Finite Group Databasebeta

← C2×#21430250 #28755253

Subgroups — C2×#21430250 #28755253

Order 15104.

2786 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14273712C211yesmaximal, characteristic
2C22×#14273705C211yesmaximal, characteristic, complemented
3#21430250C2116yesmaximal, direct product factor
4C2×#16837343C211yesmaximal, characteristic, complemented
5C2×#16837337C211yesmaximal, characteristic, complemented
6C2×#16837331C211yesmaximal, characteristic, complemented
7C2×#16837328C211yesmaximal, characteristic, complemented
8C2×#16837322C211yesmaximal, characteristic, complemented
9C2×#16837320C211yesmaximal, characteristic
10C2×#16837319C211yesmaximal, characteristic
11C2×#16837315C211yesmaximal, characteristic, complemented
12C2×#16837297C211yesmaximal, characteristic, complemented
13C2×#16837293C211yesmaximal, characteristic, complemented
14C2×#16837292C211yesmaximal, characteristic, complemented
15C2×C4×(C2×D59)⋊C4C211yesmaximal, characteristic, complemented
16C2×C59×#389C211yesmaximal, characteristic, complemented
17C23×Dic118C2211yescharacteristic
18C23×D236C2211yescharacteristic
19C23×C4×D59C2211yescharacteristic
20C2×#14273712—28no—
21C2×#14273712C2218yes—
22C2×#14273705—28no—
23C2×#14273705C2218yescomplemented
24C22×Dic59⋊C4C2211yescharacteristic
25C22×Dic59⋊C4C2211yescharacteristic
26C22×Dic59⋊C4C2211yescharacteristic
27C22×Dic59⋊C4C2211yescharacteristic
28C22×Dic59⋊C4C2211yescharacteristic
29C22×(C2×D59)⋊C4C2211yescharacteristic
30C22×(C2×D59)⋊C4C2211yescharacteristic
31C22×(C2×D59)⋊C4C2211yescharacteristic
32C22×(C2×D59)⋊C4C2211yescharacteristic
33C22×(C2×D59)⋊C4C2211yescharacteristic
34C22×(C2×D59)⋊C4C2211yescharacteristic
35C22×(C2×D59)⋊C4C2211yescharacteristic
36C22×(C2×D59)⋊C4C2211yescharacteristic
37C22×(C2×D59)⋊C4C2211yescharacteristic
38C22×(C2×D59)⋊C4C2211yescharacteristic
39C22×(C2×D59)⋊C4C2211yescharacteristic
40C22×C4×Dic59C2211yescharacteristic
41#16837343C2218yescomplemented
42#16837337C2218yescomplemented
43#16837331C2218yescomplemented
44#16837328C2218yescomplemented
45#16837322C2218yescomplemented
46#16837320C2218yes—
47#16837319C2218yes—
48#16837315C2218yescomplemented
49#16837297C2218yescomplemented
50#16837293C2218yescomplemented
51#16837292C2218yescomplemented
52C4×(C2×D59)⋊C4C2218yescomplemented
53C2×C59⋊#95C2211yescharacteristic
54C2×C59⋊#95C2211yescharacteristic
55C2×C59⋊#95C2211yescharacteristic
56C2×C59⋊#95C2211yescharacteristic
57C2×C59⋊#95C2211yescharacteristic
58C2×C59⋊#95C2211yescharacteristic
59C2×C59⋊#95C2211yescharacteristic
60C2×C59⋊#95C2211yescharacteristic
61C22×C4⋊C4×C59C2211yescharacteristic
62C22×C4⋊C4×C59C2211yescharacteristic
63C22×C4⋊C4×C59C2211yescharacteristic
64C22×C4⋊C4×C59C2211yescharacteristic
65C22×C42×C59C2211yescharacteristic
66C59×#389C2218yescomplemented
67C2×#95×C59C2211yescharacteristic
68C2×#95×C59C2211yescharacteristic
69C24×D59C2311yescharacteristic
70C24×D59C2311yescharacteristic
71C22×Dic118—24no—
72C22×Dic118—42no—
73C22×Dic118—42no—
74C22×Dic118C2314yes—
75C22×D236—24no—
76C22×D236—42no—
77C22×D236—42no—
78C22×D236C2314yes—
79C23×Dic59C2311yescharacteristic
80C23×Dic59C2311yescharacteristic
81C23×Dic59C2311yescharacteristic
82C23×Dic59C2311yescharacteristic
83C23×Dic59C2311yescharacteristic
84C23×Dic59C2311yescharacteristic
85C22×C4×D59—42no—
86C22×C4×D59—42no—
87C22×C4×D59D418yes—
88C22×C4×D59C2314yes—
89#14273712—232no—
90#14273705—232no—
91C2×Dic59⋊C4—24no—
92C2×Dic59⋊C4—24no—
93C2×Dic59⋊C4—24no—
94C2×Dic59⋊C4—24no—
95C2×Dic59⋊C4—42no—
96C2×Dic59⋊C4C2314yes—
97C2×Dic59⋊C4C2314yes—
98C2×Dic59⋊C4C2314yes—
99C2×Dic59⋊C4C2314yes—
100C2×Dic59⋊C4C2314yes—
101C2×(C2×D59)⋊C4—24no—
102C2×(C2×D59)⋊C4—24no—
103C2×(C2×D59)⋊C4—24no—
104C2×(C2×D59)⋊C4—24no—
105C2×(C2×D59)⋊C4—24no—
106C2×(C2×D59)⋊C4—24no—
107C2×(C2×D59)⋊C4—24no—
108C2×(C2×D59)⋊C4—24no—
109C2×(C2×D59)⋊C4—24no—
110C2×(C2×D59)⋊C4—42no—
111C2×(C2×D59)⋊C4—42no—
112C2×(C2×D59)⋊C4C2314yes—
113C2×(C2×D59)⋊C4C2314yes—
114C2×(C2×D59)⋊C4C2314yes—
115C2×(C2×D59)⋊C4C2314yes—
116C2×(C2×D59)⋊C4C2314yes—
117C2×(C2×D59)⋊C4C2314yes—
118C2×(C2×D59)⋊C4C2314yes—
119C2×(C2×D59)⋊C4C2314yes—
120C2×(C2×D59)⋊C4C2314yes—
121C2×(C2×D59)⋊C4C2314yes—
122C2×(C2×D59)⋊C4C2314yes—
123C2×C4×Dic59—42no—
124C2×C4×Dic59C2314yes—
125C59⋊#95C2314yes—
126C59⋊#95C2314yes—
127C59⋊#95C2314yes—
128C59⋊#95C2314yes—
129C59⋊#95C2314yes—
130C59⋊#95C2314yes—
131C59⋊#95C2314yes—
132C59⋊#95C2314yes—
133C23×C4×C59C2311yescharacteristic
134C23×C4×C59C2311yescharacteristic
135C23×C4×C59C2311yescharacteristic
136C23×C4×C59C2311yescharacteristic
137C23×C4×C59C2311yescharacteristic
138C23×C4×C59C2311yescharacteristic
139C23×C4×C59C2311yescharacteristic
140C2×C4⋊C4×C59—24no—
141C2×C4⋊C4×C59—24no—
142C2×C4⋊C4×C59—24no—
143C2×C4⋊C4×C59—42no—
144C2×C4⋊C4×C59C2314yes—
145C2×C4⋊C4×C59C2314yes—
146C2×C4⋊C4×C59C2314yes—
147C2×C4⋊C4×C59C2314yes—
148C2×C42×C59—42no—
149C2×C42×C59C2314yes—
150#95×C59C2314yes—
151#95×C59C2314yes—
152C24×C59C2411yescharacteristic
153C23×D59—22no—
154C23×D59—22no—
155C23×D59—22no—
156C23×D59—22no—
157C23×D59—22no—
158C23×D59—22no—
159C23×D59—22no—
160C23×D59—22no—
161C23×D59—22no—
162C23×D59—22no—
163C23×D59—22no—
164C23×D59—22no—
165C23×D59—22no—
166C23×D59C2×D414yes—
167C23×D59C2412yes—
168C23×D59C2412yes—
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×C59—22no—
183C22×C4×C59—22no—
184C22×C4×C59—22no—
185C22×C4×C59—22no—
186C22×C4×C59—22no—
187C22×C4×C59—22no—
188C22×C4×C59C2×D414yes—
189C22×C4×C59#4114yes—
190C22×C4×C59C2412yes—
191C22×C4×C59C2412yes—
192C22×C4×C59C2412yes—
193C22×C4×C59C2412yes—
194C22×C4×C59C2412yes—
195C22×C4×C59C2412yes—
196C22×C4×C59C2412yes—
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—22no—
213C22×Dic59C2×D414yes—
214C22×Dic59#4114yes—
215C22×Dic59C2412yes—
216C22×Dic59C2412yes—
217C22×Dic59C2412yes—
218C22×Dic59C2412yes—
219C22×Dic59C2412yes—
220C22×Dic59C2412yes—
221C2×D236—28no—
222C2×D236—44no—
223C2×D236—44no—
224C2×D236—416no—
225C2×C4×D59—416no—
226C2×C4×D59—44no—
227C2×C4×D59—44no—
228C2×C4×D59C2×D4116yes—
229C2×Dic118—28no—
230C2×Dic118—44no—
231C2×Dic118—44no—
232C2×Dic118—416no—
233C4⋊C4×C59—28no—
234C4⋊C4×C59—28no—
235C4⋊C4×C59—28no—
236C4⋊C4×C59—44no—
237C42×C59—44no—
238(C2×D59)⋊C4—28no—
239(C2×D59)⋊C4—28no—
240(C2×D59)⋊C4—28no—
241(C2×D59)⋊C4—28no—
242(C2×D59)⋊C4—28no—
243(C2×D59)⋊C4—28no—
244(C2×D59)⋊C4—28no—
245(C2×D59)⋊C4—28no—
246(C2×D59)⋊C4—28no—
247(C2×D59)⋊C4—44no—
248(C2×D59)⋊C4—44no—
249Dic59⋊C4—28no—
250Dic59⋊C4—28no—
251Dic59⋊C4—28no—
252Dic59⋊C4—28no—
253Dic59⋊C4—44no—
254C4×Dic59—44no—
255C23×C59C22×D412yes—
256C23×C59C2×#4112yes—
257C23×C59C2×#4112yes—
258C23×C59H(5,𝔽2)12yes—
259C23×C59H(5,𝔽2)12yes—
260C23×C592−1+412yes—
261C23×C592−1+412yes—
262C23×C59C2511yescharacteristic
263C22×D59—28no—
264C22×D59—28no—
265C22×D59—28no—
266C22×D59—22no—
267C22×D59—22no—
268C22×D59—22no—
269C22×D59—22no—
270C22×D59—22no—
271C22×D59—22no—
272C22×D59—22no—
273C22×D59—22no—
274C22×D59—22no—
275C22×D59—22no—
276C22×D59—22no—
277C22×D59—22no—
278C22×D59—22no—
279C22×D59—44no—
280C22×D59—44no—
281C22×D59—44no—
282C22×D59—44no—
283C22×D59—44no—
284C22×D59—44no—
285C22×D59—44no—
286C22×D59—44no—
287C22×D59—44no—
288C22×D59—44no—
289C22×D59—44no—
290C22×D59C22×D414yes—
291C2×C4×C59—28no—
292C2×C4×C59—28no—
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—22no—
308C2×C4×C59—22no—
309C2×C4×C59—22no—
310C2×C4×C59—22no—
311C2×C4×C59—22no—
312C2×C4×C59—44no—
313C2×C4×C59—44no—
314C2×C4×C59—44no—
315C2×C4×C59—44no—
316C2×C4×C59—44no—
317C2×C4×C59C22×D414yes—
318C2×C4×C59C2×#4114yes—
319C2×Dic59—28no—
320C2×Dic59—28no—
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—44no—
338C2×Dic59—44no—
339C2×Dic59—44no—
340C2×Dic59—44no—
341C2×Dic59C22×D414yes—
342C2×Dic59C2×#4114yes—
343D236—416no—
344C4×D59—416no—
345Dic118—416no—
346C2×#2663—591nomaximal, Sylow
347C22×C59#53214yes—
348C22×C59#53414yes—
349C22×C59#53614yes—
350C22×C59#53914yes—
351C22×C59#53914yes—
352C22×C59#54214yes—
353C22×C59#54214yes—
354C22×C59C23×D411yescharacteristic
355C22×C59C22×#4111yescharacteristic
356C22×C59C22×#4111yescharacteristic
357C22×C59C2×H(5,𝔽2)11yescharacteristic
358C22×C59C2×H(5,𝔽2)11yescharacteristic
359C22×C59C2×2−1+411yescharacteristic
360C22×C59C2×2−1+411yescharacteristic
361C2×D59—24no—
362C2×D59—24no—
363C2×D59—24no—
364C2×D59—416no—
365C2×D59—42no—
366C2×D59—42no—
367C2×D59—42no—
368C2×D59—42no—
369C2×D59—42no—
370C2×D59—42no—
371C2×D59—42no—
372C2×D59—42no—
373C2×D59—42no—
374C2×D59—42no—
375C2×D59—42no—
376C2×D59—88no—
377C4×C59—24no—
378C4×C59—24no—
379C4×C59—42no—
380C4×C59—42no—
381C4×C59—42no—
382C4×C59—42no—
383C4×C59—42no—
384Dic59—24no—
385Dic59—24no—
386Dic59—42no—
387Dic59—42no—
388Dic59—42no—
389Dic59—42no—
390C22×#123—591no—
391C22×C22⋊Q8—591no—
392#2663—5916no—
393C2×#400—591no—
394C2×#399—591no—
395C2×#397—591no—
396C2×#397—591no—
397C2×#395—591no—
398C2×#394—591no—
399C2×#394—591no—
400C2×#393—591no—
401C2×#389—591no—
402C2×#389D5911yescharacteristic, complemented
403C2×#388—591no—
404C2×#388—591no—
405C2×C4×C22⋊C4—591no—
406C2×C59#266318yescomplemented
407C2×C59C2×#53211yescharacteristic
408C2×C59C2×#53411yescharacteristic
409C2×C59C2×#53611yescharacteristic
410C2×C59C2×#53911yescharacteristic
411C2×C59C2×#53911yescharacteristic
412C2×C59C2×#54211yescharacteristic
413C2×C59C2×#54211yescharacteristic
414D59—44no—
415D59—82no—
416C23×Q8—591no—
417C23×D4—591no—
418C24×C4—591no—
419C2×#123—598no—
420C2×#123—1188no—
421C2×C22⋊Q8—598no—
422C2×C22⋊Q8—1188no—
423C22×C4⋊C4—591no—
424C22×C4⋊C4—591no—
425C22×C4⋊C4—591no—
426C22×C4⋊C4—591no—
427C22×C4⋊C4—591no—
428C22×C4⋊C4C2×D5911yescharacteristic
429C22×C4⋊C4C2×D5911yescharacteristic
430C22×C4⋊C4C2×D5911yescharacteristic
431C22×C4⋊C4C2×D5911yescharacteristic
432C22×C22⋊C4—591no—
433C22×C22⋊C4—591no—
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×C42C2×D5911yescharacteristic
445#400—598no—
446#399—598no—
447#397—598no—
448#397—598no—
449#395—598no—
450#394—598no—
451#394—598no—
452#393—598no—
453#389—598no—
454#389C2×D5918yescomplemented
455#388—598no—
456#388—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×#95C2×D5911yescharacteristic
467C2×#95C2×D5911yescharacteristic
468C59C2×#266311yescharacteristic, complemented, Sylow
469C25—591no—
470C25—591no—
471C22×Q8—594no—
472C22×Q8—1184no—
473C22×Q8—2362no—
474C22×Q8—2362no—
475C22×D4—594no—
476C22×D4—1184no—
477C22×D4—2362no—
478C22×D4—2362no—
479C23×C4—591no—
480C23×C4—591no—
481C23×C4—598no—
482C23×C4—594no—
483C23×C4—591no—
484C23×C4—591no—
485C23×C4—591no—
486C23×C4—591no—
487C23×C4—2362no—
488C23×C4—2362no—
489C23×C4C22×D5911yescharacteristic
490C23×C4C22×D5911yescharacteristic
491C23×C4C22×D5911yescharacteristic
492C23×C4C22×D5911yescharacteristic
493C23×C4C22×D5911yescharacteristic
494C23×C4C22×D5911yescharacteristic
495C23×C4C22×D5911yescharacteristic
496#123—11832no—
497C22⋊Q8—11832no—
498C2×C4⋊C4—24no—
499C2×C4⋊C4—24no—
500C2×C4⋊C4—24no—
501C2×C4⋊C4—42no—
502C2×C4⋊C4—594no—
503C2×C4⋊C4—594no—
504C2×C4⋊C4—594no—
505C2×C4⋊C4—594no—
506C2×C4⋊C4—594no—
507C2×C4⋊C4—1184no—
508C2×C4⋊C4—1184no—
509C2×C4⋊C4—1184no—
510C2×C4⋊C4—1184no—
511C2×C4⋊C4—2362no—
512C2×C4⋊C4C22×D5914yes—
513C2×C4⋊C4C22×D5914yes—
514C2×C4⋊C4C22×D5914yes—
515C2×C4⋊C4C22×D5914yes—
516C2×C22⋊C4—594no—
517C2×C22⋊C4—594no—
518C2×C22⋊C4—594no—
519C2×C22⋊C4—594no—
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—1184no—
528C2×C22⋊C4—1184no—
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—42no—
539C2×C42—594no—
540C2×C42—2362no—
541C2×C42C22×D5914yes—
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#95C22×D5914yes—
551#95C22×D5914yes—
552C24—594no—
553C24—592no—
554C24—592no—
555C24—1182no—
556C24—1182no—
557C24—1182no—
558C24—1182no—
559C24—1182no—
560C24—1182no—
561C24—1182no—
562C24—1182no—
563C24—1182no—
564C24—1182no—
565C24—1182no—
566C24—1182no—
567C24—1182no—
568C24C23×D5911yescharacteristic
569C2×Q8—1188no—
570C2×Q8—2364no—
571C2×Q8—2364no—
572C2×Q8—23616no—
573C2×D4—1188no—
574C2×D4—2364no—
575C2×D4—2364no—
576C2×D4—23616no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—594no—
597C22×C4—594no—
598C22×C4—592no—
599C22×C4—592no—
600C22×C4—5916no—
601C22×C4—592no—
602C22×C4—592no—
603C22×C4—592no—
604C22×C4—592no—
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—1182no—
614C22×C4—1182no—
615C22×C4—1182no—
616C22×C4—1182no—
617C22×C4—1182no—
618C22×C4—1182no—
619C22×C4—1182no—
620C22×C4—1182no—
621C22×C4—23616no—
622C22×C4—2364no—
623C22×C4—2364no—
624C22×C4#1174568514yes—
625C22×C4D4×D5914yes—
626C22×C4C23×D5912yes—
627C22×C4C23×D5912yes—
628C22×C4C23×D5912yes—
629C22×C4C23×D5912yes—
630C22×C4C23×D5912yes—
631C22×C4C23×D5912yes—
632C22×C4C23×D5912yes—
633C4⋊C4—28no—
634C4⋊C4—28no—
635C4⋊C4—28no—
636C4⋊C4—44no—
637C4⋊C4—1188no—
638C4⋊C4—1188no—
639C4⋊C4—1188no—
640C4⋊C4—1188no—
641C4⋊C4—2364no—
642C22⋊C4—1188no—
643C22⋊C4—1188no—
644C22⋊C4—1188no—
645C22⋊C4—1188no—
646C22⋊C4—1188no—
647C22⋊C4—1188no—
648C22⋊C4—1188no—
649C22⋊C4—1188no—
650C22⋊C4—1188no—
651C22⋊C4—2364no—
652C22⋊C4—2364no—
653C42—44no—
654C42—2364no—
655C23—594no—
656C23—1188no—
657C23—1188no—
658C23—1182no—
659C23—1182no—
660C23—1182no—
661C23—1188no—
662C23—1182no—
663C23—1182no—
664C23—1182no—
665C23—1182no—
666C23—1182no—
667C23—1182no—
668C23—1182no—
669C23—1182no—
670C23—1182no—
671C23—1182no—
672C23—2364no—
673C23—2364no—
674C23—2364no—
675C23—2364no—
676C23—2364no—
677C23—2364no—
678C23—2364no—
679C23—2364no—
680C23—2364no—
681C23—2364no—
682C23—2364no—
683C23C2×D4×D5912yes—
684C23#41×D5912yes—
685C23C2×#1174568512yes—
686C23#1427377212yes—
687C23#1427377312yes—
688C23#1427377512yes—
689C23#1427377512yes—
690C23C24×D5911yescharacteristic
691Q8—23616no—
692D4—23616no—
693C2×C4—28no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—28no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—44no—
715C2×C4—44no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—44no—
719C2×C4—594no—
720C2×C4—594no—
721C2×C4—1188no—
722C2×C4—1182no—
723C2×C4—1182no—
724C2×C4—1182no—
725C2×C4—1182no—
726C2×C4—1188no—
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—23616no—
740C2×C4—2364no—
741C2×C4—2364no—
742C2×C4—2364no—
743C2×C4—2364no—
744C2×C4C2×D4×D5914yes—
745C2×C4C2×#1174568514yes—
746C22—1184no—
747C22—1184no—
748C22—1184no—
749C22—4728no—
750C22—2362no—
751C22—2362no—
752C22—2362no—
753C22—2362no—
754C22—2362no—
755C22—2362no—
756C22—2362no—
757C22—2362no—
758C22—2362no—
759C22—2362no—
760C22—2362no—
761C22—23616no—
762C22#1683794914yes—
763C22#1683796014yes—
764C22#1683797714yes—
765C22#1683799914yes—
766C22#1683800014yes—
767C22#1683802214yes—
768C22#1683802414yes—
769C22C22×D4×D5911yescharacteristic
770C22C2×#41×D5911yescharacteristic
771C22C22×#1174568511yescharacteristic
772C22C2×#1427377211yescharacteristic
773C22C2×#1427377311yescharacteristic
774C22C2×#1427377511yescharacteristic
775C22C2×#1427377511yescharacteristic
776C4—24no—
777C4—24no—
778C4—42no—
779C4—42no—
780C4—42no—
781C4—42no—
782C4—42no—
783C4—1184no—
784C4—1184no—
785C4—2362no—
786C4—2362no—
787C4—2362no—
788C4—2362no—
789C2—4722no—
790C2—2364no—
791C2#2143025018yesdirect product factor
792C2C2×#1683794911yescharacteristic
793C2C2×#1683796011yescharacteristic
794C2C2×#1683797711yescharacteristic
795C2C2×#1683799911yescharacteristic
796C2C2×#1683800011yescharacteristic
797C2C2×#1683802211yescharacteristic
798C2C2×#1683802411yescharacteristic
subgroupG/H
centerC24C23×D59
commutator, cosocleC23×C59C25
FrattiniC23C24×D59
FittingC2×C59×#389C2
socleC24×C59C24
prime radicalC23×D236C22
hypercenterC2×#389D59
hypocenterC59C2×#2663
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
2. C22×#14273705C2semidirect
3. #21430250C2direct (N × H)
4. C2×#16837343C2semidirect
5. C2×#16837337C2semidirect
6. C2×#16837331C2semidirect
7. C2×#16837328C2semidirect
8. C2×#16837322C2semidirect
11. C2×#16837315C2semidirect
12. C2×#16837297C2semidirect
13. C2×#16837293C2semidirect
14. C2×#16837292C2semidirect
15. C2×C4×(C2×D59)⋊C4C2semidirect
16. C2×C59×#389C2semidirect
23. C2×#14273705C22semidirect
41. #16837343C22semidirect
42. #16837337C22semidirect
43. #16837331C22semidirect
44. #16837328C22semidirect
45. #16837322C22semidirect
48. #16837315C22semidirect
49. #16837297C22semidirect
50. #16837293C22semidirect
51. #16837292C22semidirect
52. C4×(C2×D59)⋊C4C22semidirect
66. C59×#389C22semidirect
402. C2×#389D59semidirect
406. C2×C59#2663semidirect
454. #389C2×D59semidirect
468. C59C2×#2663semidirect
791. C2#21430250direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#142737122
C22×#142737052
#214302502
C2×#168373432
C2×#168373372
C2×#168373312
C2×#168373282
C2×#168373222
C2×#168373202
C2×#168373192
C2×#168373152
C2×#168372972
C2×#168372932
C2×#168372922
C2×C4×(C2×D59)⋊C42
C2×C59×#3892
C2×#266359