Finite Group Databasebeta

← C2×#21429550 #28758985

Subgroups — C2×#21429550 #28758985

Order 15104.

2334 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
1#21429550C2116yesmaximal, direct product factor
2C2×#16837344C211yesmaximal, characteristic, complemented
3C2×#16837337C211yesmaximal, characteristic
4C2×#16837315C211yesmaximal, characteristic
5C2×#16837307C211yesmaximal, characteristic, complemented
6C2×#16837306C211yesmaximal, characteristic, complemented
7C2×#16837298C211yesmaximal, characteristic, complemented
8C2×#16837294C211yesmaximal, characteristic
9C2×#16837292C211yesmaximal, characteristic
10C2×#16837283C211yesmaximal, characteristic, complemented
11C2×#16837283C211yesmaximal, characteristic, complemented
12C2×#16837273C211yesmaximal, characteristic
13C2×#16837273C211yesmaximal, characteristic
14C2×#16837253C211yesmaximal, characteristic, complemented
15C2×#16837249C211yesmaximal, characteristic
16C2×C59×#398C211yesmaximal, characteristic, complemented
17C23×Dic118C2211yescharacteristic
18C23×C4×D59C2211yescharacteristic
19C22×C4⋊Dic59C2211yescharacteristic
20C22×Dic59⋊C4C2211yescharacteristic
21C22×Dic59⋊C4C2211yescharacteristic
22C22×Dic59⋊C4C2211yescharacteristic
23C22×Dic59⋊C4C2211yescharacteristic
24C22×(C2×D59)⋊C4C2211yescharacteristic
25C22×(C2×D59)⋊C4C2211yescharacteristic
26C22×(C2×D59)⋊C4C2211yescharacteristic
27C22×(C2×D59)⋊C4C2211yescharacteristic
28C22×(C2×D59)⋊C4C2211yescharacteristic
29C22×(C2×D59)⋊C4C2211yescharacteristic
30C22×C4×Dic59C2211yescharacteristic
31C22×C4×Dic59C2211yescharacteristic
32C22×C4×Dic59C2211yescharacteristic
33C22×C4×Dic59C2211yescharacteristic
34#16837344C2218yescomplemented
35#16837337C2218yes—
36#16837315C2218yes—
37#16837307C2218yescomplemented
38#16837306C2218yescomplemented
39#16837298C2218yescomplemented
40#16837294C2218yes—
41#16837292C2218yes—
42#16837283C2218yescomplemented
43#16837283C2218yescomplemented
44#16837273C2218yes—
45#16837273C2218yes—
46#16837253C2218yescomplemented
47#16837249C2218yes—
48C2×C59⋊#95C2211yescharacteristic
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
63C59×#398C2218yescomplemented
64C2×#95×C59C2211yescharacteristic
65C2×#95×C59C2211yescharacteristic
66C2×#95×C59C2211yescharacteristic
67C24×D59C2311yescharacteristic
68C22×Dic118—24no—
69C22×Dic118—24no—
70C22×Dic118—42no—
71C22×Dic118C2314yes—
72C23×Dic59C2311yescharacteristic
73C23×Dic59C2311yescharacteristic
74C23×Dic59C2311yescharacteristic
75C23×Dic59C2311yescharacteristic
76C23×Dic59C2311yescharacteristic
77C23×Dic59C2311yescharacteristic
78C23×Dic59C2311yescharacteristic
79C22×C4×D59—24no—
80C22×C4×D59—42no—
81C22×C4×D59—42no—
82C22×C4×D59C2314yes—
83C2×C4⋊Dic59—24no—
84C2×C4⋊Dic59C2314yes—
85C2×Dic59⋊C4—24no—
86C2×Dic59⋊C4—24no—
87C2×Dic59⋊C4—24no—
88C2×Dic59⋊C4—24no—
89C2×Dic59⋊C4C2314yes—
90C2×Dic59⋊C4C2314yes—
91C2×Dic59⋊C4C2314yes—
92C2×Dic59⋊C4C2314yes—
93C2×(C2×D59)⋊C4—24no—
94C2×(C2×D59)⋊C4—24no—
95C2×(C2×D59)⋊C4—24no—
96C2×(C2×D59)⋊C4—42no—
97C2×(C2×D59)⋊C4—42no—
98C2×(C2×D59)⋊C4Q818yescomplemented
99C2×(C2×D59)⋊C4C2314yes—
100C2×(C2×D59)⋊C4C2314yes—
101C2×(C2×D59)⋊C4C2314yes—
102C2×(C2×D59)⋊C4C2314yes—
103C2×(C2×D59)⋊C4C2314yes—
104C2×(C2×D59)⋊C4C2314yes—
105C2×C4×Dic59—24no—
106C2×C4×Dic59—42no—
107C2×C4×Dic59—42no—
108C2×C4×Dic59—42no—
109C2×C4×Dic59C2314yes—
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—
123C59⋊#95C2314yes—
124C23×C4×C59C2311yescharacteristic
125C23×C4×C59C2311yescharacteristic
126C23×C4×C59C2311yescharacteristic
127C23×C4×C59C2311yescharacteristic
128C23×C4×C59C2311yescharacteristic
129C23×C4×C59C2311yescharacteristic
130C23×C4×C59C2311yescharacteristic
131C2×C4⋊C4×C59—42no—
132C2×C4⋊C4×C59—42no—
133C2×C4⋊C4×C59—42no—
134C2×C4⋊C4×C59—42no—
135C2×C4⋊C4×C59C2314yes—
136C2×C4⋊C4×C59C2314yes—
137C2×C4⋊C4×C59C2314yes—
138C2×C4⋊C4×C59C2314yes—
139#95×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×C59—22no—
169C22×C4×C59—22no—
170C22×C4×C59C2×Q814yes—
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×Dic59C2×Q814yes—
197C22×Dic59#4114yes—
198C22×Dic59#4114yes—
199C22×Dic59#4114yes—
200C22×Dic59C2412yes—
201C22×Dic59C2412yes—
202C22×Dic59C2412yes—
203C22×Dic59C2412yes—
204C22×Dic59C2412yes—
205C22×Dic59C2412yes—
206C22×Dic59C2412yes—
207C2×C4×D59—28no—
208C2×C4×D59—44no—
209C2×C4×D59—44no—
210C2×C4×D59—416no—
211C2×Dic118—28no—
212C2×Dic118—28no—
213C2×Dic118—44no—
214C2×Dic118—416no—
215C4⋊C4×C59—44no—
216C4⋊C4×C59—44no—
217C4⋊C4×C59—44no—
218C4⋊C4×C59—44no—
219(C2×D59)⋊C4—28no—
220(C2×D59)⋊C4—28no—
221(C2×D59)⋊C4—28no—
222(C2×D59)⋊C4—44no—
223(C2×D59)⋊C4—44no—
224(C2×D59)⋊C4C2×Q8116yescomplemented
225C4⋊Dic59—28no—
226Dic59⋊C4—28no—
227Dic59⋊C4—28no—
228Dic59⋊C4—28no—
229Dic59⋊C4—28no—
230C4×Dic59—28no—
231C4×Dic59—44no—
232C4×Dic59—44no—
233C4×Dic59—44no—
234C23×C59C22×Q812yes—
235C23×C59C2×#4112yes—
236C23×C59C2×#4112yes—
237C23×C59C2×#4112yes—
238C23×C59C2×#4112yes—
239C23×C59H(5,𝔽2)12yes—
240C23×C59H(5,𝔽2)12yes—
241C23×C59C2511yescharacteristic
242C22×D59—28no—
243C22×D59—28no—
244C22×D59—28no—
245C22×D59—22no—
246C22×D59—22no—
247C22×D59—22no—
248C22×D59—22no—
249C22×D59—22no—
250C22×D59—22no—
251C22×D59—44no—
252C22×D59—44no—
253C22×D59—44no—
254C22×D59—44no—
255C22×D59C22×Q814yes—
256C2×C4×C59—28no—
257C2×C4×C59—28no—
258C2×C4×C59—22no—
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—22no—
277C2×C4×C59—44no—
278C2×C4×C59—44no—
279C2×C4×C59—44no—
280C2×C4×C59—44no—
281C2×C4×C59—44no—
282C2×C4×C59C22×Q814yes—
283C2×C4×C59C2×#4114yes—
284C2×Dic59—28no—
285C2×Dic59—28no—
286C2×Dic59—28no—
287C2×Dic59—28no—
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—44no—
306C2×Dic59—44no—
307C2×Dic59—44no—
308C2×Dic59C22×Q814yes—
309C2×Dic59C2×#4114yes—
310C2×Dic59C2×#4114yes—
311C2×Dic59C2×#4114yes—
312C4×D59—416no—
313Dic118—416no—
314C2×#2589—591nomaximal, Sylow
315C22×C59#52914yes—
316C22×C59#53314yes—
317C22×C59#53814yes—
318C22×C59#55114yes—
319C22×C59#55414yes—
320C22×C59#55414yes—
321C22×C59#55914yes—
322C22×C59C23×Q811yescharacteristic
323C22×C59C22×#4111yescharacteristic
324C22×C59C22×#4111yescharacteristic
325C22×C59C22×#4111yescharacteristic
326C22×C59C22×#4111yescharacteristic
327C22×C59C2×H(5,𝔽2)11yescharacteristic
328C22×C59C2×H(5,𝔽2)11yescharacteristic
329C2×D59—24no—
330C2×D59—24no—
331C2×D59—24no—
332C2×D59—416no—
333C2×D59—42no—
334C2×D59—42no—
335C2×D59—42no—
336C2×D59—42no—
337C4×C59—24no—
338C4×C59—24no—
339C4×C59—42no—
340C4×C59—42no—
341C4×C59—42no—
342C4×C59—42no—
343C4×C59—42no—
344Dic59—24no—
345Dic59—24no—
346Dic59—24no—
347Dic59—24no—
348Dic59—42no—
349Dic59—42no—
350Dic59—42no—
351#2589—5916no—
352C2×#400—591no—
353C2×#399—591no—
354C2×#398D5911yescharacteristic, complemented
355C2×#393—591no—
356C2×#391—591no—
357C2×#391—591no—
358C2×#389—591no—
359C2×#388—591no—
360C2×#388—591no—
361C2×#387—591no—
362C2×#387—591no—
363C2×#385—591no—
364C2×#385—591no—
365C2×C4×C4⋊C4—591no—
366C2×C4×C22⋊C4—591no—
367C2×C59#258918yescomplemented
368C2×C59C2×#52911yescharacteristic
369C2×C59C2×#53311yescharacteristic
370C2×C59C2×#53811yescharacteristic
371C2×C59C2×#55111yescharacteristic
372C2×C59C2×#55411yescharacteristic
373C2×C59C2×#55411yescharacteristic
374C2×C59C2×#55911yescharacteristic
375D59—44no—
376C23×Q8—591no—
377C24×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×C42—591no—
397#400—598no—
398#399—598no—
399#398C2×D5918yescomplemented
400#393—598no—
401#391—598no—
402#391—598no—
403#389—598no—
404#388—598no—
405#388—598no—
406#387—598no—
407#387—598no—
408#385—598no—
409#385—598no—
410C4×C4⋊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×#95—591no—
423C2×#95C2×D5911yescharacteristic
424C2×#95C2×D5911yescharacteristic
425C2×#95C2×D5911yescharacteristic
426C59C2×#258911yescharacteristic, complemented, Sylow
427C25—591no—
428C22×Q8—594no—
429C22×Q8—1184no—
430C22×Q8—1184no—
431C22×Q8—2362no—
432C23×C4—591no—
433C23×C4—591no—
434C23×C4—591no—
435C23×C4—591no—
436C23×C4—591no—
437C23×C4—591no—
438C23×C4—591no—
439C23×C4—594no—
440C23×C4—1184no—
441C23×C4—2362no—
442C23×C4—2362no—
443C23×C4C22×D5911yescharacteristic
444C23×C4C22×D5911yescharacteristic
445C23×C4C22×D5911yescharacteristic
446C23×C4C22×D5911yescharacteristic
447C23×C4C22×D5911yescharacteristic
448C23×C4C22×D5911yescharacteristic
449C23×C4C22×D5911yescharacteristic
450C2×C4⋊C4—42no—
451C2×C4⋊C4—42no—
452C2×C4⋊C4—42no—
453C2×C4⋊C4—42no—
454C2×C4⋊C4—594no—
455C2×C4⋊C4—594no—
456C2×C4⋊C4—594no—
457C2×C4⋊C4—594no—
458C2×C4⋊C4—594no—
459C2×C4⋊C4—1184no—
460C2×C4⋊C4—1184no—
461C2×C4⋊C4—1184no—
462C2×C4⋊C4—1184no—
463C2×C4⋊C4—1184no—
464C2×C4⋊C4C22×D5914yes—
465C2×C4⋊C4C22×D5914yes—
466C2×C4⋊C4C22×D5914yes—
467C2×C4⋊C4C22×D5914yes—
468C2×C22⋊C4—598no—
469C2×C22⋊C4—594no—
470C2×C22⋊C4—594no—
471C2×C22⋊C4—594no—
472C2×C22⋊C4—594no—
473C2×C22⋊C4—594no—
474C2×C22⋊C4—594no—
475C2×C22⋊C4—1184no—
476C2×C22⋊C4—1184no—
477C2×C22⋊C4—1184no—
478C2×C22⋊C4—2362no—
479C2×C22⋊C4—2362no—
480C2×C42—594no—
481C2×C42—594no—
482C2×C42—594no—
483C2×C42—594no—
484C2×C42—1184no—
485C2×C42—2362no—
486C2×C42—2362no—
487C2×C42—2362no—
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#95—594no—
499#95C22×D5914yes—
500#95C22×D5914yes—
501#95C22×D5914yes—
502C24—594no—
503C24—592no—
504C24—1182no—
505C24—1182no—
506C24—1182no—
507C24—1182no—
508C24—1182no—
509C24—1182no—
510C24C23×D5911yescharacteristic
511C2×Q8—1188no—
512C2×Q8—1188no—
513C2×Q8—2364no—
514C2×Q8—23616no—
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—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—594no—
535C22×C4—594no—
536C22×C4—594no—
537C22×C4—594no—
538C22×C4—592no—
539C22×C4—592no—
540C22×C4—592no—
541C22×C4—592no—
542C22×C4—592no—
543C22×C4—592no—
544C22×C4—592no—
545C22×C4—1188no—
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—2364no—
564C22×C4—2364no—
565C22×C4—23616no—
566C22×C4Q8×D5914yes—
567C22×C4#1174568914yes—
568C22×C4C23×D5912yes—
569C22×C4C23×D5912yes—
570C22×C4C23×D5912yes—
571C22×C4C23×D5912yes—
572C22×C4C23×D5912yes—
573C22×C4C23×D5912yes—
574C22×C4C23×D5912yes—
575C4⋊C4—44no—
576C4⋊C4—44no—
577C4⋊C4—44no—
578C4⋊C4—44no—
579C4⋊C4—1188no—
580C4⋊C4—1188no—
581C4⋊C4—1188no—
582C4⋊C4—1188no—
583C4⋊C4—1188no—
584C22⋊C4—5916no—
585C22⋊C4—1188no—
586C22⋊C4—1188no—
587C22⋊C4—1188no—
588C22⋊C4—2364no—
589C22⋊C4—2364no—
590C42—1188no—
591C42—2364no—
592C42—2364no—
593C42—2364no—
594C23—594no—
595C23—1188no—
596C23—1182no—
597C23—1182no—
598C23—1182no—
599C23—1182no—
600C23—1182no—
601C23—1182no—
602C23—1188no—
603C23—1188no—
604C23—2364no—
605C23—2364no—
606C23—2364no—
607C23—2364no—
608C23C2×Q8×D5912yes—
609C23#41×D5912yes—
610C23#41×D5912yes—
611C23#41×D5912yes—
612C23C2×#1174568912yes—
613C23#1427377212yes—
614C23#1427377212yes—
615C23C24×D5911yescharacteristic
616Q8—23616no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—28no—
622C2×C4—28no—
623C2×C4—22no—
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—44no—
639C2×C4—44no—
640C2×C4—44no—
641C2×C4—44no—
642C2×C4—44no—
643C2×C4—594no—
644C2×C4—594no—
645C2×C4—594no—
646C2×C4—594no—
647C2×C4—1188no—
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—1188no—
657C2×C4—1188no—
658C2×C4—1188no—
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—1182no—
668C2×C4—23616no—
669C2×C4—2364no—
670C2×C4—2364no—
671C2×C4—2364no—
672C2×C4C2×Q8×D5914yes—
673C2×C4C2×#1174568914yes—
674C22—1184no—
675C22—1184no—
676C22—1184no—
677C22—23616no—
678C22—2362no—
679C22—2362no—
680C22—2362no—
681C22—2362no—
682C22#1683793714yes—
683C22#1683795814yes—
684C22#1683798414yes—
685C22#1683807914yes—
686C22#1683810614yes—
687C22#1683811314yes—
688C22#1683813614yes—
689C22C22×Q8×D5911yescharacteristic
690C22C2×#41×D5911yescharacteristic
691C22C2×#41×D5911yescharacteristic
692C22C2×#41×D5911yescharacteristic
693C22C22×#1174568911yescharacteristic
694C22C2×#1427377211yescharacteristic
695C22C2×#1427377211yescharacteristic
696C4—24no—
697C4—24no—
698C4—42no—
699C4—42no—
700C4—42no—
701C4—42no—
702C4—42no—
703C4—1184no—
704C4—1184no—
705C4—1184no—
706C4—1184no—
707C4—2362no—
708C4—2362no—
709C4—2362no—
710C2—2364no—
711C2#2142955018yesdirect product factor
712C2C2×#1683793711yescharacteristic
713C2C2×#1683795811yescharacteristic
714C2C2×#1683798411yescharacteristic
715C2C2×#1683807911yescharacteristic
716C2C2×#1683810611yescharacteristic
717C2C2×#1683811311yescharacteristic
718C2C2×#1683813611yescharacteristic
subgroupG/H
centerC24C23×D59
commutator, cosocleC23×C59C25
FrattiniC23C24×D59
FittingC2×C59×#398C2
socleC24×C59C24
prime radicalC24×D59C23
hypercenterC2×#398D59
hypocenterC59C2×#2589
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
1. #21429550C2direct (N × H)
2. C2×#16837344C2semidirect
5. C2×#16837307C2semidirect
6. C2×#16837306C2semidirect
7. C2×#16837298C2semidirect
10. C2×#16837283C2semidirect
11. C2×#16837283C2semidirect
14. C2×#16837253C2semidirect
16. C2×C59×#398C2semidirect
34. #16837344C22semidirect
37. #16837307C22semidirect
38. #16837306C22semidirect
39. #16837298C22semidirect
42. #16837283C22semidirect
43. #16837283C22semidirect
46. #16837253C22semidirect
63. C59×#398C22semidirect
98. C2×(C2×D59)⋊C4Q8semidirect
224. (C2×D59)⋊C4C2×Q8semidirect
354. C2×#398D59semidirect
367. C2×C59#2589semidirect
399. #398C2×D59semidirect
426. C59C2×#2589semidirect
711. C2#21429550direct (N × H)

Maximal subgroups

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

subgroupindex
#214295502
C2×#168373442
C2×#168373372
C2×#168373152
C2×#168373072
C2×#168373062
C2×#168372982
C2×#168372942
C2×#168372922
C2×#168372832
C2×#168372732
C2×#168372532
C2×#168372492
C2×C59×#3982
C2×#258959