Finite Group Databasebeta

← #18071704

Subgroups — #18071704

Order 4864.

366 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 87 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#14565111C211yesmaximal, characteristic
3#14565106C211yesmaximal, characteristic
4#14561461C211yesmaximal, characteristic
5#14561458C211yesmaximal, characteristic
6#14561458C211yesmaximal, characteristic
7C19×#2805C211yesmaximal, characteristic
8C2×#10597264—21no—
9C2×#10597265—21no—
10C2×#10597265—21no—
11C2×#10597292—21no—
12#11926414C2211yescharacteristic
13#11926306—21no—
14#11926306—21no—
15#11926299C2211yescharacteristic
16#11926299C2211yescharacteristic
17#11926299C2211yescharacteristic
18C19×#400—21no—
19C19×#400—21no—
20C19×#395—21no—
21C19×#391C2211yescharacteristic
22C19×#389—21no—
23C19×#389C2211yescharacteristic
24C19×#389C2211yescharacteristic
25C19×#387—21no—
26C19×#387—21no—
27C22×Q8×C19D411yescharacteristic
28C2×C4⋊C4×C19—21no—
29C2×C4⋊C4×C19—21no—
30C2×C4⋊C4×C19—21no—
31C2×C4⋊C4×C19—21no—
32C2×C4⋊C4×C19D411yescharacteristic
33C2×C4⋊C4×C19D411yescharacteristic
34C2×C4⋊C4×C19D411yescharacteristic
35C2×C4⋊C4×C19D411yescharacteristic
36C2×C4⋊C4×C19D411yescharacteristic
37C2×C42×C19—21no—
38C2×C42×C19C2311yescharacteristic
39C2×C4⋊Dic19—21no—
40C2×C4⋊Dic19—21no—
41C2×C4⋊Dic19—21no—
42C22×C19⋊C8—21no—
43C22×C19⋊C8—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#10597292—42no—
55#10597265—42no—
56#10597265—42no—
57#10597264—42no—
58C2×Q8×C19—21no—
59C2×Q8×C19—21no—
60C2×Q8×C19—41no—
61C2×Q8×C19—41no—
62C22×C4×C19—21no—
63C22×C4×C19—21no—
64C22×C4×C19—21no—
65C22×C4×C19—21no—
66C22×C4×C19—21no—
67C22×C4×C19—21no—
68C22×C4×C19C2×D411yescharacteristic
69C22×C4×C19C2×D411yescharacteristic
70C22×C4×C19C2×D411yescharacteristic
71C22×Dic19—41no—
72C4⋊C4×C19—21no—
73C4⋊C4×C19—21no—
74C4⋊C4×C19—21no—
75C4⋊C4×C19—41no—
76C4⋊C4×C19—41no—
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×C19SD1612yes—
85C42×C19—41no—
86C42×C19—81no—
87C4⋊Dic19—41no—
88C4⋊Dic19—41no—
89C4⋊Dic19—41no—
90C4⋊Dic19—41no—
91C4⋊Dic19—41no—
92C4⋊Dic19—41no—
93C2×C19⋊C8—22no—
94C2×C19⋊C8—22no—
95C2×C19⋊C8—22no—
96C2×C19⋊C8—41no—
97C2×C19⋊C8—41no—
98C2×C19⋊C8—41no—
99C2×C19⋊C8—41no—
100C2×C19⋊C8—41no—
101C2×C19⋊C8—41no—
102#7807—191nomaximal, Sylow
103C23×C19#12011yescharacteristic
104Q8×C19—42no—
105Q8×C19—81no—
106C2×C4×C19—21no—
107C2×C4×C19—21no—
108C2×C4×C19—21no—
109C2×C4×C19—21no—
110C2×C4×C19—21no—
111C2×C4×C19—21no—
112C2×C4×C19—22no—
113C2×C4×C19—41no—
114C2×C4×C19—41no—
115C2×C4×C19—41no—
116C2×C4×C19—41no—
117C2×C4×C19—41no—
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×C19C2×SD1611yescharacteristic
131C2×C4×C19#13511yescharacteristic
132C2×C4×C19#13511yescharacteristic
133C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
134C2×C4×C19#13711yescharacteristic
135C2×C4×C19#13711yescharacteristic
136C2×Dic19—81no—
137C2×Dic19—81no—
138C2×Dic19—81no—
139C19⋊C8—42no—
140C19⋊C8—42no—
141C19⋊C8—42no—
142#2805D1911yescharacteristic
143#2096—191no—
144#2084—191no—
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—42no—
163C4×C19—81no—
164C4×C19—81no—
165C4×C19—81no—
166C4×C19—81no—
167C4×C19—81no—
168Dic19—161no—
169C2×#107—381no—
170C2×#106—381no—
171C2×#106—381no—
172C2×#103—381no—
173#400—21no—
174#400—21no—
175#395—21no—
176#391C2×D1911yescharacteristic
177#389—21no—
178#389C2×D1911yescharacteristic
179#389C2×D1911yescharacteristic
180#387—21no—
181#387—21no—
182#384—191no—
183#340—381no—
184#340—381no—
185#336—191no—
186#336—191no—
187#336—191no—
188C2×C19#160911yescharacteristic
189C2×C19#161111yescharacteristic
190C2×C19#161811yescharacteristic
191C2×C19#162211yescharacteristic
192C2×C19#165011yescharacteristic
193C2×C19#165311yescharacteristic
194C2×C19#166011yescharacteristic
195C22×Q8C22⋊D1911yescharacteristic
196C22×C8—381no—
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—381no—
204C2×C4⋊C4—381no—
205C2×C4⋊C4—381no—
206C2×C4⋊C4C22⋊D1911yescharacteristic
207C2×C4⋊C4C22⋊D1911yescharacteristic
208C2×C4⋊C4C22⋊D1911yescharacteristic
209C2×C4⋊C4C22⋊D1911yescharacteristic
210C2×C4⋊C4C22⋊D1911yescharacteristic
211C2×C42—21no—
212C2×C42C22×D1911yescharacteristic
213#107—762no—
214#106—762no—
215#106—762no—
216#103—762no—
217#95—21no—
218#95—21no—
219#95—21no—
220#95—21no—
221#95—21no—
222#95—21no—
223#95—21no—
224#95—21no—
225#95—21no—
226C19#780711yescharacteristic, complemented, Sylow
227C2×Q8—21no—
228C2×Q8—21no—
229C2×Q8—41no—
230C2×Q8—41no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—761no—
238C22×C4C2×C22⋊D1911yescharacteristic
239C22×C4C2×C22⋊D1911yescharacteristic
240C22×C4C2×C22⋊D1911yescharacteristic
241C2×C8—382no—
242C2×C8—382no—
243C2×C8—382no—
244C2×C8—761no—
245C2×C8—761no—
246C2×C8—761no—
247C2×C8—761no—
248C2×C8—761no—
249C2×C8—761no—
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—21no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—81no—
261C4⋊C4—81no—
262C4⋊C4—761no—
263C4⋊C4—761no—
264C4⋊C4—761no—
265C4⋊C4—761no—
266C4⋊C4—761no—
267C4⋊C4—761no—
268C4⋊C4#6452712yes—
269C42—41no—
270C42—81no—
271C23#1059739911yescharacteristic
272Q8—42no—
273Q8—81no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—22no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
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—1521no—
299C2×C4—1521no—
300C2×C4—1521no—
301C2×C4C2×#6452711yescharacteristic
302C2×C4#1059738811yescharacteristic
303C2×C4#1059739511yescharacteristic
304C2×C4#1059739611yescharacteristic
305C2×C4#1059739611yescharacteristic
306C2×C4#1059739711yescharacteristic
307C8—762no—
308C8—762no—
309C8—762no—
310C22#1192668311yescharacteristic
311C22#1192668911yescharacteristic
312C22#1192670611yescharacteristic
313C22#1192671211yescharacteristic
314C22#1192672711yescharacteristic
315C22#1192672711yescharacteristic
316C22#1192673411yescharacteristic
317C4—21no—
318C4—21no—
319C4—21no—
320C4—21no—
321C4—21no—
322C4—21no—
323C4—42no—
324C4—81no—
325C4—81no—
326C4—81no—
327C4—81no—
328C4—81no—
329C4—3041no—
330C2#1456263211yescharacteristic
331C2#1456264311yescharacteristic
332C2#1456268311yescharacteristic
333C2#1456270711yescharacteristic
334C2#1456289111yescharacteristic
335C2#1456291211yescharacteristic
336C2#1456294611yescharacteristic
subgroupG/H
centerC23#10597399
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#2805C2
socle, prime radicalC23×C19#120
hypercenter#2805D19
hypocenterC19#7807
LCSG ▷ C2×C42×C19 ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2805

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
#145651782
#145651112
#145651062
#145614612
#145614582
C19×#28052
#780719