Finite Group Databasebeta

← C2×#21434943 #29459337

Subgroups — C2×#21434943 #29459337

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×#16837981C211yesmaximal, characteristic, complemented
2C2×#16837968C211yesmaximal, characteristic, complemented
3#21434943C2116yesmaximal, direct product factor
4C2×#16837722C211yesmaximal, characteristic, complemented
5C2×#16837746C211yesmaximal, characteristic, complemented
6C2×#16837724C211yesmaximal, characteristic, complemented
7C2×#16837714C211yesmaximal, characteristic, complemented
8C2×#16837648C211yesmaximal, characteristic, complemented
9C2×#16837636C211yesmaximal, characteristic, complemented
10C2×#16837629C211yesmaximal, characteristic, complemented
11C2×#16837548C211yesmaximal, characteristic, complemented
12C2×#16837544C211yesmaximal, characteristic, complemented
13C2×#16837554C211yesmaximal, characteristic, complemented
14C2×#16837534C211yesmaximal, characteristic, complemented
15C2×#16837370C211yesmaximal, characteristic, complemented
16C2×C59×#469C211yesmaximal, characteristic, complemented
17C22×#11745685C2211yescharacteristic
18C22×#11745687C2211yescharacteristic, complemented
19C22×D4×D59C2211yescharacteristic
20C22×#11745660C2211yescharacteristic
21C22×#11745670C2211yescharacteristic
22C22×#11745669C2211yescharacteristic
23C23×C59⋊C8C2211yescharacteristic, complemented
24#16837981—24no—
25#16837981C2218yescomplemented
26#16837968—24no—
27#16837968C2218yescomplemented
28C2×#14273723—21no—
29C2×#14273713—21no—
30C2×#14273707C2211yescharacteristic
31C2×#14273706C2211yescharacteristic, complemented
32C2×#14273704—21no—
33C2×#14273702C2211yescharacteristic
34C2×#14273701C2211yescharacteristic
35C2×#14273700—21no—
36C2×#14273699—21no—
37C2×#14273698—21no—
38C2×#14273698C2211yescharacteristic
39C2×#14273698C2211yescharacteristic
40C2×#14273697—21no—
41C2×#14273695—21no—
42C2×#14273685C2211yescharacteristic
43C2×C4⋊C4×D59C2211yescharacteristic, complemented
44#16837746C2218yescomplemented
45#16837724C2218yescomplemented
46#16837722C2218yescomplemented
47#16837714C2218yescomplemented
48#16837648C2218yescomplemented
49#16837636C2218yescomplemented
50#16837629C2218yescomplemented
51#16837554C2218yescomplemented
52#16837548C2218yescomplemented
53#16837544C2218yescomplemented
54#16837534C2218yescomplemented
55C2×#14273661C2211yescharacteristic, complemented
56C2×#14273660C2211yescharacteristic, complemented
57C2×#14273658C2211yescharacteristic, complemented
58C2×#14273652C2211yescharacteristic, complemented
59C2×#14273650C2211yescharacteristic, complemented
60C2×#14273649C2211yescharacteristic
61C2×#14273648C2211yescharacteristic
62C2×#14273648C2211yescharacteristic, complemented
63C2×#14273647C2211yescharacteristic
64#16837370C2218yescomplemented
65C2×(C2×D59)⋊C8C2211yescharacteristic
66C2×(C2×D59)⋊C8C2211yescharacteristic
67C2×(C2×D59)⋊C8C2211yescharacteristic, complemented
68C2×(C2×D59)⋊C8C2211yescharacteristic, complemented
69C22×D8×C59C2211yescharacteristic
70C22×M16×C59C2211yescharacteristic, complemented
71C2×#121×C59C2211yescharacteristic
72C2×#121×C59C2211yescharacteristic, complemented
73C59×#469C2218yescomplemented
74C2×#106×C59C2211yescharacteristic, complemented
75C2×#102×C59C2211yescharacteristic
76C2×#102×C59C2211yescharacteristic, complemented
77C24×D59—21no—
78C2×#11745685—42no—
79C2×#11745685—42no—
80C2×#11745685D414yes—
81C2×#11745685C2314yes—
82C2×#11745687—22no—
83C2×#11745687—42no—
84C2×#11745687—42no—
85C2×#11745687C2314yescomplemented
86C22×Dic118D411yescharacteristic
87C22×Dic118C2311yescharacteristic
88C22×D236—21no—
89C22×D236D411yescharacteristic
90C22×D236C2311yescharacteristic
91C22×C22⋊D59—21no—
92C22×C22⋊D59—21no—
93C22×C22⋊D59—21no—
94C22×C22⋊D59—21no—
95C22×C22⋊D59—21no—
96C22×C22⋊D59D411yescharacteristic
97C22×C22⋊D59D411yescharacteristic
98C2×D4×D59—22no—
99C2×D4×D59—42no—
100C2×D4×D59—42no—
101C2×D4×D59C2314yes—
102C23×Dic59—21no—
103C22×C4×D59—21no—
104C22×C4×D59C2311yescharacteristic
105C22×C4×D59C2311yescharacteristic
106C2×#11745660—42no—
107C2×#11745660C2314yes—
108C2×#11745670—42no—
109C2×#11745670C2314yes—
110C2×#11745669—42no—
111C2×#11745669C2314yes—
112C22×C59⋊C8—42no—
113C22×C59⋊C8C2311yescharacteristic
114C22×C59⋊C8C2311yescharacteristic
115C22×C59⋊C8C2314yescomplemented
116#14273723—28no—
117#14273713—28no—
118#14273707—22no—
119#14273707C2314yes—
120#14273706—22no—
121#14273706C2314yescomplemented
122#14273704—28no—
123#14273702—22no—
124#14273702C2314yes—
125#14273701—22no—
126#14273701C2314yes—
127#14273700—28no—
128#14273699—28no—
129#14273698—28no—
130#14273698—22no—
131#14273698—22no—
132#14273698C2314yes—
133#14273698C2314yes—
134#14273697—28no—
135#14273695—28no—
136#14273685—22no—
137#14273685C2314yes—
138C2×C4⋊Dic59—21no—
139C2×C4⋊Dic59C2311yescharacteristic
140C2×C4⋊Dic59C2311yescharacteristic
141C2×Dic59⋊C4—21no—
142C2×Dic59⋊C4—21no—
143C4⋊C4×D59—22no—
144C4⋊C4×D59C2314yescomplemented
145C2×C22⋊Dic59—21no—
146C2×C22⋊Dic59—21no—
147C2×C22⋊Dic59—21no—
148C2×(C2×D59)⋊C4—21no—
149C2×(C2×D59)⋊C4—21no—
150C2×(C2×D59)⋊C4—21no—
151C2×(C2×D59)⋊C4—21no—
152C2×C4×Dic59—21no—
153#14273661C2314yescomplemented
154#14273660C2314yescomplemented
155#14273658C2314yescomplemented
156#14273652C2314yescomplemented
157#14273650C2314yescomplemented
158#14273649C2314yes—
159#14273648C2314yes—
160#14273648C2314yescomplemented
161#14273647C2314yes—
162(C2×D59)⋊C8C2314yes—
163(C2×D59)⋊C8C2314yes—
164(C2×D59)⋊C8C2314yescomplemented
165(C2×D59)⋊C8C2314yescomplemented
166C22×D4×C59—21no—
167C22×D4×C59—21no—
168C22×D4×C59C2311yescharacteristic
169C22×D4×C59C2311yescharacteristic
170C23×C4×C59C2311yescharacteristic
171C2×D8×C59—42no—
172C2×D8×C59C2314yes—
173C2×M16×C59—42no—
174C2×M16×C59C2314yescomplemented
175C22×C8×C59C2311yescharacteristic
176C22×C8×C59C2311yescharacteristic
177#121×C59—22no—
178#121×C59—22no—
179#121×C59C2314yes—
180#121×C59C2314yescomplemented
181C2×C4⋊C4×C59C2311yescharacteristic
182C2×C4⋊C4×C59C2311yescharacteristic
183C2×C22⋊C4×C59—21no—
184C2×C22⋊C4×C59—21no—
185#106×C59C2314yescomplemented
186#102×C59C2314yes—
187#102×C59C2314yescomplemented
188C24×C59—21no—
189C24×C59—21no—
190C24×C59C2×D411yescharacteristic
191C23×D59—21no—
192C23×D59—24no—
193C23×D59—44no—
194C23×D59—82no—
195C23×D59—82no—
196C23×D59C2×D411yescharacteristic
197C23×D59C2×D411yescharacteristic
198C2×D4×C59—24no—
199C2×D4×C59—24no—
200C2×D4×C59—21no—
201C2×D4×C59—21no—
202C2×D4×C59—22no—
203C2×D4×C59—22no—
204C2×D4×C59—22no—
205C2×D4×C59—22no—
206C2×D4×C59—82no—
207C2×D4×C59—82no—
208C2×D4×C59C2412yes—
209C2×D4×C59C2412yes—
210C22×C4×C59—22no—
211C22×C4×C59—22no—
212C22×C4×C59—21no—
213C22×C4×C59—21no—
214C22×C4×C59C2×D411yescharacteristic
215C22×C4×C59C2×D412yes—
216C22×C4×C59C2412yes—
217C22×C4×C59C2411yescharacteristic
218C2×C22⋊D59—24no—
219C2×C22⋊D59—24no—
220C2×C22⋊D59—24no—
221C2×C22⋊D59—24no—
222C2×C22⋊D59—24no—
223C2×C22⋊D59—42no—
224C2×C22⋊D59—42no—
225C2×C22⋊D59—44no—
226C2×C22⋊D59—44no—
227C2×C22⋊D59—82no—
228C2×C22⋊D59—82no—
229C2×C22⋊D59—82no—
230C2×C22⋊D59C2×D414yes—
231C2×C22⋊D59C2×D414yes—
232C22×Dic59—21no—
233C22×Dic59—21no—
234C22×Dic59—21no—
235C22×Dic59—24no—
236C22×Dic59—44no—
237C22×Dic59C2×D411yescharacteristic
238C22×Dic59C2×D411yescharacteristic
239#11745687—44no—
240#11745687—44no—
241#11745687—48no—
242D4×D59—44no—
243D4×D59—44no—
244D4×D59—48no—
245#11745685—48no—
246#11745685—44no—
247#11745685—44no—
248C2×D236—22no—
249C2×D236—22no—
250C2×D236—21no—
251C2×D236—24no—
252C2×D236—42no—
253C2×D236—82no—
254C2×D236C2×D414yes—
255C2×D236C2412yes—
256C2×C4×D59—22no—
257C2×C4×D59—22no—
258C2×C4×D59—22no—
259C2×C4×D59—22no—
260C2×C4×D59—24no—
261C2×C4×D59—82no—
262C2×C4×D59C2×D412yes—
263C2×C4×D59C2×D412yes—
264C2×C4×D59C2412yes—
265C2×C4×D59C2412yes—
266C2×Dic118—22no—
267C2×Dic118—22no—
268C2×Dic118—21no—
269C2×Dic118—42no—
270C2×Dic118C2×D414yes—
271C2×Dic118C2412yes—
272D8×C59—44no—
273M16×C59—44no—
274C2×C8×C59—22no—
275C2×C8×C59—22no—
276C2×C8×C59C2412yes—
277C2×C8×C59C2412yes—
278C4⋊C4×C59—21no—
279C4⋊C4×C59—21no—
280C4⋊C4×C59C2412yes—
281C4⋊C4×C59C2412yes—
282C22⋊C4×C59—24no—
283C22⋊C4×C59—24no—
284C22⋊Dic59—24no—
285C22⋊Dic59—24no—
286C22⋊Dic59—24no—
287#11745670—44no—
288#11745669—44no—
289(C2×D59)⋊C4—24no—
290(C2×D59)⋊C4—24no—
291(C2×D59)⋊C4—24no—
292(C2×D59)⋊C4—24no—
293C4⋊Dic59—21no—
294C4⋊Dic59—21no—
295C4⋊Dic59—24no—
296C4⋊Dic59C2412yes—
297C4⋊Dic59C2412yes—
298Dic59⋊C4—24no—
299Dic59⋊C4—24no—
300C4×Dic59—24no—
301C2×C59⋊C8—22no—
302C2×C59⋊C8—22no—
303C2×C59⋊C8—44no—
304C2×C59⋊C8C2412yes—
305C2×C59⋊C8C2412yes—
306#11745660—44no—
307C23×C59—22no—
308C23×C59—22no—
309C23×C59—22no—
310C23×C59—22no—
311C23×C59—22no—
312C23×C59—42no—
313C23×C59—42no—
314C23×C59—42no—
315C23×C59—42no—
316C23×C59—42no—
317C23×C59—42no—
318C23×C59C22×D412yes—
319C23×C59C22×D411yescharacteristic
320C22×D59—22no—
321C22×D59—22no—
322C22×D59—22no—
323C22×D59—22no—
324C22×D59—22no—
325C22×D59—22no—
326C22×D59—22no—
327C22×D59—48no—
328C22×D59—42no—
329C22×D59—42no—
330C22×D59—42no—
331C22×D59—84no—
332C22×D59—84no—
333C22×D59—816no—
334C22×D59C22×D412yes—
335C22×D59C22×D412yes—
336D4×C59—22no—
337D4×C59—22no—
338D4×C59—22no—
339D4×C59—22no—
340D4×C59—42no—
341D4×C59—42no—
342D4×C59—84no—
343D4×C59—84no—
344C2×C4×C59—22no—
345C2×C4×C59—24no—
346C2×C4×C59—22no—
347C2×C4×C59—22no—
348C2×C4×C59—22no—
349C2×C4×C59—22no—
350C2×C4×C59—42no—
351C2×C4×C59—42no—
352C2×C4×C59C22×D412yes—
353C2×C4×C59C22×D411yescharacteristic
354C2×C4×C59H(5,𝔽2)12yes—
355C2×C4×C59H(5,𝔽2)12yes—
356C2×C4×C59C2511yescharacteristic
357C22⋊D59—44no—
358C22⋊D59—44no—
359C22⋊D59—48no—
360C22⋊D59—48no—
361C22⋊D59—84no—
362C22⋊D59—84no—
363C22⋊D59—84no—
364C2×Dic59—22no—
365C2×Dic59—22no—
366C2×Dic59—22no—
367C2×Dic59—22no—
368C2×Dic59—22no—
369C2×Dic59—48no—
370C2×Dic59—42no—
371C2×Dic59—42no—
372C2×Dic59—42no—
373C2×Dic59C22×D412yes—
374C2×Dic59C22×D412yes—
375D236—22no—
376D236—22no—
377D236—44no—
378D236—42no—
379D236—84no—
380C4×D59—24no—
381C4×D59—24no—
382C4×D59—22no—
383C4×D59—22no—
384C4×D59—22no—
385C4×D59—22no—
386C4×D59—84no—
387Dic118—22no—
388Dic118—22no—
389Dic118—44no—
390Dic118—42no—
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—84no—
407C22×C59—84no—
408C22×C59#53412yes—
409C22×C59#57612yes—
410C22×C59#57712yes—
411C22×C59C23×D411yescharacteristic
412C2×D59—22no—
413C2×D59—22no—
414C2×D59—22no—
415C2×D59—22no—
416C2×D59—22no—
417C2×D59—22no—
418C2×D59—44no—
419C2×D59—44no—
420C2×D59—42no—
421C2×D59—42no—
422C2×D59—42no—
423C2×D59—816no—
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×#469D5911yescharacteristic, complemented
444C2×#468—591no—
445C2×#466—591no—
446C2×#465—591no—
447C2×#449—591no—
448C2×#449—591no—
449C2×#450—591no—
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×D4—591no—
465C22×SD16—591no—
466C22×SD16—591no—
467C22×D8—591no—
468C22×D8C2×D5911yescharacteristic
469C22×M16C2×D5911yescharacteristic, complemented
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—591no—
479C2×C22⋊Q8—1181no—
480C2×#121—591no—
481C2×#121—591no—
482C2×#121—591no—
483C2×#121—591no—
484C2×#121—1181no—
485C2×#121—1181no—
486C2×#121—1181no—
487C2×#121C2×D5911yescharacteristic
488C2×#121C2×D5911yescharacteristic, complemented
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#469C2×D5918yescomplemented
498#468—598no—
499#466—598no—
500#465—598no—
501#450—598no—
502#449—598no—
503#449—598no—
504#447—598no—
505C2×#107—591no—
506C2×#107—591no—
507C2×#106—591no—
508C2×#106C2×D5911yescharacteristic, complemented
509C2×#103—591no—
510C2×#103—591no—
511C2×#102—591no—
512C2×#102—591no—
513C2×#102—591no—
514C2×#102—591no—
515C2×#102C2×D5911yescharacteristic
516C2×#102C2×D5911yescharacteristic, complemented
517#408—598no—
518C2×C22⋊C8—591no—
519C2×C22⋊C8—591no—
520C2×C22⋊C8—591no—
521C2×C22⋊C8—591no—
522C59C2×#319811yescharacteristic, complemented, Sylow
523C25—1181no—
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×Q8—591no—
534C22×D4—21no—
535C22×D4—21no—
536C22×D4—591no—
537C22×D4—591no—
538C22×D4—594no—
539C22×D4—591no—
540C22×D4—591no—
541C22×D4—1181no—
542C22×D4—1182no—
543C22×D4—1181no—
544C22×D4—1181no—
545C22×D4—1181no—
546C22×D4—1181no—
547C22×D4—1181no—
548C22×D4—2362no—
549C22×D4—2362no—
550C22×D4C22×D5911yescharacteristic
551C22×D4C22×D5911yescharacteristic
552C23×C4—591no—
553C23×C4—591no—
554C23×C4—1181no—
555C23×C4—1181no—
556C23×C4C22×D5911yescharacteristic
557C2×SD16—594no—
558C2×SD16—594no—
559C2×SD16—2362no—
560C2×SD16—2362no—
561C2×D8—42no—
562C2×D8—594no—
563C2×D8—2362no—
564C2×D8C22×D5914yes—
565C2×M16—42no—
566C2×M16C22×D5914yescomplemented
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—594no—
576C22⋊Q8—594no—
577C22⋊Q8—1188no—
578C22⋊Q8—1182no—
579C22⋊Q8—1182no—
580#121—22no—
581#121—22no—
582#121—594no—
583#121—594no—
584#121—594no—
585#121—594no—
586#121—1188no—
587#121—1182no—
588#121—1182no—
589#121—1182no—
590#121—1188no—
591#121—1188no—
592#121—1182no—
593#121C22×D5914yes—
594#121C22×D5914yescomplemented
595#120—1188no—
596#120—1188no—
597#117—594no—
598#117—1182no—
599C2×C4⋊C4—591no—
600C2×C4⋊C4—591no—
601C2×C4⋊C4—594no—
602C2×C4⋊C4—1182no—
603C2×C4⋊C4—1181no—
604C2×C4⋊C4—1181no—
605C2×C4⋊C4—1181no—
606C2×C4⋊C4C22×D5911yescharacteristic
607C2×C4⋊C4C22×D5911yescharacteristic
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
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#106C22×D5914yescomplemented
622#103—594no—
623#103—594no—
624#102—594no—
625#102—594no—
626#102—594no—
627#102—594no—
628#102C22×D5914yes—
629#102C22×D5914yescomplemented
630C22⋊C8—594no—
631C22⋊C8—594no—
632C22⋊C8—594no—
633C22⋊C8—594no—
634C24—21no—
635C24—21no—
636C24—591no—
637C24—591no—
638C24—1184no—
639C24—1181no—
640C24—4722no—
641C24—4722no—
642C24—2364no—
643C24D4×D5911yescharacteristic
644#41—2368no—
645#41—2364no—
646#41—2364no—
647#41—2364no—
648#41—2364no—
649#41—2368no—
650C2×Q8—594no—
651C2×Q8—592no—
652C2×Q8—1181no—
653C2×Q8—1182no—
654C2×Q8—1182no—
655C2×Q8—2362no—
656C2×D4—24no—
657C2×D4—24no—
658C2×D4—21no—
659C2×D4—21no—
660C2×D4—22no—
661C2×D4—22no—
662C2×D4—22no—
663C2×D4—22no—
664C2×D4—82no—
665C2×D4—82no—
666C2×D4—594no—
667C2×D4—594no—
668C2×D4—594no—
669C2×D4—592no—
670C2×D4—1184no—
671C2×D4—1184no—
672C2×D4—1184no—
673C2×D4—1184no—
674C2×D4—1184no—
675C2×D4—1184no—
676C2×D4—1181no—
677C2×D4—1182no—
678C2×D4—1182no—
679C2×D4—4722no—
680C2×D4—4722no—
681C2×D4—4722no—
682C2×D4—4722no—
683C2×D4—2362no—
684C2×D4—2364no—
685C2×D4—2364no—
686C2×D4—2368no—
687C2×D4—2362no—
688C2×D4—2362no—
689C2×D4—2364no—
690C2×D4—2364no—
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—2364no—
719SD16—2364no—
720D8—44no—
721D8—2364no—
722M16—44no—
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—21no—
733C4⋊C4—21no—
734C4⋊C4—592no—
735C4⋊C4—592no—
736C4⋊C4—1184no—
737C4⋊C4—1184no—
738C4⋊C4—1181no—
739C4⋊C4—1181no—
740C4⋊C4—1184no—
741C4⋊C4C23×D5912yes—
742C4⋊C4C23×D5912yes—
743C22⋊C4—24no—
744C22⋊C4—24no—
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—42no—
759C23—42no—
760C23—42no—
761C23—42no—
762C23—42no—
763C23—42no—
764C23—592no—
765C23—592no—
766C23—1182no—
767C23—1182no—
768C23—1182no—
769C23—1182no—
770C23—1182no—
771C23—1182no—
772C23—1182no—
773C23—4724no—
774C23—4724no—
775C23—47216no—
776C23—2368no—
777C23—2362no—
778C23—2362no—
779C23—2362no—
780C23C2×D4×D5912yes—
781C23C2×D4×D5911yescharacteristic
782Q8—1182no—
783Q8—1182no—
784Q8—2364no—
785Q8—2362no—
786D4—22no—
787D4—22no—
788D4—22no—
789D4—22no—
790D4—42no—
791D4—42no—
792D4—84no—
793D4—84no—
794D4—1182no—
795D4—1182no—
796D4—4724no—
797D4—4724no—
798D4—4724no—
799D4—4724no—
800D4—2364no—
801D4—2364no—
802D4—2364no—
803D4—2368no—
804D4—2368no—
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#1427377312yes—
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—84no—
852C22—84no—
853C22—1182no—
854C22—1182no—
855C22—1182no—
856C22—1182no—
857C22—1182no—
858C22—1182no—
859C22—47216no—
860C22—4724no—
861C22—2362no—
862C22—2362no—
863C22—2362no—
864C22—2364no—
865C22—2364no—
866C22#1683796012yes—
867C22#1683820612yes—
868C22#1683821212yes—
869C22C22×D4×D5911yescharacteristic
870C4—22no—
871C4—42no—
872C4—42no—
873C4—1182no—
874C4—1182no—
875C4—2362no—
876C4—2362no—
877C4—2362no—
878C4#1683796012yes—
879C4C2×#1427377211yescharacteristic
880C4C2×#1427377311yescharacteristic
881C2—42no—
882C2—82no—
883C2—82no—
884C2—4722no—
885C2—2362no—
886C2—2362no—
887C2#2143494314yesdirect product factor
888C2C2×#1683796011yescharacteristic
889C2C2×#1683820611yescharacteristic
890C2C2×#1683821211yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#469C2
socleC23×C59C22×D4
hypercenterC2×#469D59
hypocenterC59C2×#3198
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#469

Complements

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

NH ≅ G/Ntype
1. C2×#16837981C2semidirect
2. C2×#16837968C2semidirect
3. #21434943C2direct (N × H)
4. C2×#16837722C2semidirect
5. C2×#16837746C2semidirect
6. C2×#16837724C2semidirect
7. C2×#16837714C2semidirect
8. C2×#16837648C2semidirect
9. C2×#16837636C2semidirect
10. C2×#16837629C2semidirect
11. C2×#16837548C2semidirect
12. C2×#16837544C2semidirect
13. C2×#16837554C2semidirect
14. C2×#16837534C2semidirect
15. C2×#16837370C2semidirect
16. C2×C59×#469C2semidirect
18. C22×#11745687C22semidirect
23. C23×C59⋊C8C22semidirect
25. #16837981C22semidirect
27. #16837968C22semidirect
31. C2×#14273706C22semidirect
43. C2×C4⋊C4×D59C22semidirect
44. #16837746C22semidirect
45. #16837724C22semidirect
46. #16837722C22semidirect
47. #16837714C22semidirect
48. #16837648C22semidirect
49. #16837636C22semidirect
50. #16837629C22semidirect
51. #16837554C22semidirect
52. #16837548C22semidirect
53. #16837544C22semidirect
54. #16837534C22semidirect
55. C2×#14273661C22semidirect
56. C2×#14273660C22semidirect
57. C2×#14273658C22semidirect
58. C2×#14273652C22semidirect
59. C2×#14273650C22semidirect
62. C2×#14273648C22semidirect
64. #16837370C22semidirect
67. C2×(C2×D59)⋊C8C22semidirect
68. C2×(C2×D59)⋊C8C22semidirect
70. C22×M16×C59C22semidirect
72. C2×#121×C59C22semidirect
73. C59×#469C22semidirect
74. C2×#106×C59C22semidirect
76. C2×#102×C59C22semidirect
85. C2×#11745687C23semidirect
115. C22×C59⋊C8C23semidirect
121. #14273706C23semidirect
144. C4⋊C4×D59C23semidirect
153. #14273661C23semidirect
154. #14273660C23semidirect
155. #14273658C23semidirect
156. #14273652C23semidirect
157. #14273650C23semidirect
160. #14273648C23semidirect
164. (C2×D59)⋊C8C23semidirect
165. (C2×D59)⋊C8C23semidirect
174. C2×M16×C59C23semidirect
180. #121×C59C23semidirect
185. #106×C59C23semidirect
187. #102×C59C23semidirect
443. C2×#469D59semidirect
455. C2×C59#3198semidirect
469. C22×M16C2×D59semidirect
488. C2×#121C2×D59semidirect
497. #469C2×D59semidirect
508. C2×#106C2×D59semidirect
516. C2×#102C2×D59semidirect
522. C59C2×#3198semidirect
566. C2×M16C22×D59semidirect
594. #121C22×D59semidirect
621. #106C22×D59semidirect
629. #102C22×D59semidirect
887. C2#21434943direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168379812
C2×#168379682
#214349432
C2×#168377222
C2×#168377462
C2×#168377242
C2×#168377142
C2×#168376482
C2×#168376362
C2×#168376292
C2×#168375482
C2×#168375442
C2×#168375542
C2×#168375342
C2×#168373702
C2×C59×#4692
C2×#319859