Finite Group Databasebeta

← C2×#21422654 #28556026

Subgroups — C2×#21422654 #28556026

Order 15104.

1366 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837947C211yesmaximal, characteristic
2C2×#16837452C211yesmaximal, characteristic, complemented
3C2×#16837266C211yesmaximal, characteristic, complemented
4#21422654C218yesmaximal, direct product factor
5C2×#16837137C211yesmaximal, characteristic, complemented
6C2×#16837136C211yesmaximal, characteristic, complemented
7C2×#16837135C211yesmaximal, characteristic, complemented
8C2×C59×#327C211yesmaximal, characteristic, complemented
9C22×#11745687—21no—
10#16837947—22no—
11#16837947—22no—
12#16837947C414yescomplemented
13#16837947C2214yes—
14C2×#14273726C411yescharacteristic, complemented
15C2×#14273723C411yescharacteristic, complemented
16C2×#14273713—21no—
17C2×#14273701C2211yescharacteristic
18C2×#14273699—21no—
19C2×D4×Dic59C411yescharacteristic, complemented
20C2×#14273689C411yescharacteristic, complemented
21C2×(C22⋊D59)⋊C4—21no—
22C22×Dic59⋊C4—21no—
23C22×C4×Dic59C2211yescharacteristic
24#16837452—22no—
25#16837452C2214yescomplemented
26C2×Dic59⋊C8—21no—
27C2×C22⋊(C59⋊C8)C2211yescharacteristic
28C2×C8×Dic59—21no—
29#16837266—22no—
30#16837266C2214yescomplemented
31C2×C59⋊#95—21no—
32C2×C59⋊#95C2211yescharacteristic
33#16837137C2214yescomplemented
34#16837136C2214yescomplemented
35#16837135C2214yescomplemented
36C2×#121×C59C2211yescharacteristic
37C2×C22⋊C8×C59C2211yescharacteristic
38C2×#95×C59C2211yescharacteristic
39C59×#327C2214yescomplemented
40C2×#11745687—24no—
41C2×#11745687—24no—
42C2×#11745687—44no—
43C2×#11745687—44no—
44C22×Dic118—21no—
45C22×D236C2×C411yescharacteristic
46C22×C22⋊D59—21no—
47C22×C22⋊D59—21no—
48C22×C22⋊D59—21no—
49C23×Dic59—21no—
50C23×Dic59—21no—
51C23×Dic59D411yescharacteristic
52C23×Dic59D411yescharacteristic
53C22×C4×D59—21no—
54C22×C59⋊C8—21no—
55#14273726—22no—
56#14273726C2×C414yescomplemented
57#14273723—22no—
58#14273723C2×C414yescomplemented
59#14273713—24no—
60#14273713—24no—
61#14273701—21no—
62#14273701—21no—
63#14273701C2×C412yes—
64#14273701C2312yes—
65#14273699—24no—
66#14273699—24no—
67D4×Dic59—22no—
68D4×Dic59C2×C414yescomplemented
69#14273689—22no—
70#14273689C2×C414yescomplemented
71(C22⋊D59)⋊C4—24no—
72(C22⋊D59)⋊C4—24no—
73C2×C4⋊Dic59C2×C411yescharacteristic
74C2×Dic59⋊C4—21no—
75C2×Dic59⋊C4—24no—
76C2×Dic59⋊C4—44no—
77C2×C22⋊Dic59—21no—
78C2×(C2×D59)⋊C4—21no—
79C2×(C2×D59)⋊C4—21no—
80C2×C4×Dic59C2×C411yescharacteristic
81C2×C4×Dic59C2×C412yes—
82C2×C4×Dic59C2×C411yescharacteristic
83C2×C4×Dic59D412yes—
84C2×C4×Dic59D411yescharacteristic
85C2×C4×Dic59D411yescharacteristic
86C2×C4×Dic59D412yes—
87C2×C4×Dic59C2312yes—
88Dic59⋊C8—24no—
89C22⋊(C59⋊C8)—21no—
90C22⋊(C59⋊C8)C2312yes—
91C8×Dic59—24no—
92C59⋊#95—21no—
93C59⋊#95—24no—
94C59⋊#95C2312yes—
95C22×D4×C59—21no—
96C22×D4×C59C2×C411yescharacteristic
97C23×C4×C59—21no—
98C23×C4×C59C2311yescharacteristic
99C22×C8×C59—21no—
100#121×C59—21no—
101#121×C59—21no—
102#121×C59C2×C412yes—
103#121×C59C2312yes—
104C2×C4⋊C4×C59C2×C411yescharacteristic
105C2×C22⋊C4×C59—21no—
106C22⋊C8×C59—21no—
107C22⋊C8×C59C2312yes—
108#95×C59—21no—
109#95×C59C2312yes—
110C24×C59—21no—
111C24×C59C2×D411yescharacteristic
112C23×D59—21no—
113C2×D4×C59—22no—
114C2×D4×C59—22no—
115C2×D4×C59—21no—
116C2×D4×C59—42no—
117C2×D4×C59—42no—
118C2×D4×C59—42no—
119C2×D4×C59C22×C412yes—
120C22×C4×C59—21no—
121C22×C4×C59—22no—
122C22×C4×C59—42no—
123C22×C4×C59—42no—
124C22×C4×C59—42no—
125C22×C4×C59—42no—
126C22×C4×C59C22×C411yescharacteristic
127C22×C4×C59C22×C411yescharacteristic
128C22×C4×C59C2×D411yescharacteristic
129C22×C4×C59C2×D411yescharacteristic
130C22×C4×C59C2×D411yescharacteristic
131C22×C4×C59C2411yescharacteristic
132C2×C22⋊D59—22no—
133C2×C22⋊D59—22no—
134C2×C22⋊D59—24no—
135C2×C22⋊D59—24no—
136C2×C22⋊D59—44no—
137C2×C22⋊D59—42no—
138C2×C22⋊D59—42no—
139C2×C22⋊D59—44no—
140C22×Dic59—21no—
141C22×Dic59—24no—
142C22×Dic59—22no—
143C22×Dic59—42no—
144C22×Dic59—44no—
145C22×Dic59—42no—
146C22×Dic59—42no—
147C22×Dic59—42no—
148C22×Dic59C22⋊C411yescharacteristic
149C22×Dic59C22⋊C411yescharacteristic
150C22×Dic59C22⋊C412yes—
151C22×Dic59C22⋊C411yescharacteristic
152C22×Dic59C22⋊C411yescharacteristic
153C22×Dic59C22⋊C412yes—
154C22×Dic59D814yes—
155C22×Dic59SD1614yes—
156C22×Dic59C2×D412yes—
157C22×Dic59C2×D412yes—
158#11745687—416no—
159#11745687—48no—
160#11745687—48no—
161C2×D236—21no—
162C2×D236—42no—
163C2×D236C22×C412yes—
164C2×C4×D59—24no—
165C2×C4×D59—44no—
166C2×Dic118—24no—
167C2×Dic118—44no—
168C2×C8×C59—22no—
169C2×C8×C59—42no—
170C4⋊C4×C59—21no—
171C4⋊C4×C59C22×C412yes—
172C22⋊C4×C59—22no—
173C22⋊C4×C59—22no—
174C22⋊Dic59—24no—
175(C2×D59)⋊C4—22no—
176(C2×D59)⋊C4—22no—
177(C2×D59)⋊C4—24no—
178C4⋊Dic59—21no—
179C4⋊Dic59C22×C412yes—
180Dic59⋊C4—24no—
181Dic59⋊C4—48no—
182C4×Dic59C22⋊C412yes—
183C4×Dic59C22⋊C412yes—
184C4×Dic59C22⋊C412yes—
185C4×Dic59C22⋊C412yes—
186C4×Dic59C22×C412yes—
187C4×Dic59C22×C412yes—
188C4×Dic59C2×D412yes—
189C4×Dic59C2×D412yes—
190C2×C59⋊C8—22no—
191C2×C59⋊C8—42no—
192C23×C59—22no—
193C23×C59—22no—
194C23×C59—22no—
195C23×C59—42no—
196C23×C59—42no—
197C23×C59—42no—
198C23×C59C2×C22⋊C411yescharacteristic
199C23×C59C2×C22⋊C411yescharacteristic
200C23×C59C2×D812yes—
201C23×C59C2×SD1612yes—
202C23×C59C22×D411yescharacteristic
203C22×D59—22no—
204C22×D59—42no—
205C22×D59—42no—
206C22×D59—42no—
207D4×C59—42no—
208D4×C59—42no—
209D4×C59—42no—
210D4×C59—42no—
211D4×C59—44no—
212C2×C4×C59—22no—
213C2×C4×C59—22no—
214C2×C4×C59—22no—
215C2×C4×C59—41no—
216C2×C4×C59—41no—
217C2×C4×C59—41no—
218C2×C4×C59—41no—
219C2×C4×C59—42no—
220C2×C4×C59—42no—
221C2×C4×C59—42no—
222C2×C4×C59—42no—
223C2×C4×C59—84no—
224C2×C4×C59C2×C22⋊C411yescharacteristic
225C2×C4×C59C2×C22⋊C411yescharacteristic
226C2×C4×C59C23×C411yescharacteristic
227C2×C4×C59C22×D411yescharacteristic
228C22⋊D59—48no—
229C22⋊D59—42no—
230C22⋊D59—42no—
231C22⋊D59—44no—
232C22⋊D59—48no—
233C2×Dic59—22no—
234C2×Dic59—22no—
235C2×Dic59—22no—
236C2×Dic59—42no—
237C2×Dic59—42no—
238C2×Dic59—42no—
239C2×Dic59—48no—
240C2×Dic59—42no—
241C2×Dic59—42no—
242C2×Dic59—42no—
243C2×Dic59—84no—
244C2×Dic59#10214yes—
245C2×Dic59#10214yes—
246C2×Dic59#10218yes—
247C2×Dic59C2×C22⋊C412yes—
248C2×Dic59C2×C22⋊C412yes—
249C2×Dic59C2×C22⋊C412yes—
250C2×Dic59C2×C22⋊C412yes—
251C2×Dic59C2×D814yes—
252C2×Dic59C2×SD1614yes—
253D236—42no—
254D236—42no—
255C4×D59—48no—
256Dic118—48no—
257C8×C59—42no—
258C59⋊C8—42no—
259C2×#1517—591nomaximal, Sylow
260C22×C59—21no—
261C22×C59—21no—
262C22×C59—21no—
263C22×C59—21no—
264C22×C59—24no—
265C22×C59—24no—
266C22×C59—42no—
267C22×C59—42no—
268C22×C59—42no—
269C22×C59—84no—
270C22×C59#41012yes—
271C22×C59C2×#10212yes—
272C22×C59C2×#10212yes—
273C22×C59#42112yes—
274C22×C59C22×C22⋊C411yescharacteristic
275C22×C59C22×D811yescharacteristic
276C22×C59C22×SD1611yescharacteristic
277C2×D59—42no—
278C2×D59—42no—
279C2×D59—42no—
280C2×D59—84no—
281C4×C59—21no—
282C4×C59—21no—
283C4×C59—21no—
284C4×C59—21no—
285C4×C59—42no—
286C4×C59—82no—
287Dic59—22no—
288Dic59—22no—
289Dic59—42no—
290Dic59—82no—
291Dic59C2×#10214yes—
292Dic59C2×#10214yes—
293C2×#532—591no—
294C2×#431—591no—
295C2×#382—591no—
296#1517—598no—
297C2×#327—591no—
298C2×#327—591no—
299C2×#327—591no—
300C2×#327D5911yescharacteristic, complemented
301C2×C59—21no—
302C2×C59—21no—
303C2×C59—22no—
304C2×C59—82no—
305C2×C59#151714yescomplemented
306C2×C59C2×#41011yescharacteristic
307C2×C59C22×#10211yescharacteristic
308C2×C59C2×#42111yescharacteristic
309D59—82no—
310C22×#41—1181no—
311#532—594no—
312#532—594no—
313#532—1182no—
314#532—1182no—
315C2×C4⋊Q8—591no—
316C2×#127—591no—
317C2×#124—1181no—
318C2×#121—591no—
319C2×#121—1181no—
320C2×#121C2×D5911yescharacteristic
321C2×C4×D4—591no—
322C2×C4×D4—591no—
323C2×C4×D4—1181no—
324C22×C4⋊C4—1181no—
325C22×C42—591no—
326#431—594no—
327#431—1182no—
328C2×C4⋊C8—1181no—
329C2×C22⋊C8—591no—
330C2×C22⋊C8C2×D5911yescharacteristic
331C2×C4×C8—1181no—
332#382—594no—
333#382—1182no—
334C2×#95—591no—
335C2×#95—1181no—
336C2×#95C2×D5911yescharacteristic
337#327—594no—
338#327—594no—
339#327—594no—
340#327C2×D5914yescomplemented
341C59C2×#151711yescharacteristic, complemented, Sylow
342C2×#41—1184no—
343C2×#41—1184no—
344C2×#41—2364no—
345C2×#41—2364no—
346C22×Q8—1181no—
347C22×D4—21no—
348C22×D4—591no—
349C22×D4—1181no—
350C22×D4—1181no—
351C22×D4—1181no—
352C22×D4C4×D5911yescharacteristic
353C23×C4—21no—
354C23×C4—591no—
355C23×C4—591no—
356C23×C4—1181no—
357C23×C4—1181no—
358C23×C4—1181no—
359C23×C4C22×D5911yescharacteristic
360C22×C8—21no—
361C22×C8—1181no—
362C4⋊Q8—594no—
363C4⋊Q8—1182no—
364#127—594no—
365#127—1182no—
366#124—1184no—
367#124—1184no—
368#121—21no—
369#121—21no—
370#121—592no—
371#121—592no—
372#121—1184no—
373#121—1184no—
374#121—1181no—
375#121—1181no—
376#121C4×D5912yes—
377#121C22×D5912yes—
378C4×D4—594no—
379C4×D4—594no—
380C4×D4—1184no—
381C4×D4—1184no—
382C4×D4—1182no—
383C4×D4—1182no—
384C2×C4⋊C4—591no—
385C2×C4⋊C4—1181no—
386C2×C4⋊C4—1184no—
387C2×C4⋊C4—2364no—
388C2×C4⋊C4C4×D5911yescharacteristic
389C2×C22⋊C4—21no—
390C2×C22⋊C4—1181no—
391C2×C22⋊C4—1181no—
392C2×C22⋊C4—1181no—
393C2×C42—591no—
394C2×C42—591no—
395C2×C42—592no—
396C2×C42—591no—
397C2×C42—591no—
398C2×C42—592no—
399C2×C42—592no—
400C2×C42—592no—
401C4⋊C8—1184no—
402C22⋊C8—21no—
403C22⋊C8—592no—
404C22⋊C8—1181no—
405C22⋊C8C22×D5912yes—
406C4×C8—1184no—
407#95—21no—
408#95—592no—
409#95—1184no—
410#95—1181no—
411#95C22×D5912yes—
412C24—21no—
413C24—1181no—
414C24D4×D5911yescharacteristic
415#41—23616no—
416#41—2368no—
417#41—2368no—
418C2×Q8—1184no—
419C2×Q8—2364no—
420C2×D4—22no—
421C2×D4—22no—
422C2×D4—21no—
423C2×D4—42no—
424C2×D4—42no—
425C2×D4—42no—
426C2×D4—592no—
427C2×D4—1184no—
428C2×D4—1184no—
429C2×D4—1182no—
430C2×D4—1182no—
431C2×D4—1181no—
432C2×D4—2362no—
433C2×D4—2364no—
434C2×D4—2364no—
435C2×D4—2362no—
436C2×D4—2362no—
437C2×D4C2×C4×D5912yes—
438C22×C4—21no—
439C22×C4—22no—
440C22×C4—42no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—42no—
444C22×C4—592no—
445C22×C4—591no—
446C22×C4—591no—
447C22×C4—594no—
448C22×C4—594no—
449C22×C4—592no—
450C22×C4—591no—
451C22×C4—591no—
452C22×C4—592no—
453C22×C4—592no—
454C22×C4—1184no—
455C22×C4—1184no—
456C22×C4—1181no—
457C22×C4—1182no—
458C22×C4—2364no—
459C22×C4—2364no—
460C22×C4—2362no—
461C22×C4—2362no—
462C22×C4—2362no—
463C22×C4—2362no—
464C22×C4C2×C4×D5911yescharacteristic
465C22×C4C2×C4×D5911yescharacteristic
466C22×C4D4×D5911yescharacteristic
467C22×C4D4×D5911yescharacteristic
468C22×C4D4×D5911yescharacteristic
469C22×C4C23×D5911yescharacteristic
470C2×C8—22no—
471C2×C8—42no—
472C2×C8—1182no—
473C2×C8—2362no—
474C4⋊C4—21no—
475C4⋊C4—592no—
476C4⋊C4—1184no—
477C4⋊C4—1181no—
478C4⋊C4—2368no—
479C4⋊C4C2×C4×D5912yes—
480C22⋊C4—22no—
481C22⋊C4—22no—
482C22⋊C4—1184no—
483C22⋊C4—1184no—
484C22⋊C4—1182no—
485C22⋊C4—1182no—
486C42—592no—
487C42—592no—
488C42—592no—
489C42—592no—
490C42—592no—
491C42—592no—
492C42—592no—
493C42—592no—
494C23—22no—
495C23—22no—
496C23—22no—
497C23—42no—
498C23—42no—
499C23—42no—
500C23—1182no—
501C23—2362no—
502C23—2362no—
503C23—2362no—
504C23C22⋊C4×D5911yescharacteristic
505C23C22⋊C4×D5911yescharacteristic
506C23D8×D5912yes—
507C23SD16×D5912yes—
508C23C2×D4×D5911yescharacteristic
509Q8—2368no—
510D4—42no—
511D4—42no—
512D4—44no—
513D4—42no—
514D4—42no—
515D4—2362no—
516D4—2362no—
517D4—2368no—
518D4—2368no—
519D4—2364no—
520D4—2362no—
521D4—2362no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—84no—
534C2×C4—594no—
535C2×C4—594no—
536C2×C4—598no—
537C2×C4—594no—
538C2×C4—594no—
539C2×C4—592no—
540C2×C4—592no—
541C2×C4—592no—
542C2×C4—592no—
543C2×C4—1182no—
544C2×C4—1182no—
545C2×C4—1182no—
546C2×C4—4724no—
547C2×C4—2368no—
548C2×C4—2368no—
549C2×C4—2362no—
550C2×C4—2362no—
551C2×C4—2362no—
552C2×C4—2362no—
553C2×C4—2362no—
554C2×C4—2362no—
555C2×C4C22⋊C4×D5911yescharacteristic
556C2×C4C22⋊C4×D5911yescharacteristic
557C2×C4C22×C4×D5911yescharacteristic
558C2×C4C2×D4×D5911yescharacteristic
559C8—42no—
560C8—2362no—
561C22—21no—
562C22—21no—
563C22—24no—
564C22—24no—
565C22—21no—
566C22—21no—
567C22—42no—
568C22—42no—
569C22—42no—
570C22—84no—
571C22—4724no—
572C22—2362no—
573C22—2362no—
574C22—2362no—
575C22#1683737412yes—
576C22#102×D5912yes—
577C22#102×D5912yes—
578C22#1683741712yes—
579C22C2×C22⋊C4×D5911yescharacteristic
580C22C2×D8×D5911yescharacteristic
581C22C2×SD16×D5911yescharacteristic
582C4—21no—
583C4—21no—
584C4—21no—
585C4—21no—
586C4—42no—
587C4—82no—
588C4—594no—
589C4—594no—
590C4—1182no—
591C4—1182no—
592C4—4722no—
593C4—2362no—
594C2—21no—
595C2—22no—
596C2—21no—
597C2—82no—
598C2—4722no—
599C2#2142265414yesdirect product factor
600C2C2×#1683737411yescharacteristic
601C2C2×#102×D5911yescharacteristic
602C2C2×#1683741711yescharacteristic
subgroupG/H
centerC23C22⋊C4×D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC2×C59×#327C2
socleC23×C59C2×C22⋊C4
prime radicalC2×#16837947C2
cosocleC22×C4×C59C24
hypercenterC2×#327D59
hypocenterC59C2×#1517
LCSG ▷ C2×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#327

Complements

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

NH ≅ G/Ntype
2. C2×#16837452C2semidirect
3. C2×#16837266C2semidirect
4. #21422654C2direct (N × H)
5. C2×#16837137C2semidirect
6. C2×#16837136C2semidirect
7. C2×#16837135C2semidirect
8. C2×C59×#327C2semidirect
12. #16837947C4semidirect
14. C2×#14273726C4semidirect
15. C2×#14273723C4semidirect
19. C2×D4×Dic59C4semidirect
20. C2×#14273689C4semidirect
25. #16837452C22semidirect
30. #16837266C22semidirect
33. #16837137C22semidirect
34. #16837136C22semidirect
35. #16837135C22semidirect
39. C59×#327C22semidirect
56. #14273726C2×C4semidirect
58. #14273723C2×C4semidirect
68. D4×Dic59C2×C4semidirect
70. #14273689C2×C4semidirect
300. C2×#327D59semidirect
305. C2×C59#1517semidirect
340. #327C2×D59semidirect
341. C59C2×#1517semidirect
599. C2#21422654direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168379472
C2×#168374522
C2×#168372662
#214226542
C2×#168371372
C2×#168371362
C2×#168371352
C2×C59×#3272
C2×#151759