Finite Group Databasebeta

← C2×#21436828 #29468391

Subgroups — C2×#21436828 #29468391

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×#16838129C211yesmaximal, characteristic, complemented
2C2×#16838073C211yesmaximal, characteristic
3#21436828C2116yesmaximal, direct product factor
4C2×#16837768C211yesmaximal, characteristic, complemented
5C2×#16837765C211yesmaximal, characteristic, complemented
6C2×#16837747C211yesmaximal, characteristic, complemented
7C2×#16837701C211yesmaximal, characteristic, complemented
8C2×#16837681C211yesmaximal, characteristic, complemented
9C2×#16837603C211yesmaximal, characteristic, complemented
10C2×#16837601C211yesmaximal, characteristic, complemented
11C2×#16837601C211yesmaximal, characteristic, complemented
12C2×#16837531C211yesmaximal, characteristic, complemented
13C2×#16837502C211yesmaximal, characteristic, complemented
14C2×#16837501C211yesmaximal, characteristic, complemented
15C2×#16837489C211yesmaximal, characteristic, complemented
16C2×C59×#478C211yesmaximal, characteristic, complemented
17C22×#11745685—21no—
18C22×#11745660C2211yescharacteristic
19C22×#11745660C2211yescharacteristic
20C22×#11745670C2211yescharacteristic
21#16838129—24no—
22#16838129C2218yescomplemented
23#16838073—24no—
24#16838073C2218yes—
25C2×#14273726—21no—
26C2×#14273726C2211yescharacteristic
27C2×#14273724C2211yescharacteristic
28C2×#14273723C2211yescharacteristic
29C2×#14273723C2211yescharacteristic
30C2×#14273718C2211yescharacteristic
31C2×#14273717—21no—
32C2×#14273717—21no—
33C2×#14273701—21no—
34C2×#14273700—21no—
35C2×#14273700—21no—
36C2×C4×Dic118C2211yescharacteristic
37C2×C4×Dic118C2211yescharacteristic
38C2×#14273692—21no—
39C2×#14273692C2211yescharacteristic
40C2×#14273692C2211yescharacteristic
41C2×#14273689C2211yescharacteristic
42C2×#14273689C2211yescharacteristic
43#16837768C2218yescomplemented
44#16837765C2218yescomplemented
45#16837747C2218yescomplemented
46#16837701C2218yescomplemented
47#16837681C2218yescomplemented
48#16837603C2218yescomplemented
49#16837601C2218yescomplemented
50#16837601C2218yescomplemented
51#16837531C2218yescomplemented
52#16837502C2218yescomplemented
53#16837501C2218yescomplemented
54#16837489C2218yescomplemented
55C2×#14273660C2211yescharacteristic
56C2×Dic59⋊C8C2211yescharacteristic
57C2×Dic59⋊C8C2211yescharacteristic
58C2×#14273650C2211yescharacteristic
59C2×#14273649C2211yescharacteristic
60C2×#14273649C2211yescharacteristic
61C2×#14273648C2211yescharacteristic
62C2×#14273647C2211yescharacteristic
63C2×#14273647C2211yescharacteristic
64C2×#14273647C2211yescharacteristic
65C2×#14273647C2211yescharacteristic
66C2×#14273638C2211yescharacteristic
67C2×#14273637C2211yescharacteristic
68C2×C8×Dic59C2211yescharacteristic
69C2×#125×C59C2211yescharacteristic
70C2×C4×D4×C59C2211yescharacteristic
71C59×#478C2218yescomplemented
72C2×#107×C59C2211yescharacteristic
73C2×#106×C59C2211yescharacteristic
74C2×C4⋊C8×C59C2211yescharacteristic
75C2×#102×C59C2211yescharacteristic
76C2×#102×C59C2211yescharacteristic
77C2×#11745685—28no—
78C2×#11745685—48no—
79C22×Dic118—21no—
80C22×Dic118D411yescharacteristic
81C22×Dic118C2311yescharacteristic
82C22×D236—21no—
83C22×D236—21no—
84C22×D236C2311yescharacteristic
85C22×D236C2311yescharacteristic
86C22×C22⋊D59—21no—
87C22×C22⋊D59—21no—
88C22×C22⋊D59—21no—
89C22×C22⋊D59—21no—
90C22×C4×D59—21no—
91C22×C4×D59—21no—
92C2×#11745660—24no—
93C2×#11745660—24no—
94C2×#11745660C2314yes—
95C2×#11745660C2314yes—
96C2×#11745670—24no—
97C2×#11745670C2314yes—
98C22×C59⋊C8C2311yescharacteristic
99C22×C59⋊C8C2311yescharacteristic
100#14273726—28no—
101#14273726—22no—
102#14273726C2314yes—
103#14273724—22no—
104#14273724C2314yes—
105#14273723—22no—
106#14273723—22no—
107#14273723C2314yes—
108#14273723C2314yes—
109#14273718—22no—
110#14273718C2314yes—
111#14273717—28no—
112#14273717—28no—
113#14273701—28no—
114#14273700—28no—
115#14273700—28no—
116C4×Dic118—22no—
117C4×Dic118D414yes—
118C4×Dic118C2314yes—
119C4×Dic118C2314yes—
120#14273692—28no—
121#14273692—22no—
122#14273692—22no—
123#14273692C2314yes—
124#14273692C2314yes—
125#14273689—22no—
126#14273689—22no—
127#14273689C2314yes—
128#14273689C2314yes—
129C2×C4⋊Dic59—21no—
130C2×C4⋊Dic59D411yescharacteristic
131C2×C4⋊Dic59C2311yescharacteristic
132C2×Dic59⋊C4—21no—
133C2×Dic59⋊C4—21no—
134C2×Dic59⋊C4—21no—
135C2×Dic59⋊C4—21no—
136C2×Dic59⋊C4—21no—
137C2×Dic59⋊C4D411yescharacteristic
138C2×Dic59⋊C4D411yescharacteristic
139C2×(C2×D59)⋊C4—21no—
140C2×(C2×D59)⋊C4—21no—
141C2×C4×Dic59—21no—
142C2×C4×Dic59—21no—
143C2×C4×Dic59—21no—
144C2×C4×Dic59C2311yescharacteristic
145C2×C4×Dic59C2311yescharacteristic
146#14273660C2314yes—
147Dic59⋊C8C2314yes—
148Dic59⋊C8C2314yes—
149#14273650C2314yes—
150#14273649C2314yes—
151#14273649C2314yes—
152#14273648C2314yes—
153#14273647C2314yes—
154#14273647C2314yes—
155#14273647C2314yes—
156#14273647C2314yes—
157#14273638C2314yes—
158#14273637C2314yes—
159C8×Dic59C2314yes—
160C22×D4×C59C2311yescharacteristic
161C23×C4×C59—21no—
162C22×C8×C59C2311yescharacteristic
163C22×C8×C59C2311yescharacteristic
164#125×C59—22no—
165#125×C59C2314yes—
166C4×D4×C59—22no—
167C4×D4×C59C2314yes—
168C2×C4⋊C4×C59—21no—
169C2×C4⋊C4×C59—21no—
170C2×C4⋊C4×C59C2311yescharacteristic
171C2×C4⋊C4×C59C2311yescharacteristic
172C2×C4⋊C4×C59C2311yescharacteristic
173C2×C22⋊C4×C59—21no—
174C2×C42×C59C2311yescharacteristic
175#107×C59C2314yes—
176#106×C59C2314yes—
177C4⋊C8×C59C2314yes—
178#102×C59C2314yes—
179#102×C59C2314yes—
180C24×C59—21no—
181C23×D59—21no—
182C23×D59—21no—
183C2×D4×C59—21no—
184C2×D4×C59—22no—
185C2×D4×C59—22no—
186C2×D4×C59C2412yes—
187C22×C4×C59—21no—
188C22×C4×C59—21no—
189C22×C4×C59—21no—
190C22×C4×C59—24no—
191C22×C4×C59—44no—
192C22×C4×C59C2×D411yescharacteristic
193C22×C4×C59C2×D411yescharacteristic
194C22×C4×C59C2411yescharacteristic
195C2×C22⋊D59—24no—
196C2×C22⋊D59—24no—
197C2×C22⋊D59—24no—
198C2×C22⋊D59—24no—
199C2×C22⋊D59—44no—
200C2×C22⋊D59—44no—
201C2×C22⋊D59—82no—
202C2×C22⋊D59—82no—
203C22×Dic59—21no—
204C22×Dic59—21no—
205C22×Dic59C2×D411yescharacteristic
206C22×Dic59C2×D411yescharacteristic
207C22×Dic59C2×D411yescharacteristic
208C22×Dic59C2×D411yescharacteristic
209#11745685—432no—
210C2×D236—22no—
211C2×D236—22no—
212C2×D236—22no—
213C2×D236—22no—
214C2×D236—21no—
215C2×D236—21no—
216C2×D236—24no—
217C2×D236—24no—
218C2×D236—44no—
219C2×D236—82no—
220C2×D236C2412yes—
221C2×D236C2412yes—
222C2×C4×D59—24no—
223C2×C4×D59—24no—
224C2×C4×D59—44no—
225C2×C4×D59—44no—
226C2×Dic118—21no—
227C2×Dic118—22no—
228C2×Dic118—24no—
229C2×Dic118—24no—
230C2×Dic118—44no—
231C2×Dic118C2×D414yes—
232C2×Dic118#4114yescomplemented
233C2×Dic118C2412yes—
234C2×C8×C59—22no—
235C2×C8×C59—22no—
236C2×C8×C59C2412yes—
237C2×C8×C59C2412yes—
238C4⋊C4×C59—24no—
239C4⋊C4×C59—24no—
240C4⋊C4×C59—21no—
241C4⋊C4×C59—21no—
242C4⋊C4×C59—21no—
243C4⋊C4×C59C2412yes—
244C4⋊C4×C59C2412yes—
245C4⋊C4×C59C2412yes—
246C22⋊C4×C59—24no—
247C42×C59C2×D412yes—
248C42×C59C2412yes—
249#11745670—28no—
250(C2×D59)⋊C4—24no—
251(C2×D59)⋊C4—24no—
252C4⋊Dic59—21no—
253C4⋊Dic59—24no—
254C4⋊Dic59C2×D414yes—
255C4⋊Dic59C2412yes—
256Dic59⋊C4—24no—
257Dic59⋊C4—24no—
258Dic59⋊C4—24no—
259Dic59⋊C4—24no—
260Dic59⋊C4—24no—
261Dic59⋊C4C2×D414yes—
262Dic59⋊C4C2×D414yes—
263C4×Dic59—24no—
264C4×Dic59—24no—
265C4×Dic59—24no—
266C4×Dic59C2×D412yes—
267C4×Dic59C2×D412yes—
268C4×Dic59C2412yes—
269C4×Dic59C2412yes—
270C2×C59⋊C8—22no—
271C2×C59⋊C8—22no—
272C2×C59⋊C8C2412yes—
273C2×C59⋊C8C2412yes—
274#11745660—28no—
275#11745660—28no—
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—
289D4×C59—22no—
290D4×C59—22no—
291D4×C59—42no—
292C2×C4×C59—22no—
293C2×C4×C59—22no—
294C2×C4×C59—22no—
295C2×C4×C59—22no—
296C2×C4×C59—22no—
297C2×C4×C59—48no—
298C2×C4×C59—42no—
299C2×C4×C59—42no—
300C2×C4×C59—42no—
301C2×C4×C59C22×D412yes—
302C2×C4×C59C22×D412yes—
303C2×C4×C59C22×D411yescharacteristic
304C2×C4×C59C2×#4112yes—
305C2×C4×C592−1+412yes—
306C2×C4×C59C2511yescharacteristic
307C22⋊D59—48no—
308C22⋊D59—48no—
309C22⋊D59—84no—
310C22⋊D59—84no—
311C2×Dic59—24no—
312C2×Dic59—22no—
313C2×Dic59—22no—
314C2×Dic59—22no—
315C2×Dic59—22no—
316C2×Dic59—22no—
317C2×Dic59—42no—
318C2×Dic59AGL(1,ℤ/8)14yes—
319C2×Dic59C22×D412yes—
320C2×Dic59C22×D412yes—
321C2×Dic59C22×D412yes—
322C2×Dic59C22×D412yes—
323D236—22no—
324D236—22no—
325D236—22no—
326D236—22no—
327D236—48no—
328D236—42no—
329D236—42no—
330D236—84no—
331C4×D59—48no—
332C4×D59—48no—
333Dic118—24no—
334Dic118—22no—
335Dic118—28no—
336Dic118—48no—
337Dic118C2×#4114yescomplemented
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—22no—
360C4×C59—22no—
361C4×C59—42no—
362C4×C59—42no—
363C4×C59—42no—
364C4×C59#54812yes—
365C4×C59C22×#4111yescharacteristic
366C4×C59C2×2−1+411yescharacteristic
367Dic59—24no—
368Dic59—22no—
369Dic59—22no—
370Dic59—22no—
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×#478D5911yescharacteristic, complemented
381C2×#474—591no—
382C2×#460—591no—
383C2×#460—591no—
384C2×#460—591no—
385C2×#446—591no—
386C2×#440—591no—
387C2×#440—591no—
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×SD16—591no—
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—1181no—
411C2×#125—1181no—
412C2×#125C2×D5911yescharacteristic
413C2×#121—1181no—
414C2×#121—1181no—
415C2×#121—1181no—
416C2×C4×Q8—591no—
417C2×C4×Q8—591no—
418C2×C4×Q8—591no—
419C2×C4×Q8—591no—
420C2×C4×Q8—1181no—
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#478C2×D5918yescomplemented
429#474—598no—
430#460—598no—
431#460—598no—
432#460—598no—
433#446—598no—
434#440—598no—
435#440—598no—
436C4×SD16—598no—
437C2×#107—591no—
438C2×#107C2×D5911yescharacteristic
439C2×#106C2×D5911yescharacteristic
440C2×C4⋊C8—591no—
441C2×C4⋊C8—591no—
442C2×C4⋊C8C2×D5911yescharacteristic
443C2×#103—591no—
444C2×#102—591no—
445C2×#102—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×#97—591no—
455C2×C4×C8—591no—
456C59C2×#336811yescharacteristic, complemented, Sylow
457C2×#41—1188no—
458C2×#41—2368no—
459C22×Q8—591no—
460C22×Q8—591no—
461C22×Q8—1181no—
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—594no—
475C2×SD16—594no—
476C2×SD16—594no—
477C2×SD16—1184no—
478C2×SD16—1184no—
479C2×SD16—1184no—
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—22no—
494#125—594no—
495#125—1182no—
496#125—1188no—
497#125—1188no—
498#125C22×D5914yes—
499#121—1188no—
500#121—1188no—
501#121—1188no—
502C4×Q8—594no—
503C4×Q8—594no—
504C4×Q8—594no—
505C4×Q8—594no—
506C4×Q8—594no—
507C4×Q8—1182no—
508C4×Q8—1182no—
509C4×Q8—1188no—
510C4×Q8—1182no—
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—21no—
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⋊C4C22×D5911yescharacteristic
530C2×C4⋊C4C22×D5911yescharacteristic
531C2×C4⋊C4C22×D5911yescharacteristic
532C2×C22⋊C4—21no—
533C2×C22⋊C4—1181no—
534C2×C22⋊C4—1181no—
535C2×C42—591no—
536C2×C42—591no—
537C2×C42—1181no—
538C2×C42—1181no—
539C2×C42—1181no—
540C2×C42C22×D5911yescharacteristic
541#107—594no—
542#107C22×D5914yes—
543#106C22×D5914yes—
544C4⋊C8—594no—
545C4⋊C8—594no—
546C4⋊C8C22×D5914yes—
547#103—594no—
548#102—594no—
549#102—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#97—594no—
559C4×C8—594no—
560C24—21no—
561C24—1181no—
562C24—1181no—
563#41—23632no—
564C2×Q8—594no—
565C2×Q8—594no—
566C2×Q8—592no—
567C2×Q8—1184no—
568C2×Q8—1184no—
569C2×Q8—1181no—
570C2×Q8—1182no—
571C2×Q8—2364no—
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—1188no—
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—24no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—594no—
631C4⋊C4—594no—
632C4⋊C4—594no—
633C4⋊C4—592no—
634C4⋊C4—1184no—
635C4⋊C4—1184no—
636C4⋊C4—1184no—
637C4⋊C4—1184no—
638C4⋊C4—1184no—
639C4⋊C4—1181no—
640C4⋊C4—1184no—
641C4⋊C4C23×D5912yes—
642C4⋊C4C23×D5912yes—
643C4⋊C4C23×D5912yes—
644C22⋊C4—24no—
645C22⋊C4—1184no—
646C22⋊C4—1184no—
647C42—592no—
648C42—592no—
649C42—592no—
650C42—592no—
651C42—1184no—
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—594no—
670Q8—1188no—
671Q8—1182no—
672Q8—1184no—
673Q8—2368no—
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—22no—
693C2×C4—22no—
694C2×C4—48no—
695C2×C4—42no—
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—1184no—
708C2×C4—1182no—
709C2×C4—2368no—
710C2×C4—2368no—
711C2×C4—2362no—
712C2×C4C2×D4×D5912yes—
713C2×C4C2×D4×D5912yes—
714C2×C4C2×D4×D5911yescharacteristic
715C2×C4#41×D5912yes—
716C2×C4#1427377512yes—
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#1683806212yes—
735C22AGL(1,ℤ/8)×D5912yes—
736C22#1683820912yes—
737C22C22×D4×D5911yescharacteristic
738C4—22no—
739C4—22no—
740C4—42no—
741C4—42no—
742C4—42no—
743C4—594no—
744C4—1182no—
745C4—1184no—
746C4—1182no—
747C4—1182no—
748C4—2362no—
749C4#1683806212yes—
750C4C2×#41×D5911yescharacteristic
751C4C2×#1427377511yescharacteristic
752C2—82no—
753C2—4722no—
754C2—4722no—
755C2#2143682814yesdirect product factor
756C2C2×#1683806211yescharacteristic
757C2C2×AGL(1,ℤ/8)×D5911yescharacteristic
758C2C2×#1683820911yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#478C2
socleC23×C59C22×D4
prime radicalC2×#16838073C2
hypercenterC2×#478D59
hypocenterC59C2×#3368
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#478

Complements

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

NH ≅ G/Ntype
1. C2×#16838129C2semidirect
3. #21436828C2direct (N × H)
4. C2×#16837768C2semidirect
5. C2×#16837765C2semidirect
6. C2×#16837747C2semidirect
7. C2×#16837701C2semidirect
8. C2×#16837681C2semidirect
9. C2×#16837603C2semidirect
10. C2×#16837601C2semidirect
11. C2×#16837601C2semidirect
12. C2×#16837531C2semidirect
13. C2×#16837502C2semidirect
14. C2×#16837501C2semidirect
15. C2×#16837489C2semidirect
16. C2×C59×#478C2semidirect
22. #16838129C22semidirect
43. #16837768C22semidirect
44. #16837765C22semidirect
45. #16837747C22semidirect
46. #16837701C22semidirect
47. #16837681C22semidirect
48. #16837603C22semidirect
49. #16837601C22semidirect
50. #16837601C22semidirect
51. #16837531C22semidirect
52. #16837502C22semidirect
53. #16837501C22semidirect
54. #16837489C22semidirect
71. C59×#478C22semidirect
232. C2×Dic118#41semidirect
337. Dic118C2×#41semidirect
380. C2×#478D59semidirect
390. C2×C59#3368semidirect
428. #478C2×D59semidirect
456. C59C2×#3368semidirect
755. C2#21436828direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168381292
C2×#168380732
#214368282
C2×#168377682
C2×#168377652
C2×#168377472
C2×#168377012
C2×#168376812
C2×#168376032
C2×#168376012
C2×#168375312
C2×#168375022
C2×#168375012
C2×#168374892
C2×C59×#4782
C2×#336859