Finite Group Databasebeta

← C2×#21433603 #29455579

Subgroups — C2×#21433603 #29455579

Order 15104.

2882 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14273754C211yesmaximal, characteristic
2C22×SD16×D59C211yesmaximal, characteristic, complemented
3C2×#16837977C211yesmaximal, characteristic, complemented
4C2×#16837874C211yesmaximal, characteristic, complemented
5#21433603C2116yesmaximal, direct product factor
6C2×#16837620C211yesmaximal, characteristic, complemented
7C2×#16837619C211yesmaximal, characteristic, complemented
8C2×#16837618C211yesmaximal, characteristic, complemented
9C2×#16837617C211yesmaximal, characteristic, complemented
10C2×#16837606C211yesmaximal, characteristic, complemented
11C2×#16837605C211yesmaximal, characteristic, complemented
12C2×#16837604C211yesmaximal, characteristic, complemented
13C2×#16837427C211yesmaximal, characteristic, complemented
14C2×#16837409C211yesmaximal, characteristic, complemented
15C2×#16837397C211yesmaximal, characteristic, complemented
16C2×C59×#461C211yesmaximal, characteristic, complemented
17C22×#11745689C2211yescharacteristic
18C22×Q8×D59C2211yescharacteristic
19C22×D4×D59C2211yescharacteristic
20C2×#14273754—28no—
21C2×#14273754C2218yes—
22C22×#11745660C2211yescharacteristic
23C22×#11745670C2211yescharacteristic
24C22×#11745671C2211yescharacteristic
25C22×#11745671C2211yescharacteristic
26C2×SD16×D59—28no—
27C2×SD16×D59C2218yescomplemented
28C22×D472C2211yescharacteristic
29C22×#11745669C2211yescharacteristic
30C22×#11745659C2211yescharacteristic
31C22×C8×D59C2211yescharacteristic
32#16837977—24no—
33#16837977C2218yescomplemented
34C2×#14273725C2211yescharacteristic, complemented
35C2×#14273716C2211yescharacteristic, complemented
36C2×#14273715C2211yescharacteristic, complemented
37C2×#14273712—21no—
38C2×#14273712—21no—
39C2×#14273705—21no—
40C2×#14273705—21no—
41#16837874—24no—
42#16837874C2218yescomplemented
43C2×C4×D236C2211yescharacteristic
44C2×D4×Dic59C2211yescharacteristic
45C2×#14273689C2211yescharacteristic
46C2×C4×C22⋊D59—21no—
47C2×(C22⋊D59)⋊C4—21no—
48C2×#14273685C2211yescharacteristic
49C2×#14273684C2211yescharacteristic
50C22×(C2×D59)⋊C4—21no—
51C2×C22⋊C4×D59—21no—
52#16837620C2218yescomplemented
53#16837619C2218yescomplemented
54#16837618C2218yescomplemented
55#16837617C2218yescomplemented
56#16837606C2218yescomplemented
57#16837605C2218yescomplemented
58#16837604C2218yescomplemented
59#16837427C2218yescomplemented
60C2×C4⋊(C59⋊C8)C2211yescharacteristic, complemented
61C2×Dic59⋊C8C2211yescharacteristic, complemented
62C2×Dic59⋊C8C2211yescharacteristic, complemented
63#16837409C2218yescomplemented
64#16837397C2218yescomplemented
65C2×#14273652C2211yescharacteristic, complemented
66C2×#14273651C2211yescharacteristic, complemented
67C2×#14273651C2211yescharacteristic, complemented
68C2×#14273650C2211yescharacteristic, complemented
69C2×#14273649C2211yescharacteristic, complemented
70C2×#14273647C2211yescharacteristic, complemented
71C22×SD16×C59C2211yescharacteristic
72C22×SD16×C59C2211yescharacteristic
73C2×C4⋊Q8×C59C2211yescharacteristic, complemented
74C2×C4×D4×C59C2211yescharacteristic
75C59×#461C2218yescomplemented
76C2×C4⋊C8×C59C2211yescharacteristic, complemented
77C2×#103×C59C2211yescharacteristic, complemented
78C2×#103×C59C2211yescharacteristic, complemented
79C24×D59—21no—
80C2×#11745689—22no—
81C2×#11745689—24no—
82C2×#11745689—24no—
83C2×#11745689C2314yes—
84C22×Dic118—21no—
85C22×Dic118C2311yescharacteristic
86C2×Q8×D59—22no—
87C2×Q8×D59—24no—
88C2×Q8×D59—24no—
89C2×Q8×D59C2314yes—
90C22×D236—21no—
91C22×D236C2311yescharacteristic
92C22×D236C2311yescharacteristic
93C22×C22⋊D59—21no—
94C2×D4×D59—22no—
95C2×D4×D59—24no—
96C2×D4×D59D418yes—
97C2×D4×D59C2314yes—
98C23×Dic59—21no—
99C22×C4×D59—21no—
100C22×C4×D59—21no—
101C22×C4×D59—21no—
102C22×C4×D59—21no—
103C22×C4×D59C2311yescharacteristic
104#14273754—232no—
105C2×#11745660—24no—
106C2×#11745660C2314yes—
107C2×#11745670—24no—
108C2×#11745670C2314yes—
109C2×#11745671—24no—
110C2×#11745671—24no—
111C2×#11745671C2314yes—
112C2×#11745671C2314yes—
113SD16×D59—232no—
114C2×D472—24no—
115C2×D472C2314yes—
116C2×#11745669—24no—
117C2×#11745669C2314yes—
118C2×#11745659—24no—
119C2×#11745659C2314yes—
120C22×C59⋊C8C2311yescharacteristic
121C22×C59⋊C8C2311yescharacteristic
122C2×C8×D59—24no—
123C2×C8×D59C2314yes—
124#14273725—22no—
125#14273725C2314yescomplemented
126#14273716—22no—
127#14273716C2314yescomplemented
128#14273715—22no—
129#14273715C2314yescomplemented
130#14273712—28no—
131#14273712—28no—
132#14273705—28no—
133#14273705—28no—
134C4×D236—22no—
135C4×D236C2314yes—
136D4×Dic59—22no—
137D4×Dic59C2314yes—
138#14273689—22no—
139#14273689C2314yes—
140C4×C22⋊D59—28no—
141(C22⋊D59)⋊C4—28no—
142#14273685—22no—
143#14273685C2314yes—
144#14273684D414yes—
145#14273684C2314yes—
146C2×C4⋊Dic59C2311yescharacteristic
147C2×Dic59⋊C4—21no—
148C2×Dic59⋊C4—21no—
149C2×Dic59⋊C4D411yescharacteristic
150C2×Dic59⋊C4D411yescharacteristic
151C2×C22⋊Dic59—21no—
152C2×(C2×D59)⋊C4—21no—
153C2×(C2×D59)⋊C4—21no—
154C2×(C2×D59)⋊C4—21no—
155C2×(C2×D59)⋊C4—21no—
156C2×(C2×D59)⋊C4—21no—
157C2×(C2×D59)⋊C4—21no—
158C2×(C2×D59)⋊C4—21no—
159C2×(C2×D59)⋊C4—28no—
160C2×(C2×D59)⋊C4D411yescharacteristic
161C2×(C2×D59)⋊C4D411yescharacteristic
162C22⋊C4×D59—28no—
163C2×C4×Dic59—21no—
164C2×C4×Dic59C2311yescharacteristic
165C4⋊(C59⋊C8)C2314yescomplemented
166Dic59⋊C8C2314yescomplemented
167Dic59⋊C8C2314yescomplemented
168#14273652C2314yescomplemented
169#14273651C2314yescomplemented
170#14273651C2314yescomplemented
171#14273650C2314yescomplemented
172#14273649C2314yescomplemented
173#14273647C2314yescomplemented
174C22×Q8×C59C2311yescharacteristic
175C22×Q8×C59C2311yescharacteristic
176C22×D4×C59C2311yescharacteristic
177C23×C4×C59—21no—
178C2×SD16×C59—24no—
179C2×SD16×C59—24no—
180C2×SD16×C59C2314yes—
181C2×SD16×C59C2314yes—
182C22×C8×C59C2311yescharacteristic
183C22×C8×C59C2311yescharacteristic
184C4⋊Q8×C59—22no—
185C4⋊Q8×C59C2314yescomplemented
186C4×D4×C59—22no—
187C4×D4×C59C2314yes—
188C2×C4⋊C4×C59—21no—
189C2×C4⋊C4×C59—21no—
190C2×C4⋊C4×C59C2311yescharacteristic
191C2×C22⋊C4×C59—21no—
192C2×C42×C59C2311yescharacteristic
193C4⋊C8×C59C2314yescomplemented
194#103×C59C2314yescomplemented
195#103×C59C2314yescomplemented
196C24×C59—21no—
197C23×D59—21no—
198C23×D59—28no—
199C23×D59—24no—
200C23×D59—21no—
201C23×D59—82no—
202C23×D59—82no—
203C23×D59C2×D411yescharacteristic
204C2×Q8×C59—21no—
205C2×Q8×C59—21no—
206C2×Q8×C59—22no—
207C2×Q8×C59—22no—
208C2×Q8×C59—22no—
209C2×Q8×C59—22no—
210C2×Q8×C59C2412yes—
211C2×Q8×C59C2412yes—
212C2×D4×C59—21no—
213C2×D4×C59—22no—
214C2×D4×C59C2×D414yes—
215C2×D4×C59C2412yes—
216C22×C4×C59—21no—
217C22×C4×C59—21no—
218C22×C4×C59—21no—
219C22×C4×C59—24no—
220C22×C4×C59—82no—
221C22×C4×C59C2×D411yescharacteristic
222C22×C4×C59C2×D411yescharacteristic
223C22×C4×C59C2411yescharacteristic
224C2×C22⋊D59—28no—
225C2×C22⋊D59—24no—
226C22×Dic59—21no—
227C22×Dic59—21no—
228C22×Dic59—24no—
229C22×Dic59—82no—
230C22×Dic59C2×D411yescharacteristic
231C22×Dic59C2×D411yescharacteristic
232C22×Dic59C2×D411yescharacteristic
233#11745689—28no—
234#11745689—28no—
235#11745689—48no—
236Q8×D59—28no—
237Q8×D59—28no—
238Q8×D59—48no—
239D4×D59—216no—
240D4×D59—28no—
241D4×D59C2×D4116yes—
242C2×D236—21no—
243C2×D236—22no—
244C2×D236—22no—
245C2×D236—22no—
246C2×D236—24no—
247C2×D236—21no—
248C2×D236—44no—
249C2×D236C2×D414yes—
250C2×D236C2412yes—
251C2×D236C2412yes—
252C2×C4×D59—24no—
253C2×C4×D59—24no—
254C2×C4×D59—24no—
255C2×C4×D59—24no—
256C2×C4×D59—44no—
257C2×C4×D59—44no—
258C2×C4×D59—82no—
259C2×C4×D59—82no—
260C2×C4×D59C2×D412yes—
261C2×C4×D59C2×D414yes—
262C2×C4×D59#4114yes—
263C2×C4×D59C2412yes—
264C2×Dic118—22no—
265C2×Dic118—22no—
266C2×Dic118—21no—
267C2×Dic118—24no—
268C2×Dic118—44no—
269C2×Dic118C2412yes—
270SD16×C59—28no—
271SD16×C59—28no—
272C2×C8×C59—22no—
273C2×C8×C59—22no—
274C2×C8×C59C2412yes—
275C2×C8×C59C2412yes—
276C4⋊C4×C59—24no—
277C4⋊C4×C59—24no—
278C4⋊C4×C59—21no—
279C4⋊C4×C59C2412yes—
280C22⋊C4×C59—24no—
281C42×C59C2×D412yes—
282C42×C59C2412yes—
283C22⋊Dic59—24no—
284#11745671—28no—
285#11745671—28no—
286#11745670—28no—
287#11745669—28no—
288(C2×D59)⋊C4—24no—
289(C2×D59)⋊C4—24no—
290(C2×D59)⋊C4—24no—
291(C2×D59)⋊C4—24no—
292(C2×D59)⋊C4—24no—
293(C2×D59)⋊C4—24no—
294(C2×D59)⋊C4—24no—
295(C2×D59)⋊C4C2×D414yes—
296(C2×D59)⋊C4C2×D414yes—
297C4⋊Dic59—21no—
298C4⋊Dic59C2412yes—
299Dic59⋊C4—24no—
300Dic59⋊C4—24no—
301Dic59⋊C4C2×D414yes—
302Dic59⋊C4C2×D414yes—
303C4×Dic59—24no—
304C4×Dic59C2×D412yes—
305C4×Dic59C2412yes—
306C2×C59⋊C8—22no—
307C2×C59⋊C8—22no—
308C2×C59⋊C8C2412yes—
309C2×C59⋊C8C2412yes—
310D472—28no—
311#11745660—28no—
312#11745659—28no—
313C8×D59—28no—
314C23×C59—24no—
315C23×C59—22no—
316C23×C59—42no—
317C23×C59—42no—
318C23×C59C22×D411yescharacteristic
319C22×D59—22no—
320C22×D59—22no—
321C22×D59—24no—
322C22×D59—22no—
323C22×D59—216no—
324C22×D59—22no—
325C22×D59—42no—
326C22×D59—42no—
327C22×D59—42no—
328C22×D59—42no—
329C22×D59—42no—
330C22×D59—816no—
331C22×D59—84no—
332C22×D59—84no—
333C22×D59#12114yes—
334C22×D59C22×D412yes—
335Q8×C59—22no—
336Q8×C59—22no—
337Q8×C59—22no—
338Q8×C59—22no—
339Q8×C59—42no—
340Q8×C59—42no—
341D4×C59—24no—
342D4×C59—22no—
343D4×C59C22×D414yes—
344C2×C4×C59—22no—
345C2×C4×C59—22no—
346C2×C4×C59—22no—
347C2×C4×C59—22no—
348C2×C4×C59—22no—
349C2×C4×C59—42no—
350C2×C4×C59—42no—
351C2×C4×C59—42no—
352C2×C4×C59—84no—
353C2×C4×C59C22×D412yes—
354C2×C4×C59C22×D412yes—
355C2×C4×C59C22×D411yescharacteristic
356C2×C4×C59C22×D412yes—
357C2×C4×C59C2×#4112yes—
358C2×C4×C59C2511yescharacteristic
359C22⋊D59—216no—
360C2×Dic59—22no—
361C2×Dic59—22no—
362C2×Dic59—22no—
363C2×Dic59—22no—
364C2×Dic59—42no—
365C2×Dic59—42no—
366C2×Dic59—84no—
367C2×Dic59#12114yes—
368C2×Dic59C22×D412yes—
369C2×Dic59C22×D412yes—
370C2×Dic59C22×D412yes—
371D236—24no—
372D236—22no—
373D236—22no—
374D236—22no—
375D236—48no—
376D236—42no—
377D236C22×D414yes—
378C4×D59—48no—
379C4×D59—48no—
380C4×D59—84no—
381C4×D59—84no—
382C4×D59#12118yes—
383C4×D59C22×D414yes—
384C4×D59C2×#4114yes—
385Dic118—22no—
386Dic118—22no—
387Dic118—42no—
388Dic118—48no—
389C8×C59—22no—
390C8×C59—22no—
391C59⋊C8—22no—
392C59⋊C8—22no—
393C2×#3042—591nomaximal, Sylow
394C22×C59—24no—
395C22×C59—48no—
396C22×C59—42no—
397C22×C59—42no—
398C22×C59C2×#12112yes—
399C22×C59#57712yes—
400C22×C59#57712yes—
401C22×C59C23×D411yescharacteristic
402C2×D59—28no—
403C2×D59—22no—
404C2×D59—22no—
405C2×D59—24no—
406C2×D59—48no—
407C2×D59—42no—
408C2×D59—42no—
409C2×D59—42no—
410C2×D59—42no—
411C2×D59—42no—
412C2×D59—816no—
413C2×D59—84no—
414C2×D59C2×#12114yes—
415C4×C59—22no—
416C4×C59—22no—
417C4×C59—42no—
418C4×C59—42no—
419C4×C59—42no—
420C4×C59C2×#12112yes—
421C4×C59C23×D411yescharacteristic
422C4×C59C22×#4111yescharacteristic
423Dic59—22no—
424Dic59—22no—
425Dic59—42no—
426Dic59—42no—
427Dic59C2×#12114yes—
428C22×AGL(1,ℤ/8)—591no—
429C23×SD16—591no—
430C2×#536—591no—
431C2×#518—591no—
432#3042—5916no—
433C2×#463—591no—
434C2×#463—591no—
435C2×#463—591no—
436C2×#463—591no—
437C2×#461—591no—
438C2×#461—591no—
439C2×#461—591no—
440C2×#461D5911yescharacteristic, complemented
441C2×#424—591no—
442C2×#419—591no—
443C2×#416—591no—
444C2×C59—44no—
445C2×C59#304214yescomplemented
446C2×C59C22×#12111yescharacteristic
447C2×C59C2×#57711yescharacteristic
448C2×C59C2×#57711yescharacteristic
449D59—24no—
450D59—44no—
451D59—82no—
452C22×#41—591no—
453C23×Q8—591no—
454C23×D4—591no—
455C2×AGL(1,ℤ/8)—598no—
456C2×AGL(1,ℤ/8)—1188no—
457C22×SD16—591no—
458C22×SD16—591no—
459C22×SD16—591no—
460C22×SD16—598no—
461C22×SD16—591no—
462C22×SD16—1188no—
463C22×SD16C2×D5911yescharacteristic
464C22×SD16C2×D5911yescharacteristic
465C22×D8—591no—
466C22×D8—591no—
467C22×M16—591no—
468C23×C8—591no—
469#536—598no—
470#536—1184no—
471C2×C4⋊Q8—591no—
472C2×C4⋊Q8C2×D5911yescharacteristic, complemented
473C2×#124—591no—
474C2×#124—591no—
475C2×#123—1181no—
476C2×#123—1181no—
477C2×C22⋊Q8—1181no—
478C2×C22⋊Q8—1181no—
479#518—598no—
480#518—1184no—
481C2×C4×D4—591no—
482C2×C4×D4—591no—
483C2×C4×D4—591no—
484C2×C4×D4—1181no—
485C2×C4×D4—1181no—
486C2×C4×D4C2×D5911yescharacteristic
487C2×#117—591no—
488C2×#117—591no—
489C22×C22⋊C4—1181no—
490C22×C22⋊C4—1181no—
491#463—598no—
492#463—598no—
493#463—598no—
494#463—598no—
495#461—598no—
496#461—598no—
497#461—598no—
498#461C2×D5918yescomplemented
499#424—598no—
500C2×C4⋊C8—591no—
501C2×C4⋊C8—591no—
502C2×C4⋊C8—591no—
503C2×C4⋊C8C2×D5911yescharacteristic, complemented
504#419—598no—
505#416—598no—
506C2×#103—591no—
507C2×#103—591no—
508C2×#103—591no—
509C2×#103—591no—
510C2×#103C2×D5911yescharacteristic, complemented
511C2×#103C2×D5911yescharacteristic, complemented
512C2×#102—591no—
513C2×#102—591no—
514C59C2×#304211yescharacteristic, complemented, Sylow
515C25—1181no—
516C2×#41—594no—
517C2×#41—1182no—
518C2×#41—1184no—
519C2×#41—1184no—
520C22×Q8—594no—
521C22×Q8—591no—
522C22×Q8—1181no—
523C22×Q8—1182no—
524C22×Q8—1184no—
525C22×Q8—1184no—
526C22×Q8C22×D5911yescharacteristic
527C22×Q8C22×D5911yescharacteristic
528C22×D4—598no—
529C22×D4—594no—
530C22×D4—591no—
531C22×D4—591no—
532C22×D4—1181no—
533C22×D4—1182no—
534C22×D4—1184no—
535C22×D4—1181no—
536C22×D4C22×D5911yescharacteristic
537C23×C4—21no—
538C23×C4—591no—
539C23×C4—1181no—
540C23×C4—1181no—
541C23×C4—1181no—
542C23×C4—1181no—
543C23×C4—1181no—
544AGL(1,ℤ/8)—11832no—
545C2×SD16—24no—
546C2×SD16—24no—
547C2×SD16—594no—
548C2×SD16—594no—
549C2×SD16—594no—
550C2×SD16—594no—
551C2×SD16—1184no—
552C2×SD16—11832no—
553C2×SD16—1184no—
554C2×SD16—1184no—
555C2×SD16—1184no—
556C2×SD16C22×D5914yes—
557C2×SD16C22×D5914yes—
558C2×D8—594no—
559C2×D8—594no—
560C2×D8—1184no—
561C2×D8—1184no—
562C2×M16—594no—
563C2×M16—1184no—
564C22×C8—591no—
565C22×C8—591no—
566C22×C8—594no—
567C22×C8—1184no—
568C22×C8C22×D5911yescharacteristic
569C22×C8C22×D5911yescharacteristic
570C4⋊Q8—22no—
571C4⋊Q8—594no—
572C4⋊Q8—1182no—
573C4⋊Q8C22×D5914yescomplemented
574#124—594no—
575#124—594no—
576#124—1182no—
577#124—1182no—
578#123—1188no—
579#123—1188no—
580C22⋊Q8—1188no—
581C22⋊Q8—1188no—
582C4×D4—22no—
583C4×D4—594no—
584C4×D4—594no—
585C4×D4—594no—
586C4×D4—1182no—
587C4×D4—1182no—
588C4×D4—1188no—
589C4×D4—1188no—
590C4×D4—1182no—
591C4×D4C22×D5914yes—
592#117—594no—
593#117—594no—
594#117—594no—
595#117—1182no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—591no—
599C2×C4⋊C4—591no—
600C2×C4⋊C4—591no—
601C2×C4⋊C4—1181no—
602C2×C4⋊C4—1181no—
603C2×C4⋊C4C22×D5911yescharacteristic
604C2×C22⋊C4—21no—
605C2×C22⋊C4—591no—
606C2×C22⋊C4—591no—
607C2×C22⋊C4—1188no—
608C2×C22⋊C4—1188no—
609C2×C22⋊C4—1181no—
610C2×C22⋊C4—1181no—
611C2×C22⋊C4—1181no—
612C2×C22⋊C4—1181no—
613C2×C22⋊C4—1181no—
614C2×C22⋊C4—1181no—
615C2×C22⋊C4—1181no—
616C2×C22⋊C4—1181no—
617C2×C42—591no—
618C2×C42—1181no—
619C2×C42C22×D5911yescharacteristic
620C4⋊C8—594no—
621C4⋊C8—594no—
622C4⋊C8—594no—
623C4⋊C8C22×D5914yescomplemented
624#103—594no—
625#103—594no—
626#103—594no—
627#103—594no—
628#103C22×D5914yescomplemented
629#103C22×D5914yescomplemented
630#102—594no—
631#102—594no—
632C24—21no—
633C24—591no—
634C24—1184no—
635C24—1188no—
636C24—1181no—
637C24—1181no—
638C24—4722no—
639C24—4722no—
640#41—1188no—
641#41—1188no—
642#41—2368no—
643C2×Q8—21no—
644C2×Q8—21no—
645C2×Q8—22no—
646C2×Q8—22no—
647C2×Q8—22no—
648C2×Q8—22no—
649C2×Q8—592no—
650C2×Q8—1184no—
651C2×Q8—1188no—
652C2×Q8—1188no—
653C2×Q8—1181no—
654C2×Q8—1182no—
655C2×Q8—1182no—
656C2×Q8—2364no—
657C2×Q8—2368no—
658C2×Q8C23×D5912yes—
659C2×Q8C23×D5912yes—
660C2×D4—21no—
661C2×D4—22no—
662C2×D4—5916no—
663C2×D4—594no—
664C2×D4—592no—
665C2×D4—592no—
666C2×D4—1184no—
667C2×D4—11816no—
668C2×D4—1188no—
669C2×D4—1184no—
670C2×D4—1188no—
671C2×D4—1181no—
672C2×D4—1182no—
673C2×D4—1181no—
674C2×D4—1182no—
675C2×D4—1182no—
676C2×D4—2364no—
677C2×D4D4×D5914yes—
678C2×D4C23×D5912yes—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—24no—
683C22×C4—82no—
684C22×C4—591no—
685C22×C4—592no—
686C22×C4—594no—
687C22×C4—594no—
688C22×C4—592no—
689C22×C4—591no—
690C22×C4—591no—
691C22×C4—1184no—
692C22×C4—1184no—
693C22×C4—1184no—
694C22×C4—1184no—
695C22×C4—1181no—
696C22×C4—1181no—
697C22×C4—1184no—
698C22×C4—4722no—
699C22×C4—4722no—
700C22×C4—4722no—
701C22×C4—2364no—
702C22×C4—2364no—
703C22×C4D4×D5911yescharacteristic
704C22×C4D4×D5911yescharacteristic
705C22×C4C23×D5911yescharacteristic
706SD16—28no—
707SD16—28no—
708SD16—1188no—
709SD16—1188no—
710SD16—1188no—
711SD16—1188no—
712D8—1188no—
713D8—1188no—
714M16—1188no—
715C2×C8—22no—
716C2×C8—22no—
717C2×C8—592no—
718C2×C8—592no—
719C2×C8—1188no—
720C2×C8—1182no—
721C2×C8—1182no—
722C2×C8C23×D5912yes—
723C2×C8C23×D5912yes—
724C4⋊C4—24no—
725C4⋊C4—24no—
726C4⋊C4—21no—
727C4⋊C4—594no—
728C4⋊C4—594no—
729C4⋊C4—592no—
730C4⋊C4—1184no—
731C4⋊C4—1184no—
732C4⋊C4—1181no—
733C4⋊C4C23×D5912yes—
734C22⋊C4—24no—
735C22⋊C4—594no—
736C22⋊C4—594no—
737C22⋊C4—1184no—
738C22⋊C4—1184no—
739C22⋊C4—1184no—
740C22⋊C4—1184no—
741C22⋊C4—1184no—
742C22⋊C4—1184no—
743C22⋊C4—1184no—
744C22⋊C4—1184no—
745C42—592no—
746C42—592no—
747C42—1184no—
748C42D4×D5912yes—
749C42C23×D5912yes—
750C23—24no—
751C23—22no—
752C23—42no—
753C23—42no—
754C23—594no—
755C23—592no—
756C23—11816no—
757C23—1182no—
758C23—1182no—
759C23—1184no—
760C23—1182no—
761C23—1182no—
762C23—47216no—
763C23—4724no—
764C23—4724no—
765C23—2362no—
766C23—2362no—
767C23—2362no—
768C23—2362no—
769C23—2362no—
770C23C2×D4×D5911yescharacteristic
771Q8—22no—
772Q8—22no—
773Q8—22no—
774Q8—22no—
775Q8—42no—
776Q8—42no—
777Q8—1182no—
778Q8—1182no—
779Q8—2368no—
780Q8—2362no—
781D4—24no—
782D4—22no—
783D4—594no—
784D4—11816no—
785D4—1184no—
786D4—1182no—
787D4—1182no—
788D4—1182no—
789D4—2368no—
790D4—2362no—
791D4C2×D4×D5914yes—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—84no—
801C2×C4—594no—
802C2×C4—592no—
803C2×C4—598no—
804C2×C4—594no—
805C2×C4—594no—
806C2×C4—592no—
807C2×C4—592no—
808C2×C4—1182no—
809C2×C4—1182no—
810C2×C4—1182no—
811C2×C4—1182no—
812C2×C4—4724no—
813C2×C4—4724no—
814C2×C4—4724no—
815C2×C4—2368no—
816C2×C4—2368no—
817C2×C4—2362no—
818C2×C4—2362no—
819C2×C4C2×D4×D5912yes—
820C2×C4C2×D4×D5912yes—
821C2×C4C2×D4×D5911yescharacteristic
822C2×C4C2×D4×D5912yes—
823C2×C4#41×D5912yes—
824C2×C4C24×D5911yescharacteristic
825C8—22no—
826C8—22no—
827C8—1182no—
828C8—1182no—
829C22—24no—
830C22—48no—
831C22—42no—
832C22—42no—
833C22—594no—
834C22—1188no—
835C22—1182no—
836C22—1182no—
837C22—1184no—
838C22—47216no—
839C22—4724no—
840C22—2362no—
841C22—2362no—
842C22—2362no—
843C22—2368no—
844C22—2362no—
845C22—2362no—
846C22#121×D5912yes—
847C22#1683820812yes—
848C22#1683821112yes—
849C22C22×D4×D5911yescharacteristic
850C4—22no—
851C4—22no—
852C4—42no—
853C4—42no—
854C4—42no—
855C4—594no—
856C4—1182no—
857C4—1182no—
858C4—2362no—
859C4—2362no—
860C4#121×D5912yes—
861C4C22×D4×D5911yescharacteristic
862C4C2×#41×D5911yescharacteristic
863C2—44no—
864C2—1184no—
865C2—4722no—
866C2—2364no—
867C2#2143360314yesdirect product factor
868C2C2×#121×D5911yescharacteristic
869C2C2×#1683820811yescharacteristic
870C2C2×#1683821111yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#461C2
socleC23×C59C22×D4
prime radicalC22×#14273754C2
hypercenterC2×#461D59
hypocenterC59C2×#3042
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#461

Complements

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

NH ≅ G/Ntype
2. C22×SD16×D59C2semidirect
3. C2×#16837977C2semidirect
4. C2×#16837874C2semidirect
5. #21433603C2direct (N × H)
6. C2×#16837620C2semidirect
7. C2×#16837619C2semidirect
8. C2×#16837618C2semidirect
9. C2×#16837617C2semidirect
10. C2×#16837606C2semidirect
11. C2×#16837605C2semidirect
12. C2×#16837604C2semidirect
13. C2×#16837427C2semidirect
14. C2×#16837409C2semidirect
15. C2×#16837397C2semidirect
16. C2×C59×#461C2semidirect
27. C2×SD16×D59C22semidirect
33. #16837977C22semidirect
34. C2×#14273725C22semidirect
35. C2×#14273716C22semidirect
36. C2×#14273715C22semidirect
42. #16837874C22semidirect
52. #16837620C22semidirect
53. #16837619C22semidirect
54. #16837618C22semidirect
55. #16837617C22semidirect
56. #16837606C22semidirect
57. #16837605C22semidirect
58. #16837604C22semidirect
59. #16837427C22semidirect
60. C2×C4⋊(C59⋊C8)C22semidirect
61. C2×Dic59⋊C8C22semidirect
62. C2×Dic59⋊C8C22semidirect
63. #16837409C22semidirect
64. #16837397C22semidirect
65. C2×#14273652C22semidirect
66. C2×#14273651C22semidirect
67. C2×#14273651C22semidirect
68. C2×#14273650C22semidirect
69. C2×#14273649C22semidirect
70. C2×#14273647C22semidirect
73. C2×C4⋊Q8×C59C22semidirect
75. C59×#461C22semidirect
76. C2×C4⋊C8×C59C22semidirect
77. C2×#103×C59C22semidirect
78. C2×#103×C59C22semidirect
125. #14273725C23semidirect
127. #14273716C23semidirect
129. #14273715C23semidirect
165. C4⋊(C59⋊C8)C23semidirect
166. Dic59⋊C8C23semidirect
167. Dic59⋊C8C23semidirect
168. #14273652C23semidirect
169. #14273651C23semidirect
170. #14273651C23semidirect
171. #14273650C23semidirect
172. #14273649C23semidirect
173. #14273647C23semidirect
185. C4⋊Q8×C59C23semidirect
193. C4⋊C8×C59C23semidirect
194. #103×C59C23semidirect
195. #103×C59C23semidirect
440. C2×#461D59semidirect
445. C2×C59#3042semidirect
472. C2×C4⋊Q8C2×D59semidirect
498. #461C2×D59semidirect
503. C2×C4⋊C8C2×D59semidirect
510. C2×#103C2×D59semidirect
511. C2×#103C2×D59semidirect
514. C59C2×#3042semidirect
573. C4⋊Q8C22×D59semidirect
623. C4⋊C8C22×D59semidirect
628. #103C22×D59semidirect
629. #103C22×D59semidirect
867. C2#21433603direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#142737542
C22×SD16×D592
C2×#168379772
C2×#168378742
#214336032
C2×#168376202
C2×#168376192
C2×#168376182
C2×#168376172
C2×#168376062
C2×#168376052
C2×#168376042
C2×#168374272
C2×#168374092
C2×#168373972
C2×C59×#4612
C2×#304259