Finite Group Databasebeta

← #14289555

Subgroups — #14289555

Order 1920.

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

normal subgroups only

This group has 412 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×Dic30C211yesmaximal, characteristic
2#11751122C211yesmaximal, characteristic
3#11750951C211yesmaximal, characteristic
4#11750800C211yesmaximal, characteristic
5C3×C5×Q8⋊C8C211yesmaximal, characteristic
6#11746302C211yesmaximal, characteristic
7#11746277C211yesmaximal, characteristic
8#10599060—31nomaximal, Hall
9C3×C4×C5×Q8C2211yescharacteristic
10Q8×Dic15—21no—
11C2×Dic60—22no—
12#91777—22no—
13#91777—21no—
14#91758—21no—
15#91758C2211yescharacteristic
16#91758C2211yescharacteristic
17C4×Dic30—21no—
18C4×Dic30C2211yescharacteristic
19C3×C5×C4⋊C8C2211yescharacteristic
20C3×C4×C5×C8C2211yescharacteristic
21#91119—21no—
22#91102—21no—
23#91100—21no—
24#91091—21no—
25C4⋊(C3⋊#168)C2211yescharacteristic
26#68267—51nomaximal, Hall
27Q8×Dic10—31no—
28#65310—31no—
29#65139—31no—
30#64988—31no—
31C5×Q8⋊C8D311yescharacteristic
32#64701—31no—
33#64676—31no—
34C2×C3×C5×Q8D411yescharacteristic
35C2×Dic30—21no—
36C2×Dic30—22no—
37C2×Dic30D411yescharacteristic
38C2×Dic30D412yes—
39C2×C3×C5×C8—21no—
40C2×C3×C5×C8—21no—
41C3×C5×C4⋊C4—21no—
42C3×C5×C4⋊C4D411yescharacteristic
43C3×C42×C5—21no—
44C3×C42×C5C2311yescharacteristic
45C4⋊Dic15—22no—
46C4⋊Dic15—21no—
47C4⋊Dic15—21no—
48C4⋊Dic15—21no—
49C4⋊Dic15—21no—
50C4⋊Dic15D411yescharacteristic
51#6712—22no—
52#6712—21no—
53C4×Dic15—22no—
54C4×Dic15—21no—
55C2×C3⋊#168—21no—
56Dic60—44no—
57Q8×Dic6—51no—
58#5021—51no—
59#4850—51no—
60#4699—51no—
61C3×Q8⋊C8D511yescharacteristic
62#4481—51no—
63#4456—51no—
64C4×C5×Q8C2×D311yescharacteristic
65Q8×Dic5—61no—
66C2×Dic20—62no—
67#4034—62no—
68#4034—61no—
69#4015—31no—
70#4015—31no—
71#4015—61no—
72C4×Dic10—31no—
73C4×Dic10—61no—
74C5×C4⋊C8C2×D311yescharacteristic
75C4×C5×C8C2×D311yescharacteristic
76#3967—61no—
77#3950—61no—
78#3948—61no—
79#3939—61no—
80C4⋊#168—31no—
81#1633—151noSylow
82C3×C5×Q8—21no—
83C3×C5×Q8Q1612yescomplemented
84C2×C3×C4×C5—21no—
85C2×C3×C4×C5—21no—
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×Dic15—21no—
90C2×Dic15—22no—
91C2×Dic15—21no—
92C2×Dic15—41no—
93Dic30—21no—
94Dic30—42no—
95Dic30—42no—
96Dic30—82no—
97Dic30Q1612yescomplemented
98C3×C5×C8—22no—
99C3×C5×C8—41no—
100C3⋊#168—41no—
101C3×C4×Q8C2×D511yescharacteristic
102Q8×Dic3—101no—
103C2×Dic12—102no—
104#888—102no—
105#888—101no—
106#869—51no—
107#869—51no—
108#869—101no—
109C4×Dic6—51no—
110C4×Dic6—101no—
111C3×C4⋊C8C2×D511yescharacteristic
112C3×C4×C8C2×D511yescharacteristic
113#835—101no—
114#818—101no—
115#816—101no—
116#807—101no—
117C4⋊(C3⋊C8)—51no—
118C2×C5×Q8D1211yescharacteristic
119C2×Dic10—31no—
120C2×Dic10—32no—
121C2×Dic10—61no—
122C2×Dic10—62no—
123C2×C5×C8—21no—
124C2×C5×C8—21no—
125C5×C4⋊C4—21no—
126C5×C4⋊C4D1211yescharacteristic
127C42×C5—21no—
128C42×C5C22×D311yescharacteristic
129C4⋊Dic5—31no—
130C4⋊Dic5—62no—
131C4⋊Dic5—61no—
132C4⋊Dic5—61no—
133C4⋊Dic5—61no—
134C4⋊Dic5—61no—
135#683—62no—
136#683—61no—
137C4×Dic5—62no—
138C4×Dic5—61no—
139C2×#168—61no—
140Dic20—124no—
141Q82—151no—
142#494—151no—
143#477—151no—
144#477—151no—
145#333—151no—
146Q8⋊C8—151no—
147Q8⋊C8D1511yescharacteristic
148C22×C3×C5#12011yescharacteristic
149C3×C4×C5—22no—
150C3×C4×C5—21no—
151C3×C4×C5—41no—
152C3×C4×C5C2×Q1611yescharacteristic
153C3×C4×C5C2×Q1611yescharacteristic
154C3×C4×C5#13711yescharacteristic
155C3×C4×C5#13711yescharacteristic
156Dic15—22no—
157Dic15—42no—
158Dic15—41no—
159Dic15—81no—
160C2×C3×Q8D2011yescharacteristic
161C2×Dic6—51no—
162C2×Dic6—52no—
163C2×Dic6—101no—
164C2×Dic6—102no—
165C2×C3×C8—21no—
166C2×C3×C8—21no—
167C3×C4⋊C4—21no—
168C3×C4⋊C4D2011yescharacteristic
169C3×C42—21no—
170C3×C42C22×D511yescharacteristic
171C4⋊Dic3—51no—
172C4⋊Dic3—102no—
173C4⋊Dic3—101no—
174C4⋊Dic3—101no—
175C4⋊Dic3—101no—
176C4⋊Dic3—101no—
177Dic3⋊C4—102no—
178Dic3⋊C4—101no—
179C4×Dic3—102no—
180C4×Dic3—101no—
181C2×C3⋊C8—101no—
182Dic12—204no—
183C5×Q8—21no—
184C5×Q8Dic1212yescomplemented
185C2×C4×C5—21no—
186C2×C4×C5—21no—
187C2×C4×C5C2×D1211yescharacteristic
188C2×C4×C5D3×D411yescharacteristic
189C2×C4×C5D3×D411yescharacteristic
190C2×Dic5—61no—
191C2×Dic5—61no—
192C2×Dic5—62no—
193C2×Dic5—121no—
194Dic10—32no—
195Dic10—61no—
196Dic10—122no—
197Dic10—122no—
198Dic10—242no—
199C5×C8—22no—
200C5×C8—41no—
201#168—121no—
202C2×Q16—302no—
203C4⋊Q8—151no—
204C4⋊Q8—151no—
205C4⋊Q8—301no—
206C4⋊Q8—302no—
207C4⋊Q8—301no—
208C4×Q8—151no—
209C4×Q8—301no—
210C4×Q8—301no—
211C4×Q8C2×D1511yescharacteristic
212#107—301no—
213#107—301no—
214C4⋊C8—151no—
215C4⋊C8C2×D1511yescharacteristic
216#103—301no—
217#103—301no—
218C4×C8C2×D1511yescharacteristic
219C2×C3×C5#45111yescharacteristic
220C2×C3×C5#45111yescharacteristic
221C2×C3×C5#45311yescharacteristic
222C3×Q8—21no—
223C3×Q8Dic2012yescomplemented
224C2×C3×C4—21no—
225C2×C3×C4—21no—
226C2×C3×C4C2×D2011yescharacteristic
227C2×C3×C4D4×D511yescharacteristic
228C2×C3×C4D4×D511yescharacteristic
229C2×Dic3—101no—
230C2×Dic3—101no—
231C2×Dic3—102no—
232C2×Dic3—201no—
233Dic6—52no—
234Dic6—101no—
235Dic6—202no—
236Dic6—202no—
237Dic6—402no—
238C3×C8—22no—
239C3×C8—41no—
240C3⋊C8—201no—
241C22×C5#88211yescharacteristic
242C4×C5—22no—
243C4×C5—21no—
244C4×C5—41no—
245C4×C5C2×Dic1211yescharacteristic
246C4×C5#90911yescharacteristic
247C4×C5#91511yescharacteristic
248C4×C5D3×Q1611yescharacteristic
249Dic5—62no—
250Dic5—122no—
251Dic5—121no—
252Dic5—241no—
253C2×Q8—151no—
254C2×Q8—152no—
255C2×Q8—302no—
256C2×Q8—301no—
257C2×Q8D6011yescharacteristic
258Q16—604no—
259C2×C8—21no—
260C2×C8—21no—
261C2×C8—301no—
262C4⋊C4—21no—
263C4⋊C4—151no—
264C4⋊C4—302no—
265C4⋊C4—302no—
266C4⋊C4—301no—
267C4⋊C4—301no—
268C4⋊C4—301no—
269C4⋊C4—301no—
270C4⋊C4—301no—
271C4⋊C4D6011yescharacteristic
272C42—21no—
273C42—302no—
274C42—301no—
275C42C22×D1511yescharacteristic
276C3×C5#163311yescharacteristic, complemented, Hall
277C22×C3#402811yescharacteristic
278C3×C4—22no—
279C3×C4—21no—
280C3×C4—41no—
281C3×C4C2×Dic2011yescharacteristic
282C3×C4#405511yescharacteristic
283C3×C4#406111yescharacteristic
284C3×C4D5×Q1611yescharacteristic
285Dic3—102no—
286Dic3—202no—
287Dic3—201no—
288Dic3—401no—
289C2×C5#473911yescharacteristic
290C2×C5#480911yescharacteristic
291C2×C5#482211yescharacteristic
292Q8—21no—
293Q8—152no—
294Q8—301no—
295Q8—602no—
296Q8—602no—
297Q8—1202no—
298Q8Dic6012yescomplemented
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—301no—
302C2×C4—301no—
303C2×C4—302no—
304C2×C4—601no—
305C2×C4C2×D6011yescharacteristic
306C2×C4D4×D1511yescharacteristic
307C2×C4D4×D1511yescharacteristic
308C8—22no—
309C8—41no—
310C8—601no—
311C2×C3#6502811yescharacteristic
312C2×C3#6509711yescharacteristic
313C2×C3#6511111yescharacteristic
314C5#6826711yescharacteristic, complemented, Sylow
315C22#9177111yescharacteristic
316C4—21no—
317C4—22no—
318C4—41no—
319C4—302no—
320C4—602no—
321C4—601no—
322C4—1201no—
323C4C2×Dic6011yescharacteristic
324C4#9179811yescharacteristic
325C4#9180411yescharacteristic
326C4Q16×D1511yescharacteristic
327C3#1059906011yescharacteristic, complemented, Sylow
328C2#1175084011yescharacteristic
329C2#1175091011yescharacteristic
330C2#1175092311yescharacteristic
subgroupG/H
centerC22#91771
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×Q8⋊C8C2
socle, prime radicalC22×C3×C5#120
hypercenterQ8⋊C8D15
hypocenterC3×C5#1633
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
83. C3×C5×Q8Q16semidirect
97. Dic30Q16semidirect
184. C5×Q8Dic12semidirect
223. C3×Q8Dic20semidirect
276. C3×C5#1633semidirect
298. Q8Dic60semidirect
314. C5#68267semidirect
327. C3#10599060semidirect

Maximal subgroups

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

subgroupindex
Q8×Dic302
#117511222
#117509512
#117508002
C3×C5×Q8⋊C82
#117463022
#117462772
#105990603
#682675