Finite Group Databasebeta

← #18078267

Subgroups — #18078267

Order 4864.

1010 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 1010 conjugacy classes of subgroups — too many to draw. Only its 143 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#14571922C211yesmaximal, characteristic
2C2×C4×C22⋊Dic19C211yesmaximal, characteristic
3C2×#11926282C212yesmaximal, complemented
4#14561515C212yesmaximal, complemented
5C19×#1779C211yesmaximal, characteristic
6C2×#10597370C412yescomplemented
7C2×#10597370C2211yescharacteristic
8C22×C22⋊Dic19—21no—
9C22×C4×Dic19—21no—
10#11926417—22no—
11#11926417—21no—
12#11926404C412yescomplemented
13#11926404C2211yescharacteristic
14#11926400—21no—
15C4×C22⋊Dic19—24no—
16C2×C19⋊#95C2212yes—
17#11926282—24no—
18C24×C4×C19C2211yescharacteristic
19C2×C19×C22⋊C8—22no—
20C2×C19×C22⋊C8C2212yes—
21C25×C19D411yescharacteristic
22C23×C4×C19—22no—
23C23×C4×C19—22no—
24C23×C4×C19—44no—
25C23×C4×C19C2×C412yes—
26C23×C4×C19D411yescharacteristic
27C23×C4×C19D412yes—
28C23×C4×C19C2311yescharacteristic
29C23×Dic19—22no—
30C22×Dic38C2×C411yescharacteristic
31C22×C8×C19—22no—
32C2×C22⋊Dic19—24no—
33C2×C22⋊Dic19—28no—
34C2×C22⋊Dic19—22no—
35C2×C22⋊Dic19—22no—
36C2×C22⋊Dic19—21no—
37C2×C22⋊Dic19—21no—
38C2×C4⋊Dic19C2×C411yescharacteristic
39C2×C4⋊Dic19C2×C412yes—
40#10597370—22no—
41#10597370—22no—
42#10597370—44no—
43C2×Dic19⋊C4—22no—
44C2×Dic19⋊C4—21no—
45C2×C4×Dic19—24no—
46C2×C4×Dic19—44no—
47C19×C22⋊C8—22no—
48C19×C22⋊C8—22no—
49C19×C22⋊C8—44no—
50C19⋊#95—22no—
51C19⋊#95—22no—
52C19⋊#95—21no—
53C19⋊#95D414yes—
54C24×C19—24no—
55C24×C19—21no—
56C24×C19—21no—
57C24×C19—22no—
58C24×C19—22no—
59C24×C19—42no—
60C24×C19C22⋊C412yes—
61C24×C19C2×D411yescharacteristic
62C22×C4×C19—21no—
63C22×C4×C19—21no—
64C22×C4×C19—24no—
65C22×C4×C19—24no—
66C22×C4×C19—24no—
67C22×C4×C19—24no—
68C22×C4×C19—24no—
69C22×C4×C19—42no—
70C22×C4×C19—42no—
71C22×C4×C19—42no—
72C22×C4×C19—48no—
73C22×C4×C19—48no—
74C22×C4×C19C22⋊C412yes—
75C22×C4×C19C22×C411yescharacteristic
76C22×C4×C19C2×D412yes—
77C22×C4×C19C2×D411yescharacteristic
78C22×C4×C19#4112yes—
79C22×Dic19—28no—
80C22×Dic19—24no—
81C22×Dic19—21no—
82C22×Dic19—21no—
83C22×Dic19—22no—
84C22×Dic19—44no—
85C22×Dic19—42no—
86C22×Dic19—42no—
87C2×Dic38—22no—
88C2×Dic38—42no—
89C2×C8×C19—44no—
90C2×C8×C19—42no—
91C22⋊Dic19—216no—
92C22⋊Dic19—44no—
93C22⋊Dic19—44no—
94C22⋊Dic19—41no—
95C22⋊Dic19—41no—
96C22⋊Dic19—42no—
97C4⋊Dic19—22no—
98C4⋊Dic19—42no—
99Dic19⋊C4—44no—
100Dic19⋊C4—42no—
101C4×Dic19—48no—
102#9146—191nomaximal, Sylow
103C23×C19—22no—
104C23×C19—22no—
105C23×C19—24no—
106C23×C19—24no—
107C23×C19—22no—
108C23×C19—22no—
109C23×C19—22no—
110C23×C19—22no—
111C23×C19—22no—
112C23×C19—22no—
113C23×C19—48no—
114C23×C19—48no—
115C23×C19—42no—
116C23×C19—42no—
117C23×C19—42no—
118C23×C19—42no—
119C23×C19#10414yes—
120C23×C19C2×C22⋊C411yescharacteristic
121C23×C19#12011yescharacteristic
122C23×C19#12311yescharacteristic
123C23×C19#13512yes—
124C23×C19#13712yes—
125C2×C4×C19—24no—
126C2×C4×C19—24no—
127C2×C4×C19—22no—
128C2×C4×C19—22no—
129C2×C4×C19—22no—
130C2×C4×C19—22no—
131C2×C4×C19—42no—
132C2×C4×C19—42no—
133C2×C4×C19—48no—
134C2×C4×C19—48no—
135C2×C4×C19#9914yes—
136C2×C4×C19C4×D412yes—
137C2×C4×C19#12112yes—
138C2×Dic19—28no—
139C2×Dic19—44no—
140C2×Dic19—48no—
141C2×Dic19—48no—
142C2×Dic19—44no—
143C2×Dic19—41no—
144C2×Dic19—41no—
145C2×Dic19—42no—
146C2×Dic19—42no—
147C2×Dic19—42no—
148C2×Dic19—42no—
149C2×Dic19—42no—
150Dic38—82no—
151C8×C19—82no—
152#2848—191no—
153C2×C4×C22⋊C4—191no—
154#1779D1911yescharacteristic
155C2×#328—192no—
156#1294—192no—
157C22×C19—21no—
158C22×C19—21no—
159C22×C19—21no—
160C22×C19—21no—
161C22×C19—24no—
162C22×C19—24no—
163C22×C19—24no—
164C22×C19—24no—
165C22×C19—24no—
166C22×C19—48no—
167C22×C19—48no—
168C22×C19—42no—
169C22×C19—42no—
170C22×C19—42no—
171C22×C19—42no—
172C22×C19#38611yescharacteristic
173C22×C19C2×#9912yes—
174C22×C19#41611yescharacteristic
175C22×C19#41911yescharacteristic
176C22×C19C2×#10412yes—
177C22×C19#45212yes—
178C22×C19#48512yes—
179C4×C19—22no—
180C4×C19—22no—
181C4×C19—24no—
182Dic19—48no—
183Dic19—81no—
184Dic19—81no—
185Dic19—82no—
186C24×C4C2×D1911yescharacteristic
187C2×C22⋊Q8—191no—
188C2×C22⋊Q8—192no—
189C22×C22⋊C4—381no—
190C22×C42—381no—
191C2×C22⋊C8—22no—
192C2×C22⋊C8C2×D1912yes—
193#385—381no—
194#385—382no—
195#380—192no—
196#380—191no—
197#379—381no—
198C4×C22⋊C4—384no—
199C2×#95—192no—
200#328—384no—
201C2×C19—22no—
202C2×C19—22no—
203C2×C19—44no—
204C2×C19#150112yes—
205C2×C19#150812yes—
206C2×C19#187311yescharacteristic
207C2×C19#189611yescharacteristic
208C2×C19#189811yescharacteristic
209C25D7611yescharacteristic
210C22×Q8—191no—
211C23×C4—22no—
212C23×C4—22no—
213C23×C4—44no—
214C23×C4—382no—
215C23×C4C4×D1912yes—
216C23×C4D7611yescharacteristic
217C23×C4C22⋊D1912yes—
218C23×C4C22×D1911yescharacteristic
219C22×C8—22no—
220C22⋊Q8—382no—
221C22⋊Q8—382no—
222C22⋊Q8—764no—
223C2×C4⋊C4—191no—
224C2×C4⋊C4—192no—
225C2×C4⋊C4—382no—
226C2×C4⋊C4—381no—
227C2×C22⋊C4—388no—
228C2×C22⋊C4—384no—
229C2×C22⋊C4—382no—
230C2×C22⋊C4—382no—
231C2×C22⋊C4—381no—
232C2×C22⋊C4—381no—
233C2×C42—384no—
234C2×C42—764no—
235C22⋊C8—22no—
236C22⋊C8—22no—
237C22⋊C8—44no—
238#95—194no—
239#95—382no—
240#95—382no—
241#95—381no—
242C19#914611yescharacteristic, complemented, Sylow
243C24—24no—
244C24—21no—
245C24—21no—
246C24—22no—
247C24—22no—
248C24—42no—
249C24(C2×D19)⋊C412yes—
250C24C2×D7611yescharacteristic
251C2×Q8—382no—
252C2×Q8—762no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—24no—
256C22×C4—24no—
257C22×C4—24no—
258C22×C4—24no—
259C22×C4—24no—
260C22×C4—42no—
261C22×C4—42no—
262C22×C4—42no—
263C22×C4—48no—
264C22×C4—48no—
265C22×C4—388no—
266C22×C4—384no—
267C22×C4—382no—
268C22×C4—381no—
269C22×C4—381no—
270C22×C4—764no—
271C22×C4—762no—
272C22×C4—762no—
273C22×C4(C2×D19)⋊C412yes—
274C22×C4C2×C4×D1911yescharacteristic
275C22×C4D4×D1912yes—
276C22×C4#6454312yes—
277C22×C4C2×C22⋊D1911yescharacteristic
278C2×C8—44no—
279C2×C8—42no—
280C4⋊C4—382no—
281C4⋊C4—762no—
282C4⋊C4—762no—
283C4⋊C4—764no—
284C22⋊C4—3816no—
285C22⋊C4—764no—
286C22⋊C4—764no—
287C22⋊C4—761no—
288C22⋊C4—761no—
289C22⋊C4—762no—
290C42—768no—
291C23—22no—
292C23—22no—
293C23—24no—
294C23—24no—
295C23—22no—
296C23—22no—
297C23—22no—
298C23—22no—
299C23—22no—
300C23—22no—
301C23—48no—
302C23—48no—
303C23—42no—
304C23—42no—
305C23—42no—
306C23—42no—
307C23#1059728214yes—
308C23#1059732811yescharacteristic
309C23#1059733211yescharacteristic
310C23#1059735012yes—
311C23#1059735512yes—
312C23C2×(C2×D19)⋊C411yescharacteristic
313Q8—1522no—
314C2×C4—24no—
315C2×C4—24no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—48no—
323C2×C4—48no—
324C2×C4—388no—
325C2×C4—764no—
326C2×C4—768no—
327C2×C4—768no—
328C2×C4—764no—
329C2×C4—762no—
330C2×C4—762no—
331C2×C4—762no—
332C2×C4—761no—
333C2×C4—761no—
334C2×C4—762no—
335C2×C4—762no—
336C2×C4#1059726314yes—
337C2×C4(C22⋊D19)⋊C412yes—
338C2×C4#1059738512yes—
339C8—82no—
340C22—24no—
341C22—24no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—24no—
347C22—24no—
348C22—24no—
349C22—48no—
350C22—48no—
351C22—42no—
352C22—42no—
353C22—42no—
354C22—42no—
355C22#1192642111yescharacteristic
356C22C2×#1059726312yes—
357C22#1192654111yescharacteristic
358C22#1192655411yescharacteristic
359C22C2×#1059728212yes—
360C22#1192670812yes—
361C22#1192688612yes—
362C4—22no—
363C4—24no—
364C4—22no—
365C4—768no—
366C4—1522no—
367C4—1521no—
368C4—1521no—
369C2—22no—
370C2—22no—
371C2—44no—
372C2#1456212712yes—
373C2#1456215612yes—
374C2#1456394511yescharacteristic
375C2#1456407611yescharacteristic
376C2#1456408611yescharacteristic
subgroupG/H
centerC23C2×(C2×D19)⋊C4
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1779C2
socleC23×C19C2×C22⋊C4
prime radicalC25×C19D4
cosocleC23×C4×C19C23
hypercenter#1779D19
hypocenterC19#9146
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C24×C4 ◁ #1779

Complements

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

NH ≅ G/Ntype
3. C2×#11926282C2semidirect
4. #14561515C2semidirect
6. C2×#10597370C4semidirect
12. #11926404C4semidirect
242. C19#9146semidirect

Maximal subgroups

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

subgroupindex
#145719222
C2×C4×C22⋊Dic192
C2×#119262822
#145615152
C19×#17792
#914619