Finite Group Databasebeta

← C2×#21436826 #29468389

Subgroups — C2×#21436826 #29468389

Order 15104.

2122 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×#16838128C211yesmaximal, characteristic, complemented
2C2×#16838073C211yesmaximal, characteristic
3#21436826C2116yesmaximal, direct product factor
4C2×#16837767C211yesmaximal, characteristic, complemented
5C2×#16837765C211yesmaximal, characteristic, complemented
6C2×#16837747C211yesmaximal, characteristic, complemented
7C2×#16837705C211yesmaximal, characteristic, complemented
8C2×#16837702C211yesmaximal, characteristic, complemented
9C2×#16837681C211yesmaximal, characteristic, complemented
10C2×#16837602C211yesmaximal, characteristic, complemented
11C2×#16837600C211yesmaximal, characteristic, complemented
12C2×#16837600C211yesmaximal, characteristic, complemented
13C2×#16837530C211yesmaximal, characteristic, complemented
14C2×#16837505C211yesmaximal, characteristic, complemented
15C2×#16837487C211yesmaximal, characteristic, complemented
16C2×C59×#440C211yesmaximal, characteristic, complemented
17C22×#11745685—21no—
18C22×#11745671C2211yescharacteristic
19C22×#11745671C2211yescharacteristic
20#16838128—24no—
21#16838128C2218yescomplemented
22#16838073—24no—
23#16838073C2218yes—
24C2×#14273726—21no—
25C2×#14273726C2211yescharacteristic
26C2×#14273724C2211yescharacteristic
27C2×#14273723C2211yescharacteristic
28C2×#14273723C2211yescharacteristic
29C2×#14273719—21no—
30C2×#14273719C2211yescharacteristic
31C2×#14273718—21no—
32C2×#14273718C2211yescharacteristic
33C2×#14273701—21no—
34C2×#14273700—21no—
35C2×#14273700—21no—
36C2×Q8×Dic59C2211yescharacteristic
37C2×Q8×Dic59C2211yescharacteristic
38C2×C4×Dic118—21no—
39C2×C4×Dic118C2211yescharacteristic
40C2×#14273689C2211yescharacteristic
41C2×#14273689C2211yescharacteristic
42#16837767C2218yescomplemented
43#16837765C2218yescomplemented
44#16837747C2218yescomplemented
45#16837705C2218yescomplemented
46#16837702C2218yescomplemented
47#16837681C2218yescomplemented
48#16837602C2218yescomplemented
49#16837600C2218yescomplemented
50#16837600C2218yescomplemented
51#16837530C2218yescomplemented
52#16837505C2218yescomplemented
53#16837487C2218yescomplemented
54C2×#14273660C2211yescharacteristic
55C2×#14273658C2211yescharacteristic
56C2×C4⋊(C59⋊C8)C2211yescharacteristic
57C2×Dic59⋊C8C2211yescharacteristic
58C2×Dic59⋊C8C2211yescharacteristic
59C2×#14273649C2211yescharacteristic
60C2×#14273649C2211yescharacteristic
61C2×#14273649C2211yescharacteristic
62C2×#14273649C2211yescharacteristic
63C2×#14273648C2211yescharacteristic
64C2×#14273648C2211yescharacteristic
65C2×#14273647C2211yescharacteristic
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
77C2×#11745685—28no—
78C2×#11745685—48no—
79C22×Dic118—21no—
80C22×Dic118D411yescharacteristic
81C22×D236—21no—
82C22×D236—21no—
83C22×D236C2311yescharacteristic
84C22×D236C2311yescharacteristic
85C22×C22⋊D59—21no—
86C22×C22⋊D59—21no—
87C22×C22⋊D59—21no—
88C22×C22⋊D59—21no—
89C22×C4×D59—21no—
90C22×C4×D59—21no—
91C2×#11745671—24no—
92C2×#11745671—24no—
93C2×#11745671C2314yes—
94C2×#11745671C2314yes—
95C22×C59⋊C8C2311yescharacteristic
96C22×C59⋊C8C2311yescharacteristic
97#14273726—28no—
98#14273726—22no—
99#14273726C2314yes—
100#14273724—22no—
101#14273724C2314yes—
102#14273723—22no—
103#14273723—22no—
104#14273723C2314yes—
105#14273723C2314yes—
106#14273719—22no—
107#14273719—28no—
108#14273719C2314yes—
109#14273718—28no—
110#14273718—22no—
111#14273718C2314yes—
112#14273701—28no—
113#14273700—28no—
114#14273700—28no—
115Q8×Dic59—22no—
116Q8×Dic59—22no—
117Q8×Dic59C2314yes—
118Q8×Dic59C2314yes—
119C4×Dic118—28no—
120C4×Dic118D414yes—
121C4×Dic118C2314yes—
122#14273689—22no—
123#14273689—22no—
124#14273689C2314yes—
125#14273689C2314yes—
126C2×C4⋊Dic59—21no—
127C2×C4⋊Dic59—21no—
128C2×C4⋊Dic59—21no—
129C2×C4⋊Dic59D411yescharacteristic
130C2×C4⋊Dic59C2311yescharacteristic
131C2×C4⋊Dic59C2311yescharacteristic
132C2×Dic59⋊C4—21no—
133C2×Dic59⋊C4—21no—
134C2×Dic59⋊C4—21no—
135C2×Dic59⋊C4—21no—
136C2×Dic59⋊C4D411yescharacteristic
137C2×Dic59⋊C4D411yescharacteristic
138C2×(C2×D59)⋊C4—21no—
139C2×(C2×D59)⋊C4—21no—
140C2×C4×Dic59—21no—
141C2×C4×Dic59—21no—
142C2×C4×Dic59C2311yescharacteristic
143C2×C4×Dic59C2311yescharacteristic
144#14273660C2314yes—
145#14273658C2314yes—
146C4⋊(C59⋊C8)C2314yes—
147Dic59⋊C8C2314yes—
148Dic59⋊C8C2314yes—
149#14273649C2314yes—
150#14273649C2314yes—
151#14273649C2314yes—
152#14273649C2314yes—
153#14273648C2314yes—
154#14273648C2314yes—
155#14273647C2314yes—
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—
182C23×D59—21no—
183C2×Q8×C59—21no—
184C2×Q8×C59—22no—
185C2×Q8×C59#4114yescomplemented
186C2×Q8×C59C2412yes—
187C2×D4×C59—21no—
188C2×D4×C59—22no—
189C2×D4×C59—22no—
190C2×D4×C59C2412yes—
191C22×C4×C59—21no—
192C22×C4×C59—21no—
193C22×C4×C59—21no—
194C22×C4×C59—24no—
195C22×C4×C59—44no—
196C22×C4×C59C2×D411yescharacteristic
197C22×C4×C59C2×D411yescharacteristic
198C22×C4×C59C2411yescharacteristic
199C2×C22⋊D59—24no—
200C2×C22⋊D59—24no—
201C2×C22⋊D59—24no—
202C2×C22⋊D59—24no—
203C2×C22⋊D59—44no—
204C2×C22⋊D59—44no—
205C2×C22⋊D59—82no—
206C2×C22⋊D59—82no—
207C22×Dic59—21no—
208C22×Dic59—21no—
209C22×Dic59C2×D411yescharacteristic
210C22×Dic59C2×D411yescharacteristic
211C22×Dic59C2×D411yescharacteristic
212C22×Dic59C2×D411yescharacteristic
213#11745685—432no—
214C2×D236—22no—
215C2×D236—22no—
216C2×D236—22no—
217C2×D236—22no—
218C2×D236—21no—
219C2×D236—21no—
220C2×D236—24no—
221C2×D236—24no—
222C2×D236—44no—
223C2×D236—82no—
224C2×D236C2412yes—
225C2×D236C2412yes—
226C2×C4×D59—24no—
227C2×C4×D59—24no—
228C2×C4×D59—44no—
229C2×C4×D59—44no—
230C2×Dic118—24no—
231C2×Dic118—24no—
232C2×Dic118—44no—
233C2×Dic118C2×D414yes—
234SD16×C59—28no—
235C2×C8×C59—22no—
236C2×C8×C59—22no—
237C2×C8×C59C2412yes—
238C2×C8×C59C2412yes—
239C4⋊C4×C59—24no—
240C4⋊C4×C59—21no—
241C4⋊C4×C59—21no—
242C4⋊C4×C59C2412yes—
243C4⋊C4×C59C2412yes—
244C22⋊C4×C59—24no—
245C42×C59—24no—
246C42×C59C2×D412yes—
247C42×C59C2412yes—
248#11745671—28no—
249#11745671—28no—
250(C2×D59)⋊C4—24no—
251(C2×D59)⋊C4—24no—
252C4⋊Dic59—21no—
253C4⋊Dic59—21no—
254C4⋊Dic59—24no—
255C4⋊Dic59—24no—
256C4⋊Dic59—24no—
257C4⋊Dic59C2×D414yes—
258C4⋊Dic59C2412yes—
259C4⋊Dic59C2412yes—
260Dic59⋊C4—24no—
261Dic59⋊C4—24no—
262Dic59⋊C4—24no—
263Dic59⋊C4—24no—
264Dic59⋊C4C2×D414yes—
265Dic59⋊C4C2×D414yes—
266C4×Dic59—24no—
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—22no—
277C23×C59—42no—
278C23×C59—42no—
279C23×C59—42no—
280C23×C59C22×D411yescharacteristic
281C22×D59—22no—
282C22×D59—22no—
283C22×D59—42no—
284C22×D59—42no—
285C22×D59—42no—
286C22×D59—42no—
287C22×D59—42no—
288C22×D59—42no—
289Q8×C59—24no—
290Q8×C59—22no—
291Q8×C59C2×#4114yescomplemented
292D4×C59—22no—
293D4×C59—22no—
294D4×C59—42no—
295C2×C4×C59—24no—
296C2×C4×C59—22no—
297C2×C4×C59—22no—
298C2×C4×C59—22no—
299C2×C4×C59—22no—
300C2×C4×C59—22no—
301C2×C4×C59—48no—
302C2×C4×C59—42no—
303C2×C4×C59—42no—
304C2×C4×C59C22×D412yes—
305C2×C4×C59C22×D412yes—
306C2×C4×C59C22×D411yescharacteristic
307C2×C4×C59C2×#4112yes—
308C2×C4×C592−1+412yes—
309C2×C4×C59C2511yescharacteristic
310C22⋊D59—48no—
311C22⋊D59—48no—
312C22⋊D59—84no—
313C22⋊D59—84no—
314C2×Dic59—22no—
315C2×Dic59—22no—
316C2×Dic59—22no—
317C2×Dic59—22no—
318C2×Dic59—22no—
319C2×Dic59—42no—
320C2×Dic59—42no—
321C2×Dic59AGL(1,ℤ/8)14yes—
322C2×Dic59C22×D412yes—
323C2×Dic59C22×D412yes—
324C2×Dic59C22×D412yes—
325C2×Dic59C22×D412yes—
326D236—22no—
327D236—22no—
328D236—22no—
329D236—22no—
330D236—48no—
331D236—42no—
332D236—42no—
333D236—84no—
334C4×D59—48no—
335C4×D59—48no—
336Dic118—28no—
337Dic118—48no—
338C8×C59—22no—
339C8×C59—22no—
340C59⋊C8—22no—
341C59⋊C8—22no—
342C2×#3368—591nomaximal, Sylow
343C22×C59—42no—
344C22×C59—42no—
345C22×C59—42no—
346C22×C59—84no—
347C22×C59#54812yes—
348C22×C59C2×AGL(1,ℤ/8)12yes—
349C22×C59#57712yes—
350C22×C59C23×D411yescharacteristic
351C2×D59—42no—
352C2×D59—42no—
353C2×D59—42no—
354C2×D59—42no—
355C2×D59—42no—
356C2×D59—42no—
357C2×D59—84no—
358C2×D59—84no—
359C4×C59—24no—
360C4×C59—22no—
361C4×C59—22no—
362C4×C59—42no—
363C4×C59—42no—
364C4×C59#54812yes—
365C4×C59C22×#4111yescharacteristic
366C4×C59C2×2−1+411yescharacteristic
367Dic59—22no—
368Dic59—22no—
369Dic59—22no—
370Dic59—42no—
371Dic59—42no—
372Dic59C2×AGL(1,ℤ/8)14yes—
373C2×#557—591no—
374C2×#550—591no—
375#3368—5916no—
376C2×#490—591no—
377C2×#490—591no—
378C2×#486—591no—
379C2×#478—591no—
380C2×#478—591no—
381C2×#474—591no—
382C2×#460—591no—
383C2×#460—591no—
384C2×#460—591no—
385C2×#446—591no—
386C2×#440—591no—
387C2×#440D5911yescharacteristic, complemented
388C2×C4×SD16—591no—
389C2×C59—82no—
390C2×C59#336814yescomplemented
391C2×C59C2×#54811yescharacteristic
392C2×C59C22×AGL(1,ℤ/8)11yescharacteristic
393C2×C59C2×#57711yescharacteristic
394D59—82no—
395D59—82no—
396C22×#41—1181no—
397C22×SD16—591no—
398C22×SD16—591no—
399C22×SD16C2×D5911yescharacteristic
400#557—598no—
401#557—1184no—
402#550—598no—
403#550—1184no—
404C2×C4⋊Q8—591no—
405C2×C4⋊Q8—1181no—
406C2×#127—591no—
407C2×#127—591no—
408C2×#127—591no—
409C2×#125—591no—
410C2×#125—591no—
411C2×#125—1181no—
412C2×#125—1181no—
413C2×#121—1181no—
414C2×#121—1181no—
415C2×#121—1181no—
416C2×C4×Q8—591no—
417C2×C4×Q8—591no—
418C2×C4×Q8—591no—
419C2×C4×Q8—1181no—
420C2×C4×Q8C2×D5911yescharacteristic
421C2×C4×D4—591no—
422C2×C4×D4—591no—
423C2×C4×D4C2×D5911yescharacteristic
424#490—598no—
425#490—598no—
426#486—598no—
427#478—598no—
428#478—598no—
429#474—598no—
430#460—598no—
431#460—598no—
432#460—598no—
433#446—598no—
434#440—598no—
435#440C2×D5918yescomplemented
436C4×SD16—598no—
437C2×#107—591no—
438C2×#107C2×D5911yescharacteristic
439C2×#106—591no—
440C2×C4⋊C8—591no—
441C2×C4⋊C8—591no—
442C2×C4⋊C8—591no—
443C2×#103C2×D5911yescharacteristic
444C2×#102—591no—
445C2×#102—591no—
446C2×#102—591no—
447C2×#102—591no—
448C2×#102—591no—
449C2×#102—591no—
450C2×#102—591no—
451C2×#102—591no—
452C2×#102C2×D5911yescharacteristic
453C2×#97—591no—
454C2×#97C2×D5911yescharacteristic
455C2×C4×C8—591no—
456C59C2×#336811yescharacteristic, complemented, Sylow
457C2×#41—1188no—
458C2×#41—2368no—
459C22×Q8—591no—
460C22×Q8—1181no—
461C22×Q8C22×D5911yescharacteristic
462C22×D4—591no—
463C22×D4—591no—
464C22×D4—1181no—
465C22×D4—1181no—
466C22×D4—1181no—
467C22×D4—1181no—
468C22×D4—1181no—
469C22×D4—1181no—
470C22×D4C22×D5911yescharacteristic
471C23×C4—21no—
472C23×C4—1181no—
473C23×C4—1181no—
474C2×SD16—24no—
475C2×SD16—594no—
476C2×SD16—594no—
477C2×SD16—1184no—
478C2×SD16—1184no—
479C2×SD16C22×D5914yes—
480C22×C8—591no—
481C22×C8—591no—
482C22×C8C22×D5911yescharacteristic
483C22×C8C22×D5911yescharacteristic
484C4⋊Q8—594no—
485C4⋊Q8—1182no—
486C4⋊Q8—1188no—
487#127—594no—
488#127—594no—
489#127—594no—
490#127—1182no—
491#127—1182no—
492#127—1182no—
493#125—594no—
494#125—594no—
495#125—1188no—
496#125—1182no—
497#125—1188no—
498#125—1182no—
499#121—1188no—
500#121—1188no—
501#121—1188no—
502C4×Q8—22no—
503C4×Q8—594no—
504C4×Q8—594no—
505C4×Q8—594no—
506C4×Q8—594no—
507C4×Q8—1188no—
508C4×Q8—1182no—
509C4×Q8—1182no—
510C4×Q8C22×D5914yes—
511C4×D4—22no—
512C4×D4—594no—
513C4×D4—594no—
514C4×D4—1182no—
515C4×D4—1182no—
516C4×D4C22×D5914yes—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—591no—
519C2×C4⋊C4—591no—
520C2×C4⋊C4—591no—
521C2×C4⋊C4—591no—
522C2×C4⋊C4—591no—
523C2×C4⋊C4—1181no—
524C2×C4⋊C4—1181no—
525C2×C4⋊C4—1181no—
526C2×C4⋊C4—1181no—
527C2×C4⋊C4—1181no—
528C2×C4⋊C4—1181no—
529C2×C4⋊C4—1181no—
530C2×C4⋊C4C22×D5911yescharacteristic
531C2×C4⋊C4C22×D5911yescharacteristic
532C2×C22⋊C4—21no—
533C2×C22⋊C4—1181no—
534C2×C22⋊C4—1181no—
535C2×C42—21no—
536C2×C42—591no—
537C2×C42—591no—
538C2×C42—1181no—
539C2×C42—1181no—
540C2×C42C22×D5911yescharacteristic
541#107—594no—
542#107C22×D5914yes—
543#106—594no—
544C4⋊C8—594no—
545C4⋊C8—594no—
546C4⋊C8—594no—
547#103C22×D5914yes—
548#102—594no—
549#102—594no—
550#102—594no—
551#102—594no—
552#102—594no—
553#102—594no—
554#102—594no—
555#102—594no—
556#102C22×D5914yes—
557#97—594no—
558#97C22×D5914yes—
559C4×C8—594no—
560C24—21no—
561C24—1181no—
562C24—1181no—
563#41—23632no—
564C2×Q8—21no—
565C2×Q8—22no—
566C2×Q8—594no—
567C2×Q8—1184no—
568C2×Q8—1184no—
569C2×Q8—2364no—
570C2×Q8#1174568514yescomplemented
571C2×Q8C23×D5912yes—
572C2×D4—21no—
573C2×D4—22no—
574C2×D4—22no—
575C2×D4—592no—
576C2×D4—592no—
577C2×D4—1184no—
578C2×D4—1184no—
579C2×D4—1184no—
580C2×D4—1184no—
581C2×D4—1184no—
582C2×D4—1181no—
583C2×D4—1181no—
584C2×D4—1184no—
585C2×D4—1182no—
586C2×D4—1182no—
587C2×D4—1182no—
588C2×D4—1182no—
589C2×D4—4722no—
590C2×D4—4722no—
591C2×D4—4722no—
592C2×D4—2364no—
593C2×D4—2364no—
594C2×D4—2364no—
595C2×D4C23×D5912yes—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—24no—
600C22×C4—44no—
601C22×C4—591no—
602C22×C4—591no—
603C22×C4—591no—
604C22×C4—591no—
605C22×C4—1184no—
606C22×C4—1184no—
607C22×C4—1181no—
608C22×C4—1181no—
609C22×C4—2364no—
610C22×C4—2364no—
611C22×C4D4×D5911yescharacteristic
612C22×C4D4×D5911yescharacteristic
613C22×C4C23×D5911yescharacteristic
614SD16—28no—
615SD16—1188no—
616SD16—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—24no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—594no—
629C4⋊C4—594no—
630C4⋊C4—594no—
631C4⋊C4—592no—
632C4⋊C4—592no—
633C4⋊C4—1184no—
634C4⋊C4—1184no—
635C4⋊C4—1184no—
636C4⋊C4—1184no—
637C4⋊C4—1184no—
638C4⋊C4—1181no—
639C4⋊C4—1181no—
640C4⋊C4—1184no—
641C4⋊C4—1184no—
642C4⋊C4C23×D5912yes—
643C4⋊C4C23×D5912yes—
644C22⋊C4—24no—
645C22⋊C4—1184no—
646C22⋊C4—1184no—
647C42—24no—
648C42—592no—
649C42—592no—
650C42—592no—
651C42—592no—
652C42—1184no—
653C42—1184no—
654C42D4×D5912yes—
655C42C23×D5912yes—
656C23—22no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—1182no—
661C23—1182no—
662C23—2362no—
663C23—2362no—
664C23—2362no—
665C23—2362no—
666C23—2362no—
667C23—2362no—
668C23C2×D4×D5911yescharacteristic
669Q8—22no—
670Q8—24no—
671Q8—1188no—
672Q8—2368no—
673Q8C2×#1174568514yescomplemented
674D4—22no—
675D4—22no—
676D4—42no—
677D4—1182no—
678D4—1182no—
679D4—1182no—
680D4—1182no—
681D4—4724no—
682D4—4724no—
683D4—4724no—
684D4—2368no—
685D4—2368no—
686D4—2368no—
687D4—2362no—
688D4—2362no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—24no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—48no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—594no—
699C2×C4—592no—
700C2×C4—592no—
701C2×C4—592no—
702C2×C4—592no—
703C2×C4—1182no—
704C2×C4—1182no—
705C2×C4—1182no—
706C2×C4—1182no—
707C2×C4—1182no—
708C2×C4—2368no—
709C2×C4—2368no—
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—42no—
723C22—42no—
724C22—42no—
725C22—84no—
726C22—4724no—
727C22—4724no—
728C22—2362no—
729C22—2362no—
730C22—2362no—
731C22—2362no—
732C22—2362no—
733C22—2362no—
734C22#1683806112yes—
735C22AGL(1,ℤ/8)×D5912yes—
736C22#1683821112yes—
737C22C22×D4×D5911yescharacteristic
738C4—22no—
739C4—24no—
740C4—22no—
741C4—42no—
742C4—42no—
743C4—594no—
744C4—1182no—
745C4—1182no—
746C4—1182no—
747C4—2362no—
748C4—2362no—
749C4#1683806112yes—
750C4C22×#1174568511yescharacteristic
751C4C2×#1427377411yescharacteristic
752C2—82no—
753C2—4722no—
754C2—4722no—
755C2#2143682614yesdirect product factor
756C2C2×#1683806111yescharacteristic
757C2C2×AGL(1,ℤ/8)×D5911yescharacteristic
758C2C2×#1683821111yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#440C2
socleC23×C59C22×D4
prime radicalC2×#16838073C2
hypercenterC2×#440D59
hypocenterC59C2×#3368
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×#16838128C2semidirect
3. #21436826C2direct (N × H)
4. C2×#16837767C2semidirect
5. C2×#16837765C2semidirect
6. C2×#16837747C2semidirect
7. C2×#16837705C2semidirect
8. C2×#16837702C2semidirect
9. C2×#16837681C2semidirect
10. C2×#16837602C2semidirect
11. C2×#16837600C2semidirect
12. C2×#16837600C2semidirect
13. C2×#16837530C2semidirect
14. C2×#16837505C2semidirect
15. C2×#16837487C2semidirect
16. C2×C59×#440C2semidirect
21. #16838128C22semidirect
42. #16837767C22semidirect
43. #16837765C22semidirect
44. #16837747C22semidirect
45. #16837705C22semidirect
46. #16837702C22semidirect
47. #16837681C22semidirect
48. #16837602C22semidirect
49. #16837600C22semidirect
50. #16837600C22semidirect
51. #16837530C22semidirect
52. #16837505C22semidirect
53. #16837487C22semidirect
72. C59×#440C22semidirect
185. C2×Q8×C59#41semidirect
291. Q8×C59C2×#41semidirect
387. C2×#440D59semidirect
390. C2×C59#3368semidirect
435. #440C2×D59semidirect
456. C59C2×#3368semidirect
570. C2×Q8#11745685semidirect
673. Q8C2×#11745685semidirect
755. C2#21436826direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168381282
C2×#168380732
#214368262
C2×#168377672
C2×#168377652
C2×#168377472
C2×#168377052
C2×#168377022
C2×#168376812
C2×#168376022
C2×#168376002
C2×#168375302
C2×#168375052
C2×#168374872
C2×C59×#4402
C2×#336859