Finite Group Databasebeta

← #18071697

Subgroups — #18071697

Order 4864.

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

normal subgroups only

This group has 350 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#14565193C211yesmaximal, characteristic
2#14565106C211yesmaximal, characteristic
3#14565043C211yesmaximal, characteristic
4#14561461C211yesmaximal, characteristic
5#14561458C211yesmaximal, characteristic
6#14561458C211yesmaximal, characteristic
7C19×#2805C211yesmaximal, characteristic
8C2×#10597264—21no—
9C2×#10597292—21no—
10#11926414C2211yescharacteristic
11#11926306—21no—
12#11926306—21no—
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#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—21no—
63C22×C4×C19—21no—
64C22×C4×C19—21no—
65C22×C4×C19—21no—
66C22×C4×C19C2×D411yescharacteristic
67C22×C4×C19C2×D411yescharacteristic
68C22×C4×C19C2×D411yescharacteristic
69C22×Dic19—41no—
70C4⋊C4×C19—21no—
71C4⋊C4×C19—21no—
72C4⋊C4×C19—21no—
73C4⋊C4×C19—41no—
74C4⋊C4×C19—41no—
75C4⋊C4×C19—41no—
76C4⋊C4×C19—41no—
77C4⋊C4×C19—41no—
78C4⋊C4×C19—41no—
79C4⋊C4×C19—41no—
80C4⋊C4×C19—81no—
81C4⋊C4×C19—81no—
82C4⋊C4×C19Q1612yes—
83C42×C19—41no—
84C42×C19—81no—
85C4⋊Dic19—42no—
86C4⋊Dic19—41no—
87C4⋊Dic19—41no—
88C4⋊Dic19—41no—
89C4⋊Dic19—41no—
90C2×C19⋊C8—22no—
91C2×C19⋊C8—41no—
92C2×C19⋊C8—41no—
93C2×C19⋊C8—41no—
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—22no—
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—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×C19C2×Q1611yescharacteristic
128C2×C4×C19#13511yescharacteristic
129C2×C4×C19#13511yescharacteristic
130C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
131C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
132C2×C4×C19#13711yescharacteristic
133C2×Dic19—81no—
134C2×Dic19—81no—
135C2×Dic19—81no—
136C19⋊C8—42no—
137C19⋊C8—81no—
138C19⋊C8—81no—
139#2805D1911yescharacteristic
140#2099—191no—
141#2083—191no—
142#2072—191no—
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—42no—
160C4×C19—81no—
161C4×C19—81no—
162C4×C19—81no—
163C4×C19—81no—
164C4×C19—81no—
165Dic19—161no—
166C2×#107—381no—
167C2×#103—381no—
168#400—21no—
169#400—21no—
170#395—21no—
171#391C2×D1911yescharacteristic
172#389—21no—
173#389C2×D1911yescharacteristic
174#389C2×D1911yescharacteristic
175#387—21no—
176#387—21no—
177#384—191no—
178#340—381no—
179#340—381no—
180#340—381no—
181#340—381no—
182#336—191no—
183#336—191no—
184#336—191no—
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—381no—
194C22×C8—381no—
195C22×C8—381no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—381no—
201C2×C4⋊C4—381no—
202C2×C4⋊C4—381no—
203C2×C4⋊C4C22⋊D1911yescharacteristic
204C2×C4⋊C4C22⋊D1911yescharacteristic
205C2×C4⋊C4C22⋊D1911yescharacteristic
206C2×C4⋊C4C22⋊D1911yescharacteristic
207C2×C4⋊C4C22⋊D1911yescharacteristic
208C2×C42—21no—
209C2×C42C22×D1911yescharacteristic
210#107—762no—
211#103—762no—
212#95—21no—
213#95—21no—
214#95—21no—
215#95—21no—
216#95—21no—
217#95—21no—
218#95—21no—
219#95—21no—
220#95—21no—
221C19#780611yescharacteristic, complemented, Sylow
222C2×Q8—21no—
223C2×Q8—21no—
224C2×Q8—41no—
225C2×Q8—41no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—761no—
233C22×C4C2×C22⋊D1911yescharacteristic
234C22×C4C2×C22⋊D1911yescharacteristic
235C22×C4C2×C22⋊D1911yescharacteristic
236C2×C8—382no—
237C2×C8—761no—
238C2×C8—761no—
239C2×C8—761no—
240C2×C8—761no—
241C2×C8—761no—
242C2×C8—761no—
243C2×C8—761no—
244C2×C8—761no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—81no—
256C4⋊C4—81no—
257C4⋊C4—762no—
258C4⋊C4—761no—
259C4⋊C4—761no—
260C4⋊C4—761no—
261C4⋊C4—761no—
262C4⋊C4#6452812yes—
263C42—41no—
264C42—81no—
265C23#1059739911yescharacteristic
266Q8—42no—
267Q8—81no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—22no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
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—1521no—
293C2×C4—1521no—
294C2×C4—1521no—
295C2×C4#1059738811yescharacteristic
296C2×C4C2×#6452811yescharacteristic
297C2×C4#1059739511yescharacteristic
298C2×C4#1059739511yescharacteristic
299C2×C4#1059739611yescharacteristic
300C2×C4#1059739611yescharacteristic
301C8—762no—
302C8—1521no—
303C8—1521no—
304C22#1192668911yescharacteristic
305C22#1192668911yescharacteristic
306C22#1192670011yescharacteristic
307C22#1192671711yescharacteristic
308C22#1192672211yescharacteristic
309C22#1192672711yescharacteristic
310C22#1192673411yescharacteristic
311C4—21no—
312C4—21no—
313C4—21no—
314C4—21no—
315C4—21no—
316C4—21no—
317C4—42no—
318C4—81no—
319C4—81no—
320C4—81no—
321C4—81no—
322C4—81no—
323C4—3041no—
324C2#1456263211yescharacteristic
325C2#1456264911yescharacteristic
326C2#1456267711yescharacteristic
327C2#1456274511yescharacteristic
328C2#1456284911yescharacteristic
329C2#1456287711yescharacteristic
330C2#1456296911yescharacteristic
subgroupG/H
centerC23#10597399
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#2805C2
socle, prime radicalC23×C19#120
hypercenter#2805D19
hypocenterC19#7806
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
221. C19#7806semidirect

Maximal subgroups

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

subgroupindex
#145651932
#145651062
#145650432
#145614612
#145614582
C19×#28052
#780619