Finite Group Databasebeta

← C2×#21444950 #29655635

Subgroups — C2×#21444950 #29655635

Order 15616.

1054 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840473C211yesmaximal, characteristic
2C2×#16840054C211yesmaximal, characteristic, complemented
3C2×#16840049C211yesmaximal, characteristic
4#21444950C218yesmaximal, direct product factor
5C2×#16839511C211yesmaximal, characteristic, complemented
6C2×#16839494C211yesmaximal, characteristic, complemented
7C2×#16839491C211yesmaximal, characteristic
8C2×C61×#494C211yesmaximal, characteristic, complemented
9#16840473—22no—
10#16840473—22no—
11#16840473—22no—
12#16840473C2214yes—
13C2×#14519768—21no—
14C2×#14519757—21no—
15C2×#14519753—22no—
16C2×C4×Dic122C2211yescharacteristic
17C2×C4×D244C2211yescharacteristic
18C2×#14519739—21no—
19C2×C4⋊C4×D61—21no—
20#16840054—22no—
21#16840054C2214yescomplemented
22#16840049—22no—
23#16840049C2214yes—
24C2×#14519710—21no—
25C2×#14519708—21no—
26C2×C4⋊#92418C2211yescharacteristic
27C2×C4⋊#92418C2211yescharacteristic
28C2×#14519700—21no—
29C2×#14519697—21no—
30#16839511C2214yescomplemented
31#16839494C2214yescomplemented
32#16839491C2214yes—
33C22×Q16×C61—22no—
34C2×C4⋊Q8×C61C2211yescharacteristic
35C2×C4⋊Q8×C61C2211yescharacteristic
36C61×#494—22no—
37C61×#494C2214yescomplemented
38C2×C4×C8×C61C2211yescharacteristic
39C22×Dic122D411yescharacteristic
40C22×D244D411yescharacteristic
41C22×C4×D61—21no—
42C22×C4×D61—22no—
43C22×#92418—21no—
44C22×#92418—21no—
45#14519768—24no—
46#14519768—24no—
47#14519757—24no—
48#14519757—24no—
49#14519753—28no—
50#14519753—28no—
51C4×Dic122—21no—
52C4×Dic122—21no—
53C4×Dic122D412yes—
54C4×Dic122C2312yes—
55C4×D244—21no—
56C4×D244—21no—
57C4×D244D412yes—
58C4×D244C2312yes—
59#14519739—24no—
60#14519739—24no—
61C2×C4⋊Dic61—22no—
62C2×C4⋊Dic61D411yescharacteristic
63C2×C4⋊Dic61D411yescharacteristic
64C2×#11758196—22no—
65C2×#11758196—21no—
66C4⋊C4×D61—24no—
67C4⋊C4×D61—24no—
68C2×#11758198—22no—
69C2×#11758198—21no—
70C2×C4×Dic61—21no—
71#14519710—24no—
72#14519708—24no—
73C4⋊#92418—21no—
74C4⋊#92418—21no—
75C4⋊#92418C2312yes—
76C4⋊#92418C2312yes—
77#14519700—24no—
78#14519697—24no—
79C22×Q8×C61—21no—
80C22×Q8×C61D412yes—
81C2×Q16×C61—28no—
82C2×Q16×C61—48no—
83C22×C8×C61—21no—
84C4⋊Q8×C61—21no—
85C4⋊Q8×C61—21no—
86C4⋊Q8×C61—21no—
87C4⋊Q8×C61—21no—
88C4⋊Q8×C61—21no—
89C4⋊Q8×C61D412yes—
90C4⋊Q8×C61C2312yes—
91C4⋊Q8×C61C2312yes—
92C2×C4⋊C4×C61—21no—
93C2×C4⋊C4×C61—21no—
94C2×C4⋊C4×C61—21no—
95C2×C4⋊C4×C61—21no—
96C2×C42×C61C2311yescharacteristic
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—44no—
104C2×Q8×C61—41no—
105C2×Q8×C61C2×D414yes—
106C22×C4×C61—22no—
107C22×C4×C61—41no—
108C22×C4×C61C2×D411yescharacteristic
109C22×C4×C61C2×D411yescharacteristic
110C22×C4×C61C2×D411yescharacteristic
111C22×Dic61—21no—
112C22×Dic61—21no—
113C22×Dic61—21no—
114C2×D244—21no—
115C2×D244—22no—
116C2×D244Q1614yescomplemented
117C2×D244C2×D412yes—
118C2×C4×D61—22no—
119C2×C4×D61—22no—
120C2×C4×D61—28no—
121C2×C4×D61—42no—
122C2×C4×D61—42no—
123C2×C4×D61—84no—
124C2×Dic122—22no—
125C2×Dic122—22no—
126C2×Dic122—21no—
127C2×Dic122C2×D412yes—
128Q16×C61—416no—
129C2×C8×C61—24no—
130C2×C8×C61—22no—
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#11758198—28no—
144#11758198—22no—
145#11758198—22no—
146C4⋊Dic61—28no—
147C4⋊Dic61—21no—
148C4⋊Dic61—21no—
149C4⋊Dic61C2×D412yes—
150C4⋊Dic61C2×D412yes—
151#11758196—28no—
152#11758196—22no—
153#11758196—22no—
154C4×Dic61—22no—
155C4×Dic61—22no—
156C2×#92418—22no—
157C2×#92418—22no—
158C2×#92418—42no—
159C2×#92418—42no—
160C23×C61#12011yescharacteristic
161C22×D61—22no—
162C22×D61—24no—
163C22×D61—42no—
164C22×D61—42no—
165Q8×C61—44no—
166Q8×C61—44no—
167Q8×C61—82no—
168Q8×C61—82no—
169C2×C4×C61—22no—
170C2×C4×C61—24no—
171C2×C4×C61—44no—
172C2×C4×C61—42no—
173C2×C4×C61—82no—
174C2×C4×C61#12011yescharacteristic
175C2×C4×C61#12011yescharacteristic
176C2×C4×C61#12011yescharacteristic
177C2×C4×C61C2×Q1612yes—
178C2×C4×C61#13512yes—
179C2×C4×C61#13712yes—
180C2×C4×C61#13712yes—
181C2×C4×C61C22×D411yescharacteristic
182C2×C4×C61C22×D411yescharacteristic
183C2×C4×C61C22×D411yescharacteristic
184C2×Dic61—22no—
185C2×Dic61—22no—
186C2×Dic61—22no—
187C2×Dic61—42no—
188C2×Dic61—42no—
189C2×Dic61—42no—
190D244—22no—
191D244—24no—
192D244C2×Q1614yescomplemented
193C4×D61—42no—
194C4×D61—42no—
195C4×D61—44no—
196C4×D61—88no—
197Dic122—22no—
198Dic122—22no—
199Dic122—42no—
200C8×C61—24no—
201#92418—42no—
202#92418—42no—
203C2×#1632—611nomaximal, Sylow
204C22×C61#45112yes—
205C22×C61#45212yes—
206C22×C61#45312yes—
207C22×C61C2×#12011yescharacteristic
208C2×D61—24no—
209C2×D61—48no—
210C2×D61—42no—
211C2×D61—42no—
212C4×C61—21no—
213C4×C61—21no—
214C4×C61—44no—
215C4×C61—82no—
216C4×C61#45112yes—
217C4×C61#45212yes—
218C4×C61C22×Q1611yescharacteristic
219C4×C61C2×#13511yescharacteristic
220C4×C61C2×#13711yescharacteristic
221C4×C61C2×#13711yescharacteristic
222Dic61—42no—
223Dic61—42no—
224Dic61—42no—
225C2×#554—611no—
226C2×#494D6111yescharacteristic, complemented
227C2×#477—611no—
228C2×#476—611no—
229#1632—618no—
230C2×#333—611no—
231C2×Q8⋊C8—611no—
232C2×D4⋊C8—611no—
233C2×C61#163214yescomplemented
234C2×C61C2×#45111yescharacteristic
235C2×C61C2×#45211yescharacteristic
236C2×C61C2×#45311yescharacteristic
237D61—44no—
238C22×Q16—22no—
239#554—614no—
240#554—1222no—
241#554—1222no—
242#554—1222no—
243C2×C4⋊Q8C2×D6111yescharacteristic
244C2×C4⋊Q8C2×D6111yescharacteristic
245C2×#125—1221no—
246C2×C22⋊Q8—1221no—
247C2×C22⋊Q8—1222no—
248C2×C4×Q8—611no—
249C2×C4×D4—611no—
250C2×C4×D4—1221no—
251C22×C4⋊C4—1221no—
252#494—22no—
253#494C2×D6114yescomplemented
254#477—614no—
255#477—1222no—
256#476—614no—
257#476—1222no—
258C2×#107—1221no—
259C2×#106—1221no—
260C2×C4⋊C8—611no—
261C2×C4⋊C8—611no—
262C2×#103—1221no—
263C2×#102—1221no—
264C2×C4×C8C2×D6111yescharacteristic
265#333—614no—
266Q8⋊C8—614no—
267D4⋊C8—614no—
268C61C2×#163211yescharacteristic, complemented, Sylow
269C22×Q8—21no—
270C22×Q8—611no—
271C22×Q8C22⋊D6112yes—
272C22×D4—611no—
273C23×C4—1222no—
274C23×C4—1221no—
275C2×Q16—28no—
276C2×Q16—48no—
277C22×C8—21no—
278C22×C8—1221no—
279C22×C8—1221no—
280C4⋊Q8—21no—
281C4⋊Q8—21no—
282C4⋊Q8—21no—
283C4⋊Q8—21no—
284C4⋊Q8—21no—
285C4⋊Q8C22⋊D6112yes—
286C4⋊Q8C22×D6112yes—
287C4⋊Q8C22×D6112yes—
288#125—1224no—
289#125—1224no—
290C22⋊Q8—1224no—
291C22⋊Q8—1224no—
292C22⋊Q8—1228no—
293C22⋊Q8—1228no—
294C4×Q8—612no—
295C4×Q8—612no—
296C4×Q8—1221no—
297C4×Q8—1221no—
298C4×D4—612no—
299C4×D4—612no—
300C4×D4—1224no—
301C4×D4—1224no—
302C4×D4—1221no—
303C4×D4—1221no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—21no—
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×C22⋊C4—1222no—
316C2×C22⋊C4—1221no—
317C2×C42—1221no—
318C2×C42C22×D6111yescharacteristic
319#107—1224no—
320#106—1224no—
321C4⋊C8—612no—
322C4⋊C8—612no—
323C4⋊C8—1221no—
324C4⋊C8—1221no—
325#103—1224no—
326#102—1224no—
327C4×C8—21no—
328C4×C8C22×D6112yes—
329C24—1221no—
330C2×Q8—22no—
331C2×Q8—22no—
332C2×Q8—44no—
333C2×Q8—44no—
334C2×Q8—41no—
335C2×Q8—612no—
336C2×Q8—1221no—
337C2×Q8—1222no—
338C2×Q8—1222no—
339C2×Q8C2×C22⋊D6114yes—
340C2×D4—612no—
341C2×D4—614no—
342C2×D4—1222no—
343C2×D4—1221no—
344C22×C4—22no—
345C22×C4—41no—
346C22×C4—1228no—
347C22×C4—1221no—
348C22×C4—1221no—
349C22×C4—1221no—
350C22×C4—1222no—
351C22×C4—1222no—
352C22×C4—4884no—
353C22×C4—2442no—
354C22×C4—2442no—
355C22×C4D4×D6111yescharacteristic
356C22×C4D4×D6111yescharacteristic
357C22×C4C2×C22⋊D6111yescharacteristic
358Q16—416no—
359C2×C8—24no—
360C2×C8—22no—
361C2×C8—1222no—
362C2×C8—1222no—
363C2×C8—2442no—
364C2×C8—2442no—
365C4⋊C4—22no—
366C4⋊C4—22no—
367C4⋊C4—22no—
368C4⋊C4—22no—
369C4⋊C4—22no—
370C4⋊C4—22no—
371C4⋊C4—41no—
372C4⋊C4—41no—
373C4⋊C4—612no—
374C4⋊C4—612no—
375C4⋊C4—1228no—
376C4⋊C4—1228no—
377C4⋊C4—1222no—
378C4⋊C4—1221no—
379C4⋊C4—1221no—
380C4⋊C4—1222no—
381C22⋊C4—1228no—
382C22⋊C4—1222no—
383C22⋊C4—1222no—
384C42—1222no—
385C42—1222no—
386C42D4×D6111yescharacteristic
387C42D4×D6111yescharacteristic
388C42C2×C22⋊D6111yescharacteristic
389C42C23×D6111yescharacteristic
390C23—1222no—
391C23—1224no—
392C23—2442no—
393C23—2442no—
394C23#1451974511yescharacteristic
395Q8—44no—
396Q8—44no—
397Q8—82no—
398Q8—82no—
399Q8—1222no—
400Q8—1222no—
401Q8—2442no—
402D4—614no—
403D4—1222no—
404D4—1224no—
405C2×C4—22no—
406C2×C4—24no—
407C2×C4—44no—
408C2×C4—42no—
409C2×C4—82no—
410C2×C4—1222no—
411C2×C4—1222no—
412C2×C4—1222no—
413C2×C4—4888no—
414C2×C4—2442no—
415C2×C4—2442no—
416C2×C4—2442no—
417C2×C4—2442no—
418C2×C4—2442no—
419C2×C4—2444no—
420C2×C4#1451974511yescharacteristic
421C2×C4#1451974511yescharacteristic
422C2×C4#1451974511yescharacteristic
423C2×C4Q16×D6112yes—
424C2×C4#1451980012yes—
425C2×C4#1451980912yes—
426C2×C4#1451980912yes—
427C2×C4C2×D4×D6111yescharacteristic
428C2×C4C2×D4×D6111yescharacteristic
429C2×C4C22×C22⋊D6111yescharacteristic
430C8—24no—
431C8—2442no—
432C8—2442no—
433C22—1224no—
434C22—2442no—
435C22—2448no—
436C22—2442no—
437C22#1683991612yes—
438C22#1683992312yes—
439C22#1683992912yes—
440C22C2×#1451974511yescharacteristic
441C4—21no—
442C4—21no—
443C4—44no—
444C4—82no—
445C4—2442no—
446C4—2442no—
447C4—2442no—
448C4#1683991612yes—
449C4#1683992312yes—
450C4C2×Q16×D6111yescharacteristic
451C4C2×#1451980011yescharacteristic
452C4C2×#1451980911yescharacteristic
453C4C2×#1451980911yescharacteristic
454C2—2444no—
455C2#2144495014yesdirect product factor
456C2C2×#1683991611yescharacteristic
457C2C2×#1683992311yescharacteristic
458C2C2×#1683992911yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC2×C61×#494C2
socleC23×C61#120
prime radicalC22×D244D4
hypercenterC2×#494D61
hypocenterC61C2×#1632
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#494

Complements

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

NH ≅ G/Ntype
2. C2×#16840054C2semidirect
4. #21444950C2direct (N × H)
5. C2×#16839511C2semidirect
6. C2×#16839494C2semidirect
8. C2×C61×#494C2semidirect
21. #16840054C22semidirect
30. #16839511C22semidirect
31. #16839494C22semidirect
37. C61×#494C22semidirect
116. C2×D244Q16semidirect
192. D244C2×Q16semidirect
226. C2×#494D61semidirect
233. C2×C61#1632semidirect
253. #494C2×D61semidirect
268. C61C2×#1632semidirect
455. C2#21444950direct (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×#168400542
C2×#168400492
#214449502
C2×#168395112
C2×#168394942
C2×#168394912
C2×C61×#4942
C2×#163261