Finite Group Databasebeta

← C2×#21434952 #29459346

Subgroups — C2×#21434952 #29459346

Order 15104.

2378 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837982C211yesmaximal, characteristic, complemented
2C2×#16837969C211yesmaximal, characteristic, complemented
3#21434952C2116yesmaximal, direct product factor
4C2×#16837719C211yesmaximal, characteristic, complemented
5C2×#16837740C211yesmaximal, characteristic, complemented
6C2×#16837727C211yesmaximal, characteristic, complemented
7C2×#16837714C211yesmaximal, characteristic, complemented
8C2×#16837654C211yesmaximal, characteristic, complemented
9C2×#16837645C211yesmaximal, characteristic, complemented
10C2×#16837637C211yesmaximal, characteristic, complemented
11C2×#16837628C211yesmaximal, characteristic, complemented
12C2×#16837546C211yesmaximal, characteristic, complemented
13C2×#16837546C211yesmaximal, characteristic, complemented
14C2×#16837536C211yesmaximal, characteristic, complemented
15C2×#16837367C211yesmaximal, characteristic, complemented
16C2×C59×#450C211yesmaximal, characteristic, complemented
17C22×#11745689C2211yescharacteristic, complemented
18C22×#11745685C2211yescharacteristic
19C22×#11745669C2211yescharacteristic
20C22×#11745669C2211yescharacteristic
21C22×#11745659C2211yescharacteristic, complemented
22C22×C8×D59C2211yescharacteristic, complemented
23#16837982—24no—
24#16837982C2218yescomplemented
25#16837969—24no—
26#16837969C2218yescomplemented
27C2×#14273723—21no—
28C2×#14273714—21no—
29C2×#14273705—21no—
30C2×#14273703C2211yescharacteristic, complemented
31C2×#14273702—21no—
32C2×#14273702C2211yescharacteristic, complemented
33C2×#14273701C2211yescharacteristic
34C2×#14273700—21no—
35C2×#14273700—21no—
36C2×#14273698C2211yescharacteristic
37C2×#14273698C2211yescharacteristic
38C2×#14273698C2211yescharacteristic
39C2×#14273698C2211yescharacteristic
40C2×#14273696—21no—
41C2×#14273696—21no—
42C2×#14273686C2211yescharacteristic
43C2×C4⋊C4×D59C2211yescharacteristic, complemented
44#16837740C2218yescomplemented
45#16837727C2218yescomplemented
46#16837719C2218yescomplemented
47#16837714C2218yescomplemented
48#16837654C2218yescomplemented
49#16837645C2218yescomplemented
50#16837637C2218yescomplemented
51#16837628C2218yescomplemented
52#16837546C2218yescomplemented
53#16837546C2218yescomplemented
54#16837536C2218yescomplemented
55C2×#14273661C2211yescharacteristic, complemented
56C2×#14273660C2211yescharacteristic, complemented
57C2×#14273659C2211yescharacteristic, complemented
58C2×#14273658C2211yescharacteristic, complemented
59C2×#14273651C2211yescharacteristic, complemented
60C2×#14273651C2211yescharacteristic, complemented
61C2×#14273649C2211yescharacteristic, complemented
62C2×#14273649C2211yescharacteristic, complemented
63C2×#14273648C2211yescharacteristic
64C2×#14273648C2211yescharacteristic
65#16837367C2218yescomplemented
66C2×C22⋊(C59⋊C8)C2211yescharacteristic
67C2×(C2×D59)⋊C8C2211yescharacteristic, complemented
68C2×(C2×D59)⋊C8C2211yescharacteristic, complemented
69C23×D4×C59C2211yescharacteristic
70C22×SD16×C59C2211yescharacteristic
71C22×SD16×C59C2211yescharacteristic
72C2×C22⋊Q8×C59C2211yescharacteristic
73C59×#450C2218yescomplemented
74C2×#102×C59C2211yescharacteristic
75C2×#102×C59C2211yescharacteristic
76C2×C22⋊C8×C59C2211yescharacteristic
77C2×#11745689—22no—
78C2×#11745689—42no—
79C2×#11745689—42no—
80C2×#11745689C2314yescomplemented
81C2×#11745685—42no—
82C2×#11745685—42no—
83C2×#11745685D414yes—
84C2×#11745685C2314yes—
85C22×Dic118D411yescharacteristic
86C22×D236—21no—
87C22×D236—21no—
88C22×D236D411yescharacteristic
89C22×D236C2311yescharacteristic
90C22×C22⋊D59—21no—
91C22×C22⋊D59—21no—
92C22×C22⋊D59—21no—
93C22×C22⋊D59—21no—
94C22×C22⋊D59—21no—
95C22×C22⋊D59D411yescharacteristic
96C22×C22⋊D59D411yescharacteristic
97C22×C4×D59—21no—
98C22×C4×D59—21no—
99C22×C4×D59C2311yescharacteristic
100C22×C4×D59C2311yescharacteristic
101C2×#11745669—42no—
102C2×#11745669—42no—
103C2×#11745669C2314yes—
104C2×#11745669C2314yes—
105C2×#11745659—42no—
106C2×#11745659C2314yescomplemented
107C22×C59⋊C8C2311yescharacteristic
108C22×C59⋊C8C2311yescharacteristic
109C2×C8×D59—42no—
110C2×C8×D59C2314yescomplemented
111#14273723—28no—
112#14273714—28no—
113#14273705—28no—
114#14273703—22no—
115#14273703C2314yescomplemented
116#14273702—28no—
117#14273702—22no—
118#14273702C2314yescomplemented
119#14273701—22no—
120#14273701C2314yes—
121#14273700—28no—
122#14273700—28no—
123#14273698—22no—
124#14273698—22no—
125#14273698—22no—
126#14273698—22no—
127#14273698C2314yes—
128#14273698C2314yes—
129#14273698C2314yes—
130#14273698C2314yes—
131#14273696—28no—
132#14273696—28no—
133#14273686—22no—
134#14273686C2314yes—
135C2×C4⋊Dic59C2311yescharacteristic
136C2×C4⋊Dic59C2311yescharacteristic
137C2×C4⋊Dic59C2311yescharacteristic
138C2×Dic59⋊C4—21no—
139C2×Dic59⋊C4—21no—
140C4⋊C4×D59—22no—
141C4⋊C4×D59C2314yescomplemented
142C2×C22⋊Dic59—21no—
143C2×C22⋊Dic59—21no—
144C2×C22⋊Dic59—21no—
145C2×C22⋊Dic59—21no—
146C2×C22⋊Dic59—21no—
147C2×(C2×D59)⋊C4—21no—
148C2×(C2×D59)⋊C4—21no—
149C2×(C2×D59)⋊C4—21no—
150C2×C4×Dic59—21no—
151#14273661C2314yescomplemented
152#14273660C2314yescomplemented
153#14273659C2314yescomplemented
154#14273658C2314yescomplemented
155#14273651C2314yescomplemented
156#14273651C2314yescomplemented
157#14273649C2314yescomplemented
158#14273649C2314yescomplemented
159#14273648C2314yes—
160#14273648C2314yes—
161C22⋊(C59⋊C8)C2314yes—
162(C2×D59)⋊C8C2314yescomplemented
163(C2×D59)⋊C8C2314yescomplemented
164C25×C59—21no—
165C22×Q8×C59C2311yescharacteristic
166C22×D4×C59—21no—
167C22×D4×C59—22no—
168C22×D4×C59—42no—
169C22×D4×C59—42no—
170C22×D4×C59C2311yescharacteristic
171C22×D4×C59C2311yescharacteristic
172C22×D4×C59C2314yes—
173C23×C4×C59C2311yescharacteristic
174C2×SD16×C59—42no—
175C2×SD16×C59—42no—
176C2×SD16×C59C2314yes—
177C2×SD16×C59C2314yes—
178C22×C8×C59C2311yescharacteristic
179C22×C8×C59C2311yescharacteristic
180C22⋊Q8×C59—22no—
181C22⋊Q8×C59C2314yes—
182C2×C4⋊C4×C59—21no—
183C2×C4⋊C4×C59C2311yescharacteristic
184C2×C22⋊C4×C59—21no—
185#102×C59C2314yes—
186#102×C59C2314yes—
187C22⋊C8×C59C2314yes—
188C24×C59—21no—
189C24×C59—21no—
190C24×C59—24no—
191C24×C59—44no—
192C24×C59—82no—
193C24×C59—82no—
194C24×C59C2×D411yescharacteristic
195C23×D59—21no—
196C23×D59C2×D411yescharacteristic
197C23×D59C2×D411yescharacteristic
198C2×Q8×C59—21no—
199C2×Q8×C59—22no—
200C2×Q8×C59—22no—
201C2×Q8×C59C2412yes—
202C2×D4×C59—21no—
203C2×D4×C59—21no—
204C2×D4×C59—24no—
205C2×D4×C59—22no—
206C2×D4×C59—22no—
207C2×D4×C59—22no—
208C2×D4×C59—22no—
209C2×D4×C59—44no—
210C2×D4×C59—44no—
211C2×D4×C59—44no—
212C2×D4×C59—48no—
213C2×D4×C59C2412yes—
214C2×D4×C59C2412yes—
215C22×C4×C59—22no—
216C22×C4×C59—22no—
217C22×C4×C59—21no—
218C22×C4×C59—21no—
219C22×C4×C59C2×D411yescharacteristic
220C22×C4×C59C2×D412yes—
221C22×C4×C59C2412yes—
222C22×C4×C59C2411yescharacteristic
223C2×C22⋊D59—24no—
224C2×C22⋊D59—24no—
225C2×C22⋊D59—24no—
226C2×C22⋊D59—24no—
227C2×C22⋊D59—24no—
228C2×C22⋊D59—42no—
229C2×C22⋊D59—42no—
230C2×C22⋊D59—82no—
231C2×C22⋊D59—82no—
232C2×C22⋊D59—82no—
233C2×C22⋊D59—82no—
234C2×C22⋊D59—82no—
235C2×C22⋊D59C2×D414yes—
236C2×C22⋊D59C2×D414yes—
237C22×Dic59—21no—
238C22×Dic59—21no—
239C22×Dic59—21no—
240C22×Dic59C2×D411yescharacteristic
241C22×Dic59C2×D411yescharacteristic
242#11745689—44no—
243#11745689—44no—
244#11745689—48no—
245#11745685—48no—
246#11745685—44no—
247#11745685—44no—
248C2×D236—22no—
249C2×D236—22no—
250C2×D236—24no—
251C2×D236—21no—
252C2×D236—24no—
253C2×D236—42no—
254C2×D236—44no—
255C2×D236—82no—
256C2×D236C2×D414yes—
257C2×D236C2412yes—
258C2×C4×D59—22no—
259C2×C4×D59—22no—
260C2×C4×D59—22no—
261C2×C4×D59—22no—
262C2×C4×D59—24no—
263C2×C4×D59—24no—
264C2×C4×D59—44no—
265C2×C4×D59—82no—
266C2×C4×D59C2×D412yes—
267C2×C4×D59C2×D412yes—
268C2×C4×D59C2412yes—
269C2×C4×D59C2412yes—
270C2×Dic118—42no—
271C2×Dic118C2×D414yes—
272SD16×C59—44no—
273SD16×C59—44no—
274C2×C8×C59—22no—
275C2×C8×C59—22no—
276C2×C8×C59C2412yes—
277C2×C8×C59C2412yes—
278C4⋊C4×C59—24no—
279C4⋊C4×C59—21no—
280C4⋊C4×C59C2412yes—
281C22⋊C4×C59—24no—
282C22⋊Dic59—24no—
283C22⋊Dic59—24no—
284C22⋊Dic59—24no—
285C22⋊Dic59—24no—
286C22⋊Dic59—24no—
287#11745669—44no—
288#11745669—44no—
289(C2×D59)⋊C4—24no—
290(C2×D59)⋊C4—24no—
291(C2×D59)⋊C4—24no—
292C4⋊Dic59—21no—
293C4⋊Dic59—21no—
294C4⋊Dic59—21no—
295C4⋊Dic59C2412yes—
296C4⋊Dic59C2412yes—
297C4⋊Dic59C2412yes—
298Dic59⋊C4—24no—
299Dic59⋊C4—24no—
300C4×Dic59—24no—
301C2×C59⋊C8—22no—
302C2×C59⋊C8—22no—
303C2×C59⋊C8C2412yes—
304C2×C59⋊C8C2412yes—
305#11745659—44no—
306C8×D59—44no—
307C23×C59—22no—
308C23×C59—22no—
309C23×C59—22no—
310C23×C59—22no—
311C23×C59—22no—
312C23×C59—48no—
313C23×C59—42no—
314C23×C59—42no—
315C23×C59—42no—
316C23×C59—42no—
317C23×C59—42no—
318C23×C59—42no—
319C23×C59—84no—
320C23×C59—84no—
321C23×C59—816no—
322C23×C59C22×D412yes—
323C23×C59C22×D411yescharacteristic
324C22×D59—22no—
325C22×D59—22no—
326C22×D59—22no—
327C22×D59—22no—
328C22×D59—22no—
329C22×D59—22no—
330C22×D59—22no—
331C22×D59—42no—
332C22×D59—42no—
333C22×D59—42no—
334C22×D59C22×D412yes—
335C22×D59C22×D412yes—
336Q8×C59—22no—
337Q8×C59—22no—
338Q8×C59—42no—
339D4×C59—22no—
340D4×C59—22no—
341D4×C59—22no—
342D4×C59—22no—
343D4×C59—48no—
344D4×C59—42no—
345D4×C59—42no—
346C2×C4×C59—22no—
347C2×C4×C59—24no—
348C2×C4×C59—22no—
349C2×C4×C59—22no—
350C2×C4×C59—22no—
351C2×C4×C59—22no—
352C2×C4×C59—42no—
353C2×C4×C59—42no—
354C2×C4×C59C22×D412yes—
355C2×C4×C59C22×D411yescharacteristic
356C2×C4×C59H(5,𝔽2)12yes—
357C2×C4×C59H(5,𝔽2)12yes—
358C2×C4×C59C2511yescharacteristic
359C22⋊D59—44no—
360C22⋊D59—44no—
361C22⋊D59—84no—
362C22⋊D59—84no—
363C22⋊D59—84no—
364C22⋊D59—84no—
365C22⋊D59—84no—
366C2×Dic59—22no—
367C2×Dic59—22no—
368C2×Dic59—22no—
369C2×Dic59—22no—
370C2×Dic59—22no—
371C2×Dic59—42no—
372C2×Dic59—42no—
373C2×Dic59—42no—
374C2×Dic59C22×D412yes—
375C2×Dic59C22×D412yes—
376D236—22no—
377D236—22no—
378D236—44no—
379D236—48no—
380D236—42no—
381D236—84no—
382C4×D59—24no—
383C4×D59—24no—
384C4×D59—22no—
385C4×D59—22no—
386C4×D59—22no—
387C4×D59—22no—
388C4×D59—48no—
389C4×D59—84no—
390Dic118—44no—
391C8×C59—22no—
392C8×C59—22no—
393C59⋊C8—22no—
394C59⋊C8—22no—
395C2×#3198—591nomaximal, Sylow
396C22×C59—22no—
397C22×C59—22no—
398C22×C59—22no—
399C22×C59—44no—
400C22×C59—42no—
401C22×C59—42no—
402C22×C59—42no—
403C22×C59—42no—
404C22×C59—42no—
405C22×C59—42no—
406C22×C59—816no—
407C22×C59—84no—
408C22×C59—84no—
409C22×C59#53412yes—
410C22×C59#57612yes—
411C22×C59#57712yes—
412C22×C59C23×D411yescharacteristic
413C2×D59—22no—
414C2×D59—22no—
415C2×D59—22no—
416C2×D59—22no—
417C2×D59—22no—
418C2×D59—22no—
419C2×D59—44no—
420C2×D59—44no—
421C2×D59—42no—
422C2×D59—42no—
423C2×D59—42no—
424C2×D59—84no—
425C4×C59—22no—
426C4×C59—42no—
427C4×C59—42no—
428C4×C59#53412yes—
429C4×C59C2×H(5,𝔽2)11yescharacteristic
430C4×C59C2×H(5,𝔽2)11yescharacteristic
431Dic59—22no—
432Dic59—22no—
433Dic59—42no—
434Dic59—42no—
435Dic59—42no—
436C2×#537—591no—
437C2×#535—591no—
438#3198—5916no—
439C2×#481—591no—
440C2×#485—591no—
441C2×#482—591no—
442C2×#480—591no—
443C2×#469—591no—
444C2×#468—591no—
445C2×#466—591no—
446C2×#465—591no—
447C2×#449—591no—
448C2×#449—591no—
449C2×#450D5911yescharacteristic, complemented
450C2×#447—591no—
451C2×#408—591no—
452C2×C59—42no—
453C2×C59—82no—
454C2×C59—82no—
455C2×C59#319814yescomplemented
456C2×C59C2×#53411yescharacteristic
457C2×C59C2×#57611yescharacteristic
458C2×C59C2×#57711yescharacteristic
459D59—42no—
460D59—42no—
461D59—82no—
462C22×#41—591no—
463C22×#41—591no—
464C23×D4C2×D5911yescharacteristic
465C22×SD16C2×D5911yescharacteristic
466C22×SD16C2×D5911yescharacteristic
467C22×D8—591no—
468C22×D8—591no—
469C22×M16—591no—
470C23×C8—591no—
471#537—598no—
472#537—1184no—
473#535—598no—
474#535—1184no—
475C2×#127—1181no—
476C2×#124—1181no—
477C2×C22⋊Q8—591no—
478C2×C22⋊Q8—1181no—
479C2×C22⋊Q8C2×D5911yescharacteristic
480C2×#121—591no—
481C2×#121—591no—
482C2×#121—591no—
483C2×#121—591no—
484C2×#121—591no—
485C2×#121—591no—
486C2×#121—1181no—
487C2×#121—1181no—
488C2×#121—1181no—
489C2×#120—1181no—
490C2×#120—1181no—
491C2×#117—591no—
492C22×C4⋊C4—591no—
493#485—598no—
494#482—598no—
495#481—598no—
496#480—598no—
497#469—598no—
498#468—598no—
499#466—598no—
500#465—598no—
501#450C2×D5918yescomplemented
502#449—598no—
503#449—598no—
504#447—598no—
505C2×#107—591no—
506C2×#107—591no—
507C2×#106—591no—
508C2×#106—591no—
509C2×#103—591no—
510C2×#103—591no—
511C2×#102—591no—
512C2×#102—591no—
513C2×#102—591no—
514C2×#102—591no—
515C2×#102C2×D5911yescharacteristic
516C2×#102C2×D5911yescharacteristic
517#408—598no—
518C2×C22⋊C8—591no—
519C2×C22⋊C8—591no—
520C2×C22⋊C8—591no—
521C2×C22⋊C8C2×D5911yescharacteristic
522C59C2×#319811yescharacteristic, complemented, Sylow
523C25—21no—
524C2×#41—594no—
525C2×#41—594no—
526C2×#41—594no—
527C2×#41—1182no—
528C2×#41—2362no—
529C2×#41—2362no—
530C2×#41—2362no—
531C2×#41—2362no—
532C22×Q8—591no—
533C22×Q8C22×D5911yescharacteristic
534C22×D4—21no—
535C22×D4—22no—
536C22×D4—42no—
537C22×D4—42no—
538C22×D4—591no—
539C22×D4—591no—
540C22×D4—591no—
541C22×D4—591no—
542C22×D4—1181no—
543C22×D4—1181no—
544C22×D4—1181no—
545C22×D4—1181no—
546C22×D4—1181no—
547C22×D4—1181no—
548C22×D4—1181no—
549C22×D4C22×D5911yescharacteristic
550C22×D4C22×D5911yescharacteristic
551C22×D4C22×D5914yes—
552C23×C4—591no—
553C23×C4—591no—
554C23×C4—1181no—
555C23×C4—1181no—
556C23×C4C22×D5911yescharacteristic
557C2×SD16—42no—
558C2×SD16—42no—
559C2×SD16C22×D5914yes—
560C2×SD16C22×D5914yes—
561C2×D8—594no—
562C2×D8—594no—
563C2×D8—2362no—
564C2×D8—2362no—
565C2×M16—594no—
566C2×M16—2362no—
567C22×C8—591no—
568C22×C8—591no—
569C22×C8—594no—
570C22×C8—2362no—
571C22×C8C22×D5911yescharacteristic
572C22×C8C22×D5911yescharacteristic
573#127—1188no—
574#124—1188no—
575C22⋊Q8—22no—
576C22⋊Q8—594no—
577C22⋊Q8—1188no—
578C22⋊Q8—1182no—
579C22⋊Q8C22×D5914yes—
580#121—594no—
581#121—594no—
582#121—594no—
583#121—594no—
584#121—594no—
585#121—594no—
586#121—1188no—
587#121—1188no—
588#121—1182no—
589#121—1188no—
590#121—1182no—
591#121—1182no—
592#121—1182no—
593#121—1182no—
594#121—1182no—
595#120—1188no—
596#120—1188no—
597#117—594no—
598#117—1182no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—591no—
601C2×C4⋊C4—591no—
602C2×C4⋊C4—591no—
603C2×C4⋊C4—594no—
604C2×C4⋊C4—1182no—
605C2×C4⋊C4—1181no—
606C2×C4⋊C4—1181no—
607C2×C4⋊C4C22×D5911yescharacteristic
608C2×C22⋊C4—21no—
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—1181no—
618#107—594no—
619#107—594no—
620#106—594no—
621#106—594no—
622#103—594no—
623#103—594no—
624#102—594no—
625#102—594no—
626#102—594no—
627#102—594no—
628#102C22×D5914yes—
629#102C22×D5914yes—
630C22⋊C8—594no—
631C22⋊C8—594no—
632C22⋊C8—594no—
633C22⋊C8C22×D5914yes—
634C24—21no—
635C24—21no—
636C24—24no—
637C24—44no—
638C24—82no—
639C24—82no—
640C24—591no—
641C24—591no—
642C24—1181no—
643C24D4×D5911yescharacteristic
644#41—2368no—
645#41—2364no—
646#41—2364no—
647#41—2364no—
648#41—2364no—
649#41—2368no—
650C2×Q8—21no—
651C2×Q8—22no—
652C2×Q8—22no—
653C2×Q8—594no—
654C2×Q8—2362no—
655C2×Q8C23×D5912yes—
656C2×D4—21no—
657C2×D4—21no—
658C2×D4—24no—
659C2×D4—22no—
660C2×D4—22no—
661C2×D4—22no—
662C2×D4—22no—
663C2×D4—44no—
664C2×D4—44no—
665C2×D4—44no—
666C2×D4—48no—
667C2×D4—594no—
668C2×D4—594no—
669C2×D4—594no—
670C2×D4—592no—
671C2×D4—1184no—
672C2×D4—1184no—
673C2×D4—1184no—
674C2×D4—1184no—
675C2×D4—1184no—
676C2×D4—1184no—
677C2×D4—1184no—
678C2×D4—1181no—
679C2×D4—1182no—
680C2×D4—1182no—
681C2×D4—4722no—
682C2×D4—4722no—
683C2×D4—4722no—
684C2×D4—4722no—
685C2×D4—4722no—
686C2×D4—4722no—
687C2×D4—2362no—
688C2×D4—2364no—
689C2×D4—2362no—
690C2×D4—2362no—
691C2×D4C23×D5912yes—
692C2×D4C23×D5912yes—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—591no—
698C22×C4—591no—
699C22×C4—592no—
700C22×C4—592no—
701C22×C4—592no—
702C22×C4—592no—
703C22×C4—1184no—
704C22×C4—1184no—
705C22×C4—1182no—
706C22×C4—1182no—
707C22×C4—1182no—
708C22×C4—1182no—
709C22×C4—1181no—
710C22×C4—1181no—
711C22×C4—1181no—
712C22×C4—4722no—
713C22×C4—2364no—
714C22×C4D4×D5912yes—
715C22×C4D4×D5911yescharacteristic
716C22×C4C23×D5912yes—
717C22×C4C23×D5911yescharacteristic
718SD16—44no—
719SD16—44no—
720D8—2364no—
721D8—2364no—
722M16—2364no—
723C2×C8—22no—
724C2×C8—22no—
725C2×C8—592no—
726C2×C8—592no—
727C2×C8—1182no—
728C2×C8—1182no—
729C2×C8—2364no—
730C2×C8C23×D5912yes—
731C2×C8C23×D5912yes—
732C4⋊C4—24no—
733C4⋊C4—21no—
734C4⋊C4—592no—
735C4⋊C4—592no—
736C4⋊C4—592no—
737C4⋊C4—1184no—
738C4⋊C4—1184no—
739C4⋊C4—1181no—
740C4⋊C4—1181no—
741C4⋊C4—1181no—
742C4⋊C4C23×D5912yes—
743C22⋊C4—24no—
744C22⋊C4—1184no—
745C22⋊C4—1184no—
746C22⋊C4—1184no—
747C22⋊C4—1184no—
748C22⋊C4—1184no—
749C22⋊C4—1184no—
750C22⋊C4—1184no—
751C22⋊C4—1184no—
752C42—1184no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—48no—
759C23—42no—
760C23—42no—
761C23—42no—
762C23—42no—
763C23—42no—
764C23—42no—
765C23—84no—
766C23—84no—
767C23—816no—
768C23—592no—
769C23—592no—
770C23—1182no—
771C23—1182no—
772C23—1182no—
773C23—1182no—
774C23—1182no—
775C23—1182no—
776C23—1182no—
777C23—2362no—
778C23—2362no—
779C23—2362no—
780C23C2×D4×D5912yes—
781C23C2×D4×D5911yescharacteristic
782Q8—22no—
783Q8—22no—
784Q8—42no—
785Q8—2364no—
786D4—22no—
787D4—22no—
788D4—22no—
789D4—22no—
790D4—48no—
791D4—42no—
792D4—42no—
793D4—1182no—
794D4—1182no—
795D4—4724no—
796D4—4724no—
797D4—4724no—
798D4—4724no—
799D4—4724no—
800D4—4724no—
801D4—2364no—
802D4—2368no—
803D4—2364no—
804D4—2364no—
805D4—2362no—
806C2×C4—22no—
807C2×C4—24no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—592no—
815C2×C4—592no—
816C2×C4—1182no—
817C2×C4—1182no—
818C2×C4—1184no—
819C2×C4—1184no—
820C2×C4—1182no—
821C2×C4—1182no—
822C2×C4—1182no—
823C2×C4—1182no—
824C2×C4—1182no—
825C2×C4—1182no—
826C2×C4—1182no—
827C2×C4—4724no—
828C2×C4—2368no—
829C2×C4—2362no—
830C2×C4—2362no—
831C2×C4—2362no—
832C2×C4C2×D4×D5912yes—
833C2×C4C2×D4×D5911yescharacteristic
834C2×C4#1427377212yes—
835C2×C4#1427377212yes—
836C2×C4C24×D5911yescharacteristic
837C8—22no—
838C8—22no—
839C8—1182no—
840C8—1182no—
841C22—22no—
842C22—22no—
843C22—22no—
844C22—44no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—816no—
852C22—84no—
853C22—84no—
854C22—1182no—
855C22—1182no—
856C22—1182no—
857C22—1182no—
858C22—1182no—
859C22—1182no—
860C22—4724no—
861C22—2362no—
862C22—2362no—
863C22—2362no—
864C22—2364no—
865C22—2364no—
866C22#1683796212yes—
867C22#1683820612yes—
868C22#1683820812yes—
869C22C22×D4×D5911yescharacteristic
870C4—22no—
871C4—42no—
872C4—42no—
873C4—1182no—
874C4—1182no—
875C4—2362no—
876C4—2362no—
877C4—2362no—
878C4#1683796212yes—
879C4C2×#1427377211yescharacteristic
880C4C2×#1427377211yescharacteristic
881C2—42no—
882C2—82no—
883C2—82no—
884C2—4722no—
885C2—2362no—
886C2—2362no—
887C2#2143495214yesdirect product factor
888C2C2×#1683796211yescharacteristic
889C2C2×#1683820611yescharacteristic
890C2C2×#1683820811yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#450C2
socleC23×C59C22×D4
hypercenterC2×#450D59
hypocenterC59C2×#3198
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#450

Complements

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

NH ≅ G/Ntype
1. C2×#16837982C2semidirect
2. C2×#16837969C2semidirect
3. #21434952C2direct (N × H)
4. C2×#16837719C2semidirect
5. C2×#16837740C2semidirect
6. C2×#16837727C2semidirect
7. C2×#16837714C2semidirect
8. C2×#16837654C2semidirect
9. C2×#16837645C2semidirect
10. C2×#16837637C2semidirect
11. C2×#16837628C2semidirect
12. C2×#16837546C2semidirect
13. C2×#16837546C2semidirect
14. C2×#16837536C2semidirect
15. C2×#16837367C2semidirect
16. C2×C59×#450C2semidirect
17. C22×#11745689C22semidirect
21. C22×#11745659C22semidirect
22. C22×C8×D59C22semidirect
24. #16837982C22semidirect
26. #16837969C22semidirect
30. C2×#14273703C22semidirect
32. C2×#14273702C22semidirect
43. C2×C4⋊C4×D59C22semidirect
44. #16837740C22semidirect
45. #16837727C22semidirect
46. #16837719C22semidirect
47. #16837714C22semidirect
48. #16837654C22semidirect
49. #16837645C22semidirect
50. #16837637C22semidirect
51. #16837628C22semidirect
52. #16837546C22semidirect
53. #16837546C22semidirect
54. #16837536C22semidirect
55. C2×#14273661C22semidirect
56. C2×#14273660C22semidirect
57. C2×#14273659C22semidirect
58. C2×#14273658C22semidirect
59. C2×#14273651C22semidirect
60. C2×#14273651C22semidirect
61. C2×#14273649C22semidirect
62. C2×#14273649C22semidirect
65. #16837367C22semidirect
67. C2×(C2×D59)⋊C8C22semidirect
68. C2×(C2×D59)⋊C8C22semidirect
73. C59×#450C22semidirect
80. C2×#11745689C23semidirect
106. C2×#11745659C23semidirect
110. C2×C8×D59C23semidirect
115. #14273703C23semidirect
118. #14273702C23semidirect
141. C4⋊C4×D59C23semidirect
151. #14273661C23semidirect
152. #14273660C23semidirect
153. #14273659C23semidirect
154. #14273658C23semidirect
155. #14273651C23semidirect
156. #14273651C23semidirect
157. #14273649C23semidirect
158. #14273649C23semidirect
162. (C2×D59)⋊C8C23semidirect
163. (C2×D59)⋊C8C23semidirect
449. C2×#450D59semidirect
455. C2×C59#3198semidirect
501. #450C2×D59semidirect
522. C59C2×#3198semidirect
887. C2#21434952direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168379822
C2×#168379692
#214349522
C2×#168377192
C2×#168377402
C2×#168377272
C2×#168377142
C2×#168376542
C2×#168376452
C2×#168376372
C2×#168376282
C2×#168375462
C2×#168375362
C2×#168373672
C2×C59×#4502
C2×#319859