Finite Group Databasebeta

← #37581870

Subgroups — #37581870

Order 24448.

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

normal subgroups only

This group has 724 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
1#27133498C211yesmaximal, characteristic, complemented
2#27133462C212yesmaximal, complemented
3#27133212C211yesmaximal, characteristic, complemented
4#27132844C212yesmaximal, complemented
5#27132840C211yesmaximal, characteristic, complemented
6#27132837C212yesmaximal, complemented
7#27132833C211yesmaximal, characteristic, complemented
8#27132831C211yesmaximal, characteristic, complemented
9#104×D191C212yesmaximal, complemented
10#27132644C211yesmaximal, characteristic, complemented
11#455×C191C211yesmaximal, characteristic, complemented
12#20259369—22no—
13#20259369C2212yes—
14#20259367—22no—
15#20259367—22no—
16#20259367C2211yescharacteristic
17C2×#15690288C2211yescharacteristic, complemented
18C2×#15690286—22no—
19C2×#15690286—22no—
20C2×#15690286C2211yescharacteristic
21#41×D191—22no—
22#41×D191C2212yes—
23#20259354—22no—
24#20259353C2212yescomplemented
25#20259350C2212yescomplemented
26#20259349—22no—
27#20259347C2212yescomplemented
28#20259345—22no—
29#20259343—22no—
30M16×D191C2212yescomplemented
31#20259320C2211yescharacteristic, complemented
32#20259318C2211yescharacteristic, complemented
33#20259310C2211yescharacteristic, complemented
34#20259295—22no—
35(C22⋊D191)⋊C4—22no—
36C42×D191C2211yescharacteristic, complemented
37#20259250C2212yescomplemented
38#20259249C2212yescomplemented
39#20259248C2212yescomplemented
40#20259240C2212yescomplemented
41#20259239C2211yescharacteristic, complemented
42H(5,𝔽2)×C191C2211yescharacteristic
43#137×C191C2212yescomplemented
44#124×C191C2211yescharacteristic, complemented
45#104×C191C2212yescomplemented
46#100×C191C2211yescharacteristic, complemented
47#15690288—22no—
48#15690288—22no—
49#15690288D412yescomplemented
50#15690287—24no—
51#15690287—22no—
52#15690287—22no—
53#15690287C2312yes—
54#15690286—24no—
55#15690286—24no—
56#15690286—24no—
57#15690286—22no—
58#15690286—22no—
59#15690286—24no—
60#15690286—22no—
61#15690286—22no—
62#15690286—22no—
63#15690286D412yescomplemented
64C2×Dic382—22no—
65C2×Dic382—22no—
66C2×Dic382C2311yescharacteristic
67Q8×D191—22no—
68Q8×D191D412yescomplemented
69C2×D764—21no—
70C2×D764C2311yescharacteristic
71C2×C22⋊D191—24no—
72C2×C22⋊D191—22no—
73C2×C22⋊D191—22no—
74C2×C22⋊D191—22no—
75C2×C22⋊D191D412yes—
76D4×D191—24no—
77D4×D191—22no—
78D4×D191—22no—
79D4×D191D412yescomplemented
80C22×Dic191—22no—
81C22×Dic191D412yes—
82C2×C4×D191—22no—
83C2×C4×D191—22no—
84C2×C4×D191—21no—
85C2×C4×D191—21no—
86C2×C4×D191C2311yescharacteristic
87#15690277—22no—
88#15690276—22no—
89#15690274—22no—
90#15690274—22no—
91D1528—22no—
92#15690272—22no—
93#15690271C2312yes—
94#15690270—22no—
95C8×D191—22no—
96Dic191⋊C4—22no—
97(C2×D191)⋊C4—22no—
98C4×Dic191—21no—
99C4×Dic191C2311yescharacteristic
100#41×C191—22no—
101#41×C191C2312yes—
102C2×Q8×C191C2311yescharacteristic
103C2×D4×C191—22no—
104C2×D4×C191—22no—
105C2×D4×C191C2311yescharacteristic
106Q16×C191—22no—
107SD16×C191—22no—
108M16×C191C2312yes—
109C22⋊C4×C191—22no—
110C42×C191C2311yescharacteristic
111C22×D191—22no—
112C22×D191—22no—
113C22×D191—21no—
114C22×D191C2×D411yescharacteristic
115Dic382—24no—
116Dic382—22no—
117Dic382—22no—
118Dic382C2×D412yes—
119D764—22no—
120D764—22no—
121D764—42no—
122D764C2×D412yes—
123C22⋊D191—24no—
124C22⋊D191—24no—
125C22⋊D191—22no—
126C22⋊D191—22no—
127C22⋊D191—24no—
128C22⋊D191—22no—
129C22⋊D191—44no—
130C2×Dic191—22no—
131C2×Dic191—24no—
132C2×Dic191—21no—
133C2×Dic191—22no—
134C2×Dic191—22no—
135C2×Dic191—22no—
136C2×Dic191C2×D412yes—
137C2×Dic191C2×D411yescharacteristic
138C4×D191—24no—
139C4×D191—22no—
140C4×D191—22no—
141C4×D191—22no—
142C4×D191—42no—
143C4×D191—41no—
144C4×D191—41no—
145C4×D191C2×D412yes—
146C4×D191C2×D412yes—
147C191⋊C8—22no—
148C23×C191—22no—
149C23×C191C2×D412yes—
150Q8×C191—22no—
151Q8×C191C2×D412yes—
152D4×C191—24no—
153D4×C191—22no—
154D4×C191—22no—
155D4×C191C2×D412yes—
156C2×C4×C191—22no—
157C2×C4×C191—22no—
158C2×C4×C191—21no—
159C2×C4×C191—21no—
160C2×C4×C191C2411yescharacteristic
161C8×C191—22no—
162C22×C191—22no—
163C22×C191—22no—
164C22×C191—42no—
165C22×C191—82no—
166C22×C191C22×D411yescharacteristic
167C2×D191—22no—
168C2×D191—41no—
169C2×D191—42no—
170C2×D191—41no—
171C2×D191—82no—
172C2×D191—82no—
173C2×D191#12012yes—
174C4×C191—22no—
175C4×C191—41no—
176C4×C191—41no—
177C4×C191C22×D412yes—
178Dic191—22no—
179Dic191—22no—
180Dic191—22no—
181Dic191#12011yescharacteristic
182Dic191#12011yescharacteristic
183C2×C191—21no—
184C2×C191—42no—
185C2×C191—42no—
186C2×C191C2×#12011yescharacteristic
187D191—22no—
188D191—42no—
189D191—81no—
190C191#301811yescharacteristic, complemented, Sylow
191#3018—1911nomaximal, Sylow
192#585—1911no—
193#575—1912no—
194#532—1911no—
195#456—1912no—
196#455—1911no—
197#455D19111yescharacteristic, complemented
198#454—1912no—
199#453—1911no—
200#453—1911no—
201C2×#104—1912no—
202#413—1911no—
2032−1+4—3822no—
2042−1+4—1912no—
205H(5,𝔽2)—3822no—
206H(5,𝔽2)—3822no—
207H(5,𝔽2)—1911no—
208H(5,𝔽2)C2×D19111yescharacteristic
209C2×#41—3822no—
210C2×#41—3822no—
211C2×#41—3822no—
212C2×#41—1912no—
213C2×#41—1911no—
214C2×#41—1911no—
215#137—3822no—
216#137—1912no—
217#137C2×D19112yescomplemented
218AGL(1,ℤ/8)—3822no—
219AGL(1,ℤ/8)—1912no—
220AGL(1,ℤ/8)—1912no—
221#135—3822no—
222#135—3822no—
223C2×M16—1912no—
224C4⋊Q8—1911no—
225#127—1911no—
226#124—1911no—
227#124C2×D19111yescharacteristic, complemented
228#121—3822no—
229C4×D4—3822no—
230C2×C42—1911no—
231#104—1912no—
232#104—1912no—
233#104—1912no—
234#104C2×D19112yescomplemented
235#101—1912no—
236#100—1911no—
237#100C2×D19111yescharacteristic, complemented
238#41—22no—
239#41—3824no—
240#41—3822no—
241#41—3822no—
242#41—3824no—
243#41—3824no—
244#41—3824no—
245#41—3822no—
246#41—3822no—
247#41—3822no—
248#41—3822no—
249#41—3824no—
250#41—3822no—
251#41—3822no—
252#41—3822no—
253#41—1912no—
254#41—1912no—
255#41—1912no—
256#41C22×D19112yes—
257C2×Q8—3822no—
258C2×Q8—3822no—
259C2×Q8—3822no—
260C2×Q8—1912no—
261C2×Q8—1911no—
262C2×Q8C22×D19111yescharacteristic
263C2×D4—22no—
264C2×D4—22no—
265C2×D4—3821no—
266C2×D4—3824no—
267C2×D4—3822no—
268C2×D4—3822no—
269C2×D4—3824no—
270C2×D4—3822no—
271C2×D4—3822no—
272C2×D4—3822no—
273C2×D4—1912no—
274C2×D4—1912no—
275C2×D4—1911no—
276C2×D4C22×D19111yescharacteristic
277C22×C4—3822no—
278C22×C4—3822no—
279C22×C4—3821no—
280C22×C4—3821no—
281C22×C4—3822no—
282C22×C4—1912no—
283C22×C4—1911no—
284Q16—22no—
285Q16—3822no—
286SD16—22no—
287SD16—3822no—
288SD16—3822no—
289SD16—3822no—
290D8—3822no—
291D8—3822no—
292M16—3822no—
293M16—1912no—
294M16C22×D19112yes—
295C2×C8—3822no—
296C4⋊C4—3822no—
297C22⋊C4—22no—
298C22⋊C4—3822no—
299C42—3821no—
300C42—1911no—
301C42C22×D19111yescharacteristic
302C23—22no—
303C23—3822no—
304C23—3822no—
305C23—3821no—
306C23—1911no—
307C23D4×D19112yes—
308Q8—22no—
309Q8—3824no—
310Q8—3822no—
311Q8—3822no—
312Q8—1912no—
313Q8D4×D19112yes—
314D4—24no—
315D4—22no—
316D4—22no—
317D4—3822no—
318D4—3824no—
319D4—3824no—
320D4—3822no—
321D4—3824no—
322D4—3822no—
323D4—3822no—
324D4—3822no—
325D4—1912no—
326D4—7642no—
327D4—7644no—
328D4D4×D19112yes—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—3824no—
334C2×C4—3822no—
335C2×C4—3822no—
336C2×C4—3822no—
337C2×C4—3824no—
338C2×C4—3821no—
339C2×C4—3822no—
340C2×C4—3822no—
341C2×C4—3822no—
342C2×C4—3822no—
343C2×C4—1912no—
344C2×C4—1911no—
345C2×C4—1912no—
346C2×C4—1912no—
347C2×C4—7642no—
348C2×C4—7641no—
349C2×C4—7641no—
350C2×C4C23×D19111yescharacteristic
351C8—22no—
352C8—3822no—
353C22—22no—
354C22—22no—
355C22—42no—
356C22—82no—
357C22—3822no—
358C22—1912no—
359C22—15282no—
360C22—15282no—
361C22—7641no—
362C22—7642no—
363C22—7641no—
364C22C2×D4×D19111yescharacteristic
365C4—22no—
366C4—41no—
367C4—41no—
368C4—3822no—
369C4—3822no—
370C4—3822no—
371C4—1911no—
372C4—1911no—
373C4C2×D4×D19112yes—
374C2—21no—
375C2—42no—
376C2—42no—
377C2—3822no—
378C2—15281no—
379C2—7642no—
380C2#120×D19111yescharacteristic
subgroupG/H
centerC2#120×D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#455×C191C2
socleC2×C191C2×#120
hypercenter#455D191
hypocenterC191#3018
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C2 ◁ C2×C4 ◁ #455

Complements

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

NH ≅ G/Ntype
1. #27133498C2semidirect
2. #27133462C2semidirect
3. #27133212C2semidirect
4. #27132844C2semidirect
5. #27132840C2semidirect
6. #27132837C2semidirect
7. #27132833C2semidirect
8. #27132831C2semidirect
9. #104×D191C2semidirect
10. #27132644C2semidirect
11. #455×C191C2semidirect
17. C2×#15690288C22semidirect
24. #20259353C22semidirect
25. #20259350C22semidirect
27. #20259347C22semidirect
30. M16×D191C22semidirect
31. #20259320C22semidirect
32. #20259318C22semidirect
33. #20259310C22semidirect
36. C42×D191C22semidirect
37. #20259250C22semidirect
38. #20259249C22semidirect
39. #20259248C22semidirect
40. #20259240C22semidirect
41. #20259239C22semidirect
43. #137×C191C22semidirect
44. #124×C191C22semidirect
45. #104×C191C22semidirect
46. #100×C191C22semidirect
49. #15690288D4semidirect
63. #15690286D4semidirect
68. Q8×D191D4semidirect
79. D4×D191D4semidirect
190. C191#3018semidirect
197. #455D191semidirect
217. #137C2×D191semidirect
227. #124C2×D191semidirect
234. #104C2×D191semidirect
237. #100C2×D191semidirect

Maximal subgroups

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

subgroupindex
#271334982
#271334622
#271332122
#271328442
#271328402
#271328372
#271328332
#271328312
#104×D1912
#271326442
#455×C1912
#3018191