Finite Group Databasebeta

← C2×#21425310 #28616279

Subgroups — C2×#21425310 #28616279

Order 15104.

1434 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837445C211yesmaximal, characteristic, complemented
2C22×#14273654C211yesmaximal, characteristic
3C2×#16837403C211yesmaximal, characteristic
4C22×#14273646C211yesmaximal, characteristic, complemented
5C2×#16837309C211yesmaximal, characteristic, complemented
6#21425310C218yesmaximal, direct product factor
7C2×#16837161C211yesmaximal, characteristic, complemented
8C2×C59×#536C211yesmaximal, characteristic
9C22×#11745664C2211yescharacteristic
10C22×#11745664C2211yescharacteristic
11C22×C4⋊Dic59C2211yescharacteristic
12C22×C4×Dic59C2211yescharacteristic
13#16837445—22no—
14#16837445C2214yescomplemented
15C2×#14273660—21no—
16C2×#14273658—21no—
17C2×#14273654—24no—
18C2×#14273654C2214yes—
19#16837403—22no—
20#16837403C2214yes—
21C2×#14273651—21no—
22C2×#14273648—21no—
23C2×#14273646—24no—
24C2×#14273646C2214yescomplemented
25#16837309—22no—
26#16837309C2214yescomplemented
27C2×C59⋊#95—22no—
28#16837161C2214yescomplemented
29C22×#41×C59C2211yescharacteristic
30C23×Q8×C59C2211yescharacteristic
31C59×#536—22no—
32C59×#536—22no—
33C59×#536—22no—
34C59×#536C2214yes—
35C2×C4⋊Q8×C59—21no—
36C2×#124×C59—21no—
37C2×#123×C59—22no—
38C2×C22⋊Q8×C59—21no—
39C2×C22⋊Q8×C59—21no—
40C2×#117×C59C2211yescharacteristic
41C23×Dic59—21no—
42C23×Dic59—21no—
43C2×#11745664—21no—
44C2×#11745664—22no—
45C2×#11745664—21no—
46C2×#11745664—22no—
47C2×#11745664—22no—
48C2×#11745664D414yes—
49C2×#11745664C2312yes—
50C2×#11745664C2312yes—
51C22×C59⋊C8—21no—
52C22×C59⋊C8—21no—
53C2×C4⋊Dic59—21no—
54C2×C4⋊Dic59—21no—
55C2×C4⋊Dic59—21no—
56C2×C4⋊Dic59—21no—
57C2×C4⋊Dic59—21no—
58C2×C4⋊Dic59C2312yes—
59C2×C4×Dic59—22no—
60C2×C4×Dic59—22no—
61C2×C4×Dic59—21no—
62C2×C4×Dic59C2312yes—
63#14273660—24no—
64#14273658—24no—
65#14273654—28no—
66#14273651—24no—
67#14273648—24no—
68#14273646—28no—
69C59⋊#95—28no—
70C2×#41×C59—21no—
71C2×#41×C59—21no—
72C2×#41×C59—22no—
73C2×#41×C59—22no—
74C2×#41×C59—22no—
75C2×#41×C59—22no—
76C2×#41×C59D412yes—
77C2×#41×C59C2312yes—
78C22×Q8×C59—22no—
79C22×Q8×C59—21no—
80C22×Q8×C59—21no—
81C22×Q8×C59—21no—
82C22×Q8×C59—21no—
83C22×Q8×C59—22no—
84C22×Q8×C59—22no—
85C22×Q8×C59—22no—
86C22×Q8×C59D411yescharacteristic
87C22×Q8×C59D412yes—
88C22×Q8×C59C2312yes—
89C22×D4×C59—21no—
90C22×D4×C59D411yescharacteristic
91C23×C4×C59—21no—
92C23×C4×C59D412yes—
93C23×C4×C59C2311yescharacteristic
94C4⋊Q8×C59—24no—
95C4⋊Q8×C59—24no—
96#124×C59—24no—
97#124×C59—24no—
98#123×C59—28no—
99#123×C59—28no—
100C22⋊Q8×C59—24no—
101C22⋊Q8×C59—24no—
102C22⋊Q8×C59—24no—
103C22⋊Q8×C59—24no—
104#117×C59—21no—
105#117×C59—21no—
106#117×C59D412yes—
107#117×C59C2312yes—
108C2×C4⋊C4×C59—22no—
109C2×C4⋊C4×C59—22no—
110C2×C4⋊C4×C59D411yescharacteristic
111C2×C4⋊C4×C59D411yescharacteristic
112C2×C22⋊C4×C59—22no—
113C2×C22⋊C4×C59—22no—
114C2×C22⋊C4×C59—21no—
115C2×C42×C59—21no—
116C24×C59—21no—
117C24×C59C2×D411yescharacteristic
118#41×C59—24no—
119#41×C59—24no—
120#41×C59—22no—
121#41×C59—22no—
122#41×C59—22no—
123#41×C59—22no—
124#41×C59—42no—
125#41×C59—42no—
126#41×C59—42no—
127#41×C59—42no—
128C2×Q8×C59—22no—
129C2×Q8×C59—22no—
130C2×Q8×C59—21no—
131C2×Q8×C59—24no—
132C2×Q8×C59—24no—
133C2×Q8×C59—22no—
134C2×Q8×C59—22no—
135C2×Q8×C59—22no—
136C2×Q8×C59—22no—
137C2×Q8×C59—22no—
138C2×Q8×C59—22no—
139C2×Q8×C59—22no—
140C2×Q8×C59—22no—
141C2×Q8×C59—42no—
142C2×Q8×C59—42no—
143C2×Q8×C59—42no—
144C2×Q8×C59—42no—
145C2×Q8×C59—42no—
146C2×Q8×C59—42no—
147C2×Q8×C59—42no—
148C2×Q8×C59—42no—
149C2×Q8×C59C2×D412yes—
150C2×D4×C59—22no—
151C2×D4×C59—22no—
152C2×D4×C59—21no—
153C2×D4×C59—22no—
154C2×D4×C59—22no—
155C2×D4×C59—42no—
156C2×D4×C59—42no—
157C2×D4×C59C2×D412yes—
158C22×C4×C59—21no—
159C22×C4×C59—21no—
160C22×C4×C59—22no—
161C22×C4×C59—21no—
162C22×C4×C59—22no—
163C22×C4×C59—24no—
164C22×C4×C59—24no—
165C22×C4×C59—22no—
166C22×C4×C59—22no—
167C22×C4×C59—42no—
168C22×C4×C59—42no—
169C22×C4×C59C2×D414yes—
170C22×C4×C59C2×D411yescharacteristic
171C22×C4×C59C2×D411yescharacteristic
172C22×C4×C59C2×D411yescharacteristic
173C22×C4×C59C2×D411yescharacteristic
174C22×C4×C59C2×D411yescharacteristic
175C22×C4×C59C2×D412yes—
176C22×C4×C59#4112yes—
177C22×C4×C59#4112yes—
178C22×C4×C59#4112yes—
179C22×C4×C59C2411yescharacteristic
180C22×Dic59—24no—
181C22×Dic59—22no—
182C22×Dic59—22no—
183C22×Dic59—42no—
184C22×Dic59—42no—
185C22×Dic59—44no—
186C22×Dic59—41no—
187C22×Dic59—41no—
188C4⋊C4×C59—28no—
189C4⋊C4×C59—28no—
190C4⋊C4×C59—21no—
191C4⋊C4×C59—21no—
192C4⋊C4×C59C2×D412yes—
193C4⋊C4×C59C2×D412yes—
194C22⋊C4×C59—28no—
195C22⋊C4×C59—28no—
196C22⋊C4×C59—22no—
197C22⋊C4×C59—22no—
198C42×C59—22no—
199C42×C59—22no—
200C4⋊Dic59—22no—
201C4⋊Dic59—22no—
202C4⋊Dic59—41no—
203C4⋊Dic59—41no—
204C4×Dic59—22no—
205C4×Dic59—22no—
206C4×Dic59—42no—
207#11745664—24no—
208#11745664—22no—
209#11745664—22no—
210#11745664—22no—
211#11745664—42no—
212#11745664C2×D414yes—
213C2×C59⋊C8—24no—
214C2×C59⋊C8—22no—
215C2×C59⋊C8—22no—
216C2×C59⋊C8—42no—
217C23×C59—22no—
218C23×C59—22no—
219C23×C59—22no—
220C23×C59—42no—
221C23×C59—42no—
222C23×C59—42no—
223C23×C59#12011yescharacteristic
224C23×C59#12011yescharacteristic
225C23×C59#12112yes—
226C23×C59#12312yes—
227C23×C59C22×D411yescharacteristic
228Q8×C59—22no—
229Q8×C59—22no—
230Q8×C59—42no—
231Q8×C59—42no—
232Q8×C59—42no—
233Q8×C59—42no—
234Q8×C59—44no—
235Q8×C59—44no—
236Q8×C59—42no—
237D4×C59—22no—
238D4×C59—22no—
239D4×C59—42no—
240D4×C59—42no—
241D4×C59—44no—
242D4×C59—42no—
243C2×C4×C59—22no—
244C2×C4×C59—22no—
245C2×C4×C59—24no—
246C2×C4×C59—22no—
247C2×C4×C59—24no—
248C2×C4×C59—24no—
249C2×C4×C59—44no—
250C2×C4×C59—44no—
251C2×C4×C59—42no—
252C2×C4×C59—42no—
253C2×C4×C59—42no—
254C2×C4×C59—42no—
255C2×C4×C59—42no—
256C2×C4×C59—44no—
257C2×C4×C59#12011yescharacteristic
258C2×C4×C59#12011yescharacteristic
259C2×C4×C59#12112yes—
260C2×C4×C59#12112yes—
261C2×C4×C59#12112yes—
262C2×C4×C59#12112yes—
263C2×C4×C59#12112yes—
264C2×C4×C59#12312yes—
265C2×C4×C59#12312yes—
266C2×C4×C59#12312yes—
267C2×C4×C59#12412yes—
268C2×C4×C59#12412yes—
269C2×C4×C59C22×D411yescharacteristic
270C2×C4×C59C22×D411yescharacteristic
271C2×C4×C59C22×D411yescharacteristic
272C2×C4×C59C2×#4111yescharacteristic
273C2×C4×C59C2×#4111yescharacteristic
274C2×C4×C59C2×#4111yescharacteristic
275C2×Dic59—24no—
276C2×Dic59—42no—
277C2×Dic59—48no—
278C2×Dic59—42no—
279C2×Dic59—44no—
280C2×Dic59—42no—
281C2×Dic59—82no—
282C2×Dic59—82no—
283C59⋊C8—24no—
284C59⋊C8—42no—
285C2×#2038—591nomaximal, Sylow
286C22×C59—21no—
287C22×C59—21no—
288C22×C59—21no—
289C22×C59—21no—
290C22×C59—24no—
291C22×C59—24no—
292C22×C59—42no—
293C22×C59—42no—
294C22×C59—42no—
295C22×C59—84no—
296C22×C59#39412yes—
297C22×C59#39412yes—
298C22×C59#45412yes—
299C22×C59#45612yes—
300C22×C59C2×#12011yescharacteristic
301C22×C59C2×#12111yescharacteristic
302C22×C59C2×#12311yescharacteristic
303C4×C59—44no—
304C4×C59—42no—
305C4×C59—42no—
306C4×C59—42no—
307C4×C59#39412yes—
308C4×C59#39412yes—
309C4×C59C2×#12111yescharacteristic
310C4×C59C2×#12111yescharacteristic
311C4×C59C2×#12311yescharacteristic
312C4×C59C2×#12411yescharacteristic
313Dic59—44no—
314Dic59—82no—
315C2×#536D5911yescharacteristic
316C2×#428—591no—
317C22×#104—591no—
318C2×#417—591no—
319C22×#101—591no—
320C2×#391—591no—
321#2038—598no—
322C2×#339—591no—
323C2×C59—21no—
324C2×C59—21no—
325C2×C59—22no—
326C2×C59—82no—
327C2×C59#203814yescomplemented
328C2×C59C2×#39411yescharacteristic
329C2×C59C2×#45411yescharacteristic
330C2×C59C2×#45611yescharacteristic
331C22×#41C2×D5911yescharacteristic
332C23×Q8C2×D5911yescharacteristic
333C22×M16—591no—
334C22×M16—591no—
335#536—22no—
336#536—22no—
337#536—22no—
338#536C2×D5914yes—
339C2×C4⋊Q8—21no—
340C2×#124—21no—
341C2×#123—22no—
342C2×C22⋊Q8—21no—
343C2×C22⋊Q8—21no—
344C2×#117C2×D5911yescharacteristic
345C22×C4⋊C4—591no—
346C22×C42—591no—
347#428—594no—
348#428—1182no—
349C2×#107—1181no—
350C2×#106—1181no—
351C2×#104—594no—
352C2×#104—1184no—
353#417—594no—
354#417—1182no—
355C2×#103—1181no—
356C2×#102—1181no—
357C2×#101—594no—
358C2×#101—1184no—
359#391—594no—
360#391—1182no—
361C2×#95—1182no—
362#339—594no—
363C59C2×#203811yescharacteristic, complemented, Sylow
364C2×#41—21no—
365C2×#41—21no—
366C2×#41—22no—
367C2×#41—22no—
368C2×#41—22no—
369C2×#41—22no—
370C2×#41C22⋊D5912yes—
371C2×#41C22×D5912yes—
372C22×Q8—22no—
373C22×Q8—22no—
374C22×Q8—22no—
375C22×Q8—22no—
376C22×Q8—21no—
377C22×Q8—21no—
378C22×Q8—21no—
379C22×Q8—21no—
380C22×Q8C22⋊D5911yescharacteristic
381C22×Q8C22⋊D5912yes—
382C22×Q8C22×D5912yes—
383C22×D4—21no—
384C22×D4C22⋊D5911yescharacteristic
385C23×C4—21no—
386C23×C4—1181no—
387C23×C4—1181no—
388C23×C4C22⋊D5912yes—
389C23×C4C22×D5911yescharacteristic
390C2×M16—594no—
391C2×M16—592no—
392C2×M16—592no—
393C2×M16—1182no—
394C2×M16—1181no—
395C2×M16—1181no—
396C2×M16—1182no—
397C2×M16—1182no—
398C22×C8—1181no—
399C22×C8—1181no—
400C4⋊Q8—24no—
401C4⋊Q8—24no—
402#124—24no—
403#124—24no—
404#123—28no—
405#123—28no—
406C22⋊Q8—24no—
407C22⋊Q8—24no—
408C22⋊Q8—24no—
409C22⋊Q8—24no—
410#117—21no—
411#117—21no—
412#117C22⋊D5912yes—
413#117C22×D5912yes—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—592no—
417C2×C4⋊C4—1181no—
418C2×C4⋊C4—1181no—
419C2×C4⋊C4—1181no—
420C2×C4⋊C4—1181no—
421C2×C4⋊C4—1181no—
422C2×C4⋊C4C22⋊D5911yescharacteristic
423C2×C4⋊C4C22⋊D5911yescharacteristic
424C2×C22⋊C4—22no—
425C2×C22⋊C4—22no—
426C2×C22⋊C4—21no—
427C2×C42—21no—
428C2×C42—592no—
429C2×C42—1182no—
430C2×C42—1182no—
431C2×C42—1181no—
432#107—1184no—
433#106—1184no—
434#104—1188no—
435#103—1184no—
436#102—1184no—
437#101—1188no—
438#95—1188no—
439C24—21no—
440C24C2×C22⋊D5911yescharacteristic
441#41—24no—
442#41—24no—
443#41—22no—
444#41—22no—
445#41—22no—
446#41—22no—
447#41—42no—
448#41—42no—
449#41—42no—
450#41—42no—
451C2×Q8—22no—
452C2×Q8—22no—
453C2×Q8—21no—
454C2×Q8—24no—
455C2×Q8—24no—
456C2×Q8—22no—
457C2×Q8—22no—
458C2×Q8—22no—
459C2×Q8—22no—
460C2×Q8—22no—
461C2×Q8—22no—
462C2×Q8—22no—
463C2×Q8—22no—
464C2×Q8—42no—
465C2×Q8—42no—
466C2×Q8—42no—
467C2×Q8—42no—
468C2×Q8—42no—
469C2×Q8—42no—
470C2×Q8—42no—
471C2×Q8—42no—
472C2×Q8C2×C22⋊D5912yes—
473C2×D4—22no—
474C2×D4—22no—
475C2×D4—21no—
476C2×D4—22no—
477C2×D4—22no—
478C2×D4—42no—
479C2×D4—42no—
480C2×D4C2×C22⋊D5912yes—
481C22×C4—22no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—22no—
485C22×C4—21no—
486C22×C4—24no—
487C22×C4—24no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—42no—
491C22×C4—42no—
492C22×C4—1184no—
493C22×C4—1182no—
494C22×C4—1182no—
495C22×C4—2364no—
496C22×C4—2361no—
497C22×C4—2361no—
498C22×C4—2362no—
499C22×C4—2362no—
500C22×C4D4×D5912yes—
501C22×C4#1174568712yes—
502C22×C4#1174568712yes—
503C22×C4#1174568712yes—
504C22×C4C2×C22⋊D5914yes—
505C22×C4C2×C22⋊D5911yescharacteristic
506C22×C4C2×C22⋊D5911yescharacteristic
507C22×C4C2×C22⋊D5911yescharacteristic
508C22×C4C2×C22⋊D5911yescharacteristic
509C22×C4C2×C22⋊D5911yescharacteristic
510C22×C4C23×D5911yescharacteristic
511M16—594no—
512M16—1184no—
513M16—1182no—
514M16—1182no—
515M16—1182no—
516M16—2362no—
517C2×C8—1184no—
518C2×C8—1182no—
519C2×C8—1182no—
520C2×C8—2362no—
521C4⋊C4—28no—
522C4⋊C4—28no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—1182no—
526C4⋊C4—1182no—
527C4⋊C4—2361no—
528C4⋊C4—2361no—
529C4⋊C4C2×C22⋊D5912yes—
530C4⋊C4C2×C22⋊D5912yes—
531C22⋊C4—28no—
532C22⋊C4—28no—
533C22⋊C4—22no—
534C22⋊C4—22no—
535C42—22no—
536C42—22no—
537C42—1182no—
538C42—1182no—
539C42—2362no—
540C23—22no—
541C23—22no—
542C23—22no—
543C23—42no—
544C23—42no—
545C23—42no—
546C23#1427369611yescharacteristic
547C23#1427369611yescharacteristic
548C23#1427369912yes—
549C23#1427370812yes—
550C23C22×C22⋊D5911yescharacteristic
551Q8—22no—
552Q8—22no—
553Q8—42no—
554Q8—42no—
555Q8—42no—
556Q8—42no—
557Q8—44no—
558Q8—44no—
559Q8—42no—
560D4—22no—
561D4—22no—
562D4—42no—
563D4—42no—
564D4—44no—
565D4—42no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—24no—
569C2×C4—22no—
570C2×C4—24no—
571C2×C4—24no—
572C2×C4—44no—
573C2×C4—44no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—44no—
580C2×C4—1184no—
581C2×C4—4722no—
582C2×C4—4722no—
583C2×C4—2364no—
584C2×C4—2362no—
585C2×C4—2362no—
586C2×C4—2368no—
587C2×C4—2362no—
588C2×C4#1427369611yescharacteristic
589C2×C4#1427369611yescharacteristic
590C2×C4#1427369812yes—
591C2×C4#1427369812yes—
592C2×C4#1427369912yes—
593C2×C4#1427369912yes—
594C2×C4#1427369912yes—
595C2×C4#1427370812yes—
596C2×C4#1427370812yes—
597C2×C4#1427370812yes—
598C2×C4#1427371412yes—
599C2×C4#1427371412yes—
600C2×C4C2×D4×D5911yescharacteristic
601C2×C4C22×C22⋊D5911yescharacteristic
602C2×C4C22×C22⋊D5911yescharacteristic
603C2×C4C2×#1174568711yescharacteristic
604C2×C4C2×#1174568711yescharacteristic
605C2×C4C2×#1174568711yescharacteristic
606C8—1184no—
607C8—2362no—
608C22—21no—
609C22—21no—
610C22—21no—
611C22—21no—
612C22—24no—
613C22—24no—
614C22—42no—
615C22—42no—
616C22—42no—
617C22—84no—
618C22#1683731612yes—
619C22#1683731612yes—
620C22#1683757512yes—
621C22#1683758512yes—
622C22C2×#1427369611yescharacteristic
623C22C2×#1427369911yescharacteristic
624C22C2×#1427370811yescharacteristic
625C4—42no—
626C4—42no—
627C4—44no—
628C4—42no—
629C4—4722no—
630C4—2364no—
631C4#1683731612yes—
632C4#1683731612yes—
633C4C2×#1427369811yescharacteristic
634C4C2×#1427369911yescharacteristic
635C4C2×#1427370811yescharacteristic
636C4C2×#1427371411yescharacteristic
637C2—21no—
638C2—21no—
639C2—22no—
640C2—82no—
641C2#2142531014yesdirect product factor
642C2C2×#1683731611yescharacteristic
643C2C2×#1683757511yescharacteristic
644C2C2×#1683758511yescharacteristic
subgroupG/H
centerC23#14273696
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
FittingC2×C59×#536C2
socleC23×C59#120
prime radicalC22×#41×C59C22
hypercenterC2×#536D59
hypocenterC59C2×#2038
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#536

Complements

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

NH ≅ G/Ntype
1. C2×#16837445C2semidirect
4. C22×#14273646C2semidirect
5. C2×#16837309C2semidirect
6. #21425310C2direct (N × H)
7. C2×#16837161C2semidirect
14. #16837445C22semidirect
24. C2×#14273646C22semidirect
26. #16837309C22semidirect
28. #16837161C22semidirect
327. C2×C59#2038semidirect
363. C59C2×#2038semidirect
641. C2#21425310direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168374452
C22×#142736542
C2×#168374032
C22×#142736462
C2×#168373092
#214253102
C2×#168371612
C2×C59×#5362
C2×#203859