Finite Group Databasebeta

← #18079898

Subgroups — #18079898

Order 4864.

486 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 117 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#14572715C211yesmaximal, characteristic
2#14568843C211yesmaximal, characteristic
3#14563628C211yesmaximal, characteristic
4#14562317C211yesmaximal, characteristic
5#14562315C211yesmaximal, characteristic
6#14561538C211yesmaximal, characteristic
7C19×#1303C211yesmaximal, characteristic
8C2×#10597315C2211yescharacteristic
9C2×C4×Dic38C2211yescharacteristic
10C8×Dic38—22no—
11#11926668—22no—
12#11926597C2211yescharacteristic
13#11926594—22no—
14#11926568C2211yescharacteristic
15C2×#10597281—21no—
16#11926465C414yes—
17#11926450—21no—
18#11926443—22no—
19#11926414—21no—
20#11926312—21no—
21#11926292—22no—
22#11926292—22no—
23C19×#431C2211yescharacteristic
24C19×#423C2211yescharacteristic
25C4×C4⋊C4×C19C2211yescharacteristic
26C22×Dic38C2×C412yes—
27C22×Dic38D411yescharacteristic
28C2×M16×C19—21no—
29C2×C4⋊C4×C19—21no—
30C2×C42×C19—21no—
31C2×C42×C19C2311yescharacteristic
32C2×C4⋊Dic19—21no—
33C2×C4⋊Dic19—21no—
34C2×C4⋊Dic19—24no—
35C2×C4⋊Dic19D411yescharacteristic
36C2×Dic19⋊C4C2×C412yes—
37C2×C4×Dic19D412yes—
38C2×#64520—21no—
39#10597315—21no—
40#10597315—21no—
41#10597315—21no—
42#10597315—21no—
43C4×Dic38—21no—
44C4×Dic38—21no—
45C4×Dic38—21no—
46C4×Dic38—21no—
47C19×C4⋊C8—21no—
48C19×C4⋊C8—21no—
49C19×C4⋊C8D412yes—
50C19×C22⋊C8—21no—
51C4×C8×C19—21no—
52C19×#95C2×C412yes—
53C19⋊#95—24no—
54C22⋊(C19⋊C8)—21no—
55#10597281—42no—
56Dic19⋊C8—24no—
57C8×Dic19—24no—
58C4⋊(C19⋊C8)—21no—
59C4⋊(C19⋊C8)—21no—
60C4⋊(C19⋊C8)D412yes—
61C4×C19⋊C8—21no—
62C22×C4×C19—22no—
63C22×C4×C19C22×C411yescharacteristic
64C22×C4×C19C2×D411yescharacteristic
65C22×C4×C19C2×D411yescharacteristic
66C22×Dic19—22no—
67C22×Dic19C22⋊C412yes—
68C22×Dic19C22⋊C412yes—
69C2×Dic38—21no—
70C2×Dic38—21no—
71C2×Dic38—21no—
72C2×Dic38—21no—
73C2×Dic38—22no—
74C2×Dic38—22no—
75C2×Dic38—82no—
76C2×Dic38SD1612yes—
77C2×Dic38Q1612yes—
78M16×C19—41no—
79M16×C19—41no—
80C2×C8×C19—22no—
81C2×C8×C19—41no—
82C4⋊C4×C19—24no—
83C42×C19—41no—
84C42×C19—41no—
85C42×C19C2×D411yescharacteristic
86C42×C19C2×D411yescharacteristic
87C42×C19#4111yescharacteristic
88C42×C19#4111yescharacteristic
89C4⋊Dic19—21no—
90C4⋊Dic19—21no—
91C4⋊Dic19—41no—
92C4⋊Dic19—41no—
93C4⋊Dic19—41no—
94C4⋊Dic19—41no—
95C4⋊Dic19—84no—
96Dic19⋊C4—22no—
97Dic19⋊C4—22no—
98C4×Dic19—22no—
99C4×Dic19—22no—
100#64520—41no—
101#64520—41no—
102C2×C19⋊C8—22no—
103C2×C19⋊C8—41no—
104#9392—191nomaximal, Sylow
105C23×C19C2×C22⋊C411yescharacteristic
106C2×C4×C19—22no—
107C2×C4×C19—24no—
108C2×C4×C19—41no—
109C2×C4×C19—42no—
110C2×C4×C19—42no—
111C2×C4×C19C4×D411yescharacteristic
112C2×C4×C19C4×D411yescharacteristic
113C2×C4×C19#12011yescharacteristic
114C2×C4×C19#12111yescharacteristic
115C2×C4×C19#12111yescharacteristic
116C2×C4×C19#12311yescharacteristic
117C2×C4×C19C2×SD1611yescharacteristic
118C2×C4×C19C2×Q1611yescharacteristic
119C2×C4×C19#13511yescharacteristic
120C2×C4×C19#13511yescharacteristic
121C2×Dic19—22no—
122C2×Dic19—22no—
123C2×Dic19—22no—
124C2×Dic19—42no—
125C2×Dic19—44no—
126C2×Dic19—42no—
127C2×Dic19#10314yes—
128Dic38—22no—
129Dic38—22no—
130Dic38—22no—
131Dic38—22no—
132Dic38—82no—
133Dic38—82no—
134C8×C19—42no—
135C8×C19—81no—
136C19⋊C8—42no—
137C19⋊C8—81no—
138#2982—191no—
139#2567—191no—
140#1801—191no—
141#1548—191no—
142#1548—191no—
143#1303—191no—
144#1303D1911yescharacteristic
145C22×C19—21no—
146C22×C19—21no—
147C22×C19#38611yescharacteristic
148C22×C19C2×#10311yescharacteristic
149C22×C19#41611yescharacteristic
150C4×C19—21no—
151C4×C19—21no—
152C4×C19—21no—
153C4×C19—44no—
154C4×C19#45612yes—
155C4×C19#46511yescharacteristic
156C4×C19#46511yescharacteristic
157C4×C19#46711yescharacteristic
158C4×C19#46711yescharacteristic
159Dic19—24no—
160Dic19—42no—
161Dic19—82no—
162C2×C4⋊Q8—191no—
163C2×C4×Q8—191no—
164C8×Q8—382no—
165C8×Q8—382no—
166#431—191no—
167#431—382no—
168#431C2×D1911yescharacteristic
169#423—191no—
170#423C2×D1911yescharacteristic
171C2×#101—381no—
172#395—194no—
173#391—381no—
174#389—382no—
175#384—381no—
176C4×C4⋊C4C2×D1911yescharacteristic
177#343—381no—
178#333—382no—
179#333—382no—
180C2×C19—21no—
181C2×C19—21no—
182C2×C19#188611yescharacteristic
183C2×C19#189211yescharacteristic
184C2×C19#191411yescharacteristic
185C22×Q8—191no—
186C22×Q8—192no—
187C2×M16—21no—
188C2×M16—381no—
189C4⋊Q8—381no—
190C4⋊Q8—381no—
191C4⋊Q8—381no—
192C4⋊Q8—381no—
193C4×Q8—381no—
194C4×Q8—381no—
195C4×Q8—381no—
196C4×Q8—381no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—192no—
199C2×C4⋊C4—191no—
200C2×C4⋊C4—381no—
201C2×C4⋊C4—381no—
202C2×C4⋊C4—384no—
203C2×C42—21no—
204C2×C42—192no—
205C2×C42C22×D1911yescharacteristic
206C4⋊C8—21no—
207C4⋊C8—21no—
208C4⋊C8—192no—
209C4⋊C8—384no—
210C4⋊C8—381no—
211C4⋊C8—381no—
212C4⋊C8D7612yes—
213#101—762no—
214C22⋊C8—21no—
215C22⋊C8—381no—
216C4×C8—21no—
217C4×C8—384no—
218C4×C8—381no—
219#95—384no—
220#95C4×D1912yes—
221C19#939211yescharacteristic, complemented, Sylow
222C2×Q8—192no—
223C2×Q8—192no—
224C2×Q8—381no—
225C2×Q8—381no—
226C2×Q8—381no—
227C2×Q8—381no—
228C2×Q8—382no—
229C2×Q8—382no—
230C2×Q8—1522no—
231C22×C4—22no—
232C22×C4—192no—
233C22×C4—192no—
234C22×C4—382no—
235C22×C4C2×C4×D1911yescharacteristic
236C22×C4D4×D1911yescharacteristic
237C22×C4D4×D1911yescharacteristic
238M16—41no—
239M16—41no—
240M16—761no—
241M16—761no—
242C2×C8—22no—
243C2×C8—41no—
244C2×C8—382no—
245C2×C8—761no—
246C4⋊C4—24no—
247C4⋊C4—382no—
248C4⋊C4—381no—
249C4⋊C4—382no—
250C4⋊C4—381no—
251C4⋊C4—761no—
252C4⋊C4—761no—
253C4⋊C4—761no—
254C4⋊C4—761no—
255C4⋊C4—1524no—
256C42—41no—
257C42—41no—
258C42—382no—
259C42—382no—
260C42C2×D7611yescharacteristic
261C42#6454111yescharacteristic
262C42D4×D1911yescharacteristic
263C42#6454511yescharacteristic
264C23C22⋊C4×D1911yescharacteristic
265Q8—382no—
266Q8—382no—
267Q8—382no—
268Q8—382no—
269Q8—1522no—
270Q8—1522no—
271C2×C4—22no—
272C2×C4—24no—
273C2×C4—41no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—194no—
277C2×C4—382no—
278C2×C4—382no—
279C2×C4—382no—
280C2×C4—762no—
281C2×C4—764no—
282C2×C4—762no—
283C2×C4C4×D7611yescharacteristic
284C2×C4#1059732811yescharacteristic
285C2×C4#1059733011yescharacteristic
286C2×C4#1059733911yescharacteristic
287C2×C4#1059734011yescharacteristic
288C2×C4#1059734111yescharacteristic
289C2×C4#1059735811yescharacteristic
290C2×C4SD16×D1911yescharacteristic
291C2×C4#1059736211yescharacteristic
292C2×C4Q16×D1911yescharacteristic
293C8—42no—
294C8—81no—
295C8—762no—
296C8—1521no—
297C22—21no—
298C22—21no—
299C22#1192642211yescharacteristic
300C22#103×D1911yescharacteristic
301C22#1192653711yescharacteristic
302C4—21no—
303C4—21no—
304C4—21no—
305C4—44no—
306C4—384no—
307C4—762no—
308C4—1522no—
309C4#1192672812yes—
310C4#1192677211yescharacteristic
311C4#1192677411yescharacteristic
312C4#1192678411yescharacteristic
313C4#1192678611yescharacteristic
314C2—21no—
315C2—21no—
316C2#1456402711yescharacteristic
317C2#1456405711yescharacteristic
318C2#1456418111yescharacteristic
subgroupG/H
centerC22#11926422
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1303C2
socleC22×C19#386
prime radicalC23×C19C2×C22⋊C4
cosocleC2×C42×C19C23
hypercenter#1303D19
hypocenterC19#9392
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1303

Complements

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

NH ≅ G/Ntype
221. C19#9392semidirect

Maximal subgroups

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

subgroupindex
#145727152
#145688432
#145636282
#145623172
#145623152
#145615382
C19×#13032
#939219