Finite Group Databasebeta

← #15682762

Subgroups — #15682762

Order 2944.

698 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 698 conjugacy classes of subgroups — too many to draw. Only its 133 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
12−1+4×D23C211yesmaximal, characteristic, complemented
2#13093216C212yesmaximal, complemented
3#13092992C211yesmaximal, characteristic, complemented
4#13092599C211yesmaximal, characteristic, complemented
5#13092598C212yesmaximal, complemented
6#13092592C211yesmaximal, characteristic, complemented
7#13092591C212yesmaximal, complemented
8#13092590C211yesmaximal, characteristic, complemented
9#13092432C212yesmaximal, complemented
10#101×D23C211yesmaximal, characteristic, complemented
11C23×#456C211yesmaximal, characteristic, complemented
12C23×2−1+4C2211yescharacteristic
13#10625161—22no—
14#10625161—22no—
15#10625161C2212yes—
16#41×D23—22no—
17#41×D23—22no—
18#41×D23C2212yes—
19#10625158—22no—
20#10625158C2211yescharacteristic
21C2×#67292C2211yescharacteristic
22C2×Q8×D23—22no—
23C2×Q8×D23C2211yescharacteristic
24C23×#137C2212yescomplemented
25C23×C4⋊Q8C2211yescharacteristic, complemented
26#10625120C2212yescomplemented
27#10625118C2211yescharacteristic, complemented
28#10625115C2211yescharacteristic, complemented
29#10625113C2212yescomplemented
30#10625090—22no—
31#10625089—22no—
32#10625087—22no—
33#10625085—22no—
34#10625079C2212yescomplemented
35M16×D23C2212yes—
36#10625067—22no—
37#10625065—22no—
38#10625046C2211yescharacteristic, complemented
39#10625043C2211yescharacteristic
40C23×#104C2212yescomplemented
41C23×#101C2211yescharacteristic, complemented
42#10625019C2212yescomplemented
43#10625018C2211yescharacteristic, complemented
44#10625007C2212yescomplemented
45#10625006C2212yescomplemented
46#10624987C2212yescomplemented
47#41×C23—22no—
48#41×C23—22no—
49#41×C23C2312yes—
50C2×Q8×C23—22no—
51C2×Q8×C23C2311yescharacteristic
52C2×Q8×C23C2311yescharacteristic
53#67292—22no—
54#67292—22no—
55#67292—22no—
56#67292—22no—
57#67292D412yes—
58Q8×D23—22no—
59Q8×D23—24no—
60Q8×D23—22no—
61Q8×D23—22no—
62Q8×D23—22no—
63Q8×D23—22no—
64Q8×D23D412yes—
65#67290—22no—
66#67290—24no—
67#67290—22no—
68#67290—24no—
69#67290—22no—
70#67290D412yes—
71D4×D23—22no—
72D4×D23—22no—
73D4×D23D412yes—
74#67288—24no—
75#67288—24no—
76#67288—22no—
77#67288—22no—
78#67288—22no—
79#67288C2312yes—
80C2×D92—21no—
81C2×D92C2311yescharacteristic
82C2×C4×D23—24no—
83C2×C4×D23—22no—
84C2×C4×D23—21no—
85C2×C4×D23D412yes—
86C2×C4×D23C2311yescharacteristic
87C2×Dic46—24no—
88C2×Dic46—22no—
89C2×Dic46D412yes—
90C2×Dic46C2311yescharacteristic
91Q16×C23—22no—
92SD16×C23—22no—
93M16×C23C2312yes—
94C4⋊C4×C23—22no—
95C42×C23C2311yescharacteristic
96#67275—22no—
97#67274—22no—
98#67274—22no—
99#67272—22no—
100(C2×D23)⋊C4—21no—
101(C2×D23)⋊C4—22no—
102(C2×D23)⋊C4—22no—
103Dic23⋊C4—21no—
104Dic23⋊C4—22no—
105C4×Dic23C2311yescharacteristic
106#67267C2312yes—
107D184—22no—
108#67263—22no—
109#67262—22no—
110C8×D23—22no—
111C22×D23—22no—
112C22×D23—21no—
113C22×D23C2×D411yescharacteristic
114Q8×C23—22no—
115Q8×C23—22no—
116Q8×C23—22no—
117Q8×C23C2×D412yes—
118D4×C23—22no—
119D4×C23—22no—
120D4×C23C2×D412yes—
121C2×C4×C23—24no—
122C2×C4×C23—22no—
123C2×C4×C23—21no—
124C2×C4×C23—21no—
125C2×C4×C23C2×D412yes—
126C2×C4×C23C2411yescharacteristic
127C22⋊D23—24no—
128C22⋊D23—22no—
129C22⋊D23—22no—
130C22⋊D23—22no—
131C2×Dic23—24no—
132C2×Dic23—22no—
133C2×Dic23—21no—
134C2×Dic23C2×D412yes—
135C2×Dic23C2×D411yescharacteristic
136D92—22no—
137D92—22no—
138D92—22no—
139D92—41no—
140D92—41no—
141D92C2×D412yes—
142C4×D23—24no—
143C4×D23—24no—
144C4×D23—22no—
145C4×D23—22no—
146C4×D23—22no—
147C4×D23—22no—
148C4×D23—22no—
149C4×D23—42no—
150C4×D23C2×D412yes—
151C4×D23C2×D412yes—
152Dic46—24no—
153Dic46—22no—
154Dic46—22no—
155Dic46—22no—
156Dic46—24no—
157Dic46C2×D412yes—
158C8×C23—22no—
159C23⋊C8—22no—
160#3020—231nomaximal, Sylow
161C22×C23—22no—
162C22×C23C22×D411yescharacteristic
163C2×D23—22no—
164C2×D23—41no—
165C2×D23—44no—
166C2×D23—42no—
167C2×D23—41no—
168C2×D23#12011yescharacteristic
169C2×D23#12011yescharacteristic
170C4×C23—22no—
171C4×C23—22no—
172C4×C23—41no—
173C4×C23—41no—
174C4×C23C22×D412yes—
175Dic23—22no—
176Dic23—22no—
177Dic23—41no—
178Dic23#12012yes—
179C2×2−1+4—231no—
180#575—232no—
181#536—231no—
182#456—232no—
183#456—231no—
184#456D2311yescharacteristic, complemented
185#454—231no—
186#454—232no—
187#454—231no—
188#421—232no—
189C2×#101—231no—
190C2×C23—21no—
191C2×C23—42no—
192C2×C23C2×#12011yescharacteristic
193D23—21no—
194D23—21no—
195D23—42no—
196D23—81no—
1972−1+4—232no—
1982−1+4—231no—
1992−1+4—462no—
2002−1+4—462no—
2012−1+4—462no—
2022−1+4C2×D2311yescharacteristic
203C2×#41—232no—
204C2×#41—231no—
205C2×#41—462no—
206C2×#41—462no—
207C22×Q8—231no—
208C22×Q8—462no—
209#137—232no—
210#137—462no—
211#137C2×D2312yescomplemented
212AGL(1,ℤ/8)—232no—
213AGL(1,ℤ/8)—232no—
214AGL(1,ℤ/8)—462no—
215#135—462no—
216#135—462no—
217C2×M16—232no—
218C4⋊Q8—231no—
219C4⋊Q8C2×D2311yescharacteristic, complemented
220#124—231no—
221#124—231no—
222#123—462no—
223C22⋊Q8—462no—
224#117—231no—
225#104—232no—
226#104—232no—
227#104—232no—
228#104C2×D2312yescomplemented
229#101—231no—
230#101—232no—
231#101C2×D2311yescharacteristic, complemented
232C23#302011yescharacteristic, complemented, Sylow
233#41—22no—
234#41—22no—
235#41—232no—
236#41—232no—
237#41—232no—
238#41—462no—
239#41—462no—
240#41—464no—
241#41—464no—
242#41—462no—
243#41—464no—
244#41—462no—
245#41—462no—
246#41—462no—
247#41—464no—
248#41—462no—
249#41—462no—
250#41—462no—
251#41—462no—
252#41C22×D2312yes—
253C2×Q8—22no—
254C2×Q8—232no—
255C2×Q8—231no—
256C2×Q8—232no—
257C2×Q8—462no—
258C2×Q8—464no—
259C2×Q8—462no—
260C2×Q8—462no—
261C2×Q8—462no—
262C2×Q8—462no—
263C2×Q8—464no—
264C2×Q8—462no—
265C2×Q8C22×D2311yescharacteristic
266C2×Q8C22×D2311yescharacteristic
267C2×D4—232no—
268C2×D4—231no—
269C2×D4—461no—
270C2×D4—462no—
271C2×D4—462no—
272C22×C4—231no—
273C22×C4—232no—
274C22×C4—462no—
275C22×C4—461no—
276C22×C4—464no—
277Q16—22no—
278Q16—462no—
279SD16—22no—
280SD16—462no—
281SD16—462no—
282SD16—462no—
283D8—462no—
284D8—462no—
285M16—232no—
286M16—462no—
287M16C22×D2312yes—
288C2×C8—462no—
289C4⋊C4—22no—
290C4⋊C4—461no—
291C4⋊C4—462no—
292C22⋊C4—462no—
293C22⋊C4—461no—
294C22⋊C4—462no—
295C42—231no—
296C42C22×D2311yescharacteristic
297C23—231no—
298C23—462no—
299C23—461no—
300Q8—22no—
301Q8—22no—
302Q8—22no—
303Q8—232no—
304Q8—462no—
305Q8—464no—
306Q8—464no—
307Q8—462no—
308Q8—462no—
309Q8D4×D2312yes—
310D4—22no—
311D4—22no—
312D4—232no—
313D4—462no—
314D4—462no—
315D4—462no—
316D4—462no—
317D4—464no—
318D4—462no—
319D4—462no—
320D4—921no—
321D4—921no—
322D4D4×D2312yes—
323C2×C4—24no—
324C2×C4—22no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—231no—
328C2×C4—232no—
329C2×C4—232no—
330C2×C4—232no—
331C2×C4—462no—
332C2×C4—462no—
333C2×C4—462no—
334C2×C4—462no—
335C2×C4—464no—
336C2×C4—464no—
337C2×C4—462no—
338C2×C4—464no—
339C2×C4—462no—
340C2×C4—461no—
341C2×C4—922no—
342C2×C4D4×D2312yes—
343C2×C4C23×D2311yescharacteristic
344C8—22no—
345C8—462no—
346C22—22no—
347C22—231no—
348C22—231no—
349C22—462no—
350C22—921no—
351C22—922no—
352C22—924no—
353C22—921no—
354C22C2×D4×D2311yescharacteristic
355C4—22no—
356C4—22no—
357C4—41no—
358C4—41no—
359C4—232no—
360C4—462no—
361C4—462no—
362C4—921no—
363C4C2×D4×D2312yes—
364C2—21no—
365C2—42no—
366C2—461no—
367C2—461no—
368C2—922no—
369C2—1841no—
370C2#120×D2311yescharacteristic
subgroupG/H
centerC2#120×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#456C2
socleC2×C23C2×#120
hypercenter#456D23
hypocenterC23#3020
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C2×C4 ◁ #456

Complements

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

NH ≅ G/Ntype
1. 2−1+4×D23C2semidirect
2. #13093216C2semidirect
3. #13092992C2semidirect
4. #13092599C2semidirect
5. #13092598C2semidirect
6. #13092592C2semidirect
7. #13092591C2semidirect
8. #13092590C2semidirect
9. #13092432C2semidirect
10. #101×D23C2semidirect
11. C23×#456C2semidirect
24. C23×#137C22semidirect
25. C23×C4⋊Q8C22semidirect
26. #10625120C22semidirect
27. #10625118C22semidirect
28. #10625115C22semidirect
29. #10625113C22semidirect
34. #10625079C22semidirect
38. #10625046C22semidirect
40. C23×#104C22semidirect
41. C23×#101C22semidirect
42. #10625019C22semidirect
43. #10625018C22semidirect
44. #10625007C22semidirect
45. #10625006C22semidirect
46. #10624987C22semidirect
184. #456D23semidirect
211. #137C2×D23semidirect
219. C4⋊Q8C2×D23semidirect
228. #104C2×D23semidirect
231. #101C2×D23semidirect
232. C23#3020semidirect

Maximal subgroups

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

subgroupindex
2−1+4×D232
#130932162
#130929922
#130925992
#130925982
#130925922
#130925912
#130925902
#130924322
#101×D232
C23×#4562
#302023