Finite Group Databasebeta

← C2×#21436268 #29465312

Subgroups — C2×#21436268 #29465312

Order 15104.

2158 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
1C2×#16838096C211yesmaximal, characteristic
2C2×Q8×C22⋊D59C211yesmaximal, characteristic, complemented
3#21436268C2116yesmaximal, direct product factor
4C2×#16837769C211yesmaximal, characteristic, complemented
5C2×#16837736C211yesmaximal, characteristic, complemented
6C2×#16837743C211yesmaximal, characteristic, complemented
7C2×#16837711C211yesmaximal, characteristic, complemented
8C2×#16837648C211yesmaximal, characteristic, complemented
9C2×#16837634C211yesmaximal, characteristic, complemented
10C2×#16837606C211yesmaximal, characteristic, complemented
11C2×#16837542C211yesmaximal, characteristic, complemented
12C2×#16837541C211yesmaximal, characteristic, complemented
13C2×#16837505C211yesmaximal, characteristic, complemented
14C2×#16837471C211yesmaximal, characteristic, complemented
15C2×#103×D59C211yesmaximal, characteristic, complemented
16C2×C59×#419C211yesmaximal, characteristic, complemented
17C22×Q8×D59C2211yescharacteristic
18C22×#11745660C2211yescharacteristic
19C22×#11745671C2211yescharacteristic
20C22×#11745671C2211yescharacteristic
21C22×C8×D59C2211yescharacteristic
22#16838096—24no—
23#16838096C2218yes—
24Q8×C22⋊D59—24no—
25Q8×C22⋊D59C2218yescomplemented
26C2×#14273725—21no—
27C2×#14273725C2211yescharacteristic
28C2×#14273721—21no—
29C2×#14273718C2211yescharacteristic
30C2×#14273709—21no—
31C2×#14273706—21no—
32C2×#14273706C2211yescharacteristic
33C2×#14273703—21no—
34C2×#14273703C2211yescharacteristic
35C2×#14273702C2211yescharacteristic
36C2×#14273701C2211yescharacteristic
37C2×#14273700—21no—
38C2×Q8×Dic59C2211yescharacteristic
39C2×C4×D236—21no—
40C2×#14273689C2211yescharacteristic
41C2×C4×C22⋊D59—21no—
42C2×C4×C22⋊D59C2211yescharacteristic
43C2×C4⋊C4×D59C2211yescharacteristic
44#16837769C2218yescomplemented
45#16837743C2218yescomplemented
46#16837736C2218yescomplemented
47#16837711C2218yescomplemented
48#16837648C2218yescomplemented
49#16837634C2218yescomplemented
50#16837606C2218yescomplemented
51#16837542C2218yescomplemented
52#16837541C2218yescomplemented
53#16837505C2218yescomplemented
54#16837471C2218yescomplemented
55C2×#14273661C2211yescharacteristic
56C2×#14273660C2211yescharacteristic
57C2×#14273658C2211yescharacteristic
58C2×Dic59⋊C8C2211yescharacteristic
59C2×#14273652C2211yescharacteristic
60C2×#14273651C2211yescharacteristic
61C2×#14273651C2211yescharacteristic
62C2×#14273650C2211yescharacteristic
63C2×#14273650C2211yescharacteristic
64#103×D59C2218yescomplemented
65C2×#14273649C2211yescharacteristic
66C2×C22⋊(C59⋊C8)C2211yescharacteristic
67C2×(C2×D59)⋊C8C2211yescharacteristic
68C2×#14273637C2211yescharacteristic
69C23×Q8×C59C2211yescharacteristic
70C22×M16×C59C2211yescharacteristic
71C2×#117×C59C2211yescharacteristic
72C59×#419C2218yescomplemented
73C2×#103×C59C2211yescharacteristic
74C2×#103×C59C2211yescharacteristic
75C2×#103×C59C2211yescharacteristic
76C2×#103×C59C2211yescharacteristic
77C22×Dic118—21no—
78C22×Dic118C2311yescharacteristic
79C2×Q8×D59—22no—
80C2×Q8×D59—24no—
81C2×Q8×D59—42no—
82C2×Q8×D59C2314yes—
83C22×D236—21no—
84C22×D236C2311yescharacteristic
85C22×C22⋊D59—21no—
86C22×C22⋊D59D411yescharacteristic
87C22×C4×D59—21no—
88C22×C4×D59—21no—
89C22×C4×D59—21no—
90C22×C4×D59C2311yescharacteristic
91C2×#11745660—42no—
92C2×#11745660C2314yes—
93C2×#11745671—24no—
94C2×#11745671—42no—
95C2×#11745671C2314yes—
96C2×#11745671C2314yes—
97C22×C59⋊C8C2311yescharacteristic
98C22×C59⋊C8C2311yescharacteristic
99C2×C8×D59—42no—
100C2×C8×D59C2314yes—
101#14273725—28no—
102#14273725—22no—
103#14273725C2314yes—
104#14273721—28no—
105#14273718—22no—
106#14273718C2314yes—
107#14273709—28no—
108#14273706—22no—
109#14273706—28no—
110#14273706C2314yes—
111#14273703—22no—
112#14273703—28no—
113#14273703C2314yes—
114#14273702—22no—
115#14273702C2314yes—
116#14273701—22no—
117#14273701C2314yes—
118#14273700—28no—
119Q8×Dic59—22no—
120Q8×Dic59C2314yes—
121C4×D236—28no—
122#14273689—22no—
123#14273689C2314yes—
124C4×C22⋊D59—28no—
125C4×C22⋊D59D414yes—
126C4×C22⋊D59C2314yes—
127C2×C4⋊Dic59—21no—
128C2×C4⋊Dic59—21no—
129C2×C4⋊Dic59C2311yescharacteristic
130C2×C4⋊Dic59C2311yescharacteristic
131C2×Dic59⋊C4—21no—
132C2×Dic59⋊C4—21no—
133C2×Dic59⋊C4—21no—
134C2×Dic59⋊C4—21no—
135C2×Dic59⋊C4—21no—
136C2×Dic59⋊C4—21no—
137C2×Dic59⋊C4D411yescharacteristic
138C4⋊C4×D59—22no—
139C4⋊C4×D59C2314yes—
140C2×C22⋊Dic59—21no—
141C2×C22⋊Dic59D411yescharacteristic
142C2×(C2×D59)⋊C4—21no—
143C2×(C2×D59)⋊C4—21no—
144C2×(C2×D59)⋊C4—21no—
145C2×(C2×D59)⋊C4—21no—
146C2×(C2×D59)⋊C4D411yescharacteristic
147C2×C4×Dic59—21no—
148C2×C4×Dic59C2311yescharacteristic
149#14273661C2314yes—
150#14273660C2314yes—
151#14273658C2314yes—
152Dic59⋊C8C2314yes—
153#14273652C2314yes—
154#14273651C2314yes—
155#14273651C2314yes—
156#14273650C2314yes—
157#14273650C2314yes—
158#14273649C2314yes—
159C22⋊(C59⋊C8)C2314yes—
160(C2×D59)⋊C8C2314yes—
161#14273637C2314yes—
162C22×Q8×C59—21no—
163C22×Q8×C59—22no—
164C22×Q8×C59—24no—
165C22×Q8×C59—42no—
166C22×Q8×C59C2311yescharacteristic
167C22×Q8×C59C2314yes—
168C22×Q8×C59C2311yescharacteristic
169C23×C4×C59—21no—
170C23×C4×C59C2311yescharacteristic
171C2×M16×C59—42no—
172C2×M16×C59C2314yes—
173C22×C8×C59C2311yescharacteristic
174C22×C8×C59C2311yescharacteristic
175#117×C59—22no—
176#117×C59C2314yes—
177C2×C4⋊C4×C59C2311yescharacteristic
178C2×C4⋊C4×C59C2311yescharacteristic
179C2×C22⋊C4×C59—21no—
180C2×C42×C59—21no—
181#103×C59C2314yes—
182#103×C59C2314yes—
183#103×C59C2314yes—
184#103×C59C2314yes—
185C24×C59C2×D411yescharacteristic
186C23×D59—21no—
187C23×D59C2×D411yescharacteristic
188C2×Q8×C59—21no—
189C2×Q8×C59—24no—
190C2×Q8×C59—21no—
191C2×Q8×C59—22no—
192C2×Q8×C59—28no—
193C2×Q8×C59—22no—
194C2×Q8×C59—22no—
195C2×Q8×C59—44no—
196C2×Q8×C59—44no—
197C2×Q8×C59—48no—
198C2×Q8×C59#4114yes—
199C2×Q8×C59C2412yes—
200C2×Q8×C59C2412yes—
201C22×C4×C59—21no—
202C22×C4×C59—22no—
203C22×C4×C59—22no—
204C22×C4×C59—21no—
205C22×C4×C59—21no—
206C22×C4×C59—21no—
207C22×C4×C59—24no—
208C22×C4×C59—44no—
209C22×C4×C59C2×D411yescharacteristic
210C22×C4×C59C2×D412yes—
211C22×C4×C59C2412yes—
212C22×C4×C59C2411yescharacteristic
213C2×C22⋊D59—24no—
214C2×C22⋊D59—24no—
215C2×C22⋊D59—82no—
216C2×C22⋊D59C2×D414yes—
217C22×Dic59—21no—
218C22×Dic59—21no—
219C22×Dic59—21no—
220C22×Dic59C2×D411yescharacteristic
221C22×Dic59C2×D411yescharacteristic
222C22×Dic59C2×D411yescharacteristic
223Q8×D59—28no—
224Q8×D59—44no—
225Q8×D59—48no—
226C2×D236—22no—
227C2×D236—22no—
228C2×D236—24no—
229C2×D236—21no—
230C2×D236—44no—
231C2×D236C2412yes—
232C2×C4×D59—22no—
233C2×C4×D59—22no—
234C2×C4×D59—24no—
235C2×C4×D59—24no—
236C2×C4×D59—24no—
237C2×C4×D59—44no—
238C2×C4×D59—82no—
239C2×C4×D59—82no—
240C2×C4×D59C2×D412yes—
241C2×C4×D59C2412yes—
242C2×Dic118—22no—
243C2×Dic118—22no—
244C2×Dic118—21no—
245C2×Dic118—24no—
246C2×Dic118—44no—
247C2×Dic118C2412yes—
248M16×C59—44no—
249C2×C8×C59—22no—
250C2×C8×C59—22no—
251C2×C8×C59C2412yes—
252C2×C8×C59C2412yes—
253C4⋊C4×C59—21no—
254C4⋊C4×C59—21no—
255C4⋊C4×C59C2412yes—
256C4⋊C4×C59C2412yes—
257C22⋊C4×C59—24no—
258C42×C59—24no—
259C22⋊Dic59—24no—
260C22⋊Dic59C2×D414yes—
261#11745671—28no—
262#11745671—44no—
263(C2×D59)⋊C4—24no—
264(C2×D59)⋊C4—24no—
265(C2×D59)⋊C4—24no—
266(C2×D59)⋊C4—24no—
267(C2×D59)⋊C4C2×D414yes—
268C4⋊Dic59—21no—
269C4⋊Dic59—21no—
270C4⋊Dic59—24no—
271C4⋊Dic59—24no—
272C4⋊Dic59C2412yes—
273C4⋊Dic59C2412yes—
274Dic59⋊C4—24no—
275Dic59⋊C4—24no—
276Dic59⋊C4—24no—
277Dic59⋊C4—24no—
278Dic59⋊C4—24no—
279Dic59⋊C4—24no—
280Dic59⋊C4C2×D414yes—
281C4×Dic59—24no—
282C4×Dic59C2×D412yes—
283C4×Dic59C2412yes—
284C2×C59⋊C8—22no—
285C2×C59⋊C8—22no—
286C2×C59⋊C8C2412yes—
287C2×C59⋊C8C2412yes—
288#11745660—44no—
289C8×D59—44no—
290C23×C59—22no—
291C23×C59—22no—
292C23×C59—22no—
293C23×C59C22×D412yes—
294C23×C59C22×D411yescharacteristic
295C22×D59—22no—
296C22×D59—22no—
297C22×D59—22no—
298C22×D59—42no—
299C22×D59—42no—
300C22×D59—42no—
301C22×D59#13714yes—
302C22×D59C22×D412yes—
303Q8×C59—24no—
304Q8×C59—22no—
305Q8×C59—22no—
306Q8×C59—22no—
307Q8×C59—48no—
308Q8×C59—42no—
309Q8×C59C2×#4114yes—
310C2×C4×C59—24no—
311C2×C4×C59—22no—
312C2×C4×C59—22no—
313C2×C4×C59—24no—
314C2×C4×C59—22no—
315C2×C4×C59—22no—
316C2×C4×C59—22no—
317C2×C4×C59—22no—
318C2×C4×C59—22no—
319C2×C4×C59—48no—
320C2×C4×C59—42no—
321C2×C4×C59—42no—
322C2×C4×C59—42no—
323C2×C4×C59C22×D412yes—
324C2×C4×C59C22×D411yescharacteristic
325C2×C4×C59C2×#4112yes—
326C2×C4×C59H(5,𝔽2)12yes—
327C2×C4×C59C2511yescharacteristic
328C22⋊D59—28no—
329C22⋊D59—84no—
330C2×Dic59—22no—
331C2×Dic59—22no—
332C2×Dic59—22no—
333C2×Dic59—22no—
334C2×Dic59—22no—
335C2×Dic59—22no—
336C2×Dic59—42no—
337C2×Dic59—42no—
338C2×Dic59—42no—
339C2×Dic59C22×D412yes—
340C2×Dic59C22×D412yes—
341C2×Dic59C22×D412yes—
342D236—22no—
343D236—22no—
344D236—48no—
345D236—42no—
346C4×D59—24no—
347C4×D59—22no—
348C4×D59—22no—
349C4×D59—48no—
350C4×D59—84no—
351C4×D59—84no—
352Dic118—22no—
353Dic118—22no—
354Dic118—48no—
355Dic118—42no—
356C8×C59—22no—
357C8×C59—22no—
358C59⋊C8—22no—
359C59⋊C8—22no—
360C2×#3320—591nomaximal, Sylow
361C22×C59—22no—
362C22×C59—22no—
363C22×C59—22no—
364C22×C59—44no—
365C22×C59#54612yes—
366C22×C59C2×#13712yes—
367C22×C59#57712yes—
368C22×C59C23×D411yescharacteristic
369C2×D59—22no—
370C2×D59—28no—
371C2×D59—22no—
372C2×D59—42no—
373C2×D59—42no—
374C2×D59—42no—
375C2×D59—84no—
376C2×D59C2×#13714yes—
377C4×C59—24no—
378C4×C59—22no—
379C4×C59—42no—
380C4×C59—42no—
381C4×C59—42no—
382C4×C59#54612yes—
383C4×C59C22×#4111yescharacteristic
384C4×C59C2×H(5,𝔽2)11yescharacteristic
385Dic59—22no—
386Dic59—22no—
387Dic59—22no—
388Dic59—42no—
389Dic59—42no—
390Dic59—42no—
391C2×#553—591no—
392C2×D4×Q8—591no—
393#3320—5916no—
394C2×#491—591no—
395C2×#484—591no—
396C2×#485—591no—
397C2×#479—591no—
398C2×#468—591no—
399C2×#465—591no—
400C2×#461—591no—
401C2×#448—591no—
402C2×#448—591no—
403C2×#440—591no—
404C2×#435—591no—
405C2×#419D5911yescharacteristic, complemented
406C22×#103—591no—
407C2×C59—42no—
408C2×C59#332014yescomplemented
409C2×C59C2×#54611yescharacteristic
410C2×C59C22×#13711yescharacteristic
411C2×C59C2×#57711yescharacteristic
412D59—24no—
413D59—82no—
414C23×Q8—591no—
415C23×Q8C2×D5911yescharacteristic
416C22×SD16—591no—
417C22×SD16—591no—
418C22×SD16—591no—
419C22×M16C2×D5911yescharacteristic
420C23×C8—591no—
421#553—598no—
422#553—1184no—
423D4×Q8—598no—
424D4×Q8—1184no—
425C2×C4⋊Q8—591no—
426C2×C4⋊Q8—1181no—
427C2×#126—1181no—
428C2×#125—591no—
429C2×#123—1181no—
430C2×C22⋊Q8—591no—
431C2×C22⋊Q8—591no—
432C2×C22⋊Q8—1181no—
433C2×C22⋊Q8—1181no—
434C2×#121—591no—
435C2×#121—591no—
436C2×#121—1181no—
437C2×C4×Q8—591no—
438C2×C4×D4—591no—
439C2×C4×D4—591no—
440C2×C4×D4—1181no—
441C2×C4×D4—1181no—
442C2×#117C2×D5911yescharacteristic
443C22×C4⋊C4—591no—
444#491—598no—
445#485—598no—
446#484—598no—
447#479—598no—
448#468—598no—
449#465—598no—
450#461—598no—
451#448—598no—
452#448—598no—
453#440—598no—
454#435—598no—
455C2×#107—591no—
456C2×#107—591no—
457C2×#106—591no—
458C2×C4⋊C8—591no—
459#419C2×D5918yescomplemented
460C2×#103—591no—
461C2×#103—591no—
462C2×#103—591no—
463C2×#103—591no—
464C2×#103—591no—
465C2×#103—598no—
466C2×#103C2×D5911yescharacteristic
467C2×#103C2×D5911yescharacteristic
468C2×#103C2×D5911yescharacteristic
469C2×#103C2×D5911yescharacteristic
470C2×#102—591no—
471C2×C22⋊C8—591no—
472C2×C22⋊C8—591no—
473C2×#97—591no—
474C59C2×#332011yescharacteristic, complemented, Sylow
475C22×Q8—21no—
476C22×Q8—22no—
477C22×Q8—24no—
478C22×Q8—42no—
479C22×Q8—594no—
480C22×Q8—591no—
481C22×Q8—1181no—
482C22×Q8—1182no—
483C22×Q8—1184no—
484C22×Q8—2362no—
485C22×Q8C22×D5911yescharacteristic
486C22×Q8C22×D5914yes—
487C22×Q8C22×D5911yescharacteristic
488C22×D4—591no—
489C22×D4—591no—
490C22×D4—1181no—
491C22×D4—1181no—
492C23×C4—21no—
493C23×C4—591no—
494C23×C4—1181no—
495C23×C4—1181no—
496C23×C4—1181no—
497C23×C4C22×D5911yescharacteristic
498C2×SD16—594no—
499C2×SD16—594no—
500C2×SD16—594no—
501C2×SD16—1184no—
502C2×SD16—2362no—
503C2×SD16—2362no—
504C2×M16—42no—
505C2×M16C22×D5914yes—
506C22×C8—591no—
507C22×C8—591no—
508C22×C8—594no—
509C22×C8—2362no—
510C22×C8C22×D5911yescharacteristic
511C22×C8C22×D5911yescharacteristic
512C4⋊Q8—594no—
513C4⋊Q8—1182no—
514C4⋊Q8—1188no—
515#126—1188no—
516#125—594no—
517#125—1182no—
518#123—1188no—
519C22⋊Q8—594no—
520C22⋊Q8—594no—
521C22⋊Q8—1188no—
522C22⋊Q8—1188no—
523C22⋊Q8—1182no—
524C22⋊Q8—1182no—
525#121—594no—
526#121—594no—
527#121—1188no—
528#121—1182no—
529#121—1182no—
530C4×Q8—594no—
531C4×Q8—1182no—
532C4×D4—594no—
533C4×D4—594no—
534C4×D4—594no—
535C4×D4—1188no—
536C4×D4—1182no—
537C4×D4—1188no—
538#117—22no—
539#117C22×D5914yes—
540C2×C4⋊C4—591no—
541C2×C4⋊C4—591no—
542C2×C4⋊C4—591no—
543C2×C4⋊C4—594no—
544C2×C4⋊C4—1182no—
545C2×C4⋊C4—1181no—
546C2×C4⋊C4—1181no—
547C2×C4⋊C4—1181no—
548C2×C4⋊C4—1181no—
549C2×C4⋊C4—1181no—
550C2×C4⋊C4—1181no—
551C2×C4⋊C4—1181no—
552C2×C4⋊C4—1181no—
553C2×C4⋊C4C22×D5911yescharacteristic
554C2×C4⋊C4C22×D5911yescharacteristic
555C2×C22⋊C4—21no—
556C2×C22⋊C4—591no—
557C2×C22⋊C4—591no—
558C2×C22⋊C4—1181no—
559C2×C22⋊C4—1181no—
560C2×C22⋊C4—1181no—
561C2×C22⋊C4—1181no—
562C2×C22⋊C4—1181no—
563C2×C42—21no—
564C2×C42—591no—
565C2×C42—1181no—
566#107—594no—
567#107—594no—
568#106—594no—
569C4⋊C8—594no—
570#103—594no—
571#103—594no—
572#103—594no—
573#103—594no—
574#103—594no—
575#103C22×D5914yes—
576#103C22×D5914yes—
577#103C22×D5914yes—
578#103C22×D5914yes—
579#102—594no—
580C22⋊C8—594no—
581C22⋊C8—594no—
582#97—594no—
583C24—591no—
584C24—1181no—
585C24D4×D5911yescharacteristic
586C2×Q8—21no—
587C2×Q8—24no—
588C2×Q8—21no—
589C2×Q8—22no—
590C2×Q8—28no—
591C2×Q8—22no—
592C2×Q8—22no—
593C2×Q8—44no—
594C2×Q8—44no—
595C2×Q8—48no—
596C2×Q8—592no—
597C2×Q8—1184no—
598C2×Q8—1181no—
599C2×Q8—1188no—
600C2×Q8—1182no—
601C2×Q8—1182no—
602C2×Q8—2364no—
603C2×Q8—2364no—
604C2×Q8—2368no—
605C2×Q8#1174568514yes—
606C2×Q8C23×D5912yes—
607C2×Q8C23×D5912yes—
608C2×D4—594no—
609C2×D4—592no—
610C2×D4—1184no—
611C2×D4—1184no—
612C2×D4—1184no—
613C2×D4—1181no—
614C2×D4—1182no—
615C2×D4—1182no—
616C2×D4—4722no—
617C2×D4—2364no—
618C22×C4—21no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—24no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—44no—
626C22×C4—591no—
627C22×C4—591no—
628C22×C4—591no—
629C22×C4—592no—
630C22×C4—592no—
631C22×C4—1184no—
632C22×C4—1184no—
633C22×C4—1184no—
634C22×C4—1182no—
635C22×C4—1182no—
636C22×C4—1181no—
637C22×C4—1181no—
638C22×C4—1181no—
639C22×C4—4722no—
640C22×C4—4722no—
641C22×C4—2364no—
642C22×C4D4×D5912yes—
643C22×C4D4×D5911yescharacteristic
644C22×C4C23×D5912yes—
645C22×C4C23×D5911yescharacteristic
646SD16—1188no—
647SD16—2364no—
648SD16—2364no—
649M16—44no—
650C2×C8—22no—
651C2×C8—22no—
652C2×C8—592no—
653C2×C8—592no—
654C2×C8—1182no—
655C2×C8—1182no—
656C2×C8—2364no—
657C2×C8C23×D5912yes—
658C2×C8C23×D5912yes—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—594no—
662C4⋊C4—592no—
663C4⋊C4—592no—
664C4⋊C4—1184no—
665C4⋊C4—1184no—
666C4⋊C4—1184no—
667C4⋊C4—1184no—
668C4⋊C4—1184no—
669C4⋊C4—1184no—
670C4⋊C4—1184no—
671C4⋊C4—1181no—
672C4⋊C4—1181no—
673C4⋊C4—1184no—
674C4⋊C4C23×D5912yes—
675C4⋊C4C23×D5912yes—
676C22⋊C4—24no—
677C22⋊C4—594no—
678C22⋊C4—594no—
679C22⋊C4—1184no—
680C22⋊C4—1184no—
681C22⋊C4—1184no—
682C22⋊C4—1184no—
683C22⋊C4—1184no—
684C42—24no—
685C42—592no—
686C42—592no—
687C42—1184no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—594no—
692C23—592no—
693C23—1182no—
694C23—1182no—
695C23—1182no—
696C23—2362no—
697C23—2362no—
698C23—2362no—
699C23C2×D4×D5912yes—
700C23C2×D4×D5911yescharacteristic
701Q8—22no—
702Q8—24no—
703Q8—22no—
704Q8—22no—
705Q8—48no—
706Q8—42no—
707Q8—1182no—
708Q8—1182no—
709Q8—2368no—
710Q8—2362no—
711Q8C2×#1174568514yes—
712D4—1188no—
713D4—1182no—
714D4—1182no—
715D4—4724no—
716D4—2368no—
717D4—2362no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—24no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—24no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—48no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—592no—
732C2×C4—592no—
733C2×C4—592no—
734C2×C4—1182no—
735C2×C4—1182no—
736C2×C4—1182no—
737C2×C4—1182no—
738C2×C4—1182no—
739C2×C4—1184no—
740C2×C4—1182no—
741C2×C4—1182no—
742C2×C4—1182no—
743C2×C4—4724no—
744C2×C4—4724no—
745C2×C4—2368no—
746C2×C4—2362no—
747C2×C4—2362no—
748C2×C4—2362no—
749C2×C4C2×D4×D5912yes—
750C2×C4C2×D4×D5911yescharacteristic
751C2×C4C2×#1174568512yes—
752C2×C4#1427377212yes—
753C2×C4C24×D5911yescharacteristic
754C8—22no—
755C8—22no—
756C8—1182no—
757C8—1182no—
758C22—22no—
759C22—22no—
760C22—22no—
761C22—44no—
762C22—594no—
763C22—1182no—
764C22—1188no—
765C22—1182no—
766C22—4724no—
767C22—2362no—
768C22—2362no—
769C22—2362no—
770C22#1683804212yes—
771C22#137×D5912yes—
772C22#1683821112yes—
773C22C22×D4×D5911yescharacteristic
774C4—22no—
775C4—24no—
776C4—42no—
777C4—42no—
778C4—42no—
779C4—1182no—
780C4—1182no—
781C4—1182no—
782C4—2362no—
783C4—2362no—
784C4—2362no—
785C4#1683804212yes—
786C4C22×#1174568511yescharacteristic
787C4C2×#1427377211yescharacteristic
788C2—42no—
789C2—1184no—
790C2—4722no—
791C2#2143626814yesdirect product factor
792C2C2×#1683804211yescharacteristic
793C2C2×#137×D5911yescharacteristic
794C2C2×#1683821111yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#419C2
socleC23×C59C22×D4
prime radicalC2×#16838096C2
hypercenterC2×#419D59
hypocenterC59C2×#3320
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#419

Complements

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

NH ≅ G/Ntype
2. C2×Q8×C22⋊D59C2semidirect
3. #21436268C2direct (N × H)
4. C2×#16837769C2semidirect
5. C2×#16837736C2semidirect
6. C2×#16837743C2semidirect
7. C2×#16837711C2semidirect
8. C2×#16837648C2semidirect
9. C2×#16837634C2semidirect
10. C2×#16837606C2semidirect
11. C2×#16837542C2semidirect
12. C2×#16837541C2semidirect
13. C2×#16837505C2semidirect
14. C2×#16837471C2semidirect
15. C2×#103×D59C2semidirect
16. C2×C59×#419C2semidirect
25. Q8×C22⋊D59C22semidirect
44. #16837769C22semidirect
45. #16837743C22semidirect
46. #16837736C22semidirect
47. #16837711C22semidirect
48. #16837648C22semidirect
49. #16837634C22semidirect
50. #16837606C22semidirect
51. #16837542C22semidirect
52. #16837541C22semidirect
53. #16837505C22semidirect
54. #16837471C22semidirect
64. #103×D59C22semidirect
72. C59×#419C22semidirect
405. C2×#419D59semidirect
408. C2×C59#3320semidirect
459. #419C2×D59semidirect
474. C59C2×#3320semidirect
791. C2#21436268direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168380962
C2×Q8×C22⋊D592
#214362682
C2×#168377692
C2×#168377362
C2×#168377432
C2×#168377112
C2×#168376482
C2×#168376342
C2×#168376062
C2×#168375422
C2×#168375412
C2×#168375052
C2×#168374712
C2×#103×D592
C2×C59×#4192
C2×#332059