Finite Group Databasebeta

← C2×#21436083 #29465259

Subgroups — C2×#21436083 #29465259

Order 15104.

2374 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838063C211yesmaximal, characteristic, complemented
2C2×#16838053C211yesmaximal, characteristic, complemented
3#21436083C2116yesmaximal, direct product factor
4C2×#16837763C211yesmaximal, characteristic, complemented
5C2×#16837736C211yesmaximal, characteristic, complemented
6C2×#16837715C211yesmaximal, characteristic, complemented
7C2×#16837695C211yesmaximal, characteristic, complemented
8C2×#16837651C211yesmaximal, characteristic, complemented
9C2×#16837638C211yesmaximal, characteristic, complemented
10C2×#16837620C211yesmaximal, characteristic, complemented
11C2×#16837550C211yesmaximal, characteristic, complemented
12C2×#16837541C211yesmaximal, characteristic, complemented
13C2×#16837505C211yesmaximal, characteristic, complemented
14C2×#16837473C211yesmaximal, characteristic, complemented
15C2×#16837402C211yesmaximal, characteristic, complemented
16C22×#103×C59C211yesmaximal, characteristic, complemented
17C22×#11745689C2211yescharacteristic
18C22×#11745685—21no—
19C22×#11745671C2211yescharacteristic
20C22×#11745671C2211yescharacteristic
21C22×D472C2211yescharacteristic
22C22×#11745659C2211yescharacteristic
23#16838063—24no—
24#16838063C2218yescomplemented
25#16838053—24no—
26#16838053C2218yescomplemented
27C2×#14273726C2211yescharacteristic
28C2×#14273716—21no—
29C2×#14273716C2211yescharacteristic
30C2×#14273712—21no—
31C2×#14273710—21no—
32C2×#14273705—21no—
33C2×#14273703—21no—
34C2×#14273703C2211yescharacteristic
35C2×#14273702C2211yescharacteristic
36C2×#14273701—21no—
37C2×#14273701C2211yescharacteristic
38C2×#14273701C2211yescharacteristic
39C2×Q8×Dic59C2211yescharacteristic
40C2×#14273689C2211yescharacteristic
41C2×C4×C22⋊D59—21no—
42C2×C4×C22⋊D59C2211yescharacteristic
43C2×C4⋊C4×D59C2211yescharacteristic
44#16837763C2218yescomplemented
45#16837736C2218yescomplemented
46#16837715C2218yescomplemented
47#16837695C2218yescomplemented
48#16837651C2218yescomplemented
49#16837638C2218yescomplemented
50#16837620C2218yescomplemented
51#16837550C2218yescomplemented
52#16837541C2218yescomplemented
53#16837505C2218yescomplemented
54#16837473C2218yescomplemented
55C2×#14273661C2211yescharacteristic
56C2×#14273660C2211yescharacteristic
57C2×#14273660C2211yescharacteristic
58C2×Dic59⋊C8C2211yescharacteristic
59#16837402C2218yescomplemented
60C2×#14273651C2211yescharacteristic
61C2×#14273651C2211yescharacteristic
62C2×#14273649C2211yescharacteristic
63C2×#14273649C2211yescharacteristic
64C2×#14273647C2211yescharacteristic
65C2×#14273647C2211yescharacteristic
66C2×C22⋊(C59⋊C8)C2211yescharacteristic
67C2×(C2×D59)⋊C8C2211yescharacteristic
68C2×#14273637C2211yescharacteristic
69C23×Q8×C59C2211yescharacteristic
70C23×C8×C59C2211yescharacteristic
71C22×C4⋊C4×C59C2211yescharacteristic
72C2×#103×C59C2211yescharacteristic
73C2×#103×C59C2211yescharacteristic
74C2×#103×C59C2211yescharacteristic
75C2×#103×C59C2211yescharacteristic
76C2×#103×C59C2218yescomplemented
77C2×#11745689—22no—
78C2×#11745689—24no—
79C2×#11745689—42no—
80C2×#11745689C2314yes—
81C2×#11745685—28no—
82C2×#11745685—48no—
83C22×Dic118—21no—
84C22×D236—21no—
85C22×D236—21no—
86C22×D236C2311yescharacteristic
87C22×D236C2311yescharacteristic
88C22×C22⋊D59—21no—
89C22×C22⋊D59—21no—
90C22×C22⋊D59D411yescharacteristic
91C22×C4×D59—21no—
92C22×C4×D59—21no—
93C22×C4×D59—21no—
94C22×C4×D59C2311yescharacteristic
95C2×#11745671—24no—
96C2×#11745671—42no—
97C2×#11745671C2314yes—
98C2×#11745671C2314yes—
99C2×D472—42no—
100C2×D472C2314yes—
101C2×#11745659—42no—
102C2×#11745659C2314yes—
103C22×C59⋊C8C2311yescharacteristic
104C22×C59⋊C8C2311yescharacteristic
105#14273726—22no—
106#14273726C2314yes—
107#14273716—28no—
108#14273716—22no—
109#14273716C2314yes—
110#14273712—28no—
111#14273710—28no—
112#14273705—28no—
113#14273703—22no—
114#14273703—28no—
115#14273703C2314yes—
116#14273702—22no—
117#14273702C2314yes—
118#14273701—22no—
119#14273701—22no—
120#14273701—28no—
121#14273701C2314yes—
122#14273701C2314yes—
123Q8×Dic59—22no—
124Q8×Dic59C2314yes—
125#14273689—22no—
126#14273689C2314yes—
127C4×C22⋊D59—28no—
128C4×C22⋊D59D414yes—
129C4×C22⋊D59C2314yes—
130C2×C4⋊Dic59—21no—
131C2×C4⋊Dic59C2311yescharacteristic
132C2×C4⋊Dic59C2311yescharacteristic
133C2×Dic59⋊C4—21no—
134C2×Dic59⋊C4—21no—
135C2×Dic59⋊C4—21no—
136C2×Dic59⋊C4D411yescharacteristic
137C4⋊C4×D59—22no—
138C4⋊C4×D59C2314yes—
139C2×C22⋊Dic59D411yescharacteristic
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)⋊C4D411yescharacteristic
148C2×C4×Dic59—21no—
149C2×C4×Dic59C2311yescharacteristic
150#14273661C2314yes—
151#14273660C2314yes—
152#14273660C2314yes—
153Dic59⋊C8C2314yes—
154#14273651C2314yes—
155#14273651C2314yes—
156#14273649C2314yes—
157#14273649C2314yes—
158#14273647C2314yes—
159#14273647C2314yes—
160C22⋊(C59⋊C8)C2314yes—
161(C2×D59)⋊C8C2314yes—
162#14273637C2314yes—
163C22×Q8×C59—21no—
164C22×Q8×C59—22no—
165C22×Q8×C59—24no—
166C22×Q8×C59—42no—
167C22×Q8×C59C2311yescharacteristic
168C22×Q8×C59C2314yes—
169C22×Q8×C59C2311yescharacteristic
170C23×C4×C59—21no—
171C23×C4×C59—21no—
172C23×C4×C59C2311yescharacteristic
173C22×C8×C59—42no—
174C22×C8×C59C2311yescharacteristic
175C22×C8×C59C2311yescharacteristic
176C22×C8×C59C2314yes—
177C2×C4⋊C4×C59—21no—
178C2×C4⋊C4×C59—22no—
179C2×C4⋊C4×C59C2311yescharacteristic
180C2×C4⋊C4×C59C2311yescharacteristic
181C2×C4⋊C4×C59C2314yes—
182#103×C59C2314yes—
183#103×C59C2314yes—
184#103×C59C2314yes—
185#103×C59C2314yes—
186C24×C59C2×D411yescharacteristic
187C23×D59—21no—
188C23×D59—21no—
189C23×D59C2×D411yescharacteristic
190C2×Q8×C59—21no—
191C2×Q8×C59—24no—
192C2×Q8×C59—21no—
193C2×Q8×C59—22no—
194C2×Q8×C59—28no—
195C2×Q8×C59—22no—
196C2×Q8×C59—22no—
197C2×Q8×C59—44no—
198C2×Q8×C59—44no—
199C2×Q8×C59—48no—
200C2×Q8×C59#4114yescomplemented
201C2×Q8×C59C2412yes—
202C2×Q8×C59C2412yes—
203C22×C4×C59—21no—
204C22×C4×C59—22no—
205C22×C4×C59—22no—
206C22×C4×C59—21no—
207C22×C4×C59—21no—
208C22×C4×C59—24no—
209C22×C4×C59—21no—
210C22×C4×C59—24no—
211C22×C4×C59—44no—
212C22×C4×C59—44no—
213C22×C4×C59C2×D411yescharacteristic
214C22×C4×C59C2×D412yes—
215C22×C4×C59C2412yes—
216C22×C4×C59C2411yescharacteristic
217C2×C22⋊D59—24no—
218C2×C22⋊D59—24no—
219C2×C22⋊D59—24no—
220C2×C22⋊D59—44no—
221C2×C22⋊D59—44no—
222C2×C22⋊D59C2×D414yes—
223C22×Dic59—21no—
224C22×Dic59—21no—
225C22×Dic59C2×D411yescharacteristic
226C22×Dic59C2×D411yescharacteristic
227C22×Dic59C2×D411yescharacteristic
228#11745689—28no—
229#11745689—44no—
230#11745689—48no—
231#11745685—432no—
232C2×D236—22no—
233C2×D236—22no—
234C2×D236—22no—
235C2×D236—22no—
236C2×D236—24no—
237C2×D236—24no—
238C2×D236—21no—
239C2×D236—21no—
240C2×D236—44no—
241C2×D236—44no—
242C2×D236C2412yes—
243C2×D236C2412yes—
244C2×C4×D59—22no—
245C2×C4×D59—22no—
246C2×C4×D59—24no—
247C2×C4×D59—24no—
248C2×C4×D59—24no—
249C2×C4×D59—44no—
250C2×C4×D59—44no—
251C2×C4×D59—44no—
252C2×C4×D59C2×D412yes—
253C2×C4×D59C2412yes—
254C2×Dic118—24no—
255C2×Dic118—44no—
256C2×C8×C59—22no—
257C2×C8×C59—22no—
258C2×C8×C59—44no—
259C2×C8×C59C2412yes—
260C2×C8×C59C2412yes—
261C4⋊C4×C59—21no—
262C4⋊C4×C59—21no—
263C4⋊C4×C59—24no—
264C4⋊C4×C59C2412yes—
265C4⋊C4×C59C2412yes—
266C22⋊Dic59C2×D414yes—
267#11745671—28no—
268#11745671—44no—
269(C2×D59)⋊C4—24no—
270(C2×D59)⋊C4—24no—
271(C2×D59)⋊C4—24no—
272(C2×D59)⋊C4—24no—
273(C2×D59)⋊C4—24no—
274(C2×D59)⋊C4—24no—
275(C2×D59)⋊C4—24no—
276(C2×D59)⋊C4C2×D414yes—
277C4⋊Dic59—21no—
278C4⋊Dic59—21no—
279C4⋊Dic59—24no—
280C4⋊Dic59C2412yes—
281C4⋊Dic59C2412yes—
282Dic59⋊C4—24no—
283Dic59⋊C4—24no—
284Dic59⋊C4—24no—
285Dic59⋊C4C2×D414yes—
286C4×Dic59—24no—
287C4×Dic59C2×D412yes—
288C4×Dic59C2412yes—
289C2×C59⋊C8—22no—
290C2×C59⋊C8—22no—
291C2×C59⋊C8C2412yes—
292C2×C59⋊C8C2412yes—
293D472—44no—
294#11745659—44no—
295C23×C59—22no—
296C23×C59—22no—
297C23×C59AGL(1,ℤ/8)14yes—
298C23×C59C22×D412yes—
299C23×C59C22×D411yescharacteristic
300C22×D59—22no—
301C22×D59—22no—
302C22×D59—22no—
303C22×D59—22no—
304C22×D59—22no—
305C22×D59—42no—
306C22×D59—42no—
307C22×D59—42no—
308C22×D59—42no—
309C22×D59—42no—
310C22×D59—42no—
311C22×D59C22×D412yes—
312Q8×C59—24no—
313Q8×C59—22no—
314Q8×C59—22no—
315Q8×C59—22no—
316Q8×C59—48no—
317Q8×C59—42no—
318Q8×C59C2×#4114yescomplemented
319C2×C4×C59—24no—
320C2×C4×C59—22no—
321C2×C4×C59—22no—
322C2×C4×C59—24no—
323C2×C4×C59—22no—
324C2×C4×C59—22no—
325C2×C4×C59—22no—
326C2×C4×C59—22no—
327C2×C4×C59—22no—
328C2×C4×C59—48no—
329C2×C4×C59—42no—
330C2×C4×C59—42no—
331C2×C4×C59—42no—
332C2×C4×C59—48no—
333C2×C4×C59C22×D412yes—
334C2×C4×C59C22×D411yescharacteristic
335C2×C4×C59C2×#4112yes—
336C2×C4×C59H(5,𝔽2)12yes—
337C2×C4×C59C2511yescharacteristic
338C22⋊D59—28no—
339C22⋊D59—48no—
340C22⋊D59—48no—
341C2×Dic59—22no—
342C2×Dic59—22no—
343C2×Dic59—22no—
344C2×Dic59—22no—
345C2×Dic59—22no—
346C2×Dic59—42no—
347C2×Dic59—42no—
348C2×Dic59C22×D412yes—
349C2×Dic59C22×D412yes—
350C2×Dic59C22×D412yes—
351D236—22no—
352D236—22no—
353D236—22no—
354D236—22no—
355D236—48no—
356D236—48no—
357D236—42no—
358D236—42no—
359C4×D59—24no—
360C4×D59—22no—
361C4×D59—22no—
362C4×D59—48no—
363C4×D59—48no—
364C4×D59—48no—
365Dic118—48no—
366C8×C59—22no—
367C8×C59—22no—
368C59⋊C8—22no—
369C59⋊C8—22no—
370C2×#3308—591nomaximal, Sylow
371C22×C59—22no—
372C22×C59—28no—
373C22×C59—22no—
374C22×C59#54612yes—
375C22×C59C2×AGL(1,ℤ/8)14yes—
376C22×C59C2×AGL(1,ℤ/8)12yes—
377C22×C59#57812yes—
378C22×C59C23×D411yescharacteristic
379C2×D59—22no—
380C2×D59—22no—
381C2×D59—22no—
382C2×D59—44no—
383C2×D59—42no—
384C2×D59—42no—
385C2×D59—42no—
386C2×D59—42no—
387C2×D59—42no—
388C2×D59—42no—
389C2×D59—84no—
390C2×D59—84no—
391C4×C59—24no—
392C4×C59—22no—
393C4×C59—42no—
394C4×C59—42no—
395C4×C59—42no—
396C4×C59#54612yes—
397C4×C59C22×#4111yescharacteristic
398C4×C59C2×H(5,𝔽2)11yescharacteristic
399Dic59—22no—
400Dic59—22no—
401Dic59—22no—
402Dic59—42no—
403Dic59—42no—
404C2×#548—591no—
405C2×#547—591no—
406#3308—5916no—
407C2×#489—591no—
408C2×#484—591no—
409C2×#480—591no—
410C2×#477—591no—
411C2×#468—591no—
412C2×#466—591no—
413C2×#463—591no—
414C2×#449—591no—
415C2×#448—591no—
416C2×#440—591no—
417C2×#435—591no—
418C2×#417—591no—
419C22×#103D5911yescharacteristic, complemented
420C2×C59—24no—
421C2×C59#330814yescomplemented
422C2×C59C2×#54611yescharacteristic
423C2×C59C22×AGL(1,ℤ/8)11yescharacteristic
424C2×C59C2×#57811yescharacteristic
425D59—42no—
426D59—82no—
427D59—82no—
428C22×#41—591no—
429C22×#41—1181no—
430C23×Q8C2×D5911yescharacteristic
431C22×SD16—591no—
432C22×SD16—591no—
433C22×D8—591no—
434C22×M16—591no—
435C23×C8C2×D5911yescharacteristic
436#548—598no—
437#548—1184no—
438#547—598no—
439#547—1184no—
440C2×C4⋊Q8—591no—
441C2×#124—591no—
442C2×#124—1181no—
443C2×#123—1181no—
444C2×#123—1181no—
445C2×C22⋊Q8—591no—
446C2×C22⋊Q8—1181no—
447C2×C22⋊Q8—1181no—
448C2×#121—591no—
449C2×#121—591no—
450C2×#121—591no—
451C2×#121—1181no—
452C2×C4×Q8—591no—
453C2×C4×D4—591no—
454C2×C4×D4—591no—
455C2×C4×D4—1181no—
456C22×C4⋊C4—591no—
457C22×C4⋊C4C2×D5911yescharacteristic
458#489—598no—
459#484—598no—
460#480—598no—
461#477—598no—
462#468—598no—
463#466—598no—
464#463—598no—
465#449—598no—
466#448—598no—
467#440—598no—
468#435—598no—
469C2×#107—591no—
470C2×#107—591no—
471C2×#107—591no—
472C2×C4⋊C8—591no—
473#417—598no—
474C2×#103—591no—
475C2×#103—591no—
476C2×#103C2×D5911yescharacteristic
477C2×#103C2×D5911yescharacteristic
478C2×#103C2×D5911yescharacteristic
479C2×#103C2×D5911yescharacteristic
480C2×#103C2×D5918yescomplemented
481C2×#102—591no—
482C2×#102—591no—
483C2×#102—591no—
484C2×#102—591no—
485C2×C22⋊C8—591no—
486C2×C22⋊C8—591no—
487C2×#97—591no—
488C59C2×#330811yescharacteristic, complemented, Sylow
489C2×#41—594no—
490C2×#41—1188no—
491C2×#41—1182no—
492C2×#41—1184no—
493C2×#41—2368no—
494C2×#41—2362no—
495C22×Q8—21no—
496C22×Q8—22no—
497C22×Q8—24no—
498C22×Q8—42no—
499C22×Q8—1181no—
500C22×Q8C22×D5911yescharacteristic
501C22×Q8C22×D5914yes—
502C22×Q8C22×D5911yescharacteristic
503C22×D4—591no—
504C22×D4—591no—
505C22×D4—591no—
506C22×D4—1181no—
507C22×D4—1181no—
508C22×D4—1181no—
509C22×D4—1181no—
510C23×C4—21no—
511C23×C4—21no—
512C23×C4—591no—
513C23×C4—1181no—
514C23×C4—1181no—
515C23×C4—1181no—
516C23×C4C22×D5911yescharacteristic
517C2×SD16—594no—
518C2×SD16—594no—
519C2×SD16—1184no—
520C2×SD16—2362no—
521C2×D8—594no—
522C2×D8—2362no—
523C2×M16—594no—
524C2×M16—2362no—
525C22×C8—42no—
526C22×C8—591no—
527C22×C8—591no—
528C22×C8C22×D5911yescharacteristic
529C22×C8C22×D5911yescharacteristic
530C22×C8C22×D5914yes—
531C4⋊Q8—594no—
532C4⋊Q8—1182no—
533#124—594no—
534#124—1182no—
535#124—1188no—
536#123—1188no—
537#123—1188no—
538C22⋊Q8—594no—
539C22⋊Q8—1188no—
540C22⋊Q8—1188no—
541C22⋊Q8—1182no—
542#121—594no—
543#121—594no—
544#121—594no—
545#121—1182no—
546#121—1188no—
547#121—1182no—
548#121—1182no—
549C4×Q8—594no—
550C4×Q8—1182no—
551C4×D4—594no—
552C4×D4—594no—
553C4×D4—594no—
554C4×D4—1182no—
555C4×D4—1188no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—22no—
558C2×C4⋊C4—591no—
559C2×C4⋊C4—591no—
560C2×C4⋊C4—591no—
561C2×C4⋊C4—594no—
562C2×C4⋊C4—1182no—
563C2×C4⋊C4—1181no—
564C2×C4⋊C4—1181no—
565C2×C4⋊C4—1181no—
566C2×C4⋊C4—1181no—
567C2×C4⋊C4C22×D5911yescharacteristic
568C2×C4⋊C4C22×D5911yescharacteristic
569C2×C4⋊C4C22×D5914yes—
570C2×C22⋊C4—591no—
571C2×C22⋊C4—591no—
572C2×C22⋊C4—1181no—
573C2×C22⋊C4—1181no—
574C2×C22⋊C4—1181no—
575C2×C22⋊C4—1181no—
576C2×C22⋊C4—1181no—
577C2×C22⋊C4—1181no—
578C2×C22⋊C4—1181no—
579C2×C42—591no—
580C2×C42—1181no—
581#107—594no—
582#107—594no—
583#107—594no—
584C4⋊C8—594no—
585#103—594no—
586#103—594no—
587#103C22×D5914yes—
588#103C22×D5914yes—
589#103C22×D5914yes—
590#103C22×D5914yes—
591#102—594no—
592#102—594no—
593#102—594no—
594#102—594no—
595C22⋊C8—594no—
596C22⋊C8—594no—
597#97—594no—
598C24—591no—
599C24—1181no—
600C24—1181no—
601C24D4×D5911yescharacteristic
602#41—1188no—
603#41—23632no—
604#41—2364no—
605#41—2368no—
606C2×Q8—21no—
607C2×Q8—24no—
608C2×Q8—21no—
609C2×Q8—22no—
610C2×Q8—28no—
611C2×Q8—22no—
612C2×Q8—22no—
613C2×Q8—44no—
614C2×Q8—44no—
615C2×Q8—48no—
616C2×Q8—1184no—
617C2×Q8—2364no—
618C2×Q8#1174568514yescomplemented
619C2×Q8C23×D5912yes—
620C2×Q8C23×D5912yes—
621C2×D4—594no—
622C2×D4—592no—
623C2×D4—592no—
624C2×D4—1184no—
625C2×D4—1184no—
626C2×D4—1184no—
627C2×D4—1184no—
628C2×D4—1184no—
629C2×D4—1181no—
630C2×D4—1181no—
631C2×D4—1182no—
632C2×D4—1182no—
633C2×D4—1182no—
634C2×D4—1182no—
635C2×D4—2364no—
636C2×D4—2364no—
637C2×D4—2364no—
638C2×D4—2364no—
639C22×C4—21no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—24no—
643C22×C4—24no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—44no—
648C22×C4—44no—
649C22×C4—591no—
650C22×C4—591no—
651C22×C4—591no—
652C22×C4—592no—
653C22×C4—592no—
654C22×C4—1184no—
655C22×C4—1184no—
656C22×C4—1184no—
657C22×C4—1182no—
658C22×C4—1182no—
659C22×C4—1181no—
660C22×C4—1181no—
661C22×C4—2364no—
662C22×C4—2364no—
663C22×C4—2364no—
664C22×C4D4×D5912yes—
665C22×C4D4×D5911yescharacteristic
666C22×C4C23×D5912yes—
667C22×C4C23×D5911yescharacteristic
668SD16—1188no—
669SD16—2364no—
670D8—2364no—
671M16—2364no—
672C2×C8—22no—
673C2×C8—22no—
674C2×C8—44no—
675C2×C8—592no—
676C2×C8—592no—
677C2×C8—1182no—
678C2×C8—1182no—
679C2×C8C23×D5912yes—
680C2×C8C23×D5912yes—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—24no—
684C4⋊C4—594no—
685C4⋊C4—592no—
686C4⋊C4—592no—
687C4⋊C4—1184no—
688C4⋊C4—1184no—
689C4⋊C4—1184no—
690C4⋊C4—1184no—
691C4⋊C4—1181no—
692C4⋊C4—1181no—
693C4⋊C4C23×D5912yes—
694C4⋊C4C23×D5912yes—
695C22⋊C4—594no—
696C22⋊C4—594no—
697C22⋊C4—1184no—
698C22⋊C4—1184no—
699C22⋊C4—1184no—
700C22⋊C4—1184no—
701C22⋊C4—1184no—
702C22⋊C4—1184no—
703C22⋊C4—1184no—
704C42—592no—
705C42—592no—
706C42—1184no—
707C23—22no—
708C23—22no—
709C23—592no—
710C23—1182no—
711C23—1182no—
712C23—1182no—
713C23—1182no—
714C23—1182no—
715C23—2362no—
716C23—2362no—
717C23—2362no—
718C23—2362no—
719C23—2362no—
720C23—2362no—
721C23#1427375414yes—
722C23C2×D4×D5912yes—
723C23C2×D4×D5911yescharacteristic
724Q8—22no—
725Q8—24no—
726Q8—22no—
727Q8—22no—
728Q8—48no—
729Q8—42no—
730Q8—2368no—
731Q8C2×#1174568514yescomplemented
732D4—1188no—
733D4—1182no—
734D4—1182no—
735D4—1182no—
736D4—1182no—
737D4—2368no—
738D4—2368no—
739D4—2368no—
740D4—2368no—
741D4—2362no—
742D4—2362no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—24no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—24no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—48no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—48no—
756C2×C4—42no—
757C2×C4—592no—
758C2×C4—592no—
759C2×C4—592no—
760C2×C4—1182no—
761C2×C4—1182no—
762C2×C4—1182no—
763C2×C4—1182no—
764C2×C4—1182no—
765C2×C4—1184no—
766C2×C4—1182no—
767C2×C4—1182no—
768C2×C4—2368no—
769C2×C4—2368no—
770C2×C4—2368no—
771C2×C4—2362no—
772C2×C4—2362no—
773C2×C4C2×D4×D5912yes—
774C2×C4C2×D4×D5911yescharacteristic
775C2×C4C2×#1174568512yes—
776C2×C4#1427377212yes—
777C2×C4C24×D5911yescharacteristic
778C8—22no—
779C8—22no—
780C8—1182no—
781C8—1182no—
782C22—22no—
783C22—22no—
784C22—28no—
785C22—1182no—
786C22—1182no—
787C22—1182no—
788C22—4724no—
789C22—4724no—
790C22—2362no—
791C22—2362no—
792C22—2362no—
793C22—2362no—
794C22—2362no—
795C22—2362no—
796C22—2364no—
797C22#1683804212yes—
798C22C2×#1427375414yes—
799C22C2×#1427375412yes—
800C22#1683821512yes—
801C22C22×D4×D5911yescharacteristic
802C4—22no—
803C4—24no—
804C4—42no—
805C4—42no—
806C4—42no—
807C4—1182no—
808C4—1182no—
809C4—1182no—
810C4—2362no—
811C4—2362no—
812C4#1683804212yes—
813C4C22×#1174568511yescharacteristic
814C4C2×#1427377211yescharacteristic
815C2—24no—
816C2—4722no—
817C2—4722no—
818C2—2362no—
819C2#2143608314yesdirect product factor
820C2C2×#1683804211yescharacteristic
821C2C22×#1427375411yescharacteristic
822C2C2×#1683821511yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC22×#103×C59C2
socleC23×C59C22×D4
hypercenterC22×#103D59
hypocenterC59C2×#3308
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#103

Complements

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

NH ≅ G/Ntype
1. C2×#16838063C2semidirect
2. C2×#16838053C2semidirect
3. #21436083C2direct (N × H)
4. C2×#16837763C2semidirect
5. C2×#16837736C2semidirect
6. C2×#16837715C2semidirect
7. C2×#16837695C2semidirect
8. C2×#16837651C2semidirect
9. C2×#16837638C2semidirect
10. C2×#16837620C2semidirect
11. C2×#16837550C2semidirect
12. C2×#16837541C2semidirect
13. C2×#16837505C2semidirect
14. C2×#16837473C2semidirect
15. C2×#16837402C2semidirect
16. C22×#103×C59C2semidirect
24. #16838063C22semidirect
26. #16838053C22semidirect
44. #16837763C22semidirect
45. #16837736C22semidirect
46. #16837715C22semidirect
47. #16837695C22semidirect
48. #16837651C22semidirect
49. #16837638C22semidirect
50. #16837620C22semidirect
51. #16837550C22semidirect
52. #16837541C22semidirect
53. #16837505C22semidirect
54. #16837473C22semidirect
59. #16837402C22semidirect
76. C2×#103×C59C22semidirect
200. C2×Q8×C59#41semidirect
318. Q8×C59C2×#41semidirect
419. C22×#103D59semidirect
421. C2×C59#3308semidirect
480. C2×#103C2×D59semidirect
488. C59C2×#3308semidirect
618. C2×Q8#11745685semidirect
731. Q8C2×#11745685semidirect
819. C2#21436083direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168380632
C2×#168380532
#214360832
C2×#168377632
C2×#168377362
C2×#168377152
C2×#168376952
C2×#168376512
C2×#168376382
C2×#168376202
C2×#168375502
C2×#168375412
C2×#168375052
C2×#168374732
C2×#168374022
C22×#103×C592
C2×#330859