Finite Group Databasebeta

← C2×#21436200 #29465272

Subgroups — C2×#21436200 #29465272

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×#16838110C211yesmaximal, characteristic, complemented
2C2×#16838059C211yesmaximal, characteristic
3#21436200C2116yesmaximal, direct product factor
4C2×#16837760C211yesmaximal, characteristic, complemented
5C2×#16837719C211yesmaximal, characteristic, complemented
6C2×#16837733C211yesmaximal, characteristic, complemented
7C2×#16837685C211yesmaximal, characteristic, complemented
8C2×#16837658C211yesmaximal, characteristic, complemented
9C2×#16837628C211yesmaximal, characteristic, complemented
10C2×#16837622C211yesmaximal, characteristic, complemented
11C2×#16837556C211yesmaximal, characteristic, complemented
12C2×#16837509C211yesmaximal, characteristic, complemented
13C2×#16837476C211yesmaximal, characteristic, complemented
14C2×#16837403C211yesmaximal, characteristic, complemented
15C2×#103×D59C211yesmaximal, characteristic, complemented
16C2×C59×#452C211yesmaximal, characteristic, complemented
17C22×Q8×D59C2211yescharacteristic
18C22×#11745672C2211yescharacteristic
19C22×#11745664C2211yescharacteristic
20C22×C8×D59C2211yescharacteristic
21#16838110—24no—
22#16838110C2218yescomplemented
23#16838059—24no—
24#16838059C2218yes—
25C2×#14273726C2211yescharacteristic
26C2×#14273717—21no—
27C2×#14273714—21no—
28C2×#14273714C2211yescharacteristic
29C2×#14273707—21no—
30C2×#14273706—21no—
31C2×#14273706C2211yescharacteristic
32C2×#14273704—21no—
33C2×#14273703C2211yescharacteristic
34C2×#14273698—21no—
35C2×#14273698C2211yescharacteristic
36C2×Q8×Dic59C2211yescharacteristic
37C2×Q8×Dic59C2211yescharacteristic
38C2×C4×C22⋊D59—21no—
39C2×C4×C22⋊D59C2211yescharacteristic
40C2×(C22⋊D59)⋊C4—21no—
41C22×C4⋊Dic59C2211yescharacteristic
42C2×C4⋊C4×D59C2211yescharacteristic
43#16837760C2218yescomplemented
44#16837733C2218yescomplemented
45#16837719C2218yescomplemented
46#16837685C2218yescomplemented
47#16837658C2218yescomplemented
48#16837628C2218yescomplemented
49#16837622C2218yescomplemented
50#16837556C2218yescomplemented
51#16837509C2218yescomplemented
52#16837476C2218yescomplemented
53C2×#14273659C2211yescharacteristic
54C2×#14273659C2211yescharacteristic
55C2×#14273658C2211yescharacteristic
56C2×Dic59⋊C8C2211yescharacteristic
57#16837403C2218yescomplemented
58C2×#14273652C2211yescharacteristic
59C2×#14273652C2211yescharacteristic
60C2×#14273651C2211yescharacteristic
61C2×#14273651C2211yescharacteristic
62C2×#14273651C2211yescharacteristic
63C2×#14273650C2211yescharacteristic
64#103×D59C2218yescomplemented
65C2×#14273648C2211yescharacteristic
66C2×#14273648C2211yescharacteristic
67C2×(C2×D59)⋊C8C2211yescharacteristic
68C2×#14273637C2211yescharacteristic
69C22×#41×C59C2211yescharacteristic
70C22×Q16×C59C2211yescharacteristic
71C22×SD16×C59C2211yescharacteristic
72C2×C22⋊Q8×C59C2211yescharacteristic
73C59×#452C2218yescomplemented
74C2×#103×C59C2211yescharacteristic
75C2×#102×C59C2211yescharacteristic
76C2×C22⋊C8×C59C2211yescharacteristic
77C22×Dic118—21no—
78C22×Dic118—21no—
79C22×Dic118C2311yescharacteristic
80C2×Q8×D59—22no—
81C2×Q8×D59—24no—
82C2×Q8×D59—42no—
83C2×Q8×D59C2314yes—
84C22×C22⋊D59—21no—
85C22×C22⋊D59D411yescharacteristic
86C23×Dic59—21no—
87C22×C4×D59—21no—
88C22×C4×D59—21no—
89C22×C4×D59C2311yescharacteristic
90C2×#11745672—42no—
91C2×#11745672C2314yes—
92C2×#11745664—42no—
93C2×#11745664C2314yes—
94C22×C59⋊C8C2311yescharacteristic
95C22×C59⋊C8C2311yescharacteristic
96C2×C8×D59—42no—
97C2×C8×D59C2314yes—
98#14273726—22no—
99#14273726C2314yes—
100#14273717—28no—
101#14273714—28no—
102#14273714—22no—
103#14273714C2314yes—
104#14273707—28no—
105#14273706—22no—
106#14273706—28no—
107#14273706C2314yes—
108#14273704—28no—
109#14273703—22no—
110#14273703C2314yes—
111#14273698—28no—
112#14273698—22no—
113#14273698C2314yes—
114Q8×Dic59—22no—
115Q8×Dic59—22no—
116Q8×Dic59C2314yes—
117Q8×Dic59C2314yes—
118C4×C22⋊D59—28no—
119C4×C22⋊D59D414yes—
120C4×C22⋊D59C2314yes—
121(C22⋊D59)⋊C4—28no—
122C2×C4⋊Dic59—21no—
123C2×C4⋊Dic59—22no—
124C2×C4⋊Dic59—21no—
125C2×C4⋊Dic59—21no—
126C2×C4⋊Dic59C2311yescharacteristic
127C2×C4⋊Dic59C2311yescharacteristic
128C2×C4⋊Dic59C2311yescharacteristic
129C2×C4⋊Dic59C2314yes—
130C2×Dic59⋊C4—21no—
131C2×Dic59⋊C4—21no—
132C2×Dic59⋊C4—21no—
133C2×Dic59⋊C4—21no—
134C2×Dic59⋊C4D411yescharacteristic
135C4⋊C4×D59—22no—
136C4⋊C4×D59C2314yes—
137C2×C22⋊Dic59—21no—
138C2×C22⋊Dic59—21no—
139C2×C22⋊Dic59—21no—
140C2×C22⋊Dic59—21no—
141C2×C22⋊Dic59D411yescharacteristic
142C2×(C2×D59)⋊C4—21no—
143C2×(C2×D59)⋊C4D411yescharacteristic
144C2×C4×Dic59—21no—
145C2×C4×Dic59—21no—
146C2×C4×Dic59C2311yescharacteristic
147#14273659C2314yes—
148#14273659C2314yes—
149#14273658C2314yes—
150Dic59⋊C8C2314yes—
151#14273652C2314yes—
152#14273652C2314yes—
153#14273651C2314yes—
154#14273651C2314yes—
155#14273651C2314yes—
156#14273650C2314yes—
157#14273648C2314yes—
158#14273648C2314yes—
159(C2×D59)⋊C8C2314yes—
160#14273637C2314yes—
161C2×#41×C59—22no—
162C2×#41×C59—24no—
163C2×#41×C59—42no—
164C2×#41×C59C2314yes—
165C22×Q8×C59C2311yescharacteristic
166C22×Q8×C59C2311yescharacteristic
167C22×D4×C59—21no—
168C22×D4×C59C2311yescharacteristic
169C23×C4×C59—21no—
170C23×C4×C59C2311yescharacteristic
171C2×Q16×C59—24no—
172C2×Q16×C59C2314yes—
173C2×SD16×C59—42no—
174C2×SD16×C59C2314yes—
175C22×C8×C59C2311yescharacteristic
176C22×C8×C59C2311yescharacteristic
177C22⋊Q8×C59—22no—
178C22⋊Q8×C59C2314yes—
179C2×C4⋊C4×C59—21no—
180C2×C4⋊C4×C59C2311yescharacteristic
181C2×C22⋊C4×C59—21no—
182#103×C59C2314yes—
183#102×C59C2314yes—
184C22⋊C8×C59C2314yes—
185C24×C59—21no—
186C24×C59C2×D411yescharacteristic
187C23×D59C2×D411yescharacteristic
188#41×C59—28no—
189#41×C59—44no—
190#41×C59—48no—
191C2×Q8×C59—21no—
192C2×Q8×C59—21no—
193C2×Q8×C59—22no—
194C2×Q8×C59—22no—
195C2×Q8×C59—22no—
196C2×Q8×C59#4114yes—
197C2×Q8×C59C2412yes—
198C2×Q8×C59C2412yes—
199C2×D4×C59—24no—
200C2×D4×C59—21no—
201C2×D4×C59—22no—
202C2×D4×C59—22no—
203C2×D4×C59—44no—
204C2×D4×C59C2412yes—
205C22×C4×C59—21no—
206C22×C4×C59—22no—
207C22×C4×C59—22no—
208C22×C4×C59—21no—
209C22×C4×C59—21no—
210C22×C4×C59—24no—
211C22×C4×C59—44no—
212C22×C4×C59C2×D411yescharacteristic
213C22×C4×C59C2×D412yes—
214C22×C4×C59C2412yes—
215C22×C4×C59C2411yescharacteristic
216C2×C22⋊D59—24no—
217C2×C22⋊D59—24no—
218C2×C22⋊D59—44no—
219C2×C22⋊D59C2×D414yes—
220C22×Dic59—21no—
221C22×Dic59—21no—
222C22×Dic59—21no—
223C22×Dic59—21no—
224C22×Dic59—24no—
225C22×Dic59—82no—
226C22×Dic59C2×D411yescharacteristic
227C22×Dic59C2×D411yescharacteristic
228C22×Dic59C2×D411yescharacteristic
229Q8×D59—28no—
230Q8×D59—44no—
231Q8×D59—48no—
232C2×C4×D59—22no—
233C2×C4×D59—22no—
234C2×C4×D59—24no—
235C2×C4×D59—24no—
236C2×C4×D59—44no—
237C2×C4×D59—82no—
238C2×C4×D59C2×D412yes—
239C2×C4×D59C2412yes—
240C2×Dic118—22no—
241C2×Dic118—22no—
242C2×Dic118—21no—
243C2×Dic118—24no—
244C2×Dic118—24no—
245C2×Dic118—44no—
246C2×Dic118—82no—
247C2×Dic118C2412yes—
248Q16×C59—28no—
249SD16×C59—44no—
250C2×C8×C59—22no—
251C2×C8×C59—22no—
252C2×C8×C59C2412yes—
253C2×C8×C59C2412yes—
254C4⋊C4×C59—24no—
255C4⋊C4×C59—21no—
256C4⋊C4×C59C2412yes—
257C22⋊C4×C59—24no—
258C22⋊Dic59—24no—
259C22⋊Dic59—24no—
260C22⋊Dic59—24no—
261C22⋊Dic59—24no—
262C22⋊Dic59C2×D414yes—
263#11745672—44no—
264(C2×D59)⋊C4—24no—
265(C2×D59)⋊C4C2×D414yes—
266C4⋊Dic59—21no—
267C4⋊Dic59—21no—
268C4⋊Dic59—24no—
269C4⋊Dic59—21no—
270C4⋊Dic59—24no—
271C4⋊Dic59—24no—
272C4⋊Dic59C2412yes—
273C4⋊Dic59C2412yes—
274C4⋊Dic59C2412yes—
275Dic59⋊C4—24no—
276Dic59⋊C4—24no—
277Dic59⋊C4—24no—
278Dic59⋊C4—24no—
279Dic59⋊C4C2×D414yes—
280C4×Dic59—24no—
281C4×Dic59—24no—
282C4×Dic59C2×D412yes—
283C4×Dic59C2412yes—
284#11745664—44no—
285C2×C59⋊C8—22no—
286C2×C59⋊C8—22no—
287C2×C59⋊C8C2412yes—
288C2×C59⋊C8C2412yes—
289C8×D59—44no—
290C23×C59—22no—
291C23×C59—22no—
292C23×C59—22no—
293C23×C59—22no—
294C23×C59—42no—
295C23×C59—42no—
296C23×C59—42no—
297C23×C59C22×D412yes—
298C23×C59C22×D411yescharacteristic
299C22×D59—22no—
300C22×D59—22no—
301C22×D59#13714yes—
302C22×D59C22×D412yes—
303Q8×C59—24no—
304Q8×C59—22no—
305Q8×C59—22no—
306Q8×C59—22no—
307Q8×C59—42no—
308Q8×C59C2×#4114yes—
309D4×C59—22no—
310D4×C59—22no—
311D4×C59—48no—
312D4×C59—42no—
313C2×C4×C59—24no—
314C2×C4×C59—22no—
315C2×C4×C59—22no—
316C2×C4×C59—24no—
317C2×C4×C59—22no—
318C2×C4×C59—22no—
319C2×C4×C59—22no—
320C2×C4×C59—22no—
321C2×C4×C59—48no—
322C2×C4×C59—42no—
323C2×C4×C59—42no—
324C2×C4×C59C22×D412yes—
325C2×C4×C59C22×D411yescharacteristic
326C2×C4×C59C2×#4112yes—
327C2×C4×C59H(5,𝔽2)12yes—
328C2×C4×C59C2511yescharacteristic
329C22⋊D59—28no—
330C22⋊D59—48no—
331C2×Dic59—22no—
332C2×Dic59—22no—
333C2×Dic59—22no—
334C2×Dic59—22no—
335C2×Dic59—22no—
336C2×Dic59—22no—
337C2×Dic59—22no—
338C2×Dic59—42no—
339C2×Dic59—42no—
340C2×Dic59—42no—
341C2×Dic59—42no—
342C2×Dic59—84no—
343C2×Dic59C22×D412yes—
344C2×Dic59C22×D412yes—
345C2×Dic59C22×D412yes—
346C4×D59—24no—
347C4×D59—22no—
348C4×D59—22no—
349C4×D59—48no—
350C4×D59—84no—
351Dic118—22no—
352Dic118—22no—
353Dic118—48no—
354Dic118—42no—
355Dic118—84no—
356C8×C59—22no—
357C8×C59—22no—
358C59⋊C8—22no—
359C59⋊C8—22no—
360C2×#3316—591nomaximal, Sylow
361C22×C59—22no—
362C22×C59—22no—
363C22×C59—22no—
364C22×C59—44no—
365C22×C59—42no—
366C22×C59—42no—
367C22×C59—42no—
368C22×C59—84no—
369C22×C59#54612yes—
370C22×C59C2×#13712yes—
371C22×C59#57712yes—
372C22×C59C23×D411yescharacteristic
373C2×D59—22no—
374C2×D59—28no—
375C2×D59—22no—
376C2×D59C2×#13714yes—
377C4×C59—24no—
378C4×C59—22no—
379C4×C59—42no—
380C4×C59—42no—
381C4×C59#54612yes—
382C4×C59C22×#4111yescharacteristic
383C4×C59C2×H(5,𝔽2)11yescharacteristic
384Dic59—22no—
385Dic59—22no—
386Dic59—22no—
387Dic59—42no—
388Dic59—42no—
389Dic59—42no—
390Dic59—42no—
391C2×#554—591no—
392C2×#548—591no—
393#3316—5916no—
394C2×#489—591no—
395C2×#481—591no—
396C2×#483—591no—
397C2×#475—591no—
398C2×#470—591no—
399C2×#465—591no—
400C2×#464—591no—
401C2×#452D5911yescharacteristic, complemented
402C2×#451—591no—
403C2×#441—591no—
404C2×#435—591no—
405C2×#417—591no—
406C22×#103—591no—
407C2×C59—42no—
408C2×C59—82no—
409C2×C59#331614yescomplemented
410C2×C59C2×#54611yescharacteristic
411C2×C59C22×#13711yescharacteristic
412C2×C59C2×#57711yescharacteristic
413D59—24no—
414C22×#41C2×D5911yescharacteristic
415C23×Q8—591no—
416C22×Q16—591no—
417C22×Q16C2×D5911yescharacteristic
418C22×SD16C2×D5911yescharacteristic
419C22×M16—591no—
420C23×C8—591no—
421#554—598no—
422#554—1184no—
423#548—598no—
424#548—1184no—
425C2×C4⋊Q8—591no—
426C2×#125—1181no—
427C2×#124—591no—
428C2×#124—1181no—
429C2×C22⋊Q8—591no—
430C2×C22⋊Q8—591no—
431C2×C22⋊Q8—1181no—
432C2×C22⋊Q8—1181no—
433C2×C22⋊Q8—1181no—
434C2×C22⋊Q8C2×D5911yescharacteristic
435C2×#121—591no—
436C2×#121—1181no—
437C2×C4×Q8—591no—
438C2×C4×Q8—591no—
439C2×C4×D4—591no—
440C2×C4×D4—1181no—
441C2×C4×D4—1181no—
442C22×C4⋊C4—591no—
443C22×C4⋊C4—591no—
444#489—598no—
445#483—598no—
446#481—598no—
447#475—598no—
448#470—598no—
449#465—598no—
450#464—598no—
451#452C2×D5918yescomplemented
452#451—598no—
453#441—598no—
454#435—598no—
455C2×#106—591no—
456C2×#106—591no—
457C2×#106—591no—
458C2×C4⋊C8—591no—
459#417—598no—
460C2×#103—591no—
461C2×#103—591no—
462C2×#103—591no—
463C2×#103—591no—
464C2×#103—591no—
465C2×#103—591no—
466C2×#103—598no—
467C2×#103C2×D5911yescharacteristic
468C2×#102—591no—
469C2×#102—591no—
470C2×#102C2×D5911yescharacteristic
471C2×C22⋊C8—591no—
472C2×C22⋊C8C2×D5911yescharacteristic
473C2×#97—591no—
474C59C2×#331611yescharacteristic, complemented, Sylow
475C2×#41—22no—
476C2×#41—24no—
477C2×#41—42no—
478C2×#41C22×D5914yes—
479C22×Q8—594no—
480C22×Q8—591no—
481C22×Q8—1181no—
482C22×Q8—1181no—
483C22×Q8—1182no—
484C22×Q8—1184no—
485C22×Q8—2362no—
486C22×Q8C22×D5911yescharacteristic
487C22×Q8C22×D5911yescharacteristic
488C22×D4—21no—
489C22×D4—591no—
490C22×D4—1181no—
491C22×D4C22×D5911yescharacteristic
492C23×C4—21no—
493C23×C4—591no—
494C23×C4—1181no—
495C23×C4—1181no—
496C23×C4—1181no—
497C23×C4C22×D5911yescharacteristic
498C2×Q16—24no—
499C2×Q16—594no—
500C2×Q16—2362no—
501C2×Q16C22×D5914yes—
502C2×SD16—42no—
503C2×SD16C22×D5914yes—
504C2×M16—594no—
505C2×M16—2362no—
506C22×C8—591no—
507C22×C8—591no—
508C22×C8—594no—
509C22×C8—2362no—
510C22×C8C22×D5911yescharacteristic
511C22×C8C22×D5911yescharacteristic
512C4⋊Q8—594no—
513C4⋊Q8—1182no—
514#125—1188no—
515#124—594no—
516#124—1182no—
517#124—1188no—
518C22⋊Q8—22no—
519C22⋊Q8—594no—
520C22⋊Q8—594no—
521C22⋊Q8—1188no—
522C22⋊Q8—1188no—
523C22⋊Q8—1188no—
524C22⋊Q8—1182no—
525C22⋊Q8—1182no—
526C22⋊Q8C22×D5914yes—
527#121—594no—
528#121—1182no—
529#121—1188no—
530C4×Q8—594no—
531C4×Q8—594no—
532C4×Q8—1182no—
533C4×Q8—1182no—
534C4×D4—594no—
535C4×D4—594no—
536C4×D4—1188no—
537C4×D4—1188no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—591no—
540C2×C4⋊C4—591no—
541C2×C4⋊C4—591no—
542C2×C4⋊C4—594no—
543C2×C4⋊C4—591no—
544C2×C4⋊C4—594no—
545C2×C4⋊C4—1182no—
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—1182no—
553C2×C4⋊C4—1181no—
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—591no—
564C2×C42—1181no—
565C2×C42—1181no—
566#106—594no—
567#106—594no—
568#106—594no—
569C4⋊C8—594no—
570#103—594no—
571#103—594no—
572#103—594no—
573#103—594no—
574#103—594no—
575#103—594no—
576#103C22×D5914yes—
577#102—594no—
578#102—594no—
579#102C22×D5914yes—
580C22⋊C8—594no—
581C22⋊C8C22×D5914yes—
582#97—594no—
583C24—21no—
584C24—591no—
585C24D4×D5911yescharacteristic
586#41—28no—
587#41—44no—
588#41—48no—
589C2×Q8—21no—
590C2×Q8—21no—
591C2×Q8—22no—
592C2×Q8—22no—
593C2×Q8—22no—
594C2×Q8—592no—
595C2×Q8—1184no—
596C2×Q8—1184no—
597C2×Q8—1181no—
598C2×Q8—1188no—
599C2×Q8—1182no—
600C2×Q8—1182no—
601C2×Q8—4722no—
602C2×Q8—2364no—
603C2×Q8—2364no—
604C2×Q8—2368no—
605C2×Q8#1174568714yes—
606C2×Q8C23×D5912yes—
607C2×Q8C23×D5912yes—
608C2×D4—24no—
609C2×D4—21no—
610C2×D4—22no—
611C2×D4—22no—
612C2×D4—44no—
613C2×D4—594no—
614C2×D4—1184no—
615C2×D4—1184no—
616C2×D4—2364no—
617C2×D4C23×D5912yes—
618C22×C4—21no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—24no—
624C22×C4—44no—
625C22×C4—591no—
626C22×C4—591no—
627C22×C4—591no—
628C22×C4—592no—
629C22×C4—592no—
630C22×C4—1184no—
631C22×C4—1184no—
632C22×C4—1182no—
633C22×C4—1182no—
634C22×C4—1184no—
635C22×C4—1181no—
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
646Q16—28no—
647Q16—2364no—
648SD16—44no—
649M16—2364no—
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—24no—
660C4⋊C4—21no—
661C4⋊C4—594no—
662C4⋊C4—592no—
663C4⋊C4—592no—
664C4⋊C4—592no—
665C4⋊C4—1184no—
666C4⋊C4—1184no—
667C4⋊C4—1184no—
668C4⋊C4—1184no—
669C4⋊C4—1184no—
670C4⋊C4—1181no—
671C4⋊C4—1184no—
672C4⋊C4—1181no—
673C4⋊C4—1181no—
674C4⋊C4—1184no—
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—592no—
685C42—592no—
686C42—1184no—
687C42—1184no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—594no—
696C23—592no—
697C23—1182no—
698C23—1182no—
699C23C2×D4×D5912yes—
700C23C2×D4×D5911yescharacteristic
701Q8—22no—
702Q8—24no—
703Q8—22no—
704Q8—22no—
705Q8—42no—
706Q8—1182no—
707Q8—1182no—
708Q8—4724no—
709Q8—2368no—
710Q8—2362no—
711Q8C2×#1174568714yes—
712D4—22no—
713D4—22no—
714D4—48no—
715D4—42no—
716D4—1188no—
717D4—2368no—
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—48no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—592no—
730C2×C4—592no—
731C2×C4—592no—
732C2×C4—1182no—
733C2×C4—1182no—
734C2×C4—1182no—
735C2×C4—1182no—
736C2×C4—1182no—
737C2×C4—1184no—
738C2×C4—1182no—
739C2×C4—1182no—
740C2×C4—1182no—
741C2×C4—1182no—
742C2×C4—4724no—
743C2×C4—4724no—
744C2×C4—2368no—
745C2×C4—2362no—
746C2×C4—2362no—
747C2×C4—2362no—
748C2×C4—2362no—
749C2×C4C2×D4×D5912yes—
750C2×C4C2×D4×D5911yescharacteristic
751C2×C4C2×#1174568712yes—
752C2×C4#1427377212yes—
753C2×C4C24×D5911yescharacteristic
754C8—22no—
755C8—22no—
756C8—1182no—
757C8—1182no—
758C22—22no—
759C22—22no—
760C22—22no—
761C22—44no—
762C22—42no—
763C22—42no—
764C22—42no—
765C22—84no—
766C22—594no—
767C22—1188no—
768C22—1182no—
769C22—1182no—
770C22#1683803912yes—
771C22#137×D5912yes—
772C22#1683820912yes—
773C22C22×D4×D5911yescharacteristic
774C4—22no—
775C4—24no—
776C4—42no—
777C4—42no—
778C4—1182no—
779C4—1182no—
780C4—1182no—
781C4—2362no—
782C4—2362no—
783C4—2362no—
784C4—2362no—
785C4#1683803912yes—
786C4C22×#1174568711yescharacteristic
787C4C2×#1427377211yescharacteristic
788C2—42no—
789C2—82no—
790C2—1184no—
791C2#2143620014yesdirect product factor
792C2C2×#1683803911yescharacteristic
793C2C2×#137×D5911yescharacteristic
794C2C2×#1683820911yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#452C2
socleC23×C59C22×D4
prime radicalC2×#16838059C2
hypercenterC2×#452D59
hypocenterC59C2×#3316
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
1. C2×#16838110C2semidirect
3. #21436200C2direct (N × H)
4. C2×#16837760C2semidirect
5. C2×#16837719C2semidirect
6. C2×#16837733C2semidirect
7. C2×#16837685C2semidirect
8. C2×#16837658C2semidirect
9. C2×#16837628C2semidirect
10. C2×#16837622C2semidirect
11. C2×#16837556C2semidirect
12. C2×#16837509C2semidirect
13. C2×#16837476C2semidirect
14. C2×#16837403C2semidirect
15. C2×#103×D59C2semidirect
16. C2×C59×#452C2semidirect
22. #16838110C22semidirect
43. #16837760C22semidirect
44. #16837733C22semidirect
45. #16837719C22semidirect
46. #16837685C22semidirect
47. #16837658C22semidirect
48. #16837628C22semidirect
49. #16837622C22semidirect
50. #16837556C22semidirect
51. #16837509C22semidirect
52. #16837476C22semidirect
57. #16837403C22semidirect
64. #103×D59C22semidirect
73. C59×#452C22semidirect
401. C2×#452D59semidirect
409. C2×C59#3316semidirect
451. #452C2×D59semidirect
474. C59C2×#3316semidirect
791. C2#21436200direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168381102
C2×#168380592
#214362002
C2×#168377602
C2×#168377192
C2×#168377332
C2×#168376852
C2×#168376582
C2×#168376282
C2×#168376222
C2×#168375562
C2×#168375092
C2×#168374762
C2×#168374032
C2×#103×D592
C2×C59×#4522
C2×#331659