Finite Group Databasebeta

← C2×#21436815 #29468365

Subgroups — C2×#21436815 #29468365

Order 15104.

2070 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838124C211yesmaximal, characteristic, complemented
2C2×D4×Dic118C211yesmaximal, characteristic, complemented
3#21436815C2116yesmaximal, direct product factor
4C2×#16837763C211yesmaximal, characteristic, complemented
5C2×#16837762C211yesmaximal, characteristic, complemented
6C2×#16837751C211yesmaximal, characteristic, complemented
7C2×#16837697C211yesmaximal, characteristic, complemented
8C2×#16837696C211yesmaximal, characteristic, complemented
9C2×#16837681C211yesmaximal, characteristic, complemented
10C2×#16837619C211yesmaximal, characteristic
11C2×#16837617C211yesmaximal, characteristic
12C2×#16837605C211yesmaximal, characteristic, complemented
13C2×#16837530C211yesmaximal, characteristic, complemented
14C2×#16837499C211yesmaximal, characteristic, complemented
15C2×#16837482C211yesmaximal, characteristic
16C2×C59×#440C211yesmaximal, characteristic, complemented
17C23×Dic118—21no—
18C22×#11745670C2211yescharacteristic
19C22×#11745669C2211yescharacteristic
20#16838124—24no—
21#16838124C2218yescomplemented
22D4×Dic118—24no—
23D4×Dic118C2218yescomplemented
24C2×#14273727C2211yescharacteristic
25C2×#14273726C2211yescharacteristic
26C2×#14273726C2211yescharacteristic
27C2×#14273725C2211yescharacteristic
28C2×#14273722—21no—
29C2×#14273721—21no—
30C2×#14273716C2211yescharacteristic
31C2×#14273715C2211yescharacteristic
32C2×#14273706—21no—
33C2×#14273705—21no—
34C2×#14273704—21no—
35C2×#14273704—21no—
36C2×C4×Dic118C2211yescharacteristic
37C2×#14273692C2211yescharacteristic
38C2×D4×Dic59C2211yescharacteristic
39C2×D4×Dic59C2211yescharacteristic
40C2×#14273689C2211yescharacteristic
41C2×#14273684—21no—
42#16837763C2218yescomplemented
43#16837762C2218yescomplemented
44#16837751C2218yescomplemented
45#16837697C2218yescomplemented
46#16837696C2218yescomplemented
47#16837681C2218yescomplemented
48#16837619C2218yes—
49#16837617C2218yes—
50#16837605C2218yescomplemented
51#16837530C2218yescomplemented
52#16837499C2218yescomplemented
53#16837482C2218yes—
54C2×#14273660C2211yescharacteristic
55C2×#14273660C2211yescharacteristic
56C2×C4⋊(C59⋊C8)C2211yescharacteristic
57C2×Dic59⋊C8C2211yescharacteristic
58C2×Dic59⋊C8C2211yescharacteristic
59C2×#14273652C2211yescharacteristic
60C2×#14273652C2211yescharacteristic
61C2×#14273651C2211yescharacteristic
62C2×#14273651C2211yescharacteristic
63C2×#14273650C2211yescharacteristic
64C2×#14273649C2211yescharacteristic
65C2×#14273649C2211yescharacteristic
66C2×#14273647C2211yescharacteristic
67C2×#14273637C2211yescharacteristic
68C2×C8×Dic59C2211yescharacteristic
69C22×SD16×C59C2211yescharacteristic
70C2×C4×Q8×C59C2211yescharacteristic
71C2×C4×D4×C59C2211yescharacteristic
72C59×#440C2218yescomplemented
73C2×#107×C59C2211yescharacteristic
74C2×#103×C59C2211yescharacteristic
75C2×#102×C59C2211yescharacteristic
76C2×#97×C59C2211yescharacteristic
77C22×Dic118—21no—
78C22×Dic118—21no—
79C22×Dic118—21no—
80C22×Dic118—28no—
81C22×Dic118—48no—
82C22×Dic118D411yescharacteristic
83C22×Dic118C2311yescharacteristic
84C22×D236C2311yescharacteristic
85C23×Dic59—21no—
86C23×Dic59—21no—
87C22×C4×D59—21no—
88C2×#11745670—24no—
89C2×#11745670C2314yes—
90C2×#11745669—24no—
91C2×#11745669C2314yes—
92C22×C59⋊C8C2311yescharacteristic
93C22×C59⋊C8C2311yescharacteristic
94#14273727—22no—
95#14273727C2314yes—
96#14273726—22no—
97#14273726—22no—
98#14273726C2314yes—
99#14273726C2314yes—
100#14273725—22no—
101#14273725C2314yes—
102#14273722—28no—
103#14273721—28no—
104#14273716—22no—
105#14273716C2314yes—
106#14273715—22no—
107#14273715C2314yes—
108#14273706—28no—
109#14273705—28no—
110#14273704—28no—
111#14273704—28no—
112C4×Dic118D414yes—
113C4×Dic118C2314yes—
114#14273692—22no—
115#14273692C2314yes—
116D4×Dic59—22no—
117D4×Dic59—22no—
118D4×Dic59C2314yes—
119D4×Dic59C2314yes—
120#14273689—22no—
121#14273689C2314yes—
122#14273684—28no—
123C2×C4⋊Dic59—21no—
124C2×C4⋊Dic59D411yescharacteristic
125C2×C4⋊Dic59C2311yescharacteristic
126C2×C4⋊Dic59C2311yescharacteristic
127C2×Dic59⋊C4—21no—
128C2×Dic59⋊C4—21no—
129C2×Dic59⋊C4—21no—
130C2×Dic59⋊C4—21no—
131C2×Dic59⋊C4—21no—
132C2×Dic59⋊C4D411yescharacteristic
133C2×Dic59⋊C4D411yescharacteristic
134C2×C22⋊Dic59—21no—
135C2×C22⋊Dic59—21no—
136C2×(C2×D59)⋊C4—21no—
137C2×(C2×D59)⋊C4—21no—
138C2×(C2×D59)⋊C4—21no—
139C2×(C2×D59)⋊C4—21no—
140C2×(C2×D59)⋊C4—21no—
141C2×C4×Dic59—21no—
142C2×C4×Dic59C2311yescharacteristic
143C2×C4×Dic59C2311yescharacteristic
144#14273660C2314yes—
145#14273660C2314yes—
146C4⋊(C59⋊C8)C2314yes—
147Dic59⋊C8C2314yes—
148Dic59⋊C8C2314yes—
149#14273652C2314yes—
150#14273652C2314yes—
151#14273651C2314yes—
152#14273651C2314yes—
153#14273650C2314yes—
154#14273649C2314yes—
155#14273649C2314yes—
156#14273647C2314yes—
157#14273637C2314yes—
158C8×Dic59C2314yes—
159C22×Q8×C59C2311yescharacteristic
160C22×D4×C59C2311yescharacteristic
161C23×C4×C59—21no—
162C2×SD16×C59—24no—
163C2×SD16×C59C2314yes—
164C22×C8×C59C2311yescharacteristic
165C22×C8×C59C2311yescharacteristic
166C4×Q8×C59—22no—
167C4×Q8×C59C2314yes—
168C4×D4×C59—22no—
169C4×D4×C59C2314yes—
170C2×C4⋊C4×C59—21no—
171C2×C4⋊C4×C59C2311yescharacteristic
172C2×C4⋊C4×C59C2311yescharacteristic
173C2×C22⋊C4×C59—21no—
174C2×C42×C59—21no—
175C2×C42×C59C2311yescharacteristic
176#107×C59C2314yes—
177#103×C59C2314yes—
178#102×C59C2314yes—
179#97×C59C2314yes—
180C24×C59—21no—
181C23×D59—21no—
182C2×Q8×C59—21no—
183C2×Q8×C59—22no—
184C2×Q8×C59—22no—
185C2×Q8×C59C2412yes—
186C2×D4×C59—21no—
187C2×D4×C59—22no—
188C2×D4×C59#4114yes—
189C2×D4×C59C2412yes—
190C22×C4×C59—21no—
191C22×C4×C59—21no—
192C22×C4×C59—21no—
193C22×C4×C59—24no—
194C22×C4×C59—44no—
195C22×C4×C59C2×D411yescharacteristic
196C22×C4×C59C2×D411yescharacteristic
197C22×C4×C59C2411yescharacteristic
198C22×Dic59—21no—
199C22×Dic59—21no—
200C22×Dic59—21no—
201C22×Dic59—24no—
202C22×Dic59—24no—
203C22×Dic59—44no—
204C22×Dic59—44no—
205C22×Dic59C2×D411yescharacteristic
206C22×Dic59C2×D411yescharacteristic
207C22×Dic59C2×D411yescharacteristic
208C22×Dic59C2×D411yescharacteristic
209C2×D236—22no—
210C2×D236—22no—
211C2×D236—21no—
212C2×D236C2412yes—
213C2×C4×D59—24no—
214C2×C4×D59—44no—
215C2×Dic118—24no—
216C2×Dic118—22no—
217C2×Dic118—22no—
218C2×Dic118—21no—
219C2×Dic118—24no—
220C2×Dic118—24no—
221C2×Dic118—24no—
222C2×Dic118—432no—
223C2×Dic118—44no—
224C2×Dic118—44no—
225C2×Dic118—44no—
226C2×Dic118C2×D414yes—
227C2×Dic118C2412yes—
228SD16×C59—28no—
229C2×C8×C59—22no—
230C2×C8×C59—22no—
231C2×C8×C59C2412yes—
232C2×C8×C59C2412yes—
233C4⋊C4×C59—24no—
234C4⋊C4×C59—21no—
235C4⋊C4×C59—21no—
236C4⋊C4×C59C2412yes—
237C4⋊C4×C59C2412yes—
238C22⋊C4×C59—24no—
239C42×C59—24no—
240C42×C59C2×D412yes—
241C42×C59C2412yes—
242C22⋊Dic59—24no—
243C22⋊Dic59—24no—
244#11745670—28no—
245#11745669—28no—
246(C2×D59)⋊C4—24no—
247(C2×D59)⋊C4—24no—
248(C2×D59)⋊C4—24no—
249(C2×D59)⋊C4—24no—
250(C2×D59)⋊C4—24no—
251C4⋊Dic59—24no—
252C4⋊Dic59—21no—
253C4⋊Dic59—21no—
254C4⋊Dic59C2×D414yes—
255C4⋊Dic59C2412yes—
256C4⋊Dic59C2412yes—
257Dic59⋊C4—24no—
258Dic59⋊C4—24no—
259Dic59⋊C4—24no—
260Dic59⋊C4—24no—
261Dic59⋊C4—24no—
262Dic59⋊C4C2×D414yes—
263Dic59⋊C4C2×D414yes—
264C4×Dic59—24no—
265C4×Dic59C2×D412yes—
266C4×Dic59C2×D412yes—
267C4×Dic59C2412yes—
268C4×Dic59C2412yes—
269C2×C59⋊C8—22no—
270C2×C59⋊C8—22no—
271C2×C59⋊C8C2412yes—
272C2×C59⋊C8C2412yes—
273C23×C59—24no—
274C23×C59—22no—
275C23×C59—42no—
276C23×C59—42no—
277C23×C59C22×D411yescharacteristic
278C22×D59—22no—
279C22×D59—42no—
280C22×D59—42no—
281C22×D59—42no—
282Q8×C59—22no—
283Q8×C59—22no—
284Q8×C59—42no—
285D4×C59—24no—
286D4×C59—22no—
287D4×C59C2×#4114yes—
288C2×C4×C59—22no—
289C2×C4×C59—22no—
290C2×C4×C59—22no—
291C2×C4×C59—22no—
292C2×C4×C59—22no—
293C2×C4×C59—48no—
294C2×C4×C59—42no—
295C2×C4×C59—42no—
296C2×C4×C59—42no—
297C2×C4×C59C22×D412yes—
298C2×C4×C59C22×D412yes—
299C2×C4×C59C22×D411yescharacteristic
300C2×C4×C59C2×#4112yes—
301C2×C4×C592−1+412yes—
302C2×C4×C59C2511yescharacteristic
303C2×Dic59—22no—
304C2×Dic59—22no—
305C2×Dic59—22no—
306C2×Dic59—22no—
307C2×Dic59—22no—
308C2×Dic59—22no—
309C2×Dic59—48no—
310C2×Dic59—42no—
311C2×Dic59—42no—
312C2×Dic59—42no—
313C2×Dic59—48no—
314C2×Dic59AGL(1,ℤ/8)14yes—
315C2×Dic59C22×D412yes—
316C2×Dic59C22×D412yes—
317C2×Dic59C22×D412yes—
318C2×Dic59C22×D412yes—
319D236—22no—
320D236—22no—
321D236—42no—
322C4×D59—48no—
323Dic118—28no—
324Dic118—22no—
325Dic118—22no—
326Dic118—48no—
327Dic118—48no—
328Dic118—42no—
329Dic118—48no—
330C8×C59—22no—
331C8×C59—22no—
332C59⋊C8—22no—
333C59⋊C8—22no—
334C2×#3367—591nomaximal, Sylow
335C22×C59—24no—
336C22×C59—48no—
337C22×C59—42no—
338C22×C59—42no—
339C22×C59#54812yes—
340C22×C59C2×AGL(1,ℤ/8)12yes—
341C22×C59#57812yes—
342C22×C59C23×D411yescharacteristic
343C2×D59—42no—
344C2×D59—42no—
345C2×D59—42no—
346C2×D59—84no—
347C4×C59—22no—
348C4×C59—22no—
349C4×C59—42no—
350C4×C59—42no—
351C4×C59—42no—
352C4×C59#54812yes—
353C4×C59C22×#4111yescharacteristic
354C4×C59C2×2−1+411yescharacteristic
355Dic59—22no—
356Dic59—22no—
357Dic59—22no—
358Dic59—42no—
359Dic59—42no—
360Dic59—42no—
361Dic59C2×AGL(1,ℤ/8)14yes—
362C2×#556—591no—
363C2×D4×Q8—591no—
364#3367—5916no—
365C2×#489—591no—
366C2×#489—591no—
367C2×#487—591no—
368C2×#477—591no—
369C2×#477—591no—
370C2×#474—591no—
371C2×#463—591no—
372C2×#463—591no—
373C2×#461—591no—
374C2×#446—591no—
375C2×#440—591no—
376C2×#440D5911yescharacteristic, complemented
377C2×C4×D8—591no—
378C2×C59—44no—
379C2×C59#336714yescomplemented
380C2×C59C2×#54811yescharacteristic
381C2×C59C22×AGL(1,ℤ/8)11yescharacteristic
382C2×C59C2×#57811yescharacteristic
383D59—82no—
384C23×Q8—1181no—
385C22×SD16—591no—
386C22×SD16C2×D5911yescharacteristic
387C22×D8—591no—
388#556—598no—
389#556—1184no—
390D4×Q8—598no—
391D4×Q8—1184no—
392C2×C4⋊Q8—591no—
393C2×C4⋊Q8—591no—
394C2×C4⋊Q8—591no—
395C2×C4⋊Q8—591no—
396C2×#126—1181no—
397C2×#126—1181no—
398C2×#124—591no—
399C2×#124—591no—
400C2×C22⋊Q8—1181no—
401C2×C22⋊Q8—1181no—
402C2×C22⋊Q8—1181no—
403C2×C22⋊Q8—1181no—
404C2×C4×Q8—591no—
405C2×C4×Q8—591no—
406C2×C4×Q8C2×D5911yescharacteristic
407C2×C4×D4—591no—
408C2×C4×D4—591no—
409C2×C4×D4—591no—
410C2×C4×D4C2×D5911yescharacteristic
411C2×#117—1181no—
412#489—598no—
413#489—598no—
414#487—598no—
415#477—598no—
416#477—598no—
417#474—598no—
418#463—598no—
419#463—598no—
420#461—598no—
421#446—598no—
422#440—598no—
423#440C2×D5918yescomplemented
424C4×D8—598no—
425C2×#107—591no—
426C2×#107—591no—
427C2×#107C2×D5911yescharacteristic
428C2×C4⋊C8—591no—
429C2×C4⋊C8—591no—
430C2×C4⋊C8—591no—
431C2×#103—591no—
432C2×#103—591no—
433C2×#103—591no—
434C2×#103—591no—
435C2×#103—591no—
436C2×#103C2×D5911yescharacteristic
437C2×#102—591no—
438C2×#102—591no—
439C2×#102—591no—
440C2×#102C2×D5911yescharacteristic
441C2×#97—591no—
442C2×#97C2×D5911yescharacteristic
443C2×C4×C8—591no—
444C59C2×#336711yescharacteristic, complemented, Sylow
445C22×Q8—591no—
446C22×Q8—591no—
447C22×Q8—1181no—
448C22×Q8—1181no—
449C22×Q8—1188no—
450C22×Q8—1181no—
451C22×Q8—2368no—
452C22×Q8C22×D5911yescharacteristic
453C22×D4—591no—
454C22×D4C22×D5911yescharacteristic
455C23×C4—21no—
456C23×C4—1181no—
457C23×C4—1181no—
458C23×C4—1181no—
459C2×SD16—24no—
460C2×SD16—594no—
461C2×SD16—1184no—
462C2×SD16C22×D5914yes—
463C2×D8—594no—
464C2×D8—1184no—
465C22×C8—591no—
466C22×C8—591no—
467C22×C8C22×D5911yescharacteristic
468C22×C8C22×D5911yescharacteristic
469C4⋊Q8—594no—
470C4⋊Q8—594no—
471C4⋊Q8—594no—
472C4⋊Q8—594no—
473C4⋊Q8—1182no—
474C4⋊Q8—1182no—
475C4⋊Q8—1182no—
476C4⋊Q8—1182no—
477#126—1188no—
478#126—1188no—
479#124—594no—
480#124—594no—
481#124—1182no—
482#124—1182no—
483C22⋊Q8—1188no—
484C22⋊Q8—1188no—
485C22⋊Q8—1188no—
486C22⋊Q8—1188no—
487C4×Q8—22no—
488C4×Q8—594no—
489C4×Q8—594no—
490C4×Q8—594no—
491C4×Q8—1182no—
492C4×Q8C22×D5914yes—
493C4×D4—22no—
494C4×D4—594no—
495C4×D4—594no—
496C4×D4—594no—
497C4×D4—1182no—
498C4×D4—1182no—
499C4×D4—1182no—
500C4×D4C22×D5914yes—
501#117—1188no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—591no—
504C2×C4⋊C4—591no—
505C2×C4⋊C4—591no—
506C2×C4⋊C4—591no—
507C2×C4⋊C4—591no—
508C2×C4⋊C4—1181no—
509C2×C4⋊C4—1181no—
510C2×C4⋊C4—1181no—
511C2×C4⋊C4—1181no—
512C2×C4⋊C4—1181no—
513C2×C4⋊C4—1181no—
514C2×C4⋊C4C22×D5911yescharacteristic
515C2×C4⋊C4C22×D5911yescharacteristic
516C2×C22⋊C4—21no—
517C2×C22⋊C4—1181no—
518C2×C22⋊C4—1181no—
519C2×C22⋊C4—1181no—
520C2×C22⋊C4—1181no—
521C2×C22⋊C4—1181no—
522C2×C22⋊C4—1181no—
523C2×C22⋊C4—1181no—
524C2×C42—21no—
525C2×C42—591no—
526C2×C42—591no—
527C2×C42—1181no—
528C2×C42C22×D5911yescharacteristic
529#107—594no—
530#107—594no—
531#107C22×D5914yes—
532C4⋊C8—594no—
533C4⋊C8—594no—
534C4⋊C8—594no—
535#103—594no—
536#103—594no—
537#103—594no—
538#103—594no—
539#103—594no—
540#103C22×D5914yes—
541#102—594no—
542#102—594no—
543#102—594no—
544#102C22×D5914yes—
545#97—594no—
546#97C22×D5914yes—
547C4×C8—594no—
548C24—21no—
549C24—1181no—
550C2×Q8—21no—
551C2×Q8—22no—
552C2×Q8—22no—
553C2×Q8—594no—
554C2×Q8—592no—
555C2×Q8—1184no—
556C2×Q8—1184no—
557C2×Q8—1184no—
558C2×Q8—1181no—
559C2×Q8—1184no—
560C2×Q8—1182no—
561C2×Q8—1182no—
562C2×Q8—2364no—
563C2×Q8—2364no—
564C2×Q8—2364no—
565C2×Q8—23632no—
566C2×Q8C23×D5912yes—
567C2×D4—21no—
568C2×D4—22no—
569C2×D4—592no—
570C2×D4—1181no—
571C2×D4—1182no—
572C2×D4—1182no—
573C2×D4#1174568514yes—
574C2×D4C23×D5912yes—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—24no—
579C22×C4—44no—
580C22×C4—591no—
581C22×C4—591no—
582C22×C4—591no—
583C22×C4—591no—
584C22×C4—1184no—
585C22×C4—1184no—
586C22×C4—1184no—
587C22×C4—1181no—
588C22×C4—1181no—
589C22×C4—1181no—
590C22×C4—2364no—
591C22×C4—2364no—
592C22×C4—2364no—
593C22×C4D4×D5911yescharacteristic
594C22×C4D4×D5911yescharacteristic
595C22×C4C23×D5911yescharacteristic
596SD16—28no—
597SD16—1188no—
598D8—1188no—
599C2×C8—22no—
600C2×C8—22no—
601C2×C8—592no—
602C2×C8—592no—
603C2×C8—1182no—
604C2×C8—1182no—
605C2×C8C23×D5912yes—
606C2×C8C23×D5912yes—
607C4⋊C4—24no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—594no—
611C4⋊C4—594no—
612C4⋊C4—594no—
613C4⋊C4—592no—
614C4⋊C4—592no—
615C4⋊C4—1184no—
616C4⋊C4—1184no—
617C4⋊C4—1184no—
618C4⋊C4—1184no—
619C4⋊C4—1184no—
620C4⋊C4—1181no—
621C4⋊C4—1181no—
622C4⋊C4—1184no—
623C4⋊C4C23×D5912yes—
624C4⋊C4C23×D5912yes—
625C22⋊C4—24no—
626C22⋊C4—1184no—
627C22⋊C4—1184no—
628C22⋊C4—1184no—
629C22⋊C4—1184no—
630C22⋊C4—1184no—
631C22⋊C4—1184no—
632C22⋊C4—1184no—
633C42—24no—
634C42—592no—
635C42—592no—
636C42—592no—
637C42—592no—
638C42—1184no—
639C42D4×D5912yes—
640C42C23×D5912yes—
641C23—22no—
642C23—24no—
643C23—42no—
644C23—42no—
645C23—1182no—
646C23—2362no—
647C23—2362no—
648C23—2362no—
649C23C2×D4×D5911yescharacteristic
650Q8—22no—
651Q8—22no—
652Q8—42no—
653Q8—1188no—
654Q8—1182no—
655Q8—1182no—
656Q8—2368no—
657Q8—2368no—
658Q8—2368no—
659Q8—2362no—
660D4—22no—
661D4—24no—
662D4—1182no—
663D4—1182no—
664D4—2362no—
665D4C2×#1174568514yes—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—48no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—594no—
676C2×C4—592no—
677C2×C4—592no—
678C2×C4—592no—
679C2×C4—592no—
680C2×C4—1182no—
681C2×C4—1182no—
682C2×C4—1182no—
683C2×C4—1182no—
684C2×C4—1182no—
685C2×C4—1182no—
686C2×C4—2368no—
687C2×C4—2368no—
688C2×C4—2368no—
689C2×C4—2362no—
690C2×C4—2362no—
691C2×C4—2362no—
692C2×C4C2×D4×D5912yes—
693C2×C4C2×D4×D5912yes—
694C2×C4C2×D4×D5911yescharacteristic
695C2×C4C2×#1174568512yes—
696C2×C4#1427377412yes—
697C2×C4C24×D5911yescharacteristic
698C8—22no—
699C8—22no—
700C8—1182no—
701C8—1182no—
702C22—24no—
703C22—42no—
704C22—42no—
705C22—48no—
706C22—4724no—
707C22—2362no—
708C22—2362no—
709C22—2362no—
710C22#1683806112yes—
711C22AGL(1,ℤ/8)×D5912yes—
712C22#1683821812yes—
713C22C22×D4×D5911yescharacteristic
714C4—22no—
715C4—22no—
716C4—42no—
717C4—42no—
718C4—42no—
719C4—594no—
720C4—1182no—
721C4—1182no—
722C4—1182no—
723C4—2362no—
724C4—2362no—
725C4—2362no—
726C4#1683806112yes—
727C4C22×#1174568511yescharacteristic
728C4C2×#1427377411yescharacteristic
729C2—44no—
730C2—4722no—
731C2#2143681514yesdirect product factor
732C2C2×#1683806111yescharacteristic
733C2C2×AGL(1,ℤ/8)×D5911yescharacteristic
734C2C2×#1683821811yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#440C2
socleC23×C59C22×D4
prime radicalC22×#11745669C22
hypercenterC2×#440D59
hypocenterC59C2×#3367
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
1. C2×#16838124C2semidirect
2. C2×D4×Dic118C2semidirect
3. #21436815C2direct (N × H)
4. C2×#16837763C2semidirect
5. C2×#16837762C2semidirect
6. C2×#16837751C2semidirect
7. C2×#16837697C2semidirect
8. C2×#16837696C2semidirect
9. C2×#16837681C2semidirect
12. C2×#16837605C2semidirect
13. C2×#16837530C2semidirect
14. C2×#16837499C2semidirect
16. C2×C59×#440C2semidirect
21. #16838124C22semidirect
23. D4×Dic118C22semidirect
42. #16837763C22semidirect
43. #16837762C22semidirect
44. #16837751C22semidirect
45. #16837697C22semidirect
46. #16837696C22semidirect
47. #16837681C22semidirect
50. #16837605C22semidirect
51. #16837530C22semidirect
52. #16837499C22semidirect
72. C59×#440C22semidirect
376. C2×#440D59semidirect
379. C2×C59#3367semidirect
423. #440C2×D59semidirect
444. C59C2×#3367semidirect
731. C2#21436815direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168381242
C2×D4×Dic1182
#214368152
C2×#168377632
C2×#168377622
C2×#168377512
C2×#168376972
C2×#168376962
C2×#168376812
C2×#168376192
C2×#168376172
C2×#168376052
C2×#168375302
C2×#168374992
C2×#168374822
C2×C59×#4402
C2×#336759