Finite Group Databasebeta

← C2×#21443943 #29594979

Subgroups — C2×#21443943 #29594979

Order 15616.

1154 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519692C211yesmaximal, characteristic
2C2×#16839665C211yesmaximal, characteristic
3#21443943C214yesmaximal, direct product factor
4C22×#99×C61C211yesmaximal, characteristic
5C22×C4⋊Dic61C411yescharacteristic, complemented
6C22×C22⋊Dic61—21no—
7C22×C22⋊Dic61—21no—
8C22×C22⋊Dic61—21no—
9C22×C4×Dic61C411yescharacteristic, complemented
10C2×#14519692—21no—
11C2×#14519692—22no—
12C2×#14519692C414yescomplemented
13C2×#14519692C2212yes—
14#16839665—21no—
15#16839665—21no—
16#16839665C412yescomplemented
17#16839665C2212yes—
18C23×D4×C61C2211yescharacteristic
19C22×C22⋊C4×C61—21no—
20C2×#99×C61—21no—
21C2×#99×C61—22no—
22C2×#99×C61C414yescomplemented
23C2×#99×C61C2212yes—
24C23×Dic61—21no—
25C23×Dic61—21no—
26C23×Dic61—41no—
27C2×C4⋊Dic61—21no—
28C2×C4⋊Dic61—41no—
29C2×C4⋊Dic61—41no—
30C2×C4⋊Dic61C2×C412yescomplemented
31C2×C22⋊Dic61—24no—
32C2×C22⋊Dic61—22no—
33C2×C22⋊Dic61—22no—
34C2×C22⋊Dic61—22no—
35C2×C22⋊Dic61—22no—
36C2×C22⋊Dic61—22no—
37C2×C22⋊Dic61—44no—
38C2×C22⋊Dic61—44no—
39C2×C22⋊Dic61—41no—
40C2×C22⋊Dic61—42no—
41C2×C4×Dic61—21no—
42C2×C4×Dic61—42no—
43C2×C4×Dic61C2×C412yescomplemented
44#14519692—24no—
45#14519692—22no—
46#14519692C2×C414yescomplemented
47C25×C61D411yescharacteristic
48C25×C61D411yescharacteristic
49C22×D4×C61—42no—
50C22×D4×C61—41no—
51C22×D4×C61—41no—
52C22×D4×C61C2×C412yes—
53C22×D4×C61C2×C411yescharacteristic
54C22×D4×C61C2×C412yes—
55C22×D4×C61D411yescharacteristic
56C22×D4×C61D411yescharacteristic
57C22×D4×C61D412yes—
58C22×D4×C61Q812yes—
59C22×D4×C61C2311yescharacteristic
60C23×C4×C61—41no—
61C23×C4×C61C2×C411yescharacteristic
62C2×C22⋊C4×C61—24no—
63C2×C22⋊C4×C61—22no—
64C2×C22⋊C4×C61—41no—
65C2×C22⋊C4×C61—42no—
66#99×C61—24no—
67#99×C61—22no—
68#99×C61C2×C414yescomplemented
69C24×C61—21no—
70C24×C61—21no—
71C24×C61—22no—
72C24×C61—21no—
73C24×C61—22no—
74C24×C61—21no—
75C24×C61—42no—
76C24×C61—42no—
77C24×C61—42no—
78C24×C61—42no—
79C24×C61C22⋊C411yescharacteristic
80C24×C61C22⋊C412yes—
81C24×C61C22⋊C411yescharacteristic
82C24×C61C22⋊C411yescharacteristic
83C24×C61C22⋊C412yes—
84C24×C61C4⋊C412yes—
85C24×C61C4⋊C412yes—
86C24×C61C2×D411yescharacteristic
87C24×C61C2×D411yescharacteristic
88C2×D4×C61—42no—
89C2×D4×C61—42no—
90C2×D4×C61—42no—
91C2×D4×C61—42no—
92C2×D4×C61—41no—
93C2×D4×C61—41no—
94C2×D4×C61—42no—
95C2×D4×C61—42no—
96C2×D4×C61—41no—
97C2×D4×C61—41no—
98C2×D4×C61—41no—
99C2×D4×C61—41no—
100C2×D4×C61—42no—
101C2×D4×C61—42no—
102C2×D4×C61—41no—
103C2×D4×C61—41no—
104C2×D4×C61C4212yes—
105C2×D4×C61C22⋊C412yes—
106C2×D4×C61C22⋊C412yes—
107C2×D4×C61C4⋊C412yes—
108C2×D4×C61C4⋊C412yes—
109C2×D4×C61C4⋊C412yes—
110C2×D4×C61C22×C411yescharacteristic
111C2×D4×C61C22×C411yescharacteristic
112C2×D4×C61C2×D411yescharacteristic
113C2×D4×C61C2×Q811yescharacteristic
114C22×C4×C61—22no—
115C22×C4×C61—21no—
116C22×C4×C61—21no—
117C22×C4×C61—44no—
118C22×C4×C61—42no—
119C22×C4×C61—82no—
120C22×C4×C61—82no—
121C22×C4×C61C4212yes—
122C22×C4×C61C22⋊C411yescharacteristic
123C22×C4×C61C4⋊C412yes—
124C22×C4×C61C22×C411yescharacteristic
125C22×Dic61—24no—
126C22×Dic61—22no—
127C22×Dic61—22no—
128C22×Dic61—42no—
129C22×Dic61—42no—
130C22×Dic61—42no—
131C22×Dic61—42no—
132C22×Dic61—44no—
133C22×Dic61—42no—
134C22×Dic61—41no—
135C22×Dic61—41no—
136C22×Dic61—82no—
137C22×Dic61—82no—
138C22⋊C4×C61—24no—
139C22⋊C4×C61—44no—
140C22⋊C4×C61—42no—
141C22⋊Dic61—24no—
142C22⋊Dic61—44no—
143C22⋊Dic61—44no—
144C22⋊Dic61—44no—
145C22⋊Dic61—44no—
146C22⋊Dic61—44no—
147C22⋊Dic61—42no—
148C4⋊Dic61—42no—
149C4⋊Dic61—42no—
150C4×Dic61—42no—
151C4×Dic61—42no—
152C23×C61—22no—
153C23×C61—22no—
154C23×C61—22no—
155C23×C61—22no—
156C23×C61—22no—
157C23×C61—22no—
158C23×C61—21no—
159C23×C61—21no—
160C23×C61—21no—
161C23×C61—21no—
162C23×C61—22no—
163C23×C61—22no—
164C23×C61—22no—
165C23×C61—22no—
166C23×C61—21no—
167C23×C61—21no—
168C23×C61—21no—
169C23×C61—21no—
170C23×C61—41no—
171C23×C61—41no—
172C23×C61—41no—
173C23×C61—41no—
174C23×C61—41no—
175C23×C61—41no—
176C23×C61—44no—
177C23×C61—44no—
178C23×C61—44no—
179C23×C61—44no—
180C23×C61—41no—
181C23×C61—41no—
182C23×C61—42no—
183C23×C61—42no—
184C23×C61—42no—
185C23×C61—42no—
186C23×C61—81no—
187C23×C61—81no—
188C23×C61—81no—
189C23×C61—81no—
190C23×C61—84no—
191C23×C61—84no—
192C23×C61#9512yes—
193C23×C61#9512yes—
194C23×C61#9512yes—
195C23×C61#9911yescharacteristic
196C23×C61#9912yes—
197C23×C61#9911yescharacteristic
198C23×C61C2×C22⋊C411yescharacteristic
199C23×C61C2×C22⋊C411yescharacteristic
200C23×C61C2×C22⋊C411yescharacteristic
201C23×C61C2×C4⋊C411yescharacteristic
202C23×C61C2×C4⋊C411yescharacteristic
203D4×C61—42no—
204D4×C61—42no—
205D4×C61—42no—
206D4×C61—42no—
207D4×C61—42no—
208D4×C61—42no—
209D4×C61—41no—
210D4×C61—41no—
211D4×C61—41no—
212D4×C61—41no—
213C2×C4×C61—22no—
214C2×C4×C61—22no—
215C2×C4×C61—22no—
216C2×C4×C61—22no—
217C2×C4×C61—21no—
218C2×C4×C61—21no—
219C2×C4×C61—21no—
220C2×C4×C61—21no—
221C2×C4×C61—44no—
222C2×C4×C61—82no—
223C2×C4×C61—82no—
224C2×C4×C61—88no—
225C2×C4×C61#9512yes—
226C2×C4×C61C2×C4211yescharacteristic
227C2×C4×C61C2×C4⋊C411yescharacteristic
228C2×Dic61—24no—
229C2×Dic61—42no—
230C2×Dic61—48no—
231C2×Dic61—42no—
232C2×Dic61—44no—
233C2×Dic61—42no—
234C2×Dic61—42no—
235C2×Dic61—42no—
236C2×Dic61—82no—
237C2×Dic61—82no—
238C2×Dic61—82no—
239C2×Dic61—88no—
240C2×Dic61—82no—
241C2×#1393—611nomaximal, Sylow
242C22×C61—21no—
243C22×C61—21no—
244C22×C61—21no—
245C22×C61—21no—
246C22×C61—24no—
247C22×C61—24no—
248C22×C61—21no—
249C22×C61—21no—
250C22×C61—22no—
251C22×C61—22no—
252C22×C61—21no—
253C22×C61—21no—
254C22×C61—42no—
255C22×C61—42no—
256C22×C61—41no—
257C22×C61—41no—
258C22×C61—41no—
259C22×C61—41no—
260C22×C61—41no—
261C22×C61—41no—
262C22×C61—41no—
263C22×C61—41no—
264C22×C61—41no—
265C22×C61—41no—
266C22×C61—41no—
267C22×C61—41no—
268C22×C61—44no—
269C22×C61—44no—
270C22×C61—44no—
271C22×C61—44no—
272C22×C61—81no—
273C22×C61—81no—
274C22×C61—81no—
275C22×C61—81no—
276C22×C61—82no—
277C22×C61—82no—
278C22×C61—82no—
279C22×C61—82no—
280C22×C61#34212yes—
281C22×C61#34212yes—
282C22×C61#35312yes—
283C22×C61#35412yes—
284C22×C61C2×#9511yescharacteristic
285C22×C61C2×#9911yescharacteristic
286C22×C61C2×#9911yescharacteristic
287C4×C61—22no—
288C4×C61—21no—
289C4×C61—21no—
290C4×C61—84no—
291Dic61—44no—
292Dic61—84no—
293Dic61—82no—
294C22×#99—611no—
295C22×#99D6111yescharacteristic
296C2×#390—611no—
297#1393—614no—
298C2×C61—21no—
299C2×C61—21no—
300C2×C61—22no—
301C2×C61—41no—
302C2×C61—41no—
303C2×C61—42no—
304C2×C61—42no—
305C2×C61—41no—
306C2×C61—41no—
307C2×C61#139314yescomplemented
308C2×C61C2×#34211yescharacteristic
309C2×C61C2×#35311yescharacteristic
310C2×C61C2×#35411yescharacteristic
311C23×D4C2×D6111yescharacteristic
312C22×C4⋊C4—611no—
313C22×C22⋊C4—21no—
314C22×C22⋊C4—1221no—
315C22×C22⋊C4—1221no—
316C22×C22⋊C4—1221no—
317C22×C42—611no—
318C2×#99—21no—
319C2×#99—22no—
320C2×#99—614no—
321C2×#99—612no—
322C2×#99—1221no—
323C2×#99—1222no—
324C2×#99Dic6114yescomplemented
325C2×#99C2×D6112yes—
326#390—612no—
327#390—612no—
328#390—1221no—
329#390—1221no—
330C61C2×#139311yescharacteristic, complemented, Sylow
331C25D24411yescharacteristic
332C25C22⋊D6111yescharacteristic
333C22×D4—42no—
334C22×D4—41no—
335C22×D4—41no—
336C22×D4Dic12212yes—
337C22×D4C4×D6112yes—
338C22×D4C4×D6111yescharacteristic
339C22×D4D24411yescharacteristic
340C22×D4C2×Dic6112yes—
341C22×D4C22⋊D6112yes—
342C22×D4C22⋊D6111yescharacteristic
343C22×D4C22×D6111yescharacteristic
344C23×C4—41no—
345C23×C4—1221no—
346C23×C4—1221no—
347C23×C4—2441no—
348C23×C4C4×D6111yescharacteristic
349C2×C4⋊C4—612no—
350C2×C4⋊C4—1221no—
351C2×C4⋊C4—2441no—
352C2×C4⋊C4—2441no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—22no—
355C2×C22⋊C4—42no—
356C2×C22⋊C4—41no—
357C2×C22⋊C4—1224no—
358C2×C22⋊C4—1222no—
359C2×C22⋊C4—1222no—
360C2×C22⋊C4—1222no—
361C2×C22⋊C4—1222no—
362C2×C22⋊C4—1222no—
363C2×C22⋊C4—2444no—
364C2×C22⋊C4—2444no—
365C2×C22⋊C4—2442no—
366C2×C22⋊C4—2441no—
367C2×C42—612no—
368C2×C42—1221no—
369C2×C42—2442no—
370#99—24no—
371#99—22no—
372#99—614no—
373#99—1224no—
374#99—1222no—
375#99C2×Dic6114yescomplemented
376C24—21no—
377C24—21no—
378C24—21no—
379C24—22no—
380C24—21no—
381C24—22no—
382C24—42no—
383C24—42no—
384C24—42no—
385C24—42no—
386C24#1175819612yes—
387C24C4⋊Dic6112yes—
388C24#1175819811yescharacteristic
389C24#1175819811yescharacteristic
390C24#1175819812yes—
391C24#1175819811yescharacteristic
392C24C22⋊Dic6112yes—
393C24C2×D24411yescharacteristic
394C24C2×C22⋊D6111yescharacteristic
395C2×D4—42no—
396C2×D4—42no—
397C2×D4—41no—
398C2×D4—41no—
399C2×D4—42no—
400C2×D4—42no—
401C2×D4—41no—
402C2×D4—41no—
403C2×D4—42no—
404C2×D4—42no—
405C2×D4—41no—
406C2×D4—41no—
407C2×D4—42no—
408C2×D4—42no—
409C2×D4—41no—
410C2×D4—41no—
411C2×D4C4×Dic6112yes—
412C2×D4#1175819612yes—
413C2×D4#1175819612yes—
414C2×D4C4⋊Dic6112yes—
415C2×D4#1175819812yes—
416C2×D4C22⋊Dic6112yes—
417C2×D4C2×Dic12211yescharacteristic
418C2×D4C2×C4×D6111yescharacteristic
419C2×D4C22×Dic6111yescharacteristic
420C2×D4C2×C22⋊D6111yescharacteristic
421C22×C4—22no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—42no—
425C22×C4—44no—
426C22×C4—82no—
427C22×C4—82no—
428C22×C4—1224no—
429C22×C4—1222no—
430C22×C4—1222no—
431C22×C4—4882no—
432C22×C4—4882no—
433C22×C4—2442no—
434C22×C4—2444no—
435C22×C4—2442no—
436C22×C4—2442no—
437C22×C4—2441no—
438C22×C4—2441no—
439C22×C4—2442no—
440C22×C4—2442no—
441C22×C4C4×Dic6112yes—
442C22×C4#1175819612yes—
443C22×C4#1175819811yescharacteristic
444C22×C4C2×C4×D6111yescharacteristic
445C4⋊C4—2442no—
446C4⋊C4—2442no—
447C22⋊C4—24no—
448C22⋊C4—42no—
449C22⋊C4—44no—
450C22⋊C4—1224no—
451C22⋊C4—2444no—
452C22⋊C4—2444no—
453C22⋊C4—2444no—
454C22⋊C4—2444no—
455C22⋊C4—2442no—
456C22⋊C4—2444no—
457C42—2442no—
458C42—2442no—
459C23—22no—
460C23—22no—
461C23—21no—
462C23—21no—
463C23—21no—
464C23—21no—
465C23—22no—
466C23—22no—
467C23—22no—
468C23—22no—
469C23—21no—
470C23—21no—
471C23—21no—
472C23—21no—
473C23—22no—
474C23—22no—
475C23—22no—
476C23—22no—
477C23—41no—
478C23—41no—
479C23—41no—
480C23—41no—
481C23—44no—
482C23—44no—
483C23—41no—
484C23—41no—
485C23—44no—
486C23—44no—
487C23—41no—
488C23—41no—
489C23—42no—
490C23—42no—
491C23—42no—
492C23—42no—
493C23—81no—
494C23—81no—
495C23—81no—
496C23—81no—
497C23—84no—
498C23—84no—
499C23#1451968412yes—
500C23#1451968412yes—
501C23#1451968412yes—
502C23#1451969111yescharacteristic
503C23#1451969112yes—
504C23#1451969111yescharacteristic
505C23C2×#1175819811yescharacteristic
506C23C2×#1175819811yescharacteristic
507C23C2×C22⋊Dic6111yescharacteristic
508C23C2×#1175819611yescharacteristic
509C23C2×C4⋊Dic6111yescharacteristic
510D4—42no—
511D4—42no—
512D4—42no—
513D4—42no—
514D4—42no—
515D4—42no—
516D4—41no—
517D4—41no—
518D4—41no—
519D4—41no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—44no—
529C2×C4—82no—
530C2×C4—82no—
531C2×C4—88no—
532C2×C4—1224no—
533C2×C4—4882no—
534C2×C4—4882no—
535C2×C4—4882no—
536C2×C4—4888no—
537C2×C4—4882no—
538C2×C4—2444no—
539C2×C4—2442no—
540C2×C4—2442no—
541C2×C4—2442no—
542C2×C4—2442no—
543C2×C4—2448no—
544C2×C4—2442no—
545C2×C4#1451968412yes—
546C2×C4C2×C4×Dic6111yescharacteristic
547C2×C4C2×#1175819611yescharacteristic
548C22—21no—
549C22—21no—
550C22—21no—
551C22—21no—
552C22—24no—
553C22—24no—
554C22—21no—
555C22—21no—
556C22—22no—
557C22—22no—
558C22—21no—
559C22—21no—
560C22—42no—
561C22—42no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—44no—
575C22—44no—
576C22—44no—
577C22—44no—
578C22—81no—
579C22—81no—
580C22—81no—
581C22—81no—
582C22—82no—
583C22—82no—
584C22—82no—
585C22—82no—
586C22#1683952812yes—
587C22#1683952812yes—
588C22#1683955412yes—
589C22#1683955612yes—
590C22C2×#1451968411yescharacteristic
591C22C2×#1451969111yescharacteristic
592C22C2×#1451969111yescharacteristic
593C4—22no—
594C4—21no—
595C4—21no—
596C4—84no—
597C4—4884no—
598C4—4882no—
599C4—2444no—
600C2—21no—
601C2—21no—
602C2—22no—
603C2—41no—
604C2—41no—
605C2—42no—
606C2—42no—
607C2—41no—
608C2—41no—
609C2#2144394314yesdirect product factor
610C2C2×#1683952811yescharacteristic
611C2C2×#1683955411yescharacteristic
612C2C2×#1683955611yescharacteristic
subgroupG/H
centerC23#14519691
commutatorC2×C4×C61C2×C42
FrattiniC22×D4C22×D61
FittingC22×#99×C61C2
socleC23×C61#99
prime radicalC23×D4×C61C22
cosocleC22×D4×C61C23
hypercenterC22×#99D61
hypocenterC61C2×#1393
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C24 ◁ C23×D4 ◁ C22×#99

Complements

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

NH ≅ G/Ntype
3. #21443943C2direct (N × H)
5. C22×C4⋊Dic61C4semidirect
9. C22×C4×Dic61C4semidirect
12. C2×#14519692C4semidirect
16. #16839665C4semidirect
22. C2×#99×C61C4semidirect
30. C2×C4⋊Dic61C2×C4semidirect
43. C2×C4×Dic61C2×C4semidirect
46. #14519692C2×C4semidirect
68. #99×C61C2×C4semidirect
307. C2×C61#1393semidirect
324. C2×#99Dic61semidirect
330. C61C2×#1393semidirect
375. #99C2×Dic61semidirect
609. C2#21443943direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145196922
C2×#168396652
#214439432
C22×#99×C612
C2×#139361