Finite Group Databasebeta

← C2×#21445456 #29667751

Subgroups — C2×#21445456 #29667751

Order 15616.

966 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840138C211yesmaximal, characteristic
2C2×#16840114C211yesmaximal, characteristic, complemented
3C2×#16840110C211yesmaximal, characteristic, complemented
4C2×#16840109C211yesmaximal, characteristic, complemented
5C2×#16840108C211yesmaximal, characteristic, complemented
6#21445456C218yesmaximal, direct product factor
7C2×#16839484C211yesmaximal, characteristic, complemented
8C2×C61×#492C211yesmaximal, characteristic, complemented
9C22×#11758199—22no—
10C2×#14519777C2211yescharacteristic
11C2×#14519774C2211yescharacteristic
12#16840138—22no—
13#16840138C2214yes—
14#16840114—22no—
15#16840114C2214yescomplemented
16#16840110—22no—
17#16840110C2214yescomplemented
18#16840109—22no—
19#16840109C2214yescomplemented
20#16840108—22no—
21#16840108C2214yescomplemented
22C2×#14519700—22no—
23C2×#14519699—22no—
24C2×#14519698—22no—
25C2×#14519697—22no—
26C2×C4×#92418C2211yescharacteristic
27C2×C4×#92418C2211yescharacteristic
28#16839484C2214yescomplemented
29C22×SD16×C61—22no—
30C2×C4⋊Q8×C61C2211yescharacteristic
31C2×#127×C61C2211yescharacteristic
32C61×#492—22no—
33C61×#492C2214yescomplemented
34C2×C4×C8×C61C2211yescharacteristic
35C22×Dic122—21no—
36C22×D244—21no—
37C22×D244—21no—
38C22×D244—21no—
39C2×#11758199—28no—
40C2×#11758199—48no—
41C22×#92418D412yes—
42C22×#92418D412yes—
43#14519777—21no—
44#14519777—21no—
45#14519777—21no—
46#14519777C2312yes—
47#14519774—21no—
48#14519774—21no—
49#14519774—21no—
50#14519774C2312yes—
51C2×C4⋊Dic61—21no—
52C2×C4⋊Dic61—21no—
53#14519700—28no—
54#14519699—28no—
55#14519698—28no—
56#14519697—28no—
57C4×#92418D412yes—
58C4×#92418D412yes—
59C4×#92418C2312yes—
60C4×#92418C2312yes—
61C22×Q8×C61—21no—
62C22×D4×C61—21no—
63C22×D4×C61—21no—
64C22×D4×C61—21no—
65C2×SD16×C61—28no—
66C2×SD16×C61—48no—
67C22×C8×C61D412yes—
68C4⋊Q8×C61—21no—
69C4⋊Q8×C61—21no—
70C4⋊Q8×C61—21no—
71C4⋊Q8×C61C2312yes—
72#127×C61—21no—
73#127×C61—21no—
74#127×C61—21no—
75#127×C61C2312yes—
76C2×C4⋊C4×C61—21no—
77C2×C4⋊C4×C61—21no—
78C2×C42×C61C2311yescharacteristic
79C4×C8×C61D412yes—
80C4×C8×C61C2312yes—
81C24×C61—41no—
82C23×D61—41no—
83C2×Q8×C61—22no—
84C2×Q8×C61—41no—
85C2×Q8×C61—44no—
86C2×D4×C61—22no—
87C2×D4×C61—22no—
88C2×D4×C61—22no—
89C2×D4×C61—41no—
90C2×D4×C61—41no—
91C2×D4×C61—41no—
92C2×D4×C61—44no—
93C2×D4×C61—44no—
94C2×D4×C61—44no—
95C22×C4×C61—41no—
96C22×C4×C61C2×D411yescharacteristic
97C22×C4×C61C2×D411yescharacteristic
98C22×C4×C61C2×D411yescharacteristic
99C22×Dic61—41no—
100C2×D244—22no—
101C2×D244—22no—
102C2×D244—22no—
103C2×D244—44no—
104C2×D244—44no—
105C2×D244—44no—
106C2×D244—41no—
107C2×D244—41no—
108C2×D244—41no—
109C2×Dic122—22no—
110C2×Dic122—44no—
111C2×Dic122—41no—
112SD16×C61—416no—
113C2×C8×C61—24no—
114C2×C8×C61C2×D414yes—
115C4⋊C4×C61—22no—
116C4⋊C4×C61—22no—
117C4⋊C4×C61—41no—
118C4⋊C4×C61—41no—
119C42×C61C2×D411yescharacteristic
120C42×C61C2×D411yescharacteristic
121C42×C61C2×D411yescharacteristic
122C42×C61C2411yescharacteristic
123#11758199—416no—
124C4⋊Dic61—22no—
125C4⋊Dic61—22no—
126C4⋊Dic61—41no—
127C4⋊Dic61—41no—
128C2×#92418—24no—
129C2×#92418—24no—
130C2×#92418C2×D414yes—
131C2×#92418C2×D414yes—
132C23×C61—42no—
133C23×C61—82no—
134C23×C61—82no—
135C23×C61—82no—
136C23×C61#12711yescharacteristic
137C22×D61—42no—
138C22×D61—82no—
139C22×D61—82no—
140C22×D61—82no—
141Q8×C61—44no—
142Q8×C61—82no—
143D4×C61—44no—
144D4×C61—44no—
145D4×C61—44no—
146D4×C61—82no—
147D4×C61—82no—
148D4×C61—82no—
149C2×C4×C61—42no—
150C2×C4×C61—82no—
151C2×C4×C61#12711yescharacteristic
152C2×C4×C61#12711yescharacteristic
153C2×C4×C61#12711yescharacteristic
154C2×C4×C61#13514yes—
155C2×C4×C61AGL(1,ℤ/8)14yes—
156C2×C4×C61AGL(1,ℤ/8)14yes—
157C2×C4×C61C22×D411yescharacteristic
158C2×C4×C61C22×D411yescharacteristic
159C2×C4×C61C22×D411yescharacteristic
160C2×Dic61—42no—
161C2×Dic61—82no—
162D244—44no—
163D244—44no—
164D244—44no—
165D244—82no—
166D244—82no—
167D244—82no—
168Dic122—44no—
169Dic122—82no—
170C8×C61—24no—
171#92418—24no—
172#92418—24no—
173C2×#1717—611nomaximal, Sylow
174C22×C61—82no—
175C22×C61—82no—
176C22×C61—82no—
177C22×C61—164no—
178C22×C61#49512yes—
179C22×C61#49612yes—
180C22×C61#49612yes—
181C22×C61C2×#12711yescharacteristic
182C2×D61—82no—
183C2×D61—82no—
184C2×D61—82no—
185C2×D61—164no—
186C4×C61—82no—
187C4×C61#49512yes—
188C4×C61#49612yes—
189C4×C61#49612yes—
190C4×C61C2×#13512yes—
191C4×C61C2×AGL(1,ℤ/8)12yes—
192C4×C61C2×AGL(1,ℤ/8)12yes—
193Dic61—82no—
194C2×#493—611no—
195C2×#492D6111yescharacteristic, complemented
196C2×#487—611no—
197C2×#486—611no—
198C2×#486—611no—
199C2×#486—611no—
200#1717—618no—
201C2×#322—611no—
202C2×C61—162no—
203C2×C61#171714yescomplemented
204C2×C61C2×#49511yescharacteristic
205C2×C61C2×#49611yescharacteristic
206C2×C61C2×#49611yescharacteristic
207D61—162no—
208C22×SD16—22no—
209C22×D8—1222no—
210C2×C4⋊Q8—611no—
211C2×C4⋊Q8C2×D6111yescharacteristic
212C2×#127—611no—
213C2×#127C2×D6111yescharacteristic
214#493—614no—
215#493—1222no—
216#492—22no—
217#492C2×D6114yescomplemented
218#487—614no—
219#487—1222no—
220#486—614no—
221#486—614no—
222#486—614no—
223#486—1222no—
224#486—1222no—
225#486—1222no—
226C2×#103—1222no—
227C2×#102—1222no—
228C2×#102—1222no—
229C2×#102—1222no—
230C2×C4×C8—611no—
231C2×C4×C8—611no—
232C2×C4×C8C2×D6111yescharacteristic
233#322—614no—
234C61C2×#171711yescharacteristic, complemented, Sylow
235C22×Q8—21no—
236C22×Q8—1221no—
237C22×D4—21no—
238C22×D4—21no—
239C22×D4—21no—
240C22×D4—1221no—
241C22×D4—1221no—
242C22×D4—1221no—
243C2×SD16—28no—
244C2×SD16—48no—
245C2×D8—1228no—
246C2×D8—2448no—
247C22×C8—612no—
248C22×C8—612no—
249C22×C8C22⋊D6112yes—
250C4⋊Q8—21no—
251C4⋊Q8—21no—
252C4⋊Q8—21no—
253C4⋊Q8—612no—
254C4⋊Q8—1221no—
255C4⋊Q8—1221no—
256C4⋊Q8—1221no—
257C4⋊Q8C22×D6112yes—
258#127—21no—
259#127—21no—
260#127—21no—
261#127—612no—
262#127—1221no—
263#127—1221no—
264#127—1221no—
265#127C22×D6112yes—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—1221no—
269C2×C4⋊C4—1221no—
270C2×C42C22×D6111yescharacteristic
271#103—1228no—
272#102—1228no—
273#102—1228no—
274#102—1228no—
275C4×C8—612no—
276C4×C8—612no—
277C4×C8—612no—
278C4×C8—612no—
279C4×C8C22⋊D6112yes—
280C4×C8C22×D6112yes—
281C24—41no—
282C24—2441no—
283C2×Q8—22no—
284C2×Q8—41no—
285C2×Q8—44no—
286C2×Q8—1222no—
287C2×Q8—2444no—
288C2×Q8—2441no—
289C2×D4—22no—
290C2×D4—22no—
291C2×D4—22no—
292C2×D4—41no—
293C2×D4—41no—
294C2×D4—41no—
295C2×D4—44no—
296C2×D4—44no—
297C2×D4—44no—
298C2×D4—1222no—
299C2×D4—1222no—
300C2×D4—1222no—
301C2×D4—2441no—
302C2×D4—2441no—
303C2×D4—2441no—
304C2×D4—2444no—
305C2×D4—2444no—
306C2×D4—2444no—
307C22×C4—41no—
308C22×C4—2441no—
309C22×C4D4×D6111yescharacteristic
310C22×C4D4×D6111yescharacteristic
311C22×C4C2×C22⋊D6111yescharacteristic
312SD16—416no—
313D8—24416no—
314C2×C8—24no—
315C2×C8—614no—
316C2×C8—614no—
317C2×C8—1224no—
318C2×C8—1224no—
319C2×C8C2×C22⋊D6114yes—
320C4⋊C4—22no—
321C4⋊C4—22no—
322C4⋊C4—41no—
323C4⋊C4—41no—
324C4⋊C4—1222no—
325C4⋊C4—1222no—
326C4⋊C4—2441no—
327C4⋊C4—2441no—
328C42D4×D6111yescharacteristic
329C42D4×D6111yescharacteristic
330C42C2×C22⋊D6111yescharacteristic
331C42C23×D6111yescharacteristic
332C23—42no—
333C23—82no—
334C23—82no—
335C23—82no—
336C23—4882no—
337C23—4882no—
338C23—4882no—
339C23—2442no—
340C23#1451977311yescharacteristic
341Q8—44no—
342Q8—82no—
343Q8—4882no—
344Q8—2444no—
345D4—44no—
346D4—44no—
347D4—44no—
348D4—82no—
349D4—82no—
350D4—82no—
351D4—4882no—
352D4—4882no—
353D4—4882no—
354D4—2444no—
355D4—2444no—
356D4—2444no—
357C2×C4—42no—
358C2×C4—82no—
359C2×C4—4882no—
360C2×C4—2442no—
361C2×C4#1451977311yescharacteristic
362C2×C4#1451977311yescharacteristic
363C2×C4#1451977311yescharacteristic
364C2×C4#1451979814yes—
365C2×C4#1451980314yes—
366C2×C4#1451980414yes—
367C2×C4C2×D4×D6111yescharacteristic
368C2×C4C2×D4×D6111yescharacteristic
369C2×C4C22×C22⋊D6111yescharacteristic
370C8—24no—
371C8—1224no—
372C8—1224no—
373C22—82no—
374C22—82no—
375C22—82no—
376C22—164no—
377C22—9764no—
378C22—4882no—
379C22—4882no—
380C22—4882no—
381C22#1684014312yes—
382C22#1684014812yes—
383C22#1684014912yes—
384C22C2×#1451977311yescharacteristic
385C4—82no—
386C4—4882no—
387C4#1684014312yes—
388C4#1684014812yes—
389C4#1684014912yes—
390C4C2×#1451979812yes—
391C4C2×#1451980312yes—
392C4C2×#1451980412yes—
393C2—162no—
394C2—9762no—
395C2#2144545614yesdirect product factor
396C2C2×#1684014311yescharacteristic
397C2C2×#1684014811yescharacteristic
398C2C2×#1684014911yescharacteristic
subgroupG/H
centerC23#14519773
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC2×C61×#492C2
socleC23×C61#127
prime radicalC2×#16840138C2
hypercenterC2×#492D61
hypocenterC61C2×#1717
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#492

Complements

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

NH ≅ G/Ntype
2. C2×#16840114C2semidirect
3. C2×#16840110C2semidirect
4. C2×#16840109C2semidirect
5. C2×#16840108C2semidirect
6. #21445456C2direct (N × H)
7. C2×#16839484C2semidirect
8. C2×C61×#492C2semidirect
15. #16840114C22semidirect
17. #16840110C22semidirect
19. #16840109C22semidirect
21. #16840108C22semidirect
28. #16839484C22semidirect
33. C61×#492C22semidirect
195. C2×#492D61semidirect
203. C2×C61#1717semidirect
217. #492C2×D61semidirect
234. C61C2×#1717semidirect
395. C2#21445456direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168401382
C2×#168401142
C2×#168401102
C2×#168401092
C2×#168401082
#214454562
C2×#168394842
C2×C61×#4922
C2×#171761