Finite Group Databasebeta

← C2×#21435466 #29461542

Subgroups — C2×#21435466 #29461542

Order 15104.

1898 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×#16837931C211yesmaximal, characteristic
3#21435466C2116yesmaximal, direct product factor
4C2×#16837710C211yesmaximal, characteristic, complemented
5C2×#16837709C211yesmaximal, characteristic, complemented
6C2×#16837695C211yesmaximal, characteristic, complemented
7C2×#16837690C211yesmaximal, characteristic, complemented
8C2×#16837659C211yesmaximal, characteristic, complemented
9C2×#16837657C211yesmaximal, characteristic, complemented
10C2×#16837647C211yesmaximal, characteristic
11C2×#16837645C211yesmaximal, characteristic
12C2×#16837621C211yesmaximal, characteristic, complemented
13C2×#16837610C211yesmaximal, characteristic, complemented
14C2×#16837605C211yesmaximal, characteristic, complemented
15C2×#16837424C211yesmaximal, characteristic, complemented
16C2×C59×#464C211yesmaximal, characteristic, complemented
17C22×#11745672C2211yescharacteristic
18C22×#11745670C2211yescharacteristic
19C22×#11745659C2211yescharacteristic
20C22×#11745659C2211yescharacteristic
21#16837956—24no—
22#16837956C2218yescomplemented
23C2×#14273726C2211yescharacteristic
24C2×#14273725C2211yescharacteristic
25#16837931—24no—
26#16837931C2218yes—
27C2×#14273720—21no—
28C2×#14273719C2211yescharacteristic
29C2×#14273717—21no—
30C2×#14273709—21no—
31C2×#14273707C2211yescharacteristic
32C2×#14273705—21no—
33C2×#14273703C2211yescharacteristic
34C2×#14273703C2211yescharacteristic
35C2×#14273698C2211yescharacteristic
36C2×Q8×Dic59C2211yescharacteristic
37C2×C4×Dic118—21no—
38C2×C4×Dic118C2211yescharacteristic
39C2×D4×Dic59C2211yescharacteristic
40C2×(C22⋊D59)⋊C4—21no—
41C2×#14273684—21no—
42C2×#14273683—21no—
43C2×C42×D59C2211yescharacteristic
44#16837710C2218yescomplemented
45#16837709C2218yescomplemented
46#16837695C2218yescomplemented
47#16837690C2218yescomplemented
48#16837659C2218yescomplemented
49#16837657C2218yescomplemented
50#16837647C2218yes—
51#16837645C2218yes—
52#16837621C2218yescomplemented
53#16837610C2218yescomplemented
54#16837605C2218yescomplemented
55C2×#14273661C2211yescharacteristic
56C2×#14273660C2211yescharacteristic
57C2×#14273659C2211yescharacteristic
58C2×#14273658C2211yescharacteristic
59#16837424C2218yescomplemented
60C2×C4⋊(C59⋊C8)C2211yescharacteristic
61C2×Dic59⋊C8C2211yescharacteristic
62C2×Dic59⋊C8C2211yescharacteristic
63C2×#14273652C2211yescharacteristic
64C2×#14273652C2211yescharacteristic
65C2×#14273651C2211yescharacteristic
66C2×#14273651C2211yescharacteristic
67C2×#14273651C2211yescharacteristic
68C2×#14273648C2211yescharacteristic
69C22×Q16×C59C2211yescharacteristic
70C22×SD16×C59C2211yescharacteristic
71C2×#124×C59C2211yescharacteristic
72C2×C4×Q8×C59C2211yescharacteristic
73C59×#464C2218yescomplemented
74C2×C4⋊C8×C59C2211yescharacteristic
75C2×#103×C59C2211yescharacteristic
76C2×#102×C59C2211yescharacteristic
77C22×Dic118—21no—
78C22×Dic118C2311yescharacteristic
79C22×C22⋊D59—21no—
80C23×Dic59—21no—
81C22×C4×D59D411yescharacteristic
82C22×C4×D59D411yescharacteristic
83C22×C4×D59C2311yescharacteristic
84C2×#11745672—42no—
85C2×#11745672C2314yes—
86C2×#11745670—42no—
87C2×#11745670C2314yes—
88C2×#11745659—42no—
89C2×#11745659—42no—
90C2×#11745659C2314yes—
91C2×#11745659C2314yes—
92C22×C59⋊C8C2311yescharacteristic
93C22×C59⋊C8C2311yescharacteristic
94#14273726—22no—
95#14273726C2314yes—
96#14273725—22no—
97#14273725C2314yes—
98#14273720—28no—
99#14273719—22no—
100#14273719C2314yes—
101#14273717—28no—
102#14273709—28no—
103#14273707—22no—
104#14273707C2314yes—
105#14273705—28no—
106#14273703—22no—
107#14273703—22no—
108#14273703C2314yes—
109#14273703C2314yes—
110#14273698—22no—
111#14273698C2314yes—
112Q8×Dic59—22no—
113Q8×Dic59C2314yes—
114C4×Dic118—22no—
115C4×Dic118—28no—
116C4×Dic118C2314yes—
117D4×Dic59—22no—
118D4×Dic59C2314yes—
119(C22⋊D59)⋊C4—28no—
120#14273684—28no—
121#14273683—28no—
122C2×C4⋊Dic59—21no—
123C2×C4⋊Dic59—21no—
124C2×C4⋊Dic59C2311yescharacteristic
125C2×C4⋊Dic59C2311yescharacteristic
126C2×C4⋊Dic59C2311yescharacteristic
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×Dic59⋊C4—21no—
134C2×Dic59⋊C4—21no—
135C2×C22⋊Dic59—21no—
136C2×C22⋊Dic59—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×Dic59D411yescharacteristic
143C2×C4×Dic59D411yescharacteristic
144C2×C4×Dic59C2311yescharacteristic
145C42×D59D414yes—
146C42×D59C2314yes—
147#14273661C2314yes—
148#14273660C2314yes—
149#14273659C2314yes—
150#14273658C2314yes—
151C4⋊(C59⋊C8)C2314yes—
152Dic59⋊C8C2314yes—
153Dic59⋊C8C2314yes—
154#14273652C2314yes—
155#14273652C2314yes—
156#14273651C2314yes—
157#14273651C2314yes—
158#14273651C2314yes—
159#14273648C2314yes—
160C22×Q8×C59C2311yescharacteristic
161C22×Q8×C59C2311yescharacteristic
162C22×D4×C59C2311yescharacteristic
163C2×Q16×C59—42no—
164C2×Q16×C59C2314yes—
165C2×SD16×C59—42no—
166C2×SD16×C59C2314yes—
167C22×C8×C59C2311yescharacteristic
168C22×C8×C59C2311yescharacteristic
169#124×C59—22no—
170#124×C59C2314yes—
171C4×Q8×C59—22no—
172C4×Q8×C59C2314yes—
173C2×C4⋊C4×C59—21no—
174C2×C4⋊C4×C59C2311yescharacteristic
175C2×C22⋊C4×C59—21no—
176C2×C22⋊C4×C59—21no—
177C2×C42×C59—21no—
178C2×C42×C59C2311yescharacteristic
179C4⋊C8×C59C2314yes—
180#103×C59C2314yes—
181#102×C59C2314yes—
182C24×C59—21no—
183C23×D59C2×D411yescharacteristic
184C2×Q8×C59—21no—
185C2×Q8×C59—21no—
186C2×Q8×C59—22no—
187C2×Q8×C59—22no—
188C2×Q8×C59—22no—
189C2×Q8×C59—22no—
190C2×Q8×C59C2412yes—
191C2×Q8×C59C2412yes—
192C2×D4×C59—21no—
193C2×D4×C59—22no—
194C2×D4×C59—22no—
195C2×D4×C59C2412yes—
196C22×C4×C59—21no—
197C22×C4×C59—21no—
198C22×C4×C59—21no—
199C22×C4×C59C2×D411yescharacteristic
200C22×C4×C59C2×D411yescharacteristic
201C22×C4×C59C2411yescharacteristic
202C2×C22⋊D59—24no—
203C2×C22⋊D59—44no—
204C22×Dic59—21no—
205C22×Dic59—21no—
206C22×Dic59—21no—
207C22×Dic59—21no—
208C22×Dic59—24no—
209C22×Dic59—44no—
210C22×Dic59C2×D411yescharacteristic
211C22×Dic59C2×D411yescharacteristic
212C22×Dic59C2×D411yescharacteristic
213C2×C4×D59—22no—
214C2×C4×D59—22no—
215C2×C4×D59—24no—
216C2×C4×D59—42no—
217C2×C4×D59C2×D412yes—
218C2×C4×D59C2×D414yes—
219C2×C4×D59C2×D414yes—
220C2×C4×D59C2412yes—
221C2×Dic118—22no—
222C2×Dic118—22no—
223C2×Dic118—21no—
224C2×Dic118—24no—
225C2×Dic118—44no—
226C2×Dic118C2412yes—
227Q16×C59—44no—
228SD16×C59—44no—
229C2×C8×C59—22no—
230C2×C8×C59—22no—
231C2×C8×C59C2412yes—
232C2×C8×C59C2412yes—
233C4⋊C4×C59—24no—
234C4⋊C4×C59—21no—
235C4⋊C4×C59C2412yes—
236C22⋊C4×C59—24no—
237C22⋊C4×C59—24no—
238C42×C59—24no—
239C42×C59C2×D412yes—
240C42×C59C2412yes—
241C22⋊Dic59—24no—
242C22⋊Dic59—24no—
243#11745672—44no—
244#11745670—44no—
245(C2×D59)⋊C4—24no—
246(C2×D59)⋊C4—24no—
247(C2×D59)⋊C4—24no—
248C4⋊Dic59—21no—
249C4⋊Dic59—21no—
250C4⋊Dic59—21no—
251C4⋊Dic59—24no—
252C4⋊Dic59—24no—
253C4⋊Dic59C2412yes—
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—
263Dic59⋊C4—24no—
264C4×Dic59—24no—
265C4×Dic59—24no—
266C4×Dic59C2×D412yes—
267C4×Dic59C2×D414yes—
268C4×Dic59C2×D414yes—
269C4×Dic59C2412yes—
270C2×C59⋊C8—22no—
271C2×C59⋊C8—22no—
272C2×C59⋊C8C2412yes—
273C2×C59⋊C8C2412yes—
274#11745659—44no—
275#11745659—44no—
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—22no—
288Q8×C59—22no—
289Q8×C59—42no—
290Q8×C59—42no—
291D4×C59—22no—
292D4×C59—22no—
293D4×C59—42no—
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×D412yes—
304C2×C4×C59C22×D411yescharacteristic
305C2×C4×C59H(5,𝔽2)12yes—
306C2×C4×C592−1+412yes—
307C2×C4×C59C2511yescharacteristic
308C22⋊D59—48no—
309C2×Dic59—22no—
310C2×Dic59—22no—
311C2×Dic59—22no—
312C2×Dic59—22no—
313C2×Dic59—22no—
314C2×Dic59—22no—
315C2×Dic59—42no—
316C2×Dic59—42no—
317C2×Dic59—42no—
318C2×Dic59—42no—
319C2×Dic59—48no—
320C2×Dic59#13714yes—
321C2×Dic59C22×D412yes—
322C2×Dic59C22×D412yes—
323C2×Dic59C22×D412yes—
324C4×D59—24no—
325C4×D59—22no—
326C4×D59—22no—
327C4×D59—28no—
328C4×D59—44no—
329Dic118—22no—
330Dic118—22no—
331Dic118—48no—
332Dic118—42no—
333C8×C59—22no—
334C8×C59—22no—
335C59⋊C8—22no—
336C59⋊C8—22no—
337C2×#3252—591nomaximal, Sylow
338C22×C59—42no—
339C22×C59—42no—
340C22×C59—42no—
341C22×C59—84no—
342C22×C59#53712yes—
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—22no—
352C4×C59—42no—
353C4×C59—42no—
354C4×C59—42no—
355C4×C59#53712yes—
356C4×C59C2×H(5,𝔽2)11yescharacteristic
357C4×C59C2×2−1+411yescharacteristic
358Dic59—22no—
359Dic59—22no—
360Dic59—42no—
361Dic59—42no—
362Dic59—42no—
363Dic59—42no—
364Dic59C2×#13714yes—
365C2×#533—591no—
366C2×#529—591no—
367#3252—5916no—
368C2×#479—591no—
369C2×#479—591no—
370C2×#477—591no—
371C2×#476—591no—
372C2×#470—591no—
373C2×#470—591no—
374C2×#468—591no—
375C2×#468—591no—
376C2×#464—591no—
377C2×#464D5911yescharacteristic, complemented
378C2×#462—591no—
379C2×#461—591no—
380C2×#423—591no—
381C2×C59—82no—
382C2×C59#325214yescomplemented
383C2×C59C2×#53711yescharacteristic
384C2×C59C22×#13711yescharacteristic
385C2×C59C2×#57511yescharacteristic
386D59—42no—
387C22×Q16—591no—
388C22×Q16C2×D5911yescharacteristic
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×#124C2×D5911yescharacteristic
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—591no—
414C2×C4×D4—1181no—
415C2×#117—1181no—
416C2×#117—1181no—
417C22×C42—591no—
418#479—598no—
419#479—598no—
420#477—598no—
421#476—598no—
422#470—598no—
423#470—598no—
424#468—598no—
425#468—598no—
426#464—598no—
427#464C2×D5918yescomplemented
428#462—598no—
429#461—598no—
430C2×#107—591no—
431C2×#107—591no—
432C2×#106—591no—
433C2×#106—591no—
434#423—598no—
435C2×C4⋊C8—591no—
436C2×C4⋊C8—591no—
437C2×C4⋊C8—591no—
438C2×C4⋊C8C2×D5911yescharacteristic
439C2×#103—591no—
440C2×#103—591no—
441C2×#103—591no—
442C2×#103—591no—
443C2×#103—591no—
444C2×#103C2×D5911yescharacteristic
445C2×#102—591no—
446C2×#102C2×D5911yescharacteristic
447C59C2×#325211yescharacteristic, complemented, Sylow
448C22×Q8—591no—
449C22×Q8—1181no—
450C22×Q8C22×D5911yescharacteristic
451C22×Q8C22×D5911yescharacteristic
452C22×D4—1181no—
453C22×D4C22×D5911yescharacteristic
454C23×C4—591no—
455C23×C4—591no—
456C23×C4—591no—
457C23×C4—1181no—
458C2×Q16—42no—
459C2×Q16—594no—
460C2×Q16—2362no—
461C2×Q16C22×D5914yes—
462C2×SD16—42no—
463C2×SD16—594no—
464C2×SD16—2362no—
465C2×SD16C22×D5914yes—
466C2×M16—594no—
467C2×M16—594no—
468C2×M16—2362no—
469C2×M16—2362no—
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—1188no—
481#125—1182no—
482#124—22no—
483#124C22×D5914yes—
484#123—1188no—
485C22⋊Q8—594no—
486C22⋊Q8—594no—
487C22⋊Q8—594no—
488C22⋊Q8—1182no—
489C22⋊Q8—1188no—
490C22⋊Q8—1182no—
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—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—591no—
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⋊C4—1181no—
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—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#106—594no—
541C4⋊C8—594no—
542C4⋊C8—594no—
543C4⋊C8—594no—
544C4⋊C8C22×D5914yes—
545#103—594no—
546#103—594no—
547#103—594no—
548#103—594no—
549#103—594no—
550#103C22×D5914yes—
551#102—594no—
552#102C22×D5914yes—
553C24—21no—
554C24—591no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—22no—
558C2×Q8—22no—
559C2×Q8—22no—
560C2×Q8—22no—
561C2×Q8—592no—
562C2×Q8—1184no—
563C2×Q8—1181no—
564C2×Q8—1182no—
565C2×Q8—1182no—
566C2×Q8—2364no—
567C2×Q8C23×D5912yes—
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—591no—
579C22×C4—591no—
580C22×C4—591no—
581C22×C4—594no—
582C22×C4—592no—
583C22×C4—592no—
584C22×C4—594no—
585C22×C4—1184no—
586C22×C4—1184no—
587C22×C4—1182no—
588C22×C4—1182no—
589C22×C4—1181no—
590C22×C4—1181no—
591C22×C4—1181no—
592C22×C4—1181no—
593C22×C4—2362no—
594C22×C4—2364no—
595C22×C4D4×D5911yescharacteristic
596C22×C4D4×D5911yescharacteristic
597C22×C4C23×D5911yescharacteristic
598Q16—44no—
599Q16—2364no—
600SD16—44no—
601SD16—2364no—
602M16—2364no—
603M16—2364no—
604C2×C8—22no—
605C2×C8—22no—
606C2×C8—592no—
607C2×C8—592no—
608C2×C8—1182no—
609C2×C8—1182no—
610C2×C8C23×D5912yes—
611C2×C8C23×D5912yes—
612C4⋊C4—24no—
613C4⋊C4—21no—
614C4⋊C4—592no—
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—1181no—
625C4⋊C4—1181no—
626C4⋊C4—1181no—
627C4⋊C4—1184no—
628C4⋊C4—1184no—
629C4⋊C4—1184no—
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—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—22no—
659Q8—22no—
660Q8—42no—
661Q8—42no—
662Q8—1182no—
663Q8—1182no—
664Q8—2368no—
665Q8—2362no—
666D4—22no—
667D4—22no—
668D4—42no—
669D4—2368no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—594no—
679C2×C4—592no—
680C2×C4—592no—
681C2×C4—592no—
682C2×C4—1188no—
683C2×C4—1182no—
684C2×C4—1182no—
685C2×C4—1182no—
686C2×C4—1182no—
687C2×C4—1184no—
688C2×C4—1182no—
689C2×C4—1182no—
690C2×C4—1182no—
691C2×C4—1182no—
692C2×C4—2364no—
693C2×C4—2368no—
694C2×C4—2362no—
695C2×C4—2362no—
696C2×C4—2362no—
697C2×C4—2362no—
698C2×C4C2×D4×D5912yes—
699C2×C4C2×D4×D5912yes—
700C2×C4C2×D4×D5911yescharacteristic
701C2×C4#1427377212yes—
702C2×C4#1427377412yes—
703C2×C4C24×D5911yescharacteristic
704C8—22no—
705C8—22no—
706C8—1182no—
707C8—1182no—
708C22—42no—
709C22—42no—
710C22—42no—
711C22—84no—
712C22—1182no—
713C22—1182no—
714C22—1182no—
715C22—2364no—
716C22#1683798112yes—
717C22#137×D5912yes—
718C22#1683819912yes—
719C22C22×D4×D5911yescharacteristic
720C4—22no—
721C4—22no—
722C4—42no—
723C4—42no—
724C4—42no—
725C4—594no—
726C4—1182no—
727C4—1182no—
728C4—2362no—
729C4—2362no—
730C4—2362no—
731C4—2362no—
732C4#1683798112yes—
733C4C2×#1427377211yescharacteristic
734C4C2×#1427377411yescharacteristic
735C2—82no—
736C2—2362no—
737C2#2143546614yesdirect product factor
738C2C2×#1683798111yescharacteristic
739C2C2×#137×D5911yescharacteristic
740C2C2×#1683819911yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#464C2
socleC23×C59C22×D4
prime radicalC2×#14273698C22
hypercenterC2×#464D59
hypocenterC59C2×#3252
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#464

Complements

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

NH ≅ G/Ntype
1. C2×#16837956C2semidirect
3. #21435466C2direct (N × H)
4. C2×#16837710C2semidirect
5. C2×#16837709C2semidirect
6. C2×#16837695C2semidirect
7. C2×#16837690C2semidirect
8. C2×#16837659C2semidirect
9. C2×#16837657C2semidirect
12. C2×#16837621C2semidirect
13. C2×#16837610C2semidirect
14. C2×#16837605C2semidirect
15. C2×#16837424C2semidirect
16. C2×C59×#464C2semidirect
22. #16837956C22semidirect
44. #16837710C22semidirect
45. #16837709C22semidirect
46. #16837695C22semidirect
47. #16837690C22semidirect
48. #16837659C22semidirect
49. #16837657C22semidirect
52. #16837621C22semidirect
53. #16837610C22semidirect
54. #16837605C22semidirect
59. #16837424C22semidirect
73. C59×#464C22semidirect
377. C2×#464D59semidirect
382. C2×C59#3252semidirect
427. #464C2×D59semidirect
447. C59C2×#3252semidirect
737. C2#21435466direct (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×#168379312
#214354662
C2×#168377102
C2×#168377092
C2×#168376952
C2×#168376902
C2×#168376592
C2×#168376572
C2×#168376472
C2×#168376452
C2×#168376212
C2×#168376102
C2×#168376052
C2×#168374242
C2×C59×#4642
C2×#325259