Finite Group Databasebeta

← C2×#21436776 #29468296

Subgroups — C2×#21436776 #29468296

Order 15104.

1830 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838128C211yesmaximal, characteristic, complemented
2C2×#16838121C211yesmaximal, characteristic
3#21436776C2116yesmaximal, direct product factor
4C2×#16837756C211yesmaximal, characteristic
5C2×#16837755C211yesmaximal, characteristic
6C2×#16837751C211yesmaximal, characteristic, complemented
7C2×#16837710C211yesmaximal, characteristic, complemented
8C2×#16837707C211yesmaximal, characteristic, complemented
9C2×#16837680C211yesmaximal, characteristic
10C2×#16837622C211yesmaximal, characteristic
11C2×#16837610C211yesmaximal, characteristic, complemented
12C2×#16837526C211yesmaximal, characteristic, complemented
13C2×Q16×Dic59C211yesmaximal, characteristic, complemented
14C2×C4×#11745672C211yesmaximal, characteristic, complemented
15C2×SD16×Dic59C211yesmaximal, characteristic
16C2×C59×#464C211yesmaximal, characteristic
17C22×#11745672C2211yescharacteristic
18#16838128—24no—
19#16838128C2218yescomplemented
20#16838121—24no—
21#16838121C2218yes—
22C2×#14273726—21no—
23C2×#14273726C2211yescharacteristic
24C2×#14273725C2211yescharacteristic
25C2×#14273720—21no—
26C2×#14273720—21no—
27C2×#14273719—21no—
28C2×#14273719C2211yescharacteristic
29C2×#14273718—21no—
30C2×#14273718C2211yescharacteristic
31C2×#14273714C2211yescharacteristic
32C2×#14273704—21no—
33C2×Q8×Dic59C2211yescharacteristic
34C2×Q8×Dic59C2211yescharacteristic
35C2×Q8×Dic59C2211yescharacteristic
36C2×C4×Dic118—21no—
37C2×C4×Dic118C2211yescharacteristic
38C2×C4×Dic118C2211yescharacteristic
39C2×D4×Dic59C2211yescharacteristic
40C2×#14273683—21no—
41#16837756C2218yes—
42#16837755C2218yes—
43#16837751C2218yescomplemented
44#16837710C2218yescomplemented
45#16837707C2218yescomplemented
46#16837680C2218yes—
47#16837622C2218yes—
48#16837610C2218yescomplemented
49#16837526C2218yescomplemented
50Q16×Dic59C2218yescomplemented
51C4×#11745672C2218yescomplemented
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×#14273650C2211yescharacteristic
64C2×#14273648C2211yescharacteristic
65C2×#14273648C2211yescharacteristic
66C2×C4×C59⋊C8C2211yescharacteristic
67C2×C8×Dic59C2211yescharacteristic
68C2×C8×Dic59C2211yescharacteristic
69C22×Q16×C59C2211yescharacteristic
70C22×SD16×C59C2211yescharacteristic
71C2×#124×C59C2211yescharacteristic
72C2×C4×Q8×C59C2211yescharacteristic
73C59×#464C2218yes—
74C2×C4⋊C8×C59C2211yescharacteristic
75C2×#103×C59C2211yescharacteristic
76C2×#102×C59C2211yescharacteristic
77C22×Dic118—21no—
78C22×Dic118D411yescharacteristic
79C22×Dic118C2311yescharacteristic
80C23×Dic59—21no—
81C2×#11745672—24no—
82C2×#11745672C2314yes—
83C22×C59⋊C8C2311yescharacteristic
84C22×C59⋊C8C2311yescharacteristic
85#14273726—28no—
86#14273726—22no—
87#14273726C2314yes—
88#14273725—22no—
89#14273725C2314yes—
90#14273720—28no—
91#14273720—28no—
92#14273719—22no—
93#14273719—28no—
94#14273719C2314yes—
95#14273718—28no—
96#14273718—22no—
97#14273718C2314yes—
98#14273714—22no—
99#14273714C2314yes—
100#14273704—28no—
101Q8×Dic59—22no—
102Q8×Dic59—22no—
103Q8×Dic59—22no—
104Q8×Dic59C2314yes—
105Q8×Dic59C2314yes—
106Q8×Dic59C2314yes—
107C4×Dic118—22no—
108C4×Dic118—28no—
109C4×Dic118D414yes—
110C4×Dic118C2314yes—
111C4×Dic118C2314yes—
112D4×Dic59—22no—
113D4×Dic59C2314yes—
114#14273683—28no—
115C2×C4⋊Dic59—21no—
116C2×C4⋊Dic59—21no—
117C2×C4⋊Dic59—21no—
118C2×C4⋊Dic59—21no—
119C2×C4⋊Dic59D411yescharacteristic
120C2×C4⋊Dic59C2311yescharacteristic
121C2×C4⋊Dic59C2311yescharacteristic
122C2×C4⋊Dic59C2311yescharacteristic
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⋊C4D411yescharacteristic
131C2×Dic59⋊C4D411yescharacteristic
132C2×C22⋊Dic59—21no—
133C2×C22⋊Dic59—21no—
134C2×C22⋊Dic59—21no—
135C2×C4×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#14273650C2314yes—
152#14273648C2314yes—
153#14273648C2314yes—
154C4×C59⋊C8C2314yes—
155C8×Dic59C2314yes—
156C8×Dic59C2314yes—
157C22×Q8×C59C2311yescharacteristic
158C22×Q8×C59C2311yescharacteristic
159C22×D4×C59C2311yescharacteristic
160C2×Q16×C59—24no—
161C2×Q16×C59C2314yes—
162C2×SD16×C59—24no—
163C2×SD16×C59C2314yes—
164C22×C8×C59C2311yescharacteristic
165C22×C8×C59C2311yescharacteristic
166#124×C59—22no—
167#124×C59C2314yes—
168C4×Q8×C59—22no—
169C4×Q8×C59C2314yes—
170C2×C4⋊C4×C59—21no—
171C2×C4⋊C4×C59C2311yescharacteristic
172C2×C22⋊C4×C59—21no—
173C2×C22⋊C4×C59—21no—
174C2×C42×C59—21no—
175C2×C42×C59C2311yescharacteristic
176C4⋊C8×C59C2314yes—
177#103×C59C2314yes—
178#102×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#4114yes—
186C2×Q8×C59C2412yes—
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×C59C2×D411yescharacteristic
196C22×C4×C59C2×D411yescharacteristic
197C22×C4×C59C2411yescharacteristic
198C22×Dic59—21no—
199C22×Dic59—21no—
200C22×Dic59—21no—
201C22×Dic59—21no—
202C22×Dic59—24no—
203C22×Dic59—44no—
204C22×Dic59C2×D411yescharacteristic
205C22×Dic59C2×D411yescharacteristic
206C22×Dic59C2×D411yescharacteristic
207C22×Dic59C2×D411yescharacteristic
208C2×Dic118—24no—
209C2×Dic118—22no—
210C2×Dic118—22no—
211C2×Dic118—21no—
212C2×Dic118—24no—
213C2×Dic118—44no—
214C2×Dic118C2×D414yes—
215C2×Dic118C2412yes—
216Q16×C59—28no—
217SD16×C59—28no—
218C2×C8×C59—22no—
219C2×C8×C59—22no—
220C2×C8×C59C2412yes—
221C2×C8×C59C2412yes—
222C4⋊C4×C59—24no—
223C4⋊C4×C59—21no—
224C4⋊C4×C59C2412yes—
225C22⋊C4×C59—24no—
226C22⋊C4×C59—24no—
227C42×C59—24no—
228C42×C59C2×D412yes—
229C42×C59C2412yes—
230C22⋊Dic59—24no—
231C22⋊Dic59—24no—
232C22⋊Dic59—24no—
233#11745672—28no—
234C4⋊Dic59—21no—
235C4⋊Dic59—21no—
236C4⋊Dic59—21no—
237C4⋊Dic59—24no—
238C4⋊Dic59—24no—
239C4⋊Dic59—24no—
240C4⋊Dic59—24no—
241C4⋊Dic59C2×D414yes—
242C4⋊Dic59C2412yes—
243C4⋊Dic59C2412yes—
244C4⋊Dic59C2412yes—
245Dic59⋊C4—24no—
246Dic59⋊C4—24no—
247Dic59⋊C4—24no—
248Dic59⋊C4—24no—
249Dic59⋊C4—24no—
250Dic59⋊C4—24no—
251Dic59⋊C4—24no—
252Dic59⋊C4C2×D414yes—
253Dic59⋊C4C2×D414yes—
254C4×Dic59—24no—
255C4×Dic59—24no—
256C4×Dic59—24no—
257C4×Dic59—24no—
258C4×Dic59C2×D412yes—
259C4×Dic59C2×D412yes—
260C4×Dic59C2412yes—
261C4×Dic59C2412yes—
262C2×C59⋊C8—22no—
263C2×C59⋊C8—22no—
264C2×C59⋊C8C2412yes—
265C2×C59⋊C8C2412yes—
266C23×C59—22no—
267C23×C59—42no—
268C23×C59—42no—
269C23×C59—42no—
270C23×C59C22×D411yescharacteristic
271Q8×C59—24no—
272Q8×C59—22no—
273Q8×C59—22no—
274Q8×C59—22no—
275Q8×C59—42no—
276Q8×C59C2×#4114yes—
277D4×C59—22no—
278D4×C59—22no—
279D4×C59—42no—
280C2×C4×C59—24no—
281C2×C4×C59—22no—
282C2×C4×C59—22no—
283C2×C4×C59—22no—
284C2×C4×C59—22no—
285C2×C4×C59—22no—
286C2×C4×C59—42no—
287C2×C4×C59—42no—
288C2×C4×C59C22×D412yes—
289C2×C4×C59C22×D412yes—
290C2×C4×C59C22×D411yescharacteristic
291C2×C4×C59C2×#4112yes—
292C2×C4×C592−1+412yes—
293C2×C4×C59C2511yescharacteristic
294C2×Dic59—22no—
295C2×Dic59—22no—
296C2×Dic59—22no—
297C2×Dic59—22no—
298C2×Dic59—22no—
299C2×Dic59—22no—
300C2×Dic59—22no—
301C2×Dic59—42no—
302C2×Dic59—42no—
303C2×Dic59—42no—
304C2×Dic59—42no—
305C2×Dic59—48no—
306C2×Dic59#13514yes—
307C2×Dic59C22×D412yes—
308C2×Dic59C22×D412yes—
309C2×Dic59C22×D412yes—
310C2×Dic59C22×D412yes—
311Dic118—28no—
312Dic118—22no—
313Dic118—22no—
314Dic118—42no—
315Dic118—48no—
316C8×C59—22no—
317C8×C59—22no—
318C59⋊C8—22no—
319C59⋊C8—22no—
320C2×#3364—591nomaximal, Sylow
321C22×C59—42no—
322C22×C59—42no—
323C22×C59—42no—
324C22×C59—84no—
325C22×C59#54812yes—
326C22×C59C2×#13512yes—
327C22×C59#57812yes—
328C22×C59C23×D411yescharacteristic
329C4×C59—24no—
330C4×C59—22no—
331C4×C59—22no—
332C4×C59—42no—
333C4×C59—42no—
334C4×C59#54812yes—
335C4×C59C22×#4111yescharacteristic
336C4×C59C2×2−1+411yescharacteristic
337Dic59—22no—
338Dic59—22no—
339Dic59—22no—
340Dic59—42no—
341Dic59—42no—
342Dic59—42no—
343Dic59—42no—
344Dic59C2×#13514yes—
345C2×#557—591no—
346C2×#556—591no—
347#3364—5916no—
348C2×#488—591no—
349C2×#488—591no—
350C2×#487—591no—
351C2×#479—591no—
352C2×#479—591no—
353C2×#474—591no—
354C2×#464—591no—
355C2×#464D5911yescharacteristic
356C2×#462—591no—
357C2×C8×Q8—591no—
358C2×C4×Q16—591no—
359C2×C4×Q16—591no—
360C2×C4×SD16—591no—
361C2×C59—82no—
362C2×C59#336414yescomplemented
363C2×C59C2×#54811yescharacteristic
364C2×C59C22×#13511yescharacteristic
365C2×C59C2×#57811yescharacteristic
366C22×Q16—591no—
367C22×Q16C2×D5911yescharacteristic
368C22×SD16C2×D5911yescharacteristic
369#557—598no—
370#557—1184no—
371#556—598no—
372#556—1184no—
373C2×C4⋊Q8—591no—
374C2×C4⋊Q8—591no—
375C2×C4⋊Q8—1181no—
376C2×#126—1181no—
377C2×#126—1181no—
378C2×#125—591no—
379C2×#125—591no—
380C2×#125—1181no—
381C2×#125—1181no—
382C2×#124—591no—
383C2×#124C2×D5911yescharacteristic
384C2×C22⋊Q8—1181no—
385C2×C4×Q8—591no—
386C2×C4×Q8—591no—
387C2×C4×Q8—591no—
388C2×C4×Q8—591no—
389C2×C4×Q8—591no—
390C2×C4×Q8—1181no—
391C2×C4×Q8C2×D5911yescharacteristic
392C2×C4×D4—591no—
393C2×#117—1181no—
394#488—598no—
395#488—598no—
396#487—598no—
397#479—598no—
398#479—598no—
399#474—598no—
400#464—598no—
401#464C2×D5918yes—
402#462—598no—
403C8×Q8—598no—
404C4×Q16—598no—
405C4×Q16—598no—
406C4×SD16—598no—
407C2×#107—591no—
408C2×#107—591no—
409C2×#106—591no—
410C2×C4⋊C8—591no—
411C2×C4⋊C8—591no—
412C2×C4⋊C8C2×D5911yescharacteristic
413C2×#103—591no—
414C2×#103—591no—
415C2×#103—591no—
416C2×#103—591no—
417C2×#103—591no—
418C2×#103—591no—
419C2×#103C2×D5911yescharacteristic
420C2×#102—591no—
421C2×#102—591no—
422C2×#102C2×D5911yescharacteristic
423C2×C4×C8—591no—
424C2×C4×C8—591no—
425C2×C4×C8—591no—
426C59C2×#336411yescharacteristic, complemented, Sylow
427C22×Q8—591no—
428C22×Q8—591no—
429C22×Q8—1181no—
430C22×Q8C22×D5911yescharacteristic
431C22×Q8C22×D5911yescharacteristic
432C22×D4C22×D5911yescharacteristic
433C23×C4—1181no—
434C2×Q16—24no—
435C2×Q16—594no—
436C2×Q16—1184no—
437C2×Q16C22×D5914yes—
438C2×SD16—24no—
439C2×SD16C22×D5914yes—
440C22×C8—591no—
441C22×C8—591no—
442C22×C8C22×D5911yescharacteristic
443C22×C8C22×D5911yescharacteristic
444C4⋊Q8—594no—
445C4⋊Q8—594no—
446C4⋊Q8—1182no—
447C4⋊Q8—1182no—
448C4⋊Q8—1188no—
449#126—1188no—
450#126—1188no—
451#125—594no—
452#125—594no—
453#125—1188no—
454#125—1182no—
455#125—1188no—
456#125—1182no—
457#124—22no—
458#124—594no—
459#124—1182no—
460#124C22×D5914yes—
461C22⋊Q8—1188no—
462C4×Q8—22no—
463C4×Q8—594no—
464C4×Q8—594no—
465C4×Q8—594no—
466C4×Q8—594no—
467C4×Q8—594no—
468C4×Q8—594no—
469C4×Q8—1188no—
470C4×Q8—1182no—
471C4×Q8—1182no—
472C4×Q8—1182no—
473C4×Q8—1182no—
474C4×Q8C22×D5914yes—
475C4×D4—594no—
476C4×D4—1182no—
477#117—1188no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—591no—
480C2×C4⋊C4—591no—
481C2×C4⋊C4—591no—
482C2×C4⋊C4—591no—
483C2×C4⋊C4—591no—
484C2×C4⋊C4—591no—
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⋊C4—1181no—
494C2×C4⋊C4—1181no—
495C2×C4⋊C4—1181no—
496C2×C4⋊C4C22×D5911yescharacteristic
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—1181no—
500C2×C22⋊C4—1181no—
501C2×C22⋊C4—1181no—
502C2×C42—21no—
503C2×C42—591no—
504C2×C42—591no—
505C2×C42—1181no—
506C2×C42—1181no—
507C2×C42—1181no—
508C2×C42—1181no—
509C2×C42C22×D5911yescharacteristic
510#107—594no—
511#107—594no—
512#106—594no—
513C4⋊C8—594no—
514C4⋊C8—594no—
515C4⋊C8C22×D5914yes—
516#103—594no—
517#103—594no—
518#103—594no—
519#103—594no—
520#103—594no—
521#103—594no—
522#103C22×D5914yes—
523#102—594no—
524#102—594no—
525#102C22×D5914yes—
526C4×C8—594no—
527C4×C8—594no—
528C4×C8—594no—
529C24—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—22no—
533C2×Q8—22no—
534C2×Q8—22no—
535C2×Q8—594no—
536C2×Q8—592no—
537C2×Q8—1184no—
538C2×Q8—1184no—
539C2×Q8—1181no—
540C2×Q8—1182no—
541C2×Q8—1182no—
542C2×Q8—2364no—
543C2×Q8#1174568714yes—
544C2×Q8C23×D5912yes—
545C2×Q8C23×D5912yes—
546C2×D4—21no—
547C2×D4—22no—
548C2×D4—22no—
549C2×D4C23×D5912yes—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—591no—
554C22×C4—591no—
555C22×C4—591no—
556C22×C4—591no—
557C22×C4—1184no—
558C22×C4—1181no—
559C22×C4—1181no—
560C22×C4—1181no—
561C22×C4—1181no—
562C22×C4—2364no—
563C22×C4D4×D5911yescharacteristic
564C22×C4D4×D5911yescharacteristic
565C22×C4C23×D5911yescharacteristic
566Q16—28no—
567Q16—1188no—
568SD16—28no—
569C2×C8—22no—
570C2×C8—22no—
571C2×C8—592no—
572C2×C8—592no—
573C2×C8—1182no—
574C2×C8—1182no—
575C2×C8C23×D5912yes—
576C2×C8C23×D5912yes—
577C4⋊C4—24no—
578C4⋊C4—21no—
579C4⋊C4—594no—
580C4⋊C4—594no—
581C4⋊C4—594no—
582C4⋊C4—592no—
583C4⋊C4—592no—
584C4⋊C4—592no—
585C4⋊C4—1184no—
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⋊C4—1184no—
599C4⋊C4C23×D5912yes—
600C22⋊C4—24no—
601C22⋊C4—24no—
602C22⋊C4—1184no—
603C22⋊C4—1184no—
604C22⋊C4—1184no—
605C42—24no—
606C42—592no—
607C42—592no—
608C42—592no—
609C42—592no—
610C42—1184no—
611C42—1184no—
612C42—1184no—
613C42—1184no—
614C42D4×D5912yes—
615C42C23×D5912yes—
616C23—22no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23C2×D4×D5911yescharacteristic
621Q8—22no—
622Q8—24no—
623Q8—22no—
624Q8—22no—
625Q8—42no—
626Q8—1188no—
627Q8—1182no—
628Q8—1182no—
629Q8—2368no—
630Q8—2362no—
631Q8C2×#1174568714yes—
632D4—22no—
633D4—22no—
634D4—42no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—24no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—42no—
642C2×C4—42no—
643C2×C4—594no—
644C2×C4—592no—
645C2×C4—592no—
646C2×C4—592no—
647C2×C4—592no—
648C2×C4—1182no—
649C2×C4—1182no—
650C2×C4—1182no—
651C2×C4—1182no—
652C2×C4—1182no—
653C2×C4—1182no—
654C2×C4—1182no—
655C2×C4—2368no—
656C2×C4—2362no—
657C2×C4—2362no—
658C2×C4—2362no—
659C2×C4—2362no—
660C2×C4C2×D4×D5912yes—
661C2×C4C2×D4×D5912yes—
662C2×C4C2×D4×D5911yescharacteristic
663C2×C4C2×#1174568712yes—
664C2×C4#1427377412yes—
665C2×C4C24×D5911yescharacteristic
666C8—22no—
667C8—22no—
668C8—1182no—
669C8—1182no—
670C22—42no—
671C22—42no—
672C22—42no—
673C22—84no—
674C22#1683805812yes—
675C22#135×D5912yes—
676C22#1683821812yes—
677C22C22×D4×D5911yescharacteristic
678C4—22no—
679C4—24no—
680C4—22no—
681C4—42no—
682C4—42no—
683C4—594no—
684C4—1182no—
685C4—1182no—
686C4—1182no—
687C4—2362no—
688C4—2362no—
689C4—2362no—
690C4—2362no—
691C4#1683805812yes—
692C4C22×#1174568711yescharacteristic
693C4C2×#1427377411yescharacteristic
694C2—82no—
695C2#2143677614yesdirect product factor
696C2C2×#1683805811yescharacteristic
697C2C2×#135×D5911yescharacteristic
698C2C2×#1683821811yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#464C2
socleC23×C59C22×D4
prime radicalC22×D4×C59C23
hypercenterC2×#464D59
hypocenterC59C2×#3364
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×#16838128C2semidirect
3. #21436776C2direct (N × H)
6. C2×#16837751C2semidirect
7. C2×#16837710C2semidirect
8. C2×#16837707C2semidirect
11. C2×#16837610C2semidirect
12. C2×#16837526C2semidirect
13. C2×Q16×Dic59C2semidirect
14. C2×C4×#11745672C2semidirect
19. #16838128C22semidirect
43. #16837751C22semidirect
44. #16837710C22semidirect
45. #16837707C22semidirect
48. #16837610C22semidirect
49. #16837526C22semidirect
50. Q16×Dic59C22semidirect
51. C4×#11745672C22semidirect
362. C2×C59#3364semidirect
426. C59C2×#3364semidirect
695. C2#21436776direct (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×#168381212
#214367762
C2×#168377562
C2×#168377552
C2×#168377512
C2×#168377102
C2×#168377072
C2×#168376802
C2×#168376222
C2×#168376102
C2×#168375262
C2×Q16×Dic592
C2×C4×#117456722
C2×SD16×Dic592
C2×C59×#4642
C2×#336459