Finite Group Databasebeta

← C4×#22548747 #44559185

Subgroups — C4×#22548747 #44559185

Order 32128.

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×#22548747C211yesmaximal, characteristic
2C4×#16860811C211yesmaximal, characteristic
3C4×Q8×D251C211yesmaximal, characteristic, complemented
4#30631794C211yesmaximal, characteristic, complemented
5#30631791C211yesmaximal, characteristic, complemented
6#30631790C211yesmaximal, characteristic, complemented
7#30631786C211yesmaximal, characteristic, complemented
8C4×#16860800C211yesmaximal, characteristic, complemented
9C4×#16860799C211yesmaximal, characteristic, complemented
10C4×#16860797C211yesmaximal, characteristic, complemented
11#30631728C211yesmaximal, characteristic, complemented
12#30631694C211yesmaximal, characteristic, complemented
13#30631687C211yesmaximal, characteristic
14C4×#16860793C211yesmaximal, characteristic, complemented
15C4×Q16×C251C211yesmaximal, characteristic, complemented
16C2×#16860811C2211yescharacteristic
17C2×Q8×D251C2211yescharacteristic
18#22548747C418yesdirect product factor
19C2×#16860800C2211yescharacteristic
20C2×#16860799C2211yescharacteristic
21C2×#16860797C2211yescharacteristic
22C2×#16860793C2211yescharacteristic
23C2×#16860793C2211yescharacteristic
24Q8×Dic251C2211yescharacteristic
25Q8×Dic251C2211yescharacteristic
26C4×Dic502—21no—
27C4×Dic502C2211yescharacteristic
28#22548680—21no—
29#22548680C2211yescharacteristic
30C4×D1004—21no—
31C4×D1004C2211yescharacteristic
32#22548677—21no—
33#22548677C2211yescharacteristic
34#22548673—21no—
35#22548673C2211yescharacteristic
36C4⋊C4×D251—21no—
37C4⋊C4×D251C2211yescharacteristic
38C42×D251—21no—
39C42×D251—21no—
40C42×D251C2211yescharacteristic
41#22548648C2211yescharacteristic
42#22548647C2211yescharacteristic
43#22548646C2211yescharacteristic
44#22548640C2211yescharacteristic
45#22548639C2211yescharacteristic
46#22548639C2211yescharacteristic
47#22548638C2211yescharacteristic
48#22548637C2211yescharacteristic
49#22548635C2211yescharacteristic
50#22548625C2211yescharacteristic
51#22548625C2211yescharacteristic
52C4×C251⋊C8C2211yescharacteristic
53C2×Q16×C251C2211yescharacteristic
54C4×Q8×C251C2211yescharacteristic
55C4×Q8×C251C2211yescharacteristic
56#107×C251C2211yescharacteristic
57#103×C251C2211yescharacteristic
58#103×C251C2211yescharacteristic
59C4×C8×C251C2211yescharacteristic
60#16860811—22no—
61#16860811C2×C414yes—
62C2×Dic502—21no—
63C2×Dic502C2311yescharacteristic
64Q8×D251—22no—
65Q8×D251C2×C414yescomplemented
66C2×D1004—21no—
67C2×D1004C2311yescharacteristic
68C2×C4×D251—21no—
69C2×C4×D251—21no—
70C2×C4×D251—21no—
71C2×C4×D251—21no—
72C2×C4×D251—21no—
73C2×C4×D251D411yescharacteristic
74C2×C4×D251D411yescharacteristic
75C2×C4×D251C2311yescharacteristic
76#16860800C2×C414yescomplemented
77#16860799C2×C414yescomplemented
78#16860797C2×C414yescomplemented
79#16860793—22no—
80#16860793C2×C414yescomplemented
81C2×C251⋊C8C2311yescharacteristic
82C2×C251⋊C8C2311yescharacteristic
83C4⋊Dic251—21no—
84C4⋊Dic251—21no—
85C4⋊Dic251C2311yescharacteristic
86C4⋊Dic251C2311yescharacteristic
87Dic251⋊C4—21no—
88Dic251⋊C4—21no—
89Dic251⋊C4—21no—
90(C2×D251)⋊C4—21no—
91(C2×D251)⋊C4—21no—
92(C2×D251)⋊C4—21no—
93C4×Dic251—21no—
94C4×Dic251—21no—
95C4×Dic251—21no—
96C4×Dic251—21no—
97C4×Dic251—21no—
98C4×Dic251D411yescharacteristic
99C4×Dic251D411yescharacteristic
100C4×Dic251C2311yescharacteristic
101C2×Q8×C251C2311yescharacteristic
102C2×Q8×C251C2311yescharacteristic
103Q16×C251C2×C414yescomplemented
104C2×C8×C251C2311yescharacteristic
105C2×C8×C251C2311yescharacteristic
106C4⋊C4×C251—21no—
107C4⋊C4×C251—21no—
108C4⋊C4×C251C2311yescharacteristic
109C4⋊C4×C251C2311yescharacteristic
110C42×C251—21no—
111C42×C251—21no—
112C42×C251C2311yescharacteristic
113C22×D251—21no—
114C22×D251C2×D411yescharacteristic
115Dic502—21no—
116Dic502—24no—
117Dic502C22×C412yes—
118D1004—24no—
119D1004—21no—
120D1004C22×C412yes—
121C2×Dic251—21no—
122C2×Dic251—21no—
123C2×Dic251—21no—
124C2×Dic251C2×D411yescharacteristic
125C2×Dic251C2×D411yescharacteristic
126C2×Dic251C2×D411yescharacteristic
127C4×D251—24no—
128C4×D251—22no—
129C4×D251—24no—
130C4×D251—41no—
131C4×D251—42no—
132C4×D251—42no—
133C4×D251—42no—
134C4×D251C22×C412yes—
135C4×D251#4112yes—
136C251⋊C8—21no—
137C251⋊C8C22×C412yes—
138Q8×C251—21no—
139Q8×C251—21no—
140Q8×C251C22×C412yes—
141Q8×C251C22×C412yes—
142C2×C4×C251—21no—
143C2×C4×C251—21no—
144C2×C4×C251—21no—
145C2×C4×C251—21no—
146C2×C4×C251C2×D411yescharacteristic
147C2×C4×C251C2×D411yescharacteristic
148C2×C4×C251C2411yescharacteristic
149C8×C251—21no—
150C8×C251C22×C412yes—
151C22×C251C22×D411yescharacteristic
152C2×D251—21no—
153C2×D251—21no—
154C2×D251—22no—
155C2×D251—41no—
156C2×D251—41no—
157C2×D251C4×D412yes—
158C4×C251—22no—
159C4×C251—22no—
160C4×C251—21no—
161C4×C251—41no—
162C4×C251—41no—
163C4×C251#13712yescomplemented
164C4×C251C23×C411yescharacteristic
165C4×C251C2×#4111yescharacteristic
166Dic251—22no—
167Dic251—21no—
168Dic251—21no—
169Dic251—41no—
170Dic251—41no—
171Dic251C4×D412yes—
172C2×C251C2×C4×D411yescharacteristic
173C2×C251C2×#13711yescharacteristic
174C2×C251#57511yescharacteristic
175D251—22no—
176D251—42no—
177C251C4×#13711yescharacteristic, complemented, Sylow
178C4×#137—2511nomaximal, Sylow
179C2×#137—2511no—
180C4×#41—2511no—
181C2×C4×Q8—2511no—
182#441—2511no—
183#441—2511no—
184#440—2511no—
185#440—2511no—
186C4×Q16—2511no—
187C4×Q16D25111yescharacteristic, complemented
188C4×SD16—2511no—
189C4×SD16—2511no—
190#428—2511no—
191#419—2511no—
192#417—2511no—
193C4×M16—2511no—
194C2×#41—2511no—
195C22×Q8—2511no—
196#137—2518no—
197C2×Q16—2511no—
198C2×Q16C2×D25111yescharacteristic
199C2×SD16—2511no—
200C2×SD16—2511no—
201C2×M16—2511no—
202C2×M16—2511no—
203C4×Q8—5021no—
204C4×Q8—5021no—
205C4×Q8—2511no—
206C4×Q8—2511no—
207C4×Q8—2511no—
208C4×Q8—2511no—
209C4×Q8C2×D25111yescharacteristic
210C4×Q8C2×D25111yescharacteristic
211C4×D4—5021no—
212C4×D4—5021no—
213C4×D4—2511no—
214C4×D4—2511no—
215#117—5021no—
216#117—2511no—
217C2×C4⋊C4—5021no—
218C2×C4⋊C4—2511no—
219C2×C42—5021no—
220C2×C42—5021no—
221C2×C42—2511no—
222#107—2511no—
223#107C2×D25111yescharacteristic
224#106—2511no—
225#106—2511no—
226#103—2511no—
227#103—2511no—
228#103—2511no—
229#103—2511no—
230#103C2×D25111yescharacteristic
231#103C2×D25111yescharacteristic
232#102—2511no—
233#102—2511no—
234#97—2511no—
235#97—2511no—
236C4×C8—2511no—
237C4×C8C2×D25111yescharacteristic
238#41—5022no—
239#41—2514no—
240C2×Q8—5021no—
241C2×Q8—5022no—
242C2×Q8—2514no—
243C2×Q8—2511no—
244C2×Q8C22×D25111yescharacteristic
245C2×Q8C22×D25111yescharacteristic
246C2×D4—5021no—
247C2×D4—2511no—
248C22×C4—5021no—
249C22×C4—5021no—
250C22×C4—5021no—
251C22×C4—5021no—
252C22×C4—5021no—
253C22×C4—2511no—
254C22×C4—2511no—
255C22×C4—2511no—
256Q16—2514no—
257Q16C4×D25114yescomplemented
258SD16—2514no—
259SD16—2514no—
260M16—5022no—
261M16—2514no—
262C2×C8—2511no—
263C2×C8—2511no—
264C2×C8C22×D25111yescharacteristic
265C2×C8C22×D25111yescharacteristic
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—5021no—
269C4⋊C4—5021no—
270C4⋊C4—5021no—
271C4⋊C4—5021no—
272C4⋊C4—5021no—
273C4⋊C4—2511no—
274C4⋊C4—2511no—
275C4⋊C4C22×D25111yescharacteristic
276C4⋊C4C22×D25111yescharacteristic
277C22⋊C4—5021no—
278C22⋊C4—5021no—
279C22⋊C4—5021no—
280C42—21no—
281C42—21no—
282C42—5021no—
283C42—5021no—
284C42—5021no—
285C42—5021no—
286C42—5021no—
287C42—2511no—
288C42—2511no—
289C42—2511no—
290C42C22×D25111yescharacteristic
291C23—5021no—
292C23—2511no—
293Q8—21no—
294Q8—21no—
295Q8—5024no—
296Q8—5021no—
297Q8—2512no—
298Q8C2×C4×D25112yes—
299Q8C2×C4×D25112yes—
300D4—5024no—
301D4—5021no—
302D4—2512no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—10041no—
308C2×C4—10042no—
309C2×C4—10042no—
310C2×C4—10042no—
311C2×C4—5024no—
312C2×C4—5024no—
313C2×C4—5021no—
314C2×C4—5021no—
315C2×C4—5021no—
316C2×C4—5022no—
317C2×C4—2511no—
318C2×C4—2511no—
319C2×C4—2511no—
320C2×C4—2512no—
321C2×C4—2512no—
322C2×C4D4×D25111yescharacteristic
323C2×C4D4×D25111yescharacteristic
324C2×C4C23×D25111yescharacteristic
325C8—21no—
326C8—5021no—
327C8—2512no—
328C8C2×C4×D25112yes—
329C22—10041no—
330C22—10041no—
331C22—5022no—
332C22—5021no—
333C22—5021no—
334C22—2512no—
335C22C2×D4×D25111yescharacteristic
336C4—21no—
337C4—22no—
338C4—22no—
339C4—41no—
340C4—41no—
341C4—10041no—
342C4—10041no—
343C4—5021no—
344C4—5021no—
345C4—5022no—
346C4—2512no—
347C4#2254874712yesdirect product factor
348C4C22×C4×D25111yescharacteristic
349C4#41×D25111yescharacteristic
350C2—10042no—
351C2—5022no—
352C2C4×D4×D25111yescharacteristic
353C2C2×#2254874711yescharacteristic
354C2#3063248411yescharacteristic
subgroupG/H
centerC2×C4D4×D251
commutatorC4×C251C23×C4
FrattiniC2×C4C23×D251
FittingC4×Q16×C251C2
socleC22×C251C22×D4
prime radicalC2×#16860811C22
cosocleC2×C4×C251C24
hypercenterC4×Q16D251
hypocenterC251C4×#137
LCSG ▷ C4×C251 ▷ C2×C251 ▷ C251
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
3. C4×Q8×D251C2semidirect
4. #30631794C2semidirect
5. #30631791C2semidirect
6. #30631790C2semidirect
7. #30631786C2semidirect
8. C4×#16860800C2semidirect
9. C4×#16860799C2semidirect
10. C4×#16860797C2semidirect
11. #30631728C2semidirect
12. #30631694C2semidirect
14. C4×#16860793C2semidirect
15. C4×Q16×C251C2semidirect
18. #22548747C4direct (N × H)
65. Q8×D251C2×C4semidirect
76. #16860800C2×C4semidirect
77. #16860799C2×C4semidirect
78. #16860797C2×C4semidirect
80. #16860793C2×C4semidirect
103. Q16×C251C2×C4semidirect
163. C4×C251#137semidirect
177. C251C4×#137semidirect
187. C4×Q16D251semidirect
257. Q16C4×D251semidirect
347. C4#22548747direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#225487472
C4×#168608112
C4×Q8×D2512
#306317942
#306317912
#306317902
#306317862
C4×#168608002
C4×#168607992
C4×#168607972
#306317282
#306316942
#306316872
C4×#168607932
C4×Q16×C2512
C4×#137251