Finite Group Databasebeta

← #18071694

Subgroups — #18071694

Order 4864.

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

normal subgroups only

This group has 350 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#14571590C211yesmaximal, characteristic
2#14565192C211yesmaximal, characteristic
3#14565107C211yesmaximal, characteristic
4#14561461C211yesmaximal, characteristic
5#14561459C211yesmaximal, characteristic
6#14561457C211yesmaximal, characteristic
7C19×#2072C211yesmaximal, characteristic
8C2×#10597264—21no—
9#11926486—21no—
10#11926484—21no—
11#11926463—21no—
12#11926442C2211yescharacteristic
13#11926442C2211yescharacteristic
14#11926441—21no—
15#11926427—21no—
16#11926425—21no—
17#11926306—21no—
18#11926306—21no—
19#11926306—21no—
20#11926299C2211yescharacteristic
21#11926299C2211yescharacteristic
22C2×C19×#103—21no—
23C19×#391C2211yescharacteristic
24C19×#384C2211yescharacteristic
25C19×#340—21no—
26C19×#336C2211yescharacteristic
27C22×Q8×C19D411yescharacteristic
28C22×C8×C19—21no—
29C2×C4⋊C4×C19—21no—
30C2×C4⋊C4×C19—21no—
31C2×C4⋊C4×C19—21no—
32C2×C4⋊C4×C19D411yescharacteristic
33C2×C42×C19C2311yescharacteristic
34C2×C4⋊Dic19D411yescharacteristic
35C2×C4⋊Dic19D411yescharacteristic
36C2×C4⋊Dic19D411yescharacteristic
37C2×C4⋊Dic19D411yescharacteristic
38C2×Dic19⋊C4—21no—
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×#103—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#10597264—42no—
56C2×Q8×C19—21no—
57C2×Q8×C19—21no—
58C2×Q8×C19—41no—
59C2×Q8×C19—41no—
60C22×C4×C19—21no—
61C22×C4×C19—21no—
62C22×C4×C19—41no—
63C22×C4×C19C2×D411yescharacteristic
64C22×C4×C19C2×D411yescharacteristic
65C22×C4×C19C2×D411yescharacteristic
66C22×Dic19—21no—
67C22×Dic19—21no—
68C22×Dic19—21no—
69C22×Dic19—21no—
70C2×C8×C19—41no—
71C2×C8×C19—41no—
72C2×C8×C19—41no—
73C4⋊C4×C19—41no—
74C4⋊C4×C19—42no—
75C4⋊C4×C19—41no—
76C4⋊C4×C19—41no—
77C4⋊C4×C19—41no—
78C4⋊C4×C19—41no—
79C42×C19—41no—
80C4⋊Dic19—21no—
81C4⋊Dic19—21no—
82C4⋊Dic19—21no—
83C4⋊Dic19—41no—
84C4⋊Dic19—41no—
85C4⋊Dic19Q1612yes—
86Dic19⋊C4—41no—
87Dic19⋊C4—41no—
88Dic19⋊C4—41no—
89Dic19⋊C4—41no—
90Dic19⋊C4—81no—
91Dic19⋊C4—81no—
92C4×Dic19—81no—
93C2×C19⋊C8—22no—
94C2×C19⋊C8—41no—
95C2×C19⋊C8—41no—
96C2×C19⋊C8—41no—
97C2×C19⋊C8—41no—
98C2×C19⋊C8—41no—
99#7806—191nomaximal, Sylow
100C23×C19#12011yescharacteristic
101Q8×C19—42no—
102Q8×C19—81no—
103C2×C4×C19—21no—
104C2×C4×C19—21no—
105C2×C4×C19—21no—
106C2×C4×C19—21no—
107C2×C4×C19—21no—
108C2×C4×C19—21no—
109C2×C4×C19—41no—
110C2×C4×C19—41no—
111C2×C4×C19—41no—
112C2×C4×C19—41no—
113C2×C4×C19—41no—
114C2×C4×C19—41no—
115C2×C4×C19—81no—
116C2×C4×C19—81no—
117C2×C4×C19—81no—
118C2×C4×C19C2×Q1611yescharacteristic
119C2×C4×C19#13511yescharacteristic
120C2×C4×C19#13511yescharacteristic
121C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
122C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
123C2×C4×C19#13711yescharacteristic
124C2×Dic19—22no—
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—41no—
135C2×Dic19—41no—
136C8×C19—81no—
137C19⋊C8—42no—
138C19⋊C8—81no—
139#2805—191no—
140#2099—191no—
141#2083—191no—
142#2072D1911yescharacteristic
143#1272—191no—
144#1271—191no—
145#1271—191no—
146C22×C19#44911yescharacteristic
147C22×C19#44911yescharacteristic
148C22×C19#45111yescharacteristic
149C22×C19#45411yescharacteristic
150C22×C19#45511yescharacteristic
151C22×C19#45611yescharacteristic
152C22×C19#45811yescharacteristic
153C4×C19—21no—
154C4×C19—21no—
155C4×C19—21no—
156C4×C19—21no—
157C4×C19—21no—
158C4×C19—21no—
159C4×C19—81no—
160C4×C19—81no—
161C4×C19—161no—
162Dic19—42no—
163Dic19—81no—
164Dic19—81no—
165Dic19—81no—
166C2×#107—381no—
167C2×#103—21no—
168#400—381no—
169#400—381no—
170#395—381no—
171#391C2×D1911yescharacteristic
172#389—191no—
173#389—191no—
174#389—381no—
175#387—381no—
176#387—381no—
177#384C2×D1911yescharacteristic
178#340—21no—
179#340—381no—
180#340—381no—
181#340—381no—
182#336—191no—
183#336—191no—
184#336C2×D1911yescharacteristic
185C2×C19#160911yescharacteristic
186C2×C19#161211yescharacteristic
187C2×C19#161711yescharacteristic
188C2×C19#162811yescharacteristic
189C2×C19#164411yescharacteristic
190C2×C19#164811yescharacteristic
191C2×C19#166411yescharacteristic
192C22×Q8C22⋊D1911yescharacteristic
193C22×C8—21no—
194C22×C8—381no—
195C22×C8—381no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—191no—
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⋊C4C22⋊D1911yescharacteristic
208C2×C42—381no—
209C2×C42C22×D1911yescharacteristic
210#107—762no—
211#103—42no—
212#95—21no—
213#95—21no—
214#95—381no—
215#95—381no—
216#95—381no—
217#95—381no—
218#95—381no—
219#95—381no—
220#95—381no—
221C19#780611yescharacteristic, complemented, Sylow
222C2×Q8—21no—
223C2×Q8—21no—
224C2×Q8—41no—
225C2×Q8—41no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—41no—
229C22×C4—381no—
230C22×C4—381no—
231C22×C4—381no—
232C22×C4—381no—
233C22×C4D4×D1911yescharacteristic
234C22×C4D4×D1911yescharacteristic
235C22×C4C2×C22⋊D1911yescharacteristic
236C2×C8—41no—
237C2×C8—41no—
238C2×C8—41no—
239C2×C8—382no—
240C2×C8—761no—
241C2×C8—761no—
242C2×C8—761no—
243C2×C8—761no—
244C2×C8—761no—
245C4⋊C4—41no—
246C4⋊C4—42no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—192no—
252C4⋊C4—381no—
253C4⋊C4—381no—
254C4⋊C4—381no—
255C4⋊C4—761no—
256C4⋊C4—761no—
257C4⋊C4—761no—
258C4⋊C4—761no—
259C4⋊C4—761no—
260C4⋊C4—761no—
261C4⋊C4—1521no—
262C4⋊C4—1521no—
263C42—41no—
264C42—1521no—
265C23#1059738311yescharacteristic
266Q8—42no—
267Q8—81no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—81no—
281C2×C4—81no—
282C2×C4—81no—
283C2×C4—382no—
284C2×C4—761no—
285C2×C4—761no—
286C2×C4—761no—
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#1059736011yescharacteristic
296C2×C4#1059736211yescharacteristic
297C2×C4Q16×D1911yescharacteristic
298C2×C4#1059736411yescharacteristic
299C2×C4#1059737811yescharacteristic
300C2×C4#1059739611yescharacteristic
301C8—81no—
302C8—762no—
303C8—1521no—
304C22#1192668711yescharacteristic
305C22#1192668811yescharacteristic
306C22#1192669811yescharacteristic
307C22#1192671511yescharacteristic
308C22#1192672111yescharacteristic
309C22#1192672511yescharacteristic
310C22#1192673311yescharacteristic
311C4—21no—
312C4—21no—
313C4—21no—
314C4—21no—
315C4—21no—
316C4—21no—
317C4—81no—
318C4—81no—
319C4—161no—
320C4—762no—
321C4—1521no—
322C4—1521no—
323C4—1521no—
324C2#1456263111yescharacteristic
325C2#1456264711yescharacteristic
326C2#1456267511yescharacteristic
327C2#1456274411yescharacteristic
328C2#1456284611yescharacteristic
329C2#1456287511yescharacteristic
330C2#1456296811yescharacteristic
subgroupG/H
centerC23#10597383
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#2072C2
socle, prime radicalC23×C19#120
hypercenter#2072D19
hypocenterC19#7806
LCSG ▷ C2×C42×C19 ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2072

Complements

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

NH ≅ G/Ntype
221. C19#7806semidirect

Maximal subgroups

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

subgroupindex
#145715902
#145651922
#145651072
#145614612
#145614592
#145614572
C19×#20722
#780619