Finite Group Databasebeta

← C2×#21432241 #28795072

Subgroups — C2×#21432241 #28795072

Order 15104.

2174 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#21432241C2116yesmaximal, direct product factor
2C2×#16837334C211yesmaximal, characteristic, complemented
3C2×#16837331C211yesmaximal, characteristic, complemented
4C2×#16837331C211yesmaximal, characteristic, complemented
5C2×#16837330C211yesmaximal, characteristic, complemented
6C2×#16837325C211yesmaximal, characteristic, complemented
7C2×#16837324C211yesmaximal, characteristic, complemented
8C2×#16837322C211yesmaximal, characteristic, complemented
9C2×#16837318C211yesmaximal, characteristic
10C2×#16837318C211yesmaximal, characteristic
11C2×#16837315C211yesmaximal, characteristic, complemented
12C2×#16837314C211yesmaximal, characteristic, complemented
13C2×#16837302C211yesmaximal, characteristic
14C2×#16837287C211yesmaximal, characteristic, complemented
15C2×#16837285C211yesmaximal, characteristic, complemented
16C2×C59×#397C211yesmaximal, characteristic, complemented
17C23×Dic118C2211yescharacteristic
18C23×C22⋊D59C2211yescharacteristic
19C22×C4⋊Dic59C2211yescharacteristic
20C22×C4⋊Dic59C2211yescharacteristic
21C22×C4⋊Dic59C2211yescharacteristic
22C22×Dic59⋊C4C2211yescharacteristic
23C22×Dic59⋊C4C2211yescharacteristic
24C22×Dic59⋊C4C2211yescharacteristic
25C22×Dic59⋊C4C2211yescharacteristic
26C22×C22⋊Dic59C2211yescharacteristic
27C22×C22⋊Dic59C2211yescharacteristic
28C22×C22⋊Dic59C2211yescharacteristic
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×C4×Dic59C2211yescharacteristic
36#16837334C2218yescomplemented
37#16837331C2218yescomplemented
38#16837331C2218yescomplemented
39#16837330C2218yescomplemented
40#16837325C2218yescomplemented
41#16837324C2218yescomplemented
42#16837322C2218yescomplemented
43#16837318C2218yes—
44#16837318C2218yes—
45#16837315C2218yescomplemented
46#16837314C2218yescomplemented
47#16837302C2218yes—
48#16837287C2218yescomplemented
49#16837285C2218yescomplemented
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
59C22×C4⋊C4×C59C2211yescharacteristic
60C22×C22⋊C4×C59C2211yescharacteristic
61C22×C22⋊C4×C59C2211yescharacteristic
62C22×C22⋊C4×C59C2211yescharacteristic
63C59×#397C2218yescomplemented
64C2×#95×C59C2211yescharacteristic
65C2×#95×C59C2211yescharacteristic
66C2×#95×C59C2211yescharacteristic
67C24×D59C2311yescharacteristic
68C22×Dic118—42no—
69C22×Dic118—42no—
70C22×Dic118—42no—
71C22×Dic118C2314yes—
72C22×C22⋊D59—24no—
73C22×C22⋊D59—42no—
74C22×C22⋊D59—42no—
75C22×C22⋊D59C2314yes—
76C23×Dic59C2311yescharacteristic
77C23×Dic59C2311yescharacteristic
78C23×Dic59C2311yescharacteristic
79C23×Dic59C2311yescharacteristic
80C23×Dic59C2311yescharacteristic
81C23×Dic59C2311yescharacteristic
82C23×Dic59C2311yescharacteristic
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⋊C4—42no—
91C2×Dic59⋊C4—42no—
92C2×Dic59⋊C4—42no—
93C2×Dic59⋊C4C2314yes—
94C2×Dic59⋊C4C2314yes—
95C2×Dic59⋊C4C2314yes—
96C2×Dic59⋊C4C2314yes—
97C2×C22⋊Dic59—42no—
98C2×C22⋊Dic59—42no—
99C2×C22⋊Dic59—42no—
100C2×C22⋊Dic59C2314yes—
101C2×C22⋊Dic59C2314yes—
102C2×C22⋊Dic59C2314yes—
103C2×(C2×D59)⋊C4—42no—
104C2×(C2×D59)⋊C4—42no—
105C2×(C2×D59)⋊C4—42no—
106C2×(C2×D59)⋊C4—42no—
107C2×(C2×D59)⋊C4—42no—
108C2×(C2×D59)⋊C4—42no—
109C2×(C2×D59)⋊C4C2314yes—
110C2×(C2×D59)⋊C4C2314yes—
111C2×(C2×D59)⋊C4C2314yes—
112C2×(C2×D59)⋊C4C2314yes—
113C2×(C2×D59)⋊C4C2314yes—
114C2×(C2×D59)⋊C4C2314yes—
115C2×C4×Dic59—42no—
116C2×C4×Dic59C2314yes—
117C59⋊#95C2314yes—
118C59⋊#95C2314yes—
119C59⋊#95C2314yes—
120C59⋊#95C2314yes—
121C59⋊#95C2314yes—
122C59⋊#95C2314yes—
123C59⋊#95C2314yes—
124C59⋊#95C2314yes—
125C59⋊#95C2314yes—
126C25×C59C2311yescharacteristic
127C23×C4×C59C2311yescharacteristic
128C23×C4×C59C2311yescharacteristic
129C23×C4×C59C2311yescharacteristic
130C23×C4×C59C2311yescharacteristic
131C23×C4×C59C2311yescharacteristic
132C23×C4×C59C2311yescharacteristic
133C2×C4⋊C4×C59—42no—
134C2×C4⋊C4×C59C2314yes—
135C2×C22⋊C4×C59—42no—
136C2×C22⋊C4×C59—42no—
137C2×C22⋊C4×C59—42no—
138C2×C22⋊C4×C59C2314yes—
139C2×C22⋊C4×C59C2314yes—
140C2×C22⋊C4×C59C2314yes—
141#95×C59C2314yes—
142#95×C59C2314yes—
143#95×C59C2314yes—
144C24×C59—22no—
145C24×C59—22no—
146C24×C59—22no—
147C24×C59—22no—
148C24×C59—22no—
149C24×C59—22no—
150C24×C59—22no—
151C24×C59C2412yes—
152C24×C59C2411yescharacteristic
153C23×D59—22no—
154C23×D59—22no—
155C23×D59—22no—
156C23×D59—22no—
157C23×D59—22no—
158C23×D59—22no—
159C23×D59—22no—
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×C59C2412yes—
180C22×C4×C59C2412yes—
181C22×C4×C59C2412yes—
182C22×C4×C59C2412yes—
183C22×C4×C59C2412yes—
184C22×C4×C59C2412yes—
185C2×C22⋊D59—28no—
186C2×C22⋊D59—44no—
187C2×C22⋊D59—44no—
188C2×C22⋊D59—416no—
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—22no—
206C22×Dic59—22no—
207C22×Dic59—22no—
208C22×Dic59—22no—
209C22×Dic59#4114yes—
210C22×Dic59C2412yes—
211C22×Dic59C2412yes—
212C22×Dic59C2412yes—
213C22×Dic59C2412yes—
214C22×Dic59C2412yes—
215C22×Dic59C2412yes—
216C22×Dic59C2412yes—
217C2×Dic118—44no—
218C2×Dic118—44no—
219C2×Dic118—44no—
220C2×Dic118—416no—
221C4⋊C4×C59—44no—
222C22⋊C4×C59—44no—
223C22⋊C4×C59—44no—
224C22⋊C4×C59—44no—
225C22⋊Dic59—44no—
226C22⋊Dic59—44no—
227C22⋊Dic59—44no—
228(C2×D59)⋊C4—44no—
229(C2×D59)⋊C4—44no—
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—
238Dic59⋊C4—44no—
239Dic59⋊C4—44no—
240Dic59⋊C4—44no—
241C4×Dic59—44no—
242C23×C59—22no—
243C23×C59—22no—
244C23×C59—22no—
245C23×C59—22no—
246C23×C59—22no—
247C23×C59—22no—
248C23×C59—22no—
249C23×C59—44no—
250C23×C59—44no—
251C23×C59—44no—
252C23×C59—44no—
253C23×C59—44no—
254C23×C59—44no—
255C23×C59—44no—
256C23×C59C2×#4112yes—
257C23×C59H(5,𝔽2)12yes—
258C23×C59H(5,𝔽2)12yes—
259C23×C59H(5,𝔽2)12yes—
260C23×C59H(5,𝔽2)12yes—
261C23×C592−1+412yes—
262C23×C592−1+412yes—
263C23×C59C2511yescharacteristic
264C22×D59—22no—
265C22×D59—22no—
266C22×D59—22no—
267C22×D59—22no—
268C22×D59—22no—
269C22×D59—22no—
270C22×D59—22no—
271C22×D59—44no—
272C22×D59—44no—
273C22×D59—44no—
274C22×D59—44no—
275C22×D59—44no—
276C22×D59—44no—
277C22×D59—44no—
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—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—44no—
297C2×C4×C59—44no—
298C2×C4×C59—44no—
299C2×C4×C59—44no—
300C2×C4×C59—44no—
301C2×C4×C59—44no—
302C22⋊D59—416no—
303C2×Dic59—28no—
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—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×Dic59—44no—
329C2×Dic59—44no—
330C2×Dic59C2×#4114yes—
331Dic118—416no—
332C2×#2830—591nomaximal, Sylow
333C22×C59—42no—
334C22×C59—42no—
335C22×C59—42no—
336C22×C59—42no—
337C22×C59—42no—
338C22×C59—42no—
339C22×C59—42no—
340C22×C59—88no—
341C22×C59#53814yes—
342C22×C59#54214yes—
343C22×C59#54214yes—
344C22×C59#56014yes—
345C22×C59#56214yes—
346C22×C59#56214yes—
347C22×C59#56314yes—
348C22×C59C22×#4111yescharacteristic
349C22×C59C2×H(5,𝔽2)11yescharacteristic
350C22×C59C2×H(5,𝔽2)11yescharacteristic
351C22×C59C2×H(5,𝔽2)11yescharacteristic
352C22×C59C2×H(5,𝔽2)11yescharacteristic
353C22×C59C2×2−1+411yescharacteristic
354C22×C59C2×2−1+411yescharacteristic
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—42no—
364C4×C59—42no—
365C4×C59—42no—
366C4×C59—42no—
367C4×C59—42no—
368C4×C59—42no—
369Dic59—24no—
370Dic59—42no—
371Dic59—42no—
372Dic59—42no—
373Dic59—42no—
374Dic59—42no—
375Dic59—42no—
376#2830—5916no—
377C2×#398—591no—
378C2×#397—591no—
379C2×#397—591no—
380C2×#397—591no—
381C2×#397D5911yescharacteristic, complemented
382C2×#396—591no—
383C2×#396—591no—
384C2×#395—591no—
385C2×#394—591no—
386C2×#394—591no—
387C2×#393—591no—
388C2×#393—591no—
389C2×#390—591no—
390C2×#387—591no—
391C2×#387—591no—
392C2×C59—82no—
393C2×C59#283018yescomplemented
394C2×C59C2×#53811yescharacteristic
395C2×C59C2×#54211yescharacteristic
396C2×C59C2×#54211yescharacteristic
397C2×C59C2×#56011yescharacteristic
398C2×C59C2×#56211yescharacteristic
399C2×C59C2×#56211yescharacteristic
400C2×C59C2×#56311yescharacteristic
401D59—82no—
402C23×Q8—591no—
403C23×D4—591no—
404C22×C4⋊C4—591no—
405C22×C4⋊C4—591no—
406C22×C4⋊C4—591no—
407C22×C4⋊C4—591no—
408C22×C4⋊C4—591no—
409C22×C4⋊C4—591no—
410C22×C4⋊C4—591no—
411C22×C4⋊C4C2×D5911yescharacteristic
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×C22⋊C4C2×D5911yescharacteristic
422C22×C22⋊C4C2×D5911yescharacteristic
423C22×C22⋊C4C2×D5911yescharacteristic
424C22×C42—591no—
425#398—598no—
426#397—598no—
427#397—598no—
428#397—598no—
429#397C2×D5918yescomplemented
430#396—598no—
431#396—598no—
432#395—598no—
433#394—598no—
434#394—598no—
435#393—598no—
436#393—598no—
437#390—598no—
438#387—598no—
439#387—598no—
440C2×#95—591no—
441C2×#95—591no—
442C2×#95—591no—
443C2×#95—591no—
444C2×#95—591no—
445C2×#95—591no—
446C2×#95—591no—
447C2×#95—591no—
448C2×#95—591no—
449C2×#95C2×D5911yescharacteristic
450C2×#95C2×D5911yescharacteristic
451C2×#95C2×D5911yescharacteristic
452C59C2×#283011yescharacteristic, complemented, Sylow
453C25—591no—
454C25C22×D5911yescharacteristic
455C22×Q8—594no—
456C22×Q8—2362no—
457C22×Q8—2362no—
458C22×Q8—2362no—
459C22×D4—594no—
460C22×D4—1184no—
461C22×D4—2362no—
462C22×D4—2362no—
463C23×C4—591no—
464C23×C4—591no—
465C23×C4—591no—
466C23×C4—591no—
467C23×C4—591no—
468C23×C4—591no—
469C23×C4—591no—
470C23×C4C22×D5911yescharacteristic
471C23×C4C22×D5911yescharacteristic
472C23×C4C22×D5911yescharacteristic
473C23×C4C22×D5911yescharacteristic
474C23×C4C22×D5911yescharacteristic
475C23×C4C22×D5911yescharacteristic
476C2×C4⋊C4—42no—
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—1184no—
485C2×C4⋊C4—1184no—
486C2×C4⋊C4—2362no—
487C2×C4⋊C4—2362no—
488C2×C4⋊C4—2362no—
489C2×C4⋊C4—2362no—
490C2×C4⋊C4—2362no—
491C2×C4⋊C4C22×D5914yes—
492C2×C22⋊C4—42no—
493C2×C22⋊C4—42no—
494C2×C22⋊C4—42no—
495C2×C22⋊C4—594no—
496C2×C22⋊C4—594no—
497C2×C22⋊C4—594no—
498C2×C22⋊C4—594no—
499C2×C22⋊C4—594no—
500C2×C22⋊C4—594no—
501C2×C22⋊C4—594no—
502C2×C22⋊C4—594no—
503C2×C22⋊C4—594no—
504C2×C22⋊C4—2362no—
505C2×C22⋊C4—2362no—
506C2×C22⋊C4—2362no—
507C2×C22⋊C4—2362no—
508C2×C22⋊C4—2362no—
509C2×C22⋊C4—2362no—
510C2×C22⋊C4—2362no—
511C2×C22⋊C4—2362no—
512C2×C22⋊C4—2362no—
513C2×C22⋊C4C22×D5914yes—
514C2×C22⋊C4C22×D5914yes—
515C2×C22⋊C4C22×D5914yes—
516C2×C42—594no—
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#95—594no—
526#95—594no—
527#95C22×D5914yes—
528#95C22×D5914yes—
529#95C22×D5914yes—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—22no—
534C24—22no—
535C24—22no—
536C24—22no—
537C24—592no—
538C24—1182no—
539C24—1182no—
540C24—1182no—
541C24—1182no—
542C24—1182no—
543C24—1182no—
544C24—1182no—
545C24C23×D5912yes—
546C24C23×D5911yescharacteristic
547C2×Q8—2364no—
548C2×Q8—2364no—
549C2×Q8—2364no—
550C2×Q8—23616no—
551C2×D4—1188no—
552C2×D4—2364no—
553C2×D4—2364no—
554C2×D4—23616no—
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—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—594no—
574C22×C4—592no—
575C22×C4—592no—
576C22×C4—592no—
577C22×C4—592no—
578C22×C4—592no—
579C22×C4—592no—
580C22×C4—592no—
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—1182no—
596C22×C4—1182no—
597C22×C4—1182no—
598C22×C4—1182no—
599C22×C4—1182no—
600C22×C4—1182no—
601C22×C4C23×D5912yes—
602C22×C4C23×D5912yes—
603C22×C4C23×D5912yes—
604C22×C4C23×D5912yes—
605C22×C4C23×D5912yes—
606C22×C4C23×D5912yes—
607C4⋊C4—44no—
608C4⋊C4—1188no—
609C4⋊C4—1188no—
610C4⋊C4—2364no—
611C4⋊C4—2364no—
612C4⋊C4—2364no—
613C4⋊C4—2364no—
614C4⋊C4—2364no—
615C22⋊C4—44no—
616C22⋊C4—44no—
617C22⋊C4—44no—
618C22⋊C4—2364no—
619C22⋊C4—2364no—
620C22⋊C4—2364no—
621C22⋊C4—2364no—
622C22⋊C4—2364no—
623C22⋊C4—2364no—
624C22⋊C4—2364no—
625C22⋊C4—2364no—
626C22⋊C4—2364no—
627C42—2364no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—44no—
636C23—44no—
637C23—44no—
638C23—44no—
639C23—44no—
640C23—44no—
641C23—44no—
642C23—1182no—
643C23—1182no—
644C23—1182no—
645C23—1182no—
646C23—1182no—
647C23—1182no—
648C23—1182no—
649C23—2364no—
650C23—2364no—
651C23—2364no—
652C23—2364no—
653C23—2364no—
654C23—2364no—
655C23—2364no—
656C23#41×D5912yes—
657C23#1427377212yes—
658C23#1427377212yes—
659C23#1427377312yes—
660C23#1427377312yes—
661C23#1427377412yes—
662C23#1427377412yes—
663C23C24×D5911yescharacteristic
664Q8—23616no—
665D4—23616no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
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—44no—
685C2×C4—44no—
686C2×C4—44no—
687C2×C4—44no—
688C2×C4—44no—
689C2×C4—44no—
690C2×C4—594no—
691C2×C4—1182no—
692C2×C4—1182no—
693C2×C4—1188no—
694C2×C4—1182no—
695C2×C4—1182no—
696C2×C4—1182no—
697C2×C4—1182no—
698C2×C4—1182no—
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—1182no—
712C2×C4—2364no—
713C2×C4—2364no—
714C2×C4—2364no—
715C2×C4—2364no—
716C2×C4—2364no—
717C2×C4—2364no—
718C22—42no—
719C22—42no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—88no—
726C22—4728no—
727C22—2362no—
728C22—2362no—
729C22—2362no—
730C22—2362no—
731C22—2362no—
732C22—2362no—
733C22—2362no—
734C22#1683799114yes—
735C22#1683801614yes—
736C22#1683802014yes—
737C22#1683814014yes—
738C22#1683814914yes—
739C22#1683814914yes—
740C22#1683815414yes—
741C22C2×#41×D5911yescharacteristic
742C22C2×#1427377211yescharacteristic
743C22C2×#1427377211yescharacteristic
744C22C2×#1427377311yescharacteristic
745C22C2×#1427377311yescharacteristic
746C22C2×#1427377411yescharacteristic
747C22C2×#1427377411yescharacteristic
748C4—42no—
749C4—42no—
750C4—42no—
751C4—42no—
752C4—42no—
753C4—42no—
754C4—1184no—
755C4—2362no—
756C4—2362no—
757C4—2362no—
758C4—2362no—
759C4—2362no—
760C4—2362no—
761C2—82no—
762C2—4722no—
763C2#2143224118yesdirect product factor
764C2C2×#1683799111yescharacteristic
765C2C2×#1683801611yescharacteristic
766C2C2×#1683802011yescharacteristic
767C2C2×#1683814011yescharacteristic
768C2C2×#1683814911yescharacteristic
769C2C2×#1683814911yescharacteristic
770C2C2×#1683815411yescharacteristic
subgroupG/H
centerC24C23×D59
commutator, cosocleC23×C59C25
FrattiniC23C24×D59
FittingC2×C59×#397C2
socleC24×C59C24
prime radicalC23×C22⋊D59C22
hypercenterC2×#397D59
hypocenterC59C2×#2830
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C24 ◁ C2×#397

Complements

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

NH ≅ G/Ntype
1. #21432241C2direct (N × H)
2. C2×#16837334C2semidirect
3. C2×#16837331C2semidirect
4. C2×#16837331C2semidirect
5. C2×#16837330C2semidirect
6. C2×#16837325C2semidirect
7. C2×#16837324C2semidirect
8. C2×#16837322C2semidirect
11. C2×#16837315C2semidirect
12. C2×#16837314C2semidirect
14. C2×#16837287C2semidirect
15. C2×#16837285C2semidirect
16. C2×C59×#397C2semidirect
36. #16837334C22semidirect
37. #16837331C22semidirect
38. #16837331C22semidirect
39. #16837330C22semidirect
40. #16837325C22semidirect
41. #16837324C22semidirect
42. #16837322C22semidirect
45. #16837315C22semidirect
46. #16837314C22semidirect
48. #16837287C22semidirect
49. #16837285C22semidirect
63. C59×#397C22semidirect
381. C2×#397D59semidirect
393. C2×C59#2830semidirect
429. #397C2×D59semidirect
452. C59C2×#2830semidirect
763. C2#21432241direct (N × H)

Maximal subgroups

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

subgroupindex
#214322412
C2×#168373342
C2×#168373312
C2×#168373302
C2×#168373252
C2×#168373242
C2×#168373222
C2×#168373182
C2×#168373152
C2×#168373142
C2×#168373022
C2×#168372872
C2×#168372852
C2×C59×#3972
C2×#283059