Finite Group Databasebeta

← #18071387

Subgroups — #18071387

Order 4864.

436 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 83 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#14571594C211yesmaximal, characteristic
2#14564965C211yesmaximal, characteristic
3#14564735C211yesmaximal, characteristic
4#14561461C211yesmaximal, characteristic
5#14561460C211yesmaximal, characteristic
6#14561459C211yesmaximal, characteristic
7C19×#2024C211yesmaximal, characteristic
8C22×#64528—21no—
9C2×#10597265—21no—
10C2×#10597292—21no—
11#11926478—21no—
12#11926478—21no—
13#11926463—21no—
14#11926450C2211yescharacteristic
15#11926448—21no—
16#11926442C2211yescharacteristic
17#11926439—21no—
18#11926429—21no—
19#11926306—21no—
20#11926299C2211yescharacteristic
21#11926299C2211yescharacteristic
22C2×C19×C4⋊Q8C2211yescharacteristic
23C2×C19×#103—21no—
24C19×#391C2211yescharacteristic
25C19×#340—21no—
26C19×#336C2211yescharacteristic
27C22×Q8×C19—21no—
28C22×Q8×C19D411yescharacteristic
29C22×Dic38D411yescharacteristic
30C22×C8×C19—21no—
31C19×C4⋊Q8—42no—
32C2×C4⋊C4×C19—21no—
33C2×C4⋊C4×C19—21no—
34C2×C4⋊C4×C19D411yescharacteristic
35C2×C42×C19C2311yescharacteristic
36C2×#64528—42no—
37C2×#64528—42no—
38C2×#64528—42no—
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×Dic19⋊C4—21no—
47C2×C4×Dic19—21no—
48C22×C19⋊C8—21no—
49C22×C19⋊C8—21no—
50C19×#103—42no—
51C19×#95—21no—
52C19×#95—21no—
53#10597292—42no—
54C19⋊#95—21no—
55C19⋊#95—21no—
56C19⋊#95—21no—
57C19⋊#95—21no—
58C19⋊#95—21no—
59C19⋊#95—21no—
60#10597265—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—
81C2×Dic38—21no—
82C2×Dic38—41no—
83C2×Dic38—41no—
84C2×Dic38SD1612yes—
85C2×C8×C19—41no—
86C2×C8×C19—41no—
87C2×C8×C19—41no—
88C4⋊C4×C19—22no—
89C4⋊C4×C19—22no—
90C4⋊C4×C19—41no—
91C4⋊C4×C19—41no—
92C4⋊C4×C19—41no—
93C42×C19—41no—
94#64528—48no—
95C4⋊Dic19—21no—
96C4⋊Dic19—41no—
97C4⋊Dic19—41no—
98C4⋊Dic19Q1612yescomplemented
99Dic19⋊C4—41no—
100Dic19⋊C4—41no—
101Dic19⋊C4—81no—
102Dic19⋊C4—81no—
103Dic19⋊C4—81no—
104Dic19⋊C4—81no—
105C4×Dic19—81no—
106C2×C19⋊C8—22no—
107C2×C19⋊C8—22no—
108C2×C19⋊C8—41no—
109C2×C19⋊C8—41no—
110C2×C19⋊C8—41no—
111C2×C19⋊C8—41no—
112#7761—191nomaximal, Sylow
113C23×C19#12011yescharacteristic
114Q8×C19—42no—
115Q8×C19—42no—
116Q8×C19—42no—
117Q8×C19—81no—
118Q8×C19—81no—
119Q8×C19—81no—
120C2×C4×C19—21no—
121C2×C4×C19—21no—
122C2×C4×C19—21no—
123C2×C4×C19—21no—
124C2×C4×C19—21no—
125C2×C4×C19—21no—
126C2×C4×C19—41no—
127C2×C4×C19—41no—
128C2×C4×C19—41no—
129C2×C4×C19—41no—
130C2×C4×C19—41no—
131C2×C4×C19—41no—
132C2×C4×C19—42no—
133C2×C4×C19—81no—
134C2×C4×C19—81no—
135C2×C4×C19C2×SD1611yescharacteristic
136C2×C4×C19C2×Q1611yescharacteristic
137C2×C4×C19#13511yescharacteristic
138C2×C4×C19#13711yescharacteristic
139C2×C4×C19#13711yescharacteristic
140C2×C4×C19#13711yescharacteristic
141C2×Dic19—22no—
142C2×Dic19—22no—
143C2×Dic19—41no—
144C2×Dic19—41no—
145C2×Dic19—41no—
146C2×Dic19—41no—
147C2×Dic19—41no—
148C2×Dic19—41no—
149C2×Dic19—41no—
150C2×Dic19—41no—
151C2×Dic19—41no—
152C2×Dic19—41no—
153Dic38—42no—
154Dic38—81no—
155C8×C19—81no—
156C19⋊C8—42no—
157C19⋊C8—42no—
158#2806—191no—
159#2058—191no—
160#2024D1911yescharacteristic
161#2016—191no—
162#1272—191no—
163#1272—191no—
164#1271—191no—
165C22×C19#44811yescharacteristic
166C22×C19#45111yescharacteristic
167C22×C19#45211yescharacteristic
168C22×C19#45311yescharacteristic
169C22×C19#45511yescharacteristic
170C22×C19#45611yescharacteristic
171C22×C19B(4,𝔽2)11yescharacteristic
172C4×C19—21no—
173C4×C19—21no—
174C4×C19—21no—
175C4×C19—21no—
176C4×C19—21no—
177C4×C19—21no—
178C4×C19—82no—
179C4×C19—81no—
180C4×C19—81no—
181Dic19—42no—
182Dic19—42no—
183Dic19—81no—
184Dic19—81no—
185C22×Q16—381no—
186C2×C4⋊Q8C2×D1911yescharacteristic
187C2×#106—381no—
188C2×#103—21no—
189C2×#103—381no—
190#398—381no—
191#398—381no—
192#395—381no—
193#391—191no—
194#391—381no—
195#391C2×D1911yescharacteristic
196#389—191no—
197#389—381no—
198#387—381no—
199#340—21no—
200#340—381no—
201#336—191no—
202#336—191no—
203#336C2×D1911yescharacteristic
204C2×C19#159611yescharacteristic
205C2×C19#160511yescharacteristic
206C2×C19#160611yescharacteristic
207C2×C19#163211yescharacteristic
208C2×C19#164511yescharacteristic
209C2×C19#165311yescharacteristic
210C2×C19#166111yescharacteristic
211C22×Q8—21no—
212C22×Q8—191no—
213C22×Q8C22⋊D1911yescharacteristic
214C2×Q16—762no—
215C2×Q16—762no—
216C2×Q16—762no—
217C22×C8—21no—
218C22×C8—381no—
219C22×C8—381no—
220C4⋊Q8—42no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—191no—
224C2×C4⋊C4—191no—
225C2×C4⋊C4—191no—
226C2×C4⋊C4—381no—
227C2×C4⋊C4—381no—
228C2×C4⋊C4—381no—
229C2×C4⋊C4—381no—
230C2×C4⋊C4—381no—
231C2×C4⋊C4C22⋊D1911yescharacteristic
232C2×C42—381no—
233C2×C42C22×D1911yescharacteristic
234#106—762no—
235#103—42no—
236#103—762no—
237#95—21no—
238#95—21no—
239#95—381no—
240#95—381no—
241#95—381no—
242#95—381no—
243#95—381no—
244#95—381no—
245C19#776111yescharacteristic, complemented, Sylow
246C2×Q8—22no—
247C2×Q8—21no—
248C2×Q8—21no—
249C2×Q8—41no—
250C2×Q8—41no—
251C2×Q8—41no—
252C2×Q8—41no—
253C2×Q8—41no—
254C2×Q8—41no—
255C2×Q8—41no—
256C2×Q8—192no—
257C2×Q8—381no—
258C2×Q8—761no—
259C2×Q8—761no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—41no—
263C22×C4—381no—
264C22×C4—381no—
265C22×C4—381no—
266C22×C4—381no—
267C22×C4D4×D1911yescharacteristic
268C22×C4D4×D1911yescharacteristic
269C22×C4C2×C22⋊D1911yescharacteristic
270Q16—768no—
271C2×C8—41no—
272C2×C8—41no—
273C2×C8—41no—
274C2×C8—382no—
275C2×C8—382no—
276C2×C8—761no—
277C2×C8—761no—
278C2×C8—761no—
279C2×C8—761no—
280C4⋊C4—22no—
281C4⋊C4—22no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—192no—
286C4⋊C4—381no—
287C4⋊C4—761no—
288C4⋊C4—761no—
289C4⋊C4—761no—
290C4⋊C4—761no—
291C4⋊C4—1521no—
292C4⋊C4—1521no—
293C4⋊C4—1521no—
294C4⋊C4—1521no—
295C42—41no—
296C42—1521no—
297C23#1059738311yescharacteristic
298Q8—42no—
299Q8—42no—
300Q8—42no—
301Q8—81no—
302Q8—81no—
303Q8—81no—
304Q8—762no—
305Q8—1521no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—42no—
318C2×C4—41no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4—382no—
322C2×C4—382no—
323C2×C4—761no—
324C2×C4—761no—
325C2×C4—761no—
326C2×C4—761no—
327C2×C4—761no—
328C2×C4—761no—
329C2×C4—761no—
330C2×C4—761no—
331C2×C4—761no—
332C2×C4—761no—
333C2×C4SD16×D1911yescharacteristic
334C2×C4#1059736111yescharacteristic
335C2×C4Q16×D1911yescharacteristic
336C2×C4#1059736411yescharacteristic
337C2×C4#1059738811yescharacteristic
338C2×C4#1059739611yescharacteristic
339C8—81no—
340C8—762no—
341C8—762no—
342C22#1192668111yescharacteristic
343C22#1192669811yescharacteristic
344C22#1192670411yescharacteristic
345C22#1192671011yescharacteristic
346C22#1192672111yescharacteristic
347C22#1192672511yescharacteristic
348C22#1192673011yescharacteristic
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—21no—
355C4—81no—
356C4—81no—
357C4—82no—
358C4—762no—
359C4—762no—
360C4—1521no—
361C4—1521no—
362C2#1456255611yescharacteristic
363C2#1456260711yescharacteristic
364C2#1456261311yescharacteristic
365C2#1456276811yescharacteristic
366C2#1456285311yescharacteristic
367C2#1456291111yescharacteristic
368C2#1456295111yescharacteristic
subgroupG/H
centerC23#10597383
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#2024C2
socle, prime radicalC23×C19#120
hypercenter#2024D19
hypocenterC19#7761
LCSG ▷ C2×C42×C19 ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2024

Complements

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

NH ≅ G/Ntype
98. C4⋊Dic19Q16semidirect
245. C19#7761semidirect

Maximal subgroups

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

subgroupindex
#145715942
#145649652
#145647352
#145614612
#145614602
#145614592
C19×#20242
#776119