Finite Group Databasebeta

← C2×#21432952 #29452822

Subgroups — C2×#21432952 #29452822

Order 15104.

2870 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×SD16×D59C211yesmaximal, characteristic
2C2×#16837878C211yesmaximal, characteristic, complemented
3C2×#16837874C211yesmaximal, characteristic
4#21432952C2116yesmaximal, direct product factor
5C2×#16837504C211yesmaximal, characteristic, complemented
6C2×#16837503C211yesmaximal, characteristic, complemented
7C2×#16837501C211yesmaximal, characteristic, complemented
8C2×#16837493C211yesmaximal, characteristic, complemented
9C2×C4×#11745671C211yesmaximal, characteristic, complemented
10C2×C4×#11745670C211yesmaximal, characteristic, complemented
11C2×#16837487C211yesmaximal, characteristic, complemented
12C2×#16837439C211yesmaximal, characteristic, complemented
13C2×#16837409C211yesmaximal, characteristic, complemented
14C2×#16837405C211yesmaximal, characteristic
15C2×#16837359C211yesmaximal, characteristic, complemented
16C2×C59×#440C211yesmaximal, characteristic, complemented
17C22×Q8×D59C2211yescharacteristic
18C22×D4×D59C2211yescharacteristic
19C22×#11745660C2211yescharacteristic
20C22×#11745670C2211yescharacteristic
21C22×#11745671C2211yescharacteristic
22C2×SD16×D59C4116yescomplemented
23C2×SD16×D59C2218yes—
24C22×#11745659C2211yescharacteristic
25C22×C8×D59C2211yescharacteristic
26#16837878—24no—
27#16837878C2218yescomplemented
28#16837874—24no—
29#16837874C2218yes—
30C2×Q8×Dic59C2211yescharacteristic, complemented
31C2×C4×Dic118—21no—
32C2×C4×Dic118C2211yescharacteristic, complemented
33C2×#14273692—21no—
34C2×#14273692C2211yescharacteristic, complemented
35C2×C4×D236C2211yescharacteristic
36C2×D4×Dic59C2211yescharacteristic
37C2×#14273689C2211yescharacteristic
38C2×C4×C22⋊D59—21no—
39C2×(C22⋊D59)⋊C4—21no—
40C2×#14273685—21no—
41C2×#14273685C2211yescharacteristic
42C2×#14273685C2211yescharacteristic
43C2×#14273684—21no—
44C2×#14273684C2211yescharacteristic
45C22×(C2×D59)⋊C4—21no—
46C2×C22⋊C4×D59—21no—
47#16837504C2218yescomplemented
48#16837503C2218yescomplemented
49#16837501C2218yescomplemented
50#16837493C2218yescomplemented
51C4×#11745671C2218yescomplemented
52C4×#11745670C2218yescomplemented
53#16837487C2218yescomplemented
54#16837439C2218yescomplemented
55C2×#14273661C2211yescharacteristic, complemented
56C2×#14273658C2211yescharacteristic, complemented
57C2×#14273658C2211yescharacteristic, complemented
58#16837409C2218yescomplemented
59#16837405C2218yes—
60C2×#14273652C2211yescharacteristic, complemented
61C2×#14273651C2211yescharacteristic, complemented
62C2×#14273650C2211yescharacteristic, complemented
63C2×#14273649C2211yescharacteristic
64C2×#14273648C2211yescharacteristic
65C2×#14273647C2211yescharacteristic
66#16837359C2218yescomplemented
67C2×#14273637C2211yescharacteristic, complemented
68C2×C4×C59⋊C8C2211yescharacteristic, complemented
69C2×C8×Dic59C2211yescharacteristic, complemented
70C22×SD16×C59C2211yescharacteristic
71C2×C4×Q8×C59C2211yescharacteristic, complemented
72C2×C4×D4×C59C2211yescharacteristic
73C59×#440C2218yescomplemented
74C2×#107×C59C2211yescharacteristic, complemented
75C2×#103×C59C2211yescharacteristic, complemented
76C2×#102×C59C2211yescharacteristic
77C2×#97×C59C2211yescharacteristic, complemented
78C24×D59—21no—
79C22×Dic118—21no—
80C22×Dic118C2311yescharacteristic
81C2×Q8×D59—22no—
82C2×Q8×D59—24no—
83C2×Q8×D59C2×C418yescomplemented
84C2×Q8×D59C2314yes—
85C22×D236C2311yescharacteristic
86C22×C22⋊D59—21no—
87C2×D4×D59—22no—
88C2×D4×D59—24no—
89C2×D4×D59C2×C418yes—
90C2×D4×D59C2314yes—
91C23×Dic59—21no—
92C22×C4×D59—21no—
93C22×C4×D59—21no—
94C22×C4×D59—21no—
95C22×C4×D59C2311yescharacteristic
96C2×#11745660C2×C418yescomplemented
97C2×#11745660C2314yes—
98C2×#11745670C2×C418yescomplemented
99C2×#11745670C2314yes—
100C2×#11745671C2×C418yescomplemented
101C2×#11745671C2314yes—
102SD16×D59C2×C4164yescomplemented
103C2×#11745659—24no—
104C2×#11745659C2314yes—
105C22×C59⋊C8C2311yescharacteristic
106C22×C59⋊C8C2311yescharacteristic
107C2×C8×D59C2×C418yescomplemented
108C2×C8×D59C2314yes—
109Q8×Dic59—22no—
110Q8×Dic59C2314yescomplemented
111C4×Dic118—22no—
112C4×Dic118—28no—
113C4×Dic118C2314yescomplemented
114#14273692—28no—
115#14273692—22no—
116#14273692C2314yescomplemented
117C4×D236—22no—
118C4×D236C2314yes—
119D4×Dic59—22no—
120D4×Dic59C2314yes—
121#14273689—22no—
122#14273689C2314yes—
123C4×C22⋊D59—28no—
124(C22⋊D59)⋊C4—28no—
125#14273685—22no—
126#14273685—22no—
127#14273685—28no—
128#14273685C2314yes—
129#14273685C2314yes—
130#14273684—28no—
131#14273684D414yes—
132#14273684C2314yes—
133C2×C4⋊Dic59—21no—
134C2×C4⋊Dic59C2311yescharacteristic
135C2×C4⋊Dic59C2311yescharacteristic
136C2×Dic59⋊C4—21no—
137C2×Dic59⋊C4—21no—
138C2×Dic59⋊C4D411yescharacteristic
139C2×Dic59⋊C4D411yescharacteristic
140C2×C22⋊Dic59—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—28no—
146C2×(C2×D59)⋊C4D411yescharacteristic
147C2×(C2×D59)⋊C4D411yescharacteristic
148C22⋊C4×D59—28no—
149C2×C4×Dic59—21no—
150C2×C4×Dic59—21no—
151C2×C4×Dic59—21no—
152C2×C4×Dic59—21no—
153C2×C4×Dic59—21no—
154C2×C4×Dic59C2311yescharacteristic
155#14273661C2314yescomplemented
156#14273658C2314yescomplemented
157#14273658C2314yescomplemented
158#14273652C2314yescomplemented
159#14273651C2314yescomplemented
160#14273650C2314yescomplemented
161#14273649C2314yes—
162#14273648C2314yes—
163#14273647C2314yes—
164#14273637C2314yescomplemented
165C4×C59⋊C8C2314yescomplemented
166C8×Dic59C2314yescomplemented
167C22×Q8×C59C2311yescharacteristic
168C22×D4×C59C2311yescharacteristic
169C23×C4×C59—21no—
170C2×SD16×C59C2×C418yescomplemented
171C2×SD16×C59C2314yes—
172C22×C8×C59C2311yescharacteristic
173C22×C8×C59C2311yescharacteristic
174C4×Q8×C59—22no—
175C4×Q8×C59C2314yescomplemented
176C4×D4×C59—22no—
177C4×D4×C59C2314yes—
178C2×C4⋊C4×C59—21no—
179C2×C4⋊C4×C59C2311yescharacteristic
180C2×C4⋊C4×C59C2311yescharacteristic
181C2×C22⋊C4×C59—21no—
182C2×C42×C59—21no—
183C2×C42×C59C2311yescharacteristic
184#107×C59C2314yescomplemented
185#103×C59C2314yescomplemented
186#102×C59C2314yes—
187#97×C59C2314yescomplemented
188C24×C59—21no—
189C23×D59—21no—
190C23×D59—28no—
191C23×D59—24no—
192C23×D59—82no—
193C23×D59—82no—
194C23×D59C2×D411yescharacteristic
195C2×Q8×C59—21no—
196C2×Q8×C59—22no—
197C2×Q8×C59C22×C414yes—
198C2×Q8×C59C2412yes—
199C2×D4×C59—21no—
200C2×D4×C59—22no—
201C2×D4×C59C22×C414yes—
202C2×D4×C59C2412yes—
203C22×C4×C59—21no—
204C22×C4×C59—21no—
205C22×C4×C59—21no—
206C22×C4×C59—24no—
207C22×C4×C59—82no—
208C22×C4×C59C2×D411yescharacteristic
209C22×C4×C59C2×D411yescharacteristic
210C22×C4×C59C2411yescharacteristic
211C2×C22⋊D59—28no—
212C2×C22⋊D59—24no—
213C22×Dic59—21no—
214C22×Dic59—21no—
215C22×Dic59—21no—
216C22×Dic59—24no—
217C22×Dic59—82no—
218C22×Dic59C2×D411yescharacteristic
219C22×Dic59C2×D411yescharacteristic
220C22×Dic59C2×D411yescharacteristic
221Q8×D59—216no—
222Q8×D59—28no—
223Q8×D59C22×C4116yescomplemented
224D4×D59—216no—
225D4×D59—28no—
226D4×D59C22×C4116yes—
227C2×D236—21no—
228C2×D236—22no—
229C2×D236C22×C414yes—
230C2×D236C2412yes—
231C2×C4×D59—28no—
232C2×C4×D59—24no—
233C2×C4×D59—24no—
234C2×C4×D59—24no—
235C2×C4×D59—82no—
236C2×C4×D59—82no—
237C2×C4×D59C22×C414yes—
238C2×C4×D59C2×D412yes—
239C2×C4×D59#4114yes—
240C2×C4×D59C2412yes—
241C2×Dic118—21no—
242C2×Dic118—22no—
243C2×Dic118—28no—
244C2×Dic118—24no—
245C2×Dic118C22×C414yes—
246C2×Dic118C2412yes—
247SD16×C59C22×C4116yescomplemented
248C2×C8×C59—22no—
249C2×C8×C59C22×C414yes—
250C2×C8×C59C2412yes—
251C2×C8×C59C2412yes—
252C4⋊C4×C59—24no—
253C4⋊C4×C59—21no—
254C4⋊C4×C59—21no—
255C4⋊C4×C59C2412yes—
256C4⋊C4×C59C2412yes—
257C22⋊C4×C59—24no—
258C42×C59—24no—
259C42×C59C2×D412yes—
260C42×C59C2412yes—
261C22⋊Dic59—24no—
262#11745671C22×C4116yescomplemented
263#11745670C22×C4116yescomplemented
264(C2×D59)⋊C4—24no—
265(C2×D59)⋊C4—24no—
266(C2×D59)⋊C4—24no—
267(C2×D59)⋊C4—24no—
268(C2×D59)⋊C4C2×D414yes—
269(C2×D59)⋊C4C2×D414yes—
270C4⋊Dic59—21no—
271C4⋊Dic59—21no—
272C4⋊Dic59—24no—
273C4⋊Dic59C2412yes—
274C4⋊Dic59C2412yes—
275Dic59⋊C4—24no—
276Dic59⋊C4—24no—
277Dic59⋊C4C2×D414yes—
278Dic59⋊C4C2×D414yes—
279C4×Dic59—24no—
280C4×Dic59—24no—
281C4×Dic59—24no—
282C4×Dic59—24no—
283C4×Dic59—24no—
284C4×Dic59C2×D412yes—
285C4×Dic59C2412yes—
286C2×C59⋊C8—22no—
287C2×C59⋊C8C22×C414yes—
288C2×C59⋊C8C2412yes—
289C2×C59⋊C8C2412yes—
290#11745660C22×C4116yescomplemented
291#11745659—28no—
292C8×D59C22×C4116yescomplemented
293C23×C59—24no—
294C23×C59—22no—
295C23×C59—42no—
296C23×C59—42no—
297C23×C59C22×D411yescharacteristic
298C22×D59—22no—
299C22×D59—22no—
300C22×D59—24no—
301C22×D59—22no—
302C22×D59—216no—
303C22×D59—42no—
304C22×D59—42no—
305C22×D59—816no—
306C22×D59—84no—
307C22×D59—84no—
308C22×D59C4×D414yes—
309C22×D59C22×D412yes—
310Q8×C59—24no—
311Q8×C59—22no—
312Q8×C59C23×C414yes—
313D4×C59—24no—
314D4×C59—22no—
315D4×C59C23×C414yes—
316C2×C4×C59—24no—
317C2×C4×C59—22no—
318C2×C4×C59—22no—
319C2×C4×C59—22no—
320C2×C4×C59—22no—
321C2×C4×C59—22no—
322C2×C4×C59—42no—
323C2×C4×C59—42no—
324C2×C4×C59—84no—
325C2×C4×C59C23×C412yes—
326C2×C4×C59C22×D412yes—
327C2×C4×C59C22×D412yes—
328C2×C4×C59C22×D411yescharacteristic
329C2×C4×C59C2×#4112yes—
330C2×C4×C59C2511yescharacteristic
331C22⋊D59—216no—
332C2×Dic59—24no—
333C2×Dic59—22no—
334C2×Dic59—22no—
335C2×Dic59—22no—
336C2×Dic59—22no—
337C2×Dic59—22no—
338C2×Dic59—42no—
339C2×Dic59—42no—
340C2×Dic59—84no—
341C2×Dic59C4×D414yes—
342C2×Dic59C22×D412yes—
343C2×Dic59C22×D412yes—
344C2×Dic59C22×D412yes—
345D236—24no—
346D236—22no—
347D236C23×C414yes—
348C4×D59—216no—
349C4×D59—84no—
350C4×D59—84no—
351C4×D59C4×D418yes—
352C4×D59C23×C414yes—
353C4×D59C2×#4114yes—
354Dic118—24no—
355Dic118—22no—
356Dic118—216no—
357Dic118C23×C414yes—
358C8×C59—22no—
359C8×C59C23×C414yes—
360C59⋊C8—22no—
361C59⋊C8C23×C414yes—
362C2×#2949—591nomaximal, Sylow
363C22×C59—24no—
364C22×C59—48no—
365C22×C59—42no—
366C22×C59—42no—
367C22×C59C2×C4×D412yes—
368C22×C59#57712yes—
369C22×C59#57712yes—
370C22×C59C23×D411yescharacteristic
371C2×D59—28no—
372C2×D59—22no—
373C2×D59—22no—
374C2×D59—24no—
375C2×D59—48no—
376C2×D59—42no—
377C2×D59—42no—
378C2×D59—816no—
379C2×D59C2×C4×D414yes—
380C4×C59—24no—
381C4×C59—22no—
382C4×C59—22no—
383C4×C59—42no—
384C4×C59—42no—
385C4×C59C2×C4×D412yes—
386C4×C59C24×C411yescharacteristic
387C4×C59C22×#4111yescharacteristic
388Dic59—24no—
389Dic59—22no—
390Dic59—22no—
391Dic59—42no—
392Dic59—42no—
393Dic59C2×C4×D414yes—
394C23×SD16—591no—
395C2×#519—591no—
396C2×#518—591no—
397#2949—5916no—
398C2×#440—591no—
399C2×#440—591no—
400C2×#440—591no—
401C2×#440D5911yescharacteristic, complemented
402C2×C4×SD16—591no—
403C2×C4×SD16—591no—
404C2×C4×SD16—591no—
405C2×C4×SD16—591no—
406C2×#427—591no—
407C2×#419—591no—
408C2×#418—591no—
409C2×#405—591no—
410C2×C59—44no—
411C2×C59#294914yescomplemented
412C2×C59C22×C4×D411yescharacteristic
413C2×C59C2×#57711yescharacteristic
414C2×C59C2×#57711yescharacteristic
415D59—24no—
416D59—44no—
417C23×Q8—591no—
418C23×D4—591no—
419C22×SD16—591no—
420C22×SD16—591no—
421C22×SD16—5916no—
422C22×SD16—598no—
423C22×SD16—591no—
424C22×SD16C2×D5911yescharacteristic
425C22×M16—591no—
426C23×C8—591no—
427#519—598no—
428#519—1184no—
429#518—598no—
430#518—1184no—
431C2×C4×Q8—591no—
432C2×C4×Q8—591no—
433C2×C4×Q8—591no—
434C2×C4×Q8—1181no—
435C2×C4×Q8—1181no—
436C2×C4×Q8C2×D5911yescharacteristic, complemented
437C2×C4×D4—591no—
438C2×C4×D4—591no—
439C2×C4×D4—591no—
440C2×C4×D4—1181no—
441C2×C4×D4—1181no—
442C2×C4×D4C2×D5911yescharacteristic
443C2×#117—591no—
444C2×#117—591no—
445C2×#117—591no—
446C2×#117—1181no—
447C2×#117—1181no—
448C22×C22⋊C4—1181no—
449C22×C22⋊C4—1181no—
450#440—598no—
451#440—598no—
452#440—598no—
453#440C2×D5918yescomplemented
454C4×SD16—598no—
455C4×SD16—598no—
456C4×SD16—598no—
457C4×SD16—598no—
458#427—598no—
459C2×#107—591no—
460C2×#107C2×D5911yescharacteristic, complemented
461C2×#106—591no—
462C2×#106—591no—
463#419—598no—
464#418—598no—
465C2×#103—591no—
466C2×#103—591no—
467C2×#103—591no—
468C2×#103C2×D5911yescharacteristic, complemented
469C2×#102—591no—
470C2×#102—591no—
471C2×#102—591no—
472C2×#102C2×D5911yescharacteristic
473#405—598no—
474C2×#97—591no—
475C2×#97C2×D5911yescharacteristic, complemented
476C2×C4×C8—591no—
477C2×C4×C8—591no—
478C59C2×#294911yescharacteristic, complemented, Sylow
479C25—1181no—
480C22×Q8—598no—
481C22×Q8—594no—
482C22×Q8—591no—
483C22×Q8—1181no—
484C22×Q8—1182no—
485C22×Q8—1184no—
486C22×Q8C22×D5911yescharacteristic
487C22×D4—598no—
488C22×D4—594no—
489C22×D4—591no—
490C22×D4—1182no—
491C22×D4—1184no—
492C22×D4—1181no—
493C22×D4C22×D5911yescharacteristic
494C23×C4—21no—
495C23×C4—591no—
496C23×C4—1181no—
497C23×C4—1181no—
498C23×C4—1181no—
499C23×C4—1181no—
500C2×SD16—598no—
501C2×SD16—594no—
502C2×SD16—598no—
503C2×SD16—594no—
504C2×SD16—5964no—
505C2×SD16—598no—
506C2×SD16—594no—
507C2×SD16C4×D5918yescomplemented
508C2×SD16C22×D5914yes—
509C2×M16—594no—
510C2×M16—1184no—
511C22×C8—591no—
512C22×C8—598no—
513C22×C8—594no—
514C22×C8—591no—
515C22×C8C22×D5911yescharacteristic
516C22×C8C22×D5911yescharacteristic
517C4×Q8—22no—
518C4×Q8—594no—
519C4×Q8—594no—
520C4×Q8—594no—
521C4×Q8—1188no—
522C4×Q8—1182no—
523C4×Q8—1182no—
524C4×Q8—1188no—
525C4×Q8—1182no—
526C4×Q8C22×D5914yescomplemented
527C4×D4—22no—
528C4×D4—594no—
529C4×D4—594no—
530C4×D4—594no—
531C4×D4—1182no—
532C4×D4—1182no—
533C4×D4—1188no—
534C4×D4—1188no—
535C4×D4—1182no—
536C4×D4C22×D5914yes—
537#117—594no—
538#117—594no—
539#117—594no—
540#117—594no—
541#117—1188no—
542#117—1188no—
543#117—1182no—
544#117—1182no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—591no—
547C2×C4⋊C4—591no—
548C2×C4⋊C4—591no—
549C2×C4⋊C4—591no—
550C2×C4⋊C4—1181no—
551C2×C4⋊C4—1181no—
552C2×C4⋊C4—1181no—
553C2×C4⋊C4C22×D5911yescharacteristic
554C2×C4⋊C4C22×D5911yescharacteristic
555C2×C22⋊C4—21no—
556C2×C22⋊C4—591no—
557C2×C22⋊C4—591no—
558C2×C22⋊C4—1188no—
559C2×C22⋊C4—1188no—
560C2×C22⋊C4—1181no—
561C2×C22⋊C4—1181no—
562C2×C22⋊C4—1181no—
563C2×C22⋊C4—1181no—
564C2×C22⋊C4—1181no—
565C2×C42—21no—
566C2×C42—591no—
567C2×C42—1181no—
568C2×C42—1181no—
569C2×C42—1181no—
570C2×C42—1181no—
571C2×C42—1181no—
572C2×C42C22×D5911yescharacteristic
573#107—594no—
574#107C22×D5914yescomplemented
575#106—594no—
576#106—594no—
577#103—594no—
578#103—594no—
579#103—594no—
580#103C22×D5914yescomplemented
581#102—594no—
582#102—594no—
583#102—594no—
584#102C22×D5914yes—
585#97—594no—
586#97C22×D5914yescomplemented
587C4×C8—594no—
588C4×C8—594no—
589C24—21no—
590C24—591no—
591C24—1184no—
592C24—1188no—
593C24—1181no—
594C24—4722no—
595C24—4722no—
596C2×Q8—21no—
597C2×Q8—22no—
598C2×Q8—5916no—
599C2×Q8—594no—
600C2×Q8—592no—
601C2×Q8—1184no—
602C2×Q8—1188no—
603C2×Q8—1188no—
604C2×Q8—11816no—
605C2×Q8—1181no—
606C2×Q8—1182no—
607C2×Q8C2×C4×D5914yes—
608C2×Q8C23×D5912yes—
609C2×D4—21no—
610C2×D4—22no—
611C2×D4—5916no—
612C2×D4—594no—
613C2×D4—592no—
614C2×D4—1188no—
615C2×D4—11816no—
616C2×D4—1184no—
617C2×D4—1188no—
618C2×D4—1181no—
619C2×D4—1182no—
620C2×D4C2×C4×D5914yes—
621C2×D4C23×D5912yes—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—24no—
626C22×C4—82no—
627C22×C4—591no—
628C22×C4—594no—
629C22×C4—592no—
630C22×C4—594no—
631C22×C4—592no—
632C22×C4—591no—
633C22×C4—591no—
634C22×C4—1184no—
635C22×C4—1184no—
636C22×C4—1188no—
637C22×C4—1184no—
638C22×C4—1181no—
639C22×C4—1181no—
640C22×C4—1181no—
641C22×C4—1184no—
642C22×C4—4722no—
643C22×C4—4722no—
644C22×C4—4722no—
645C22×C4D4×D5911yescharacteristic
646C22×C4D4×D5911yescharacteristic
647C22×C4C23×D5911yescharacteristic
648SD16—5916no—
649SD16—5916no—
650SD16—5916no—
651SD16C2×C4×D59116yescomplemented
652M16—1188no—
653C2×C8—22no—
654C2×C8—594no—
655C2×C8—592no—
656C2×C8—5916no—
657C2×C8—592no—
658C2×C8—1182no—
659C2×C8C2×C4×D5914yes—
660C2×C8C23×D5912yes—
661C2×C8C23×D5912yes—
662C4⋊C4—24no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—594no—
666C4⋊C4—594no—
667C4⋊C4—592no—
668C4⋊C4—592no—
669C4⋊C4—1184no—
670C4⋊C4—1184no—
671C4⋊C4—1181no—
672C4⋊C4—1181no—
673C4⋊C4—1184no—
674C4⋊C4C23×D5912yes—
675C4⋊C4C23×D5912yes—
676C22⋊C4—24no—
677C22⋊C4—594no—
678C22⋊C4—594no—
679C22⋊C4—1184no—
680C22⋊C4—1184no—
681C22⋊C4—1184no—
682C22⋊C4—1184no—
683C22⋊C4—1184no—
684C42—24no—
685C42—592no—
686C42—592no—
687C42—1184no—
688C42—1184no—
689C42—1184no—
690C42—1184no—
691C42—1184no—
692C42D4×D5912yes—
693C42C23×D5912yes—
694C23—22no—
695C23—24no—
696C23—42no—
697C23—42no—
698C23—592no—
699C23—594no—
700C23—11816no—
701C23—1182no—
702C23—1182no—
703C23—1182no—
704C23—1184no—
705C23—47216no—
706C23—4724no—
707C23—4724no—
708C23—2362no—
709C23—2362no—
710C23C2×D4×D5911yescharacteristic
711Q8—22no—
712Q8—24no—
713Q8—594no—
714Q8—11816no—
715Q8—1182no—
716Q8—1184no—
717Q8C22×C4×D5914yes—
718D4—22no—
719D4—24no—
720D4—594no—
721D4—11816no—
722D4—1182no—
723D4—1184no—
724D4C22×C4×D5914yes—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—24no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—84no—
734C2×C4—592no—
735C2×C4—594no—
736C2×C4—594no—
737C2×C4—594no—
738C2×C4—598no—
739C2×C4—592no—
740C2×C4—592no—
741C2×C4—11816no—
742C2×C4—1182no—
743C2×C4—1182no—
744C2×C4—1182no—
745C2×C4—1184no—
746C2×C4—1182no—
747C2×C4—1182no—
748C2×C4—4724no—
749C2×C4—4724no—
750C2×C4—4724no—
751C2×C4—2362no—
752C2×C4—2362no—
753C2×C4C22×C4×D5912yes—
754C2×C4C2×D4×D5912yes—
755C2×C4C2×D4×D5912yes—
756C2×C4C2×D4×D5911yescharacteristic
757C2×C4#41×D5912yes—
758C2×C4C24×D5911yescharacteristic
759C8—22no—
760C8—594no—
761C8—1182no—
762C8C22×C4×D5914yes—
763C22—24no—
764C22—48no—
765C22—42no—
766C22—42no—
767C22—594no—
768C22—1188no—
769C22—1182no—
770C22—1182no—
771C22—1184no—
772C22—47216no—
773C22—2368no—
774C22—2362no—
775C22—2362no—
776C22C4×D4×D5912yes—
777C22#1683821112yes—
778C22#1683821212yes—
779C22C22×D4×D5911yescharacteristic
780C4—24no—
781C4—22no—
782C4—22no—
783C4—42no—
784C4—42no—
785C4—594no—
786C4—1184no—
787C4—1182no—
788C4—1182no—
789C4—2362no—
790C4—2362no—
791C4C4×D4×D5912yes—
792C4C23×C4×D5911yescharacteristic
793C4C2×#41×D5911yescharacteristic
794C2—44no—
795C2—1184no—
796C2—2364no—
797C2#2143295214yesdirect product factor
798C2C2×C4×D4×D5911yescharacteristic
799C2C2×#1683821111yescharacteristic
800C2C2×#1683821211yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutatorC4×C59C24×C4
FrattiniC2×C4C24×D59
FittingC2×C59×#440C2
socleC23×C59C22×D4
prime radicalC22×D4×D59C22
cosocleC2×C4×C59C25
hypercenterC2×#440D59
hypocenterC59C2×#2949
LCSG ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
2. C2×#16837878C2semidirect
4. #21432952C2direct (N × H)
5. C2×#16837504C2semidirect
6. C2×#16837503C2semidirect
7. C2×#16837501C2semidirect
8. C2×#16837493C2semidirect
9. C2×C4×#11745671C2semidirect
10. C2×C4×#11745670C2semidirect
11. C2×#16837487C2semidirect
12. C2×#16837439C2semidirect
13. C2×#16837409C2semidirect
15. C2×#16837359C2semidirect
16. C2×C59×#440C2semidirect
22. C2×SD16×D59C4semidirect
27. #16837878C22semidirect
30. C2×Q8×Dic59C22semidirect
32. C2×C4×Dic118C22semidirect
34. C2×#14273692C22semidirect
47. #16837504C22semidirect
48. #16837503C22semidirect
49. #16837501C22semidirect
50. #16837493C22semidirect
51. C4×#11745671C22semidirect
52. C4×#11745670C22semidirect
53. #16837487C22semidirect
54. #16837439C22semidirect
55. C2×#14273661C22semidirect
56. C2×#14273658C22semidirect
57. C2×#14273658C22semidirect
58. #16837409C22semidirect
60. C2×#14273652C22semidirect
61. C2×#14273651C22semidirect
62. C2×#14273650C22semidirect
66. #16837359C22semidirect
67. C2×#14273637C22semidirect
68. C2×C4×C59⋊C8C22semidirect
69. C2×C8×Dic59C22semidirect
71. C2×C4×Q8×C59C22semidirect
73. C59×#440C22semidirect
74. C2×#107×C59C22semidirect
75. C2×#103×C59C22semidirect
77. C2×#97×C59C22semidirect
83. C2×Q8×D59C2×C4semidirect
96. C2×#11745660C2×C4semidirect
98. C2×#11745670C2×C4semidirect
100. C2×#11745671C2×C4semidirect
102. SD16×D59C2×C4semidirect
107. C2×C8×D59C2×C4semidirect
110. Q8×Dic59C23semidirect
113. C4×Dic118C23semidirect
116. #14273692C23semidirect
155. #14273661C23semidirect
156. #14273658C23semidirect
157. #14273658C23semidirect
158. #14273652C23semidirect
159. #14273651C23semidirect
160. #14273650C23semidirect
164. #14273637C23semidirect
165. C4×C59⋊C8C23semidirect
166. C8×Dic59C23semidirect
170. C2×SD16×C59C2×C4semidirect
175. C4×Q8×C59C23semidirect
184. #107×C59C23semidirect
185. #103×C59C23semidirect
187. #97×C59C23semidirect
223. Q8×D59C22×C4semidirect
247. SD16×C59C22×C4semidirect
262. #11745671C22×C4semidirect
263. #11745670C22×C4semidirect
290. #11745660C22×C4semidirect
292. C8×D59C22×C4semidirect
401. C2×#440D59semidirect
411. C2×C59#2949semidirect
436. C2×C4×Q8C2×D59semidirect
453. #440C2×D59semidirect
460. C2×#107C2×D59semidirect
468. C2×#103C2×D59semidirect
475. C2×#97C2×D59semidirect
478. C59C2×#2949semidirect
507. C2×SD16C4×D59semidirect
526. C4×Q8C22×D59semidirect
574. #107C22×D59semidirect
580. #103C22×D59semidirect
586. #97C22×D59semidirect
651. SD16C2×C4×D59semidirect
797. C2#21432952direct (N × H)

Maximal subgroups

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

subgroupindex
C22×SD16×D592
C2×#168378782
C2×#168378742
#214329522
C2×#168375042
C2×#168375032
C2×#168375012
C2×#168374932
C2×C4×#117456712
C2×C4×#117456702
C2×#168374872
C2×#168374392
C2×#168374092
C2×#168374052
C2×#168373592
C2×C59×#4402
C2×#294959