Finite Group Databasebeta

← #18082677

Subgroups — #18082677

Order 4864.

430 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14571996C211yesmaximal, characteristic
2#14563751C211yesmaximal, characteristic
3C4⋊C8×Dic19C211yesmaximal, 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×C8×Dic19—21no—
12#11926443—21no—
13#11926443—21no—
14#11926440—21no—
15#11926440—21no—
16#11926414C2211yescharacteristic
17#11926409C412yes—
18C42×Dic19C2211yescharacteristic
19#11926298—21no—
20#11926298—21no—
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—
51C8×Dic19—42no—
52C4⋊(C19⋊C8)—21no—
53C4⋊(C19⋊C8)—21no—
54C4⋊(C19⋊C8)—21no—
55C4⋊(C19⋊C8)Q812yes—
56C22×C4×C19—22no—
57C22×C4×C19C22×C411yescharacteristic
58C22×C4×C19C2×D411yescharacteristic
59C22×C4×C19C2×D411yescharacteristic
60C22×Dic19—22no—
61C22×Dic19C22⋊C411yescharacteristic
62C22×Dic19C22⋊C411yescharacteristic
63C22×Dic19C22⋊C411yescharacteristic
64C22×Dic19C22⋊C411yescharacteristic
65C2×C8×C19—22no—
66C2×C8×C19—41no—
67C2×C8×C19—41no—
68C2×C8×C19—41no—
69C2×C8×C19—41no—
70C2×C8×C19—41no—
71C4⋊C4×C19—42no—
72C4⋊C4×C19—41no—
73C4⋊C4×C19—41no—
74C4⋊C4×C19—41no—
75C4⋊C4×C19—41no—
76C42×C19C2×Q811yescharacteristic
77C42×C19C2×Q811yescharacteristic
78C42×C19#4111yescharacteristic
79C42×C19#4111yescharacteristic
80C4⋊Dic19—41no—
81C4⋊Dic19—41no—
82C4⋊Dic19—41no—
83C4⋊Dic19—41no—
84C4⋊Dic19—44no—
85C4⋊Dic19—42no—
86Dic19⋊C4—44no—
87C4×Dic19—21no—
88C4×Dic19—21no—
89C4×Dic19—21no—
90C4×Dic19—21no—
91C4×Dic19—21no—
92C4×Dic19—21no—
93C4×Dic19—21no—
94C4×Dic19—21no—
95C4×Dic19—22no—
96C4×Dic19—22no—
97C2×C19⋊C8—22no—
98C2×C19⋊C8—41no—
99C2×C19⋊C8—41no—
100C2×C19⋊C8—41no—
101C2×C19⋊C8—41no—
102C2×C19⋊C8—41no—
103#9901—191nomaximal, Sylow
104C23×C19C2×C22⋊C411yescharacteristic
105C2×C4×C19—21no—
106C2×C4×C19—21no—
107C2×C4×C19—42no—
108C2×C4×C19—42no—
109C2×C4×C19—42no—
110C2×C4×C19C4×Q811yescharacteristic
111C2×C4×C19C4×Q811yescharacteristic
112C2×C4×C19C22⋊Q811yescharacteristic
113C2×C4×C19C22⋊Q811yescharacteristic
114C2×C4×C19#12411yescharacteristic
115C2×C4×C19C4⋊Q811yescharacteristic
116C2×C4×C19#13511yescharacteristic
117C2×C4×C19#13511yescharacteristic
118C2×C4×C19#13511yescharacteristic
119C2×C4×C19#13511yescharacteristic
120C2×C4×C19#13511yescharacteristic
121C2×C4×C19#13511yescharacteristic
122C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
123C2×C4×C19#13711yescharacteristic
124C2×Dic19—21no—
125C2×Dic19—21no—
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—42no—
135C2×Dic19—42no—
136C2×Dic19—42no—
137C2×Dic19#10012yes—
138C2×Dic19#10112yes—
139C8×C19—42no—
140C8×C19—81no—
141C19⋊C8—42no—
142C19⋊C8—81no—
143#2859—191no—
144#1831—191no—
145C4×C4⋊C8—191no—
146#1296—191no—
147#1296—191no—
148#1296—191no—
149#1296D1911yescharacteristic
150C22×C19#39111yescharacteristic
151C22×C19C2×#10011yescharacteristic
152C22×C19C2×#10111yescharacteristic
153C22×C19#41611yescharacteristic
154C22×C19#41611yescharacteristic
155C22×C19#41611yescharacteristic
156C22×C19#41711yescharacteristic
157C4×C19—21no—
158C4×C19—21no—
159C4×C19—82no—
160C4×C19#47811yescharacteristic
161C4×C19#47811yescharacteristic
162C4×C19#47911yescharacteristic
163C4×C19#47911yescharacteristic
164C4×C19#48811yescharacteristic
165C4×C19#48811yescharacteristic
166C4×C19#49911yescharacteristic
167C4×C19#49911yescharacteristic
168Dic19—22no—
169Dic19—22no—
170Dic19—41no—
171Dic19—41no—
172Dic19—82no—
173C2×#125—192no—
174C2×C4⋊C8—191no—
175C2×C4⋊C8—191no—
176C2×C4⋊C8C2×D1911yescharacteristic
177C2×C4⋊C8C2×D1911yescharacteristic
178C2×C4×C8—381no—
179#389—381no—
180#389—381no—
181#389—381no—
182#389—381no—
183#384—191no—
184#384C2×D1911yescharacteristic
185#382—192no—
186C43—191no—
187#336—381no—
188#336—381no—
189#336—381no—
190C2×C19#154311yescharacteristic
191C2×C19#154411yescharacteristic
192C2×C19#155111yescharacteristic
193C2×C19#155211yescharacteristic
194C2×C19#198911yescharacteristic
195C2×C19#199111yescharacteristic
196C2×C19#199711yescharacteristic
197C22×C8—21no—
198C22×C8—21no—
199C22×C8—381no—
200C22×C8—381no—
201#125—764no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—192no—
205C2×C4⋊C4—382no—
206C2×C4⋊C4—382no—
207C2×C4⋊C4—381no—
208C2×C4⋊C4—381no—
209C2×C4⋊C4C4×D1912yes—
210C2×C42—191no—
211C2×C42—191no—
212C2×C42—191no—
213C2×C42—191no—
214C2×C42—191no—
215C2×C42—191no—
216C2×C42C22×D1911yescharacteristic
217C4⋊C8—21no—
218C4⋊C8—21no—
219C4⋊C8—21no—
220C4⋊C8—192no—
221C4⋊C8—381no—
222C4⋊C8—381no—
223C4⋊C8—381no—
224C4⋊C8Dic3812yes—
225C4×C8—762no—
226#95—382no—
227#95—382no—
228C19#990111yescharacteristic, complemented, Sylow
229C22×C4—22no—
230C22×C4—191no—
231C22×C4—191no—
232C22×C4—191no—
233C22×C4—191no—
234C22×C4—382no—
235C22×C4C2×C4×D1911yescharacteristic
236C22×C4D4×D1911yescharacteristic
237C22×C4D4×D1911yescharacteristic
238C2×C8—22no—
239C2×C8—41no—
240C2×C8—41no—
241C2×C8—41no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—382no—
245C2×C8—761no—
246C2×C8—761no—
247C2×C8—761no—
248C2×C8—761no—
249C2×C8—761no—
250C4⋊C4—42no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—762no—
256C4⋊C4—764no—
257C4⋊C4—764no—
258C4⋊C4—761no—
259C4⋊C4—761no—
260C4⋊C4—761no—
261C4⋊C4—761no—
262C42—382no—
263C42—382no—
264C42—381no—
265C42—381no—
266C42—381no—
267C42—381no—
268C42—381no—
269C42—381no—
270C42—381no—
271C42—381no—
272C42C2×Dic3811yescharacteristic
273C42#6454111yescharacteristic
274C42#6454311yescharacteristic
275C42Q8×D1911yescharacteristic
276C23C22⋊C4×D1911yescharacteristic
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—192no—
283C2×C4—192no—
284C2×C4—381no—
285C2×C4—381no—
286C2×C4—381no—
287C2×C4—381no—
288C2×C4—381no—
289C2×C4—381no—
290C2×C4—381no—
291C2×C4—381no—
292C2×C4—381no—
293C2×C4—381no—
294C2×C4—762no—
295C2×C4—762no—
296C2×C4—762no—
297C2×C4C4×Dic3811yescharacteristic
298C2×C4#1059732411yescharacteristic
299C2×C4#1059733111yescharacteristic
300C2×C4#1059733311yescharacteristic
301C2×C4#1059733411yescharacteristic
302C2×C4#1059734211yescharacteristic
303C2×C4#1059735811yescharacteristic
304C2×C4#1059735811yescharacteristic
305C2×C4#1059736011yescharacteristic
306C2×C4#1059736211yescharacteristic
307C2×C4#1059736211yescharacteristic
308C2×C4#1059736211yescharacteristic
309C2×C4#1059736411yescharacteristic
310C2×C4#1059736511yescharacteristic
311C8—42no—
312C8—81no—
313C8—762no—
314C8—1521no—
315C22#1192644811yescharacteristic
316C22#100×D1911yescharacteristic
317C22#101×D1911yescharacteristic
318C22#1192653711yescharacteristic
319C22#1192653711yescharacteristic
320C22#1192653911yescharacteristic
321C22#1192654411yescharacteristic
322C4—21no—
323C4—21no—
324C4—82no—
325C4—382no—
326C4—382no—
327C4—761no—
328C4—761no—
329C4—1522no—
330C4#1192684211yescharacteristic
331C4#1192684311yescharacteristic
332C4#1192684911yescharacteristic
333C4#1192685011yescharacteristic
334C4#1192689711yescharacteristic
335C4#1192690011yescharacteristic
336C4#1192694411yescharacteristic
337C4#1192694511yescharacteristic
338C2#1456229411yescharacteristic
339C2#1456229811yescharacteristic
340C2#1456232911yescharacteristic
341C2#1456233211yescharacteristic
342C2#1456459111yescharacteristic
343C2#1456459811yescharacteristic
344C2#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#9901
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
228. C19#9901semidirect

Maximal subgroups

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

subgroupindex
#145719962
#145637512
C4⋊C8×Dic192
#145615192
#145615182
C19×#12962
#990119