Finite Group Databasebeta

← C2×#21461145 #30610413

Subgroups — C2×#21461145 #30610413

Order 15616.

1714 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840781C211yesmaximal, characteristic, complemented
2C2×#16840766C211yesmaximal, characteristic, complemented
3#21461145C218yesmaximal, direct product factor
4C2×#16840610C212yesmaximal, complemented
5C2×D4⋊#92420C212yesmaximal, complemented
6C2×C4×D4×D61C211yesmaximal, characteristic
7C22×#11758213—21no—
8#16840781—22no—
9#16840781C2214yescomplemented
10#16840766—22no—
11#16840766C2214yescomplemented
12C2×C4⋊#92420—21no—
13C2×C4⋊#92420—21no—
14C2×C4⋊#92420C2212yescomplemented
15C2×#14519834—21no—
16C2×C4×#92420C2212yescomplemented
17#16840610C2218yescomplemented
18D4⋊#92420C2218yescomplemented
19C22×D4×D61C411yescharacteristic
20C23×C4×D61—21no—
21C2×C4×D244C411yescharacteristic
22C2×D4×Dic61C2211yescharacteristic
23C2×#14519739C2211yescharacteristic
24C2×C4×C22⋊D61—21no—
25C2×#14519737—21no—
26C4×D4×D61—22no—
27C4×D4×D61—22no—
28C4×D4×D61C414yes—
29C4×D4×D61C2214yes—
30C2×C4⋊C4×D61C411yescharacteristic
31C2×C22⋊C4×D61—21no—
32C2×C42×D61C2211yescharacteristic
33C2×C4×D4×C61C411yescharacteristic
34C2×#11758213—24no—
35C2×#11758213—44no—
36C22×#92420—22no—
37C22×#92420—22no—
38C4⋊#92420—24no—
39C4⋊#92420—24no—
40C4⋊#92420—22no—
41C4⋊#92420C2314yescomplemented
42#14519834—24no—
43C4×#92420—22no—
44C4×#92420C2314yescomplemented
45C24×D61—21no—
46C22×D244C2×C411yescharacteristic
47C22×C22⋊D61—21no—
48C2×D4×D61—24no—
49C2×D4×D61—24no—
50C2×D4×D61—22no—
51C2×D4×D61C2×C414yes—
52C23×Dic61—21no—
53C22×C4×D61—21no—
54C22×C4×D61—21no—
55C22×C4×D61—21no—
56C22×C4×D61—24no—
57C22×C4×D61—24no—
58C22×C4×D61—44no—
59C22×C4×D61—44no—
60C22×C4×D61C2×C411yescharacteristic
61C22×C4×D61D411yescharacteristic
62C22×C4×D61D411yescharacteristic
63C4×D244—22no—
64C4×D244C2×C414yes—
65D4×Dic61—21no—
66D4×Dic61—21no—
67D4×Dic61C2×C412yes—
68D4×Dic61C2312yes—
69#14519739—21no—
70#14519739—21no—
71#14519739C2×C412yes—
72#14519739C2312yes—
73C4×C22⋊D61—24no—
74C4×C22⋊D61—24no—
75#14519737—24no—
76#14519737—24no—
77C2×C4⋊Dic61C2×C411yescharacteristic
78C2×#11758196—21no—
79C4⋊C4×D61—22no—
80C4⋊C4×D61C2×C414yes—
81C2×C22⋊Dic61—21no—
82C2×#11758198—21no—
83C2×#11758198—21no—
84C22⋊C4×D61—24no—
85C22⋊C4×D61—24no—
86C2×C4×Dic61D411yescharacteristic
87C2×C4×Dic61D411yescharacteristic
88C2×C4×Dic61C2311yescharacteristic
89C42×D61C2×C412yes—
90C42×D61D412yes—
91C42×D61D412yes—
92C42×D61C2312yes—
93C22×D4×C61C2×C411yescharacteristic
94C23×C4×C61—21no—
95C4×D4×C61—22no—
96C4×D4×C61C2×C414yes—
97C2×C4⋊C4×C61C2×C411yescharacteristic
98C2×C22⋊C4×C61—21no—
99C2×C42×C61C2×C411yescharacteristic
100C24×C61—21no—
101C23×D61—28no—
102C23×D61—21no—
103C23×D61—24no—
104C23×D61—44no—
105C23×D61—44no—
106C23×D61C22⋊C411yescharacteristic
107C2×D4×C61—21no—
108C2×D4×C61—22no—
109C2×D4×C61M1614yescomplemented
110C2×D4×C61C22×C412yes—
111C22×C4×C61—21no—
112C22×C4×C61—24no—
113C22×C4×C61—44no—
114C22×C4×C61C22⋊C411yescharacteristic
115C22×C4×C61C22⋊C411yescharacteristic
116C22×C4×C61C22×C411yescharacteristic
117C2×C22⋊D61—28no—
118C2×C22⋊D61—24no—
119C22×Dic61—21no—
120C22×Dic61—22no—
121C22×Dic61—22no—
122C22×Dic61—42no—
123C22×Dic61—42no—
124C22×Dic61C22⋊C411yescharacteristic
125C22×Dic61C2×D411yescharacteristic
126C22×Dic61C2×D411yescharacteristic
127D4×D61—216no—
128D4×D61—28no—
129D4×D61—28no—
130C2×D244—21no—
131C2×D244—22no—
132C2×D244M1614yescomplemented
133C2×D244C22×C412yes—
134C2×C4×D61—22no—
135C2×C4×D61—22no—
136C2×C4×D61—24no—
137C2×C4×D61—24no—
138C2×C4×D61—22no—
139C2×C4×D61—22no—
140C2×C4×D61—42no—
141C2×C4×D61—44no—
142C2×C4×D61—44no—
143C2×C4×D61—42no—
144C2×C4×D61—42no—
145C2×C4×D61—416no—
146C2×C4×D61—48no—
147C2×C4×D61—48no—
148C2×C4×D61C22⋊C412yes—
149C2×C4×D61C22⋊C412yes—
150C2×C4×D61C22⋊C412yes—
151C2×C4×D61D814yes—
152C2×C4×D61SD1614yes—
153C2×C4×D61C22×C412yes—
154C2×C4×D61C2×D412yes—
155C2×C4×D61C2×D412yes—
156C2×#92420—24no—
157C2×#92420—24no—
158C2×#92420—44no—
159C2×#92420—44no—
160#11758213—48no—
161C4⋊C4×C61—21no—
162C4⋊C4×C61C22×C412yes—
163C22⋊C4×C61—24no—
164C42×C61C22⋊C412yes—
165C42×C61C22×C412yes—
166C22⋊Dic61—22no—
167C22⋊Dic61—22no—
168#11758198—24no—
169#11758198—22no—
170#11758198—22no—
171C4⋊Dic61—21no—
172C4⋊Dic61C22×C412yes—
173#11758196—24no—
174C4×Dic61C22⋊C412yes—
175C4×Dic61C22⋊C412yes—
176C4×Dic61C22×C411yescharacteristic
177C4×Dic61C2×D411yescharacteristic
178C4×Dic61C2×D411yescharacteristic
179C4×Dic61C2×D412yes—
180C4×Dic61C2×D412yes—
181C4×Dic61C2411yescharacteristic
182C23×C61—22no—
183C23×C61—24no—
184C23×C61—42no—
185C23×C61—42no—
186C23×C61C2×C22⋊C411yescharacteristic
187C22×D61—22no—
188C22×D61—22no—
189C22×D61—216no—
190C22×D61—22no—
191C22×D61—24no—
192C22×D61—48no—
193C22×D61—432no—
194C22×D61—42no—
195C22×D61—42no—
196C22×D61—48no—
197C22×D61#10214yes—
198C22×D61C2×C22⋊C412yes—
199D4×C61—22no—
200D4×C61—24no—
201D4×C61C2×M1614yescomplemented
202C2×C4×C61—22no—
203C2×C4×C61—22no—
204C2×C4×C61—42no—
205C2×C4×C61—48no—
206C2×C4×C61#10214yes—
207C2×C4×C61C2×C22⋊C412yes—
208C2×C4×C61C2×C22⋊C411yescharacteristic
209C2×C4×C61C2×C22⋊C412yes—
210C2×C4×C61C2×M1612yes—
211C2×C4×C61C2×M1612yes—
212C2×C4×C61C23×C411yescharacteristic
213C22⋊D61—216no—
214C2×Dic61—22no—
215C2×Dic61—22no—
216C2×Dic61—22no—
217C2×Dic61—42no—
218C2×Dic61—42no—
219C2×Dic61—42no—
220C2×Dic61—44no—
221C2×Dic61C2×C22⋊C411yescharacteristic
222C2×Dic61C2×C22⋊C412yes—
223C2×Dic61C2×C22⋊C411yescharacteristic
224C2×Dic61C2×D812yes—
225C2×Dic61C2×SD1612yes—
226C2×Dic61C22×D411yescharacteristic
227C2×Dic61C22×D411yescharacteristic
228D244—22no—
229D244—24no—
230D244C2×M1614yescomplemented
231C4×D61—22no—
232C4×D61—22no—
233C4×D61—24no—
234C4×D61—42no—
235C4×D61—42no—
236C4×D61—48no—
237C4×D61—48no—
238C4×D61—42no—
239C4×D61—42no—
240C4×D61—44no—
241C4×D61#10218yes—
242C4×D61C2×D814yes—
243C4×D61C2×SD1614yes—
244#92420—44no—
245#92420—44no—
246C2×#1486—611nomaximal, Sylow
247C22×C61—24no—
248C22×C61—42no—
249C22×C61—42no—
250C22×C61—48no—
251C22×C61#40712yes—
252C22×C61C2×#10212yes—
253C22×C61#42112yes—
254C22×C61C22×C22⋊C411yescharacteristic
255C2×D61—22no—
256C2×D61—22no—
257C2×D61—28no—
258C2×D61—24no—
259C2×D61—432no—
260C2×D61—42no—
261C2×D61—42no—
262C2×D61—48no—
263C2×D61C2×#10214yes—
264C4×C61—22no—
265C4×C61—42no—
266C4×C61#40712yes—
267C4×C61C2×#10214yes—
268C4×C61C22×M1611yescharacteristic
269C4×C61C22×M1611yescharacteristic
270Dic61—22no—
271Dic61—21no—
272Dic61—21no—
273Dic61—42no—
274Dic61C2×#10212yes—
275Dic61C22×D811yescharacteristic
276Dic61C22×SD1611yescharacteristic
277C22×C4×D4—611no—
278C2×#431—611no—
279C2×#423—611no—
280#1486—618no—
281C2×D4⋊C8—612no—
282C2×D4⋊C8—612no—
283C2×C61—44no—
284C2×C61#148614yescomplemented
285C2×C61C2×#40711yescharacteristic
286C2×C61C22×#10211yescharacteristic
287C2×C61C2×#42111yescharacteristic
288D61—24no—
289D61—44no—
290C23×D4—611no—
291C24×C4—1221no—
292C22×M16—1221no—
293C2×C4×D4—611no—
294C2×C4×D4—614no—
295C2×C4×D4—614no—
296C2×C4×D4—611no—
297C2×C4×D4—611no—
298C2×C4×D4—1221no—
299C2×C4×D4—1222no—
300C2×C4×D4—1222no—
301C2×C4×D4—1221no—
302C2×C4×D4#692311yescharacteristic
303C22×C4⋊C4—611no—
304C22×C22⋊C4—1221no—
305C22×C42—611no—
306#431—614no—
307#431—1222no—
308#423—614no—
309#423—1222no—
310C2×C4⋊C8—612no—
311C2×C4⋊C8—1221no—
312C2×C4⋊C8—1221no—
313C2×C22⋊C8—1221no—
314C2×C4×C8—612no—
315D4⋊C8—618no—
316D4⋊C8—618no—
317C61C2×#148611yescharacteristic, complemented, Sylow
318C25—1221no—
319C22×D4—614no—
320C22×D4—611no—
321C22×D4—1222no—
322C22×D4—1221no—
323C22×D4—1224no—
324C22×D4—1224no—
325C22×D4C2×#692311yescharacteristic
326C23×C4—21no—
327C23×C4—611no—
328C23×C4—611no—
329C23×C4—611no—
330C23×C4—1221no—
331C23×C4—1224no—
332C23×C4—1224no—
333C23×C4—1221no—
334C23×C4—1221no—
335C23×C4—1221no—
336C23×C4—2444no—
337C23×C4—2444no—
338C2×M16—1224no—
339C2×M16—2444no—
340C22×C8—1222no—
341C22×C8—1222no—
342C4×D4—22no—
343C4×D4—612no—
344C4×D4—612no—
345C4×D4—612no—
346C4×D4—612no—
347C4×D4—614no—
348C4×D4—1224no—
349C4×D4—1224no—
350C4×D4—1221no—
351C4×D4—1221no—
352C4×D4—1224no—
353C4×D4—1224no—
354C4×D4—1221no—
355C4×D4—1221no—
356C4×D4—1222no—
357C4×D4C2×#692314yes—
358C2×C4⋊C4—611no—
359C2×C4⋊C4—614no—
360C2×C4⋊C4—1222no—
361C2×C4⋊C4—1221no—
362C2×C4⋊C4C2×#692311yescharacteristic
363C2×C22⋊C4—21no—
364C2×C22⋊C4—1224no—
365C2×C22⋊C4—1224no—
366C2×C22⋊C4—1221no—
367C2×C22⋊C4—1221no—
368C2×C22⋊C4—1221no—
369C2×C42—611no—
370C2×C42—611no—
371C2×C42—611no—
372C2×C42—612no—
373C2×C42—612no—
374C2×C42—612no—
375C2×C42—612no—
376C2×C42C2×#692311yescharacteristic
377C4⋊C8—614no—
378C4⋊C8—1222no—
379C4⋊C8—1224no—
380C4⋊C8—1224no—
381C22⋊C8—1224no—
382C4×C8—614no—
383C4×C8—1222no—
384C24—21no—
385C24—611no—
386C24—1224no—
387C24—1228no—
388C24—1221no—
389C24—2444no—
390C24—2444no—
391C2×D4—21no—
392C2×D4—22no—
393C2×D4—614no—
394C2×D4—612no—
395C2×D4—1224no—
396C2×D4—1228no—
397C2×D4—12216no—
398C2×D4—1228no—
399C2×D4—1228no—
400C2×D4—1221no—
401C2×D4—1222no—
402C2×D4#1175821314yescomplemented
403C2×D4C22×#692312yes—
404C22×C4—21no—
405C22×C4—24no—
406C22×C4—44no—
407C22×C4—611no—
408C22×C4—614no—
409C22×C4—614no—
410C22×C4—612no—
411C22×C4—612no—
412C22×C4—611no—
413C22×C4—611no—
414C22×C4—612no—
415C22×C4—612no—
416C22×C4—612no—
417C22×C4—612no—
418C22×C4—1222no—
419C22×C4—1222no—
420C22×C4—1224no—
421C22×C4—1222no—
422C22×C4—1222no—
423C22×C4—1222no—
424C22×C4—1222no—
425C22×C4—1221no—
426C22×C4—1224no—
427C22×C4—2442no—
428C22×C4—2442no—
429C22×C4—2442no—
430C22×C4—24416no—
431C22×C4—2448no—
432C22×C4—2448no—
433C22×C4—2444no—
434C22×C4—2442no—
435C22×C4—2442no—
436C22×C4—2444no—
437C22×C4C22⋊#692311yescharacteristic
438C22×C4C22⋊#692311yescharacteristic
439C22×C4C22×#692311yescharacteristic
440M16—2448no—
441C2×C8—1224no—
442C2×C8—1224no—
443C2×C8—2444no—
444C2×C8—2444no—
445C4⋊C4—21no—
446C4⋊C4—612no—
447C4⋊C4—1224no—
448C4⋊C4—1221no—
449C4⋊C4C22×#692312yes—
450C22⋊C4—24no—
451C22⋊C4—1222no—
452C22⋊C4—1222no—
453C22⋊C4—1222no—
454C22⋊C4—1222no—
455C22⋊C4—1224no—
456C42—611no—
457C42—611no—
458C42—612no—
459C42—612no—
460C42—612no—
461C42—612no—
462C42—611no—
463C42—611no—
464C42C22⋊#692312yes—
465C42C22×#692312yes—
466C23—24no—
467C23—22no—
468C23—42no—
469C23—42no—
470C23—614no—
471C23—612no—
472C23—12216no—
473C23—1222no—
474C23—1222no—
475C23—1224no—
476C23—1222no—
477C23—2448no—
478C23—24432no—
479C23—2448no—
480C23—2442no—
481C23—2442no—
482C23C2×C22⋊#692311yescharacteristic
483D4—24no—
484D4—22no—
485D4—614no—
486D4—12216no—
487D4—1224no—
488D4—1222no—
489D4C2×#1175821314yescomplemented
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—42no—
493C2×C4—48no—
494C2×C4—612no—
495C2×C4—612no—
496C2×C4—611no—
497C2×C4—611no—
498C2×C4—618no—
499C2×C4—614no—
500C2×C4—614no—
501C2×C4—611no—
502C2×C4—612no—
503C2×C4—611no—
504C2×C4—1222no—
505C2×C4—1222no—
506C2×C4—1224no—
507C2×C4—1222no—
508C2×C4—1222no—
509C2×C4—1222no—
510C2×C4—2442no—
511C2×C4—2442no—
512C2×C4—2442no—
513C2×C4—2442no—
514C2×C4—2444no—
515C2×C4—2448no—
516C2×C4—2442no—
517C2×C4—2442no—
518C2×C4—2444no—
519C2×C4—2442no—
520C2×C4—2448no—
521C2×C4#1451983914yes—
522C2×C4C2×C22⋊#692312yes—
523C2×C4C2×C22⋊#692311yescharacteristic
524C2×C4C2×C22⋊#692312yes—
525C2×C4D61⋊M1612yes—
526C2×C4C2×#1175821312yes—
527C2×C4C23×#692311yescharacteristic
528C8—2444no—
529C8—2444no—
530C22—24no—
531C22—48no—
532C22—42no—
533C22—42no—
534C22—614no—
535C22—1222no—
536C22—1228no—
537C22—1222no—
538C22—1224no—
539C22—24432no—
540C22—2448no—
541C22—2442no—
542C22—2442no—
543C22#1684073312yes—
544C22C2×#1451983912yes—
545C22#1684075912yes—
546C22C22×C22⋊#692311yescharacteristic
547C4—22no—
548C4—42no—
549C4—611no—
550C4—611no—
551C4—612no—
552C4—1222no—
553C4—1221no—
554C4—1221no—
555C4—2442no—
556C4#1684073312yes—
557C4C2×#1451983914yes—
558C4C2×D61⋊M1611yescharacteristic
559C4C22×#1175821311yescharacteristic
560C2—44no—
561C2—1224no—
562C2—2444no—
563C2#2146114514yesdirect product factor
564C2C2×#1684073311yescharacteristic
565C2C22×#1451983911yescharacteristic
566C2C2×#1684075911yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC2×C4×D4×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC22×D4×D61C4
cosocleC4×Dic61C24
hypercenterC2×C4×D4#6923
hypocenterC61C2×#1486
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×#16840781C2semidirect
2. C2×#16840766C2semidirect
3. #21461145C2direct (N × H)
4. C2×#16840610C2semidirect
5. C2×D4⋊#92420C2semidirect
9. #16840781C22semidirect
11. #16840766C22semidirect
14. C2×C4⋊#92420C22semidirect
16. C2×C4×#92420C22semidirect
17. #16840610C22semidirect
18. D4⋊#92420C22semidirect
41. C4⋊#92420C23semidirect
44. C4×#92420C23semidirect
109. C2×D4×C61M16semidirect
132. C2×D244M16semidirect
201. D4×C61C2×M16semidirect
230. D244C2×M16semidirect
284. C2×C61#1486semidirect
317. C61C2×#1486semidirect
402. C2×D4#11758213semidirect
489. D4C2×#11758213semidirect
563. C2#21461145direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168407812
C2×#168407662
#214611452
C2×#168406102
C2×D4⋊#924202
C2×C4×D4×D612
C2×#148661