Finite Group Databasebeta

← #18078815

Subgroups — #18078815

Order 4864.

550 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 550 conjugacy classes of subgroups — too many to draw. Only its 111 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#14573639C211yesmaximal, characteristic
2#14566096C211yesmaximal, characteristic
3#14564613C211yesmaximal, characteristic, complemented
4#14562061C211yesmaximal, characteristic
5#14561538C211yesmaximal, characteristic, complemented
6#14561467C211yesmaximal, characteristic, complemented
7C19×#1503C211yesmaximal, characteristic, complemented
8C2×C4×D76C2211yescharacteristic
9C2×#10597318—21no—
10#11926872—21no—
11#11926831C412yescomplemented
12#11926746C412yescomplemented
13#11926694—21no—
14C4×#64527—22no—
15#11926597C2211yescharacteristic
16#11926568C2211yescharacteristic
17#11926445—21no—
18#11926440—21no—
19#11926433—22no—
20C4×(C2×D19)⋊C4—21no—
21C42×Dic19C2211yescharacteristic
22#11926303—21no—
23#11926303—21no—
24#11926273—22no—
25C19×#533C2211yescharacteristic
26C19×#431C2211yescharacteristic
27C4×C4⋊C4×C19C2211yescharacteristic
28C19×#328—22no—
29C22×D76D411yescharacteristic
30C22×C4×D19—21no—
31C19×C4⋊Q8C2×C411yescharacteristic
32C19×C4⋊Q8C2×C411yescharacteristic
33C19×#125—21no—
34C19×C22⋊Q8—21no—
35C19×C22⋊Q8—21no—
36C4×Q8×C19—21no—
37C4×Q8×C19—21no—
38C19×#117—21no—
39C2×C4⋊C4×C19—21no—
40C2×C42×C19—21no—
41C2×C42×C19C2311yescharacteristic
42C2×#64527—22no—
43C2×(C2×D19)⋊C4—21no—
44C2×(C2×D19)⋊C4—22no—
45C2×(C2×D19)⋊C4—22no—
46C2×C4⋊Dic19D411yescharacteristic
47C2×Dic19⋊C4—22no—
48C2×C4×Dic19—21no—
49C2×C4×Dic19—21no—
50C2×C4×Dic19D411yescharacteristic
51C2×C4×Dic19D411yescharacteristic
52C2×#64520—21no—
53C4×D76—21no—
54C4×D76—21no—
55C4×D76C2×C412yes—
56C4×D76D412yes—
57#10597318—42no—
58#10597318—42no—
59C19×C4⋊C8—21no—
60C19×C22⋊C8—21no—
61C4×C8×C19—21no—
62C19×#95D412yes—
63#10597292—22no—
64C19⋊#95—22no—
65C22⋊(C19⋊C8)—21no—
66#10597266—22no—
67#10597265—22no—
68C4⋊(C19⋊C8)—21no—
69C4⋊(C19⋊C8)—21no—
70C4⋊(C19⋊C8)C2×C412yes—
71C4×C19⋊C8—21no—
72C23×D19—21no—
73C2×Q8×C19—21no—
74C2×Q8×C19—21no—
75C22×C4×C19—22no—
76C22×C4×C19C2×D411yescharacteristic
77C22×C4×C19C2×D411yescharacteristic
78C22×C4×C19C2×D411yescharacteristic
79C22×Dic19—21no—
80C22×Dic19—21no—
81C22×Dic19—21no—
82C2×D76—21no—
83C2×D76—42no—
84C2×D76C22⋊C412yes—
85C2×C4×D19—22no—
86C2×C4×D19—22no—
87C2×C4×D19—41no—
88C2×C4×D19—41no—
89C2×C4×D19—41no—
90C2×C4×D19—41no—
91C2×C8×C19—41no—
92C4⋊C4×C19—21no—
93C4⋊C4×C19—21no—
94C4⋊C4×C19—21no—
95C4⋊C4×C19—21no—
96C4⋊C4×C19—42no—
97C4⋊C4×C19—41no—
98C4⋊C4×C19—41no—
99C22⋊C4×C19—41no—
100C42×C19—41no—
101C42×C19—41no—
102C42×C19—41no—
103C42×C19C22×C411yescharacteristic
104C42×C19C2×D411yescharacteristic
105C42×C19#4111yescharacteristic
106C42×C19#4111yescharacteristic
107#64527—44no—
108(C2×D19)⋊C4—22no—
109(C2×D19)⋊C4—22no—
110(C2×D19)⋊C4—44no—
111(C2×D19)⋊C4—44no—
112C4⋊Dic19—21no—
113C4⋊Dic19C22⋊C412yes—
114Dic19⋊C4—44no—
115C4×Dic19—21no—
116C4×Dic19—21no—
117C4×Dic19—21no—
118C4×Dic19—42no—
119C4×Dic19—42no—
120C4×Dic19SD1612yescomplemented
121#64520—41no—
122#64520—41no—
123C2×C19⋊C8—22no—
124C2×C19⋊C8—41no—
125#9235—191nomaximal, Sylow
126C23×C19#12011yescharacteristic
127C22×D19—22no—
128C22×D19—42no—
129C22×D19—42no—
130C22×D19—41no—
131C22×D19—41no—
132Q8×C19—42no—
133Q8×C19—81no—
134C2×C4×C19—22no—
135C2×C4×C19—41no—
136C2×C4×C19—42no—
137C2×C4×C19—42no—
138C2×C4×C19—41no—
139C2×C4×C19—41no—
140C2×C4×C19—42no—
141C2×C4×C19C2×C22⋊C411yescharacteristic
142C2×C4×C19C4×D411yescharacteristic
143C2×C4×C19C4×D411yescharacteristic
144C2×C4×C19#12111yescharacteristic
145C2×C4×C19#12111yescharacteristic
146C2×C4×C19#12311yescharacteristic
147C2×C4×C19C2×SD1611yescharacteristic
148C2×C4×C19#13511yescharacteristic
149C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
150C2×C4×C19#13711yescharacteristic
151C2×Dic19—22no—
152C2×Dic19—22no—
153C2×Dic19—22no—
154C2×Dic19—41no—
155C2×Dic19—41no—
156C2×Dic19—41no—
157C2×Dic19—41no—
158C2×Dic19—41no—
159C2×Dic19—41no—
160D76—22no—
161D76—22no—
162D76—42no—
163C4×D19—42no—
164C4×D19—42no—
165C4×D19—42no—
166C4×D19—42no—
167C8×C19—81no—
168C19⋊C8—42no—
169C19⋊C8—81no—
170#3101—191no—
171#2293—191no—
172#1994—191no—
173#1503D1911yescharacteristic, complemented
174#1486—191no—
175#1303—191no—
176#1276—191no—
177C22×C19—21no—
178C22×C19—21no—
179C22×C19#38611yescharacteristic
180C22×C19#45011yescharacteristic
181C22×C19#45211yescharacteristic
182C2×D19—42no—
183C2×D19—42no—
184C2×D19—42no—
185C2×D19—82no—
186C2×D19—82no—
187C4×C19—21no—
188C4×C19—21no—
189C4×C19—21no—
190C4×C19—82no—
191C4×C19—81no—
192C4×C19—81no—
193C4×C19#42112yes—
194C4×C19C4×SD1611yescharacteristic
195C4×C19#44011yescharacteristic
196C4×C19#46111yescharacteristic
197C4×C19#46311yescharacteristic
198Dic19—42no—
199Dic19—42no—
200Dic19—42no—
201#533C2×D1911yescharacteristic
202C2×C4×D4—191no—
203C2×#117—381no—
204#483—381no—
205#476—192no—
206#461—192no—
207#450—381no—
208C4×SD16—382no—
209#431—191no—
210#431C2×D1911yescharacteristic
211#423—191no—
212#390—381no—
213#389—381no—
214#388—382no—
215C4×C4⋊C4C2×D1911yescharacteristic
216C4×C22⋊C4—381no—
217C43—191no—
218#339—381no—
219#339—381no—
220#328—22no—
221D4⋊C8—382no—
222C2×C19—21no—
223C2×C19—21no—
224C2×C19#187711yescharacteristic
225C2×C19#189711yescharacteristic
226C2×C19#190611yescharacteristic
227D19—82no—
228C22×D4—191no—
229C23×C4—381no—
230C2×SD16—382no—
231C2×M16—381no—
232C4⋊Q8C4×D1911yescharacteristic
233C4⋊Q8C4×D1911yescharacteristic
234#125—21no—
235C22⋊Q8—21no—
236C22⋊Q8—21no—
237C4×Q8—21no—
238C4×Q8—21no—
239C4×D4—192no—
240C4×D4—192no—
241C4×D4—381no—
242C4×D4—381no—
243#117—21no—
244#117—762no—
245#117—762no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—191no—
248C2×C4⋊C4—382no—
249C2×C22⋊C4—381no—
250C2×C22⋊C4—382no—
251C2×C22⋊C4—382no—
252C2×C42—21no—
253C2×C42—191no—
254C2×C42—191no—
255C2×C42—381no—
256C2×C42—381no—
257C2×C42C22×D1911yescharacteristic
258#106—382no—
259C4⋊C8—21no—
260C4⋊C8—192no—
261C4⋊C8—381no—
262C4⋊C8—381no—
263#103—382no—
264#102—382no—
265C22⋊C8—21no—
266C22⋊C8—381no—
267C4×C8—21no—
268C4×C8—381no—
269#95—382no—
270#95C22⋊D1912yes—
271C19#923511yescharacteristic, complemented, Sylow
272C24—381no—
273C2×Q8—21no—
274C2×Q8—21no—
275C2×D4—192no—
276C2×D4—381no—
277C2×D4—762no—
278C22×C4—22no—
279C22×C4—381no—
280C22×C4—381no—
281C22×C4—381no—
282C22×C4—382no—
283C22×C4—382no—
284C22×C4—761no—
285C22×C4—761no—
286C22×C4—761no—
287C22×C4—761no—
288C22×C4D4×D1911yescharacteristic
289C22×C4D4×D1911yescharacteristic
290C22×C4C2×C22⋊D1911yescharacteristic
291SD16—764no—
292M16—761no—
293M16—761no—
294C2×C8—41no—
295C2×C8—382no—
296C2×C8—761no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—42no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—192no—
305C4⋊C4—381no—
306C4⋊C4—764no—
307C22⋊C4—41no—
308C22⋊C4—382no—
309C22⋊C4—382no—
310C22⋊C4—764no—
311C22⋊C4—764no—
312C42—41no—
313C42—41no—
314C42—41no—
315C42—192no—
316C42—381no—
317C42—381no—
318C42—381no—
319C42—762no—
320C42—762no—
321C42C2×C4×D1911yescharacteristic
322C42#6454111yescharacteristic
323C42D4×D1911yescharacteristic
324C42#6454311yescharacteristic
325C23—382no—
326C23—762no—
327C23—762no—
328C23—761no—
329C23—761no—
330C23#1059738311yescharacteristic
331Q8—42no—
332Q8—81no—
333D4—382no—
334D4—382no—
335D4—762no—
336C2×C4—22no—
337C2×C4—41no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—42no—
343C2×C4—382no—
344C2×C4—382no—
345C2×C4—382no—
346C2×C4—761no—
347C2×C4—761no—
348C2×C4—761no—
349C2×C4—761no—
350C2×C4—761no—
351C2×C4—761no—
352C2×C4—762no—
353C2×C4—762no—
354C2×C4—762no—
355C2×C4—762no—
356C2×C4C22⋊C4×D1911yescharacteristic
357C2×C4(C22⋊D19)⋊C411yescharacteristic
358C2×C4#1059732911yescharacteristic
359C2×C4#1059733011yescharacteristic
360C2×C4SD16×D1911yescharacteristic
361C2×C4#1059736011yescharacteristic
362C2×C4#1059736411yescharacteristic
363C2×C4#1059736511yescharacteristic
364C2×C4C4×C22⋊D1911yescharacteristic
365C2×C4#1059738411yescharacteristic
366C8—81no—
367C8—762no—
368C8—1521no—
369C22—21no—
370C22—21no—
371C22—762no—
372C22—762no—
373C22—762no—
374C22—1522no—
375C22—1522no—
376C22#1192642011yescharacteristic
377C22#1192669311yescharacteristic
378C22#1192670511yescharacteristic
379C4—21no—
380C4—21no—
381C4—21no—
382C4—82no—
383C4—81no—
384C4—81no—
385C4—762no—
386C4—762no—
387C4—762no—
388C4#1192655912yes—
389C4#1192662911yescharacteristic
390C4#1192664711yescharacteristic
391C4#1192674811yescharacteristic
392C4#1192676211yescharacteristic
393C2—21no—
394C2—21no—
395C2—1522no—
396C2#1456396611yescharacteristic
397C2#1456408011yescharacteristic
398C2#1456413311yescharacteristic
subgroupG/H
centerC2×C4#10597330
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1503C2
socleC22×C19#386
prime radicalC22×D76D4
cosocleC2×C42×C19C23
hypercenter#1503D19
hypocenterC19#9235
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1503

Complements

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

NH ≅ G/Ntype
3. #14564613C2semidirect
5. #14561538C2semidirect
6. #14561467C2semidirect
7. C19×#1503C2semidirect
11. #11926831C4semidirect
12. #11926746C4semidirect
120. C4×Dic19SD16semidirect
173. #1503D19semidirect
271. C19#9235semidirect

Maximal subgroups

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

subgroupindex
#145736392
#145660962
#145646132
#145620612
#145615382
#145614672
C19×#15032
#923519