Finite Group Databasebeta

← C4×#16837947 #28747213

Subgroups — C4×#16837947 #28747213

Order 15104.

3526 conjugacy classes of subgroups.

The subgroup lattice has 1148 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837947C211yesmaximal, characteristic
2C2×C4×#11745687C212yesmaximal, complemented
3#21426667C211yesmaximal, characteristic, complemented
4C4×#14273726C211yesmaximal, characteristic, complemented
5#21426660C211yesmaximal, characteristic, complemented
6C4×#14273723C211yesmaximal, characteristic, complemented
7#21426637C212yesmaximal, complemented
8C4×#14273713C212yesmaximal, complemented
9#121×Dic59C211yesmaximal, characteristic, complemented
10C4×#14273701C211yesmaximal, characteristic, complemented
11#21426606C212yesmaximal, complemented
12C4×#14273699C212yesmaximal, complemented
13#21426602C211yesmaximal, characteristic, complemented
14#21426581C212yesmaximal, complemented
15#21426558C211yesmaximal, characteristic, complemented
16#21426556C212yesmaximal, complemented
17#21426554C211yesmaximal, characteristic, complemented
18#21426498C211yesmaximal, characteristic, complemented
19C4×D4×Dic59C211yesmaximal, characteristic, complemented
20C4×#14273689C211yesmaximal, characteristic, complemented
21C4×(C22⋊D59)⋊C4C212yesmaximal, complemented
22C2×C42×Dic59C211yesmaximal, characteristic, complemented
23C4×#121×C59C211yesmaximal, characteristic, complemented
24C22×#11745687C2212yes—
25#16837947C4116yesdirect product factor
26C2×#14273726C2211yescharacteristic
27C2×#14273723C2211yescharacteristic
28C2×#14273713C2212yes—
29C2×#14273701C2211yescharacteristic
30C2×#14273699C2212yes—
31C4×#11745687—216no—
32C2×C4×Dic118C2212yes—
33C2×#14273692C2212yes—
34C2×C4×D236C2211yescharacteristic
35C2×D4×Dic59C2211yescharacteristic
36C2×D4×Dic59C2212yes—
37C2×D4×Dic59C2211yescharacteristic
38C2×#14273689C2211yescharacteristic
39C2×#14273689C2211yescharacteristic
40C2×C4×C22⋊D59C2212yes—
41C2×C4×C22⋊D59C2212yes—
42C2×C4×C22⋊D59C2212yes—
43C2×(C22⋊D59)⋊C4C2212yes—
44C2×(C22⋊D59)⋊C4C2212yes—
45C2×(C22⋊D59)⋊C4C2212yes—
46C2×(C22⋊D59)⋊C4C2212yes—
47C2×#14273685C2212yes—
48C2×#14273683C2212yes—
49C2×#14273683C2212yes—
50C22×C4×Dic59C2212yes—
51C22×C4×Dic59C2211yescharacteristic
52C22×C4×Dic59C2211yescharacteristic
53C22×C4×Dic59C2211yescharacteristic
54C22×C4×Dic59C2211yescharacteristic
55C22×C4×Dic59C2211yescharacteristic
56C22×C4×Dic59C2211yescharacteristic
57C2×C42×D59C2212yes—
58#16837306C2212yes—
59#16837306C2212yes—
60#16837305C2211yescharacteristic
61#16837304C2211yescharacteristic
62#16837303C2211yescharacteristic
63#16837302C2212yes—
64#16837302C2212yes—
65#16837302C2212yes—
66#16837302C2212yes—
67#16837301C2211yescharacteristic
68#16837300C2211yescharacteristic
69#16837299C2212yes—
70#16837298C2211yescharacteristic
71#16837297C2212yes—
72#16837296C2212yes—
73#16837295C2212yes—
74#16837294C2212yes—
75#16837293C2212yes—
76#16837292C2212yes—
77#16837291C2212yes—
78#16837290C2212yes—
79#16837282C2212yes—
80#16837281C2212yes—
81#16837279C2212yes—
82#16837271C2211yescharacteristic
83#16837271C2211yescharacteristic
84#16837266C2212yes—
85#16837262C2211yescharacteristic
86#16837260C2212yes—
87C4⋊C4×Dic59C2211yescharacteristic
88C4⋊C4×Dic59C2211yescharacteristic
89C4⋊C4×Dic59C2211yescharacteristic
90C4⋊C4×Dic59C2211yescharacteristic
91C4×Dic59⋊C4C2212yes—
92C4×C4⋊Dic59C2211yescharacteristic
93#16837253C2212yes—
94#16837253C2212yes—
95C22⋊C4×Dic59C2212yes—
96C22⋊C4×Dic59C2212yes—
97C22⋊C4×Dic59C2212yes—
98C22⋊C4×Dic59C2212yes—
99C4×(C2×D59)⋊C4C2212yes—
100C4×(C2×D59)⋊C4C2212yes—
101C4×C22⋊Dic59C2212yes—
102#16837249C2212yes—
103#16837249C2212yes—
104#16837249C2212yes—
105#16837249C2212yes—
106C42×Dic59C2211yescharacteristic
107C42×Dic59C2211yescharacteristic
108C42×Dic59C2211yescharacteristic
109C42×Dic59C2211yescharacteristic
110C42×Dic59C2211yescharacteristic
111C42×Dic59C2211yescharacteristic
112C42×Dic59C2211yescharacteristic
113C42×Dic59C2211yescharacteristic
114C2×#121×C59C2211yescharacteristic
115C2×C4×D4×C59C2211yescharacteristic
116C2×C4×D4×C59C2212yes—
117C22×C42×C59C2211yescharacteristic
118C59×#390C2211yescharacteristic
119C59×#389C2211yescharacteristic
120C59×#388C2212yes—
121C59×#386C2212yes—
122C59×#380C2211yescharacteristic
123C4×C4⋊C4×C59C2211yescharacteristic
124C4×C22⋊C4×C59C2212yes—
125C2×#11745687—28no—
126C2×#11745687—28no—
127C2×#11745687C2×C4116yescomplemented
128C22×Dic118C2312yes—
129C22×D236C2311yescharacteristic
130C22×C22⋊D59C2312yes—
131C22×C22⋊D59C2312yes—
132C22×C22⋊D59C2312yes—
133C23×Dic59C2312yes—
134C23×Dic59C2311yescharacteristic
135C23×Dic59C2311yescharacteristic
136C23×Dic59C2312yes—
137C23×Dic59C2311yescharacteristic
138C23×Dic59C2311yescharacteristic
139C22×C4×D59C2312yes—
140C22×C4×D59C2312yes—
141C22×C4×D59C2312yes—
142#14273726C2×C418yescomplemented
143#14273723C2×C418yescomplemented
144#14273713C2×C4116yescomplemented
145#14273701C2×C418yescomplemented
146#14273699C2×C4116yescomplemented
147C4×Dic118—28no—
148#14273692—28no—
149C4×D236—24no—
150D4×Dic59—28no—
151D4×Dic59—24no—
152D4×Dic59C2×C418yescomplemented
153#14273689—24no—
154#14273689C2×C418yescomplemented
155C4×C22⋊D59—28no—
156C4×C22⋊D59—28no—
157C4×C22⋊D59—28no—
158(C22⋊D59)⋊C4—28no—
159(C22⋊D59)⋊C4—28no—
160(C22⋊D59)⋊C4—28no—
161(C22⋊D59)⋊C4C2×C4116yescomplemented
162#14273685—28no—
163#14273683—28no—
164#14273683—28no—
165C2×C4⋊Dic59C2311yescharacteristic
166C2×C4⋊Dic59C2311yescharacteristic
167C2×C4⋊Dic59C2312yes—
168C2×C4⋊Dic59C2311yescharacteristic
169C2×Dic59⋊C4C2312yes—
170C2×Dic59⋊C4C2312yes—
171C2×Dic59⋊C4C2312yes—
172C2×Dic59⋊C4C2312yes—
173C2×Dic59⋊C4C2312yes—
174C2×Dic59⋊C4C2312yes—
175C2×Dic59⋊C4C2312yes—
176C2×C22⋊Dic59C2312yes—
177C2×C22⋊Dic59C2312yes—
178C2×C22⋊Dic59C2312yes—
179C2×C22⋊Dic59C2312yes—
180C2×C22⋊Dic59C2312yes—
181C2×(C2×D59)⋊C4C2312yes—
182C2×(C2×D59)⋊C4C2312yes—
183C2×(C2×D59)⋊C4C2312yes—
184C2×(C2×D59)⋊C4C2312yes—
185C2×(C2×D59)⋊C4C2312yes—
186C2×(C2×D59)⋊C4C2312yes—
187C2×(C2×D59)⋊C4C2312yes—
188C2×(C2×D59)⋊C4C2312yes—
189C2×C4×Dic59—24no—
190C2×C4×Dic59—28no—
191C2×C4×Dic59—24no—
192C2×C4×Dic59—24no—
193C2×C4×Dic59—24no—
194C2×C4×Dic59C2×C418yescomplemented
195C2×C4×Dic59D418yescomplemented
196C2×C4×Dic59C2311yescharacteristic
197C2×C4×Dic59C2311yescharacteristic
198C2×C4×Dic59C2311yescharacteristic
199C2×C4×Dic59C2311yescharacteristic
200C2×C4×Dic59C2311yescharacteristic
201C2×C4×Dic59C2311yescharacteristic
202C2×C4×Dic59C2311yescharacteristic
203C2×C4×Dic59C2311yescharacteristic
204C2×C4×Dic59C2311yescharacteristic
205C2×C4×Dic59C2311yescharacteristic
206C2×C4×Dic59C2311yescharacteristic
207C2×C4×Dic59C2311yescharacteristic
208C2×C4×Dic59C2311yescharacteristic
209C2×C4×Dic59C2312yes—
210C2×C4×Dic59C2312yes—
211C2×C4×Dic59C2312yes—
212C2×C4×Dic59C2312yes—
213C2×C4×Dic59C2312yes—
214C2×C4×Dic59C2311yescharacteristic
215C2×C4×Dic59C2311yescharacteristic
216C2×C4×Dic59C2311yescharacteristic
217C2×C4×Dic59C2311yescharacteristic
218C2×C4×Dic59C2311yescharacteristic
219C2×C4×Dic59C2311yescharacteristic
220C2×C4×Dic59C2311yescharacteristic
221C2×C4×Dic59C2311yescharacteristic
222C2×C4×Dic59C2311yescharacteristic
223C2×C4×Dic59C2311yescharacteristic
224C2×C4×Dic59C2311yescharacteristic
225C42×D59—28no—
226C59⋊#95C2312yes—
227C59⋊#95C2312yes—
228C59⋊#95C2312yes—
229C59⋊#95C2312yes—
230C59⋊#95C2312yes—
231C59⋊#95C2312yes—
232C59⋊#95C2312yes—
233C59⋊#95C2312yes—
234C59⋊#95C2312yes—
235C22×D4×C59C2312yes—
236C22×D4×C59C2311yescharacteristic
237C23×C4×C59C2312yes—
238C23×C4×C59C2311yescharacteristic
239C23×C4×C59C2311yescharacteristic
240C23×C4×C59C2311yescharacteristic
241#121×C59C2×C418yescomplemented
242C4×D4×C59—28no—
243C4×D4×C59—24no—
244C2×C4⋊C4×C59C2311yescharacteristic
245C2×C4⋊C4×C59C2311yescharacteristic
246C2×C4⋊C4×C59C2312yes—
247C2×C4⋊C4×C59C2311yescharacteristic
248C2×C22⋊C4×C59C2312yes—
249C2×C22⋊C4×C59C2312yes—
250C2×C22⋊C4×C59C2312yes—
251C2×C22⋊C4×C59C2312yes—
252C2×C22⋊C4×C59C2312yes—
253C2×C42×C59—24no—
254C2×C42×C59C2311yescharacteristic
255C2×C42×C59C2312yes—
256C2×C42×C59C2311yescharacteristic
257C2×C42×C59C2311yescharacteristic
258C2×C42×C59C2311yescharacteristic
259#95×C59C2312yes—
260#95×C59C2312yes—
261#95×C59C2312yes—
262C24×C59C2412yes—
263C24×C59C2411yescharacteristic
264C23×D59C2412yes—
265C2×D4×C59—24no—
266C2×D4×C59—24no—
267C2×D4×C59—22no—
268C2×D4×C59—22no—
269C2×D4×C59C22×C414yes—
270C2×D4×C59C22×C418yes—
271C22×C4×C59—22no—
272C22×C4×C59—22no—
273C22×C4×C59—22no—
274C22×C4×C59—22no—
275C22×C4×C59—22no—
276C22×C4×C59—22no—
277C22×C4×C59—22no—
278C22×C4×C59—24no—
279C22×C4×C59—24no—
280C22×C4×C59—24no—
281C22×C4×C59C22×C414yes—
282C22×C4×C59C2×D414yes—
283C22×C4×C59C2412yes—
284C22×C4×C59C2412yes—
285C22×C4×C59C2411yescharacteristic
286C22×C4×C59C2412yes—
287C22×C4×C59C2411yescharacteristic
288C22×C4×C59C2411yescharacteristic
289C22×C4×C59C2411yescharacteristic
290C22×C4×C59C2411yescharacteristic
291C22×C4×C59C2411yescharacteristic
292C2×C22⋊D59—24no—
293C2×C22⋊D59—24no—
294C2×C22⋊D59—24no—
295C2×C22⋊D59—24no—
296C2×C22⋊D59—24no—
297C2×C22⋊D59—24no—
298C2×C22⋊D59C22×C418yes—
299C2×C22⋊D59C22×C418yes—
300C2×C22⋊D59C22×C418yes—
301C22×Dic59—22no—
302C22×Dic59—24no—
303C22×Dic59—22no—
304C22×Dic59—22no—
305C22×Dic59—22no—
306C22×Dic59—22no—
307C22×Dic59—22no—
308C22×Dic59—22no—
309C22×Dic59—24no—
310C22×Dic59—24no—
311C22×Dic59—24no—
312C22×Dic59—24no—
313C22×Dic59C22×C414yes—
314C22×Dic59C22×C418yes—
315C22×Dic59C22×C414yes—
316C22×Dic59C2×D414yes—
317C22×Dic59C2×D414yes—
318C22×Dic59#4114yes—
319C22×Dic59C2412yes—
320C22×Dic59C2412yes—
321C22×Dic59C2411yescharacteristic
322C22×Dic59C2412yes—
323C22×Dic59C2411yescharacteristic
324C22×Dic59C2411yescharacteristic
325C22×Dic59C2411yescharacteristic
326C22×Dic59C2411yescharacteristic
327C22×Dic59C2411yescharacteristic
328C22×Dic59C2411yescharacteristic
329C22×Dic59C2411yescharacteristic
330#11745687—264no—
331C2×D236—22no—
332C2×D236—22no—
333C2×D236C22×C414yes—
334C2×C4×D59—24no—
335C2×C4×D59—24no—
336C2×C4×D59—24no—
337C2×C4×D59—24no—
338C2×C4×D59—24no—
339C2×C4×D59—24no—
340C2×C4×D59—24no—
341C2×C4×D59—24no—
342C2×C4×D59C22×C418yes—
343C2×Dic118—24no—
344C2×Dic118—24no—
345C2×Dic118C22×C418yes—
346C4⋊C4×C59—24no—
347C4⋊C4×C59—22no—
348C4⋊C4×C59—22no—
349C4⋊C4×C59C22×C414yes—
350C22⋊C4×C59—24no—
351C22⋊C4×C59—24no—
352C22⋊C4×C59—24no—
353C22⋊C4×C59—24no—
354C22⋊C4×C59C22×C418yes—
355C42×C59—24no—
356C42×C59—22no—
357C42×C59—22no—
358C42×C59—22no—
359C42×C59#4114yescomplemented
360C22⋊Dic59—24no—
361C22⋊Dic59—24no—
362C22⋊Dic59—24no—
363C22⋊Dic59—24no—
364C22⋊Dic59C22×C418yes—
365(C2×D59)⋊C4—24no—
366(C2×D59)⋊C4—24no—
367(C2×D59)⋊C4—24no—
368(C2×D59)⋊C4—24no—
369(C2×D59)⋊C4—24no—
370(C2×D59)⋊C4—24no—
371(C2×D59)⋊C4C22×C418yes—
372(C2×D59)⋊C4C22×C418yes—
373C4⋊Dic59—22no—
374C4⋊Dic59—22no—
375C4⋊Dic59—24no—
376C4⋊Dic59C22×C414yes—
377Dic59⋊C4—24no—
378Dic59⋊C4—24no—
379Dic59⋊C4—24no—
380Dic59⋊C4—24no—
381Dic59⋊C4—24no—
382Dic59⋊C4—24no—
383Dic59⋊C4C22×C418yes—
384C4×Dic59—24no—
385C4×Dic59—22no—
386C4×Dic59—22no—
387C4×Dic59—22no—
388C4×Dic59—24no—
389C4×Dic59—24no—
390C4×Dic59—24no—
391C4×Dic59—24no—
392C4×Dic59—22no—
393C4×Dic59—22no—
394C4×Dic59—22no—
395C4×Dic59—22no—
396C4×Dic59—22no—
397C4×Dic59—22no—
398C4×Dic59—22no—
399C4×Dic59—22no—
400C4×Dic59—22no—
401C4×Dic59—22no—
402C4×Dic59C22×C414yes—
403C4×Dic59C22×C414yes—
404C4×Dic59C22×C414yes—
405C4×Dic59C22×C414yes—
406C4×Dic59C2×D414yes—
407C4×Dic59C2×D414yes—
408C4×Dic59C2×D414yes—
409C4×Dic59C2×D414yes—
410C4×Dic59#4114yescomplemented
411C4×Dic59#4114yescomplemented
412C4×Dic59#4114yescomplemented
413C23×C59—21no—
414C23×C59—21no—
415C23×C59—21no—
416C23×C59—21no—
417C23×C59—22no—
418C23×C59—22no—
419C23×C59—22no—
420C23×C59—22no—
421C23×C59—22no—
422C23×C59—22no—
423C23×C59C23×C414yes—
424C23×C59C23×C412yes—
425C23×C59C22×D412yes—
426C23×C59C2×#4112yes—
427C23×C59C2511yescharacteristic
428C22×D59—22no—
429C22×D59—22no—
430C22×D59—22no—
431C22×D59—22no—
432C22×D59—22no—
433C22×D59—22no—
434C22×D59C23×C414yes—
435D4×C59—216no—
436D4×C59—28no—
437C2×C4×C59—28no—
438C2×C4×C59—22no—
439C2×C4×C59—21no—
440C2×C4×C59—21no—
441C2×C4×C59—21no—
442C2×C4×C59—21no—
443C2×C4×C59—21no—
444C2×C4×C59—21no—
445C2×C4×C59—21no—
446C2×C4×C59—21no—
447C2×C4×C59—22no—
448C2×C4×C59—28no—
449C2×C4×C59—28no—
450C2×C4×C59—22no—
451C2×C4×C59—22no—
452C2×C4×C59—22no—
453C2×C4×C59—22no—
454C2×C4×C59—22no—
455C2×C4×C59—22no—
456C2×C4×C59—48no—
457C2×C4×C59C23×C412yes—
458C2×C4×C59C23×C414yes—
459C2×C4×C59C23×C412yes—
460C2×C4×C59C22×D412yes—
461C2×C4×C59C22×D412yes—
462C2×C4×C59C2×#4112yes—
463C2×C4×C59C2×#4112yes—
464C2×C4×C59C2×#4112yes—
465C2×C4×C59C2×#4112yes—
466C2×C4×C59C2×#4112yes—
467C2×C4×C59C2×#4112yes—
468C22⋊D59—216no—
469C22⋊D59—216no—
470C22⋊D59—216no—
471C2×Dic59—28no—
472C2×Dic59—22no—
473C2×Dic59—21no—
474C2×Dic59—21no—
475C2×Dic59—21no—
476C2×Dic59—21no—
477C2×Dic59—21no—
478C2×Dic59—21no—
479C2×Dic59—21no—
480C2×Dic59—21no—
481C2×Dic59—22no—
482C2×Dic59—216no—
483C2×Dic59—28no—
484C2×Dic59—28no—
485C2×Dic59—22no—
486C2×Dic59—22no—
487C2×Dic59—22no—
488C2×Dic59—22no—
489C2×Dic59—22no—
490C2×Dic59—22no—
491C2×Dic59—48no—
492C2×Dic59C4×D4116yescomplemented
493C2×Dic59C23×C412yes—
494C2×Dic59C23×C414yes—
495C2×Dic59C23×C412yes—
496C2×Dic59C23×C412yes—
497C2×Dic59C23×C412yes—
498C2×Dic59C22×D412yes—
499C2×Dic59C22×D412yes—
500C2×Dic59C22×D412yes—
501C2×Dic59C22×D412yes—
502C2×Dic59C2×#4112yes—
503C2×Dic59C2×#4112yes—
504C2×Dic59C2×#4112yes—
505C2×Dic59C2×#4112yes—
506C2×Dic59C2×#4112yes—
507C2×Dic59C2×#4112yes—
508C2×Dic59C2×#4112yes—
509C2×Dic59C2×#4112yes—
510D236—28no—
511C4×D59—216no—
512C4×D59—48no—
513C4×D59—48no—
514Dic118—216no—
515C4×#532—591nomaximal, Sylow
516C22×C59—22no—
517C22×C59—22no—
518C22×C59—22no—
519C22×C59—22no—
520C22×C59—22no—
521C22×C59—22no—
522C22×C59—24no—
523C22×C59—24no—
524C22×C59—24no—
525C22×C59—42no—
526C22×C59—42no—
527C22×C59—42no—
528C22×C59—42no—
529C22×C59C2×C4×D414yes—
530C22×C59C24×C411yescharacteristic
531C22×C59C23×D411yescharacteristic
532C22×C59C22×#4111yescharacteristic
533C22×C59C22×#4111yescharacteristic
534C22×C59C22×#4111yescharacteristic
535C22×C59C22×#4111yescharacteristic
536C22×C59C22×#4111yescharacteristic
537C2×D59—24no—
538C2×D59—24no—
539C2×D59—24no—
540C2×D59—42no—
541C2×D59—42no—
542C2×D59—42no—
543C2×D59—42no—
544C4×C59—24no—
545C4×C59—22no—
546C4×C59—22no—
547C4×C59—22no—
548C4×C59—22no—
549C4×C59—42no—
550C4×C59—42no—
551C4×C59C4×#4114yescomplemented
552C4×C59#53214yescomplemented
553Dic59—24no—
554Dic59—22no—
555Dic59—22no—
556Dic59—22no—
557Dic59—22no—
558Dic59—42no—
559Dic59—42no—
560Dic59C2×C4×D414yes—
561Dic59C2×C4×D414yes—
562Dic59C4×#4114yescomplemented
563Dic59#53214yescomplemented
564C2×#532—591no—
565C2×C4×#41—592no—
566C4×C4⋊Q8—591no—
567C4×C4⋊Q8—591no—
568C4×#127—591no—
569C4×#127—591no—
570C4×#124—592no—
571C4×#124—592no—
572C4×#121—591no—
573C4×#121—592no—
574C4×#121—591no—
575C4×#121—591no—
576C4×#121—592no—
577C4×#121D5911yescharacteristic, complemented
578#2297—592no—
579#2293—591no—
580#2293—591no—
581#2293—592no—
582#2285—591no—
583C42×D4—591no—
584C42×D4—592no—
585C42×D4—591no—
586C2×C43—591no—
587C2×C59—24no—
588C2×C59—44no—
589C2×C59C22×C4×D411yescharacteristic
590C2×C59C2×C4×#4111yescharacteristic
591C2×C59C2×C4×#4111yescharacteristic
592C2×C59C2×#53211yescharacteristic
593C2×C59C2×#53211yescharacteristic
594C2×C59#344411yescharacteristic
595C2×C59#344411yescharacteristic
596D59—44no—
597C22×#41—592no—
598#532—5916no—
599C2×C4⋊Q8—591no—
600C2×#127—591no—
601C2×#124—592no—
602C2×#121—592no—
603C2×#121—591no—
604C2×#121C2×D5911yescharacteristic
605C4×#41—11816no—
606C2×C4×Q8—592no—
607C2×C4×Q8—592no—
608C2×C4×D4—591no—
609C2×C4×D4—591no—
610C2×C4×D4—592no—
611C2×C4×D4—592no—
612C2×C4×D4—592no—
613C2×C4×D4—592no—
614C2×C4×D4—591no—
615C2×C4×D4—591no—
616C2×C4×D4—592no—
617C2×C4×D4—592no—
618C2×C4×D4—592no—
619C2×C4×D4—592no—
620C2×C4×D4—591no—
621C2×C4×D4C2×D5911yescharacteristic
622C2×C4×D4C2×D5912yes—
623C2×#117—592no—
624C2×#117—592no—
625C2×#117—592no—
626C22×C42—591no—
627C22×C42—591no—
628C22×C42—592no—
629C22×C42—591no—
630C22×C42—591no—
631C22×C42—591no—
632C22×C42—591no—
633C22×C42—592no—
634C22×C42C2×D5911yescharacteristic
635#391—592no—
636#391—592no—
637#390—591no—
638#390—591no—
639#390—592no—
640#390—592no—
641#390—592no—
642#390—592no—
643#390—591no—
644#390C2×D5911yescharacteristic
645#389—592no—
646#389—591no—
647#389—591no—
648#389—591no—
649#389—592no—
650#389C2×D5911yescharacteristic
651#388—592no—
652#388—592no—
653#388—592no—
654#388—592no—
655#388—592no—
656#388—592no—
657#388—592no—
658#388C2×D5912yes—
659#386—592no—
660#386—592no—
661#386—592no—
662#386C2×D5912yes—
663#384—591no—
664#384—591no—
665#382—592no—
666#380—591no—
667#380—592no—
668#380C2×D5911yescharacteristic
669C4×C4⋊C4—591no—
670C4×C4⋊C4—591no—
671C4×C4⋊C4—591no—
672C4×C4⋊C4—591no—
673C4×C4⋊C4—591no—
674C4×C4⋊C4—592no—
675C4×C4⋊C4—592no—
676C4×C4⋊C4—592no—
677C4×C4⋊C4C2×D5911yescharacteristic
678C4×C22⋊C4—592no—
679C4×C22⋊C4—592no—
680C4×C22⋊C4—592no—
681C4×C22⋊C4—592no—
682C4×C22⋊C4—592no—
683C4×C22⋊C4—592no—
684C4×C22⋊C4—592no—
685C4×C22⋊C4—592no—
686C4×C22⋊C4—592no—
687C4×C22⋊C4—592no—
688C4×C22⋊C4—592no—
689C4×C22⋊C4C2×D5912yes—
690C43—591no—
691C43—591no—
692C43—591no—
693C43—591no—
694C43—591no—
695C43—591no—
696C43—591no—
697C43—591no—
698C59C4×#53211yescharacteristic, complemented, Sylow
699C2×#41—5916no—
700C2×#41—1188no—
701C2×#41—1188no—
702C22×Q8—592no—
703C22×D4—592no—
704C22×D4—592no—
705C22×D4—592no—
706C22×D4—591no—
707C22×D4C22×D5911yescharacteristic
708C22×D4C22×D5912yes—
709C23×C4—591no—
710C23×C4—592no—
711C23×C4—591no—
712C23×C4—591no—
713C23×C4—592no—
714C23×C4—592no—
715C23×C4—591no—
716C23×C4—592no—
717C23×C4—592no—
718C23×C4C22×D5911yescharacteristic
719C23×C4C22×D5912yes—
720C23×C4C22×D5911yescharacteristic
721C23×C4C22×D5911yescharacteristic
722C4⋊Q8—598no—
723#127—598no—
724#124—5916no—
725#121—5916no—
726#121—598no—
727#121C4×D5918yescomplemented
728C4×Q8—1188no—
729C4×Q8—1188no—
730C4×D4—28no—
731C4×D4—24no—
732C4×D4—598no—
733C4×D4—598no—
734C4×D4—5916no—
735C4×D4—1188no—
736C4×D4—1188no—
737C4×D4—1184no—
738C4×D4—1188no—
739C4×D4—1188no—
740C4×D4—1184no—
741C4×D4—1188no—
742C4×D4—1188no—
743C4×D4—1188no—
744C4×D4—1184no—
745#117—1188no—
746#117—1188no—
747#117—1188no—
748C2×C4⋊C4—592no—
749C2×C4⋊C4—591no—
750C2×C4⋊C4—592no—
751C2×C4⋊C4—592no—
752C2×C4⋊C4—592no—
753C2×C4⋊C4—592no—
754C2×C4⋊C4—592no—
755C2×C4⋊C4—592no—
756C2×C4⋊C4—592no—
757C2×C4⋊C4—591no—
758C2×C4⋊C4—591no—
759C2×C4⋊C4C22×D5912yes—
760C2×C4⋊C4C22×D5911yescharacteristic
761C2×C4⋊C4C22×D5911yescharacteristic
762C2×C4⋊C4C22×D5911yescharacteristic
763C2×C22⋊C4—592no—
764C2×C22⋊C4—592no—
765C2×C22⋊C4—592no—
766C2×C22⋊C4—592no—
767C2×C22⋊C4—592no—
768C2×C22⋊C4—592no—
769C2×C22⋊C4—592no—
770C2×C22⋊C4—592no—
771C2×C22⋊C4—592no—
772C2×C22⋊C4—592no—
773C2×C22⋊C4—592no—
774C2×C22⋊C4—592no—
775C2×C22⋊C4—592no—
776C2×C22⋊C4C22×D5912yes—
777C2×C22⋊C4C22×D5912yes—
778C2×C22⋊C4C22×D5912yes—
779C2×C22⋊C4C22×D5912yes—
780C2×C22⋊C4C22×D5912yes—
781C2×C42—24no—
782C2×C42—598no—
783C2×C42—598no—
784C2×C42—591no—
785C2×C42—591no—
786C2×C42—591no—
787C2×C42—591no—
788C2×C42—591no—
789C2×C42—591no—
790C2×C42—591no—
791C2×C42—591no—
792C2×C42—591no—
793C2×C42—591no—
794C2×C42—591no—
795C2×C42—592no—
796C2×C42—592no—
797C2×C42—592no—
798C2×C42—592no—
799C2×C42—591no—
800C2×C42—591no—
801C2×C42—591no—
802C2×C42—591no—
803C2×C42—591no—
804C2×C42—591no—
805C2×C42—591no—
806C2×C42—591no—
807C2×C42—591no—
808C2×C42—591no—
809C2×C42—591no—
810C2×C42—591no—
811C2×C42—592no—
812C2×C42—591no—
813C2×C42—1188no—
814C2×C42—1188no—
815C2×C42—1184no—
816C2×C42—1184no—
817C2×C42—1184no—
818C2×C42—1184no—
819C2×C42C22×D5911yescharacteristic
820C2×C42C22×D5911yescharacteristic
821C2×C42C22×D5912yes—
822C2×C42C22×D5911yescharacteristic
823C2×C42C22×D5911yescharacteristic
824#95—592no—
825#95—592no—
826#95—592no—
827#95—592no—
828#95—592no—
829#95—592no—
830#95—592no—
831#95—592no—
832#95—592no—
833#95C22×D5912yes—
834#95C22×D5912yes—
835#95C22×D5912yes—
836C24—592no—
837C24C23×D5912yes—
838C24C23×D5911yescharacteristic
839#41—11864no—
840C2×Q8—598no—
841C2×Q8—1184no—
842C2×Q8—1184no—
843C2×D4—24no—
844C2×D4—24no—
845C2×D4—22no—
846C2×D4—22no—
847C2×D4—598no—
848C2×D4—598no—
849C2×D4—598no—
850C2×D4—594no—
851C2×D4—1184no—
852C2×D4—1184no—
853C2×D4—1184no—
854C2×D4—1184no—
855C2×D4—1184no—
856C2×D4—1184no—
857C2×D4—1182no—
858C2×D4—1182no—
859C2×D4C2×C4×D5914yes—
860C2×D4C2×C4×D5918yes—
861C22×C4—22no—
862C22×C4—22no—
863C22×C4—22no—
864C22×C4—22no—
865C22×C4—22no—
866C22×C4—22no—
867C22×C4—22no—
868C22×C4—24no—
869C22×C4—24no—
870C22×C4—24no—
871C22×C4—594no—
872C22×C4—594no—
873C22×C4—594no—
874C22×C4—591no—
875C22×C4—591no—
876C22×C4—591no—
877C22×C4—591no—
878C22×C4—594no—
879C22×C4—598no—
880C22×C4—594no—
881C22×C4—591no—
882C22×C4—591no—
883C22×C4—591no—
884C22×C4—592no—
885C22×C4—591no—
886C22×C4—598no—
887C22×C4—592no—
888C22×C4—592no—
889C22×C4—1184no—
890C22×C4—1184no—
891C22×C4—1184no—
892C22×C4—1184no—
893C22×C4—1184no—
894C22×C4—1184no—
895C22×C4—1182no—
896C22×C4—1182no—
897C22×C4—1182no—
898C22×C4—1182no—
899C22×C4—1182no—
900C22×C4—1182no—
901C22×C4—1184no—
902C22×C4—1184no—
903C22×C4—1184no—
904C22×C4—1184no—
905C22×C4—1182no—
906C22×C4—1184no—
907C22×C4—1184no—
908C22×C4—1184no—
909C22×C4C2×C4×D5914yes—
910C22×C4D4×D5914yes—
911C22×C4C23×D5912yes—
912C22×C4C23×D5912yes—
913C22×C4C23×D5911yescharacteristic
914C22×C4C23×D5912yes—
915C22×C4C23×D5911yescharacteristic
916C22×C4C23×D5911yescharacteristic
917C22×C4C23×D5911yescharacteristic
918C22×C4C23×D5911yescharacteristic
919C22×C4C23×D5911yescharacteristic
920C4⋊C4—24no—
921C4⋊C4—22no—
922C4⋊C4—22no—
923C4⋊C4—598no—
924C4⋊C4—594no—
925C4⋊C4—1184no—
926C4⋊C4—1184no—
927C4⋊C4—1184no—
928C4⋊C4—1184no—
929C4⋊C4—1184no—
930C4⋊C4—1184no—
931C4⋊C4—1184no—
932C4⋊C4—1182no—
933C4⋊C4—1182no—
934C4⋊C4C2×C4×D5914yes—
935C22⋊C4—24no—
936C22⋊C4—24no—
937C22⋊C4—24no—
938C22⋊C4—24no—
939C22⋊C4—598no—
940C22⋊C4—598no—
941C22⋊C4—598no—
942C22⋊C4—1184no—
943C22⋊C4—1184no—
944C22⋊C4—1184no—
945C22⋊C4—1184no—
946C22⋊C4—1184no—
947C22⋊C4—1184no—
948C22⋊C4—1184no—
949C22⋊C4—1184no—
950C22⋊C4—1184no—
951C22⋊C4—1184no—
952C22⋊C4C2×C4×D5918yes—
953C42—24no—
954C42—22no—
955C42—22no—
956C42—22no—
957C42—594no—
958C42—594no—
959C42—594no—
960C42—594no—
961C42—594no—
962C42—594no—
963C42—594no—
964C42—594no—
965C42—594no—
966C42—594no—
967C42—594no—
968C42—1184no—
969C42—1184no—
970C42—1184no—
971C42—1184no—
972C42—1182no—
973C42—1182no—
974C42—1182no—
975C42—1182no—
976C42—1182no—
977C42—1182no—
978C42—1182no—
979C42—1182no—
980C42—1182no—
981C42—1182no—
982C42—1184no—
983C42—1182no—
984C42—1182no—
985C42—1182no—
986C42#1174568714yescomplemented
987C23—21no—
988C23—21no—
989C23—21no—
990C23—21no—
991C23—22no—
992C23—22no—
993C23—22no—
994C23—22no—
995C23—22no—
996C23—22no—
997C23—594no—
998C23—1182no—
999C23—1182no—
1000C23—1182no—
1001C23—1182no—
1002C23—1182no—
1003C23—1182no—
1004C23C22×C4×D5914yes—
1005C23C22×C4×D5912yes—
1006C23C2×D4×D5912yes—
1007C23#41×D5912yes—
1008C23C24×D5911yescharacteristic
1009Q8—11816no—
1010D4—216no—
1011D4—28no—
1012D4—11816no—
1013D4—11816no—
1014D4—11816no—
1015D4—1188no—
1016C2×C4—28no—
1017C2×C4—22no—
1018C2×C4—21no—
1019C2×C4—21no—
1020C2×C4—21no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—22no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—28no—
1028C2×C4—28no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—48no—
1036C2×C4—592no—
1037C2×C4—592no—
1038C2×C4—592no—
1039C2×C4—592no—
1040C2×C4—592no—
1041C2×C4—592no—
1042C2×C4—592no—
1043C2×C4—592no—
1044C2×C4—592no—
1045C2×C4—592no—
1046C2×C4—592no—
1047C2×C4—592no—
1048C2×C4—5916no—
1049C2×C4—592no—
1050C2×C4—594no—
1051C2×C4—592no—
1052C2×C4—592no—
1053C2×C4—592no—
1054C2×C4—11816no—
1055C2×C4—1188no—
1056C2×C4—1188no—
1057C2×C4—11816no—
1058C2×C4—1188no—
1059C2×C4—1182no—
1060C2×C4—1181no—
1061C2×C4—1181no—
1062C2×C4—1181no—
1063C2×C4—1181no—
1064C2×C4—1181no—
1065C2×C4—1181no—
1066C2×C4—1181no—
1067C2×C4—1181no—
1068C2×C4—1182no—
1069C2×C4—1182no—
1070C2×C4—1182no—
1071C2×C4—1182no—
1072C2×C4—1182no—
1073C2×C4—1182no—
1074C2×C4—1182no—
1075C2×C4—2368no—
1076C2×C4—2368no—
1077C2×C4—2368no—
1078C2×C4C22×C4×D5912yes—
1079C2×C4C22×C4×D5914yes—
1080C2×C4C22×C4×D5912yes—
1081C2×C4C2×D4×D5912yes—
1082C2×C4C2×D4×D5912yes—
1083C2×C4#41×D5912yes—
1084C2×C4#41×D5912yes—
1085C2×C4#41×D5912yes—
1086C2×C4C2×#1174568712yes—
1087C2×C4C2×#1174568712yes—
1088C2×C4C2×#1174568712yes—
1089C22—22no—
1090C22—22no—
1091C22—22no—
1092C22—22no—
1093C22—22no—
1094C22—22no—
1095C22—24no—
1096C22—24no—
1097C22—24no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—1184no—
1103C22—1184no—
1104C22—1184no—
1105C22—2362no—
1106C22—2362no—
1107C22—2362no—
1108C22—2362no—
1109C22C4×D4×D5914yes—
1110C22C23×C4×D5911yescharacteristic
1111C22C22×D4×D5911yescharacteristic
1112C22C2×#41×D5911yescharacteristic
1113C22C2×#41×D5911yescharacteristic
1114C22C2×#41×D5911yescharacteristic
1115C22C2×#41×D5911yescharacteristic
1116C22C22×#1174568711yescharacteristic
1117C4—24no—
1118C4—22no—
1119C4—22no—
1120C4—22no—
1121C4—22no—
1122C4—42no—
1123C4—42no—
1124C4—594no—
1125C4—594no—
1126C4—594no—
1127C4—594no—
1128C4—1184no—
1129C4—1182no—
1130C4—1182no—
1131C4—1182no—
1132C4—1182no—
1133C4—2362no—
1134C4—2362no—
1135C4C4×#1174568714yescomplemented
1136C4#1683794714yesdirect product factor
1137C2—24no—
1138C2—44no—
1139C2—2364no—
1140C2C2×C4×D4×D5911yescharacteristic
1141C2C4×#41×D5911yescharacteristic
1142C2C2×C4×#1174568711yescharacteristic
1143C2#532×D5911yescharacteristic
1144C2C2×#1683794711yescharacteristic
1145C2#2143738811yescharacteristic
1146C2#2143739011yescharacteristic
subgroupG/H
centerC22×C4C23×D59
commutatorC22×C59C24×C4
FrattiniC23C24×D59
FittingC4×#121×C59C2
socle, cosocleC23×C59C25
prime radicalC2×#16837947C2
hypercenterC4×#121D59
hypocenterC59C4×#532
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C4×#121

Complements

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

NH ≅ G/Ntype
2. C2×C4×#11745687C2semidirect
3. #21426667C2semidirect
4. C4×#14273726C2semidirect
5. #21426660C2semidirect
6. C4×#14273723C2semidirect
7. #21426637C2semidirect
8. C4×#14273713C2semidirect
9. #121×Dic59C2semidirect
10. C4×#14273701C2semidirect
11. #21426606C2semidirect
12. C4×#14273699C2semidirect
13. #21426602C2semidirect
14. #21426581C2semidirect
15. #21426558C2semidirect
16. #21426556C2semidirect
17. #21426554C2semidirect
18. #21426498C2semidirect
19. C4×D4×Dic59C2semidirect
20. C4×#14273689C2semidirect
21. C4×(C22⋊D59)⋊C4C2semidirect
22. C2×C42×Dic59C2semidirect
23. C4×#121×C59C2semidirect
25. #16837947C4direct (N × H)
127. C2×#11745687C2×C4semidirect
142. #14273726C2×C4semidirect
143. #14273723C2×C4semidirect
144. #14273713C2×C4semidirect
145. #14273701C2×C4semidirect
146. #14273699C2×C4semidirect
152. D4×Dic59C2×C4semidirect
154. #14273689C2×C4semidirect
161. (C22⋊D59)⋊C4C2×C4semidirect
194. C2×C4×Dic59C2×C4semidirect
195. C2×C4×Dic59D4semidirect
241. #121×C59C2×C4semidirect
359. C42×C59#41semidirect
410. C4×Dic59#41semidirect
411. C4×Dic59#41semidirect
412. C4×Dic59#41semidirect
492. C2×Dic59C4×D4semidirect
551. C4×C59C4×#41semidirect
552. C4×C59#532semidirect
562. Dic59C4×#41semidirect
563. Dic59#532semidirect
577. C4×#121D59semidirect
698. C59C4×#532semidirect
727. #121C4×D59semidirect
986. C42#11745687semidirect
1135. C4C4×#11745687semidirect
1136. C4#16837947direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168379472
C2×C4×#117456872
#214266672
C4×#142737262
#214266602
C4×#142737232
#214266372
C4×#142737132
#121×Dic592
C4×#142737012
#214266062
C4×#142736992
#214266022
#214265812
#214265582
#214265562
#214265542
#214264982
C4×D4×Dic592
C4×#142736892
C4×(C22⋊D59)⋊C42
C2×C42×Dic592
C4×#121×C592
C4×#53259