Finite Group Databasebeta

← #18073901

Subgroups — #18073901

Order 4864.

874 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 874 conjugacy classes of subgroups — too many to draw. Only its 139 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
1C22×#10597322C211yesmaximal, characteristic
2#14563703C211yesmaximal, characteristic, complemented
3C2×#11926269C212yesmaximal, complemented
4C2×#11926267C212yesmaximal
5C19×#1817C211yesmaximal, characteristic, complemented
6C2×#10597322—24no—
7C2×#10597322—24no—
8C2×#10597322—22no—
9C2×#10597322—22no—
10C22×Dic19⋊C4C411yescharacteristic
11C22×Dic19⋊C4C411yescharacteristic
12C22×Dic19⋊C4C2211yescharacteristic
13C22×(C2×D19)⋊C4C411yescharacteristic
14C22×(C2×D19)⋊C4C411yescharacteristic
15C22×(C2×D19)⋊C4C2211yescharacteristic
16C2×C22⋊(C19⋊C8)C2212yes—
17#11926299—22no—
18#11926269—24no—
19#11926267—24no—
20C22×C42×C19C2211yescharacteristic
21C2×C19×C22⋊C8C2212yes—
22C19×#336—22no—
23C24×D19C2×C411yescharacteristic
24C23×C4×C19C2×C411yescharacteristic
25C23×C4×C19C2×C411yescharacteristic
26C23×C4×C19C2311yescharacteristic
27C23×Dic19C2×C411yescharacteristic
28C23×Dic19C2×C411yescharacteristic
29C23×Dic19C2×C411yescharacteristic
30C22×C8×C19—22no—
31C2×C42×C19—22no—
32C2×C42×C19—22no—
33C2×C42×C19D412yes—
34C2×C42×C19D412yes—
35C2×(C2×D19)⋊C4—22no—
36C2×(C2×D19)⋊C4—22no—
37C2×(C2×D19)⋊C4—22no—
38C2×(C2×D19)⋊C4—22no—
39C2×(C2×D19)⋊C4—21no—
40C2×(C2×D19)⋊C4—22no—
41C2×(C2×D19)⋊C4—21no—
42C2×(C2×D19)⋊C4—22no—
43C2×(C2×D19)⋊C4—22no—
44C2×(C2×D19)⋊C4D414yes—
45C2×Dic19⋊C4—22no—
46C2×Dic19⋊C4—22no—
47C2×Dic19⋊C4—21no—
48C2×Dic19⋊C4—22no—
49C2×Dic19⋊C4—21no—
50C2×Dic19⋊C4—22no—
51C2×Dic19⋊C4—22no—
52C2×Dic19⋊C4—22no—
53C2×Dic19⋊C4—22no—
54C2×Dic19⋊C4D414yes—
55C22×C19⋊C8—22no—
56#10597322—216no—
57#10597322—216no—
58C19×C22⋊C8—22no—
59C19×C22⋊C8—22no—
60C22⋊(C19⋊C8)—22no—
61C22⋊(C19⋊C8)—22no—
62C24×C19C22×C411yescharacteristic
63C23×D19—21no—
64C23×D19—21no—
65C23×D19—22no—
66C23×D19—22no—
67C23×D19—42no—
68C23×D19—42no—
69C23×D19C22⋊C412yes—
70C22×C4×C19—21no—
71C22×C4×C19—21no—
72C22×C4×C19—21no—
73C22×C4×C19—21no—
74C22×C4×C19—22no—
75C22×C4×C19—22no—
76C22×C4×C19—42no—
77C22×C4×C19—42no—
78C22×C4×C19C22⋊C412yes—
79C22×C4×C19C22⋊C412yes—
80C22×C4×C19C2×D411yescharacteristic
81C22×C4×C19C2×D412yes—
82C22×C4×C19C2×D412yes—
83C22×C4×C19C2×D411yescharacteristic
84C22×Dic19—21no—
85C22×Dic19—21no—
86C22×Dic19—21no—
87C22×Dic19—21no—
88C22×Dic19—21no—
89C22×Dic19—21no—
90C22×Dic19—22no—
91C22×Dic19—22no—
92C22×Dic19—42no—
93C22×Dic19—42no—
94C22×Dic19C22⋊C412yes—
95C22×Dic19C22⋊C412yes—
96C22×Dic19C22⋊C412yes—
97C2×C8×C19—44no—
98C2×C8×C19—42no—
99C42×C19—24no—
100C42×C19—24no—
101(C2×D19)⋊C4—28no—
102(C2×D19)⋊C4—28no—
103(C2×D19)⋊C4—24no—
104(C2×D19)⋊C4—24no—
105Dic19⋊C4—28no—
106Dic19⋊C4—28no—
107Dic19⋊C4—24no—
108Dic19⋊C4—24no—
109C2×C19⋊C8—44no—
110C2×C19⋊C8—42no—
111#8309—191nomaximal, Sylow
112C23×C19—22no—
113C23×C19—22no—
114C23×C19C2×C22⋊C411yescharacteristic
115C23×C19C2×C22⋊C411yescharacteristic
116C23×C19C2×C22⋊C411yescharacteristic
117C23×C19#13112yes—
118C23×C19#13112yes—
119C22×D19—22no—
120C22×D19—24no—
121C22×D19—42no—
122C22×D19—42no—
123C22×D19—42no—
124C22×D19—41no—
125C22×D19—41no—
126C22×D19—42no—
127C22×D19—42no—
128C22×D19—42no—
129C22×D19—42no—
130C22×D19—84no—
131C22×D19—84no—
132C2×C4×C19—22no—
133C2×C4×C19—22no—
134C2×C4×C19—22no—
135C2×C4×C19—22no—
136C2×C4×C19—22no—
137C2×C4×C19—22no—
138C2×C4×C19—24no—
139C2×C4×C19—42no—
140C2×C4×C19—42no—
141C2×C4×C19—42no—
142C2×C4×C19—42no—
143C2×C4×C19—42no—
144C2×C4×C19—42no—
145C2×C4×C19#12012yes—
146C2×C4×C19#12012yes—
147C2×Dic19—22no—
148C2×Dic19—22no—
149C2×Dic19—22no—
150C2×Dic19—24no—
151C2×Dic19—42no—
152C2×Dic19—42no—
153C2×Dic19—42no—
154C2×Dic19—41no—
155C2×Dic19—41no—
156C2×Dic19—42no—
157C2×Dic19—42no—
158C2×Dic19—42no—
159C2×Dic19—42no—
160C8×C19—82no—
161C19⋊C8—82no—
162C22×#126—191no—
163#1817—191no—
164#1817D1911yescharacteristic, complemented
165C2×#324—192no—
166C2×#323—192no—
167C22×C19—24no—
168C22×C19—24no—
169C22×C19—21no—
170C22×C19—21no—
171C22×C19—21no—
172C22×C19—21no—
173C22×C19#37911yescharacteristic
174C22×C19#40812yes—
175C22×C19#40812yes—
176C22×C19#40811yescharacteristic
177C22×C19#40811yescharacteristic
178C22×C19#41012yes—
179C22×C19#41312yes—
180C2×D19—42no—
181C2×D19—42no—
182C2×D19—42no—
183C2×D19—84no—
184C2×D19—82no—
185C2×D19—82no—
186C2×D19—84no—
187C4×C19—22no—
188C4×C19—22no—
189C4×C19—42no—
190C4×C19—42no—
191Dic19—42no—
192Dic19—42no—
193Dic19—42no—
194C2×#126—384no—
195C2×#126—384no—
196C2×#126—382no—
197C2×#126—382no—
198C22×C4⋊C4—191no—
199C22×C4⋊C4—191no—
200C22×C4⋊C4—191no—
201C22×C22⋊C4—191no—
202C22×C22⋊C4—191no—
203C22×C22⋊C4—191no—
204C22×C42C2×D1911yescharacteristic
205C2×C22⋊C8—192no—
206C2×C22⋊C8C2×D1912yes—
207#336—22no—
208#336—382no—
209#324—384no—
210#323—384no—
211C2×C19—22no—
212C2×C19—22no—
213C2×C19#147312yes—
214C2×C19#147312yes—
215C2×C19#178011yescharacteristic
216C2×C19#178211yescharacteristic
217C2×C19#178511yescharacteristic
218D19—82no—
219C25—191no—
220C23×C4—191no—
221C23×C4—191no—
222C23×C4—191no—
223C23×C4C4×D1911yescharacteristic
224C23×C4C4×D1911yescharacteristic
225C23×C4C22×D1911yescharacteristic
226C22×C8—22no—
227C22×C8—382no—
228#126—3816no—
229#126—3816no—
230C2×C4⋊C4—194no—
231C2×C4⋊C4—382no—
232C2×C4⋊C4—382no—
233C2×C4⋊C4—382no—
234C2×C4⋊C4—382no—
235C2×C4⋊C4—382no—
236C2×C4⋊C4—382no—
237C2×C4⋊C4—381no—
238C2×C4⋊C4—382no—
239C2×C4⋊C4—381no—
240C2×C22⋊C4—194no—
241C2×C22⋊C4—382no—
242C2×C22⋊C4—382no—
243C2×C22⋊C4—382no—
244C2×C22⋊C4—382no—
245C2×C22⋊C4—382no—
246C2×C22⋊C4—382no—
247C2×C22⋊C4—381no—
248C2×C22⋊C4—382no—
249C2×C22⋊C4—381no—
250C2×C42—22no—
251C2×C42—22no—
252C2×C42D7612yes—
253C2×C42C22⋊D1912yes—
254C22⋊C8—22no—
255C22⋊C8—22no—
256C22⋊C8—382no—
257C22⋊C8—382no—
258C19#830911yescharacteristic, complemented, Sylow
259C24—192no—
260C24—381no—
261C24—381no—
262C24—382no—
263C24—382no—
264C24—762no—
265C24—762no—
266C24C2×C4×D1911yescharacteristic
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—22no—
272C22×C4—22no—
273C22×C4—42no—
274C22×C4—42no—
275C22×C4—192no—
276C22×C4—192no—
277C22×C4—192no—
278C22×C4—381no—
279C22×C4—381no—
280C22×C4—381no—
281C22×C4—382no—
282C22×C4—382no—
283C22×C4—381no—
284C22×C4—381no—
285C22×C4—381no—
286C22×C4—762no—
287C22×C4—762no—
288C22×C4(C2×D19)⋊C412yes—
289C22×C4(C2×D19)⋊C412yes—
290C22×C4C2×D7611yescharacteristic
291C22×C4D4×D1912yes—
292C22×C4D4×D1912yes—
293C22×C4C2×C22⋊D1911yescharacteristic
294C2×C8—44no—
295C2×C8—42no—
296C2×C8—764no—
297C2×C8—762no—
298C4⋊C4—388no—
299C4⋊C4—388no—
300C4⋊C4—384no—
301C4⋊C4—384no—
302C22⋊C4—388no—
303C22⋊C4—388no—
304C22⋊C4—384no—
305C22⋊C4—384no—
306C42—24no—
307C42—24no—
308C23—22no—
309C23—22no—
310C23—382no—
311C23—384no—
312C23—762no—
313C23—762no—
314C23—762no—
315C23—762no—
316C23—762no—
317C23—761no—
318C23—761no—
319C23—762no—
320C23—762no—
321C23—1524no—
322C23—1524no—
323C23C22⋊C4×D1911yescharacteristic
324C23C22⋊C4×D1911yescharacteristic
325C23#1059734712yes—
326C23#1059735312yes—
327C23C2×(C2×D19)⋊C411yescharacteristic
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—22no—
333C2×C4—22no—
334C2×C4—24no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—382no—
342C2×C4—382no—
343C2×C4—382no—
344C2×C4—384no—
345C2×C4—762no—
346C2×C4—762no—
347C2×C4—762no—
348C2×C4—761no—
349C2×C4—761no—
350C2×C4—762no—
351C2×C4—762no—
352C2×C4—762no—
353C2×C4—762no—
354C2×C4#1059732812yes—
355C2×C4#1059738312yes—
356C8—82no—
357C8—1522no—
358C22—24no—
359C22—24no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—762no—
365C22—762no—
366C22—762no—
367C22—1524no—
368C22—1524no—
369C22—1522no—
370C22—1522no—
371C22#1192639911yescharacteristic
372C22#1192650912yes—
373C22#1192650912yes—
374C22#1192651011yescharacteristic
375C22#1192651211yescharacteristic
376C22#1192651712yes—
377C22#1192652612yes—
378C4—22no—
379C4—22no—
380C4—42no—
381C4—42no—
382C4—762no—
383C4—762no—
384C4—762no—
385C2—22no—
386C2—22no—
387C2—1522no—
388C2#1456200212yes—
389C2#1456200512yes—
390C2#1456354611yescharacteristic
391C2#1456355211yescharacteristic
392C2#1456356111yescharacteristic
subgroupG/H
centerC23C2×(C2×D19)⋊C4
commutatorC24×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1817C2
socleC23×C19C2×C22⋊C4
prime radicalC24×D19C2×C4
cosocleC23×C4×C19C23
hypercenter#1817D19
hypocenterC19#8309
LCSG ▷ C24×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1817

Complements

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

NH ≅ G/Ntype
2. #14563703C2semidirect
3. C2×#11926269C2semidirect
5. C19×#1817C2semidirect
164. #1817D19semidirect
258. C19#8309semidirect

Maximal subgroups

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

subgroupindex
C22×#105973222
#145637032
C2×#119262692
C2×#119262672
C19×#18172
#830919