Finite Group Databasebeta

← C2×#21458698 #30560456

Subgroups — C2×#21458698 #30560456

Order 15616.

1842 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840487C211yesmaximal, characteristic, complemented
2C2×#16840469C211yesmaximal, characteristic
3#21458698C2116yesmaximal, direct product factor
4C2×#16840163C212yesmaximal, complemented
5C2×#16840158C211yesmaximal, characteristic, complemented
6C2×#16840068C212yesmaximal, complemented
7C2×#16840058C211yesmaximal, characteristic, complemented
8C2×#16840060C212yesmaximal
9C2×#16839886C211yesmaximal, characteristic, complemented
10C2×#16839853C212yesmaximal
11C2×C4×#11758200C211yesmaximal, characteristic
12C2×C61×#474C211yesmaximal, characteristic
13C22×#11758200C2211yescharacteristic
14#16840487—24no—
15#16840487C2218yescomplemented
16#16840469—24no—
17#16840469C2218yes—
18C2×#14519777C2211yescharacteristic
19C2×#14519775—21no—
20C2×#14519768C2212yes—
21C2×#14519768C2212yes—
22C2×#14519767—22no—
23C2×#14519756—21no—
24C2×#14519754—22no—
25C2×Q8×Dic61—21no—
26C2×C4×Dic122C2211yescharacteristic
27C2×C4×Dic122C2211yescharacteristic
28C2×#14519742C2212yes—
29C2×D4×Dic61C2212yes—
30C22×C4⋊Dic61—21no—
31#16840163C22116yescomplemented
32#16840158C2218yescomplemented
33#16840068C22116yescomplemented
34#16840060C22116yes—
35#16840058C2218yescomplemented
36#16839886C2218yescomplemented
37#16839853C22116yes—
38C4×#11758200C2218yes—
39C2×#14519711C2212yes—
40C2×#14519708C2212yes—
41C2×#14519708C2212yes—
42C2×#14519708C2211yescharacteristic
43C2×#14519706C2212yes—
44C2×#14519702C2212yes—
45C2×#14519700C2211yescharacteristic
46C2×#14519698C2211yescharacteristic
47C2×C4×#92418C2211yescharacteristic
48C2×C8×Dic61C2212yes—
49C2×C4⋊Q8×C61C2211yescharacteristic
50C2×C4×D4×C61C2211yescharacteristic
51C61×#474C2218yes—
52C2×#107×C61C2212yes—
53C2×C4⋊C8×C61C2211yescharacteristic
54C2×#102×C61C2212yes—
55C22×Dic122—21no—
56C22×Dic122D411yescharacteristic
57C22×Dic122C2311yescharacteristic
58C23×Dic61—22no—
59C2×#11758200Q818yescomplemented
60C2×#11758200C2314yes—
61C22×#92418C2311yescharacteristic
62C22×#92418C2311yescharacteristic
63#14519777—22no—
64#14519777C2314yes—
65#14519775—28no—
66#14519768—24no—
67#14519768—24no—
68#14519768C2318yes—
69#14519768C2318yes—
70#14519767—216no—
71#14519756—28no—
72#14519754—216no—
73Q8×Dic61—28no—
74C4×Dic122—22no—
75C4×Dic122D414yes—
76C4×Dic122C2314yes—
77C4×Dic122C2314yes—
78#14519742—24no—
79#14519742C2318yes—
80D4×Dic61—24no—
81D4×Dic61C2318yes—
82C2×C4⋊Dic61—21no—
83C2×C4⋊Dic61—22no—
84C2×C4⋊Dic61—22no—
85C2×C4⋊Dic61—28no—
86C2×C4⋊Dic61D411yescharacteristic
87C2×C4⋊Dic61C2312yes—
88C2×C4⋊Dic61C2311yescharacteristic
89C2×#11758196—21no—
90C2×#11758196—22no—
91C2×#11758196—22no—
92C2×#11758196—22no—
93C2×#11758196D412yes—
94C2×C22⋊Dic61—22no—
95C2×C4×Dic61—21no—
96C2×C4×Dic61—22no—
97C2×C4×Dic61C2312yes—
98#14519711C2318yes—
99#14519708C2318yes—
100#14519708C2314yes—
101#14519708C2318yes—
102#14519706C2318yes—
103#14519702C2318yes—
104#14519700C2314yes—
105#14519698C2314yes—
106C4×#92418C2314yes—
107C8×Dic61C2318yes—
108C22×Q8×C61—21no—
109C22×D4×C61C2311yescharacteristic
110C23×C4×C61—21no—
111C22×C8×C61C2312yes—
112C4⋊Q8×C61—22no—
113C4⋊Q8×C61C2314yes—
114C4×D4×C61—22no—
115C4×D4×C61C2314yes—
116C2×C4⋊C4×C61—21no—
117C2×C4⋊C4×C61C2312yes—
118C2×C4⋊C4×C61C2311yescharacteristic
119C2×C22⋊C4×C61—21no—
120C2×C42×C61C2311yescharacteristic
121#107×C61C2318yes—
122C4⋊C8×C61C2314yes—
123#102×C61C2318yes—
124C24×C61—21no—
125C2×Q8×C61—24no—
126C2×Q8×C61—44no—
127C2×D4×C61—21no—
128C2×D4×C61—22no—
129C2×D4×C61C2×Q814yes—
130C2×D4×C61C2412yes—
131C22×C4×C61—21no—
132C22×C4×C61—22no—
133C22×C4×C61—24no—
134C22×C4×C61—44no—
135C22×C4×C61C2×D411yescharacteristic
136C22×C4×C61C2×D411yescharacteristic
137C22×C4×C61C2411yescharacteristic
138C22×Dic61—21no—
139C22×Dic61—22no—
140C22×Dic61—21no—
141C22×Dic61—28no—
142C22×Dic61—84no—
143C22×Dic61C2×D412yes—
144C22×Dic61C2×D412yes—
145C2×Dic122—24no—
146C2×Dic122—21no—
147C2×Dic122—22no—
148C2×Dic122—24no—
149C2×Dic122—82no—
150C2×Dic122C2×D414yes—
151C2×Dic122C2×Q814yes—
152C2×Dic122C2412yes—
153C2×C8×C61—24no—
154C2×C8×C61C2414yes—
155C4⋊C4×C61—24no—
156C4⋊C4×C61—21no—
157C4⋊C4×C61—22no—
158C4⋊C4×C61C2414yes—
159C4⋊C4×C61C2412yes—
160C22⋊C4×C61—24no—
161C42×C61C2×D412yes—
162C42×C61C2412yes—
163C22⋊Dic61—28no—
164#11758200C2×Q8116yescomplemented
165C4⋊Dic61—24no—
166C4⋊Dic61—22no—
167C4⋊Dic61—21no—
168C4⋊Dic61—28no—
169C4⋊Dic61—28no—
170C4⋊Dic61C2×D414yes—
171C4⋊Dic61C2412yes—
172C4⋊Dic61C2414yes—
173#11758196—24no—
174#11758196—28no—
175#11758196—28no—
176#11758196—28no—
177#11758196C2×D418yes—
178C4×Dic61—24no—
179C4×Dic61—28no—
180C4×Dic61C2×D414yes—
181C4×Dic61C2414yes—
182C2×#92418—22no—
183C2×#92418C2×Q814yes—
184C2×#92418C2412yes—
185C2×#92418C2412yes—
186C23×C61—24no—
187C23×C61—22no—
188C23×C61—42no—
189C23×C61—42no—
190C23×C61C22×D411yescharacteristic
191Q8×C61—48no—
192D4×C61—24no—
193D4×C61—22no—
194D4×C61C22×Q814yes—
195C2×C4×C61—22no—
196C2×C4×C61—24no—
197C2×C4×C61—22no—
198C2×C4×C61—42no—
199C2×C4×C61—44no—
200C2×C4×C61—48no—
201C2×C4×C61#13514yes—
202C2×C4×C61C22×D412yes—
203C2×C4×C61C22×D411yescharacteristic
204C2×C4×C61C22×D412yes—
205C2×C4×C61C22×Q812yes—
206C2×C4×C612−1+412yes—
207C2×C4×C61C2511yescharacteristic
208C2×Dic61—24no—
209C2×Dic61—24no—
210C2×Dic61—24no—
211C2×Dic61—22no—
212C2×Dic61—22no—
213C2×Dic61—24no—
214C2×Dic61—44no—
215C2×Dic61—42no—
216C2×Dic61—88no—
217C2×Dic61C22×D414yes—
218C2×Dic61C22×D414yes—
219Dic122—24no—
220Dic122—28no—
221Dic122—22no—
222Dic122—84no—
223Dic122C22×Q814yes—
224C8×C61—24no—
225#92418—22no—
226#92418C22×Q814yes—
227C2×#3381—611nomaximal, Sylow
228C22×C61—24no—
229C22×C61—48no—
230C22×C61—42no—
231C22×C61—42no—
232C22×C61D4×Q812yes—
233C22×C61C2×#13512yes—
234C22×C61#57712yes—
235C22×C61C23×D411yescharacteristic
236C4×C61—22no—
237C4×C61—42no—
238C4×C61—44no—
239C4×C61D4×Q812yes—
240C4×C61C2×#13514yes—
241C4×C61C23×Q811yescharacteristic
242C4×C61C2×2−1+411yescharacteristic
243Dic61—24no—
244Dic61—24no—
245Dic61—24no—
246Dic61—44no—
247Dic61—42no—
248C2×#557—611no—
249C2×#554—611no—
250#3381—6116no—
251C2×#499—612no—
252C2×#498—611no—
253C2×#479—612no—
254C2×#477—611no—
255C2×#478—612no—
256C2×#474D6111yescharacteristic
257C2×C8×Q8—611no—
258C2×C4×SD16—612no—
259C2×C4×SD16—611no—
260C2×C61—44no—
261C2×C61#338114yescomplemented
262C2×C61C2×D4×Q811yescharacteristic
263C2×C61C22×#13511yescharacteristic
264C2×C61C2×#57711yescharacteristic
265C22×SD16—611no—
266#557—618no—
267#557—1224no—
268#554—618no—
269#554—1224no—
270C2×C4⋊Q8—611no—
271C2×C4⋊Q8—1221no—
272C2×C4⋊Q8C2×D6111yescharacteristic
273C2×#125—612no—
274C2×#125—612no—
275C2×#125—1222no—
276C2×C22⋊Q8—1222no—
277C2×C22⋊Q8—1221no—
278C2×C4×Q8—611no—
279C2×C4×Q8—612no—
280C2×C4×Q8—611no—
281C2×C4×Q8—1221no—
282C2×C4×D4—612no—
283C2×C4×D4C2×D6111yescharacteristic
284C22×C4⋊C4—1221no—
285#499—6116no—
286#498—618no—
287#479—6116no—
288#478—6116no—
289#477—618no—
290#474C2×D6118yes—
291C8×Q8—618no—
292C4×SD16—618no—
293C4×SD16—6116no—
294C2×#107—612no—
295C2×#107C2×D6112yes—
296C2×#106—612no—
297C2×#106—612no—
298C2×#106—611no—
299C2×C4⋊C8—612no—
300C2×C4⋊C8C2×D6111yescharacteristic
301C2×#103—612no—
302C2×#103—611no—
303C2×#102—611no—
304C2×#102C2×D6112yes—
305C2×C4×C8—612no—
306C2×C4×C8—611no—
307C61C2×#338111yescharacteristic, complemented, Sylow
308C22×Q8—21no—
309C22×Q8—611no—
310C22×Q8—611no—
311C22×Q8—1221no—
312C22×D4C22×D6111yescharacteristic
313C23×C4—21no—
314C23×C4—1222no—
315C2×SD16—618no—
316C2×SD16—614no—
317C22×C8—611no—
318C22×C8—611no—
319C22×C8C22×D6112yes—
320C4⋊Q8—22no—
321C4⋊Q8—614no—
322C4⋊Q8—1228no—
323C4⋊Q8—1222no—
324C4⋊Q8C22×D6114yes—
325#125—618no—
326#125—618no—
327#125—1224no—
328#125—1224no—
329#125—12216no—
330C22⋊Q8—12216no—
331C22⋊Q8—1228no—
332C4×Q8—614no—
333C4×Q8—614no—
334C4×Q8—618no—
335C4×Q8—614no—
336C4×Q8—1224no—
337C4×Q8—1228no—
338C4×Q8—1222no—
339C4×D4—22no—
340C4×D4—618no—
341C4×D4—1224no—
342C4×D4C22×D6114yes—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—611no—
345C2×C4⋊C4—612no—
346C2×C4⋊C4—612no—
347C2×C4⋊C4—611no—
348C2×C4⋊C4—1228no—
349C2×C4⋊C4—1222no—
350C2×C4⋊C4—1222no—
351C2×C4⋊C4—1222no—
352C2×C4⋊C4—1222no—
353C2×C4⋊C4—1222no—
354C2×C4⋊C4—1221no—
355C2×C4⋊C4—1221no—
356C2×C4⋊C4C22×D6111yescharacteristic
357C2×C4⋊C4C22×D6112yes—
358C2×C22⋊C4—21no—
359C2×C22⋊C4—1222no—
360C2×C42—612no—
361C2×C42—1222no—
362C2×C42—1221no—
363C2×C42C22×D6111yescharacteristic
364#107—618no—
365#107C22×D6118yes—
366#106—618no—
367#106—614no—
368#106—618no—
369C4⋊C8—618no—
370C4⋊C8C22×D6114yes—
371#103—618no—
372#103—614no—
373#102—614no—
374#102C22×D6118yes—
375C4×C8—618no—
376C4×C8—614no—
377C24—21no—
378C2×Q8—24no—
379C2×Q8—44no—
380C2×Q8—614no—
381C2×Q8—614no—
382C2×Q8—612no—
383C2×Q8—1221no—
384C2×Q8—1224no—
385C2×Q8—1222no—
386C2×Q8—1224no—
387C2×Q8—4882no—
388C2×D4—21no—
389C2×D4—22no—
390C2×D4Q8×D6114yes—
391C2×D4C23×D6112yes—
392C22×C4—22no—
393C22×C4—21no—
394C22×C4—24no—
395C22×C4—44no—
396C22×C4—612no—
397C22×C4—612no—
398C22×C4—1228no—
399C22×C4—1221no—
400C22×C4—1221no—
401C22×C4—1222no—
402C22×C4—4884no—
403C22×C4D4×D6111yescharacteristic
404C22×C4D4×D6111yescharacteristic
405C22×C4C23×D6111yescharacteristic
406SD16—6116no—
407C2×C8—24no—
408C2×C8—614no—
409C2×C8—612no—
410C2×C8—612no—
411C2×C8—1222no—
412C2×C8C23×D6114yes—
413C4⋊C4—24no—
414C4⋊C4—21no—
415C4⋊C4—22no—
416C4⋊C4—614no—
417C4⋊C4—618no—
418C4⋊C4—612no—
419C4⋊C4—614no—
420C4⋊C4—1228no—
421C4⋊C4—1228no—
422C4⋊C4—1228no—
423C4⋊C4—1228no—
424C4⋊C4—1228no—
425C4⋊C4—1222no—
426C4⋊C4—1221no—
427C4⋊C4—1224no—
428C4⋊C4—1224no—
429C4⋊C4C23×D6114yes—
430C4⋊C4C23×D6112yes—
431C22⋊C4—24no—
432C22⋊C4—1228no—
433C42—614no—
434C42—614no—
435C42—1228no—
436C42—1224no—
437C42D4×D6112yes—
438C42C23×D6112yes—
439C23—22no—
440C23—24no—
441C23—42no—
442C23—42no—
443C23C2×D4×D6111yescharacteristic
444Q8—48no—
445Q8—614no—
446Q8—1228no—
447Q8—1222no—
448Q8—1224no—
449Q8—4884no—
450D4—22no—
451D4—24no—
452D4C2×Q8×D6114yes—
453C2×C4—22no—
454C2×C4—24no—
455C2×C4—22no—
456C2×C4—42no—
457C2×C4—44no—
458C2×C4—48no—
459C2×C4—614no—
460C2×C4—614no—
461C2×C4—1224no—
462C2×C4—1224no—
463C2×C4—1222no—
464C2×C4—1224no—
465C2×C4—1222no—
466C2×C4—1224no—
467C2×C4—4888no—
468C2×C4—2442no—
469C2×C4—2444no—
470C2×C4#1451979614yes—
471C2×C4C2×D4×D6112yes—
472C2×C4C2×D4×D6112yes—
473C2×C4C2×D4×D6111yescharacteristic
474C2×C4C2×Q8×D6112yes—
475C2×C4#1451982412yes—
476C2×C4C24×D6111yescharacteristic
477C8—24no—
478C8—614no—
479C8—1222no—
480C22—24no—
481C22—48no—
482C22—42no—
483C22—42no—
484C22#1684042512yes—
485C22C2×#1451979612yes—
486C22#1684057112yes—
487C22C22×D4×D6111yescharacteristic
488C4—22no—
489C4—42no—
490C4—44no—
491C4—1224no—
492C4—1224no—
493C4—1224no—
494C4—2444no—
495C4—2442no—
496C4#1684042512yes—
497C4C2×#1451979614yes—
498C4C22×Q8×D6111yescharacteristic
499C4C2×#1451982411yescharacteristic
500C2—44no—
501C2#2145869814yesdirect product factor
502C2C2×#1684042511yescharacteristic
503C2C22×#1451979611yescharacteristic
504C2C2×#1684057111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#474C2
socleC23×C61C22×D4
prime radicalC22×D4×C61C23
hypercenterC2×#474D61
hypocenterC61C2×#3381
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#474

Complements

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

NH ≅ G/Ntype
1. C2×#16840487C2semidirect
3. #21458698C2direct (N × H)
4. C2×#16840163C2semidirect
5. C2×#16840158C2semidirect
6. C2×#16840068C2semidirect
7. C2×#16840058C2semidirect
9. C2×#16839886C2semidirect
15. #16840487C22semidirect
31. #16840163C22semidirect
32. #16840158C22semidirect
33. #16840068C22semidirect
35. #16840058C22semidirect
36. #16839886C22semidirect
59. C2×#11758200Q8semidirect
164. #11758200C2×Q8semidirect
261. C2×C61#3381semidirect
307. C61C2×#3381semidirect
501. C2#21458698direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404872
C2×#168404692
#214586982
C2×#168401632
C2×#168401582
C2×#168400682
C2×#168400582
C2×#168400602
C2×#168398862
C2×#168398532
C2×C4×#117582002
C2×C61×#4742
C2×#338161