Finite Group Databasebeta

← #18087160

Subgroups — #18087160

Order 4864.

386 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14564596C211yesmaximal, characteristic
2#14564558C211yesmaximal, characteristic
3#14564398C211yesmaximal, characteristic
4C2×#11926297C211yesmaximal, characteristic
5C2×#11926289C211yesmaximal, characteristic
6#14561519C211yesmaximal, characteristic
7C19×#1939C211yesmaximal, characteristic
8C2×#10597315C2211yescharacteristic
9C2×#10597265—21no—
10C2×C4⋊(C19⋊C8)C2211yescharacteristic
11C2×C4⋊(C19⋊C8)C2211yescharacteristic
12C2×#10597267—21no—
13C2×#10597267—21no—
14#11926414C2211yescharacteristic
15#11926307—21no—
16#11926307—21no—
17#11926306—21no—
18#11926297—22no—
19#11926289—22no—
20C2×C19×C4⋊C8—21no—
21C2×C19×C4⋊C8C2211yescharacteristic
22C2×C4×C8×C19C2211yescharacteristic
23C4×C4⋊C4×C19C2211yescharacteristic
24C19×#336—21no—
25C22×Dic38—21no—
26C22×C8×C19—21no—
27C22×C8×C19D411yescharacteristic
28C22×C8×C19D411yescharacteristic
29C2×C4⋊C4×C19D411yescharacteristic
30C2×C4⋊C4×C19D411yescharacteristic
31C2×C42×C19—21no—
32C2×C42×C19C2311yescharacteristic
33C2×C4⋊Dic19—21no—
34C2×C4⋊Dic19—21no—
35C2×C4⋊Dic19—21no—
36C2×C4⋊Dic19—21no—
37C2×C4⋊Dic19—21no—
38C22×C19⋊C8—21no—
39C22×C19⋊C8—21no—
40#10597315—21no—
41#10597315—21no—
42#10597315—21no—
43#10597315Q812yes—
44C19×C4⋊C8—21no—
45C19×C4⋊C8—21no—
46C19×C4⋊C8—42no—
47C4×C8×C19—21no—
48C4×C8×C19—21no—
49C19×#95—21no—
50#10597267—42no—
51#10597267—42no—
52#10597265—42no—
53C4⋊(C19⋊C8)—21no—
54C4⋊(C19⋊C8)—21no—
55C4⋊(C19⋊C8)—21no—
56C4⋊(C19⋊C8)D412yes—
57C22×C4×C19—21no—
58C22×C4×C19—21no—
59C22×C4×C19C2×D411yescharacteristic
60C22×C4×C19C2×D411yescharacteristic
61C22×C4×C19#4111yescharacteristic
62C22×Dic19—41no—
63C22×Dic19—41no—
64C2×Dic38—22no—
65C2×Dic38—41no—
66C2×Dic38—41no—
67C2×Dic38—41no—
68C2×Dic38—41no—
69C2×Dic38—41no—
70C2×C8×C19—21no—
71C2×C8×C19—21no—
72C2×C8×C19—21no—
73C2×C8×C19—21no—
74C2×C8×C19—21no—
75C2×C8×C19—41no—
76C2×C8×C19—41no—
77C2×C8×C19—41no—
78C2×C8×C19SD1612yes—
79C4⋊C4×C19—21no—
80C4⋊C4×C19—21no—
81C4⋊C4×C19—21no—
82C4⋊C4×C19D812yes—
83C42×C19—41no—
84C42×C19—41no—
85C42×C19C2×D411yescharacteristic
86C42×C19C2×Q811yescharacteristic
87C42×C19#4111yescharacteristic
88C42×C19#4111yescharacteristic
89C4⋊Dic19—22no—
90C4⋊Dic19—22no—
91C4⋊Dic19—41no—
92C4⋊Dic19—41no—
93C4⋊Dic19—41no—
94C4⋊Dic19—41no—
95C4⋊Dic19—41no—
96C4⋊Dic19—41no—
97C4⋊Dic19—81no—
98C2×C19⋊C8—22no—
99C2×C19⋊C8—41no—
100C2×C19⋊C8—41no—
101C2×C19⋊C8—41no—
102C2×C19⋊C8—41no—
103C2×C19⋊C8—41no—
104#10602—191nomaximal, Sylow
105C23×C19#12111yescharacteristic
106C2×C4×C19—21no—
107C2×C4×C19—21no—
108C2×C4×C19—22no—
109C2×C4×C19—41no—
110C2×C4×C19—41no—
111C2×C4×C19—41no—
112C2×C4×C19—41no—
113C2×C4×C19—41no—
114C2×C4×C19#12111yescharacteristic
115C2×C4×C19#12111yescharacteristic
116C2×C4×C19C22⋊Q811yescharacteristic
117C2×C4×C19C22⋊Q811yescharacteristic
118C2×C4×C19C22⋊Q811yescharacteristic
119C2×C4×C19#12611yescharacteristic
120C2×C4×C19C2×D811yescharacteristic
121C2×C4×C19C2×SD1611yescharacteristic
122C2×C4×C19#13511yescharacteristic
123C2×C4×C19#13511yescharacteristic
124C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
125C2×C4×C19#13711yescharacteristic
126C2×C4×C19#13711yescharacteristic
127C2×C4×C19#13711yescharacteristic
128C2×Dic19—42no—
129C2×Dic19—81no—
130C2×Dic19—81no—
131C2×Dic19—81no—
132C2×Dic19—81no—
133C2×Dic19—81no—
134Dic38—42no—
135Dic38—42no—
136Dic38—81no—
137Dic38—81no—
138C8×C19—22no—
139C8×C19—41no—
140C8×C19—81no—
141C19⋊C8—42no—
142C19⋊C8—81no—
143#1990—191no—
144#1981—191no—
145#1948—191no—
146#1939D1911yescharacteristic
147C2×#335—191no—
148C2×#332—191no—
149#1296—191no—
150C22×C19#39611yescharacteristic
151C22×C19#46111yescharacteristic
152C22×C19#46411yescharacteristic
153C22×C19#46611yescharacteristic
154C22×C19#46811yescharacteristic
155C22×C19#47111yescharacteristic
156C22×C19#47311yescharacteristic
157C4×C19—21no—
158C4×C19—21no—
159C4×C19—42no—
160C4×C19—81no—
161C4×C19#45911yescharacteristic
162C4×C19#46411yescharacteristic
163C4×C19#46511yescharacteristic
164C4×C19#47011yescharacteristic
165C4×C19#47411yescharacteristic
166C4×C19#47511yescharacteristic
167C4×C19#47811yescharacteristic
168C4×C19#47911yescharacteristic
169Dic19—82no—
170Dic19—161no—
171C2×C4⋊Q8—191no—
172C2×#106—381no—
173C2×C4⋊C8—21no—
174C2×C4⋊C8—191no—
175C2×C4⋊C8—191no—
176C2×C4⋊C8C2×D1911yescharacteristic
177C2×#103—381no—
178C2×#103—381no—
179C2×C4×C8C2×D1911yescharacteristic
180#384—191no—
181C4×C4⋊C4C2×D1911yescharacteristic
182#340—381no—
183#340—381no—
184#340—381no—
185#336—21no—
186#335—382no—
187#332—382no—
188C2×C19#167311yescharacteristic
189C2×C19#168211yescharacteristic
190C2×C19#169111yescharacteristic
191C2×C19#170011yescharacteristic
192C2×C19#206411yescharacteristic
193C2×C19#206611yescharacteristic
194C2×C19#206711yescharacteristic
195C22×Q8—381no—
196C22×C8—21no—
197C22×C8—381no—
198C22×C8—381no—
199C22×C8C22⋊D1911yescharacteristic
200C22×C8C22⋊D1911yescharacteristic
201C4⋊Q8—192no—
202C4⋊Q8—381no—
203C4⋊Q8—381no—
204C4⋊Q8—381no—
205C2×C4⋊C4—381no—
206C2×C4⋊C4—381no—
207C2×C4⋊C4—381no—
208C2×C4⋊C4—381no—
209C2×C4⋊C4—381no—
210C2×C4⋊C4D7611yescharacteristic
211C2×C4⋊C4D7611yescharacteristic
212C2×C42—21no—
213C2×C42C22×D1911yescharacteristic
214#106—762no—
215C4⋊C8—21no—
216C4⋊C8—21no—
217C4⋊C8—42no—
218C4⋊C8—192no—
219C4⋊C8—381no—
220C4⋊C8—381no—
221C4⋊C8—381no—
222#103—762no—
223#103—762no—
224C4×C8—21no—
225C4×C8—21no—
226#95—21no—
227C19#1060211yescharacteristic, complemented, Sylow
228C2×Q8—382no—
229C2×Q8—761no—
230C2×Q8—761no—
231C2×Q8—761no—
232C2×Q8—761no—
233C2×Q8—761no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—761no—
237C22×C4—761no—
238C22×C4C2×D7611yescharacteristic
239C22×C4#6454111yescharacteristic
240C22×C4C2×C22⋊D1911yescharacteristic
241C2×C8—21no—
242C2×C8—21no—
243C2×C8—21no—
244C2×C8—21no—
245C2×C8—21no—
246C2×C8—41no—
247C2×C8—41no—
248C2×C8—41no—
249C2×C8—382no—
250C2×C8—761no—
251C2×C8—761no—
252C2×C8—761no—
253C2×C8—761no—
254C2×C8—761no—
255C2×C8#6452612yes—
256C4⋊C4—21no—
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—382no—
260C4⋊C4—382no—
261C4⋊C4—761no—
262C4⋊C4—761no—
263C4⋊C4—761no—
264C4⋊C4—761no—
265C4⋊C4—761no—
266C4⋊C4—761no—
267C4⋊C4—1521no—
268C4⋊C4D15212yes—
269C42—41no—
270C42—41no—
271C42D4×D1911yescharacteristic
272C42#6454311yescharacteristic
273C42Q8×D1911yescharacteristic
274C42#6454511yescharacteristic
275C23#1059737611yescharacteristic
276Q8—762no—
277Q8—762no—
278Q8—1521no—
279Q8—1521no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—22no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—762no—
289C2×C4—1521no—
290C2×C4—1521no—
291C2×C4—1521no—
292C2×C4—1521no—
293C2×C4—1521no—
294C2×C4#1059734111yescharacteristic
295C2×C4#1059734211yescharacteristic
296C2×C4#1059734311yescharacteristic
297C2×C4#1059734411yescharacteristic
298C2×C4C2×D15211yescharacteristic
299C2×C4#1059735011yescharacteristic
300C2×C4#1059735411yescharacteristic
301C2×C4#1059735511yescharacteristic
302C2×C4C2×#6452611yescharacteristic
303C2×C4#1059738511yescharacteristic
304C2×C4#1059738811yescharacteristic
305C2×C4#1059739211yescharacteristic
306C2×C4#1059739611yescharacteristic
307C2×C4#1059739711yescharacteristic
308C8—22no—
309C8—41no—
310C8—81no—
311C8—762no—
312C8—1521no—
313C22#1192646611yescharacteristic
314C22#1192674911yescharacteristic
315C22#1192676611yescharacteristic
316C22#1192678011yescharacteristic
317C22#1192679011yescharacteristic
318C22#1192680711yescharacteristic
319C22#1192681911yescharacteristic
320C4—21no—
321C4—21no—
322C4—42no—
323C4—81no—
324C4—3041no—
325C4—1522no—
326C4#1192674011yescharacteristic
327C4#1192676711yescharacteristic
328C4#1192677111yescharacteristic
329C4#1192680011yescharacteristic
330C4#1192682511yescharacteristic
331C4#1192682611yescharacteristic
332C4#1192684511yescharacteristic
333C4#1192684811yescharacteristic
334C2#1456302411yescharacteristic
335C2#1456307911yescharacteristic
336C2#1456313411yescharacteristic
337C2#1456318911yescharacteristic
338C2#1456500111yescharacteristic
339C2#1456501311yescharacteristic
340C2#1456502211yescharacteristic
subgroupG/H
centerC23#10597376
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#1939C2
socle, prime radicalC23×C19#121
hypercenter#1939D19
hypocenterC19#10602
LCSG ▷ C2×C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1939

Complements

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

NH ≅ G/Ntype
227. C19#10602semidirect

Maximal subgroups

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

subgroupindex
#145645962
#145645582
#145643982
C2×#119262972
C2×#119262892
#145615192
C19×#19392
#1060219