Finite Group Databasebeta

← #18071671

Subgroups — #18071671

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#14571620C211yesmaximal, characteristic
2#14565177C211yesmaximal, characteristic
3#14565108C211yesmaximal, characteristic
4#14565106C211yesmaximal, characteristic
5#14561460C211yesmaximal, characteristic
6#14561457C211yesmaximal, characteristic
7C19×#1271C211yesmaximal, characteristic
8C2×#10597275—21no—
9C2×#10597264—21no—
10C2×#10597274—21no—
11C2×#10597273—21no—
12#11926486—21no—
13#11926475—21no—
14#11926474—21no—
15#11926450C2211yescharacteristic
16#11926448—21no—
17#11926442C2211yescharacteristic
18#11926430—21no—
19#11926425—21no—
20#11926414C2211yescharacteristic
21#11926307—21no—
22#11926306—21no—
23#11926299C2211yescharacteristic
24C19×#389C2211yescharacteristic
25C19×#336C2211yescharacteristic
26C19×#336C2211yescharacteristic
27C22×Dic38D411yescharacteristic
28C22×C8×C19—21no—
29C22×C8×C19—21no—
30C2×C4⋊C4×C19—21no—
31C2×C4⋊C4×C19D411yescharacteristic
32C2×C4⋊C4×C19D411yescharacteristic
33C2×C42×C19C2311yescharacteristic
34C2×C4⋊Dic19—21no—
35C2×C4⋊Dic19—21no—
36C2×C4⋊Dic19—21no—
37C2×C4⋊Dic19D411yescharacteristic
38C2×C4⋊Dic19D411yescharacteristic
39C2×C4⋊Dic19D411yescharacteristic
40C2×Dic19⋊C4—21no—
41C2×Dic19⋊C4—21no—
42C2×Dic19⋊C4—21no—
43C2×C4×Dic19—21no—
44C22×C19⋊C8—21no—
45C19×#95—21no—
46C19⋊#95—21no—
47C19⋊#95—21no—
48C19⋊#95—21no—
49C19⋊#95—21no—
50C19⋊#95—21no—
51C19⋊#95—21no—
52C19⋊#95—21no—
53C19⋊#95—21no—
54#10597275—42no—
55#10597274—42no—
56#10597273—42no—
57#10597264—42no—
58C22×C4×C19—21no—
59C22×C4×C19—21no—
60C22×C4×C19C2×D411yescharacteristic
61C22×C4×C19C2×D411yescharacteristic
62C22×C4×C19C2×D411yescharacteristic
63C22×Dic19—21no—
64C22×Dic19—21no—
65C22×Dic19—21no—
66C22×Dic19—21no—
67C22×Dic19—41no—
68C2×Dic38—21no—
69C2×Dic38—41no—
70C2×Dic38—41no—
71C2×Dic38Q1612yes—
72C2×C8×C19—22no—
73C2×C8×C19—22no—
74C2×C8×C19—41no—
75C2×C8×C19—41no—
76C2×C8×C19—41no—
77C2×C8×C19—41no—
78C4⋊C4×C19—21no—
79C4⋊C4×C19—21no—
80C4⋊C4×C19—41no—
81C4⋊C4×C19—41no—
82C4⋊C4×C19—41no—
83C42×C19—41no—
84C4⋊Dic19—21no—
85C4⋊Dic19—21no—
86C4⋊Dic19—41no—
87C4⋊Dic19—41no—
88C4⋊Dic19—41no—
89C4⋊Dic19—41no—
90C4⋊Dic19—41no—
91C4⋊Dic19—41no—
92C4⋊Dic19—41no—
93C4⋊Dic19—41no—
94Dic19⋊C4—41no—
95Dic19⋊C4—41no—
96Dic19⋊C4—81no—
97Dic19⋊C4—81no—
98C4×Dic19—81no—
99C2×C19⋊C8—22no—
100C2×C19⋊C8—41no—
101C2×C19⋊C8—41no—
102#7802—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×C19C2×Q1611yescharacteristic
117C2×C4×C19#13511yescharacteristic
118C2×C4×C19#13511yescharacteristic
119C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
120C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
121C2×C4×C19#13711yescharacteristic
122C2×Dic19—22no—
123C2×Dic19—41no—
124C2×Dic19—41no—
125C2×Dic19—41no—
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—81no—
135C2×Dic19—81no—
136C2×Dic19—81no—
137Dic38—42no—
138Dic38—81no—
139C8×C19—42no—
140C8×C19—42no—
141C19⋊C8—42no—
142#2809—191no—
143#2096—191no—
144#2083—191no—
145#2083—191no—
146#1272—191no—
147#1271—191no—
148#1271D1911yescharacteristic
149C22×C19#44911yescharacteristic
150C22×C19#44911yescharacteristic
151C22×C19#45111yescharacteristic
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—
164Dic19—42no—
165Dic19—81no—
166Dic19—81no—
167Dic19—81no—
168Dic19—161no—
169C2×#107—381no—
170C2×#107—381no—
171C2×#106—381no—
172C2×#103—381no—
173#400—381no—
174#398—381no—
175#398—381no—
176#391—191no—
177#391—381no—
178#389—191no—
179#389C2×D1911yescharacteristic
180#387—381no—
181#387—381no—
182#384—191no—
183#340—381no—
184#340—381no—
185#336—191no—
186#336C2×D1911yescharacteristic
187#336C2×D1911yescharacteristic
188C2×C19#160911yescharacteristic
189C2×C19#160911yescharacteristic
190C2×C19#161411yescharacteristic
191C2×C19#162411yescharacteristic
192C2×C19#164811yescharacteristic
193C2×C19#164811yescharacteristic
194C2×C19#166011yescharacteristic
195C22×Q8—191no—
196C22×C8—21no—
197C22×C8—21no—
198C22×C8—381no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—191no—
201C2×C4⋊C4—191no—
202C2×C4⋊C4—191no—
203C2×C4⋊C4—381no—
204C2×C4⋊C4—381no—
205C2×C4⋊C4—381no—
206C2×C4⋊C4—381no—
207C2×C4⋊C4—381no—
208C2×C4⋊C4—381no—
209C2×C4⋊C4D7611yescharacteristic
210C2×C4⋊C4D7611yescharacteristic
211C2×C42—381no—
212C2×C42C22×D1911yescharacteristic
213#107—762no—
214#107—762no—
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#780211yescharacteristic, complemented, Sylow
227C2×Q8—192no—
228C2×Q8—381no—
229C2×Q8—761no—
230C2×Q8—761no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—381no—
234C22×C4—381no—
235C22×C4—381no—
236C22×C4—381no—
237C22×C4—761no—
238C22×C4C2×D7611yescharacteristic
239C22×C4D4×D1911yescharacteristic
240C22×C4D4×D1911yescharacteristic
241C2×C8—22no—
242C2×C8—22no—
243C2×C8—41no—
244C2×C8—41no—
245C2×C8—41no—
246C2×C8—41no—
247C2×C8—382no—
248C2×C8—761no—
249C2×C8—761no—
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—381no—
256C4⋊C4—381no—
257C4⋊C4—761no—
258C4⋊C4—761no—
259C4⋊C4—761no—
260C4⋊C4—761no—
261C4⋊C4—761no—
262C4⋊C4—761no—
263C4⋊C4—761no—
264C4⋊C4—761no—
265C4⋊C4—761no—
266C4⋊C4—761no—
267C4⋊C4—1521no—
268C4⋊C4—1521no—
269C42—41no—
270C42—1521no—
271C23#1059732811yescharacteristic
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—382no—
287C2×C4—761no—
288C2×C4—761no—
289C2×C4—761no—
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—1521no—
299C2×C4—1521no—
300C2×C4—1521no—
301C2×C4#1059735011yescharacteristic
302C2×C4#1059735411yescharacteristic
303C2×C4#1059735711yescharacteristic
304C2×C4#1059736111yescharacteristic
305C2×C4#1059736211yescharacteristic
306C2×C4Q16×D1911yescharacteristic
307C8—42no—
308C8—42no—
309C8—762no—
310C22#1192669011yescharacteristic
311C22#1192669111yescharacteristic
312C22#1192670111yescharacteristic
313C22#1192671311yescharacteristic
314C22#1192672811yescharacteristic
315C22#1192672911yescharacteristic
316C22#1192673511yescharacteristic
317C4—21no—
318C4—21no—
319C4—21no—
320C4—21no—
321C4—21no—
322C4—21no—
323C4—81no—
324C4—81no—
325C4—3041no—
326C4—762no—
327C4—1521no—
328C4—1521no—
329C4—1521no—
330C2#1456263311yescharacteristic
331C2#1456263411yescharacteristic
332C2#1456266111yescharacteristic
333C2#1456272011yescharacteristic
334C2#1456287811yescharacteristic
335C2#1456287911yescharacteristic
336C2#1456294811yescharacteristic
subgroupG/H
centerC23#10597328
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#1271C2
socle, prime radicalC23×C19#120
hypercenter#1271D19
hypocenterC19#7802
LCSG ▷ C2×C42×C19 ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

Complements

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

NH ≅ G/Ntype
226. C19#7802semidirect

Maximal subgroups

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

subgroupindex
#145716202
#145651772
#145651082
#145651062
#145614602
#145614572
C19×#12712
#780219