Finite Group Databasebeta

← C2×#21436598 #29467286

Subgroups — C2×#21436598 #29467286

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×#16838117C211yesmaximal, characteristic, complemented
2C2×#16838098C211yesmaximal, characteristic, complemented
3#21436598C2116yesmaximal, direct product factor
4C2×#16837811C211yesmaximal, characteristic, complemented
5C2×#16837727C211yesmaximal, characteristic, complemented
6C2×#16837727C211yesmaximal, characteristic, complemented
7C2×#16837727C211yesmaximal, characteristic, complemented
8C2×#16837716C211yesmaximal, characteristic, complemented
9C2×#16837703C211yesmaximal, characteristic, complemented
10C2×#16837683C211yesmaximal, characteristic, complemented
11C2×#16837655C211yesmaximal, characteristic, complemented
12C2×#16837638C211yesmaximal, characteristic, complemented
13C2×#16837515C211yesmaximal, characteristic, complemented
14C2×#16837444C211yesmaximal, characteristic, complemented
15C2×#16837440C211yesmaximal, characteristic, complemented
16C2×C59×#435C211yesmaximal, characteristic, complemented
17C22×D472C2211yescharacteristic
18#16838117—24no—
19#16838117C2218yescomplemented
20#16838098—24no—
21#16838098C2218yescomplemented
22C2×#14273727C2211yescharacteristic
23C2×#14273722—21no—
24C2×#14273719C2211yescharacteristic
25C2×#14273713—21no—
26C2×#14273713—21no—
27C2×#14273709—21no—
28C2×#14273701C2211yescharacteristic
29C2×#14273701C2211yescharacteristic
30C2×#14273701C2211yescharacteristic
31C2×#14273701C2211yescharacteristic
32C2×#14273699—21no—
33C2×#14273698—21no—
34C2×C4×D236C2211yescharacteristic
35C2×C4×D236C2211yescharacteristic
36C2×(C22⋊D59)⋊C4—21no—
37C2×#14273686C2211yescharacteristic
38C2×#14273686C2211yescharacteristic
39C2×#14273686C2211yescharacteristic
40C2×#14273685—21no—
41C22×C4⋊Dic59C2211yescharacteristic
42#16837811C2218yescomplemented
43#16837727C2218yescomplemented
44#16837727C2218yescomplemented
45#16837727C2218yescomplemented
46#16837716C2218yescomplemented
47#16837703C2218yescomplemented
48#16837683C2218yescomplemented
49#16837655C2218yescomplemented
50#16837638C2218yescomplemented
51#16837515C2218yescomplemented
52#16837444C2218yescomplemented
53#16837440C2218yescomplemented
54C2×#14273661C2211yescharacteristic
55C2×#14273661C2211yescharacteristic
56C2×#14273661C2211yescharacteristic
57C2×#14273661C2211yescharacteristic
58C2×#14273661C2211yescharacteristic
59C2×#14273659C2211yescharacteristic
60C2×#14273659C2211yescharacteristic
61C2×#14273659C2211yescharacteristic
62C2×#14273659C2211yescharacteristic
63C2×#14273649C2211yescharacteristic
64C2×#14273649C2211yescharacteristic
65C2×#14273649C2211yescharacteristic
66C2×#14273649C2211yescharacteristic
67C2×#14273649C2211yescharacteristic
68C2×#14273649C2211yescharacteristic
69C22×M16×C59C2211yescharacteristic
70C23×C8×C59C2211yescharacteristic
71C2×C4×D4×C59C2211yescharacteristic
72C59×#435C2218yescomplemented
73C2×C4⋊C8×C59C2211yescharacteristic
74C2×C22⋊C8×C59C2211yescharacteristic
75C2×C22⋊C8×C59C2211yescharacteristic
76C2×#97×C59C2211yescharacteristic
77C22×Dic118—21no—
78C22×D236C2311yescharacteristic
79C22×D236C2311yescharacteristic
80C22×C22⋊D59—21no—
81C22×C22⋊D59—21no—
82C22×C22⋊D59—21no—
83C22×C22⋊D59—21no—
84C23×Dic59—21no—
85C22×C4×D59—21no—
86C22×C4×D59—21no—
87C2×D472—24no—
88C2×D472C2314yes—
89#14273727—22no—
90#14273727C2314yes—
91#14273722—28no—
92#14273719—22no—
93#14273719C2314yes—
94#14273713—28no—
95#14273713—28no—
96#14273709—28no—
97#14273701—22no—
98#14273701—22no—
99#14273701—22no—
100#14273701—22no—
101#14273701C2314yes—
102#14273701C2314yes—
103#14273701C2314yes—
104#14273701C2314yes—
105#14273699—28no—
106#14273698—28no—
107C4×D236—22no—
108C4×D236—22no—
109C4×D236C2314yes—
110C4×D236C2314yes—
111(C22⋊D59)⋊C4—28no—
112#14273686—22no—
113#14273686—22no—
114#14273686—22no—
115#14273686C2314yes—
116#14273686C2314yes—
117#14273686C2314yes—
118#14273685—28no—
119C2×C4⋊Dic59—21no—
120C2×C4⋊Dic59—21no—
121C2×C4⋊Dic59—22no—
122C2×C4⋊Dic59C2311yescharacteristic
123C2×C4⋊Dic59C2311yescharacteristic
124C2×C4⋊Dic59C2311yescharacteristic
125C2×C4⋊Dic59C2311yescharacteristic
126C2×C4⋊Dic59C2311yescharacteristic
127C2×C4⋊Dic59C2311yescharacteristic
128C2×C4⋊Dic59C2314yes—
129C2×Dic59⋊C4—21no—
130C2×Dic59⋊C4—21no—
131C2×C22⋊Dic59—21no—
132C2×C22⋊Dic59—21no—
133C2×C22⋊Dic59—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)⋊C4—21no—
140C2×C4×Dic59—21no—
141C2×C4×Dic59—21no—
142C2×C4×Dic59—21no—
143#14273661C2314yes—
144#14273661C2314yes—
145#14273661C2314yes—
146#14273661C2314yes—
147#14273661C2314yes—
148#14273659C2314yes—
149#14273659C2314yes—
150#14273659C2314yes—
151#14273659C2314yes—
152#14273649C2314yes—
153#14273649C2314yes—
154#14273649C2314yes—
155#14273649C2314yes—
156#14273649C2314yes—
157#14273649C2314yes—
158C22×D4×C59D411yescharacteristic
159C23×C4×C59C2311yescharacteristic
160C23×C4×C59C2311yescharacteristic
161C2×M16×C59—24no—
162C2×M16×C59C2314yes—
163C22×C8×C59—24no—
164C22×C8×C59C2314yes—
165C22×C8×C59C2311yescharacteristic
166C22×C8×C59C2311yescharacteristic
167C22×C8×C59C2311yescharacteristic
168C22×C8×C59C2311yescharacteristic
169C4×D4×C59D414yes—
170C4×D4×C59C2314yes—
171C2×C4⋊C4×C59D411yescharacteristic
172C2×C22⋊C4×C59D411yescharacteristic
173C2×C22⋊C4×C59D411yescharacteristic
174C2×C42×C59C2311yescharacteristic
175C4⋊C8×C59C2314yes—
176C22⋊C8×C59C2314yes—
177C22⋊C8×C59C2314yes—
178#97×C59C2314yes—
179C24×C59C2×D411yescharacteristic
180C24×C59C2×D411yescharacteristic
181C23×D59—21no—
182C23×D59—21no—
183C2×D4×C59—42no—
184C2×D4×C59C2×D414yes—
185C22×C4×C59—22no—
186C22×C4×C59—22no—
187C22×C4×C59—22no—
188C22×C4×C59—22no—
189C22×C4×C59C2×D411yescharacteristic
190C22×C4×C59C2×D411yescharacteristic
191C22×C4×C59C2×D411yescharacteristic
192C22×C4×C59C2×D411yescharacteristic
193C22×C4×C59C2×D412yes—
194C22×C4×C59C2×D412yes—
195C22×C4×C59C2412yes—
196C22×C4×C59C2412yes—
197C22×C4×C59C2411yescharacteristic
198C2×C22⋊D59—24no—
199C2×C22⋊D59—24no—
200C2×C22⋊D59—24no—
201C2×C22⋊D59—24no—
202C2×C22⋊D59—44no—
203C2×C22⋊D59—82no—
204C2×C22⋊D59—82no—
205C2×C22⋊D59—82no—
206C22×Dic59—21no—
207C22×Dic59—21no—
208C22×Dic59—21no—
209C22×Dic59—21no—
210C22×Dic59—21no—
211C22×Dic59—21no—
212C22×Dic59—24no—
213C22×Dic59—82no—
214C2×D236—22no—
215C2×D236—22no—
216C2×D236—22no—
217C2×D236—22no—
218C2×D236—21no—
219C2×D236—21no—
220C2×D236C2412yes—
221C2×D236C2412yes—
222C2×C4×D59—24no—
223C2×C4×D59—24no—
224C2×C4×D59—44no—
225C2×C4×D59—82no—
226C2×Dic118—24no—
227C2×Dic118—82no—
228M16×C59—28no—
229C2×C8×C59—22no—
230C2×C8×C59—22no—
231C2×C8×C59—22no—
232C2×C8×C59—28no—
233C2×C8×C59#4114yes—
234C2×C8×C59C2412yes—
235C2×C8×C59C2412yes—
236C2×C8×C59C2412yes—
237C2×C8×C59C2412yes—
238C4⋊C4×C59C2×D414yes—
239C22⋊C4×C59C2×D414yes—
240C22⋊C4×C59C2×D414yes—
241C42×C59C2×D412yes—
242C42×C59C2412yes—
243C22⋊Dic59—24no—
244C22⋊Dic59—24no—
245C22⋊Dic59—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—
252C4⋊Dic59—21no—
253C4⋊Dic59—21no—
254C4⋊Dic59—24no—
255C4⋊Dic59—24no—
256C4⋊Dic59—21no—
257C4⋊Dic59—21no—
258C4⋊Dic59—21no—
259C4⋊Dic59—21no—
260C4⋊Dic59C2412yes—
261C4⋊Dic59C2412yes—
262C4⋊Dic59C2412yes—
263C4⋊Dic59C2412yes—
264C4⋊Dic59C2412yes—
265C4⋊Dic59C2412yes—
266Dic59⋊C4—24no—
267Dic59⋊C4—24no—
268C4×Dic59—24no—
269C4×Dic59—24no—
270C4×Dic59—24no—
271D472—28no—
272C23×C59—22no—
273C23×C59—22no—
274C23×C59—22no—
275C23×C59—22no—
276C23×C59—22no—
277C23×C59—22no—
278C23×C59C22×D412yes—
279C23×C59C22×D412yes—
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—44no—
290C2×C4×C59—22no—
291C2×C4×C59—22no—
292C2×C4×C59—22no—
293C2×C4×C59—22no—
294C2×C4×C59—24no—
295C2×C4×C59—24no—
296C2×C4×C59—22no—
297C2×C4×C59—22no—
298C2×C4×C59—22no—
299C2×C4×C59—22no—
300C2×C4×C59C22×D412yes—
301C2×C4×C59C22×D412yes—
302C2×C4×C59C22×D412yes—
303C2×C4×C59C22×D412yes—
304C2×C4×C59C22×D411yescharacteristic
305C2×C4×C59C2×#4112yes—
306C2×C4×C592−1+412yes—
307C2×C4×C59C2511yescharacteristic
308C22⋊D59—48no—
309C22⋊D59—84no—
310C22⋊D59—84no—
311C22⋊D59—84no—
312C2×Dic59—22no—
313C2×Dic59—22no—
314C2×Dic59—22no—
315C2×Dic59—22no—
316C2×Dic59—22no—
317C2×Dic59—22no—
318C2×Dic59—42no—
319C2×Dic59—42no—
320C2×Dic59—42no—
321C2×Dic59—42no—
322C2×Dic59—42no—
323C2×Dic59—42no—
324C2×Dic59—84no—
325D236—22no—
326D236—22no—
327D236—22no—
328D236—22no—
329D236—42no—
330D236—42no—
331C4×D59—48no—
332C4×D59—84no—
333Dic118—84no—
334C8×C59—22no—
335C8×C59—22no—
336C8×C59—22no—
337C8×C59C2×#4114yes—
338C2×#3347—591nomaximal, Sylow
339C22×C59—22no—
340C22×C59—22no—
341C22×C59—22no—
342C22×C59—22no—
343C22×C59—22no—
344C22×C59—22no—
345C22×C59—44no—
346C22×C59—44no—
347C22×C59#54712yes—
348C22×C59#57512yes—
349C22×C59#57612yes—
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—22no—
362C4×C59—22no—
363C4×C59#54712yes—
364C4×C59C22×#4111yescharacteristic
365C4×C59C2×2−1+411yescharacteristic
366Dic59—42no—
367Dic59—42no—
368Dic59—42no—
369Dic59—42no—
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×#435D5911yescharacteristic, complemented
386C2×#428—591no—
387C2×#427—591no—
388C2×C59—42no—
389C2×C59—42no—
390C2×C59#334714yescomplemented
391C2×C59C2×#54711yescharacteristic
392C2×C59C2×#57511yescharacteristic
393C2×C59C2×#57611yescharacteristic
394D59—82no—
395D59—82no—
396C22×D8—591no—
397C22×M16C2×D5911yescharacteristic
398C23×C8C2×D5911yescharacteristic
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—1181no—
418C2×C4×D4C2×D5911yescharacteristic
419C2×#117—591no—
420C2×#117—591no—
421C2×#117—591no—
422C2×#117—1181no—
423C22×C4⋊C4—591no—
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#435C2×D5918yescomplemented
435#428—598no—
436#427—598no—
437C2×#107—591no—
438C2×#107—591no—
439C2×#107—591no—
440C2×#107—591no—
441C2×#107—591no—
442C2×#106—591no—
443C2×#106—591no—
444C2×#106—591no—
445C2×#106—591no—
446C2×C4⋊C8C2×D5911yescharacteristic
447C2×#102—591no—
448C2×#102—591no—
449C2×#102—591no—
450C2×#102—591no—
451C2×#102—591no—
452C2×#102—591no—
453C2×C22⋊C8C2×D5911yescharacteristic
454C2×C22⋊C8C2×D5911yescharacteristic
455C2×#97C2×D5911yescharacteristic
456C59C2×#334711yescharacteristic, complemented, Sylow
457C22×Q8—1181no—
458C22×D4—591no—
459C22×D4—591no—
460C22×D4—1181no—
461C22×D4—1181no—
462C22×D4—1181no—
463C22×D4—1181no—
464C22×D4D23611yescharacteristic
465C23×C4—1181no—
466C23×C4—1181no—
467C23×C4—1181no—
468C23×C4C22×D5911yescharacteristic
469C23×C4C22×D5911yescharacteristic
470C2×D8—594no—
471C2×D8—1184no—
472C2×M16—24no—
473C2×M16C22×D5914yes—
474C22×C8—24no—
475C22×C8C22×D5911yescharacteristic
476C22×C8C22×D5914yes—
477C22×C8C22×D5911yescharacteristic
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—1188no—
494#121—1182no—
495#121—1182no—
496#121—1182no—
497#121—1182no—
498C4×D4—594no—
499C4×D4—594no—
500C4×D4—1188no—
501C4×D4—1182no—
502C4×D4—1182no—
503C4×D4D23614yes—
504C4×D4C22×D5914yes—
505#117—594no—
506#117—594no—
507#117—594no—
508#117—1182no—
509#117—1182no—
510#117—1182no—
511#117—1188no—
512C2×C4⋊C4—591no—
513C2×C4⋊C4—591no—
514C2×C4⋊C4—594no—
515C2×C4⋊C4—591no—
516C2×C4⋊C4—591no—
517C2×C4⋊C4—591no—
518C2×C4⋊C4—591no—
519C2×C4⋊C4—1181no—
520C2×C4⋊C4—1182no—
521C2×C4⋊C4—1181no—
522C2×C4⋊C4—1181no—
523C2×C4⋊C4—1181no—
524C2×C4⋊C4D23611yescharacteristic
525C2×C22⋊C4—1181no—
526C2×C22⋊C4—1181no—
527C2×C22⋊C4—1181no—
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⋊C4D23611yescharacteristic
535C2×C22⋊C4D23611yescharacteristic
536C2×C42—1181no—
537C2×C42—1181no—
538C2×C42—1181no—
539C2×C42C22×D5911yescharacteristic
540#107—594no—
541#107—594no—
542#107—594no—
543#107—594no—
544#107—594no—
545#106—594no—
546#106—594no—
547#106—594no—
548#106—594no—
549C4⋊C8C22×D5914yes—
550#102—594no—
551#102—594no—
552#102—594no—
553#102—594no—
554#102—594no—
555#102—594no—
556C22⋊C8C22×D5914yes—
557C22⋊C8C22×D5914yes—
558#97C22×D5914yes—
559C24—1181no—
560C24—1181no—
561C24C2×D23611yescharacteristic
562C24C2×D23611yescharacteristic
563C2×Q8—1184no—
564C2×Q8—4722no—
565C2×D4—42no—
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—2364no—
582C2×D4C2×D23614yes—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—1184no—
588C22×C4—1181no—
589C22×C4—1181no—
590C22×C4—1181no—
591C22×C4—1181no—
592C22×C4—1181no—
593C22×C4—1181no—
594C22×C4—1184no—
595C22×C4—1184no—
596C22×C4—4722no—
597C22×C4—4722no—
598C22×C4—2364no—
599C22×C4C2×D23612yes—
600C22×C4C2×D23612yes—
601C22×C4C2×D23611yescharacteristic
602C22×C4C2×D23611yescharacteristic
603C22×C4C2×D23611yescharacteristic
604C22×C4C2×D23611yescharacteristic
605C22×C4C23×D5912yes—
606C22×C4C23×D5912yes—
607C22×C4C23×D5911yescharacteristic
608D8—1188no—
609M16—28no—
610C2×C8—22no—
611C2×C8—22no—
612C2×C8—22no—
613C2×C8—28no—
614C2×C8#1174568714yes—
615C2×C8C23×D5912yes—
616C2×C8C23×D5912yes—
617C2×C8C23×D5912yes—
618C2×C8C23×D5912yes—
619C4⋊C4—592no—
620C4⋊C4—592no—
621C4⋊C4—592no—
622C4⋊C4—592no—
623C4⋊C4—592no—
624C4⋊C4—592no—
625C4⋊C4—1181no—
626C4⋊C4—1181no—
627C4⋊C4—1184no—
628C4⋊C4—1181no—
629C4⋊C4—1181no—
630C4⋊C4—1181no—
631C4⋊C4—1181no—
632C4⋊C4—1184no—
633C4⋊C4—1184no—
634C4⋊C4—1184no—
635C4⋊C4C2×D23614yes—
636C22⋊C4—1184no—
637C22⋊C4—1184no—
638C22⋊C4—1184no—
639C22⋊C4—1184no—
640C22⋊C4—1184no—
641C22⋊C4—1184no—
642C22⋊C4—1184no—
643C22⋊C4—1184no—
644C22⋊C4—1184no—
645C22⋊C4C2×D23614yes—
646C22⋊C4C2×D23614yes—
647C42—1184no—
648C42—1184no—
649C42—1184no—
650C42C2×D23612yes—
651C42C23×D5912yes—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—1182no—
659C23—1182no—
660C23—2362no—
661C23—2362no—
662C23—2362no—
663C23—2362no—
664C23—2362no—
665C23—2362no—
666C23C22×D23612yes—
667C23C22×D23612yes—
668C23C22×D23611yescharacteristic
669Q8—4724no—
670D4—44no—
671D4—1182no—
672D4—1182no—
673D4—1182no—
674D4—1182no—
675D4—4724no—
676D4—4724no—
677D4—4724no—
678D4—2368no—
679D4—2362no—
680D4—2362no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—1182no—
692C2×C4—1182no—
693C2×C4—1182no—
694C2×C4—1182no—
695C2×C4—1182no—
696C2×C4—1182no—
697C2×C4—4724no—
698C2×C4—4724no—
699C2×C4—2368no—
700C2×C4—2362no—
701C2×C4—2362no—
702C2×C4—2362no—
703C2×C4—2362no—
704C2×C4—2362no—
705C2×C4—2362no—
706C2×C4C22×D23612yes—
707C2×C4C22×D23612yes—
708C2×C4C22×D23612yes—
709C2×C4C22×D23612yes—
710C2×C4C22×D23611yescharacteristic
711C2×C4C2×#1174568712yes—
712C2×C4#1427377412yes—
713C2×C4C24×D5911yescharacteristic
714C8—22no—
715C8—22no—
716C8—22no—
717C8C2×#1174568714yes—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—44no—
725C22—44no—
726C22—4724no—
727C22—4724no—
728C22—2362no—
729C22—2362no—
730C22—2362no—
731C22—2362no—
732C22—2362no—
733C22—2362no—
734C22#1683805612yes—
735C22#1683820212yes—
736C22#1683820712yes—
737C22C23×D23611yescharacteristic
738C4—22no—
739C4—22no—
740C4—22no—
741C4—22no—
742C4—2362no—
743C4—2362no—
744C4—2362no—
745C4—2362no—
746C4—2362no—
747C4—2362no—
748C4#1683805612yes—
749C4C22×#1174568711yescharacteristic
750C4C2×#1427377411yescharacteristic
751C2—42no—
752C2—42no—
753C2—4722no—
754C2—4722no—
755C2#2143659814yesdirect product factor
756C2C2×#1683805611yescharacteristic
757C2C2×#1683820211yescharacteristic
758C2C2×#1683820711yescharacteristic
subgroupG/H
centerC23C22×D236
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#435C2
socleC23×C59C22×D4
hypercenterC2×#435D59
hypocenterC59C2×#3347
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C2×#16838117C2semidirect
2. C2×#16838098C2semidirect
3. #21436598C2direct (N × H)
4. C2×#16837811C2semidirect
5. C2×#16837727C2semidirect
6. C2×#16837727C2semidirect
7. C2×#16837727C2semidirect
8. C2×#16837716C2semidirect
9. C2×#16837703C2semidirect
10. C2×#16837683C2semidirect
11. C2×#16837655C2semidirect
12. C2×#16837638C2semidirect
13. C2×#16837515C2semidirect
14. C2×#16837444C2semidirect
15. C2×#16837440C2semidirect
16. C2×C59×#435C2semidirect
19. #16838117C22semidirect
21. #16838098C22semidirect
42. #16837811C22semidirect
43. #16837727C22semidirect
44. #16837727C22semidirect
45. #16837727C22semidirect
46. #16837716C22semidirect
47. #16837703C22semidirect
48. #16837683C22semidirect
49. #16837655C22semidirect
50. #16837638C22semidirect
51. #16837515C22semidirect
52. #16837444C22semidirect
53. #16837440C22semidirect
72. C59×#435C22semidirect
385. C2×#435D59semidirect
390. C2×C59#3347semidirect
434. #435C2×D59semidirect
456. C59C2×#3347semidirect
755. C2#21436598direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168381172
C2×#168380982
#214365982
C2×#168378112
C2×#168377272
C2×#168377162
C2×#168377032
C2×#168376832
C2×#168376552
C2×#168376382
C2×#168375152
C2×#168374442
C2×#168374402
C2×C59×#4352
C2×#334759