Finite Group Databasebeta

← C2×#21436872 #29468347

Subgroups — C2×#21436872 #29468347

Order 15104.

1854 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838127C211yesmaximal, characteristic, complemented
2C2×#16838111C211yesmaximal, characteristic
3#21436872C2116yesmaximal, direct product factor
4C2×#16837770C211yesmaximal, characteristic, complemented
5C2×#16837769C211yesmaximal, characteristic, complemented
6C2×#16837751C211yesmaximal, characteristic, complemented
7C2×#16837710C211yesmaximal, characteristic, complemented
8C2×#16837707C211yesmaximal, characteristic, complemented
9C2×#16837695C211yesmaximal, characteristic, complemented
10C2×#16837605C211yesmaximal, characteristic
11C2×#16837605C211yesmaximal, characteristic
12C2×#16837531C211yesmaximal, characteristic, complemented
13C2×#16837503C211yesmaximal, characteristic
14C2×#16837502C211yesmaximal, characteristic
15C2×SD16×Dic59C211yesmaximal, characteristic
16C2×C59×#461C211yesmaximal, characteristic
17C22×#11745670C2211yescharacteristic
18#16838127—24no—
19#16838127C2218yescomplemented
20#16838111—24no—
21#16838111C2218yes—
22C2×#14273726C2211yescharacteristic
23C2×#14273725C2211yescharacteristic
24C2×#14273725C2211yescharacteristic
25C2×#14273719C2211yescharacteristic
26C2×#14273718—21no—
27C2×#14273718C2211yescharacteristic
28C2×#14273717—21no—
29C2×#14273717—21no—
30C2×#14273706—21no—
31C2×#14273704—21no—
32C2×#14273704—21no—
33C2×Q8×Dic59C2211yescharacteristic
34C2×Q8×Dic59C2211yescharacteristic
35C2×C4×Dic118C2211yescharacteristic
36C2×C4×Dic118C2211yescharacteristic
37C2×#14273692—21no—
38C2×D4×Dic59C2211yescharacteristic
39C2×D4×Dic59C2211yescharacteristic
40C22×Dic59⋊C4—21no—
41#16837770C2218yescomplemented
42#16837769C2218yescomplemented
43#16837751C2218yescomplemented
44#16837710C2218yescomplemented
45#16837707C2218yescomplemented
46#16837695C2218yescomplemented
47#16837605C2218yes—
48#16837605C2218yes—
49#16837531C2218yescomplemented
50#16837503C2218yes—
51#16837502C2218yes—
52SD16×Dic59C2218yes—
53C2×#14273661C2211yescharacteristic
54C2×#14273660C2211yescharacteristic
55C2×#14273659C2211yescharacteristic
56C2×Dic59⋊C8C2211yescharacteristic
57C2×Dic59⋊C8C2211yescharacteristic
58C2×#14273652C2211yescharacteristic
59C2×#14273652C2211yescharacteristic
60C2×#14273651C2211yescharacteristic
61C2×#14273651C2211yescharacteristic
62C2×#14273651C2211yescharacteristic
63C2×#14273651C2211yescharacteristic
64C2×#14273650C2211yescharacteristic
65C2×#14273648C2211yescharacteristic
66C2×#14273638C2211yescharacteristic
67C2×#14273637C2211yescharacteristic
68C2×C8×Dic59C2211yescharacteristic
69C22×SD16×C59C2211yescharacteristic
70C22×SD16×C59C2211yescharacteristic
71C2×C4⋊Q8×C59C2211yescharacteristic
72C2×C4×D4×C59C2211yescharacteristic
73C59×#461C2218yes—
74C2×C4⋊C8×C59C2211yescharacteristic
75C2×#103×C59C2211yescharacteristic
76C2×#103×C59C2211yescharacteristic
77C22×Dic118—21no—
78C22×Dic118D411yescharacteristic
79C22×Dic118C2311yescharacteristic
80C23×Dic59—21no—
81C23×Dic59—21no—
82C2×#11745670—24no—
83C2×#11745670C2314yes—
84C22×C59⋊C8C2311yescharacteristic
85C22×C59⋊C8C2311yescharacteristic
86#14273726—22no—
87#14273726C2314yes—
88#14273725—22no—
89#14273725—22no—
90#14273725C2314yes—
91#14273725C2314yes—
92#14273719—22no—
93#14273719C2314yes—
94#14273718—28no—
95#14273718—22no—
96#14273718C2314yes—
97#14273717—28no—
98#14273717—28no—
99#14273706—28no—
100#14273704—28no—
101#14273704—28no—
102Q8×Dic59—22no—
103Q8×Dic59—22no—
104Q8×Dic59C2314yes—
105Q8×Dic59C2314yes—
106C4×Dic118—22no—
107C4×Dic118D414yes—
108C4×Dic118C2314yes—
109C4×Dic118C2314yes—
110#14273692—28no—
111D4×Dic59—22no—
112D4×Dic59—22no—
113D4×Dic59C2314yes—
114D4×Dic59C2314yes—
115C2×C4⋊Dic59—21no—
116C2×C4⋊Dic59—21no—
117C2×C4⋊Dic59—21no—
118C2×C4⋊Dic59D411yescharacteristic
119C2×C4⋊Dic59C2311yescharacteristic
120C2×C4⋊Dic59C2311yescharacteristic
121C2×C4⋊Dic59C2311yescharacteristic
122C2×Dic59⋊C4—21no—
123C2×Dic59⋊C4—21no—
124C2×Dic59⋊C4—21no—
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—28no—
132C2×Dic59⋊C4D411yescharacteristic
133C2×Dic59⋊C4D411yescharacteristic
134C2×C22⋊Dic59—21no—
135C2×C22⋊Dic59—21no—
136C2×C4×Dic59—21no—
137C2×C4×Dic59—21no—
138C2×C4×Dic59—21no—
139C2×C4×Dic59C2311yescharacteristic
140C2×C4×Dic59C2311yescharacteristic
141#14273661C2314yes—
142#14273660C2314yes—
143#14273659C2314yes—
144Dic59⋊C8C2314yes—
145Dic59⋊C8C2314yes—
146#14273652C2314yes—
147#14273652C2314yes—
148#14273651C2314yes—
149#14273651C2314yes—
150#14273651C2314yes—
151#14273651C2314yes—
152#14273650C2314yes—
153#14273648C2314yes—
154#14273638C2314yes—
155#14273637C2314yes—
156C8×Dic59C2314yes—
157C22×Q8×C59C2311yescharacteristic
158C22×Q8×C59C2311yescharacteristic
159C22×D4×C59C2311yescharacteristic
160C23×C4×C59—21no—
161C2×SD16×C59—24no—
162C2×SD16×C59—24no—
163C2×SD16×C59C2314yes—
164C2×SD16×C59C2314yes—
165C22×C8×C59C2311yescharacteristic
166C22×C8×C59C2311yescharacteristic
167C4⋊Q8×C59—22no—
168C4⋊Q8×C59C2314yes—
169C4×D4×C59—22no—
170C4×D4×C59C2314yes—
171C2×C4⋊C4×C59—21no—
172C2×C4⋊C4×C59—21no—
173C2×C4⋊C4×C59C2311yescharacteristic
174C2×C22⋊C4×C59—21no—
175C2×C42×C59C2311yescharacteristic
176C4⋊C8×C59C2314yes—
177#103×C59C2314yes—
178#103×C59C2314yes—
179C24×C59—21no—
180C2×Q8×C59—21no—
181C2×Q8×C59—21no—
182C2×Q8×C59—22no—
183C2×Q8×C59—22no—
184C2×Q8×C59—22no—
185C2×Q8×C59—22no—
186C2×Q8×C59C2412yes—
187C2×Q8×C59C2412yes—
188C2×D4×C59—21no—
189C2×D4×C59—22no—
190C2×D4×C59#4114yes—
191C2×D4×C59C2412yes—
192C22×C4×C59—21no—
193C22×C4×C59—21no—
194C22×C4×C59—21no—
195C22×C4×C59—24no—
196C22×C4×C59—82no—
197C22×C4×C59C2×D411yescharacteristic
198C22×C4×C59C2×D411yescharacteristic
199C22×C4×C59C2411yescharacteristic
200C22×Dic59—21no—
201C22×Dic59—21no—
202C22×Dic59—21no—
203C22×Dic59—21no—
204C22×Dic59—24no—
205C22×Dic59—24no—
206C22×Dic59—44no—
207C22×Dic59—82no—
208C22×Dic59C2×D411yescharacteristic
209C22×Dic59C2×D411yescharacteristic
210C22×Dic59C2×D411yescharacteristic
211C22×Dic59C2×D411yescharacteristic
212C2×Dic118—24no—
213C2×Dic118—22no—
214C2×Dic118—22no—
215C2×Dic118—21no—
216C2×Dic118—24no—
217C2×Dic118—82no—
218C2×Dic118C2×D414yes—
219C2×Dic118C2412yes—
220SD16×C59—28no—
221SD16×C59—28no—
222C2×C8×C59—22no—
223C2×C8×C59—22no—
224C2×C8×C59C2412yes—
225C2×C8×C59C2412yes—
226C4⋊C4×C59—24no—
227C4⋊C4×C59—24no—
228C4⋊C4×C59—21no—
229C4⋊C4×C59C2412yes—
230C22⋊C4×C59—24no—
231C42×C59C2×D412yes—
232C42×C59C2412yes—
233C22⋊Dic59—24no—
234C22⋊Dic59—24no—
235#11745670—28no—
236C4⋊Dic59—21no—
237C4⋊Dic59—21no—
238C4⋊Dic59—21no—
239C4⋊Dic59—24no—
240C4⋊Dic59—24no—
241C4⋊Dic59—24no—
242C4⋊Dic59C2×D414yes—
243C4⋊Dic59C2412yes—
244C4⋊Dic59C2412yes—
245C4⋊Dic59C2412yes—
246Dic59⋊C4—24no—
247Dic59⋊C4—24no—
248Dic59⋊C4—24no—
249Dic59⋊C4—24no—
250Dic59⋊C4—24no—
251Dic59⋊C4—24no—
252Dic59⋊C4—24no—
253Dic59⋊C4—24no—
254Dic59⋊C4—24no—
255Dic59⋊C4C2×D414yes—
256Dic59⋊C4C2×D414yes—
257C4×Dic59—24no—
258C4×Dic59—24no—
259C4×Dic59—24no—
260C4×Dic59C2×D412yes—
261C4×Dic59C2×D412yes—
262C4×Dic59C2412yes—
263C4×Dic59C2412yes—
264C2×C59⋊C8—22no—
265C2×C59⋊C8—22no—
266C2×C59⋊C8C2412yes—
267C2×C59⋊C8C2412yes—
268C23×C59—24no—
269C23×C59—22no—
270C23×C59—42no—
271C23×C59—42no—
272C23×C59C22×D411yescharacteristic
273Q8×C59—22no—
274Q8×C59—22no—
275Q8×C59—22no—
276Q8×C59—22no—
277Q8×C59—42no—
278Q8×C59—42no—
279D4×C59—24no—
280D4×C59—22no—
281D4×C59C2×#4114yes—
282C2×C4×C59—22no—
283C2×C4×C59—22no—
284C2×C4×C59—22no—
285C2×C4×C59—22no—
286C2×C4×C59—22no—
287C2×C4×C59—42no—
288C2×C4×C59—42no—
289C2×C4×C59—42no—
290C2×C4×C59—84no—
291C2×C4×C59C22×D412yes—
292C2×C4×C59C22×D412yes—
293C2×C4×C59C22×D411yescharacteristic
294C2×C4×C59C2×#4112yes—
295C2×C4×C592−1+412yes—
296C2×C4×C59C2511yescharacteristic
297C2×Dic59—22no—
298C2×Dic59—22no—
299C2×Dic59—22no—
300C2×Dic59—22no—
301C2×Dic59—22no—
302C2×Dic59—22no—
303C2×Dic59—22no—
304C2×Dic59—42no—
305C2×Dic59—42no—
306C2×Dic59—42no—
307C2×Dic59—42no—
308C2×Dic59—48no—
309C2×Dic59—84no—
310C2×Dic59#13714yes—
311C2×Dic59C22×D412yes—
312C2×Dic59C22×D412yes—
313C2×Dic59C22×D412yes—
314C2×Dic59C22×D412yes—
315Dic118—28no—
316Dic118—22no—
317Dic118—22no—
318Dic118—42no—
319Dic118—84no—
320C8×C59—22no—
321C8×C59—22no—
322C59⋊C8—22no—
323C59⋊C8—22no—
324C2×#3372—591nomaximal, Sylow
325C22×C59—24no—
326C22×C59—48no—
327C22×C59—42no—
328C22×C59—42no—
329C22×C59#54812yes—
330C22×C59C2×#13712yes—
331C22×C59#57712yes—
332C22×C59C23×D411yescharacteristic
333C4×C59—22no—
334C4×C59—22no—
335C4×C59—42no—
336C4×C59—42no—
337C4×C59—42no—
338C4×C59#54812yes—
339C4×C59C22×#4111yescharacteristic
340C4×C59C2×2−1+411yescharacteristic
341Dic59—22no—
342Dic59—22no—
343Dic59—22no—
344Dic59—42no—
345Dic59—42no—
346Dic59—42no—
347Dic59—42no—
348Dic59C2×#13714yes—
349C2×#557—591no—
350C2×#554—591no—
351#3372—5916no—
352C2×#491—591no—
353C2×#491—591no—
354C2×#487—591no—
355C2×#479—591no—
356C2×#479—591no—
357C2×#477—591no—
358C2×#461—591no—
359C2×#461—591no—
360C2×#461D5911yescharacteristic
361C2×#446—591no—
362C2×#440—591no—
363C2×#440—591no—
364C2×C4×SD16—591no—
365C2×C59—44no—
366C2×C59#337214yescomplemented
367C2×C59C2×#54811yescharacteristic
368C2×C59C22×#13711yescharacteristic
369C2×C59C2×#57711yescharacteristic
370C22×SD16—591no—
371C22×SD16C2×D5911yescharacteristic
372C22×SD16C2×D5911yescharacteristic
373#557—598no—
374#557—1184no—
375#554—598no—
376#554—1184no—
377C2×C4⋊Q8—591no—
378C2×C4⋊Q8—591no—
379C2×C4⋊Q8—591no—
380C2×C4⋊Q8C2×D5911yescharacteristic
381C2×#125—591no—
382C2×#125—591no—
383C2×#125—1181no—
384C2×#125—1181no—
385C2×#125—1181no—
386C2×C22⋊Q8—1181no—
387C2×C22⋊Q8—1181no—
388C2×C22⋊Q8—1181no—
389C2×C4×Q8—591no—
390C2×C4×Q8—591no—
391C2×C4×Q8—591no—
392C2×C4×Q8—591no—
393C2×C4×Q8—1181no—
394C2×C4×D4—591no—
395C2×C4×D4—591no—
396C2×C4×D4C2×D5911yescharacteristic
397C22×C4⋊C4—1181no—
398#491—598no—
399#491—598no—
400#487—598no—
401#479—598no—
402#479—598no—
403#477—598no—
404#461—598no—
405#461—598no—
406#461C2×D5918yes—
407#446—598no—
408#440—598no—
409#440—598no—
410C4×SD16—598no—
411C2×#107—591no—
412C2×#107—591no—
413C2×#106—591no—
414C2×C4⋊C8—591no—
415C2×C4⋊C8—591no—
416C2×C4⋊C8C2×D5911yescharacteristic
417C2×#103—591no—
418C2×#103—591no—
419C2×#103—591no—
420C2×#103—591no—
421C2×#103—591no—
422C2×#103—591no—
423C2×#103—591no—
424C2×#103C2×D5911yescharacteristic
425C2×#103C2×D5911yescharacteristic
426C2×#102—591no—
427C2×#97—591no—
428C2×#97—591no—
429C2×C4×C8—591no—
430C59C2×#337211yescharacteristic, complemented, Sylow
431C22×Q8—591no—
432C22×Q8—591no—
433C22×Q8—1181no—
434C22×Q8C22×D5911yescharacteristic
435C22×Q8C22×D5911yescharacteristic
436C22×D4C22×D5911yescharacteristic
437C23×C4—21no—
438C23×C4—1181no—
439C23×C4—1181no—
440C2×SD16—24no—
441C2×SD16—24no—
442C2×SD16—594no—
443C2×SD16—1184no—
444C2×SD16C22×D5914yes—
445C2×SD16C22×D5914yes—
446C22×C8—591no—
447C22×C8—591no—
448C22×C8C22×D5911yescharacteristic
449C22×C8C22×D5911yescharacteristic
450C4⋊Q8—22no—
451C4⋊Q8—594no—
452C4⋊Q8—594no—
453C4⋊Q8—594no—
454C4⋊Q8—1182no—
455C4⋊Q8—1182no—
456C4⋊Q8—1182no—
457C4⋊Q8C22×D5914yes—
458#125—594no—
459#125—594no—
460#125—1182no—
461#125—1188no—
462#125—1188no—
463#125—1188no—
464#125—1182no—
465C22⋊Q8—1188no—
466C22⋊Q8—1188no—
467C22⋊Q8—1188no—
468C4×Q8—594no—
469C4×Q8—594no—
470C4×Q8—594no—
471C4×Q8—594no—
472C4×Q8—594no—
473C4×Q8—1182no—
474C4×Q8—1182no—
475C4×Q8—1188no—
476C4×Q8—1182no—
477C4×D4—22no—
478C4×D4—594no—
479C4×D4—594no—
480C4×D4—1182no—
481C4×D4—1182no—
482C4×D4C22×D5914yes—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—591no—
486C2×C4⋊C4—591no—
487C2×C4⋊C4—591no—
488C2×C4⋊C4—591no—
489C2×C4⋊C4—591no—
490C2×C4⋊C4—591no—
491C2×C4⋊C4—1188no—
492C2×C4⋊C4—1181no—
493C2×C4⋊C4—1181no—
494C2×C4⋊C4—1181no—
495C2×C4⋊C4—1181no—
496C2×C4⋊C4—1181no—
497C2×C4⋊C4—1181no—
498C2×C4⋊C4—1181no—
499C2×C4⋊C4—1181no—
500C2×C4⋊C4—1181no—
501C2×C4⋊C4—1181no—
502C2×C4⋊C4—1181no—
503C2×C4⋊C4—1181no—
504C2×C4⋊C4C22×D5911yescharacteristic
505C2×C22⋊C4—21no—
506C2×C22⋊C4—1181no—
507C2×C22⋊C4—1181no—
508C2×C42—591no—
509C2×C42—591no—
510C2×C42—1181no—
511C2×C42—1181no—
512C2×C42—1181no—
513C2×C42C22×D5911yescharacteristic
514#107—594no—
515#107—594no—
516#106—594no—
517C4⋊C8—594no—
518C4⋊C8—594no—
519C4⋊C8C22×D5914yes—
520#103—594no—
521#103—594no—
522#103—594no—
523#103—594no—
524#103—594no—
525#103—594no—
526#103—594no—
527#103C22×D5914yes—
528#103C22×D5914yes—
529#102—594no—
530#97—594no—
531#97—594no—
532C4×C8—594no—
533C24—21no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8—22no—
537C2×Q8—22no—
538C2×Q8—22no—
539C2×Q8—22no—
540C2×Q8—594no—
541C2×Q8—592no—
542C2×Q8—1184no—
543C2×Q8—1184no—
544C2×Q8—1181no—
545C2×Q8—1182no—
546C2×Q8—1182no—
547C2×Q8—4722no—
548C2×Q8C23×D5912yes—
549C2×Q8C23×D5912yes—
550C2×D4—21no—
551C2×D4—22no—
552C2×D4#1174568714yes—
553C2×D4C23×D5912yes—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—24no—
558C22×C4—82no—
559C22×C4—591no—
560C22×C4—591no—
561C22×C4—591no—
562C22×C4—591no—
563C22×C4—1184no—
564C22×C4—1184no—
565C22×C4—1181no—
566C22×C4—1181no—
567C22×C4—1181no—
568C22×C4—1181no—
569C22×C4—4722no—
570C22×C4—2364no—
571C22×C4D4×D5911yescharacteristic
572C22×C4D4×D5911yescharacteristic
573C22×C4C23×D5911yescharacteristic
574SD16—28no—
575SD16—28no—
576SD16—1188no—
577C2×C8—22no—
578C2×C8—22no—
579C2×C8—592no—
580C2×C8—592no—
581C2×C8—1182no—
582C2×C8—1182no—
583C2×C8C23×D5912yes—
584C2×C8C23×D5912yes—
585C4⋊C4—24no—
586C4⋊C4—24no—
587C4⋊C4—21no—
588C4⋊C4—594no—
589C4⋊C4—594no—
590C4⋊C4—594no—
591C4⋊C4—592no—
592C4⋊C4—592no—
593C4⋊C4—592no—
594C4⋊C4—1184no—
595C4⋊C4—1184no—
596C4⋊C4—1184no—
597C4⋊C4—1184no—
598C4⋊C4—1184no—
599C4⋊C4—1184no—
600C4⋊C4—1184no—
601C4⋊C4—1184no—
602C4⋊C4—1184no—
603C4⋊C4—1181no—
604C4⋊C4—1181no—
605C4⋊C4—1181no—
606C4⋊C4—1184no—
607C4⋊C4—1184no—
608C4⋊C4—1184no—
609C4⋊C4C23×D5912yes—
610C22⋊C4—24no—
611C22⋊C4—1184no—
612C22⋊C4—1184no—
613C42—592no—
614C42—592no—
615C42—592no—
616C42—592no—
617C42—1184no—
618C42—1184no—
619C42—1184no—
620C42D4×D5912yes—
621C42C23×D5912yes—
622C23—22no—
623C23—24no—
624C23—42no—
625C23—42no—
626C23C2×D4×D5911yescharacteristic
627Q8—22no—
628Q8—22no—
629Q8—22no—
630Q8—22no—
631Q8—42no—
632Q8—42no—
633Q8—1188no—
634Q8—1182no—
635Q8—1182no—
636Q8—4724no—
637Q8—2362no—
638D4—22no—
639D4—24no—
640D4C2×#1174568714yes—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—42no—
647C2×C4—42no—
648C2×C4—42no—
649C2×C4—84no—
650C2×C4—594no—
651C2×C4—592no—
652C2×C4—592no—
653C2×C4—592no—
654C2×C4—592no—
655C2×C4—1182no—
656C2×C4—1182no—
657C2×C4—1182no—
658C2×C4—1182no—
659C2×C4—1182no—
660C2×C4—1182no—
661C2×C4—1182no—
662C2×C4—4724no—
663C2×C4—2368no—
664C2×C4—2362no—
665C2×C4—2362no—
666C2×C4—2362no—
667C2×C4—2362no—
668C2×C4C2×D4×D5912yes—
669C2×C4C2×D4×D5912yes—
670C2×C4C2×D4×D5911yescharacteristic
671C2×C4C2×#1174568712yes—
672C2×C4#1427377412yes—
673C2×C4C24×D5911yescharacteristic
674C8—22no—
675C8—22no—
676C8—1182no—
677C8—1182no—
678C22—24no—
679C22—42no—
680C22—42no—
681C22—48no—
682C22#1683805812yes—
683C22#137×D5912yes—
684C22#1683820812yes—
685C22C22×D4×D5911yescharacteristic
686C4—22no—
687C4—22no—
688C4—42no—
689C4—42no—
690C4—42no—
691C4—594no—
692C4—1182no—
693C4—1182no—
694C4—1182no—
695C4—2362no—
696C4—2362no—
697C4—2362no—
698C4—2362no—
699C4#1683805812yes—
700C4C22×#1174568711yescharacteristic
701C4C2×#1427377411yescharacteristic
702C2—44no—
703C2#2143687214yesdirect product factor
704C2C2×#1683805811yescharacteristic
705C2C2×#137×D5911yescharacteristic
706C2C2×#1683820811yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#461C2
socleC23×C59C22×D4
prime radicalC22×D4×C59C23
hypercenterC2×#461D59
hypocenterC59C2×#3372
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#461

Complements

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

NH ≅ G/Ntype
1. C2×#16838127C2semidirect
3. #21436872C2direct (N × H)
4. C2×#16837770C2semidirect
5. C2×#16837769C2semidirect
6. C2×#16837751C2semidirect
7. C2×#16837710C2semidirect
8. C2×#16837707C2semidirect
9. C2×#16837695C2semidirect
12. C2×#16837531C2semidirect
19. #16838127C22semidirect
41. #16837770C22semidirect
42. #16837769C22semidirect
43. #16837751C22semidirect
44. #16837710C22semidirect
45. #16837707C22semidirect
46. #16837695C22semidirect
49. #16837531C22semidirect
366. C2×C59#3372semidirect
430. C59C2×#3372semidirect
703. C2#21436872direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168381272
C2×#168381112
#214368722
C2×#168377702
C2×#168377692
C2×#168377512
C2×#168377102
C2×#168377072
C2×#168376952
C2×#168376052
C2×#168375312
C2×#168375032
C2×#168375022
C2×SD16×Dic592
C2×C59×#4612
C2×#337259