Finite Group Databasebeta

← C2×#21460666 #30596398

Subgroups — C2×#21460666 #30596398

Order 15616.

1118 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840733C211yesmaximal, characteristic
2C2×C4×C22⋊#6923C211yesmaximal, characteristic
3#21460666C214yesmaximal, direct product factor
4C2×#16839624C211yesmaximal, characteristic
5C22×#11758213—21no—
6C22×C22⋊#6923—21no—
7C22×C4×#6923C412yescomplemented
8#16840733—21no—
9#16840733—21no—
10#16840733C412yescomplemented
11#16840733C2212yes—
12C2×#14519834C412yescomplemented
13C2×C22⋊#92420—21no—
14C4×C22⋊#6923—21no—
15C4×C22⋊#6923—21no—
16C4×C22⋊#6923C412yescomplemented
17C4×C22⋊#6923C2212yes—
18C2×(C2×#6923)⋊C4—21no—
19C23×C4×D61C2211yescharacteristic
20C22×#11758198—21no—
21#16839624—21no—
22#16839624—21no—
23#16839624C412yescomplemented
24#16839624C2212yes—
25C2×#14519684—21no—
26C2×#14519684C411yescharacteristic, complemented
27C2×#95×C61C411yescharacteristic, complemented
28C23×#6923—22no—
29C2×#11758213—22no—
30C2×#11758213—22no—
31C2×#11758213—44no—
32C22×#92420—22no—
33C2×C22⋊#6923—24no—
34C2×C22⋊#6923—24no—
35C2×C22⋊#6923—22no—
36C2×C22⋊#6923—22no—
37C2×C4×#6923—22no—
38C2×C4×#6923—44no—
39C2×C4×#6923C2×C414yescomplemented
40#14519834—22no—
41#14519834C2×C414yescomplemented
42C22⋊#92420—22no—
43C22⋊#92420—22no—
44(C2×#6923)⋊C4—22no—
45(C2×#6923)⋊C4—22no—
46C24×D61D411yescharacteristic
47C23×Dic61—21no—
48C23×Dic61D411yescharacteristic
49C22×C4×D61—44no—
50C22×C4×D61C2×C411yescharacteristic
51C22×C4×D61C2×C411yescharacteristic
52C22×C4×D61C2×C411yescharacteristic
53C22×C4×D61C2×C411yescharacteristic
54C22×C4×D61C2×C411yescharacteristic
55C22×C4×D61D411yescharacteristic
56C22×C4×D61D411yescharacteristic
57C22×C4×D61D411yescharacteristic
58C22×C4×D61D411yescharacteristic
59C22×C4×D61Q811yescharacteristic
60C22×C4×D61Q811yescharacteristic
61C22×C4×D61C2311yescharacteristic
62C2×#11758198—22no—
63C2×#11758198—22no—
64C2×#11758198—44no—
65#14519684—21no—
66#14519684—22no—
67#14519684—22no—
68#14519684C2×C412yescomplemented
69C23×C4×C61—21no—
70C23×C4×C61C2×C411yescharacteristic
71#95×C61—21no—
72#95×C61C2×C412yescomplemented
73C24×C61C22⋊C411yescharacteristic
74C23×D61—22no—
75C23×D61—22no—
76C23×D61—24no—
77C23×D61—42no—
78C23×D61C22⋊C411yescharacteristic
79C23×D61C22⋊C411yescharacteristic
80C23×D61C22⋊C411yescharacteristic
81C23×D61C4⋊C411yescharacteristic
82C23×D61C4⋊C411yescharacteristic
83C23×D61C2×D411yescharacteristic
84C22×#6923—28no—
85C22×#6923—24no—
86C22×#6923—44no—
87C22×#6923—44no—
88C22×C4×C61—22no—
89C22×C4×C61—42no—
90C22×C4×C61—42no—
91C22×C4×C61—42no—
92C22×C4×C61—42no—
93C22×C4×C61C4211yescharacteristic
94C22×C4×C61C4211yescharacteristic
95C22×C4×C61C22⋊C411yescharacteristic
96C22×C4×C61C4⋊C411yescharacteristic
97C22×C4×C61C4⋊C411yescharacteristic
98C22×C4×C61C22×C411yescharacteristic
99C22×Dic61—22no—
100C22×Dic61—42no—
101C22×Dic61—42no—
102C22×Dic61—42no—
103C22×Dic61—42no—
104C22×Dic61C22⋊C411yescharacteristic
105C22×Dic61C22⋊C411yescharacteristic
106C22×Dic61C22⋊C411yescharacteristic
107C22×Dic61C4⋊C411yescharacteristic
108C22×Dic61C4⋊C411yescharacteristic
109C22×Dic61C2×D411yescharacteristic
110C2×C4×D61—24no—
111C2×C4×D61—24no—
112C2×C4×D61—42no—
113C2×C4×D61—42no—
114C2×C4×D61—42no—
115C2×C4×D61—42no—
116C2×C4×D61—42no—
117C2×C4×D61—42no—
118C2×C4×D61—42no—
119C2×C4×D61—42no—
120C2×C4×D61—42no—
121C2×C4×D61—42no—
122C2×C4×D61C4211yescharacteristic
123C2×C4×D61C4211yescharacteristic
124C2×C4×D61C22⋊C411yescharacteristic
125C2×C4×D61C22⋊C411yescharacteristic
126C2×C4×D61C22⋊C411yescharacteristic
127C2×C4×D61C22⋊C411yescharacteristic
128C2×C4×D61C4⋊C411yescharacteristic
129C2×C4×D61C4⋊C411yescharacteristic
130C2×C4×D61C4⋊C411yescharacteristic
131C2×C4×D61C4⋊C411yescharacteristic
132C2×C4×D61C4⋊C411yescharacteristic
133C2×C4×D61C4⋊C411yescharacteristic
134C2×C4×D61C22×C411yescharacteristic
135C2×C4×D61C22×C411yescharacteristic
136C2×C4×D61C2×D411yescharacteristic
137C2×C4×D61C2×Q811yescharacteristic
138C22⋊#6923—28no—
139C22⋊#6923—24no—
140C22⋊#6923—24no—
141C2×#92420—24no—
142C2×#92420—44no—
143C4×#6923—44no—
144C4×#6923—44no—
145#11758213—44no—
146#11758213—44no—
147#11758198—44no—
148#11758198—44no—
149C23×C61—22no—
150C23×C61—22no—
151C23×C61#9511yescharacteristic
152C23×C61#9511yescharacteristic
153C23×C61#10412yes—
154C23×C61#10412yes—
155C23×C61C2×C22⋊C411yescharacteristic
156C22×D61—22no—
157C22×D61—22no—
158C22×D61—22no—
159C22×D61—22no—
160C22×D61—22no—
161C22×D61—22no—
162C22×D61—22no—
163C22×D61—21no—
164C22×D61—21no—
165C22×D61—21no—
166C22×D61—21no—
167C22×D61—22no—
168C22×D61—22no—
169C22×D61—22no—
170C22×D61—22no—
171C22×D61—41no—
172C22×D61—41no—
173C22×D61—41no—
174C22×D61—41no—
175C22×D61—48no—
176C22×D61—48no—
177C22×D61#9511yescharacteristic
178C22×D61#9511yescharacteristic
179C22×D61#9914yes—
180C22×D61C2×C22⋊C411yescharacteristic
181C22×D61C2×C4⋊C411yescharacteristic
182C2×#6923—28no—
183C2×#6923—416no—
184C2×#6923—44no—
185C2×#6923—44no—
186C2×C4×C61—22no—
187C2×C4×C61—22no—
188C2×C4×C61—41no—
189C2×C4×C61—41no—
190C2×C4×C61—41no—
191C2×C4×C61—41no—
192C2×C4×C61—42no—
193C2×C4×C61—42no—
194C2×C4×C61—42no—
195C2×C4×C61—84no—
196C2×C4×C61#9511yescharacteristic
197C2×C4×C61#9511yescharacteristic
198C2×C4×C61C2×C4211yescharacteristic
199C2×C4×C61C2×C4⋊C411yescharacteristic
200C2×Dic61—22no—
201C2×Dic61—22no—
202C2×Dic61—41no—
203C2×Dic61—41no—
204C2×Dic61—41no—
205C2×Dic61—41no—
206C2×Dic61—42no—
207C2×Dic61—42no—
208C2×Dic61—42no—
209C2×Dic61—84no—
210C2×Dic61#9511yescharacteristic
211C2×Dic61#9511yescharacteristic
212C2×Dic61C2×C22⋊C411yescharacteristic
213C2×Dic61C2×C4⋊C411yescharacteristic
214C4×D61—22no—
215C4×D61—22no—
216C4×D61—22no—
217C4×D61—22no—
218C4×D61—22no—
219C4×D61—22no—
220C4×D61—22no—
221C4×D61—22no—
222C4×D61—41no—
223C4×D61—41no—
224C4×D61—41no—
225C4×D61—41no—
226C4×D61—41no—
227C4×D61—41no—
228C4×D61—41no—
229C4×D61—41no—
230#92420—44no—
231C2×#1284—611nomaximal, Sylow
232C22×C61—24no—
233C22×C61—24no—
234C22×C61—21no—
235C22×C61—21no—
236C22×C61—21no—
237C22×C61—21no—
238C22×C61H(3,ℤ/4)12yes—
239C22×C61#33912yes—
240C22×C61#33912yes—
241C22×C61#34212yes—
242C22×C61C2×#9511yescharacteristic
243C22×C61C2×#10411yescharacteristic
244C22×C61C2×#10411yescharacteristic
245C2×D61—28no—
246C2×D61—21no—
247C2×D61—21no—
248C2×D61—21no—
249C2×D61—21no—
250C2×D61—21no—
251C2×D61—21no—
252C2×D61—21no—
253C2×D61—21no—
254C2×D61—21no—
255C2×D61—21no—
256C2×D61—42no—
257C2×D61—42no—
258C2×D61—44no—
259C2×D61—42no—
260C2×D61—42no—
261C2×D61—44no—
262C2×D61—44no—
263C2×D61#34212yes—
264C2×D61C2×#9912yes—
265#6923—48no—
266C4×C61—21no—
267C4×C61—21no—
268C4×C61—21no—
269C4×C61—21no—
270C4×C61—82no—
271Dic61—21no—
272Dic61—21no—
273Dic61—21no—
274Dic61—21no—
275Dic61—82no—
276C2×#407—611no—
277C2×#381—611no—
278C2×C4×C22⋊C4—611no—
279#1284—614no—
280C2×C61—21no—
281C2×C61—21no—
282C2×C61—22no—
283C2×C61#128414yescomplemented
284C2×C61C2×H(3,ℤ/4)11yescharacteristic
285C2×C61C2×#33911yescharacteristic
286C2×C61C2×#34211yescharacteristic
287D61—22no—
288D61—22no—
289D61—41no—
290D61—41no—
291C24×C4—611no—
292C22×M16—1221no—
293C22×C22⋊C4—1221no—
294C22×C22⋊C4—1221no—
295C22×C42—612no—
296#407—612no—
297#407—612no—
298#407—1221no—
299#407—1221no—
300C2×C22⋊C8—612no—
301C2×C22⋊C8—1221no—
302#381—612no—
303#381—612no—
304#381—1221no—
305#381—1221no—
306C4×C22⋊C4—612no—
307C4×C22⋊C4—612no—
308C4×C22⋊C4—1221no—
309C4×C22⋊C4—1221no—
310C2×#95—611no—
311C2×#95—1221no—
312C2×#95—1221no—
313C2×#95#692311yescharacteristic, complemented
314C61C2×#128411yescharacteristic, complemented, Sylow
315C25—611no—
316C23×C4—21no—
317C23×C4—611no—
318C23×C4—611no—
319C23×C4—611no—
320C23×C4—611no—
321C23×C4—611no—
322C23×C4—611no—
323C23×C4—611no—
324C23×C4—611no—
325C23×C4—611no—
326C23×C4—611no—
327C23×C4—611no—
328C23×C4—611no—
329C23×C4—611no—
330C23×C4—1222no—
331C23×C4—1221no—
332C23×C4—2444no—
333C23×C4C2×#692311yescharacteristic
334C2×M16—1222no—
335C2×M16—1222no—
336C2×M16—2444no—
337C22×C8—1222no—
338C2×C22⋊C4—1222no—
339C2×C22⋊C4—1222no—
340C2×C22⋊C4—1224no—
341C2×C22⋊C4—1224no—
342C2×C22⋊C4—1222no—
343C2×C22⋊C4—1222no—
344C2×C22⋊C4—2444no—
345C2×C42—614no—
346C2×C42—1222no—
347C2×C42—2444no—
348C22⋊C8—614no—
349C22⋊C8—1222no—
350C22⋊C8—1222no—
351C22⋊C8—1222no—
352#95—21no—
353#95—612no—
354#95—1222no—
355#95—1222no—
356#95—1222no—
357#95—1222no—
358#95—1221no—
359#95C2×#692312yescomplemented
360C24—611no—
361C24—611no—
362C24—611no—
363C24—611no—
364C24—611no—
365C24—611no—
366C24—1224no—
367C24—1222no—
368C24—1222no—
369C24—2442no—
370C24C22⋊#692311yescharacteristic
371C22×C4—22no—
372C22×C4—42no—
373C22×C4—42no—
374C22×C4—42no—
375C22×C4—42no—
376C22×C4—611no—
377C22×C4—611no—
378C22×C4—611no—
379C22×C4—611no—
380C22×C4—611no—
381C22×C4—611no—
382C22×C4—611no—
383C22×C4—611no—
384C22×C4—611no—
385C22×C4—611no—
386C22×C4—611no—
387C22×C4—611no—
388C22×C4—611no—
389C22×C4—611no—
390C22×C4—611no—
391C22×C4—611no—
392C22×C4—611no—
393C22×C4—611no—
394C22×C4—611no—
395C22×C4—611no—
396C22×C4—611no—
397C22×C4—611no—
398C22×C4—1224no—
399C22×C4—1224no—
400C22×C4—1224no—
401C22×C4—1228no—
402C22×C4—1222no—
403C22×C4—2442no—
404C22×C4—2442no—
405C22×C4—2442no—
406C22×C4—2442no—
407C22×C4—2442no—
408C22×C4—2442no—
409C22×C4—2442no—
410C22×C4—2442no—
411C22×C4—2442no—
412C22×C4—2442no—
413C22×C4—2442no—
414C22×C4—2442no—
415C22×C4—2442no—
416C22×C4—2442no—
417C22×C4—2444no—
418C22×C4—2444no—
419C22×C4C4×#692311yescharacteristic
420C22×C4C4×#692311yescharacteristic
421C22×C4C4⋊#692311yescharacteristic
422C22×C4C4⋊#692311yescharacteristic
423C22×C4C22⋊#692311yescharacteristic
424C22×C4C22×#692311yescharacteristic
425M16—2444no—
426M16—2444no—
427C2×C8—1224no—
428C2×C8—2444no—
429C22⋊C4—1224no—
430C22⋊C4—1224no—
431C22⋊C4—1228no—
432C22⋊C4—2444no—
433C22⋊C4—2444no—
434C42—2444no—
435C42—2444no—
436C23—22no—
437C23—22no—
438C23—614no—
439C23—611no—
440C23—611no—
441C23—611no—
442C23—611no—
443C23—1222no—
444C23—1222no—
445C23—1222no—
446C23—1222no—
447C23—1222no—
448C23—1222no—
449C23—1221no—
450C23—1221no—
451C23—1221no—
452C23—1221no—
453C23—1222no—
454C23—1222no—
455C23—1222no—
456C23—1222no—
457C23—1222no—
458C23—2441no—
459C23—2441no—
460C23—2441no—
461C23—2441no—
462C23—2448no—
463C23—2448no—
464C23(C2×#6923)⋊C411yescharacteristic
465C23(C2×#6923)⋊C411yescharacteristic
466C23#1451984112yes—
467C23#1451984212yes—
468C23C2×C22⋊#692311yescharacteristic
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—84no—
479C2×C4—611no—
480C2×C4—611no—
481C2×C4—611no—
482C2×C4—611no—
483C2×C4—1222no—
484C2×C4—1222no—
485C2×C4—1222no—
486C2×C4—1222no—
487C2×C4—1222no—
488C2×C4—1222no—
489C2×C4—1222no—
490C2×C4—1222no—
491C2×C4—1222no—
492C2×C4—1222no—
493C2×C4—1228no—
494C2×C4—4884no—
495C2×C4—2441no—
496C2×C4—2441no—
497C2×C4—2441no—
498C2×C4—2441no—
499C2×C4—2441no—
500C2×C4—2441no—
501C2×C4—2441no—
502C2×C4—2441no—
503C2×C4—2441no—
504C2×C4—2441no—
505C2×C4—2441no—
506C2×C4—2441no—
507C2×C4—2442no—
508C2×C4—2442no—
509C2×C4—2442no—
510C2×C4—2444no—
511C2×C4—24416no—
512C2×C4—2444no—
513C2×C4(C2×#6923)⋊C411yescharacteristic
514C2×C4(C2×#6923)⋊C411yescharacteristic
515C2×C4C2×C4×#692311yescharacteristic
516C2×C4C2×C4⋊#692311yescharacteristic
517C8—2444no—
518C22—21no—
519C22—21no—
520C22—24no—
521C22—24no—
522C22—21no—
523C22—21no—
524C22—612no—
525C22—612no—
526C22—1228no—
527C22—1221no—
528C22—1221no—
529C22—1221no—
530C22—1221no—
531C22—1221no—
532C22—1221no—
533C22—1221no—
534C22—1221no—
535C22—1221no—
536C22—1221no—
537C22—2442no—
538C22—2442no—
539C22—2442no—
540C22—2442no—
541C22—2444no—
542C22—2444no—
543C22—2444no—
544C22#1684062912yes—
545C22#1684063212yes—
546C22#1684063212yes—
547C22#1684063912yes—
548C22C2×(C2×#6923)⋊C411yescharacteristic
549C22C2×#1451984111yescharacteristic
550C22C2×#1451984211yescharacteristic
551C4—21no—
552C4—21no—
553C4—21no—
554C4—21no—
555C4—82no—
556C4—1221no—
557C4—1221no—
558C4—1221no—
559C4—1221no—
560C4—4882no—
561C4—2448no—
562C2—21no—
563C2—21no—
564C2—22no—
565C2—1222no—
566C2—1222no—
567C2—2441no—
568C2—2441no—
569C2#2146066614yesdirect product factor
570C2C2×#1684062911yescharacteristic
571C2C2×#1684063211yescharacteristic
572C2C2×#1684063911yescharacteristic
subgroupG/H
centerC23(C2×#6923)⋊C4
commutatorC2×C4×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC2×#95×C61C4
socleC23×C61#95
prime radicalC24×D61D4
cosocleC22×C4×D61C23
hypercenterC2×#95#6923
hypocenterC61C2×#1284
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
3. #21460666C2direct (N × H)
7. C22×C4×#6923C4semidirect
10. #16840733C4semidirect
12. C2×#14519834C4semidirect
16. C4×C22⋊#6923C4semidirect
23. #16839624C4semidirect
26. C2×#14519684C4semidirect
27. C2×#95×C61C4semidirect
39. C2×C4×#6923C2×C4semidirect
41. #14519834C2×C4semidirect
68. #14519684C2×C4semidirect
72. #95×C61C2×C4semidirect
283. C2×C61#1284semidirect
313. C2×#95#6923semidirect
314. C61C2×#1284semidirect
359. #95C2×#6923semidirect
569. C2#21460666direct (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×C4×C22⋊#69232
#214606662
C2×#168396242
C2×#128461