Finite Group Databasebeta

← #18081605

Subgroups — #18081605

Order 4864.

602 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14571991C211yesmaximal, characteristic
2#14563751C211yesmaximal, characteristic, complemented
3C4⋊C8×Dic19C211yesmaximal, characteristic, complemented
4C2×#11926292C211yesmaximal, characteristic, complemented
5C2×#11926292C211yesmaximal, characteristic, complemented
6C2×#11926288C211yesmaximal, characteristic
7C2×C19×#331C211yesmaximal, characteristic
8C2×#10597315C2211yescharacteristic
9C2×#10597382C414yes—
10C2×C4⋊(C19⋊C8)C2211yescharacteristic
11C2×C4⋊(C19⋊C8)C2211yescharacteristic
12C2×C8×Dic19—21no—
13#11926447—21no—
14#11926447—22no—
15#11926447—21no—
16C42×Dic19C2211yescharacteristic
17#11926298—21no—
18#11926298—22no—
19#11926292—22no—
20#11926292—22no—
21#11926288—22no—
22C2×C19×#127C2211yescharacteristic
23C2×C19×C4⋊C8C2211yescharacteristic
24C2×C19×C4⋊C8C2211yescharacteristic
25C19×#331—22no—
26C22×D4×C19—21no—
27C22×D4×C19—21no—
28C22×D4×C19C2×C412yes—
29C22×Dic38C2×C412yes—
30C22×C8×C19—21no—
31C22×C8×C19—21no—
32C19×#127—21no—
33C19×#127—21no—
34C19×#127—21no—
35C19×#127—21no—
36C2×C42×C19C2311yescharacteristic
37C2×C22⋊Dic19—24no—
38C2×C22⋊Dic19—24no—
39#10597382—48no—
40C2×C4⋊Dic19—21no—
41C2×C4⋊Dic19—21no—
42C2×C4×Dic19C2×C412yes—
43C2×C4×Dic19D411yescharacteristic
44C2×C4×Dic19D412yes—
45C2×C4×Dic19D411yescharacteristic
46C22×C19⋊C8—21no—
47C22×C19⋊C8—21no—
48#10597315—21no—
49#10597315—21no—
50#10597315—21no—
51#10597315—21no—
52C19×C4⋊C8—21no—
53C19×C4⋊C8—21no—
54C19×C4⋊C8—21no—
55C19×C4⋊C8D412yes—
56C8×Dic19—42no—
57C4⋊(C19⋊C8)—21no—
58C4⋊(C19⋊C8)—21no—
59C4⋊(C19⋊C8)—21no—
60C4⋊(C19⋊C8)D412yes—
61C24×C19—22no—
62C2×D4×C19—22no—
63C2×D4×C19—22no—
64C2×D4×C19—44no—
65C2×D4×C19—41no—
66C2×D4×C19—41no—
67C2×D4×C19—41no—
68C2×D4×C19—41no—
69C2×D4×C19—41no—
70C2×D4×C19—42no—
71C2×D4×C19—41no—
72C2×D4×C19—42no—
73C2×D4×C19—41no—
74C2×D4×C19—41no—
75C22×C4×C19C22×C411yescharacteristic
76C22×C4×C19C2×D411yescharacteristic
77C22×C4×C19C2×D411yescharacteristic
78C22×Dic19—22no—
79C22×Dic19C22⋊C412yes—
80C22×Dic19C22⋊C412yes—
81C2×Dic38—22no—
82C2×Dic38—22no—
83C2×Dic38—44no—
84C2×C8×C19—22no—
85C2×C8×C19—41no—
86C2×C8×C19—41no—
87C2×C8×C19—41no—
88C2×C8×C19—42no—
89C42×C19C2×D411yescharacteristic
90C42×C19C2×D411yescharacteristic
91C42×C19#4111yescharacteristic
92C42×C19#4111yescharacteristic
93C22⋊Dic19—48no—
94C22⋊Dic19—48no—
95C4⋊Dic19—41no—
96C4⋊Dic19—41no—
97C4⋊Dic19—41no—
98C4⋊Dic19—41no—
99C4×Dic19—22no—
100C4×Dic19—21no—
101C4×Dic19—22no—
102C4×Dic19—21no—
103C4×Dic19—21no—
104C4×Dic19—21no—
105C4×Dic19—24no—
106C2×C19⋊C8—22no—
107C2×C19⋊C8—41no—
108C2×C19⋊C8—41no—
109C2×C19⋊C8—41no—
110C2×C19⋊C8—42no—
111#9699—191nomaximal, Sylow
112C23×C19—42no—
113C23×C19—44no—
114C23×C19—42no—
115C23×C19—44no—
116C23×C19—42no—
117C23×C19C2×C22⋊C411yescharacteristic
118D4×C19—82no—
119D4×C19—82no—
120D4×C19—81no—
121D4×C19—81no—
122D4×C19—81no—
123D4×C19—81no—
124D4×C19—82no—
125D4×C19—81no—
126D4×C19—81no—
127C2×C4×C19—22no—
128C2×C4×C19C4×D411yescharacteristic
129C2×C4×C19C4×D411yescharacteristic
130C2×C4×C19#12111yescharacteristic
131C2×C4×C19#12111yescharacteristic
132C2×C4×C19#12411yescharacteristic
133C2×C4×C19#12711yescharacteristic
134C2×C4×C19#13511yescharacteristic
135C2×C4×C19#13512yes—
136C2×C4×C19#13511yescharacteristic
137C2×C4×C19#13512yes—
138C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
139C2×C4×C19#13711yescharacteristic
140C2×Dic19—22no—
141C2×Dic19—22no—
142C2×Dic19—22no—
143C2×Dic19—22no—
144C2×Dic19—22no—
145C2×Dic19—42no—
146C2×Dic19—44no—
147C2×Dic19#10014yes—
148Dic38—82no—
149Dic38—82no—
150C8×C19—42no—
151C8×C19—81no—
152C19⋊C8—42no—
153C19⋊C8—81no—
154#2858—191no—
155#1831—191no—
156C4×C4⋊C8—191no—
157C2×#333—191no—
158C2×#333—191no—
159C2×#331—191no—
160C2×#331D1911yescharacteristic
161C22×C19—84no—
162C22×C19—84no—
163C22×C19—82no—
164C22×C19—82no—
165C22×C19—82no—
166C22×C19#39011yescharacteristic
167C22×C19C2×#10012yes—
168C22×C19#41611yescharacteristic
169C22×C19#41612yes—
170C22×C19#41711yescharacteristic
171C4×C19—21no—
172C4×C19—21no—
173C4×C19#46311yescharacteristic
174C4×C19#46311yescharacteristic
175C4×C19#46411yescharacteristic
176C4×C19#46411yescharacteristic
177C4×C19#48812yes—
178C4×C19#49511yescharacteristic
179C4×C19#49511yescharacteristic
180Dic19—24no—
181Dic19—42no—
182Dic19—82no—
183C2×C4⋊Q8—191no—
184C2×#127C2×D1911yescharacteristic
185C2×#124—194no—
186C2×C4⋊C8—191no—
187C2×C4⋊C8—191no—
188C2×C4⋊C8C2×D1911yescharacteristic
189C2×C4⋊C8C2×D1911yescharacteristic
190C2×C4×C8—381no—
191#390—382no—
192#390—381no—
193#390—381no—
194C43—191no—
195#336—382no—
196#336—381no—
197#333—382no—
198#333—382no—
199#331—22no—
200#331—382no—
201C2×C19—162no—
202C2×C19#154312yes—
203C2×C19#155112yes—
204C2×C19#195811yescharacteristic
205C2×C19#196511yescharacteristic
206C2×C19#198311yescharacteristic
207C22×Q8—192no—
208C22×D4—21no—
209C22×D4—21no—
210C22×D4C4×D1912yes—
211C22×C8—21no—
212C22×C8—21no—
213C22×C8—381no—
214C22×C8—381no—
215C4⋊Q8—381no—
216C4⋊Q8—381no—
217C4⋊Q8—381no—
218C4⋊Q8—381no—
219#127—21no—
220#127—21no—
221#127—21no—
222#127—21no—
223#124—768no—
224C2×C4⋊C4—381no—
225C2×C4⋊C4—381no—
226C2×C22⋊C4—384no—
227C2×C22⋊C4—384no—
228C2×C42—192no—
229C2×C42—192no—
230C2×C42—191no—
231C2×C42—191no—
232C2×C42C22×D1911yescharacteristic
233C4⋊C8—21no—
234C4⋊C8—21no—
235C4⋊C8—21no—
236C4⋊C8—192no—
237C4⋊C8—381no—
238C4⋊C8—381no—
239C4⋊C8—381no—
240C4⋊C8C22⋊D1912yes—
241C4×C8—762no—
242C19#969911yescharacteristic, complemented, Sylow
243C24—22no—
244C2×Q8—382no—
245C2×Q8—382no—
246C2×Q8—764no—
247C2×D4—22no—
248C2×D4—22no—
249C2×D4—44no—
250C2×D4—41no—
251C2×D4—41no—
252C2×D4—41no—
253C2×D4—41no—
254C2×D4—41no—
255C2×D4—42no—
256C2×D4—41no—
257C2×D4—41no—
258C2×D4—42no—
259C2×D4—41no—
260C22×C4—192no—
261C22×C4—192no—
262C22×C4—382no—
263C22×C4C2×C4×D1911yescharacteristic
264C22×C4D4×D1911yescharacteristic
265C22×C4D4×D1911yescharacteristic
266C2×C8—22no—
267C2×C8—41no—
268C2×C8—41no—
269C2×C8—41no—
270C2×C8—42no—
271C2×C8—382no—
272C2×C8—761no—
273C2×C8—761no—
274C2×C8—761no—
275C2×C8—762no—
276C4⋊C4—761no—
277C4⋊C4—761no—
278C4⋊C4—761no—
279C4⋊C4—761no—
280C22⋊C4—768no—
281C22⋊C4—768no—
282C42—384no—
283C42—381no—
284C42—382no—
285C42—381no—
286C42—381no—
287C42—382no—
288C42—381no—
289C42#6454111yescharacteristic
290C42D4×D1911yescharacteristic
291C42#6454311yescharacteristic
292C42C2×C22⋊D1911yescharacteristic
293C23—44no—
294C23—42no—
295C23—42no—
296C23—42no—
297C23—44no—
298C23C22⋊C4×D1911yescharacteristic
299Q8—1522no—
300Q8—1522no—
301D4—82no—
302D4—82no—
303D4—82no—
304D4—81no—
305D4—81no—
306D4—81no—
307D4—81no—
308D4—81no—
309D4—81no—
310C2×C4—22no—
311C2×C4—194no—
312C2×C4—382no—
313C2×C4—382no—
314C2×C4—382no—
315C2×C4—382no—
316C2×C4—382no—
317C2×C4—762no—
318C2×C4—764no—
319C2×C4(C22⋊D19)⋊C411yescharacteristic
320C2×C4#1059733011yescharacteristic
321C2×C4#1059733111yescharacteristic
322C2×C4#1059735711yescharacteristic
323C2×C4#1059735812yes—
324C2×C4#1059735811yescharacteristic
325C2×C4#1059736111yescharacteristic
326C2×C4#1059736212yes—
327C2×C4#1059736211yescharacteristic
328C2×C4C4×C22⋊D1911yescharacteristic
329C2×C4#1059738511yescharacteristic
330C2×C4#1059738611yescharacteristic
331C8—42no—
332C8—81no—
333C8—762no—
334C8—1521no—
335C22—84no—
336C22—82no—
337C22—82no—
338C22—82no—
339C22—84no—
340C22#1192644411yescharacteristic
341C22#100×D1912yes—
342C22#1192653712yes—
343C22#1192653711yescharacteristic
344C22#1192654211yescharacteristic
345C4—21no—
346C4—21no—
347C4—384no—
348C4—762no—
349C4—1522no—
350C4#1192675711yescharacteristic
351C4#1192675811yescharacteristic
352C4#1192676411yescharacteristic
353C4#1192676511yescharacteristic
354C4#1192689712yes—
355C4#1192692511yescharacteristic
356C4#1192692711yescharacteristic
357C2—162no—
358C2#1456229412yes—
359C2#1456232712yes—
360C2#1456444511yescharacteristic
361C2#1456447311yescharacteristic
362C2#1456456611yescharacteristic
subgroupG/H
centerC23C22⋊C4×D19
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC2×C19×#331C2
socleC23×C19C2×C22⋊C4
prime radicalC2×C19×#127C22
cosocleC2×C42×C19C23
hypercenterC2×#331D19
hypocenterC19#9699
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#331

Complements

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

NH ≅ G/Ntype
2. #14563751C2semidirect
3. C4⋊C8×Dic19C2semidirect
4. C2×#11926292C2semidirect
5. C2×#11926292C2semidirect
242. C19#9699semidirect

Maximal subgroups

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

subgroupindex
#145719912
#145637512
C4⋊C8×Dic192
C2×#119262922
C2×#119262882
C2×C19×#3312
#969919