Finite Group Databasebeta

← C2×#21434695 #29458459

Subgroups — C2×#21434695 #29458459

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×#16837954C211yesmaximal, characteristic, complemented
2C2×#16837933C211yesmaximal, characteristic
3#21434695C2116yesmaximal, direct product factor
4C2×#16837810C211yesmaximal, characteristic, complemented
5C2×#16837793C211yesmaximal, characteristic, complemented
6C2×#16837769C211yesmaximal, characteristic, complemented
7C2×#16837760C211yesmaximal, characteristic, complemented
8C2×#16837660C211yesmaximal, characteristic, complemented
9C2×#16837658C211yesmaximal, characteristic, complemented
10C2×#16837646C211yesmaximal, characteristic
11C2×#16837496C211yesmaximal, characteristic, complemented
12C2×#16837494C211yesmaximal, characteristic, complemented
13C2×#16837493C211yesmaximal, characteristic, complemented
14C2×SD16×Dic59C211yesmaximal, characteristic, complemented
15C2×M16×Dic59C211yesmaximal, characteristic, complemented
16C2×C59×#468C211yesmaximal, characteristic
17C22×Dic236C2211yescharacteristic
18C22×#11745672C2211yescharacteristic
19C22×#11745670C2211yescharacteristic
20C22×#11745664C2211yescharacteristic
21#16837954—24no—
22#16837954C2218yescomplemented
23C2×#14273726C2211yescharacteristic
24C2×#14273725C2211yescharacteristic
25#16837933—24no—
26#16837933C2218yes—
27C2×#14273720—21no—
28C2×#14273718C2211yescharacteristic
29C2×#14273717—21no—
30C2×#14273714C2211yescharacteristic
31C2×#14273708—21no—
32C2×#14273706C2211yescharacteristic
33C2×#14273706C2211yescharacteristic
34C2×#14273704—21no—
35C2×Q8×Dic59C2211yescharacteristic
36C2×#14273692—21no—
37C2×#14273692C2211yescharacteristic
38C2×#14273692C2211yescharacteristic
39C2×D4×Dic59—21no—
40C2×D4×Dic59C2211yescharacteristic
41C2×#14273683—21no—
42C2×#14273683—21no—
43C22×C4×Dic59C2211yescharacteristic
44#16837810C2218yescomplemented
45#16837793C2218yescomplemented
46#16837769C2218yescomplemented
47#16837760C2218yescomplemented
48#16837660C2218yescomplemented
49#16837658C2218yescomplemented
50#16837646C2218yes—
51#16837496C2218yescomplemented
52#16837494C2218yescomplemented
53#16837493C2218yescomplemented
54SD16×Dic59C2218yescomplemented
55C2×#14273660C2211yescharacteristic
56C2×#14273659C2211yescharacteristic
57C2×#14273658C2211yescharacteristic
58C2×#14273652C2211yescharacteristic
59C2×#14273652C2211yescharacteristic
60C2×#14273651C2211yescharacteristic
61C2×#14273650C2211yescharacteristic
62C2×#14273650C2211yescharacteristic
63C2×#14273648C2211yescharacteristic
64M16×Dic59C2218yescomplemented
65C2×#14273637C2211yescharacteristic
66C2×#14273637C2211yescharacteristic
67C2×C8×Dic59C2211yescharacteristic
68C2×C8×Dic59C2211yescharacteristic
69C22×SD16×C59C2211yescharacteristic
70C22×M16×C59C2211yescharacteristic
71C2×C22⋊Q8×C59C2211yescharacteristic
72C2×#121×C59C2211yescharacteristic
73C59×#468C2218yes—
74C2×#107×C59C2211yescharacteristic
75C2×#103×C59C2211yescharacteristic
76C2×#102×C59C2211yescharacteristic
77C22×Dic118—21no—
78C22×Dic118C2311yescharacteristic
79C22×Dic118C2311yescharacteristic
80C23×Dic59—21no—
81C23×Dic59D411yescharacteristic
82C23×Dic59D411yescharacteristic
83C2×Dic236—24no—
84C2×Dic236C2314yes—
85C2×#11745672—24no—
86C2×#11745672C2314yes—
87C2×#11745670—24no—
88C2×#11745670C2314yes—
89C2×#11745664—24no—
90C2×#11745664C2314yes—
91C22×C59⋊C8C2311yescharacteristic
92C22×C59⋊C8C2311yescharacteristic
93#14273726—22no—
94#14273726C2314yes—
95#14273725—22no—
96#14273725C2314yes—
97#14273720—28no—
98#14273718—22no—
99#14273718C2314yes—
100#14273717—28no—
101#14273714—22no—
102#14273714C2314yes—
103#14273708—28no—
104#14273706—22no—
105#14273706—22no—
106#14273706C2314yes—
107#14273706C2314yes—
108#14273704—28no—
109Q8×Dic59—22no—
110Q8×Dic59C2314yes—
111#14273692—22no—
112#14273692—22no—
113#14273692—28no—
114#14273692C2314yes—
115#14273692C2314yes—
116D4×Dic59—28no—
117D4×Dic59—22no—
118D4×Dic59C2314yes—
119#14273683—28no—
120#14273683—28no—
121C2×C4⋊Dic59—21no—
122C2×C4⋊Dic59—21no—
123C2×C4⋊Dic59C2311yescharacteristic
124C2×C4⋊Dic59C2311yescharacteristic
125C2×Dic59⋊C4—21no—
126C2×Dic59⋊C4—21no—
127C2×Dic59⋊C4—21no—
128C2×Dic59⋊C4—21no—
129C2×Dic59⋊C4—21no—
130C2×Dic59⋊C4—21no—
131C2×Dic59⋊C4—21no—
132C2×Dic59⋊C4—21no—
133C2×C22⋊Dic59—21no—
134C2×C22⋊Dic59—21no—
135C2×C22⋊Dic59—21no—
136C2×C22⋊Dic59—21no—
137C2×C22⋊Dic59—21no—
138C2×C4×Dic59—21no—
139C2×C4×Dic59—21no—
140C2×C4×Dic59—21no—
141C2×C4×Dic59D411yescharacteristic
142C2×C4×Dic59D414yes—
143C2×C4×Dic59D411yescharacteristic
144C2×C4×Dic59C2311yescharacteristic
145C2×C4×Dic59C2314yes—
146C2×C4×Dic59C2311yescharacteristic
147#14273660C2314yes—
148#14273659C2314yes—
149#14273658C2314yes—
150#14273652C2314yes—
151#14273652C2314yes—
152#14273651C2314yes—
153#14273650C2314yes—
154#14273650C2314yes—
155#14273648C2314yes—
156#14273637C2314yes—
157#14273637C2314yes—
158C8×Dic59C2314yes—
159C8×Dic59C2314yes—
160C22×Q8×C59C2311yescharacteristic
161C22×D4×C59—21no—
162C22×D4×C59C2311yescharacteristic
163C23×C4×C59C2311yescharacteristic
164C2×SD16×C59—24no—
165C2×SD16×C59C2314yes—
166C2×M16×C59—24no—
167C2×M16×C59C2314yes—
168C22×C8×C59C2311yescharacteristic
169C22×C8×C59C2311yescharacteristic
170C22⋊Q8×C59—22no—
171C22⋊Q8×C59C2314yes—
172#121×C59—22no—
173#121×C59C2314yes—
174C2×C4⋊C4×C59—21no—
175C2×C4⋊C4×C59C2311yescharacteristic
176C2×C4⋊C4×C59C2311yescharacteristic
177C2×C22⋊C4×C59—21no—
178C2×C22⋊C4×C59—21no—
179#107×C59C2314yes—
180#103×C59C2314yes—
181#102×C59C2314yes—
182C24×C59—21no—
183C24×C59C2×D411yescharacteristic
184C2×Q8×C59—21no—
185C2×Q8×C59—22no—
186C2×Q8×C59—22no—
187C2×Q8×C59C2412yes—
188C2×D4×C59—24no—
189C2×D4×C59—21no—
190C2×D4×C59—22no—
191C2×D4×C59—22no—
192C2×D4×C59—44no—
193C2×D4×C59C2412yes—
194C22×C4×C59—22no—
195C22×C4×C59—22no—
196C22×C4×C59—21no—
197C22×C4×C59—21no—
198C22×C4×C59—21no—
199C22×C4×C59C2×D411yescharacteristic
200C22×C4×C59C2×D412yes—
201C22×C4×C59C2412yes—
202C22×C4×C59C2411yescharacteristic
203C22×Dic59—24no—
204C22×Dic59—21no—
205C22×Dic59—21no—
206C22×Dic59—21no—
207C22×Dic59—21no—
208C22×Dic59—24no—
209C22×Dic59—42no—
210C22×Dic59—44no—
211C22×Dic59C2×D411yescharacteristic
212C22×Dic59C2×D411yescharacteristic
213C22×Dic59C2×D411yescharacteristic
214C22×Dic59C2×D414yes—
215C22×Dic59C2×D414yes—
216C22×Dic59C2×D411yescharacteristic
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—
228M16×C59—28no—
229C2×C8×C59—22no—
230C2×C8×C59#4114yes—
231C2×C8×C59C2412yes—
232C2×C8×C59C2412yes—
233C4⋊C4×C59—24no—
234C4⋊C4×C59—21no—
235C4⋊C4×C59—21no—
236C4⋊C4×C59C2412yes—
237C4⋊C4×C59C2412yes—
238C22⋊C4×C59—24no—
239C22⋊C4×C59—24no—
240C22⋊Dic59—24no—
241C22⋊Dic59—24no—
242C22⋊Dic59—24no—
243C22⋊Dic59—24no—
244C22⋊Dic59—24no—
245#11745672—28no—
246#11745670—28no—
247C4⋊Dic59—21no—
248C4⋊Dic59—21no—
249C4⋊Dic59—24no—
250C4⋊Dic59—24no—
251C4⋊Dic59C2412yes—
252C4⋊Dic59C2412yes—
253Dic59⋊C4—24no—
254Dic59⋊C4—24no—
255Dic59⋊C4—24no—
256Dic59⋊C4—24no—
257Dic59⋊C4—24no—
258Dic59⋊C4—24no—
259Dic59⋊C4—24no—
260Dic59⋊C4—24no—
261C4×Dic59—24no—
262C4×Dic59—24no—
263C4×Dic59—24no—
264C4×Dic59C2×D414yes—
265C4×Dic59C2×D412yes—
266C4×Dic59C2×D412yes—
267C4×Dic59C2×D414yes—
268C4×Dic59C2412yes—
269C4×Dic59C2412yes—
270#11745664—28no—
271C2×C59⋊C8—22no—
272C2×C59⋊C8#4114yes—
273C2×C59⋊C8C2412yes—
274C2×C59⋊C8C2412yes—
275Dic236—28no—
276C23×C59—22no—
277C23×C59—22no—
278C23×C59—22no—
279C23×C59—22no—
280C23×C59—42no—
281C23×C59—42no—
282C23×C59—42no—
283C23×C59C22×D412yes—
284C23×C59C22×D411yescharacteristic
285Q8×C59—22no—
286Q8×C59—22no—
287Q8×C59—42no—
288D4×C59—22no—
289D4×C59—22no—
290D4×C59—48no—
291D4×C59—42no—
292C2×C4×C59—22no—
293C2×C4×C59—24no—
294C2×C4×C59—22no—
295C2×C4×C59—22no—
296C2×C4×C59—22no—
297C2×C4×C59—22no—
298C2×C4×C59—22no—
299C2×C4×C59—42no—
300C2×C4×C59—42no—
301C2×C4×C59—42no—
302C2×C4×C59C22×D412yes—
303C2×C4×C59C22×D411yescharacteristic
304C2×C4×C59C2×#4112yes—
305C2×C4×C59C2×#4112yes—
306C2×C4×C59C2511yescharacteristic
307C2×Dic59—22no—
308C2×Dic59—22no—
309C2×Dic59—22no—
310C2×Dic59—28no—
311C2×Dic59—22no—
312C2×Dic59—22no—
313C2×Dic59—22no—
314C2×Dic59—22no—
315C2×Dic59—44no—
316C2×Dic59—42no—
317C2×Dic59—42no—
318C2×Dic59—42no—
319C2×Dic59—42no—
320C2×Dic59—48no—
321C2×Dic59#13714yes—
322C2×Dic59C22×D412yes—
323C2×Dic59C22×D412yes—
324C2×Dic59C22×D412yes—
325C2×Dic59C22×D412yes—
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—22no—
339C22×C59—22no—
340C22×C59—22no—
341C22×C59—44no—
342C22×C59—42no—
343C22×C59—42no—
344C22×C59—42no—
345C22×C59—84no—
346C22×C59#53212yes—
347C22×C59C2×#13712yes—
348C22×C59#57512yes—
349C22×C59C23×D411yescharacteristic
350C4×C59—22no—
351C4×C59—42no—
352C4×C59—42no—
353C4×C59—42no—
354C4×C59#53212yes—
355C4×C59C22×#4111yescharacteristic
356C4×C59C22×#4111yescharacteristic
357Dic59—22no—
358Dic59—22no—
359Dic59—22no—
360Dic59—42no—
361Dic59—42no—
362Dic59—42no—
363Dic59—42no—
364Dic59C2×#13714yes—
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×#468D5911yescharacteristic
376C2×C4×Q16—591no—
377C2×C4×Q16—591no—
378C2×C4×SD16—591no—
379C2×C4×SD16—591no—
380C2×C4×M16—591no—
381C2×C59—42no—
382C2×C59—82no—
383C2×C59#317214yescomplemented
384C2×C59C2×#53211yescharacteristic
385C2×C59C22×#13711yescharacteristic
386C2×C59C2×#57511yescharacteristic
387C22×Q16—591no—
388C22×Q16—591no—
389C22×SD16—591no—
390C22×SD16C2×D5911yescharacteristic
391C22×M16—591no—
392C22×M16C2×D5911yescharacteristic
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—1181no—
407C2×C22⋊Q8C2×D5911yescharacteristic
408C2×#121C2×D5911yescharacteristic
409C2×C4×Q8—591no—
410C2×C4×Q8—591no—
411C2×C4×Q8—591no—
412C2×C4×Q8—1181no—
413C2×C4×D4—591no—
414C2×C4×D4—1181no—
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#468C2×D5918yes—
426C4×Q16—598no—
427C4×Q16—598no—
428C4×SD16—598no—
429C4×SD16—598no—
430C2×#107—591no—
431C2×#107C2×D5911yescharacteristic
432C2×#106—591no—
433C2×#106—591no—
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×C8—591no—
447C59C2×#317211yescharacteristic, complemented, Sylow
448C22×Q8—591no—
449C22×Q8—591no—
450C22×Q8—1181no—
451C22×Q8C22×D5911yescharacteristic
452C22×D4—21no—
453C22×D4C22×D5911yescharacteristic
454C23×C4—591no—
455C23×C4—591no—
456C23×C4—1181no—
457C23×C4C22×D5911yescharacteristic
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—24no—
467C2×M16—594no—
468C2×M16—1184no—
469C2×M16C22×D5914yes—
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—22no—
486C22⋊Q8—594no—
487C22⋊Q8—594no—
488C22⋊Q8—1188no—
489C22⋊Q8—1182no—
490C22⋊Q8—1182no—
491C22⋊Q8C22×D5914yes—
492#121—22no—
493#121C22×D5914yes—
494C4×Q8—594no—
495C4×Q8—594no—
496C4×Q8—594no—
497C4×Q8—1182no—
498C4×Q8—1182no—
499C4×Q8—1188no—
500C4×Q8—1182no—
501C4×D4—594no—
502C4×D4—1182no—
503C4×D4—1188no—
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—21no—
523C2×C22⋊C4—1181no—
524C2×C22⋊C4—1181no—
525C2×C22⋊C4—1181no—
526C2×C22⋊C4—1181no—
527C2×C22⋊C4—1181no—
528C2×C42—591no—
529C2×C42—591no—
530C2×C42—594no—
531C2×C42—591no—
532C2×C42—591no—
533C2×C42—594no—
534C2×C42—1181no—
535C2×C42—1181no—
536C2×C42—1181no—
537#107—594no—
538#107C22×D5914yes—
539#106—594no—
540#106—594no—
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×C8—594no—
553C24—21no—
554C24D4×D5911yescharacteristic
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—24no—
570C2×D4—21no—
571C2×D4—22no—
572C2×D4—22no—
573C2×D4—44no—
574C2×D4C23×D5912yes—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—591no—
581C22×C4—594no—
582C22×C4—591no—
583C22×C4—591no—
584C22×C4—591no—
585C22×C4—594no—
586C22×C4—1184no—
587C22×C4—1184no—
588C22×C4—1181no—
589C22×C4—1181no—
590C22×C4—1181no—
591C22×C4—1181no—
592C22×C4—2364no—
593C22×C4—2362no—
594C22×C4D4×D5912yes—
595C22×C4D4×D5911yescharacteristic
596C22×C4C23×D5912yes—
597C22×C4C23×D5911yescharacteristic
598Q16—1188no—
599Q16—1188no—
600SD16—28no—
601SD16—1188no—
602M16—28no—
603M16—1188no—
604C2×C8—22no—
605C2×C8—594no—
606C2×C8—592no—
607C2×C8—592no—
608C2×C8—1182no—
609C2×C8#1174568714yes—
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—24no—
633C22⋊C4—1184no—
634C22⋊C4—1184no—
635C22⋊C4—1184no—
636C22⋊C4—1184no—
637C22⋊C4—1184no—
638C42—594no—
639C42—592no—
640C42—592no—
641C42—594no—
642C42—592no—
643C42—592no—
644C42—1184no—
645C42—1184no—
646C42—1184no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23C2×D4×D5912yes—
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—48no—
669D4—42no—
670C2×C4—22no—
671C2×C4—24no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—594no—
681C2×C4—592no—
682C2×C4—592no—
683C2×C4—592no—
684C2×C4—592no—
685C2×C4—1188no—
686C2×C4—1182no—
687C2×C4—1182no—
688C2×C4—1182no—
689C2×C4—1182no—
690C2×C4—1182no—
691C2×C4—1182no—
692C2×C4—1182no—
693C2×C4—2368no—
694C2×C4—2364no—
695C2×C4—2362no—
696C2×C4—2362no—
697C2×C4—2362no—
698C2×C4—2362no—
699C2×C4C2×D4×D5912yes—
700C2×C4C2×D4×D5911yescharacteristic
701C2×C4#41×D5912yes—
702C2×C4C2×#1174568712yes—
703C2×C4C24×D5911yescharacteristic
704C8—22no—
705C8—594no—
706C8—1182no—
707C8C2×#1174568714yes—
708C22—22no—
709C22—22no—
710C22—22no—
711C22—44no—
712C22—42no—
713C22—42no—
714C22—42no—
715C22—84no—
716C22#1683794712yes—
717C22#137×D5912yes—
718C22#1683819812yes—
719C22C22×D4×D5911yescharacteristic
720C4—22no—
721C4—42no—
722C4—42no—
723C4—42no—
724C4—594no—
725C4—1182no—
726C4—1182no—
727C4—1182no—
728C4—2362no—
729C4—2362no—
730C4—2362no—
731C4—2362no—
732C4#1683794712yes—
733C4C2×#41×D5911yescharacteristic
734C4C22×#1174568711yescharacteristic
735C2—42no—
736C2—82no—
737C2#2143469514yesdirect product factor
738C2C2×#1683794711yescharacteristic
739C2C2×#137×D5911yescharacteristic
740C2C2×#1683819811yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#468C2
socleC23×C59C22×D4
prime radicalC2×#121×C59C22
hypercenterC2×#468D59
hypocenterC59C2×#3172
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#468

Complements

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

NH ≅ G/Ntype
1. C2×#16837954C2semidirect
3. #21434695C2direct (N × H)
4. C2×#16837810C2semidirect
5. C2×#16837793C2semidirect
6. C2×#16837769C2semidirect
7. C2×#16837760C2semidirect
8. C2×#16837660C2semidirect
9. C2×#16837658C2semidirect
11. C2×#16837496C2semidirect
12. C2×#16837494C2semidirect
13. C2×#16837493C2semidirect
14. C2×SD16×Dic59C2semidirect
15. C2×M16×Dic59C2semidirect
22. #16837954C22semidirect
44. #16837810C22semidirect
45. #16837793C22semidirect
46. #16837769C22semidirect
47. #16837760C22semidirect
48. #16837660C22semidirect
49. #16837658C22semidirect
51. #16837496C22semidirect
52. #16837494C22semidirect
53. #16837493C22semidirect
54. SD16×Dic59C22semidirect
64. M16×Dic59C22semidirect
383. C2×C59#3172semidirect
447. C59C2×#3172semidirect
737. C2#21434695direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168379542
C2×#168379332
#214346952
C2×#168378102
C2×#168377932
C2×#168377692
C2×#168377602
C2×#168376602
C2×#168376582
C2×#168376462
C2×#168374962
C2×#168374942
C2×#168374932
C2×SD16×Dic592
C2×M16×Dic592
C2×C59×#4682
C2×#317259