Finite Group Databasebeta

← #14288964

Subgroups — #14288964

Order 1920.

472 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 93 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#11756338C211yesmaximal, characteristic, complemented
2#11751128C211yesmaximal, characteristic, complemented
3#11750944C211yesmaximal, characteristic
4#11750794C211yesmaximal, characteristic, complemented
5C3×C5×Q8⋊C8C211yesmaximal, characteristic, complemented
6#11746302C211yesmaximal, characteristic, complemented
7#11746280C211yesmaximal, characteristic, complemented
8#10599037—31nomaximal, Hall
9C3×C4×C5×Q8C2211yescharacteristic
10#91835—21no—
11C2×#6717—21no—
12C2×D120—21no—
13C2×#6706—22no—
14#91785—22no—
15C4⋊C4×D15—21no—
16#91763C2211yescharacteristic
17C4×D60—21no—
18C4×D60C2211yescharacteristic
19#91759—21no—
20#91758C2211yescharacteristic
21C3×C5×C4⋊C8C2211yescharacteristic
22C3×C4×C5×C8C2211yescharacteristic
23#91105—21no—
24#91093—21no—
25C4⋊(C3⋊#168)C2211yescharacteristic
26#68244—51nomaximal, Hall
27#65913—31no—
28#65316—31no—
29#65132—31no—
30#64982—31no—
31C5×Q8⋊C8D311yescharacteristic, complemented
32#64701—31no—
33#64679—31no—
34C2×C3×C5×Q8D411yescharacteristic
35C2×D60—21no—
36C2×D60—21no—
37C2×D60—21no—
38C2×D60D411yescharacteristic
39C2×C4×D15—21no—
40C2×C4×D15—22no—
41C2×Dic30D412yes—
42C2×C3×C5×C8—21no—
43C2×C3×C5×C8—21no—
44C3×C5×C4⋊C4—21no—
45C3×C5×C4⋊C4D411yescharacteristic
46C3×C42×C5—21no—
47C3×C42×C5C2311yescharacteristic
48#6717—42no—
49#6714—22no—
50#6714—21no—
51C4⋊Dic15—21no—
52C4⋊Dic15—21no—
53C4⋊Dic15D411yescharacteristic
54#6712—22no—
55#6712—22no—
56C2×C3⋊#168—21no—
57D120—42no—
58#6706—44no—
59#5579—51no—
60#5027—51no—
61#4843—51no—
62#4693—51no—
63C3×Q8⋊C8D511yescharacteristic, complemented
64#4481—51no—
65#4459—51no—
66C4×C5×Q8C2×D311yescharacteristic
67#4092—61no—
68C2×#688—61no—
69C2×D40—61no—
70C2×#677—62no—
71#4042—62no—
72D5×C4⋊C4—61no—
73#4020—31no—
74C4×D20—31no—
75C4×D20—61no—
76#4016—61no—
77#4015—31no—
78C5×C4⋊C8C2×D311yescharacteristic
79C4×C5×C8C2×D311yescharacteristic
80#3953—61no—
81#3941—61no—
82C4⋊#168—31no—
83#1622—151noSylow
84C22×D15—21no—
85C22×D15—41no—
86C3×C5×Q8—21no—
87C3×C5×Q8—21no—
88C2×C3×C4×C5—21no—
89C2×C3×C4×C5—21no—
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×C3×C4×C5C2×D411yescharacteristic
92C2×C3×C4×C5C2×D411yescharacteristic
93C2×Dic15—21no—
94C2×Dic15—22no—
95D60—21no—
96D60—42no—
97D60—41no—
98D60—41no—
99D60—41no—
100D60—41no—
101D60SD1612yescomplemented
102C4×D15—41no—
103C4×D15—41no—
104C4×D15—82no—
105Dic30—42no—
106C3×C5×C8—22no—
107C3×C5×C8—41no—
108C3⋊#168—41no—
109C3×C4×Q8C2×D511yescharacteristic
110#946—101no—
111C2×#215—101no—
112C2×D24—101no—
113C2×#204—102no—
114#896—102no—
115D3×C4⋊C4—101no—
116#874—51no—
117C4×D12—51no—
118C4×D12—101no—
119#870—101no—
120#869—51no—
121C3×C4⋊C8C2×D511yescharacteristic
122C3×C4×C8C2×D511yescharacteristic
123#821—101no—
124#809—101no—
125C4⋊(C3⋊C8)—51no—
126C2×C5×Q8D1211yescharacteristic
127C2×D20—31no—
128C2×D20—61no—
129C2×D20—61no—
130C2×D20—61no—
131C2×C4×D5—61no—
132C2×C4×D5—62no—
133C2×Dic10—32no—
134C2×C5×C8—21no—
135C2×C5×C8—21no—
136C5×C4⋊C4—21no—
137C5×C4⋊C4D1211yescharacteristic
138C42×C5—21no—
139C42×C5C22×D311yescharacteristic
140#688—122no—
141#685—62no—
142#685—61no—
143C4⋊Dic5—31no—
144C4⋊Dic5—61no—
145C4⋊Dic5—61no—
146#683—62no—
147#683—62no—
148C2×#168—61no—
149D40—122no—
150#677—124no—
151#554—151no—
152#492—151no—
153#460—151no—
154#459—151no—
155#333—151no—
156Q8⋊C8D1511yescharacteristic, complemented
157D4⋊C8—151no—
158C22×C3×C5#12011yescharacteristic
159C2×D15—22no—
160C2×D15—41no—
161C2×D15—41no—
162C2×D15—81no—
163C2×D15—81no—
164C2×D15—81no—
165C3×C4×C5—21no—
166C3×C4×C5—41no—
167C3×C4×C5—41no—
168C3×C4×C5C2×SD1611yescharacteristic
169C3×C4×C5#13511yescharacteristic
170C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
171C3×C4×C5#13711yescharacteristic
172Dic15—41no—
173Dic15—42no—
174C2×C3×Q8D2011yescharacteristic
175C2×D12—51no—
176C2×D12—101no—
177C2×D12—101no—
178C2×D12—101no—
179C2×C4×D3—101no—
180C2×C4×D3—102no—
181C2×Dic6—52no—
182C2×C3×C8—21no—
183C2×C3×C8—21no—
184C3×C4⋊C4—21no—
185C3×C4⋊C4D2011yescharacteristic
186C3×C42—21no—
187C3×C42C22×D511yescharacteristic
188#215—202no—
189(C2×D3)⋊C4—102no—
190(C2×D3)⋊C4—101no—
191C4⋊Dic3—51no—
192C4⋊Dic3—101no—
193C4⋊Dic3—101no—
194Dic3⋊C4—102no—
195Dic3⋊C4—102no—
196C2×C3⋊C8—101no—
197D24—202no—
198#204—204no—
199C22×D5—61no—
200C22×D5—121no—
201C5×Q8—21no—
202C5×Q8—21no—
203C2×C4×C5—21no—
204C2×C4×C5—21no—
205C2×C4×C5C2×D1211yescharacteristic
206C2×C4×C5D3×D411yescharacteristic
207C2×C4×C5D3×D411yescharacteristic
208C2×Dic5—61no—
209C2×Dic5—62no—
210D20—32no—
211D20—61no—
212D20—122no—
213D20—121no—
214D20—121no—
215D20—121no—
216D20—121no—
217C4×D5—121no—
218C4×D5—121no—
219C4×D5—242no—
220Dic10—122no—
221C5×C8—22no—
222C5×C8—41no—
223#168—121no—
224C2×SD16—302no—
225C2×SD16—301no—
226C2×D8—301no—
227C4⋊Q8—151no—
228#127—151no—
229#125—301no—
230C22⋊Q8—302no—
231C22⋊Q8—301no—
232C4×Q8C2×D1511yescharacteristic
233C4×D4—151no—
234C4×D4—301no—
235C2×C4⋊C4—301no—
236C4⋊C8—151no—
237C4⋊C8C2×D1511yescharacteristic
238#102—301no—
239#102—301no—
240C4×C8C2×D1511yescharacteristic
241C2×C3×C5#44811yescharacteristic
242C2×C3×C5#44911yescharacteristic
243C2×C3×C5#45311yescharacteristic
244D15—42no—
245D15—161no—
246C22×D3—101no—
247C22×D3—201no—
248C3×Q8—21no—
249C3×Q8—21no—
250C2×C3×C4—21no—
251C2×C3×C4—21no—
252C2×C3×C4C2×D2011yescharacteristic
253C2×C3×C4D4×D511yescharacteristic
254C2×C3×C4D4×D511yescharacteristic
255C2×Dic3—101no—
256C2×Dic3—102no—
257D12—52no—
258D12—101no—
259D12—202no—
260D12—201no—
261D12—201no—
262D12—201no—
263D12—201no—
264C4×D3—201no—
265C4×D3—201no—
266C4×D3—402no—
267Dic6—202no—
268C3×C8—22no—
269C3×C8—41no—
270C3⋊C8—201no—
271C22×C5#88211yescharacteristic
272C2×D5—62no—
273C2×D5—121no—
274C2×D5—121no—
275C2×D5—241no—
276C2×D5—241no—
277C2×D5—241no—
278C4×C5—21no—
279C4×C5—41no—
280C4×C5—41no—
281C4×C5#90411yescharacteristic
282C4×C5#90811yescharacteristic
283C4×C5D3×SD1611yescharacteristic
284C4×C5#91811yescharacteristic
285Dic5—121no—
286Dic5—122no—
287C2×Q8—152no—
288C2×Q8D6011yescharacteristic
289C2×D4—151no—
290C2×D4—301no—
291C2×D4—301no—
292C2×D4—301no—
293C22×C4—302no—
294C22×C4—301no—
295SD16—604no—
296SD16—602no—
297D8—602no—
298C2×C8—21no—
299C2×C8—21no—
300C2×C8—301no—
301C4⋊C4—21no—
302C4⋊C4—151no—
303C4⋊C4—302no—
304C4⋊C4—302no—
305C4⋊C4—301no—
306C4⋊C4—301no—
307C4⋊C4D6011yescharacteristic
308C22⋊C4—302no—
309C22⋊C4—301no—
310C42—21no—
311C42C22×D1511yescharacteristic
312C3×C5#162211yescharacteristic, complemented, Hall
313C22×C3#402811yescharacteristic
314C2×D3—102no—
315C2×D3—201no—
316C2×D3—201no—
317C2×D3—401no—
318C2×D3—401no—
319C2×D3—401no—
320C3×C4—21no—
321C3×C4—41no—
322C3×C4—41no—
323C3×C4#405011yescharacteristic
324C3×C4#405411yescharacteristic
325C3×C4D5×SD1611yescharacteristic
326C3×C4#406411yescharacteristic
327Dic3—202no—
328Dic3—201no—
329C2×C5#473411yescharacteristic
330C2×C5#480611yescharacteristic
331C2×C5#482211yescharacteristic
332D5—122no—
333D5—481no—
334C23—301no—
335C23—601no—
336Q8—21no—
337Q8—21no—
338Q8—602no—
339D4—152no—
340D4—301no—
341D4—602no—
342D4—601no—
343D4—601no—
344D4—601no—
345D4—601no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—301no—
349C2×C4—302no—
350C2×C4—601no—
351C2×C4—601no—
352C2×C4—1202no—
353C2×C4C2×D6011yescharacteristic
354C2×C4D4×D1511yescharacteristic
355C2×C4D4×D1511yescharacteristic
356C8—22no—
357C8—41no—
358C8—601no—
359C2×C3#6502311yescharacteristic
360C2×C3#6509511yescharacteristic
361C2×C3#6511111yescharacteristic
362D3—202no—
363D3—801no—
364C5#6824411yescharacteristic, complemented, Sylow
365C22—302no—
366C22—601no—
367C22—601no—
368C22—1201no—
369C22—1201no—
370C22—1201no—
371C22#9177111yescharacteristic
372C4—21no—
373C4—41no—
374C4—41no—
375C4—602no—
376C4—601no—
377C4#9179311yescharacteristic
378C4#9179711yescharacteristic
379C4SD16×D1511yescharacteristic
380C4#9180711yescharacteristic
381C3#1059903711yescharacteristic, complemented, Sylow
382C2—602no—
383C2—2401no—
384C2#1175083511yescharacteristic
385C2#1175090711yescharacteristic
386C2#1175092311yescharacteristic
subgroupG/H
centerC22#91771
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×Q8⋊C8C2
socleC22×C3×C5#120
prime radical#11750944C2
hypercenterQ8⋊C8D15
hypocenterC3×C5#1622
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
1. #11756338C2semidirect
2. #11751128C2semidirect
4. #11750794C2semidirect
5. C3×C5×Q8⋊C8C2semidirect
6. #11746302C2semidirect
7. #11746280C2semidirect
31. C5×Q8⋊C8D3semidirect
63. C3×Q8⋊C8D5semidirect
101. D60SD16semidirect
156. Q8⋊C8D15semidirect
312. C3×C5#1622semidirect
364. C5#68244semidirect
381. C3#10599037semidirect

Maximal subgroups

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

subgroupindex
#117563382
#117511282
#117509442
#117507942
C3×C5×Q8⋊C82
#117463022
#117462802
#105990373
#682445