Finite Group Databasebeta

← C2×#21445030 #29655682

Subgroups — C2×#21445030 #29655682

Order 15616.

1022 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840473C211yesmaximal, characteristic
2C2×#16840039C211yesmaximal, characteristic
3C2×#16839969C211yesmaximal, characteristic, complemented
4#21445030C218yesmaximal, direct product factor
5C2×#16839511C211yesmaximal, characteristic, complemented
6C2×#16839494C211yesmaximal, characteristic, complemented
7C2×#16839491C211yesmaximal, characteristic
8C2×C61×#487C211yesmaximal, characteristic, complemented
9C22×#11758202—21no—
10#16840473—22no—
11#16840473—22no—
12#16840473—22no—
13#16840473C2214yes—
14C2×#14519768—21no—
15C2×#14519757—21no—
16C2×#14519753—22no—
17C2×C4×Dic122C2211yescharacteristic
18C2×C4×D244C2211yescharacteristic
19C2×#14519739—21no—
20C2×C4⋊C4×D61—21no—
21#16840039—22no—
22#16840039C2214yes—
23#16839969—22no—
24#16839969C2214yescomplemented
25C2×#14519710—21no—
26C2×C4⋊#92418C2211yescharacteristic
27C2×C4⋊#92418C2211yescharacteristic
28C2×#14519701—21no—
29C2×#14519697—21no—
30#16839511C2214yescomplemented
31#16839494C2214yescomplemented
32#16839491C2214yes—
33C2×C4⋊Q8×C61C2211yescharacteristic
34C2×C4⋊Q8×C61C2211yescharacteristic
35C61×#487—22no—
36C61×#487C2214yescomplemented
37C2×#103×C61—22no—
38C2×C4×C8×C61C2211yescharacteristic
39C22×Dic122D411yescharacteristic
40C22×D244D411yescharacteristic
41C22×C4×D61—21no—
42C22×C4×D61—22no—
43C2×#11758202—24no—
44C2×#11758202—44no—
45C22×#92418—21no—
46C22×#92418—21no—
47#14519768—24no—
48#14519768—24no—
49#14519757—24no—
50#14519757—24no—
51#14519753—28no—
52#14519753—28no—
53C4×Dic122—21no—
54C4×Dic122—21no—
55C4×Dic122D412yes—
56C4×Dic122C2312yes—
57C4×D244—21no—
58C4×D244—21no—
59C4×D244D412yes—
60C4×D244C2312yes—
61#14519739—24no—
62#14519739—24no—
63C2×C4⋊Dic61—22no—
64C2×C4⋊Dic61D411yescharacteristic
65C2×C4⋊Dic61D411yescharacteristic
66C2×#11758196—22no—
67C2×#11758196—21no—
68C4⋊C4×D61—24no—
69C4⋊C4×D61—24no—
70C2×#11758198—22no—
71C2×#11758198—21no—
72C2×C4×Dic61—21no—
73#14519710—24no—
74C4⋊#92418—21no—
75C4⋊#92418—21no—
76C4⋊#92418C2312yes—
77C4⋊#92418C2312yes—
78#14519701—24no—
79#14519697—24no—
80C22×Q8×C61—21no—
81C22×Q8×C61D412yes—
82C22×C8×C61—21no—
83C4⋊Q8×C61—21no—
84C4⋊Q8×C61—21no—
85C4⋊Q8×C61—21no—
86C4⋊Q8×C61—21no—
87C4⋊Q8×C61—21no—
88C4⋊Q8×C61D412yes—
89C4⋊Q8×C61C2312yes—
90C4⋊Q8×C61C2312yes—
91C2×C4⋊C4×C61—21no—
92C2×C4⋊C4×C61—21no—
93C2×C4⋊C4×C61—21no—
94C2×C4⋊C4×C61—21no—
95C2×C42×C61C2311yescharacteristic
96#103×C61—28no—
97C4×C8×C61—21no—
98C4×C8×C61C2312yes—
99C23×D61—21no—
100C2×Q8×C61—22no—
101C2×Q8×C61—22no—
102C2×Q8×C61—44no—
103C2×Q8×C61—41no—
104C2×Q8×C61—42no—
105C2×Q8×C61—42no—
106C2×Q8×C61C2×D414yes—
107C22×C4×C61—22no—
108C22×C4×C61—41no—
109C22×C4×C61C2×D411yescharacteristic
110C22×C4×C61C2×D411yescharacteristic
111C22×C4×C61C2×D411yescharacteristic
112C22×Dic61—21no—
113C22×Dic61—21no—
114C22×Dic61—21no—
115C2×D244—21no—
116C2×D244—22no—
117C2×D244Q1614yescomplemented
118C2×D244C2×D412yes—
119C2×C4×D61—22no—
120C2×C4×D61—22no—
121C2×C4×D61—28no—
122C2×C4×D61—42no—
123C2×C4×D61—42no—
124C2×C4×D61—84no—
125C2×Dic122—22no—
126C2×Dic122—22no—
127C2×Dic122—21no—
128C2×Dic122C2×D412yes—
129C2×C8×C61—22no—
130C2×C8×C61—42no—
131C4⋊C4×C61—22no—
132C4⋊C4×C61—22no—
133C4⋊C4×C61—22no—
134C4⋊C4×C61—22no—
135C4⋊C4×C61—22no—
136C4⋊C4×C61—22no—
137C4⋊C4×C61—41no—
138C4⋊C4×C61—41no—
139C42×C61C2×D411yescharacteristic
140C42×C61C2×D411yescharacteristic
141C42×C61C2×D411yescharacteristic
142C42×C61C2411yescharacteristic
143#11758202—48no—
144#11758198—28no—
145#11758198—22no—
146#11758198—22no—
147C4⋊Dic61—28no—
148C4⋊Dic61—21no—
149C4⋊Dic61—21no—
150C4⋊Dic61C2×D412yes—
151C4⋊Dic61C2×D412yes—
152#11758196—28no—
153#11758196—22no—
154#11758196—22no—
155C4×Dic61—22no—
156C4×Dic61—22no—
157C2×#92418—22no—
158C2×#92418—22no—
159C2×#92418—42no—
160C2×#92418—42no—
161C23×C61#12011yescharacteristic
162C22×D61—22no—
163C22×D61—24no—
164C22×D61—42no—
165C22×D61—42no—
166Q8×C61—44no—
167Q8×C61—42no—
168Q8×C61—42no—
169Q8×C61—82no—
170Q8×C61—82no—
171C2×C4×C61—22no—
172C2×C4×C61—24no—
173C2×C4×C61—44no—
174C2×C4×C61—42no—
175C2×C4×C61—82no—
176C2×C4×C61#12011yescharacteristic
177C2×C4×C61#12011yescharacteristic
178C2×C4×C61#12011yescharacteristic
179C2×C4×C61C2×Q1612yes—
180C2×C4×C61#13512yes—
181C2×C4×C61AGL(1,ℤ/8)12yes—
182C2×C4×C61#13712yes—
183C2×C4×C61C22×D411yescharacteristic
184C2×C4×C61C22×D411yescharacteristic
185C2×C4×C61C22×D411yescharacteristic
186C2×Dic61—22no—
187C2×Dic61—22no—
188C2×Dic61—22no—
189C2×Dic61—42no—
190C2×Dic61—42no—
191C2×Dic61—42no—
192D244—22no—
193D244—24no—
194D244C2×Q1614yescomplemented
195C4×D61—42no—
196C4×D61—42no—
197C4×D61—44no—
198C4×D61—88no—
199Dic122—22no—
200Dic122—22no—
201Dic122—42no—
202C8×C61—42no—
203#92418—42no—
204#92418—42no—
205C2×#1644—611nomaximal, Sylow
206C22×C61#44912yes—
207C22×C61#45112yes—
208C22×C61#45512yes—
209C22×C61C2×#12011yescharacteristic
210C2×D61—24no—
211C2×D61—48no—
212C2×D61—42no—
213C2×D61—42no—
214C4×C61—21no—
215C4×C61—21no—
216C4×C61—44no—
217C4×C61—82no—
218C4×C61#44912yes—
219C4×C61#45112yes—
220C4×C61C22×Q1611yescharacteristic
221C4×C61C2×#13511yescharacteristic
222C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
223C4×C61C2×#13711yescharacteristic
224Dic61—42no—
225Dic61—42no—
226Dic61—42no—
227C2×#554—611no—
228C2×#487D6111yescharacteristic, complemented
229C2×#474—611no—
230C2×#462—611no—
231#1644—618no—
232C2×#333—611no—
233C2×Q8⋊C8—611no—
234C2×D4⋊C8—611no—
235C2×C61#164414yescomplemented
236C2×C61C2×#45111yescharacteristic
237C2×C61C2×#44911yescharacteristic
238C2×C61C2×#45511yescharacteristic
239D61—44no—
240C22×Q16—1221no—
241#554—614no—
242#554—1222no—
243#554—1222no—
244#554—1222no—
245C2×C4⋊Q8C2×D6111yescharacteristic
246C2×C4⋊Q8C2×D6111yescharacteristic
247C2×#125—1221no—
248C2×C22⋊Q8—1221no—
249C2×C22⋊Q8—1222no—
250C2×C4×Q8—611no—
251C2×C4×D4—611no—
252C2×C4×D4—1221no—
253C22×C4⋊C4—1221no—
254#487—22no—
255#487C2×D6114yescomplemented
256#474—614no—
257#474—1222no—
258#462—614no—
259#462—1222no—
260C2×#107—1221no—
261C2×C4⋊C8—611no—
262C2×C4⋊C8—611no—
263C2×#103—22no—
264C2×#103—1221no—
265C2×#102—1221no—
266C2×C4×C8C2×D6111yescharacteristic
267#333—614no—
268Q8⋊C8—614no—
269D4⋊C8—614no—
270C61C2×#164411yescharacteristic, complemented, Sylow
271C22×Q8—21no—
272C22×Q8—611no—
273C22×Q8C22⋊D6112yes—
274C22×D4—611no—
275C23×C4—1222no—
276C23×C4—1221no—
277C2×Q16—1224no—
278C2×Q16—2444no—
279C22×C8—21no—
280C22×C8—1221no—
281C22×C8—1221no—
282C4⋊Q8—21no—
283C4⋊Q8—21no—
284C4⋊Q8—21no—
285C4⋊Q8—21no—
286C4⋊Q8—21no—
287C4⋊Q8C22⋊D6112yes—
288C4⋊Q8C22×D6112yes—
289C4⋊Q8C22×D6112yes—
290#125—1224no—
291#125—1224no—
292C22⋊Q8—1224no—
293C22⋊Q8—1224no—
294C22⋊Q8—1228no—
295C22⋊Q8—1228no—
296C4×Q8—612no—
297C4×Q8—612no—
298C4×Q8—1221no—
299C4×Q8—1221no—
300C4×D4—612no—
301C4×D4—612no—
302C4×D4—1224no—
303C4×D4—1224no—
304C4×D4—1221no—
305C4×D4—1221no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—611no—
311C2×C4⋊C4—611no—
312C2×C4⋊C4—1224no—
313C2×C4⋊C4—1224no—
314C2×C4⋊C4—1222no—
315C2×C4⋊C4—1222no—
316C2×C4⋊C4—1221no—
317C2×C22⋊C4—1222no—
318C2×C22⋊C4—1221no—
319C2×C42—1221no—
320C2×C42C22×D6111yescharacteristic
321#107—1224no—
322C4⋊C8—612no—
323C4⋊C8—612no—
324C4⋊C8—1221no—
325C4⋊C8—1221no—
326#103—28no—
327#103—1224no—
328#102—1224no—
329C4×C8—21no—
330C4×C8C22×D6112yes—
331C24—1221no—
332C2×Q8—22no—
333C2×Q8—22no—
334C2×Q8—44no—
335C2×Q8—41no—
336C2×Q8—42no—
337C2×Q8—42no—
338C2×Q8—612no—
339C2×Q8—1221no—
340C2×Q8—1222no—
341C2×Q8—1222no—
342C2×Q8C2×C22⋊D6114yes—
343C2×D4—612no—
344C2×D4—614no—
345C2×D4—1222no—
346C2×D4—1221no—
347C22×C4—22no—
348C22×C4—41no—
349C22×C4—1228no—
350C22×C4—1221no—
351C22×C4—1221no—
352C22×C4—1221no—
353C22×C4—1222no—
354C22×C4—1222no—
355C22×C4—4884no—
356C22×C4—2442no—
357C22×C4—2442no—
358C22×C4D4×D6111yescharacteristic
359C22×C4D4×D6111yescharacteristic
360C22×C4C2×C22⋊D6111yescharacteristic
361Q16—2448no—
362C2×C8—22no—
363C2×C8—42no—
364C2×C8—1222no—
365C2×C8—1222no—
366C2×C8—2442no—
367C2×C8—2442no—
368C4⋊C4—22no—
369C4⋊C4—22no—
370C4⋊C4—22no—
371C4⋊C4—22no—
372C4⋊C4—22no—
373C4⋊C4—22no—
374C4⋊C4—41no—
375C4⋊C4—41no—
376C4⋊C4—612no—
377C4⋊C4—612no—
378C4⋊C4—1228no—
379C4⋊C4—1228no—
380C4⋊C4—1222no—
381C4⋊C4—1221no—
382C4⋊C4—1221no—
383C4⋊C4—1222no—
384C22⋊C4—1228no—
385C22⋊C4—1222no—
386C22⋊C4—1222no—
387C42—1222no—
388C42—1222no—
389C42D4×D6111yescharacteristic
390C42D4×D6111yescharacteristic
391C42C2×C22⋊D6111yescharacteristic
392C42C23×D6111yescharacteristic
393C23—1222no—
394C23—1224no—
395C23—2442no—
396C23—2442no—
397C23#1451974511yescharacteristic
398Q8—44no—
399Q8—42no—
400Q8—42no—
401Q8—82no—
402Q8—82no—
403Q8—1222no—
404Q8—1222no—
405Q8—2442no—
406D4—614no—
407D4—1222no—
408D4—1224no—
409C2×C4—22no—
410C2×C4—24no—
411C2×C4—44no—
412C2×C4—42no—
413C2×C4—82no—
414C2×C4—1222no—
415C2×C4—1222no—
416C2×C4—1222no—
417C2×C4—4888no—
418C2×C4—2442no—
419C2×C4—2442no—
420C2×C4—2442no—
421C2×C4—2442no—
422C2×C4—2442no—
423C2×C4—2444no—
424C2×C4#1451974511yescharacteristic
425C2×C4#1451974511yescharacteristic
426C2×C4#1451974511yescharacteristic
427C2×C4Q16×D6112yes—
428C2×C4#1451979812yes—
429C2×C4#1451980412yes—
430C2×C4#1451980912yes—
431C2×C4C2×D4×D6111yescharacteristic
432C2×C4C2×D4×D6111yescharacteristic
433C2×C4C22×C22⋊D6111yescharacteristic
434C8—42no—
435C8—2442no—
436C8—2442no—
437C22—1224no—
438C22—2442no—
439C22—2448no—
440C22—2442no—
441C22#1683990612yes—
442C22#1683991612yes—
443C22#1683993912yes—
444C22C2×#1451974511yescharacteristic
445C4—21no—
446C4—21no—
447C4—44no—
448C4—82no—
449C4—2442no—
450C4—2442no—
451C4—2442no—
452C4#1683990612yes—
453C4#1683991612yes—
454C4C2×Q16×D6111yescharacteristic
455C4C2×#1451979811yescharacteristic
456C4C2×#1451980411yescharacteristic
457C4C2×#1451980911yescharacteristic
458C2—2444no—
459C2#2144503014yesdirect product factor
460C2C2×#1683991611yescharacteristic
461C2C2×#1683990611yescharacteristic
462C2C2×#1683993911yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC2×C61×#487C2
socleC23×C61#120
prime radicalC22×D244D4
hypercenterC2×#487D61
hypocenterC61C2×#1644
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#487

Complements

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

NH ≅ G/Ntype
3. C2×#16839969C2semidirect
4. #21445030C2direct (N × H)
5. C2×#16839511C2semidirect
6. C2×#16839494C2semidirect
8. C2×C61×#487C2semidirect
24. #16839969C22semidirect
30. #16839511C22semidirect
31. #16839494C22semidirect
36. C61×#487C22semidirect
117. C2×D244Q16semidirect
194. D244C2×Q16semidirect
228. C2×#487D61semidirect
235. C2×C61#1644semidirect
255. #487C2×D61semidirect
270. C61C2×#1644semidirect
459. C2#21445030direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404732
C2×#168400392
C2×#168399692
#214450302
C2×#168395112
C2×#168394942
C2×#168394912
C2×C61×#4872
C2×#164461