Finite Group Databasebeta

← #18081894

Subgroups — #18081894

Order 4864.

394 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14574145C211yesmaximal, characteristic
2#14563504C211yesmaximal, characteristic
3#14562381C211yesmaximal, characteristic
4#14562133C211yesmaximal, characteristic
5#14562039C211yesmaximal, characteristic
6#14562038C211yesmaximal, characteristic
7C19×#1503C211yesmaximal, characteristic
8#11927101C2211yescharacteristic
9#11926947C411yescharacteristic, complemented
10#11926947C411yescharacteristic, complemented
11#11926943—21no—
12#11926943—21no—
13#11926940C411yescharacteristic, complemented
14#11926940C411yescharacteristic, complemented
15#11926597C2211yescharacteristic
16#11926580—21no—
17#11926580—21no—
18C2×C4⋊(C19⋊C8)C2211yescharacteristic
19C2×#10597260—21no—
20C2×C4×C19⋊C8C2211yescharacteristic
21#11926299—21no—
22#11926296—21no—
23#11926294—21no—
24#11926280—22no—
25#11926276—22no—
26Q8⋊(C19⋊C8)—22no—
27C19×#533C2211yescharacteristic
28C19×#431C2211yescharacteristic
29C4×C4⋊C4×C19C2211yescharacteristic
30C19×#328—22no—
31C19×C4⋊Q8C2×C411yescharacteristic
32C19×C4⋊Q8C2×C411yescharacteristic
33C19×#125—21no—
34C19×C22⋊Q8—21no—
35C19×C22⋊Q8—21no—
36C4×Q8×C19—21no—
37C4×Q8×C19—21no—
38C19×#117—21no—
39C2×C4⋊C4×C19—21no—
40C2×C42×C19—21no—
41C2×C42×C19C2311yescharacteristic
42#10597372—21no—
43#10597370—21no—
44#10597370—21no—
45C22×C19⋊C8—21no—
46C22×C19⋊C8D411yescharacteristic
47C22×C19⋊C8D411yescharacteristic
48#10597316—21no—
49#10597315C2×C411yescharacteristic
50#10597315C2×C411yescharacteristic
51C4×Dic38—21no—
52C4×Dic38—21no—
53C19×C4⋊C8—21no—
54C19×C22⋊C8—21no—
55C4×C8×C19—21no—
56C19×#95D412yes—
57C22⋊(C19⋊C8)—21no—
58#10597265—21no—
59#10597265—21no—
60#10597265—21no—
61#10597265—21no—
62#10597264—21no—
63#10597264—21no—
64#10597264—21no—
65#10597264—21no—
66C4⋊(C19⋊C8)—21no—
67C4⋊(C19⋊C8)—21no—
68C4⋊(C19⋊C8)D412yes—
69#10597260—42no—
70C4×C19⋊C8—21no—
71C4×C19⋊C8C2×C411yescharacteristic
72C4×C19⋊C8C2×C411yescharacteristic
73C4×C19⋊C8D411yescharacteristic
74C4×C19⋊C8D411yescharacteristic
75C2×Q8×C19—21no—
76C2×Q8×C19—21no—
77C22×C4×C19—22no—
78C22×C4×C19C2×D411yescharacteristic
79C22×C4×C19C2×D411yescharacteristic
80C22×C4×C19#4111yescharacteristic
81C2×Dic38—21no—
82C2×Dic38—21no—
83C2×C8×C19—41no—
84C4⋊C4×C19—21no—
85C4⋊C4×C19—21no—
86C4⋊C4×C19—21no—
87C4⋊C4×C19—21no—
88C4⋊C4×C19—42no—
89C4⋊C4×C19—41no—
90C4⋊C4×C19—41no—
91C22⋊C4×C19—41no—
92C42×C19—41no—
93C42×C19—41no—
94C42×C19—41no—
95C42×C19C22×C411yescharacteristic
96C42×C19C2×D411yescharacteristic
97C42×C19C2×D411yescharacteristic
98C42×C19#4111yescharacteristic
99C22⋊Dic19—41no—
100C4⋊Dic19—21no—
101C4⋊Dic19—21no—
102C4⋊Dic19—21no—
103C4⋊Dic19—21no—
104Dic19⋊C4—41no—
105Dic19⋊C4—41no—
106C4×Dic19—41no—
107C2×C19⋊C8—21no—
108C2×C19⋊C8—21no—
109C2×C19⋊C8—22no—
110C2×C19⋊C8—41no—
111C2×C19⋊C8—41no—
112C2×C19⋊C8—41no—
113C2×C19⋊C8C22⋊C411yescharacteristic
114C2×C19⋊C8C22⋊C411yescharacteristic
115C2×C19⋊C8C22⋊C411yescharacteristic
116C2×C19⋊C8C22⋊C411yescharacteristic
117C2×C19⋊C8SD1612yes—
118C2×C19⋊C8Q1612yes—
119#9752—191nomaximal, Sylow
120C23×C19#12111yescharacteristic
121Q8×C19—42no—
122Q8×C19—81no—
123C2×C4×C19—22no—
124C2×C4×C19—41no—
125C2×C4×C19—42no—
126C2×C4×C19—42no—
127C2×C4×C19—41no—
128C2×C4×C19—41no—
129C2×C4×C19—42no—
130C2×C4×C19C2×C22⋊C411yescharacteristic
131C2×C4×C19C4×D411yescharacteristic
132C2×C4×C19C4×D411yescharacteristic
133C2×C4×C19#12111yescharacteristic
134C2×C4×C19#12411yescharacteristic
135C2×C4×C19#12711yescharacteristic
136C2×C4×C19C2×SD1611yescharacteristic
137C2×C4×C19C2×Q1611yescharacteristic
138C2×C4×C19#13711yescharacteristic
139C2×C4×C19#13711yescharacteristic
140C2×Dic19—41no—
141C2×Dic19—41no—
142Dic38—42no—
143Dic38—81no—
144C8×C19—81no—
145C19⋊C8—21no—
146C19⋊C8—21no—
147C19⋊C8—42no—
148C19⋊C8—81no—
149C19⋊C8#10312yes—
150C19⋊C8#10312yes—
151#3160—191no—
152#1770—191no—
153#1564—191no—
154#1503—191no—
155#1503D1911yescharacteristic
156#1481—191no—
157#1481—191no—
158C22×C19—21no—
159C22×C19—21no—
160C22×C19#39011yescharacteristic
161C22×C19#46111yescharacteristic
162C22×C19#46211yescharacteristic
163C4×C19—21no—
164C4×C19—21no—
165C4×C19—21no—
166C4×C19—82no—
167C4×C19—81no—
168C4×C19—81no—
169C4×C19C2×#10311yescharacteristic
170C4×C19#41911yescharacteristic
171C4×C19#44412yes—
172C4×C19#46111yescharacteristic
173C4×C19#46211yescharacteristic
174Dic19—81no—
175Dic19—81no—
176#533—191no—
177#533C2×D1911yescharacteristic
178#500—191no—
179#500—191no—
180#499—381no—
181#499—381no—
182#498—191no—
183#498—191no—
184#431—191no—
185#431C2×D1911yescharacteristic
186#427—381no—
187#427—381no—
188C2×C4⋊C8—191no—
189C2×#97—381no—
190C2×C4×C8—191no—
191C4×C4⋊C4C2×D1911yescharacteristic
192#336—381no—
193#335—381no—
194#334—381no—
195#328—22no—
196#328—382no—
197Q8⋊C8—382no—
198Q8⋊C8—382no—
199C2×C19—21no—
200C2×C19—21no—
201C2×C19#197511yescharacteristic
202C2×C19#197611yescharacteristic
203C2×C19#198111yescharacteristic
204C22×C8—191no—
205C22×C8—191no—
206C22×C8—381no—
207C4⋊Q8—191no—
208C4⋊Q8—191no—
209C4⋊Q8C4×D1911yescharacteristic
210C4⋊Q8C4×D1911yescharacteristic
211#125—21no—
212#125—381no—
213C22⋊Q8—21no—
214C22⋊Q8—21no—
215C22⋊Q8—381no—
216C22⋊Q8—381no—
217C4×Q8—21no—
218C4×Q8—21no—
219C4×Q8—381no—
220C4×Q8—381no—
221#117—21no—
222#117—381no—
223C2×C4⋊C4—21no—
224C2×C42—21no—
225C2×C42C22×D1911yescharacteristic
226#107—381no—
227#107—381no—
228#107—381no—
229#107—381no—
230#106—381no—
231#106—381no—
232#106—381no—
233#106—381no—
234C4⋊C8—21no—
235C4⋊C8—192no—
236C4⋊C8—381no—
237C4⋊C8—381no—
238C22⋊C8—21no—
239C22⋊C8—381no—
240#97—762no—
241C4×C8—21no—
242C4×C8—191no—
243C4×C8—191no—
244C4×C8—191no—
245C4×C8—191no—
246C4×C8—381no—
247#95C22⋊D1912yes—
248C19#975211yescharacteristic, complemented, Sylow
249C2×Q8—21no—
250C2×Q8—21no—
251C2×Q8—381no—
252C2×Q8—381no—
253C22×C4—22no—
254C22×C4D4×D1911yescharacteristic
255C22×C4#6454311yescharacteristic
256C22×C4C2×C22⋊D1911yescharacteristic
257C2×C8—41no—
258C2×C8—191no—
259C2×C8—191no—
260C2×C8—192no—
261C2×C8—192no—
262C2×C8—191no—
263C2×C8—191no—
264C2×C8—381no—
265C2×C8—381no—
266C2×C8—382no—
267C2×C8—761no—
268C2×C8—761no—
269C2×C8—761no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—42no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—381no—
278C4⋊C4—381no—
279C4⋊C4—381no—
280C4⋊C4—381no—
281C4⋊C4—761no—
282C4⋊C4—761no—
283C22⋊C4—41no—
284C22⋊C4—761no—
285C42—41no—
286C42—41no—
287C42—41no—
288C42—761no—
289C42C2×C4×D1911yescharacteristic
290C42#6454111yescharacteristic
291C42D4×D1911yescharacteristic
292C42D4×D1911yescharacteristic
293C23#1059738511yescharacteristic
294Q8—42no—
295Q8—81no—
296Q8—762no—
297Q8—1521no—
298C2×C4—22no—
299C2×C4—41no—
300C2×C4—42no—
301C2×C4—42no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—42no—
305C2×C4—761no—
306C2×C4—761no—
307C2×C4C22⋊C4×D1911yescharacteristic
308C2×C4(C22⋊D19)⋊C411yescharacteristic
309C2×C4#1059733011yescharacteristic
310C2×C4#1059733111yescharacteristic
311C2×C4SD16×D1911yescharacteristic
312C2×C4#1059736111yescharacteristic
313C2×C4Q16×D1911yescharacteristic
314C2×C4#1059736411yescharacteristic
315C2×C4C4×C22⋊D1911yescharacteristic
316C2×C4#1059738611yescharacteristic
317C8—81no—
318C8—192no—
319C8—192no—
320C8—381no—
321C8—381no—
322C8—762no—
323C8—1521no—
324C22—21no—
325C22—21no—
326C22#1192644411yescharacteristic
327C22#1192674711yescharacteristic
328C22#1192675211yescharacteristic
329C4—21no—
330C4—21no—
331C4—21no—
332C4—82no—
333C4—81no—
334C4—81no—
335C4—1521no—
336C4—1521no—
337C4#103×D1911yescharacteristic
338C4#1192655111yescharacteristic
339C4#1192666312yes—
340C4#1192674811yescharacteristic
341C4#1192675311yescharacteristic
342C2—21no—
343C2—21no—
344C2#1456452511yescharacteristic
345C2#1456453011yescharacteristic
346C2#1456455611yescharacteristic
subgroupG/H
centerC2×C4#10597330
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1503C2
socleC22×C19#390
prime radicalC23×C19#121
cosocleC2×C42×C19C23
hypercenter#1503D19
hypocenterC19#9752
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1503

Complements

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

NH ≅ G/Ntype
9. #11926947C4semidirect
10. #11926947C4semidirect
13. #11926940C4semidirect
14. #11926940C4semidirect
248. C19#9752semidirect

Maximal subgroups

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

subgroupindex
#145741452
#145635042
#145623812
#145621332
#145620392
#145620382
C19×#15032
#975219