Finite Group Databasebeta

← #18071718

Subgroups — #18071718

Order 4864.

378 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 91 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#14565178C211yesmaximal, characteristic
2#14565106C211yesmaximal, characteristic
3#14565043C211yesmaximal, characteristic
4#14561461C211yesmaximal, characteristic
5#14561461C211yesmaximal, characteristic
6#14561458C211yesmaximal, characteristic
7C19×#2806C211yesmaximal, characteristic
8C2×#10597264—21no—
9C2×#10597265—21no—
10C2×#10597292—21no—
11C2×#10597292—21no—
12#11926414C2211yescharacteristic
13#11926306—21no—
14#11926306—21no—
15#11926299C2211yescharacteristic
16#11926299C2211yescharacteristic
17#11926299C2211yescharacteristic
18C19×#398—21no—
19C19×#398—21no—
20C19×#395—21no—
21C19×#391—21no—
22C19×#391C2211yescharacteristic
23C19×#391C2211yescharacteristic
24C19×#389—21no—
25C19×#389C2211yescharacteristic
26C19×#387—21no—
27C22×Q8×C19D411yescharacteristic
28C22×Q8×C19D411yescharacteristic
29C2×C4⋊C4×C19—21no—
30C2×C4⋊C4×C19—21no—
31C2×C4⋊C4×C19—21no—
32C2×C4⋊C4×C19—21no—
33C2×C4⋊C4×C19—21no—
34C2×C4⋊C4×C19D411yescharacteristic
35C2×C4⋊C4×C19D411yescharacteristic
36C2×C4⋊C4×C19D411yescharacteristic
37C2×C4⋊C4×C19D411yescharacteristic
38C2×C42×C19—21no—
39C2×C42×C19C2311yescharacteristic
40C2×C4⋊Dic19—21no—
41C2×C4⋊Dic19—21no—
42C2×C4⋊Dic19—21no—
43C22×C19⋊C8—21no—
44C22×C19⋊C8—21no—
45C22×C19⋊C8—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#10597292—42no—
55#10597292—42no—
56#10597265—42no—
57#10597264—42no—
58C2×Q8×C19—21no—
59C2×Q8×C19—21no—
60C2×Q8×C19—21no—
61C2×Q8×C19—41no—
62C2×Q8×C19—41no—
63C2×Q8×C19—41no—
64C2×Q8×C19—41no—
65C2×Q8×C19Q1612yes—
66C22×C4×C19—21no—
67C22×C4×C19—21no—
68C22×C4×C19—21no—
69C22×C4×C19—21no—
70C22×C4×C19—21no—
71C22×C4×C19—21no—
72C22×C4×C19C2×D411yescharacteristic
73C22×C4×C19C2×D411yescharacteristic
74C22×C4×C19C2×D411yescharacteristic
75C22×Dic19—41no—
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—81no—
83C4⋊C4×C19—81no—
84C4⋊C4×C19—81no—
85C4⋊C4×C19—81no—
86C4⋊C4×C19SD1612yes—
87C42×C19—41no—
88C42×C19—81no—
89C4⋊Dic19—41no—
90C4⋊Dic19—41no—
91C4⋊Dic19—41no—
92C4⋊Dic19—41no—
93C4⋊Dic19—41no—
94C4⋊Dic19—41no—
95C2×C19⋊C8—22no—
96C2×C19⋊C8—22no—
97C2×C19⋊C8—41no—
98C2×C19⋊C8—41no—
99C2×C19⋊C8—41no—
100C2×C19⋊C8—41no—
101C2×C19⋊C8—41no—
102C2×C19⋊C8—41no—
103C2×C19⋊C8—41no—
104#7809—191nomaximal, Sylow
105C23×C19#12011yescharacteristic
106Q8×C19—42no—
107Q8×C19—42no—
108Q8×C19—81no—
109Q8×C19—81no—
110C2×C4×C19—21no—
111C2×C4×C19—21no—
112C2×C4×C19—21no—
113C2×C4×C19—21no—
114C2×C4×C19—21no—
115C2×C4×C19—21no—
116C2×C4×C19—22no—
117C2×C4×C19—22no—
118C2×C4×C19—41no—
119C2×C4×C19—41no—
120C2×C4×C19—41no—
121C2×C4×C19—41no—
122C2×C4×C19—41no—
123C2×C4×C19—41no—
124C2×C4×C19—41no—
125C2×C4×C19—41no—
126C2×C4×C19—41no—
127C2×C4×C19—41no—
128C2×C4×C19—41no—
129C2×C4×C19—41no—
130C2×C4×C19—41no—
131C2×C4×C19—41no—
132C2×C4×C19—41no—
133C2×C4×C19—41no—
134C2×C4×C19C2×SD1611yescharacteristic
135C2×C4×C19C2×Q1611yescharacteristic
136C2×C4×C19#13511yescharacteristic
137C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
138C2×C4×C19#13711yescharacteristic
139C2×C4×C19#13711yescharacteristic
140C2×Dic19—81no—
141C2×Dic19—81no—
142C2×Dic19—81no—
143C19⋊C8—42no—
144C19⋊C8—42no—
145C19⋊C8—81no—
146#2806D1911yescharacteristic
147#2096—191no—
148#2083—191no—
149#2072—191no—
150#1272—191no—
151#1272—191no—
152#1271—191no—
153C22×C19#44811yescharacteristic
154C22×C19#44911yescharacteristic
155C22×C19#45111yescharacteristic
156C22×C19#45311yescharacteristic
157C22×C19#45511yescharacteristic
158C22×C19#45611yescharacteristic
159C22×C19#45811yescharacteristic
160C4×C19—21no—
161C4×C19—21no—
162C4×C19—21no—
163C4×C19—21no—
164C4×C19—21no—
165C4×C19—21no—
166C4×C19—42no—
167C4×C19—42no—
168C4×C19—81no—
169C4×C19—81no—
170C4×C19—81no—
171C4×C19—81no—
172Dic19—161no—
173C2×#107—381no—
174C2×#106—381no—
175C2×#103—381no—
176C2×#103—381no—
177#398—21no—
178#398—21no—
179#395—21no—
180#391—21no—
181#391C2×D1911yescharacteristic
182#391C2×D1911yescharacteristic
183#389—21no—
184#389C2×D1911yescharacteristic
185#387—21no—
186#384—191no—
187#340—381no—
188#340—381no—
189#336—191no—
190#336—191no—
191#336—191no—
192C2×C19#161111yescharacteristic
193C2×C19#161211yescharacteristic
194C2×C19#161411yescharacteristic
195C2×C19#162211yescharacteristic
196C2×C19#164511yescharacteristic
197C2×C19#164811yescharacteristic
198C2×C19#166111yescharacteristic
199C22×Q8C22⋊D1911yescharacteristic
200C22×Q8C22⋊D1911yescharacteristic
201C22×C8—381no—
202C22×C8—381no—
203C22×C8—381no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—381no—
210C2×C4⋊C4—381no—
211C2×C4⋊C4—381no—
212C2×C4⋊C4C22⋊D1911yescharacteristic
213C2×C4⋊C4C22⋊D1911yescharacteristic
214C2×C4⋊C4C22⋊D1911yescharacteristic
215C2×C4⋊C4C22⋊D1911yescharacteristic
216C2×C42—21no—
217C2×C42C22×D1911yescharacteristic
218#107—762no—
219#106—762no—
220#103—762no—
221#103—762no—
222#95—21no—
223#95—21no—
224#95—21no—
225#95—21no—
226#95—21no—
227#95—21no—
228#95—21no—
229#95—21no—
230C19#780911yescharacteristic, complemented, Sylow
231C2×Q8—21no—
232C2×Q8—21no—
233C2×Q8—21no—
234C2×Q8—41no—
235C2×Q8—41no—
236C2×Q8—41no—
237C2×Q8—41no—
238C2×Q8#6452812yes—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—761no—
246C22×C4C2×C22⋊D1911yescharacteristic
247C22×C4C2×C22⋊D1911yescharacteristic
248C22×C4C2×C22⋊D1911yescharacteristic
249C2×C8—382no—
250C2×C8—382no—
251C2×C8—761no—
252C2×C8—761no—
253C2×C8—761no—
254C2×C8—761no—
255C2×C8—761no—
256C2×C8—761no—
257C2×C8—761no—
258C4⋊C4—21no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—81no—
265C4⋊C4—81no—
266C4⋊C4—81no—
267C4⋊C4—81no—
268C4⋊C4—761no—
269C4⋊C4—761no—
270C4⋊C4—761no—
271C4⋊C4—761no—
272C4⋊C4—761no—
273C4⋊C4—761no—
274C4⋊C4#6452712yes—
275C42—41no—
276C42—81no—
277C23#1059739911yescharacteristic
278Q8—42no—
279Q8—42no—
280Q8—81no—
281Q8—81no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—1521no—
307C2×C4—1521no—
308C2×C4—1521no—
309C2×C4C2×#6452711yescharacteristic
310C2×C4#1059738811yescharacteristic
311C2×C4#1059738811yescharacteristic
312C2×C4C2×#6452811yescharacteristic
313C2×C4#1059739511yescharacteristic
314C2×C4#1059739611yescharacteristic
315C8—762no—
316C8—762no—
317C8—1521no—
318C22#1192668311yescharacteristic
319C22#1192668911yescharacteristic
320C22#1192670011yescharacteristic
321C22#1192671211yescharacteristic
322C22#1192672211yescharacteristic
323C22#1192672711yescharacteristic
324C22#1192673411yescharacteristic
325C4—21no—
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—42no—
332C4—42no—
333C4—81no—
334C4—81no—
335C4—81no—
336C4—81no—
337C4—3041no—
338C2#1456264311yescharacteristic
339C2#1456264911yescharacteristic
340C2#1456266011yescharacteristic
341C2#1456270711yescharacteristic
342C2#1456285611yescharacteristic
343C2#1456287711yescharacteristic
344C2#1456295211yescharacteristic
subgroupG/H
centerC23#10597399
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#2806C2
socle, prime radicalC23×C19#120
hypercenter#2806D19
hypocenterC19#7809
LCSG ▷ C2×C42×C19 ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2806

Complements

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

NH ≅ G/Ntype
230. C19#7809semidirect

Maximal subgroups

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

subgroupindex
#145651782
#145651062
#145650432
#145614612
#145614582
C19×#28062
#780919