Finite Group Databasebeta

← C2×#21429764 #28760118

Subgroups — C2×#21429764 #28760118

Order 15104.

2270 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21429764C2116yesmaximal, direct product factor
2C2×#16837324C211yesmaximal, characteristic
3C2×#16837324C211yesmaximal, characteristic
4C2×#16837324C211yesmaximal, characteristic
5C2×#16837324C211yesmaximal, characteristic
6C2×#16837301C211yesmaximal, characteristic, complemented
7C2×#16837300C211yesmaximal, characteristic, complemented
8C2×#16837297C211yesmaximal, characteristic, complemented
9C2×#16837289C211yesmaximal, characteristic, complemented
10C2×#16837288C211yesmaximal, characteristic, complemented
11C2×#16837285C211yesmaximal, characteristic, complemented
12C2×#16837283C211yesmaximal, characteristic, complemented
13C2×#16837264C211yesmaximal, characteristic
14C2×C4×(C2×D59)⋊C4C211yesmaximal, characteristic
15C2×#16837249C211yesmaximal, characteristic
16C2×C59×#389C211yesmaximal, characteristic, complemented
17C23×C4×D59C2211yescharacteristic
18C22×C4⋊Dic59C2211yescharacteristic
19C22×C4⋊Dic59C2211yescharacteristic
20C22×C4⋊Dic59C2211yescharacteristic
21C22×C4⋊Dic59C2211yescharacteristic
22C22×Dic59⋊C4C2211yescharacteristic
23C22×Dic59⋊C4C2211yescharacteristic
24C22×Dic59⋊C4C2211yescharacteristic
25C22×Dic59⋊C4C2211yescharacteristic
26C22×(C2×D59)⋊C4C2211yescharacteristic
27C22×(C2×D59)⋊C4C2211yescharacteristic
28C22×(C2×D59)⋊C4C2211yescharacteristic
29C22×(C2×D59)⋊C4C2211yescharacteristic
30C22×(C2×D59)⋊C4C2211yescharacteristic
31C22×(C2×D59)⋊C4C2211yescharacteristic
32C22×C4×Dic59C2211yescharacteristic
33C22×C4×Dic59C2211yescharacteristic
34C22×C4×Dic59C2211yescharacteristic
35#16837324C2218yes—
36#16837324C2218yes—
37#16837324C2218yes—
38#16837324C2218yes—
39#16837301C2218yescomplemented
40#16837300C2218yescomplemented
41#16837297C2218yescomplemented
42#16837289C2218yescomplemented
43#16837288C2218yescomplemented
44#16837285C2218yescomplemented
45#16837283C2218yescomplemented
46#16837264C2218yes—
47C4×(C2×D59)⋊C4C2218yes—
48#16837249C2218yes—
49C2×C59⋊#95C2211yescharacteristic
50C2×C59⋊#95C2211yescharacteristic
51C2×C59⋊#95C2211yescharacteristic
52C2×C59⋊#95C2211yescharacteristic
53C2×C59⋊#95C2211yescharacteristic
54C2×C59⋊#95C2211yescharacteristic
55C2×C59⋊#95C2211yescharacteristic
56C2×C59⋊#95C2211yescharacteristic
57C2×C59⋊#95C2211yescharacteristic
58C2×C59⋊#95C2211yescharacteristic
59C22×C4⋊C4×C59C2211yescharacteristic
60C22×C4⋊C4×C59C2211yescharacteristic
61C22×C4⋊C4×C59C2211yescharacteristic
62C22×C4⋊C4×C59C2211yescharacteristic
63C22×C42×C59C2211yescharacteristic
64C59×#389C2218yescomplemented
65C2×#95×C59C2211yescharacteristic
66C2×#95×C59C2211yescharacteristic
67C24×D59C2311yescharacteristic
68C23×Dic59C2311yescharacteristic
69C23×Dic59C2311yescharacteristic
70C23×Dic59C2311yescharacteristic
71C23×Dic59C2311yescharacteristic
72C23×Dic59C2311yescharacteristic
73C23×Dic59C2311yescharacteristic
74C23×Dic59C2311yescharacteristic
75C22×C4×D59—42no—
76C22×C4×D59—42no—
77C22×C4×D59Q818yes—
78C22×C4×D59C2314yes—
79C2×C4⋊Dic59—24no—
80C2×C4⋊Dic59—24no—
81C2×C4⋊Dic59—42no—
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—42no—
91C2×Dic59⋊C4C2314yes—
92C2×Dic59⋊C4C2314yes—
93C2×Dic59⋊C4C2314yes—
94C2×Dic59⋊C4C2314yes—
95C2×(C2×D59)⋊C4—24no—
96C2×(C2×D59)⋊C4—24no—
97C2×(C2×D59)⋊C4—24no—
98C2×(C2×D59)⋊C4—24no—
99C2×(C2×D59)⋊C4—42no—
100C2×(C2×D59)⋊C4—42no—
101C2×(C2×D59)⋊C4C2314yes—
102C2×(C2×D59)⋊C4C2314yes—
103C2×(C2×D59)⋊C4C2314yes—
104C2×(C2×D59)⋊C4C2314yes—
105C2×(C2×D59)⋊C4C2314yes—
106C2×(C2×D59)⋊C4C2314yes—
107C2×C4×Dic59—42no—
108C2×C4×Dic59—42no—
109C2×C4×Dic59—42no—
110C2×C4×Dic59C2314yes—
111C2×C4×Dic59C2314yes—
112C2×C4×Dic59C2314yes—
113C59⋊#95C2314yes—
114C59⋊#95C2314yes—
115C59⋊#95C2314yes—
116C59⋊#95C2314yes—
117C59⋊#95C2314yes—
118C59⋊#95C2314yes—
119C59⋊#95C2314yes—
120C59⋊#95C2314yes—
121C59⋊#95C2314yes—
122C59⋊#95C2314yes—
123C23×C4×C59C2311yescharacteristic
124C23×C4×C59C2311yescharacteristic
125C23×C4×C59C2311yescharacteristic
126C23×C4×C59C2311yescharacteristic
127C23×C4×C59C2311yescharacteristic
128C23×C4×C59C2311yescharacteristic
129C23×C4×C59C2311yescharacteristic
130C2×C4⋊C4×C59—24no—
131C2×C4⋊C4×C59—24no—
132C2×C4⋊C4×C59—24no—
133C2×C4⋊C4×C59—42no—
134C2×C4⋊C4×C59C2314yes—
135C2×C4⋊C4×C59C2314yes—
136C2×C4⋊C4×C59C2314yes—
137C2×C4⋊C4×C59C2314yes—
138C2×C42×C59—42no—
139C2×C42×C59C2314yes—
140#95×C59C2314yes—
141#95×C59C2314yes—
142C24×C59C2411yescharacteristic
143C23×D59—22no—
144C23×D59—22no—
145C23×D59—22no—
146C23×D59—22no—
147C23×D59—22no—
148C23×D59—22no—
149C23×D59C2×Q814yes—
150C23×D59C2412yes—
151C22×C4×C59—22no—
152C22×C4×C59—22no—
153C22×C4×C59—22no—
154C22×C4×C59—22no—
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×C59C2×Q814yes—
169C22×C4×C59#4114yes—
170C22×C4×C59#4114yes—
171C22×C4×C59#4114yes—
172C22×C4×C59C2412yes—
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×Dic59C2×Q814yes—
199C22×Dic59#4114yes—
200C22×Dic59C2412yes—
201C22×Dic59C2412yes—
202C22×Dic59C2412yes—
203C22×Dic59C2412yes—
204C22×Dic59C2412yes—
205C22×Dic59C2412yes—
206C22×Dic59C2412yes—
207C2×C4×D59—416no—
208C2×C4×D59—44no—
209C2×C4×D59—44no—
210C2×C4×D59C2×Q8116yes—
211C4⋊C4×C59—28no—
212C4⋊C4×C59—28no—
213C4⋊C4×C59—28no—
214C4⋊C4×C59—44no—
215C42×C59—44no—
216(C2×D59)⋊C4—28no—
217(C2×D59)⋊C4—28no—
218(C2×D59)⋊C4—28no—
219(C2×D59)⋊C4—28no—
220(C2×D59)⋊C4—44no—
221(C2×D59)⋊C4—44no—
222C4⋊Dic59—28no—
223C4⋊Dic59—28no—
224C4⋊Dic59—44no—
225C4⋊Dic59—44no—
226Dic59⋊C4—28no—
227Dic59⋊C4—28no—
228Dic59⋊C4—28no—
229Dic59⋊C4—44no—
230C4×Dic59—44no—
231C4×Dic59—44no—
232C4×Dic59—44no—
233C23×C59C22×Q812yes—
234C23×C59C2×#4112yes—
235C23×C59C2×#4112yes—
236C23×C59C2×#4112yes—
237C23×C59C2×#4112yes—
238C23×C59H(5,𝔽2)12yes—
239C23×C59H(5,𝔽2)12yes—
240C23×C59C2511yescharacteristic
241C22×D59—28no—
242C22×D59—28no—
243C22×D59—28no—
244C22×D59—22no—
245C22×D59—22no—
246C22×D59—22no—
247C22×D59—22no—
248C22×D59—22no—
249C22×D59—22no—
250C22×D59—44no—
251C22×D59—44no—
252C22×D59—44no—
253C22×D59—44no—
254C22×D59C22×Q814yes—
255C2×C4×C59—28no—
256C2×C4×C59—28no—
257C2×C4×C59—28no—
258C2×C4×C59—28no—
259C2×C4×C59—22no—
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×C59C22×Q814yes—
280C2×C4×C59C2×#4114yes—
281C2×C4×C59C2×#4114yes—
282C2×C4×C59C2×#4114yes—
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—44no—
305C2×Dic59—44no—
306C2×Dic59—44no—
307C2×Dic59—44no—
308C2×Dic59—44no—
309C2×Dic59C22×Q814yes—
310C2×Dic59C2×#4114yes—
311C4×D59—416no—
312C2×#2608—591nomaximal, Sylow
313C22×C59#53314yes—
314C22×C59#53314yes—
315C22×C59#54314yes—
316C22×C59#55314yes—
317C22×C59#55314yes—
318C22×C59#55314yes—
319C22×C59#55314yes—
320C22×C59C23×Q811yescharacteristic
321C22×C59C22×#4111yescharacteristic
322C22×C59C22×#4111yescharacteristic
323C22×C59C22×#4111yescharacteristic
324C22×C59C22×#4111yescharacteristic
325C22×C59C2×H(5,𝔽2)11yescharacteristic
326C22×C59C2×H(5,𝔽2)11yescharacteristic
327C2×D59—24no—
328C2×D59—24no—
329C2×D59—24no—
330C2×D59—416no—
331C2×D59—42no—
332C2×D59—42no—
333C2×D59—42no—
334C2×D59—42no—
335C4×C59—24no—
336C4×C59—24no—
337C4×C59—24no—
338C4×C59—24no—
339C4×C59—42no—
340C4×C59—42no—
341C4×C59—42no—
342Dic59—24no—
343Dic59—24no—
344Dic59—42no—
345Dic59—42no—
346Dic59—42no—
347Dic59—42no—
348Dic59—42no—
349#2608—5916no—
350C2×#396—591no—
351C2×#396—591no—
352C2×#396—591no—
353C2×#396—591no—
354C2×#389—591no—
355C2×#389—591no—
356C2×#389—591no—
357C2×#389D5911yescharacteristic, complemented
358C2×#387—591no—
359C2×#387—591no—
360C2×#387—591no—
361C2×#387—591no—
362C2×#381—591no—
363C2×C4×C22⋊C4—591no—
364C2×C4×C22⋊C4—591no—
365C2×C59#260818yescomplemented
366C2×C59C2×#53311yescharacteristic
367C2×C59C2×#53311yescharacteristic
368C2×C59C2×#54311yescharacteristic
369C2×C59C2×#55311yescharacteristic
370C2×C59C2×#55311yescharacteristic
371C2×C59C2×#55311yescharacteristic
372C2×C59C2×#55311yescharacteristic
373D59—44no—
374C24×C4—591no—
375C22×C4⋊C4—591no—
376C22×C4⋊C4—591no—
377C22×C4⋊C4—591no—
378C22×C4⋊C4—591no—
379C22×C4⋊C4—591no—
380C22×C4⋊C4—591no—
381C22×C4⋊C4—591no—
382C22×C4⋊C4—591no—
383C22×C4⋊C4C2×D5911yescharacteristic
384C22×C4⋊C4C2×D5911yescharacteristic
385C22×C4⋊C4C2×D5911yescharacteristic
386C22×C4⋊C4C2×D5911yescharacteristic
387C22×C22⋊C4—591no—
388C22×C22⋊C4—591no—
389C22×C22⋊C4—591no—
390C22×C22⋊C4—591no—
391C22×C22⋊C4—591no—
392C22×C22⋊C4—591no—
393C22×C42—591no—
394C22×C42—591no—
395C22×C42—591no—
396C22×C42C2×D5911yescharacteristic
397#396—598no—
398#396—598no—
399#396—598no—
400#396—598no—
401#389—598no—
402#389—598no—
403#389—598no—
404#389C2×D5918yescomplemented
405#387—598no—
406#387—598no—
407#387—598no—
408#387—598no—
409#381—598no—
410C4×C22⋊C4—598no—
411C4×C22⋊C4—598no—
412C2×#95—591no—
413C2×#95—591no—
414C2×#95—591no—
415C2×#95—591no—
416C2×#95—591no—
417C2×#95—591no—
418C2×#95—591no—
419C2×#95—591no—
420C2×#95—591no—
421C2×#95—591no—
422C2×#95C2×D5911yescharacteristic
423C2×#95C2×D5911yescharacteristic
424C59C2×#260811yescharacteristic, complemented, Sylow
425C25—591no—
426C23×C4—591no—
427C23×C4—591no—
428C23×C4—598no—
429C23×C4—594no—
430C23×C4—591no—
431C23×C4—591no—
432C23×C4—591no—
433C23×C4—591no—
434C23×C4—591no—
435C23×C4—2362no—
436C23×C4—2362no—
437C23×C4C22×D5911yescharacteristic
438C23×C4C22×D5911yescharacteristic
439C23×C4C22×D5911yescharacteristic
440C23×C4C22×D5911yescharacteristic
441C23×C4C22×D5911yescharacteristic
442C23×C4C22×D5911yescharacteristic
443C23×C4C22×D5911yescharacteristic
444C2×C4⋊C4—24no—
445C2×C4⋊C4—24no—
446C2×C4⋊C4—24no—
447C2×C4⋊C4—42no—
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—1184no—
457C2×C4⋊C4—1184no—
458C2×C4⋊C4—1184no—
459C2×C4⋊C4—1184no—
460C2×C4⋊C4—1184no—
461C2×C4⋊C4—2362no—
462C2×C4⋊C4—2362no—
463C2×C4⋊C4—2362no—
464C2×C4⋊C4C22×D5914yes—
465C2×C4⋊C4C22×D5914yes—
466C2×C4⋊C4C22×D5914yes—
467C2×C4⋊C4C22×D5914yes—
468C2×C22⋊C4—594no—
469C2×C22⋊C4—594no—
470C2×C22⋊C4—594no—
471C2×C22⋊C4—594no—
472C2×C22⋊C4—594no—
473C2×C22⋊C4—594no—
474C2×C22⋊C4—1184no—
475C2×C22⋊C4—1184no—
476C2×C22⋊C4—1184no—
477C2×C22⋊C4—1184no—
478C2×C22⋊C4—2362no—
479C2×C22⋊C4—2362no—
480C2×C42—42no—
481C2×C42—594no—
482C2×C42—594no—
483C2×C42—594no—
484C2×C42—2362no—
485C2×C42—2362no—
486C2×C42—2362no—
487C2×C42C22×D5914yes—
488#95—594no—
489#95—594no—
490#95—594no—
491#95—594no—
492#95—594no—
493#95—594no—
494#95—594no—
495#95—594no—
496#95—594no—
497#95—594no—
498#95C22×D5914yes—
499#95C22×D5914yes—
500C24—594no—
501C24—592no—
502C24—1182no—
503C24—1182no—
504C24—1182no—
505C24—1182no—
506C24—1182no—
507C24—1182no—
508C24C23×D5911yescharacteristic
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
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—594no—
527C22×C4—594no—
528C22×C4—592no—
529C22×C4—592no—
530C22×C4—5916no—
531C22×C4—592no—
532C22×C4—592no—
533C22×C4—592no—
534C22×C4—592no—
535C22×C4—592no—
536C22×C4—1182no—
537C22×C4—1182no—
538C22×C4—1182no—
539C22×C4—1182no—
540C22×C4—1182no—
541C22×C4—1182no—
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—2364no—
556C22×C4—2364no—
557C22×C4—23616no—
558C22×C4#1174568514yes—
559C22×C4#1174568714yes—
560C22×C4Q8×D5914yes—
561C22×C4#1174568914yes—
562C22×C4C23×D5912yes—
563C22×C4C23×D5912yes—
564C22×C4C23×D5912yes—
565C22×C4C23×D5912yes—
566C22×C4C23×D5912yes—
567C22×C4C23×D5912yes—
568C22×C4C23×D5912yes—
569C4⋊C4—28no—
570C4⋊C4—28no—
571C4⋊C4—28no—
572C4⋊C4—44no—
573C4⋊C4—1188no—
574C4⋊C4—1188no—
575C4⋊C4—1188no—
576C4⋊C4—1188no—
577C4⋊C4—1188no—
578C4⋊C4—2364no—
579C4⋊C4—2364no—
580C4⋊C4—2364no—
581C22⋊C4—1188no—
582C22⋊C4—1188no—
583C22⋊C4—1188no—
584C22⋊C4—1188no—
585C22⋊C4—2364no—
586C22⋊C4—2364no—
587C42—44no—
588C42—2364no—
589C42—2364no—
590C42—2364no—
591C23—594no—
592C23—1188no—
593C23—1188no—
594C23—1182no—
595C23—1182no—
596C23—1182no—
597C23—1182no—
598C23—1182no—
599C23—1182no—
600C23—1188no—
601C23—2364no—
602C23—2364no—
603C23—2364no—
604C23—2364no—
605C23C2×Q8×D5912yes—
606C23#41×D5912yes—
607C23C2×#1174568712yes—
608C23C2×#1174568512yes—
609C23C2×#1174568912yes—
610C23#1427377212yes—
611C23#1427377312yes—
612C23C24×D5911yescharacteristic
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—28no—
622C2×C4—28no—
623C2×C4—28no—
624C2×C4—28no—
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—44no—
635C2×C4—44no—
636C2×C4—44no—
637C2×C4—594no—
638C2×C4—594no—
639C2×C4—1182no—
640C2×C4—1182no—
641C2×C4—1182no—
642C2×C4—1182no—
643C2×C4—1188no—
644C2×C4—1188no—
645C2×C4—1182no—
646C2×C4—1182no—
647C2×C4—1182no—
648C2×C4—1182no—
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—1182no—
658C2×C4—1182no—
659C2×C4—1182no—
660C2×C4—23616no—
661C2×C4—2364no—
662C2×C4—2364no—
663C2×C4—2364no—
664C2×C4—2364no—
665C2×C4—2364no—
666C2×C4C2×Q8×D5914yes—
667C2×C4C2×#1174568714yes—
668C2×C4C2×#1174568514yes—
669C2×C4C2×#1174568914yes—
670C22—1184no—
671C22—1184no—
672C22—1184no—
673C22—23616no—
674C22—2362no—
675C22—2362no—
676C22—2362no—
677C22—2362no—
678C22#1683795614yes—
679C22#1683795714yes—
680C22#1683802714yes—
681C22#1683809514yes—
682C22#1683809814yes—
683C22#1683810014yes—
684C22#1683810514yes—
685C22C22×Q8×D5911yescharacteristic
686C22C2×#41×D5911yescharacteristic
687C22C22×#1174568711yescharacteristic
688C22C22×#1174568511yescharacteristic
689C22C22×#1174568911yescharacteristic
690C22C2×#1427377211yescharacteristic
691C22C2×#1427377311yescharacteristic
692C4—24no—
693C4—24no—
694C4—24no—
695C4—24no—
696C4—42no—
697C4—42no—
698C4—42no—
699C4—1184no—
700C4—1184no—
701C4—2362no—
702C4—2362no—
703C4—2362no—
704C4—2362no—
705C4—2362no—
706C2—2364no—
707C2#2142976418yesdirect product factor
708C2C2×#1683795611yescharacteristic
709C2C2×#1683795711yescharacteristic
710C2C2×#1683802711yescharacteristic
711C2C2×#1683809511yescharacteristic
712C2C2×#1683809811yescharacteristic
713C2C2×#1683810011yescharacteristic
714C2C2×#1683810511yescharacteristic
subgroupG/H
centerC24C23×D59
commutator, cosocleC23×C59C25
FrattiniC23C24×D59
FittingC2×C59×#389C2
socleC24×C59C24
prime radicalC24×D59C23
hypercenterC2×#389D59
hypocenterC59C2×#2608
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
1. #21429764C2direct (N × H)
6. C2×#16837301C2semidirect
7. C2×#16837300C2semidirect
8. C2×#16837297C2semidirect
9. C2×#16837289C2semidirect
10. C2×#16837288C2semidirect
11. C2×#16837285C2semidirect
12. C2×#16837283C2semidirect
16. C2×C59×#389C2semidirect
39. #16837301C22semidirect
40. #16837300C22semidirect
41. #16837297C22semidirect
42. #16837289C22semidirect
43. #16837288C22semidirect
44. #16837285C22semidirect
45. #16837283C22semidirect
64. C59×#389C22semidirect
357. C2×#389D59semidirect
365. C2×C59#2608semidirect
404. #389C2×D59semidirect
424. C59C2×#2608semidirect
707. C2#21429764direct (N × H)

Maximal subgroups

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

subgroupindex
#214297642
C2×#168373242
C2×#168373012
C2×#168373002
C2×#168372972
C2×#168372892
C2×#168372882
C2×#168372852
C2×#168372832
C2×#168372642
C2×C4×(C2×D59)⋊C42
C2×#168372492
C2×C59×#3892
C2×#260859