Finite Group Databasebeta

← C2×#21445034 #29655686

Subgroups — C2×#21445034 #29655686

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×#16840112C211yesmaximal, characteristic, complemented
3C2×#16840043C211yesmaximal, characteristic
4C2×#16839973C211yesmaximal, characteristic, complemented
5#21445034C218yesmaximal, direct product factor
6C2×#16839492C211yesmaximal, characteristic, complemented
7C2×#16839489C211yesmaximal, characteristic
8C2×C61×#333C211yesmaximal, characteristic, complemented
9C22×Dic244—21no—
10#16840473—22no—
11#16840473—22no—
12#16840473—22no—
13#16840473C2214yes—
14C2×#14519777C2211yescharacteristic
15C2×#14519768—21no—
16C2×#14519757—21no—
17C2×#14519753—22no—
18C2×C4×Dic122C2211yescharacteristic
19C2×C4×D244C2211yescharacteristic
20C2×#14519739—21no—
21C2×C4⋊C4×D61—21no—
22#16840112—22no—
23#16840112C2214yescomplemented
24#16840043—22no—
25#16840043C2214yes—
26#16839973—22no—
27#16839973C2214yescomplemented
28C2×#14519711—21no—
29C2×#14519702—21no—
30C2×#14519701—22no—
31C2×#14519699—21no—
32C2×C4×#92418C2211yescharacteristic
33#16839492C2214yescomplemented
34#16839489C2214yes—
35C2×C4⋊Q8×C61C2211yescharacteristic
36C2×C4⋊C8×C61C2211yescharacteristic
37C2×C4⋊C8×C61C2211yescharacteristic
38C61×#333C2214yescomplemented
39C22×Dic122—21no—
40C22×Dic122D411yescharacteristic
41C22×D244D411yescharacteristic
42C22×C4×D61—21no—
43C22×C4×D61—22no—
44C2×Dic244—24no—
45C2×Dic244—44no—
46C22×#92418—21no—
47#14519777—21no—
48#14519777—21no—
49#14519777—21no—
50#14519777C2312yes—
51#14519768—24no—
52#14519768—24no—
53#14519757—24no—
54#14519757—24no—
55#14519753—28no—
56#14519753—28no—
57C4×Dic122—21no—
58C4×Dic122—21no—
59C4×Dic122D412yes—
60C4×Dic122C2312yes—
61C4×D244—21no—
62C4×D244—21no—
63C4×D244D412yes—
64C4×D244C2312yes—
65#14519739—24no—
66#14519739—24no—
67C2×C4⋊Dic61—22no—
68C2×C4⋊Dic61—21no—
69C2×C4⋊Dic61—21no—
70C2×C4⋊Dic61D411yescharacteristic
71C2×C4⋊Dic61D411yescharacteristic
72C2×#11758196—22no—
73C2×#11758196—21no—
74C4⋊C4×D61—24no—
75C4⋊C4×D61—24no—
76C2×#11758198—22no—
77C2×#11758198—21no—
78C2×C4×Dic61—21no—
79#14519711—24no—
80#14519702—24no—
81#14519701—28no—
82#14519699—24no—
83C4×#92418—21no—
84C4×#92418C2312yes—
85C22×Q8×C61D412yes—
86C22×C8×C61—21no—
87C22×C8×C61—21no—
88C4⋊Q8×C61—21no—
89C4⋊Q8×C61—21no—
90C4⋊Q8×C61D412yes—
91C4⋊Q8×C61C2312yes—
92C2×C4⋊C4×C61—21no—
93C2×C4⋊C4×C61—21no—
94C2×C42×C61C2311yescharacteristic
95C4⋊C8×C61—21no—
96C4⋊C8×C61—21no—
97C4⋊C8×C61C2312yes—
98C4⋊C8×C61C2312yes—
99C23×D61—21no—
100C2×Q8×C61—22no—
101C2×Q8×C61—44no—
102C2×Q8×C61C2×D414yes—
103C22×C4×C61—22no—
104C22×C4×C61C2×D411yescharacteristic
105C22×C4×C61C2×D411yescharacteristic
106C22×C4×C61C2×D411yescharacteristic
107C22×Dic61—21no—
108C22×Dic61—21no—
109C22×Dic61—21no—
110C22×Dic61—41no—
111C2×D244—21no—
112C2×D244—22no—
113C2×D244Q1614yescomplemented
114C2×D244C2×D412yes—
115C2×C4×D61—22no—
116C2×C4×D61—22no—
117C2×C4×D61—28no—
118C2×C4×D61—42no—
119C2×C4×D61—42no—
120C2×C4×D61—84no—
121C2×Dic122—22no—
122C2×Dic122—22no—
123C2×Dic122—21no—
124C2×Dic122—22no—
125C2×Dic122—42no—
126C2×Dic122—42no—
127C2×Dic122—41no—
128C2×Dic122C2×D412yes—
129C2×C8×C61—22no—
130C2×C8×C61—22no—
131C2×C8×C61—42no—
132C2×C8×C61—42no—
133C4⋊C4×C61—22no—
134C4⋊C4×C61—22no—
135C4⋊C4×C61—22no—
136C4⋊C4×C61—22no—
137C42×C61C2×D411yescharacteristic
138C42×C61C2×D411yescharacteristic
139C42×C61C2×D411yescharacteristic
140C42×C61C2411yescharacteristic
141#11758198—28no—
142#11758198—22no—
143#11758198—22no—
144C4⋊Dic61—28no—
145C4⋊Dic61—21no—
146C4⋊Dic61—21no—
147C4⋊Dic61—22no—
148C4⋊Dic61—22no—
149C4⋊Dic61—41no—
150C4⋊Dic61—41no—
151C4⋊Dic61C2×D412yes—
152C4⋊Dic61C2×D412yes—
153#11758196—28no—
154#11758196—22no—
155#11758196—22no—
156C4×Dic61—22no—
157C4×Dic61—22no—
158C2×#92418—22no—
159C2×#92418—42no—
160Dic244—48no—
161C23×C61#12011yescharacteristic
162C22×D61—22no—
163C22×D61—24no—
164C22×D61—42no—
165C22×D61—42no—
166Q8×C61—44no—
167Q8×C61—82no—
168C2×C4×C61—22no—
169C2×C4×C61—24no—
170C2×C4×C61—44no—
171C2×C4×C61#12011yescharacteristic
172C2×C4×C61#12011yescharacteristic
173C2×C4×C61#12011yescharacteristic
174C2×C4×C61C2×Q1612yes—
175C2×C4×C61#13512yes—
176C2×C4×C61AGL(1,ℤ/8)12yes—
177C2×C4×C61#13712yes—
178C2×C4×C61C22×D411yescharacteristic
179C2×C4×C61C22×D411yescharacteristic
180C2×C4×C61C22×D411yescharacteristic
181C2×Dic61—22no—
182C2×Dic61—22no—
183C2×Dic61—22no—
184C2×Dic61—42no—
185C2×Dic61—42no—
186C2×Dic61—42no—
187C2×Dic61—42no—
188C2×Dic61—82no—
189D244—22no—
190D244—24no—
191D244C2×Q1614yescomplemented
192C4×D61—42no—
193C4×D61—42no—
194C4×D61—44no—
195C4×D61—88no—
196Dic122—22no—
197Dic122—22no—
198Dic122—42no—
199Dic122—42no—
200Dic122—42no—
201Dic122—82no—
202C8×C61—42no—
203C8×C61—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#44912yes—
218C4×C61#45112yes—
219C4×C61C22×Q1611yescharacteristic
220C4×C61C2×#13511yescharacteristic
221C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
222C4×C61C2×#13711yescharacteristic
223Dic61—42no—
224Dic61—42no—
225Dic61—42no—
226Dic61—82no—
227C2×#554—611no—
228C2×#487—611no—
229C2×#474—611no—
230C2×#462—611no—
231#1644—618no—
232C2×#333D6111yescharacteristic, complemented
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⋊Q8—611no—
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—614no—
255#487—1222no—
256#474—614no—
257#474—1222no—
258#462—614no—
259#462—1222no—
260C2×#107—1221no—
261C2×C4⋊C8C2×D6111yescharacteristic
262C2×C4⋊C8C2×D6111yescharacteristic
263C2×#103—1221no—
264C2×#103—1222no—
265C2×#102—1221no—
266C2×C4×C8—611no—
267#333C2×D6114yescomplemented
268Q8⋊C8—614no—
269D4⋊C8—614no—
270C61C2×#164411yescharacteristic, complemented, Sylow
271C22×Q8—611no—
272C22×Q8—1221no—
273C22×Q8D24412yes—
274C22×D4—611no—
275C23×C4—1222no—
276C23×C4—1221no—
277C2×Q16—1224no—
278C2×Q16—2444no—
279C22×C8—21no—
280C22×C8—21no—
281C22×C8—1221no—
282C4⋊Q8—21no—
283C4⋊Q8—21no—
284C4⋊Q8—612no—
285C4⋊Q8—1221no—
286C4⋊Q8—1221no—
287C4⋊Q8—1221no—
288C4⋊Q8D24412yes—
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—611no—
309C2×C4⋊C4—611no—
310C2×C4⋊C4—1224no—
311C2×C4⋊C4—1224no—
312C2×C4⋊C4—1222no—
313C2×C4⋊C4—1222no—
314C2×C4⋊C4—1221no—
315C2×C4⋊C4—1221no—
316C2×C4⋊C4—1221no—
317C2×C22⋊C4—1222no—
318C2×C22⋊C4—1221no—
319C2×C42—1221no—
320C2×C42C22×D6111yescharacteristic
321#107—1224no—
322C4⋊C8—21no—
323C4⋊C8—21no—
324C4⋊C8C22×D6112yes—
325C4⋊C8C22×D6112yes—
326#103—1224no—
327#103—1228no—
328#102—1224no—
329C4×C8—612no—
330C4×C8—1221no—
331C24—1221no—
332C2×Q8—22no—
333C2×Q8—44no—
334C2×Q8—612no—
335C2×Q8—1221no—
336C2×Q8—1222no—
337C2×Q8—1222no—
338C2×Q8—1222no—
339C2×Q8—2442no—
340C2×Q8—2442no—
341C2×Q8—2441no—
342C2×Q8C2×D24414yes—
343C2×D4—612no—
344C2×D4—614no—
345C2×D4—1221no—
346C2×D4—1222no—
347C22×C4—22no—
348C22×C4—1228no—
349C22×C4—1221no—
350C22×C4—1221no—
351C22×C4—1221no—
352C22×C4—1222no—
353C22×C4—1222no—
354C22×C4—4884no—
355C22×C4—2441no—
356C22×C4—2442no—
357C22×C4—2442no—
358C22×C4C2×D24411yescharacteristic
359C22×C4D4×D6111yescharacteristic
360C22×C4D4×D6111yescharacteristic
361Q16—2448no—
362C2×C8—22no—
363C2×C8—22no—
364C2×C8—42no—
365C2×C8—42no—
366C2×C8—1222no—
367C2×C8—2442no—
368C4⋊C4—22no—
369C4⋊C4—22no—
370C4⋊C4—22no—
371C4⋊C4—22no—
372C4⋊C4—612no—
373C4⋊C4—612no—
374C4⋊C4—1228no—
375C4⋊C4—1228no—
376C4⋊C4—1222no—
377C4⋊C4—1221no—
378C4⋊C4—1221no—
379C4⋊C4—1222no—
380C4⋊C4—1222no—
381C4⋊C4—1222no—
382C4⋊C4—2441no—
383C4⋊C4—2441no—
384C22⋊C4—1228no—
385C22⋊C4—1222no—
386C22⋊C4—1222no—
387C42—1222no—
388C42—1222no—
389C42C2×D24411yescharacteristic
390C42D4×D6111yescharacteristic
391C42D4×D6111yescharacteristic
392C42C23×D6111yescharacteristic
393C23—1222no—
394C23—1224no—
395C23—2442no—
396C23—2442no—
397C23#1451974711yescharacteristic
398Q8—44no—
399Q8—82no—
400Q8—1222no—
401Q8—1222no—
402Q8—4882no—
403Q8—2442no—
404Q8—2442no—
405Q8—2442no—
406D4—614no—
407D4—1222no—
408D4—1224no—
409C2×C4—22no—
410C2×C4—24no—
411C2×C4—44no—
412C2×C4—1222no—
413C2×C4—1222no—
414C2×C4—1222no—
415C2×C4—4888no—
416C2×C4—4882no—
417C2×C4—2442no—
418C2×C4—2442no—
419C2×C4—2442no—
420C2×C4—2442no—
421C2×C4—2442no—
422C2×C4—2442no—
423C2×C4—2444no—
424C2×C4#1451974711yescharacteristic
425C2×C4#1451974711yescharacteristic
426C2×C4#1451974711yescharacteristic
427C2×C4Q16×D6112yes—
428C2×C4#1451980012yes—
429C2×C4#1451980412yes—
430C2×C4#1451980612yes—
431C2×C4C2×D4×D6111yescharacteristic
432C2×C4C2×D4×D6111yescharacteristic
433C2×C4C22×D24411yescharacteristic
434C8—42no—
435C8—42no—
436C8—2442no—
437C22—1224no—
438C22—2442no—
439C22—2448no—
440C22—2442no—
441C22#1683991012yes—
442C22#1683991912yes—
443C22#1683994212yes—
444C22C2×#1451974711yescharacteristic
445C4—21no—
446C4—21no—
447C4—44no—
448C4—4882no—
449C4—2442no—
450C4—2442no—
451C4—2442no—
452C4#1683991012yes—
453C4#1683991912yes—
454C4C2×Q16×D6111yescharacteristic
455C4C2×#1451980011yescharacteristic
456C4C2×#1451980411yescharacteristic
457C4C2×#1451980611yescharacteristic
458C2—2444no—
459C2#2144503414yesdirect product factor
460C2C2×#1683991911yescharacteristic
461C2C2×#1683991011yescharacteristic
462C2C2×#1683994211yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC2×C61×#333C2
socleC23×C61#120
prime radicalC22×D244D4
hypercenterC2×#333D61
hypocenterC61C2×#1644
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#333

Complements

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

NH ≅ G/Ntype
2. C2×#16840112C2semidirect
4. C2×#16839973C2semidirect
5. #21445034C2direct (N × H)
6. C2×#16839492C2semidirect
8. C2×C61×#333C2semidirect
23. #16840112C22semidirect
27. #16839973C22semidirect
33. #16839492C22semidirect
38. C61×#333C22semidirect
113. C2×D244Q16semidirect
191. D244C2×Q16semidirect
232. C2×#333D61semidirect
235. C2×C61#1644semidirect
267. #333C2×D61semidirect
270. C61C2×#1644semidirect
459. C2#21445034direct (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×#168401122
C2×#168400432
C2×#168399732
#214450342
C2×#168394922
C2×#168394892
C2×C61×#3332
C2×#164461