Finite Group Databasebeta

← #18085485

Subgroups — #18085485

Order 4864.

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

normal subgroups only

This group has 574 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#14574456C211yesmaximal, characteristic
2#14568120C211yesmaximal, characteristic
3#14568114C211yesmaximal, characteristic
4#14563713C211yesmaximal, characteristic
5#14562156C211yesmaximal, characteristic
6#14561521C211yesmaximal, characteristic
7C19×#1508C211yesmaximal, characteristic
8C2×#10597370C2211yescharacteristic
9C22×C4⋊Dic19C2211yescharacteristic
10#11926874—21no—
11#11926872—21no—
12#11926800—22no—
13#11926700—21no—
14#11926699—21no—
15#11926508C2211yescharacteristic
16#11926484—22no—
17#11926474—22no—
18#11926451—21no—
19#11926450—21no—
20#11926416—22no—
21#11926413—21no—
22#11926410—21no—
23#11926405—22no—
24C4×C22⋊Dic19C2211yescharacteristic
25#11926312—22no—
26#11926282—22no—
27C2×C19×C22⋊Q8C2211yescharacteristic
28C19×#407C2211yescharacteristic
29C4×C22⋊C4×C19C2211yescharacteristic
30C19×#328—22no—
31C22×Q8×C19D411yescharacteristic
32C23×C4×C19C2311yescharacteristic
33C23×Dic19D412yes—
34C22×Dic38D411yescharacteristic
35C2×M16×C19—21no—
36C19×C22⋊Q8—21no—
37C19×C22⋊Q8—21no—
38C19×C22⋊Q8—21no—
39C19×C22⋊Q8—21no—
40C2×C4⋊C4×C19—21no—
41C2×C4⋊C4×C19D411yescharacteristic
42C2×C22⋊C4×C19—21no—
43C2×C22⋊C4×C19—21no—
44C2×C42×C19—21no—
45C2×C22⋊Dic19—21no—
46C2×C22⋊Dic19—21no—
47C2×#64528—22no—
48C2×C4⋊Dic19—21no—
49C2×C4⋊Dic19—21no—
50C2×C4⋊Dic19—21no—
51C2×C4⋊Dic19—21no—
52C2×C4⋊Dic19—21no—
53C2×C4⋊Dic19—21no—
54C2×C4⋊Dic19D411yescharacteristic
55#10597370—21no—
56#10597370—21no—
57#10597370—21no—
58#10597370—21no—
59C2×Dic19⋊C4—21no—
60C2×Dic19⋊C4—24no—
61C2×C4×Dic19—21no—
62C2×#64520D412yes—
63C19×C22⋊C8—21no—
64C19×C22⋊C8—21no—
65C19×#95D412yes—
66#10597292—22no—
67C19⋊#95—24no—
68C19⋊#95—24no—
69C19⋊#95—24no—
70C19⋊#95D412yes—
71C22⋊(C19⋊C8)—21no—
72C22⋊(C19⋊C8)—21no—
73#10597267—22no—
74#10597265—22no—
75C24×C19C2×D411yescharacteristic
76C2×Q8×C19—21no—
77C2×Q8×C19—21no—
78C2×Q8×C19—42no—
79C22×C4×C19—22no—
80C22×C4×C19—21no—
81C22×C4×C19—21no—
82C22×C4×C19—42no—
83C22×C4×C19C2×D411yescharacteristic
84C22×C4×C19C2×D411yescharacteristic
85C22×C4×C19C2×D411yescharacteristic
86C22×C4×C19C2×D411yescharacteristic
87C22×C4×C19C2×D411yescharacteristic
88C22×C4×C19#4111yescharacteristic
89C22×Dic19—22no—
90C22×Dic19—21no—
91C22×Dic19—21no—
92C22×Dic19—22no—
93C22×Dic19—22no—
94C22×Dic19—22no—
95C22×Dic19—44no—
96C2×Dic38—21no—
97C2×Dic38—21no—
98C2×Dic38—42no—
99M16×C19—42no—
100C2×C8×C19—41no—
101C4⋊C4×C19—21no—
102C4⋊C4×C19—21no—
103C4⋊C4×C19—41no—
104C4⋊C4×C19—41no—
105C22⋊C4×C19—42no—
106C22⋊C4×C19—41no—
107C22⋊C4×C19—41no—
108C42×C19—42no—
109C22⋊Dic19—24no—
110C22⋊Dic19—41no—
111C22⋊Dic19—41no—
112#64528—82no—
113C4⋊Dic19—21no—
114C4⋊Dic19—21no—
115C4⋊Dic19—41no—
116C4⋊Dic19—41no—
117C4⋊Dic19—41no—
118C4⋊Dic19—41no—
119Dic19⋊C4—41no—
120Dic19⋊C4—41no—
121Dic19⋊C4—84no—
122C4×Dic19—42no—
123#64520—42no—
124C2×C19⋊C8—22no—
125#10335—191nomaximal, Sylow
126C23×C19—22no—
127C23×C19—22no—
128C23×C19—41no—
129C23×C19#12011yescharacteristic
130C23×C19#12011yescharacteristic
131C23×C19#12111yescharacteristic
132Q8×C19—42no—
133Q8×C19—81no—
134C2×C4×C19—22no—
135C2×C4×C19—22no—
136C2×C4×C19—22no—
137C2×C4×C19—41no—
138C2×C4×C19—41no—
139C2×C4×C19—41no—
140C2×C4×C19—42no—
141C2×C4×C19—42no—
142C2×C4×C19—42no—
143C2×C4×C19—41no—
144C2×C4×C19—41no—
145C2×C4×C19—42no—
146C2×C4×C19—42no—
147C2×C4×C19#12011yescharacteristic
148C2×C4×C19#12111yescharacteristic
149C2×C4×C19#12111yescharacteristic
150C2×C4×C19#12711yescharacteristic
151C2×Dic19—24no—
152C2×Dic19—42no—
153C2×Dic19—42no—
154C2×Dic19—42no—
155C2×Dic19—44no—
156C2×Dic19—41no—
157C2×Dic19—41no—
158C2×Dic19—42no—
159C2×Dic19—44no—
160C2×Dic19—42no—
161C2×Dic19—82no—
162Dic38—42no—
163Dic38—81no—
164C8×C19—81no—
165C19⋊C8—42no—
166#3195—191no—
167#2503—191no—
168#2502—191no—
169#1821—191no—
170#1508—191no—
171#1508D1911yescharacteristic
172#1297—191no—
173C22×C19—21no—
174C22×C19—21no—
175C22×C19—21no—
176C22×C19—21no—
177C22×C19—21no—
178C22×C19—21no—
179C22×C19—21no—
180C22×C19—44no—
181C22×C19#39211yescharacteristic
182C22×C19#45512yes—
183C22×C19#45612yes—
184C4×C19—21no—
185C4×C19—21no—
186C4×C19—21no—
187C4×C19—82no—
188C4×C19—81no—
189C4×C19—81no—
190C4×C19#45812yes—
191Dic19—44no—
192Dic19—82no—
193Dic19—81no—
194Dic19—81no—
195C2×C22⋊Q8—191no—
196C2×C22⋊Q8C2×D1911yescharacteristic
197C22×C4⋊C4—191no—
198#483—381no—
199#483—381no—
200#470—382no—
201#451—381no—
202#451—381no—
203#407—191no—
204#407C2×D1911yescharacteristic
205#400—382no—
206#398—382no—
207#391—381no—
208#391—381no—
209#385—382no—
210#384—381no—
211#382—381no—
212#381—382no—
213C4×C22⋊C4—191no—
214C4×C22⋊C4C2×D1911yescharacteristic
215#343—382no—
216#328—22no—
217#328—382no—
218C2×C19—22no—
219C2×C19—22no—
220C2×C19—41no—
221C2×C19#200411yescharacteristic
222C2×C19#200511yescharacteristic
223C2×C19#202211yescharacteristic
224C22×Q8—191no—
225C22×Q8D7611yescharacteristic
226C23×C4—192no—
227C23×C4C22×D1911yescharacteristic
228C2×Q16—382no—
229C2×M16—21no—
230C2×M16—192no—
231C22⋊Q8—21no—
232C22⋊Q8—21no—
233C22⋊Q8—21no—
234C22⋊Q8—21no—
235C22⋊Q8—381no—
236C22⋊Q8—381no—
237C22⋊Q8—381no—
238C22⋊Q8—381no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—191no—
241C2×C4⋊C4—381no—
242C2×C4⋊C4—381no—
243C2×C4⋊C4—381no—
244C2×C4⋊C4—381no—
245C2×C4⋊C4—381no—
246C2×C4⋊C4—381no—
247C2×C4⋊C4—381no—
248C2×C4⋊C4—384no—
249C2×C4⋊C4D7611yescharacteristic
250C2×C22⋊C4—21no—
251C2×C22⋊C4—21no—
252C2×C22⋊C4—381no—
253C2×C22⋊C4—381no—
254C2×C42—21no—
255C2×C42—381no—
256#106—382no—
257#103—382no—
258#103—382no—
259C22⋊C8—21no—
260C22⋊C8—21no—
261C22⋊C8—381no—
262C22⋊C8—381no—
263#95—192no—
264#95—384no—
265#95—384no—
266#95—384no—
267#95C22⋊D1912yes—
268C19#1033511yescharacteristic, complemented, Sylow
269C24D4×D1911yescharacteristic
270C2×Q8—21no—
271C2×Q8—21no—
272C2×Q8—42no—
273C2×Q8—381no—
274C2×Q8—381no—
275C2×Q8—762no—
276C22×C4—22no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—42no—
280C22×C4—382no—
281C22×C4—381no—
282C22×C4—381no—
283C22×C4—382no—
284C22×C4—382no—
285C22×C4—382no—
286C22×C4—764no—
287C22×C4C2×D7611yescharacteristic
288C22×C4#6454111yescharacteristic
289C22×C4D4×D1911yescharacteristic
290C22×C4D4×D1911yescharacteristic
291C22×C4D4×D1911yescharacteristic
292C22×C4C2×C22⋊D1911yescharacteristic
293Q16—1522no—
294M16—42no—
295M16—762no—
296C2×C8—41no—
297C2×C8—382no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—381no—
303C4⋊C4—381no—
304C4⋊C4—761no—
305C4⋊C4—761no—
306C4⋊C4—761no—
307C4⋊C4—761no—
308C4⋊C4—761no—
309C4⋊C4—761no—
310C4⋊C4—1524no—
311C22⋊C4—42no—
312C22⋊C4—41no—
313C22⋊C4—41no—
314C22⋊C4—384no—
315C22⋊C4—761no—
316C22⋊C4—761no—
317C42—42no—
318C42—762no—
319C23—22no—
320C23—22no—
321C23—41no—
322C23#1059732811yescharacteristic
323C23#1059733011yescharacteristic
324C23#1059738311yescharacteristic
325Q8—42no—
326Q8—81no—
327Q8—762no—
328Q8—1521no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—384no—
343C2×C4—762no—
344C2×C4—762no—
345C2×C4—764no—
346C2×C4—762no—
347C2×C4—761no—
348C2×C4—761no—
349C2×C4—762no—
350C2×C4—764no—
351C2×C4—762no—
352C2×C4—1522no—
353C2×C4#1059732811yescharacteristic
354C2×C4#1059733011yescharacteristic
355C2×C4#1059737611yescharacteristic
356C2×C4#1059738611yescharacteristic
357C8—81no—
358C8—762no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—44no—
367C22#1192645311yescharacteristic
368C22#1192672312yes—
369C22#1192672512yes—
370C4—21no—
371C4—21no—
372C4—21no—
373C4—82no—
374C4—81no—
375C4—81no—
376C4—764no—
377C4—1522no—
378C4—1521no—
379C4—1521no—
380C4#1192673512yes—
381C2—22no—
382C2—22no—
383C2—41no—
384C2#1456466311yescharacteristic
385C2#1456467211yescharacteristic
386C2#1456476511yescharacteristic
subgroupG/H
centerC22#11926453
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC19×#1508C2
socleC22×C19#392
prime radicalC24×C19C2×D4
hypercenter#1508D19
hypocenterC19#10335
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1508

Complements

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

NH ≅ G/Ntype
268. C19#10335semidirect

Maximal subgroups

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

subgroupindex
#145744562
#145681202
#145681142
#145637132
#145621562
#145615212
C19×#15082
#1033519