Finite Group Databasebeta

← C2×#21426879 #28747576

Subgroups — C2×#21426879 #28747576

Order 15104.

2982 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14273711C211yesmaximal, characteristic
2#21426879C2116yesmaximal, direct product factor
3C2×#16837302C211yesmaximal, characteristic
4C2×#16837300C211yesmaximal, characteristic, complemented
5C2×#16837295C211yesmaximal, characteristic, complemented
6C2×#16837294C211yesmaximal, characteristic, complemented
7C2×#16837291C211yesmaximal, characteristic, complemented
8C2×#16837287C211yesmaximal, characteristic, complemented
9C2×#16837285C211yesmaximal, characteristic, complemented
10C2×#16837278C211yesmaximal, characteristic
11C2×#16837273C211yesmaximal, characteristic, complemented
12C2×#16837260C211yesmaximal, characteristic, complemented
13C2×C4⋊C4×Dic59C211yesmaximal, characteristic, complemented
14C2×C22⋊C4×Dic59C211yesmaximal, characteristic, complemented
15C2×C4×(C2×D59)⋊C4C211yesmaximal, characteristic, complemented
16C2×C59×#388C211yesmaximal, characteristic, complemented
17C23×C22⋊D59C2211yescharacteristic
18C24×Dic59C2211yescharacteristic
19C23×C4×D59C2211yescharacteristic
20C2×#14273711C4116yescomplemented
21C2×#14273711C2218yes—
22C22×C4⋊Dic59C2211yescharacteristic
23C22×C4⋊Dic59C2211yescharacteristic
24C22×C4⋊Dic59C2211yescharacteristic
25C22×Dic59⋊C4C2211yescharacteristic
26C22×Dic59⋊C4C2211yescharacteristic
27C22×Dic59⋊C4C2211yescharacteristic
28C22×C22⋊Dic59C2211yescharacteristic
29C22×C22⋊Dic59C2211yescharacteristic
30C22×(C2×D59)⋊C4C2211yescharacteristic
31C22×(C2×D59)⋊C4C2211yescharacteristic
32C22×(C2×D59)⋊C4C2211yescharacteristic
33C22×(C2×D59)⋊C4C2211yescharacteristic
34C22×(C2×D59)⋊C4C2211yescharacteristic
35C22×C4×Dic59C2211yescharacteristic
36C22×C4×Dic59C2211yescharacteristic
37C22×C4×Dic59C2211yescharacteristic
38C22×C4×Dic59C2211yescharacteristic
39#16837302C2218yes—
40#16837300C2218yescomplemented
41#16837295C2218yescomplemented
42#16837294C2218yescomplemented
43#16837291C2218yescomplemented
44#16837287C2218yescomplemented
45#16837285C2218yescomplemented
46#16837278C2218yes—
47#16837273C2218yescomplemented
48#16837260C2218yescomplemented
49C4⋊C4×Dic59C2218yescomplemented
50C22⋊C4×Dic59C2218yescomplemented
51C4×(C2×D59)⋊C4C2218yescomplemented
52C2×C59⋊#95C2211yescharacteristic
53C2×C59⋊#95C2211yescharacteristic
54C2×C59⋊#95C2211yescharacteristic
55C2×C59⋊#95C2211yescharacteristic
56C2×C59⋊#95C2211yescharacteristic
57C2×C59⋊#95C2211yescharacteristic
58C2×C59⋊#95C2211yescharacteristic
59C2×C59⋊#95C2211yescharacteristic
60C22×C4⋊C4×C59C2211yescharacteristic
61C22×C22⋊C4×C59C2211yescharacteristic
62C22×C22⋊C4×C59C2211yescharacteristic
63C22×C22⋊C4×C59C2211yescharacteristic
64C22×C42×C59C2211yescharacteristic
65C59×#388C2218yescomplemented
66C2×#95×C59C2211yescharacteristic
67C2×#95×C59C2211yescharacteristic
68C24×D59C2311yescharacteristic
69C22×C22⋊D59—42no—
70C22×C22⋊D59—42no—
71C22×C22⋊D59C2×C418yes—
72C22×C22⋊D59C2314yes—
73C23×Dic59—42no—
74C23×Dic59—42no—
75C23×Dic59C2×C418yescomplemented
76C23×Dic59C2311yescharacteristic
77C23×Dic59C2311yescharacteristic
78C23×Dic59C2311yescharacteristic
79C23×Dic59C2311yescharacteristic
80C23×Dic59C2311yescharacteristic
81C23×Dic59C2311yescharacteristic
82C23×Dic59C2311yescharacteristic
83C23×Dic59C2314yes—
84C22×C4×D59—24no—
85C22×C4×D59—42no—
86C22×C4×D59—42no—
87C22×C4×D59C2314yes—
88#14273711C2×C4164yescomplemented
89C2×C4⋊Dic59—42no—
90C2×C4⋊Dic59C2×C418yescomplemented
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⋊C4C2314yes—
99C2×Dic59⋊C4C2314yes—
100C2×Dic59⋊C4C2314yes—
101C2×C22⋊Dic59—24no—
102C2×C22⋊Dic59—42no—
103C2×C22⋊Dic59C2314yes—
104C2×C22⋊Dic59C2314yes—
105C2×(C2×D59)⋊C4—24no—
106C2×(C2×D59)⋊C4—42no—
107C2×(C2×D59)⋊C4—42no—
108C2×(C2×D59)⋊C4C2×C418yes—
109C2×(C2×D59)⋊C4C2×C418yes—
110C2×(C2×D59)⋊C4C2314yes—
111C2×(C2×D59)⋊C4C2314yes—
112C2×(C2×D59)⋊C4C2314yes—
113C2×(C2×D59)⋊C4C2314yes—
114C2×(C2×D59)⋊C4C2314yes—
115C2×C4×Dic59—24no—
116C2×C4×Dic59—42no—
117C2×C4×Dic59—42no—
118C2×C4×Dic59—42no—
119C2×C4×Dic59C2314yes—
120C2×C4×Dic59C2314yes—
121C2×C4×Dic59C2314yes—
122C2×C4×Dic59C2314yes—
123C59⋊#95C2314yes—
124C59⋊#95C2314yes—
125C59⋊#95C2314yes—
126C59⋊#95C2314yes—
127C59⋊#95C2314yes—
128C59⋊#95C2314yes—
129C59⋊#95C2314yes—
130C59⋊#95C2314yes—
131C25×C59C2311yescharacteristic
132C23×C4×C59C2311yescharacteristic
133C23×C4×C59C2311yescharacteristic
134C23×C4×C59C2311yescharacteristic
135C23×C4×C59C2311yescharacteristic
136C23×C4×C59C2311yescharacteristic
137C23×C4×C59C2311yescharacteristic
138C2×C4⋊C4×C59—24no—
139C2×C4⋊C4×C59C2314yes—
140C2×C22⋊C4×C59—24no—
141C2×C22⋊C4×C59—42no—
142C2×C22⋊C4×C59C2×C418yescomplemented
143C2×C22⋊C4×C59C2314yes—
144C2×C22⋊C4×C59C2314yes—
145C2×C22⋊C4×C59C2314yes—
146C2×C42×C59—42no—
147C2×C42×C59C2314yes—
148#95×C59C2314yes—
149#95×C59C2314yes—
150C24×C59—22no—
151C24×C59—22no—
152C24×C59—22no—
153C24×C59—22no—
154C24×C59—22no—
155C24×C59—22no—
156C24×C59C22×C414yes—
157C24×C59C2412yes—
158C24×C59C2411yescharacteristic
159C23×D59—22no—
160C23×D59—22no—
161C23×D59—22no—
162C23×D59—22no—
163C23×D59—22no—
164C23×D59—22no—
165C23×D59C22×C414yes—
166C23×D59C2412yes—
167C22×C4×C59—22no—
168C22×C4×C59—22no—
169C22×C4×C59—22no—
170C22×C4×C59—22no—
171C22×C4×C59—22no—
172C22×C4×C59—22no—
173C22×C4×C59—22no—
174C22×C4×C59—22no—
175C22×C4×C59—22no—
176C22×C4×C59—22no—
177C22×C4×C59—22no—
178C22×C4×C59—22no—
179C22×C4×C59—22no—
180C22×C4×C59—22no—
181C22×C4×C59—22no—
182C22×C4×C59C22×C414yes—
183C22×C4×C59C22×C414yes—
184C22×C4×C59#4114yes—
185C22×C4×C59C2412yes—
186C22×C4×C59C2412yes—
187C22×C4×C59C2412yes—
188C22×C4×C59C2412yes—
189C22×C4×C59C2412yes—
190C22×C4×C59C2412yes—
191C2×C22⋊D59—416no—
192C2×C22⋊D59—44no—
193C2×C22⋊D59—44no—
194C2×C22⋊D59C22×C4116yes—
195C22×Dic59—22no—
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—22no—
207C22×Dic59—22no—
208C22×Dic59—22no—
209C22×Dic59—22no—
210C22×Dic59—22no—
211C22×Dic59—22no—
212C22×Dic59—416no—
213C22×Dic59—44no—
214C22×Dic59—44no—
215C22×Dic59C22×C414yes—
216C22×Dic59C22×C414yes—
217C22×Dic59C22×C414yes—
218C22×Dic59C22×C4116yescomplemented
219C22×Dic59#4114yes—
220C22×Dic59C2412yes—
221C22×Dic59C2412yes—
222C22×Dic59C2412yes—
223C22×Dic59C2412yes—
224C22×Dic59C2412yes—
225C22×Dic59C2412yes—
226C22×Dic59C2412yes—
227C2×C4×D59—28no—
228C2×C4×D59—44no—
229C2×C4×D59—44no—
230C2×C4×D59—416no—
231C4⋊C4×C59—28no—
232C22⋊C4×C59—28no—
233C22⋊C4×C59—44no—
234C22⋊C4×C59C22×C4116yescomplemented
235C42×C59—44no—
236C22⋊Dic59—28no—
237C22⋊Dic59—44no—
238(C2×D59)⋊C4—28no—
239(C2×D59)⋊C4—44no—
240(C2×D59)⋊C4—44no—
241(C2×D59)⋊C4C22×C4116yes—
242(C2×D59)⋊C4C22×C4116yes—
243C4⋊Dic59—44no—
244C4⋊Dic59C22×C4116yescomplemented
245C4⋊Dic59C22×C4116yescomplemented
246Dic59⋊C4—44no—
247Dic59⋊C4—44no—
248Dic59⋊C4—44no—
249C4×Dic59—28no—
250C4×Dic59—44no—
251C4×Dic59—44no—
252C4×Dic59—44no—
253C23×C59—28no—
254C23×C59—28no—
255C23×C59—28no—
256C23×C59—22no—
257C23×C59—22no—
258C23×C59—22no—
259C23×C59—22no—
260C23×C59—22no—
261C23×C59—22no—
262C23×C59—44no—
263C23×C59—44no—
264C23×C59—44no—
265C23×C59—44no—
266C23×C59C23×C414yes—
267C23×C59C23×C412yes—
268C23×C59C2×#4112yes—
269C23×C59C2×#4112yes—
270C23×C59H(5,𝔽2)12yes—
271C23×C59H(5,𝔽2)12yes—
272C23×C59H(5,𝔽2)12yes—
273C23×C592−1+412yes—
274C23×C59C2511yescharacteristic
275C22×D59—28no—
276C22×D59—28no—
277C22×D59—28no—
278C22×D59—22no—
279C22×D59—22no—
280C22×D59—22no—
281C22×D59—22no—
282C22×D59—22no—
283C22×D59—22no—
284C22×D59—44no—
285C22×D59—44no—
286C22×D59—44no—
287C22×D59—44no—
288C22×D59C23×C414yes—
289C2×C4×C59—28no—
290C2×C4×C59—28no—
291C2×C4×C59—28no—
292C2×C4×C59—22no—
293C2×C4×C59—22no—
294C2×C4×C59—22no—
295C2×C4×C59—22no—
296C2×C4×C59—22no—
297C2×C4×C59—22no—
298C2×C4×C59—22no—
299C2×C4×C59—22no—
300C2×C4×C59—22no—
301C2×C4×C59—22no—
302C2×C4×C59—22no—
303C2×C4×C59—22no—
304C2×C4×C59—22no—
305C2×C4×C59—22no—
306C2×C4×C59—22no—
307C2×C4×C59—44no—
308C2×C4×C59—44no—
309C2×C4×C59—44no—
310C2×C4×C59C23×C414yes—
311C2×C4×C59C23×C414yes—
312C2×C4×C59C2×#4114yes—
313C22⋊D59—416no—
314C2×Dic59—28no—
315C2×Dic59—28no—
316C2×Dic59—28no—
317C2×Dic59—28no—
318C2×Dic59—22no—
319C2×Dic59—22no—
320C2×Dic59—22no—
321C2×Dic59—22no—
322C2×Dic59—22no—
323C2×Dic59—22no—
324C2×Dic59—22no—
325C2×Dic59—22no—
326C2×Dic59—22no—
327C2×Dic59—22no—
328C2×Dic59—22no—
329C2×Dic59—22no—
330C2×Dic59—22no—
331C2×Dic59—22no—
332C2×Dic59—22no—
333C2×Dic59—22no—
334C2×Dic59—22no—
335C2×Dic59—416no—
336C2×Dic59—44no—
337C2×Dic59—44no—
338C2×Dic59—44no—
339C2×Dic59C23×C414yes—
340C2×Dic59C23×C414yes—
341C2×Dic59C23×C414yes—
342C2×Dic59C2×#4114yes—
343C4×D59—416no—
344C2×#2335—591nomaximal, Sylow
345C22×C59—24no—
346C22×C59—24no—
347C22×C59—24no—
348C22×C59—416no—
349C22×C59—42no—
350C22×C59—42no—
351C22×C59—42no—
352C22×C59—42no—
353C22×C59C4×#4114yes—
354C22×C59#51814yes—
355C22×C59#52014yes—
356C22×C59#53814yes—
357C22×C59#53914yes—
358C22×C59#54014yes—
359C22×C59#54214yes—
360C22×C59C24×C411yescharacteristic
361C22×C59C22×#4111yescharacteristic
362C22×C59C22×#4111yescharacteristic
363C22×C59C2×H(5,𝔽2)11yescharacteristic
364C22×C59C2×H(5,𝔽2)11yescharacteristic
365C22×C59C2×H(5,𝔽2)11yescharacteristic
366C22×C59C2×2−1+411yescharacteristic
367C2×D59—24no—
368C2×D59—24no—
369C2×D59—24no—
370C2×D59—416no—
371C2×D59—42no—
372C2×D59—42no—
373C2×D59—42no—
374C2×D59—42no—
375C4×C59—24no—
376C4×C59—24no—
377C4×C59—24no—
378C4×C59—42no—
379C4×C59—42no—
380C4×C59—42no—
381Dic59—24no—
382Dic59—24no—
383Dic59—24no—
384Dic59—24no—
385Dic59—42no—
386Dic59—42no—
387Dic59—42no—
388C22×#123—591no—
389#2335—5916no—
390C2×#390—591no—
391C2×#389—591no—
392C2×#388—591no—
393C2×#388—591no—
394C2×#388—591no—
395C2×#388D5911yescharacteristic, complemented
396C2×#387—591no—
397C2×#387—591no—
398C2×#386—591no—
399C2×#385—591no—
400C2×#380—591no—
401C2×C4×C4⋊C4—591no—
402C2×C4×C22⋊C4—591no—
403C2×C4×C22⋊C4—591no—
404C2×C59—44no—
405C2×C59#233518yescomplemented
406C2×C59C2×C4×#4111yescharacteristic
407C2×C59C2×#51811yescharacteristic
408C2×C59C2×#52011yescharacteristic
409C2×C59C2×#53811yescharacteristic
410C2×C59C2×#53911yescharacteristic
411C2×C59C2×#54011yescharacteristic
412C2×C59C2×#54211yescharacteristic
413D59—44no—
414C23×D4—591no—
415C24×C4—591no—
416C24×C4—591no—
417C2×#123—5916no—
418C2×#123—598no—
419C22×C4⋊C4—591no—
420C22×C4⋊C4—591no—
421C22×C4⋊C4—591no—
422C22×C4⋊C4—591no—
423C22×C4⋊C4—591no—
424C22×C4⋊C4—591no—
425C22×C4⋊C4C2×D5911yescharacteristic
426C22×C22⋊C4—591no—
427C22×C22⋊C4—591no—
428C22×C22⋊C4—591no—
429C22×C22⋊C4—591no—
430C22×C22⋊C4—591no—
431C22×C22⋊C4—591no—
432C22×C22⋊C4—591no—
433C22×C22⋊C4C2×D5911yescharacteristic
434C22×C22⋊C4C2×D5911yescharacteristic
435C22×C22⋊C4C2×D5911yescharacteristic
436C22×C42—591no—
437C22×C42—591no—
438C22×C42—591no—
439C22×C42—591no—
440C22×C42C2×D5911yescharacteristic
441#390—598no—
442#389—598no—
443#388—598no—
444#388—598no—
445#388—598no—
446#388C2×D5918yescomplemented
447#387—598no—
448#387—598no—
449#386—598no—
450#385—598no—
451#380—598no—
452C4×C4⋊C4—598no—
453C4×C22⋊C4—598no—
454C4×C22⋊C4—598no—
455C2×#95—591no—
456C2×#95—591no—
457C2×#95—591no—
458C2×#95—591no—
459C2×#95—591no—
460C2×#95—591no—
461C2×#95—591no—
462C2×#95—591no—
463C2×#95C2×D5911yescharacteristic
464C2×#95C2×D5911yescharacteristic
465C59C2×#233511yescharacteristic, complemented, Sylow
466C25—591no—
467C25C22×D5911yescharacteristic
468C22×D4—598no—
469C22×D4—594no—
470C22×D4—2362no—
471C22×D4—2362no—
472C23×C4—591no—
473C23×C4—591no—
474C23×C4—591no—
475C23×C4—591no—
476C23×C4—598no—
477C23×C4—594no—
478C23×C4—591no—
479C23×C4—591no—
480C23×C4—591no—
481C23×C4—594no—
482C23×C4—1184no—
483C23×C4—2362no—
484C23×C4—2362no—
485C23×C4—2362no—
486C23×C4—2362no—
487C23×C4C22×D5911yescharacteristic
488C23×C4C22×D5911yescharacteristic
489C23×C4C22×D5911yescharacteristic
490C23×C4C22×D5911yescharacteristic
491C23×C4C22×D5911yescharacteristic
492C23×C4C22×D5911yescharacteristic
493#123—5964no—
494C2×C4⋊C4—24no—
495C2×C4⋊C4—598no—
496C2×C4⋊C4—598no—
497C2×C4⋊C4—594no—
498C2×C4⋊C4—594no—
499C2×C4⋊C4—594no—
500C2×C4⋊C4—594no—
501C2×C4⋊C4—594no—
502C2×C4⋊C4—594no—
503C2×C4⋊C4—2362no—
504C2×C4⋊C4—2362no—
505C2×C4⋊C4—2362no—
506C2×C4⋊C4—2362no—
507C2×C4⋊C4C22×D5914yes—
508C2×C22⋊C4—24no—
509C2×C22⋊C4—42no—
510C2×C22⋊C4—598no—
511C2×C22⋊C4—598no—
512C2×C22⋊C4—594no—
513C2×C22⋊C4—594no—
514C2×C22⋊C4—594no—
515C2×C22⋊C4—594no—
516C2×C22⋊C4—594no—
517C2×C22⋊C4—594no—
518C2×C22⋊C4—594no—
519C2×C22⋊C4—1184no—
520C2×C22⋊C4—1184no—
521C2×C22⋊C4—2362no—
522C2×C22⋊C4—2362no—
523C2×C22⋊C4—2362no—
524C2×C22⋊C4C4×D5918yescomplemented
525C2×C22⋊C4C22×D5914yes—
526C2×C22⋊C4C22×D5914yes—
527C2×C22⋊C4C22×D5914yes—
528C2×C42—42no—
529C2×C42—594no—
530C2×C42—594no—
531C2×C42—594no—
532C2×C42—594no—
533C2×C42—1184no—
534C2×C42—2362no—
535C2×C42—2362no—
536C2×C42—2362no—
537C2×C42C22×D5914yes—
538#95—594no—
539#95—594no—
540#95—594no—
541#95—594no—
542#95—594no—
543#95—594no—
544#95—594no—
545#95—594no—
546#95C22×D5914yes—
547#95C22×D5914yes—
548C24—22no—
549C24—22no—
550C24—22no—
551C24—22no—
552C24—22no—
553C24—22no—
554C24—594no—
555C24—592no—
556C24—1182no—
557C24—1182no—
558C24—1182no—
559C24—1182no—
560C24—1182no—
561C24—1182no—
562C24C2×C4×D5914yes—
563C24C23×D5912yes—
564C24C23×D5911yescharacteristic
565C2×D4—5916no—
566C2×D4—2364no—
567C2×D4—2364no—
568C2×D4—23616no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—594no—
585C22×C4—594no—
586C22×C4—594no—
587C22×C4—594no—
588C22×C4—592no—
589C22×C4—592no—
590C22×C4—592no—
591C22×C4—592no—
592C22×C4—5916no—
593C22×C4—592no—
594C22×C4—592no—
595C22×C4—592no—
596C22×C4—1182no—
597C22×C4—1182no—
598C22×C4—1182no—
599C22×C4—1182no—
600C22×C4—1182no—
601C22×C4—1182no—
602C22×C4—1182no—
603C22×C4—1182no—
604C22×C4—1182no—
605C22×C4—1182no—
606C22×C4—1182no—
607C22×C4—1182no—
608C22×C4—1182no—
609C22×C4—1182no—
610C22×C4—1182no—
611C22×C4—1182no—
612C22×C4—1182no—
613C22×C4—1188no—
614C22×C4—2364no—
615C22×C4—2364no—
616C22×C4—23616no—
617C22×C4—2364no—
618C22×C4—2364no—
619C22×C4—23616no—
620C22×C4C2×C4×D5914yes—
621C22×C4C2×C4×D5914yes—
622C22×C4#1174568714yes—
623C22×C4C23×D5912yes—
624C22×C4C23×D5912yes—
625C22×C4C23×D5912yes—
626C22×C4C23×D5912yes—
627C22×C4C23×D5912yes—
628C22×C4C23×D5912yes—
629C4⋊C4—28no—
630C4⋊C4—5916no—
631C4⋊C4—5916no—
632C4⋊C4—2364no—
633C4⋊C4—2364no—
634C4⋊C4—2364no—
635C4⋊C4—2364no—
636C22⋊C4—28no—
637C22⋊C4—44no—
638C22⋊C4—5916no—
639C22⋊C4—5916no—
640C22⋊C4—1188no—
641C22⋊C4—1188no—
642C22⋊C4—2364no—
643C22⋊C4—2364no—
644C22⋊C4—2364no—
645C22⋊C4C2×C4×D59116yescomplemented
646C42—44no—
647C42—1188no—
648C42—2364no—
649C42—2364no—
650C42—2364no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—28no—
658C23—28no—
659C23—28no—
660C23—44no—
661C23—44no—
662C23—44no—
663C23—44no—
664C23—594no—
665C23—1182no—
666C23—1182no—
667C23—1182no—
668C23—1182no—
669C23—1182no—
670C23—1182no—
671C23—1188no—
672C23—1188no—
673C23—1188no—
674C23—2364no—
675C23—2364no—
676C23—2364no—
677C23—2364no—
678C23C22×C4×D5914yes—
679C23C22×C4×D5912yes—
680C23#41×D5912yes—
681C23C2×#1174568712yes—
682C23#1427377212yes—
683C23#1427377312yes—
684C23#1427377312yes—
685C23#1427377412yes—
686C23C24×D5911yescharacteristic
687D4—23616no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—28no—
695C2×C4—28no—
696C2×C4—28no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—44no—
707C2×C4—44no—
708C2×C4—44no—
709C2×C4—594no—
710C2×C4—594no—
711C2×C4—594no—
712C2×C4—594no—
713C2×C4—1182no—
714C2×C4—1182no—
715C2×C4—1182no—
716C2×C4—1182no—
717C2×C4—1182no—
718C2×C4—1182no—
719C2×C4—1182no—
720C2×C4—1182no—
721C2×C4—1188no—
722C2×C4—1188no—
723C2×C4—1188no—
724C2×C4—1188no—
725C2×C4—1182no—
726C2×C4—1182no—
727C2×C4—1182no—
728C2×C4—1182no—
729C2×C4—1182no—
730C2×C4—1182no—
731C2×C4—1182no—
732C2×C4—1182no—
733C2×C4—1182no—
734C2×C4—23616no—
735C2×C4—23616no—
736C2×C4—2364no—
737C2×C4—2364no—
738C2×C4—2364no—
739C2×C4C22×C4×D5914yes—
740C2×C4C22×C4×D5914yes—
741C2×C4C2×#1174568714yes—
742C22—24no—
743C22—24no—
744C22—24no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—416no—
749C22—42no—
750C22—1184no—
751C22—1184no—
752C22—1184no—
753C22—2362no—
754C22—2362no—
755C22—2362no—
756C22—23616no—
757C22—2362no—
758C22C4×#1174568714yes—
759C22#1683787614yes—
760C22#1683788114yes—
761C22#1683798914yes—
762C22#1683799314yes—
763C22#1683800414yes—
764C22#1683802114yes—
765C22C23×C4×D5911yescharacteristic
766C22C2×#41×D5911yescharacteristic
767C22C22×#1174568711yescharacteristic
768C22C2×#1427377211yescharacteristic
769C22C2×#1427377311yescharacteristic
770C22C2×#1427377311yescharacteristic
771C22C2×#1427377411yescharacteristic
772C4—24no—
773C4—24no—
774C4—24no—
775C4—42no—
776C4—42no—
777C4—42no—
778C4—1184no—
779C4—1184no—
780C4—1184no—
781C4—1184no—
782C4—2362no—
783C4—2362no—
784C4—2362no—
785C2—44no—
786C2—2364no—
787C2#2142687918yesdirect product factor
788C2C2×C4×#1174568711yescharacteristic
789C2C2×#1683787611yescharacteristic
790C2C2×#1683788111yescharacteristic
791C2C2×#1683798911yescharacteristic
792C2C2×#1683799311yescharacteristic
793C2C2×#1683800411yescharacteristic
794C2C2×#1683802111yescharacteristic
subgroupG/H
centerC24C23×D59
commutatorC22×C59C24×C4
FrattiniC23C24×D59
FittingC2×C59×#388C2
socleC24×C59C24
prime radicalC23×C22⋊D59C22
cosocleC23×C59C25
hypercenterC2×#388D59
hypocenterC59C2×#2335
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. #21426879C2direct (N × H)
4. C2×#16837300C2semidirect
5. C2×#16837295C2semidirect
6. C2×#16837294C2semidirect
7. C2×#16837291C2semidirect
8. C2×#16837287C2semidirect
9. C2×#16837285C2semidirect
11. C2×#16837273C2semidirect
12. C2×#16837260C2semidirect
13. C2×C4⋊C4×Dic59C2semidirect
14. C2×C22⋊C4×Dic59C2semidirect
15. C2×C4×(C2×D59)⋊C4C2semidirect
16. C2×C59×#388C2semidirect
20. C2×#14273711C4semidirect
40. #16837300C22semidirect
41. #16837295C22semidirect
42. #16837294C22semidirect
43. #16837291C22semidirect
44. #16837287C22semidirect
45. #16837285C22semidirect
47. #16837273C22semidirect
48. #16837260C22semidirect
49. C4⋊C4×Dic59C22semidirect
50. C22⋊C4×Dic59C22semidirect
51. C4×(C2×D59)⋊C4C22semidirect
65. C59×#388C22semidirect
75. C23×Dic59C2×C4semidirect
88. #14273711C2×C4semidirect
90. C2×C4⋊Dic59C2×C4semidirect
91. C2×C4⋊Dic59C2×C4semidirect
142. C2×C22⋊C4×C59C2×C4semidirect
218. C22×Dic59C22×C4semidirect
234. C22⋊C4×C59C22×C4semidirect
244. C4⋊Dic59C22×C4semidirect
245. C4⋊Dic59C22×C4semidirect
395. C2×#388D59semidirect
405. C2×C59#2335semidirect
446. #388C2×D59semidirect
465. C59C2×#2335semidirect
524. C2×C22⋊C4C4×D59semidirect
645. C22⋊C4C2×C4×D59semidirect
787. C2#21426879direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#142737112
#214268792
C2×#168373022
C2×#168373002
C2×#168372952
C2×#168372942
C2×#168372912
C2×#168372872
C2×#168372852
C2×#168372782
C2×#168372732
C2×#168372602
C2×C4⋊C4×Dic592
C2×C22⋊C4×Dic592
C2×C4×(C2×D59)⋊C42
C2×C59×#3882
C2×#233559