Finite Group Databasebeta

← #15682770

Subgroups — #15682770

Order 2944.

736 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 736 conjugacy classes of subgroups — too many to draw. Only its 145 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
1#13093253C211yesmaximal, characteristic, complemented
2C2×#10625079C211yesmaximal, characteristic, complemented
3C2×#10625120C211yesmaximal, characteristic, complemented
4#13092986C211yesmaximal, characteristic, complemented
5#13092591C214yesmaximal, complemented
6#13092586C214yesmaximal, complemented
7#13092435C211yesmaximal, characteristic, complemented
8#13092399C211yesmaximal, characteristic, complemented
9C23×#421C211yesmaximal, characteristic, complemented
10C2×#41×C23C2211yescharacteristic
11#10625161—21no—
12#10625161C2212yescomplemented
13#10625160—21no—
14#10625160C2212yescomplemented
15#41×D23—22no—
16#41×D23—22no—
17#10625158—21no—
18#10625155—21no—
19#10625155—22no—
20C2×#67288—22no—
21C2×#67288C2211yescharacteristic
22C2×#67288C2211yescharacteristic
23C22×D92C2211yescharacteristic, complemented
24C2×M16×C23C2211yescharacteristic, complemented
25C23×#117C2211yescharacteristic, complemented
26#10625120—22no—
27#10625120C2214yescomplemented
28C2×#67274—21no—
29C2×#67272—21no—
30C2×#67267C2211yescharacteristic, complemented
31#10625079—22no—
32#10625079C2214yescomplemented
33C2×D184—21no—
34C2×#67263—21no—
35#10625066—22no—
36#10625053—22no—
37#10625046C2212yescomplemented
38#10625045C2212yescomplemented
39C23×#104C2214yescomplemented
40#10625006C2212yescomplemented
41#10625005C2212yescomplemented
42#10624987C2214yescomplemented
43C23×D23—21no—
44#41×C23—21no—
45#41×C23—21no—
46#41×C23D412yescomplemented
47#41×C23C2312yes—
48C2×Q8×C23D411yescharacteristic, complemented
49C2×D4×C23—21no—
50C2×D4×C23D411yescharacteristic, complemented
51C22×C4×C23—21no—
52C22×C4×C23C2311yescharacteristic
53C2×C22⋊D23—24no—
54C2×C22⋊D23—21no—
55C2×C22⋊D23D412yes—
56#67292—22no—
57#67292—22no—
58Q8×D23—22no—
59Q8×D23—22no—
60#67290—24no—
61#67290—22no—
62#67290—22no—
63#67290—24no—
64D4×D23—24no—
65D4×D23—22no—
66D4×D23—24no—
67D4×D23—22no—
68#67288—24no—
69#67288—24no—
70#67288—21no—
71#67288—21no—
72#67288—21no—
73#67288—21no—
74#67288—21no—
75#67288—21no—
76#67288—22no—
77#67288—22no—
78#67288D412yescomplemented
79#67288C2312yes—
80C2×D92—22no—
81C2×D92—21no—
82C2×D92—21no—
83C2×D92—21no—
84C2×D92—21no—
85C2×D92—21no—
86C2×D92—24no—
87C2×D92D411yescharacteristic, complemented
88C2×D92C2312yes—
89C2×D92C2311yescharacteristic
90C2×C4×D23—24no—
91C2×C4×D23—21no—
92C2×C4×D23D412yes—
93C2×Dic46—22no—
94C2×Dic46D411yescharacteristic, complemented
95C2×Dic46C2311yescharacteristic
96M16×C23—21no—
97M16×C23C2312yes—
98C2×C8×C23—21no—
99C4⋊C4×C23—21no—
100C22⋊C4×C23—21no—
101C42×C23C2312yes—
102#67274—24no—
103#67272—24no—
104(C2×D23)⋊C4—24no—
105#67267—21no—
106#67267C2312yes—
107C2×C23⋊C8—21no—
108D184—24no—
109#67263—24no—
110C23×C23—21no—
111C23×C23C2×D411yescharacteristic
112C22×D23—24no—
113C22×D23—21no—
114C22×D23—22no—
115C22×D23—41no—
116C22×D23—41no—
117C22×D23—82no—
118C22×D23C2×D412yes—
119Q8×C23—21no—
120Q8×C23C2×D412yes—
121D4×C23—22no—
122D4×C23—22no—
123D4×C23—21no—
124D4×C23C2×D412yes—
125C2×C4×C23—21no—
126C2×C4×C23—22no—
127C2×C4×C23—22no—
128C2×C4×C23—22no—
129C2×C4×C23C2×D411yescharacteristic
130C2×C4×C23C2×D411yescharacteristic
131C2×C4×C23C2×D411yescharacteristic
132C2×C4×C23C2×D411yescharacteristic
133C2×C4×C23C2×D411yescharacteristic
134C2×C4×C23C2411yescharacteristic
135C22⋊D23—24no—
136C22⋊D23—24no—
137C22⋊D23—22no—
138C22⋊D23—22no—
139C22⋊D23—22no—
140C22⋊D23—22no—
141C2×Dic23—24no—
142C2×Dic23—21no—
143C2×Dic23C2×D412yes—
144D92—24no—
145D92—21no—
146D92—21no—
147D92—21no—
148D92—22no—
149D92—22no—
150D92—41no—
151D92—41no—
152D92—84no—
153D92C2×D412yes—
154C4×D23—24no—
155C4×D23—24no—
156C4×D23—22no—
157C4×D23—22no—
158C4×D23—22no—
159C4×D23—22no—
160Dic46—24no—
161Dic46—21no—
162Dic46—21no—
163Dic46—21no—
164Dic46C2×D412yes—
165C8×C23—22no—
166C23⋊C8—22no—
167#3021—231nomaximal, Sylow
168C22×C23—22no—
169C22×C23—41no—
170C22×C23—81no—
171C22×C23#12011yescharacteristic
172C22×C23#12011yescharacteristic
173C22×C23C22×D411yescharacteristic
174C2×D23—22no—
175C2×D23—22no—
176C2×D23—42no—
177C2×D23—44no—
178C2×D23—42no—
179C2×D23—81no—
180C2×D23—84no—
181C2×D23—82no—
182C2×D23—82no—
183C4×C23—22no—
184C4×C23—42no—
185C4×C23#12011yescharacteristic
186C4×C23#12011yescharacteristic
187C4×C23C22×D411yescharacteristic
188C4×C23C22×D411yescharacteristic
189Dic23—22no—
190Dic23—22no—
191#585—231no—
192C2×AGL(1,ℤ/8)—231no—
193C2×AGL(1,ℤ/8)—231no—
194#535—231no—
195#454—234no—
196#453—234no—
197#421—231no—
198#421D2311yescharacteristic, complemented
199#413—231no—
200C2×C23—21no—
201C2×C23—21no—
202C2×C23—21no—
203C2×C23—42no—
204C2×C23C2×#12011yescharacteristic
205D23—42no—
206D23—42no—
207D23—82no—
2082−1+4—232no—
2092−1+4—461no—
2102−1+4—461no—
211H(5,𝔽2)—232no—
212H(5,𝔽2)—462no—
213H(5,𝔽2)—461no—
214H(5,𝔽2)—461no—
215C2×#41—231no—
216C2×#41—231no—
217C2×#41—462no—
218C2×#41—462no—
219C2×#41—462no—
220C2×#41C2×D2311yescharacteristic
221C22×D4—231no—
222AGL(1,ℤ/8)—234no—
223AGL(1,ℤ/8)—234no—
224AGL(1,ℤ/8)—462no—
225AGL(1,ℤ/8)—462no—
226C2×SD16—461no—
227C2×SD16—461no—
228C2×D8—461no—
229C2×D8—461no—
230C2×M16—231no—
231C2×M16C2×D2311yescharacteristic, complemented
232#127—232no—
233#124—232no—
234#121—462no—
235#120—462no—
236#117C2×D2311yescharacteristic, complemented
237#104—234no—
238#104C2×D2314yescomplemented
239#101—232no—
240#100—232no—
241C23#302111yescharacteristic, complemented, Sylow
242C24—461no—
243#41—21no—
244#41—21no—
245#41—232no—
246#41—232no—
247#41—462no—
248#41—462no—
249#41—464no—
250#41—464no—
251#41—464no—
252#41—464no—
253#41—462no—
254#41—462no—
255#41—462no—
256#41—462no—
257#41—461no—
258#41—461no—
259#41—461no—
260#41—461no—
261#41—461no—
262#41—461no—
263#41D9212yescomplemented
264#41C22×D2312yes—
265C2×Q8—231no—
266C2×Q8—231no—
267C2×Q8—462no—
268C2×Q8—462no—
269C2×Q8—462no—
270C2×Q8D9211yescharacteristic, complemented
271C2×D4—21no—
272C2×D4—232no—
273C2×D4—231no—
274C2×D4—231no—
275C2×D4—232no—
276C2×D4—462no—
277C2×D4—464no—
278C2×D4—464no—
279C2×D4—464no—
280C2×D4—462no—
281C2×D4—464no—
282C2×D4—461no—
283C2×D4—462no—
284C2×D4—461no—
285C2×D4—461no—
286C2×D4—461no—
287C2×D4—461no—
288C2×D4—461no—
289C2×D4D9211yescharacteristic, complemented
290C22×C4—21no—
291C22×C4—232no—
292C22×C4—464no—
293C22×C4—461no—
294C22×C4C22×D2311yescharacteristic
295SD16—464no—
296SD16—464no—
297D8—464no—
298D8—464no—
299M16—21no—
300M16—232no—
301M16—461no—
302M16C22×D2312yes—
303C2×C8—21no—
304C2×C8—461no—
305C4⋊C4—21no—
306C22⋊C4—21no—
307C22⋊C4—464no—
308C42C22×D2312yes—
309C23—21no—
310C23—232no—
311C23—464no—
312C23—461no—
313C23—462no—
314C23—921no—
315C23—921no—
316C23—1842no—
317C23D4×D2311yescharacteristic
318Q8—21no—
319Q8—232no—
320Q8—464no—
321Q8—461no—
322Q8—461no—
323Q8—461no—
324Q8C2×D9212yes—
325D4—22no—
326D4—22no—
327D4—21no—
328D4—232no—
329D4—464no—
330D4—464no—
331D4—464no—
332D4—462no—
333D4—462no—
334D4—462no—
335D4—462no—
336D4—461no—
337D4—461no—
338D4—462no—
339D4—461no—
340D4—462no—
341D4—921no—
342D4—921no—
343D4—1844no—
344D4C2×D9212yes—
345C2×C4—21no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—22no—
349C2×C4—232no—
350C2×C4—464no—
351C2×C4—464no—
352C2×C4—464no—
353C2×C4—461no—
354C2×C4—462no—
355C2×C4—462no—
356C2×C4—462no—
357C2×C4—462no—
358C2×C4C2×D9211yescharacteristic
359C2×C4C2×D9211yescharacteristic
360C2×C4D4×D2311yescharacteristic
361C2×C4D4×D2311yescharacteristic
362C2×C4D4×D2311yescharacteristic
363C2×C4C23×D2311yescharacteristic
364C8—22no—
365C8—462no—
366C22—22no—
367C22—41no—
368C22—81no—
369C22—462no—
370C22—462no—
371C22—922no—
372C22—924no—
373C22—922no—
374C22—1841no—
375C22—1842no—
376C22—1842no—
377C22—1844no—
378C22#1062505311yescharacteristic
379C22#1062505311yescharacteristic
380C22C2×D4×D2311yescharacteristic
381C4—22no—
382C4—42no—
383C4—462no—
384C4—462no—
385C4#1062505311yescharacteristic
386C4#1062505311yescharacteristic
387C4C22×D9211yescharacteristic
388C4C2×D4×D2311yescharacteristic
389C2—21no—
390C2—21no—
391C2—21no—
392C2—42no—
393C2—922no—
394C2—922no—
395C2—1842no—
396C2C2×#1062505311yescharacteristic
subgroupG/H
centerC2C2×#10625053
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#421C2
socleC2×C23C2×#120
hypercenter#421D23
hypocenterC23#3021
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C22×C4 ◁ #421

Complements

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

NH ≅ G/Ntype
1. #13093253C2semidirect
2. C2×#10625079C2semidirect
3. C2×#10625120C2semidirect
4. #13092986C2semidirect
5. #13092591C2semidirect
6. #13092586C2semidirect
7. #13092435C2semidirect
8. #13092399C2semidirect
9. C23×#421C2semidirect
12. #10625161C22semidirect
14. #10625160C22semidirect
23. C22×D92C22semidirect
24. C2×M16×C23C22semidirect
25. C23×#117C22semidirect
27. #10625120C22semidirect
30. C2×#67267C22semidirect
32. #10625079C22semidirect
37. #10625046C22semidirect
38. #10625045C22semidirect
39. C23×#104C22semidirect
40. #10625006C22semidirect
41. #10625005C22semidirect
42. #10624987C22semidirect
46. #41×C23D4semidirect
48. C2×Q8×C23D4semidirect
50. C2×D4×C23D4semidirect
78. #67288D4semidirect
87. C2×D92D4semidirect
94. C2×Dic46D4semidirect
198. #421D23semidirect
231. C2×M16C2×D23semidirect
236. #117C2×D23semidirect
238. #104C2×D23semidirect
241. C23#3021semidirect
263. #41D92semidirect
270. C2×Q8D92semidirect
289. C2×D4D92semidirect

Maximal subgroups

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

subgroupindex
#130932532
C2×#106250792
C2×#106251202
#130929862
#130925912
#130925862
#130924352
#130923992
C23×#4212
#302123