Finite Group Databasebeta

← C2×#21437020 #29469193

Subgroups — C2×#21437020 #29469193

Order 15104.

2006 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838128C211yesmaximal, characteristic, complemented
2C2×#16838067C211yesmaximal, characteristic
3#21437020C2116yesmaximal, direct product factor
4C2×#16837810C211yesmaximal, characteristic, complemented
5C2×#16837808C211yesmaximal, characteristic, complemented
6C2×#16837806C211yesmaximal, characteristic, complemented
7C2×#16837695C211yesmaximal, characteristic, complemented
8C2×#16837685C211yesmaximal, characteristic, complemented
9C2×#16837705C211yesmaximal, characteristic
10C2×#16837703C211yesmaximal, characteristic
11C2×#16837681C211yesmaximal, characteristic
12C2×#16837531C211yesmaximal, characteristic, complemented
13C2×#16837505C211yesmaximal, characteristic
14C2×#16837500C211yesmaximal, characteristic
15C2×#16837487C211yesmaximal, characteristic
16C2×C59×#477C211yesmaximal, characteristic, complemented
17C22×Q8×D59—21no—
18C22×#11745671C2211yescharacteristic
19#16838128—24no—
20#16838128C2218yescomplemented
21#16838067—24no—
22#16838067C2218yes—
23C2×#14273726—21no—
24C2×#14273726C2211yescharacteristic
25C2×#14273726C2211yescharacteristic
26C2×#14273726C2211yescharacteristic
27C2×#14273719—21no—
28C2×#14273719C2211yescharacteristic
29C2×#14273718—21no—
30C2×#14273718C2211yescharacteristic
31C2×#14273705—21no—
32C2×#14273705—21no—
33C2×#14273703—21no—
34C2×Q8×Dic59C2211yescharacteristic
35C2×Q8×Dic59C2211yescharacteristic
36C2×C4×Dic118—21no—
37C2×C4×Dic118C2211yescharacteristic
38C2×C4×D236C2211yescharacteristic
39C2×#14273689C2211yescharacteristic
40C2×#14273689C2211yescharacteristic
41#16837810C2218yescomplemented
42#16837808C2218yescomplemented
43#16837806C2218yescomplemented
44#16837705C2218yes—
45#16837703C2218yes—
46#16837695C2218yescomplemented
47#16837685C2218yescomplemented
48#16837681C2218yes—
49#16837531C2218yescomplemented
50#16837505C2218yes—
51#16837500C2218yes—
52#16837487C2218yes—
53C2×#14273661C2211yescharacteristic
54C2×#14273660C2211yescharacteristic
55C2×#14273660C2211yescharacteristic
56C2×#14273660C2211yescharacteristic
57C2×#14273659C2211yescharacteristic
58C2×#14273658C2211yescharacteristic
59C2×#14273658C2211yescharacteristic
60C2×Dic59⋊C8C2211yescharacteristic
61C2×Dic59⋊C8C2211yescharacteristic
62C2×#14273651C2211yescharacteristic
63C2×#14273649C2211yescharacteristic
64C2×#14273649C2211yescharacteristic
65C2×#14273647C2211yescharacteristic
66C2×#14273638C2211yescharacteristic
67C2×#14273637C2211yescharacteristic
68C2×C8×Dic59C2211yescharacteristic
69C2×C4⋊Q8×C59C2211yescharacteristic
70C2×C4×Q8×C59C2211yescharacteristic
71C59×#477C2218yescomplemented
72C2×#107×C59C2211yescharacteristic
73C2×#107×C59C2211yescharacteristic
74C2×C4⋊C8×C59C2211yescharacteristic
75C2×#103×C59C2211yescharacteristic
76C2×#103×C59C2211yescharacteristic
77C22×Dic118—21no—
78C22×Dic118—21no—
79C22×Dic118—21no—
80C22×Dic118D411yescharacteristic
81C2×Q8×D59—28no—
82C2×Q8×D59—48no—
83C22×D236C2311yescharacteristic
84C22×C4×D59—21no—
85C22×C4×D59—21no—
86C22×C4×D59—21no—
87C2×#11745671Q818yescomplemented
88C2×#11745671C2314yes—
89C22×C59⋊C8C2311yescharacteristic
90C22×C59⋊C8C2311yescharacteristic
91#14273726—28no—
92#14273726—22no—
93#14273726—22no—
94#14273726—22no—
95#14273726C2314yes—
96#14273726C2314yes—
97#14273726C2314yes—
98#14273719—22no—
99#14273719—28no—
100#14273719C2314yes—
101#14273718—28no—
102#14273718—22no—
103#14273718C2314yes—
104#14273705—28no—
105#14273705—28no—
106#14273703—28no—
107Q8×Dic59—22no—
108Q8×Dic59—22no—
109Q8×Dic59C2314yes—
110Q8×Dic59C2314yes—
111C4×Dic118—28no—
112C4×Dic118D414yes—
113C4×Dic118C2314yes—
114C4×D236—22no—
115C4×D236C2314yes—
116#14273689—22no—
117#14273689—22no—
118#14273689C2314yes—
119#14273689C2314yes—
120C2×C4⋊Dic59—21no—
121C2×C4⋊Dic59—21no—
122C2×C4⋊Dic59—21no—
123C2×C4⋊Dic59D411yescharacteristic
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⋊C4D411yescharacteristic
134C2×Dic59⋊C4D411yescharacteristic
135C2×(C2×D59)⋊C4—21no—
136C2×(C2×D59)⋊C4—21no—
137C2×(C2×D59)⋊C4—21no—
138C2×C4×Dic59—21no—
139C2×C4×Dic59—21no—
140C2×C4×Dic59C2311yescharacteristic
141C2×C4×Dic59C2311yescharacteristic
142#14273661C2314yes—
143#14273660C2314yes—
144#14273660C2314yes—
145#14273660C2314yes—
146#14273659C2314yes—
147#14273658C2314yes—
148#14273658C2314yes—
149Dic59⋊C8C2314yes—
150Dic59⋊C8C2314yes—
151#14273651C2314yes—
152#14273649C2314yes—
153#14273649C2314yes—
154#14273647C2314yes—
155#14273638C2314yes—
156#14273637C2314yes—
157C8×Dic59C2314yes—
158C22×Q8×C59—21no—
159C22×Q8×C59C2311yescharacteristic
160C22×C8×C59C2311yescharacteristic
161C22×C8×C59C2311yescharacteristic
162C4⋊Q8×C59—22no—
163C4⋊Q8×C59C2314yes—
164C4×Q8×C59—22no—
165C4×Q8×C59C2314yes—
166C2×C4⋊C4×C59—21no—
167C2×C4⋊C4×C59—21no—
168C2×C4⋊C4×C59C2311yescharacteristic
169C2×C4⋊C4×C59C2311yescharacteristic
170C2×C4⋊C4×C59C2311yescharacteristic
171C2×C42×C59—21no—
172C2×C42×C59C2311yescharacteristic
173#107×C59C2314yes—
174#107×C59C2314yes—
175C4⋊C8×C59C2314yes—
176#103×C59C2314yes—
177#103×C59C2314yes—
178C23×D59—21no—
179C2×Q8×C59—21no—
180C2×Q8×C59—24no—
181C2×Q8×C59—22no—
182C2×Q8×C59—44no—
183C2×Q8×C59C2×Q814yescomplemented
184C2×Q8×C59C2412yes—
185C22×C4×C59—21no—
186C22×C4×C59—21no—
187C22×C4×C59—21no—
188C22×C4×C59—21no—
189C22×C4×C59C2×D411yescharacteristic
190C22×C4×C59C2×D411yescharacteristic
191C22×C4×C59C2411yescharacteristic
192C22×Dic59—21no—
193C22×Dic59—21no—
194C22×Dic59—21no—
195C22×Dic59C2×D411yescharacteristic
196C22×Dic59C2×D411yescharacteristic
197C22×Dic59C2×D411yescharacteristic
198C22×Dic59C2×D411yescharacteristic
199Q8×D59—432no—
200C2×D236—21no—
201C2×D236—22no—
202C2×D236C2×Q814yes—
203C2×D236C2412yes—
204C2×C4×D59—24no—
205C2×C4×D59—24no—
206C2×C4×D59—24no—
207C2×C4×D59—44no—
208C2×C4×D59—44no—
209C2×C4×D59—44no—
210C2×Dic118—24no—
211C2×Dic118—24no—
212C2×Dic118—24no—
213C2×Dic118—24no—
214C2×Dic118—44no—
215C2×Dic118—44no—
216C2×Dic118—44no—
217C2×Dic118C2×D414yes—
218C2×C8×C59—22no—
219C2×C8×C59—22no—
220C2×C8×C59C2412yes—
221C2×C8×C59C2412yes—
222C4⋊C4×C59—24no—
223C4⋊C4×C59—24no—
224C4⋊C4×C59—21no—
225C4⋊C4×C59—21no—
226C4⋊C4×C59—21no—
227C4⋊C4×C59C2412yes—
228C4⋊C4×C59C2412yes—
229C4⋊C4×C59C2412yes—
230C42×C59—24no—
231C42×C59C2×D412yes—
232C42×C59C2412yes—
233#11745671C2×Q8116yescomplemented
234(C2×D59)⋊C4—24no—
235(C2×D59)⋊C4—24no—
236(C2×D59)⋊C4—24no—
237C4⋊Dic59—21no—
238C4⋊Dic59—21no—
239C4⋊Dic59—21no—
240C4⋊Dic59—24no—
241C4⋊Dic59—24no—
242C4⋊Dic59—24no—
243C4⋊Dic59C2×D414yes—
244C4⋊Dic59C2412yes—
245C4⋊Dic59C2412yes—
246C4⋊Dic59C2412yes—
247Dic59⋊C4—24no—
248Dic59⋊C4—24no—
249Dic59⋊C4—24no—
250Dic59⋊C4—24no—
251Dic59⋊C4—24no—
252Dic59⋊C4—24no—
253Dic59⋊C4C2×D414yes—
254Dic59⋊C4C2×D414yes—
255C4×Dic59—24no—
256C4×Dic59—24no—
257C4×Dic59C2×D412yes—
258C4×Dic59C2×D412yes—
259C4×Dic59C2412yes—
260C4×Dic59C2412yes—
261C2×C59⋊C8—22no—
262C2×C59⋊C8C2×Q814yescomplemented
263C2×C59⋊C8C2412yes—
264C2×C59⋊C8C2412yes—
265C23×C59C22×D411yescharacteristic
266C22×D59—24no—
267C22×D59—22no—
268C22×D59—42no—
269C22×D59—42no—
270Q8×C59—24no—
271Q8×C59—22no—
272Q8×C59—48no—
273Q8×C59C22×Q814yescomplemented
274C2×C4×C59—24no—
275C2×C4×C59—22no—
276C2×C4×C59—22no—
277C2×C4×C59—22no—
278C2×C4×C59—22no—
279C2×C4×C59—22no—
280C2×C4×C59—22no—
281C2×C4×C59—42no—
282C2×C4×C59—42no—
283C2×C4×C59—42no—
284C2×C4×C59C22×D412yes—
285C2×C4×C59C22×D412yes—
286C2×C4×C59C22×D411yescharacteristic
287C2×C4×C59C22×Q812yes—
288C2×C4×C592−1+412yes—
289C2×C4×C59C2511yescharacteristic
290C2×Dic59—22no—
291C2×Dic59—22no—
292C2×Dic59—22no—
293C2×Dic59—22no—
294C2×Dic59—22no—
295C2×Dic59—22no—
296C2×Dic59—42no—
297C2×Dic59—42no—
298C2×Dic59—42no—
299C2×Dic59AGL(1,ℤ/8)14yes—
300C2×Dic59C22×D412yes—
301C2×Dic59C22×D412yes—
302C2×Dic59C22×D412yes—
303C2×Dic59C22×D412yes—
304D236—24no—
305D236—22no—
306D236C22×Q814yes—
307C4×D59—48no—
308C4×D59—48no—
309C4×D59—48no—
310Dic118—28no—
311Dic118—48no—
312Dic118—48no—
313Dic118—48no—
314C8×C59—22no—
315C8×C59—22no—
316C59⋊C8—22no—
317C59⋊C8C22×Q814yescomplemented
318C2×#3386—591nomaximal, Sylow
319C22×C59D4×Q812yes—
320C22×C59C2×AGL(1,ℤ/8)12yes—
321C22×C59#57812yes—
322C22×C59C23×D411yescharacteristic
323C2×D59—24no—
324C2×D59—48no—
325C2×D59—42no—
326C2×D59—42no—
327C4×C59—24no—
328C4×C59—22no—
329C4×C59—22no—
330C4×C59—42no—
331C4×C59—42no—
332C4×C59—42no—
333C4×C59D4×Q812yes—
334C4×C59C23×Q811yescharacteristic
335C4×C59C2×2−1+411yescharacteristic
336Dic59—22no—
337Dic59—22no—
338Dic59—22no—
339Dic59—42no—
340Dic59—42no—
341Dic59—42no—
342Dic59C2×AGL(1,ℤ/8)14yes—
343C2×#557—591no—
344C2×D4×Q8—591no—
345#3386—5916no—
346C2×#501—591no—
347C2×#501—591no—
348C2×#500—591no—
349C2×#477—591no—
350C2×#477D5911yescharacteristic, complemented
351C2×#475—591no—
352C2×#478—591no—
353C2×#478—591no—
354C2×#474—591no—
355C2×#446—591no—
356C2×#440—591no—
357C2×#440—591no—
358C2×C4×SD16—591no—
359C2×C59#338614yescomplemented
360C2×C59C2×D4×Q811yescharacteristic
361C2×C59C22×AGL(1,ℤ/8)11yescharacteristic
362C2×C59C2×#57811yescharacteristic
363D59—44no—
364C23×Q8—1181no—
365C22×SD16—591no—
366#557—598no—
367#557—1184no—
368D4×Q8—598no—
369D4×Q8—1184no—
370C2×C4⋊Q8—591no—
371C2×C4⋊Q8—591no—
372C2×C4⋊Q8—591no—
373C2×C4⋊Q8—1181no—
374C2×C4⋊Q8C2×D5911yescharacteristic
375C2×#125—591no—
376C2×#125—591no—
377C2×#125—1181no—
378C2×#125—1181no—
379C2×C22⋊Q8—1181no—
380C2×C22⋊Q8—1181no—
381C2×C22⋊Q8—1181no—
382C2×C4×Q8—591no—
383C2×C4×Q8—591no—
384C2×C4×Q8—591no—
385C2×C4×Q8—1181no—
386C2×C4×Q8C2×D5911yescharacteristic
387C2×C4×D4—591no—
388C2×C4×D4—591no—
389C2×C4×D4—591no—
390#501—598no—
391#501—598no—
392#500—598no—
393#478—598no—
394#478—598no—
395#477—598no—
396#477C2×D5918yescomplemented
397#475—598no—
398#474—598no—
399#446—598no—
400#440—598no—
401#440—598no—
402C4×SD16—598no—
403C2×#107—591no—
404C2×#107—591no—
405C2×#107—591no—
406C2×#107—591no—
407C2×#107C2×D5911yescharacteristic
408C2×#107C2×D5911yescharacteristic
409C2×#106—591no—
410C2×#106—591no—
411C2×#106—591no—
412C2×C4⋊C8—591no—
413C2×C4⋊C8—591no—
414C2×C4⋊C8C2×D5911yescharacteristic
415C2×#103—591no—
416C2×#103C2×D5911yescharacteristic
417C2×#103C2×D5911yescharacteristic
418C2×#102—591no—
419C2×#102—591no—
420C2×#102—591no—
421C2×#97—591no—
422C2×#97—591no—
423C2×C4×C8—591no—
424C59C2×#338611yescharacteristic, complemented, Sylow
425C22×Q8—21no—
426C22×Q8—591no—
427C22×Q8—1181no—
428C22×Q8—1181no—
429C22×Q8—1181no—
430C22×Q8—1188no—
431C22×Q8—2368no—
432C22×Q8C22×D5911yescharacteristic
433C22×D4—591no—
434C23×C4—1181no—
435C23×C4—1181no—
436C23×C4—1181no—
437C2×SD16—598no—
438C2×SD16—594no—
439C22×C8—591no—
440C22×C8—591no—
441C22×C8C22×D5911yescharacteristic
442C22×C8C22×D5911yescharacteristic
443C4⋊Q8—22no—
444C4⋊Q8—594no—
445C4⋊Q8—594no—
446C4⋊Q8—594no—
447C4⋊Q8—1182no—
448C4⋊Q8—1182no—
449C4⋊Q8—1182no—
450C4⋊Q8—1188no—
451C4⋊Q8C22×D5914yes—
452#125—594no—
453#125—594no—
454#125—1188no—
455#125—1182no—
456#125—1188no—
457#125—1182no—
458C22⋊Q8—1188no—
459C22⋊Q8—1188no—
460C22⋊Q8—1188no—
461C4×Q8—22no—
462C4×Q8—594no—
463C4×Q8—594no—
464C4×Q8—594no—
465C4×Q8—594no—
466C4×Q8—1188no—
467C4×Q8—1182no—
468C4×Q8—1182no—
469C4×Q8C22×D5914yes—
470C4×D4—594no—
471C4×D4—594no—
472C4×D4—594no—
473C4×D4—1182no—
474C4×D4—1182no—
475C4×D4—1182no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—591no—
479C2×C4⋊C4—591no—
480C2×C4⋊C4—591no—
481C2×C4⋊C4—591no—
482C2×C4⋊C4—591no—
483C2×C4⋊C4—591no—
484C2×C4⋊C4—1181no—
485C2×C4⋊C4—1181no—
486C2×C4⋊C4—1181no—
487C2×C4⋊C4—1181no—
488C2×C4⋊C4—1181no—
489C2×C4⋊C4—1181no—
490C2×C4⋊C4—1181no—
491C2×C4⋊C4—1181no—
492C2×C4⋊C4—1181no—
493C2×C4⋊C4C22×D5911yescharacteristic
494C2×C4⋊C4C22×D5911yescharacteristic
495C2×C4⋊C4C22×D5911yescharacteristic
496C2×C22⋊C4—1181no—
497C2×C22⋊C4—1181no—
498C2×C22⋊C4—1181no—
499C2×C42—21no—
500C2×C42—591no—
501C2×C42—591no—
502C2×C42—1181no—
503C2×C42—1181no—
504C2×C42C22×D5911yescharacteristic
505#107—594no—
506#107—594no—
507#107—594no—
508#107—594no—
509#107C22×D5914yes—
510#107C22×D5914yes—
511#106—594no—
512#106—594no—
513#106—594no—
514C4⋊C8—594no—
515C4⋊C8—594no—
516C4⋊C8C22×D5914yes—
517#103—594no—
518#103C22×D5914yes—
519#103C22×D5914yes—
520#102—594no—
521#102—594no—
522#102—594no—
523#97—594no—
524#97—594no—
525C4×C8—594no—
526C24—1181no—
527C2×Q8—21no—
528C2×Q8—24no—
529C2×Q8—22no—
530C2×Q8—44no—
531C2×Q8—594no—
532C2×Q8—1184no—
533C2×Q8—1184no—
534C2×Q8—1184no—
535C2×Q8—1184no—
536C2×Q8—2364no—
537C2×Q8—2364no—
538C2×Q8—2364no—
539C2×Q8—23632no—
540C2×Q8Q8×D5914yescomplemented
541C2×Q8C23×D5912yes—
542C2×D4—594no—
543C2×D4—592no—
544C2×D4—1181no—
545C2×D4—1182no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—591no—
551C22×C4—591no—
552C22×C4—591no—
553C22×C4—591no—
554C22×C4—1184no—
555C22×C4—1184no—
556C22×C4—1181no—
557C22×C4—1181no—
558C22×C4—1181no—
559C22×C4—1184no—
560C22×C4—2364no—
561C22×C4—2364no—
562C22×C4—2364no—
563C22×C4D4×D5911yescharacteristic
564C22×C4D4×D5911yescharacteristic
565C22×C4C23×D5911yescharacteristic
566SD16—5916no—
567C2×C8—22no—
568C2×C8—22no—
569C2×C8—594no—
570C2×C8—592no—
571C2×C8—592no—
572C2×C8—1182no—
573C2×C8C23×D5912yes—
574C2×C8C23×D5912yes—
575C4⋊C4—24no—
576C4⋊C4—24no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—594no—
581C4⋊C4—594no—
582C4⋊C4—594no—
583C4⋊C4—592no—
584C4⋊C4—592no—
585C4⋊C4—592no—
586C4⋊C4—1184no—
587C4⋊C4—1184no—
588C4⋊C4—1184no—
589C4⋊C4—1184no—
590C4⋊C4—1184no—
591C4⋊C4—1184no—
592C4⋊C4—1184no—
593C4⋊C4—1181no—
594C4⋊C4—1181no—
595C4⋊C4—1181no—
596C4⋊C4—1184no—
597C4⋊C4—1184no—
598C4⋊C4C23×D5912yes—
599C4⋊C4C23×D5912yes—
600C4⋊C4C23×D5912yes—
601C22⋊C4—1184no—
602C22⋊C4—1184no—
603C22⋊C4—1184no—
604C42—24no—
605C42—592no—
606C42—592no—
607C42—592no—
608C42—592no—
609C42—1184no—
610C42—1184no—
611C42D4×D5912yes—
612C42C23×D5912yes—
613C23—1182no—
614C23—1184no—
615C23—2362no—
616C23—2362no—
617C23C2×D4×D5911yescharacteristic
618Q8—22no—
619Q8—24no—
620Q8—48no—
621Q8—1188no—
622Q8—2368no—
623Q8—2368no—
624Q8—2368no—
625Q8C2×Q8×D5914yescomplemented
626D4—594no—
627D4—1182no—
628D4—1184no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—24no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4—42no—
639C2×C4—594no—
640C2×C4—592no—
641C2×C4—592no—
642C2×C4—592no—
643C2×C4—592no—
644C2×C4—1182no—
645C2×C4—1182no—
646C2×C4—1182no—
647C2×C4—1182no—
648C2×C4—1182no—
649C2×C4—1182no—
650C2×C4—2368no—
651C2×C4—2368no—
652C2×C4—2368no—
653C2×C4—2362no—
654C2×C4—2362no—
655C2×C4—2362no—
656C2×C4C2×D4×D5912yes—
657C2×C4C2×D4×D5912yes—
658C2×C4C2×D4×D5911yescharacteristic
659C2×C4C2×Q8×D5912yes—
660C2×C4#1427377412yes—
661C2×C4C24×D5911yescharacteristic
662C8—22no—
663C8—22no—
664C8—594no—
665C8—1182no—
666C22—1184no—
667C22—2368no—
668C22—2362no—
669C22—2362no—
670C22#1683806512yes—
671C22AGL(1,ℤ/8)×D5912yes—
672C22#1683821512yes—
673C22C22×D4×D5911yescharacteristic
674C4—22no—
675C4—24no—
676C4—22no—
677C4—42no—
678C4—42no—
679C4—42no—
680C4—594no—
681C4—1182no—
682C4—1182no—
683C4—1182no—
684C4—2362no—
685C4—2362no—
686C4—2362no—
687C4#1683806512yes—
688C4C22×Q8×D5911yescharacteristic
689C4C2×#1427377411yescharacteristic
690C2—2364no—
691C2#2143702014yesdirect product factor
692C2C2×#1683806511yescharacteristic
693C2C2×AGL(1,ℤ/8)×D5911yescharacteristic
694C2C2×#1683821511yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#477C2
socleC23×C59C22×D4
prime radicalC22×D236C23
hypercenterC2×#477D59
hypocenterC59C2×#3386
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#477

Complements

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

NH ≅ G/Ntype
1. C2×#16838128C2semidirect
3. #21437020C2direct (N × H)
4. C2×#16837810C2semidirect
5. C2×#16837808C2semidirect
6. C2×#16837806C2semidirect
7. C2×#16837695C2semidirect
8. C2×#16837685C2semidirect
12. C2×#16837531C2semidirect
16. C2×C59×#477C2semidirect
20. #16838128C22semidirect
41. #16837810C22semidirect
42. #16837808C22semidirect
43. #16837806C22semidirect
46. #16837695C22semidirect
47. #16837685C22semidirect
49. #16837531C22semidirect
71. C59×#477C22semidirect
87. C2×#11745671Q8semidirect
183. C2×Q8×C59C2×Q8semidirect
233. #11745671C2×Q8semidirect
262. C2×C59⋊C8C2×Q8semidirect
273. Q8×C59C22×Q8semidirect
317. C59⋊C8C22×Q8semidirect
350. C2×#477D59semidirect
359. C2×C59#3386semidirect
396. #477C2×D59semidirect
424. C59C2×#3386semidirect
540. C2×Q8Q8×D59semidirect
625. Q8C2×Q8×D59semidirect
691. C2#21437020direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168381282
C2×#168380672
#214370202
C2×#168378102
C2×#168378082
C2×#168378062
C2×#168376952
C2×#168376852
C2×#168377052
C2×#168377032
C2×#168376812
C2×#168375312
C2×#168375052
C2×#168375002
C2×#168374872
C2×C59×#4772
C2×#338659