Finite Group Databasebeta

← #18086322

Subgroups — #18086322

Order 4864.

366 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 93 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#14573440C211yesmaximal, characteristic
2#14562409C211yesmaximal, characteristic
3#14562293C211yesmaximal, characteristic
4#14562198C211yesmaximal, characteristic
5#14561959C211yesmaximal, characteristic
6#14561493C211yesmaximal, characteristic
7C19×#1805C211yesmaximal, characteristic
8#11927101C2211yescharacteristic
9#11926851—22no—
10#11926839—21no—
11#11926829—21no—
12#11926597C2211yescharacteristic
13#11926597C2211yescharacteristic
14#11926584—21no—
15#11926568C2211yescharacteristic
16#11926553—21no—
17#11926296—22no—
18#11926292—21no—
19#11926289—21no—
20#11926280—22no—
21#11926270—22no—
22C2×C4×Q8×C19C2211yescharacteristic
23C2×C19×C4⋊C8C2211yescharacteristic
24C2×C19×#103—21no—
25C19×#382C2211yescharacteristic
26C19×#340—21no—
27C22×Q8×C19D411yescharacteristic
28C22×C8×C19—21no—
29C4×Q8×C19—21no—
30C4×Q8×C19—21no—
31C4×Q8×C19—21no—
32C4×Q8×C19—21no—
33C2×C4⋊C4×C19—21no—
34C2×C4⋊C4×C19—21no—
35C2×C4⋊C4×C19D411yescharacteristic
36C2×C42×C19—21no—
37C2×C42×C19C2311yescharacteristic
38#10597372—21no—
39#10597370—21no—
40#10597370—21no—
41C2×#64520—21no—
42#10597316—21no—
43#10597315D411yescharacteristic
44#10597315D411yescharacteristic
45C4×Dic38—21no—
46C4×Dic38—21no—
47C19×C4⋊C8—21no—
48C19×C4⋊C8—21no—
49C19×#103—42no—
50C19×#95—21no—
51C19×#95—21no—
52#10597292—22no—
53#10597292—22no—
54C22⋊(C19⋊C8)—21no—
55C22⋊(C19⋊C8)D412yes—
56#10597265—22no—
57#10597264—22no—
58C4⋊(C19⋊C8)—21no—
59C4⋊(C19⋊C8)—21no—
60C4⋊(C19⋊C8)—21no—
61C4⋊(C19⋊C8)D412yes—
62C4×C19⋊C8—21no—
63C4×C19⋊C8—21no—
64C2×Q8×C19—21no—
65C2×Q8×C19—21no—
66C2×Q8×C19—21no—
67C2×Q8×C19—21no—
68C2×Q8×C19—21no—
69C2×Q8×C19Q1612yes—
70C22×C4×C19—21no—
71C22×C4×C19—21no—
72C22×C4×C19—41no—
73C22×C4×C19C2×D411yescharacteristic
74C22×C4×C19C2×D411yescharacteristic
75C22×C4×C19#4111yescharacteristic
76C2×Dic38—21no—
77C2×Dic38—21no—
78C2×C8×C19—41no—
79C2×C8×C19—41no—
80C2×C8×C19—41no—
81C4⋊C4×C19—21no—
82C4⋊C4×C19—21no—
83C4⋊C4×C19—41no—
84C4⋊C4×C19—41no—
85C4⋊C4×C19—41no—
86C4⋊C4×C19—41no—
87C42×C19—41no—
88C42×C19—41no—
89C42×C19C2×D411yescharacteristic
90C42×C19C2×D411yescharacteristic
91C42×C19#4111yescharacteristic
92C42×C19#4111yescharacteristic
93C22⋊Dic19—41no—
94C4⋊Dic19—21no—
95C4⋊Dic19—21no—
96C4⋊Dic19—21no—
97C4⋊Dic19—21no—
98Dic19⋊C4—41no—
99Dic19⋊C4—41no—
100C4×Dic19—41no—
101#64520—41no—
102#64520—41no—
103C2×C19⋊C8—22no—
104C2×C19⋊C8—22no—
105C2×C19⋊C8—41no—
106#10471—191nomaximal, Sylow
107C23×C19#12111yescharacteristic
108Q8×C19—22no—
109Q8×C19—22no—
110Q8×C19—41no—
111Q8×C19—41no—
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—81no—
119C2×C4×C19—81no—
120C2×C4×C19—81no—
121C2×C4×C19—81no—
122C2×C4×C19#12011yescharacteristic
123C2×C4×C19#12111yescharacteristic
124C2×C4×C19#12111yescharacteristic
125C2×C4×C19#12311yescharacteristic
126C2×C4×C19#12311yescharacteristic
127C2×C4×C19#12411yescharacteristic
128C2×C4×C19C2×Q1611yescharacteristic
129C2×C4×C19#13511yescharacteristic
130C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
131C2×C4×C19#13711yescharacteristic
132C2×Dic19—41no—
133C2×Dic19—41no—
134Dic38—81no—
135Dic38—81no—
136C8×C19—81no—
137C19⋊C8—42no—
138C19⋊C8—42no—
139C19⋊C8—81no—
140#3078—191no—
141#1805D1911yescharacteristic
142#1571—191no—
143#1542—191no—
144#1518—191no—
145#1461—191no—
146#1286—191no—
147C22×C19—21no—
148C22×C19—21no—
149C22×C19#39411yescharacteristic
150C22×C19#46711yescharacteristic
151C22×C19#46811yescharacteristic
152C4×C19—21no—
153C4×C19—21no—
154C4×C19—21no—
155C4×C19—21no—
156C4×C19—42no—
157C4×C19—81no—
158C4×C19—161no—
159C4×C19#44911yescharacteristic
160C4×C19#45111yescharacteristic
161C4×C19#48411yescharacteristic
162C4×C19#48511yescharacteristic
163Dic19—81no—
164Dic19—81no—
165#533—191no—
166C2×C4×Q8C2×D1911yescharacteristic
167#479—382no—
168#477—381no—
169#475—381no—
170#431—191no—
171#431—191no—
172#428—381no—
173#423—191no—
174C2×C4⋊C8C2×D1911yescharacteristic
175#419—381no—
176C2×#103—21no—
177#382C2×D1911yescharacteristic
178#340—21no—
179#335—382no—
180#333—381no—
181#332—381no—
182#328—382no—
183#324—382no—
184C2×C19—21no—
185C2×C19—21no—
186C2×C19#203611yescharacteristic
187C2×C19#204911yescharacteristic
188C2×C19#205311yescharacteristic
189C22×Q8C22⋊D1911yescharacteristic
190C2×M16—381no—
191C22×C8—21no—
192C4⋊Q8—191no—
193C4⋊Q8—191no—
194#125—381no—
195C22⋊Q8—381no—
196C22⋊Q8—381no—
197C4×Q8—21no—
198C4×Q8—21no—
199C4×Q8—21no—
200C4×Q8—21no—
201C4×Q8—381no—
202C4×Q8—381no—
203#117—381no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4C22⋊D1911yescharacteristic
207C2×C42—21no—
208C2×C42C22×D1911yescharacteristic
209#107—382no—
210#106—382no—
211C4⋊C8—21no—
212C4⋊C8—21no—
213C4⋊C8—192no—
214C4⋊C8—381no—
215C4⋊C8—381no—
216C4⋊C8—381no—
217#103—42no—
218#103—382no—
219#103—382no—
220C22⋊C8—192no—
221C22⋊C8—381no—
222C4×C8—381no—
223C4×C8—381no—
224#95—21no—
225#95—21no—
226C19#1047111yescharacteristic, complemented, Sylow
227C2×Q8—21no—
228C2×Q8—21no—
229C2×Q8—21no—
230C2×Q8—21no—
231C2×Q8—21no—
232C2×Q8—381no—
233C2×Q8—381no—
234C2×Q8#6452812yes—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—41no—
238C22×C4D4×D1911yescharacteristic
239C22×C4#6454311yescharacteristic
240C22×C4C2×C22⋊D1911yescharacteristic
241M16—761no—
242M16—761no—
243C2×C8—41no—
244C2×C8—41no—
245C2×C8—41no—
246C2×C8—382no—
247C2×C8—382no—
248C2×C8—761no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—381no—
256C4⋊C4—381no—
257C4⋊C4—381no—
258C4⋊C4—381no—
259C4⋊C4—761no—
260C4⋊C4—761no—
261C22⋊C4—761no—
262C42—41no—
263C42—41no—
264C42—761no—
265C42#6454111yescharacteristic
266C42#6454111yescharacteristic
267C42D4×D1911yescharacteristic
268C42D4×D1911yescharacteristic
269C23#1059738511yescharacteristic
270Q8—22no—
271Q8—22no—
272Q8—41no—
273Q8—41no—
274Q8—1521no—
275Q8—1521no—
276C2×C4—22no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—81no—
283C2×C4—81no—
284C2×C4—81no—
285C2×C4—81no—
286C2×C4—761no—
287C2×C4—761no—
288C2×C4#1059732911yescharacteristic
289C2×C4#1059733011yescharacteristic
290C2×C4#1059733011yescharacteristic
291C2×C4#1059733111yescharacteristic
292C2×C4#1059737511yescharacteristic
293C2×C4#1059737811yescharacteristic
294C2×C4#1059738311yescharacteristic
295C2×C4C2×#6452811yescharacteristic
296C2×C4#1059739611yescharacteristic
297C2×C4#1059739711yescharacteristic
298C8—81no—
299C8—762no—
300C8—762no—
301C8—1521no—
302C22—21no—
303C22—21no—
304C22#1192645911yescharacteristic
305C22#1192678311yescharacteristic
306C22#1192678811yescharacteristic
307C4—21no—
308C4—21no—
309C4—21no—
310C4—21no—
311C4—42no—
312C4—81no—
313C4—161no—
314C4—1521no—
315C4—1521no—
316C4#1192668711yescharacteristic
317C4#1192669911yescharacteristic
318C4#1192687911yescharacteristic
319C4#1192688511yescharacteristic
320C2—21no—
321C2—21no—
322C2#1456483811yescharacteristic
323C2#1456491311yescharacteristic
324C2#1456493911yescharacteristic
subgroupG/H
centerC22#11926459
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#1805C2
socleC22×C19#394
prime radicalC23×C19#121
hypercenter#1805D19
hypocenterC19#10471
LCSG ▷ C2×C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1805

Complements

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

NH ≅ G/Ntype
226. C19#10471semidirect

Maximal subgroups

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

subgroupindex
#145734402
#145624092
#145622932
#145621982
#145619592
#145614932
C19×#18052
#1047119