Finite Group Databasebeta

← #18081911

Subgroups — #18081911

Order 4864.

394 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14574145C211yesmaximal, characteristic
2#14563797C211yesmaximal, characteristic
3#14562200C211yesmaximal, characteristic
4#14562199C211yesmaximal, characteristic
5#14562198C211yesmaximal, characteristic
6#14561919C211yesmaximal, characteristic
7C19×#1518C211yesmaximal, 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×#10597264—21no—
19C2×#10597265—21no—
20C2×C4×C19⋊C8C2211yescharacteristic
21#11926410C2211yescharacteristic
22#11926282—22no—
23#11926281—22no—
24#11926280—22no—
25#11926266—21no—
26C8×C19⋊C8—21no—
27C19×#533C2211yescharacteristic
28C19×#431C2211yescharacteristic
29C19×#382C2211yescharacteristic
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×C19C2311yescharacteristic
41#10597372—21no—
42C2×C4⋊Dic19—21no—
43#10597370—21no—
44#10597370—21no—
45C22×C19⋊C8D411yescharacteristic
46C22×C19⋊C8D411yescharacteristic
47#10597316—21no—
48#10597315C2×C411yescharacteristic
49#10597315C2×C411yescharacteristic
50C4×Dic38—21no—
51C4×Dic38—21no—
52C19×C4⋊C8—21no—
53C19×C22⋊C8D412yes—
54C4×C8×C19—21no—
55C19×#95—21no—
56C19×#95—21no—
57C19⋊#95—21no—
58C19⋊#95—21no—
59C22⋊(C19⋊C8)D412yes—
60#10597265—21no—
61#10597265—21no—
62#10597265—21no—
63#10597265—21no—
64#10597265—42no—
65#10597264—21no—
66#10597264—21no—
67#10597264—21no—
68#10597264—21no—
69#10597264—42no—
70C4⋊(C19⋊C8)—21no—
71C4×C19⋊C8—21no—
72C4×C19⋊C8C2×C411yescharacteristic
73C4×C19⋊C8C2×C411yescharacteristic
74C4×C19⋊C8D411yescharacteristic
75C4×C19⋊C8D411yescharacteristic
76C2×Q8×C19—21no—
77C2×Q8×C19—21no—
78C22×C4×C19—41no—
79C22×C4×C19C2×D411yescharacteristic
80C22×C4×C19C2×D411yescharacteristic
81C22×C4×C19C2×D411yescharacteristic
82C22×Dic19—41no—
83C2×Dic38—21no—
84C2×Dic38—21no—
85C2×C8×C19—22no—
86C4⋊C4×C19—21no—
87C4⋊C4×C19—21no—
88C4⋊C4×C19—21no—
89C4⋊C4×C19—21no—
90C4⋊C4×C19—41no—
91C4⋊C4×C19—41no—
92C4⋊C4×C19—41no—
93C4⋊C4×C19—41no—
94C22⋊C4×C19—41no—
95C42×C19—41no—
96C42×C19C22×C411yescharacteristic
97C42×C19C2×D411yescharacteristic
98C42×C19#4111yescharacteristic
99C42×C19#4111yescharacteristic
100C22⋊Dic19—41no—
101C4⋊Dic19—21no—
102C4⋊Dic19—21no—
103C4⋊Dic19—21no—
104C4⋊Dic19—21no—
105C4⋊Dic19—41no—
106C4⋊Dic19—41no—
107Dic19⋊C4—41no—
108Dic19⋊C4—41no—
109C4×Dic19—41no—
110C2×C19⋊C8—22no—
111C2×C19⋊C8C22⋊C411yescharacteristic
112C2×C19⋊C8C22⋊C411yescharacteristic
113C2×C19⋊C8C22⋊C411yescharacteristic
114C2×C19⋊C8C22⋊C411yescharacteristic
115C2×C19⋊C8SD1612yes—
116C2×C19⋊C8SD1612yes—
117C2×C19⋊C8Q1612yes—
118C2×C19⋊C8Q1612yes—
119#9755—191nomaximal, Sylow
120C23×C19#12711yescharacteristic
121Q8×C19—81no—
122Q8×C19—81no—
123C2×C4×C19—41no—
124C2×C4×C19—41no—
125C2×C4×C19—41no—
126C2×C4×C19—41no—
127C2×C4×C19—81no—
128C2×C4×C19—81no—
129C2×C4×C19—81no—
130C2×C4×C19C2×C22⋊C411yescharacteristic
131C2×C4×C19C4×D411yescharacteristic
132C2×C4×C19C4×D411yescharacteristic
133C2×C4×C19#12111yescharacteristic
134C2×C4×C19#12111yescharacteristic
135C2×C4×C19#12411yescharacteristic
136C2×C4×C19C2×SD1611yescharacteristic
137C2×C4×C19C2×SD1611yescharacteristic
138C2×C4×C19C2×Q1611yescharacteristic
139C2×C4×C19C2×Q1611yescharacteristic
140C2×Dic19—41no—
141C2×Dic19—41no—
142C2×Dic19—81no—
143C2×Dic19—81no—
144C2×Dic19—81no—
145Dic38—81no—
146Dic38—81no—
147C8×C19—42no—
148C19⋊C8—42no—
149C19⋊C8#10312yes—
150C19⋊C8#10312yes—
151C19⋊C8#10312yes—
152C19⋊C8#10312yes—
153#3160—191no—
154#1846—191no—
155#1518—191no—
156#1518—191no—
157#1518—191no—
158#1518D1911yescharacteristic
159#1450—191no—
160C22×C19—21no—
161C22×C19—21no—
162C22×C19#39011yescharacteristic
163C22×C19#49211yescharacteristic
164C22×C19#49411yescharacteristic
165C4×C19—21no—
166C4×C19—21no—
167C4×C19—21no—
168C4×C19—21no—
169C4×C19—81no—
170C4×C19—81no—
171C4×C19—161no—
172C4×C19C2×#10311yescharacteristic
173C4×C19C2×#10311yescharacteristic
174C4×C19#48711yescharacteristic
175C4×C19#48711yescharacteristic
176Dic19—81no—
177Dic19—81no—
178Dic19—161no—
179#533—191no—
180#533C2×D1911yescharacteristic
181#500—191no—
182#500—191no—
183#499—381no—
184#499—381no—
185#498—191no—
186#498—191no—
187#431—191no—
188#431C2×D1911yescharacteristic
189#427—381no—
190#427—381no—
191C2×#107—381no—
192C2×#106—381no—
193C2×C4×C8—191no—
194#382—191no—
195#382C2×D1911yescharacteristic
196#328—22no—
197#328—382no—
198#328—382no—
199#328—382no—
200#322—381no—
201C82—381no—
202C2×C19—21no—
203C2×C19—21no—
204C2×C19#195611yescharacteristic
205C2×C19#197611yescharacteristic
206C2×C19#197611yescharacteristic
207C22×C8—191no—
208C22×C8—191no—
209C4⋊Q8—191no—
210C4⋊Q8—191no—
211C4⋊Q8C4×D1911yescharacteristic
212C4⋊Q8C4×D1911yescharacteristic
213#125—21no—
214#125—381no—
215C22⋊Q8—21no—
216C22⋊Q8—21no—
217C22⋊Q8—381no—
218C22⋊Q8—381no—
219C4×Q8—21no—
220C4×Q8—21no—
221C4×Q8—381no—
222C4×Q8—381no—
223#117—21no—
224#117—381no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—381no—
227C2×C42C22×D1911yescharacteristic
228#107—381no—
229#107—381no—
230#107—381no—
231#107—381no—
232#107—762no—
233#106—381no—
234#106—381no—
235#106—381no—
236#106—381no—
237#106—762no—
238C4⋊C8—21no—
239C4⋊C8—381no—
240C22⋊C8—192no—
241C22⋊C8C22⋊D1912yes—
242C4×C8—21no—
243C4×C8—191no—
244C4×C8—191no—
245C4×C8—191no—
246C4×C8—191no—
247C4×C8—381no—
248#95—21no—
249#95—21no—
250#95—381no—
251#95—381no—
252C19#975511yescharacteristic, complemented, Sylow
253C2×Q8—21no—
254C2×Q8—21no—
255C2×Q8—381no—
256C2×Q8—381no—
257C22×C4—41no—
258C22×C4—761no—
259C22×C4D4×D1911yescharacteristic
260C22×C4D4×D1911yescharacteristic
261C22×C4C2×C22⋊D1911yescharacteristic
262C2×C8—22no—
263C2×C8—191no—
264C2×C8—191no—
265C2×C8—191no—
266C2×C8—191no—
267C2×C8—192no—
268C2×C8—192no—
269C2×C8—192no—
270C2×C8—192no—
271C2×C8—382no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—381no—
281C4⋊C4—381no—
282C4⋊C4—381no—
283C4⋊C4—381no—
284C4⋊C4—761no—
285C4⋊C4—761no—
286C4⋊C4—761no—
287C4⋊C4—761no—
288C22⋊C4—41no—
289C22⋊C4—761no—
290C42—41no—
291C42—761no—
292C42C2×C4×D1911yescharacteristic
293C42#6454111yescharacteristic
294C42D4×D1911yescharacteristic
295C42#6454311yescharacteristic
296C23#1059738611yescharacteristic
297Q8—81no—
298Q8—81no—
299Q8—1521no—
300Q8—1521no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—81no—
306C2×C4—81no—
307C2×C4—81no—
308C2×C4—761no—
309C2×C4—761no—
310C2×C4—1521no—
311C2×C4—1521no—
312C2×C4—1521no—
313C2×C4C22⋊C4×D1911yescharacteristic
314C2×C4(C22⋊D19)⋊C411yescharacteristic
315C2×C4#1059733011yescharacteristic
316C2×C4#1059733111yescharacteristic
317C2×C4SD16×D1911yescharacteristic
318C2×C4SD16×D1911yescharacteristic
319C2×C4Q16×D1911yescharacteristic
320C2×C4Q16×D1911yescharacteristic
321C2×C4C4×C22⋊D1911yescharacteristic
322C2×C4#1059738511yescharacteristic
323C8—42no—
324C8—192no—
325C8—192no—
326C8—192no—
327C8—192no—
328C8—762no—
329C22—21no—
330C22—21no—
331C22#1192644411yescharacteristic
332C22#1192691511yescharacteristic
333C22#1192692211yescharacteristic
334C4—21no—
335C4—21no—
336C4—21no—
337C4—21no—
338C4—81no—
339C4—81no—
340C4—161no—
341C4—3041no—
342C4—1521no—
343C4—1521no—
344C4#103×D1911yescharacteristic
345C4#103×D1911yescharacteristic
346C4#1192689311yescharacteristic
347C4#1192689311yescharacteristic
348C2—21no—
349C2—21no—
350C2#1456443511yescharacteristic
351C2#1456453011yescharacteristic
352C2#1456453211yescharacteristic
subgroupG/H
centerC22#11926444
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1518C2
socleC22×C19#390
prime radicalC23×C19#127
cosocleC2×C42×C19C23
hypercenter#1518D19
hypocenterC19#9755
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1518

Complements

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

NH ≅ G/Ntype
9. #11926947C4semidirect
10. #11926947C4semidirect
13. #11926940C4semidirect
14. #11926940C4semidirect
252. C19#9755semidirect

Maximal subgroups

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

subgroupindex
#145741452
#145637972
#145622002
#145621992
#145621982
#145619192
C19×#15182
#975519