Finite Group Databasebeta

← #14289762

Subgroups — #14289762

Order 1920.

456 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 101 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
1Q8×D60C211yesmaximal, characteristic
2#11751122C211yesmaximal, characteristic, complemented
3#11750943C211yesmaximal, characteristic
4#11750782C211yesmaximal, characteristic, complemented
5C3×C5×Q8⋊C8C211yesmaximal, characteristic, complemented
6#11746307C211yesmaximal, characteristic, complemented
7#11746280C211yesmaximal, characteristic
8#10599062—31nomaximal, Hall
9C2×Q8×D15—21no—
10C3×C4×C5×Q8C2211yescharacteristic
11#91786—21no—
12#91786—22no—
13C4×D60—21no—
14C4×D60C2211yescharacteristic
15#91758—21no—
16#91758C2211yescharacteristic
17#91758C2211yescharacteristic
18C3×C5×C4⋊C8C2211yescharacteristic
19C3×C4×C5×C8C2211yescharacteristic
20#91119—21no—
21#91105—21no—
22#91101—21no—
23#91100—22no—
24#91091—21no—
25C4⋊(C3⋊#168)C2211yescharacteristic
26#68269—51nomaximal, Hall
27Q8×D20—31no—
28#65310—31no—
29#65131—31no—
30#64970—31no—
31C5×Q8⋊C8D311yescharacteristic, complemented
32#64706—31no—
33#64679—31no—
34C2×C3×C5×Q8D411yescharacteristic
35Q8×D15—42no—
36Q8×D15—42no—
37C2×D60D411yescharacteristic
38C2×C4×D15—22no—
39C2×C4×D15—21no—
40C2×Dic30—22no—
41C2×Dic30—21no—
42C2×Dic30—21no—
43C2×C3×C5×C8—21no—
44C2×C3×C5×C8—21no—
45C3×C5×C4⋊C4—21no—
46C3×C5×C4⋊C4D411yescharacteristic
47C3×C42×C5—21no—
48C3×C42×C5C2311yescharacteristic
49#6714—22no—
50#6714—21no—
51C4⋊Dic15—22no—
52C4⋊Dic15—21no—
53C4⋊Dic15—21no—
54C4⋊Dic15—21no—
55C4⋊Dic15D411yescharacteristic
56C4⋊Dic15D412yes—
57C2×C3⋊#168—21no—
58Q8×D12—51no—
59#5021—51no—
60#4842—51no—
61#4681—51no—
62C3×Q8⋊C8D511yescharacteristic, complemented
63#4486—51no—
64#4459—51no—
65C2×Q8×D5—61no—
66C4×C5×Q8C2×D311yescharacteristic
67#4043—62no—
68#4043—61no—
69C4×D20—31no—
70C4×D20—61no—
71#4015—31no—
72#4015—31no—
73#4015—61no—
74C5×C4⋊C8C2×D311yescharacteristic
75C4×C5×C8C2×D311yescharacteristic
76#3967—61no—
77#3953—61no—
78#3949—61no—
79#3948—62no—
80#3939—61no—
81C4⋊#168—31no—
82#1637—151noSylow
83C22×D15—21no—
84C3×C5×Q8—21no—
85C3×C5×Q8SD1612yes—
86C2×C3×C4×C5—21no—
87C2×C3×C4×C5—21no—
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×Dic15—21no—
92C2×Dic15—22no—
93C2×Dic15—41no—
94D60—21no—
95D60Q1612yes—
96C4×D15—44no—
97C4×D15—41no—
98C4×D15—41no—
99Dic30—44no—
100Dic30—41no—
101Dic30—41no—
102Dic30—42no—
103C3×C5×C8—41no—
104C3×C5×C8—41no—
105C3⋊#168—41no—
106C2×D3×Q8—101no—
107C3×C4×Q8C2×D511yescharacteristic
108#897—102no—
109#897—101no—
110C4×D12—51no—
111C4×D12—101no—
112#869—51no—
113#869—51no—
114#869—101no—
115C3×C4⋊C8C2×D511yescharacteristic
116C3×C4×C8C2×D511yescharacteristic
117#835—101no—
118#821—101no—
119#817—101no—
120#816—102no—
121#807—101no—
122C4⋊(C3⋊C8)—51no—
123C2×C5×Q8D1211yescharacteristic
124Q8×D5—122no—
125Q8×D5—122no—
126C2×D20—31no—
127C2×C4×D5—62no—
128C2×C4×D5—61no—
129C2×Dic10—62no—
130C2×Dic10—61no—
131C2×Dic10—61no—
132C2×C5×C8—21no—
133C2×C5×C8—21no—
134C5×C4⋊C4—21no—
135C5×C4⋊C4D1211yescharacteristic
136C42×C5—21no—
137C42×C5C22×D311yescharacteristic
138#685—62no—
139#685—61no—
140C4⋊Dic5—32no—
141C4⋊Dic5—31no—
142C4⋊Dic5—62no—
143C4⋊Dic5—61no—
144C4⋊Dic5—61no—
145C4⋊Dic5—61no—
146C2×#168—61no—
147D4×Q8—151no—
148#487—151no—
149#477—151no—
150#476—151no—
151#332—151no—
152Q8⋊C8D1511yescharacteristic, complemented
153D4⋊C8—151no—
154C22×C3×C5#12011yescharacteristic
155C2×D15—22no—
156C2×D15—41no—
157C2×D15—41no—
158C3×C4×C5—22no—
159C3×C4×C5—21no—
160C3×C4×C5—41no—
161C3×C4×C5C2×SD1611yescharacteristic
162C3×C4×C5C2×Q1611yescharacteristic
163C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
164C3×C4×C5#13711yescharacteristic
165Dic15—41no—
166Dic15—42no—
167Dic15—81no—
168C2×C3×Q8D2011yescharacteristic
169D3×Q8—202no—
170D3×Q8—202no—
171C2×D12—51no—
172C2×C4×D3—102no—
173C2×C4×D3—101no—
174C2×Dic6—102no—
175C2×Dic6—101no—
176C2×Dic6—101no—
177C2×C3×C8—21no—
178C2×C3×C8—21no—
179C3×C4⋊C4—21no—
180C3×C4⋊C4D2011yescharacteristic
181C3×C42—21no—
182C3×C42C22×D511yescharacteristic
183(C2×D3)⋊C4—102no—
184(C2×D3)⋊C4—101no—
185C4⋊Dic3—52no—
186C4⋊Dic3—51no—
187C4⋊Dic3—102no—
188C4⋊Dic3—101no—
189C4⋊Dic3—101no—
190C4⋊Dic3—101no—
191C2×C3⋊C8—101no—
192C22×D5—61no—
193C5×Q8—21no—
194C5×Q8#20412yes—
195C2×C4×C5—21no—
196C2×C4×C5—21no—
197C2×C4×C5C2×D1211yescharacteristic
198C2×C4×C5D3×D411yescharacteristic
199C2×C4×C5D3×D411yescharacteristic
200C2×Dic5—62no—
201C2×Dic5—61no—
202C2×Dic5—121no—
203D20—32no—
204D20—61no—
205C4×D5—124no—
206C4×D5—121no—
207C4×D5—121no—
208Dic10—124no—
209Dic10—121no—
210Dic10—121no—
211Dic10—122no—
212C5×C8—41no—
213C5×C8—41no—
214#168—121no—
215C22×Q8—301no—
216C4⋊Q8—151no—
217C4⋊Q8—151no—
218C4⋊Q8—301no—
219C22⋊Q8—302no—
220C22⋊Q8—301no—
221C4×Q8C2×D1511yescharacteristic
222C4×D4—151no—
223C4×D4—301no—
224#107—301no—
225#106—301no—
226C4⋊C8—151no—
227C4⋊C8C2×D1511yescharacteristic
228#103—302no—
229#103—301no—
230#102—301no—
231C4×C8C2×D1511yescharacteristic
232C2×C3×C5#45011yescharacteristic
233C2×C3×C5#45111yescharacteristic
234C2×C3×C5#45411yescharacteristic
235D15—42no—
236C22×D3—101no—
237C3×Q8—21no—
238C3×Q8#67712yes—
239C2×C3×C4—21no—
240C2×C3×C4—21no—
241C2×C3×C4C2×D2011yescharacteristic
242C2×C3×C4D4×D511yescharacteristic
243C2×C3×C4D4×D511yescharacteristic
244C2×Dic3—102no—
245C2×Dic3—101no—
246C2×Dic3—201no—
247D12—52no—
248D12—101no—
249C4×D3—204no—
250C4×D3—201no—
251C4×D3—201no—
252Dic6—204no—
253Dic6—201no—
254Dic6—201no—
255Dic6—202no—
256C3×C8—41no—
257C3×C8—41no—
258C3⋊C8—201no—
259C22×C5#88211yescharacteristic
260C2×D5—62no—
261C2×D5—121no—
262C2×D5—121no—
263C4×C5—22no—
264C4×C5—21no—
265C4×C5—41no—
266C4×C5C2×#20411yescharacteristic
267C4×C5#90811yescharacteristic
268C4×C5#91511yescharacteristic
269C4×C5D3×Q1611yescharacteristic
270Dic5—121no—
271Dic5—122no—
272Dic5—241no—
273C2×Q8—302no—
274C2×Q8—301no—
275C2×Q8—301no—
276C2×Q8—602no—
277C2×Q8—602no—
278C2×Q8D6011yescharacteristic
279C2×D4—151no—
280C22×C4—302no—
281C22×C4—301no—
282C2×C8—21no—
283C2×C8—21no—
284C2×C8—301no—
285C4⋊C4—21no—
286C4⋊C4—152no—
287C4⋊C4—151no—
288C4⋊C4—302no—
289C4⋊C4—301no—
290C4⋊C4—301no—
291C4⋊C4—301no—
292C4⋊C4D6011yescharacteristic
293C22⋊C4—302no—
294C22⋊C4—301no—
295C42—21no—
296C42C22×D1511yescharacteristic
297C3×C5#163711yescharacteristic, complemented, Hall
298C22×C3#402811yescharacteristic
299C2×D3—102no—
300C2×D3—201no—
301C2×D3—201no—
302C3×C4—21no—
303C3×C4—22no—
304C3×C4—41no—
305C3×C4C2×#67711yescharacteristic
306C3×C4#405411yescharacteristic
307C3×C4#406111yescharacteristic
308C3×C4D5×Q1611yescharacteristic
309Dic3—201no—
310Dic3—202no—
311Dic3—401no—
312C2×C5#473111yescharacteristic
313C2×C5#480911yescharacteristic
314C2×C5#482711yescharacteristic
315D5—122no—
316C23—301no—
317Q8—21no—
318Q8—604no—
319Q8—602no—
320Q8—601no—
321Q8—601no—
322Q8#670612yes—
323D4—152no—
324D4—301no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—302no—
328C2×C4—301no—
329C2×C4—604no—
330C2×C4—601no—
331C2×C4—601no—
332C2×C4—601no—
333C2×C4C2×D6011yescharacteristic
334C2×C4D4×D1511yescharacteristic
335C2×C4D4×D1511yescharacteristic
336C8—41no—
337C8—41no—
338C8—601no—
339C2×C3#6502011yescharacteristic
340C2×C3#6509711yescharacteristic
341C2×C3#6511611yescharacteristic
342D3—202no—
343C5#6826911yescharacteristic, complemented, Sylow
344C22—302no—
345C22—601no—
346C22—601no—
347C22#9177111yescharacteristic
348C4—21no—
349C4—22no—
350C4—41no—
351C4—602no—
352C4—601no—
353C4—1201no—
354C4C2×#670611yescharacteristic
355C4#9179711yescharacteristic
356C4#9180411yescharacteristic
357C4Q16×D1511yescharacteristic
358C3#1059906211yescharacteristic, complemented, Sylow
359C2—602no—
360C2#1175083211yescharacteristic
361C2#1175091011yescharacteristic
362C2#1175092811yescharacteristic
subgroupG/H
centerC22#91771
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×Q8⋊C8C2
socleC22×C3×C5#120
prime radicalC2×D60D4
hypercenterQ8⋊C8D15
hypocenterC3×C5#1637
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
2. #11751122C2semidirect
4. #11750782C2semidirect
5. C3×C5×Q8⋊C8C2semidirect
6. #11746307C2semidirect
31. C5×Q8⋊C8D3semidirect
62. C3×Q8⋊C8D5semidirect
152. Q8⋊C8D15semidirect
297. C3×C5#1637semidirect
343. C5#68269semidirect
358. C3#10599062semidirect

Maximal subgroups

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

subgroupindex
Q8×D602
#117511222
#117509432
#117507822
C3×C5×Q8⋊C82
#117463072
#117462802
#105990623
#682695