Finite Group Databasebeta

← C2×#21461087 #30610045

Subgroups — C2×#21461087 #30610045

Order 15616.

1490 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840733C211yesmaximal, characteristic, complemented
2C2×D61⋊(C22⋊C8)C211yesmaximal, characteristic, complemented
3#21461087C218yesmaximal, direct product factor
4C2×#16840608C212yesmaximal, complemented
5C2×#16840606C212yesmaximal, complemented
6C22×#14519762C211yesmaximal, characteristic
7C22×#11758213—21no—
8C22×D61⋊C8—21no—
9#16840733—22no—
10#16840733C2214yescomplemented
11C2×#14519834—21no—
12C2×#14519834—21no—
13D61⋊(C22⋊C8)—22no—
14D61⋊(C22⋊C8)C2214yescomplemented
15C2×C22⋊#92420C2212yes—
16C2×C22⋊#92420C2212yes—
17#16840608C2218yescomplemented
18#16840606C2218yescomplemented
19C23×D244C411yescharacteristic
20C23×C4×D61C2211yescharacteristic
21C2×#14519762—21no—
22C2×#14519762—21no—
23C2×#14519762—22no—
24C2×#14519762—21no—
25C2×#14519762—21no—
26C2×#14519762—22no—
27C2×#14519762C414yes—
28C2×#14519762C2214yes—
29C22×#11758196C2211yescharacteristic
30C22×#11758198C411yescharacteristic
31C22×#11758198C411yescharacteristic
32C22×#11758198C2211yescharacteristic
33C22×C4⋊C4×C61C411yescharacteristic
34C2×#11758213—24no—
35C2×#11758213—44no—
36C2×D61⋊C8—24no—
37C2×D61⋊C8—44no—
38C22×#92420—22no—
39C22×#92420—22no—
40#14519834—24no—
41#14519834—24no—
42C22⋊#92420—22no—
43C22⋊#92420—22no—
44C22⋊#92420C2314yes—
45C22⋊#92420C2314yes—
46C24×D61C2×C411yescharacteristic
47C24×D61C2×C411yescharacteristic
48C22×D244—21no—
49C22×D244—22no—
50C22×D244—21no—
51C22×D244—44no—
52C22×D244C2×C414yes—
53C23×Dic61C2×C411yescharacteristic
54C23×Dic61C2311yescharacteristic
55C22×C4×D61—44no—
56C22×C4×D61C2×C412yes—
57C22×C4×D61D411yescharacteristic
58C22×C4×D61D411yescharacteristic
59C22×C4×D61D412yes—
60C22×C4×D61D411yescharacteristic
61C22×C4×D61D411yescharacteristic
62C22×C4×D61D412yes—
63C22×C4×D61C2312yes—
64#14519762—24no—
65#14519762—24no—
66#14519762—24no—
67#14519762—24no—
68#14519762—24no—
69#14519762—24no—
70#14519762—24no—
71#14519762—24no—
72C2×#11758196—21no—
73C2×#11758196—21no—
74C2×#11758196—21no—
75C2×#11758196—21no—
76C2×#11758196C2×C412yes—
77C2×#11758196C2312yes—
78C2×#11758198—21no—
79C2×#11758198—22no—
80C2×#11758198—21no—
81C2×#11758198—21no—
82C2×#11758198—21no—
83C2×#11758198—22no—
84C2×#11758198—21no—
85C2×#11758198—21no—
86C2×#11758198—21no—
87C2×#11758198—21no—
88C2×#11758198C2×C414yes—
89C2×#11758198C2×C414yes—
90C2×#11758198C2×C412yes—
91C2×#11758198C2312yes—
92C23×C4×C61C2×C411yescharacteristic
93C23×C4×C61C2×C411yescharacteristic
94C23×C4×C61C2×C411yescharacteristic
95C2×C4⋊C4×C61—21no—
96C2×C4⋊C4×C61—21no—
97C2×C4⋊C4×C61—22no—
98C2×C4⋊C4×C61C2×C414yes—
99C24×C61C22×C411yescharacteristic
100C23×D61—24no—
101C23×D61—24no—
102C23×D61—21no—
103C23×D61—21no—
104C23×D61—24no—
105C23×D61—42no—
106C23×D61—42no—
107C23×D61—42no—
108C23×D61C22⋊C411yescharacteristic
109C23×D61C22⋊C412yes—
110C23×D61C22⋊C411yescharacteristic
111C23×D61C22×C412yes—
112C23×D61C22×C412yes—
113C22×C4×C61—21no—
114C22×C4×C61—21no—
115C22×C4×C61—21no—
116C22×C4×C61—21no—
117C22×C4×C61—42no—
118C22×C4×C61—42no—
119C22×C4×C61—42no—
120C22×C4×C61C22⋊C411yescharacteristic
121C22×C4×C61C22⋊C411yescharacteristic
122C22×C4×C61C22⋊C412yes—
123C22×C4×C61C22×C412yes—
124C22×C4×C61C22×C412yes—
125C22×C4×C61C22×C412yes—
126C22×Dic61—21no—
127C22×Dic61—21no—
128C22×Dic61—24no—
129C22×Dic61—42no—
130C22×Dic61C22×C412yes—
131C22×Dic61C22×C411yescharacteristic
132C22×Dic61C2×D411yescharacteristic
133C22×Dic61C2×D411yescharacteristic
134C22×Dic61C2×D411yescharacteristic
135C22×Dic61C2×D411yescharacteristic
136C22×Dic61C2411yescharacteristic
137C2×D244—24no—
138C2×D244—24no—
139C2×D244—44no—
140C2×D244—48no—
141C2×D244—44no—
142C2×D244—48no—
143C2×C4×D61—24no—
144C2×C4×D61—24no—
145C2×C4×D61—44no—
146C2×C4×D61—44no—
147C2×C4×D61—44no—
148C2×C4×D61—44no—
149C2×C4×D61—42no—
150C2×C4×D61—42no—
151C2×C4×D61C22⋊C412yes—
152C2×C4×D61C22⋊C412yes—
153C2×C4×D61C22⋊C412yes—
154C2×C4×D61C22⋊C412yes—
155C2×C4×D61C2×D412yes—
156C2×C4×D61C2×D412yes—
157C2×C4×D61C2×D412yes—
158C2×C4×D61C2×D412yes—
159C2×#92420—24no—
160C2×#92420—24no—
161C2×#92420—44no—
162C2×#92420—44no—
163#11758213—48no—
164D61⋊C8—48no—
165C4⋊C4×C61—24no—
166C4⋊C4×C61—24no—
167#11758198—24no—
168#11758198—24no—
169#11758198—24no—
170#11758198—24no—
171#11758198—22no—
172#11758198—22no—
173#11758198—22no—
174#11758198—22no—
175#11758196—22no—
176#11758196—22no—
177#11758196—22no—
178#11758196—22no—
179C23×C61—22no—
180C23×C61—22no—
181C23×C61C2×C22⋊C411yescharacteristic
182C23×C61C2×C22⋊C411yescharacteristic
183C23×C61#13114yes—
184C23×C61C23×C411yescharacteristic
185C22×D61—22no—
186C22×D61—22no—
187C22×D61—24no—
188C22×D61—24no—
189C22×D61—22no—
190C22×D61—22no—
191C22×D61—22no—
192C22×D61—24no—
193C22×D61—24no—
194C22×D61—22no—
195C22×D61—24no—
196C22×D61—42no—
197C22×D61—42no—
198C22×D61—416no—
199C22×D61—42no—
200C22×D61—42no—
201C22×D61—42no—
202C22×D61—42no—
203C22×D61—42no—
204C22×D61—42no—
205C22×D61—42no—
206C22×D61—42no—
207C22×D61—88no—
208C22×D61#9914yes—
209C22×D61C2×C22⋊C412yes—
210C22×D61C2×C22⋊C412yes—
211C2×C4×C61—22no—
212C2×C4×C61—22no—
213C2×C4×C61—22no—
214C2×C4×C61—22no—
215C2×C4×C61—42no—
216C2×C4×C61—42no—
217C2×C4×C61—42no—
218C2×C4×C61—42no—
219C2×C4×C61—42no—
220C2×C4×C61—42no—
221C2×C4×C61—42no—
222C2×C4×C61—42no—
223C2×C4×C61C2×C22⋊C412yes—
224C2×C4×C61C2×C22⋊C412yes—
225C2×Dic61—22no—
226C2×Dic61—22no—
227C2×Dic61—22no—
228C2×Dic61—24no—
229C2×Dic61—41no—
230C2×Dic61—41no—
231C2×Dic61—41no—
232C2×Dic61—41no—
233C2×Dic61—42no—
234C2×Dic61—42no—
235C2×Dic61C2×C22⋊C411yescharacteristic
236C2×Dic61C2×C22⋊C411yescharacteristic
237C2×Dic61C22×D411yescharacteristic
238C2×Dic61C22×D411yescharacteristic
239D244—48no—
240D244—48no—
241C4×D61—24no—
242C4×D61—24no—
243C4×D61—24no—
244C4×D61—24no—
245C4×D61—42no—
246C4×D61—42no—
247C4×D61—42no—
248C4×D61—42no—
249#92420—44no—
250#92420—44no—
251C2×#1468—611nomaximal, Sylow
252C22×C61—21no—
253C22×C61—21no—
254C22×C61—21no—
255C22×C61—21no—
256C22×C61—28no—
257C22×C61#40812yes—
258C22×C61#40812yes—
259C22×C61C2×#9912yes—
260C22×C61#41312yes—
261C22×C61C22×C22⋊C411yescharacteristic
262C22×C61C2×#13112yes—
263C2×D61—22no—
264C2×D61—22no—
265C2×D61—28no—
266C2×D61—22no—
267C2×D61—22no—
268C2×D61—22no—
269C2×D61—48no—
270C2×D61—48no—
271C2×D61—44no—
272C2×D61—42no—
273C2×D61—42no—
274C2×D61—42no—
275C2×D61—84no—
276C2×D61—84no—
277C2×D61—84no—
278C2×D61C2×#9914yes—
279C4×C61—22no—
280C4×C61—22no—
281C4×C61—42no—
282C4×C61—42no—
283Dic61—21no—
284Dic61—21no—
285Dic61—21no—
286Dic61—21no—
287Dic61—42no—
288C22×#123—611no—
289C2×#407—611no—
290C22×C22⋊C8—611no—
291#1468—618no—
292C2×#324—612no—
293C2×#323—612no—
294C2×C61—22no—
295C2×C61—22no—
296C2×C61#146814yescomplemented
297C2×C61C2×#40811yescharacteristic
298C2×C61C22×#9911yescharacteristic
299C2×C61C2×#41311yescharacteristic
300D61—24no—
301D61—42no—
302D61—82no—
303C23×D4—611no—
304C24×C4—611no—
305C22×M16—1221no—
306C23×C8—1221no—
307C2×#123—614no—
308C2×#123—614no—
309C2×#123—1221no—
310C2×#123—1221no—
311C2×#123—1222no—
312C2×#123—1221no—
313C2×#123—1221no—
314C2×#123—1222no—
315C22×C4⋊C4—611no—
316C22×C4⋊C4#692311yescharacteristic
317C22×C22⋊C4—611no—
318C22×C22⋊C4—611no—
319C22×C22⋊C4—611no—
320#407—614no—
321#407—1222no—
322C2×C22⋊C8—612no—
323C2×C22⋊C8—612no—
324C2×C22⋊C8—614no—
325C2×C22⋊C8—1222no—
326C2×C22⋊C8—1221no—
327C2×C22⋊C8—1221no—
328#324—618no—
329#323—618no—
330C61C2×#146811yescharacteristic, complemented, Sylow
331C25—611no—
332C25—611no—
333C22×D4—614no—
334C22×D4—1222no—
335C22×D4—1221no—
336C22×D4—1221no—
337C22×D4—2444no—
338C23×C4—611no—
339C23×C4—611no—
340C23×C4—611no—
341C23×C4—611no—
342C23×C4—611no—
343C23×C4—612no—
344C23×C4—612no—
345C23×C4—612no—
346C23×C4—612no—
347C23×C4—611no—
348C23×C4—2444no—
349C23×C4C2×#692311yescharacteristic
350C23×C4C2×#692311yescharacteristic
351C23×C4C2×#692311yescharacteristic
352C2×M16—1224no—
353C2×M16—2444no—
354C22×C8—1222no—
355C22×C8—1222no—
356C22×C8—1224no—
357C22×C8—2444no—
358#123—1224no—
359#123—1224no—
360#123—1224no—
361#123—1224no—
362#123—1224no—
363#123—1224no—
364#123—1224no—
365#123—1224no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—612no—
370C2×C4⋊C4—612no—
371C2×C4⋊C4—1221no—
372C2×C4⋊C4—1221no—
373C2×C4⋊C4—1221no—
374C2×C4⋊C4—1221no—
375C2×C4⋊C4C2×#692314yes—
376C2×C22⋊C4—612no—
377C2×C22⋊C4—612no—
378C2×C22⋊C4—614no—
379C2×C22⋊C4—614no—
380C2×C22⋊C4—1221no—
381C2×C22⋊C4—1221no—
382C2×C22⋊C4—1221no—
383C2×C22⋊C4—1221no—
384C2×C22⋊C4—1222no—
385C2×C22⋊C4—1221no—
386C2×C22⋊C4—1221no—
387C2×C22⋊C4—1222no—
388C2×C22⋊C4—1221no—
389C2×C22⋊C4—1221no—
390C22⋊C8—614no—
391C22⋊C8—614no—
392C22⋊C8—1222no—
393C22⋊C8—1222no—
394C22⋊C8—1224no—
395C22⋊C8—1224no—
396C24—611no—
397C24—611no—
398C24—612no—
399C24—612no—
400C24—612no—
401C24—1224no—
402C24—1224no—
403C24—1224no—
404C24—1221no—
405C24—1221no—
406C24—2442no—
407C24—2442no—
408C24—2442no—
409C24C22×#692311yescharacteristic
410C2×D4—1224no—
411C2×D4—1224no—
412C2×D4—2444no—
413C2×D4—2448no—
414C2×D4—2444no—
415C2×D4—2448no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—42no—
421C22×C4—42no—
422C22×C4—42no—
423C22×C4—611no—
424C22×C4—611no—
425C22×C4—611no—
426C22×C4—611no—
427C22×C4—611no—
428C22×C4—611no—
429C22×C4—612no—
430C22×C4—612no—
431C22×C4—612no—
432C22×C4—612no—
433C22×C4—612no—
434C22×C4—612no—
435C22×C4—612no—
436C22×C4—612no—
437C22×C4—612no—
438C22×C4—1224no—
439C22×C4—1224no—
440C22×C4—1221no—
441C22×C4—1221no—
442C22×C4—1224no—
443C22×C4—2442no—
444C22×C4—2442no—
445C22×C4—2444no—
446C22×C4—2444no—
447C22×C4—2444no—
448C22×C4—2444no—
449C22×C4—2442no—
450C22×C4C22⋊#692311yescharacteristic
451C22×C4C22⋊#692311yescharacteristic
452C22×C4C22⋊#692312yes—
453C22×C4C22×#692312yes—
454C22×C4C22×#692312yes—
455C22×C4C22×#692312yes—
456M16—2448no—
457C2×C8—1224no—
458C2×C8—1224no—
459C2×C8—2448no—
460C2×C8—2444no—
461C2×C8—2444no—
462C4⋊C4—24no—
463C4⋊C4—24no—
464C4⋊C4—1222no—
465C4⋊C4—1222no—
466C4⋊C4—1222no—
467C4⋊C4—1222no—
468C22⋊C4—1222no—
469C22⋊C4—1222no—
470C22⋊C4—1222no—
471C22⋊C4—1222no—
472C22⋊C4—1224no—
473C22⋊C4—1224no—
474C22⋊C4—1224no—
475C22⋊C4—1224no—
476C23—22no—
477C23—22no—
478C23—614no—
479C23—612no—
480C23—612no—
481C23—1224no—
482C23—1224no—
483C23—1222no—
484C23—1222no—
485C23—1224no—
486C23—1222no—
487C23—1222no—
488C23—1222no—
489C23—1224no—
490C23—1224no—
491C23—1222no—
492C23—4888no—
493C23—2442no—
494C23—2442no—
495C23—24416no—
496C23—2442no—
497C23—2442no—
498C23—2442no—
499C23—2442no—
500C23—2442no—
501C23—2442no—
502C23—2442no—
503C23—2442no—
504C23C2×C22⋊#692311yescharacteristic
505C23C2×C22⋊#692311yescharacteristic
506C23#1451986514yes—
507C23C23×#692311yescharacteristic
508D4—2448no—
509D4—2448no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—611no—
523C2×C4—611no—
524C2×C4—611no—
525C2×C4—611no—
526C2×C4—1224no—
527C2×C4—1224no—
528C2×C4—1224no—
529C2×C4—1224no—
530C2×C4—1222no—
531C2×C4—1222no—
532C2×C4—1222no—
533C2×C4—1224no—
534C2×C4—2442no—
535C2×C4—2442no—
536C2×C4—2442no—
537C2×C4—2442no—
538C2×C4—2441no—
539C2×C4—2441no—
540C2×C4—2441no—
541C2×C4—2441no—
542C2×C4—2442no—
543C2×C4—2442no—
544C2×C4C2×C22⋊#692312yes—
545C2×C4C2×C22⋊#692312yes—
546C8—2444no—
547C8—2444no—
548C22—28no—
549C22—21no—
550C22—21no—
551C22—21no—
552C22—21no—
553C22—614no—
554C22—1228no—
555C22—1222no—
556C22—1222no—
557C22—1222no—
558C22—1222no—
559C22—1222no—
560C22—4884no—
561C22—4884no—
562C22—4884no—
563C22—2448no—
564C22—2448no—
565C22—2442no—
566C22—2442no—
567C22—2442no—
568C22—2444no—
569C22#1684073712yes—
570C22#1684073712yes—
571C22D61⋊#9912yes—
572C22#1684074812yes—
573C22C22×C22⋊#692311yescharacteristic
574C22C2×#1451986512yes—
575C4—22no—
576C4—22no—
577C4—42no—
578C4—42no—
579C4—1221no—
580C4—1221no—
581C4—1221no—
582C4—1221no—
583C4—2442no—
584C2—22no—
585C2—22no—
586C2—1224no—
587C2—4882no—
588C2—2442no—
589C2#2146108714yesdirect product factor
590C2C2×#1684073711yescharacteristic
591C2C2×D61⋊#9911yescharacteristic
592C2C2×#1684074811yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC22×C4⋊C4×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC23×D244C4
cosocleC22×Dic61C24
hypercenterC22×C4⋊C4#6923
hypocenterC61C2×#1468
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#16840733C2semidirect
2. C2×D61⋊(C22⋊C8)C2semidirect
3. #21461087C2direct (N × H)
4. C2×#16840608C2semidirect
5. C2×#16840606C2semidirect
10. #16840733C22semidirect
14. D61⋊(C22⋊C8)C22semidirect
17. #16840608C22semidirect
18. #16840606C22semidirect
296. C2×C61#1468semidirect
330. C61C2×#1468semidirect
589. C2#21461087direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168407332
C2×D61⋊(C22⋊C8)2
#214610872
C2×#168406082
C2×#168406062
C22×#145197622
C2×#146861