Finite Group Databasebeta

← #18071539

Subgroups — #18071539

Order 4864.

424 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 81 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#14571590C211yesmaximal, characteristic
2#14564965C211yesmaximal, characteristic
3#14564960C211yesmaximal, characteristic
4#14561461C211yesmaximal, characteristic
5#14561459C211yesmaximal, characteristic
6#14561457C211yesmaximal, characteristic
7C19×#2016C211yesmaximal, characteristic
8C2×#10597264—21no—
9C2×#10597265—21no—
10#11926486—21no—
11#11926484—21no—
12#11926463—21no—
13#11926442C2211yescharacteristic
14#11926442C2211yescharacteristic
15#11926441—21no—
16#11926427—21no—
17#11926425—21no—
18#11926306—21no—
19#11926306—21no—
20#11926299C2211yescharacteristic
21#11926299C2211yescharacteristic
22C22×Q16×C19—21no—
23C2×C19×C4⋊Q8C2211yescharacteristic
24C2×C19×#103—21no—
25C19×#391C2211yescharacteristic
26C19×#336C2211yescharacteristic
27C22×Q8×C19—21no—
28C22×Q8×C19D411yescharacteristic
29C2×Q16×C19—42no—
30C2×Q16×C19—42no—
31C2×Q16×C19—42no—
32C22×C8×C19—21no—
33C19×C4⋊Q8—42no—
34C2×C4⋊C4×C19—21no—
35C2×C4⋊C4×C19—21no—
36C2×C4⋊C4×C19D411yescharacteristic
37C2×C42×C19C2311yescharacteristic
38C2×C4⋊Dic19D411yescharacteristic
39C2×C4⋊Dic19D411yescharacteristic
40C2×C4⋊Dic19D411yescharacteristic
41C2×C4⋊Dic19D411yescharacteristic
42C2×Dic19⋊C4—21no—
43C2×Dic19⋊C4—21no—
44C2×Dic19⋊C4—21no—
45C2×Dic19⋊C4—21no—
46C2×C4×Dic19—21no—
47C22×C19⋊C8—21no—
48C22×C19⋊C8—21no—
49C19×#103—42no—
50C19×#95—21no—
51C19×#95—21no—
52C19⋊#95—21no—
53C19⋊#95—21no—
54C19⋊#95—21no—
55C19⋊#95—21no—
56C19⋊#95—21no—
57C19⋊#95—21no—
58C19⋊#95—21no—
59#10597265—42no—
60#10597264—42no—
61C2×Q8×C19—22no—
62C2×Q8×C19—21no—
63C2×Q8×C19—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—
70C2×Q8×C19—41no—
71C22×C4×C19—21no—
72C22×C4×C19—21no—
73C22×C4×C19—41no—
74C22×C4×C19C2×D411yescharacteristic
75C22×C4×C19C2×D411yescharacteristic
76C22×C4×C19C2×D411yescharacteristic
77C22×Dic19—21no—
78C22×Dic19—21no—
79C22×Dic19—21no—
80C22×Dic19—21no—
81Q16×C19—48no—
82C2×C8×C19—22no—
83C2×C8×C19—41no—
84C2×C8×C19—41no—
85C4⋊C4×C19—22no—
86C4⋊C4×C19—22no—
87C4⋊C4×C19—41no—
88C4⋊C4×C19—41no—
89C4⋊C4×C19—41no—
90C42×C19—41no—
91C4⋊Dic19—21no—
92C4⋊Dic19—21no—
93C4⋊Dic19—21no—
94C4⋊Dic19—41no—
95C4⋊Dic19—41no—
96C4⋊Dic19Q1612yescomplemented
97Dic19⋊C4—41no—
98Dic19⋊C4—41no—
99Dic19⋊C4—41no—
100Dic19⋊C4—41no—
101Dic19⋊C4—81no—
102Dic19⋊C4—81no—
103C4×Dic19—81no—
104C2×C19⋊C8—22no—
105C2×C19⋊C8—22no—
106C2×C19⋊C8—41no—
107C2×C19⋊C8—41no—
108C2×C19⋊C8—41no—
109C2×C19⋊C8—41no—
110#7783—191nomaximal, Sylow
111C23×C19#12011yescharacteristic
112Q8×C19—42no—
113Q8×C19—42no—
114Q8×C19—42no—
115Q8×C19—81no—
116Q8×C19—81no—
117Q8×C19—81no—
118C2×C4×C19—21no—
119C2×C4×C19—21no—
120C2×C4×C19—21no—
121C2×C4×C19—21no—
122C2×C4×C19—21no—
123C2×C4×C19—21no—
124C2×C4×C19—41no—
125C2×C4×C19—41no—
126C2×C4×C19—41no—
127C2×C4×C19—41no—
128C2×C4×C19—41no—
129C2×C4×C19—41no—
130C2×C4×C19—42no—
131C2×C4×C19—81no—
132C2×C4×C19—81no—
133C2×C4×C19C2×Q1611yescharacteristic
134C2×C4×C19#13511yescharacteristic
135C2×C4×C19#13511yescharacteristic
136C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
137C2×C4×C19#13711yescharacteristic
138C2×C4×C19#13711yescharacteristic
139C2×Dic19—22no—
140C2×Dic19—41no—
141C2×Dic19—41no—
142C2×Dic19—41no—
143C2×Dic19—41no—
144C2×Dic19—41no—
145C2×Dic19—41no—
146C2×Dic19—41no—
147C2×Dic19—41no—
148C2×Dic19—41no—
149C2×Dic19—41no—
150C2×Dic19—41no—
151C8×C19—42no—
152C19⋊C8—42no—
153C19⋊C8—42no—
154#2805—191no—
155#2058—191no—
156#2057—191no—
157#2016D1911yescharacteristic
158#1272—191no—
159#1271—191no—
160#1271—191no—
161C22×C19#44911yescharacteristic
162C22×C19#45111yescharacteristic
163C22×C19#45211yescharacteristic
164C22×C19#45311yescharacteristic
165C22×C19#45611yescharacteristic
166C22×C19#45611yescharacteristic
167C22×C19B(4,𝔽2)11yescharacteristic
168C4×C19—21no—
169C4×C19—21no—
170C4×C19—21no—
171C4×C19—21no—
172C4×C19—21no—
173C4×C19—21no—
174C4×C19—81no—
175C4×C19—82no—
176C4×C19—81no—
177Dic19—42no—
178Dic19—81no—
179Dic19—81no—
180Dic19—81no—
181C22×Q16—21no—
182C2×C4⋊Q8C2×D1911yescharacteristic
183C2×#107—381no—
184C2×#106—381no—
185C2×#103—21no—
186#400—381no—
187#400—381no—
188#395—381no—
189#391C2×D1911yescharacteristic
190#389—191no—
191#389—191no—
192#389—381no—
193#387—381no—
194#387—381no—
195#340—381no—
196#340—381no—
197#336—191no—
198#336—191no—
199#336C2×D1911yescharacteristic
200C2×C19#160011yescharacteristic
201C2×C19#160311yescharacteristic
202C2×C19#160511yescharacteristic
203C2×C19#163211yescharacteristic
204C2×C19#164811yescharacteristic
205C2×C19#165211yescharacteristic
206C2×C19#166011yescharacteristic
207C22×Q8—21no—
208C22×Q8C22⋊D1911yescharacteristic
209C2×Q16—42no—
210C2×Q16—42no—
211C2×Q16—42no—
212C22×C8—21no—
213C22×C8—381no—
214C22×C8—381no—
215C4⋊Q8—42no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—191no—
219C2×C4⋊C4—191no—
220C2×C4⋊C4—191no—
221C2×C4⋊C4—191no—
222C2×C4⋊C4—381no—
223C2×C4⋊C4—381no—
224C2×C4⋊C4—381no—
225C2×C4⋊C4—381no—
226C2×C4⋊C4C22⋊D1911yescharacteristic
227C2×C42—381no—
228C2×C42C22×D1911yescharacteristic
229#107—762no—
230#106—762no—
231#103—42no—
232#95—21no—
233#95—21no—
234#95—381no—
235#95—381no—
236#95—381no—
237#95—381no—
238#95—381no—
239#95—381no—
240#95—381no—
241C19#778311yescharacteristic, complemented, Sylow
242C2×Q8—22no—
243C2×Q8—21no—
244C2×Q8—21no—
245C2×Q8—41no—
246C2×Q8—41no—
247C2×Q8—41no—
248C2×Q8—41no—
249C2×Q8—41no—
250C2×Q8—41no—
251C2×Q8—41no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—41no—
255C22×C4—381no—
256C22×C4—381no—
257C22×C4—381no—
258C22×C4—381no—
259C22×C4D4×D1911yescharacteristic
260C22×C4D4×D1911yescharacteristic
261C22×C4C2×C22⋊D1911yescharacteristic
262Q16—48no—
263C2×C8—22no—
264C2×C8—41no—
265C2×C8—41no—
266C2×C8—382no—
267C2×C8—382no—
268C2×C8—761no—
269C2×C8—761no—
270C2×C8—761no—
271C2×C8—761no—
272C4⋊C4—22no—
273C4⋊C4—22no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—192no—
278C4⋊C4—381no—
279C4⋊C4—381no—
280C4⋊C4—381no—
281C4⋊C4—761no—
282C4⋊C4—761no—
283C4⋊C4—761no—
284C4⋊C4—761no—
285C4⋊C4—761no—
286C4⋊C4—761no—
287C4⋊C4—1521no—
288C4⋊C4—1521no—
289C42—41no—
290C42—1521no—
291C23#1059738311yescharacteristic
292Q8—42no—
293Q8—42no—
294Q8—42no—
295Q8—81no—
296Q8—81no—
297Q8—81no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—42no—
310C2×C4—41no—
311C2×C4—81no—
312C2×C4—81no—
313C2×C4—382no—
314C2×C4—761no—
315C2×C4—761no—
316C2×C4—761no—
317C2×C4—761no—
318C2×C4—761no—
319C2×C4—761no—
320C2×C4—761no—
321C2×C4—761no—
322C2×C4—761no—
323C2×C4—761no—
324C2×C4—761no—
325C2×C4Q16×D1911yescharacteristic
326C2×C4#1059736411yescharacteristic
327C2×C4#1059736411yescharacteristic
328C2×C4#1059736511yescharacteristic
329C2×C4#1059737811yescharacteristic
330C2×C4#1059739611yescharacteristic
331C8—42no—
332C8—762no—
333C8—762no—
334C22#1192668711yescharacteristic
335C22#1192669811yescharacteristic
336C22#1192670511yescharacteristic
337C22#1192671111yescharacteristic
338C22#1192672511yescharacteristic
339C22#1192672511yescharacteristic
340C22#1192673011yescharacteristic
341C4—21no—
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—81no—
348C4—82no—
349C4—81no—
350C4—762no—
351C4—1521no—
352C4—1521no—
353C4—1521no—
354C2#1456257911yescharacteristic
355C2#1456259711yescharacteristic
356C2#1456260711yescharacteristic
357C2#1456276611yescharacteristic
358C2#1456287511yescharacteristic
359C2#1456290311yescharacteristic
360C2#1456294411yescharacteristic
subgroupG/H
centerC23#10597383
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#2016C2
socle, prime radicalC23×C19#120
hypercenter#2016D19
hypocenterC19#7783
LCSG ▷ C2×C42×C19 ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2016

Complements

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

NH ≅ G/Ntype
96. C4⋊Dic19Q16semidirect
241. C19#7783semidirect

Maximal subgroups

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

subgroupindex
#145715902
#145649652
#145649602
#145614612
#145614592
#145614572
C19×#20162
#778319