Finite Group Databasebeta

← C2×#13092586 #15682722

Subgroups — C2×#13092586 #15682722

Order 2944.

844 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 844 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10625160C211yesmaximal, characteristic, complemented
2C2×#10625079C211yesmaximal, characteristic, complemented
3C2×#10625120C211yesmaximal, characteristic, complemented
4C2×#10625045C211yesmaximal, characteristic, complemented
5#13092586C218yesmaximal, direct product factor
6C2×#10624987C211yesmaximal, characteristic, complemented
7C2×#10625005C211yesmaximal, characteristic, complemented
8C2×C23×#104C211yesmaximal, characteristic, complemented
9C2×#41×C23C2211yescharacteristic
10#10625160—22no—
11#10625160—22no—
12#10625160—22no—
13#10625160C2214yescomplemented
14C2×#67292—21no—
15C2×D4×D23—22no—
16C2×D4×D23—21no—
17C2×#67288—21no—
18C2×#67288C2211yescharacteristic
19C22×D92—21no—
20C22×D92—22no—
21C22×D92C2211yescharacteristic
22C22×D92C2211yescharacteristic, complemented
23C2×M16×C23C2211yescharacteristic, complemented
24C2×C42×C23C2211yescharacteristic, complemented
25#10625120—22no—
26#10625120C2214yescomplemented
27C2×#67274—21no—
28C2×#67272—21no—
29C2×#67267C2211yescharacteristic, complemented
30#10625079—22no—
31#10625079C2214yescomplemented
32C2×D184—21no—
33C2×#67263—21no—
34#10625045—22no—
35#10625045C2214yescomplemented
36C23×#104C2214yescomplemented
37#10625005C2214yescomplemented
38#10624987C2214yescomplemented
39C23×D23—22no—
40C23×D23—21no—
41C23×D23D412yes—
42#41×C23—21no—
43#41×C23—21no—
44#41×C23D412yescomplemented
45#41×C23C2312yes—
46C2×Q8×C23D411yescharacteristic, complemented
47C2×D4×C23—21no—
48C2×D4×C23D411yescharacteristic, complemented
49C22×C4×C23—21no—
50C22×C4×C23—21no—
51C22×C4×C23C2311yescharacteristic
52C2×C22⋊D23—22no—
53C2×C22⋊D23—21no—
54#67292—24no—
55#67292—24no—
56D4×D23—28no—
57D4×D23—24no—
58D4×D23—28no—
59D4×D23—24no—
60#67288—24no—
61#67288—21no—
62#67288—21no—
63#67288—24no—
64#67288D412yescomplemented
65#67288C2312yes—
66C2×D92—22no—
67C2×D92—24no—
68C2×D92—21no—
69C2×D92—21no—
70C2×D92—21no—
71C2×D92—21no—
72C2×D92—24no—
73C2×D92—21no—
74C2×D92—21no—
75C2×D92—21no—
76C2×D92—21no—
77C2×D92—28no—
78C2×D92—21no—
79C2×D92—48no—
80C2×D92D412yes—
81C2×D92D411yescharacteristic, complemented
82C2×D92C2312yes—
83C2×D92C2312yescomplemented
84C2×C4×D23—22no—
85C2×C4×D23—21no—
86C2×Dic46D411yescharacteristic, complemented
87M16×C23—21no—
88M16×C23C2312yescomplemented
89C2×C8×C23—21no—
90C42×C23—21no—
91C42×C23C2312yescomplemented
92#67274—24no—
93#67272—24no—
94#67267—21no—
95#67267C2312yescomplemented
96C2×C23⋊C8—21no—
97D184—24no—
98#67263—24no—
99C23×C23—21no—
100C23×C23C2×D411yescharacteristic
101C22×D23—22no—
102C22×D23—21no—
103C22×D23—28no—
104C22×D23—22no—
105C22×D23—22no—
106C22×D23—44no—
107C22×D23—44no—
108C22×D23—41no—
109C22×D23—41no—
110C22×D23—84no—
111C22×D23C2×D414yes—
112Q8×C23—21no—
113Q8×C23C2×D412yescomplemented
114D4×C23—22no—
115D4×C23—22no—
116D4×C23—21no—
117D4×C23C2×D412yescomplemented
118C2×C4×C23—24no—
119C2×C4×C23—21no—
120C2×C4×C23—22no—
121C2×C4×C23—22no—
122C2×C4×C23—22no—
123C2×C4×C23C2×D411yescharacteristic
124C2×C4×C23C2×D411yescharacteristic
125C2×C4×C23C2×D411yescharacteristic
126C2×C4×C23C2×D411yescharacteristic
127C2×C4×C23C2×D411yescharacteristic
128C2×C4×C23C2411yescharacteristic
129C22⋊D23—28no—
130C22⋊D23—22no—
131C22⋊D23—22no—
132C2×Dic23—21no—
133D92—28no—
134D92—22no—
135D92—21no—
136D92—22no—
137D92—22no—
138D92—22no—
139D92—22no—
140D92—22no—
141D92—416no—
142D92—41no—
143D92—41no—
144D92C2×D412yescomplemented
145C4×D23—28no—
146C4×D23—22no—
147C4×D23—22no—
148Dic46—21no—
149Dic46C2×D412yescomplemented
150C8×C23—22no—
151C23⋊C8—22no—
152C2×#453—231nomaximal, Sylow
153C22×C23—22no—
154C22×C23—22no—
155C22×C23—42no—
156C22×C23#12011yescharacteristic
157C22×C23#12011yescharacteristic
158C22×C23C22×D411yescharacteristic
159C2×D23—24no—
160C2×D23—22no—
161C2×D23—44no—
162C2×D23—42no—
163C2×D23—44no—
164C2×D23—44no—
165C2×D23—42no—
166C2×D23—82no—
167C2×D23—88no—
168C2×D23—82no—
169C2×D23—82no—
170C4×C23—24no—
171C4×C23—22no—
172C4×C23#12011yescharacteristic
173C4×C23#12011yescharacteristic
174C4×C23C22×D411yescharacteristic
175C4×C23C22×D411yescharacteristic
176Dic23—22no—
177C2×H(5,𝔽2)—231no—
178C2×AGL(1,ℤ/8)—231no—
179C2×AGL(1,ℤ/8)—231no—
180C2×#127—231no—
181#453—238no—
182C2×#104—231no—
183C2×#104D2311yescharacteristic, complemented
184C2×#100—231no—
185C2×C23—21no—
186C2×C23—21no—
187C2×C23—42no—
188C2×C23#45312yescomplemented
189C2×C23C2×#12011yescharacteristic
190D23—44no—
191D23—42no—
192D23—82no—
193H(5,𝔽2)—234no—
194H(5,𝔽2)—462no—
195H(5,𝔽2)—462no—
196H(5,𝔽2)—462no—
197C2×#41—231no—
198C2×#41—461no—
199C2×#41—461no—
200C2×#41C2×D2311yescharacteristic
201C22×D4—231no—
202C22×D4—231no—
203C22×D4—461no—
204C22×D4—462no—
205C22×D4—462no—
206C22×D4—461no—
207AGL(1,ℤ/8)—234no—
208AGL(1,ℤ/8)—234no—
209AGL(1,ℤ/8)—462no—
210AGL(1,ℤ/8)—462no—
211C2×SD16—461no—
212C2×SD16—461no—
213C2×D8—461no—
214C2×D8—461no—
215C2×M16—231no—
216C2×M16C2×D2311yescharacteristic, complemented
217#127—234no—
218#127—462no—
219C2×C42C2×D2311yescharacteristic, complemented
220#104—234no—
221#104C2×D2314yescomplemented
222#100—234no—
223C23C2×#45311yescharacteristic, complemented, Sylow
224C24—232no—
225C24—462no—
226C24—461no—
227#41—21no—
228#41—21no—
229#41—232no—
230#41—232no—
231#41—464no—
232#41—464no—
233#41—464no—
234#41—464no—
235#41—461no—
236#41—461no—
237#41D9212yescomplemented
238#41C22×D2312yes—
239C2×Q8—231no—
240C2×Q8D9211yescharacteristic, complemented
241C2×D4—21no—
242C2×D4—231no—
243C2×D4—232no—
244C2×D4—232no—
245C2×D4—232no—
246C2×D4—464no—
247C2×D4—462no—
248C2×D4—464no—
249C2×D4—468no—
250C2×D4—468no—
251C2×D4—468no—
252C2×D4—464no—
253C2×D4—462no—
254C2×D4—461no—
255C2×D4—464no—
256C2×D4—461no—
257C2×D4—461no—
258C2×D4—461no—
259C2×D4—461no—
260C2×D4—461no—
261C2×D4—461no—
262C2×D4—461no—
263C2×D4—461no—
264C2×D4—461no—
265C2×D4—928no—
266C2×D4D9211yescharacteristic, complemented
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—462no—
270C22×C4—461no—
271C22×C4C22×D2311yescharacteristic
272SD16—464no—
273SD16—464no—
274D8—464no—
275D8—464no—
276M16—21no—
277M16—232no—
278M16—461no—
279M16C22×D2312yescomplemented
280C2×C8—21no—
281C2×C8—461no—
282C42—21no—
283C42C22×D2312yescomplemented
284C23—21no—
285C23—234no—
286C23—468no—
287C23—461no—
288C23—462no—
289C23—462no—
290C23—462no—
291C23—924no—
292C23—924no—
293C23—921no—
294C23—921no—
295C23—1844no—
296C23D4×D2311yescharacteristic
297Q8—21no—
298Q8—232no—
299Q8—461no—
300Q8C2×D9212yescomplemented
301D4—22no—
302D4—22no—
303D4—21no—
304D4—232no—
305D4—468no—
306D4—468no—
307D4—462no—
308D4—462no—
309D4—461no—
310D4—462no—
311D4—462no—
312D4—462no—
313D4—462no—
314D4—462no—
315D4—462no—
316D4—9216no—
317D4—921no—
318D4—921no—
319D4C2×D9212yescomplemented
320C2×C4—24no—
321C2×C4—21no—
322C2×C4—22no—
323C2×C4—22no—
324C2×C4—22no—
325C2×C4—468no—
326C2×C4—461no—
327C2×C4—462no—
328C2×C4—462no—
329C2×C4C2×D9211yescharacteristic
330C2×C4C2×D9211yescharacteristic
331C2×C4D4×D2311yescharacteristic
332C2×C4D4×D2311yescharacteristic
333C2×C4D4×D2311yescharacteristic
334C2×C4C23×D2311yescharacteristic
335C8—22no—
336C8—462no—
337C22—22no—
338C22—22no—
339C22—42no—
340C22—462no—
341C22—464no—
342C22—924no—
343C22—924no—
344C22—924no—
345C22—922no—
346C22—922no—
347C22—1842no—
348C22—1842no—
349C22—1848no—
350C22—1842no—
351C22#1062505311yescharacteristic
352C22#1062505311yescharacteristic
353C22C2×D4×D2311yescharacteristic
354C4—24no—
355C4—22no—
356C4—462no—
357C4#1062505311yescharacteristic
358C4#1062505311yescharacteristic
359C4C22×D9211yescharacteristic
360C4C2×D4×D2311yescharacteristic
361C2—21no—
362C2—21no—
363C2—42no—
364C2—924no—
365C2—922no—
366C2—1842no—
367C2#1309258612yesdirect product factor
368C2C2×#1062505311yescharacteristic
subgroupG/H
centerC22#10625053
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC2×C23×#104C2
socleC22×C23#120
hypercenterC2×#104D23
hypocenterC23C2×#453
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
1. C2×#10625160C2semidirect
2. C2×#10625079C2semidirect
3. C2×#10625120C2semidirect
4. C2×#10625045C2semidirect
5. #13092586C2direct (N × H)
6. C2×#10624987C2semidirect
7. C2×#10625005C2semidirect
8. C2×C23×#104C2semidirect
13. #10625160C22semidirect
22. C22×D92C22semidirect
23. C2×M16×C23C22semidirect
24. C2×C42×C23C22semidirect
26. #10625120C22semidirect
29. C2×#67267C22semidirect
31. #10625079C22semidirect
35. #10625045C22semidirect
36. C23×#104C22semidirect
37. #10625005C22semidirect
38. #10624987C22semidirect
44. #41×C23D4semidirect
46. C2×Q8×C23D4semidirect
48. C2×D4×C23D4semidirect
64. #67288D4semidirect
81. C2×D92D4semidirect
83. C2×D92C23semidirect
86. C2×Dic46D4semidirect
88. M16×C23C23semidirect
91. C42×C23C23semidirect
95. #67267C23semidirect
113. Q8×C23C2×D4semidirect
117. D4×C23C2×D4semidirect
144. D92C2×D4semidirect
149. Dic46C2×D4semidirect
183. C2×#104D23semidirect
188. C2×C23#453semidirect
216. C2×M16C2×D23semidirect
219. C2×C42C2×D23semidirect
221. #104C2×D23semidirect
223. C23C2×#453semidirect
237. #41D92semidirect
240. C2×Q8D92semidirect
266. C2×D4D92semidirect
279. M16C22×D23semidirect
283. C42C22×D23semidirect
300. Q8C2×D92semidirect
319. D4C2×D92semidirect
367. C2#13092586direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106251602
C2×#106250792
C2×#106251202
C2×#106250452
#130925862
C2×#106249872
C2×#106250052
C2×C23×#1042
C2×#45323