Finite Group Databasebeta

← C2×#21436282 #29465439

Subgroups — C2×#21436282 #29465439

Order 15104.

2178 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838117C211yesmaximal, characteristic, complemented
2#21436282C2116yesmaximal, direct product factor
3C2×#16837761C211yesmaximal, characteristic, complemented
4C2×#16837740C211yesmaximal, characteristic, complemented
5C2×#16837723C211yesmaximal, characteristic, complemented
6C2×#16837687C211yesmaximal, characteristic, complemented
7C2×#16837653C211yesmaximal, characteristic, complemented
8C2×#16837633C211yesmaximal, characteristic, complemented
9C2×#16837614C211yesmaximal, characteristic, complemented
10C2×#16837547C211yesmaximal, characteristic, complemented
11C2×#16837541C211yesmaximal, characteristic, complemented
12C2×#16837500C211yesmaximal, characteristic, complemented
13C2×#16837474C211yesmaximal, characteristic, complemented
14C2×#16837411C211yesmaximal, characteristic, complemented
15C2×#16837398C211yesmaximal, characteristic, complemented
16C2×C59×#548C211yesmaximal, characteristic, complemented
17C22×#11745671C2211yescharacteristic
18C22×#11745671C2211yescharacteristic
19C22×#11745669C2211yescharacteristic
20C22×#11745664C2211yescharacteristic
21C23×C59⋊C8C2211yescharacteristic
22#16838117—24no—
23#16838117C2218yescomplemented
24C2×#14273727C2211yescharacteristic
25C2×#14273713—21no—
26C2×#14273713—21no—
27C2×#14273701C2211yescharacteristic
28C2×#14273701C2211yescharacteristic
29C2×#14273698—21no—
30C2×C4×D236C2211yescharacteristic
31C2×#14273686C2211yescharacteristic
32C2×#14273686C2211yescharacteristic
33C2×#14273685—21no—
34#16837761C2218yescomplemented
35#16837740C2218yescomplemented
36#16837723C2218yescomplemented
37#16837687C2218yescomplemented
38#16837653C2218yescomplemented
39#16837633C2218yescomplemented
40#16837614C2218yescomplemented
41#16837547C2218yescomplemented
42#16837541C2218yescomplemented
43#16837500C2218yescomplemented
44#16837474C2218yescomplemented
45C2×#14273660C2211yescharacteristic
46C2×#14273658C2211yescharacteristic
47C2×#14273658C2211yescharacteristic
48C2×C4⋊(C59⋊C8)C2211yescharacteristic
49#16837411C2218yescomplemented
50#16837398C2218yescomplemented
51C2×#14273651C2211yescharacteristic
52C2×#14273651C2211yescharacteristic
53C2×#14273651C2211yescharacteristic
54C2×#14273651C2211yescharacteristic
55C2×#14273651C2211yescharacteristic
56C2×#14273651C2211yescharacteristic
57C2×#14273648C2211yescharacteristic
58C2×#14273648C2211yescharacteristic
59C2×#14273648C2211yescharacteristic
60C2×#14273647C2211yescharacteristic
61C2×C22⋊(C59⋊C8)C2211yescharacteristic
62C2×C22⋊(C59⋊C8)C2211yescharacteristic
63C2×#14273638C2211yescharacteristic
64C22×#41×C59C2211yescharacteristic
65C23×Q8×C59C2211yescharacteristic
66C59×#548—24no—
67C59×#548C2218yescomplemented
68C2×#124×C59—21no—
69C2×#124×C59C2211yescharacteristic
70C2×C22⋊Q8×C59—21no—
71C2×C22⋊Q8×C59C2211yescharacteristic
72C2×#121×C59—21no—
73C2×#121×C59C2211yescharacteristic
74C2×C4×Q8×C59C2211yescharacteristic
75C2×C4×D4×C59—21no—
76C2×C4×D4×C59C2211yescharacteristic
77C22×Dic118—21no—
78C22×D236C2311yescharacteristic
79C22×C22⋊D59—21no—
80C22×C22⋊D59—21no—
81C22×C4×D59—21no—
82C2×#11745671—24no—
83C2×#11745671—42no—
84C2×#11745671C2314yes—
85C2×#11745671C2314yes—
86C2×#11745669—42no—
87C2×#11745669C2314yes—
88C2×#11745664—42no—
89C2×#11745664C2314yes—
90C22×C59⋊C8—42no—
91C22×C59⋊C8C2311yescharacteristic
92C22×C59⋊C8C2311yescharacteristic
93C22×C59⋊C8C2311yescharacteristic
94C22×C59⋊C8C2311yescharacteristic
95C22×C59⋊C8C2314yes—
96#14273727—22no—
97#14273727C2314yes—
98#14273713—28no—
99#14273713—28no—
100#14273701—22no—
101#14273701—22no—
102#14273701C2314yes—
103#14273701C2314yes—
104#14273698—28no—
105C4×D236—22no—
106C4×D236C2314yes—
107#14273686—22no—
108#14273686—22no—
109#14273686C2314yes—
110#14273686C2314yes—
111#14273685—28no—
112C2×C4⋊Dic59—21no—
113C2×C4⋊Dic59C2311yescharacteristic
114C2×C4⋊Dic59C2311yescharacteristic
115C2×C4⋊Dic59C2311yescharacteristic
116C2×C22⋊Dic59—21no—
117C2×C22⋊Dic59—21no—
118C2×(C2×D59)⋊C4—21no—
119C2×(C2×D59)⋊C4—21no—
120C2×(C2×D59)⋊C4—21no—
121C2×C4×Dic59—21no—
122C2×C4×Dic59—21no—
123#14273660C2314yes—
124#14273658C2314yes—
125#14273658C2314yes—
126C4⋊(C59⋊C8)C2314yes—
127#14273651C2314yes—
128#14273651C2314yes—
129#14273651C2314yes—
130#14273651C2314yes—
131#14273651C2314yes—
132#14273651C2314yes—
133#14273648C2314yes—
134#14273648C2314yes—
135#14273648C2314yes—
136#14273647C2314yes—
137C22⋊(C59⋊C8)C2314yes—
138C22⋊(C59⋊C8)C2314yes—
139#14273638C2314yes—
140C2×#41×C59—22no—
141C2×#41×C59—24no—
142C2×#41×C59—42no—
143C2×#41×C59C2314yes—
144C22×Q8×C59—21no—
145C22×Q8×C59—22no—
146C22×Q8×C59—24no—
147C22×Q8×C59—42no—
148C22×Q8×C59C2311yescharacteristic
149C22×Q8×C59C2314yes—
150C22×Q8×C59C2311yescharacteristic
151C22×D4×C59—21no—
152C22×D4×C59—21no—
153C22×D4×C59D411yescharacteristic
154C22×D4×C59C2311yescharacteristic
155C23×C4×C59—21no—
156C23×C4×C59—21no—
157C23×C4×C59C2311yescharacteristic
158C23×C4×C59C2311yescharacteristic
159#124×C59—28no—
160#124×C59—22no—
161#124×C59C2314yes—
162C22⋊Q8×C59—22no—
163C22⋊Q8×C59—28no—
164C22⋊Q8×C59C2314yes—
165#121×C59—28no—
166#121×C59—22no—
167#121×C59C2314yes—
168C4×Q8×C59—22no—
169C4×Q8×C59C2314yes—
170C4×D4×C59—28no—
171C4×D4×C59D414yes—
172C4×D4×C59C2314yes—
173C2×C4⋊C4×C59—21no—
174C2×C4⋊C4×C59—21no—
175C2×C4⋊C4×C59D411yescharacteristic
176C2×C4⋊C4×C59C2311yescharacteristic
177C2×C22⋊C4×C59—21no—
178C2×C22⋊C4×C59—21no—
179C2×C22⋊C4×C59—21no—
180C2×C22⋊C4×C59—21no—
181C2×C22⋊C4×C59D411yescharacteristic
182C2×C22⋊C4×C59D411yescharacteristic
183C2×C42×C59—21no—
184C2×C42×C59C2311yescharacteristic
185C24×C59—21no—
186C24×C59C2×D411yescharacteristic
187C24×C59C2×D411yescharacteristic
188C23×D59—21no—
189#41×C59—28no—
190#41×C59—44no—
191#41×C59—48no—
192C2×Q8×C59—21no—
193C2×Q8×C59—24no—
194C2×Q8×C59—21no—
195C2×Q8×C59—22no—
196C2×Q8×C59—28no—
197C2×Q8×C59—22no—
198C2×Q8×C59—22no—
199C2×Q8×C59—44no—
200C2×Q8×C59—44no—
201C2×Q8×C59—48no—
202C2×Q8×C59#4114yes—
203C2×Q8×C59C2412yes—
204C2×Q8×C59C2412yes—
205C2×D4×C59—24no—
206C2×D4×C59—24no—
207C2×D4×C59—21no—
208C2×D4×C59—22no—
209C2×D4×C59—22no—
210C2×D4×C59—42no—
211C2×D4×C59—44no—
212C2×D4×C59—44no—
213C2×D4×C59C2×D414yes—
214C2×D4×C59C2412yes—
215C22×C4×C59—21no—
216C22×C4×C59—22no—
217C22×C4×C59—22no—
218C22×C4×C59—22no—
219C22×C4×C59—22no—
220C22×C4×C59—21no—
221C22×C4×C59—21no—
222C22×C4×C59—24no—
223C22×C4×C59—24no—
224C22×C4×C59—44no—
225C22×C4×C59—44no—
226C22×C4×C59C2×D411yescharacteristic
227C22×C4×C59C2×D411yescharacteristic
228C22×C4×C59C2×D411yescharacteristic
229C22×C4×C59C2×D411yescharacteristic
230C22×C4×C59C2×D412yes—
231C22×C4×C59C2×D412yes—
232C22×C4×C59C2412yes—
233C22×C4×C59C2412yes—
234C22×C4×C59C2411yescharacteristic
235C2×C22⋊D59—24no—
236C2×C22⋊D59—24no—
237C2×C22⋊D59—82no—
238C2×C22⋊D59—82no—
239C22×Dic59—21no—
240C22×Dic59—21no—
241C22×Dic59—21no—
242C2×D236—22no—
243C2×D236—22no—
244C2×D236—21no—
245C2×D236C2412yes—
246C2×C4×D59—24no—
247C2×C4×D59—44no—
248C2×Dic118—24no—
249C2×Dic118—82no—
250C4⋊C4×C59—24no—
251C4⋊C4×C59—24no—
252C4⋊C4×C59—21no—
253C4⋊C4×C59C2×D414yes—
254C4⋊C4×C59C2412yes—
255C22⋊C4×C59—24no—
256C22⋊C4×C59—24no—
257C22⋊C4×C59—24no—
258C22⋊C4×C59—24no—
259C22⋊C4×C59C2×D414yes—
260C22⋊C4×C59C2×D414yes—
261C42×C59—24no—
262C42×C59C2×D412yes—
263C42×C59C2412yes—
264C22⋊Dic59—24no—
265C22⋊Dic59—24no—
266#11745671—28no—
267#11745671—44no—
268#11745669—44no—
269(C2×D59)⋊C4—24no—
270(C2×D59)⋊C4—24no—
271(C2×D59)⋊C4—24no—
272C4⋊Dic59—24no—
273C4⋊Dic59—21no—
274C4⋊Dic59—21no—
275C4⋊Dic59—21no—
276C4⋊Dic59C2412yes—
277C4⋊Dic59C2412yes—
278C4⋊Dic59C2412yes—
279C4×Dic59—24no—
280C4×Dic59—24no—
281#11745664—44no—
282C2×C59⋊C8—22no—
283C2×C59⋊C8—22no—
284C2×C59⋊C8—22no—
285C2×C59⋊C8—22no—
286C2×C59⋊C8—44no—
287C2×C59⋊C8C2412yes—
288C2×C59⋊C8C2412yes—
289C2×C59⋊C8C2412yes—
290C2×C59⋊C8C2412yes—
291C23×C59—22no—
292C23×C59—22no—
293C23×C59—22no—
294C23×C59—22no—
295C23×C59—22no—
296C23×C59—22no—
297C23×C59—22no—
298C23×C59—42no—
299C23×C59—42no—
300C23×C59—42no—
301C23×C59C22×D412yes—
302C23×C59C22×D412yes—
303C23×C59C22×D411yescharacteristic
304C22×D59—22no—
305C22×D59—42no—
306C22×D59—42no—
307C22×D59—42no—
308Q8×C59—24no—
309Q8×C59—22no—
310Q8×C59—22no—
311Q8×C59—22no—
312Q8×C59—48no—
313Q8×C59—42no—
314Q8×C59C2×#4114yes—
315D4×C59—22no—
316D4×C59—22no—
317D4×C59—44no—
318D4×C59—48no—
319D4×C59—48no—
320D4×C59—42no—
321C2×C4×C59—22no—
322C2×C4×C59—22no—
323C2×C4×C59—24no—
324C2×C4×C59—22no—
325C2×C4×C59—22no—
326C2×C4×C59—22no—
327C2×C4×C59—24no—
328C2×C4×C59—24no—
329C2×C4×C59—22no—
330C2×C4×C59—22no—
331C2×C4×C59—22no—
332C2×C4×C59—22no—
333C2×C4×C59—22no—
334C2×C4×C59—22no—
335C2×C4×C59—48no—
336C2×C4×C59—48no—
337C2×C4×C59—42no—
338C2×C4×C59—42no—
339C2×C4×C59C22×D412yes—
340C2×C4×C59C22×D412yes—
341C2×C4×C59C22×D412yes—
342C2×C4×C59C22×D412yes—
343C2×C4×C59C22×D411yescharacteristic
344C2×C4×C59C2×#4112yes—
345C2×C4×C59H(5,𝔽2)12yes—
346C2×C4×C59C2511yescharacteristic
347C22⋊D59—84no—
348C22⋊D59—84no—
349C2×Dic59—22no—
350C2×Dic59—22no—
351C2×Dic59—22no—
352C2×Dic59—42no—
353C2×Dic59—42no—
354C2×Dic59—42no—
355D236—22no—
356D236—22no—
357D236—42no—
358C4×D59—48no—
359Dic118—84no—
360C59⋊C8—22no—
361C59⋊C8—22no—
362C59⋊C8—22no—
363C59⋊C8—22no—
364C2×#3321—591nomaximal, Sylow
365C22×C59—22no—
366C22×C59—22no—
367C22×C59—22no—
368C22×C59—22no—
369C22×C59—22no—
370C22×C59—22no—
371C22×C59—44no—
372C22×C59—44no—
373C22×C59—42no—
374C22×C59—42no—
375C22×C59—42no—
376C22×C59—84no—
377C22×C59#54612yes—
378C22×C59#57512yes—
379C22×C59#57712yes—
380C22×C59C23×D411yescharacteristic
381C2×D59—42no—
382C2×D59—42no—
383C2×D59—42no—
384C2×D59—84no—
385C4×C59—22no—
386C4×C59—22no—
387C4×C59—24no—
388C4×C59—22no—
389C4×C59—22no—
390C4×C59—42no—
391C4×C59—42no—
392C4×C59#54612yes—
393C4×C59C22×#4111yescharacteristic
394C4×C59C2×H(5,𝔽2)11yescharacteristic
395Dic59—42no—
396Dic59—42no—
397Dic59—42no—
398C2×#555—591no—
399C2×#548D5911yescharacteristic, complemented
400#3321—5916no—
401C2×#489—591no—
402C2×#485—591no—
403C2×#482—591no—
404C2×#475—591no—
405C2×#469—591no—
406C2×#465—591no—
407C2×#463—591no—
408C2×#449—591no—
409C2×#448—591no—
410C2×#440—591no—
411C2×#435—591no—
412C2×#419—591no—
413C2×#416—591no—
414C2×C59—42no—
415C2×C59—42no—
416C2×C59—82no—
417C2×C59#332114yescomplemented
418C2×C59C2×#54611yescharacteristic
419C2×C59C2×#57511yescharacteristic
420C2×C59C2×#57711yescharacteristic
421D59—82no—
422C22×#41C2×D5911yescharacteristic
423C23×Q8C2×D5911yescharacteristic
424C22×SD16—591no—
425C22×SD16—591no—
426C22×D8—591no—
427C22×M16—591no—
428C23×C8—591no—
429#555—598no—
430#555—1184no—
431#548—24no—
432#548C2×D5918yescomplemented
433C2×C4⋊Q8—591no—
434C2×#124—21no—
435C2×#124—1181no—
436C2×#124—1181no—
437C2×#124C2×D5911yescharacteristic
438C2×C22⋊Q8—21no—
439C2×C22⋊Q8C2×D5911yescharacteristic
440C2×#121—21no—
441C2×#121—591no—
442C2×#121—591no—
443C2×#121—1181no—
444C2×#121C2×D5911yescharacteristic
445C2×C4×Q8C2×D5911yescharacteristic
446C2×C4×D4—21no—
447C2×C4×D4—591no—
448C2×C4×D4C2×D5911yescharacteristic
449C2×#117—591no—
450C2×#117—591no—
451C2×#117—1181no—
452#489—598no—
453#485—598no—
454#482—598no—
455#475—598no—
456#469—598no—
457#465—598no—
458#463—598no—
459#449—598no—
460#448—598no—
461#440—598no—
462#435—598no—
463C2×#107—591no—
464C2×#106—591no—
465C2×#106—591no—
466C2×C4⋊C8—591no—
467#419—598no—
468#416—598no—
469C2×#103—591no—
470C2×#103—591no—
471C2×#103—591no—
472C2×#103—591no—
473C2×#103—591no—
474C2×#103—591no—
475C2×#102—591no—
476C2×#102—591no—
477C2×#102—591no—
478C2×#102—591no—
479C2×C22⋊C8—591no—
480C2×C22⋊C8—591no—
481C2×#97—591no—
482C59C2×#332111yescharacteristic, complemented, Sylow
483C2×#41—22no—
484C2×#41—24no—
485C2×#41—42no—
486C2×#41C22×D5914yes—
487C22×Q8—21no—
488C22×Q8—22no—
489C22×Q8—24no—
490C22×Q8—42no—
491C22×Q8—1181no—
492C22×Q8C22×D5911yescharacteristic
493C22×Q8C22×D5914yes—
494C22×Q8C22×D5911yescharacteristic
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—591no—
498C22×D4—1181no—
499C22×D4—1181no—
500C22×D4C22⋊D5911yescharacteristic
501C22×D4C22×D5911yescharacteristic
502C23×C4—21no—
503C23×C4—21no—
504C23×C4—1181no—
505C23×C4C22×D5911yescharacteristic
506C23×C4C22×D5911yescharacteristic
507C2×SD16—594no—
508C2×SD16—594no—
509C2×SD16—1184no—
510C2×SD16—2362no—
511C2×D8—594no—
512C2×D8—2362no—
513C2×M16—594no—
514C2×M16—2362no—
515C22×C8—591no—
516C22×C8—591no—
517C22×C8—591no—
518C22×C8—591no—
519C22×C8—594no—
520C22×C8—2362no—
521C4⋊Q8—594no—
522C4⋊Q8—1182no—
523#124—28no—
524#124—22no—
525#124—1188no—
526#124—1188no—
527#124C22×D5914yes—
528C22⋊Q8—22no—
529C22⋊Q8—28no—
530C22⋊Q8C22×D5914yes—
531#121—28no—
532#121—22no—
533#121—594no—
534#121—594no—
535#121—1188no—
536#121—1182no—
537#121—1182no—
538#121C22×D5914yes—
539C4×Q8—22no—
540C4×Q8C22×D5914yes—
541C4×D4—28no—
542C4×D4—594no—
543C4×D4—1182no—
544C4×D4C22⋊D5914yes—
545C4×D4C22×D5914yes—
546#117—594no—
547#117—594no—
548#117—1182no—
549#117—1182no—
550#117—1188no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—591no—
554C2×C4⋊C4—591no—
555C2×C4⋊C4—591no—
556C2×C4⋊C4—1181no—
557C2×C4⋊C4C22⋊D5911yescharacteristic
558C2×C4⋊C4C22×D5911yescharacteristic
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—1181no—
564C2×C22⋊C4—1181no—
565C2×C22⋊C4—1181no—
566C2×C22⋊C4—1181no—
567C2×C22⋊C4—1181no—
568C2×C22⋊C4C22⋊D5911yescharacteristic
569C2×C22⋊C4C22⋊D5911yescharacteristic
570C2×C42—21no—
571C2×C42—1181no—
572C2×C42—1181no—
573C2×C42C22×D5911yescharacteristic
574#107—594no—
575#106—594no—
576#106—594no—
577C4⋊C8—594no—
578#103—594no—
579#103—594no—
580#103—594no—
581#103—594no—
582#103—594no—
583#103—594no—
584#102—594no—
585#102—594no—
586#102—594no—
587#102—594no—
588C22⋊C8—594no—
589C22⋊C8—594no—
590#97—594no—
591C24—21no—
592C24—1181no—
593C24C2×C22⋊D5911yescharacteristic
594C24C2×C22⋊D5911yescharacteristic
595#41—28no—
596#41—44no—
597#41—48no—
598C2×Q8—21no—
599C2×Q8—24no—
600C2×Q8—21no—
601C2×Q8—22no—
602C2×Q8—28no—
603C2×Q8—22no—
604C2×Q8—22no—
605C2×Q8—44no—
606C2×Q8—44no—
607C2×Q8—48no—
608C2×Q8—1184no—
609C2×Q8—4722no—
610C2×Q8#1174568714yes—
611C2×Q8C23×D5912yes—
612C2×Q8C23×D5912yes—
613C2×D4—24no—
614C2×D4—24no—
615C2×D4—21no—
616C2×D4—22no—
617C2×D4—22no—
618C2×D4—42no—
619C2×D4—44no—
620C2×D4—44no—
621C2×D4—592no—
622C2×D4—1184no—
623C2×D4—1184no—
624C2×D4—1181no—
625C2×D4—1182no—
626C2×D4—1182no—
627C2×D4—4722no—
628C2×D4—4722no—
629C2×D4C2×C22⋊D5914yes—
630C2×D4C23×D5912yes—
631C22×C4—21no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—24no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—24no—
640C22×C4—44no—
641C22×C4—44no—
642C22×C4—1181no—
643C22×C4—1181no—
644C22×C4—1181no—
645C22×C4—1184no—
646C22×C4—2364no—
647C22×C4C2×C22⋊D5912yes—
648C22×C4C2×C22⋊D5912yes—
649C22×C4C2×C22⋊D5911yescharacteristic
650C22×C4C2×C22⋊D5911yescharacteristic
651C22×C4C2×C22⋊D5911yescharacteristic
652C22×C4C2×C22⋊D5911yescharacteristic
653C22×C4C23×D5912yes—
654C22×C4C23×D5912yes—
655C22×C4C23×D5911yescharacteristic
656SD16—1188no—
657SD16—2364no—
658D8—2364no—
659M16—2364no—
660C2×C8—592no—
661C2×C8—592no—
662C2×C8—592no—
663C2×C8—592no—
664C2×C8—1182no—
665C2×C8—1182no—
666C2×C8—1182no—
667C2×C8—1182no—
668C2×C8—2364no—
669C4⋊C4—24no—
670C4⋊C4—24no—
671C4⋊C4—21no—
672C4⋊C4—592no—
673C4⋊C4—592no—
674C4⋊C4—592no—
675C4⋊C4—1181no—
676C4⋊C4—1181no—
677C4⋊C4—1181no—
678C4⋊C4—1184no—
679C4⋊C4C2×C22⋊D5914yes—
680C4⋊C4C23×D5912yes—
681C22⋊C4—24no—
682C22⋊C4—24no—
683C22⋊C4—24no—
684C22⋊C4—24no—
685C22⋊C4—1184no—
686C22⋊C4—1184no—
687C22⋊C4—1184no—
688C22⋊C4—1184no—
689C22⋊C4—1184no—
690C22⋊C4C2×C22⋊D5914yes—
691C22⋊C4C2×C22⋊D5914yes—
692C42—24no—
693C42—1184no—
694C42—1184no—
695C42C2×C22⋊D5912yes—
696C42C23×D5912yes—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—1182no—
708C23—2362no—
709C23—2362no—
710C23—2362no—
711C23C22×C22⋊D5912yes—
712C23C22×C22⋊D5912yes—
713C23C22×C22⋊D5911yescharacteristic
714Q8—22no—
715Q8—24no—
716Q8—22no—
717Q8—22no—
718Q8—48no—
719Q8—42no—
720Q8—4724no—
721Q8C2×#1174568714yes—
722D4—22no—
723D4—22no—
724D4—44no—
725D4—48no—
726D4—48no—
727D4—42no—
728D4—1182no—
729D4—1182no—
730D4—4724no—
731D4—4724no—
732D4—2362no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—24no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—48no—
748C2×C4—48no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—1182no—
752C2×C4—1182no—
753C2×C4—1182no—
754C2×C4—2368no—
755C2×C4—2362no—
756C2×C4—2362no—
757C2×C4—2362no—
758C2×C4C22×C22⋊D5912yes—
759C2×C4C22×C22⋊D5912yes—
760C2×C4C22×C22⋊D5912yes—
761C2×C4C22×C22⋊D5912yes—
762C2×C4C22×C22⋊D5911yescharacteristic
763C2×C4C2×#1174568712yes—
764C2×C4#1427377212yes—
765C2×C4C24×D5911yescharacteristic
766C8—1182no—
767C8—1182no—
768C8—1182no—
769C8—1182no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—44no—
777C22—44no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—84no—
782C22—4724no—
783C22—2362no—
784C22—2362no—
785C22—2362no—
786C22#1683804612yes—
787C22#1683820012yes—
788C22#1683821012yes—
789C22C23×C22⋊D5911yescharacteristic
790C4—22no—
791C4—22no—
792C4—24no—
793C4—22no—
794C4—22no—
795C4—42no—
796C4—42no—
797C4—2362no—
798C4—2362no—
799C4—2362no—
800C4#1683804612yes—
801C4C22×#1174568711yescharacteristic
802C4C2×#1427377211yescharacteristic
803C2—42no—
804C2—42no—
805C2—82no—
806C2—4722no—
807C2#2143628214yesdirect product factor
808C2C2×#1683804611yescharacteristic
809C2C2×#1683820011yescharacteristic
810C2C2×#1683821011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#548C2
socleC23×C59C22×D4
hypercenterC2×#548D59
hypocenterC59C2×#3321
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C2×#16838117C2semidirect
2. #21436282C2direct (N × H)
3. C2×#16837761C2semidirect
4. C2×#16837740C2semidirect
5. C2×#16837723C2semidirect
6. C2×#16837687C2semidirect
7. C2×#16837653C2semidirect
8. C2×#16837633C2semidirect
9. C2×#16837614C2semidirect
10. C2×#16837547C2semidirect
11. C2×#16837541C2semidirect
12. C2×#16837500C2semidirect
13. C2×#16837474C2semidirect
14. C2×#16837411C2semidirect
15. C2×#16837398C2semidirect
16. C2×C59×#548C2semidirect
23. #16838117C22semidirect
34. #16837761C22semidirect
35. #16837740C22semidirect
36. #16837723C22semidirect
37. #16837687C22semidirect
38. #16837653C22semidirect
39. #16837633C22semidirect
40. #16837614C22semidirect
41. #16837547C22semidirect
42. #16837541C22semidirect
43. #16837500C22semidirect
44. #16837474C22semidirect
49. #16837411C22semidirect
50. #16837398C22semidirect
67. C59×#548C22semidirect
399. C2×#548D59semidirect
417. C2×C59#3321semidirect
432. #548C2×D59semidirect
482. C59C2×#3321semidirect
807. C2#21436282direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168381172
#214362822
C2×#168377612
C2×#168377402
C2×#168377232
C2×#168376872
C2×#168376532
C2×#168376332
C2×#168376142
C2×#168375472
C2×#168375412
C2×#168375002
C2×#168374742
C2×#168374112
C2×#168373982
C2×C59×#5482
C2×#332159