Finite Group Databasebeta

← C2×#21428305 #28757185

Subgroups — C2×#21428305 #28757185

Order 15104.

2638 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14273720C211yesmaximal, characteristic
2C22×#14273683C211yesmaximal, characteristic
3#21428305C2116yesmaximal, direct product factor
4C2×#16837336C211yesmaximal, characteristic, complemented
5C2×#16837336C211yesmaximal, characteristic, complemented
6C2×#16837330C211yesmaximal, characteristic
7C2×#16837299C211yesmaximal, characteristic, complemented
8C2×#16837298C211yesmaximal, characteristic, complemented
9C2×#16837290C211yesmaximal, characteristic
10C2×#16837288C211yesmaximal, characteristic, complemented
11C2×#16837285C211yesmaximal, characteristic, complemented
12C2×#16837284C211yesmaximal, characteristic, complemented
13C2×#16837277C211yesmaximal, characteristic
14C2×#16837274C211yesmaximal, characteristic
15C2×#16837253C211yesmaximal, characteristic, complemented
16C2×C59×#397C211yesmaximal, characteristic
17C24×Dic59C2211yescharacteristic
18C2×#14273720—28no—
19C2×#14273720C2218yes—
20C2×#14273683—28no—
21C2×#14273683C2218yes—
22C22×C4⋊Dic59C2211yescharacteristic
23C22×C4⋊Dic59C2211yescharacteristic
24C22×C4⋊Dic59C2211yescharacteristic
25C22×Dic59⋊C4C2211yescharacteristic
26C22×Dic59⋊C4C2211yescharacteristic
27C22×Dic59⋊C4C2211yescharacteristic
28C22×Dic59⋊C4C2211yescharacteristic
29C22×Dic59⋊C4C2211yescharacteristic
30C22×Dic59⋊C4C2211yescharacteristic
31C22×Dic59⋊C4C2211yescharacteristic
32C22×Dic59⋊C4C2211yescharacteristic
33C22×C22⋊Dic59C2211yescharacteristic
34C22×C22⋊Dic59C2211yescharacteristic
35C22×C22⋊Dic59C2211yescharacteristic
36C22×C4×Dic59C2211yescharacteristic
37C22×C4×Dic59C2211yescharacteristic
38C22×C4×Dic59C2211yescharacteristic
39C22×C4×Dic59C2211yescharacteristic
40#16837336C2218yescomplemented
41#16837336C2218yescomplemented
42#16837330C2218yes—
43#16837299C2218yescomplemented
44#16837298C2218yescomplemented
45#16837290C2218yes—
46#16837288C2218yescomplemented
47#16837285C2218yescomplemented
48#16837284C2218yescomplemented
49#16837277C2218yes—
50#16837274C2218yes—
51#16837253C2218yescomplemented
52C2×C59⋊#95C2211yescharacteristic
53C2×C59⋊#95C2211yescharacteristic
54C2×C59⋊#95C2211yescharacteristic
55C2×C59⋊#95C2211yescharacteristic
56C2×C59⋊#95C2211yescharacteristic
57C2×C59⋊#95C2211yescharacteristic
58C2×C59⋊#95C2211yescharacteristic
59C2×C59⋊#95C2211yescharacteristic
60C2×C59⋊#95C2211yescharacteristic
61C22×C4⋊C4×C59C2211yescharacteristic
62C22×C22⋊C4×C59C2211yescharacteristic
63C22×C22⋊C4×C59C2211yescharacteristic
64C22×C22⋊C4×C59C2211yescharacteristic
65C59×#397C2218yes—
66C2×#95×C59C2211yescharacteristic
67C2×#95×C59C2211yescharacteristic
68C2×#95×C59C2211yescharacteristic
69C23×Dic59—24no—
70C23×Dic59—24no—
71C23×Dic59—24no—
72C23×Dic59C2314yes—
73C23×Dic59C2311yescharacteristic
74C23×Dic59C2311yescharacteristic
75C23×Dic59C2311yescharacteristic
76C23×Dic59C2311yescharacteristic
77C23×Dic59C2311yescharacteristic
78C23×Dic59C2311yescharacteristic
79C23×Dic59C2311yescharacteristic
80C23×Dic59C2311yescharacteristic
81#14273720—232no—
82#14273683—232no—
83C2×C4⋊Dic59—24no—
84C2×C4⋊Dic59—24no—
85C2×C4⋊Dic59—24no—
86C2×C4⋊Dic59C2314yes—
87C2×C4⋊Dic59C2314yes—
88C2×C4⋊Dic59C2314yes—
89C2×Dic59⋊C4—24no—
90C2×Dic59⋊C4—24no—
91C2×Dic59⋊C4—24no—
92C2×Dic59⋊C4—24no—
93C2×Dic59⋊C4—24no—
94C2×Dic59⋊C4—24no—
95C2×Dic59⋊C4—24no—
96C2×Dic59⋊C4—24no—
97C2×Dic59⋊C4C2314yes—
98C2×Dic59⋊C4C2314yes—
99C2×Dic59⋊C4C2314yes—
100C2×Dic59⋊C4C2314yes—
101C2×Dic59⋊C4C2314yes—
102C2×Dic59⋊C4C2314yes—
103C2×Dic59⋊C4C2314yes—
104C2×Dic59⋊C4C2314yes—
105C2×C22⋊Dic59—24no—
106C2×C22⋊Dic59—24no—
107C2×C22⋊Dic59D418yes—
108C2×C22⋊Dic59C2314yes—
109C2×C22⋊Dic59C2314yes—
110C2×C22⋊Dic59C2314yes—
111C2×C4×Dic59—24no—
112C2×C4×Dic59—24no—
113C2×C4×Dic59—24no—
114C2×C4×Dic59—24no—
115C2×C4×Dic59C2314yes—
116C2×C4×Dic59C2314yes—
117C2×C4×Dic59C2314yes—
118C2×C4×Dic59C2314yes—
119C59⋊#95C2314yes—
120C59⋊#95C2314yes—
121C59⋊#95C2314yes—
122C59⋊#95C2314yes—
123C59⋊#95C2314yes—
124C59⋊#95C2314yes—
125C59⋊#95C2314yes—
126C59⋊#95C2314yes—
127C59⋊#95C2314yes—
128C25×C59C2311yescharacteristic
129C23×C4×C59C2311yescharacteristic
130C23×C4×C59C2311yescharacteristic
131C23×C4×C59C2311yescharacteristic
132C23×C4×C59C2311yescharacteristic
133C23×C4×C59C2311yescharacteristic
134C23×C4×C59C2311yescharacteristic
135C2×C4⋊C4×C59—24no—
136C2×C4⋊C4×C59C2314yes—
137C2×C22⋊C4×C59—24no—
138C2×C22⋊C4×C59—24no—
139C2×C22⋊C4×C59—24no—
140C2×C22⋊C4×C59C2314yes—
141C2×C22⋊C4×C59C2314yes—
142C2×C22⋊C4×C59C2314yes—
143#95×C59C2314yes—
144#95×C59C2314yes—
145#95×C59C2314yes—
146C24×C59—22no—
147C24×C59—22no—
148C24×C59—22no—
149C24×C59—22no—
150C24×C59—22no—
151C24×C59—22no—
152C24×C59C2×D414yes—
153C24×C59C2412yes—
154C24×C59C2411yescharacteristic
155C22×C4×C59—22no—
156C22×C4×C59—22no—
157C22×C4×C59—22no—
158C22×C4×C59—22no—
159C22×C4×C59—22no—
160C22×C4×C59—22no—
161C22×C4×C59—22no—
162C22×C4×C59—22no—
163C22×C4×C59—22no—
164C22×C4×C59—22no—
165C22×C4×C59—22no—
166C22×C4×C59—22no—
167C22×C4×C59—22no—
168C22×C4×C59—22no—
169C22×C4×C59—22no—
170C22×C4×C59—22no—
171C22×C4×C59—22no—
172C22×C4×C59#4114yes—
173C22×C4×C59C2412yes—
174C22×C4×C59C2412yes—
175C22×C4×C59C2412yes—
176C22×C4×C59C2412yes—
177C22×C4×C59C2412yes—
178C22×C4×C59C2412yes—
179C22×Dic59—232no—
180C22×Dic59—22no—
181C22×Dic59—22no—
182C22×Dic59—28no—
183C22×Dic59—22no—
184C22×Dic59—22no—
185C22×Dic59—22no—
186C22×Dic59—22no—
187C22×Dic59—22no—
188C22×Dic59—22no—
189C22×Dic59—22no—
190C22×Dic59—22no—
191C22×Dic59—28no—
192C22×Dic59—28no—
193C22×Dic59—22no—
194C22×Dic59—22no—
195C22×Dic59—22no—
196C22×Dic59—22no—
197C22×Dic59—22no—
198C22×Dic59—22no—
199C22×Dic59—22no—
200C22×Dic59—22no—
201C22×Dic59—22no—
202C22×Dic59C2×D414yes—
203C22×Dic59C2×D414yes—
204C22×Dic59#4114yes—
205C22×Dic59#4114yes—
206C22×Dic59#4114yes—
207C22×Dic59C2412yes—
208C22×Dic59C2412yes—
209C22×Dic59C2412yes—
210C22×Dic59C2412yes—
211C22×Dic59C2412yes—
212C22×Dic59C2412yes—
213C22×Dic59C2412yes—
214C22×Dic59C2412yes—
215C4⋊C4×C59—28no—
216C22⋊C4×C59—28no—
217C22⋊C4×C59—28no—
218C22⋊C4×C59—28no—
219C22⋊Dic59—28no—
220C22⋊Dic59—28no—
221C22⋊Dic59C2×D4116yes—
222C4⋊Dic59—28no—
223C4⋊Dic59—28no—
224C4⋊Dic59—28no—
225Dic59⋊C4—28no—
226Dic59⋊C4—28no—
227Dic59⋊C4—28no—
228Dic59⋊C4—28no—
229Dic59⋊C4—28no—
230Dic59⋊C4—28no—
231Dic59⋊C4—28no—
232Dic59⋊C4—28no—
233C4×Dic59—28no—
234C4×Dic59—28no—
235C4×Dic59—28no—
236C4×Dic59—28no—
237C23×C59—28no—
238C23×C59—28no—
239C23×C59—28no—
240C23×C59—22no—
241C23×C59—22no—
242C23×C59—22no—
243C23×C59—22no—
244C23×C59—22no—
245C23×C59—22no—
246C23×C59—44no—
247C23×C59—44no—
248C23×C59—44no—
249C23×C59—44no—
250C23×C59C22×D414yes—
251C23×C59C22×D412yes—
252C23×C59C2×#4112yes—
253C23×C59C2×#4112yes—
254C23×C59C2×#4112yes—
255C23×C59C2×#4112yes—
256C23×C592−1+412yes—
257C23×C592−1+412yes—
258C23×C59C2511yescharacteristic
259C2×C4×C59—28no—
260C2×C4×C59—22no—
261C2×C4×C59—22no—
262C2×C4×C59—22no—
263C2×C4×C59—22no—
264C2×C4×C59—22no—
265C2×C4×C59—22no—
266C2×C4×C59—22no—
267C2×C4×C59—22no—
268C2×C4×C59—22no—
269C2×C4×C59—22no—
270C2×C4×C59—22no—
271C2×C4×C59—22no—
272C2×C4×C59—22no—
273C2×C4×C59—22no—
274C2×C4×C59—22no—
275C2×C4×C59—22no—
276C2×C4×C59—22no—
277C2×C4×C59—44no—
278C2×C4×C59—44no—
279C2×C4×C59—44no—
280C2×C4×C59—44no—
281C2×C4×C59—44no—
282C2×C4×C59C2×#4114yes—
283C2×Dic59—232no—
284C2×Dic59—28no—
285C2×Dic59—28no—
286C2×Dic59—28no—
287C2×Dic59—28no—
288C2×Dic59—28no—
289C2×Dic59—22no—
290C2×Dic59—22no—
291C2×Dic59—22no—
292C2×Dic59—22no—
293C2×Dic59—22no—
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—22no—
303C2×Dic59—22no—
304C2×Dic59—22no—
305C2×Dic59—22no—
306C2×Dic59—22no—
307C2×Dic59—22no—
308C2×Dic59—44no—
309C2×Dic59—44no—
310C2×Dic59—44no—
311C2×Dic59C22×D414yes—
312C2×Dic59C22×D414yes—
313C2×Dic59C2×#4114yes—
314C2×Dic59C2×#4114yes—
315C2×Dic59C2×#4114yes—
316C2×#2478—591nomaximal, Sylow
317C22×C59—24no—
318C22×C59—24no—
319C22×C59—24no—
320C22×C59—42no—
321C22×C59—42no—
322C22×C59—42no—
323C22×C59—42no—
324C22×C59—416no—
325C22×C59#52514yes—
326C22×C59#52914yes—
327C22×C59#54114yes—
328C22×C59#54714yes—
329C22×C59#54714yes—
330C22×C59#55214yes—
331C22×C59#55614yes—
332C22×C59C23×D411yescharacteristic
333C22×C59C22×#4111yescharacteristic
334C22×C59C22×#4111yescharacteristic
335C22×C59C22×#4111yescharacteristic
336C22×C59C22×#4111yescharacteristic
337C22×C59C2×2−1+411yescharacteristic
338C22×C59C2×2−1+411yescharacteristic
339C4×C59—24no—
340C4×C59—42no—
341C4×C59—42no—
342C4×C59—42no—
343C4×C59—42no—
344C4×C59—42no—
345Dic59—24no—
346Dic59—24no—
347Dic59—24no—
348Dic59—24no—
349Dic59—24no—
350Dic59—42no—
351Dic59—42no—
352Dic59—42no—
353C22×#126—591no—
354C22×#117—591no—
355#2478—5916no—
356C2×#398—591no—
357C2×#398—591no—
358C2×#397—591no—
359C2×#397D5911yescharacteristic
360C2×#389—591no—
361C2×#389—591no—
362C2×#388—591no—
363C2×#387—591no—
364C2×#387—591no—
365C2×#387—591no—
366C2×#385—591no—
367C2×#385—591no—
368C2×C4×C4⋊C4—591no—
369C2×C59—44no—
370C2×C59#247818yescomplemented
371C2×C59C2×#52511yescharacteristic
372C2×C59C2×#52911yescharacteristic
373C2×C59C2×#54111yescharacteristic
374C2×C59C2×#54711yescharacteristic
375C2×C59C2×#54711yescharacteristic
376C2×C59C2×#55211yescharacteristic
377C2×C59C2×#55611yescharacteristic
378C24×C4—591no—
379C2×#126—598no—
380C2×#126—1188no—
381C2×#117—598no—
382C2×#117—1188no—
383C22×C4⋊C4—591no—
384C22×C4⋊C4—591no—
385C22×C4⋊C4—591no—
386C22×C4⋊C4—591no—
387C22×C4⋊C4—591no—
388C22×C4⋊C4—591no—
389C22×C4⋊C4—591no—
390C22×C4⋊C4—591no—
391C22×C4⋊C4—591no—
392C22×C4⋊C4—591no—
393C22×C4⋊C4—591no—
394C22×C4⋊C4C2×D5911yescharacteristic
395C22×C22⋊C4—591no—
396C22×C22⋊C4—591no—
397C22×C22⋊C4—591no—
398C22×C22⋊C4C2×D5911yescharacteristic
399C22×C22⋊C4C2×D5911yescharacteristic
400C22×C22⋊C4C2×D5911yescharacteristic
401C22×C42—591no—
402C22×C42—591no—
403C22×C42—591no—
404C22×C42—591no—
405#398—598no—
406#398—598no—
407#397—598no—
408#397C2×D5918yes—
409#389—598no—
410#389—598no—
411#388—598no—
412#387—598no—
413#387—598no—
414#387—598no—
415#385—598no—
416#385—598no—
417C4×C4⋊C4—598no—
418C2×#95—591no—
419C2×#95—591no—
420C2×#95—591no—
421C2×#95—591no—
422C2×#95—591no—
423C2×#95—591no—
424C2×#95—591no—
425C2×#95—591no—
426C2×#95—591no—
427C2×#95C2×D5911yescharacteristic
428C2×#95C2×D5911yescharacteristic
429C2×#95C2×D5911yescharacteristic
430C59C2×#247811yescharacteristic, complemented, Sylow
431C25C22×D5911yescharacteristic
432C23×C4—591no—
433C23×C4—591no—
434C23×C4—591no—
435C23×C4—591no—
436C23×C4—591no—
437C23×C4—594no—
438C23×C4—591no—
439C23×C4—591no—
440C23×C4—591no—
441C23×C4—1184no—
442C23×C4—1184no—
443C23×C4—1184no—
444C23×C4C22×D5911yescharacteristic
445C23×C4C22×D5911yescharacteristic
446C23×C4C22×D5911yescharacteristic
447C23×C4C22×D5911yescharacteristic
448C23×C4C22×D5911yescharacteristic
449C23×C4C22×D5911yescharacteristic
450#126—11832no—
451#117—11832no—
452C2×C4⋊C4—24no—
453C2×C4⋊C4—594no—
454C2×C4⋊C4—594no—
455C2×C4⋊C4—594no—
456C2×C4⋊C4—594no—
457C2×C4⋊C4—594no—
458C2×C4⋊C4—594no—
459C2×C4⋊C4—594no—
460C2×C4⋊C4—594no—
461C2×C4⋊C4—594no—
462C2×C4⋊C4—594no—
463C2×C4⋊C4—594no—
464C2×C4⋊C4—1184no—
465C2×C4⋊C4—1184no—
466C2×C4⋊C4—1184no—
467C2×C4⋊C4—1184no—
468C2×C4⋊C4—1184no—
469C2×C4⋊C4—1184no—
470C2×C4⋊C4—1184no—
471C2×C4⋊C4—1184no—
472C2×C4⋊C4—1184no—
473C2×C4⋊C4—1184no—
474C2×C4⋊C4—1184no—
475C2×C4⋊C4C22×D5914yes—
476C2×C22⋊C4—24no—
477C2×C22⋊C4—24no—
478C2×C22⋊C4—24no—
479C2×C22⋊C4—598no—
480C2×C22⋊C4—594no—
481C2×C22⋊C4—594no—
482C2×C22⋊C4—594no—
483C2×C22⋊C4—1184no—
484C2×C22⋊C4—1184no—
485C2×C22⋊C4C22×D5914yes—
486C2×C22⋊C4C22×D5914yes—
487C2×C22⋊C4C22×D5914yes—
488C2×C42—594no—
489C2×C42—594no—
490C2×C42—594no—
491C2×C42—594no—
492C2×C42—1184no—
493C2×C42—1184no—
494C2×C42—1184no—
495C2×C42—1184no—
496#95—594no—
497#95—594no—
498#95—594no—
499#95—594no—
500#95—594no—
501#95—594no—
502#95—594no—
503#95—594no—
504#95—594no—
505#95C22×D5914yes—
506#95C22×D5914yes—
507#95C22×D5914yes—
508C24—22no—
509C24—22no—
510C24—22no—
511C24—22no—
512C24—22no—
513C24—22no—
514C24D4×D5914yes—
515C24C23×D5912yes—
516C24C23×D5911yescharacteristic
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—594no—
535C22×C4—594no—
536C22×C4—594no—
537C22×C4—594no—
538C22×C4—594no—
539C22×C4—592no—
540C22×C4—592no—
541C22×C4—592no—
542C22×C4—592no—
543C22×C4—592no—
544C22×C4—592no—
545C22×C4—592no—
546C22×C4—592no—
547C22×C4—1188no—
548C22×C4—1188no—
549C22×C4—11832no—
550C22×C4—1182no—
551C22×C4—1182no—
552C22×C4—1188no—
553C22×C4—1182no—
554C22×C4—1182no—
555C22×C4—1182no—
556C22×C4—1182no—
557C22×C4—1182no—
558C22×C4—1182no—
559C22×C4—1182no—
560C22×C4—1182no—
561C22×C4—1182no—
562C22×C4—1182no—
563C22×C4—1182no—
564C22×C4—1182no—
565C22×C4—1182no—
566C22×C4—1182no—
567C22×C4—1182no—
568C22×C4—1182no—
569C22×C4—1182no—
570C22×C4#1174568714yes—
571C22×C4C23×D5912yes—
572C22×C4C23×D5912yes—
573C22×C4C23×D5912yes—
574C22×C4C23×D5912yes—
575C22×C4C23×D5912yes—
576C22×C4C23×D5912yes—
577C4⋊C4—28no—
578C4⋊C4—1188no—
579C4⋊C4—1188no—
580C4⋊C4—1188no—
581C4⋊C4—1188no—
582C4⋊C4—1188no—
583C4⋊C4—1188no—
584C4⋊C4—1188no—
585C4⋊C4—1188no—
586C4⋊C4—1188no—
587C4⋊C4—1188no—
588C4⋊C4—1188no—
589C22⋊C4—28no—
590C22⋊C4—28no—
591C22⋊C4—28no—
592C22⋊C4—5916no—
593C22⋊C4—1188no—
594C22⋊C4—1188no—
595C42—1188no—
596C42—1188no—
597C42—1188no—
598C42—1188no—
599C23—28no—
600C23—22no—
601C23—22no—
602C23—22no—
603C23—22no—
604C23—22no—
605C23—22no—
606C23—28no—
607C23—28no—
608C23—44no—
609C23—44no—
610C23—44no—
611C23—44no—
612C23C2×D4×D5914yes—
613C23C2×D4×D5912yes—
614C23#41×D5912yes—
615C23#41×D5912yes—
616C23#41×D5912yes—
617C23C2×#1174568712yes—
618C23#1427377412yes—
619C23#1427377412yes—
620C23C24×D5911yescharacteristic
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—28no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—44no—
640C2×C4—44no—
641C2×C4—44no—
642C2×C4—44no—
643C2×C4—44no—
644C2×C4—594no—
645C2×C4—594no—
646C2×C4—594no—
647C2×C4—594no—
648C2×C4—594no—
649C2×C4—11832no—
650C2×C4—1188no—
651C2×C4—1188no—
652C2×C4—1188no—
653C2×C4—1182no—
654C2×C4—1182no—
655C2×C4—1182no—
656C2×C4—1182no—
657C2×C4—1182no—
658C2×C4—1182no—
659C2×C4—1182no—
660C2×C4—1182no—
661C2×C4—1182no—
662C2×C4—1182no—
663C2×C4—1188no—
664C2×C4—1188no—
665C2×C4—1182no—
666C2×C4—1182no—
667C2×C4—1182no—
668C2×C4—1182no—
669C2×C4—1182no—
670C2×C4—1182no—
671C2×C4—1182no—
672C2×C4—1182no—
673C2×C4—1182no—
674C2×C4—2364no—
675C2×C4—2364no—
676C2×C4—2364no—
677C2×C4C2×#1174568714yes—
678C22—24no—
679C22—24no—
680C22—24no—
681C22—42no—
682C22—416no—
683C22—42no—
684C22—42no—
685C22—42no—
686C22#1683791014yes—
687C22#1683793114yes—
688C22#1683800914yes—
689C22#1683805014yes—
690C22#1683805214yes—
691C22#1683808914yes—
692C22#1683811914yes—
693C22C22×D4×D5911yescharacteristic
694C22C2×#41×D5911yescharacteristic
695C22C2×#41×D5911yescharacteristic
696C22C2×#41×D5911yescharacteristic
697C22C22×#1174568711yescharacteristic
698C22C2×#1427377411yescharacteristic
699C22C2×#1427377411yescharacteristic
700C4—24no—
701C4—42no—
702C4—42no—
703C4—42no—
704C4—42no—
705C4—42no—
706C4—1184no—
707C4—1184no—
708C4—1184no—
709C4—1184no—
710C4—1184no—
711C4—2362no—
712C4—2362no—
713C4—2362no—
714C2—44no—
715C2#2142830518yesdirect product factor
716C2C2×#1683791011yescharacteristic
717C2C2×#1683793111yescharacteristic
718C2C2×#1683800911yescharacteristic
719C2C2×#1683805011yescharacteristic
720C2C2×#1683805211yescharacteristic
721C2C2×#1683808911yescharacteristic
722C2C2×#1683811911yescharacteristic
subgroupG/H
centerC24C23×D59
commutator, cosocleC23×C59C25
FrattiniC23C24×D59
FittingC2×C59×#397C2
socleC24×C59C24
prime radicalC25×C59C23
hypercenterC2×#397D59
hypocenterC59C2×#2478
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C24 ◁ C2×#397

Complements

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

NH ≅ G/Ntype
3. #21428305C2direct (N × H)
4. C2×#16837336C2semidirect
5. C2×#16837336C2semidirect
7. C2×#16837299C2semidirect
8. C2×#16837298C2semidirect
10. C2×#16837288C2semidirect
11. C2×#16837285C2semidirect
12. C2×#16837284C2semidirect
15. C2×#16837253C2semidirect
40. #16837336C22semidirect
41. #16837336C22semidirect
43. #16837299C22semidirect
44. #16837298C22semidirect
46. #16837288C22semidirect
47. #16837285C22semidirect
48. #16837284C22semidirect
51. #16837253C22semidirect
370. C2×C59#2478semidirect
430. C59C2×#2478semidirect
715. C2#21428305direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#142737202
C22×#142736832
#214283052
C2×#168373362
C2×#168373302
C2×#168372992
C2×#168372982
C2×#168372902
C2×#168372882
C2×#168372852
C2×#168372842
C2×#168372772
C2×#168372742
C2×#168372532
C2×C59×#3972
C2×#247859