Finite Group Databasebeta

← C2×#21444963 #29655900

Subgroups — C2×#21444963 #29655900

Order 15616.

1074 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840477C211yesmaximal, characteristic
2C2×#16840141C211yesmaximal, characteristic, complemented
3C2×#16840049C211yesmaximal, characteristic, complemented
4#21444963C218yesmaximal, direct product factor
5C2×#16839510C211yesmaximal, characteristic, complemented
6C2×D4⋊#92418C211yesmaximal, characteristic, complemented
7C2×#16839489C211yesmaximal, characteristic, complemented
8C2×C61×#476C211yesmaximal, characteristic, complemented
9C22×#11758202—22no—
10#16840477—22no—
11#16840477—22no—
12#16840477—22no—
13#16840477C2214yes—
14C2×#14519777C2211yescharacteristic
15C2×#14519763—22no—
16C2×#14519751—21no—
17C2×#14519748—21no—
18C2×C4×D244C2211yescharacteristic
19C2×#14519736—21no—
20C2×#14519735—21no—
21#16840141—22no—
22#16840141C2214yescomplemented
23#16840049—22no—
24#16840049C2214yescomplemented
25C2×#14519708—21no—
26C2×C4⋊#92418C2211yescharacteristic
27C2×#14519697—21no—
28C2×C4×#92418C2211yescharacteristic
29#16839510C2214yescomplemented
30D4⋊#92418C2214yescomplemented
31#16839489C2214yescomplemented
32C2×C4⋊Q8×C61C2211yescharacteristic
33C2×C4×D4×C61C2211yescharacteristic
34C61×#476—22no—
35C61×#476C2214yescomplemented
36C2×#106×C61—21no—
37C2×C4⋊C8×C61C2211yescharacteristic
38C2×#102×C61—21no—
39C22×Dic122D412yes—
40C22×D244D411yescharacteristic
41C22×C22⋊D61—22no—
42C22×C4×D61—21no—
43C2×#11758202—28no—
44C2×#11758202—48no—
45C22×#92418—21no—
46C22×#92418—21no—
47#14519777—21no—
48#14519777—21no—
49#14519777D412yes—
50#14519777C2312yes—
51#14519763—28no—
52#14519763—28no—
53#14519751—24no—
54#14519751—24no—
55#14519748—24no—
56#14519748—24no—
57C4×D244—21no—
58C4×D244—21no—
59C4×D244D412yes—
60C4×D244C2312yes—
61#14519736—24no—
62#14519736—24no—
63#14519735—24no—
64#14519735—24no—
65C2×C4⋊Dic61—21no—
66C2×C4⋊Dic61—21no—
67C2×C4⋊Dic61D411yescharacteristic
68C2×C22⋊Dic61—22no—
69C2×#11758198—22no—
70C2×#11758198—21no—
71C2×C4×Dic61—22no—
72#14519708—24no—
73C4⋊#92418—21no—
74C4⋊#92418C2312yes—
75#14519697—24no—
76C4×#92418—21no—
77C4×#92418C2312yes—
78C22×Q8×C61—21no—
79C22×D4×C61D411yescharacteristic
80C23×C4×C61—21no—
81C22×C8×C61—21no—
82C4⋊Q8×C61—21no—
83C4⋊Q8×C61—21no—
84C4⋊Q8×C61—21no—
85C4⋊Q8×C61C2312yes—
86C4×D4×C61—21no—
87C4×D4×C61—21no—
88C4×D4×C61D412yes—
89C4×D4×C61C2312yes—
90C2×C4⋊C4×C61—21no—
91C2×C4⋊C4×C61—21no—
92C2×C4⋊C4×C61D411yescharacteristic
93C2×C22⋊C4×C61—21no—
94C2×C42×C61C2311yescharacteristic
95#106×C61—24no—
96C4⋊C8×C61—21no—
97C4⋊C8×C61C2312yes—
98#102×C61—24no—
99C24×C61—21no—
100C23×D61—21no—
101C2×Q8×C61—22no—
102C2×Q8×C61—44no—
103C2×Q8×C61—41no—
104C2×D4×C61—21no—
105C2×D4×C61—22no—
106C2×D4×C61—22no—
107C2×D4×C61C2×D412yes—
108C22×C4×C61—21no—
109C22×C4×C61—22no—
110C22×C4×C61—22no—
111C22×C4×C61—42no—
112C22×C4×C61—42no—
113C22×C4×C61—41no—
114C22×C4×C61C2×D411yescharacteristic
115C22×C4×C61C2×D411yescharacteristic
116C22×C4×C61C2×D411yescharacteristic
117C2×C22⋊D61—28no—
118C2×C22⋊D61—84no—
119C22×Dic61—21no—
120C22×Dic61—22no—
121C2×D244—22no—
122C2×D244—22no—
123C2×D244—21no—
124C2×D244C2×D412yes—
125C2×C4×D61—22no—
126C2×C4×D61—22no—
127C2×C4×D61—42no—
128C2×C4×D61—42no—
129C2×Dic122—22no—
130C2×Dic122—44no—
131C2×Dic122C2×D414yes—
132C2×C8×C61—22no—
133C2×C8×C61—42no—
134C4⋊C4×C61—21no—
135C4⋊C4×C61—22no—
136C4⋊C4×C61—22no—
137C4⋊C4×C61—41no—
138C4⋊C4×C61—41no—
139C4⋊C4×C61C2×D412yes—
140C22⋊C4×C61—22no—
141C22⋊C4×C61—22no—
142C42×C61C2×D411yescharacteristic
143C42×C61C2×D411yescharacteristic
144C42×C61C2×D411yescharacteristic
145C42×C61C2411yescharacteristic
146C22⋊Dic61—28no—
147#11758202—416no—
148#11758198—28no—
149#11758198—22no—
150#11758198—22no—
151C4⋊Dic61—22no—
152C4⋊Dic61—22no—
153C4⋊Dic61—21no—
154C4⋊Dic61—22no—
155C4⋊Dic61—22no—
156C4⋊Dic61C2×D412yes—
157C4×Dic61—28no—
158C2×#92418—24no—
159C2×#92418—22no—
160C2×#92418—22no—
161C2×#92418—42no—
162C23×C61—22no—
163C23×C61—42no—
164C23×C61—42no—
165C23×C61—42no—
166C23×C61#12011yescharacteristic
167C22×D61—22no—
168C22×D61—42no—
169C22×D61—42no—
170C22×D61—42no—
171Q8×C61—44no—
172Q8×C61—82no—
173D4×C61—22no—
174D4×C61—22no—
175D4×C61—42no—
176C2×C4×C61—22no—
177C2×C4×C61—22no—
178C2×C4×C61—42no—
179C2×C4×C61—42no—
180C2×C4×C61—42no—
181C2×C4×C61—44no—
182C2×C4×C61—42no—
183C2×C4×C61—82no—
184C2×C4×C61#12011yescharacteristic
185C2×C4×C61#12011yescharacteristic
186C2×C4×C61#12011yescharacteristic
187C2×C4×C61#13512yes—
188C2×C4×C61#13512yes—
189C2×C4×C61#13712yes—
190C2×C4×C61#13712yes—
191C2×C4×C61C22×D411yescharacteristic
192C2×C4×C61C22×D411yescharacteristic
193C2×C4×C61C22×D411yescharacteristic
194C22⋊D61—88no—
195C2×Dic61—22no—
196C2×Dic61—24no—
197C2×Dic61—42no—
198C2×Dic61—44no—
199D244—22no—
200D244—22no—
201D244—42no—
202C4×D61—42no—
203C4×D61—42no—
204C4×D61—44no—
205Dic122—44no—
206Dic122—82no—
207C8×C61—42no—
208#92418—24no—
209#92418—42no—
210C2×#1634—611nomaximal, Sylow
211C22×C61—42no—
212C22×C61—42no—
213C22×C61—42no—
214C22×C61—84no—
215C22×C61#45212yes—
216C22×C61#45212yes—
217C22×C61#45312yes—
218C22×C61C2×#12011yescharacteristic
219C2×D61—42no—
220C2×D61—42no—
221C2×D61—42no—
222C2×D61—84no—
223C4×C61—21no—
224C4×C61—21no—
225C4×C61—42no—
226C4×C61—82no—
227C4×C61#45212yes—
228C4×C61#45212yes—
229C4×C61C2×#13511yescharacteristic
230C4×C61C2×#13511yescharacteristic
231C4×C61C2×#13711yescharacteristic
232C4×C61C2×#13711yescharacteristic
233Dic61—42no—
234Dic61—44no—
235C2×#555—611no—
236C2×#494—611no—
237C2×#476—611no—
238C2×#476D6111yescharacteristic, complemented
239#1634—618no—
240C2×#333—611no—
241C2×D4⋊C8—611no—
242C2×D4⋊C8—611no—
243C2×C61—82no—
244C2×C61#163414yescomplemented
245C2×C61C2×#45211yescharacteristic
246C2×C61C2×#45211yescharacteristic
247C2×C61C2×#45311yescharacteristic
248D61—82no—
249C22×Q16—1222no—
250#555—614no—
251#555—1222no—
252#555—1222no—
253#555—1222no—
254C2×C4⋊Q8—611no—
255C2×C4⋊Q8C2×D6111yescharacteristic
256C2×#124—1222no—
257C2×#121—1221no—
258C2×#121—1221no—
259C2×C4×D4—611no—
260C2×C4×D4C2×D6111yescharacteristic
261C2×#117—1221no—
262C2×#117—1221no—
263#494—614no—
264#494—1222no—
265#476—22no—
266#476—614no—
267#476—1222no—
268#476C2×D6114yescomplemented
269C2×#106—21no—
270C2×#106—1221no—
271C2×C4⋊C8—611no—
272C2×C4⋊C8C2×D6111yescharacteristic
273C2×#102—21no—
274C2×#102—1221no—
275C2×C4×C8—611no—
276#333—614no—
277D4⋊C8—614no—
278D4⋊C8—614no—
279C61C2×#163411yescharacteristic, complemented, Sylow
280C22×Q8—21no—
281C22×Q8—612no—
282C22×D4—611no—
283C22×D4—1222no—
284C22×D4C22⋊D6111yescharacteristic
285C23×C4—21no—
286C23×C4—1221no—
287C2×Q16—1228no—
288C2×Q16—2448no—
289C22×C8—21no—
290C22×C8—1221no—
291C22×C8—1221no—
292C4⋊Q8—21no—
293C4⋊Q8—21no—
294C4⋊Q8—21no—
295C4⋊Q8—612no—
296C4⋊Q8—612no—
297C4⋊Q8—1221no—
298C4⋊Q8—1221no—
299C4⋊Q8C22×D6112yes—
300#124—1228no—
301#124—1228no—
302#121—1224no—
303#121—1224no—
304#121—1224no—
305#121—1224no—
306C4×D4—21no—
307C4×D4—21no—
308C4×D4—612no—
309C4×D4—612no—
310C4×D4—1221no—
311C4×D4—1221no—
312C4×D4C22⋊D6112yes—
313C4×D4C22×D6112yes—
314#117—1224no—
315#117—1224no—
316#117—1224no—
317#117—1224no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—611no—
321C2×C4⋊C4—1221no—
322C2×C4⋊C4—1221no—
323C2×C4⋊C4C22⋊D6111yescharacteristic
324C2×C22⋊C4—21no—
325C2×C22⋊C4—1222no—
326C2×C22⋊C4—1222no—
327C2×C22⋊C4—1221no—
328C2×C42—1222no—
329C2×C42C22×D6111yescharacteristic
330#106—24no—
331#106—1224no—
332C4⋊C8—21no—
333C4⋊C8—612no—
334C4⋊C8—1221no—
335C4⋊C8C22×D6112yes—
336#102—24no—
337#102—1224no—
338C4×C8—612no—
339C4×C8—1221no—
340C24—21no—
341C24—1221no—
342C2×Q8—22no—
343C2×Q8—44no—
344C2×Q8—41no—
345C2×Q8—614no—
346C2×Q8—1222no—
347C2×Q8—2444no—
348C2×D4—22no—
349C2×D4—21no—
350C2×D4—22no—
351C2×D4—612no—
352C2×D4—1228no—
353C2×D4—1221no—
354C2×D4—1222no—
355C2×D4—1222no—
356C2×D4—4884no—
357C2×D4C2×C22⋊D6112yes—
358C22×C4—21no—
359C22×C4—22no—
360C22×C4—22no—
361C22×C4—42no—
362C22×C4—42no—
363C22×C4—41no—
364C22×C4—1221no—
365C22×C4—1222no—
366C22×C4—1222no—
367C22×C4—1222no—
368C22×C4—2442no—
369C22×C4—2442no—
370C22×C4D4×D6111yescharacteristic
371C22×C4D4×D6111yescharacteristic
372C22×C4C2×C22⋊D6111yescharacteristic
373Q16—24416no—
374C2×C8—22no—
375C2×C8—42no—
376C2×C8—1224no—
377C2×C8—1222no—
378C2×C8—1222no—
379C2×C8—2442no—
380C4⋊C4—21no—
381C4⋊C4—22no—
382C4⋊C4—22no—
383C4⋊C4—41no—
384C4⋊C4—41no—
385C4⋊C4—612no—
386C4⋊C4—1222no—
387C4⋊C4—1222no—
388C4⋊C4—1221no—
389C4⋊C4—1222no—
390C4⋊C4—1222no—
391C4⋊C4C2×C22⋊D6112yes—
392C22⋊C4—22no—
393C22⋊C4—22no—
394C22⋊C4—1228no—
395C22⋊C4—1228no—
396C22⋊C4—1222no—
397C22⋊C4—1222no—
398C42—1228no—
399C42D4×D6111yescharacteristic
400C42D4×D6111yescharacteristic
401C42C2×C22⋊D6111yescharacteristic
402C42C23×D6111yescharacteristic
403C23—22no—
404C23—42no—
405C23—42no—
406C23—42no—
407C23—1222no—
408C23—2442no—
409C23—2442no—
410C23—2442no—
411C23#1451974511yescharacteristic
412Q8—44no—
413Q8—82no—
414Q8—4882no—
415Q8—2444no—
416D4—22no—
417D4—22no—
418D4—42no—
419D4—1222no—
420D4—1222no—
421D4—4888no—
422D4—2442no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—44no—
429C2×C4—42no—
430C2×C4—82no—
431C2×C4—1222no—
432C2×C4—1224no—
433C2×C4—2442no—
434C2×C4—2444no—
435C2×C4—2442no—
436C2×C4—2442no—
437C2×C4—2444no—
438C2×C4#1451974511yescharacteristic
439C2×C4#1451974511yescharacteristic
440C2×C4#1451974511yescharacteristic
441C2×C4#1451979712yes—
442C2×C4#1451979812yes—
443C2×C4#1451980612yes—
444C2×C4#1451980812yes—
445C2×C4C2×D4×D6111yescharacteristic
446C2×C4C2×D4×D6111yescharacteristic
447C2×C4C22×C22⋊D6111yescharacteristic
448C8—42no—
449C8—1224no—
450C8—2442no—
451C22—42no—
452C22—42no—
453C22—42no—
454C22—84no—
455C22—4884no—
456C22—2442no—
457C22—2442no—
458C22—2442no—
459C22#1683992112yes—
460C22#1683992212yes—
461C22#1683992812yes—
462C22C2×#1451974511yescharacteristic
463C4—21no—
464C4—21no—
465C4—42no—
466C4—82no—
467C4—2444no—
468C4—2442no—
469C4#1683992112yes—
470C4#1683992212yes—
471C4C2×#1451979711yescharacteristic
472C4C2×#1451979811yescharacteristic
473C4C2×#1451980611yescharacteristic
474C4C2×#1451980811yescharacteristic
475C2—82no—
476C2—4882no—
477C2#2144496314yesdirect product factor
478C2C2×#1683992111yescharacteristic
479C2C2×#1683992211yescharacteristic
480C2C2×#1683992811yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC2×C61×#476C2
socleC23×C61#120
prime radicalC2×#16840477C2
hypercenterC2×#476D61
hypocenterC61C2×#1634
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#476

Complements

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

NH ≅ G/Ntype
2. C2×#16840141C2semidirect
3. C2×#16840049C2semidirect
4. #21444963C2direct (N × H)
5. C2×#16839510C2semidirect
6. C2×D4⋊#92418C2semidirect
7. C2×#16839489C2semidirect
8. C2×C61×#476C2semidirect
22. #16840141C22semidirect
24. #16840049C22semidirect
29. #16839510C22semidirect
30. D4⋊#92418C22semidirect
31. #16839489C22semidirect
35. C61×#476C22semidirect
238. C2×#476D61semidirect
244. C2×C61#1634semidirect
268. #476C2×D61semidirect
279. C61C2×#1634semidirect
477. C2#21444963direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404772
C2×#168401412
C2×#168400492
#214449632
C2×#168395102
C2×D4⋊#924182
C2×#168394892
C2×C61×#4762
C2×#163461