Finite Group Databasebeta

← C2×#21436233 #29465243

Subgroups — C2×#21436233 #29465243

Order 15104.

2642 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838100C211yesmaximal, characteristic, complemented
2C2×D4×C22⋊D59C211yesmaximal, characteristic, complemented
3#21436233C2116yesmaximal, direct product factor
4C2×#16837765C211yesmaximal, characteristic, complemented
5C2×#16837720C211yesmaximal, characteristic, complemented
6C2×#16837724C211yesmaximal, characteristic, complemented
7C2×#16837700C211yesmaximal, characteristic, complemented
8C2×#16837654C211yesmaximal, characteristic, complemented
9C2×#16837638C211yesmaximal, characteristic, complemented
10C2×#16837596C211yesmaximal, characteristic, complemented
11C2×#16837537C211yesmaximal, characteristic, complemented
12C2×#16837536C211yesmaximal, characteristic, complemented
13C2×#16837511C211yesmaximal, characteristic, complemented
14C2×#16837473C211yesmaximal, characteristic, complemented
15C2×#16837405C211yesmaximal, characteristic, complemented
16C22×#102×C59C211yesmaximal, characteristic, complemented
17C23×C22⋊D59—21no—
18C22×D4×D59C2211yescharacteristic
19C22×D472C2211yescharacteristic, complemented
20C22×#11745669C2211yescharacteristic
21C22×#11745669C2211yescharacteristic, complemented
22C22×#11745659C2211yescharacteristic, complemented
23#16838100—24no—
24#16838100C2218yescomplemented
25D4×C22⋊D59—24no—
26D4×C22⋊D59C2218yescomplemented
27C2×#14273723C2211yescharacteristic
28C2×#14273722—21no—
29C2×#14273718C2211yescharacteristic, complemented
30C2×#14273712—21no—
31C2×#14273702C2211yescharacteristic, complemented
32C2×#14273701—21no—
33C2×#14273701C2211yescharacteristic
34C2×#14273701C2211yescharacteristic, complemented
35C2×#14273699—21no—
36C2×#14273698C2211yescharacteristic
37C2×#14273696—21no—
38C2×#14273695—21no—
39C2×D4×Dic59C2211yescharacteristic
40C2×#14273689C2211yescharacteristic, complemented
41C2×C4×C22⋊D59—21no—
42C2×C4×C22⋊D59C2211yescharacteristic
43C2×#14273685C2211yescharacteristic, complemented
44#16837765C2218yescomplemented
45#16837724C2218yescomplemented
46#16837720C2218yescomplemented
47#16837700C2218yescomplemented
48#16837654C2218yescomplemented
49#16837638C2218yescomplemented
50#16837596C2218yescomplemented
51#16837537C2218yescomplemented
52#16837536C2218yescomplemented
53#16837511C2218yescomplemented
54#16837473C2218yescomplemented
55C2×#14273661C2211yescharacteristic, complemented
56C2×#14273658C2211yescharacteristic, complemented
57C2×#14273658C2211yescharacteristic, complemented
58C2×Dic59⋊C8C2211yescharacteristic, complemented
59#16837405C2218yescomplemented
60C2×#14273649C2211yescharacteristic, complemented
61C2×#14273649C2211yescharacteristic, complemented
62C2×#14273648C2211yescharacteristic
63C2×#14273648C2211yescharacteristic, complemented
64C2×#14273647C2211yescharacteristic, complemented
65C2×#14273647C2211yescharacteristic, complemented
66C2×C22⋊(C59⋊C8)C2211yescharacteristic, complemented
67C2×(C2×D59)⋊C8C2211yescharacteristic, complemented
68C2×#14273637C2211yescharacteristic, complemented
69C23×D4×C59C2211yescharacteristic
70C23×C8×C59C2211yescharacteristic, complemented
71C22×C4⋊C4×C59C2211yescharacteristic, complemented
72C2×#102×C59C2211yescharacteristic
73C2×#102×C59C2211yescharacteristic
74C2×#102×C59C2218yescomplemented
75C2×#102×C59C2211yescharacteristic, complemented
76C2×#102×C59C2211yescharacteristic, complemented
77C24×D59—21no—
78C22×D236—21no—
79C22×D236C2311yescharacteristic
80C22×D236C2311yescharacteristic
81C22×C22⋊D59—21no—
82C22×C22⋊D59—21no—
83C22×C22⋊D59—21no—
84C22×C22⋊D59—28no—
85C22×C22⋊D59—21no—
86C22×C22⋊D59—21no—
87C22×C22⋊D59—21no—
88C22×C22⋊D59—48no—
89C22×C22⋊D59D411yescharacteristic
90C2×D4×D59—24no—
91C2×D4×D59—22no—
92C2×D4×D59—42no—
93C2×D4×D59C2314yes—
94C23×Dic59—21no—
95C22×C4×D59—21no—
96C22×C4×D59C2311yescharacteristic
97C2×D472—42no—
98C2×D472C2314yescomplemented
99C2×#11745669—24no—
100C2×#11745669—42no—
101C2×#11745669C2314yes—
102C2×#11745669C2314yescomplemented
103C2×#11745659—42no—
104C2×#11745659C2314yescomplemented
105C22×C59⋊C8C2311yescharacteristic
106C22×C59⋊C8C2311yescharacteristic
107#14273723—22no—
108#14273723C2314yes—
109#14273722—28no—
110#14273718—22no—
111#14273718C2314yescomplemented
112#14273712—28no—
113#14273702—22no—
114#14273702C2314yescomplemented
115#14273701—22no—
116#14273701—22no—
117#14273701—28no—
118#14273701C2314yes—
119#14273701C2314yescomplemented
120#14273699—28no—
121#14273698—22no—
122#14273698C2314yes—
123#14273696—28no—
124#14273695—28no—
125D4×Dic59—22no—
126D4×Dic59C2314yes—
127#14273689—22no—
128#14273689C2314yescomplemented
129C4×C22⋊D59—28no—
130C4×C22⋊D59D414yes—
131C4×C22⋊D59C2314yes—
132#14273685—22no—
133#14273685C2314yescomplemented
134C2×C4⋊Dic59—21no—
135C2×C4⋊Dic59C2311yescharacteristic
136C2×C4⋊Dic59C2311yescharacteristic
137C2×Dic59⋊C4—21no—
138C2×Dic59⋊C4D411yescharacteristic
139C2×C22⋊Dic59—21no—
140C2×C22⋊Dic59—21no—
141C2×C22⋊Dic59D411yescharacteristic
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#14273661C2314yescomplemented
151#14273658C2314yescomplemented
152#14273658C2314yescomplemented
153Dic59⋊C8C2314yescomplemented
154#14273649C2314yescomplemented
155#14273649C2314yescomplemented
156#14273648C2314yes—
157#14273648C2314yescomplemented
158#14273647C2314yescomplemented
159#14273647C2314yescomplemented
160C22⋊(C59⋊C8)C2314yescomplemented
161(C2×D59)⋊C8C2314yescomplemented
162#14273637C2314yescomplemented
163C25×C59—21no—
164C22×D4×C59—24no—
165C22×D4×C59—21no—
166C22×D4×C59—22no—
167C22×D4×C59—42no—
168C22×D4×C59C2311yescharacteristic
169C22×D4×C59C2314yes—
170C22×D4×C59C2311yescharacteristic
171C23×C4×C59—21no—
172C23×C4×C59C2311yescharacteristic
173C22×C8×C59—42no—
174C22×C8×C59C2311yescharacteristic
175C22×C8×C59C2311yescharacteristic
176C22×C8×C59C2314yescomplemented
177C2×C4⋊C4×C59—21no—
178C2×C4⋊C4×C59—22no—
179C2×C4⋊C4×C59C2311yescharacteristic
180C2×C4⋊C4×C59C2311yescharacteristic
181C2×C4⋊C4×C59C2314yescomplemented
182#102×C59C2314yes—
183#102×C59C2314yes—
184#102×C59C2314yescomplemented
185#102×C59C2314yescomplemented
186C24×C59—21no—
187C24×C59—21no—
188C24×C59—24no—
189C24×C59—44no—
190C24×C59—44no—
191C24×C59—82no—
192C24×C59C2×D411yescharacteristic
193C23×D59—21no—
194C23×D59—21no—
195C23×D59—24no—
196C23×D59—44no—
197C23×D59—44no—
198C23×D59—82no—
199C23×D59C2×D411yescharacteristic
200C2×D4×C59—28no—
201C2×D4×C59—21no—
202C2×D4×C59—24no—
203C2×D4×C59—21no—
204C2×D4×C59—22no—
205C2×D4×C59—22no—
206C2×D4×C59—22no—
207C2×D4×C59—44no—
208C2×D4×C59—48no—
209C2×D4×C59—44no—
210C2×D4×C59#4114yes—
211C2×D4×C59C2412yes—
212C2×D4×C59C2412yes—
213C22×C4×C59—22no—
214C22×C4×C59—22no—
215C22×C4×C59—21no—
216C22×C4×C59—21no—
217C22×C4×C59—24no—
218C22×C4×C59—82no—
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—24no—
229C2×C22⋊D59—24no—
230C2×C22⋊D59—44no—
231C2×C22⋊D59—44no—
232C2×C22⋊D59—432no—
233C2×C22⋊D59—44no—
234C2×C22⋊D59—44no—
235C2×C22⋊D59—44no—
236C2×C22⋊D59—82no—
237C2×C22⋊D59C2×D414yes—
238C22×Dic59—21no—
239C22×Dic59—21no—
240C22×Dic59—24no—
241C22×Dic59—44no—
242C22×Dic59C2×D411yescharacteristic
243C22×Dic59C2×D411yescharacteristic
244C22×Dic59C2×D411yescharacteristic
245D4×D59—28no—
246D4×D59—44no—
247D4×D59—48no—
248C2×D236—22no—
249C2×D236—22no—
250C2×D236—22no—
251C2×D236—22no—
252C2×D236—21no—
253C2×D236—21no—
254C2×D236—24no—
255C2×D236—82no—
256C2×D236C2412yes—
257C2×D236C2412yes—
258C2×C4×D59—22no—
259C2×C4×D59—22no—
260C2×C4×D59—24no—
261C2×C4×D59—82no—
262C2×C4×D59C2×D412yes—
263C2×C4×D59C2412yes—
264C2×C8×C59—22no—
265C2×C8×C59—22no—
266C2×C8×C59—44no—
267C2×C8×C59C2412yes—
268C2×C8×C59C2412yes—
269C4⋊C4×C59—21no—
270C4⋊C4×C59—21no—
271C4⋊C4×C59—24no—
272C4⋊C4×C59C2412yes—
273C4⋊C4×C59C2412yes—
274C22⋊Dic59—24no—
275C22⋊Dic59—24no—
276C22⋊Dic59C2×D414yes—
277#11745669—28no—
278#11745669—44no—
279(C2×D59)⋊C4—24no—
280(C2×D59)⋊C4—24no—
281(C2×D59)⋊C4—24no—
282(C2×D59)⋊C4—24no—
283(C2×D59)⋊C4—24no—
284(C2×D59)⋊C4C2×D414yes—
285C4⋊Dic59—21no—
286C4⋊Dic59—21no—
287C4⋊Dic59—24no—
288C4⋊Dic59C2412yes—
289C4⋊Dic59C2412yes—
290Dic59⋊C4—24no—
291Dic59⋊C4C2×D414yes—
292C4×Dic59—24no—
293C4×Dic59C2×D412yes—
294C4×Dic59C2412yes—
295C2×C59⋊C8—22no—
296C2×C59⋊C8—22no—
297C2×C59⋊C8C2412yes—
298C2×C59⋊C8C2412yes—
299D472—44no—
300#11745659—44no—
301C23×C59—22no—
302C23×C59—22no—
303C23×C59—24no—
304C23×C59—22no—
305C23×C59—22no—
306C23×C59—48no—
307C23×C59—42no—
308C23×C59—42no—
309C23×C59—42no—
310C23×C59—48no—
311C23×C59—42no—
312C23×C59—42no—
313C23×C59—84no—
314C23×C59—816no—
315C23×C59AGL(1,ℤ/8)14yes—
316C23×C59C22×D412yes—
317C23×C59C22×D411yescharacteristic
318C22×D59—22no—
319C22×D59—22no—
320C22×D59—22no—
321C22×D59—22no—
322C22×D59—22no—
323C22×D59—48no—
324C22×D59—48no—
325C22×D59—42no—
326C22×D59—42no—
327C22×D59—42no—
328C22×D59—42no—
329C22×D59—42no—
330C22×D59—42no—
331C22×D59—84no—
332C22×D59—816no—
333C22×D59C22×D412yes—
334D4×C59—24no—
335D4×C59—22no—
336D4×C59—22no—
337D4×C59—22no—
338D4×C59—48no—
339D4×C59—42no—
340D4×C59C2×#4114yes—
341C2×C4×C59—22no—
342C2×C4×C59—24no—
343C2×C4×C59—22no—
344C2×C4×C59—22no—
345C2×C4×C59—22no—
346C2×C4×C59—22no—
347C2×C4×C59—42no—
348C2×C4×C59—42no—
349C2×C4×C59—84no—
350C2×C4×C59C22×D412yes—
351C2×C4×C59C22×D411yescharacteristic
352C2×C4×C59C2×#4112yes—
353C2×C4×C59H(5,𝔽2)12yes—
354C2×C4×C59C2511yescharacteristic
355C22⋊D59—28no—
356C22⋊D59—48no—
357C22⋊D59—48no—
358C22⋊D59—48no—
359C22⋊D59—48no—
360C22⋊D59—48no—
361C22⋊D59—84no—
362C2×Dic59—22no—
363C2×Dic59—22no—
364C2×Dic59—22no—
365C2×Dic59—22no—
366C2×Dic59—22no—
367C2×Dic59—48no—
368C2×Dic59—42no—
369C2×Dic59—42no—
370C2×Dic59C22×D412yes—
371C2×Dic59C22×D412yes—
372C2×Dic59C22×D412yes—
373D236—22no—
374D236—22no—
375D236—22no—
376D236—22no—
377D236—42no—
378D236—42no—
379D236—84no—
380C4×D59—24no—
381C4×D59—22no—
382C4×D59—22no—
383C4×D59—84no—
384C8×C59—22no—
385C8×C59—22no—
386C59⋊C8—22no—
387C59⋊C8—22no—
388C2×#3318—591nomaximal, Sylow
389C22×C59—22no—
390C22×C59—28no—
391C22×C59—22no—
392C22×C59—24no—
393C22×C59—48no—
394C22×C59—42no—
395C22×C59—42no—
396C22×C59—42no—
397C22×C59—42no—
398C22×C59—42no—
399C22×C59—816no—
400C22×C59—84no—
401C22×C59#54612yes—
402C22×C59C2×AGL(1,ℤ/8)14yes—
403C22×C59C2×AGL(1,ℤ/8)12yes—
404C22×C59#57612yes—
405C22×C59C23×D411yescharacteristic
406C2×D59—22no—
407C2×D59—22no—
408C2×D59—22no—
409C2×D59—44no—
410C2×D59—42no—
411C2×D59—42no—
412C2×D59—42no—
413C2×D59—42no—
414C2×D59—42no—
415C2×D59—42no—
416C2×D59—816no—
417C2×D59—84no—
418C2×D59—84no—
419C4×C59—22no—
420C4×C59—42no—
421C4×C59—42no—
422C4×C59#54612yes—
423C4×C59C22×#4111yescharacteristic
424C4×C59C2×H(5,𝔽2)11yescharacteristic
425Dic59—22no—
426Dic59—22no—
427Dic59—22no—
428Dic59—42no—
429Dic59—42no—
430C2×#553—591no—
431C2×D42—591no—
432#3318—5916no—
433C2×#490—591no—
434C2×#481—591no—
435C2×#482—591no—
436C2×#478—591no—
437C2×#469—591no—
438C2×#466—591no—
439C2×#459—591no—
440C2×#447—591no—
441C2×#447—591no—
442C2×#442—591no—
443C2×#435—591no—
444C2×#418—591no—
445C22×#102D5911yescharacteristic, complemented
446C2×C59—24no—
447C2×C59—44no—
448C2×C59—82no—
449C2×C59#331814yescomplemented
450C2×C59C2×#54611yescharacteristic
451C2×C59C22×AGL(1,ℤ/8)11yescharacteristic
452C2×C59C2×#57611yescharacteristic
453D59—42no—
454D59—82no—
455D59—82no—
456C23×D4—591no—
457C23×D4—1181no—
458C23×D4C2×D5911yescharacteristic
459C22×D8—591no—
460C22×D8—591no—
461C22×D8—591no—
462C22×M16—591no—
463C23×C8C2×D5911yescharacteristic, complemented
464#553—598no—
465#553—1184no—
466D42—598no—
467D42—1184no—
468C2×#127—591no—
469C2×#126—1181no—
470C2×#125—591no—
471C2×#123—1181no—
472C2×#121—591no—
473C2×#121—591no—
474C2×#121—591no—
475C2×#121—591no—
476C2×#121—1181no—
477C2×#121—1181no—
478C2×#120—1181no—
479C2×#120—1181no—
480C2×C4×D4—591no—
481C2×C4×D4—591no—
482C2×C4×D4—591no—
483C2×C4×D4—1181no—
484C2×#117—591no—
485C22×C4⋊C4C2×D5911yescharacteristic, complemented
486#490—598no—
487#482—598no—
488#481—598no—
489#478—598no—
490#469—598no—
491#466—598no—
492#459—598no—
493#447—598no—
494#447—598no—
495#442—598no—
496#435—598no—
497C2×#107—591no—
498C2×#106—591no—
499C2×#106—591no—
500C2×C4⋊C8—591no—
501#418—598no—
502C2×#102—591no—
503C2×#102—591no—
504C2×#102—591no—
505C2×#102—591no—
506C2×#102—591no—
507C2×#102—591no—
508C2×#102C2×D5911yescharacteristic
509C2×#102C2×D5911yescharacteristic
510C2×#102C2×D5918yescomplemented
511C2×#102C2×D5911yescharacteristic, complemented
512C2×#102C2×D5911yescharacteristic, complemented
513C2×C22⋊C8—591no—
514C2×C22⋊C8—591no—
515C2×#97—591no—
516C59C2×#331811yescharacteristic, complemented, Sylow
517C25—21no—
518C25—1181no—
519C22×D4—24no—
520C22×D4—21no—
521C22×D4—22no—
522C22×D4—42no—
523C22×D4—591no—
524C22×D4—594no—
525C22×D4—591no—
526C22×D4—591no—
527C22×D4—1181no—
528C22×D4—1182no—
529C22×D4—1181no—
530C22×D4—1181no—
531C22×D4—1181no—
532C22×D4—1188no—
533C22×D4—1184no—
534C22×D4—1181no—
535C22×D4—1181no—
536C22×D4—1181no—
537C22×D4—2362no—
538C22×D4—2368no—
539C22×D4C22×D5911yescharacteristic
540C22×D4C22×D5914yes—
541C22×D4C22×D5911yescharacteristic
542C23×C4—21no—
543C23×C4—591no—
544C23×C4—1181no—
545C23×C4—1181no—
546C23×C4C22×D5911yescharacteristic
547C2×D8—594no—
548C2×D8—594no—
549C2×D8—594no—
550C2×D8—1184no—
551C2×D8—2362no—
552C2×D8—2362no—
553C2×M16—594no—
554C2×M16—2362no—
555C22×C8—42no—
556C22×C8—591no—
557C22×C8—591no—
558C22×C8C22×D5911yescharacteristic
559C22×C8C22×D5911yescharacteristic
560C22×C8C22×D5914yescomplemented
561#127—594no—
562#127—1182no—
563#126—1188no—
564#125—594no—
565#125—1182no—
566#123—1188no—
567#121—594no—
568#121—594no—
569#121—594no—
570#121—594no—
571#121—1182no—
572#121—1188no—
573#121—1188no—
574#121—1182no—
575#121—1182no—
576#121—1182no—
577#120—1188no—
578#120—1188no—
579C4×D4—594no—
580C4×D4—594no—
581C4×D4—594no—
582C4×D4—594no—
583C4×D4—1182no—
584C4×D4—1182no—
585C4×D4—1188no—
586#117—594no—
587#117—1182no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—22no—
590C2×C4⋊C4—591no—
591C2×C4⋊C4—591no—
592C2×C4⋊C4—591no—
593C2×C4⋊C4—1181no—
594C2×C4⋊C4—1181no—
595C2×C4⋊C4C22×D5911yescharacteristic
596C2×C4⋊C4C22×D5911yescharacteristic
597C2×C4⋊C4C22×D5914yescomplemented
598C2×C22⋊C4—591no—
599C2×C22⋊C4—591no—
600C2×C22⋊C4—1181no—
601C2×C22⋊C4—1181no—
602C2×C22⋊C4—1181no—
603C2×C22⋊C4—1181no—
604C2×C22⋊C4—1181no—
605C2×C22⋊C4—1181no—
606C2×C22⋊C4—1181no—
607C2×C42—591no—
608C2×C42—1181no—
609#107—594no—
610#106—594no—
611#106—594no—
612C4⋊C8—594no—
613#102—594no—
614#102—594no—
615#102—594no—
616#102—594no—
617#102—594no—
618#102—594no—
619#102C22×D5914yes—
620#102C22×D5914yes—
621#102C22×D5914yescomplemented
622#102C22×D5914yescomplemented
623C22⋊C8—594no—
624C22⋊C8—594no—
625#97—594no—
626C24—21no—
627C24—21no—
628C24—24no—
629C24—44no—
630C24—44no—
631C24—82no—
632C24—591no—
633C24—1184no—
634C24—1181no—
635C24—1181no—
636C24—4722no—
637C24—2364no—
638C24—2364no—
639C24D4×D5911yescharacteristic
640C2×D4—28no—
641C2×D4—21no—
642C2×D4—24no—
643C2×D4—21no—
644C2×D4—22no—
645C2×D4—22no—
646C2×D4—22no—
647C2×D4—44no—
648C2×D4—48no—
649C2×D4—44no—
650C2×D4—594no—
651C2×D4—592no—
652C2×D4—592no—
653C2×D4—1184no—
654C2×D4—1184no—
655C2×D4—1184no—
656C2×D4—1184no—
657C2×D4—1184no—
658C2×D4—1188no—
659C2×D4—1184no—
660C2×D4—1184no—
661C2×D4—1184no—
662C2×D4—1181no—
663C2×D4—1181no—
664C2×D4—1182no—
665C2×D4—1182no—
666C2×D4—1182no—
667C2×D4—1182no—
668C2×D4—4722no—
669C2×D4—4722no—
670C2×D4—2364no—
671C2×D4—2368no—
672C2×D4—2364no—
673C2×D4—2364no—
674C2×D4—23632no—
675C2×D4—2364no—
676C2×D4—2364no—
677C2×D4—2364no—
678C2×D4#1174568514yes—
679C2×D4C23×D5912yes—
680C2×D4C23×D5912yes—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—24no—
686C22×C4—82no—
687C22×C4—591no—
688C22×C4—591no—
689C22×C4—591no—
690C22×C4—592no—
691C22×C4—592no—
692C22×C4—1184no—
693C22×C4—1184no—
694C22×C4—1182no—
695C22×C4—1182no—
696C22×C4—1181no—
697C22×C4—1181no—
698C22×C4—4722no—
699C22×C4—2364no—
700C22×C4D4×D5912yes—
701C22×C4D4×D5911yescharacteristic
702C22×C4C23×D5912yes—
703C22×C4C23×D5911yescharacteristic
704D8—1188no—
705D8—2364no—
706D8—2364no—
707M16—2364no—
708C2×C8—22no—
709C2×C8—22no—
710C2×C8—44no—
711C2×C8—592no—
712C2×C8—592no—
713C2×C8—1182no—
714C2×C8—1182no—
715C2×C8C23×D5912yes—
716C2×C8C23×D5912yes—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—24no—
720C4⋊C4—594no—
721C4⋊C4—592no—
722C4⋊C4—592no—
723C4⋊C4—1184no—
724C4⋊C4—1184no—
725C4⋊C4—1181no—
726C4⋊C4—1181no—
727C4⋊C4C23×D5912yes—
728C4⋊C4C23×D5912yes—
729C22⋊C4—594no—
730C22⋊C4—594no—
731C22⋊C4—1184no—
732C22⋊C4—1184no—
733C22⋊C4—1184no—
734C22⋊C4—1184no—
735C22⋊C4—1184no—
736C22⋊C4—1184no—
737C22⋊C4—1184no—
738C42—592no—
739C42—592no—
740C42—1184no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—24no—
745C23—22no—
746C23—48no—
747C23—42no—
748C23—42no—
749C23—48no—
750C23—42no—
751C23—42no—
752C23—42no—
753C23—84no—
754C23—816no—
755C23—592no—
756C23—1182no—
757C23—1182no—
758C23—1182no—
759C23—1182no—
760C23—1182no—
761C23—4724no—
762C23—47216no—
763C23—2368no—
764C23—2368no—
765C23—2362no—
766C23—2362no—
767C23—2362no—
768C23—2362no—
769C23—2362no—
770C23—2362no—
771C23#1427375414yes—
772C23C2×D4×D5912yes—
773C23C2×D4×D5911yescharacteristic
774D4—22no—
775D4—22no—
776D4—22no—
777D4—24no—
778D4—48no—
779D4—42no—
780D4—1188no—
781D4—1182no—
782D4—1182no—
783D4—1182no—
784D4—1182no—
785D4—4724no—
786D4—4724no—
787D4—2368no—
788D4—2368no—
789D4—2368no—
790D4—2368no—
791D4—2368no—
792D4—2362no—
793D4—2362no—
794D4C2×#1174568514yes—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—24no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—84no—
804C2×C4—592no—
805C2×C4—592no—
806C2×C4—592no—
807C2×C4—1182no—
808C2×C4—1182no—
809C2×C4—1182no—
810C2×C4—1182no—
811C2×C4—1182no—
812C2×C4—1184no—
813C2×C4—1182no—
814C2×C4—1182no—
815C2×C4—4724no—
816C2×C4—2368no—
817C2×C4—2362no—
818C2×C4—2362no—
819C2×C4C2×D4×D5912yes—
820C2×C4C2×D4×D5911yescharacteristic
821C2×C4C2×#1174568512yes—
822C2×C4#1427377212yes—
823C2×C4C24×D5911yescharacteristic
824C8—22no—
825C8—22no—
826C8—1182no—
827C8—1182no—
828C22—28no—
829C22—22no—
830C22—22no—
831C22—24no—
832C22—48no—
833C22—42no—
834C22—42no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—816no—
839C22—84no—
840C22—1182no—
841C22—1182no—
842C22—1182no—
843C22—47216no—
844C22—4724no—
845C22—4724no—
846C22—2362no—
847C22—2362no—
848C22—2362no—
849C22—2362no—
850C22—2362no—
851C22—2362no—
852C22—2364no—
853C22#1683804212yes—
854C22C2×#1427375414yes—
855C22C2×#1427375412yes—
856C22#1683820312yes—
857C22C22×D4×D5911yescharacteristic
858C4—22no—
859C4—42no—
860C4—42no—
861C4—1182no—
862C4—1182no—
863C4—1182no—
864C4—2362no—
865C4—2362no—
866C4#1683804212yes—
867C4C22×#1174568511yescharacteristic
868C4C2×#1427377211yescharacteristic
869C2—24no—
870C2—44no—
871C2—82no—
872C2—4722no—
873C2—4722no—
874C2—2362no—
875C2#2143623314yesdirect product factor
876C2C2×#1683804211yescharacteristic
877C2C22×#1427375411yescharacteristic
878C2C2×#1683820311yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC22×#102×C59C2
socleC23×C59C22×D4
hypercenterC22×#102D59
hypocenterC59C2×#3318
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#102

Complements

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

NH ≅ G/Ntype
1. C2×#16838100C2semidirect
2. C2×D4×C22⋊D59C2semidirect
3. #21436233C2direct (N × H)
4. C2×#16837765C2semidirect
5. C2×#16837720C2semidirect
6. C2×#16837724C2semidirect
7. C2×#16837700C2semidirect
8. C2×#16837654C2semidirect
9. C2×#16837638C2semidirect
10. C2×#16837596C2semidirect
11. C2×#16837537C2semidirect
12. C2×#16837536C2semidirect
13. C2×#16837511C2semidirect
14. C2×#16837473C2semidirect
15. C2×#16837405C2semidirect
16. C22×#102×C59C2semidirect
19. C22×D472C22semidirect
21. C22×#11745669C22semidirect
22. C22×#11745659C22semidirect
24. #16838100C22semidirect
26. D4×C22⋊D59C22semidirect
29. C2×#14273718C22semidirect
31. C2×#14273702C22semidirect
34. C2×#14273701C22semidirect
40. C2×#14273689C22semidirect
43. C2×#14273685C22semidirect
44. #16837765C22semidirect
45. #16837724C22semidirect
46. #16837720C22semidirect
47. #16837700C22semidirect
48. #16837654C22semidirect
49. #16837638C22semidirect
50. #16837596C22semidirect
51. #16837537C22semidirect
52. #16837536C22semidirect
53. #16837511C22semidirect
54. #16837473C22semidirect
55. C2×#14273661C22semidirect
56. C2×#14273658C22semidirect
57. C2×#14273658C22semidirect
58. C2×Dic59⋊C8C22semidirect
59. #16837405C22semidirect
60. C2×#14273649C22semidirect
61. C2×#14273649C22semidirect
63. C2×#14273648C22semidirect
64. C2×#14273647C22semidirect
65. C2×#14273647C22semidirect
66. C2×C22⋊(C59⋊C8)C22semidirect
67. C2×(C2×D59)⋊C8C22semidirect
68. C2×#14273637C22semidirect
70. C23×C8×C59C22semidirect
71. C22×C4⋊C4×C59C22semidirect
74. C2×#102×C59C22semidirect
75. C2×#102×C59C22semidirect
76. C2×#102×C59C22semidirect
98. C2×D472C23semidirect
102. C2×#11745669C23semidirect
104. C2×#11745659C23semidirect
111. #14273718C23semidirect
114. #14273702C23semidirect
119. #14273701C23semidirect
128. #14273689C23semidirect
133. #14273685C23semidirect
150. #14273661C23semidirect
151. #14273658C23semidirect
152. #14273658C23semidirect
153. Dic59⋊C8C23semidirect
154. #14273649C23semidirect
155. #14273649C23semidirect
157. #14273648C23semidirect
158. #14273647C23semidirect
159. #14273647C23semidirect
160. C22⋊(C59⋊C8)C23semidirect
161. (C2×D59)⋊C8C23semidirect
162. #14273637C23semidirect
176. C22×C8×C59C23semidirect
181. C2×C4⋊C4×C59C23semidirect
184. #102×C59C23semidirect
185. #102×C59C23semidirect
445. C22×#102D59semidirect
449. C2×C59#3318semidirect
463. C23×C8C2×D59semidirect
485. C22×C4⋊C4C2×D59semidirect
510. C2×#102C2×D59semidirect
511. C2×#102C2×D59semidirect
512. C2×#102C2×D59semidirect
516. C59C2×#3318semidirect
560. C22×C8C22×D59semidirect
597. C2×C4⋊C4C22×D59semidirect
621. #102C22×D59semidirect
622. #102C22×D59semidirect
875. C2#21436233direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168381002
C2×D4×C22⋊D592
#214362332
C2×#168377652
C2×#168377202
C2×#168377242
C2×#168377002
C2×#168376542
C2×#168376382
C2×#168375962
C2×#168375372
C2×#168375362
C2×#168375112
C2×#168374732
C2×#168374052
C22×#102×C592
C2×#331859