Finite Group Databasebeta

← C2×#21428351 #28756311

Subgroups — C2×#21428351 #28756311

Order 15104.

3114 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14273722C211yesmaximal, characteristic, complemented
2#21428351C2116yesmaximal, direct product factor
3C2×#16837341C211yesmaximal, characteristic, complemented
4C2×#16837340C211yesmaximal, characteristic, complemented
5C2×#16837328C211yesmaximal, characteristic, complemented
6C2×#16837324C211yesmaximal, characteristic, complemented
7C2×#16837292C211yesmaximal, characteristic, complemented
8C2×#16837288C211yesmaximal, characteristic, complemented
9C2×#16837283C211yesmaximal, characteristic, complemented
10C2×#16837281C211yesmaximal, characteristic
11C2×#16837281C211yesmaximal, characteristic
12C2×#16837281C211yesmaximal, characteristic
13C2×#16837275C211yesmaximal, characteristic, complemented
14C2×#16837262C211yesmaximal, characteristic, complemented
15C2×C4×C22⋊Dic59C211yesmaximal, characteristic, complemented
16C23×C4⋊C4×C59C211yesmaximal, characteristic, complemented
17C23×C22⋊D59C2211yescharacteristic
18C2×#14273722—28no—
19C2×#14273722C2218yescomplemented
20C22×C4⋊Dic59C2211yescharacteristic
21C22×C4⋊Dic59C2211yescharacteristic
22C22×Dic59⋊C4C2211yescharacteristic
23C22×Dic59⋊C4C2211yescharacteristic
24C22×C22⋊Dic59C2211yescharacteristic
25C22×C22⋊Dic59C2211yescharacteristic
26C22×C22⋊Dic59C2211yescharacteristic
27C22×(C2×D59)⋊C4C2211yescharacteristic
28C22×(C2×D59)⋊C4C2211yescharacteristic
29C22×(C2×D59)⋊C4C2211yescharacteristic
30C22×(C2×D59)⋊C4C2211yescharacteristic
31C22×(C2×D59)⋊C4C2211yescharacteristic
32C22×(C2×D59)⋊C4C2211yescharacteristic
33C22×C4×Dic59C2211yescharacteristic
34C22×C4×Dic59C2211yescharacteristic
35#16837341C2218yescomplemented
36#16837340C2218yescomplemented
37#16837328C2218yescomplemented
38#16837324C2218yescomplemented
39#16837292C2218yescomplemented
40#16837288C2218yescomplemented
41#16837283C2218yescomplemented
42#16837281C2218yes—
43#16837281C2218yes—
44#16837281C2218yes—
45#16837275C2218yescomplemented
46#16837262C2218yescomplemented
47C4×C22⋊Dic59C2218yescomplemented
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⋊#95C2211yescharacteristic
60C24×C4×C59C2211yescharacteristic
61C24×C4×C59C2211yescharacteristic
62C24×C4×C59C2211yescharacteristic
63C22×C4⋊C4×C59—28no—
64C22×C4⋊C4×C59C2211yescharacteristic
65C22×C4⋊C4×C59C2211yescharacteristic
66C22×C4⋊C4×C59C2211yescharacteristic
67C22×C4⋊C4×C59C2211yescharacteristic
68C22×C4⋊C4×C59C2218yescomplemented
69C24×D59C2311yescharacteristic
70C22×C22⋊D59—24no—
71C22×C22⋊D59—24no—
72C22×C22⋊D59—24no—
73C22×C22⋊D59C2314yes—
74C23×Dic59C2311yescharacteristic
75C23×Dic59C2311yescharacteristic
76C23×Dic59C2311yescharacteristic
77C23×Dic59C2311yescharacteristic
78C23×Dic59C2311yescharacteristic
79C23×Dic59C2311yescharacteristic
80C23×Dic59C2311yescharacteristic
81#14273722—232no—
82C2×C4⋊Dic59—24no—
83C2×C4⋊Dic59—42no—
84C2×C4⋊Dic59C2314yes—
85C2×C4⋊Dic59C2314yes—
86C2×Dic59⋊C4—24no—
87C2×Dic59⋊C4—24no—
88C2×Dic59⋊C4C2314yes—
89C2×Dic59⋊C4C2314yes—
90C2×C22⋊Dic59—24no—
91C2×C22⋊Dic59—24no—
92C2×C22⋊Dic59—24no—
93C2×C22⋊Dic59C2314yes—
94C2×C22⋊Dic59C2314yes—
95C2×C22⋊Dic59C2314yes—
96C2×(C2×D59)⋊C4—24no—
97C2×(C2×D59)⋊C4—24no—
98C2×(C2×D59)⋊C4—24no—
99C2×(C2×D59)⋊C4—24no—
100C2×(C2×D59)⋊C4—42no—
101C2×(C2×D59)⋊C4—42no—
102C2×(C2×D59)⋊C4C2314yes—
103C2×(C2×D59)⋊C4C2314yes—
104C2×(C2×D59)⋊C4C2314yes—
105C2×(C2×D59)⋊C4C2314yes—
106C2×(C2×D59)⋊C4C2314yes—
107C2×(C2×D59)⋊C4C2314yes—
108C2×C4×Dic59—24no—
109C2×C4×Dic59—42no—
110C2×C4×Dic59C2314yes—
111C2×C4×Dic59C2314yes—
112C59⋊#95C2314yes—
113C59⋊#95C2314yes—
114C59⋊#95C2314yes—
115C59⋊#95C2314yes—
116C59⋊#95C2314yes—
117C59⋊#95C2314yes—
118C59⋊#95C2314yes—
119C59⋊#95C2314yes—
120C59⋊#95C2314yes—
121C59⋊#95C2314yes—
122C59⋊#95C2314yes—
123C59⋊#95C2314yes—
124C25×C59C2311yescharacteristic
125C23×C4×C59—24no—
126C23×C4×C59—24no—
127C23×C4×C59—24no—
128C23×C4×C59—24no—
129C23×C4×C59—24no—
130C23×C4×C59—24no—
131C23×C4×C59—24no—
132C23×C4×C59—42no—
133C23×C4×C59—42no—
134C23×C4×C59C2311yescharacteristic
135C23×C4×C59C2311yescharacteristic
136C23×C4×C59C2314yes—
137C23×C4×C59C2314yes—
138C23×C4×C59C2314yes—
139C23×C4×C59C2311yescharacteristic
140C23×C4×C59C2311yescharacteristic
141C23×C4×C59C2311yescharacteristic
142C23×C4×C59C2311yescharacteristic
143C2×C4⋊C4×C59—24no—
144C2×C4⋊C4×C59—24no—
145C2×C4⋊C4×C59—24no—
146C2×C4⋊C4×C59—232no—
147C2×C4⋊C4×C59D418yescomplemented
148C2×C4⋊C4×C59C2314yes—
149C2×C4⋊C4×C59C2314yes—
150C2×C4⋊C4×C59C2314yes—
151C2×C4⋊C4×C59C2314yes—
152C24×C59—22no—
153C24×C59—22no—
154C24×C59—22no—
155C24×C59—22no—
156C24×C59#4114yes—
157C24×C59#4114yes—
158C24×C59#4114yes—
159C24×C59C2412yes—
160C24×C59C2411yescharacteristic
161C23×D59—22no—
162C23×D59—22no—
163C23×D59—22no—
164C23×D59—22no—
165C23×D59—22no—
166C23×D59—22no—
167C23×D59—22no—
168C23×D59C2412yes—
169C22×C4×C59—232no—
170C22×C4×C59—22no—
171C22×C4×C59—28no—
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—28no—
180C22×C4×C59—28no—
181C22×C4×C59—22no—
182C22×C4×C59—22no—
183C22×C4×C59—28no—
184C22×C4×C59—28no—
185C22×C4×C59—22no—
186C22×C4×C59—22no—
187C22×C4×C59—22no—
188C22×C4×C59—22no—
189C22×C4×C59—28no—
190C22×C4×C59—28no—
191C22×C4×C59—44no—
192C22×C4×C59—44no—
193C22×C4×C59—416no—
194C22×C4×C59—416no—
195C22×C4×C59C2×D414yes—
196C22×C4×C59C2×D414yes—
197C22×C4×C59C2×D414yes—
198C22×C4×C59#4114yes—
199C22×C4×C59C2412yes—
200C22×C4×C59C2412yes—
201C22×C4×C59C2412yes—
202C22×C4×C59C2412yes—
203C22×C4×C59C2412yes—
204C22×C4×C59C2412yes—
205C2×C22⋊D59—28no—
206C2×C22⋊D59—28no—
207C2×C22⋊D59—28no—
208C2×C22⋊D59—416no—
209C22×Dic59—22no—
210C22×Dic59—22no—
211C22×Dic59—22no—
212C22×Dic59—22no—
213C22×Dic59—22no—
214C22×Dic59—22no—
215C22×Dic59—22no—
216C22×Dic59—22no—
217C22×Dic59—22no—
218C22×Dic59—22no—
219C22×Dic59—22no—
220C22×Dic59—22no—
221C22×Dic59—22no—
222C22×Dic59—22no—
223C22×Dic59—22no—
224C22×Dic59—22no—
225C22×Dic59—22no—
226C22×Dic59—22no—
227C22×Dic59—22no—
228C22×Dic59—22no—
229C22×Dic59—22no—
230C22×Dic59C2412yes—
231C22×Dic59C2412yes—
232C22×Dic59C2412yes—
233C22×Dic59C2412yes—
234C22×Dic59C2412yes—
235C22×Dic59C2412yes—
236C22×Dic59C2412yes—
237C4⋊C4×C59—28no—
238C4⋊C4×C59—28no—
239C4⋊C4×C59—28no—
240C4⋊C4×C59C2×D4116yescomplemented
241C22⋊Dic59—28no—
242C22⋊Dic59—28no—
243C22⋊Dic59—28no—
244(C2×D59)⋊C4—28no—
245(C2×D59)⋊C4—28no—
246(C2×D59)⋊C4—28no—
247(C2×D59)⋊C4—28no—
248(C2×D59)⋊C4—44no—
249(C2×D59)⋊C4—44no—
250C4⋊Dic59—28no—
251C4⋊Dic59—44no—
252Dic59⋊C4—28no—
253Dic59⋊C4—28no—
254C4×Dic59—28no—
255C4×Dic59—44no—
256C23×C59—28no—
257C23×C59—28no—
258C23×C59—28no—
259C23×C59—28no—
260C23×C59—28no—
261C23×C59—28no—
262C23×C59—22no—
263C23×C59—22no—
264C23×C59—22no—
265C23×C59—22no—
266C23×C59#126116yescomplemented
267C23×C59C22×D412yes—
268C23×C59C2×#4114yes—
269C23×C59C2×#4112yes—
270C23×C59C2×#4114yes—
271C23×C59C2×#4112yes—
272C23×C59C2×#4112yes—
273C23×C59C2×#4114yes—
274C23×C59C2×#4112yes—
275C23×C59H(5,𝔽2)12yes—
276C23×C592−1+412yes—
277C23×C59C2511yescharacteristic
278C22×D59—22no—
279C22×D59—22no—
280C22×D59—22no—
281C22×D59—22no—
282C22×D59—22no—
283C22×D59—22no—
284C22×D59—22no—
285C22×D59—44no—
286C22×D59—44no—
287C22×D59—44no—
288C22×D59—44no—
289C22×D59—44no—
290C22×D59—44no—
291C22×D59—44no—
292C2×C4×C59—232no—
293C2×C4×C59—28no—
294C2×C4×C59—28no—
295C2×C4×C59—28no—
296C2×C4×C59—28no—
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—22no—
308C2×C4×C59—22no—
309C2×C4×C59—22no—
310C2×C4×C59—22no—
311C2×C4×C59—416no—
312C2×C4×C59—416no—
313C2×C4×C59—44no—
314C2×C4×C59—44no—
315C2×C4×C59C22×D414yes—
316C2×C4×C59C22×D414yes—
317C2×C4×C59C22×D414yes—
318C2×C4×C59C2×#4114yes—
319C22⋊D59—416no—
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—22no—
336C2×Dic59—22no—
337C2×Dic59—22no—
338C2×Dic59—22no—
339C2×Dic59—22no—
340C2×Dic59—22no—
341C2×Dic59—44no—
342C2×Dic59—44no—
343C2×Dic59—44no—
344C2×Dic59—44no—
345C2×Dic59—44no—
346C2×Dic59—44no—
347C2×Dic59—44no—
348C2×#2481—591nomaximal, Sylow
349C22×C59—24no—
350C22×C59—24no—
351C22×C59—24no—
352C22×C59—24no—
353C22×C59—24no—
354C22×C59—24no—
355C22×C59—232no—
356C22×C59#52514yes—
357C22×C59C2×#12614yes—
358C22×C59C2×#12618yescomplemented
359C22×C59#53914yes—
360C22×C59#54614yes—
361C22×C59#54814yes—
362C22×C59#55214yes—
363C22×C59#55314yes—
364C22×C59C23×D411yescharacteristic
365C22×C59C22×#4111yescharacteristic
366C22×C59C22×#4111yescharacteristic
367C22×C59C22×#4111yescharacteristic
368C22×C59C22×#4111yescharacteristic
369C22×C59C2×H(5,𝔽2)11yescharacteristic
370C22×C59C2×2−1+411yescharacteristic
371C2×D59—42no—
372C2×D59—42no—
373C2×D59—42no—
374C2×D59—42no—
375C2×D59—42no—
376C2×D59—42no—
377C2×D59—42no—
378C2×D59—88no—
379C4×C59—24no—
380C4×C59—24no—
381C4×C59—24no—
382C4×C59—24no—
383C4×C59—42no—
384C4×C59—42no—
385Dic59—42no—
386Dic59—42no—
387Dic59—42no—
388Dic59—42no—
389Dic59—42no—
390Dic59—42no—
391Dic59—42no—
392C22×#126—591no—
393C23×C4⋊C4D5911yescharacteristic, complemented
394#2481—5916no—
395C2×#400—591no—
396C2×#400—591no—
397C2×#397—591no—
398C2×#396—591no—
399C2×#388—591no—
400C2×#387—591no—
401C2×#387—591no—
402C2×#386—591no—
403C2×#386—591no—
404C2×#386—591no—
405C2×#385—591no—
406C2×#380—591no—
407C2×C4×C22⋊C4—591no—
408C2×C59—28no—
409C2×C59#248118yescomplemented
410C2×C59C2×#52511yescharacteristic
411C2×C59C22×#12611yescharacteristic
412C2×C59C2×#53911yescharacteristic
413C2×C59C2×#54611yescharacteristic
414C2×C59C2×#54811yescharacteristic
415C2×C59C2×#55211yescharacteristic
416C2×C59C2×#55311yescharacteristic
417D59—82no—
418C23×D4—591no—
419C24×C4C2×D5911yescharacteristic
420C24×C4C2×D5911yescharacteristic
421C24×C4C2×D5911yescharacteristic
422C2×#126—598no—
423C2×#126—1188no—
424C22×C4⋊C4—28no—
425C22×C4⋊C4—591no—
426C22×C4⋊C4—591no—
427C22×C4⋊C4—591no—
428C22×C4⋊C4—591no—
429C22×C4⋊C4C2×D5911yescharacteristic
430C22×C4⋊C4C2×D5911yescharacteristic
431C22×C4⋊C4C2×D5911yescharacteristic
432C22×C4⋊C4C2×D5911yescharacteristic
433C22×C4⋊C4C2×D5918yescomplemented
434C22×C22⋊C4—591no—
435C22×C22⋊C4—591no—
436C22×C22⋊C4—591no—
437C22×C22⋊C4—591no—
438C22×C22⋊C4—591no—
439C22×C22⋊C4—591no—
440C22×C22⋊C4—591no—
441C22×C22⋊C4—591no—
442C22×C22⋊C4—591no—
443C22×C42—591no—
444C22×C42—591no—
445#400—598no—
446#400—598no—
447#397—598no—
448#396—598no—
449#388—598no—
450#387—598no—
451#387—598no—
452#386—598no—
453#386—598no—
454#386—598no—
455#385—598no—
456#380—598no—
457C4×C22⋊C4—598no—
458C2×#95—591no—
459C2×#95—591no—
460C2×#95—591no—
461C2×#95—591no—
462C2×#95—591no—
463C2×#95—591no—
464C2×#95—591no—
465C2×#95—591no—
466C2×#95—591no—
467C2×#95—591no—
468C2×#95—591no—
469C2×#95—591no—
470C59C2×#248111yescharacteristic, complemented, Sylow
471C25—591no—
472C25C22×D5911yescharacteristic
473C22×D4—594no—
474C22×D4—1184no—
475C22×D4—1184no—
476C22×D4—1184no—
477C23×C4—24no—
478C23×C4—24no—
479C23×C4—24no—
480C23×C4—24no—
481C23×C4—24no—
482C23×C4—24no—
483C23×C4—24no—
484C23×C4—42no—
485C23×C4—42no—
486C23×C4—591no—
487C23×C4—591no—
488C23×C4—591no—
489C23×C4—591no—
490C23×C4—591no—
491C23×C4—591no—
492C23×C4—591no—
493C23×C4C22×D5914yes—
494C23×C4C22×D5911yescharacteristic
495C23×C4C22×D5911yescharacteristic
496C23×C4C22×D5914yes—
497C23×C4C22×D5914yes—
498C23×C4C22×D5911yescharacteristic
499C23×C4C22×D5911yescharacteristic
500C23×C4C22×D5911yescharacteristic
501C23×C4C22×D5911yescharacteristic
502#126—11832no—
503C2×C4⋊C4—24no—
504C2×C4⋊C4—24no—
505C2×C4⋊C4—24no—
506C2×C4⋊C4—232no—
507C2×C4⋊C4—594no—
508C2×C4⋊C4—594no—
509C2×C4⋊C4—594no—
510C2×C4⋊C4—594no—
511C2×C4⋊C4—1184no—
512C2×C4⋊C4—1184no—
513C2×C4⋊C4—1184no—
514C2×C4⋊C4—2362no—
515C2×C4⋊C4C22⋊D5918yescomplemented
516C2×C4⋊C4C22×D5914yes—
517C2×C4⋊C4C22×D5914yes—
518C2×C4⋊C4C22×D5914yes—
519C2×C4⋊C4C22×D5914yes—
520C2×C22⋊C4—594no—
521C2×C22⋊C4—594no—
522C2×C22⋊C4—594no—
523C2×C22⋊C4—594no—
524C2×C22⋊C4—594no—
525C2×C22⋊C4—594no—
526C2×C22⋊C4—594no—
527C2×C22⋊C4—594no—
528C2×C22⋊C4—594no—
529C2×C22⋊C4—1184no—
530C2×C22⋊C4—1184no—
531C2×C22⋊C4—1184no—
532C2×C22⋊C4—1184no—
533C2×C22⋊C4—1184no—
534C2×C22⋊C4—1184no—
535C2×C22⋊C4—1184no—
536C2×C22⋊C4—2362no—
537C2×C22⋊C4—2362no—
538C2×C42—594no—
539C2×C42—594no—
540C2×C42—1184no—
541C2×C42—2362no—
542#95—594no—
543#95—594no—
544#95—594no—
545#95—594no—
546#95—594no—
547#95—594no—
548#95—594no—
549#95—594no—
550#95—594no—
551#95—594no—
552#95—594no—
553#95—594no—
554C24—22no—
555C24—22no—
556C24—22no—
557C24—22no—
558C24—592no—
559C24—1182no—
560C24—1182no—
561C24—1182no—
562C24—1182no—
563C24—1182no—
564C24—1182no—
565C24—1182no—
566C24#1174568514yes—
567C24#1174568714yes—
568C24#1174568914yes—
569C24C23×D5912yes—
570C24C23×D5911yescharacteristic
571C2×D4—1188no—
572C2×D4—1188no—
573C2×D4—1188no—
574C2×D4—23616no—
575C22×C4—232no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—28no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—28no—
586C22×C4—28no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—28no—
590C22×C4—28no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—28no—
596C22×C4—28no—
597C22×C4—44no—
598C22×C4—44no—
599C22×C4—416no—
600C22×C4—416no—
601C22×C4—592no—
602C22×C4—592no—
603C22×C4—592no—
604C22×C4—592no—
605C22×C4—592no—
606C22×C4—592no—
607C22×C4—592no—
608C22×C4—1182no—
609C22×C4—1182no—
610C22×C4—1182no—
611C22×C4—1182no—
612C22×C4—1182no—
613C22×C4—1182no—
614C22×C4—1182no—
615C22×C4—1182no—
616C22×C4—1182no—
617C22×C4—1182no—
618C22×C4—1182no—
619C22×C4—1182no—
620C22×C4—1182no—
621C22×C4—1182no—
622C22×C4—1182no—
623C22×C4—1182no—
624C22×C4—1182no—
625C22×C4—1182no—
626C22×C4—1182no—
627C22×C4—1182no—
628C22×C4—1182no—
629C22×C4#1174568514yes—
630C22×C4C2×C22⋊D5914yes—
631C22×C4C2×C22⋊D5914yes—
632C22×C4C2×C22⋊D5914yes—
633C22×C4C23×D5912yes—
634C22×C4C23×D5912yes—
635C22×C4C23×D5912yes—
636C22×C4C23×D5912yes—
637C22×C4C23×D5912yes—
638C22×C4C23×D5912yes—
639C4⋊C4—28no—
640C4⋊C4—28no—
641C4⋊C4—28no—
642C4⋊C4—1188no—
643C4⋊C4—1188no—
644C4⋊C4—1188no—
645C4⋊C4—2364no—
646C4⋊C4C2×C22⋊D59116yescomplemented
647C22⋊C4—1188no—
648C22⋊C4—1188no—
649C22⋊C4—1188no—
650C22⋊C4—1188no—
651C22⋊C4—1188no—
652C22⋊C4—1188no—
653C22⋊C4—1188no—
654C22⋊C4—2364no—
655C22⋊C4—2364no—
656C42—1188no—
657C42—2364no—
658C23—28no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—28no—
664C23—28no—
665C23—28no—
666C23—28no—
667C23—28no—
668C23—1182no—
669C23—1182no—
670C23—1182no—
671C23—1182no—
672C23—1182no—
673C23—1182no—
674C23—1182no—
675C23—2364no—
676C23—2364no—
677C23—2364no—
678C23—2364no—
679C23—2364no—
680C23—2364no—
681C23—2364no—
682C23#14273722116yescomplemented
683C23C22×C22⋊D5912yes—
684C23C2×#1174568714yes—
685C23C2×#1174568712yes—
686C23C2×#1174568514yes—
687C23C2×#1174568512yes—
688C23C2×#1174568512yes—
689C23C2×#1174568914yes—
690C23C2×#1174568912yes—
691C23#1427377212yes—
692C23#1427377512yes—
693C23C24×D5911yescharacteristic
694D4—23616no—
695C2×C4—232no—
696C2×C4—28no—
697C2×C4—28no—
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—28no—
707C2×C4—28no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—416no—
715C2×C4—416no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—1182no—
719C2×C4—1182no—
720C2×C4—1182no—
721C2×C4—1182no—
722C2×C4—1182no—
723C2×C4—1182no—
724C2×C4—1182no—
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—1182no—
735C2×C4—1182no—
736C2×C4—1182no—
737C2×C4—1182no—
738C2×C4—1182no—
739C2×C4—2364no—
740C2×C4—2364no—
741C2×C4—2364no—
742C2×C4—2364no—
743C2×C4—2364no—
744C2×C4—2364no—
745C2×C4—2364no—
746C2×C4C22×C22⋊D5914yes—
747C2×C4C22×C22⋊D5914yes—
748C2×C4C22×C22⋊D5914yes—
749C2×C4C2×#1174568514yes—
750C22—24no—
751C22—24no—
752C22—24no—
753C22—232no—
754C22—24no—
755C22—24no—
756C22—24no—
757C22—4728no—
758C22—2362no—
759C22—2362no—
760C22—2362no—
761C22—2362no—
762C22—2362no—
763C22—2362no—
764C22—2362no—
765C22#1683791314yes—
766C22C2×#1427372214yes—
767C22C2×#1427372218yescomplemented
768C22#1683799914yes—
769C22#1683804614yes—
770C22#1683806314yes—
771C22#1683808714yes—
772C22#1683810014yes—
773C22C23×C22⋊D5911yescharacteristic
774C22C22×#1174568711yescharacteristic
775C22C22×#1174568511yescharacteristic
776C22C22×#1174568511yescharacteristic
777C22C22×#1174568911yescharacteristic
778C22C2×#1427377211yescharacteristic
779C22C2×#1427377511yescharacteristic
780C4—24no—
781C4—24no—
782C4—24no—
783C4—24no—
784C4—42no—
785C4—42no—
786C4—2362no—
787C4—2362no—
788C4—2362no—
789C4—2362no—
790C4—2362no—
791C4—2362no—
792C4—2362no—
793C2—28no—
794C2—4722no—
795C2#2142835118yesdirect product factor
796C2C2×#1683791311yescharacteristic
797C2C22×#1427372211yescharacteristic
798C2C2×#1683799911yescharacteristic
799C2C2×#1683804611yescharacteristic
800C2C2×#1683806311yescharacteristic
801C2C2×#1683808711yescharacteristic
802C2C2×#1683810011yescharacteristic
subgroupG/H
centerC24C23×D59
commutator, cosocleC23×C59C25
FrattiniC23C24×D59
FittingC23×C4⋊C4×C59C2
socleC24×C59C24
prime radicalC23×C22⋊D59C22
hypercenterC23×C4⋊C4D59
hypocenterC59C2×#2481
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C24 ◁ C23×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#14273722C2semidirect
2. #21428351C2direct (N × H)
3. C2×#16837341C2semidirect
4. C2×#16837340C2semidirect
5. C2×#16837328C2semidirect
6. C2×#16837324C2semidirect
7. C2×#16837292C2semidirect
8. C2×#16837288C2semidirect
9. C2×#16837283C2semidirect
13. C2×#16837275C2semidirect
14. C2×#16837262C2semidirect
15. C2×C4×C22⋊Dic59C2semidirect
16. C23×C4⋊C4×C59C2semidirect
19. C2×#14273722C22semidirect
35. #16837341C22semidirect
36. #16837340C22semidirect
37. #16837328C22semidirect
38. #16837324C22semidirect
39. #16837292C22semidirect
40. #16837288C22semidirect
41. #16837283C22semidirect
45. #16837275C22semidirect
46. #16837262C22semidirect
47. C4×C22⋊Dic59C22semidirect
68. C22×C4⋊C4×C59C22semidirect
147. C2×C4⋊C4×C59D4semidirect
240. C4⋊C4×C59C2×D4semidirect
266. C23×C59#126semidirect
358. C22×C59C2×#126semidirect
393. C23×C4⋊C4D59semidirect
409. C2×C59#2481semidirect
433. C22×C4⋊C4C2×D59semidirect
470. C59C2×#2481semidirect
515. C2×C4⋊C4C22⋊D59semidirect
646. C4⋊C4C2×C22⋊D59semidirect
682. C23#14273722semidirect
767. C22C2×#14273722semidirect
795. C2#21428351direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#142737222
#214283512
C2×#168373412
C2×#168373402
C2×#168373282
C2×#168373242
C2×#168372922
C2×#168372882
C2×#168372832
C2×#168372812
C2×#168372752
C2×#168372622
C2×C4×C22⋊Dic592
C23×C4⋊C4×C592
C2×#248159