Finite Group Databasebeta

← C2×#21462095 #30623959

Subgroups — C2×#21462095 #30623959

Order 15616.

1510 conjugacy classes of subgroups; only the 216 normal subgroups are shown.

normal subgroups only

This group has 1510 conjugacy classes of subgroups — too many to draw. Only its 216 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D61⋊#99C212yesmaximal, complemented
2#21462095C218yesmaximal, direct product factor
3C2×#16840669C212yesmaximal, complemented
4C2×#16840666C212yesmaximal, complemented
5C2×#16840325C211yesmaximal, characteristic
6C22×C22⋊#6923—22no—
7C2×#14519836C2214yes—
8D61⋊#99—24no—
9D61⋊#99C2218yescomplemented
10C2×#14519835—22no—
11#16840669C2218yescomplemented
12#16840666C2218yescomplemented
13C22×#11758224C411yescharacteristic, complemented
14C22×D4×D61C2211yescharacteristic
15#16840325—24no—
16#16840325C414yescomplemented
17#16840325C2214yes—
18C2×#14519773C2211yescharacteristic
19C2×#14519765C2211yescharacteristic
20C2×#14519764C411yescharacteristic, complemented
21C2×#14519749—22no—
22C2×#14519745—22no—
23C2×#14519734C411yescharacteristic, complemented
24C2×#127×C61C411yescharacteristic, complemented
25C23×#6923—42no—
26C2×C22⋊#6923—24no—
27C2×C22⋊#6923—28no—
28C2×C22⋊#6923—44no—
29C2×C22⋊#6923—42no—
30#14519836—24no—
31#14519836C2318yes—
32#14519835—28no—
33C24×D61D412yes—
34C2×#11758224—22no—
35C2×#11758224—42no—
36C2×#11758224—42no—
37C2×#11758224C2×C414yescomplemented
38C22×Dic122C2×C411yescharacteristic, complemented
39C22×D244C2311yescharacteristic
40C22×C22⋊D61—21no—
41C22×C22⋊D61—22no—
42C22×C22⋊D61D412yes—
43C2×D4×D61—42no—
44C2×D4×D61—42no—
45C2×D4×D61C2×C412yes—
46C2×D4×D61D414yes—
47C2×D4×D61C2312yes—
48C23×Dic61—21no—
49C22×C4×D61C2×C411yescharacteristic
50#14519773—22no—
51#14519773C2×C412yescomplemented
52#14519773C2312yes—
53#14519765—22no—
54#14519765C2×C412yescomplemented
55#14519765C2312yes—
56#14519764—22no—
57#14519764C2×C414yescomplemented
58#14519749—28no—
59#14519749—28no—
60#14519745—28no—
61#14519745—28no—
62#14519734—22no—
63#14519734C2×C414yescomplemented
64C2×#11758196—21no—
65C2×C22⋊Dic61—22no—
66C2×#11758198—21no—
67C2×#11758198—22no—
68C2×C4×Dic61C2×C411yescharacteristic, complemented
69C22×D4×C61—22no—
70C22×D4×C61C2×C411yescharacteristic
71C22×D4×C61C2×C411yescharacteristic, complemented
72#127×C61—22no—
73#127×C61C2×C414yescomplemented
74C2×C42×C61C2×C411yescharacteristic, complemented
75C24×C61—21no—
76C24×C61C22⋊C412yes—
77C23×D61—22no—
78C23×D61—22no—
79C23×D61—24no—
80C23×D61—84no—
81C23×D61C22⋊C414yes—
82C23×D61C22⋊C411yescharacteristic
83C23×D61C2×D412yes—
84C23×D61C2×D414yes—
85C22×#6923—44no—
86C22×#6923—48no—
87C22×#6923—88no—
88C2×D4×C61—28no—
89C2×D4×C61—21no—
90C2×D4×C61—41no—
91C2×D4×C61—41no—
92C2×D4×C61—41no—
93C2×D4×C61—41no—
94C2×D4×C61—84no—
95C2×D4×C61C22⋊C412yes—
96C2×D4×C61C22×C412yes—
97C2×D4×C61C22×C412yescomplemented
98C22×C4×C61—21no—
99C22×C4×C61C22×C411yescharacteristic
100C2×C22⋊D61—24no—
101C2×C22⋊D61—24no—
102C2×C22⋊D61—24no—
103C2×C22⋊D61—42no—
104C2×C22⋊D61—42no—
105C2×C22⋊D61—42no—
106C2×C22⋊D61—42no—
107C2×C22⋊D61—84no—
108C2×C22⋊D61C22⋊C414yes—
109C2×C22⋊D61C2×D414yes—
110C22×Dic61—21no—
111C22×Dic61—21no—
112C22×Dic61—24no—
113C22×Dic61—42no—
114C22×Dic61—42no—
115C22×Dic61C22⋊C411yescharacteristic
116#11758224—48no—
117#11758224—48no—
118D4×D61—44no—
119D4×D61—44no—
120D4×D61—44no—
121D4×D61—44no—
122C2×D244—41no—
123C2×D244—41no—
124C2×D244C22×C411yescharacteristic
125C2×D244C2×D412yes—
126C2×D244C2411yescharacteristic
127C2×C4×D61—22no—
128C2×C4×D61—22no—
129C2×C4×D61C22⋊C412yes—
130C2×C4×D61C22×C412yes—
131C2×Dic122—21no—
132C2×Dic122—41no—
133C2×Dic122—41no—
134C2×Dic122C22×C412yescomplemented
135C22⋊#6923—28no—
136C22⋊#6923—44no—
137C22⋊#6923—48no—
138C42×C61—21no—
139C42×C61C22×C412yescomplemented
140C22⋊Dic61—28no—
141#11758198—24no—
142#11758198—24no—
143#11758198—24no—
144#11758196—24no—
145C4×Dic61—21no—
146C4×Dic61C22×C412yescomplemented
147C23×C61—22no—
148C23×C61—22no—
149C23×C61—22no—
150C23×C61—44no—
151C23×C61—44no—
152C23×C61—41no—
153C23×C61—41no—
154C23×C61C2×C22⋊C411yescharacteristic
155C23×C61C2×C22⋊C414yes—
156C22×D61—22no—
157C22×D61—22no—
158C22×D61—24no—
159C22×D61—24no—
160C22×D61—24no—
161C22×D61—24no—
162C22×D61—42no—
163C22×D61—48no—
164C22×D61—44no—
165C22×D61—84no—
166C22×D61—84no—
167C22×D61—84no—
168C22×D61—88no—
169C22×D61#9912yes—
170C22×D61#9912yes—
171C22×D61C2×C22⋊C412yes—
172C22×D61C2×C22⋊C412yes—
173C22×D61C22×D412yes—
174C2×#6923—48no—
175C2×#6923—816no—
176C2×#6923—88no—
177D4×C61—42no—
178D4×C61—42no—
179D4×C61—42no—
180D4×C61—42no—
181D4×C61—88no—
182C2×C4×C61—21no—
183C2×C4×C61—21no—
184C2×C4×C61—22no—
185C2×C4×C61—42no—
186C2×C4×C61C2×C22⋊C411yescharacteristic
187C2×C4×C61C23×C411yescharacteristic
188C22⋊D61—44no—
189C22⋊D61—44no—
190C22⋊D61—48no—
191C22⋊D61—84no—
192C22⋊D61—84no—
193C2×Dic61—21no—
194C2×Dic61—21no—
195C2×Dic61—22no—
196C2×Dic61—22no—
197C2×Dic61—48no—
198C2×Dic61—42no—
199C2×Dic61—41no—
200C2×Dic61—41no—
201C2×Dic61C2×C22⋊C412yes—
202D244—41no—
203D244—42no—
204D244—41no—
205C4×D61—24no—
206C4×D61—24no—
207Dic122—42no—
208Dic122—42no—
209C2×#2127—611nomaximal, Sylow
210C22×C61—22no—
211C22×C61—24no—
212C22×C61—44no—
213C22×C61—44no—
214C22×C61—44no—
215C22×C61—42no—
216C22×C61—82no—
217C22×C61—82no—
218C22×C61—82no—
219C22×C61C2×#9911yescharacteristic
220C22×C61C2×#9911yescharacteristic
221C22×C61C22×C22⋊C411yescharacteristic
222C2×D61—24no—
223C2×D61—22no—
224C2×D61—22no—
225C2×D61—42no—
226C2×D61—42no—
227C2×D61—48no—
228C2×D61—48no—
229C2×D61—44no—
230C2×D61—42no—
231C2×D61—42no—
232C2×D61—84no—
233C2×D61—84no—
234C2×D61—82no—
235C2×D61C2×#9914yes—
236#6923—88no—
237C4×C61—21no—
238C4×C61—21no—
239C4×C61—42no—
240Dic61—22no—
241Dic61—42no—
242Dic61—42no—
243C2×#535—611no—
244C22×#99—612no—
245#2127—618no—
246C2×#354—612no—
247C2×#353—612no—
248C2×C61—21no—
249C2×C61—21no—
250C2×C61—44no—
251C2×C61—82no—
252C2×C61#212712yescomplemented
253C2×C61C22×#9911yescharacteristic
254D61—24no—
255D61—42no—
256D61—42no—
257C22×#41—611no—
258C23×D4—611no—
259#535—614no—
260#535—614no—
261#535—1224no—
262C2×#127—611no—
263C2×#127#692311yescharacteristic, complemented
264C2×#124—611no—
265C2×#124—611no—
266C2×#121—1222no—
267C2×#120—1222no—
268C2×#117—611no—
269C22×C22⋊C4—1222no—
270C2×#99—618no—
271C2×#99—614no—
272C2×#99—1222no—
273C2×#99—1224no—
274#354—618no—
275#353—618no—
276C61C2×#212711yescharacteristic, complemented, Sylow
277C25—612no—
278C2×#41—614no—
279C2×#41—1222no—
280C2×#41—2442no—
281C2×#41—2442no—
282C22×Q8—611no—
283C22×D4—22no—
284C22×D4—612no—
285C22×D4—614no—
286C22×D4—612no—
287C22×D4—612no—
288C22×D4—611no—
289C22×D4—1222no—
290C22×D4—1221no—
291C22×D4—2442no—
292C22×D4—2442no—
293C22×D4C2×#692311yescharacteristic
294C22×D4C2×#692311yescharacteristic, complemented
295C23×C4—611no—
296C23×C4—1221no—
297C23×C4—2442no—
298#127—22no—
299#127—612no—
300#127—612no—
301#127—1222no—
302#127C2×#692314yescomplemented
303#124—614no—
304#124—612no—
305#124—612no—
306#124—1222no—
307#124—1222no—
308#121—1228no—
309#121—1228no—
310#120—1228no—
311#120—1228no—
312#117—614no—
313#117—1222no—
314C2×C4⋊C4—1221no—
315C2×C22⋊C4—1221no—
316C2×C22⋊C4—1222no—
317C2×C22⋊C4—1222no—
318C2×C22⋊C4—1228no—
319C2×C22⋊C4—1224no—
320C2×C22⋊C4—2442no—
321C2×C22⋊C4—2444no—
322C2×C42—611no—
323C2×C42C2×#692311yescharacteristic, complemented
324#99—618no—
325#99—1228no—
326#99—1224no—
327C24—21no—
328C24—611no—
329C24—614no—
330C24—614no—
331C24—612no—
332C24—1222no—
333C24—1224no—
334C24—1222no—
335C24—4884no—
336C24C22⋊#692312yes—
337#41—2448no—
338#41—2448no—
339C2×Q8—612no—
340C2×Q8—1221no—
341C2×Q8—2441no—
342C2×Q8—2441no—
343C2×D4—28no—
344C2×D4—21no—
345C2×D4—41no—
346C2×D4—41no—
347C2×D4—41no—
348C2×D4—41no—
349C2×D4—84no—
350C2×D4—614no—
351C2×D4—614no—
352C2×D4—612no—
353C2×D4—611no—
354C2×D4—611no—
355C2×D4—1224no—
356C2×D4—1224no—
357C2×D4—1224no—
358C2×D4—4884no—
359C2×D4—2441no—
360C2×D4—2441no—
361C2×D4—2444no—
362C2×D4—2444no—
363C2×D4—2444no—
364C2×D4—2444no—
365C2×D4—2442no—
366C2×D4—2442no—
367C2×D4—2442no—
368C2×D4—2442no—
369C2×D4C22⋊#692312yes—
370C2×D4C22×#692312yes—
371C2×D4C22×#692312yescomplemented
372C22×C4—21no—
373C22×C4—611no—
374C22×C4—612no—
375C22×C4—612no—
376C22×C4—1222no—
377C22×C4—1222no—
378C22×C4—1224no—
379C22×C4—1221no—
380C22×C4—1221no—
381C22×C4—4888no—
382C22×C4—2442no—
383C22×C4—2442no—
384C22×C4—2448no—
385C22×C4—2444no—
386C22×C4C22×#692311yescharacteristic
387C4⋊C4—1224no—
388C22⋊C4—1224no—
389C22⋊C4—1224no—
390C22⋊C4—1224no—
391C22⋊C4—1228no—
392C22⋊C4—1228no—
393C22⋊C4—2448no—
394C22⋊C4—2444no—
395C42—21no—
396C42—612no—
397C42—1221no—
398C42C22×#692312yescomplemented
399C23—22no—
400C23—22no—
401C23—22no—
402C23—44no—
403C23—44no—
404C23—41no—
405C23—41no—
406C23—612no—
407C23—612no—
408C23—612no—
409C23—612no—
410C23—612no—
411C23—1224no—
412C23—1224no—
413C23—1224no—
414C23—1224no—
415C23—1222no—
416C23—1222no—
417C23—4884no—
418C23—4884no—
419C23—4884no—
420C23—4888no—
421C23—2442no—
422C23—2444no—
423C23—2448no—
424C23C2×C22⋊#692314yes—
425C23C2×C22⋊#692311yescharacteristic
426Q8—2442no—
427Q8—2442no—
428D4—42no—
429D4—42no—
430D4—42no—
431D4—42no—
432D4—88no—
433D4—4884no—
434D4—4884no—
435D4—2442no—
436D4—2441no—
437D4—2441no—
438D4—2444no—
439D4—2444no—
440D4—2448no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—22no—
444C2×C4—42no—
445C2×C4—612no—
446C2×C4—1224no—
447C2×C4—1224no—
448C2×C4—1221no—
449C2×C4—1221no—
450C2×C4—1222no—
451C2×C4—1222no—
452C2×C4—48816no—
453C2×C4—4888no—
454C2×C4—2448no—
455C2×C4—2448no—
456C2×C4—2442no—
457C2×C4—2441no—
458C2×C4—2441no—
459C2×C4C2×C22⋊#692311yescharacteristic
460C2×C4C23×#692311yescharacteristic
461C22—22no—
462C22—24no—
463C22—44no—
464C22—44no—
465C22—44no—
466C22—42no—
467C22—82no—
468C22—82no—
469C22—82no—
470C22—614no—
471C22—1224no—
472C22—1222no—
473C22—1222no—
474C22—4882no—
475C22—4884no—
476C22—4884no—
477C22—2442no—
478C22—2442no—
479C22—2442no—
480C22—2442no—
481C22—2448no—
482C22—2448no—
483C22—2444no—
484C22D61⋊#9911yescharacteristic
485C22D61⋊#9911yescharacteristic
486C22C22×C22⋊#692311yescharacteristic
487C4—21no—
488C4—21no—
489C4—42no—
490C4—1222no—
491C4—4888no—
492C4—2442no—
493C4—2442no—
494C2—21no—
495C2—21no—
496C2—44no—
497C2—82no—
498C2—1224no—
499C2—2442no—
500C2—2442no—
501C2#2146209512yesdirect product factor
502C2C2×D61⋊#9911yescharacteristic
subgroupG/H
centerC22D61⋊#99
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC2×#127×C61C4
socleC22×C61C2×#99
prime radicalC2×#16840325C2
cosocleC2×D244C24
hypercenterC2×#127#6923
hypocenterC61C2×#2127
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ C2×#127

Complements

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

NH ≅ G/Ntype
1. C2×D61⋊#99C2semidirect
2. #21462095C2direct (N × H)
3. C2×#16840669C2semidirect
4. C2×#16840666C2semidirect
9. D61⋊#99C22semidirect
11. #16840669C22semidirect
12. #16840666C22semidirect
13. C22×#11758224C4semidirect
16. #16840325C4semidirect
20. C2×#14519764C4semidirect
23. C2×#14519734C4semidirect
24. C2×#127×C61C4semidirect
37. C2×#11758224C2×C4semidirect
38. C22×Dic122C2×C4semidirect
51. #14519773C2×C4semidirect
54. #14519765C2×C4semidirect
57. #14519764C2×C4semidirect
63. #14519734C2×C4semidirect
68. C2×C4×Dic61C2×C4semidirect
71. C22×D4×C61C2×C4semidirect
73. #127×C61C2×C4semidirect
74. C2×C42×C61C2×C4semidirect
97. C2×D4×C61C22×C4semidirect
134. C2×Dic122C22×C4semidirect
139. C42×C61C22×C4semidirect
146. C4×Dic61C22×C4semidirect
252. C2×C61#2127semidirect
263. C2×#127#6923semidirect
276. C61C2×#2127semidirect
294. C22×D4C2×#6923semidirect
302. #127C2×#6923semidirect
323. C2×C42C2×#6923semidirect
371. C2×D4C22×#6923semidirect
398. C42C22×#6923semidirect
501. C2#21462095direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D61⋊#992
#214620952
C2×#168406692
C2×#168406662
C2×#168403252
C2×#212761