Finite Group Databasebeta

← C4×#10625089 #15682217

Subgroups — C4×#10625089 #15682217

Order 2944.

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×#10625089C211yesmaximal, characteristic
2C4×#67292C211yesmaximal, characteristic
3C4×Q8×D23C211yesmaximal, characteristic, complemented
4#13092524C211yesmaximal, characteristic, complemented
5#13092521C211yesmaximal, characteristic, complemented
6#13092520C211yesmaximal, characteristic, complemented
7#13092516C211yesmaximal, characteristic, complemented
8C4×#67275C211yesmaximal, characteristic, complemented
9C4×#67263C211yesmaximal, characteristic, complemented
10C4×#67274C211yesmaximal, characteristic, complemented
11#13092458C211yesmaximal, characteristic, complemented
12#13092424C211yesmaximal, characteristic, complemented
13#13092417C211yesmaximal, characteristic
14C4×#67262C211yesmaximal, characteristic, complemented
15C4×Q16×C23C211yesmaximal, characteristic, complemented
16C2×#67292C2211yescharacteristic
17C2×Q8×D23C2211yescharacteristic
18C2×Q16×C23C2211yescharacteristic
19C4×Q8×C23C2211yescharacteristic
20C4×Q8×C23C2211yescharacteristic
21Q8×Dic23C2211yescharacteristic
22Q8×Dic23C2211yescharacteristic
23C2×#67275C2211yescharacteristic
24C2×#67274C2211yescharacteristic
25#10625089C418yesdirect product factor
26C2×#67263C2211yescharacteristic
27C2×#67262C2211yescharacteristic
28C2×#67262C2211yescharacteristic
29#10625064—21no—
30#10625064C2211yescharacteristic
31#10625063—21no—
32#10625063C2211yescharacteristic
33C4⋊C4×D23—21no—
34C4⋊C4×D23C2211yescharacteristic
35#10625058—21no—
36#10625058C2211yescharacteristic
37C4×D92—21no—
38C4×D92C2211yescharacteristic
39C42×D23—21no—
40C42×D23—21no—
41C42×D23C2211yescharacteristic
42C4×Dic46—21no—
43C4×Dic46C2211yescharacteristic
44C23×#107C2211yescharacteristic
45C23×#103C2211yescharacteristic
46C23×#103C2211yescharacteristic
47C4×C8×C23C2211yescharacteristic
48#10625017C2211yescharacteristic
49#10625017C2211yescharacteristic
50#10625003C2211yescharacteristic
51#10624999C2211yescharacteristic
52#10624998C2211yescharacteristic
53#10624997C2211yescharacteristic
54#10624997C2211yescharacteristic
55#10624992C2211yescharacteristic
56#10624991C2211yescharacteristic
57#10624990C2211yescharacteristic
58#10624989C2211yescharacteristic
59C4×C23⋊C8C2211yescharacteristic
60C2×Q8×C23C2311yescharacteristic
61C2×Q8×C23C2311yescharacteristic
62#67292—22no—
63#67292C2×C414yes—
64Q8×D23—22no—
65Q8×D23C2×C414yescomplemented
66C2×D92—21no—
67C2×D92C2311yescharacteristic
68C2×C4×D23—21no—
69C2×C4×D23—21no—
70C2×C4×D23—21no—
71C2×C4×D23—21no—
72C2×C4×D23—21no—
73C2×C4×D23D411yescharacteristic
74C2×C4×D23D411yescharacteristic
75C2×C4×D23C2311yescharacteristic
76C2×Dic46—21no—
77C2×Dic46C2311yescharacteristic
78Q16×C23C2×C414yescomplemented
79C2×C8×C23C2311yescharacteristic
80C2×C8×C23C2311yescharacteristic
81C4⋊C4×C23—21no—
82C4⋊C4×C23—21no—
83C4⋊C4×C23C2311yescharacteristic
84C4⋊C4×C23C2311yescharacteristic
85C42×C23—21no—
86C42×C23—21no—
87C42×C23C2311yescharacteristic
88#67275C2×C414yescomplemented
89#67274C2×C414yescomplemented
90(C2×D23)⋊C4—21no—
91(C2×D23)⋊C4—21no—
92(C2×D23)⋊C4—21no—
93C4⋊Dic23—21no—
94C4⋊Dic23—21no—
95C4⋊Dic23C2311yescharacteristic
96C4⋊Dic23C2311yescharacteristic
97Dic23⋊C4—21no—
98Dic23⋊C4—21no—
99Dic23⋊C4—21no—
100C4×Dic23—21no—
101C4×Dic23—21no—
102C4×Dic23—21no—
103C4×Dic23—21no—
104C4×Dic23—21no—
105C4×Dic23D411yescharacteristic
106C4×Dic23D411yescharacteristic
107C4×Dic23C2311yescharacteristic
108C2×C23⋊C8C2311yescharacteristic
109C2×C23⋊C8C2311yescharacteristic
110#67263C2×C414yescomplemented
111#67262—22no—
112#67262C2×C414yescomplemented
113C22×D23—21no—
114C22×D23C2×D411yescharacteristic
115Q8×C23—21no—
116Q8×C23—21no—
117Q8×C23C22×C412yes—
118Q8×C23C22×C412yes—
119C2×C4×C23—21no—
120C2×C4×C23—21no—
121C2×C4×C23—21no—
122C2×C4×C23—21no—
123C2×C4×C23C2×D411yescharacteristic
124C2×C4×C23C2×D411yescharacteristic
125C2×C4×C23C2411yescharacteristic
126C2×Dic23—21no—
127C2×Dic23—21no—
128C2×Dic23—21no—
129C2×Dic23C2×D411yescharacteristic
130C2×Dic23C2×D411yescharacteristic
131C2×Dic23C2×D411yescharacteristic
132D92—24no—
133D92—21no—
134D92C22×C412yes—
135C4×D23—24no—
136C4×D23—22no—
137C4×D23—24no—
138C4×D23—41no—
139C4×D23—42no—
140C4×D23—42no—
141C4×D23—42no—
142C4×D23C22×C412yes—
143C4×D23#4112yes—
144Dic46—21no—
145Dic46—24no—
146Dic46C22×C412yes—
147C8×C23—21no—
148C8×C23C22×C412yes—
149C23⋊C8—21no—
150C23⋊C8C22×C412yes—
151C4×#137—231nomaximal, Sylow
152C22×C23C22×D411yescharacteristic
153C2×D23—21no—
154C2×D23—21no—
155C2×D23—22no—
156C2×D23—41no—
157C2×D23—41no—
158C2×D23C4×D412yes—
159C4×C23—22no—
160C4×C23—22no—
161C4×C23—21no—
162C4×C23—41no—
163C4×C23—41no—
164C4×C23#13712yescomplemented
165C4×C23C23×C411yescharacteristic
166C4×C23C2×#4111yescharacteristic
167Dic23—22no—
168Dic23—21no—
169Dic23—21no—
170Dic23—41no—
171Dic23—41no—
172Dic23C4×D412yes—
173C2×#137—231no—
174C4×#41—231no—
175C2×C4×Q8—231no—
176#441—231no—
177#441—231no—
178#440—231no—
179#440—231no—
180C4×Q16—231no—
181C4×Q16D2311yescharacteristic, complemented
182C4×SD16—231no—
183C4×SD16—231no—
184#428—231no—
185#419—231no—
186#417—231no—
187C4×M16—231no—
188C2×C23C2×C4×D411yescharacteristic
189C2×C23C2×#13711yescharacteristic
190C2×C23#57511yescharacteristic
191D23—22no—
192D23—42no—
193C2×#41—231no—
194C22×Q8—231no—
195#137—238no—
196C2×Q16—231no—
197C2×Q16C2×D2311yescharacteristic
198C2×SD16—231no—
199C2×SD16—231no—
200C2×M16—231no—
201C2×M16—231no—
202C4×Q8—231no—
203C4×Q8—231no—
204C4×Q8—231no—
205C4×Q8—231no—
206C4×Q8—461no—
207C4×Q8—461no—
208C4×Q8C2×D2311yescharacteristic
209C4×Q8C2×D2311yescharacteristic
210C4×D4—231no—
211C4×D4—231no—
212C4×D4—461no—
213C4×D4—461no—
214#117—231no—
215#117—461no—
216C2×C4⋊C4—231no—
217C2×C4⋊C4—461no—
218C2×C42—231no—
219C2×C42—461no—
220C2×C42—461no—
221#107—231no—
222#107C2×D2311yescharacteristic
223#106—231no—
224#106—231no—
225#103—231no—
226#103—231no—
227#103—231no—
228#103—231no—
229#103C2×D2311yescharacteristic
230#103C2×D2311yescharacteristic
231#102—231no—
232#102—231no—
233#97—231no—
234#97—231no—
235C4×C8—231no—
236C4×C8C2×D2311yescharacteristic
237C23C4×#13711yescharacteristic, complemented, Sylow
238#41—234no—
239#41—462no—
240C2×Q8—234no—
241C2×Q8—231no—
242C2×Q8—461no—
243C2×Q8—462no—
244C2×Q8C22×D2311yescharacteristic
245C2×Q8C22×D2311yescharacteristic
246C2×D4—231no—
247C2×D4—461no—
248C22×C4—231no—
249C22×C4—231no—
250C22×C4—231no—
251C22×C4—461no—
252C22×C4—461no—
253C22×C4—461no—
254C22×C4—461no—
255C22×C4—461no—
256Q16—234no—
257Q16C4×D2314yescomplemented
258SD16—234no—
259SD16—234no—
260M16—234no—
261M16—462no—
262C2×C8—231no—
263C2×C8—231no—
264C2×C8C22×D2311yescharacteristic
265C2×C8C22×D2311yescharacteristic
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—231no—
269C4⋊C4—231no—
270C4⋊C4—461no—
271C4⋊C4—461no—
272C4⋊C4—461no—
273C4⋊C4—461no—
274C4⋊C4—461no—
275C4⋊C4C22×D2311yescharacteristic
276C4⋊C4C22×D2311yescharacteristic
277C22⋊C4—461no—
278C22⋊C4—461no—
279C22⋊C4—461no—
280C42—21no—
281C42—21no—
282C42—231no—
283C42—231no—
284C42—231no—
285C42—461no—
286C42—461no—
287C42—461no—
288C42—461no—
289C42—461no—
290C42C22×D2311yescharacteristic
291C23—231no—
292C23—461no—
293Q8—21no—
294Q8—21no—
295Q8—232no—
296Q8—464no—
297Q8—461no—
298Q8C2×C4×D2312yes—
299Q8C2×C4×D2312yes—
300D4—232no—
301D4—464no—
302D4—461no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—231no—
308C2×C4—232no—
309C2×C4—232no—
310C2×C4—231no—
311C2×C4—231no—
312C2×C4—464no—
313C2×C4—464no—
314C2×C4—461no—
315C2×C4—462no—
316C2×C4—461no—
317C2×C4—461no—
318C2×C4—921no—
319C2×C4—922no—
320C2×C4—922no—
321C2×C4—922no—
322C2×C4D4×D2311yescharacteristic
323C2×C4D4×D2311yescharacteristic
324C2×C4C23×D2311yescharacteristic
325C8—21no—
326C8—232no—
327C8—461no—
328C8C2×C4×D2312yes—
329C22—232no—
330C22—461no—
331C22—461no—
332C22—462no—
333C22—921no—
334C22—921no—
335C22C2×D4×D2311yescharacteristic
336C4—22no—
337C4—22no—
338C4—21no—
339C4—41no—
340C4—41no—
341C4—232no—
342C4—462no—
343C4—461no—
344C4—461no—
345C4—921no—
346C4—921no—
347C4#1062508912yesdirect product factor
348C4C22×C4×D2311yescharacteristic
349C4#41×D2311yescharacteristic
350C2—462no—
351C2—922no—
352C2C4×D4×D2311yescharacteristic
353C2C2×#1062508911yescharacteristic
354C2#1309321411yescharacteristic
subgroupG/H
centerC2×C4D4×D23
commutatorC4×C23C23×C4
FrattiniC2×C4C23×D23
FittingC4×Q16×C23C2
socleC22×C23C22×D4
prime radicalC2×#67292C22
cosocleC2×C4×C23C24
hypercenterC4×Q16D23
hypocenterC23C4×#137
LCSG ▷ C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
3. C4×Q8×D23C2semidirect
4. #13092524C2semidirect
5. #13092521C2semidirect
6. #13092520C2semidirect
7. #13092516C2semidirect
8. C4×#67275C2semidirect
9. C4×#67263C2semidirect
10. C4×#67274C2semidirect
11. #13092458C2semidirect
12. #13092424C2semidirect
14. C4×#67262C2semidirect
15. C4×Q16×C23C2semidirect
25. #10625089C4direct (N × H)
65. Q8×D23C2×C4semidirect
78. Q16×C23C2×C4semidirect
88. #67275C2×C4semidirect
89. #67274C2×C4semidirect
110. #67263C2×C4semidirect
112. #67262C2×C4semidirect
164. C4×C23#137semidirect
181. C4×Q16D23semidirect
237. C23C4×#137semidirect
257. Q16C4×D23semidirect
347. C4#10625089direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106250892
C4×#672922
C4×Q8×D232
#130925242
#130925212
#130925202
#130925162
C4×#672752
C4×#672632
C4×#672742
#130924582
#130924242
#130924172
C4×#672622
C4×Q16×C232
C4×#13723