Finite Group Databasebeta

← C2×#21436317 #29465507

Subgroups — C2×#21436317 #29465507

Order 15104.

2254 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838093C211yesmaximal, characteristic, complemented
2C2×#16838047C211yesmaximal, characteristic
3#21436317C2116yesmaximal, direct product factor
4C2×#16837757C211yesmaximal, characteristic, complemented
5C2×#16837722C211yesmaximal, characteristic, complemented
6C2×#16837746C211yesmaximal, characteristic, complemented
7C2×#16837702C211yesmaximal, characteristic, complemented
8C2×#16837659C211yesmaximal, characteristic, complemented
9C2×#16837651C211yesmaximal, characteristic, complemented
10C2×#16837624C211yesmaximal, characteristic, complemented
11C2×#16837561C211yesmaximal, characteristic, complemented
12C2×#16837551C211yesmaximal, characteristic, complemented
13C2×#16837481C211yesmaximal, characteristic, complemented
14C2×#16837400C211yesmaximal, characteristic, complemented
15C2×#16837405C211yesmaximal, characteristic, complemented
16C2×C4×SD16×C59C211yesmaximal, characteristic, complemented
17C22×#11745687C2211yescharacteristic
18C22×D4×D59C2211yescharacteristic
19C22×#11745672C2211yescharacteristic, complemented
20C22×#11745671C2211yescharacteristic
21C22×#11745659C2211yescharacteristic
22C22×#11745659C2211yescharacteristic, complemented
23#16838093—24no—
24#16838093C2218yescomplemented
25#16838047—24no—
26#16838047C2218yes—
27C2×#14273721—21no—
28C2×#14273719C2211yescharacteristic, complemented
29C2×#14273717—21no—
30C2×#14273715C2211yescharacteristic
31C2×#14273712—21no—
32C2×#14273711—21no—
33C2×#14273707C2211yescharacteristic
34C2×#14273703C2211yescharacteristic
35C2×#14273703C2211yescharacteristic, complemented
36C2×#14273702C2211yescharacteristic
37C2×#14273701—21no—
38C2×#14273697—21no—
39C2×C4×D236C2211yescharacteristic
40C2×#14273685C2211yescharacteristic
41C2×#14273684—21no—
42C2×C4⋊C4×D59C2211yescharacteristic, complemented
43C22×(C2×D59)⋊C4—21no—
44#16837757C2218yescomplemented
45#16837746C2218yescomplemented
46#16837722C2218yescomplemented
47#16837702C2218yescomplemented
48#16837659C2218yescomplemented
49#16837651C2218yescomplemented
50#16837624C2218yescomplemented
51#16837561C2218yescomplemented
52#16837551C2218yescomplemented
53#16837481C2218yescomplemented
54C2×#14273660C2211yescharacteristic, complemented
55C2×#14273658C2211yescharacteristic, complemented
56C2×C4⋊(C59⋊C8)C2211yescharacteristic, complemented
57#16837405C2218yescomplemented
58#16837400C2218yescomplemented
59C2×#14273652C2211yescharacteristic, complemented
60C2×#14273652C2211yescharacteristic, complemented
61C2×#14273650C2211yescharacteristic, complemented
62C2×#14273649C2211yescharacteristic
63C2×#14273649C2211yescharacteristic
64C2×#14273648C2211yescharacteristic
65C2×#14273648C2211yescharacteristic
66C2×#14273647C2211yescharacteristic
67C2×(C2×D59)⋊C8C2211yescharacteristic
68C2×(C2×D59)⋊C8C2211yescharacteristic, complemented
69C22×SD16×C59C2211yescharacteristic
70C2×C4×Q8×C59C2211yescharacteristic, complemented
71C2×C4×D4×C59C2211yescharacteristic
72C4×SD16×C59C2218yescomplemented
73C2×#106×C59C2211yescharacteristic, complemented
74C2×#103×C59C2211yescharacteristic, complemented
75C2×#102×C59C2211yescharacteristic
76C2×C4×C8×C59C2211yescharacteristic, complemented
77C24×D59—21no—
78C2×#11745687—24no—
79C2×#11745687—22no—
80C2×#11745687—42no—
81C2×#11745687C2314yes—
82C22×Dic118C2311yescharacteristic
83C22×D236—21no—
84C22×D236D411yescharacteristic
85C22×D236C2311yescharacteristic
86C22×C22⋊D59—21no—
87C22×C22⋊D59—21no—
88C2×D4×D59—24no—
89C2×D4×D59—22no—
90C2×D4×D59—42no—
91C2×D4×D59C2314yes—
92C23×Dic59—21no—
93C22×C4×D59—21no—
94C22×C4×D59C2311yescharacteristic
95C22×C4×D59C2311yescharacteristic
96C2×#11745672—42no—
97C2×#11745672C2314yescomplemented
98C2×#11745671—42no—
99C2×#11745671C2314yes—
100C2×#11745659—42no—
101C2×#11745659—42no—
102C2×#11745659C2314yes—
103C2×#11745659C2314yescomplemented
104C22×C59⋊C8C2311yescharacteristic
105C22×C59⋊C8C2311yescharacteristic
106#14273721—28no—
107#14273719—22no—
108#14273719C2314yescomplemented
109#14273717—28no—
110#14273715—22no—
111#14273715C2314yes—
112#14273712—28no—
113#14273711—28no—
114#14273707—22no—
115#14273707C2314yes—
116#14273703—22no—
117#14273703—22no—
118#14273703C2314yes—
119#14273703C2314yescomplemented
120#14273702—22no—
121#14273702C2314yes—
122#14273701—28no—
123#14273697—28no—
124C4×D236D414yes—
125C4×D236C2314yes—
126#14273685—22no—
127#14273685C2314yes—
128#14273684—28no—
129C2×C4⋊Dic59—21no—
130C2×C4⋊Dic59D411yescharacteristic
131C2×C4⋊Dic59C2311yescharacteristic
132C2×C4⋊Dic59C2311yescharacteristic
133C2×Dic59⋊C4—21no—
134C2×Dic59⋊C4—21no—
135C2×Dic59⋊C4—21no—
136C2×Dic59⋊C4—21no—
137C2×Dic59⋊C4—21no—
138C4⋊C4×D59—22no—
139C4⋊C4×D59C2314yescomplemented
140C2×(C2×D59)⋊C4—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—21no—
146C2×(C2×D59)⋊C4—21no—
147C2×(C2×D59)⋊C4—28no—
148C2×(C2×D59)⋊C4D411yescharacteristic
149C2×(C2×D59)⋊C4D411yescharacteristic
150C2×C4×Dic59—21no—
151#14273660C2314yescomplemented
152#14273658C2314yescomplemented
153C4⋊(C59⋊C8)C2314yescomplemented
154#14273652C2314yescomplemented
155#14273652C2314yescomplemented
156#14273650C2314yescomplemented
157#14273649C2314yes—
158#14273649C2314yes—
159#14273648C2314yes—
160#14273648C2314yes—
161#14273647C2314yes—
162(C2×D59)⋊C8C2314yes—
163(C2×D59)⋊C8C2314yescomplemented
164C22×Q8×C59C2311yescharacteristic
165C22×D4×C59C2311yescharacteristic
166C23×C4×C59—21no—
167C2×SD16×C59—24no—
168C2×SD16×C59C2314yes—
169C22×C8×C59C2311yescharacteristic
170C22×C8×C59C2311yescharacteristic
171C4×Q8×C59—22no—
172C4×Q8×C59C2314yescomplemented
173C4×D4×C59—22no—
174C4×D4×C59C2314yes—
175C2×C4⋊C4×C59—21no—
176C2×C4⋊C4×C59C2311yescharacteristic
177C2×C4⋊C4×C59C2311yescharacteristic
178C2×C22⋊C4×C59—21no—
179C2×C42×C59—21no—
180C2×C42×C59C2311yescharacteristic
181#106×C59C2314yescomplemented
182#103×C59C2314yescomplemented
183#102×C59C2314yes—
184C4×C8×C59C2314yescomplemented
185C24×C59—21no—
186C23×D59—21no—
187C23×D59—24no—
188C23×D59—44no—
189C23×D59—44no—
190C23×D59—82no—
191C23×D59C2×D411yescharacteristic
192C23×D59C2×D411yescharacteristic
193C2×Q8×C59—21no—
194C2×Q8×C59—22no—
195C2×Q8×C59—22no—
196C2×Q8×C59C2412yes—
197C2×D4×C59—21no—
198C2×D4×C59—22no—
199C2×D4×C59#4114yes—
200C2×D4×C59C2412yes—
201C22×C4×C59—21no—
202C22×C4×C59—21no—
203C22×C4×C59—21no—
204C22×C4×C59—24no—
205C22×C4×C59—82no—
206C22×C4×C59C2×D411yescharacteristic
207C22×C4×C59C2×D411yescharacteristic
208C22×C4×C59C2411yescharacteristic
209C2×C22⋊D59—24no—
210C2×C22⋊D59—24no—
211C2×C22⋊D59—44no—
212C2×C22⋊D59—44no—
213C22×Dic59—21no—
214C22×Dic59—21no—
215C22×Dic59—21no—
216C22×Dic59—24no—
217C22×Dic59—44no—
218C22×Dic59C2×D411yescharacteristic
219C22×Dic59C2×D411yescharacteristic
220#11745687—28no—
221#11745687—44no—
222#11745687—48no—
223D4×D59—28no—
224D4×D59—44no—
225D4×D59—48no—
226C2×D236—22no—
227C2×D236—22no—
228C2×D236—21no—
229C2×D236—24no—
230C2×D236—42no—
231C2×D236—82no—
232C2×D236C2×D414yes—
233C2×D236C2412yes—
234C2×C4×D59—22no—
235C2×C4×D59—22no—
236C2×C4×D59—22no—
237C2×C4×D59—22no—
238C2×C4×D59—24no—
239C2×C4×D59—44no—
240C2×C4×D59C2×D412yes—
241C2×C4×D59C2×D412yes—
242C2×C4×D59C2412yes—
243C2×C4×D59C2412yes—
244C2×Dic118—22no—
245C2×Dic118—22no—
246C2×Dic118—21no—
247C2×Dic118C2412yes—
248SD16×C59—28no—
249C2×C8×C59—22no—
250C2×C8×C59—22no—
251C2×C8×C59C2412yes—
252C2×C8×C59C2412yes—
253C4⋊C4×C59—24no—
254C4⋊C4×C59—21no—
255C4⋊C4×C59—21no—
256C4⋊C4×C59C2412yes—
257C4⋊C4×C59C2412yes—
258C22⋊C4×C59—24no—
259C42×C59—24no—
260C42×C59C2×D412yes—
261C42×C59C2412yes—
262#11745672—44no—
263#11745671—44no—
264(C2×D59)⋊C4—24no—
265(C2×D59)⋊C4—24no—
266(C2×D59)⋊C4—24no—
267(C2×D59)⋊C4—24no—
268(C2×D59)⋊C4—24no—
269(C2×D59)⋊C4—24no—
270(C2×D59)⋊C4—24no—
271(C2×D59)⋊C4C2×D414yes—
272(C2×D59)⋊C4C2×D414yes—
273C4⋊Dic59—21no—
274C4⋊Dic59—21no—
275C4⋊Dic59—24no—
276C4⋊Dic59C2×D414yes—
277C4⋊Dic59C2412yes—
278C4⋊Dic59C2412yes—
279Dic59⋊C4—24no—
280Dic59⋊C4—24no—
281Dic59⋊C4—24no—
282Dic59⋊C4—24no—
283Dic59⋊C4—24no—
284C4×Dic59—24no—
285C2×C59⋊C8—22no—
286C2×C59⋊C8—22no—
287C2×C59⋊C8C2412yes—
288C2×C59⋊C8C2412yes—
289#11745659—44no—
290#11745659—44no—
291C23×C59—24no—
292C23×C59—22no—
293C23×C59—42no—
294C23×C59—42no—
295C23×C59C22×D411yescharacteristic
296C22×D59—22no—
297C22×D59—22no—
298C22×D59—22no—
299C22×D59—22no—
300C22×D59—22no—
301C22×D59—22no—
302C22×D59—22no—
303C22×D59—48no—
304C22×D59—48no—
305C22×D59—42no—
306C22×D59—42no—
307C22×D59—42no—
308C22×D59—84no—
309C22×D59—816no—
310C22×D59C22×D412yes—
311C22×D59C22×D412yes—
312Q8×C59—22no—
313Q8×C59—22no—
314Q8×C59—42no—
315D4×C59—24no—
316D4×C59—22no—
317D4×C59C2×#4114yes—
318C2×C4×C59—22no—
319C2×C4×C59—22no—
320C2×C4×C59—22no—
321C2×C4×C59—22no—
322C2×C4×C59—22no—
323C2×C4×C59—42no—
324C2×C4×C59—42no—
325C2×C4×C59—42no—
326C2×C4×C59—84no—
327C2×C4×C59C22×D412yes—
328C2×C4×C59C22×D412yes—
329C2×C4×C59C22×D411yescharacteristic
330C2×C4×C59C2×#4112yes—
331C2×C4×C59H(5,𝔽2)12yes—
332C2×C4×C59C2511yescharacteristic
333C22⋊D59—48no—
334C22⋊D59—48no—
335C2×Dic59—22no—
336C2×Dic59—22no—
337C2×Dic59—22no—
338C2×Dic59—22no—
339C2×Dic59—22no—
340C2×Dic59—48no—
341C2×Dic59—42no—
342C2×Dic59—42no—
343C2×Dic59—42no—
344C2×Dic59C22×D412yes—
345C2×Dic59C22×D412yes—
346D236—22no—
347D236—22no—
348D236—44no—
349D236—42no—
350D236—84no—
351C4×D59—24no—
352C4×D59—24no—
353C4×D59—22no—
354C4×D59—22no—
355C4×D59—22no—
356C4×D59—22no—
357C4×D59—48no—
358Dic118—22no—
359Dic118—22no—
360Dic118—42no—
361C8×C59—22no—
362C8×C59—22no—
363C59⋊C8—22no—
364C59⋊C8—22no—
365C2×#3323—591nomaximal, Sylow
366C22×C59—24no—
367C22×C59—48no—
368C22×C59—42no—
369C22×C59—42no—
370C22×C59#54612yes—
371C22×C59#57512yes—
372C22×C59#57712yes—
373C22×C59C23×D411yescharacteristic
374C2×D59—22no—
375C2×D59—22no—
376C2×D59—22no—
377C2×D59—22no—
378C2×D59—22no—
379C2×D59—22no—
380C2×D59—44no—
381C2×D59—44no—
382C2×D59—42no—
383C2×D59—42no—
384C2×D59—42no—
385C2×D59—816no—
386C2×D59—84no—
387C4×C59—22no—
388C4×C59—22no—
389C4×C59—42no—
390C4×C59—42no—
391C4×C59—42no—
392C4×C59#54612yes—
393C4×C59C22×#4111yescharacteristic
394C4×C59C2×H(5,𝔽2)11yescharacteristic
395Dic59—22no—
396Dic59—22no—
397Dic59—42no—
398Dic59—42no—
399Dic59—42no—
400C2×#552—591no—
401C2×#546—591no—
402#3323—5916no—
403C2×#488—591no—
404C2×#481—591no—
405C2×#485—591no—
406C2×#478—591no—
407C2×#470—591no—
408C2×#468—591no—
409C2×#464—591no—
410C2×#452—591no—
411C2×#450—591no—
412C2×C4×SD16D5911yescharacteristic, complemented
413C2×#436—591no—
414C2×#417—591no—
415C2×#418—591no—
416C2×C59—44no—
417C2×C59#332314yescomplemented
418C2×C59C2×#54611yescharacteristic
419C2×C59C2×#57511yescharacteristic
420C2×C59C2×#57711yescharacteristic
421D59—42no—
422D59—42no—
423D59—82no—
424C22×#41—591no—
425C23×D4—591no—
426C22×Q16—591no—
427C22×SD16—591no—
428C22×SD16C2×D5911yescharacteristic
429C22×M16—591no—
430C22×M16—591no—
431#552—598no—
432#552—1184no—
433#546—598no—
434#546—1184no—
435C2×#126—1181no—
436C2×#125—591no—
437C2×#125—1181no—
438C2×#124—591no—
439C2×#123—1181no—
440C2×#123—1181no—
441C2×C22⋊Q8—591no—
442C2×C22⋊Q8—591no—
443C2×C22⋊Q8—591no—
444C2×#121—591no—
445C2×#121—1181no—
446C2×#120—1181no—
447C2×C4×Q8C2×D5911yescharacteristic, complemented
448C2×C4×D4—591no—
449C2×C4×D4C2×D5911yescharacteristic
450C2×#117—591no—
451C2×#117—1181no—
452C22×C4⋊C4—591no—
453C22×C22⋊C4—1181no—
454#488—598no—
455#485—598no—
456#481—598no—
457#478—598no—
458#470—598no—
459#468—598no—
460#464—598no—
461#452—598no—
462#450—598no—
463C4×SD16C2×D5918yescomplemented
464#436—598no—
465C2×#107—591no—
466C2×#106—591no—
467C2×#106C2×D5911yescharacteristic, complemented
468C2×C4⋊C8—591no—
469#418—598no—
470#417—598no—
471C2×#103—591no—
472C2×#103—591no—
473C2×#103—591no—
474C2×#103C2×D5911yescharacteristic, complemented
475C2×#102—591no—
476C2×#102—591no—
477C2×#102—591no—
478C2×#102—591no—
479C2×#102—591no—
480C2×#102C2×D5911yescharacteristic
481C2×C22⋊C8—591no—
482C2×C22⋊C8—591no—
483C2×C4×C8C2×D5911yescharacteristic, complemented
484C59C2×#332311yescharacteristic, complemented, Sylow
485C25—1181no—
486C2×#41—594no—
487C2×#41—1182no—
488C2×#41—1184no—
489C2×#41—2362no—
490C22×Q8—591no—
491C22×Q8C22×D5911yescharacteristic
492C22×D4—594no—
493C22×D4—591no—
494C22×D4—591no—
495C22×D4—1181no—
496C22×D4—1182no—
497C22×D4—1181no—
498C22×D4—1184no—
499C22×D4—1181no—
500C22×D4—2362no—
501C22×D4C22×D5911yescharacteristic
502C23×C4—21no—
503C23×C4—591no—
504C23×C4—591no—
505C23×C4—1181no—
506C23×C4—1181no—
507C2×Q16—594no—
508C2×Q16—2362no—
509C2×SD16—24no—
510C2×SD16—594no—
511C2×SD16—2362no—
512C2×SD16C22×D5914yes—
513C2×M16—594no—
514C2×M16—594no—
515C2×M16—2362no—
516C2×M16—2362no—
517C22×C8—591no—
518C22×C8—591no—
519C22×C8C22×D5911yescharacteristic
520C22×C8C22×D5911yescharacteristic
521#126—1188no—
522#125—594no—
523#125—1188no—
524#125—1182no—
525#124—594no—
526#124—1182no—
527#123—1188no—
528#123—1188no—
529C22⋊Q8—594no—
530C22⋊Q8—594no—
531C22⋊Q8—594no—
532C22⋊Q8—1182no—
533C22⋊Q8—1182no—
534C22⋊Q8—1182no—
535#121—594no—
536#121—1188no—
537#121—1182no—
538#120—1188no—
539C4×Q8—22no—
540C4×Q8C22×D5914yescomplemented
541C4×D4—22no—
542C4×D4—594no—
543C4×D4—594no—
544C4×D4C22×D5914yes—
545#117—594no—
546#117—1188no—
547#117—1182no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—591no—
550C2×C4⋊C4—591no—
551C2×C4⋊C4—591no—
552C2×C4⋊C4—594no—
553C2×C4⋊C4—1182no—
554C2×C4⋊C4—1181no—
555C2×C4⋊C4—1181no—
556C2×C4⋊C4—1181no—
557C2×C4⋊C4—1181no—
558C2×C4⋊C4—1181no—
559C2×C4⋊C4—1181no—
560C2×C4⋊C4C22×D5911yescharacteristic
561C2×C4⋊C4C22×D5911yescharacteristic
562C2×C22⋊C4—21no—
563C2×C22⋊C4—591no—
564C2×C22⋊C4—591no—
565C2×C22⋊C4—1188no—
566C2×C22⋊C4—1181no—
567C2×C22⋊C4—1181no—
568C2×C22⋊C4—1181no—
569C2×C22⋊C4—1181no—
570C2×C22⋊C4—1181no—
571C2×C22⋊C4—1181no—
572C2×C22⋊C4—1181no—
573C2×C42—21no—
574C2×C42—1181no—
575C2×C42C22×D5911yescharacteristic
576#107—594no—
577#106—594no—
578#106C22×D5914yescomplemented
579C4⋊C8—594no—
580#103—594no—
581#103—594no—
582#103—594no—
583#103C22×D5914yescomplemented
584#102—594no—
585#102—594no—
586#102—594no—
587#102—594no—
588#102—594no—
589#102C22×D5914yes—
590C22⋊C8—594no—
591C22⋊C8—594no—
592C4×C8C22×D5914yescomplemented
593C24—21no—
594C24—591no—
595C24—591no—
596C24—1184no—
597C24—1181no—
598C24—4722no—
599C24—2364no—
600C24—2364no—
601#41—1188no—
602#41—2364no—
603#41—2368no—
604C2×Q8—21no—
605C2×Q8—22no—
606C2×Q8—22no—
607C2×Q8—592no—
608C2×Q8—1181no—
609C2×Q8—1182no—
610C2×Q8—1182no—
611C2×Q8C23×D5912yes—
612C2×D4—21no—
613C2×D4—22no—
614C2×D4—594no—
615C2×D4—592no—
616C2×D4—1184no—
617C2×D4—1184no—
618C2×D4—1188no—
619C2×D4—1184no—
620C2×D4—1181no—
621C2×D4—1182no—
622C2×D4—1182no—
623C2×D4—4722no—
624C2×D4—2362no—
625C2×D4—2364no—
626C2×D4—2368no—
627C2×D4—2364no—
628C2×D4—2364no—
629C2×D4#1174568514yes—
630C2×D4C23×D5912yes—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—24no—
635C22×C4—82no—
636C22×C4—591no—
637C22×C4—591no—
638C22×C4—592no—
639C22×C4—592no—
640C22×C4—592no—
641C22×C4—592no—
642C22×C4—1184no—
643C22×C4—1184no—
644C22×C4—1182no—
645C22×C4—1182no—
646C22×C4—1182no—
647C22×C4—1182no—
648C22×C4—1181no—
649C22×C4—1181no—
650C22×C4—1181no—
651C22×C4—2364no—
652C22×C4—2364no—
653C22×C4D4×D5911yescharacteristic
654C22×C4D4×D5911yescharacteristic
655C22×C4C23×D5911yescharacteristic
656Q16—2364no—
657SD16—28no—
658SD16—2364no—
659M16—2364no—
660M16—2364no—
661C2×C8—22no—
662C2×C8—22no—
663C2×C8—592no—
664C2×C8—592no—
665C2×C8—1182no—
666C2×C8—1182no—
667C2×C8C23×D5912yes—
668C2×C8C23×D5912yes—
669C4⋊C4—24no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—594no—
673C4⋊C4—592no—
674C4⋊C4—592no—
675C4⋊C4—1184no—
676C4⋊C4—1184no—
677C4⋊C4—1184no—
678C4⋊C4—1184no—
679C4⋊C4—1181no—
680C4⋊C4—1181no—
681C4⋊C4—1184no—
682C4⋊C4—1184no—
683C4⋊C4C23×D5912yes—
684C4⋊C4C23×D5912yes—
685C22⋊C4—24no—
686C22⋊C4—594no—
687C22⋊C4—594no—
688C22⋊C4—1184no—
689C22⋊C4—1184no—
690C22⋊C4—1184no—
691C22⋊C4—1184no—
692C22⋊C4—1184no—
693C22⋊C4—1184no—
694C22⋊C4—1184no—
695C42—24no—
696C42—1184no—
697C42D4×D5912yes—
698C42C23×D5912yes—
699C23—22no—
700C23—24no—
701C23—42no—
702C23—42no—
703C23—592no—
704C23—592no—
705C23—1182no—
706C23—1182no—
707C23—1182no—
708C23—1182no—
709C23—1182no—
710C23—1182no—
711C23—1182no—
712C23—4724no—
713C23—47216no—
714C23—2368no—
715C23—2368no—
716C23—2362no—
717C23—2362no—
718C23—2362no—
719C23C2×D4×D5911yescharacteristic
720Q8—22no—
721Q8—22no—
722Q8—42no—
723Q8—1182no—
724Q8—1182no—
725Q8—2362no—
726D4—22no—
727D4—24no—
728D4—1182no—
729D4—1182no—
730D4—4724no—
731D4—2364no—
732D4—2368no—
733D4—2368no—
734D4—2362no—
735D4C2×#1174568514yes—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—84no—
745C2×C4—592no—
746C2×C4—592no—
747C2×C4—1182no—
748C2×C4—1182no—
749C2×C4—1182no—
750C2×C4—1182no—
751C2×C4—1182no—
752C2×C4—1182no—
753C2×C4—1184no—
754C2×C4—1184no—
755C2×C4—1182no—
756C2×C4—1182no—
757C2×C4—1182no—
758C2×C4—2368no—
759C2×C4—2368no—
760C2×C4—2362no—
761C2×C4—2362no—
762C2×C4—2362no—
763C2×C4C2×D4×D5912yes—
764C2×C4C2×D4×D5912yes—
765C2×C4C2×D4×D5911yescharacteristic
766C2×C4C2×#1174568512yes—
767C2×C4#1427377312yes—
768C2×C4C24×D5911yescharacteristic
769C8—22no—
770C8—22no—
771C8—1182no—
772C8—1182no—
773C22—24no—
774C22—42no—
775C22—42no—
776C22—48no—
777C22—1182no—
778C22—1182no—
779C22—1182no—
780C22—1182no—
781C22—1182no—
782C22—1182no—
783C22—47216no—
784C22—4724no—
785C22—2362no—
786C22—2362no—
787C22—2362no—
788C22—2364no—
789C22—2364no—
790C22#1683804812yes—
791C22#1683819912yes—
792C22#1683820812yes—
793C22C22×D4×D5911yescharacteristic
794C4—22no—
795C4—22no—
796C4—42no—
797C4—42no—
798C4—42no—
799C4—1182no—
800C4—1182no—
801C4—2362no—
802C4—2362no—
803C4—2362no—
804C4#1683804812yes—
805C4C22×#1174568511yescharacteristic
806C4C2×#1427377311yescharacteristic
807C2—44no—
808C2—4722no—
809C2—2362no—
810C2—2362no—
811C2#2143631714yesdirect product factor
812C2C2×#1683804811yescharacteristic
813C2C2×#1683819911yescharacteristic
814C2C2×#1683820811yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C4×SD16×C59C2
socleC23×C59C22×D4
prime radicalC2×#16838047C2
hypercenterC2×C4×SD16D59
hypocenterC59C2×#3323
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#16838093C2semidirect
3. #21436317C2direct (N × H)
4. C2×#16837757C2semidirect
5. C2×#16837722C2semidirect
6. C2×#16837746C2semidirect
7. C2×#16837702C2semidirect
8. C2×#16837659C2semidirect
9. C2×#16837651C2semidirect
10. C2×#16837624C2semidirect
11. C2×#16837561C2semidirect
12. C2×#16837551C2semidirect
13. C2×#16837481C2semidirect
14. C2×#16837400C2semidirect
15. C2×#16837405C2semidirect
16. C2×C4×SD16×C59C2semidirect
19. C22×#11745672C22semidirect
22. C22×#11745659C22semidirect
24. #16838093C22semidirect
28. C2×#14273719C22semidirect
35. C2×#14273703C22semidirect
42. C2×C4⋊C4×D59C22semidirect
44. #16837757C22semidirect
45. #16837746C22semidirect
46. #16837722C22semidirect
47. #16837702C22semidirect
48. #16837659C22semidirect
49. #16837651C22semidirect
50. #16837624C22semidirect
51. #16837561C22semidirect
52. #16837551C22semidirect
53. #16837481C22semidirect
54. C2×#14273660C22semidirect
55. C2×#14273658C22semidirect
56. C2×C4⋊(C59⋊C8)C22semidirect
57. #16837405C22semidirect
58. #16837400C22semidirect
59. C2×#14273652C22semidirect
60. C2×#14273652C22semidirect
61. C2×#14273650C22semidirect
68. C2×(C2×D59)⋊C8C22semidirect
70. C2×C4×Q8×C59C22semidirect
72. C4×SD16×C59C22semidirect
73. C2×#106×C59C22semidirect
74. C2×#103×C59C22semidirect
76. C2×C4×C8×C59C22semidirect
97. C2×#11745672C23semidirect
103. C2×#11745659C23semidirect
108. #14273719C23semidirect
119. #14273703C23semidirect
139. C4⋊C4×D59C23semidirect
151. #14273660C23semidirect
152. #14273658C23semidirect
153. C4⋊(C59⋊C8)C23semidirect
154. #14273652C23semidirect
155. #14273652C23semidirect
156. #14273650C23semidirect
163. (C2×D59)⋊C8C23semidirect
172. C4×Q8×C59C23semidirect
181. #106×C59C23semidirect
182. #103×C59C23semidirect
184. C4×C8×C59C23semidirect
412. C2×C4×SD16D59semidirect
417. C2×C59#3323semidirect
447. C2×C4×Q8C2×D59semidirect
463. C4×SD16C2×D59semidirect
467. C2×#106C2×D59semidirect
474. C2×#103C2×D59semidirect
483. C2×C4×C8C2×D59semidirect
484. C59C2×#3323semidirect
540. C4×Q8C22×D59semidirect
578. #106C22×D59semidirect
583. #103C22×D59semidirect
592. C4×C8C22×D59semidirect
811. C2#21436317direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168380932
C2×#168380472
#214363172
C2×#168377572
C2×#168377222
C2×#168377462
C2×#168377022
C2×#168376592
C2×#168376512
C2×#168376242
C2×#168375612
C2×#168375512
C2×#168374812
C2×#168374002
C2×#168374052
C2×C4×SD16×C592
C2×#332359