Finite Group Databasebeta

← C2×#21436531 #29467215

Subgroups — C2×#21436531 #29467215

Order 15104.

2094 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838086C211yesmaximal, characteristic, complemented
2C2×#16838052C211yesmaximal, characteristic
3#21436531C2116yesmaximal, direct product factor
4C2×#16837810C211yesmaximal, characteristic, complemented
5C2×#16837735C211yesmaximal, characteristic, complemented
6C2×#16837723C211yesmaximal, characteristic, complemented
7C2×#16837731C211yesmaximal, characteristic, complemented
8C2×#16837714C211yesmaximal, characteristic, complemented
9C2×#16837695C211yesmaximal, characteristic, complemented
10C2×#16837704C211yesmaximal, characteristic, complemented
11C2×#16837628C211yesmaximal, characteristic, complemented
12C2×#16837503C211yesmaximal, characteristic, complemented
13C2×#16837471C211yesmaximal, characteristic, complemented
14C2×#16837444C211yesmaximal, characteristic, complemented
15C2×#107×D59C211yesmaximal, characteristic, complemented
16C2×C59×#468C211yesmaximal, characteristic, complemented
17C22×#11745687—21no—
18C22×C8×D59C2211yescharacteristic
19#16838086—24no—
20#16838086C2218yescomplemented
21#16838052—24no—
22#16838052C2218yes—
23C2×#14273726C2211yescharacteristic
24C2×#14273720—21no—
25C2×#14273718C2211yescharacteristic
26C2×#14273717—21no—
27C2×#14273709—21no—
28C2×#14273709—21no—
29C2×#14273708—21no—
30C2×#14273704—21no—
31C2×#14273703C2211yescharacteristic
32C2×#14273698C2211yescharacteristic
33C2×Q8×Dic59C2211yescharacteristic
34C2×D4×Dic59C2211yescharacteristic
35C2×C4×C22⋊D59C2211yescharacteristic
36C2×#14273686C2211yescharacteristic
37C2×#14273685—21no—
38C22×C4⋊Dic59C2211yescharacteristic
39C2×C4⋊C4×D59C2211yescharacteristic
40C2×C4⋊C4×D59C2211yescharacteristic
41#16837810C2218yescomplemented
42#16837735C2218yescomplemented
43#16837731C2218yescomplemented
44#16837723C2218yescomplemented
45#16837714C2218yescomplemented
46#16837704C2218yescomplemented
47#16837695C2218yescomplemented
48#16837628C2218yescomplemented
49#16837503C2218yescomplemented
50#16837471C2218yescomplemented
51#16837444C2218yescomplemented
52C2×#14273661C2211yescharacteristic
53C2×#14273661C2211yescharacteristic
54C2×#14273660C2211yescharacteristic
55C2×#14273660C2211yescharacteristic
56C2×#14273660C2211yescharacteristic
57#107×D59C2218yescomplemented
58C2×#14273659C2211yescharacteristic
59C2×#14273659C2211yescharacteristic
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
70C22×M16×C59C2211yescharacteristic
71C2×C22⋊Q8×C59C2211yescharacteristic
72C2×#121×C59C2211yescharacteristic
73C59×#468C2218yescomplemented
74C2×#107×C59C2211yescharacteristic
75C2×#103×C59C2211yescharacteristic
76C2×#102×C59C2211yescharacteristic
77C2×#11745687—28no—
78C2×#11745687—48no—
79C22×Dic118—21no—
80C22×C22⋊D59—21no—
81C22×C22⋊D59D411yescharacteristic
82C23×Dic59—21no—
83C23×Dic59—21no—
84C22×C4×D59—21no—
85C22×C4×D59—21no—
86C22×C4×D59C2311yescharacteristic
87C22×C59⋊C8C2311yescharacteristic
88C22×C59⋊C8C2311yescharacteristic
89C2×C8×D59—24no—
90C2×C8×D59C2314yes—
91#14273726—22no—
92#14273726C2314yes—
93#14273720—28no—
94#14273718—22no—
95#14273718C2314yes—
96#14273717—28no—
97#14273709—28no—
98#14273709—28no—
99#14273708—28no—
100#14273704—28no—
101#14273703—22no—
102#14273703C2314yes—
103#14273698—22no—
104#14273698C2314yes—
105Q8×Dic59—22no—
106Q8×Dic59C2314yes—
107D4×Dic59—22no—
108D4×Dic59C2314yes—
109C4×C22⋊D59D414yes—
110C4×C22⋊D59C2314yes—
111#14273686—22no—
112#14273686C2314yes—
113#14273685—28no—
114C2×C4⋊Dic59—21no—
115C2×C4⋊Dic59—22no—
116C2×C4⋊Dic59—21no—
117C2×C4⋊Dic59—21no—
118C2×C4⋊Dic59C2311yescharacteristic
119C2×C4⋊Dic59C2311yescharacteristic
120C2×C4⋊Dic59C2311yescharacteristic
121C2×C4⋊Dic59C2311yescharacteristic
122C2×C4⋊Dic59C2314yes—
123C2×Dic59⋊C4—21no—
124C2×Dic59⋊C4—21no—
125C2×Dic59⋊C4—21no—
126C2×Dic59⋊C4—21no—
127C2×Dic59⋊C4—21no—
128C2×Dic59⋊C4D411yescharacteristic
129C4⋊C4×D59—22no—
130C4⋊C4×D59—22no—
131C4⋊C4×D59C2314yes—
132C4⋊C4×D59C2314yes—
133C2×C22⋊Dic59—21no—
134C2×C22⋊Dic59—21no—
135C2×C22⋊Dic59—21no—
136C2×C22⋊Dic59D411yescharacteristic
137C2×(C2×D59)⋊C4—21no—
138C2×(C2×D59)⋊C4D411yescharacteristic
139C2×C4×Dic59—21no—
140C2×C4×Dic59—21no—
141C2×C4×Dic59C2311yescharacteristic
142#14273661C2314yes—
143#14273661C2314yes—
144#14273660C2314yes—
145#14273660C2314yes—
146#14273660C2314yes—
147#14273659C2314yes—
148#14273659C2314yes—
149#14273658C2314yes—
150Dic59⋊C8C2314yes—
151#14273651C2314yes—
152#14273651C2314yes—
153#14273648C2314yes—
154#14273648C2314yes—
155C22⋊(C59⋊C8)C2314yes—
156(C2×D59)⋊C8C2314yes—
157#14273637C2314yes—
158C22×Q8×C59C2311yescharacteristic
159C22×D4×C59—21no—
160C22×D4×C59C2311yescharacteristic
161C23×C4×C59C2311yescharacteristic
162C2×SD16×C59—24no—
163C2×SD16×C59C2314yes—
164C2×M16×C59—24no—
165C2×M16×C59C2314yes—
166C22×C8×C59C2311yescharacteristic
167C22×C8×C59C2311yescharacteristic
168C22⋊Q8×C59—22no—
169C22⋊Q8×C59C2314yes—
170#121×C59—22no—
171#121×C59C2314yes—
172C2×C4⋊C4×C59—21no—
173C2×C4⋊C4×C59C2311yescharacteristic
174C2×C4⋊C4×C59C2311yescharacteristic
175C2×C22⋊C4×C59—21no—
176C2×C22⋊C4×C59—21no—
177#107×C59C2314yes—
178#103×C59C2314yes—
179#102×C59C2314yes—
180C24×C59—21no—
181C24×C59C2×D411yescharacteristic
182C23×D59C2×D411yescharacteristic
183C2×Q8×C59—21no—
184C2×Q8×C59—22no—
185C2×Q8×C59—22no—
186C2×Q8×C59C2412yes—
187C2×D4×C59—24no—
188C2×D4×C59—21no—
189C2×D4×C59—22no—
190C2×D4×C59—22no—
191C2×D4×C59—44no—
192C2×D4×C59C2412yes—
193C22×C4×C59—22no—
194C22×C4×C59—22no—
195C22×C4×C59—21no—
196C22×C4×C59—21no—
197C22×C4×C59—21no—
198C22×C4×C59C2×D411yescharacteristic
199C22×C4×C59C2×D412yes—
200C22×C4×C59C2412yes—
201C22×C4×C59C2411yescharacteristic
202C2×C22⋊D59—24no—
203C2×C22⋊D59—24no—
204C2×C22⋊D59—44no—
205C2×C22⋊D59C2×D414yes—
206C22×Dic59—21no—
207C22×Dic59—21no—
208C22×Dic59—21no—
209C22×Dic59—21no—
210C22×Dic59—24no—
211C22×Dic59—24no—
212C22×Dic59—44no—
213C22×Dic59—44no—
214C22×Dic59C2×D411yescharacteristic
215C22×Dic59C2×D411yescharacteristic
216C22×Dic59C2×D411yescharacteristic
217#11745687—432no—
218C2×C4×D59—22no—
219C2×C4×D59—22no—
220C2×C4×D59—24no—
221C2×C4×D59—24no—
222C2×C4×D59—44no—
223C2×C4×D59—44no—
224C2×C4×D59C2×D412yes—
225C2×C4×D59C2412yes—
226C2×Dic118—24no—
227C2×Dic118—44no—
228SD16×C59—28no—
229M16×C59—28no—
230C2×C8×C59—22no—
231C2×C8×C59#4114yescomplemented
232C2×C8×C59C2412yes—
233C2×C8×C59C2412yes—
234C4⋊C4×C59—24no—
235C4⋊C4×C59—21no—
236C4⋊C4×C59—21no—
237C4⋊C4×C59C2412yes—
238C4⋊C4×C59C2412yes—
239C22⋊C4×C59—24no—
240C22⋊C4×C59—24no—
241C22⋊Dic59—24no—
242C22⋊Dic59—24no—
243C22⋊Dic59—24no—
244C22⋊Dic59C2×D414yes—
245(C2×D59)⋊C4—24no—
246(C2×D59)⋊C4C2×D414yes—
247C4⋊Dic59—21no—
248C4⋊Dic59—21no—
249C4⋊Dic59—21no—
250C4⋊Dic59—24no—
251C4⋊Dic59—21no—
252C4⋊Dic59—24no—
253C4⋊Dic59—24no—
254C4⋊Dic59C2412yes—
255C4⋊Dic59C2412yes—
256C4⋊Dic59C2412yes—
257C4⋊Dic59C2412yes—
258Dic59⋊C4—24no—
259Dic59⋊C4—24no—
260Dic59⋊C4—24no—
261Dic59⋊C4—24no—
262Dic59⋊C4—24no—
263Dic59⋊C4C2×D414yes—
264C4×Dic59—24no—
265C4×Dic59—24no—
266C4×Dic59C2×D412yes—
267C4×Dic59C2412yes—
268C2×C59⋊C8—22no—
269C2×C59⋊C8—22no—
270C2×C59⋊C8C2412yes—
271C2×C59⋊C8C2412yes—
272C8×D59—28no—
273C23×C59—22no—
274C23×C59—22no—
275C23×C59—22no—
276C23×C59—22no—
277C23×C59—42no—
278C23×C59—42no—
279C23×C59—42no—
280C23×C59C22×D412yes—
281C23×C59C22×D411yescharacteristic
282C22×D59—22no—
283C22×D59—22no—
284C22×D59AGL(1,ℤ/8)14yes—
285C22×D59C22×D412yes—
286Q8×C59—22no—
287Q8×C59—22no—
288Q8×C59—42no—
289D4×C59—22no—
290D4×C59—22no—
291D4×C59—48no—
292D4×C59—42no—
293C2×C4×C59—22no—
294C2×C4×C59—24no—
295C2×C4×C59—22no—
296C2×C4×C59—22no—
297C2×C4×C59—22no—
298C2×C4×C59—22no—
299C2×C4×C59—22no—
300C2×C4×C59—42no—
301C2×C4×C59—42no—
302C2×C4×C59—42no—
303C2×C4×C59C22×D412yes—
304C2×C4×C59C22×D411yescharacteristic
305C2×C4×C59C2×#4112yes—
306C2×C4×C592−1+412yes—
307C2×C4×C59C2511yescharacteristic
308C22⋊D59—28no—
309C22⋊D59—48no—
310C2×Dic59—22no—
311C2×Dic59—22no—
312C2×Dic59—22no—
313C2×Dic59—22no—
314C2×Dic59—22no—
315C2×Dic59—22no—
316C2×Dic59—22no—
317C2×Dic59—48no—
318C2×Dic59—48no—
319C2×Dic59—42no—
320C2×Dic59—42no—
321C2×Dic59—42no—
322C2×Dic59—42no—
323C2×Dic59C22×D412yes—
324C2×Dic59C22×D412yes—
325C2×Dic59C22×D412yes—
326C4×D59—24no—
327C4×D59—22no—
328C4×D59—22no—
329C4×D59—48no—
330C4×D59—48no—
331Dic118—48no—
332C8×C59—22no—
333C8×C59C2×#4114yescomplemented
334C59⋊C8—22no—
335C59⋊C8—22no—
336C2×#3343—591nomaximal, Sylow
337C22×C59—22no—
338C22×C59—22no—
339C22×C59—22no—
340C22×C59—44no—
341C22×C59—42no—
342C22×C59—42no—
343C22×C59—42no—
344C22×C59—84no—
345C22×C59#54712yes—
346C22×C59C2×AGL(1,ℤ/8)12yes—
347C22×C59#57812yes—
348C22×C59C23×D411yescharacteristic
349C2×D59—28no—
350C2×D59—22no—
351C2×D59—22no—
352C2×D59C2×AGL(1,ℤ/8)14yes—
353C4×C59—22no—
354C4×C59—42no—
355C4×C59—42no—
356C4×C59—42no—
357C4×C59#54712yes—
358C4×C59C22×#4111yescharacteristic
359C4×C59C2×2−1+411yescharacteristic
360Dic59—22no—
361Dic59—22no—
362Dic59—22no—
363Dic59—42no—
364Dic59—42no—
365Dic59—42no—
366Dic59—42no—
367C2×#552—591no—
368C2×#547—591no—
369#3343—5916no—
370C2×#501—591no—
371C2×#484—591no—
372C2×#482—591no—
373C2×#483—591no—
374C2×#480—591no—
375C2×#477—591no—
376C2×#478—591no—
377C2×#468D5911yescharacteristic, complemented
378C2×#465—591no—
379C2×#440—591no—
380C2×#435—591no—
381C2×#428—591no—
382C22×#107—591no—
383C2×C59—42no—
384C2×C59—82no—
385C2×C59#334314yescomplemented
386C2×C59C2×#54711yescharacteristic
387C2×C59C22×AGL(1,ℤ/8)11yescharacteristic
388C2×C59C2×#57811yescharacteristic
389D59—24no—
390C22×#41—1181no—
391C22×SD16C2×D5911yescharacteristic
392C22×M16C2×D5911yescharacteristic
393C23×C8—591no—
394#552—598no—
395#552—1184no—
396#547—598no—
397#547—1184no—
398C2×C4⋊Q8—591no—
399C2×#126—1181no—
400C2×#125—591no—
401C2×#125—1181no—
402C2×#123—1181no—
403C2×#123—1181no—
404C2×#123—1181no—
405C2×C22⋊Q8—591no—
406C2×C22⋊Q8—1181no—
407C2×C22⋊Q8C2×D5911yescharacteristic
408C2×#121—591no—
409C2×#121C2×D5911yescharacteristic
410C2×C4×Q8—591no—
411C2×C4×D4—591no—
412C2×C4×D4—591no—
413C2×#117—591no—
414C2×#117—1181no—
415C22×C4⋊C4—591no—
416C22×C4⋊C4—591no—
417C22×C4⋊C4—591no—
418#501—598no—
419#484—598no—
420#483—598no—
421#482—598no—
422#480—598no—
423#478—598no—
424#477—598no—
425#468C2×D5918yescomplemented
426#465—598no—
427#440—598no—
428#435—598no—
429#428—598no—
430C2×#107—591no—
431C2×#107—591no—
432C2×#107—591no—
433C2×#107—591no—
434C2×#107—591no—
435C2×#107—598no—
436C2×#107C2×D5911yescharacteristic
437C2×#106—591no—
438C2×#106—591no—
439C2×#106—591no—
440C2×C4⋊C8—591no—
441C2×#103—591no—
442C2×#103—591no—
443C2×#103C2×D5911yescharacteristic
444C2×#102—591no—
445C2×#102—591no—
446C2×#102C2×D5911yescharacteristic
447C2×C22⋊C8—591no—
448C2×C22⋊C8—591no—
449C2×#97—591no—
450C59C2×#334311yescharacteristic, complemented, Sylow
451C2×#41—1188no—
452C2×#41—2368no—
453C22×Q8—1181no—
454C22×Q8C22×D5911yescharacteristic
455C22×D4—21no—
456C22×D4—591no—
457C22×D4—1181no—
458C22×D4C22×D5911yescharacteristic
459C23×C4—591no—
460C23×C4—1181no—
461C23×C4—1181no—
462C23×C4—1181no—
463C23×C4—1181no—
464C23×C4C22×D5911yescharacteristic
465C2×SD16—24no—
466C2×SD16C22×D5914yes—
467C2×M16—24no—
468C2×M16C22×D5914yes—
469C22×C8—591no—
470C22×C8—591no—
471C22×C8—594no—
472C22×C8—1184no—
473C22×C8C22×D5911yescharacteristic
474C22×C8C22×D5911yescharacteristic
475C4⋊Q8—594no—
476C4⋊Q8—1182no—
477#126—1188no—
478#125—594no—
479#125—1182no—
480#125—1188no—
481#123—1188no—
482#123—1188no—
483#123—1188no—
484C22⋊Q8—22no—
485C22⋊Q8—594no—
486C22⋊Q8—1188no—
487C22⋊Q8—1182no—
488C22⋊Q8C22×D5914yes—
489#121—22no—
490#121—594no—
491#121—1182no—
492#121C22×D5914yes—
493C4×Q8—594no—
494C4×Q8—1182no—
495C4×D4—594no—
496C4×D4—594no—
497C4×D4—594no—
498C4×D4—1182no—
499#117—594no—
500#117—1188no—
501#117—1182no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—591no—
504C2×C4⋊C4—591no—
505C2×C4⋊C4—591no—
506C2×C4⋊C4—591no—
507C2×C4⋊C4—594no—
508C2×C4⋊C4—591no—
509C2×C4⋊C4—594no—
510C2×C4⋊C4—594no—
511C2×C4⋊C4—1182no—
512C2×C4⋊C4—1182no—
513C2×C4⋊C4—1181no—
514C2×C4⋊C4—1181no—
515C2×C4⋊C4—1181no—
516C2×C4⋊C4—1181no—
517C2×C4⋊C4—1181no—
518C2×C4⋊C4—1181no—
519C2×C4⋊C4—1181no—
520C2×C4⋊C4—1181no—
521C2×C4⋊C4—1182no—
522C2×C4⋊C4C22×D5911yescharacteristic
523C2×C4⋊C4C22×D5911yescharacteristic
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—591no—
527C2×C22⋊C4—591no—
528C2×C22⋊C4—1181no—
529C2×C22⋊C4—1181no—
530C2×C22⋊C4—1181no—
531C2×C22⋊C4—1181no—
532C2×C42—591no—
533C2×C42—1181no—
534C2×C42—1181no—
535#107—594no—
536#107—594no—
537#107—594no—
538#107—594no—
539#107—594no—
540#107C22×D5914yes—
541#106—594no—
542#106—594no—
543#106—594no—
544C4⋊C8—594no—
545#103—594no—
546#103—594no—
547#103C22×D5914yes—
548#102—594no—
549#102—594no—
550#102C22×D5914yes—
551C22⋊C8—594no—
552C22⋊C8—594no—
553#97—594no—
554C24—21no—
555C24—591no—
556C24D4×D5911yescharacteristic
557#41—23632no—
558C2×Q8—21no—
559C2×Q8—22no—
560C2×Q8—22no—
561C2×Q8—1184no—
562C2×Q8—2364no—
563C2×Q8C23×D5912yes—
564C2×D4—24no—
565C2×D4—21no—
566C2×D4—22no—
567C2×D4—22no—
568C2×D4—44no—
569C2×D4—594no—
570C2×D4—1184no—
571C2×D4—1184no—
572C2×D4—2364no—
573C2×D4C23×D5912yes—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—591no—
580C22×C4—591no—
581C22×C4—591no—
582C22×C4—592no—
583C22×C4—592no—
584C22×C4—1184no—
585C22×C4—1184no—
586C22×C4—1184no—
587C22×C4—1182no—
588C22×C4—1182no—
589C22×C4—1184no—
590C22×C4—1181no—
591C22×C4—1181no—
592C22×C4—1181no—
593C22×C4—1181no—
594C22×C4—2364no—
595C22×C4—2364no—
596C22×C4—2364no—
597C22×C4—2364no—
598C22×C4D4×D5912yes—
599C22×C4D4×D5911yescharacteristic
600C22×C4C23×D5912yes—
601C22×C4C23×D5911yescharacteristic
602SD16—28no—
603M16—28no—
604C2×C8—22no—
605C2×C8—592no—
606C2×C8—592no—
607C2×C8—1182no—
608C2×C8—1182no—
609C2×C8—1188no—
610C2×C8#1174568714yescomplemented
611C2×C8C23×D5912yes—
612C2×C8C23×D5912yes—
613C4⋊C4—24no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—594no—
617C4⋊C4—592no—
618C4⋊C4—592no—
619C4⋊C4—592no—
620C4⋊C4—592no—
621C4⋊C4—1184no—
622C4⋊C4—1184no—
623C4⋊C4—1184no—
624C4⋊C4—1184no—
625C4⋊C4—1184no—
626C4⋊C4—1184no—
627C4⋊C4—1184no—
628C4⋊C4—1181no—
629C4⋊C4—1181no—
630C4⋊C4—1181no—
631C4⋊C4—1184no—
632C4⋊C4—1181no—
633C4⋊C4C23×D5912yes—
634C4⋊C4C23×D5912yes—
635C22⋊C4—24no—
636C22⋊C4—24no—
637C22⋊C4—594no—
638C22⋊C4—594no—
639C22⋊C4—1184no—
640C22⋊C4—1184no—
641C22⋊C4—1184no—
642C22⋊C4—1184no—
643C42—592no—
644C42—592no—
645C42—1184no—
646C42—1184no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—594no—
655C23—592no—
656C23—1182no—
657C23—1182no—
658C23C2×D4×D5912yes—
659C23C2×D4×D5911yescharacteristic
660Q8—22no—
661Q8—22no—
662Q8—42no—
663Q8—2368no—
664D4—22no—
665D4—22no—
666D4—48no—
667D4—42no—
668D4—1188no—
669D4—2368no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—24no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—592no—
681C2×C4—592no—
682C2×C4—592no—
683C2×C4—1182no—
684C2×C4—1182no—
685C2×C4—1182no—
686C2×C4—1182no—
687C2×C4—1182no—
688C2×C4—1184no—
689C2×C4—1182no—
690C2×C4—1182no—
691C2×C4—1182no—
692C2×C4—1182no—
693C2×C4—2368no—
694C2×C4—2368no—
695C2×C4—2368no—
696C2×C4—2368no—
697C2×C4—2362no—
698C2×C4—2362no—
699C2×C4—2362no—
700C2×C4—2362no—
701C2×C4C2×D4×D5912yes—
702C2×C4C2×D4×D5911yescharacteristic
703C2×C4C2×#1174568712yes—
704C2×C4#1427377412yes—
705C2×C4C24×D5911yescharacteristic
706C8—22no—
707C8—1182no—
708C8—1182no—
709C8C2×#1174568714yescomplemented
710C22—22no—
711C22—22no—
712C22—22no—
713C22—44no—
714C22—42no—
715C22—42no—
716C22—42no—
717C22—84no—
718C22—594no—
719C22—1182no—
720C22—1188no—
721C22—1182no—
722C22#1683805212yes—
723C22AGL(1,ℤ/8)×D5912yes—
724C22#1683821812yes—
725C22C22×D4×D5911yescharacteristic
726C4—22no—
727C4—42no—
728C4—42no—
729C4—42no—
730C4—1182no—
731C4—1182no—
732C4—1182no—
733C4—2362no—
734C4—2362no—
735C4—2362no—
736C4—2362no—
737C4#1683805212yes—
738C4C22×#1174568711yescharacteristic
739C4C2×#1427377411yescharacteristic
740C2—42no—
741C2—82no—
742C2—1184no—
743C2#2143653114yesdirect product factor
744C2C2×#1683805211yescharacteristic
745C2C2×AGL(1,ℤ/8)×D5911yescharacteristic
746C2C2×#1683821811yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#468C2
socleC23×C59C22×D4
prime radicalC2×#16838052C2
hypercenterC2×#468D59
hypocenterC59C2×#3343
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#468

Complements

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

NH ≅ G/Ntype
1. C2×#16838086C2semidirect
3. #21436531C2direct (N × H)
4. C2×#16837810C2semidirect
5. C2×#16837735C2semidirect
6. C2×#16837723C2semidirect
7. C2×#16837731C2semidirect
8. C2×#16837714C2semidirect
9. C2×#16837695C2semidirect
10. C2×#16837704C2semidirect
11. C2×#16837628C2semidirect
12. C2×#16837503C2semidirect
13. C2×#16837471C2semidirect
14. C2×#16837444C2semidirect
15. C2×#107×D59C2semidirect
16. C2×C59×#468C2semidirect
20. #16838086C22semidirect
41. #16837810C22semidirect
42. #16837735C22semidirect
43. #16837731C22semidirect
44. #16837723C22semidirect
45. #16837714C22semidirect
46. #16837704C22semidirect
47. #16837695C22semidirect
48. #16837628C22semidirect
49. #16837503C22semidirect
50. #16837471C22semidirect
51. #16837444C22semidirect
57. #107×D59C22semidirect
73. C59×#468C22semidirect
231. C2×C8×C59#41semidirect
333. C8×C59C2×#41semidirect
377. C2×#468D59semidirect
385. C2×C59#3343semidirect
425. #468C2×D59semidirect
450. C59C2×#3343semidirect
610. C2×C8#11745687semidirect
709. C8C2×#11745687semidirect
743. C2#21436531direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168380862
C2×#168380522
#214365312
C2×#168378102
C2×#168377352
C2×#168377232
C2×#168377312
C2×#168377142
C2×#168376952
C2×#168377042
C2×#168376282
C2×#168375032
C2×#168374712
C2×#168374442
C2×#107×D592
C2×C59×#4682
C2×#334359