Finite Group Databasebeta

← #18079906

Subgroups — #18079906

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#14568624C211yesmaximal, characteristic
3#14563628C211yesmaximal, characteristic
4#14562307C211yesmaximal, characteristic
5#14561537C211yesmaximal, characteristic
6#14561536C211yesmaximal, characteristic
7C19×#1546C211yesmaximal, characteristic
8C2×#10597390—21no—
9C2×C4×Dic38C2211yescharacteristic
10C8×Dic38—22no—
11#11926668—22no—
12#11926597C2211yescharacteristic
13#11926594—22no—
14#11926568C2211yescharacteristic
15C2×#10597281—21no—
16#11926475C414yes—
17#11926451—21no—
18#11926440—22no—
19C4×C4⋊Dic19C2211yescharacteristic
20#11926312—21no—
21#11926290—22no—
22C2×C19×C4⋊Q8C2211yescharacteristic
23C19×#431C2211yescharacteristic
24C19×#423C2211yescharacteristic
25C19×#332—22no—
26C22×Q8×C19—21no—
27C22×Dic38D411yescharacteristic
28C2×M16×C19—21no—
29C19×C4⋊Q8—21no—
30C19×C4⋊Q8—21no—
31C19×C4⋊Q8—21no—
32C19×C4⋊Q8—21no—
33C2×C4⋊C4×C19—21no—
34C2×C4⋊C4×C19C2×C412yes—
35C2×C42×C19C2311yescharacteristic
36#10597390—42no—
37#10597390—42no—
38C2×C4⋊Dic19—21no—
39C2×C4⋊Dic19D411yescharacteristic
40C2×Dic19⋊C4—24no—
41C2×Dic19⋊C4C2×C412yes—
42C2×C4×Dic19—21no—
43C2×C4×Dic19D412yes—
44C2×#64520—21no—
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⋊#95—24no—
55C19⋊#95C2×C412yes—
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—
64C2×Q8×C19—41no—
65C2×Q8×C19—41no—
66C2×Q8×C19—41no—
67C2×Q8×C19—41no—
68C2×Q8×C19—41no—
69C2×Q8×C19—41no—
70C22×C4×C19—22no—
71C22×C4×C19C22×C411yescharacteristic
72C22×C4×C19C2×D411yescharacteristic
73C22×C4×C19C2×D411yescharacteristic
74C22×Dic19—22no—
75C22×Dic19C22⋊C412yes—
76C22×Dic19C22⋊C412yes—
77C2×Dic38—21no—
78C2×Dic38—21no—
79C2×Dic38—21no—
80C2×Dic38—21no—
81C2×Dic38D812yes—
82C2×Dic38SD1612yes—
83M16×C19—41no—
84M16×C19—41no—
85C2×C8×C19—22no—
86C2×C8×C19—41no—
87C4⋊C4×C19—22no—
88C4⋊C4×C19—22no—
89C4⋊C4×C19—41no—
90C4⋊C4×C19—41no—
91C42×C19C2×D411yescharacteristic
92C42×C19C2×D411yescharacteristic
93C42×C19#4111yescharacteristic
94C42×C19#4111yescharacteristic
95C4⋊Dic19—24no—
96C4⋊Dic19—21no—
97C4⋊Dic19—21no—
98Dic19⋊C4—22no—
99Dic19⋊C4—22no—
100Dic19⋊C4—48no—
101C4×Dic19—22no—
102C4×Dic19—22no—
103C4×Dic19—41no—
104C4×Dic19—41no—
105#64520—41no—
106#64520—41no—
107C2×C19⋊C8—22no—
108C2×C19⋊C8—41no—
109#9394—191nomaximal, Sylow
110C23×C19C2×C22⋊C411yescharacteristic
111Q8×C19—81no—
112Q8×C19—81no—
113Q8×C19—81no—
114Q8×C19—81no—
115C2×C4×C19—22no—
116C2×C4×C19—41no—
117C2×C4×C19—42no—
118C2×C4×C19—42no—
119C2×C4×C19—42no—
120C2×C4×C19C4×D411yescharacteristic
121C2×C4×C19C4×D411yescharacteristic
122C2×C4×C19#12011yescharacteristic
123C2×C4×C19#12111yescharacteristic
124C2×C4×C19#12111yescharacteristic
125C2×C4×C19#12311yescharacteristic
126C2×C4×C19C2×D811yescharacteristic
127C2×C4×C19C2×SD1611yescharacteristic
128C2×C4×C19#13511yescharacteristic
129C2×C4×C19#13511yescharacteristic
130C2×Dic19—22no—
131C2×Dic19—22no—
132C2×Dic19—24no—
133C2×Dic19—22no—
134C2×Dic19—42no—
135C2×Dic19—42no—
136C2×Dic19—42no—
137C2×Dic19#10214yes—
138Dic38—22no—
139Dic38—22no—
140Dic38—22no—
141Dic38—22no—
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#1546D1911yescharacteristic
151#1303—191no—
152#1303—191no—
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—82no—
162C4×C19#45612yes—
163C4×C19#46511yescharacteristic
164C4×C19#46511yescharacteristic
165C4×C19#46611yescharacteristic
166C4×C19#46611yescharacteristic
167Dic19—24no—
168Dic19—44no—
169Dic19—42no—
170C2×C4⋊Q8—381no—
171C2×C4⋊Q8C2×D1911yescharacteristic
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⋊C4—191no—
185#343—381no—
186#332—22no—
187#332—382no—
188C2×C19—21no—
189C2×C19—21no—
190C2×C19#188611yescharacteristic
191C2×C19#189311yescharacteristic
192C2×C19#191511yescharacteristic
193C22×Q8—21no—
194C22×Q8—191no—
195C2×M16—21no—
196C2×M16—381no—
197C4⋊Q8—21no—
198C4⋊Q8—21no—
199C4⋊Q8—21no—
200C4⋊Q8—21no—
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—381no—
211C2×C4⋊C4—384no—
212C2×C4⋊C4C4×D1912yes—
213C2×C42—192no—
214C2×C42—381no—
215C2×C42C22×D1911yescharacteristic
216C4⋊C8—21no—
217C4⋊C8—21no—
218C4⋊C8—192no—
219C4⋊C8—384no—
220C4⋊C8—381no—
221C4⋊C8—381no—
222C4⋊C8C22⋊D1912yes—
223#101—762no—
224C22⋊C8—21no—
225C22⋊C8—381no—
226C4×C8—21no—
227C4×C8—384no—
228C4×C8—381no—
229#95—192no—
230#95—384no—
231C19#939411yescharacteristic, complemented, Sylow
232C2×Q8—41no—
233C2×Q8—41no—
234C2×Q8—41no—
235C2×Q8—41no—
236C2×Q8—41no—
237C2×Q8—41no—
238C2×Q8—192no—
239C2×Q8—192no—
240C2×Q8—381no—
241C2×Q8—381no—
242C2×Q8—381no—
243C2×Q8—381no—
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—22no—
260C4⋊C4—22no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—384no—
264C4⋊C4—381no—
265C4⋊C4—382no—
266C4⋊C4—381no—
267C4⋊C4—382no—
268C4⋊C4—768no—
269C42—382no—
270C42—382no—
271C42—761no—
272C42—761no—
273C42#6454111yescharacteristic
274C42D4×D1911yescharacteristic
275C42#6454311yescharacteristic
276C42C2×C22⋊D1911yescharacteristic
277C23C22⋊C4×D1911yescharacteristic
278Q8—81no—
279Q8—81no—
280Q8—81no—
281Q8—81no—
282Q8—382no—
283Q8—382no—
284Q8—382no—
285Q8—382no—
286C2×C4—22no—
287C2×C4—41no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—42no—
291C2×C4—194no—
292C2×C4—382no—
293C2×C4—382no—
294C2×C4—384no—
295C2×C4—382no—
296C2×C4—762no—
297C2×C4—762no—
298C2×C4—762no—
299C2×C4(C22⋊D19)⋊C411yescharacteristic
300C2×C4#1059732911yescharacteristic
301C2×C4#1059733011yescharacteristic
302C2×C4D8×D1911yescharacteristic
303C2×C4#1059735811yescharacteristic
304C2×C4SD16×D1911yescharacteristic
305C2×C4#1059736211yescharacteristic
306C2×C4C4×C22⋊D1911yescharacteristic
307C2×C4#1059738311yescharacteristic
308C2×C4#1059738411yescharacteristic
309C8—42no—
310C8—81no—
311C8—762no—
312C8—1521no—
313C22—21no—
314C22—21no—
315C22#1192642011yescharacteristic
316C22#102×D1911yescharacteristic
317C22#1192653711yescharacteristic
318C4—21no—
319C4—21no—
320C4—21no—
321C4—82no—
322C4—384no—
323C4—764no—
324C4—762no—
325C4#1192672512yes—
326C4#1192677011yescharacteristic
327C4#1192677211yescharacteristic
328C4#1192677711yescharacteristic
329C4#1192677911yescharacteristic
330C2—21no—
331C2—21no—
332C2#1456402511yescharacteristic
333C2#1456406011yescharacteristic
334C2#1456418411yescharacteristic
subgroupG/H
centerC22#11926420
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1546C2
socleC22×C19#386
prime radicalC23×C19C2×C22⋊C4
cosocleC2×C42×C19C23
hypercenter#1546D19
hypocenterC19#9394
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1546

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
#145686242
#145636282
#145623072
#145615372
#145615362
C19×#15462
#939419