Finite Group Databasebeta

← C2×#21436587 #29467274

Subgroups — C2×#21436587 #29467274

Order 15104.

1942 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838110C211yesmaximal, characteristic, complemented
2C2×#16838104C211yesmaximal, characteristic
3#21436587C2116yesmaximal, direct product factor
4C2×#16837809C211yesmaximal, characteristic, complemented
5C2×#16837735C211yesmaximal, characteristic, complemented
6C2×#16837718C211yesmaximal, characteristic, complemented
7C2×#16837742C211yesmaximal, characteristic, complemented
8C2×#16837714C211yesmaximal, characteristic, complemented
9C2×#16837711C211yesmaximal, characteristic, complemented
10C2×#16837680C211yesmaximal, characteristic, complemented
11C2×#16837645C211yesmaximal, characteristic, complemented
12C2×#16837503C211yesmaximal, characteristic, complemented
13C2×#16837473C211yesmaximal, characteristic, complemented
14C2×#16837441C211yesmaximal, characteristic, complemented
15C22×#14273661C211yesmaximal, characteristic, complemented
16C2×C59×#465C211yesmaximal, characteristic, complemented
17C22×#11745659C2211yescharacteristic
18#16838110—24no—
19#16838110C2218yescomplemented
20#16838104—24no—
21#16838104C2218yes—
22C2×#14273726C2211yescharacteristic
23C2×#14273720—21no—
24C2×#14273718C2211yescharacteristic
25C2×#14273717—21no—
26C2×#14273711—21no—
27C2×#14273707—21no—
28C2×#14273704—21no—
29C2×#14273703C2211yescharacteristic
30C2×#14273699—21no—
31C2×#14273698C2211yescharacteristic
32C2×Q8×Dic59C2211yescharacteristic
33C2×D4×Dic59—21no—
34C2×D4×Dic59C2211yescharacteristic
35C2×C4×C22⋊D59C2211yescharacteristic
36C2×(C22⋊D59)⋊C4—21no—
37C2×#14273685C2211yescharacteristic
38C22×C4⋊Dic59C2211yescharacteristic
39C22×C4⋊Dic59C2211yescharacteristic
40C2×C4⋊C4×D59C2211yescharacteristic
41#16837809C2218yescomplemented
42#16837742C2218yescomplemented
43#16837735C2218yescomplemented
44#16837718C2218yescomplemented
45#16837714C2218yescomplemented
46#16837711C2218yescomplemented
47#16837680C2218yescomplemented
48#16837645C2218yescomplemented
49#16837503C2218yescomplemented
50#16837473C2218yescomplemented
51#16837441C2218yescomplemented
52C2×#14273661C2211yescharacteristic
53C2×#14273661C2211yescharacteristic
54C2×#14273661C2211yescharacteristic
55C2×#14273661C2211yescharacteristic
56C2×#14273661C2218yescomplemented
57C2×#14273660C2211yescharacteristic
58C2×#14273660C2211yescharacteristic
59C2×#14273658C2211yescharacteristic
60C2×#14273658C2211yescharacteristic
61C2×Dic59⋊C8C2211yescharacteristic
62C2×#14273651C2211yescharacteristic
63C2×#14273651C2211yescharacteristic
64C2×#14273648C2211yescharacteristic
65C2×#14273648C2211yescharacteristic
66C2×C22⋊(C59⋊C8)C2211yescharacteristic
67C2×(C2×D59)⋊C8C2211yescharacteristic
68C2×#14273637C2211yescharacteristic
69C22×SD16×C59C2211yescharacteristic
70C23×C8×C59C2211yescharacteristic
71C2×C22⋊Q8×C59C2211yescharacteristic
72C2×#121×C59C2211yescharacteristic
73C59×#465C2218yescomplemented
74C2×#106×C59C2211yescharacteristic
75C2×#103×C59C2211yescharacteristic
76C2×#102×C59C2211yescharacteristic
77C22×Dic118—21no—
78C22×C22⋊D59—21no—
79C22×C22⋊D59D411yescharacteristic
80C23×Dic59—21no—
81C23×Dic59—21no—
82C23×Dic59—21no—
83C22×C4×D59—21no—
84C22×C4×D59C2311yescharacteristic
85C2×#11745659—24no—
86C2×#11745659C2314yes—
87C22×C59⋊C8C2311yescharacteristic
88C22×C59⋊C8C2311yescharacteristic
89#14273726—22no—
90#14273726C2314yes—
91#14273720—28no—
92#14273718—22no—
93#14273718C2314yes—
94#14273717—28no—
95#14273711—28no—
96#14273707—28no—
97#14273704—28no—
98#14273703—22no—
99#14273703C2314yes—
100#14273699—28no—
101#14273698—22no—
102#14273698C2314yes—
103Q8×Dic59—22no—
104Q8×Dic59C2314yes—
105D4×Dic59—28no—
106D4×Dic59—22no—
107D4×Dic59C2314yes—
108C4×C22⋊D59D414yes—
109C4×C22⋊D59C2314yes—
110(C22⋊D59)⋊C4—28no—
111#14273685—22no—
112#14273685C2314yes—
113C2×C4⋊Dic59—21no—
114C2×C4⋊Dic59—21no—
115C2×C4⋊Dic59—22no—
116C2×C4⋊Dic59—22no—
117C2×C4⋊Dic59—21no—
118C2×C4⋊Dic59—21no—
119C2×C4⋊Dic59C2311yescharacteristic
120C2×C4⋊Dic59C2311yescharacteristic
121C2×C4⋊Dic59C2311yescharacteristic
122C2×C4⋊Dic59C2311yescharacteristic
123C2×C4⋊Dic59C2314yes—
124C2×C4⋊Dic59C2314yes—
125C2×Dic59⋊C4—21no—
126C2×Dic59⋊C4—21no—
127C2×Dic59⋊C4—21no—
128C2×Dic59⋊C4—21no—
129C2×Dic59⋊C4D411yescharacteristic
130C4⋊C4×D59—22no—
131C4⋊C4×D59C2314yes—
132C2×C22⋊Dic59—21no—
133C2×C22⋊Dic59—21no—
134C2×C22⋊Dic59D411yescharacteristic
135C2×(C2×D59)⋊C4—21no—
136C2×(C2×D59)⋊C4—21no—
137C2×(C2×D59)⋊C4D411yescharacteristic
138C2×C4×Dic59—21no—
139C2×C4×Dic59—21no—
140C2×C4×Dic59C2311yescharacteristic
141#14273661C2314yes—
142#14273661C2314yes—
143#14273661C2314yes—
144#14273661C2314yes—
145#14273660C2314yes—
146#14273660C2314yes—
147#14273658C2314yes—
148#14273658C2314yes—
149Dic59⋊C8C2314yes—
150#14273651C2314yes—
151#14273651C2314yes—
152#14273648C2314yes—
153#14273648C2314yes—
154C22⋊(C59⋊C8)C2314yes—
155(C2×D59)⋊C8C2314yes—
156#14273637C2314yes—
157C22×Q8×C59C2311yescharacteristic
158C22×D4×C59—21no—
159C22×D4×C59C2311yescharacteristic
160C23×C4×C59C2311yescharacteristic
161C2×SD16×C59—24no—
162C2×SD16×C59C2314yes—
163C22×C8×C59—24no—
164C22×C8×C59C2311yescharacteristic
165C22×C8×C59C2314yes—
166C22×C8×C59C2311yescharacteristic
167C22⋊Q8×C59—22no—
168C22⋊Q8×C59C2314yes—
169#121×C59—22no—
170#121×C59C2314yes—
171C2×C4⋊C4×C59—21no—
172C2×C4⋊C4×C59C2311yescharacteristic
173C2×C4⋊C4×C59C2311yescharacteristic
174C2×C22⋊C4×C59—21no—
175C2×C22⋊C4×C59—21no—
176#106×C59C2314yes—
177#103×C59C2314yes—
178#102×C59C2314yes—
179C24×C59—21no—
180C24×C59C2×D411yescharacteristic
181C23×D59C2×D411yescharacteristic
182C2×Q8×C59—21no—
183C2×Q8×C59—22no—
184C2×Q8×C59—22no—
185C2×Q8×C59C2412yes—
186C2×D4×C59—24no—
187C2×D4×C59—21no—
188C2×D4×C59—22no—
189C2×D4×C59—22no—
190C2×D4×C59—44no—
191C2×D4×C59C2412yes—
192C22×C4×C59—22no—
193C22×C4×C59—22no—
194C22×C4×C59—21no—
195C22×C4×C59—21no—
196C22×C4×C59—21no—
197C22×C4×C59C2×D411yescharacteristic
198C22×C4×C59C2×D412yes—
199C22×C4×C59C2412yes—
200C22×C4×C59C2411yescharacteristic
201C2×C22⋊D59—24no—
202C2×C22⋊D59—24no—
203C2×C22⋊D59—82no—
204C2×C22⋊D59C2×D414yes—
205C22×Dic59—21no—
206C22×Dic59—21no—
207C22×Dic59—21no—
208C22×Dic59—21no—
209C22×Dic59—24no—
210C22×Dic59—24no—
211C22×Dic59—24no—
212C22×Dic59—82no—
213C22×Dic59—82no—
214C22×Dic59—82no—
215C22×Dic59C2×D411yescharacteristic
216C22×Dic59C2×D411yescharacteristic
217C22×Dic59C2×D411yescharacteristic
218C2×C4×D59—22no—
219C2×C4×D59—22no—
220C2×C4×D59—24no—
221C2×C4×D59—82no—
222C2×C4×D59C2×D412yes—
223C2×C4×D59C2412yes—
224C2×Dic118—24no—
225C2×Dic118—82no—
226SD16×C59—28no—
227C2×C8×C59—22no—
228C2×C8×C59—28no—
229C2×C8×C59#4114yes—
230C2×C8×C59C2412yes—
231C2×C8×C59C2412yes—
232C4⋊C4×C59—24no—
233C4⋊C4×C59—21no—
234C4⋊C4×C59—21no—
235C4⋊C4×C59C2412yes—
236C4⋊C4×C59C2412yes—
237C22⋊C4×C59—24no—
238C22⋊C4×C59—24no—
239C22⋊Dic59—24no—
240C22⋊Dic59—24no—
241C22⋊Dic59C2×D414yes—
242(C2×D59)⋊C4—24no—
243(C2×D59)⋊C4—24no—
244(C2×D59)⋊C4C2×D414yes—
245C4⋊Dic59—21no—
246C4⋊Dic59—21no—
247C4⋊Dic59—21no—
248C4⋊Dic59—21no—
249C4⋊Dic59—24no—
250C4⋊Dic59—24no—
251C4⋊Dic59—24no—
252C4⋊Dic59—24no—
253C4⋊Dic59C2412yes—
254C4⋊Dic59C2412yes—
255C4⋊Dic59C2412yes—
256C4⋊Dic59C2412yes—
257Dic59⋊C4—24no—
258Dic59⋊C4—24no—
259Dic59⋊C4—24no—
260Dic59⋊C4—24no—
261Dic59⋊C4C2×D414yes—
262C4×Dic59—24no—
263C4×Dic59—24no—
264C4×Dic59C2×D412yes—
265C4×Dic59C2412yes—
266C2×C59⋊C8—22no—
267C2×C59⋊C8—22no—
268C2×C59⋊C8C2412yes—
269C2×C59⋊C8C2412yes—
270#11745659—28no—
271C23×C59—22no—
272C23×C59—22no—
273C23×C59—22no—
274C23×C59—42no—
275C23×C59—42no—
276C23×C59—42no—
277C23×C59#13714yes—
278C23×C59C22×D412yes—
279C23×C59C22×D411yescharacteristic
280C22×D59—22no—
281C22×D59—22no—
282C22×D59—22no—
283C22×D59C22×D412yes—
284Q8×C59—22no—
285Q8×C59—22no—
286Q8×C59—42no—
287D4×C59—22no—
288D4×C59—22no—
289D4×C59—48no—
290D4×C59—42no—
291C2×C4×C59—22no—
292C2×C4×C59—24no—
293C2×C4×C59—22no—
294C2×C4×C59—22no—
295C2×C4×C59—22no—
296C2×C4×C59—22no—
297C2×C4×C59—22no—
298C2×C4×C59—42no—
299C2×C4×C59—42no—
300C2×C4×C59—42no—
301C2×C4×C59C22×D412yes—
302C2×C4×C59C22×D411yescharacteristic
303C2×C4×C59C2×#4112yes—
304C2×C4×C592−1+412yes—
305C2×C4×C59C2511yescharacteristic
306C22⋊D59—28no—
307C22⋊D59—84no—
308C2×Dic59—22no—
309C2×Dic59—22no—
310C2×Dic59—22no—
311C2×Dic59—22no—
312C2×Dic59—22no—
313C2×Dic59—22no—
314C2×Dic59—22no—
315C2×Dic59—42no—
316C2×Dic59—42no—
317C2×Dic59—42no—
318C2×Dic59—42no—
319C2×Dic59—84no—
320C2×Dic59—84no—
321C2×Dic59—84no—
322C2×Dic59C22×D412yes—
323C2×Dic59C22×D412yes—
324C2×Dic59C22×D412yes—
325C4×D59—24no—
326C4×D59—22no—
327C4×D59—22no—
328C4×D59—84no—
329Dic118—84no—
330C8×C59—22no—
331C8×C59C2×#4114yes—
332C59⋊C8—22no—
333C59⋊C8—22no—
334C2×#3346—591nomaximal, Sylow
335C22×C59—28no—
336C22×C59—22no—
337C22×C59—22no—
338C22×C59—42no—
339C22×C59—42no—
340C22×C59—42no—
341C22×C59—84no—
342C22×C59#54712yes—
343C22×C59C2×#13714yes—
344C22×C59C2×#13712yes—
345C22×C59#57612yes—
346C22×C59C23×D411yescharacteristic
347C2×D59—22no—
348C2×D59—22no—
349C2×D59—22no—
350C2×D59—44no—
351C4×C59—22no—
352C4×C59—42no—
353C4×C59—42no—
354C4×C59—42no—
355C4×C59#54712yes—
356C4×C59C22×#4111yescharacteristic
357C4×C59C2×2−1+411yescharacteristic
358Dic59—22no—
359Dic59—22no—
360Dic59—22no—
361Dic59—42no—
362Dic59—42no—
363Dic59—42no—
364Dic59—42no—
365C2×#554—591no—
366C2×#553—591no—
367#3346—5916no—
368C2×#501—591no—
369C2×#484—591no—
370C2×#481—591no—
371C2×#485—591no—
372C2×#480—591no—
373C2×#479—591no—
374C2×#474—591no—
375C2×#468—591no—
376C2×#465D5911yescharacteristic, complemented
377C2×#440—591no—
378C2×#435—591no—
379C2×#428—591no—
380C22×#107—591no—
381C2×C59—24no—
382C2×C59—82no—
383C2×C59#334614yescomplemented
384C2×C59C2×#54711yescharacteristic
385C2×C59C22×#13711yescharacteristic
386C2×C59C2×#57611yescharacteristic
387D59—42no—
388C22×SD16C2×D5911yescharacteristic
389C22×M16—591no—
390C23×C8C2×D5911yescharacteristic
391#554—598no—
392#554—1184no—
393#553—598no—
394#553—1184no—
395C2×C4⋊Q8—591no—
396C2×#126—1181no—
397C2×#125—591no—
398C2×#125—1181no—
399C2×#123—1181no—
400C2×C22⋊Q8—591no—
401C2×C22⋊Q8—1181no—
402C2×C22⋊Q8—1181no—
403C2×C22⋊Q8C2×D5911yescharacteristic
404C2×#121—591no—
405C2×#121—1181no—
406C2×#121C2×D5911yescharacteristic
407C2×C4×Q8—591no—
408C2×C4×D4—591no—
409C2×C4×D4—591no—
410C2×C4×D4—1181no—
411C2×C4×D4—1181no—
412C2×#117—591no—
413C22×C4⋊C4—591no—
414C22×C4⋊C4—591no—
415C22×C4⋊C4—591no—
416#501—598no—
417#485—598no—
418#484—598no—
419#481—598no—
420#480—598no—
421#479—598no—
422#474—598no—
423#468—598no—
424#465C2×D5918yescomplemented
425#440—598no—
426#435—598no—
427#428—598no—
428C2×#107—591no—
429C2×#107—591no—
430C2×#107—598no—
431C2×#107—591no—
432C2×#107—591no—
433C2×#107—591no—
434C2×#107—591no—
435C2×#106—591no—
436C2×#106—591no—
437C2×#106C2×D5911yescharacteristic
438C2×C4⋊C8—591no—
439C2×#103—591no—
440C2×#103—591no—
441C2×#103C2×D5911yescharacteristic
442C2×#102—591no—
443C2×#102—591no—
444C2×#102C2×D5911yescharacteristic
445C2×C22⋊C8—591no—
446C2×C22⋊C8—591no—
447C2×#97—591no—
448C59C2×#334611yescharacteristic, complemented, Sylow
449C22×Q8—1181no—
450C22×Q8C22×D5911yescharacteristic
451C22×D4—21no—
452C22×D4—591no—
453C22×D4—1181no—
454C22×D4C22×D5911yescharacteristic
455C23×C4—591no—
456C23×C4—1181no—
457C23×C4—1181no—
458C23×C4—1181no—
459C23×C4—1181no—
460C23×C4C22×D5911yescharacteristic
461C2×SD16—24no—
462C2×SD16C22×D5914yes—
463C2×M16—594no—
464C2×M16—1184no—
465C22×C8—24no—
466C22×C8—591no—
467C22×C8—591no—
468C22×C8C22×D5911yescharacteristic
469C22×C8C22×D5914yes—
470C22×C8C22×D5911yescharacteristic
471C4⋊Q8—594no—
472C4⋊Q8—1182no—
473#126—1188no—
474#125—594no—
475#125—1182no—
476#125—1188no—
477#123—1188no—
478C22⋊Q8—22no—
479C22⋊Q8—594no—
480C22⋊Q8—1188no—
481C22⋊Q8—1188no—
482C22⋊Q8—1182no—
483C22⋊Q8C22×D5914yes—
484#121—22no—
485#121—594no—
486#121—1182no—
487#121—1188no—
488#121C22×D5914yes—
489C4×Q8—594no—
490C4×Q8—1182no—
491C4×D4—594no—
492C4×D4—594no—
493C4×D4—594no—
494C4×D4—1182no—
495C4×D4—1188no—
496C4×D4—1188no—
497#117—594no—
498#117—1182no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—591no—
501C2×C4⋊C4—591no—
502C2×C4⋊C4—591no—
503C2×C4⋊C4—591no—
504C2×C4⋊C4—591no—
505C2×C4⋊C4—594no—
506C2×C4⋊C4—594no—
507C2×C4⋊C4—594no—
508C2×C4⋊C4—1182no—
509C2×C4⋊C4—1181no—
510C2×C4⋊C4—1181no—
511C2×C4⋊C4—1181no—
512C2×C4⋊C4—1181no—
513C2×C4⋊C4—1181no—
514C2×C4⋊C4—1181no—
515C2×C4⋊C4—1181no—
516C2×C4⋊C4—1181no—
517C2×C4⋊C4—1182no—
518C2×C4⋊C4—1182no—
519C2×C4⋊C4C22×D5911yescharacteristic
520C2×C4⋊C4C22×D5911yescharacteristic
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—591no—
524C2×C22⋊C4—591no—
525C2×C22⋊C4—1181no—
526C2×C22⋊C4—1181no—
527C2×C22⋊C4—1181no—
528C2×C22⋊C4—1181no—
529C2×C42—591no—
530C2×C42—1181no—
531C2×C42—1181no—
532#107—594no—
533#107—594no—
534#107—594no—
535#107—594no—
536#107—594no—
537#107—594no—
538#106—594no—
539#106—594no—
540#106C22×D5914yes—
541C4⋊C8—594no—
542#103—594no—
543#103—594no—
544#103C22×D5914yes—
545#102—594no—
546#102—594no—
547#102C22×D5914yes—
548C22⋊C8—594no—
549C22⋊C8—594no—
550#97—594no—
551C24—21no—
552C24—591no—
553C24D4×D5911yescharacteristic
554C2×Q8—21no—
555C2×Q8—22no—
556C2×Q8—22no—
557C2×Q8—1184no—
558C2×Q8—4722no—
559C2×Q8C23×D5912yes—
560C2×D4—24no—
561C2×D4—21no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—44no—
565C2×D4—594no—
566C2×D4—1184no—
567C2×D4—1184no—
568C2×D4—4722no—
569C2×D4C23×D5912yes—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—591no—
576C22×C4—591no—
577C22×C4—591no—
578C22×C4—592no—
579C22×C4—592no—
580C22×C4—1184no—
581C22×C4—1184no—
582C22×C4—1182no—
583C22×C4—1182no—
584C22×C4—1184no—
585C22×C4—1184no—
586C22×C4—1181no—
587C22×C4—1181no—
588C22×C4—1181no—
589C22×C4—1181no—
590C22×C4—4722no—
591C22×C4—4722no—
592C22×C4—4722no—
593C22×C4—4722no—
594C22×C4D4×D5912yes—
595C22×C4D4×D5911yescharacteristic
596C22×C4C23×D5912yes—
597C22×C4C23×D5911yescharacteristic
598SD16—28no—
599M16—1188no—
600C2×C8—22no—
601C2×C8—28no—
602C2×C8—592no—
603C2×C8—592no—
604C2×C8—1182no—
605C2×C8—1182no—
606C2×C8#1174568714yes—
607C2×C8C23×D5912yes—
608C2×C8C23×D5912yes—
609C4⋊C4—24no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—594no—
613C4⋊C4—592no—
614C4⋊C4—592no—
615C4⋊C4—592no—
616C4⋊C4—592no—
617C4⋊C4—1184no—
618C4⋊C4—1184no—
619C4⋊C4—1184no—
620C4⋊C4—1184no—
621C4⋊C4—1184no—
622C4⋊C4—1184no—
623C4⋊C4—1181no—
624C4⋊C4—1181no—
625C4⋊C4—1181no—
626C4⋊C4—1184no—
627C4⋊C4—1181no—
628C4⋊C4—1184no—
629C4⋊C4C23×D5912yes—
630C4⋊C4C23×D5912yes—
631C22⋊C4—24no—
632C22⋊C4—24no—
633C22⋊C4—594no—
634C22⋊C4—594no—
635C22⋊C4—1184no—
636C22⋊C4—1184no—
637C22⋊C4—1184no—
638C22⋊C4—1184no—
639C42—592no—
640C42—592no—
641C42—1184no—
642C42—1184no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—592no—
650C23—1182no—
651C23—1182no—
652C23—1182no—
653C23#1427375614yes—
654C23C2×D4×D5912yes—
655C23C2×D4×D5911yescharacteristic
656Q8—22no—
657Q8—22no—
658Q8—42no—
659Q8—4724no—
660D4—22no—
661D4—22no—
662D4—48no—
663D4—42no—
664D4—1188no—
665D4—4724no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—24no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—592no—
677C2×C4—592no—
678C2×C4—592no—
679C2×C4—1182no—
680C2×C4—1182no—
681C2×C4—1182no—
682C2×C4—1182no—
683C2×C4—1182no—
684C2×C4—1184no—
685C2×C4—1182no—
686C2×C4—1182no—
687C2×C4—1182no—
688C2×C4—1182no—
689C2×C4—4724no—
690C2×C4—4724no—
691C2×C4—4724no—
692C2×C4—4724no—
693C2×C4—2362no—
694C2×C4—2362no—
695C2×C4—2362no—
696C2×C4—2362no—
697C2×C4C2×D4×D5912yes—
698C2×C4C2×D4×D5911yescharacteristic
699C2×C4C2×#1174568712yes—
700C2×C4#1427377412yes—
701C2×C4C24×D5911yescharacteristic
702C8—22no—
703C8—1182no—
704C8—1182no—
705C8C2×#1174568714yes—
706C22—22no—
707C22—22no—
708C22—28no—
709C22—42no—
710C22—42no—
711C22—42no—
712C22—84no—
713C22—1182no—
714C22—1182no—
715C22—1182no—
716C22—2364no—
717C22#1683805212yes—
718C22C2×#1427375614yes—
719C22C2×#1427375612yes—
720C22#1683820412yes—
721C22C22×D4×D5911yescharacteristic
722C4—22no—
723C4—42no—
724C4—42no—
725C4—42no—
726C4—1182no—
727C4—1182no—
728C4—1182no—
729C4—2362no—
730C4—2362no—
731C4—2362no—
732C4—2362no—
733C4#1683805212yes—
734C4C22×#1174568711yescharacteristic
735C4C2×#1427377411yescharacteristic
736C2—24no—
737C2—82no—
738C2—2362no—
739C2#2143658714yesdirect product factor
740C2C2×#1683805211yescharacteristic
741C2C22×#1427375611yescharacteristic
742C2C2×#1683820411yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#465C2
socleC23×C59C22×D4
prime radicalC2×#16838104C2
hypercenterC2×#465D59
hypocenterC59C2×#3346
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#465

Complements

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

NH ≅ G/Ntype
1. C2×#16838110C2semidirect
3. #21436587C2direct (N × H)
4. C2×#16837809C2semidirect
5. C2×#16837735C2semidirect
6. C2×#16837718C2semidirect
7. C2×#16837742C2semidirect
8. C2×#16837714C2semidirect
9. C2×#16837711C2semidirect
10. C2×#16837680C2semidirect
11. C2×#16837645C2semidirect
12. C2×#16837503C2semidirect
13. C2×#16837473C2semidirect
14. C2×#16837441C2semidirect
15. C22×#14273661C2semidirect
16. C2×C59×#465C2semidirect
19. #16838110C22semidirect
41. #16837809C22semidirect
42. #16837742C22semidirect
43. #16837735C22semidirect
44. #16837718C22semidirect
45. #16837714C22semidirect
46. #16837711C22semidirect
47. #16837680C22semidirect
48. #16837645C22semidirect
49. #16837503C22semidirect
50. #16837473C22semidirect
51. #16837441C22semidirect
56. C2×#14273661C22semidirect
73. C59×#465C22semidirect
376. C2×#465D59semidirect
383. C2×C59#3346semidirect
424. #465C2×D59semidirect
448. C59C2×#3346semidirect
739. C2#21436587direct (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×#168381042
#214365872
C2×#168378092
C2×#168377352
C2×#168377182
C2×#168377422
C2×#168377142
C2×#168377112
C2×#168376802
C2×#168376452
C2×#168375032
C2×#168374732
C2×#168374412
C22×#142736612
C2×C59×#4652
C2×#334659