Finite Group Databasebeta

← C2×#21436628 #29467318

Subgroups — C2×#21436628 #29467318

Order 15104.

1834 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838122C211yesmaximal, characteristic
2C2×#16838092C211yesmaximal, characteristic
3#21436628C2116yesmaximal, direct product factor
4C2×#16837811C211yesmaximal, characteristic, complemented
5C2×#16837738C211yesmaximal, characteristic, complemented
6C2×#16837744C211yesmaximal, characteristic, complemented
7C2×#16837744C211yesmaximal, characteristic, complemented
8C2×#16837744C211yesmaximal, characteristic, complemented
9C2×#16837710C211yesmaximal, characteristic, complemented
10C2×#16837698C211yesmaximal, characteristic, complemented
11C2×#16837660C211yesmaximal, characteristic, complemented
12C2×#16837643C211yesmaximal, characteristic, complemented
13C2×#16837510C211yesmaximal, characteristic, complemented
14C2×#16837444C211yesmaximal, characteristic, complemented
15C2×#16837440C211yesmaximal, characteristic, complemented
16C2×C59×#435C211yesmaximal, characteristic
17C22×Dic236C2211yescharacteristic
18#16838122—24no—
19#16838122C2218yes—
20#16838092—24no—
21#16838092C2218yes—
22C2×#14273727C2211yescharacteristic
23C2×#14273720—21no—
24C2×#14273720—21no—
25C2×#14273720—21no—
26C2×#14273719C2211yescharacteristic
27C2×#14273717—21no—
28C2×#14273714—21no—
29C2×#14273708—21no—
30C2×#14273706C2211yescharacteristic
31C2×#14273706C2211yescharacteristic
32C2×#14273706C2211yescharacteristic
33C2×#14273706C2211yescharacteristic
34C2×C4×Dic118C2211yescharacteristic
35C2×C4×Dic118C2211yescharacteristic
36C2×#14273692—21no—
37C2×#14273686C2211yescharacteristic
38C2×#14273686C2211yescharacteristic
39C2×#14273686C2211yescharacteristic
40C2×#14273683—21no—
41C22×C4⋊Dic59C2211yescharacteristic
42#16837811C2218yescomplemented
43#16837744C2218yescomplemented
44#16837744C2218yescomplemented
45#16837744C2218yescomplemented
46#16837738C2218yescomplemented
47#16837710C2218yescomplemented
48#16837698C2218yescomplemented
49#16837660C2218yescomplemented
50#16837643C2218yescomplemented
51#16837510C2218yescomplemented
52#16837444C2218yescomplemented
53#16837440C2218yescomplemented
54C2×#14273661C2211yescharacteristic
55C2×#14273661C2211yescharacteristic
56C2×#14273661C2211yescharacteristic
57C2×#14273661C2211yescharacteristic
58C2×#14273661C2211yescharacteristic
59C2×#14273659C2211yescharacteristic
60C2×#14273659C2211yescharacteristic
61C2×#14273659C2211yescharacteristic
62C2×#14273659C2211yescharacteristic
63C2×#14273652C2211yescharacteristic
64C2×#14273652C2211yescharacteristic
65C2×#14273652C2211yescharacteristic
66C2×#14273652C2211yescharacteristic
67C2×#14273652C2211yescharacteristic
68C2×#14273652C2211yescharacteristic
69C22×M16×C59C2211yescharacteristic
70C23×C8×C59C2211yescharacteristic
71C2×C4×D4×C59C2211yescharacteristic
72C59×#435C2218yes—
73C2×C4⋊C8×C59C2211yescharacteristic
74C2×C22⋊C8×C59C2211yescharacteristic
75C2×C22⋊C8×C59C2211yescharacteristic
76C2×#97×C59C2211yescharacteristic
77C22×Dic118—21no—
78C22×Dic118C2311yescharacteristic
79C22×Dic118C2311yescharacteristic
80C23×Dic59—21no—
81C2×Dic236—24no—
82C2×Dic236C2314yes—
83#14273727—22no—
84#14273727C2314yes—
85#14273720—28no—
86#14273720—28no—
87#14273720—28no—
88#14273719—22no—
89#14273719C2314yes—
90#14273717—28no—
91#14273714—28no—
92#14273708—28no—
93#14273706—22no—
94#14273706—22no—
95#14273706—22no—
96#14273706—22no—
97#14273706C2314yes—
98#14273706C2314yes—
99#14273706C2314yes—
100#14273706C2314yes—
101C4×Dic118—22no—
102C4×Dic118—22no—
103C4×Dic118C2314yes—
104C4×Dic118C2314yes—
105#14273692—28no—
106#14273686—22no—
107#14273686—22no—
108#14273686—22no—
109#14273686C2314yes—
110#14273686C2314yes—
111#14273686C2314yes—
112#14273683—28no—
113C2×C4⋊Dic59—21no—
114C2×C4⋊Dic59—21no—
115C2×C4⋊Dic59—22no—
116C2×C4⋊Dic59C2311yescharacteristic
117C2×C4⋊Dic59C2311yescharacteristic
118C2×C4⋊Dic59C2311yescharacteristic
119C2×C4⋊Dic59C2311yescharacteristic
120C2×C4⋊Dic59C2311yescharacteristic
121C2×C4⋊Dic59C2311yescharacteristic
122C2×C4⋊Dic59C2314yes—
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×C22⋊Dic59—21no—
132C2×C22⋊Dic59—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×Dic59—21no—
142C2×C4×Dic59—21no—
143#14273661C2314yes—
144#14273661C2314yes—
145#14273661C2314yes—
146#14273661C2314yes—
147#14273661C2314yes—
148#14273659C2314yes—
149#14273659C2314yes—
150#14273659C2314yes—
151#14273659C2314yes—
152#14273652C2314yes—
153#14273652C2314yes—
154#14273652C2314yes—
155#14273652C2314yes—
156#14273652C2314yes—
157#14273652C2314yes—
158C22×D4×C59D411yescharacteristic
159C23×C4×C59C2311yescharacteristic
160C23×C4×C59C2311yescharacteristic
161C2×M16×C59—24no—
162C2×M16×C59C2314yes—
163C22×C8×C59—24no—
164C22×C8×C59C2314yes—
165C22×C8×C59C2311yescharacteristic
166C22×C8×C59C2311yescharacteristic
167C22×C8×C59C2311yescharacteristic
168C22×C8×C59C2311yescharacteristic
169C4×D4×C59D414yes—
170C4×D4×C59C2314yes—
171C2×C4⋊C4×C59D411yescharacteristic
172C2×C22⋊C4×C59D411yescharacteristic
173C2×C22⋊C4×C59D411yescharacteristic
174C2×C42×C59C2311yescharacteristic
175C4⋊C8×C59C2314yes—
176C22⋊C8×C59C2314yes—
177C22⋊C8×C59C2314yes—
178#97×C59C2314yes—
179C24×C59C2×D411yescharacteristic
180C24×C59C2×D411yescharacteristic
181C2×D4×C59—42no—
182C2×D4×C59C2×D414yes—
183C22×C4×C59—22no—
184C22×C4×C59—22no—
185C22×C4×C59—22no—
186C22×C4×C59—22no—
187C22×C4×C59C2×D411yescharacteristic
188C22×C4×C59C2×D411yescharacteristic
189C22×C4×C59C2×D411yescharacteristic
190C22×C4×C59C2×D411yescharacteristic
191C22×C4×C59C2×D412yes—
192C22×C4×C59C2×D412yes—
193C22×C4×C59C2412yes—
194C22×C4×C59C2412yes—
195C22×C4×C59C2411yescharacteristic
196C22×Dic59—21no—
197C22×Dic59—21no—
198C22×Dic59—21no—
199C22×Dic59—21no—
200C22×Dic59—21no—
201C22×Dic59—21no—
202C22×Dic59—21no—
203C22×Dic59—21no—
204C22×Dic59—24no—
205C22×Dic59—44no—
206C2×Dic118—22no—
207C2×Dic118—22no—
208C2×Dic118—22no—
209C2×Dic118—22no—
210C2×Dic118—24no—
211C2×Dic118—21no—
212C2×Dic118—21no—
213C2×Dic118—44no—
214C2×Dic118C2412yes—
215C2×Dic118C2412yes—
216M16×C59—28no—
217C2×C8×C59—22no—
218C2×C8×C59—22no—
219C2×C8×C59—22no—
220C2×C8×C59—28no—
221C2×C8×C59#4114yes—
222C2×C8×C59C2412yes—
223C2×C8×C59C2412yes—
224C2×C8×C59C2412yes—
225C2×C8×C59C2412yes—
226C4⋊C4×C59C2×D414yes—
227C22⋊C4×C59C2×D414yes—
228C22⋊C4×C59C2×D414yes—
229C42×C59C2×D412yes—
230C42×C59C2412yes—
231C22⋊Dic59—24no—
232C22⋊Dic59—24no—
233C22⋊Dic59—24no—
234C22⋊Dic59—24no—
235C22⋊Dic59—24no—
236C22⋊Dic59—24no—
237C22⋊Dic59—24no—
238C4⋊Dic59—21no—
239C4⋊Dic59—21no—
240C4⋊Dic59—24no—
241C4⋊Dic59—24no—
242C4⋊Dic59—21no—
243C4⋊Dic59—21no—
244C4⋊Dic59—21no—
245C4⋊Dic59—21no—
246C4⋊Dic59C2412yes—
247C4⋊Dic59C2412yes—
248C4⋊Dic59C2412yes—
249C4⋊Dic59C2412yes—
250C4⋊Dic59C2412yes—
251C4⋊Dic59C2412yes—
252Dic59⋊C4—24no—
253Dic59⋊C4—24no—
254Dic59⋊C4—24no—
255Dic59⋊C4—24no—
256Dic59⋊C4—24no—
257Dic59⋊C4—24no—
258Dic59⋊C4—24no—
259Dic59⋊C4—24no—
260C4×Dic59—24no—
261C4×Dic59—24no—
262C4×Dic59—24no—
263C4×Dic59—24no—
264C4×Dic59—24no—
265Dic236—28no—
266C23×C59—22no—
267C23×C59—22no—
268C23×C59—22no—
269C23×C59—22no—
270C23×C59—22no—
271C23×C59—22no—
272C23×C59C22×D412yes—
273C23×C59C22×D412yes—
274C23×C59C22×D411yescharacteristic
275D4×C59—44no—
276C2×C4×C59—22no—
277C2×C4×C59—22no—
278C2×C4×C59—22no—
279C2×C4×C59—22no—
280C2×C4×C59—24no—
281C2×C4×C59—24no—
282C2×C4×C59—22no—
283C2×C4×C59—22no—
284C2×C4×C59—22no—
285C2×C4×C59—22no—
286C2×C4×C59C22×D412yes—
287C2×C4×C59C22×D412yes—
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—22no—
302C2×Dic59—48no—
303C2×Dic59—42no—
304C2×Dic59—42no—
305C2×Dic59—42no—
306C2×Dic59—42no—
307C2×Dic59—42no—
308C2×Dic59—42no—
309C2×Dic59—42no—
310C2×Dic59—42no—
311Dic118—22no—
312Dic118—22no—
313Dic118—22no—
314Dic118—22no—
315Dic118—48no—
316Dic118—42no—
317Dic118—42no—
318C8×C59—22no—
319C8×C59—22no—
320C8×C59—22no—
321C8×C59C2×#4114yes—
322C2×#3349—591nomaximal, Sylow
323C22×C59—22no—
324C22×C59—22no—
325C22×C59—22no—
326C22×C59—22no—
327C22×C59—22no—
328C22×C59—22no—
329C22×C59—44no—
330C22×C59—44no—
331C22×C59#54712yes—
332C22×C59#57512yes—
333C22×C59#57812yes—
334C22×C59C23×D411yescharacteristic
335C4×C59—22no—
336C4×C59—22no—
337C4×C59—22no—
338C4×C59—22no—
339C4×C59#54712yes—
340C4×C59C22×#4111yescharacteristic
341C4×C59C2×2−1+411yescharacteristic
342Dic59—42no—
343Dic59—42no—
344Dic59—42no—
345Dic59—42no—
346Dic59—42no—
347Dic59—42no—
348Dic59—42no—
349Dic59—42no—
350C2×#556—591no—
351C2×#552—591no—
352#3349—5916no—
353C2×#501—591no—
354C2×#484—591no—
355C2×#485—591no—
356C2×#485—591no—
357C2×#485—591no—
358C2×#479—591no—
359C2×#477—591no—
360C2×#470—591no—
361C2×#467—591no—
362C2×#441—591no—
363C2×#435D5911yescharacteristic
364C2×#428—591no—
365C2×#427—591no—
366C2×C59—42no—
367C2×C59—42no—
368C2×C59#334914yescomplemented
369C2×C59C2×#54711yescharacteristic
370C2×C59C2×#57511yescharacteristic
371C2×C59C2×#57811yescharacteristic
372C22×Q16—591no—
373C22×M16C2×D5911yescharacteristic
374C23×C8C2×D5911yescharacteristic
375#556—598no—
376#556—1184no—
377#552—598no—
378#552—1184no—
379C2×C4⋊Q8—591no—
380C2×#126—1181no—
381C2×#126—1181no—
382C2×#126—1181no—
383C2×#125—591no—
384C2×#125—1181no—
385C2×#124—1181no—
386C2×#123—1181no—
387C2×C22⋊Q8—591no—
388C2×C22⋊Q8—591no—
389C2×C22⋊Q8—591no—
390C2×C22⋊Q8—591no—
391C2×C4×Q8—591no—
392C2×C4×Q8—591no—
393C2×C4×Q8—1181no—
394C2×C4×D4C2×D5911yescharacteristic
395C2×#117—591no—
396C2×#117—591no—
397C2×#117—591no—
398C2×#117—1181no—
399C22×C4⋊C4—591no—
400#501—598no—
401#485—598no—
402#485—598no—
403#485—598no—
404#484—598no—
405#479—598no—
406#477—598no—
407#470—598no—
408#467—598no—
409#441—598no—
410#435C2×D5918yes—
411#428—598no—
412#427—598no—
413C2×#107—591no—
414C2×#107—591no—
415C2×#107—591no—
416C2×#107—591no—
417C2×#107—591no—
418C2×#106—591no—
419C2×#106—591no—
420C2×#106—591no—
421C2×#106—591no—
422C2×C4⋊C8C2×D5911yescharacteristic
423C2×#103—591no—
424C2×#103—591no—
425C2×#103—591no—
426C2×#103—591no—
427C2×#103—591no—
428C2×#103—591no—
429C2×C22⋊C8C2×D5911yescharacteristic
430C2×C22⋊C8C2×D5911yescharacteristic
431C2×#97C2×D5911yescharacteristic
432C59C2×#334911yescharacteristic, complemented, Sylow
433C22×Q8—591no—
434C22×Q8—591no—
435C22×Q8—1181no—
436C22×D4D23611yescharacteristic
437C23×C4—1181no—
438C23×C4C22×D5911yescharacteristic
439C23×C4C22×D5911yescharacteristic
440C2×Q16—594no—
441C2×Q16—1184no—
442C2×M16—24no—
443C2×M16C22×D5914yes—
444C22×C8—24no—
445C22×C8C22×D5911yescharacteristic
446C22×C8C22×D5914yes—
447C22×C8C22×D5911yescharacteristic
448C22×C8C22×D5911yescharacteristic
449C22×C8C22×D5911yescharacteristic
450C4⋊Q8—594no—
451C4⋊Q8—1182no—
452#126—1188no—
453#126—1188no—
454#126—1188no—
455#125—594no—
456#125—1188no—
457#125—1182no—
458#124—1188no—
459#123—1188no—
460C22⋊Q8—594no—
461C22⋊Q8—594no—
462C22⋊Q8—594no—
463C22⋊Q8—594no—
464C22⋊Q8—1182no—
465C22⋊Q8—1182no—
466C22⋊Q8—1182no—
467C22⋊Q8—1182no—
468C4×Q8—594no—
469C4×Q8—594no—
470C4×Q8—1188no—
471C4×Q8—1182no—
472C4×Q8—1182no—
473C4×D4D23614yes—
474C4×D4C22×D5914yes—
475#117—594no—
476#117—594no—
477#117—594no—
478#117—1182no—
479#117—1182no—
480#117—1182no—
481#117—1188no—
482C2×C4⋊C4—591no—
483C2×C4⋊C4—591no—
484C2×C4⋊C4—594no—
485C2×C4⋊C4—591no—
486C2×C4⋊C4—591no—
487C2×C4⋊C4—591no—
488C2×C4⋊C4—591no—
489C2×C4⋊C4—1181no—
490C2×C4⋊C4—1182no—
491C2×C4⋊C4—1181no—
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⋊C4D23611yescharacteristic
501C2×C22⋊C4—1181no—
502C2×C22⋊C4—1181no—
503C2×C22⋊C4—1181no—
504C2×C22⋊C4—1181no—
505C2×C22⋊C4—1181no—
506C2×C22⋊C4—1181no—
507C2×C22⋊C4—1181no—
508C2×C22⋊C4D23611yescharacteristic
509C2×C22⋊C4D23611yescharacteristic
510C2×C42—1181no—
511C2×C42—1181no—
512C2×C42—1181no—
513C2×C42—1181no—
514C2×C42—1181no—
515C2×C42C22×D5911yescharacteristic
516#107—594no—
517#107—594no—
518#107—594no—
519#107—594no—
520#107—594no—
521#106—594no—
522#106—594no—
523#106—594no—
524#106—594no—
525C4⋊C8C22×D5914yes—
526#103—594no—
527#103—594no—
528#103—594no—
529#103—594no—
530#103—594no—
531#103—594no—
532C22⋊C8C22×D5914yes—
533C22⋊C8C22×D5914yes—
534#97C22×D5914yes—
535C24C2×D23611yescharacteristic
536C24C2×D23611yescharacteristic
537C2×Q8—592no—
538C2×Q8—592no—
539C2×Q8—1181no—
540C2×Q8—1181no—
541C2×Q8—1184no—
542C2×Q8—1182no—
543C2×Q8—1182no—
544C2×Q8—1182no—
545C2×Q8—1182no—
546C2×Q8—2364no—
547C2×D4—42no—
548C2×D4C2×D23614yes—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—1184no—
554C22×C4—1181no—
555C22×C4—1181no—
556C22×C4—1181no—
557C22×C4—1181no—
558C22×C4—1181no—
559C22×C4—1181no—
560C22×C4—1181no—
561C22×C4—1181no—
562C22×C4—2364no—
563C22×C4C2×D23612yes—
564C22×C4C2×D23612yes—
565C22×C4C2×D23611yescharacteristic
566C22×C4C2×D23611yescharacteristic
567C22×C4C2×D23611yescharacteristic
568C22×C4C2×D23611yescharacteristic
569C22×C4C23×D5912yes—
570C22×C4C23×D5912yes—
571C22×C4C23×D5911yescharacteristic
572Q16—1188no—
573M16—28no—
574C2×C8—22no—
575C2×C8—22no—
576C2×C8—22no—
577C2×C8—28no—
578C2×C8#1174568714yes—
579C2×C8C23×D5912yes—
580C2×C8C23×D5912yes—
581C2×C8C23×D5912yes—
582C2×C8C23×D5912yes—
583C4⋊C4—592no—
584C4⋊C4—592no—
585C4⋊C4—592no—
586C4⋊C4—592no—
587C4⋊C4—592no—
588C4⋊C4—592no—
589C4⋊C4—1181no—
590C4⋊C4—1181no—
591C4⋊C4—1184no—
592C4⋊C4—1181no—
593C4⋊C4—1181no—
594C4⋊C4—1181no—
595C4⋊C4—1181no—
596C4⋊C4—1184no—
597C4⋊C4—1184no—
598C4⋊C4—1184no—
599C4⋊C4—1184no—
600C4⋊C4—1184no—
601C4⋊C4—1184no—
602C4⋊C4—1184no—
603C4⋊C4—1184no—
604C4⋊C4—1184no—
605C4⋊C4C2×D23614yes—
606C22⋊C4—1184no—
607C22⋊C4—1184no—
608C22⋊C4—1184no—
609C22⋊C4—1184no—
610C22⋊C4—1184no—
611C22⋊C4—1184no—
612C22⋊C4—1184no—
613C22⋊C4C2×D23614yes—
614C22⋊C4C2×D23614yes—
615C42—1184no—
616C42—1184no—
617C42—1184no—
618C42—1184no—
619C42—1184no—
620C42C2×D23612yes—
621C42C23×D5912yes—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23C22×D23612yes—
629C23C22×D23612yes—
630C23C22×D23611yescharacteristic
631Q8—1182no—
632Q8—1182no—
633Q8—1182no—
634Q8—1182no—
635Q8—2368no—
636Q8—2362no—
637Q8—2362no—
638D4—44no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—24no—
648C2×C4—24no—
649C2×C4—1182no—
650C2×C4—1182no—
651C2×C4—1182no—
652C2×C4—1182no—
653C2×C4—1182no—
654C2×C4—1182no—
655C2×C4—1182no—
656C2×C4—1182no—
657C2×C4—2368no—
658C2×C4—2362no—
659C2×C4—2362no—
660C2×C4—2362no—
661C2×C4—2362no—
662C2×C4—2362no—
663C2×C4—2362no—
664C2×C4—2362no—
665C2×C4—2362no—
666C2×C4C22×D23612yes—
667C2×C4C22×D23612yes—
668C2×C4C22×D23612yes—
669C2×C4C22×D23612yes—
670C2×C4C22×D23611yescharacteristic
671C2×C4C2×#1174568712yes—
672C2×C4#1427377412yes—
673C2×C4C24×D5911yescharacteristic
674C8—22no—
675C8—22no—
676C8—22no—
677C8C2×#1174568714yes—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—22no—
682C22—22no—
683C22—22no—
684C22—44no—
685C22—44no—
686C22#1683805612yes—
687C22#1683820212yes—
688C22#1683821912yes—
689C22C23×D23611yescharacteristic
690C4—22no—
691C4—22no—
692C4—22no—
693C4—22no—
694C4—2362no—
695C4—2362no—
696C4—2362no—
697C4—2362no—
698C4—2362no—
699C4—2362no—
700C4—2362no—
701C4—2362no—
702C4#1683805612yes—
703C4C22×#1174568711yescharacteristic
704C4C2×#1427377411yescharacteristic
705C2—42no—
706C2—42no—
707C2#2143662814yesdirect product factor
708C2C2×#1683805611yescharacteristic
709C2C2×#1683820211yescharacteristic
710C2C2×#1683821911yescharacteristic
subgroupG/H
centerC23C22×D236
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#435C2
socleC23×C59C22×D4
prime radicalC22×D4×C59D4
hypercenterC2×#435D59
hypocenterC59C2×#3349
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
3. #21436628C2direct (N × H)
4. C2×#16837811C2semidirect
5. C2×#16837738C2semidirect
6. C2×#16837744C2semidirect
7. C2×#16837744C2semidirect
8. C2×#16837744C2semidirect
9. C2×#16837710C2semidirect
10. C2×#16837698C2semidirect
11. C2×#16837660C2semidirect
12. C2×#16837643C2semidirect
13. C2×#16837510C2semidirect
14. C2×#16837444C2semidirect
15. C2×#16837440C2semidirect
42. #16837811C22semidirect
43. #16837744C22semidirect
44. #16837744C22semidirect
45. #16837744C22semidirect
46. #16837738C22semidirect
47. #16837710C22semidirect
48. #16837698C22semidirect
49. #16837660C22semidirect
50. #16837643C22semidirect
51. #16837510C22semidirect
52. #16837444C22semidirect
53. #16837440C22semidirect
368. C2×C59#3349semidirect
432. C59C2×#3349semidirect
707. C2#21436628direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168381222
C2×#168380922
#214366282
C2×#168378112
C2×#168377382
C2×#168377442
C2×#168377102
C2×#168376982
C2×#168376602
C2×#168376432
C2×#168375102
C2×#168374442
C2×#168374402
C2×C59×#4352
C2×#334959