Finite Group Databasebeta

← #18071767

Subgroups — #18071767

Order 4864.

410 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 87 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#14570666C211yesmaximal, characteristic
2#14565179C211yesmaximal, characteristic
3#14565112C211yesmaximal, characteristic
4#14561460C211yesmaximal, characteristic
5#14561458C211yesmaximal, characteristic
6#14561457C211yesmaximal, characteristic
7C19×#2084C211yesmaximal, characteristic
8C2×#10597334—21no—
9C2×#10597265—21no—
10C2×#10597265—21no—
11C2×#10597267—21no—
12#11926477—21no—
13#11926465—21no—
14#11926464—21no—
15#11926450C2211yescharacteristic
16#11926442C2211yescharacteristic
17#11926430—21no—
18#11926427—21no—
19#11926306—21no—
20#11926299C2211yescharacteristic
21#11926299C2211yescharacteristic
22C2×C19×#106—21no—
23C19×#389C2211yescharacteristic
24C19×#384C2211yescharacteristic
25C19×#340—21no—
26C19×#336C2211yescharacteristic
27C22×Dic38—21no—
28C22×Dic38D411yescharacteristic
29C22×C8×C19—21no—
30C2×C4⋊C4×C19—21no—
31C2×C4⋊C4×C19—21no—
32C2×C4⋊C4×C19—21no—
33C2×C4⋊C4×C19—21no—
34C2×C4⋊C4×C19D411yescharacteristic
35C2×C4⋊C4×C19D411yescharacteristic
36C2×C42×C19C2311yescharacteristic
37C2×C4⋊Dic19—21no—
38C2×C4⋊Dic19D411yescharacteristic
39C2×C4⋊Dic19D411yescharacteristic
40C2×C4⋊Dic19D411yescharacteristic
41C2×Dic19⋊C4—21no—
42C2×Dic19⋊C4—21no—
43C2×Dic19⋊C4—21no—
44C2×C4×Dic19—21no—
45C22×C19⋊C8—21no—
46C22×C19⋊C8—21no—
47#10597334—42no—
48#10597334—42no—
49C19×#106—42no—
50C19×#95—21no—
51C19⋊#95—21no—
52C19⋊#95—21no—
53C19⋊#95—21no—
54C19⋊#95—21no—
55C19⋊#95—21no—
56C19⋊#95—21no—
57#10597267—42no—
58#10597265—42no—
59#10597265—42no—
60C22×C4×C19—21no—
61C22×C4×C19—21no—
62C22×C4×C19—41no—
63C22×C4×C19C2×D411yescharacteristic
64C22×C4×C19C2×D411yescharacteristic
65C22×C4×C19C2×D411yescharacteristic
66C22×Dic19—21no—
67C22×Dic19—21no—
68C22×Dic19—21no—
69C22×Dic19—21no—
70C2×Dic38—21no—
71C2×Dic38—41no—
72C2×Dic38—41no—
73C2×Dic38—42no—
74C2×Dic38—81no—
75C2×Dic38—81no—
76C2×Dic38SD1612yes—
77C2×C8×C19—22no—
78C2×C8×C19—41no—
79C2×C8×C19—41no—
80C4⋊C4×C19—21no—
81C4⋊C4×C19—41no—
82C4⋊C4×C19—41no—
83C4⋊C4×C19—41no—
84C4⋊C4×C19—41no—
85C4⋊C4×C19—41no—
86C4⋊C4×C19—41no—
87C4⋊C4×C19—41no—
88C4⋊C4×C19—41no—
89C4⋊C4×C19—41no—
90C4⋊C4×C19SD1612yes—
91C42×C19—41no—
92C4⋊Dic19—21no—
93C4⋊Dic19—42no—
94C4⋊Dic19—41no—
95C4⋊Dic19—41no—
96C4⋊Dic19SD1612yes—
97Dic19⋊C4—42no—
98Dic19⋊C4—41no—
99Dic19⋊C4—41no—
100Dic19⋊C4—81no—
101C4×Dic19—42no—
102C2×C19⋊C8—22no—
103C2×C19⋊C8—22no—
104C2×C19⋊C8—41no—
105C2×C19⋊C8—41no—
106C2×C19⋊C8—41no—
107C2×C19⋊C8—41no—
108#7817—191nomaximal, Sylow
109C23×C19#12011yescharacteristic
110C2×C4×C19—21no—
111C2×C4×C19—21no—
112C2×C4×C19—21no—
113C2×C4×C19—21no—
114C2×C4×C19—21no—
115C2×C4×C19—21no—
116C2×C4×C19—22no—
117C2×C4×C19—41no—
118C2×C4×C19—41no—
119C2×C4×C19—41no—
120C2×C4×C19—41no—
121C2×C4×C19—41no—
122C2×C4×C19—81no—
123C2×C4×C19—81no—
124C2×C4×C19—81no—
125C2×C4×C19C2×SD1611yescharacteristic
126C2×C4×C19C2×SD1611yescharacteristic
127C2×C4×C19C2×SD1611yescharacteristic
128C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
129C2×C4×C19#13711yescharacteristic
130C2×C4×C19#13711yescharacteristic
131C2×Dic19—22no—
132C2×Dic19—22no—
133C2×Dic19—41no—
134C2×Dic19—41no—
135C2×Dic19—41no—
136C2×Dic19—41no—
137C2×Dic19—41no—
138C2×Dic19—41no—
139C2×Dic19—41no—
140C2×Dic19—41no—
141C2×Dic19—41no—
142C2×Dic19—41no—
143Dic38—42no—
144Dic38—81no—
145Dic38—84no—
146C8×C19—42no—
147C19⋊C8—42no—
148C19⋊C8—42no—
149#2734—191no—
150#2096—191no—
151#2084—191no—
152#2084D1911yescharacteristic
153#1272—191no—
154#1271—191no—
155#1271—191no—
156C22×C19#44811yescharacteristic
157C22×C19#44811yescharacteristic
158C22×C19#45011yescharacteristic
159C22×C19#45311yescharacteristic
160C22×C19#45611yescharacteristic
161C22×C19#45611yescharacteristic
162C22×C19#45811yescharacteristic
163C4×C19—21no—
164C4×C19—21no—
165C4×C19—21no—
166C4×C19—21no—
167C4×C19—21no—
168C4×C19—21no—
169C4×C19—42no—
170C4×C19—81no—
171C4×C19—161no—
172Dic19—42no—
173Dic19—42no—
174Dic19—81no—
175Dic19—81no—
176C2×C4⋊Q8—381no—
177C2×#106—21no—
178C2×#106—381no—
179C2×#106—381no—
180C2×#103—381no—
181#398—381no—
182#395—381no—
183#395—381no—
184#391—191no—
185#389—191no—
186#389C2×D1911yescharacteristic
187#387—381no—
188#387—381no—
189#384C2×D1911yescharacteristic
190#340—21no—
191#340—381no—
192#336—191no—
193#336—191no—
194#336C2×D1911yescharacteristic
195C2×C19#161111yescharacteristic
196C2×C19#161111yescharacteristic
197C2×C19#161311yescharacteristic
198C2×C19#162311yescharacteristic
199C2×C19#165111yescharacteristic
200C2×C19#165111yescharacteristic
201C2×C19#166011yescharacteristic
202C22×Q8—191no—
203C22×Q8—381no—
204C22×C8—21no—
205C22×C8—381no—
206C22×C8—381no—
207C4⋊Q8—762no—
208C4⋊Q8—762no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—191no—
214C2×C4⋊C4—191no—
215C2×C4⋊C4—191no—
216C2×C4⋊C4—381no—
217C2×C4⋊C4—381no—
218C2×C4⋊C4—381no—
219C2×C4⋊C4—381no—
220C2×C4⋊C4C22⋊D1911yescharacteristic
221C2×C4⋊C4C22⋊D1911yescharacteristic
222C2×C42—381no—
223C2×C42C22×D1911yescharacteristic
224#106—42no—
225#106—762no—
226#106—762no—
227#103—762no—
228#95—21no—
229#95—381no—
230#95—381no—
231#95—381no—
232#95—381no—
233#95—381no—
234#95—381no—
235C19#781711yescharacteristic, complemented, Sylow
236C2×Q8—192no—
237C2×Q8—381no—
238C2×Q8—761no—
239C2×Q8—761no—
240C2×Q8—762no—
241C2×Q8—1521no—
242C2×Q8—1521no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—41no—
246C22×C4—381no—
247C22×C4—381no—
248C22×C4—381no—
249C22×C4—381no—
250C22×C4D4×D1911yescharacteristic
251C22×C4D4×D1911yescharacteristic
252C22×C4C2×C22⋊D1911yescharacteristic
253C2×C8—22no—
254C2×C8—41no—
255C2×C8—41no—
256C2×C8—382no—
257C2×C8—382no—
258C2×C8—761no—
259C2×C8—761no—
260C2×C8—761no—
261C2×C8—761no—
262C4⋊C4—21no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—192no—
273C4⋊C4—381no—
274C4⋊C4—761no—
275C4⋊C4—761no—
276C4⋊C4—762no—
277C4⋊C4—762no—
278C4⋊C4—761no—
279C4⋊C4—761no—
280C4⋊C4—1521no—
281C4⋊C4#6452612yes—
282C42—41no—
283C42—762no—
284C23#1059738311yescharacteristic
285Q8—762no—
286Q8—1521no—
287Q8—1524no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—22no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—81no—
301C2×C4—81no—
302C2×C4—81no—
303C2×C4—382no—
304C2×C4—382no—
305C2×C4—761no—
306C2×C4—761no—
307C2×C4—761no—
308C2×C4—761no—
309C2×C4—761no—
310C2×C4—761no—
311C2×C4—761no—
312C2×C4—761no—
313C2×C4—761no—
314C2×C4—761no—
315C2×C4SD16×D1911yescharacteristic
316C2×C4SD16×D1911yescharacteristic
317C2×C4#1059736011yescharacteristic
318C2×C4#1059736111yescharacteristic
319C2×C4C2×#6452611yescharacteristic
320C2×C4#1059739711yescharacteristic
321C8—42no—
322C8—762no—
323C8—762no—
324C22#1192668111yescharacteristic
325C22#1192668211yescharacteristic
326C22#1192669311yescharacteristic
327C22#1192671011yescharacteristic
328C22#1192672511yescharacteristic
329C22#1192672611yescharacteristic
330C22#1192673311yescharacteristic
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—21no—
336C4—21no—
337C4—42no—
338C4—81no—
339C4—161no—
340C4—762no—
341C4—762no—
342C4—1521no—
343C4—1521no—
344C2#1456264111yescharacteristic
345C2#1456264211yescharacteristic
346C2#1456265311yescharacteristic
347C2#1456271211yescharacteristic
348C2#1456289511yescharacteristic
349C2#1456289611yescharacteristic
350C2#1456294511yescharacteristic
subgroupG/H
centerC23#10597383
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#2084C2
socle, prime radicalC23×C19#120
hypercenter#2084D19
hypocenterC19#7817
LCSG ▷ C2×C42×C19 ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2084

Complements

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

NH ≅ G/Ntype
235. C19#7817semidirect

Maximal subgroups

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

subgroupindex
#145706662
#145651792
#145651122
#145614602
#145614582
#145614572
C19×#20842
#781719