Finite Group Databasebeta

← #14288996

Subgroups — #14288996

Order 1920.

472 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 90 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
2C5×#5027C211yesmaximal, characteristic, complemented
3#11747066C211yesmaximal, characteristic, complemented
4#11747045C211yesmaximal, characteristic
5C3×Q8⋊#168C211yesmaximal, characteristic, complemented
6#11745863C211yesmaximal, characteristic, complemented
7#11745839C211yesmaximal, characteristic, complemented
8#10601821—31nomaximal, Hall
9C3×C4×C5×Q8C2211yescharacteristic
10#91835—21no—
11#91785—22no—
12C4⋊C4×D15—21no—
13C4×D60—21no—
14C4×D60C2211yescharacteristic
15#91759—21no—
16#91758C2211yescharacteristic
17C2×C5×#215—21no—
18C5×#874C2211yescharacteristic
19C2×#6659—22no—
20C2×#6654—21no—
21C5×#809—21no—
22C5×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×C4⋊#168C2211yescharacteristic
24C3×C4×#168C2211yescharacteristic
25#90967—21no—
26#68244—51nomaximal, Hall
27#65913—31no—
28C5×#460—31no—
29#65365—31no—
30#65361—31no—
31Q8⋊#168D311yescharacteristic, complemented
32#64703—31no—
33#64701—31no—
34C2×C3×C5×Q8D411yescharacteristic
35C2×D60D411yescharacteristic
36C2×C4×D15—21no—
37C2×C4×D15—22no—
38C2×Dic30D412yes—
39C2×C5×D12—21no—
40C2×C5×D12—21no—
41C2×C5×D12—21no—
42C3×C5×C4⋊C4—21no—
43C3×C5×C4⋊C4D411yescharacteristic
44C3×C42×C5—21no—
45C3×C42×C5C2311yescharacteristic
46#6714—22no—
47#6714—21no—
48C4⋊Dic15—21no—
49C4⋊Dic15—21no—
50C4⋊Dic15D411yescharacteristic
51#6712—22no—
52#6712—22no—
53C5×#215—42no—
54C2×C5×C3⋊C8—21no—
55C2×C3×#168—21no—
56C2×C3×#168—21no—
57#6659—44no—
58#6654—42no—
59#5579—51no—
60#5027D511yescharacteristic, complemented
61#4843—51no—
62#4693—51no—
63C3×Q8⋊C8—51no—
64#4481—51no—
65#4459—51no—
66C2×C5×SD16—61no—
67C5×#127—31no—
68C4×C5×Q8C2×D311yescharacteristic
69#4092—61no—
70C2×#687—62no—
71C2×#686—61no—
72#4042—62no—
73D5×C4⋊C4—61no—
74C4×D20—31no—
75C4×D20—61no—
76#4016—61no—
77#4015—31no—
78C5×C4⋊C8—31no—
79C5×#102—61no—
80#3964—61no—
81C4⋊#168C2×D311yescharacteristic
82C4×#168C2×D311yescharacteristic
83#1622—151noSylow
84C22×D15—21no—
85C22×C5×D3—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—
96D60SD1612yescomplemented
97C4×D15—41no—
98C4×D15—41no—
99C4×D15—82no—
100Dic30—42no—
101C5×D12—42no—
102C5×D12—41no—
103C5×D12—41no—
104C5×D12—41no—
105C5×D12—41no—
106C3×#168—22no—
107C3×#168—41no—
108C5×C3⋊C8—41no—
109C3×C4×Q8C2×D511yescharacteristic
110#946—101no—
111C2×#215—21no—
112C2×D24—101no—
113C2×#204—102no—
114#896—102no—
115D3×C4⋊C4—101no—
116#874C2×D511yescharacteristic
117C4×D12—51no—
118C4×D12—101no—
119#870—101no—
120#869—51no—
121C3×C4⋊C8—51no—
122C3×C4×C8—51no—
123#821—101no—
124#809—21no—
125C4⋊(C3⋊C8)C2×D511yescharacteristic
126C2×C5×Q8D1211yescharacteristic
127C2×C5×D4—61no—
128C2×C5×D4—61no—
129C2×C5×D4—61no—
130C2×D20—31no—
131C2×C4×D5—61no—
132C2×C4×D5—62no—
133C2×Dic10—32no—
134C5×SD16—122no—
135C2×C5×C8—61no—
136C5×C4⋊C4—21no—
137C5×C4⋊C4D1211yescharacteristic
138C42×C5—21no—
139C42×C5C22×D311yescharacteristic
140#687—124no—
141#686—122no—
142#685—62no—
143#685—61no—
144C4⋊Dic5—31no—
145C4⋊Dic5—61no—
146C4⋊Dic5—61no—
147#683—62no—
148#683—62no—
149C2×#168—21no—
150C2×#168—21no—
151#554—151no—
152#492—151no—
153#460—31no—
154#459—151no—
155#333—151no—
156Q8⋊C8—51no—
157D4⋊C8—151no—
158C22×C3×C5#12011yescharacteristic
159C2×D15—22no—
160C2×D15—41no—
161C2×D15—41no—
162C2×C5×D3—81no—
163C2×C5×D3—81no—
164C2×C5×D3—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×Q8C22⋊D511yescharacteristic
175C2×D12—21no—
176C2×D12—21no—
177C2×D12—21no—
178C2×D12—51no—
179C2×C4×D3—101no—
180C2×C4×D3—102no—
181C2×Dic6—52no—
182C2×C3×C8—101no—
183C2×C3×C8—101no—
184C3×C4⋊C4—21no—
185C3×C4⋊C4C22⋊D511yescharacteristic
186C3×C42—21no—
187C3×C42C22×D511yescharacteristic
188#215—42no—
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—21no—
197D24—202no—
198#204—204no—
199C23×C5—121no—
200C22×D5—61no—
201C5×Q8—21no—
202C5×Q8—21no—
203C5×D4—122no—
204C5×D4—121no—
205C5×D4—121no—
206C5×D4—121no—
207C5×D4—121no—
208C2×C4×C5—21no—
209C2×C4×C5—21no—
210C2×C4×C5C2×D1211yescharacteristic
211C2×C4×C5D3×D411yescharacteristic
212C2×C4×C5D3×D411yescharacteristic
213C2×Dic5—61no—
214C2×Dic5—62no—
215D20—32no—
216D20—61no—
217C4×D5—121no—
218C4×D5—121no—
219C4×D5—242no—
220Dic10—122no—
221C5×C8—121no—
222#168—22no—
223#168—41no—
224C2×SD16—61no—
225C2×SD16—302no—
226C2×D8—301no—
227C4⋊Q8—151no—
228#127—31no—
229#125—301no—
230C22⋊Q8—302no—
231C22⋊Q8—301no—
232C4×Q8D3×D511yescharacteristic
233C4×D4—151no—
234C4×D4—301no—
235C2×C4⋊C4—301no—
236C4⋊C8—31no—
237C4⋊C8—51no—
238#102—61no—
239#102—301no—
240C4×C8—51no—
241C2×C3×C5#44811yescharacteristic
242C2×C3×C5#44911yescharacteristic
243C2×C3×C5#45311yescharacteristic
244D15—42no—
245C5×D3—161no—
246C22×D3—41no—
247C22×D3—101no—
248C3×Q8—21no—
249C3×Q8—21no—
250C2×C3×C4—21no—
251C2×C3×C4—21no—
252C2×C3×C4D4×D511yescharacteristic
253C2×C3×C4D4×D511yescharacteristic
254C2×C3×C4C2×C22⋊D511yescharacteristic
255C2×Dic3—101no—
256C2×Dic3—102no—
257D12—42no—
258D12—41no—
259D12—41no—
260D12—41no—
261D12—41no—
262D12—52no—
263D12—101no—
264C4×D3—201no—
265C4×D3—201no—
266C4×D3—402no—
267Dic6—202no—
268C3×C8—102no—
269C3×C8—201no—
270C3⋊C8—41no—
271C22×C5—241no—
272C22×C5—241no—
273C22×C5—241no—
274C22×C5#88211yescharacteristic
275C2×D5—62no—
276C2×D5—121no—
277C2×D5—121no—
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×Q8#120311yescharacteristic
289C2×D4—61no—
290C2×D4—61no—
291C2×D4—61no—
292C2×D4—151no—
293C22×C4—302no—
294C22×C4—301no—
295SD16—122no—
296SD16—604no—
297D8—602no—
298C2×C8—61no—
299C2×C8—101no—
300C2×C8—101no—
301C4⋊C4—21no—
302C4⋊C4—151no—
303C4⋊C4—302no—
304C4⋊C4—302no—
305C4⋊C4—301no—
306C4⋊C4—301no—
307C4⋊C4#120311yescharacteristic
308C22⋊C4—302no—
309C22⋊C4—301no—
310C42—21no—
311C42C2×D3×D511yescharacteristic
312C3×C5#162211yescharacteristic, complemented, Hall
313C22×C3#408311yescharacteristic
314C2×D3—81no—
315C2×D3—81no—
316C2×D3—81no—
317C2×D3—102no—
318C2×D3—201no—
319C2×D3—201no—
320C3×C4—21no—
321C3×C4—41no—
322C3×C4—41no—
323C3×C4D5×SD1611yescharacteristic
324C3×C4#406111yescharacteristic
325C3×C4#407811yescharacteristic
326C3×C4#409611yescharacteristic
327Dic3—201no—
328Dic3—202no—
329C2×C5—481no—
330C2×C5#473411yescharacteristic
331C2×C5#480611yescharacteristic
332C2×C5#482211yescharacteristic
333D5—122no—
334C23—121no—
335C23—301no—
336Q8—21no—
337Q8—21no—
338Q8—602no—
339D4—122no—
340D4—121no—
341D4—121no—
342D4—121no—
343D4—121no—
344D4—152no—
345D4—301no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—301no—
349C2×C4—302no—
350C2×C4—601no—
351C2×C4—601no—
352C2×C4—1202no—
353C2×C4C2×#120311yescharacteristic
354C2×C4#679011yescharacteristic
355C2×C4#679011yescharacteristic
356C8—102no—
357C8—121no—
358C8—201no—
359C2×C3#6532611yescharacteristic
360C2×C3#6545911yescharacteristic
361C2×C3#6548711yescharacteristic
362D3—161no—
363D3—202no—
364C5#6824411yescharacteristic, complemented, Sylow
365C22—241no—
366C22—241no—
367C22—241no—
368C22—302no—
369C22—601no—
370C22—601no—
371C22#9157311yescharacteristic
372C4—21no—
373C4—41no—
374C4—41no—
375C4—602no—
376C4—601no—
377C4#9130311yescharacteristic
378C4#9130411yescharacteristic
379C4#9150511yescharacteristic
380C4#9152411yescharacteristic
381C3#1060182111yescharacteristic, complemented, Sylow
382C2—481no—
383C2—602no—
384C2#1174852611yescharacteristic
385C2#1174928711yescharacteristic
386C2#1174942211yescharacteristic
subgroupG/H
centerC22#91573
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×Q8C22
socleC22×C3×C5#120
prime radical#11747045C2
hypercenterC4×Q8D3×D5
hypocenterC3×C5#1622
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. #11756338C2semidirect
2. C5×#5027C2semidirect
3. #11747066C2semidirect
5. C3×Q8⋊#168C2semidirect
6. #11745863C2semidirect
7. #11745839C2semidirect
31. Q8⋊#168D3semidirect
60. #5027D5semidirect
96. D60SD16semidirect
312. C3×C5#1622semidirect
364. C5#68244semidirect
381. C3#10601821semidirect

Maximal subgroups

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

subgroupindex
#117563382
C5×#50272
#117470662
#117470452
C3×Q8⋊#1682
#117458632
#117458392
#106018213
#682445