Finite Group Databasebeta

← C2×#21434698 #29458462

Subgroups — C2×#21434698 #29458462

Order 15104.

1986 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837956C211yesmaximal, characteristic, complemented
2C2×#16837934C211yesmaximal, characteristic
3#21434698C2116yesmaximal, direct product factor
4C2×#16837809C211yesmaximal, characteristic, complemented
5C2×#16837793C211yesmaximal, characteristic, complemented
6C2×#16837769C211yesmaximal, characteristic, complemented
7C2×#16837760C211yesmaximal, characteristic, complemented
8C2×#16837661C211yesmaximal, characteristic, complemented
9C2×#16837659C211yesmaximal, characteristic, complemented
10C2×#16837647C211yesmaximal, characteristic
11C2×#16837645C211yesmaximal, characteristic
12C2×C4×Dic236C211yesmaximal, characteristic, complemented
13C2×C4×#11745672C211yesmaximal, characteristic, complemented
14C2×C4×#11745670C211yesmaximal, characteristic, complemented
15C2×C4×#11745659C211yesmaximal, characteristic, complemented
16C2×C4×SD16×C59C211yesmaximal, characteristic, complemented
17C22×Dic236C2211yescharacteristic
18C22×#11745672C2211yescharacteristic
19C22×#11745670C2211yescharacteristic
20C22×#11745659C2211yescharacteristic
21C22×#11745659C2211yescharacteristic
22#16837956—24no—
23#16837956C2218yescomplemented
24C2×#14273726C2211yescharacteristic
25C2×#14273725C2211yescharacteristic
26#16837934—24no—
27#16837934C2218yes—
28C2×#14273720—21no—
29C2×#14273718C2211yescharacteristic
30C2×#14273717—21no—
31C2×#14273714C2211yescharacteristic
32C2×#14273709—21no—
33C2×#14273707C2211yescharacteristic
34C2×#14273707C2211yescharacteristic
35C2×#14273705—21no—
36C2×#14273703C2211yescharacteristic
37C2×#14273698C2211yescharacteristic
38C2×C4×Dic118—21no—
39C2×C4×Dic118C2211yescharacteristic
40C2×C4×Dic118C2211yescharacteristic
41C2×C4×C22⋊D59—21no—
42C2×#14273686—21no—
43C2×#14273684—21no—
44C2×C42×D59C2211yescharacteristic
45#16837809C2218yescomplemented
46#16837793C2218yescomplemented
47#16837769C2218yescomplemented
48#16837760C2218yescomplemented
49#16837661C2218yescomplemented
50#16837659C2218yescomplemented
51#16837647C2218yes—
52#16837645C2218yes—
53C4×Dic236C2218yescomplemented
54C4×#11745672C2218yescomplemented
55C4×#11745670C2218yescomplemented
56C2×#14273661C2211yescharacteristic
57C2×#14273660C2211yescharacteristic
58C2×#14273658C2211yescharacteristic
59C2×#14273652C2211yescharacteristic
60C2×#14273652C2211yescharacteristic
61C2×#14273651C2211yescharacteristic
62C2×#14273650C2211yescharacteristic
63C2×#14273650C2211yescharacteristic
64C2×#14273648C2211yescharacteristic
65C4×#11745659C2218yescomplemented
66C2×#14273637C2211yescharacteristic
67C2×#14273637C2211yescharacteristic
68C2×C4×C59⋊C8C2211yescharacteristic
69C22×SD16×C59C2211yescharacteristic
70C2×C4×Q8×C59C2211yescharacteristic
71C2×C4×D4×C59C2211yescharacteristic
72C4×SD16×C59C2218yescomplemented
73C2×#106×C59C2211yescharacteristic
74C2×#103×C59C2211yescharacteristic
75C2×#102×C59C2211yescharacteristic
76C2×C4×C8×C59C2211yescharacteristic
77C22×Dic118—21no—
78C22×Dic118C2311yescharacteristic
79C22×Dic118C2311yescharacteristic
80C22×C22⋊D59—21no—
81C22×C4×D59D411yescharacteristic
82C22×C4×D59D411yescharacteristic
83C22×C4×D59C2311yescharacteristic
84C2×Dic236—24no—
85C2×Dic236C2314yes—
86C2×#11745672—24no—
87C2×#11745672C2314yes—
88C2×#11745670—24no—
89C2×#11745670C2314yes—
90C2×#11745659—24no—
91C2×#11745659—24no—
92C2×#11745659C2314yes—
93C2×#11745659C2314yes—
94C22×C59⋊C8C2311yescharacteristic
95C22×C59⋊C8C2311yescharacteristic
96#14273726—22no—
97#14273726C2314yes—
98#14273725—22no—
99#14273725C2314yes—
100#14273720—28no—
101#14273718—22no—
102#14273718C2314yes—
103#14273717—28no—
104#14273714—22no—
105#14273714C2314yes—
106#14273709—28no—
107#14273707—22no—
108#14273707—22no—
109#14273707C2314yes—
110#14273707C2314yes—
111#14273705—28no—
112#14273703—22no—
113#14273703C2314yes—
114#14273698—22no—
115#14273698C2314yes—
116C4×Dic118—22no—
117C4×Dic118—22no—
118C4×Dic118—28no—
119C4×Dic118C2314yes—
120C4×Dic118C2314yes—
121C4×C22⋊D59—28no—
122#14273686—28no—
123#14273684—28no—
124C2×C4⋊Dic59—21no—
125C2×C4⋊Dic59—21no—
126C2×C4⋊Dic59—21no—
127C2×C4⋊Dic59C2311yescharacteristic
128C2×C4⋊Dic59C2311yescharacteristic
129C2×Dic59⋊C4—21no—
130C2×Dic59⋊C4—21no—
131C2×Dic59⋊C4—21no—
132C2×Dic59⋊C4—21no—
133C2×Dic59⋊C4—21no—
134C2×Dic59⋊C4—21no—
135C2×Dic59⋊C4—21no—
136C2×C22⋊Dic59—21no—
137C2×C22⋊Dic59—21no—
138C2×C22⋊Dic59—21no—
139C2×(C2×D59)⋊C4—21no—
140C2×(C2×D59)⋊C4—21no—
141C2×(C2×D59)⋊C4—21no—
142C2×C4×Dic59—21no—
143C2×C4×Dic59—21no—
144C2×C4×Dic59D411yescharacteristic
145C2×C4×Dic59D411yescharacteristic
146C2×C4×Dic59C2311yescharacteristic
147C42×D59D414yes—
148C42×D59C2314yes—
149#14273661C2314yes—
150#14273660C2314yes—
151#14273658C2314yes—
152#14273652C2314yes—
153#14273652C2314yes—
154#14273651C2314yes—
155#14273650C2314yes—
156#14273650C2314yes—
157#14273648C2314yes—
158#14273637C2314yes—
159#14273637C2314yes—
160C4×C59⋊C8C2314yes—
161C22×Q8×C59C2311yescharacteristic
162C22×D4×C59C2311yescharacteristic
163C23×C4×C59—21no—
164C2×SD16×C59—24no—
165C2×SD16×C59C2314yes—
166C22×C8×C59C2311yescharacteristic
167C22×C8×C59C2311yescharacteristic
168C4×Q8×C59—22no—
169C4×Q8×C59C2314yes—
170C4×D4×C59—22no—
171C4×D4×C59C2314yes—
172C2×C4⋊C4×C59—21no—
173C2×C4⋊C4×C59C2311yescharacteristic
174C2×C4⋊C4×C59C2311yescharacteristic
175C2×C22⋊C4×C59—21no—
176C2×C42×C59—21no—
177C2×C42×C59C2311yescharacteristic
178#106×C59C2314yes—
179#103×C59C2314yes—
180#102×C59C2314yes—
181C4×C8×C59C2314yes—
182C24×C59—21no—
183C23×D59C2×D411yescharacteristic
184C2×Q8×C59—21no—
185C2×Q8×C59—22no—
186C2×Q8×C59—22no—
187C2×Q8×C59C2412yes—
188C2×D4×C59—21no—
189C2×D4×C59—22no—
190C2×D4×C59—22no—
191C2×D4×C59C2412yes—
192C22×C4×C59—21no—
193C22×C4×C59—21no—
194C22×C4×C59—21no—
195C22×C4×C59—24no—
196C22×C4×C59—44no—
197C22×C4×C59C2×D411yescharacteristic
198C22×C4×C59C2×D411yescharacteristic
199C22×C4×C59C2411yescharacteristic
200C2×C22⋊D59—24no—
201C2×C22⋊D59—44no—
202C22×Dic59—21no—
203C22×Dic59—21no—
204C22×Dic59—21no—
205C22×Dic59—21no—
206C22×Dic59C2×D411yescharacteristic
207C22×Dic59C2×D411yescharacteristic
208C22×Dic59C2×D411yescharacteristic
209C2×C4×D59—24no—
210C2×C4×D59—22no—
211C2×C4×D59—22no—
212C2×C4×D59—42no—
213C2×C4×D59C2×D412yes—
214C2×C4×D59C2×D414yes—
215C2×C4×D59C2×D414yes—
216C2×C4×D59C2412yes—
217C2×Dic118—22no—
218C2×Dic118—22no—
219C2×Dic118—22no—
220C2×Dic118—22no—
221C2×Dic118—21no—
222C2×Dic118—21no—
223C2×Dic118—24no—
224C2×Dic118—44no—
225C2×Dic118C2412yes—
226C2×Dic118C2412yes—
227SD16×C59—28no—
228C2×C8×C59—22no—
229C2×C8×C59#4114yes—
230C2×C8×C59C2412yes—
231C2×C8×C59C2412yes—
232C4⋊C4×C59—24no—
233C4⋊C4×C59—21no—
234C4⋊C4×C59—21no—
235C4⋊C4×C59C2412yes—
236C4⋊C4×C59C2412yes—
237C22⋊C4×C59—24no—
238C42×C59—24no—
239C42×C59C2×D412yes—
240C42×C59C2412yes—
241C22⋊Dic59—24no—
242C22⋊Dic59—24no—
243C22⋊Dic59—24no—
244#11745672—28no—
245#11745670—28no—
246(C2×D59)⋊C4—24no—
247(C2×D59)⋊C4—24no—
248(C2×D59)⋊C4—24no—
249C4⋊Dic59—21no—
250C4⋊Dic59—21no—
251C4⋊Dic59—24no—
252C4⋊Dic59—24no—
253C4⋊Dic59—24no—
254C4⋊Dic59C2412yes—
255C4⋊Dic59C2412yes—
256Dic59⋊C4—24no—
257Dic59⋊C4—24no—
258Dic59⋊C4—24no—
259Dic59⋊C4—24no—
260Dic59⋊C4—24no—
261Dic59⋊C4—24no—
262Dic59⋊C4—24no—
263C4×Dic59—24no—
264C4×Dic59—24no—
265C4×Dic59C2×D412yes—
266C4×Dic59C2×D414yes—
267C4×Dic59C2×D414yes—
268C4×Dic59C2412yes—
269C2×C59⋊C8—22no—
270C2×C59⋊C8#4114yes—
271C2×C59⋊C8C2412yes—
272C2×C59⋊C8C2412yes—
273Dic236—28no—
274#11745659—28no—
275#11745659—28no—
276C23×C59—22no—
277C23×C59—42no—
278C23×C59—42no—
279C23×C59—42no—
280C23×C59C22×D411yescharacteristic
281C22×D59—22no—
282C22×D59—22no—
283C22×D59—22no—
284C22×D59C22×D412yes—
285Q8×C59—22no—
286Q8×C59—22no—
287Q8×C59—42no—
288D4×C59—22no—
289D4×C59—22no—
290D4×C59—42no—
291C2×C4×C59—22no—
292C2×C4×C59—22no—
293C2×C4×C59—22no—
294C2×C4×C59—22no—
295C2×C4×C59—42no—
296C2×C4×C59—42no—
297C2×C4×C59—42no—
298C2×C4×C59—48no—
299C2×C4×C59#13714yes—
300C2×C4×C59C22×D412yes—
301C2×C4×C59C22×D411yescharacteristic
302C2×C4×C59C22×D412yes—
303C2×C4×C59C2×#4112yes—
304C2×C4×C59C2×#4112yes—
305C2×C4×C59C2511yescharacteristic
306C22⋊D59—48no—
307C2×Dic59—22no—
308C2×Dic59—22no—
309C2×Dic59—22no—
310C2×Dic59—22no—
311C2×Dic59—22no—
312C2×Dic59—22no—
313C2×Dic59—22no—
314C2×Dic59—42no—
315C2×Dic59—42no—
316C2×Dic59—42no—
317C2×Dic59—42no—
318C2×Dic59C22×D412yes—
319C2×Dic59C22×D412yes—
320C2×Dic59C22×D412yes—
321C4×D59—24no—
322C4×D59—28no—
323C4×D59—22no—
324C4×D59—22no—
325C4×D59—44no—
326Dic118—22no—
327Dic118—22no—
328Dic118—22no—
329Dic118—22no—
330Dic118—48no—
331Dic118—42no—
332Dic118—42no—
333C8×C59—22no—
334C8×C59C2×#4114yes—
335C59⋊C8—22no—
336C59⋊C8C2×#4114yes—
337C2×#3172—591nomaximal, Sylow
338C22×C59—42no—
339C22×C59—42no—
340C22×C59—42no—
341C22×C59—84no—
342C22×C59#53212yes—
343C22×C59C2×#13712yes—
344C22×C59#57512yes—
345C22×C59C23×D411yescharacteristic
346C2×D59—22no—
347C2×D59—22no—
348C2×D59—22no—
349C2×D59—44no—
350C4×C59—22no—
351C4×C59—42no—
352C4×C59—42no—
353C4×C59—42no—
354C4×C59#53212yes—
355C4×C59C2×#13714yes—
356C4×C59C22×#4111yescharacteristic
357C4×C59C22×#4111yescharacteristic
358Dic59—22no—
359Dic59—22no—
360Dic59—22no—
361Dic59—42no—
362Dic59—42no—
363Dic59—42no—
364Dic59—42no—
365C2×#533—591no—
366C2×#529—591no—
367#3172—5916no—
368C2×#501—591no—
369C2×#497—591no—
370C2×#491—591no—
371C2×#489—591no—
372C2×#470—591no—
373C2×#470—591no—
374C2×#468—591no—
375C2×#468—591no—
376C2×C4×Q16—591no—
377C2×C4×Q16—591no—
378C2×C4×SD16—591no—
379C2×C4×SD16D5911yescharacteristic, complemented
380C2×C4×M16—591no—
381C2×C59—82no—
382C2×C59#317214yescomplemented
383C2×C59C2×#53211yescharacteristic
384C2×C59C22×#13711yescharacteristic
385C2×C59C2×#57511yescharacteristic
386D59—42no—
387C22×Q16—591no—
388C22×Q16—591no—
389C22×SD16—591no—
390C22×SD16C2×D5911yescharacteristic
391C22×M16—591no—
392C22×M16—591no—
393#533—598no—
394#533—1184no—
395C2×C4⋊Q8—591no—
396C2×C4⋊Q8—591no—
397#529—598no—
398#529—1184no—
399C2×#126—1181no—
400C2×#125—591no—
401C2×#125—1181no—
402C2×#124—591no—
403C2×#123—1181no—
404C2×C22⋊Q8—591no—
405C2×C22⋊Q8—591no—
406C2×C22⋊Q8—591no—
407C2×C22⋊Q8—1181no—
408C2×#121—591no—
409C2×C4×Q8—591no—
410C2×C4×Q8—591no—
411C2×C4×Q8—1181no—
412C2×C4×Q8C2×D5911yescharacteristic
413C2×C4×D4—1181no—
414C2×C4×D4C2×D5911yescharacteristic
415C2×#117—1181no—
416C2×#117—1181no—
417C22×C42—591no—
418#501—598no—
419#497—598no—
420#491—598no—
421#489—598no—
422#470—598no—
423#470—598no—
424#468—598no—
425#468—598no—
426C4×Q16—598no—
427C4×Q16—598no—
428C4×SD16—598no—
429C4×SD16C2×D5918yescomplemented
430C2×#107—591no—
431C2×#107—591no—
432C2×#106—591no—
433C2×#106C2×D5911yescharacteristic
434C2×#103—591no—
435C2×#103—591no—
436C2×#103—591no—
437C2×#103—591no—
438C2×#103—591no—
439C2×#103C2×D5911yescharacteristic
440C2×#102—591no—
441C2×#102C2×D5911yescharacteristic
442C4×M16—598no—
443C2×#97—591no—
444C2×#97—591no—
445C2×C4×C8—591no—
446C2×C4×C8C2×D5911yescharacteristic
447C59C2×#317211yescharacteristic, complemented, Sylow
448C22×Q8—591no—
449C22×Q8—591no—
450C22×Q8—1181no—
451C22×Q8C22×D5911yescharacteristic
452C22×D4—1181no—
453C22×D4C22×D5911yescharacteristic
454C23×C4—21no—
455C23×C4—591no—
456C23×C4—591no—
457C23×C4—591no—
458C2×Q16—594no—
459C2×Q16—594no—
460C2×Q16—1184no—
461C2×Q16—1184no—
462C2×SD16—24no—
463C2×SD16—594no—
464C2×SD16—1184no—
465C2×SD16C22×D5914yes—
466C2×M16—594no—
467C2×M16—594no—
468C2×M16—1184no—
469C2×M16—1184no—
470C22×C8—591no—
471C22×C8—591no—
472C22×C8C22×D5911yescharacteristic
473C22×C8C22×D5911yescharacteristic
474C4⋊Q8—594no—
475C4⋊Q8—594no—
476C4⋊Q8—1182no—
477C4⋊Q8—1182no—
478#126—1188no—
479#125—594no—
480#125—1182no—
481#125—1188no—
482#124—594no—
483#124—1182no—
484#123—1188no—
485C22⋊Q8—594no—
486C22⋊Q8—594no—
487C22⋊Q8—594no—
488C22⋊Q8—1182no—
489C22⋊Q8—1182no—
490C22⋊Q8—1188no—
491C22⋊Q8—1182no—
492#121—594no—
493#121—1182no—
494C4×Q8—22no—
495C4×Q8—594no—
496C4×Q8—594no—
497C4×Q8—1188no—
498C4×Q8—1182no—
499C4×Q8—1182no—
500C4×Q8C22×D5914yes—
501C4×D4—22no—
502C4×D4—1188no—
503C4×D4C22×D5914yes—
504#117—1188no—
505#117—1188no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—591no—
508C2×C4⋊C4—591no—
509C2×C4⋊C4—1181no—
510C2×C4⋊C4—1181no—
511C2×C4⋊C4—1181no—
512C2×C4⋊C4—1181no—
513C2×C4⋊C4—1181no—
514C2×C4⋊C4—1181no—
515C2×C4⋊C4—1181no—
516C2×C4⋊C4—1181no—
517C2×C4⋊C4—1181no—
518C2×C4⋊C4—1181no—
519C2×C4⋊C4C22×D5911yescharacteristic
520C2×C4⋊C4C22×D5911yescharacteristic
521C2×C22⋊C4—21no—
522C2×C22⋊C4—1181no—
523C2×C22⋊C4—1181no—
524C2×C22⋊C4—1181no—
525C2×C22⋊C4—1181no—
526C2×C22⋊C4—1181no—
527C2×C22⋊C4—1181no—
528C2×C42—21no—
529C2×C42—591no—
530C2×C42—591no—
531C2×C42—591no—
532C2×C42—594no—
533C2×C42—594no—
534C2×C42—1181no—
535C2×C42—1181no—
536C2×C42C22×D5911yescharacteristic
537#107—594no—
538#107—594no—
539#106—594no—
540#106C22×D5914yes—
541#103—594no—
542#103—594no—
543#103—594no—
544#103—594no—
545#103—594no—
546#103C22×D5914yes—
547#102—594no—
548#102C22×D5914yes—
549#97—594no—
550#97—594no—
551C4×C8—594no—
552C4×C8C22×D5914yes—
553C24—21no—
554C24—591no—
555C2×Q8—21no—
556C2×Q8—22no—
557C2×Q8—22no—
558C2×Q8—592no—
559C2×Q8—592no—
560C2×Q8—1184no—
561C2×Q8—1181no—
562C2×Q8—1181no—
563C2×Q8—1182no—
564C2×Q8—1182no—
565C2×Q8—1182no—
566C2×Q8—1182no—
567C2×Q8—2364no—
568C2×Q8C23×D5912yes—
569C2×D4—21no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—1184no—
573C2×D4—2364no—
574C2×D4C23×D5912yes—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—24no—
579C22×C4—44no—
580C22×C4—591no—
581C22×C4—591no—
582C22×C4—591no—
583C22×C4—594no—
584C22×C4—592no—
585C22×C4—592no—
586C22×C4—594no—
587C22×C4—1184no—
588C22×C4—1182no—
589C22×C4—1182no—
590C22×C4—1181no—
591C22×C4—1181no—
592C22×C4—1181no—
593C22×C4—1181no—
594C22×C4—2362no—
595C22×C4D4×D5911yescharacteristic
596C22×C4D4×D5911yescharacteristic
597C22×C4C23×D5911yescharacteristic
598Q16—1188no—
599Q16—1188no—
600SD16—28no—
601SD16—1188no—
602M16—1188no—
603M16—1188no—
604C2×C8—22no—
605C2×C8—594no—
606C2×C8—592no—
607C2×C8—592no—
608C2×C8—1182no—
609C2×C8#1174568514yes—
610C2×C8C23×D5912yes—
611C2×C8C23×D5912yes—
612C4⋊C4—24no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—592no—
616C4⋊C4—592no—
617C4⋊C4—1184no—
618C4⋊C4—1184no—
619C4⋊C4—1184no—
620C4⋊C4—1184no—
621C4⋊C4—1184no—
622C4⋊C4—1184no—
623C4⋊C4—1184no—
624C4⋊C4—1184no—
625C4⋊C4—1181no—
626C4⋊C4—1181no—
627C4⋊C4—1184no—
628C4⋊C4—1184no—
629C4⋊C4C23×D5912yes—
630C4⋊C4C23×D5912yes—
631C22⋊C4—24no—
632C22⋊C4—1184no—
633C22⋊C4—1184no—
634C22⋊C4—1184no—
635C22⋊C4—1184no—
636C22⋊C4—1184no—
637C22⋊C4—1184no—
638C42—24no—
639C42—594no—
640C42—592no—
641C42—594no—
642C42—592no—
643C42—1184no—
644C42—1184no—
645C42D4×D5912yes—
646C42C23×D5912yes—
647C23—22no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—592no—
652C23—1182no—
653C23—1182no—
654C23—1182no—
655C23C2×D4×D5911yescharacteristic
656Q8—22no—
657Q8—22no—
658Q8—42no—
659Q8—1182no—
660Q8—1182no—
661Q8—1182no—
662Q8—1182no—
663Q8—2368no—
664Q8—2362no—
665Q8—2362no—
666D4—22no—
667D4—22no—
668D4—42no—
669D4—2368no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—48no—
678C2×C4—592no—
679C2×C4—592no—
680C2×C4—592no—
681C2×C4—1182no—
682C2×C4—1182no—
683C2×C4—1182no—
684C2×C4—1188no—
685C2×C4—1184no—
686C2×C4—1182no—
687C2×C4—1182no—
688C2×C4—1182no—
689C2×C4—1182no—
690C2×C4—1182no—
691C2×C4—1182no—
692C2×C4—2364no—
693C2×C4—2362no—
694C2×C4—2362no—
695C2×C4—2362no—
696C2×C4—2362no—
697C2×C4#1427375614yes—
698C2×C4C2×D4×D5912yes—
699C2×C4C2×D4×D5912yes—
700C2×C4C2×D4×D5911yescharacteristic
701C2×C4#41×D5912yes—
702C2×C4C2×#1174568512yes—
703C2×C4C24×D5911yescharacteristic
704C8—22no—
705C8—594no—
706C8—1182no—
707C8C2×#1174568514yes—
708C22—42no—
709C22—42no—
710C22—42no—
711C22—84no—
712C22—1182no—
713C22—1182no—
714C22—1182no—
715C22—2364no—
716C22#1683794912yes—
717C22C2×#1427375612yes—
718C22#1683819912yes—
719C22C22×D4×D5911yescharacteristic
720C4—22no—
721C4—42no—
722C4—42no—
723C4—42no—
724C4—1182no—
725C4—1182no—
726C4—1182no—
727C4—2362no—
728C4—2362no—
729C4—2362no—
730C4—2362no—
731C4#1683794912yes—
732C4C2×#1427375614yes—
733C4C2×#41×D5911yescharacteristic
734C4C22×#1174568511yescharacteristic
735C2—82no—
736C2—2362no—
737C2#2143469814yesdirect product factor
738C2C2×#1683794911yescharacteristic
739C2C22×#1427375611yescharacteristic
740C2C2×#1683819911yescharacteristic
subgroupG/H
centerC22×C4D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C4×SD16×C59C2
socleC23×C59C22×D4
prime radicalC2×#14273698C22
hypercenterC2×C4×SD16D59
hypocenterC59C2×#3172
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#16837956C2semidirect
3. #21434698C2direct (N × H)
4. C2×#16837809C2semidirect
5. C2×#16837793C2semidirect
6. C2×#16837769C2semidirect
7. C2×#16837760C2semidirect
8. C2×#16837661C2semidirect
9. C2×#16837659C2semidirect
12. C2×C4×Dic236C2semidirect
13. C2×C4×#11745672C2semidirect
14. C2×C4×#11745670C2semidirect
15. C2×C4×#11745659C2semidirect
16. C2×C4×SD16×C59C2semidirect
23. #16837956C22semidirect
45. #16837809C22semidirect
46. #16837793C22semidirect
47. #16837769C22semidirect
48. #16837760C22semidirect
49. #16837661C22semidirect
50. #16837659C22semidirect
53. C4×Dic236C22semidirect
54. C4×#11745672C22semidirect
55. C4×#11745670C22semidirect
65. C4×#11745659C22semidirect
72. C4×SD16×C59C22semidirect
379. C2×C4×SD16D59semidirect
382. C2×C59#3172semidirect
429. C4×SD16C2×D59semidirect
447. C59C2×#3172semidirect
737. C2#21434698direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168379562
C2×#168379342
#214346982
C2×#168378092
C2×#168377932
C2×#168377692
C2×#168377602
C2×#168376612
C2×#168376592
C2×#168376472
C2×#168376452
C2×C4×Dic2362
C2×C4×#117456722
C2×C4×#117456702
C2×C4×#117456592
C2×C4×SD16×C592
C2×#317259