Finite Group Databasebeta

← #18082698

Subgroups — #18082698

Order 4864.

438 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14571996C211yesmaximal, characteristic
2#14563786C211yesmaximal, characteristic
3#14563490C211yesmaximal, characteristic
4#14561519C211yesmaximal, characteristic
5#14561519C211yesmaximal, characteristic
6#14561518C211yesmaximal, characteristic
7C19×#1296C211yesmaximal, characteristic
8C2×#10597336C412yes—
9C2×C4⋊(C19⋊C8)C2211yescharacteristic
10C2×C4⋊(C19⋊C8)C2211yescharacteristic
11C2×Dic19⋊C8—21no—
12C2×Dic19⋊C8—21no—
13C2×#10597272—21no—
14#11926443—21no—
15#11926443—21no—
16#11926440—21no—
17#11926440—21no—
18#11926414C2211yescharacteristic
19#11926409C412yes—
20C42×Dic19C2211yescharacteristic
21#11926298—21no—
22C2×C19×C4⋊C8C2211yescharacteristic
23C2×C19×C4⋊C8C2211yescharacteristic
24C19×#384C2211yescharacteristic
25C22×C8×C19—21no—
26C22×C8×C19—21no—
27C2×C4⋊C4×C19—21no—
28C2×C4⋊C4×C19—21no—
29C2×C4⋊C4×C19C2×C412yes—
30C2×C42×C19C2311yescharacteristic
31C2×C4⋊Dic19—21no—
32C2×C4⋊Dic19—21no—
33C2×C4⋊Dic19—22no—
34C2×C4⋊Dic19C2×C412yes—
35C2×Dic19⋊C4—22no—
36C2×C4×Dic19C2×C411yescharacteristic
37C2×C4×Dic19C2×C411yescharacteristic
38C2×C4×Dic19D411yescharacteristic
39C2×C4×Dic19D411yescharacteristic
40C2×C4×Dic19D411yescharacteristic
41C2×C4×Dic19D411yescharacteristic
42C22×C19⋊C8—21no—
43C22×C19⋊C8—21no—
44#10597336—44no—
45C19×C4⋊C8—21no—
46C19×C4⋊C8—21no—
47C19×C4⋊C8—21no—
48C19×C4⋊C8Q812yes—
49C19⋊#95—22no—
50C19⋊#95—22no—
51#10597272—42no—
52Dic19⋊C8—42no—
53Dic19⋊C8—42no—
54C4⋊(C19⋊C8)—21no—
55C4⋊(C19⋊C8)—21no—
56C4⋊(C19⋊C8)—21no—
57C4⋊(C19⋊C8)Q812yes—
58C22×C4×C19—22no—
59C22×C4×C19C22×C411yescharacteristic
60C22×C4×C19C2×D411yescharacteristic
61C22×C4×C19C2×D411yescharacteristic
62C22×Dic19—22no—
63C22×Dic19C22⋊C411yescharacteristic
64C22×Dic19C22⋊C411yescharacteristic
65C22×Dic19C22⋊C411yescharacteristic
66C22×Dic19C22⋊C411yescharacteristic
67C2×C8×C19—22no—
68C2×C8×C19—41no—
69C2×C8×C19—41no—
70C2×C8×C19—41no—
71C2×C8×C19—41no—
72C2×C8×C19—41no—
73C4⋊C4×C19—42no—
74C4⋊C4×C19—41no—
75C4⋊C4×C19—41no—
76C4⋊C4×C19—41no—
77C4⋊C4×C19—41no—
78C42×C19C2×Q811yescharacteristic
79C42×C19C2×Q811yescharacteristic
80C42×C19#4111yescharacteristic
81C42×C19#4111yescharacteristic
82C4⋊Dic19—44no—
83C4⋊Dic19—41no—
84C4⋊Dic19—41no—
85C4⋊Dic19—41no—
86C4⋊Dic19—41no—
87C4⋊Dic19—42no—
88Dic19⋊C4—44no—
89C4×Dic19—21no—
90C4×Dic19—21no—
91C4×Dic19—21no—
92C4×Dic19—21no—
93C4×Dic19—21no—
94C4×Dic19—21no—
95C4×Dic19—21no—
96C4×Dic19—21no—
97C4×Dic19—22no—
98C4×Dic19—22no—
99C2×C19⋊C8—22no—
100C2×C19⋊C8—41no—
101C2×C19⋊C8—41no—
102C2×C19⋊C8—41no—
103C2×C19⋊C8—41no—
104C2×C19⋊C8—41no—
105#9906—191nomaximal, Sylow
106C23×C19C2×C22⋊C411yescharacteristic
107C2×C4×C19—21no—
108C2×C4×C19—21no—
109C2×C4×C19—42no—
110C2×C4×C19—42no—
111C2×C4×C19—42no—
112C2×C4×C19C4×Q811yescharacteristic
113C2×C4×C19C4×Q811yescharacteristic
114C2×C4×C19C22⋊Q811yescharacteristic
115C2×C4×C19C22⋊Q811yescharacteristic
116C2×C4×C19#12411yescharacteristic
117C2×C4×C19C4⋊Q811yescharacteristic
118C2×C4×C19#13511yescharacteristic
119C2×C4×C19#13511yescharacteristic
120C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
121C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
122C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
123C2×C4×C19#13711yescharacteristic
124C2×C4×C19#13711yescharacteristic
125C2×C4×C19#13711yescharacteristic
126C2×Dic19—21no—
127C2×Dic19—21no—
128C2×Dic19—21no—
129C2×Dic19—21no—
130C2×Dic19—21no—
131C2×Dic19—21no—
132C2×Dic19—21no—
133C2×Dic19—21no—
134C2×Dic19—21no—
135C2×Dic19—21no—
136C2×Dic19—42no—
137C2×Dic19—42no—
138C2×Dic19—42no—
139C2×Dic19#10012yes—
140C2×Dic19#10112yes—
141C8×C19—42no—
142C8×C19—81no—
143C19⋊C8—42no—
144C19⋊C8—81no—
145#2859—191no—
146#1842—191no—
147#1767—191no—
148#1296—191no—
149#1296—191no—
150#1296—191no—
151#1296D1911yescharacteristic
152C22×C19#39111yescharacteristic
153C22×C19C2×#10011yescharacteristic
154C22×C19C2×#10111yescharacteristic
155C22×C19#41611yescharacteristic
156C22×C19#41711yescharacteristic
157C22×C19#41711yescharacteristic
158C22×C19#41711yescharacteristic
159C4×C19—21no—
160C4×C19—21no—
161C4×C19—82no—
162C4×C19#47811yescharacteristic
163C4×C19#47811yescharacteristic
164C4×C19#47911yescharacteristic
165C4×C19#47911yescharacteristic
166C4×C19#49011yescharacteristic
167C4×C19#49111yescharacteristic
168C4×C19#50111yescharacteristic
169C4×C19#50111yescharacteristic
170Dic19—22no—
171Dic19—22no—
172Dic19—41no—
173Dic19—41no—
174Dic19—82no—
175C2×#125—192no—
176C2×C4⋊C8—191no—
177C2×C4⋊C8—191no—
178C2×C4⋊C8—381no—
179C2×C4⋊C8—381no—
180C2×C4⋊C8C2×D1911yescharacteristic
181C2×C4⋊C8C2×D1911yescharacteristic
182C2×#97—381no—
183#389—381no—
184#389—381no—
185#389—381no—
186#389—381no—
187#384—191no—
188#384C2×D1911yescharacteristic
189#382—192no—
190C43—191no—
191#336—381no—
192C2×C19#155111yescharacteristic
193C2×C19#155211yescharacteristic
194C2×C19#156011yescharacteristic
195C2×C19#156111yescharacteristic
196C2×C19#198911yescharacteristic
197C2×C19#199211yescharacteristic
198C2×C19#199711yescharacteristic
199C22×C8—21no—
200C22×C8—21no—
201C22×C8—381no—
202C22×C8—381no—
203#125—764no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—192no—
207C2×C4⋊C4—382no—
208C2×C4⋊C4—382no—
209C2×C4⋊C4—381no—
210C2×C4⋊C4—381no—
211C2×C4⋊C4C4×D1912yes—
212C2×C42—191no—
213C2×C42—191no—
214C2×C42—191no—
215C2×C42—191no—
216C2×C42—191no—
217C2×C42—191no—
218C2×C42C22×D1911yescharacteristic
219C4⋊C8—21no—
220C4⋊C8—21no—
221C4⋊C8—21no—
222C4⋊C8—192no—
223C4⋊C8—381no—
224C4⋊C8—381no—
225C4⋊C8—381no—
226C4⋊C8—762no—
227C4⋊C8—762no—
228C4⋊C8Dic3812yes—
229#97—762no—
230#95—382no—
231#95—382no—
232C19#990611yescharacteristic, complemented, Sylow
233C22×C4—22no—
234C22×C4—191no—
235C22×C4—191no—
236C22×C4—191no—
237C22×C4—191no—
238C22×C4—382no—
239C22×C4C2×C4×D1911yescharacteristic
240C22×C4D4×D1911yescharacteristic
241C22×C4D4×D1911yescharacteristic
242C2×C8—22no—
243C2×C8—41no—
244C2×C8—41no—
245C2×C8—41no—
246C2×C8—41no—
247C2×C8—41no—
248C2×C8—382no—
249C2×C8—761no—
250C2×C8—761no—
251C2×C8—761no—
252C2×C8—761no—
253C2×C8—761no—
254C4⋊C4—42no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—762no—
260C4⋊C4—764no—
261C4⋊C4—764no—
262C4⋊C4—761no—
263C4⋊C4—761no—
264C4⋊C4—761no—
265C4⋊C4—761no—
266C42—382no—
267C42—382no—
268C42—381no—
269C42—381no—
270C42—381no—
271C42—381no—
272C42—381no—
273C42—381no—
274C42—381no—
275C42—381no—
276C42C2×Dic3811yescharacteristic
277C42#6454111yescharacteristic
278C42#6454311yescharacteristic
279C42Q8×D1911yescharacteristic
280C23C22⋊C4×D1911yescharacteristic
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—192no—
287C2×C4—192no—
288C2×C4—381no—
289C2×C4—381no—
290C2×C4—381no—
291C2×C4—381no—
292C2×C4—381no—
293C2×C4—381no—
294C2×C4—381no—
295C2×C4—381no—
296C2×C4—381no—
297C2×C4—381no—
298C2×C4—762no—
299C2×C4—762no—
300C2×C4—762no—
301C2×C4C4×Dic3811yescharacteristic
302C2×C4#1059732411yescharacteristic
303C2×C4#1059733111yescharacteristic
304C2×C4#1059733311yescharacteristic
305C2×C4#1059733411yescharacteristic
306C2×C4#1059734211yescharacteristic
307C2×C4#1059735711yescharacteristic
308C2×C4#1059735811yescharacteristic
309C2×C4#1059736011yescharacteristic
310C2×C4#1059736011yescharacteristic
311C2×C4#1059736111yescharacteristic
312C2×C4#1059736211yescharacteristic
313C2×C4#1059736411yescharacteristic
314C2×C4#1059736411yescharacteristic
315C8—42no—
316C8—81no—
317C8—762no—
318C8—1521no—
319C22#1192644811yescharacteristic
320C22#100×D1911yescharacteristic
321C22#101×D1911yescharacteristic
322C22#1192653711yescharacteristic
323C22#1192654211yescharacteristic
324C22#1192654411yescharacteristic
325C22#1192654411yescharacteristic
326C4—21no—
327C4—21no—
328C4—82no—
329C4—382no—
330C4—382no—
331C4—761no—
332C4—761no—
333C4—1522no—
334C4#1192684211yescharacteristic
335C4#1192684311yescharacteristic
336C4#1192684911yescharacteristic
337C4#1192685011yescharacteristic
338C4#1192690711yescharacteristic
339C4#1192691111yescharacteristic
340C4#1192695111yescharacteristic
341C4#1192695211yescharacteristic
342C2#1456232711yescharacteristic
343C2#1456233211yescharacteristic
344C2#1456236911yescharacteristic
345C2#1456237111yescharacteristic
346C2#1456459111yescharacteristic
347C2#1456460211yescharacteristic
348C2#1456462211yescharacteristic
subgroupG/H
centerC23C22⋊C4×D19
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1296C2
socle, prime radicalC23×C19C2×C22⋊C4
cosocleC2×C42×C19C23
hypercenter#1296D19
hypocenterC19#9906
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
232. C19#9906semidirect

Maximal subgroups

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

subgroupindex
#145719962
#145637862
#145634902
#145615192
#145615182
C19×#12962
#990619