Finite Group Databasebeta

← C2×#21430261 #28755488

Subgroups — C2×#21430261 #28755488

Order 15104.

2354 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14273720C211yesmaximal, characteristic
2C22×#14273717C211yesmaximal, characteristic, complemented
3#21430261C2116yesmaximal, direct product factor
4C2×#16837343C211yesmaximal, characteristic, complemented
5C2×#16837338C211yesmaximal, characteristic
6C2×#16837336C211yesmaximal, characteristic, complemented
7C2×#16837336C211yesmaximal, characteristic, complemented
8C2×#16837334C211yesmaximal, characteristic, complemented
9C2×#16837330C211yesmaximal, characteristic
10C2×#16837325C211yesmaximal, characteristic
11C2×#16837325C211yesmaximal, characteristic
12C2×#16837300C211yesmaximal, characteristic, complemented
13C2×#16837297C211yesmaximal, characteristic, complemented
14C2×#16837296C211yesmaximal, characteristic
15C2×C4×Dic59⋊C4C211yesmaximal, characteristic, complemented
16C2×C59×#388C211yesmaximal, characteristic
17C2×#14273720—28no—
18C2×#14273720C2218yes—
19C2×#14273717—28no—
20C2×#14273717C2218yescomplemented
21C22×C4⋊Dic59C2211yescharacteristic
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×Dic59⋊C4C2211yescharacteristic
34C22×Dic59⋊C4C2211yescharacteristic
35C22×C22⋊Dic59C2211yescharacteristic
36C22×C22⋊Dic59C2211yescharacteristic
37C22×C22⋊Dic59C2211yescharacteristic
38C22×C22⋊Dic59C2211yescharacteristic
39C22×C4×Dic59C2211yescharacteristic
40C22×C4×Dic59C2211yescharacteristic
41#16837343C2218yescomplemented
42#16837338C2218yes—
43#16837336C2218yescomplemented
44#16837336C2218yescomplemented
45#16837334C2218yescomplemented
46#16837330C2218yes—
47#16837325C2218yes—
48#16837325C2218yes—
49#16837300C2218yescomplemented
50#16837297C2218yescomplemented
51#16837296C2218yes—
52C4×Dic59⋊C4C2218yescomplemented
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
65C22×C42×C59C2211yescharacteristic
66C59×#388C2218yes—
67C2×#95×C59C2211yescharacteristic
68C2×#95×C59C2211yescharacteristic
69C23×Dic59C2311yescharacteristic
70C23×Dic59C2311yescharacteristic
71C23×Dic59C2311yescharacteristic
72C23×Dic59C2311yescharacteristic
73C23×Dic59C2311yescharacteristic
74C23×Dic59C2311yescharacteristic
75C23×Dic59C2311yescharacteristic
76C23×Dic59C2311yescharacteristic
77#14273720—232no—
78#14273717—232no—
79C2×C4⋊Dic59—24no—
80C2×C4⋊Dic59—24no—
81C2×C4⋊Dic59—24no—
82C2×C4⋊Dic59—42no—
83C2×C4⋊Dic59C2314yes—
84C2×C4⋊Dic59C2314yes—
85C2×C4⋊Dic59C2314yes—
86C2×C4⋊Dic59C2314yes—
87C2×Dic59⋊C4—24no—
88C2×Dic59⋊C4—24no—
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—42no—
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×Dic59⋊C4C2314yes—
106C2×Dic59⋊C4C2314yes—
107C2×C22⋊Dic59—24no—
108C2×C22⋊Dic59—24no—
109C2×C22⋊Dic59—24no—
110C2×C22⋊Dic59—42no—
111C2×C22⋊Dic59C2314yes—
112C2×C22⋊Dic59C2314yes—
113C2×C22⋊Dic59C2314yes—
114C2×C22⋊Dic59C2314yes—
115C2×C4×Dic59—42no—
116C2×C4×Dic59D418yes—
117C2×C4×Dic59C2314yes—
118C2×C4×Dic59C2314yes—
119C59⋊#95C2314yes—
120C59⋊#95C2314yes—
121C59⋊#95C2314yes—
122C59⋊#95C2314yes—
123C59⋊#95C2314yes—
124C59⋊#95C2314yes—
125C59⋊#95C2314yes—
126C59⋊#95C2314yes—
127C25×C59C2311yescharacteristic
128C23×C4×C59C2311yescharacteristic
129C23×C4×C59C2311yescharacteristic
130C23×C4×C59C2311yescharacteristic
131C23×C4×C59C2311yescharacteristic
132C23×C4×C59C2311yescharacteristic
133C23×C4×C59C2311yescharacteristic
134C2×C4⋊C4×C59—24no—
135C2×C4⋊C4×C59C2314yes—
136C2×C22⋊C4×C59—24no—
137C2×C22⋊C4×C59—24no—
138C2×C22⋊C4×C59—42no—
139C2×C22⋊C4×C59C2314yes—
140C2×C22⋊C4×C59C2314yes—
141C2×C22⋊C4×C59C2314yes—
142C2×C42×C59—42no—
143C2×C42×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×C59—22no—
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×C59C2×D414yes—
172C22×C4×C59#4114yes—
173C22×C4×C59C2412yes—
174C22×C4×C59C2412yes—
175C22×C4×C59C2412yes—
176C22×C4×C59C2412yes—
177C22×C4×C59C2412yes—
178C22×C4×C59C2412yes—
179C22×Dic59—22no—
180C22×Dic59—22no—
181C22×Dic59—22no—
182C22×Dic59—22no—
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—22no—
192C22×Dic59—22no—
193C22×Dic59—22no—
194C22×Dic59—22no—
195C22×Dic59—22no—
196C22×Dic59—22no—
197C22×Dic59—22no—
198C22×Dic59—22no—
199C22×Dic59—22no—
200C22×Dic59C2×D414yes—
201C22×Dic59C2×D414yes—
202C22×Dic59#4114yes—
203C22×Dic59C2412yes—
204C22×Dic59C2412yes—
205C22×Dic59C2412yes—
206C22×Dic59C2412yes—
207C22×Dic59C2412yes—
208C22×Dic59C2412yes—
209C22×Dic59C2412yes—
210C22×Dic59C2412yes—
211C4⋊C4×C59—28no—
212C22⋊C4×C59—28no—
213C22⋊C4×C59—28no—
214C22⋊C4×C59—44no—
215C42×C59—44no—
216C22⋊Dic59—28no—
217C22⋊Dic59—28no—
218C22⋊Dic59—28no—
219C22⋊Dic59—44no—
220C4⋊Dic59—28no—
221C4⋊Dic59—28no—
222C4⋊Dic59—28no—
223C4⋊Dic59—44no—
224Dic59⋊C4—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—
233Dic59⋊C4—44no—
234C4×Dic59—44no—
235C4×Dic59C2×D4116yes—
236C23×C59—22no—
237C23×C59—22no—
238C23×C59—22no—
239C23×C59—22no—
240C23×C59—22no—
241C23×C59—22no—
242C23×C59—22no—
243C23×C59—44no—
244C23×C59—44no—
245C23×C59—44no—
246C23×C59—44no—
247C23×C59—44no—
248C23×C59—44no—
249C23×C59—44no—
250C23×C59C22×D412yes—
251C23×C59C2×#4112yes—
252C23×C59C2×#4112yes—
253C23×C59H(5,𝔽2)12yes—
254C23×C592−1+412yes—
255C23×C592−1+412yes—
256C23×C592−1+412yes—
257C23×C59C2511yescharacteristic
258C2×C4×C59—28no—
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—44no—
277C2×C4×C59—44no—
278C2×C4×C59—44no—
279C2×C4×C59—44no—
280C2×C4×C59C22×D414yes—
281C2×C4×C59C2×#4114yes—
282C2×Dic59—28no—
283C2×Dic59—28no—
284C2×Dic59—28no—
285C2×Dic59—22no—
286C2×Dic59—22no—
287C2×Dic59—22no—
288C2×Dic59—22no—
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—44no—
307C2×Dic59—44no—
308C2×Dic59—44no—
309C2×Dic59—44no—
310C2×Dic59—44no—
311C2×Dic59C22×D414yes—
312C2×Dic59C22×D414yes—
313C2×Dic59C2×#4114yes—
314C2×#2664—591nomaximal, Sylow
315C22×C59—42no—
316C22×C59—42no—
317C22×C59—42no—
318C22×C59—42no—
319C22×C59—42no—
320C22×C59—42no—
321C22×C59—42no—
322C22×C59—88no—
323C22×C59#53214yes—
324C22×C59#53614yes—
325C22×C59#53714yes—
326C22×C59#53914yes—
327C22×C59#53914yes—
328C22×C59#54114yes—
329C22×C59#54114yes—
330C22×C59C23×D411yescharacteristic
331C22×C59C22×#4111yescharacteristic
332C22×C59C22×#4111yescharacteristic
333C22×C59C2×H(5,𝔽2)11yescharacteristic
334C22×C59C2×2−1+411yescharacteristic
335C22×C59C2×2−1+411yescharacteristic
336C22×C59C2×2−1+411yescharacteristic
337C4×C59—24no—
338C4×C59—24no—
339C4×C59—42no—
340C4×C59—42no—
341C4×C59—42no—
342C4×C59—42no—
343Dic59—24no—
344Dic59—24no—
345Dic59—24no—
346Dic59—42no—
347Dic59—42no—
348Dic59—42no—
349Dic59—42no—
350Dic59—42no—
351C22×#126—591no—
352C22×#125—591no—
353#2664—5916no—
354C2×#400—591no—
355C2×#399—591no—
356C2×#398—591no—
357C2×#398—591no—
358C2×#398—591no—
359C2×#397—591no—
360C2×#396—591no—
361C2×#396—591no—
362C2×#389—591no—
363C2×#389—591no—
364C2×#388—591no—
365C2×#388D5911yescharacteristic
366C2×C4×C4⋊C4—591no—
367C2×C59—82no—
368C2×C59#266418yescomplemented
369C2×C59C2×#53211yescharacteristic
370C2×C59C2×#53611yescharacteristic
371C2×C59C2×#53711yescharacteristic
372C2×C59C2×#53911yescharacteristic
373C2×C59C2×#53911yescharacteristic
374C2×C59C2×#54111yescharacteristic
375C2×C59C2×#54111yescharacteristic
376C2×#126—598no—
377C2×#126—1188no—
378C2×#125—598no—
379C2×#125—1188no—
380C22×C4⋊C4—591no—
381C22×C4⋊C4—591no—
382C22×C4⋊C4—591no—
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⋊C4—591no—
399C22×C22⋊C4C2×D5911yescharacteristic
400C22×C22⋊C4C2×D5911yescharacteristic
401C22×C22⋊C4C2×D5911yescharacteristic
402C22×C42—591no—
403C22×C42—591no—
404C22×C42C2×D5911yescharacteristic
405#400—598no—
406#399—598no—
407#398—598no—
408#398—598no—
409#398—598no—
410#397—598no—
411#396—598no—
412#396—598no—
413#389—598no—
414#389—598no—
415#388—598no—
416#388C2×D5918yes—
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×#95C2×D5911yescharacteristic
427C2×#95C2×D5911yescharacteristic
428C59C2×#266411yescharacteristic, complemented, Sylow
429C25C22×D5911yescharacteristic
430C23×C4—591no—
431C23×C4—591no—
432C23×C4—591no—
433C23×C4—591no—
434C23×C4—591no—
435C23×C4—591no—
436C23×C4—591no—
437C23×C4—591no—
438C23×C4C22×D5911yescharacteristic
439C23×C4C22×D5911yescharacteristic
440C23×C4C22×D5911yescharacteristic
441C23×C4C22×D5911yescharacteristic
442C23×C4C22×D5911yescharacteristic
443C23×C4C22×D5911yescharacteristic
444#126—11832no—
445#125—11832no—
446C2×C4⋊C4—24no—
447C2×C4⋊C4—594no—
448C2×C4⋊C4—594no—
449C2×C4⋊C4—594no—
450C2×C4⋊C4—594no—
451C2×C4⋊C4—594no—
452C2×C4⋊C4—594no—
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—1184no—
462C2×C4⋊C4—1184no—
463C2×C4⋊C4—1184no—
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—2362no—
474C2×C4⋊C4—2362no—
475C2×C4⋊C4C22×D5914yes—
476C2×C22⋊C4—24no—
477C2×C22⋊C4—24no—
478C2×C22⋊C4—42no—
479C2×C22⋊C4—594no—
480C2×C22⋊C4—594no—
481C2×C22⋊C4—594no—
482C2×C22⋊C4—594no—
483C2×C22⋊C4—1184no—
484C2×C22⋊C4—1184no—
485C2×C22⋊C4—1184no—
486C2×C22⋊C4—2362no—
487C2×C22⋊C4C22×D5914yes—
488C2×C22⋊C4C22×D5914yes—
489C2×C22⋊C4C22×D5914yes—
490C2×C42—42no—
491C2×C42—598no—
492C2×C42—594no—
493C2×C42—594no—
494C2×C42—2362no—
495C2×C42C22×D5914yes—
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#95C22×D5914yes—
505#95C22×D5914yes—
506C24—22no—
507C24—22no—
508C24—22no—
509C24—22no—
510C24—22no—
511C24—22no—
512C24—22no—
513C24C23×D5912yes—
514C24C23×D5911yescharacteristic
515C22×C4—22no—
516C22×C4—22no—
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—594no—
532C22×C4—594no—
533C22×C4—594no—
534C22×C4—592no—
535C22×C4—592no—
536C22×C4—592no—
537C22×C4—592no—
538C22×C4—592no—
539C22×C4—592no—
540C22×C4—592no—
541C22×C4—592no—
542C22×C4—1182no—
543C22×C4—1182no—
544C22×C4—1182no—
545C22×C4—1182no—
546C22×C4—1182no—
547C22×C4—1182no—
548C22×C4—1182no—
549C22×C4—1182no—
550C22×C4—1182no—
551C22×C4—1182no—
552C22×C4—1182no—
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#1174568514yes—
564C22×C4D4×D5914yes—
565C22×C4C23×D5912yes—
566C22×C4C23×D5912yes—
567C22×C4C23×D5912yes—
568C22×C4C23×D5912yes—
569C22×C4C23×D5912yes—
570C22×C4C23×D5912yes—
571C4⋊C4—28no—
572C4⋊C4—1188no—
573C4⋊C4—1188no—
574C4⋊C4—1188no—
575C4⋊C4—1188no—
576C4⋊C4—1188no—
577C4⋊C4—1188no—
578C4⋊C4—1188no—
579C4⋊C4—1188no—
580C4⋊C4—1188no—
581C4⋊C4—1188no—
582C4⋊C4—1188no—
583C4⋊C4—1188no—
584C4⋊C4—2364no—
585C4⋊C4—2364no—
586C22⋊C4—28no—
587C22⋊C4—28no—
588C22⋊C4—44no—
589C22⋊C4—1188no—
590C22⋊C4—1188no—
591C22⋊C4—1188no—
592C22⋊C4—2364no—
593C42—44no—
594C42—5916no—
595C42—2364no—
596C23—22no—
597C23—22no—
598C23—22no—
599C23—22no—
600C23—22no—
601C23—22no—
602C23—22no—
603C23—44no—
604C23—44no—
605C23—44no—
606C23—44no—
607C23—44no—
608C23—44no—
609C23—44no—
610C23C2×D4×D5912yes—
611C23#41×D5912yes—
612C23C2×#1174568512yes—
613C23#1427377212yes—
614C23#1427377412yes—
615C23#1427377412yes—
616C23#1427377412yes—
617C23C24×D5911yescharacteristic
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—28no—
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—44no—
637C2×C4—44no—
638C2×C4—44no—
639C2×C4—44no—
640C2×C4—594no—
641C2×C4—594no—
642C2×C4—594no—
643C2×C4—1188no—
644C2×C4—1182no—
645C2×C4—1188no—
646C2×C4—1182no—
647C2×C4—1182no—
648C2×C4—1182no—
649C2×C4—1182no—
650C2×C4—1182no—
651C2×C4—1188no—
652C2×C4—1182no—
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—1182no—
664C2×C4—1182no—
665C2×C4—1182no—
666C2×C4—1182no—
667C2×C4—2364no—
668C2×C4—2364no—
669C2×C4—2364no—
670C2×C4—2364no—
671C2×C4—2364no—
672C2×C4C2×D4×D5914yes—
673C2×C4C2×#1174568514yes—
674C22—42no—
675C22—42no—
676C22—42no—
677C22—42no—
678C22—42no—
679C22—42no—
680C22—42no—
681C22—88no—
682C22#1683794914yes—
683C22#1683797214yes—
684C22#1683797914yes—
685C22#1683799414yes—
686C22#1683799514yes—
687C22#1683800914yes—
688C22#1683801414yes—
689C22C22×D4×D5911yescharacteristic
690C22C2×#41×D5911yescharacteristic
691C22C22×#1174568511yescharacteristic
692C22C2×#1427377211yescharacteristic
693C22C2×#1427377411yescharacteristic
694C22C2×#1427377411yescharacteristic
695C22C2×#1427377411yescharacteristic
696C4—24no—
697C4—24no—
698C4—42no—
699C4—42no—
700C4—42no—
701C4—42no—
702C4—1184no—
703C4—1184no—
704C4—1184no—
705C4—2362no—
706C4—2362no—
707C4—2362no—
708C4—2362no—
709C4—2362no—
710C2—82no—
711C2#2143026118yesdirect product factor
712C2C2×#1683794911yescharacteristic
713C2C2×#1683797211yescharacteristic
714C2C2×#1683797911yescharacteristic
715C2C2×#1683799411yescharacteristic
716C2C2×#1683799511yescharacteristic
717C2C2×#1683800911yescharacteristic
718C2C2×#1683801411yescharacteristic
subgroupG/H
centerC24C23×D59
commutator, cosocleC23×C59C25
FrattiniC23C24×D59
FittingC2×C59×#388C2
socleC24×C59C24
prime radicalC25×C59C23
hypercenterC2×#388D59
hypocenterC59C2×#2664
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C22×#14273717C2semidirect
3. #21430261C2direct (N × H)
4. C2×#16837343C2semidirect
6. C2×#16837336C2semidirect
7. C2×#16837336C2semidirect
8. C2×#16837334C2semidirect
12. C2×#16837300C2semidirect
13. C2×#16837297C2semidirect
15. C2×C4×Dic59⋊C4C2semidirect
20. C2×#14273717C22semidirect
41. #16837343C22semidirect
43. #16837336C22semidirect
44. #16837336C22semidirect
45. #16837334C22semidirect
49. #16837300C22semidirect
50. #16837297C22semidirect
52. C4×Dic59⋊C4C22semidirect
368. C2×C59#2664semidirect
428. C59C2×#2664semidirect
711. C2#21430261direct (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×#142737172
#214302612
C2×#168373432
C2×#168373382
C2×#168373362
C2×#168373342
C2×#168373302
C2×#168373252
C2×#168373002
C2×#168372972
C2×#168372962
C2×C4×Dic59⋊C42
C2×C59×#3882
C2×#266459