Finite Group Databasebeta

← #18085264

Subgroups — #18085264

Order 4864.

504 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 107 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#14574788C211yesmaximal, characteristic
2#14574786C211yesmaximal, characteristic
3#14572012C211yesmaximal, characteristic
4#14564611C211yesmaximal, characteristic
5#14562321C211yesmaximal, characteristic
6#14561467C211yesmaximal, characteristic
7C19×#1549C211yesmaximal, characteristic
8#11927101C2211yescharacteristic
9C2×#10597315C2211yescharacteristic
10#11926949—21no—
11#11926947—21no—
12#11926896—21no—
13#11926895—21no—
14#11926880—22no—
15#11926879—22no—
16#11926840—22no—
17#11926836—22no—
18#11926597C2211yescharacteristic
19#11926451—22no—
20#11926449—22no—
21#11926409—22no—
22C42×Dic19C2211yescharacteristic
23#11926305—22no—
24#11926289—22no—
25C2×C19×C4⋊Q8C2211yescharacteristic
26C19×#431C2211yescharacteristic
27C19×#423C2211yescharacteristic
28C19×#332—22no—
29C22×Q8×C19—21no—
30C22×Dic38—21no—
31C2×M16×C19—21no—
32C19×C4⋊Q8—21no—
33C19×C4⋊Q8—21no—
34C19×C4⋊Q8—21no—
35C19×C4⋊Q8—21no—
36C2×C4⋊C4×C19—21no—
37C2×C4⋊C4×C19D412yes—
38C2×C42×C19C2311yescharacteristic
39#10597372—21no—
40C2×C4⋊Dic19—21no—
41C2×C4⋊Dic19D412yes—
42#10597370—21no—
43#10597370—21no—
44C2×C4×Dic19—21no—
45C2×C4×Dic19—21no—
46C2×C4×Dic19D412yes—
47#10597316—21no—
48#10597315—21no—
49#10597315—21no—
50#10597315—21no—
51#10597315—21no—
52#10597315D411yescharacteristic
53#10597315D411yescharacteristic
54C4×Dic38—21no—
55C4×Dic38—21no—
56C19×C4⋊C8—21no—
57C19×C4⋊C8—21no—
58C19×C4⋊C8D412yes—
59C19×C22⋊C8—21no—
60C4×C8×C19—21no—
61C19⋊#95—28no—
62C22⋊(C19⋊C8)—21no—
63#10597275—24no—
64#10597273—24no—
65#10597267—24no—
66#10597264—24no—
67C4⋊(C19⋊C8)D412yes—
68C4×C19⋊C8—21no—
69C2×Q8×C19—44no—
70C2×Q8×C19—41no—
71C2×Q8×C19—41no—
72C22×C4×C19—22no—
73C22×C4×C19C2×D411yescharacteristic
74C22×C4×C19C2×D411yescharacteristic
75C22×C4×C19C2×D411yescharacteristic
76C22×Dic19—22no—
77C22×Dic19—22no—
78C2×Dic38—21no—
79C2×Dic38—21no—
80C2×Dic38—44no—
81C2×Dic38—41no—
82C2×Dic38—41no—
83M16×C19—42no—
84C2×C8×C19—22no—
85C2×C8×C19—41no—
86C4⋊C4×C19—22no—
87C4⋊C4×C19—22no—
88C4⋊C4×C19—41no—
89C4⋊C4×C19—41no—
90C42×C19C2×D411yescharacteristic
91C42×C19C2×D411yescharacteristic
92C42×C19C2×D411yescharacteristic
93C42×C19#4111yescharacteristic
94C22⋊Dic19—41no—
95C4⋊Dic19—21no—
96C4⋊Dic19—22no—
97C4⋊Dic19—21no—
98C4⋊Dic19—22no—
99C4⋊Dic19—21no—
100C4⋊Dic19—21no—
101C4⋊Dic19—41no—
102C4⋊Dic19—41no—
103Dic19⋊C4—41no—
104Dic19⋊C4—41no—
105C4×Dic19—22no—
106C4×Dic19—42no—
107C4×Dic19—42no—
108C4×Dic19—41no—
109C4×Dic19Q1614yes—
110C2×C19⋊C8—22no—
111#10295—191nomaximal, Sylow
112C23×C19#12011yescharacteristic
113Q8×C19—82no—
114Q8×C19—82no—
115C2×C4×C19—22no—
116C2×C4×C19—22no—
117C2×C4×C19—44no—
118C2×C4×C19—42no—
119C2×C4×C19#12011yescharacteristic
120C2×C4×C19#12011yescharacteristic
121C2×C4×C19#12111yescharacteristic
122C2×C4×C19#12111yescharacteristic
123C2×C4×C19#12111yescharacteristic
124C2×C4×C19#12711yescharacteristic
125C2×C4×C19C2×Q1612yes—
126C2×C4×C19#13712yes—
127C2×Dic19—24no—
128C2×Dic19—42no—
129C2×Dic19—42no—
130C2×Dic19—44no—
131C2×Dic19—41no—
132C2×Dic19—41no—
133C2×Dic19—42no—
134Dic38—42no—
135Dic38—42no—
136Dic38—82no—
137Dic38—82no—
138C8×C19—42no—
139C8×C19—81no—
140C19⋊C8—42no—
141#3230—191no—
142#3230—191no—
143#2862—191no—
144#1994—191no—
145#1549—191no—
146#1549D1911yescharacteristic
147#1276—191no—
148C22×C19—21no—
149C22×C19—21no—
150C22×C19#39211yescharacteristic
151C22×C19#45112yes—
152C4×C19—21no—
153C4×C19—21no—
154C4×C19—82no—
155C4×C19#45412yes—
156C4×C19#45412yes—
157C4×C19#46212yes—
158C4×C19#49411yescharacteristic
159C4×C19#49711yescharacteristic
160Dic19—44no—
161Dic19—81no—
162Dic19—81no—
163Dic19—82no—
164#533—191no—
165C2×C4⋊Q8—191no—
166C2×C4⋊Q8C2×D1911yescharacteristic
167#500—381no—
168#500—381no—
169#487—381no—
170#487—381no—
171#484—382no—
172#484—382no—
173#477—382no—
174#477—382no—
175#431—191no—
176#431C2×D1911yescharacteristic
177#423C2×D1911yescharacteristic
178#391—382no—
179#391—382no—
180#382—382no—
181C43—191no—
182#339—382no—
183#332—22no—
184#332—382no—
185C2×C19—22no—
186C2×C19#200311yescharacteristic
187C2×C19#200311yescharacteristic
188C2×C19#201611yescharacteristic
189C22×Q8—21no—
190C22×Q8—381no—
191C2×M16—21no—
192C4⋊Q8—21no—
193C4⋊Q8—21no—
194C4⋊Q8—21no—
195C4⋊Q8—21no—
196C4⋊Q8—191no—
197C4⋊Q8—191no—
198C4⋊Q8—381no—
199C4⋊Q8—381no—
200C4⋊Q8—381no—
201C4⋊Q8—381no—
202#125—381no—
203C22⋊Q8—381no—
204C22⋊Q8—381no—
205C4×Q8—381no—
206C4×Q8—381no—
207#117—381no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—192no—
210C2×C4⋊C4—381no—
211C2×C4⋊C4D7612yes—
212C2×C42—192no—
213C2×C42—381no—
214C2×C42—381no—
215C2×C42C22×D1911yescharacteristic
216#107—384no—
217#107—384no—
218C4⋊C8—21no—
219C4⋊C8—21no—
220C4⋊C8—192no—
221C4⋊C8C22⋊D1912yes—
222#103—384no—
223#103—384no—
224C22⋊C8—21no—
225C22⋊C8—381no—
226C4×C8—21no—
227C4×C8—381no—
228#95—388no—
229C19#1029511yescharacteristic, complemented, Sylow
230C2×Q8—44no—
231C2×Q8—41no—
232C2×Q8—41no—
233C2×Q8—381no—
234C2×Q8—381no—
235C2×Q8—764no—
236C2×Q8—761no—
237C2×Q8—761no—
238C22×C4—22no—
239C22×C4—382no—
240C22×C4—382no—
241C22×C4C2×D7611yescharacteristic
242C22×C4D4×D1911yescharacteristic
243C22×C4D4×D1911yescharacteristic
244M16—42no—
245C2×C8—22no—
246C2×C8—41no—
247C2×C8—382no—
248C4⋊C4—22no—
249C4⋊C4—22no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—382no—
253C4⋊C4—381no—
254C4⋊C4—381no—
255C4⋊C4—382no—
256C4⋊C4—381no—
257C4⋊C4—381no—
258C4⋊C4—761no—
259C4⋊C4—761no—
260C4⋊C4—761no—
261C4⋊C4—761no—
262C22⋊C4—761no—
263C42—194no—
264C42—382no—
265C42—762no—
266C42—762no—
267C42—761no—
268C42#6454111yescharacteristic
269C42D4×D1911yescharacteristic
270C42D4×D1911yescharacteristic
271C42C2×C22⋊D1911yescharacteristic
272C23#1059732811yescharacteristic
273Q8—82no—
274Q8—82no—
275Q8—762no—
276Q8—762no—
277Q8—1522no—
278Q8—1522no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—44no—
282C2×C4—42no—
283C2×C4—384no—
284C2×C4—762no—
285C2×C4—762no—
286C2×C4—764no—
287C2×C4—761no—
288C2×C4—761no—
289C2×C4—762no—
290C2×C4#1059732811yescharacteristic
291C2×C4#1059733011yescharacteristic
292C2×C4#1059733011yescharacteristic
293C2×C4#1059736112yes—
294C2×C4Q16×D1912yes—
295C2×C4#1059737611yescharacteristic
296C2×C4#1059738311yescharacteristic
297C2×C4#1059738611yescharacteristic
298C8—42no—
299C8—81no—
300C8—762no—
301C22—21no—
302C22—21no—
303C22#1192645311yescharacteristic
304C22#1192670112yes—
305C4—21no—
306C4—21no—
307C4—82no—
308C4—764no—
309C4—1521no—
310C4—1522no—
311C4—1521no—
312C4#1192671512yes—
313C4#1192671912yes—
314C4#1192675312yes—
315C4#1192692211yescharacteristic
316C4#1192693511yescharacteristic
317C2—22no—
318C2#1456465811yescharacteristic
319C2#1456465911yescharacteristic
320C2#1456473611yescharacteristic
subgroupG/H
centerC22#11926453
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#1549C2
socleC22×C19#392
prime radicalC23×C19#120
hypercenter#1549D19
hypocenterC19#10295
LCSG ▷ C2×C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1549

Complements

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

NH ≅ G/Ntype
229. C19#10295semidirect

Maximal subgroups

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

subgroupindex
#145747882
#145747862
#145720122
#145646112
#145623212
#145614672
C19×#15492
#1029519