Finite Group Databasebeta

← C2×#21436889 #29468377

Subgroups — C2×#21436889 #29468377

Order 15104.

2134 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838135C211yesmaximal, characteristic, complemented
2C2×D4×Dic118C211yesmaximal, characteristic, complemented
3#21436889C2116yesmaximal, direct product factor
4C2×#16837762C211yesmaximal, characteristic, complemented
5C2×#16837760C211yesmaximal, characteristic, complemented
6C2×#16837747C211yesmaximal, characteristic, complemented
7C2×#16837686C211yesmaximal, characteristic, complemented
8C2×#16837692C211yesmaximal, characteristic, complemented
9C2×#16837691C211yesmaximal, characteristic, complemented
10C2×#16837617C211yesmaximal, characteristic, complemented
11C2×#16837615C211yesmaximal, characteristic, complemented
12C2×#16837595C211yesmaximal, characteristic
13C2×#16837530C211yesmaximal, characteristic, complemented
14C2×#16837511C211yesmaximal, characteristic, complemented
15C2×#16837493C211yesmaximal, characteristic, complemented
16C2×C59×#442C211yesmaximal, characteristic, complemented
17C23×Dic118—21no—
18C22×#11745670C2211yescharacteristic
19C22×#11745669C2211yescharacteristic
20#16838135—24no—
21#16838135C2218yescomplemented
22D4×Dic118—24no—
23D4×Dic118C2218yescomplemented
24C2×#14273727C2211yescharacteristic
25C2×#14273726C2211yescharacteristic
26C2×#14273726C2211yescharacteristic
27C2×#14273723C2211yescharacteristic
28C2×#14273715C2211yescharacteristic
29C2×#14273714C2211yescharacteristic
30C2×#14273713—21no—
31C2×#14273710—21no—
32C2×#14273709—21no—
33C2×#14273706—21no—
34C2×#14273704—21no—
35C2×#14273704—21no—
36C2×C4×Dic118C2211yescharacteristic
37C2×#14273692C2211yescharacteristic
38C2×D4×Dic59C2211yescharacteristic
39C2×D4×Dic59C2211yescharacteristic
40C2×#14273689C2211yescharacteristic
41C2×C4×C22⋊D59—21no—
42#16837762C2218yescomplemented
43#16837760C2218yescomplemented
44#16837747C2218yescomplemented
45#16837692C2218yescomplemented
46#16837691C2218yescomplemented
47#16837686C2218yescomplemented
48#16837617C2218yescomplemented
49#16837615C2218yescomplemented
50#16837595C2218yes—
51#16837530C2218yescomplemented
52#16837511C2218yescomplemented
53#16837493C2218yescomplemented
54C2×#14273658C2211yescharacteristic
55C2×#14273658C2211yescharacteristic
56C2×C4⋊(C59⋊C8)C2211yescharacteristic
57C2×Dic59⋊C8C2211yescharacteristic
58C2×Dic59⋊C8C2211yescharacteristic
59C2×#14273652C2211yescharacteristic
60C2×#14273652C2211yescharacteristic
61C2×#14273650C2211yescharacteristic
62C2×#14273649C2211yescharacteristic
63C2×#14273649C2211yescharacteristic
64C2×#14273648C2211yescharacteristic
65C2×#14273648C2211yescharacteristic
66C2×#14273647C2211yescharacteristic
67C2×#14273637C2211yescharacteristic
68C2×C8×Dic59C2211yescharacteristic
69C22×D8×C59C2211yescharacteristic
70C2×C4×D4×C59C2211yescharacteristic
71C2×C4×D4×C59C2211yescharacteristic
72C59×#442C2218yescomplemented
73C2×#106×C59C2211yescharacteristic
74C2×#102×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
85C22×C22⋊D59—21no—
86C22×C22⋊D59—21no—
87C23×Dic59—21no—
88C23×Dic59—21no—
89C22×C4×D59—21no—
90C2×#11745670—24no—
91C2×#11745670C2314yes—
92C2×#11745669—24no—
93C2×#11745669C2314yes—
94C22×C59⋊C8C2311yescharacteristic
95C22×C59⋊C8C2311yescharacteristic
96#14273727—22no—
97#14273727C2314yes—
98#14273726—22no—
99#14273726—22no—
100#14273726C2314yes—
101#14273726C2314yes—
102#14273723—22no—
103#14273723C2314yes—
104#14273715—22no—
105#14273715C2314yes—
106#14273714—22no—
107#14273714C2314yes—
108#14273713—28no—
109#14273710—28no—
110#14273709—28no—
111#14273706—28no—
112#14273704—28no—
113#14273704—28no—
114C4×Dic118D414yes—
115C4×Dic118C2314yes—
116#14273692—22no—
117#14273692C2314yes—
118D4×Dic59—22no—
119D4×Dic59—22no—
120D4×Dic59C2314yes—
121D4×Dic59C2314yes—
122#14273689—22no—
123#14273689C2314yes—
124C4×C22⋊D59—28no—
125C2×C4⋊Dic59—21no—
126C2×C4⋊Dic59D411yescharacteristic
127C2×C4⋊Dic59C2311yescharacteristic
128C2×C4⋊Dic59C2311yescharacteristic
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×C22⋊Dic59—21no—
137C2×C22⋊Dic59—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#14273658C2314yes—
145#14273658C2314yes—
146C4⋊(C59⋊C8)C2314yes—
147Dic59⋊C8C2314yes—
148Dic59⋊C8C2314yes—
149#14273652C2314yes—
150#14273652C2314yes—
151#14273650C2314yes—
152#14273649C2314yes—
153#14273649C2314yes—
154#14273648C2314yes—
155#14273648C2314yes—
156#14273647C2314yes—
157#14273637C2314yes—
158C8×Dic59C2314yes—
159C22×D4×C59C2311yescharacteristic
160C22×D4×C59C2311yescharacteristic
161C23×C4×C59—21no—
162C23×C4×C59—21no—
163C2×D8×C59—24no—
164C2×D8×C59C2314yes—
165C22×C8×C59C2311yescharacteristic
166C22×C8×C59C2311yescharacteristic
167C4×D4×C59—22no—
168C4×D4×C59—22no—
169C4×D4×C59C2314yes—
170C4×D4×C59C2314yes—
171C2×C4⋊C4×C59C2311yescharacteristic
172C2×C4⋊C4×C59C2311yescharacteristic
173C2×C22⋊C4×C59—21no—
174C2×C22⋊C4×C59—21no—
175C2×C42×C59C2311yescharacteristic
176#106×C59C2314yes—
177#102×C59C2314yes—
178#102×C59C2314yes—
179#97×C59C2314yes—
180C24×C59—21no—
181C24×C59—21no—
182C23×D59—21no—
183C2×D4×C59—21no—
184C2×D4×C59—21no—
185C2×D4×C59—22no—
186C2×D4×C59—22no—
187C2×D4×C59—22no—
188C2×D4×C59#4114yes—
189C2×D4×C59C2412yes—
190C2×D4×C59C2412yes—
191C22×C4×C59—21no—
192C22×C4×C59—21no—
193C22×C4×C59—24no—
194C22×C4×C59—24no—
195C22×C4×C59—44no—
196C22×C4×C59—82no—
197C22×C4×C59C2×D411yescharacteristic
198C22×C4×C59C2×D411yescharacteristic
199C22×C4×C59C2411yescharacteristic
200C2×C22⋊D59—24no—
201C2×C22⋊D59—24no—
202C2×C22⋊D59—44no—
203C2×C22⋊D59—82no—
204C22×Dic59—21no—
205C22×Dic59—21no—
206C22×Dic59—21no—
207C22×Dic59—24no—
208C22×Dic59—24no—
209C22×Dic59—44no—
210C22×Dic59—44no—
211C22×Dic59C2×D411yescharacteristic
212C22×Dic59C2×D411yescharacteristic
213C22×Dic59C2×D411yescharacteristic
214C22×Dic59C2×D411yescharacteristic
215C2×D236—22no—
216C2×D236—22no—
217C2×D236—21no—
218C2×D236C2412yes—
219C2×C4×D59—24no—
220C2×C4×D59—82no—
221C2×Dic118—24no—
222C2×Dic118—22no—
223C2×Dic118—22no—
224C2×Dic118—21no—
225C2×Dic118—24no—
226C2×Dic118—24no—
227C2×Dic118—24no—
228C2×Dic118—432no—
229C2×Dic118—44no—
230C2×Dic118—44no—
231C2×Dic118—44no—
232C2×Dic118C2×D414yes—
233C2×Dic118C2412yes—
234D8×C59—28no—
235C2×C8×C59—22no—
236C2×C8×C59—22no—
237C2×C8×C59C2412yes—
238C2×C8×C59C2412yes—
239C4⋊C4×C59—21no—
240C4⋊C4×C59—21no—
241C4⋊C4×C59C2412yes—
242C4⋊C4×C59C2412yes—
243C22⋊C4×C59—24no—
244C22⋊C4×C59—24no—
245C42×C59C2×D412yes—
246C42×C59C2412yes—
247C22⋊Dic59—24no—
248C22⋊Dic59—24no—
249C22⋊Dic59—24no—
250C22⋊Dic59—24no—
251#11745670—28no—
252#11745669—28no—
253(C2×D59)⋊C4—24no—
254(C2×D59)⋊C4—24no—
255(C2×D59)⋊C4—24no—
256C4⋊Dic59—24no—
257C4⋊Dic59—21no—
258C4⋊Dic59—21no—
259C4⋊Dic59C2×D414yes—
260C4⋊Dic59C2412yes—
261C4⋊Dic59C2412yes—
262Dic59⋊C4—24no—
263Dic59⋊C4—24no—
264Dic59⋊C4—24no—
265Dic59⋊C4C2×D414yes—
266Dic59⋊C4C2×D414yes—
267C4×Dic59—24no—
268C4×Dic59C2×D412yes—
269C4×Dic59C2×D412yes—
270C4×Dic59C2412yes—
271C4×Dic59C2412yes—
272C2×C59⋊C8—22no—
273C2×C59⋊C8—22no—
274C2×C59⋊C8C2412yes—
275C2×C59⋊C8C2412yes—
276C23×C59—24no—
277C23×C59—22no—
278C23×C59—22no—
279C23×C59—42no—
280C23×C59—42no—
281C23×C59—42no—
282C23×C59—42no—
283C23×C59—42no—
284C23×C59C22×D411yescharacteristic
285C22×D59—22no—
286C22×D59—42no—
287C22×D59—42no—
288C22×D59—42no—
289D4×C59—24no—
290D4×C59—22no—
291D4×C59—22no—
292D4×C59—22no—
293D4×C59—42no—
294D4×C59C2×#4114yes—
295C2×C4×C59—22no—
296C2×C4×C59—22no—
297C2×C4×C59—22no—
298C2×C4×C59—22no—
299C2×C4×C59—48no—
300C2×C4×C59—42no—
301C2×C4×C59—42no—
302C2×C4×C59—84no—
303C2×C4×C59C22×D412yes—
304C2×C4×C59C22×D412yes—
305C2×C4×C59C22×D411yescharacteristic
306C2×C4×C59C2×#4112yes—
307C2×C4×C592−1+412yes—
308C2×C4×C59C2511yescharacteristic
309C22⋊D59—48no—
310C22⋊D59—84no—
311C2×Dic59—22no—
312C2×Dic59—22no—
313C2×Dic59—22no—
314C2×Dic59—22no—
315C2×Dic59—22no—
316C2×Dic59—22no—
317C2×Dic59—48no—
318C2×Dic59—42no—
319C2×Dic59—42no—
320C2×Dic59—42no—
321C2×Dic59—48no—
322C2×Dic59AGL(1,ℤ/8)14yes—
323C2×Dic59C22×D412yes—
324C2×Dic59C22×D412yes—
325C2×Dic59C22×D412yes—
326C2×Dic59C22×D412yes—
327D236—22no—
328D236—22no—
329D236—42no—
330C4×D59—84no—
331Dic118—28no—
332Dic118—22no—
333Dic118—22no—
334Dic118—48no—
335Dic118—48no—
336Dic118—42no—
337Dic118—48no—
338C8×C59—22no—
339C8×C59—22no—
340C59⋊C8—22no—
341C59⋊C8—22no—
342C2×#3373—591nomaximal, Sylow
343C22×C59—24no—
344C22×C59—48no—
345C22×C59—42no—
346C22×C59—42no—
347C22×C59—42no—
348C22×C59—42no—
349C22×C59—42no—
350C22×C59—84no—
351C22×C59#54812yes—
352C22×C59C2×AGL(1,ℤ/8)12yes—
353C22×C59#57712yes—
354C22×C59C23×D411yescharacteristic
355C2×D59—42no—
356C2×D59—42no—
357C2×D59—42no—
358C2×D59—84no—
359C4×C59—22no—
360C4×C59—22no—
361C4×C59—42no—
362C4×C59—42no—
363C4×C59#54812yes—
364C4×C59C22×#4111yescharacteristic
365C4×C59C2×2−1+411yescharacteristic
366Dic59—22no—
367Dic59—22no—
368Dic59—22no—
369Dic59—42no—
370Dic59—42no—
371Dic59—42no—
372Dic59C2×AGL(1,ℤ/8)14yes—
373C2×#559—591no—
374C2×D4×Q8—591no—
375#3373—5916no—
376C2×#489—591no—
377C2×#489—591no—
378C2×#486—591no—
379C2×#475—591no—
380C2×#476—591no—
381C2×#476—591no—
382C2×#463—591no—
383C2×#463—591no—
384C2×#459—591no—
385C2×#446—591no—
386C2×#442—591no—
387C2×#442D5911yescharacteristic, complemented
388C2×C4×SD16—591no—
389C2×C59—44no—
390C2×C59—82no—
391C2×C59#337314yescomplemented
392C2×C59C2×#54811yescharacteristic
393C2×C59C22×AGL(1,ℤ/8)11yescharacteristic
394C2×C59C2×#57711yescharacteristic
395D59—82no—
396C23×Q8—1181no—
397C22×SD16—591no—
398C22×D8—591no—
399C22×D8C2×D5911yescharacteristic
400#559—598no—
401#559—1184no—
402D4×Q8—598no—
403D4×Q8—1184no—
404C2×C4⋊Q8—591no—
405C2×C4⋊Q8—591no—
406C2×C4⋊Q8—591no—
407C2×#127—591no—
408C2×#124—591no—
409C2×#124—591no—
410C2×#124—1181no—
411C2×#123—1181no—
412C2×#123—1181no—
413C2×C22⋊Q8—1181no—
414C2×C22⋊Q8—1181no—
415C2×C22⋊Q8—1181no—
416C2×C4×Q8—591no—
417C2×C4×Q8—591no—
418C2×C4×D4—591no—
419C2×C4×D4—591no—
420C2×C4×D4—591no—
421C2×C4×D4—1181no—
422C2×C4×D4C2×D5911yescharacteristic
423C2×C4×D4C2×D5911yescharacteristic
424#489—598no—
425#489—598no—
426#486—598no—
427#476—598no—
428#476—598no—
429#475—598no—
430#463—598no—
431#463—598no—
432#459—598no—
433#446—598no—
434#442—598no—
435#442C2×D5918yescomplemented
436C4×SD16—598no—
437C2×#106—591no—
438C2×#106—591no—
439C2×#106C2×D5911yescharacteristic
440C2×C4⋊C8—591no—
441C2×C4⋊C8—591no—
442C2×C4⋊C8—591no—
443C2×#103—591no—
444C2×#103—591no—
445C2×#103—591no—
446C2×#102—591no—
447C2×#102—591no—
448C2×#102—591no—
449C2×#102—591no—
450C2×#102—591no—
451C2×#102C2×D5911yescharacteristic
452C2×#102C2×D5911yescharacteristic
453C2×#97—591no—
454C2×#97C2×D5911yescharacteristic
455C2×C4×C8—591no—
456C59C2×#337311yescharacteristic, complemented, Sylow
457C22×Q8—591no—
458C22×Q8—591no—
459C22×Q8—1181no—
460C22×Q8—1181no—
461C22×Q8—1188no—
462C22×Q8—1181no—
463C22×Q8—2368no—
464C22×D4—591no—
465C22×D4—1181no—
466C22×D4—1181no—
467C22×D4C22×D5911yescharacteristic
468C22×D4C22×D5911yescharacteristic
469C23×C4—21no—
470C23×C4—21no—
471C23×C4—1181no—
472C23×C4—1181no—
473C23×C4—1181no—
474C2×SD16—594no—
475C2×SD16—1184no—
476C2×D8—24no—
477C2×D8—594no—
478C2×D8—1184no—
479C2×D8C22×D5914yes—
480C22×C8—591no—
481C22×C8—591no—
482C22×C8C22×D5911yescharacteristic
483C22×C8C22×D5911yescharacteristic
484C4⋊Q8—594no—
485C4⋊Q8—594no—
486C4⋊Q8—594no—
487C4⋊Q8—1182no—
488C4⋊Q8—1182no—
489C4⋊Q8—1182no—
490#127—594no—
491#127—1182no—
492#124—594no—
493#124—594no—
494#124—1182no—
495#124—1188no—
496#124—1182no—
497#123—1188no—
498#123—1188no—
499C22⋊Q8—1188no—
500C22⋊Q8—1188no—
501C22⋊Q8—1188no—
502C4×Q8—594no—
503C4×Q8—594no—
504C4×Q8—594no—
505C4×Q8—1182no—
506C4×D4—22no—
507C4×D4—22no—
508C4×D4—594no—
509C4×D4—594no—
510C4×D4—594no—
511C4×D4—1182no—
512C4×D4—1182no—
513C4×D4—1182no—
514C4×D4—1188no—
515C4×D4C22×D5914yes—
516C4×D4C22×D5914yes—
517C2×C4⋊C4—591no—
518C2×C4⋊C4—591no—
519C2×C4⋊C4—591no—
520C2×C4⋊C4—591no—
521C2×C4⋊C4—591no—
522C2×C4⋊C4—1181no—
523C2×C4⋊C4—1181no—
524C2×C4⋊C4—1181no—
525C2×C4⋊C4—1181no—
526C2×C4⋊C4C22×D5911yescharacteristic
527C2×C4⋊C4C22×D5911yescharacteristic
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—1181no—
531C2×C22⋊C4—1181no—
532C2×C22⋊C4—1181no—
533C2×C22⋊C4—1181no—
534C2×C22⋊C4—1181no—
535C2×C22⋊C4—1181no—
536C2×C22⋊C4—1181no—
537C2×C42—591no—
538C2×C42—591no—
539C2×C42—1181no—
540C2×C42C22×D5911yescharacteristic
541#106—594no—
542#106—594no—
543#106C22×D5914yes—
544C4⋊C8—594no—
545C4⋊C8—594no—
546C4⋊C8—594no—
547#103—594no—
548#103—594no—
549#103—594no—
550#102—594no—
551#102—594no—
552#102—594no—
553#102—594no—
554#102—594no—
555#102C22×D5914yes—
556#102C22×D5914yes—
557#97—594no—
558#97C22×D5914yes—
559C4×C8—594no—
560C24—21no—
561C24—21no—
562C24—1181no—
563C2×Q8—594no—
564C2×Q8—592no—
565C2×Q8—1184no—
566C2×Q8—1184no—
567C2×Q8—1184no—
568C2×Q8—1181no—
569C2×Q8—1184no—
570C2×Q8—1182no—
571C2×Q8—1182no—
572C2×Q8—2364no—
573C2×Q8—2364no—
574C2×Q8—2364no—
575C2×Q8—23632no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4—592no—
582C2×D4—1184no—
583C2×D4—1184no—
584C2×D4—1181no—
585C2×D4—1182no—
586C2×D4—1182no—
587C2×D4—4722no—
588C2×D4—2364no—
589C2×D4#1174568514yes—
590C2×D4C23×D5912yes—
591C2×D4C23×D5912yes—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—24no—
595C22×C4—24no—
596C22×C4—44no—
597C22×C4—82no—
598C22×C4—591no—
599C22×C4—591no—
600C22×C4—591no—
601C22×C4—591no—
602C22×C4—1184no—
603C22×C4—1184no—
604C22×C4—1184no—
605C22×C4—1181no—
606C22×C4—1181no—
607C22×C4—1181no—
608C22×C4—4722no—
609C22×C4—2364no—
610C22×C4—2364no—
611C22×C4D4×D5911yescharacteristic
612C22×C4D4×D5911yescharacteristic
613C22×C4C23×D5911yescharacteristic
614SD16—1188no—
615D8—28no—
616D8—1188no—
617C2×C8—22no—
618C2×C8—22no—
619C2×C8—592no—
620C2×C8—592no—
621C2×C8—1182no—
622C2×C8—1182no—
623C2×C8C23×D5912yes—
624C2×C8C23×D5912yes—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—594no—
628C4⋊C4—594no—
629C4⋊C4—594no—
630C4⋊C4—592no—
631C4⋊C4—592no—
632C4⋊C4—1184no—
633C4⋊C4—1184no—
634C4⋊C4—1184no—
635C4⋊C4—1181no—
636C4⋊C4—1181no—
637C4⋊C4—1184no—
638C4⋊C4C23×D5912yes—
639C4⋊C4C23×D5912yes—
640C22⋊C4—24no—
641C22⋊C4—24no—
642C22⋊C4—1184no—
643C22⋊C4—1184no—
644C22⋊C4—1184no—
645C22⋊C4—1184no—
646C22⋊C4—1184no—
647C22⋊C4—1184no—
648C22⋊C4—1184no—
649C42—592no—
650C42—592no—
651C42—592no—
652C42—592no—
653C42—1184no—
654C42D4×D5912yes—
655C42C23×D5912yes—
656C23—22no—
657C23—24no—
658C23—22no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—1182no—
665C23—2362no—
666C23—2362no—
667C23—2362no—
668C23C2×D4×D5911yescharacteristic
669Q8—1188no—
670Q8—1182no—
671Q8—1182no—
672Q8—2368no—
673Q8—2368no—
674Q8—2368no—
675Q8—2362no—
676D4—22no—
677D4—22no—
678D4—22no—
679D4—24no—
680D4—42no—
681D4—1182no—
682D4—1182no—
683D4—4724no—
684D4—2368no—
685D4—2362no—
686D4C2×#1174568514yes—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—48no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—84no—
695C2×C4—594no—
696C2×C4—592no—
697C2×C4—592no—
698C2×C4—592no—
699C2×C4—592no—
700C2×C4—1182no—
701C2×C4—1182no—
702C2×C4—1182no—
703C2×C4—1182no—
704C2×C4—1182no—
705C2×C4—1182no—
706C2×C4—4724no—
707C2×C4—2368no—
708C2×C4—2368no—
709C2×C4—2362no—
710C2×C4—2362no—
711C2×C4—2362no—
712C2×C4C2×D4×D5912yes—
713C2×C4C2×D4×D5912yes—
714C2×C4C2×D4×D5911yescharacteristic
715C2×C4C2×#1174568512yes—
716C2×C4#1427377412yes—
717C2×C4C24×D5911yescharacteristic
718C8—22no—
719C8—22no—
720C8—1182no—
721C8—1182no—
722C22—24no—
723C22—42no—
724C22—42no—
725C22—48no—
726C22—42no—
727C22—42no—
728C22—42no—
729C22—84no—
730C22—4724no—
731C22—2362no—
732C22—2362no—
733C22—2362no—
734C22#1683806112yes—
735C22AGL(1,ℤ/8)×D5912yes—
736C22#1683821212yes—
737C22C22×D4×D5911yescharacteristic
738C4—22no—
739C4—22no—
740C4—42no—
741C4—42no—
742C4—594no—
743C4—1182no—
744C4—1182no—
745C4—1182no—
746C4—2362no—
747C4—2362no—
748C4—2362no—
749C4#1683806112yes—
750C4C22×#1174568511yescharacteristic
751C4C2×#1427377411yescharacteristic
752C2—44no—
753C2—82no—
754C2—4722no—
755C2#2143688914yesdirect product factor
756C2C2×#1683806111yescharacteristic
757C2C2×AGL(1,ℤ/8)×D5911yescharacteristic
758C2C2×#1683821211yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#442C2
socleC23×C59C22×D4
prime radicalC2×#16837595C2
hypercenterC2×#442D59
hypocenterC59C2×#3373
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#442

Complements

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

NH ≅ G/Ntype
1. C2×#16838135C2semidirect
2. C2×D4×Dic118C2semidirect
3. #21436889C2direct (N × H)
4. C2×#16837762C2semidirect
5. C2×#16837760C2semidirect
6. C2×#16837747C2semidirect
7. C2×#16837686C2semidirect
8. C2×#16837692C2semidirect
9. C2×#16837691C2semidirect
10. C2×#16837617C2semidirect
11. C2×#16837615C2semidirect
13. C2×#16837530C2semidirect
14. C2×#16837511C2semidirect
15. C2×#16837493C2semidirect
16. C2×C59×#442C2semidirect
21. #16838135C22semidirect
23. D4×Dic118C22semidirect
42. #16837762C22semidirect
43. #16837760C22semidirect
44. #16837747C22semidirect
45. #16837692C22semidirect
46. #16837691C22semidirect
47. #16837686C22semidirect
48. #16837617C22semidirect
49. #16837615C22semidirect
51. #16837530C22semidirect
52. #16837511C22semidirect
53. #16837493C22semidirect
72. C59×#442C22semidirect
387. C2×#442D59semidirect
391. C2×C59#3373semidirect
435. #442C2×D59semidirect
456. C59C2×#3373semidirect
755. C2#21436889direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168381352
C2×D4×Dic1182
#214368892
C2×#168377622
C2×#168377602
C2×#168377472
C2×#168376862
C2×#168376922
C2×#168376912
C2×#168376172
C2×#168376152
C2×#168375952
C2×#168375302
C2×#168375112
C2×#168374932
C2×C59×#4422
C2×#337359