Finite Group Databasebeta

← #18079908

Subgroups — #18079908

Order 4864.

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

normal subgroups only

This group has 506 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#14568623C211yesmaximal, characteristic
3#14563628C211yesmaximal, characteristic
4#14562308C211yesmaximal, characteristic
5#14562306C211yesmaximal, characteristic
6#14561538C211yesmaximal, characteristic
7C19×#1303C211yesmaximal, characteristic
8C2×#10597315—21no—
9C2×#10597315C2211yescharacteristic
10C2×C4×Dic38C2211yescharacteristic
11C8×Dic38—22no—
12#11926668—22no—
13#11926597C2211yescharacteristic
14#11926594—22no—
15#11926568C2211yescharacteristic
16C2×#10597281—21no—
17#11926476C414yes—
18#11926450—21no—
19#11926443—22no—
20#11926312—21no—
21#11926291—22no—
22#11926289—22no—
23C19×#431C2211yescharacteristic
24C19×#423C2211yescharacteristic
25C4×C4⋊C4×C19C2211yescharacteristic
26C22×Dic38—21no—
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—24no—
34C2×C4⋊Dic19C2×C412yes—
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—
43#10597315—42no—
44#10597315—42no—
45C4×Dic38—21no—
46C4×Dic38—21no—
47C4×Dic38—21no—
48C4×Dic38—21no—
49C19×C4⋊C8—21no—
50C19×C4⋊C8—21no—
51C19×C4⋊C8D412yes—
52C19×C22⋊C8—21no—
53C4×C8×C19—21no—
54C19×#95C2×C412yes—
55C19⋊#95—24no—
56C22⋊(C19⋊C8)—21no—
57#10597281—42no—
58Dic19⋊C8—24no—
59C8×Dic19—24no—
60C4⋊(C19⋊C8)—21no—
61C4⋊(C19⋊C8)—21no—
62C4⋊(C19⋊C8)D412yes—
63C4×C19⋊C8—21no—
64C22×C4×C19—22no—
65C22×C4×C19C22×C411yescharacteristic
66C22×C4×C19C2×D411yescharacteristic
67C22×C4×C19C2×D411yescharacteristic
68C22×Dic19—22no—
69C22×Dic19C22⋊C412yes—
70C22×Dic19C22⋊C412yes—
71C2×Dic38—21no—
72C2×Dic38—21no—
73C2×Dic38—21no—
74C2×Dic38—21no—
75C2×Dic38—41no—
76C2×Dic38—41no—
77C2×Dic38—41no—
78C2×Dic38—41no—
79C2×Dic38—41no—
80C2×Dic38—41no—
81C2×Dic38D812yes—
82C2×Dic38SD1612yes—
83M16×C19—41no—
84M16×C19—41no—
85C2×C8×C19—22no—
86C2×C8×C19—41no—
87C4⋊C4×C19—24no—
88C42×C19—41no—
89C42×C19—41no—
90C42×C19C2×D411yescharacteristic
91C42×C19C2×D411yescharacteristic
92C42×C19#4111yescharacteristic
93C42×C19#4111yescharacteristic
94C4⋊Dic19—21no—
95C4⋊Dic19—21no—
96C4⋊Dic19—22no—
97C4⋊Dic19—22no—
98C4⋊Dic19—41no—
99C4⋊Dic19—41no—
100C4⋊Dic19—48no—
101Dic19⋊C4—22no—
102Dic19⋊C4—22no—
103C4×Dic19—22no—
104C4×Dic19—22no—
105#64520—41no—
106#64520—41no—
107C2×C19⋊C8—22no—
108C2×C19⋊C8—41no—
109#9394—191nomaximal, Sylow
110C23×C19C2×C22⋊C411yescharacteristic
111C2×C4×C19—22no—
112C2×C4×C19—24no—
113C2×C4×C19—41no—
114C2×C4×C19—42no—
115C2×C4×C19—42no—
116C2×C4×C19C4×D411yescharacteristic
117C2×C4×C19C4×D411yescharacteristic
118C2×C4×C19#12011yescharacteristic
119C2×C4×C19#12111yescharacteristic
120C2×C4×C19#12111yescharacteristic
121C2×C4×C19#12311yescharacteristic
122C2×C4×C19C2×D811yescharacteristic
123C2×C4×C19C2×SD1611yescharacteristic
124C2×C4×C19#13511yescharacteristic
125C2×C4×C19#13511yescharacteristic
126C2×Dic19—22no—
127C2×Dic19—22no—
128C2×Dic19—22no—
129C2×Dic19—42no—
130C2×Dic19—42no—
131C2×Dic19—42no—
132C2×Dic19—42no—
133C2×Dic19#10214yes—
134Dic38—22no—
135Dic38—22no—
136Dic38—22no—
137Dic38—22no—
138Dic38—81no—
139Dic38—81no—
140Dic38—81no—
141Dic38—81no—
142C8×C19—42no—
143C8×C19—81no—
144C19⋊C8—42no—
145C19⋊C8—81no—
146#2982—191no—
147#2546—191no—
148#1801—191no—
149#1546—191no—
150#1546—191no—
151#1303—191no—
152#1303D1911yescharacteristic
153C22×C19—21no—
154C22×C19—21no—
155C22×C19#38611yescharacteristic
156C22×C19C2×#10211yescharacteristic
157C22×C19#41611yescharacteristic
158C4×C19—21no—
159C4×C19—21no—
160C4×C19—21no—
161C4×C19—44no—
162C4×C19#45612yes—
163C4×C19#46511yescharacteristic
164C4×C19#46511yescharacteristic
165C4×C19#46611yescharacteristic
166C4×C19#46611yescharacteristic
167Dic19—24no—
168Dic19—42no—
169Dic19—82no—
170C2×C4⋊Q8—191no—
171C2×C4⋊Q8—381no—
172C2×C4×Q8—191no—
173C8×Q8—382no—
174C8×Q8—382no—
175#431—191no—
176#431—382no—
177#431C2×D1911yescharacteristic
178#423—191no—
179#423C2×D1911yescharacteristic
180C2×#101—381no—
181#398—194no—
182#391—381no—
183#389—382no—
184C4×C4⋊C4C2×D1911yescharacteristic
185#343—381no—
186#332—382no—
187#332—382no—
188C2×C19—21no—
189C2×C19—21no—
190C2×C19#188611yescharacteristic
191C2×C19#189311yescharacteristic
192C2×C19#191511yescharacteristic
193C22×Q8—191no—
194C22×Q8—381no—
195C2×M16—21no—
196C2×M16—381no—
197C4⋊Q8—381no—
198C4⋊Q8—381no—
199C4⋊Q8—381no—
200C4⋊Q8—381no—
201C4⋊Q8—762no—
202C4⋊Q8—762no—
203C4×Q8—381no—
204C4×Q8—381no—
205C4×Q8—381no—
206C4×Q8—381no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—192no—
209C2×C4⋊C4—191no—
210C2×C4⋊C4—192no—
211C2×C4⋊C4—384no—
212C2×C4⋊C4—381no—
213C2×C42—21no—
214C2×C42—192no—
215C2×C42C22×D1911yescharacteristic
216C4⋊C8—21no—
217C4⋊C8—21no—
218C4⋊C8—192no—
219C4⋊C8—384no—
220C4⋊C8—381no—
221C4⋊C8—381no—
222C4⋊C8D7612yes—
223#101—762no—
224C22⋊C8—21no—
225C22⋊C8—381no—
226C4×C8—21no—
227C4×C8—384no—
228C4×C8—381no—
229#95—384no—
230#95C4×D1912yes—
231C19#939411yescharacteristic, complemented, Sylow
232C2×Q8—192no—
233C2×Q8—192no—
234C2×Q8—381no—
235C2×Q8—381no—
236C2×Q8—381no—
237C2×Q8—381no—
238C2×Q8—761no—
239C2×Q8—761no—
240C2×Q8—761no—
241C2×Q8—761no—
242C2×Q8—761no—
243C2×Q8—761no—
244C22×C4—22no—
245C22×C4—192no—
246C22×C4—192no—
247C22×C4—382no—
248C22×C4C2×C4×D1911yescharacteristic
249C22×C4D4×D1911yescharacteristic
250C22×C4D4×D1911yescharacteristic
251M16—41no—
252M16—41no—
253M16—761no—
254M16—761no—
255C2×C8—22no—
256C2×C8—41no—
257C2×C8—382no—
258C2×C8—761no—
259C4⋊C4—24no—
260C4⋊C4—382no—
261C4⋊C4—381no—
262C4⋊C4—382no—
263C4⋊C4—381no—
264C4⋊C4—382no—
265C4⋊C4—382no—
266C4⋊C4—768no—
267C4⋊C4—761no—
268C4⋊C4—761no—
269C42—41no—
270C42—41no—
271C42—382no—
272C42—382no—
273C42C2×D7611yescharacteristic
274C42#6454111yescharacteristic
275C42D4×D1911yescharacteristic
276C42#6454511yescharacteristic
277C23C22⋊C4×D1911yescharacteristic
278Q8—382no—
279Q8—382no—
280Q8—382no—
281Q8—382no—
282Q8—1521no—
283Q8—1521no—
284Q8—1521no—
285Q8—1521no—
286C2×C4—22no—
287C2×C4—24no—
288C2×C4—41no—
289C2×C4—42no—
290C2×C4—42no—
291C2×C4—194no—
292C2×C4—382no—
293C2×C4—382no—
294C2×C4—382no—
295C2×C4—762no—
296C2×C4—762no—
297C2×C4—762no—
298C2×C4—762no—
299C2×C4C4×D7611yescharacteristic
300C2×C4#1059732811yescharacteristic
301C2×C4#1059733011yescharacteristic
302C2×C4#1059733911yescharacteristic
303C2×C4#1059734011yescharacteristic
304C2×C4#1059734111yescharacteristic
305C2×C4D8×D1911yescharacteristic
306C2×C4SD16×D1911yescharacteristic
307C2×C4#1059736211yescharacteristic
308C2×C4#1059736511yescharacteristic
309C8—42no—
310C8—81no—
311C8—762no—
312C8—1521no—
313C22—21no—
314C22—21no—
315C22#1192642211yescharacteristic
316C22#102×D1911yescharacteristic
317C22#1192653911yescharacteristic
318C4—21no—
319C4—21no—
320C4—21no—
321C4—44no—
322C4—384no—
323C4—762no—
324C4—1522no—
325C4#1192672812yes—
326C4#1192677411yescharacteristic
327C4#1192677611yescharacteristic
328C4#1192677911yescharacteristic
329C4#1192678111yescharacteristic
330C2—21no—
331C2—21no—
332C2#1456402711yescharacteristic
333C2#1456406211yescharacteristic
334C2#1456418611yescharacteristic
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#9394
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
231. C19#9394semidirect

Maximal subgroups

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

subgroupindex
#145727152
#145686232
#145636282
#145623082
#145623062
#145615382
C19×#13032
#939419