Finite Group Databasebeta

← C2×#21426824 #28747506

Subgroups — C2×#21426824 #28747506

Order 15104.

2982 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14273704C211yesmaximal, characteristic
2#21426824C2116yesmaximal, direct product factor
3C2×#16837308C211yesmaximal, characteristic, complemented
4C2×#16837306C211yesmaximal, characteristic, complemented
5C2×#16837300C211yesmaximal, characteristic, complemented
6C2×#16837299C211yesmaximal, characteristic, complemented
7C2×#16837289C211yesmaximal, characteristic, complemented
8C2×#16837286C211yesmaximal, characteristic, complemented
9C2×#16837286C211yesmaximal, characteristic, complemented
10C2×#16837285C211yesmaximal, characteristic, complemented
11C2×#16837277C211yesmaximal, characteristic
12C2×#16837274C211yesmaximal, characteristic
13C2×#16837260C211yesmaximal, characteristic
14C2×C4×C22⋊Dic59C211yesmaximal, characteristic
15C22×C59⋊#95C211yesmaximal, characteristic
16C2×C4×C22⋊C4×C59C211yesmaximal, characteristic
17C23×Dic118C2211yescharacteristic
18C24×Dic59C2211yescharacteristic
19C24×Dic59C2211yescharacteristic
20C2×#14273704C4116yescomplemented
21C2×#14273704C2218yes—
22C22×C4⋊Dic59C2211yescharacteristic
23C22×C4⋊Dic59C2211yescharacteristic
24C22×C4⋊Dic59C2211yescharacteristic
25C22×Dic59⋊C4C2211yescharacteristic
26C22×Dic59⋊C4C2211yescharacteristic
27C22×Dic59⋊C4C2211yescharacteristic
28C22×Dic59⋊C4C2211yescharacteristic
29C22×Dic59⋊C4C2211yescharacteristic
30C22×Dic59⋊C4C2211yescharacteristic
31C22×C22⋊Dic59C2211yescharacteristic
32C22×C22⋊Dic59C2211yescharacteristic
33C22×C4×Dic59C2211yescharacteristic
34C22×C4×Dic59C2211yescharacteristic
35#16837308C2218yescomplemented
36#16837306C2218yescomplemented
37#16837300C2218yescomplemented
38#16837299C2218yescomplemented
39#16837289C2218yescomplemented
40#16837286C2218yescomplemented
41#16837286C2218yescomplemented
42#16837285C2218yescomplemented
43#16837277C2218yes—
44#16837274C2218yes—
45#16837260C2218yes—
46C4×C22⋊Dic59C2218yes—
47C2×C59⋊#95C2211yescharacteristic
48C2×C59⋊#95C2211yescharacteristic
49C2×C59⋊#95C2211yescharacteristic
50C2×C59⋊#95C2211yescharacteristic
51C2×C59⋊#95C2211yescharacteristic
52C2×C59⋊#95C2211yescharacteristic
53C2×C59⋊#95C2211yescharacteristic
54C2×C59⋊#95C2211yescharacteristic
55C2×C59⋊#95C2211yescharacteristic
56C2×C59⋊#95C2211yescharacteristic
57C2×C59⋊#95C2211yescharacteristic
58C2×C59⋊#95C2211yescharacteristic
59C2×C59⋊#95C2218yes—
60C24×C4×C59C2211yescharacteristic
61C22×C22⋊C4×C59C2211yescharacteristic
62C22×C22⋊C4×C59C2211yescharacteristic
63C22×C42×C59C2211yescharacteristic
64C22×C42×C59C2211yescharacteristic
65C4×C22⋊C4×C59C2218yes—
66C2×#95×C59C2211yescharacteristic
67C2×#95×C59C2211yescharacteristic
68C22×Dic118—42no—
69C22×Dic118—42no—
70C22×Dic118C2×C418yescomplemented
71C22×Dic118C2314yes—
72C23×Dic59—24no—
73C23×Dic59—42no—
74C23×Dic59—42no—
75C23×Dic59—42no—
76C23×Dic59—42no—
77C23×Dic59C2×C418yes—
78C23×Dic59C2311yescharacteristic
79C23×Dic59C2311yescharacteristic
80C23×Dic59C2311yescharacteristic
81C23×Dic59C2311yescharacteristic
82C23×Dic59C2311yescharacteristic
83C23×Dic59C2311yescharacteristic
84C23×Dic59C2311yescharacteristic
85C23×Dic59C2311yescharacteristic
86C23×Dic59C2314yes—
87C23×Dic59C2314yes—
88#14273704C2×C4164yescomplemented
89C2×C4⋊Dic59—42no—
90C2×C4⋊Dic59—42no—
91C2×C4⋊Dic59C2×C418yescomplemented
92C2×C4⋊Dic59C2314yes—
93C2×C4⋊Dic59C2314yes—
94C2×C4⋊Dic59C2314yes—
95C2×Dic59⋊C4—42no—
96C2×Dic59⋊C4—42no—
97C2×Dic59⋊C4—42no—
98C2×Dic59⋊C4—42no—
99C2×Dic59⋊C4C2×C418yescomplemented
100C2×Dic59⋊C4C2×C418yescomplemented
101C2×Dic59⋊C4C2314yes—
102C2×Dic59⋊C4C2314yes—
103C2×Dic59⋊C4C2314yes—
104C2×Dic59⋊C4C2314yes—
105C2×Dic59⋊C4C2314yes—
106C2×Dic59⋊C4C2314yes—
107C2×C22⋊Dic59—24no—
108C2×C22⋊Dic59C2×C418yes—
109C2×C22⋊Dic59C2314yes—
110C2×C22⋊Dic59C2314yes—
111C2×C4×Dic59—42no—
112C2×C4×Dic59—42no—
113C2×C4×Dic59C2314yes—
114C2×C4×Dic59C2314yes—
115C59⋊#95C2314yes—
116C59⋊#95C2314yes—
117C59⋊#95C2314yes—
118C59⋊#95C2314yes—
119C59⋊#95C2314yes—
120C59⋊#95C2314yes—
121C59⋊#95C2314yes—
122C59⋊#95C2314yes—
123C59⋊#95C2314yes—
124C59⋊#95C2314yes—
125C59⋊#95C2314yes—
126C59⋊#95C2314yes—
127C25×C59C2311yescharacteristic
128C23×C4×C59—42no—
129C23×C4×C59—42no—
130C23×C4×C59Q818yescomplemented
131C23×C4×C59C2311yescharacteristic
132C23×C4×C59C2311yescharacteristic
133C23×C4×C59C2311yescharacteristic
134C23×C4×C59C2311yescharacteristic
135C23×C4×C59C2311yescharacteristic
136C23×C4×C59C2311yescharacteristic
137C23×C4×C59C2314yes—
138C2×C22⋊C4×C59—24no—
139C2×C22⋊C4×C59C2×C418yes—
140C2×C22⋊C4×C59C2314yes—
141C2×C22⋊C4×C59C2314yes—
142C2×C42×C59—42no—
143C2×C42×C59—42no—
144C2×C42×C59C2314yes—
145C2×C42×C59C2314yes—
146#95×C59C2314yes—
147#95×C59C2314yes—
148C24×C59—22no—
149C24×C59—22no—
150C24×C59—22no—
151C24×C59—22no—
152C24×C59C22×C414yes—
153C24×C59C2×Q814yes—
154C24×C59#4114yes—
155C24×C59C2412yes—
156C24×C59C2411yescharacteristic
157C22×C4×C59—22no—
158C22×C4×C59—22no—
159C22×C4×C59—22no—
160C22×C4×C59—22no—
161C22×C4×C59—22no—
162C22×C4×C59—22no—
163C22×C4×C59—22no—
164C22×C4×C59—22no—
165C22×C4×C59—22no—
166C22×C4×C59—22no—
167C22×C4×C59—22no—
168C22×C4×C59—22no—
169C22×C4×C59—22no—
170C22×C4×C59—22no—
171C22×C4×C59—416no—
172C22×C4×C59—44no—
173C22×C4×C59—44no—
174C22×C4×C59C22×C414yes—
175C22×C4×C59C22×C414yes—
176C22×C4×C59C2×Q814yes—
177C22×C4×C59C2×Q814yes—
178C22×C4×C59C2×Q8116yescomplemented
179C22×C4×C59C2412yes—
180C22×C4×C59C2412yes—
181C22×C4×C59C2412yes—
182C22×C4×C59C2412yes—
183C22×C4×C59C2412yes—
184C22×C4×C59C2412yes—
185C22×Dic59—22no—
186C22×Dic59—22no—
187C22×Dic59—22no—
188C22×Dic59—22no—
189C22×Dic59—22no—
190C22×Dic59—22no—
191C22×Dic59—22no—
192C22×Dic59—22no—
193C22×Dic59—22no—
194C22×Dic59—22no—
195C22×Dic59—28no—
196C22×Dic59—22no—
197C22×Dic59—22no—
198C22×Dic59—22no—
199C22×Dic59—22no—
200C22×Dic59—22no—
201C22×Dic59—22no—
202C22×Dic59—22no—
203C22×Dic59—22no—
204C22×Dic59—22no—
205C22×Dic59—22no—
206C22×Dic59—416no—
207C22×Dic59—44no—
208C22×Dic59—44no—
209C22×Dic59—44no—
210C22×Dic59—44no—
211C22×Dic59—416no—
212C22×Dic59C22×C414yes—
213C22×Dic59C22×C414yes—
214C22×Dic59C22×C414yes—
215C22×Dic59C22×C414yes—
216C22×Dic59C22×C4116yes—
217C22×Dic59C2412yes—
218C22×Dic59C2412yes—
219C22×Dic59C2412yes—
220C22×Dic59C2412yes—
221C22×Dic59C2412yes—
222C22×Dic59C2412yes—
223C22×Dic59C2412yes—
224C22×Dic59C2412yes—
225C2×Dic118—416no—
226C2×Dic118—44no—
227C2×Dic118—44no—
228C2×Dic118C22×C4116yescomplemented
229C22⋊C4×C59—28no—
230C22⋊C4×C59C22×C4116yes—
231C42×C59—44no—
232C42×C59—44no—
233C22⋊Dic59—28no—
234C22⋊Dic59C22×C4116yes—
235C4⋊Dic59—44no—
236C4⋊Dic59—44no—
237C4⋊Dic59C22×C4116yescomplemented
238Dic59⋊C4—44no—
239Dic59⋊C4—44no—
240Dic59⋊C4—44no—
241Dic59⋊C4—44no—
242Dic59⋊C4C22×C4116yescomplemented
243Dic59⋊C4C22×C4116yescomplemented
244C4×Dic59—44no—
245C4×Dic59—44no—
246C23×C59—28no—
247C23×C59—28no—
248C23×C59—28no—
249C23×C59—28no—
250C23×C59—28no—
251C23×C59—28no—
252C23×C59—22no—
253C23×C59—22no—
254C23×C59—22no—
255C23×C59—22no—
256C23×C59C4×Q8116yes—
257C23×C59C23×C414yes—
258C23×C59C23×C412yes—
259C23×C59C22×Q814yes—
260C23×C59C22×Q812yes—
261C23×C59C2×#4114yes—
262C23×C59C2×#4112yes—
263C23×C59H(5,𝔽2)12yes—
264C23×C59H(5,𝔽2)12yes—
265C23×C59H(5,𝔽2)12yes—
266C23×C592−1+412yes—
267C23×C59C2511yescharacteristic
268C2×C4×C59—28no—
269C2×C4×C59—28no—
270C2×C4×C59—28no—
271C2×C4×C59—28no—
272C2×C4×C59—22no—
273C2×C4×C59—22no—
274C2×C4×C59—22no—
275C2×C4×C59—22no—
276C2×C4×C59—22no—
277C2×C4×C59—22no—
278C2×C4×C59—22no—
279C2×C4×C59—22no—
280C2×C4×C59—22no—
281C2×C4×C59—22no—
282C2×C4×C59—22no—
283C2×C4×C59—22no—
284C2×C4×C59—22no—
285C2×C4×C59—22no—
286C2×C4×C59—416no—
287C2×C4×C59—44no—
288C2×C4×C59—44no—
289C2×C4×C59C23×C414yes—
290C2×C4×C59C23×C414yes—
291C2×C4×C59C22×Q814yes—
292C2×C4×C59C22×Q814yes—
293C2×Dic59—28no—
294C2×Dic59—28no—
295C2×Dic59—28no—
296C2×Dic59—28no—
297C2×Dic59—22no—
298C2×Dic59—22no—
299C2×Dic59—22no—
300C2×Dic59—22no—
301C2×Dic59—22no—
302C2×Dic59—22no—
303C2×Dic59—22no—
304C2×Dic59—22no—
305C2×Dic59—22no—
306C2×Dic59—22no—
307C2×Dic59—22no—
308C2×Dic59—22no—
309C2×Dic59—22no—
310C2×Dic59—22no—
311C2×Dic59—22no—
312C2×Dic59—22no—
313C2×Dic59—22no—
314C2×Dic59—22no—
315C2×Dic59—22no—
316C2×Dic59—22no—
317C2×Dic59—416no—
318C2×Dic59—416no—
319C2×Dic59—44no—
320C2×Dic59—44no—
321C2×Dic59—44no—
322C2×Dic59—44no—
323C2×Dic59C23×C414yes—
324C2×Dic59C23×C414yes—
325C2×Dic59C23×C414yes—
326C2×Dic59C23×C414yes—
327Dic118—416no—
328C2×#2329—591nomaximal, Sylow
329C22×C59—232no—
330C22×C59—24no—
331C22×C59—24no—
332C22×C59—24no—
333C22×C59—24no—
334C22×C59—24no—
335C22×C59—24no—
336C22×C59C2×C4×Q818yes—
337C22×C59C2×C4×Q814yes—
338C22×C59#51814yes—
339C22×C59#52014yes—
340C22×C59#53814yes—
341C22×C59#53914yes—
342C22×C59#54314yes—
343C22×C59#54414yes—
344C22×C59C24×C411yescharacteristic
345C22×C59C23×Q811yescharacteristic
346C22×C59C22×#4111yescharacteristic
347C22×C59C2×H(5,𝔽2)11yescharacteristic
348C22×C59C2×H(5,𝔽2)11yescharacteristic
349C22×C59C2×H(5,𝔽2)11yescharacteristic
350C22×C59C2×2−1+411yescharacteristic
351C4×C59—24no—
352C4×C59—24no—
353C4×C59—24no—
354C4×C59—24no—
355C4×C59—42no—
356C4×C59—42no—
357Dic59—24no—
358Dic59—24no—
359Dic59—24no—
360Dic59—24no—
361Dic59—42no—
362Dic59—42no—
363Dic59—42no—
364Dic59—42no—
365C22×C22⋊Q8—591no—
366#2329—5916no—
367C2×#391—591no—
368C2×#391—591no—
369C2×#389—591no—
370C2×#389—591no—
371C2×#387—591no—
372C2×#387—591no—
373C2×#387—591no—
374C2×#387—591no—
375C2×#385—591no—
376C2×#385—591no—
377C2×#380—591no—
378C2×C4×C22⋊C4—591no—
379C2×C4×C22⋊C4D5911yescharacteristic
380C22×#95—591no—
381C2×C59—28no—
382C2×C59#232918yescomplemented
383C2×C59C22×C4×Q811yescharacteristic
384C2×C59C2×#51811yescharacteristic
385C2×C59C2×#52011yescharacteristic
386C2×C59C2×#53811yescharacteristic
387C2×C59C2×#53911yescharacteristic
388C2×C59C2×#54311yescharacteristic
389C2×C59C2×#54411yescharacteristic
390C23×Q8—591no—
391C24×C4—591no—
392C24×C4—591no—
393C24×C4C2×D5911yescharacteristic
394C2×C22⋊Q8—5916no—
395C2×C22⋊Q8—598no—
396C22×C4⋊C4—591no—
397C22×C4⋊C4—591no—
398C22×C4⋊C4—591no—
399C22×C4⋊C4—591no—
400C22×C4⋊C4—591no—
401C22×C4⋊C4—591no—
402C22×C4⋊C4—591no—
403C22×C4⋊C4—591no—
404C22×C4⋊C4—591no—
405C22×C22⋊C4—591no—
406C22×C22⋊C4—591no—
407C22×C22⋊C4C2×D5911yescharacteristic
408C22×C22⋊C4C2×D5911yescharacteristic
409C22×C42—591no—
410C22×C42—591no—
411C22×C42C2×D5911yescharacteristic
412C22×C42C2×D5911yescharacteristic
413#391—598no—
414#391—598no—
415#389—598no—
416#389—598no—
417#387—598no—
418#387—598no—
419#387—598no—
420#387—598no—
421#385—598no—
422#385—598no—
423#380—598no—
424C4×C22⋊C4—598no—
425C4×C22⋊C4C2×D5918yes—
426C2×#95—598no—
427C2×#95—591no—
428C2×#95—591no—
429C2×#95—591no—
430C2×#95—591no—
431C2×#95—591no—
432C2×#95—591no—
433C2×#95—591no—
434C2×#95—591no—
435C2×#95—591no—
436C2×#95—591no—
437C2×#95—591no—
438C2×#95—591no—
439C2×#95C2×D5911yescharacteristic
440C2×#95C2×D5911yescharacteristic
441C59C2×#232911yescharacteristic, complemented, Sylow
442C25C22×D5911yescharacteristic
443C22×Q8—598no—
444C22×Q8—594no—
445C22×Q8—2362no—
446C22×Q8—2362no—
447C23×C4—42no—
448C23×C4—42no—
449C23×C4—591no—
450C23×C4—591no—
451C23×C4—591no—
452C23×C4—591no—
453C23×C4—598no—
454C23×C4—594no—
455C23×C4—591no—
456C23×C4—591no—
457C23×C4—591no—
458C23×C4—591no—
459C23×C4—594no—
460C23×C4—1184no—
461C23×C4—2362no—
462C23×C4—2362no—
463C23×C4—2362no—
464C23×C4—2362no—
465C23×C4Dic11818yescomplemented
466C23×C4C22×D5911yescharacteristic
467C23×C4C22×D5911yescharacteristic
468C23×C4C22×D5911yescharacteristic
469C23×C4C22×D5911yescharacteristic
470C23×C4C22×D5911yescharacteristic
471C23×C4C22×D5911yescharacteristic
472C23×C4C22×D5914yes—
473C22⋊Q8—5964no—
474C2×C4⋊C4—598no—
475C2×C4⋊C4—598no—
476C2×C4⋊C4—598no—
477C2×C4⋊C4—594no—
478C2×C4⋊C4—594no—
479C2×C4⋊C4—594no—
480C2×C4⋊C4—594no—
481C2×C4⋊C4—594no—
482C2×C4⋊C4—594no—
483C2×C4⋊C4—594no—
484C2×C4⋊C4—594no—
485C2×C4⋊C4—594no—
486C2×C4⋊C4—2362no—
487C2×C4⋊C4—2362no—
488C2×C4⋊C4—2362no—
489C2×C4⋊C4—2362no—
490C2×C4⋊C4—2362no—
491C2×C4⋊C4—2362no—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—598no—
494C2×C22⋊C4—594no—
495C2×C22⋊C4—594no—
496C2×C22⋊C4—1184no—
497C2×C22⋊C4C4×D5918yes—
498C2×C22⋊C4C22×D5914yes—
499C2×C22⋊C4C22×D5914yes—
500C2×C42—42no—
501C2×C42—42no—
502C2×C42—594no—
503C2×C42—594no—
504C2×C42—2362no—
505C2×C42—2362no—
506C2×C42C22×D5914yes—
507C2×C42C22×D5914yes—
508#95—594no—
509#95—594no—
510#95—594no—
511#95—594no—
512#95—594no—
513#95—594no—
514#95—594no—
515#95—594no—
516#95—594no—
517#95—594no—
518#95—594no—
519#95—594no—
520#95C22×D5914yes—
521#95C22×D5914yes—
522C24—22no—
523C24—22no—
524C24—22no—
525C24—22no—
526C24C2×Dic11814yes—
527C24C2×C4×D5914yes—
528C24#1174568514yes—
529C24C23×D5912yes—
530C24C23×D5911yescharacteristic
531C2×Q8—5916no—
532C2×Q8—2364no—
533C2×Q8—2364no—
534C2×Q8—23616no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—416no—
550C22×C4—44no—
551C22×C4—44no—
552C22×C4—594no—
553C22×C4—594no—
554C22×C4—594no—
555C22×C4—594no—
556C22×C4—592no—
557C22×C4—592no—
558C22×C4—592no—
559C22×C4—592no—
560C22×C4—5916no—
561C22×C4—592no—
562C22×C4—592no—
563C22×C4—592no—
564C22×C4—592no—
565C22×C4—1182no—
566C22×C4—1182no—
567C22×C4—1182no—
568C22×C4—1182no—
569C22×C4—1182no—
570C22×C4—1182no—
571C22×C4—1182no—
572C22×C4—1182no—
573C22×C4—1182no—
574C22×C4—1182no—
575C22×C4—1188no—
576C22×C4—1182no—
577C22×C4—1182no—
578C22×C4—1182no—
579C22×C4—1182no—
580C22×C4—1182no—
581C22×C4—1182no—
582C22×C4—1182no—
583C22×C4—1182no—
584C22×C4—1182no—
585C22×C4—1182no—
586C22×C4—2364no—
587C22×C4—2364no—
588C22×C4—23616no—
589C22×C4—2364no—
590C22×C4—2364no—
591C22×C4—23616no—
592C22×C4C2×Dic11814yes—
593C22×C4C2×Dic11814yes—
594C22×C4C2×Dic118116yescomplemented
595C22×C4C2×C4×D5914yes—
596C22×C4C2×C4×D5914yes—
597C22×C4C23×D5912yes—
598C22×C4C23×D5912yes—
599C22×C4C23×D5912yes—
600C22×C4C23×D5912yes—
601C22×C4C23×D5912yes—
602C22×C4C23×D5912yes—
603C4⋊C4—5916no—
604C4⋊C4—5916no—
605C4⋊C4—5916no—
606C4⋊C4—2364no—
607C4⋊C4—2364no—
608C4⋊C4—2364no—
609C4⋊C4—2364no—
610C4⋊C4—2364no—
611C4⋊C4—2364no—
612C22⋊C4—28no—
613C22⋊C4—5916no—
614C22⋊C4—1188no—
615C22⋊C4C2×C4×D59116yes—
616C42—44no—
617C42—44no—
618C42—2364no—
619C42—2364no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—28no—
625C23—28no—
626C23—28no—
627C23—28no—
628C23—28no—
629C23—28no—
630C23C4×Dic118116yes—
631C23C22×C4×D5914yes—
632C23C22×C4×D5912yes—
633C23C22×Dic11814yes—
634C23C22×Dic11812yes—
635C23C2×#1174568514yes—
636C23C2×#1174568512yes—
637C23#1427377212yes—
638C23#1427377212yes—
639C23#1427377312yes—
640C23#1427377412yes—
641C23C24×D5911yescharacteristic
642Q8—23616no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—28no—
652C2×C4—28no—
653C2×C4—28no—
654C2×C4—28no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—416no—
662C2×C4—44no—
663C2×C4—44no—
664C2×C4—594no—
665C2×C4—594no—
666C2×C4—594no—
667C2×C4—594no—
668C2×C4—1182no—
669C2×C4—1182no—
670C2×C4—1182no—
671C2×C4—1182no—
672C2×C4—1182no—
673C2×C4—1182no—
674C2×C4—1182no—
675C2×C4—1182no—
676C2×C4—1188no—
677C2×C4—1188no—
678C2×C4—1188no—
679C2×C4—1188no—
680C2×C4—1182no—
681C2×C4—1182no—
682C2×C4—1182no—
683C2×C4—1182no—
684C2×C4—1182no—
685C2×C4—1182no—
686C2×C4—1182no—
687C2×C4—1182no—
688C2×C4—1182no—
689C2×C4—1182no—
690C2×C4—1182no—
691C2×C4—1182no—
692C2×C4—23616no—
693C2×C4—23616no—
694C2×C4—2364no—
695C2×C4—2364no—
696C2×C4—2364no—
697C2×C4—2364no—
698C2×C4C22×C4×D5914yes—
699C2×C4C22×C4×D5914yes—
700C2×C4C22×Dic11814yes—
701C2×C4C22×Dic11814yes—
702C22—24no—
703C22—24no—
704C22—24no—
705C22—24no—
706C22—24no—
707C22—232no—
708C22—24no—
709C22C2×C4×Dic11818yes—
710C22C2×C4×Dic11814yes—
711C22#1683787414yes—
712C22#1683788114yes—
713C22#1683798514yes—
714C22#1683799414yes—
715C22#1683802814yes—
716C22#1683803014yes—
717C22C23×C4×D5911yescharacteristic
718C22C23×Dic11811yescharacteristic
719C22C22×#1174568511yescharacteristic
720C22C2×#1427377211yescharacteristic
721C22C2×#1427377211yescharacteristic
722C22C2×#1427377311yescharacteristic
723C22C2×#1427377411yescharacteristic
724C4—24no—
725C4—24no—
726C4—24no—
727C4—24no—
728C4—42no—
729C4—42no—
730C4—1184no—
731C4—1184no—
732C4—1184no—
733C4—1184no—
734C4—2362no—
735C4—2362no—
736C4—2362no—
737C4—2362no—
738C2—28no—
739C2#2142682418yesdirect product factor
740C2C22×C4×Dic11811yescharacteristic
741C2C2×#1683787411yescharacteristic
742C2C2×#1683788111yescharacteristic
743C2C2×#1683798511yescharacteristic
744C2C2×#1683799411yescharacteristic
745C2C2×#1683802811yescharacteristic
746C2C2×#1683803011yescharacteristic
subgroupG/H
centerC24C23×D59
commutatorC22×C59C24×C4
FrattiniC23C24×D59
FittingC2×C4×C22⋊C4×C59C2
socleC24×C59C24
prime radicalC25×C59C23
cosocleC23×C59C25
hypercenterC2×C4×C22⋊C4D59
hypocenterC59C2×#2329
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #21426824C2direct (N × H)
3. C2×#16837308C2semidirect
4. C2×#16837306C2semidirect
5. C2×#16837300C2semidirect
6. C2×#16837299C2semidirect
7. C2×#16837289C2semidirect
8. C2×#16837286C2semidirect
9. C2×#16837286C2semidirect
10. C2×#16837285C2semidirect
20. C2×#14273704C4semidirect
35. #16837308C22semidirect
36. #16837306C22semidirect
37. #16837300C22semidirect
38. #16837299C22semidirect
39. #16837289C22semidirect
40. #16837286C22semidirect
41. #16837286C22semidirect
42. #16837285C22semidirect
70. C22×Dic118C2×C4semidirect
88. #14273704C2×C4semidirect
91. C2×C4⋊Dic59C2×C4semidirect
99. C2×Dic59⋊C4C2×C4semidirect
100. C2×Dic59⋊C4C2×C4semidirect
130. C23×C4×C59Q8semidirect
178. C22×C4×C59C2×Q8semidirect
228. C2×Dic118C22×C4semidirect
237. C4⋊Dic59C22×C4semidirect
242. Dic59⋊C4C22×C4semidirect
243. Dic59⋊C4C22×C4semidirect
382. C2×C59#2329semidirect
441. C59C2×#2329semidirect
465. C23×C4Dic118semidirect
594. C22×C4C2×Dic118semidirect
739. C2#21426824direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#142737042
#214268242
C2×#168373082
C2×#168373062
C2×#168373002
C2×#168372992
C2×#168372892
C2×#168372862
C2×#168372852
C2×#168372772
C2×#168372742
C2×#168372602
C2×C4×C22⋊Dic592
C22×C59⋊#952
C2×C4×C22⋊C4×C592
C2×#232959