Finite Group Databasebeta

← C2×#21434773 #29458567

Subgroups — C2×#21434773 #29458567

Order 15104.

2034 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×#16838007C211yesmaximal, characteristic, complemented
2#21434773C2116yesmaximal, direct product factor
3C2×#16837808C211yesmaximal, characteristic, complemented
4C2×#16837792C211yesmaximal, characteristic, complemented
5C2×#16837756C211yesmaximal, characteristic, complemented
6C2×#16837750C211yesmaximal, characteristic, complemented
7C2×#16837653C211yesmaximal, characteristic, complemented
8C2×#16837650C211yesmaximal, characteristic, complemented
9C2×#16837636C211yesmaximal, characteristic, complemented
10C2×#16837633C211yesmaximal, characteristic, complemented
11C2×#16837512C211yesmaximal, characteristic, complemented
12C2×#16837500C211yesmaximal, characteristic, complemented
13C2×C4×#11745671C211yesmaximal, characteristic, complemented
14C2×C4×#11745669C211yesmaximal, characteristic, complemented
15C2×#16837358C211yesmaximal, characteristic, complemented
16C2×C59×#542C211yesmaximal, characteristic, complemented
17C22×#11745671C2211yescharacteristic
18C22×#11745671C2211yescharacteristic
19C22×#11745669C2211yescharacteristic
20C22×#11745669C2211yescharacteristic
21C22×#11745664C2211yescharacteristic
22C23×C59⋊C8C2211yescharacteristic
23#16838007—24no—
24#16838007C2218yescomplemented
25C2×#14273724C2211yescharacteristic
26C2×#14273719C2211yescharacteristic
27C2×#14273712—21no—
28C2×#14273712—21no—
29C2×#14273701C2211yescharacteristic
30C2×#14273701C2211yescharacteristic
31C2×#14273700—21no—
32C2×#14273700—21no—
33C2×C4×D236C2211yescharacteristic
34C2×C4×D236C2211yescharacteristic
35#16837808C2218yescomplemented
36#16837792C2218yescomplemented
37#16837756C2218yescomplemented
38#16837750C2218yescomplemented
39#16837653C2218yescomplemented
40#16837650C2218yescomplemented
41#16837636C2218yescomplemented
42#16837633C2218yescomplemented
43#16837512C2218yescomplemented
44#16837500C2218yescomplemented
45C4×#11745671C2218yescomplemented
46C4×#11745669C2218yescomplemented
47C2×#14273660C2211yescharacteristic
48C2×#14273660C2211yescharacteristic
49C2×#14273658C2211yescharacteristic
50C2×#14273658C2211yescharacteristic
51C2×#14273651C2211yescharacteristic
52C2×#14273651C2211yescharacteristic
53C2×#14273648C2211yescharacteristic
54C2×#14273648C2211yescharacteristic
55C2×#14273647C2211yescharacteristic
56C2×#14273647C2211yescharacteristic
57C2×#14273647C2211yescharacteristic
58C2×#14273647C2211yescharacteristic
59#16837358C2218yescomplemented
60C2×#14273638C2211yescharacteristic
61C2×#14273638C2211yescharacteristic
62C2×C4×C59⋊C8C2211yescharacteristic
63C2×C4×C59⋊C8C2211yescharacteristic
64C59×#542—24no—
65C59×#542C2218yescomplemented
66C2×C4⋊Q8×C59C2211yescharacteristic
67C2×#126×C59—21no—
68C2×#124×C59—21no—
69C2×#124×C59C2211yescharacteristic
70C2×#123×C59—21no—
71C2×C22⋊Q8×C59—21no—
72C2×C22⋊Q8×C59C2211yescharacteristic
73C2×#121×C59C2211yescharacteristic
74C2×C4×Q8×C59C2211yescharacteristic
75C2×C4×D4×C59C2211yescharacteristic
76C2×#117×C59C2211yescharacteristic
77C22×D236—21no—
78C22×D236—21no—
79C22×D236C2311yescharacteristic
80C22×D236C2311yescharacteristic
81C22×C22⋊D59—21no—
82C22×C22⋊D59—21no—
83C22×C4×D59—21no—
84C22×C4×D59—21no—
85C2×#11745671—24no—
86C2×#11745671—24no—
87C2×#11745671C2314yes—
88C2×#11745671C2314yes—
89C2×#11745669—24no—
90C2×#11745669—24no—
91C2×#11745669C2314yes—
92C2×#11745669C2314yes—
93C2×#11745664—24no—
94C2×#11745664C2314yes—
95C22×C59⋊C8—24no—
96C22×C59⋊C8C2314yes—
97C22×C59⋊C8C2311yescharacteristic
98C22×C59⋊C8C2311yescharacteristic
99C22×C59⋊C8C2311yescharacteristic
100C22×C59⋊C8C2311yescharacteristic
101#14273724—22no—
102#14273724C2314yes—
103#14273719—22no—
104#14273719C2314yes—
105#14273712—28no—
106#14273712—28no—
107#14273701—22no—
108#14273701—22no—
109#14273701C2314yes—
110#14273701C2314yes—
111#14273700—28no—
112#14273700—28no—
113C4×D236—22no—
114C4×D236—22no—
115C4×D236C2314yes—
116C4×D236C2314yes—
117C2×C4⋊Dic59C2311yescharacteristic
118C2×C4⋊Dic59C2311yescharacteristic
119C2×Dic59⋊C4—21no—
120C2×Dic59⋊C4—21no—
121C2×(C2×D59)⋊C4—21no—
122C2×(C2×D59)⋊C4—21no—
123C2×(C2×D59)⋊C4—21no—
124C2×(C2×D59)⋊C4—21no—
125#14273660C2314yes—
126#14273660C2314yes—
127#14273658C2314yes—
128#14273658C2314yes—
129#14273651C2314yes—
130#14273651C2314yes—
131#14273648C2314yes—
132#14273648C2314yes—
133#14273647C2314yes—
134#14273647C2314yes—
135#14273647C2314yes—
136#14273647C2314yes—
137#14273638C2314yes—
138#14273638C2314yes—
139C4×C59⋊C8C2314yes—
140C4×C59⋊C8C2314yes—
141C22×Q8×C59—21no—
142C22×Q8×C59C2311yescharacteristic
143C22×D4×C59—21no—
144C22×D4×C59C2311yescharacteristic
145C23×C4×C59—21no—
146C23×C4×C59C2311yescharacteristic
147C4⋊Q8×C59—22no—
148C4⋊Q8×C59C2314yes—
149#126×C59—28no—
150#124×C59—28no—
151#124×C59—22no—
152#124×C59C2314yes—
153#123×C59—28no—
154C22⋊Q8×C59—22no—
155C22⋊Q8×C59—28no—
156C22⋊Q8×C59C2314yes—
157#121×C59—22no—
158#121×C59C2314yes—
159C4×Q8×C59—22no—
160C4×Q8×C59C2314yes—
161C4×D4×C59—22no—
162C4×D4×C59C2314yes—
163#117×C59D414yes—
164#117×C59C2314yes—
165C2×C4⋊C4×C59—21no—
166C2×C4⋊C4×C59—21no—
167C2×C4⋊C4×C59—21no—
168C2×C4⋊C4×C59D411yescharacteristic
169C2×C4⋊C4×C59D411yescharacteristic
170C2×C4⋊C4×C59C2311yescharacteristic
171C2×C4⋊C4×C59C2311yescharacteristic
172C2×C22⋊C4×C59—21no—
173C2×C22⋊C4×C59—21no—
174C2×C22⋊C4×C59—21no—
175C2×C22⋊C4×C59—21no—
176C2×C22⋊C4×C59—21no—
177C2×C22⋊C4×C59D411yescharacteristic
178C2×C22⋊C4×C59D411yescharacteristic
179C2×C42×C59—21no—
180C2×C42×C59C2311yescharacteristic
181C2×C42×C59C2311yescharacteristic
182C24×C59—21no—
183C24×C59C2×D411yescharacteristic
184C23×D59—21no—
185C23×D59—21no—
186C2×Q8×C59—21no—
187C2×Q8×C59—24no—
188C2×Q8×C59—22no—
189C2×Q8×C59—22no—
190C2×Q8×C59—82no—
191C2×Q8×C59C2412yes—
192C2×D4×C59—24no—
193C2×D4×C59—21no—
194C2×D4×C59—22no—
195C2×D4×C59—22no—
196C2×D4×C59—82no—
197C2×D4×C59C2412yes—
198C22×C4×C59—22no—
199C22×C4×C59—22no—
200C22×C4×C59—21no—
201C22×C4×C59—21no—
202C22×C4×C59—21no—
203C22×C4×C59—24no—
204C22×C4×C59—82no—
205C22×C4×C59C2×D411yescharacteristic
206C22×C4×C59C2×D411yescharacteristic
207C22×C4×C59C2×D411yescharacteristic
208C22×C4×C59C2×D411yescharacteristic
209C22×C4×C59C2×D411yescharacteristic
210C22×C4×C59C2×D412yes—
211C22×C4×C59C2412yes—
212C22×C4×C59C2411yescharacteristic
213C2×C22⋊D59—24no—
214C2×C22⋊D59—24no—
215C2×C22⋊D59—82no—
216C2×C22⋊D59—82no—
217C22×Dic59—21no—
218C22×Dic59—21no—
219C2×D236—22no—
220C2×D236—22no—
221C2×D236—22no—
222C2×D236—22no—
223C2×D236—21no—
224C2×D236—21no—
225C2×D236—24no—
226C2×D236—24no—
227C2×D236—82no—
228C2×D236—82no—
229C2×D236C2412yes—
230C2×D236C2412yes—
231C2×C4×D59—24no—
232C2×C4×D59—24no—
233C2×C4×D59—82no—
234C2×C4×D59—82no—
235C4⋊C4×C59—24no—
236C4⋊C4×C59—24no—
237C4⋊C4×C59—24no—
238C4⋊C4×C59—21no—
239C4⋊C4×C59—21no—
240C4⋊C4×C59C2×D414yes—
241C4⋊C4×C59C2×D414yes—
242C4⋊C4×C59C2412yes—
243C4⋊C4×C59C2412yes—
244C22⋊C4×C59—24no—
245C22⋊C4×C59—24no—
246C22⋊C4×C59—24no—
247C22⋊C4×C59—24no—
248C22⋊C4×C59—24no—
249C22⋊C4×C59C2×D414yes—
250C22⋊C4×C59C2×D414yes—
251C42×C59—24no—
252C42×C59C2×D412yes—
253C42×C59C2×D412yes—
254C42×C59C2412yes—
255C42×C59C2412yes—
256#11745671—28no—
257#11745671—28no—
258#11745669—28no—
259#11745669—28no—
260(C2×D59)⋊C4—24no—
261(C2×D59)⋊C4—24no—
262(C2×D59)⋊C4—24no—
263(C2×D59)⋊C4—24no—
264C4⋊Dic59—21no—
265C4⋊Dic59—21no—
266C4⋊Dic59C2412yes—
267C4⋊Dic59C2412yes—
268Dic59⋊C4—24no—
269Dic59⋊C4—24no—
270#11745664—28no—
271C2×C59⋊C8—22no—
272C2×C59⋊C8—22no—
273C2×C59⋊C8—28no—
274C2×C59⋊C8#4114yes—
275C2×C59⋊C8#4114yes—
276C2×C59⋊C8C2412yes—
277C2×C59⋊C8C2412yes—
278C2×C59⋊C8C2412yes—
279C2×C59⋊C8C2412yes—
280C23×C59—22no—
281C23×C59—22no—
282C23×C59—22no—
283C23×C59—22no—
284C23×C59—42no—
285C23×C59—42no—
286C23×C59—42no—
287C23×C59C22×D412yes—
288C23×C59C22×D411yescharacteristic
289C22×D59—22no—
290C22×D59—22no—
291C22×D59—42no—
292C22×D59—42no—
293C22×D59—42no—
294C22×D59—42no—
295C22×D59—42no—
296C22×D59—42no—
297Q8×C59—22no—
298Q8×C59—22no—
299Q8×C59—42no—
300Q8×C59—84no—
301D4×C59—22no—
302D4×C59—22no—
303D4×C59—42no—
304D4×C59—84no—
305C2×C4×C59—22no—
306C2×C4×C59—22no—
307C2×C4×C59—22no—
308C2×C4×C59—22no—
309C2×C4×C59—22no—
310C2×C4×C59—24no—
311C2×C4×C59—22no—
312C2×C4×C59—22no—
313C2×C4×C59—22no—
314C2×C4×C59—22no—
315C2×C4×C59—22no—
316C2×C4×C59—42no—
317C2×C4×C59—42no—
318C2×C4×C59—42no—
319C2×C4×C59—84no—
320C2×C4×C59C22×D412yes—
321C2×C4×C59C22×D412yes—
322C2×C4×C59C22×D412yes—
323C2×C4×C59C22×D412yes—
324C2×C4×C59C22×D412yes—
325C2×C4×C59C22×D411yescharacteristic
326C2×C4×C59C2×#4112yes—
327C2×C4×C59C2×#4112yes—
328C2×C4×C59C2511yescharacteristic
329C22⋊D59—84no—
330C22⋊D59—84no—
331C2×Dic59—22no—
332C2×Dic59—22no—
333C2×Dic59—42no—
334C2×Dic59—42no—
335D236—22no—
336D236—22no—
337D236—22no—
338D236—22no—
339D236—42no—
340D236—42no—
341D236—84no—
342D236—84no—
343C4×D59—84no—
344C4×D59—84no—
345C59⋊C8—22no—
346C59⋊C8—22no—
347C59⋊C8C2×#4114yes—
348C59⋊C8C2×#4114yes—
349C2×#3179—591nomaximal, Sylow
350C22×C59—22no—
351C22×C59—22no—
352C22×C59—22no—
353C22×C59—44no—
354C22×C59—42no—
355C22×C59—42no—
356C22×C59—42no—
357C22×C59—84no—
358C22×C59#53212yes—
359C22×C59#57612yes—
360C22×C59#57712yes—
361C22×C59C23×D411yescharacteristic
362C2×D59—42no—
363C2×D59—42no—
364C2×D59—42no—
365C2×D59—42no—
366C2×D59—42no—
367C2×D59—42no—
368C2×D59—84no—
369C2×D59—84no—
370C4×C59—22no—
371C4×C59—22no—
372C4×C59—22no—
373C4×C59—22no—
374C4×C59—22no—
375C4×C59—42no—
376C4×C59—42no—
377C4×C59—42no—
378C4×C59#53212yes—
379C4×C59C22×#4111yescharacteristic
380C4×C59C22×#4111yescharacteristic
381Dic59—42no—
382Dic59—42no—
383C2×#542D5911yescharacteristic, complemented
384C2×#540—591no—
385#3179—5916no—
386C2×#501—591no—
387C2×#496—591no—
388C2×#488—591no—
389C2×#486—591no—
390C2×#469—591no—
391C2×#468—591no—
392C2×#466—591no—
393C2×#465—591no—
394C2×#442—591no—
395C2×#440—591no—
396C2×C4×SD16—591no—
397C2×C4×D8—591no—
398C2×#405—591no—
399C2×C59—42no—
400C2×C59—82no—
401C2×C59#317914yescomplemented
402C2×C59C2×#53211yescharacteristic
403C2×C59C2×#57611yescharacteristic
404C2×C59C2×#57711yescharacteristic
405D59—82no—
406D59—82no—
407C22×SD16—591no—
408C22×SD16—591no—
409C22×D8—591no—
410C22×D8—591no—
411C22×M16—591no—
412C23×C8—591no—
413#542—24no—
414#542C2×D5918yescomplemented
415#540—598no—
416#540—1184no—
417C2×C4⋊Q8C2×D5911yescharacteristic
418C2×#127—591no—
419C2×#126—21no—
420C2×#125—591no—
421C2×#124—21no—
422C2×#124C2×D5911yescharacteristic
423C2×#123—21no—
424C2×#123—1181no—
425C2×#123—1181no—
426C2×C22⋊Q8—21no—
427C2×C22⋊Q8C2×D5911yescharacteristic
428C2×#121—591no—
429C2×#121—591no—
430C2×#121—1181no—
431C2×#121—1181no—
432C2×#121C2×D5911yescharacteristic
433C2×C4×Q8C2×D5911yescharacteristic
434C2×C4×D4—591no—
435C2×C4×D4—591no—
436C2×C4×D4C2×D5911yescharacteristic
437C2×#117C2×D5911yescharacteristic
438#501—598no—
439#496—598no—
440#488—598no—
441#486—598no—
442#469—598no—
443#468—598no—
444#466—598no—
445#465—598no—
446#442—598no—
447#440—598no—
448C4×SD16—598no—
449C4×D8—598no—
450C2×#107—591no—
451C2×#107—591no—
452C2×#106—591no—
453C2×#106—591no—
454C2×#103—591no—
455C2×#103—591no—
456C2×#102—591no—
457C2×#102—591no—
458C2×#102—591no—
459C2×#102—591no—
460C2×#102—591no—
461C2×#102—591no—
462#405—598no—
463C2×#97—591no—
464C2×#97—591no—
465C2×C4×C8—591no—
466C2×C4×C8—591no—
467C59C2×#317911yescharacteristic, complemented, Sylow
468C22×Q8—21no—
469C22×Q8C22×D5911yescharacteristic
470C22×D4—21no—
471C22×D4—591no—
472C22×D4—591no—
473C22×D4—1181no—
474C22×D4—1181no—
475C22×D4—1181no—
476C22×D4—1181no—
477C22×D4C22×D5911yescharacteristic
478C23×C4—21no—
479C23×C4—1181no—
480C23×C4—1181no—
481C23×C4C22×D5911yescharacteristic
482C2×SD16—594no—
483C2×SD16—594no—
484C2×SD16—1184no—
485C2×SD16—1184no—
486C2×D8—594no—
487C2×D8—594no—
488C2×D8—1184no—
489C2×D8—1184no—
490C2×M16—594no—
491C2×M16—1184no—
492C22×C8—591no—
493C22×C8—591no—
494C22×C8—591no—
495C22×C8—594no—
496C22×C8—591no—
497C22×C8—1184no—
498C4⋊Q8—22no—
499C4⋊Q8C22×D5914yes—
500#127—594no—
501#127—1182no—
502#126—28no—
503#125—594no—
504#125—1182no—
505#124—28no—
506#124—22no—
507#124C22×D5914yes—
508#123—28no—
509#123—1188no—
510#123—1188no—
511C22⋊Q8—22no—
512C22⋊Q8—28no—
513C22⋊Q8C22×D5914yes—
514#121—22no—
515#121—594no—
516#121—594no—
517#121—1182no—
518#121—1182no—
519#121—1188no—
520#121—1188no—
521#121C22×D5914yes—
522C4×Q8—22no—
523C4×Q8C22×D5914yes—
524C4×D4—22no—
525C4×D4—594no—
526C4×D4—594no—
527C4×D4—1182no—
528C4×D4—1182no—
529C4×D4C22×D5914yes—
530#117C22⋊D5914yes—
531#117C22×D5914yes—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—591no—
536C2×C4⋊C4—591no—
537C2×C4⋊C4—1181no—
538C2×C4⋊C4—1181no—
539C2×C4⋊C4C22⋊D5911yescharacteristic
540C2×C4⋊C4C22⋊D5911yescharacteristic
541C2×C4⋊C4C22×D5911yescharacteristic
542C2×C4⋊C4C22×D5911yescharacteristic
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—1181no—
549C2×C22⋊C4—1181no—
550C2×C22⋊C4—1181no—
551C2×C22⋊C4—1181no—
552C2×C22⋊C4C22⋊D5911yescharacteristic
553C2×C22⋊C4C22⋊D5911yescharacteristic
554C2×C42—21no—
555C2×C42C22×D5911yescharacteristic
556C2×C42C22×D5911yescharacteristic
557#107—594no—
558#107—594no—
559#106—594no—
560#106—594no—
561#103—594no—
562#103—594no—
563#102—594no—
564#102—594no—
565#102—594no—
566#102—594no—
567#102—594no—
568#102—594no—
569#97—594no—
570#97—594no—
571C4×C8—594no—
572C4×C8—594no—
573C24—21no—
574C24—1181no—
575C24—1181no—
576C24C2×C22⋊D5911yescharacteristic
577C2×Q8—21no—
578C2×Q8—24no—
579C2×Q8—22no—
580C2×Q8—22no—
581C2×Q8—82no—
582C2×Q8C23×D5912yes—
583C2×D4—24no—
584C2×D4—21no—
585C2×D4—22no—
586C2×D4—22no—
587C2×D4—82no—
588C2×D4—592no—
589C2×D4—592no—
590C2×D4—1184no—
591C2×D4—1184no—
592C2×D4—1184no—
593C2×D4—1184no—
594C2×D4—1181no—
595C2×D4—1181no—
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×D4C23×D5912yes—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—24no—
611C22×C4—82no—
612C22×C4—1181no—
613C22×C4—1181no—
614C22×C4—1184no—
615C22×C4—1184no—
616C22×C4—4722no—
617C22×C4—4722no—
618C22×C4C2×C22⋊D5912yes—
619C22×C4C2×C22⋊D5911yescharacteristic
620C22×C4C2×C22⋊D5911yescharacteristic
621C22×C4C2×C22⋊D5911yescharacteristic
622C22×C4C2×C22⋊D5911yescharacteristic
623C22×C4C2×C22⋊D5911yescharacteristic
624C22×C4C23×D5912yes—
625C22×C4C23×D5911yescharacteristic
626SD16—1188no—
627SD16—1188no—
628D8—1188no—
629D8—1188no—
630M16—1188no—
631C2×C8—594no—
632C2×C8—594no—
633C2×C8—592no—
634C2×C8—592no—
635C2×C8—592no—
636C2×C8—592no—
637C2×C8—1188no—
638C2×C8—1182no—
639C2×C8—1182no—
640C4⋊C4—24no—
641C4⋊C4—24no—
642C4⋊C4—24no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—592no—
646C4⋊C4—592no—
647C4⋊C4—1181no—
648C4⋊C4—1181no—
649C4⋊C4—1184no—
650C4⋊C4—1184no—
651C4⋊C4C2×C22⋊D5914yes—
652C4⋊C4C2×C22⋊D5914yes—
653C4⋊C4C23×D5912yes—
654C4⋊C4C23×D5912yes—
655C22⋊C4—24no—
656C22⋊C4—24no—
657C22⋊C4—24no—
658C22⋊C4—24no—
659C22⋊C4—24no—
660C22⋊C4—1184no—
661C22⋊C4—1184no—
662C22⋊C4—1184no—
663C22⋊C4—1184no—
664C22⋊C4C2×C22⋊D5914yes—
665C22⋊C4C2×C22⋊D5914yes—
666C42—24no—
667C42C2×C22⋊D5912yes—
668C42C2×C22⋊D5912yes—
669C42C23×D5912yes—
670C42C23×D5912yes—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—1182no—
679C23—1182no—
680C23—2362no—
681C23—2362no—
682C23—2362no—
683C23—2362no—
684C23—2362no—
685C23—2362no—
686C23C22×C22⋊D5912yes—
687C23C22×C22⋊D5911yescharacteristic
688Q8—22no—
689Q8—22no—
690Q8—42no—
691Q8—84no—
692D4—22no—
693D4—22no—
694D4—42no—
695D4—84no—
696D4—1182no—
697D4—1182no—
698D4—1182no—
699D4—1182no—
700D4—4724no—
701D4—4724no—
702D4—4724no—
703D4—4724no—
704D4—2362no—
705D4—2362no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—24no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—84no—
721C2×C4—1182no—
722C2×C4—1182no—
723C2×C4—4724no—
724C2×C4—4724no—
725C2×C4—2362no—
726C2×C4—2362no—
727C2×C4C22×C22⋊D5912yes—
728C2×C4C22×C22⋊D5912yes—
729C2×C4C22×C22⋊D5912yes—
730C2×C4C22×C22⋊D5912yes—
731C2×C4C22×C22⋊D5912yes—
732C2×C4C22×C22⋊D5911yescharacteristic
733C2×C4#41×D5912yes—
734C2×C4#41×D5912yes—
735C2×C4C24×D5911yescharacteristic
736C8—594no—
737C8—594no—
738C8—1182no—
739C8—1182no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—44no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—84no—
748C22—4724no—
749C22—4724no—
750C22—2362no—
751C22—2362no—
752C22—2362no—
753C22—2362no—
754C22—2362no—
755C22—2362no—
756C22#1683794812yes—
757C22#1683820512yes—
758C22#1683821012yes—
759C22C23×C22⋊D5911yescharacteristic
760C4—22no—
761C4—22no—
762C4—22no—
763C4—22no—
764C4—22no—
765C4—42no—
766C4—42no—
767C4—42no—
768C4—2362no—
769C4—2362no—
770C4#1683794812yes—
771C4C2×#41×D5911yescharacteristic
772C4C2×#41×D5911yescharacteristic
773C2—42no—
774C2—82no—
775C2—4722no—
776C2—4722no—
777C2#2143477314yesdirect product factor
778C2C2×#1683794811yescharacteristic
779C2C2×#1683820511yescharacteristic
780C2C2×#1683821011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#542C2
socleC23×C59C22×D4
hypercenterC2×#542D59
hypocenterC59C2×#3179
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. C2×#16838007C2semidirect
2. #21434773C2direct (N × H)
3. C2×#16837808C2semidirect
4. C2×#16837792C2semidirect
5. C2×#16837756C2semidirect
6. C2×#16837750C2semidirect
7. C2×#16837653C2semidirect
8. C2×#16837650C2semidirect
9. C2×#16837636C2semidirect
10. C2×#16837633C2semidirect
11. C2×#16837512C2semidirect
12. C2×#16837500C2semidirect
13. C2×C4×#11745671C2semidirect
14. C2×C4×#11745669C2semidirect
15. C2×#16837358C2semidirect
16. C2×C59×#542C2semidirect
24. #16838007C22semidirect
35. #16837808C22semidirect
36. #16837792C22semidirect
37. #16837756C22semidirect
38. #16837750C22semidirect
39. #16837653C22semidirect
40. #16837650C22semidirect
41. #16837636C22semidirect
42. #16837633C22semidirect
43. #16837512C22semidirect
44. #16837500C22semidirect
45. C4×#11745671C22semidirect
46. C4×#11745669C22semidirect
59. #16837358C22semidirect
65. C59×#542C22semidirect
383. C2×#542D59semidirect
401. C2×C59#3179semidirect
414. #542C2×D59semidirect
467. C59C2×#3179semidirect
777. C2#21434773direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168380072
#214347732
C2×#168378082
C2×#168377922
C2×#168377562
C2×#168377502
C2×#168376532
C2×#168376502
C2×#168376362
C2×#168376332
C2×#168375122
C2×#168375002
C2×C4×#117456712
C2×C4×#117456692
C2×#168373582
C2×C59×#5422
C2×#317959