Finite Group Databasebeta

← C2×#21437162 #29469695

Subgroups — C2×#21437162 #29469695

Order 15104.

2002 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838137C211yesmaximal, characteristic, complemented
2#21437162C2116yesmaximal, direct product factor
3C2×#16837794C211yesmaximal, characteristic, complemented
4C2×#16837792C211yesmaximal, characteristic
5C2×#16837784C211yesmaximal, characteristic, complemented
6C2×#16837624C211yesmaximal, characteristic, complemented
7C2×#16837621C211yesmaximal, characteristic, complemented
8C2×#16837602C211yesmaximal, characteristic, complemented
9C2×#16837617C211yesmaximal, characteristic, complemented
10C2×#16837614C211yesmaximal, characteristic, complemented
11C2×#16837604C211yesmaximal, characteristic, complemented
12C2×#16837533C211yesmaximal, characteristic, complemented
13C2×#16837512C211yesmaximal, characteristic, complemented
14C2×#16837507C211yesmaximal, characteristic, complemented
15C2×C4×#11745671C211yesmaximal, characteristic, complemented
16C2×C59×#556C211yesmaximal, characteristic, complemented
17C22×#11745672C2211yescharacteristic
18C22×#11745672C2211yescharacteristic
19C22×#11745670C2211yescharacteristic
20C22×#11745671C2211yescharacteristic
21C22×#11745671C2211yescharacteristic
22C22×#11745671C2211yescharacteristic
23C22×#11745671C2211yescharacteristic
24C22×#11745669C2211yescharacteristic
25C22×#11745669C2211yescharacteristic
26#16838137—24no—
27#16838137C2218yescomplemented
28C2×#14273724C2211yescharacteristic
29C2×#14273716—21no—
30C2×#14273715C2211yescharacteristic
31C2×#14273715C2211yescharacteristic
32C2×#14273712—21no—
33C2×#14273712—21no—
34C2×C4×Dic118C2211yescharacteristic
35C2×C4×D236C2211yescharacteristic
36C2×C4×D236C2211yescharacteristic
37C2×#14273689—21no—
38#16837794C2218yescomplemented
39#16837792C2218yes—
40#16837784C2218yescomplemented
41#16837624C2218yescomplemented
42#16837621C2218yescomplemented
43#16837617C2218yescomplemented
44#16837614C2218yescomplemented
45#16837604C2218yescomplemented
46#16837602C2218yescomplemented
47#16837533C2218yescomplemented
48#16837512C2218yescomplemented
49#16837507C2218yescomplemented
50C4×#11745671C2218yescomplemented
51C2×#14273658C2211yescharacteristic
52C2×C4⋊(C59⋊C8)C2211yescharacteristic
53C2×C4⋊(C59⋊C8)C2211yescharacteristic
54C2×C4⋊(C59⋊C8)C2211yescharacteristic
55C2×#14273651C2211yescharacteristic
56C2×#14273651C2211yescharacteristic
57C2×#14273650C2211yescharacteristic
58C2×#14273648C2211yescharacteristic
59C2×#14273647C2211yescharacteristic
60C2×#14273647C2211yescharacteristic
61C2×#14273638C2211yescharacteristic
62C2×#14273638C2211yescharacteristic
63C2×C4×C59⋊C8C2211yescharacteristic
64C59×#556—24no—
65C59×#556C2218yescomplemented
66C2×C4⋊Q8×C59C2211yescharacteristic
67C2×#126×C59—21no—
68C2×#126×C59—21no—
69C2×#124×C59C2211yescharacteristic
70C2×#124×C59C2211yescharacteristic
71C2×C22⋊Q8×C59—21no—
72C2×C4×Q8×C59C2211yescharacteristic
73C2×C4×Q8×C59C2211yescharacteristic
74C2×C4×Q8×C59C2211yescharacteristic
75C2×C4×D4×C59C2211yescharacteristic
76C2×#117×C59—21no—
77C22×Dic118C2311yescharacteristic
78C22×D236—21no—
79C22×D236—21no—
80C22×D236C2311yescharacteristic
81C22×D236C2311yescharacteristic
82C22×C4×D59—21no—
83C22×C4×D59—21no—
84C2×#11745672—24no—
85C2×#11745672—42no—
86C2×#11745672C2314yes—
87C2×#11745672C2314yes—
88C2×#11745670—42no—
89C2×#11745670C2314yes—
90C2×#11745671—24no—
91C2×#11745671—42no—
92C2×#11745671—42no—
93C2×#11745671—42no—
94C2×#11745671C2314yes—
95C2×#11745671C2314yes—
96C2×#11745671C2314yes—
97C2×#11745671C2314yes—
98C2×#11745669—24no—
99C2×#11745669—42no—
100C2×#11745669C2314yes—
101C2×#11745669C2314yes—
102C22×C59⋊C8C2311yescharacteristic
103C22×C59⋊C8C2311yescharacteristic
104C22×C59⋊C8C2311yescharacteristic
105C22×C59⋊C8C2311yescharacteristic
106#14273724—22no—
107#14273724C2314yes—
108#14273716—28no—
109#14273715—22no—
110#14273715—22no—
111#14273715C2314yes—
112#14273715C2314yes—
113#14273712—28no—
114#14273712—28no—
115C4×Dic118—22no—
116C4×Dic118C2314yes—
117C4×D236—22no—
118C4×D236—22no—
119C4×D236C2314yes—
120C4×D236C2314yes—
121#14273689—28no—
122C2×C4⋊Dic59C2311yescharacteristic
123C2×Dic59⋊C4—21no—
124C2×(C2×D59)⋊C4—21no—
125C2×(C2×D59)⋊C4—21no—
126C2×(C2×D59)⋊C4—21no—
127C2×(C2×D59)⋊C4—21no—
128C2×(C2×D59)⋊C4—21no—
129C2×(C2×D59)⋊C4—21no—
130C2×C4×Dic59—21no—
131#14273658C2314yes—
132C4⋊(C59⋊C8)C2314yes—
133C4⋊(C59⋊C8)C2314yes—
134C4⋊(C59⋊C8)C2314yes—
135#14273651C2314yes—
136#14273651C2314yes—
137#14273650C2314yes—
138#14273648C2314yes—
139#14273647C2314yes—
140#14273647C2314yes—
141#14273638C2314yes—
142#14273638C2314yes—
143C4×C59⋊C8C2314yes—
144C22×Q8×C59D411yescharacteristic
145C22×Q8×C59C2311yescharacteristic
146C22×Q8×C59C2311yescharacteristic
147C22×D4×C59C2311yescharacteristic
148C23×C4×C59—21no—
149C4⋊Q8×C59—22no—
150C4⋊Q8×C59C2314yes—
151#126×C59—28no—
152#126×C59—28no—
153#124×C59—22no—
154#124×C59—22no—
155#124×C59C2314yes—
156#124×C59C2314yes—
157C22⋊Q8×C59—28no—
158C4×Q8×C59—22no—
159C4×Q8×C59—22no—
160C4×Q8×C59D414yes—
161C4×Q8×C59C2314yes—
162C4×Q8×C59C2314yes—
163C4×Q8×C59C2314yes—
164C4×D4×C59—22no—
165C4×D4×C59C2314yes—
166#117×C59—28no—
167C2×C4⋊C4×C59—21no—
168C2×C4⋊C4×C59—21no—
169C2×C4⋊C4×C59—21no—
170C2×C4⋊C4×C59—21no—
171C2×C4⋊C4×C59D411yescharacteristic
172C2×C4⋊C4×C59D411yescharacteristic
173C2×C4⋊C4×C59D411yescharacteristic
174C2×C4⋊C4×C59C2311yescharacteristic
175C2×C22⋊C4×C59—21no—
176C2×C22⋊C4×C59—21no—
177C2×C22⋊C4×C59—21no—
178C2×C22⋊C4×C59—21no—
179C2×C22⋊C4×C59—21no—
180C2×C42×C59—21no—
181C2×C42×C59—21no—
182C2×C42×C59C2311yescharacteristic
183C2×C42×C59C2311yescharacteristic
184C2×C42×C59C2311yescharacteristic
185C24×C59—21no—
186C23×D59—21no—
187C23×D59—21no—
188C2×Q8×C59—21no—
189C2×Q8×C59—21no—
190C2×Q8×C59—22no—
191C2×Q8×C59—22no—
192C2×Q8×C59—22no—
193C2×Q8×C59—22no—
194C2×Q8×C59—42no—
195C2×Q8×C59C2×D414yes—
196C2×Q8×C59C2412yes—
197C2×Q8×C59C2412yes—
198C2×D4×C59—21no—
199C2×D4×C59—22no—
200C2×D4×C59—22no—
201C2×D4×C59C2412yes—
202C22×C4×C59—21no—
203C22×C4×C59—21no—
204C22×C4×C59—21no—
205C22×C4×C59—24no—
206C22×C4×C59—44no—
207C22×C4×C59C2×D411yescharacteristic
208C22×C4×C59C2×D411yescharacteristic
209C22×C4×C59C2×D411yescharacteristic
210C22×C4×C59C2×D411yescharacteristic
211C22×C4×C59C2×D411yescharacteristic
212C22×C4×C59C2×D411yescharacteristic
213C22×C4×C59C2411yescharacteristic
214C22×Dic59—21no—
215C22×Dic59—21no—
216C2×D236—22no—
217C2×D236—22no—
218C2×D236—22no—
219C2×D236—22no—
220C2×D236—24no—
221C2×D236—21no—
222C2×D236—21no—
223C2×D236—24no—
224C2×D236—44no—
225C2×D236—82no—
226C2×D236C2412yes—
227C2×D236C2412yes—
228C2×C4×D59—24no—
229C2×C4×D59—24no—
230C2×C4×D59—82no—
231C2×C4×D59—82no—
232C2×Dic118—22no—
233C2×Dic118—22no—
234C2×Dic118—21no—
235C2×Dic118C2412yes—
236C4⋊C4×C59—24no—
237C4⋊C4×C59—24no—
238C4⋊C4×C59—24no—
239C4⋊C4×C59—24no—
240C4⋊C4×C59—21no—
241C4⋊C4×C59C2×D414yes—
242C4⋊C4×C59C2×D414yes—
243C4⋊C4×C59C2×D414yes—
244C4⋊C4×C59C2412yes—
245C22⋊C4×C59—24no—
246C22⋊C4×C59—24no—
247C22⋊C4×C59—24no—
248C22⋊C4×C59—24no—
249C22⋊C4×C59—24no—
250C42×C59—24no—
251C42×C59—24no—
252C42×C59C2×D412yes—
253C42×C59C2×D412yes—
254C42×C59C2×D412yes—
255C42×C59C2412yes—
256C42×C59C2412yes—
257C42×C59C2412yes—
258#11745672—28no—
259#11745672—44no—
260#11745671—28no—
261#11745671—44no—
262#11745671—44no—
263#11745671—44no—
264#11745670—44no—
265#11745669—28no—
266#11745669—44no—
267(C2×D59)⋊C4—24no—
268(C2×D59)⋊C4—24no—
269(C2×D59)⋊C4—24no—
270(C2×D59)⋊C4—24no—
271(C2×D59)⋊C4—24no—
272(C2×D59)⋊C4—24no—
273C4⋊Dic59—21no—
274C4⋊Dic59C2412yes—
275Dic59⋊C4—24no—
276C4×Dic59—24no—
277C2×C59⋊C8—22no—
278C2×C59⋊C8—22no—
279C2×C59⋊C8—22no—
280C2×C59⋊C8#4114yes—
281C2×C59⋊C8C2412yes—
282C2×C59⋊C8C2412yes—
283C2×C59⋊C8C2412yes—
284C2×C59⋊C8C2412yes—
285C23×C59—22no—
286C23×C59—42no—
287C23×C59—42no—
288C23×C59—42no—
289C23×C59C22×D411yescharacteristic
290C22×D59—22no—
291C22×D59—22no—
292C22×D59—42no—
293C22×D59—42no—
294C22×D59—42no—
295C22×D59—42no—
296C22×D59—42no—
297C22×D59—42no—
298Q8×C59—22no—
299Q8×C59—22no—
300Q8×C59—22no—
301Q8×C59—22no—
302Q8×C59—44no—
303Q8×C59—42no—
304Q8×C59—42no—
305D4×C59—22no—
306D4×C59—22no—
307D4×C59—42no—
308C2×C4×C59—22no—
309C2×C4×C59—22no—
310C2×C4×C59—22no—
311C2×C4×C59—22no—
312C2×C4×C59—22no—
313C2×C4×C59—22no—
314C2×C4×C59—22no—
315C2×C4×C59—22no—
316C2×C4×C59—22no—
317C2×C4×C59—48no—
318C2×C4×C59—42no—
319C2×C4×C59—42no—
320C2×C4×C59—42no—
321C2×C4×C59C22×D412yes—
322C2×C4×C59C22×D412yes—
323C2×C4×C59C22×D412yes—
324C2×C4×C59C22×D412yes—
325C2×C4×C59C22×D412yes—
326C2×C4×C59C22×D412yes—
327C2×C4×C59C22×D411yescharacteristic
328C2×C4×C59C2×#4112yes—
329C2×C4×C59H(5,𝔽2)12yes—
330C2×C4×C59C2511yescharacteristic
331C2×Dic59—22no—
332C2×Dic59—22no—
333C2×Dic59—42no—
334C2×Dic59—42no—
335D236—22no—
336D236—22no—
337D236—22no—
338D236—22no—
339D236—48no—
340D236—42no—
341D236—42no—
342D236—84no—
343C4×D59—84no—
344C4×D59—84no—
345Dic118—22no—
346Dic118—22no—
347Dic118—42no—
348C59⋊C8—22no—
349C59⋊C8—22no—
350C59⋊C8—22no—
351C59⋊C8C2×#4114yes—
352C2×#3401—591nomaximal, Sylow
353C22×C59—42no—
354C22×C59—42no—
355C22×C59—42no—
356C22×C59—84no—
357C22×C59#55012yes—
358C22×C59#57512yes—
359C22×C59#57712yes—
360C22×C59C23×D411yescharacteristic
361C2×D59—42no—
362C2×D59—42no—
363C2×D59—42no—
364C2×D59—42no—
365C2×D59—42no—
366C2×D59—42no—
367C2×D59—84no—
368C2×D59—84no—
369C4×C59—22no—
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#55012yes—
379C4×C59C22×#4111yescharacteristic
380C4×C59C2×H(5,𝔽2)11yescharacteristic
381Dic59—42no—
382Dic59—42no—
383C2×#559—591no—
384C2×#556D5911yescharacteristic, complemented
385#3401—5916no—
386C2×#497—591no—
387C2×#496—591no—
388C2×#495—591no—
389C2×#464—591no—
390C2×#464—591no—
391C2×#460—591no—
392C2×#463—591no—
393C2×#463—591no—
394C2×#461—591no—
395C2×#446—591no—
396C2×#442—591no—
397C2×#441—591no—
398C2×C4×SD16—591no—
399C2×C59—82no—
400C2×C59#340114yescomplemented
401C2×C59C2×#55011yescharacteristic
402C2×C59C2×#57511yescharacteristic
403C2×C59C2×#57711yescharacteristic
404D59—82no—
405D59—82no—
406C22×Q16—591no—
407C22×Q16—591no—
408C22×SD16—591no—
409C22×SD16—591no—
410C22×SD16—591no—
411C22×SD16—591no—
412C22×SD16—591no—
413C22×D8—591no—
414C22×D8—591no—
415#559—598no—
416#559—1184no—
417#556—24no—
418#556C2×D5918yescomplemented
419C2×C4⋊Q8C2×D5911yescharacteristic
420C2×#127—591no—
421C2×#126—21no—
422C2×#126—21no—
423C2×#124—591no—
424C2×#124—591no—
425C2×#124—1181no—
426C2×#124C2×D5911yescharacteristic
427C2×#124C2×D5911yescharacteristic
428C2×#123—1181no—
429C2×#123—1181no—
430C2×C22⋊Q8—21no—
431C2×C4×Q8—591no—
432C2×C4×Q8C2×D5911yescharacteristic
433C2×C4×Q8C2×D5911yescharacteristic
434C2×C4×Q8C2×D5911yescharacteristic
435C2×C4×D4—591no—
436C2×C4×D4—591no—
437C2×C4×D4—1181no—
438C2×C4×D4C2×D5911yescharacteristic
439C2×#117—21no—
440#497—598no—
441#496—598no—
442#495—598no—
443#464—598no—
444#464—598no—
445#463—598no—
446#463—598no—
447#461—598no—
448#460—598no—
449#446—598no—
450#442—598no—
451#441—598no—
452C4×SD16—598no—
453C2×#106—591no—
454C2×C4⋊C8—591no—
455C2×C4⋊C8—591no—
456C2×C4⋊C8—591no—
457C2×#103—591no—
458C2×#103—591no—
459C2×#103—591no—
460C2×#102—591no—
461C2×#102—591no—
462C2×#102—591no—
463C2×#97—591no—
464C2×#97—591no—
465C2×C4×C8—591no—
466C59C2×#340111yescharacteristic, complemented, Sylow
467C22×Q8—591no—
468C22×Q8C22⋊D5911yescharacteristic
469C22×Q8C22×D5911yescharacteristic
470C22×Q8C22×D5911yescharacteristic
471C22×D4—591no—
472C22×D4—591no—
473C22×D4—1181no—
474C22×D4—1181no—
475C22×D4C22×D5911yescharacteristic
476C23×C4—21no—
477C23×C4—1181no—
478C23×C4—1181no—
479C2×Q16—594no—
480C2×Q16—594no—
481C2×Q16—1184no—
482C2×Q16—2362no—
483C2×SD16—594no—
484C2×SD16—594no—
485C2×SD16—594no—
486C2×SD16—594no—
487C2×SD16—594no—
488C2×SD16—1184no—
489C2×SD16—2362no—
490C2×SD16—2362no—
491C2×SD16—2362no—
492C2×SD16—2362no—
493C2×D8—594no—
494C2×D8—594no—
495C2×D8—1184no—
496C2×D8—2362no—
497C22×C8—591no—
498C22×C8—591no—
499C22×C8—591no—
500C22×C8—591no—
501C4⋊Q8—22no—
502C4⋊Q8C22×D5914yes—
503#127—594no—
504#127—1182no—
505#126—28no—
506#126—28no—
507#124—22no—
508#124—22no—
509#124—594no—
510#124—594no—
511#124—1188no—
512#124—1182no—
513#124—1182no—
514#124C22×D5914yes—
515#124C22×D5914yes—
516#123—1188no—
517#123—1188no—
518C22⋊Q8—28no—
519C4×Q8—22no—
520C4×Q8—22no—
521C4×Q8—594no—
522C4×Q8—1182no—
523C4×Q8C22⋊D5914yes—
524C4×Q8C22×D5914yes—
525C4×Q8C22×D5914yes—
526C4×Q8C22×D5914yes—
527C4×D4—22no—
528C4×D4—594no—
529C4×D4—594no—
530C4×D4—1188no—
531C4×D4—1182no—
532C4×D4—1182no—
533C4×D4C22×D5914yes—
534#117—28no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—591no—
540C2×C4⋊C4—1181no—
541C2×C4⋊C4C22⋊D5911yescharacteristic
542C2×C4⋊C4C22⋊D5911yescharacteristic
543C2×C4⋊C4C22⋊D5911yescharacteristic
544C2×C4⋊C4C22×D5911yescharacteristic
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—1181no—
551C2×C22⋊C4—1181no—
552C2×C22⋊C4—1181no—
553C2×C22⋊C4—1181no—
554C2×C22⋊C4—1181no—
555C2×C22⋊C4—1181no—
556C2×C42—21no—
557C2×C42—21no—
558C2×C42—1181no—
559C2×C42C22×D5911yescharacteristic
560C2×C42C22×D5911yescharacteristic
561C2×C42C22×D5911yescharacteristic
562#106—594no—
563C4⋊C8—594no—
564C4⋊C8—594no—
565C4⋊C8—594no—
566#103—594no—
567#103—594no—
568#103—594no—
569#102—594no—
570#102—594no—
571#102—594no—
572#97—594no—
573#97—594no—
574C4×C8—594no—
575C24—21no—
576C24—1181no—
577C24—1181no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—22no—
581C2×Q8—22no—
582C2×Q8—22no—
583C2×Q8—22no—
584C2×Q8—42no—
585C2×Q8—592no—
586C2×Q8—1181no—
587C2×Q8—1182no—
588C2×Q8—1182no—
589C2×Q8C2×C22⋊D5914yes—
590C2×Q8C23×D5912yes—
591C2×Q8C23×D5912yes—
592C2×D4—21no—
593C2×D4—22no—
594C2×D4—22no—
595C2×D4—592no—
596C2×D4—592no—
597C2×D4—1184no—
598C2×D4—1184no—
599C2×D4—1181no—
600C2×D4—1181no—
601C2×D4—1182no—
602C2×D4—1182no—
603C2×D4—1182no—
604C2×D4—1182no—
605C2×D4—4722no—
606C2×D4—2364no—
607C2×D4C23×D5912yes—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—24no—
612C22×C4—44no—
613C22×C4—1181no—
614C22×C4—1181no—
615C22×C4—1184no—
616C22×C4—1184no—
617C22×C4—4722no—
618C22×C4—4722no—
619C22×C4C2×C22⋊D5911yescharacteristic
620C22×C4C2×C22⋊D5911yescharacteristic
621C22×C4C2×C22⋊D5911yescharacteristic
622C22×C4C2×C22⋊D5911yescharacteristic
623C22×C4C2×C22⋊D5911yescharacteristic
624C22×C4C2×C22⋊D5911yescharacteristic
625C22×C4C23×D5911yescharacteristic
626Q16—1188no—
627Q16—2364no—
628SD16—1188no—
629SD16—2364no—
630SD16—2364no—
631SD16—2364no—
632SD16—2364no—
633D8—1188no—
634D8—2364no—
635C2×C8—594no—
636C2×C8—592no—
637C2×C8—592no—
638C2×C8—592no—
639C2×C8—592no—
640C2×C8—1182no—
641C2×C8—1182no—
642C2×C8—1182no—
643C4⋊C4—24no—
644C4⋊C4—24no—
645C4⋊C4—24no—
646C4⋊C4—24no—
647C4⋊C4—21no—
648C4⋊C4—592no—
649C4⋊C4—1181no—
650C4⋊C4—1184no—
651C4⋊C4C2×C22⋊D5914yes—
652C4⋊C4C2×C22⋊D5914yes—
653C4⋊C4C2×C22⋊D5914yes—
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⋊C4—1184no—
665C22⋊C4—1184no—
666C42—24no—
667C42—24no—
668C42—1184no—
669C42C2×C22⋊D5912yes—
670C42C2×C22⋊D5912yes—
671C42C2×C22⋊D5912yes—
672C42C23×D5912yes—
673C42C23×D5912yes—
674C42C23×D5912yes—
675C23—22no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—1182no—
680C23—1182no—
681C23—2362no—
682C23—2362no—
683C23—2362no—
684C23—2362no—
685C23—2362no—
686C23—2362no—
687C23C22×C22⋊D5911yescharacteristic
688Q8—22no—
689Q8—22no—
690Q8—22no—
691Q8—22no—
692Q8—44no—
693Q8—42no—
694Q8—42no—
695Q8—1182no—
696Q8—1182no—
697Q8—2362no—
698D4—22no—
699D4—22no—
700D4—42no—
701D4—1182no—
702D4—1182no—
703D4—1182no—
704D4—1182no—
705D4—4724no—
706D4—2368no—
707D4—2362no—
708D4—2362no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—48no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—1182no—
723C2×C4—1182no—
724C2×C4—4724no—
725C2×C4—4724no—
726C2×C4—2362no—
727C2×C4—2362no—
728C2×C4C22×C22⋊D5912yes—
729C2×C4C22×C22⋊D5912yes—
730C2×C4C22×C22⋊D5912yes—
731C2×C4C22×C22⋊D5912yes—
732C2×C4C22×C22⋊D5912yes—
733C2×C4C22×C22⋊D5912yes—
734C2×C4C22×C22⋊D5911yescharacteristic
735C2×C4#41×D5912yes—
736C2×C4#1427377312yes—
737C2×C4C24×D5911yescharacteristic
738C8—594no—
739C8—1182no—
740C8—1182no—
741C8—1182no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—84no—
746C22—4724no—
747C22—4724no—
748C22—2362no—
749C22—2362no—
750C22—2362no—
751C22—2362no—
752C22—2362no—
753C22—2362no—
754C22#1683807112yes—
755C22#1683820012yes—
756C22#1683821012yes—
757C22C23×C22⋊D5911yescharacteristic
758C4—22no—
759C4—22no—
760C4—22no—
761C4—22no—
762C4—22no—
763C4—22no—
764C4—42no—
765C4—42no—
766C4—42no—
767C4—2362no—
768C4—2362no—
769C4#1683807112yes—
770C4C2×#41×D5911yescharacteristic
771C4C2×#1427377311yescharacteristic
772C2—82no—
773C2—4722no—
774C2—4722no—
775C2#2143716214yesdirect product factor
776C2C2×#1683807111yescharacteristic
777C2C2×#1683820011yescharacteristic
778C2C2×#1683821011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#556C2
socleC23×C59C22×D4
prime radicalC2×#16837792C2
hypercenterC2×#556D59
hypocenterC59C2×#3401
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. C2×#16838137C2semidirect
2. #21437162C2direct (N × H)
3. C2×#16837794C2semidirect
5. C2×#16837784C2semidirect
6. C2×#16837624C2semidirect
7. C2×#16837621C2semidirect
8. C2×#16837602C2semidirect
9. C2×#16837617C2semidirect
10. C2×#16837614C2semidirect
11. C2×#16837604C2semidirect
12. C2×#16837533C2semidirect
13. C2×#16837512C2semidirect
14. C2×#16837507C2semidirect
15. C2×C4×#11745671C2semidirect
16. C2×C59×#556C2semidirect
27. #16838137C22semidirect
38. #16837794C22semidirect
40. #16837784C22semidirect
41. #16837624C22semidirect
42. #16837621C22semidirect
43. #16837617C22semidirect
44. #16837614C22semidirect
45. #16837604C22semidirect
46. #16837602C22semidirect
47. #16837533C22semidirect
48. #16837512C22semidirect
49. #16837507C22semidirect
50. C4×#11745671C22semidirect
65. C59×#556C22semidirect
384. C2×#556D59semidirect
400. C2×C59#3401semidirect
418. #556C2×D59semidirect
466. C59C2×#3401semidirect
775. C2#21437162direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168381372
#214371622
C2×#168377942
C2×#168377922
C2×#168377842
C2×#168376242
C2×#168376212
C2×#168376022
C2×#168376172
C2×#168376142
C2×#168376042
C2×#168375332
C2×#168375122
C2×#168375072
C2×C4×#117456712
C2×C59×#5562
C2×#340159