Finite Group Databasebeta

← C2×#21429610 #28759255

Subgroups — C2×#21429610 #28759255

Order 15104.

2442 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21429610C2116yesmaximal, direct product factor
2C2×#16837331C211yesmaximal, characteristic, complemented
3C2×#16837329C211yesmaximal, characteristic, complemented
4C2×#16837319C211yesmaximal, characteristic
5C2×#16837303C211yesmaximal, characteristic
6C2×#16837294C211yesmaximal, characteristic, complemented
7C2×#16837294C211yesmaximal, characteristic, complemented
8C2×#16837294C211yesmaximal, characteristic, complemented
9C2×#16837294C211yesmaximal, characteristic, complemented
10C2×#16837288C211yesmaximal, characteristic, complemented
11C2×#16837285C211yesmaximal, characteristic, complemented
12C2×#16837280C211yesmaximal, characteristic
13C2×#16837276C211yesmaximal, characteristic, complemented
14C2×C4⋊C4×Dic59C211yesmaximal, characteristic, complemented
15C2×#16837249C211yesmaximal, characteristic, complemented
16C2×C59×#400C211yesmaximal, characteristic, complemented
17C23×D236C2211yescharacteristic
18C23×C4×D59C2211yescharacteristic
19C22×C4⋊Dic59C2211yescharacteristic
20C22×C4⋊Dic59C2211yescharacteristic
21C22×C4⋊Dic59C2211yescharacteristic
22C22×Dic59⋊C4C2211yescharacteristic
23C22×(C2×D59)⋊C4C2211yescharacteristic
24C22×(C2×D59)⋊C4C2211yescharacteristic
25C22×(C2×D59)⋊C4C2211yescharacteristic
26C22×(C2×D59)⋊C4C2211yescharacteristic
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×(C2×D59)⋊C4C2211yescharacteristic
34C22×C4×Dic59C2211yescharacteristic
35C22×C4×Dic59C2211yescharacteristic
36C22×C4×Dic59C2211yescharacteristic
37C22×C4×Dic59C2211yescharacteristic
38#16837331C2218yescomplemented
39#16837329C2218yescomplemented
40#16837319C2218yes—
41#16837303C2218yes—
42#16837294C2218yescomplemented
43#16837294C2218yescomplemented
44#16837294C2218yescomplemented
45#16837294C2218yescomplemented
46#16837288C2218yescomplemented
47#16837285C2218yescomplemented
48#16837280C2218yes—
49#16837276C2218yescomplemented
50C4⋊C4×Dic59C2218yescomplemented
51#16837249C2218yescomplemented
52C2×C59⋊#95C2211yescharacteristic
53C2×C59⋊#95C2211yescharacteristic
54C2×C59⋊#95C2211yescharacteristic
55C2×C59⋊#95C2211yescharacteristic
56C2×C59⋊#95C2211yescharacteristic
57C2×C59⋊#95C2211yescharacteristic
58C2×C59⋊#95C2211yescharacteristic
59C22×C4⋊C4×C59C2211yescharacteristic
60C22×C4⋊C4×C59C2211yescharacteristic
61C59×#400C2218yescomplemented
62C2×#95×C59C2211yescharacteristic
63C2×#95×C59C2211yescharacteristic
64C2×#95×C59C2211yescharacteristic
65C2×#95×C59C2211yescharacteristic
66C2×#95×C59C2211yescharacteristic
67C24×D59C2311yescharacteristic
68C24×D59C2311yescharacteristic
69C22×D236—24no—
70C22×D236—24no—
71C22×D236—42no—
72C22×D236C2314yes—
73C23×Dic59C2311yescharacteristic
74C23×Dic59C2311yescharacteristic
75C23×Dic59C2311yescharacteristic
76C23×Dic59C2311yescharacteristic
77C23×Dic59C2311yescharacteristic
78C23×Dic59C2311yescharacteristic
79C22×C4×D59—24no—
80C22×C4×D59—42no—
81C22×C4×D59—42no—
82C22×C4×D59C2314yes—
83C2×C4⋊Dic59—24no—
84C2×C4⋊Dic59—24no—
85C2×C4⋊Dic59—42no—
86C2×C4⋊Dic59C2314yes—
87C2×C4⋊Dic59C2314yes—
88C2×C4⋊Dic59C2314yes—
89C2×Dic59⋊C4—42no—
90C2×Dic59⋊C4C2314yes—
91C2×(C2×D59)⋊C4—24no—
92C2×(C2×D59)⋊C4—24no—
93C2×(C2×D59)⋊C4—24no—
94C2×(C2×D59)⋊C4—24no—
95C2×(C2×D59)⋊C4—24no—
96C2×(C2×D59)⋊C4—24no—
97C2×(C2×D59)⋊C4—24no—
98C2×(C2×D59)⋊C4—42no—
99C2×(C2×D59)⋊C4—42no—
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×(C2×D59)⋊C4C2314yes—
109C2×(C2×D59)⋊C4C2314yes—
110C2×(C2×D59)⋊C4C2314yes—
111C2×(C2×D59)⋊C4C2314yes—
112C2×(C2×D59)⋊C4C2314yes—
113C2×C4×Dic59—24no—
114C2×C4×Dic59—42no—
115C2×C4×Dic59—42no—
116C2×C4×Dic59—42no—
117C2×C4×Dic59C2314yes—
118C2×C4×Dic59C2314yes—
119C2×C4×Dic59C2314yes—
120C2×C4×Dic59C2314yes—
121C59⋊#95C2314yes—
122C59⋊#95C2314yes—
123C59⋊#95C2314yes—
124C59⋊#95C2314yes—
125C59⋊#95C2314yes—
126C59⋊#95C2314yes—
127C59⋊#95C2314yes—
128C23×C4×C59C2311yescharacteristic
129C23×C4×C59C2311yescharacteristic
130C23×C4×C59C2311yescharacteristic
131C23×C4×C59C2311yescharacteristic
132C23×C4×C59C2311yescharacteristic
133C23×C4×C59C2311yescharacteristic
134C23×C4×C59C2311yescharacteristic
135C2×C4⋊C4×C59—24no—
136C2×C4⋊C4×C59—24no—
137C2×C4⋊C4×C59C2314yes—
138C2×C4⋊C4×C59C2314yes—
139#95×C59C2314yes—
140#95×C59C2314yes—
141#95×C59C2314yes—
142#95×C59C2314yes—
143#95×C59C2314yes—
144C24×C59C2411yescharacteristic
145C23×D59—22no—
146C23×D59—22no—
147C23×D59—22no—
148C23×D59—22no—
149C23×D59—22no—
150C23×D59—22no—
151C23×D59—22no—
152C23×D59—22no—
153C23×D59—22no—
154C23×D59—22no—
155C23×D59—22no—
156C23×D59—22no—
157C23×D59—22no—
158C23×D59#4114yes—
159C23×D59C2412yes—
160C23×D59C2412yes—
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—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#4114yes—
181C22×C4×C59#4114yes—
182C22×C4×C59C2412yes—
183C22×C4×C59C2412yes—
184C22×C4×C59C2412yes—
185C22×C4×C59C2412yes—
186C22×C4×C59C2412yes—
187C22×C4×C59C2412yes—
188C22×C4×C59C2412yes—
189C22×Dic59—22no—
190C22×Dic59—22no—
191C22×Dic59—22no—
192C22×Dic59—22no—
193C22×Dic59—22no—
194C22×Dic59—22no—
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#4114yes—
206C22×Dic59#4114yes—
207C22×Dic59C2412yes—
208C22×Dic59C2412yes—
209C22×Dic59C2412yes—
210C22×Dic59C2412yes—
211C22×Dic59C2412yes—
212C22×Dic59C2412yes—
213C2×D236—28no—
214C2×D236—28no—
215C2×D236—44no—
216C2×D236—416no—
217C2×C4×D59—28no—
218C2×C4×D59—44no—
219C2×C4×D59—44no—
220C2×C4×D59—416no—
221C4⋊C4×C59—28no—
222C4⋊C4×C59—28no—
223(C2×D59)⋊C4—28no—
224(C2×D59)⋊C4—28no—
225(C2×D59)⋊C4—28no—
226(C2×D59)⋊C4—28no—
227(C2×D59)⋊C4—28no—
228(C2×D59)⋊C4—28no—
229(C2×D59)⋊C4—28no—
230(C2×D59)⋊C4—44no—
231(C2×D59)⋊C4—44no—
232(C2×D59)⋊C4—44no—
233(C2×D59)⋊C4—44no—
234C4⋊Dic59—28no—
235C4⋊Dic59—28no—
236C4⋊Dic59—44no—
237Dic59⋊C4—44no—
238C4×Dic59—28no—
239C4×Dic59—44no—
240C4×Dic59—44no—
241C4×Dic59—44no—
242C23×C59C2×#4112yes—
243C23×C59C2×#4112yes—
244C23×C59C2×#4112yes—
245C23×C59C2×#4112yes—
246C23×C59C2×#4112yes—
247C23×C59H(5,𝔽2)12yes—
248C23×C59H(5,𝔽2)12yes—
249C23×C59C2511yescharacteristic
250C22×D59—28no—
251C22×D59—28no—
252C22×D59—28no—
253C22×D59—22no—
254C22×D59—22no—
255C22×D59—22no—
256C22×D59—22no—
257C22×D59—22no—
258C22×D59—22no—
259C22×D59—22no—
260C22×D59—22no—
261C22×D59—22no—
262C22×D59—22no—
263C22×D59—22no—
264C22×D59—22no—
265C22×D59—22no—
266C22×D59—44no—
267C22×D59—44no—
268C22×D59—44no—
269C22×D59—44no—
270C22×D59—44no—
271C22×D59—44no—
272C22×D59—44no—
273C22×D59—44no—
274C22×D59—44no—
275C22×D59—44no—
276C22×D59—44no—
277C22×D59C2×#4114yes—
278C2×C4×C59—28no—
279C2×C4×C59—28no—
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—22no—
287C2×C4×C59—22no—
288C2×C4×C59—22no—
289C2×C4×C59—22no—
290C2×C4×C59—22no—
291C2×C4×C59—22no—
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—44no—
300C2×C4×C59—44no—
301C2×C4×C59—44no—
302C2×C4×C59—44no—
303C2×C4×C59—44no—
304C2×C4×C59C2×#4114yes—
305C2×C4×C59C2×#4114yes—
306C2×Dic59—28no—
307C2×Dic59—28no—
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—22no—
318C2×Dic59—22no—
319C2×Dic59—22no—
320C2×Dic59—22no—
321C2×Dic59—22no—
322C2×Dic59—22no—
323C2×Dic59—22no—
324C2×Dic59—44no—
325C2×Dic59—44no—
326C2×Dic59—44no—
327C2×Dic59—44no—
328C2×Dic59C2×#4114yes—
329C2×Dic59C2×#4114yes—
330D236—416no—
331C4×D59—416no—
332C2×#2595—591nomaximal, Sylow
333C22×C59#52914yes—
334C22×C59#52914yes—
335C22×C59#53814yes—
336C22×C59#55114yes—
337C22×C59#55314yes—
338C22×C59#55314yes—
339C22×C59#55914yes—
340C22×C59C22×#4111yescharacteristic
341C22×C59C22×#4111yescharacteristic
342C22×C59C22×#4111yescharacteristic
343C22×C59C22×#4111yescharacteristic
344C22×C59C22×#4111yescharacteristic
345C22×C59C2×H(5,𝔽2)11yescharacteristic
346C22×C59C2×H(5,𝔽2)11yescharacteristic
347C2×D59—24no—
348C2×D59—24no—
349C2×D59—24no—
350C2×D59—416no—
351C2×D59—42no—
352C2×D59—42no—
353C2×D59—42no—
354C2×D59—42no—
355C2×D59—42no—
356C2×D59—42no—
357C2×D59—42no—
358C2×D59—42no—
359C2×D59—42no—
360C2×D59—42no—
361C2×D59—42no—
362C2×D59—88no—
363C4×C59—24no—
364C4×C59—24no—
365C4×C59—42no—
366C4×C59—42no—
367C4×C59—42no—
368C4×C59—42no—
369C4×C59—42no—
370Dic59—24no—
371Dic59—24no—
372Dic59—42no—
373Dic59—42no—
374Dic59—42no—
375Dic59—42no—
376#2595—5916no—
377C2×#400D5911yescharacteristic, complemented
378C2×#397—591no—
379C2×#397—591no—
380C2×#394—591no—
381C2×#390—591no—
382C2×#388—591no—
383C2×#388—591no—
384C2×#388—591no—
385C2×#388—591no—
386C2×#387—591no—
387C2×#387—591no—
388C2×#386—591no—
389C2×#385—591no—
390C2×C4×C4⋊C4—591no—
391C2×C4×C22⋊C4—591no—
392C2×C59#259518yescomplemented
393C2×C59C2×#52911yescharacteristic
394C2×C59C2×#52911yescharacteristic
395C2×C59C2×#53811yescharacteristic
396C2×C59C2×#55111yescharacteristic
397C2×C59C2×#55311yescharacteristic
398C2×C59C2×#55311yescharacteristic
399C2×C59C2×#55911yescharacteristic
400D59—44no—
401D59—82no—
402C23×D4—591no—
403C24×C4—591no—
404C22×C4⋊C4—591no—
405C22×C4⋊C4—591no—
406C22×C4⋊C4—591no—
407C22×C4⋊C4—591no—
408C22×C4⋊C4C2×D5911yescharacteristic
409C22×C4⋊C4C2×D5911yescharacteristic
410C22×C22⋊C4—591no—
411C22×C22⋊C4—591no—
412C22×C22⋊C4—591no—
413C22×C22⋊C4—591no—
414C22×C22⋊C4—591no—
415C22×C22⋊C4—591no—
416C22×C22⋊C4—591no—
417C22×C22⋊C4—591no—
418C22×C22⋊C4—591no—
419C22×C22⋊C4—591no—
420C22×C22⋊C4—591no—
421C22×C42—591no—
422C22×C42—591no—
423C22×C42—591no—
424C22×C42—591no—
425#400C2×D5918yescomplemented
426#397—598no—
427#397—598no—
428#394—598no—
429#390—598no—
430#388—598no—
431#388—598no—
432#388—598no—
433#388—598no—
434#387—598no—
435#387—598no—
436#386—598no—
437#385—598no—
438C4×C4⋊C4—598no—
439C4×C22⋊C4—598no—
440C2×#95—591no—
441C2×#95—591no—
442C2×#95—591no—
443C2×#95—591no—
444C2×#95—591no—
445C2×#95—591no—
446C2×#95—591no—
447C2×#95C2×D5911yescharacteristic
448C2×#95C2×D5911yescharacteristic
449C2×#95C2×D5911yescharacteristic
450C2×#95C2×D5911yescharacteristic
451C2×#95C2×D5911yescharacteristic
452C59C2×#259511yescharacteristic, complemented, Sylow
453C25—591no—
454C25—591no—
455C22×D4—594no—
456C22×D4—1184no—
457C22×D4—1184no—
458C22×D4—2362no—
459C23×C4—591no—
460C23×C4—591no—
461C23×C4—591no—
462C23×C4—591no—
463C23×C4—591no—
464C23×C4—591no—
465C23×C4—594no—
466C23×C4—1184no—
467C23×C4—2362no—
468C23×C4—2362no—
469C23×C4C22×D5911yescharacteristic
470C23×C4C22×D5911yescharacteristic
471C23×C4C22×D5911yescharacteristic
472C23×C4C22×D5911yescharacteristic
473C23×C4C22×D5911yescharacteristic
474C23×C4C22×D5911yescharacteristic
475C23×C4C22×D5911yescharacteristic
476C2×C4⋊C4—24no—
477C2×C4⋊C4—24no—
478C2×C4⋊C4—594no—
479C2×C4⋊C4—594no—
480C2×C4⋊C4—594no—
481C2×C4⋊C4—594no—
482C2×C4⋊C4—1184no—
483C2×C4⋊C4—1184no—
484C2×C4⋊C4—2362no—
485C2×C4⋊C4—2362no—
486C2×C4⋊C4C22×D5914yes—
487C2×C4⋊C4C22×D5914yes—
488C2×C22⋊C4—594no—
489C2×C22⋊C4—594no—
490C2×C22⋊C4—594no—
491C2×C22⋊C4—594no—
492C2×C22⋊C4—594no—
493C2×C22⋊C4—594no—
494C2×C22⋊C4—594no—
495C2×C22⋊C4—594no—
496C2×C22⋊C4—594no—
497C2×C22⋊C4—594no—
498C2×C22⋊C4—594no—
499C2×C22⋊C4—1184no—
500C2×C22⋊C4—1184no—
501C2×C22⋊C4—1184no—
502C2×C22⋊C4—1184no—
503C2×C22⋊C4—1184no—
504C2×C22⋊C4—1184no—
505C2×C22⋊C4—1184no—
506C2×C22⋊C4—2362no—
507C2×C22⋊C4—2362no—
508C2×C22⋊C4—2362no—
509C2×C22⋊C4—2362no—
510C2×C42—594no—
511C2×C42—594no—
512C2×C42—594no—
513C2×C42—594no—
514C2×C42—1184no—
515C2×C42—2362no—
516C2×C42—2362no—
517C2×C42—2362no—
518#95—594no—
519#95—594no—
520#95—594no—
521#95—594no—
522#95—594no—
523#95—594no—
524#95—594no—
525#95C22×D5914yes—
526#95C22×D5914yes—
527#95C22×D5914yes—
528#95C22×D5914yes—
529#95C22×D5914yes—
530C24—594no—
531C24—592no—
532C24—592no—
533C24—1182no—
534C24—1182no—
535C24—1182no—
536C24—1182no—
537C24—1182no—
538C24—1182no—
539C24—1182no—
540C24—1182no—
541C24—1182no—
542C24—1182no—
543C24—1182no—
544C24—1182no—
545C24—1182no—
546C24C23×D5911yescharacteristic
547C2×D4—1188no—
548C2×D4—1188no—
549C2×D4—2364no—
550C2×D4—23616no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—594no—
571C22×C4—594no—
572C22×C4—592no—
573C22×C4—592no—
574C22×C4—592no—
575C22×C4—592no—
576C22×C4—592no—
577C22×C4—592no—
578C22×C4—1188no—
579C22×C4—1182no—
580C22×C4—1182no—
581C22×C4—1182no—
582C22×C4—1182no—
583C22×C4—1182no—
584C22×C4—1182no—
585C22×C4—1182no—
586C22×C4—1182no—
587C22×C4—1182no—
588C22×C4—1182no—
589C22×C4—1182no—
590C22×C4—1182no—
591C22×C4—1182no—
592C22×C4—1182no—
593C22×C4—1182no—
594C22×C4—1182no—
595C22×C4—2364no—
596C22×C4—2364no—
597C22×C4—23616no—
598C22×C4#1174568714yes—
599C22×C4#1174568914yes—
600C22×C4C23×D5912yes—
601C22×C4C23×D5912yes—
602C22×C4C23×D5912yes—
603C22×C4C23×D5912yes—
604C22×C4C23×D5912yes—
605C22×C4C23×D5912yes—
606C22×C4C23×D5912yes—
607C4⋊C4—28no—
608C4⋊C4—28no—
609C4⋊C4—1188no—
610C4⋊C4—1188no—
611C4⋊C4—2364no—
612C4⋊C4—2364no—
613C22⋊C4—1188no—
614C22⋊C4—1188no—
615C22⋊C4—1188no—
616C22⋊C4—1188no—
617C22⋊C4—1188no—
618C22⋊C4—1188no—
619C22⋊C4—1188no—
620C22⋊C4—2364no—
621C22⋊C4—2364no—
622C22⋊C4—2364no—
623C22⋊C4—2364no—
624C42—1188no—
625C42—2364no—
626C42—2364no—
627C42—2364no—
628C23—594no—
629C23—1188no—
630C23—1182no—
631C23—1182no—
632C23—1182no—
633C23—1182no—
634C23—1182no—
635C23—1182no—
636C23—1188no—
637C23—1188no—
638C23—1182no—
639C23—1182no—
640C23—1182no—
641C23—1182no—
642C23—1182no—
643C23—1182no—
644C23—1182no—
645C23—2364no—
646C23—2364no—
647C23—2364no—
648C23—2364no—
649C23—2364no—
650C23—2364no—
651C23—2364no—
652C23—2364no—
653C23—2364no—
654C23—2364no—
655C23—2364no—
656C23#41×D5912yes—
657C23#41×D5912yes—
658C23#41×D5912yes—
659C23C2×#1174568712yes—
660C23C2×#1174568912yes—
661C23#1427377312yes—
662C23#1427377312yes—
663C23C24×D5911yescharacteristic
664D4—23616no—
665C2×C4—28no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—28no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—44no—
687C2×C4—44no—
688C2×C4—44no—
689C2×C4—44no—
690C2×C4—44no—
691C2×C4—594no—
692C2×C4—594no—
693C2×C4—1182no—
694C2×C4—1182no—
695C2×C4—1182no—
696C2×C4—1182no—
697C2×C4—1188no—
698C2×C4—1188no—
699C2×C4—1182no—
700C2×C4—1182no—
701C2×C4—1182no—
702C2×C4—1182no—
703C2×C4—1182no—
704C2×C4—1182no—
705C2×C4—1182no—
706C2×C4—1182no—
707C2×C4—1182no—
708C2×C4—1182no—
709C2×C4—1182no—
710C2×C4—1182no—
711C2×C4—23616no—
712C2×C4—2364no—
713C2×C4—2364no—
714C2×C4—2364no—
715C2×C4—2364no—
716C2×C4C2×#1174568714yes—
717C2×C4C2×#1174568914yes—
718C22—1184no—
719C22—1184no—
720C22—1184no—
721C22—4728no—
722C22—2362no—
723C22—2362no—
724C22—2362no—
725C22—2362no—
726C22—2362no—
727C22—2362no—
728C22—2362no—
729C22—23616no—
730C22—2362no—
731C22—2362no—
732C22—2362no—
733C22—2362no—
734C22#1683793514yes—
735C22#1683793814yes—
736C22#1683799114yes—
737C22#1683807514yes—
738C22#1683810514yes—
739C22#1683810514yes—
740C22#1683813414yes—
741C22C2×#41×D5911yescharacteristic
742C22C2×#41×D5911yescharacteristic
743C22C2×#41×D5911yescharacteristic
744C22C22×#1174568711yescharacteristic
745C22C22×#1174568911yescharacteristic
746C22C2×#1427377311yescharacteristic
747C22C2×#1427377311yescharacteristic
748C4—24no—
749C4—24no—
750C4—42no—
751C4—42no—
752C4—42no—
753C4—42no—
754C4—42no—
755C4—1184no—
756C4—1184no—
757C4—2362no—
758C4—2362no—
759C4—2362no—
760C4—2362no—
761C2—4722no—
762C2—2364no—
763C2#2142961018yesdirect product factor
764C2C2×#1683793511yescharacteristic
765C2C2×#1683793811yescharacteristic
766C2C2×#1683799111yescharacteristic
767C2C2×#1683807511yescharacteristic
768C2C2×#1683810511yescharacteristic
769C2C2×#1683810511yescharacteristic
770C2C2×#1683813411yescharacteristic
subgroupG/H
centerC24C23×D59
commutator, cosocleC23×C59C25
FrattiniC23C24×D59
FittingC2×C59×#400C2
socleC24×C59C24
prime radicalC23×D236C22
hypercenterC2×#400D59
hypocenterC59C2×#2595
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C24 ◁ C2×#400

Complements

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

NH ≅ G/Ntype
1. #21429610C2direct (N × H)
2. C2×#16837331C2semidirect
3. C2×#16837329C2semidirect
6. C2×#16837294C2semidirect
7. C2×#16837294C2semidirect
8. C2×#16837294C2semidirect
9. C2×#16837294C2semidirect
10. C2×#16837288C2semidirect
11. C2×#16837285C2semidirect
13. C2×#16837276C2semidirect
14. C2×C4⋊C4×Dic59C2semidirect
15. C2×#16837249C2semidirect
16. C2×C59×#400C2semidirect
38. #16837331C22semidirect
39. #16837329C22semidirect
42. #16837294C22semidirect
43. #16837294C22semidirect
44. #16837294C22semidirect
45. #16837294C22semidirect
46. #16837288C22semidirect
47. #16837285C22semidirect
49. #16837276C22semidirect
50. C4⋊C4×Dic59C22semidirect
51. #16837249C22semidirect
61. C59×#400C22semidirect
377. C2×#400D59semidirect
392. C2×C59#2595semidirect
425. #400C2×D59semidirect
452. C59C2×#2595semidirect
763. C2#21429610direct (N × H)

Maximal subgroups

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

subgroupindex
#214296102
C2×#168373312
C2×#168373292
C2×#168373192
C2×#168373032
C2×#168372942
C2×#168372882
C2×#168372852
C2×#168372802
C2×#168372762
C2×C4⋊C4×Dic592
C2×#168372492
C2×C59×#4002
C2×#259559