666C42—1184no—
667C42C2×D23612yes—
668C42C2×D23612yes—
669C42C23×D5912yes—
670C42C23×D5912yes—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—1182no—
675C23—1182no—
676C23—1182no—
677C23—2362no—
678C23—2362no—
679C23—2362no—
680C23—2362no—
681C23—2362no—
682C23—2362no—
683C23—2362no—
684C23—2362no—
685C23—2362no—
686C23C22×D23612yes—
687C23C22×D23611yescharacteristic
688Q8—1182no—
689Q8—1182no—
690Q8—4724no—
691Q8—2362no—
692D4—1182no—
693D4—1182no—
694D4—1182no—
695D4—1182no—
696D4—1182no—
697D4—1182no—
698D4—4724no—
699D4—4724no—
700D4—4724no—
701D4—4724no—
702D4—4724no—
703D4—2362no—
704D4—2362no—
705D4—2362no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—24no—
714C2×C4—1182no—
715C2×C4—1182no—
716C2×C4—1182no—
717C2×C4—1182no—
718C2×C4—1182no—
719C2×C4—4724no—
720C2×C4—4724no—
721C2×C4—4724no—
722C2×C4—2362no—
723C2×C4—2362no—
724C2×C4—2362no—
725C2×C4—2362no—
726C2×C4—2362no—
727C2×C4C22×D23612yes—
728C2×C4C22×D23612yes—
729C2×C4C22×D23612yes—
730C2×C4C22×D23612yes—
731C2×C4C22×D23612yes—
732C2×C4C22×D23611yescharacteristic
733C2×C4#1427377212yes—
734C2×C4#1427377512yes—
735C2×C4C24×D5911yescharacteristic
736C8—22no—
737C8—22no—
738C8—22no—
739C8—22no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—44no—
744C22—4724no—
745C22—4724no—
746C22—4724no—
747C22—2362no—
748C22—2362no—
749C22—2362no—
750C22—2362no—
751C22—2362no—
752C22—2362no—
753C22—2362no—
754C22—2362no—
755C22—2362no—
756C22#1683798312yes—
757C22#1683820712yes—
758C22#1683821412yes—
759C22C23×D23611yescharacteristic
760C4—22no—
761C4—22no—
762C4—22no—
763C4—22no—
764C4—22no—
765C4—2362no—
766C4—2362no—
767C4—2362no—
768C4—2362no—
769C4—2362no—
770C4#1683798312yes—
771C4C2×#1427377211yescharacteristic
772C4C2×#1427377511yescharacteristic
773C2—42no—
774C2—4722no—
775C2—4722no—
776C2—4722no—
777C2#2143550914yesdirect product factor
778C2C2×#1683798311yescharacteristic
779C2C2×#1683820711yescharacteristic
780C2C2×#1683821411yescharacteristic
subgroupG/H
centerC23C22×D236
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#424C2
socleC23×C59C22×D4
hypercenterC2×#424D59
hypocenterC59C2×#3257
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#424

Complements

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

NH ≅ G/Ntype
1. C2×#16838023C2semidirect
2. C2×#16838007C2semidirect
3. #21435509C2direct (N × H)
4. C2×#16837710C2semidirect
5. C2×#16837703C2semidirect
6. C2×#16837693C2semidirect
7. C2×#16837683C2semidirect
8. C2×#16837655C2semidirect
9. C2×#16837648C2semidirect
10. C2×#16837638C2semidirect
11. C2×#16837631C2semidirect
12. C2×#16837603C2semidirect
13. C2×#16837618C2semidirect
14. C2×#16837618C2semidirect
15. C2×#16837598C2semidirect
16. C2×C59×#424C2semidirect
22. #16838023C22semidirect
24. #16838007C22semidirect
45. #16837710C22semidirect
46. #16837703C22semidirect
47. #16837693C22semidirect
48. #16837683C22semidirect
49. #16837655C22semidirect
50. #16837648C22semidirect
51. #16837638C22semidirect
52. #16837631C22semidirect
53. #16837618C22semidirect
54. #16837618C22semidirect
55. #16837603C22semidirect
56. #16837598C22semidirect
72. C59×#424C22semidirect
398. C2×#424D59semidirect
400. C2×C59#3257semidirect
454. #424C2×D59semidirect
467. C59C2×#3257semidirect
777. C2#21435509direct (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×#168380072
#214355092
C2×#168377102
C2×#168377032
C2×#168376932
C2×#168376832
C2×#168376552
C2×#168376482
C2×#168376382
C2×#168376312
C2×#168376032
C2×#168376182
C2×#168375982
C2×C59×#4242
C2×#325759