Finite Group Databasebeta

← C2×#21436597 #29467285

Subgroups — C2×#21436597 #29467285

Order 15104.

1962 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×#16838115C211yesmaximal, characteristic, complemented
2C2×#16838100C211yesmaximal, characteristic, complemented
3#21436597C2116yesmaximal, direct product factor
4C2×#16837810C211yesmaximal, characteristic, complemented
5C2×#16837729C211yesmaximal, characteristic, complemented
6C2×#16837728C211yesmaximal, characteristic, complemented
7C2×#16837726C211yesmaximal, characteristic, complemented
8C2×#16837715C211yesmaximal, characteristic, complemented
9C2×#16837701C211yesmaximal, characteristic, complemented
10C2×#16837681C211yesmaximal, characteristic, complemented
11C2×#16837655C211yesmaximal, characteristic, complemented
12C2×#16837639C211yesmaximal, characteristic, complemented
13C2×#16837513C211yesmaximal, characteristic, complemented
14C2×#16837471C211yesmaximal, characteristic, complemented
15C2×#16837437C211yesmaximal, characteristic, complemented
16C2×C59×#428C211yesmaximal, characteristic, complemented
17C22×D472C2211yescharacteristic
18C22×C8×D59C2211yescharacteristic
19#16838115—24no—
20#16838115C2218yescomplemented
21#16838100—24no—
22#16838100C2218yescomplemented
23C2×#14273726C2211yescharacteristic
24C2×#14273722—21no—
25C2×#14273718C2211yescharacteristic
26C2×#14273715—21no—
27C2×#14273713—21no—
28C2×#14273712—21no—
29C2×#14273702C2211yescharacteristic
30C2×#14273702C2211yescharacteristic
31C2×#14273701—21no—
32C2×#14273701C2211yescharacteristic
33C2×#14273701C2211yescharacteristic
34C2×#14273700—21no—
35C2×#14273689C2211yescharacteristic
36C2×#14273689C2211yescharacteristic
37C2×C4×C22⋊D59—21no—
38C2×C4×C22⋊D59C2211yescharacteristic
39C2×#14273685C2211yescharacteristic
40C2×#14273685C2211yescharacteristic
41C2×#14273684—21no—
42#16837810C2218yescomplemented
43#16837729C2218yescomplemented
44#16837728C2218yescomplemented
45#16837726C2218yescomplemented
46#16837715C2218yescomplemented
47#16837701C2218yescomplemented
48#16837681C2218yescomplemented
49#16837655C2218yescomplemented
50#16837639C2218yescomplemented
51#16837513C2218yescomplemented
52#16837471C2218yescomplemented
53#16837437C2218yescomplemented
54C2×#14273660C2211yescharacteristic
55C2×#14273660C2211yescharacteristic
56C2×#14273660C2211yescharacteristic
57C2×#14273659C2211yescharacteristic
58C2×#14273658C2211yescharacteristic
59C2×Dic59⋊C8C2211yescharacteristic
60C2×#14273649C2211yescharacteristic
61C2×#14273649C2211yescharacteristic
62C2×#14273647C2211yescharacteristic
63C2×#14273647C2211yescharacteristic
64C2×#14273647C2211yescharacteristic
65C2×#14273647C2211yescharacteristic
66C2×C22⋊(C59⋊C8)C2211yescharacteristic
67C2×(C2×D59)⋊C8C2211yescharacteristic
68C2×#14273637C2211yescharacteristic
69C22×M16×C59C2211yescharacteristic
70C2×#117×C59C2211yescharacteristic
71C22×C4⋊C4×C59C2211yescharacteristic
72C59×#428C2218yescomplemented
73C2×#107×C59C2211yescharacteristic
74C2×#107×C59C2211yescharacteristic
75C2×#106×C59C2211yescharacteristic
76C2×#106×C59C2211yescharacteristic
77C22×Dic118—21no—
78C22×D236—21no—
79C22×D236—21no—
80C22×D236C2311yescharacteristic
81C22×D236C2311yescharacteristic
82C22×C22⋊D59—21no—
83C22×C22⋊D59—21no—
84C22×C22⋊D59D411yescharacteristic
85C22×C4×D59—21no—
86C22×C4×D59—21no—
87C22×C4×D59C2311yescharacteristic
88C2×D472—24no—
89C2×D472C2314yes—
90C22×C59⋊C8C2311yescharacteristic
91C22×C59⋊C8C2311yescharacteristic
92C2×C8×D59—24no—
93C2×C8×D59C2314yes—
94#14273726—22no—
95#14273726C2314yes—
96#14273722—28no—
97#14273718—22no—
98#14273718C2314yes—
99#14273715—28no—
100#14273713—28no—
101#14273712—28no—
102#14273702—22no—
103#14273702—22no—
104#14273702C2314yes—
105#14273702C2314yes—
106#14273701—22no—
107#14273701—22no—
108#14273701—28no—
109#14273701C2314yes—
110#14273701C2314yes—
111#14273700—28no—
112#14273689—22no—
113#14273689—22no—
114#14273689C2314yes—
115#14273689C2314yes—
116C4×C22⋊D59—28no—
117C4×C22⋊D59D414yes—
118C4×C22⋊D59C2314yes—
119#14273685—22no—
120#14273685—22no—
121#14273685C2314yes—
122#14273685C2314yes—
123#14273684—28no—
124C2×C4⋊Dic59—21no—
125C2×C4⋊Dic59C2311yescharacteristic
126C2×C4⋊Dic59C2311yescharacteristic
127C2×Dic59⋊C4—21no—
128C2×Dic59⋊C4—21no—
129C2×Dic59⋊C4D411yescharacteristic
130C2×C22⋊Dic59D411yescharacteristic
131C2×(C2×D59)⋊C4—21no—
132C2×(C2×D59)⋊C4—21no—
133C2×(C2×D59)⋊C4—21no—
134C2×(C2×D59)⋊C4—21no—
135C2×(C2×D59)⋊C4—21no—
136C2×(C2×D59)⋊C4—21no—
137C2×(C2×D59)⋊C4—21no—
138C2×(C2×D59)⋊C4—21no—
139C2×(C2×D59)⋊C4D411yescharacteristic
140C2×C4×Dic59—21no—
141C2×C4×Dic59—21no—
142C2×C4×Dic59C2311yescharacteristic
143#14273660C2314yes—
144#14273660C2314yes—
145#14273660C2314yes—
146#14273659C2314yes—
147#14273658C2314yes—
148Dic59⋊C8C2314yes—
149#14273649C2314yes—
150#14273649C2314yes—
151#14273647C2314yes—
152#14273647C2314yes—
153#14273647C2314yes—
154#14273647C2314yes—
155C22⋊(C59⋊C8)C2314yes—
156(C2×D59)⋊C8C2314yes—
157#14273637C2314yes—
158C23×C4×C59—21no—
159C23×C4×C59C2311yescharacteristic
160C2×M16×C59—24no—
161C2×M16×C59C2314yes—
162C22×C8×C59C2311yescharacteristic
163C22×C8×C59C2311yescharacteristic
164#117×C59—22no—
165#117×C59C2314yes—
166C2×C4⋊C4×C59—21no—
167C2×C4⋊C4×C59—22no—
168C2×C4⋊C4×C59C2311yescharacteristic
169C2×C4⋊C4×C59C2311yescharacteristic
170C2×C4⋊C4×C59C2311yescharacteristic
171C2×C4⋊C4×C59C2311yescharacteristic
172C2×C4⋊C4×C59C2314yes—
173C2×C22⋊C4×C59—21no—
174C2×C42×C59—21no—
175#107×C59C2314yes—
176#107×C59C2314yes—
177#106×C59C2314yes—
178#106×C59C2314yes—
179C24×C59C2×D411yescharacteristic
180C23×D59—21no—
181C23×D59—21no—
182C23×D59C2×D411yescharacteristic
183C22×C4×C59—22no—
184C22×C4×C59—22no—
185C22×C4×C59—21no—
186C22×C4×C59—21no—
187C22×C4×C59—21no—
188C22×C4×C59—21no—
189C22×C4×C59—24no—
190C22×C4×C59—82no—
191C22×C4×C59C2×D411yescharacteristic
192C22×C4×C59C2×D412yes—
193C22×C4×C59C2412yes—
194C22×C4×C59C2411yescharacteristic
195C2×C22⋊D59—24no—
196C2×C22⋊D59—24no—
197C2×C22⋊D59—42no—
198C2×C22⋊D59—44no—
199C2×C22⋊D59—82no—
200C2×C22⋊D59C2×D414yes—
201C22×Dic59—21no—
202C22×Dic59—21no—
203C22×Dic59C2×D411yescharacteristic
204C22×Dic59C2×D411yescharacteristic
205C22×Dic59C2×D411yescharacteristic
206C2×D236—22no—
207C2×D236—22no—
208C2×D236—22no—
209C2×D236—22no—
210C2×D236—21no—
211C2×D236—21no—
212C2×D236—24no—
213C2×D236—24no—
214C2×D236—82no—
215C2×D236—82no—
216C2×D236C2412yes—
217C2×D236C2412yes—
218C2×C4×D59—22no—
219C2×C4×D59—22no—
220C2×C4×D59—24no—
221C2×C4×D59—24no—
222C2×C4×D59—44no—
223C2×C4×D59—82no—
224C2×C4×D59C2×D412yes—
225C2×C4×D59C2412yes—
226C2×Dic118—24no—
227C2×Dic118—82no—
228M16×C59—28no—
229C2×C8×C59—22no—
230C2×C8×C59#4114yes—
231C2×C8×C59C2412yes—
232C2×C8×C59C2412yes—
233C4⋊C4×C59—21no—
234C4⋊C4×C59—21no—
235C4⋊C4×C59—24no—
236C4⋊C4×C59—21no—
237C4⋊C4×C59—21no—
238C4⋊C4×C59C2412yes—
239C4⋊C4×C59C2412yes—
240C4⋊C4×C59C2412yes—
241C4⋊C4×C59C2412yes—
242C22⋊C4×C59—24no—
243C42×C59—24no—
244C22⋊Dic59C2×D414yes—
245(C2×D59)⋊C4—24no—
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—
251(C2×D59)⋊C4—24no—
252(C2×D59)⋊C4—24no—
253(C2×D59)⋊C4C2×D414yes—
254C4⋊Dic59—21no—
255C4⋊Dic59—21no—
256C4⋊Dic59—24no—
257C4⋊Dic59C2412yes—
258C4⋊Dic59C2412yes—
259Dic59⋊C4—24no—
260Dic59⋊C4—24no—
261Dic59⋊C4C2×D414yes—
262C4×Dic59—24no—
263C4×Dic59—24no—
264C4×Dic59C2×D412yes—
265C4×Dic59C2412yes—
266C2×C59⋊C8—22no—
267C2×C59⋊C8—22no—
268C2×C59⋊C8C2412yes—
269C2×C59⋊C8C2412yes—
270D472—28no—
271C8×D59—28no—
272C23×C59—22no—
273C23×C59—22no—
274C23×C59—22no—
275C23×C59C22×D412yes—
276C23×C59C22×D411yescharacteristic
277C22×D59—22no—
278C22×D59—22no—
279C22×D59—22no—
280C22×D59—22no—
281C22×D59—22no—
282C22×D59—42no—
283C22×D59—42no—
284C22×D59—42no—
285C22×D59—42no—
286C22×D59—42no—
287C22×D59—42no—
288C22×D59C22×D412yes—
289C2×C4×C59—22no—
290C2×C4×C59—24no—
291C2×C4×C59—22no—
292C2×C4×C59—22no—
293C2×C4×C59—22no—
294C2×C4×C59—22no—
295C2×C4×C59—22no—
296C2×C4×C59—22no—
297C2×C4×C59—42no—
298C2×C4×C59—42no—
299C2×C4×C59—42no—
300C2×C4×C59—42no—
301C2×C4×C59—84no—
302C2×C4×C59C22×D412yes—
303C2×C4×C59C22×D411yescharacteristic
304C2×C4×C59C2×#4112yes—
305C2×C4×C592−1+412yes—
306C2×C4×C59C2511yescharacteristic
307C22⋊D59—44no—
308C22⋊D59—48no—
309C22⋊D59—84no—
310C2×Dic59—22no—
311C2×Dic59—22no—
312C2×Dic59—22no—
313C2×Dic59—22no—
314C2×Dic59—22no—
315C2×Dic59—42no—
316C2×Dic59—42no—
317C2×Dic59C22×D412yes—
318C2×Dic59C22×D412yes—
319C2×Dic59C22×D412yes—
320D236—22no—
321D236—22no—
322D236—22no—
323D236—22no—
324D236—42no—
325D236—42no—
326D236—84no—
327D236—84no—
328C4×D59—24no—
329C4×D59—22no—
330C4×D59—22no—
331C4×D59—48no—
332C4×D59—84no—
333Dic118—84no—
334C8×C59—22no—
335C8×C59C2×#4114yes—
336C59⋊C8—22no—
337C59⋊C8—22no—
338C2×#3347—591nomaximal, Sylow
339C22×C59—22no—
340C22×C59—22no—
341C22×C59—22no—
342C22×C59—44no—
343C22×C59#54712yes—
344C22×C59#57512yes—
345C22×C59#57612yes—
346C22×C59C23×D411yescharacteristic
347C2×D59—22no—
348C2×D59—22no—
349C2×D59—22no—
350C2×D59—44no—
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—42no—
361C4×C59—42no—
362C4×C59—42no—
363C4×C59—42no—
364C4×C59#54712yes—
365C4×C59C22×#4111yescharacteristic
366C4×C59C2×2−1+411yescharacteristic
367Dic59—22no—
368Dic59—22no—
369Dic59—22no—
370Dic59—42no—
371Dic59—42no—
372C2×#555—591no—
373C2×#553—591no—
374#3347—5916no—
375C2×#501—591no—
376C2×#482—591no—
377C2×#482—591no—
378C2×#482—591no—
379C2×#480—591no—
380C2×#478—591no—
381C2×#474—591no—
382C2×#469—591no—
383C2×#466—591no—
384C2×#442—591no—
385C2×#435—591no—
386C2×#428D5911yescharacteristic, complemented
387C2×#427—591no—
388C2×C59—42no—
389C2×C59#334714yescomplemented
390C2×C59C2×#54711yescharacteristic
391C2×C59C2×#57511yescharacteristic
392C2×C59C2×#57611yescharacteristic
393D59—42no—
394D59—82no—
395D59—82no—
396C22×D8—591no—
397C22×M16C2×D5911yescharacteristic
398C23×C8—591no—
399#555—598no—
400#555—1184no—
401#553—598no—
402#553—1184no—
403C2×C4⋊Q8—591no—
404C2×#126—1181no—
405C2×#125—591no—
406C2×#124—1181no—
407C2×#124—1181no—
408C2×#123—1181no—
409C2×#121—591no—
410C2×#121—591no—
411C2×#121—591no—
412C2×#121—591no—
413C2×#121—1181no—
414C2×#121—1181no—
415C2×C4×D4—591no—
416C2×C4×D4—591no—
417C2×C4×D4—591no—
418C2×C4×D4—1181no—
419C2×#117—591no—
420C2×#117—591no—
421C2×#117—1181no—
422C2×#117C2×D5911yescharacteristic
423C22×C4⋊C4C2×D5911yescharacteristic
424#501—598no—
425#482—598no—
426#482—598no—
427#482—598no—
428#480—598no—
429#478—598no—
430#474—598no—
431#469—598no—
432#466—598no—
433#442—598no—
434#435—598no—
435#428C2×D5918yescomplemented
436#427—598no—
437C2×#107—591no—
438C2×#107—591no—
439C2×#107—591no—
440C2×#107C2×D5911yescharacteristic
441C2×#107C2×D5911yescharacteristic
442C2×#106—591no—
443C2×#106—591no—
444C2×#106C2×D5911yescharacteristic
445C2×#106C2×D5911yescharacteristic
446C2×C4⋊C8—591no—
447C2×#102—591no—
448C2×#102—591no—
449C2×#102—591no—
450C2×#102—591no—
451C2×#102—591no—
452C2×#102—591no—
453C2×C22⋊C8—591no—
454C2×C22⋊C8—591no—
455C2×#97—591no—
456C59C2×#334711yescharacteristic, complemented, Sylow
457C22×Q8—1181no—
458C22×D4—591no—
459C22×D4—591no—
460C22×D4—591no—
461C22×D4—1181no—
462C22×D4—1181no—
463C22×D4—1181no—
464C22×D4—1181no—
465C23×C4—21no—
466C23×C4—591no—
467C23×C4—1181no—
468C23×C4—1181no—
469C23×C4C22×D5911yescharacteristic
470C2×D8—594no—
471C2×D8—1184no—
472C2×M16—24no—
473C2×M16C22×D5914yes—
474C22×C8—591no—
475C22×C8—591no—
476C22×C8—594no—
477C22×C8—1184no—
478C22×C8C22×D5911yescharacteristic
479C22×C8C22×D5911yescharacteristic
480C4⋊Q8—594no—
481C4⋊Q8—1182no—
482#126—1188no—
483#125—594no—
484#125—1182no—
485#124—1188no—
486#124—1188no—
487#123—1188no—
488#121—594no—
489#121—594no—
490#121—594no—
491#121—594no—
492#121—1188no—
493#121—1182no—
494#121—1182no—
495#121—1188no—
496#121—1182no—
497#121—1182no—
498C4×D4—594no—
499C4×D4—594no—
500C4×D4—594no—
501C4×D4—594no—
502C4×D4—1182no—
503C4×D4—1182no—
504C4×D4—1188no—
505#117—22no—
506#117—594no—
507#117—594no—
508#117—1188no—
509#117—1182no—
510#117—1182no—
511#117C22×D5914yes—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—22no—
514C2×C4⋊C4—591no—
515C2×C4⋊C4—591no—
516C2×C4⋊C4—591no—
517C2×C4⋊C4—1181no—
518C2×C4⋊C4—1181no—
519C2×C4⋊C4—1181no—
520C2×C4⋊C4C22×D5911yescharacteristic
521C2×C4⋊C4C22×D5911yescharacteristic
522C2×C4⋊C4C22×D5914yes—
523C2×C4⋊C4C22×D5911yescharacteristic
524C2×C4⋊C4C22×D5911yescharacteristic
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×C22⋊C4—1181no—
533C2×C22⋊C4—1181no—
534C2×C22⋊C4—1181no—
535C2×C22⋊C4—1181no—
536C2×C42—21no—
537C2×C42—591no—
538C2×C42—1181no—
539C2×C42—1181no—
540#107—594no—
541#107—594no—
542#107—594no—
543#107C22×D5914yes—
544#107C22×D5914yes—
545#106—594no—
546#106—594no—
547#106C22×D5914yes—
548#106C22×D5914yes—
549C4⋊C8—594no—
550#102—594no—
551#102—594no—
552#102—594no—
553#102—594no—
554#102—594no—
555#102—594no—
556C22⋊C8—594no—
557C22⋊C8—594no—
558#97—594no—
559C24—591no—
560C24—1181no—
561C24—1181no—
562C24D4×D5911yescharacteristic
563C2×Q8—1184no—
564C2×Q8—4722no—
565C2×D4—594no—
566C2×D4—592no—
567C2×D4—592no—
568C2×D4—1184no—
569C2×D4—1184no—
570C2×D4—1184no—
571C2×D4—1184no—
572C2×D4—1181no—
573C2×D4—1181no—
574C2×D4—1182no—
575C2×D4—1182no—
576C2×D4—1182no—
577C2×D4—1182no—
578C2×D4—4722no—
579C2×D4—4722no—
580C2×D4—4722no—
581C2×D4—2362no—
582C2×D4—2364no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—24no—
590C22×C4—82no—
591C22×C4—591no—
592C22×C4—591no—
593C22×C4—591no—
594C22×C4—592no—
595C22×C4—592no—
596C22×C4—1184no—
597C22×C4—1184no—
598C22×C4—1182no—
599C22×C4—1182no—
600C22×C4—1181no—
601C22×C4—1181no—
602C22×C4—4722no—
603C22×C4—2364no—
604C22×C4D4×D5912yes—
605C22×C4D4×D5911yescharacteristic
606C22×C4C23×D5912yes—
607C22×C4C23×D5911yescharacteristic
608D8—1188no—
609M16—28no—
610C2×C8—22no—
611C2×C8—592no—
612C2×C8—592no—
613C2×C8—1182no—
614C2×C8—1182no—
615C2×C8—1188no—
616C2×C8#1174568514yes—
617C2×C8C23×D5912yes—
618C2×C8C23×D5912yes—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—24no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—594no—
625C4⋊C4—592no—
626C4⋊C4—592no—
627C4⋊C4—1184no—
628C4⋊C4—1184no—
629C4⋊C4—1184no—
630C4⋊C4—1181no—
631C4⋊C4—1181no—
632C4⋊C4C23×D5912yes—
633C4⋊C4C23×D5912yes—
634C4⋊C4C23×D5912yes—
635C4⋊C4C23×D5912yes—
636C22⋊C4—24no—
637C22⋊C4—594no—
638C22⋊C4—594no—
639C22⋊C4—1184no—
640C22⋊C4—1184no—
641C22⋊C4—1184no—
642C22⋊C4—1184no—
643C22⋊C4—1184no—
644C22⋊C4—1184no—
645C22⋊C4—1184no—
646C22⋊C4—1184no—
647C42—24no—
648C42—592no—
649C42—592no—
650C42—1184no—
651C42—1184no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—592no—
656C23—1182no—
657C23—1182no—
658C23—1182no—
659C23—1182no—
660C23—1182no—
661C23—2362no—
662C23—2362no—
663C23—2362no—
664C23—2362no—
665C23—2362no—
666C23—2362no—
667C23C2×D4×D5912yes—
668C23C2×D4×D5911yescharacteristic
669Q8—4724no—
670D4—1182no—
671D4—1182no—
672D4—1182no—
673D4—1182no—
674D4—4724no—
675D4—4724no—
676D4—4724no—
677D4—2364no—
678D4—2368no—
679D4—2362no—
680D4—2362no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—24no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—84no—
694C2×C4—592no—
695C2×C4—592no—
696C2×C4—592no—
697C2×C4—1182no—
698C2×C4—1182no—
699C2×C4—1182no—
700C2×C4—1182no—
701C2×C4—1182no—
702C2×C4—1184no—
703C2×C4—1182no—
704C2×C4—1182no—
705C2×C4—4724no—
706C2×C4—2368no—
707C2×C4—2362no—
708C2×C4—2362no—
709C2×C4C2×D4×D5912yes—
710C2×C4C2×D4×D5911yescharacteristic
711C2×C4C2×#1174568512yes—
712C2×C4#1427377512yes—
713C2×C4C24×D5911yescharacteristic
714C8—22no—
715C8—1182no—
716C8—1182no—
717C8C2×#1174568514yes—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—44no—
722C22—1182no—
723C22—1182no—
724C22—1182no—
725C22—4724no—
726C22—4724no—
727C22—2362no—
728C22—2362no—
729C22—2362no—
730C22—2362no—
731C22—2362no—
732C22—2362no—
733C22—2364no—
734C22#1683805312yes—
735C22#1683820112yes—
736C22#1683820612yes—
737C22C22×D4×D5911yescharacteristic
738C4—22no—
739C4—42no—
740C4—42no—
741C4—42no—
742C4—42no—
743C4—1182no—
744C4—1182no—
745C4—1182no—
746C4—2362no—
747C4—2362no—
748C4#1683805312yes—
749C4C22×#1174568511yescharacteristic
750C4C2×#1427377511yescharacteristic
751C2—42no—
752C2—4722no—
753C2—4722no—
754C2—2362no—
755C2#2143659714yesdirect product factor
756C2C2×#1683805311yescharacteristic
757C2C2×#1683820111yescharacteristic
758C2C2×#1683820611yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#428C2
socleC23×C59C22×D4
hypercenterC2×#428D59
hypocenterC59C2×#3347
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#428

Complements

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

NH ≅ G/Ntype
1. C2×#16838115C2semidirect
2. C2×#16838100C2semidirect
3. #21436597C2direct (N × H)
4. C2×#16837810C2semidirect
5. C2×#16837729C2semidirect
6. C2×#16837728C2semidirect
7. C2×#16837726C2semidirect
8. C2×#16837715C2semidirect
9. C2×#16837701C2semidirect
10. C2×#16837681C2semidirect
11. C2×#16837655C2semidirect
12. C2×#16837639C2semidirect
13. C2×#16837513C2semidirect
14. C2×#16837471C2semidirect
15. C2×#16837437C2semidirect
16. C2×C59×#428C2semidirect
20. #16838115C22semidirect
22. #16838100C22semidirect
42. #16837810C22semidirect
43. #16837729C22semidirect
44. #16837728C22semidirect
45. #16837726C22semidirect
46. #16837715C22semidirect
47. #16837701C22semidirect
48. #16837681C22semidirect
49. #16837655C22semidirect
50. #16837639C22semidirect
51. #16837513C22semidirect
52. #16837471C22semidirect
53. #16837437C22semidirect
72. C59×#428C22semidirect
386. C2×#428D59semidirect
389. C2×C59#3347semidirect
435. #428C2×D59semidirect
456. C59C2×#3347semidirect
755. C2#21436597direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168381152
C2×#168381002
#214365972
C2×#168378102
C2×#168377292
C2×#168377282
C2×#168377262
C2×#168377152
C2×#168377012
C2×#168376812
C2×#168376552
C2×#168376392
C2×#168375132
C2×#168374712
C2×#168374372
C2×C59×#4282
C2×#334759