Finite Group Databasebeta

← C4×#15692287 #27179952

Subgroups — C4×#15692287 #27179952

Order 12928.

484 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15692287C211yesmaximal, characteristic
2C4×#13108075C211yesmaximal, characteristic
3C4×Q8×D101C211yesmaximal, characteristic, complemented
4#20265284C211yesmaximal, characteristic, complemented
5#20265281C211yesmaximal, characteristic, complemented
6#20265280C211yesmaximal, characteristic, complemented
7#20265276C211yesmaximal, characteristic, complemented
8C4×#13108064C211yesmaximal, characteristic, complemented
9C4×#13108063C211yesmaximal, characteristic, complemented
10C4×#13108061C211yesmaximal, characteristic, complemented
11#20265218C211yesmaximal, characteristic, complemented
12#20265184C211yesmaximal, characteristic, complemented
13#20265177C211yesmaximal, characteristic
14C4×#13108057C211yesmaximal, characteristic, complemented
15C4×Q16×C101C211yesmaximal, characteristic, complemented
16C2×#13108075C2211yescharacteristic
17C2×Q8×D101C2211yescharacteristic
18#15692287C418yesdirect product factor
19C2×#13108064C2211yescharacteristic
20C2×#13108063C2211yescharacteristic
21C2×#13108061C2211yescharacteristic
22C2×#13108057C2211yescharacteristic
23C2×#13108057C2211yescharacteristic
24Q8×Dic101C2211yescharacteristic
25Q8×Dic101C2211yescharacteristic
26C4×Dic202—21no—
27C4×Dic202C2211yescharacteristic
28#15692220—21no—
29#15692220C2211yescharacteristic
30C4×D404—21no—
31C4×D404C2211yescharacteristic
32#15692217—21no—
33#15692217C2211yescharacteristic
34#15692213—21no—
35#15692213C2211yescharacteristic
36C4⋊C4×D101—21no—
37C4⋊C4×D101C2211yescharacteristic
38C42×D101—21no—
39C42×D101—21no—
40C42×D101C2211yescharacteristic
41#15692188C2211yescharacteristic
42#15692187C2211yescharacteristic
43#15692186C2211yescharacteristic
44#15692180C2211yescharacteristic
45#15692179C2211yescharacteristic
46#15692179C2211yescharacteristic
47#15692178C2211yescharacteristic
48#15692177C2211yescharacteristic
49#15692175C2211yescharacteristic
50#15692165C2211yescharacteristic
51#15692165C2211yescharacteristic
52C4×#11717579C2211yescharacteristic
53C2×Q16×C101C2211yescharacteristic
54C4×Q8×C101C2211yescharacteristic
55C4×Q8×C101C2211yescharacteristic
56#107×C101C2211yescharacteristic
57#103×C101C2211yescharacteristic
58#103×C101C2211yescharacteristic
59C4×C8×C101C2211yescharacteristic
60#13108075—22no—
61#13108075C2×C414yes—
62C2×Dic202—21no—
63C2×Dic202C2311yescharacteristic
64Q8×D101—22no—
65Q8×D101C2×C414yescomplemented
66C2×D404—21no—
67C2×D404C2311yescharacteristic
68C2×C4×D101—21no—
69C2×C4×D101—21no—
70C2×C4×D101—21no—
71C2×C4×D101—21no—
72C2×C4×D101—21no—
73C2×C4×D101D411yescharacteristic
74C2×C4×D101D411yescharacteristic
75C2×C4×D101C2311yescharacteristic
76#13108064C2×C414yescomplemented
77#13108063C2×C414yescomplemented
78#13108061C2×C414yescomplemented
79#13108057—22no—
80#13108057C2×C414yescomplemented
81C2×#11717579C2311yescharacteristic
82C2×#11717579C2311yescharacteristic
83C4⋊Dic101—21no—
84C4⋊Dic101—21no—
85C4⋊Dic101C2311yescharacteristic
86C4⋊Dic101C2311yescharacteristic
87#13108053—21no—
88#13108053—21no—
89#13108053—21no—
90#13108051—21no—
91#13108051—21no—
92#13108051—21no—
93C4×Dic101—21no—
94C4×Dic101—21no—
95C4×Dic101—21no—
96C4×Dic101—21no—
97C4×Dic101—21no—
98C4×Dic101D411yescharacteristic
99C4×Dic101D411yescharacteristic
100C4×Dic101C2311yescharacteristic
101C2×Q8×C101C2311yescharacteristic
102C2×Q8×C101C2311yescharacteristic
103Q16×C101C2×C414yescomplemented
104C2×C8×C101C2311yescharacteristic
105C2×C8×C101C2311yescharacteristic
106C4⋊C4×C101—21no—
107C4⋊C4×C101—21no—
108C4⋊C4×C101C2311yescharacteristic
109C4⋊C4×C101C2311yescharacteristic
110C42×C101—21no—
111C42×C101—21no—
112C42×C101C2311yescharacteristic
113C22×D101—21no—
114C22×D101C2×D411yescharacteristic
115Q8×C101—21no—
116Q8×C101—21no—
117Q8×C101C22×C412yes—
118Q8×C101C22×C412yes—
119C2×C4×C101—21no—
120C2×C4×C101—21no—
121C2×C4×C101—21no—
122C2×C4×C101—21no—
123C2×C4×C101C2×D411yescharacteristic
124C2×C4×C101C2×D411yescharacteristic
125C2×C4×C101C2411yescharacteristic
126C2×Dic101—21no—
127C2×Dic101—21no—
128C2×Dic101—21no—
129C2×Dic101C2×D411yescharacteristic
130C2×Dic101C2×D411yescharacteristic
131C2×Dic101C2×D411yescharacteristic
132D404—24no—
133D404—21no—
134D404C22×C412yes—
135C4×D101—24no—
136C4×D101—22no—
137C4×D101—24no—
138C4×D101—41no—
139C4×D101—42no—
140C4×D101—42no—
141C4×D101—42no—
142C4×D101C22×C412yes—
143C4×D101#4112yes—
144Dic202—21no—
145Dic202—24no—
146Dic202C22×C412yes—
147C8×C101—21no—
148C8×C101C22×C412yes—
149#11717579—21no—
150#11717579C22×C412yes—
151C22×C101C22×D411yescharacteristic
152C2×D101—21no—
153C2×D101—21no—
154C2×D101—22no—
155C2×D101—41no—
156C2×D101—41no—
157C2×D101C4×D412yes—
158C4×C101—22no—
159C4×C101—22no—
160C4×C101—21no—
161C4×C101—41no—
162C4×C101—41no—
163C4×C101#13712yescomplemented
164C4×C101C23×C411yescharacteristic
165C4×C101C2×#4111yescharacteristic
166Dic101—22no—
167Dic101—21no—
168Dic101—21no—
169Dic101—41no—
170Dic101—41no—
171Dic101C4×D412yes—
172C2×C101C2×C4×D411yescharacteristic
173C2×C101C2×#13711yescharacteristic
174C2×C101#57511yescharacteristic
175D101—22no—
176D101—42no—
177C4×#137—1011nomaximal, Sylow
178C101C4×#13711yescharacteristic, complemented, Sylow
179C2×#137—1011no—
180C4×#41—1011no—
181C2×C4×Q8—1011no—
182#441—1011no—
183#441—1011no—
184#440—1011no—
185#440—1011no—
186C4×Q16—1011no—
187C4×Q16D10111yescharacteristic, complemented
188C4×SD16—1011no—
189C4×SD16—1011no—
190#428—1011no—
191#419—1011no—
192#417—1011no—
193C4×M16—1011no—
194C2×#41—1011no—
195C22×Q8—1011no—
196#137—1018no—
197C2×Q16—1011no—
198C2×Q16C2×D10111yescharacteristic
199C2×SD16—1011no—
200C2×SD16—1011no—
201C2×M16—1011no—
202C2×M16—1011no—
203C4×Q8—1011no—
204C4×Q8—1011no—
205C4×Q8—1011no—
206C4×Q8—1011no—
207C4×Q8—2021no—
208C4×Q8—2021no—
209C4×Q8C2×D10111yescharacteristic
210C4×Q8C2×D10111yescharacteristic
211C4×D4—1011no—
212C4×D4—1011no—
213C4×D4—2021no—
214C4×D4—2021no—
215#117—1011no—
216#117—2021no—
217C2×C4⋊C4—1011no—
218C2×C4⋊C4—2021no—
219C2×C42—1011no—
220C2×C42—2021no—
221C2×C42—2021no—
222#107—1011no—
223#107C2×D10111yescharacteristic
224#106—1011no—
225#106—1011no—
226#103—1011no—
227#103—1011no—
228#103—1011no—
229#103—1011no—
230#103C2×D10111yescharacteristic
231#103C2×D10111yescharacteristic
232#102—1011no—
233#102—1011no—
234#97—1011no—
235#97—1011no—
236C4×C8—1011no—
237C4×C8C2×D10111yescharacteristic
238#41—1014no—
239#41—2022no—
240C2×Q8—1014no—
241C2×Q8—1011no—
242C2×Q8—2021no—
243C2×Q8—2022no—
244C2×Q8C22×D10111yescharacteristic
245C2×Q8C22×D10111yescharacteristic
246C2×D4—1011no—
247C2×D4—2021no—
248C22×C4—1011no—
249C22×C4—1011no—
250C22×C4—1011no—
251C22×C4—2021no—
252C22×C4—2021no—
253C22×C4—2021no—
254C22×C4—2021no—
255C22×C4—2021no—
256Q16—1014no—
257Q16C4×D10114yescomplemented
258SD16—1014no—
259SD16—1014no—
260M16—1014no—
261M16—2022no—
262C2×C8—1011no—
263C2×C8—1011no—
264C2×C8C22×D10111yescharacteristic
265C2×C8C22×D10111yescharacteristic
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—1011no—
269C4⋊C4—1011no—
270C4⋊C4—2021no—
271C4⋊C4—2021no—
272C4⋊C4—2021no—
273C4⋊C4—2021no—
274C4⋊C4—2021no—
275C4⋊C4C22×D10111yescharacteristic
276C4⋊C4C22×D10111yescharacteristic
277C22⋊C4—2021no—
278C22⋊C4—2021no—
279C22⋊C4—2021no—
280C42—21no—
281C42—21no—
282C42—1011no—
283C42—1011no—
284C42—1011no—
285C42—2021no—
286C42—2021no—
287C42—2021no—
288C42—2021no—
289C42—2021no—
290C42C22×D10111yescharacteristic
291C23—1011no—
292C23—2021no—
293Q8—21no—
294Q8—21no—
295Q8—1012no—
296Q8—2024no—
297Q8—2021no—
298Q8C2×C4×D10112yes—
299Q8C2×C4×D10112yes—
300D4—1012no—
301D4—2024no—
302D4—2021no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—1011no—
308C2×C4—1012no—
309C2×C4—1012no—
310C2×C4—1011no—
311C2×C4—1011no—
312C2×C4—4041no—
313C2×C4—4042no—
314C2×C4—4042no—
315C2×C4—4042no—
316C2×C4—2024no—
317C2×C4—2024no—
318C2×C4—2021no—
319C2×C4—2021no—
320C2×C4—2021no—
321C2×C4—2022no—
322C2×C4D4×D10111yescharacteristic
323C2×C4D4×D10111yescharacteristic
324C2×C4C23×D10111yescharacteristic
325C8—21no—
326C8—1012no—
327C8—2021no—
328C8C2×C4×D10112yes—
329C22—1012no—
330C22—4041no—
331C22—4041no—
332C22—2022no—
333C22—2021no—
334C22—2021no—
335C22C2×D4×D10111yescharacteristic
336C4—22no—
337C4—22no—
338C4—21no—
339C4—41no—
340C4—41no—
341C4—1012no—
342C4—4041no—
343C4—4041no—
344C4—2022no—
345C4—2021no—
346C4—2021no—
347C4#1569228712yesdirect product factor
348C4C22×C4×D10111yescharacteristic
349C4#41×D10111yescharacteristic
350C2—4042no—
351C2—2022no—
352C2C4×D4×D10111yescharacteristic
353C2C2×#1569228711yescharacteristic
354C2#2026597411yescharacteristic
subgroupG/H
centerC2×C4D4×D101
commutatorC4×C101C23×C4
FrattiniC2×C4C23×D101
FittingC4×Q16×C101C2
socleC22×C101C22×D4
prime radicalC2×#13108075C22
cosocleC2×C4×C101C24
hypercenterC4×Q16D101
hypocenterC101C4×#137
LCSG ▷ C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
3. C4×Q8×D101C2semidirect
4. #20265284C2semidirect
5. #20265281C2semidirect
6. #20265280C2semidirect
7. #20265276C2semidirect
8. C4×#13108064C2semidirect
9. C4×#13108063C2semidirect
10. C4×#13108061C2semidirect
11. #20265218C2semidirect
12. #20265184C2semidirect
14. C4×#13108057C2semidirect
15. C4×Q16×C101C2semidirect
18. #15692287C4direct (N × H)
65. Q8×D101C2×C4semidirect
76. #13108064C2×C4semidirect
77. #13108063C2×C4semidirect
78. #13108061C2×C4semidirect
80. #13108057C2×C4semidirect
103. Q16×C101C2×C4semidirect
163. C4×C101#137semidirect
178. C101C4×#137semidirect
187. C4×Q16D101semidirect
257. Q16C4×D101semidirect
347. C4#15692287direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156922872
C4×#131080752
C4×Q8×D1012
#202652842
#202652812
#202652802
#202652762
C4×#131080642
C4×#131080632
C4×#131080612
#202652182
#202651842
#202651772
C4×#131080572
C4×Q16×C1012
C4×#137101