Finite Group Databasebeta

← #18071701

Subgroups — #18071701

Order 4864.

366 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 81 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14571585C211yesmaximal, characteristic
2#14565179C211yesmaximal, characteristic
3#14565107C211yesmaximal, characteristic
4#14561460C211yesmaximal, characteristic
5#14561459C211yesmaximal, characteristic
6#14561458C211yesmaximal, characteristic
7C19×#2084C211yesmaximal, characteristic
8C2×#10597264—21no—
9C2×#10597265—21no—
10C2×#10597267—21no—
11#11926486—21no—
12#11926482—21no—
13#11926464—21no—
14#11926450C2211yescharacteristic
15#11926442C2211yescharacteristic
16#11926439—21no—
17#11926430—21no—
18#11926429—21no—
19#11926306—21no—
20#11926299C2211yescharacteristic
21#11926299C2211yescharacteristic
22C2×C19×#106—21no—
23C19×#389C2211yescharacteristic
24C19×#384C2211yescharacteristic
25C19×#340—21no—
26C19×#336C2211yescharacteristic
27C22×Dic38D411yescharacteristic
28C22×C8×C19—21no—
29C2×C4⋊C4×C19—21no—
30C2×C4⋊C4×C19—21no—
31C2×C4⋊C4×C19—21no—
32C2×C4⋊C4×C19—21no—
33C2×C4⋊C4×C19D411yescharacteristic
34C2×C4⋊C4×C19D411yescharacteristic
35C2×C42×C19C2311yescharacteristic
36C2×C4⋊Dic19D411yescharacteristic
37C2×C4⋊Dic19D411yescharacteristic
38C2×C4⋊Dic19D411yescharacteristic
39C2×Dic19⋊C4—21no—
40C2×Dic19⋊C4—21no—
41C2×Dic19⋊C4—21no—
42C2×C4×Dic19—21no—
43C22×C19⋊C8—21no—
44C22×C19⋊C8—21no—
45C19×#106—42no—
46C19×#95—21no—
47C19⋊#95—21no—
48C19⋊#95—21no—
49C19⋊#95—21no—
50C19⋊#95—21no—
51C19⋊#95—21no—
52C19⋊#95—21no—
53C19⋊#95—21no—
54C19⋊#95—21no—
55#10597267—42no—
56#10597265—42no—
57#10597264—42no—
58C22×C4×C19—21no—
59C22×C4×C19—21no—
60C22×C4×C19—41no—
61C22×C4×C19C2×D411yescharacteristic
62C22×C4×C19C2×D411yescharacteristic
63C22×C4×C19C2×D411yescharacteristic
64C22×Dic19—21no—
65C22×Dic19—21no—
66C22×Dic19—21no—
67C22×Dic19—21no—
68C2×Dic38—21no—
69C2×Dic38—21no—
70C2×Dic38—41no—
71C2×Dic38—41no—
72C2×C8×C19—22no—
73C2×C8×C19—41no—
74C2×C8×C19—41no—
75C4⋊C4×C19—21no—
76C4⋊C4×C19—21no—
77C4⋊C4×C19—41no—
78C4⋊C4×C19—41no—
79C4⋊C4×C19—41no—
80C4⋊C4×C19—41no—
81C4⋊C4×C19—41no—
82C4⋊C4×C19—41no—
83C4⋊C4×C19—41no—
84C4⋊C4×C19—41no—
85C4⋊C4×C19—41no—
86C42×C19—41no—
87C4⋊Dic19—21no—
88C4⋊Dic19—41no—
89C4⋊Dic19—41no—
90C4⋊Dic19SD1612yes—
91Dic19⋊C4—41no—
92Dic19⋊C4—41no—
93Dic19⋊C4—81no—
94Dic19⋊C4—81no—
95C4×Dic19—81no—
96C2×C19⋊C8—22no—
97C2×C19⋊C8—22no—
98C2×C19⋊C8—41no—
99C2×C19⋊C8—41no—
100C2×C19⋊C8—41no—
101C2×C19⋊C8—41no—
102#7807—191nomaximal, Sylow
103C23×C19#12011yescharacteristic
104C2×C4×C19—21no—
105C2×C4×C19—21no—
106C2×C4×C19—21no—
107C2×C4×C19—21no—
108C2×C4×C19—21no—
109C2×C4×C19—21no—
110C2×C4×C19—41no—
111C2×C4×C19—41no—
112C2×C4×C19—41no—
113C2×C4×C19—41no—
114C2×C4×C19—41no—
115C2×C4×C19—41no—
116C2×C4×C19—81no—
117C2×C4×C19—81no—
118C2×C4×C19—81no—
119C2×C4×C19C2×SD1611yescharacteristic
120C2×C4×C19#13511yescharacteristic
121C2×C4×C19#13511yescharacteristic
122C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
123C2×C4×C19#13711yescharacteristic
124C2×C4×C19#13711yescharacteristic
125C2×Dic19—22no—
126C2×Dic19—41no—
127C2×Dic19—41no—
128C2×Dic19—41no—
129C2×Dic19—41no—
130C2×Dic19—41no—
131C2×Dic19—41no—
132C2×Dic19—41no—
133C2×Dic19—41no—
134C2×Dic19—41no—
135C2×Dic19—41no—
136C2×Dic19—41no—
137Dic38—42no—
138Dic38—81no—
139C8×C19—42no—
140C19⋊C8—42no—
141C19⋊C8—42no—
142#2805—191no—
143#2096—191no—
144#2084D1911yescharacteristic
145#2083—191no—
146#1272—191no—
147#1271—191no—
148#1271—191no—
149C22×C19#44811yescharacteristic
150C22×C19#44911yescharacteristic
151C22×C19#45211yescharacteristic
152C22×C19#45311yescharacteristic
153C22×C19#45611yescharacteristic
154C22×C19#45611yescharacteristic
155C22×C19#45811yescharacteristic
156C4×C19—21no—
157C4×C19—21no—
158C4×C19—21no—
159C4×C19—21no—
160C4×C19—21no—
161C4×C19—21no—
162C4×C19—81no—
163C4×C19—81no—
164C4×C19—161no—
165Dic19—42no—
166Dic19—81no—
167Dic19—81no—
168Dic19—81no—
169C2×#107—381no—
170C2×#106—21no—
171C2×#106—381no—
172C2×#103—381no—
173#400—381no—
174#400—381no—
175#395—381no—
176#391—191no—
177#389—191no—
178#389—381no—
179#389C2×D1911yescharacteristic
180#387—381no—
181#387—381no—
182#384C2×D1911yescharacteristic
183#340—21no—
184#340—381no—
185#336—191no—
186#336—191no—
187#336C2×D1911yescharacteristic
188C2×C19#160911yescharacteristic
189C2×C19#161111yescharacteristic
190C2×C19#161811yescharacteristic
191C2×C19#162211yescharacteristic
192C2×C19#165011yescharacteristic
193C2×C19#165311yescharacteristic
194C2×C19#166011yescharacteristic
195C22×Q8—191no—
196C22×C8—21no—
197C22×C8—381no—
198C22×C8—381no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—191no—
204C2×C4⋊C4—191no—
205C2×C4⋊C4—191no—
206C2×C4⋊C4—381no—
207C2×C4⋊C4—381no—
208C2×C4⋊C4—381no—
209C2×C4⋊C4C22⋊D1911yescharacteristic
210C2×C4⋊C4C22⋊D1911yescharacteristic
211C2×C42—381no—
212C2×C42C22×D1911yescharacteristic
213#107—762no—
214#106—42no—
215#106—762no—
216#103—762no—
217#95—21no—
218#95—381no—
219#95—381no—
220#95—381no—
221#95—381no—
222#95—381no—
223#95—381no—
224#95—381no—
225#95—381no—
226C19#780711yescharacteristic, complemented, Sylow
227C2×Q8—381no—
228C2×Q8—381no—
229C2×Q8—761no—
230C2×Q8—761no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—41no—
234C22×C4—381no—
235C22×C4—381no—
236C22×C4—381no—
237C22×C4—381no—
238C22×C4D4×D1911yescharacteristic
239C22×C4D4×D1911yescharacteristic
240C22×C4C2×C22⋊D1911yescharacteristic
241C2×C8—22no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—382no—
245C2×C8—382no—
246C2×C8—761no—
247C2×C8—761no—
248C2×C8—761no—
249C2×C8—761no—
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—192no—
262C4⋊C4—381no—
263C4⋊C4—761no—
264C4⋊C4—761no—
265C4⋊C4—761no—
266C4⋊C4—761no—
267C4⋊C4—1521no—
268C4⋊C4—1521no—
269C42—41no—
270C42—1521no—
271C23#1059738311yescharacteristic
272Q8—762no—
273Q8—1521no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—81no—
287C2×C4—81no—
288C2×C4—81no—
289C2×C4—382no—
290C2×C4—761no—
291C2×C4—761no—
292C2×C4—761no—
293C2×C4—761no—
294C2×C4—761no—
295C2×C4—761no—
296C2×C4—761no—
297C2×C4—761no—
298C2×C4—761no—
299C2×C4—761no—
300C2×C4—761no—
301C2×C4SD16×D1911yescharacteristic
302C2×C4#1059736111yescharacteristic
303C2×C4#1059736111yescharacteristic
304C2×C4#1059736211yescharacteristic
305C2×C4#1059737811yescharacteristic
306C2×C4#1059739611yescharacteristic
307C8—42no—
308C8—762no—
309C8—762no—
310C22#1192668111yescharacteristic
311C22#1192668711yescharacteristic
312C22#1192670311yescharacteristic
313C22#1192671011yescharacteristic
314C22#1192672511yescharacteristic
315C22#1192672611yescharacteristic
316C22#1192673311yescharacteristic
317C4—21no—
318C4—21no—
319C4—21no—
320C4—21no—
321C4—21no—
322C4—21no—
323C4—81no—
324C4—81no—
325C4—161no—
326C4—762no—
327C4—1521no—
328C4—1521no—
329C4—1521no—
330C2#1456263011yescharacteristic
331C2#1456264111yescharacteristic
332C2#1456268011yescharacteristic
333C2#1456270611yescharacteristic
334C2#1456288911yescharacteristic
335C2#1456290911yescharacteristic
336C2#1456294511yescharacteristic
subgroupG/H
centerC23#10597383
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#2084C2
socle, prime radicalC23×C19#120
hypercenter#2084D19
hypocenterC19#7807
LCSG ▷ C2×C42×C19 ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2084

Complements

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

NH ≅ G/Ntype
226. C19#7807semidirect

Maximal subgroups

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

subgroupindex
#145715852
#145651792
#145651072
#145614602
#145614592
#145614582
C19×#20842
#780719