Finite Group Databasebeta

← C4×#15692284 #27179946

Subgroups — C4×#15692284 #27179946

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×#15692284C211yesmaximal, characteristic
2C4×#13108073C211yesmaximal, characteristic
3C4×Q8×D101C211yesmaximal, characteristic, complemented
4#20265283C211yesmaximal, characteristic, complemented
5#20265281C211yesmaximal, characteristic, complemented
6#20265278C211yesmaximal, characteristic, complemented
7#20265274C211yesmaximal, characteristic, complemented
8C4×Dic404C211yesmaximal, characteristic, complemented
9C4×#13108064C211yesmaximal, characteristic, complemented
10C4×#13108062C211yesmaximal, characteristic, complemented
11#20265216C211yesmaximal, characteristic, complemented
12#20265184C211yesmaximal, characteristic, complemented
13#20265175C211yesmaximal, characteristic
14C4×#13108057C211yesmaximal, characteristic, complemented
15C4×SD16×C101C211yesmaximal, characteristic, complemented
16C2×#13108073C2211yescharacteristic
17C2×Q8×D101C2211yescharacteristic
18#15692284C418yesdirect product factor
19C2×Dic404C2211yescharacteristic
20C2×#13108064C2211yescharacteristic
21C2×#13108062C2211yescharacteristic
22C2×#13108057C2211yescharacteristic
23C2×#13108057C2211yescharacteristic
24Q8×Dic101C2211yescharacteristic
25C4×Dic202—21no—
26C4×Dic202C2211yescharacteristic
27C4×Dic202C2211yescharacteristic
28#15692220—21no—
29#15692220C2211yescharacteristic
30#15692220C2211yescharacteristic
31D4×Dic101C2211yescharacteristic
32C4×C22⋊D101—21no—
33#15692215—21no—
34#15692213C2211yescharacteristic
35#15692211—21no—
36C4⋊C4×D101—21no—
37C4⋊C4×D101C2211yescharacteristic
38C2×C4×Dic101—21no—
39C42×D101—21no—
40C42×D101C2211yescharacteristic
41#15692189C2211yescharacteristic
42#15692188C2211yescharacteristic
43#15692186C2211yescharacteristic
44#15692180C2211yescharacteristic
45#15692180C2211yescharacteristic
46#15692179C2211yescharacteristic
47#15692178C2211yescharacteristic
48#15692178C2211yescharacteristic
49#15692176C2211yescharacteristic
50#15692165C2211yescharacteristic
51#15692165C2211yescharacteristic
52C4×#11717579C2211yescharacteristic
53C2×SD16×C101C2211yescharacteristic
54C4×Q8×C101C2211yescharacteristic
55C4×D4×C101C2211yescharacteristic
56#106×C101C2211yescharacteristic
57#103×C101C2211yescharacteristic
58#102×C101C2211yescharacteristic
59C4×C8×C101C2211yescharacteristic
60#13108073—22no—
61#13108073C2×C414yes—
62C2×Dic202—21no—
63C2×Dic202C2311yescharacteristic
64C2×Dic202C2311yescharacteristic
65Q8×D101—22no—
66Q8×D101C2×C414yescomplemented
67C2×C22⋊D101—21no—
68C22×Dic101—21no—
69C22×Dic101—21no—
70C2×C4×D101—21no—
71C2×C4×D101—21no—
72C2×C4×D101D411yescharacteristic
73C2×C4×D101D411yescharacteristic
74C2×C4×D101C2311yescharacteristic
75Dic404C2×C414yescomplemented
76#13108064C2×C414yescomplemented
77#13108062C2×C414yescomplemented
78#13108057—22no—
79#13108057C2×C414yescomplemented
80C2×#11717579C2311yescharacteristic
81C2×#11717579C2311yescharacteristic
82C4⋊Dic101—21no—
83C4⋊Dic101C2311yescharacteristic
84C4⋊Dic101C2311yescharacteristic
85#13108053—21no—
86#13108053—21no—
87#13108053—21no—
88#13108053—21no—
89#13108053—21no—
90C22⋊Dic101—21no—
91#13108051—21no—
92C4×Dic101—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×D4×C101C2311yescharacteristic
103C22×C4×C101—21no—
104SD16×C101C2×C414yescomplemented
105C2×C8×C101C2311yescharacteristic
106C2×C8×C101C2311yescharacteristic
107C4⋊C4×C101—21no—
108C4⋊C4×C101C2311yescharacteristic
109C4⋊C4×C101C2311yescharacteristic
110C22⋊C4×C101—21no—
111C42×C101—21no—
112C42×C101C2311yescharacteristic
113C23×C101—21no—
114C22×D101C2×D411yescharacteristic
115Q8×C101—21no—
116Q8×C101C22×C412yes—
117D4×C101—21no—
118D4×C101C22×C412yes—
119C2×C4×C101—21no—
120C2×C4×C101—21no—
121C2×C4×C101—21no—
122C2×C4×C101—42no—
123C2×C4×C101C2×D411yescharacteristic
124C2×C4×C101C2×D411yescharacteristic
125C2×C4×C101C2411yescharacteristic
126C22⋊D101—24no—
127C2×Dic101—21no—
128C2×Dic101—21no—
129C2×Dic101—24no—
130C2×Dic101—21no—
131C2×Dic101—21no—
132C2×Dic101—42no—
133C2×Dic101C2×D411yescharacteristic
134C2×Dic101C2×D411yescharacteristic
135C2×Dic101C2×D411yescharacteristic
136C4×D101—24no—
137C4×D101—22no—
138C4×D101—41no—
139C4×D101—42no—
140C4×D101C22×C412yes—
141C4×D101#4112yes—
142Dic202—21no—
143Dic202—21no—
144Dic202—24no—
145Dic202C22×C412yes—
146Dic202C22×C412yes—
147C8×C101—21no—
148C8×C101C22×C412yes—
149#11717579—21no—
150#11717579C22×C412yes—
151C22×C101—22no—
152C22×C101—41no—
153C22×C101—41no—
154C22×C101C22×D411yescharacteristic
155C2×D101—21no—
156C2×D101—21no—
157C2×D101C4×D412yes—
158C4×C101—22no—
159C4×C101—21no—
160C4×C101—41no—
161C4×C101—41no—
162C4×C101#13712yescomplemented
163C4×C101C23×C411yescharacteristic
164C4×C101C2×#4111yescharacteristic
165Dic101—22no—
166Dic101—22no—
167Dic101—21no—
168Dic101—21no—
169Dic101—41no—
170Dic101—41no—
171Dic101C4×D412yes—
172C2×C101—42no—
173C2×C101C2×C4×D411yescharacteristic
174C2×C101C2×#13711yescharacteristic
175C2×C101#57511yescharacteristic
176D101—22no—
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×Q16—1011no—
188C4×SD16—1011no—
189C4×SD16D10111yescharacteristic, complemented
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×Q16—1011no—
199C2×SD16—1011no—
200C2×SD16C2×D10111yescharacteristic
201C2×M16—1011no—
202C2×M16—1011no—
203C4×Q8—1011no—
204C4×Q8—1011no—
205C4×Q8—1011no—
206C4×Q8—1011no—
207C4×Q8—1011no—
208C4×Q8—2021no—
209C4×Q8—2021no—
210C4×Q8C2×D10111yescharacteristic
211C4×D4—1011no—
212C4×D4—2021no—
213C4×D4—2021no—
214C4×D4C2×D10111yescharacteristic
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#107—1011no—
224#106—1011no—
225#106C2×D10111yescharacteristic
226#103—1011no—
227#103—1011no—
228#103—1011no—
229#103—1011no—
230#103—1011no—
231#103C2×D10111yescharacteristic
232#102—1011no—
233#102C2×D10111yescharacteristic
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—1011no—
243C2×Q8—2021no—
244C2×Q8—2022no—
245C2×Q8C22×D10111yescharacteristic
246C2×D4—2021no—
247C2×D4C22×D10111yescharacteristic
248C22×C4—21no—
249C22×C4—1011no—
250C22×C4—1011no—
251C22×C4—1011no—
252C22×C4—2021no—
253C22×C4—2021no—
254C22×C4—2021no—
255C22×C4—2021no—
256Q16—1014no—
257Q16—1014no—
258SD16—1014no—
259SD16C4×D10114yescomplemented
260M16—1014no—
261M16—2022no—
262C2×C8—1011no—
263C2×C8—1011no—
264C2×C8C22×D10111yescharacteristic
265C2×C8C22×D10111yescharacteristic
266C4⋊C4—21no—
267C4⋊C4—1011no—
268C4⋊C4—1011no—
269C4⋊C4—2021no—
270C4⋊C4—2021no—
271C4⋊C4—2021no—
272C4⋊C4—2021no—
273C4⋊C4—2021no—
274C4⋊C4—2021no—
275C4⋊C4C22×D10111yescharacteristic
276C4⋊C4C22×D10111yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—2021no—
279C22⋊C4—2021no—
280C42—21no—
281C42—1011no—
282C42—1011no—
283C42—1011no—
284C42—2021no—
285C42—2021no—
286C42—2021no—
287C42—2021no—
288C42—2021no—
289C42—2021no—
290C42C22×D10111yescharacteristic
291C23—21no—
292C23—1011no—
293Q8—21no—
294Q8—1012no—
295Q8—1012no—
296Q8—2024no—
297Q8—2021no—
298Q8—2021no—
299Q8C2×C4×D10112yes—
300D4—21no—
301D4—2024no—
302D4C2×C4×D10112yes—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—42no—
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—2024no—
316C2×C4—2024no—
317C2×C4—2021no—
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—22no—
330C22—41no—
331C22—41no—
332C22—1012no—
333C22—2021no—
334C22—2021no—
335C22C2×D4×D10111yescharacteristic
336C4—22no—
337C4—21no—
338C4—41no—
339C4—41no—
340C4—1012no—
341C4—4041no—
342C4—4041no—
343C4—2022no—
344C4—2022no—
345C4—2021no—
346C4—2021no—
347C4#1569228412yesdirect product factor
348C4C22×C4×D10111yescharacteristic
349C4#41×D10111yescharacteristic
350C2—42no—
351C2—2022no—
352C2C4×D4×D10111yescharacteristic
353C2C2×#1569228411yescharacteristic
354C2#2026597411yescharacteristic
subgroupG/H
centerC2×C4D4×D101
commutatorC4×C101C23×C4
FrattiniC2×C4C23×D101
FittingC4×SD16×C101C2
socleC22×C101C22×D4
prime radicalC2×#13108073C22
cosocleC2×C4×C101C24
hypercenterC4×SD16D101
hypocenterC101C4×#137
LCSG ▷ C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
3. C4×Q8×D101C2semidirect
4. #20265283C2semidirect
5. #20265281C2semidirect
6. #20265278C2semidirect
7. #20265274C2semidirect
8. C4×Dic404C2semidirect
9. C4×#13108064C2semidirect
10. C4×#13108062C2semidirect
11. #20265216C2semidirect
12. #20265184C2semidirect
14. C4×#13108057C2semidirect
15. C4×SD16×C101C2semidirect
18. #15692284C4direct (N × H)
66. Q8×D101C2×C4semidirect
75. Dic404C2×C4semidirect
76. #13108064C2×C4semidirect
77. #13108062C2×C4semidirect
79. #13108057C2×C4semidirect
104. SD16×C101C2×C4semidirect
162. C4×C101#137semidirect
178. C101C4×#137semidirect
189. C4×SD16D101semidirect
259. SD16C4×D101semidirect
347. C4#15692284direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156922842
C4×#131080732
C4×Q8×D1012
#202652832
#202652812
#202652782
#202652742
C4×Dic4042
C4×#131080642
C4×#131080622
#202652162
#202651842
#202651752
C4×#131080572
C4×SD16×C1012
C4×#137101