Finite Group Databasebeta

← #18078796

Subgroups — #18078796

Order 4864.

566 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14573675C211yesmaximal, characteristic
2C42×Dic38C211yesmaximal, characteristic
3#14564612C211yesmaximal, characteristic
4#14562135C211yesmaximal, characteristic
5#14562065C211yesmaximal, characteristic
6#14561537C211yesmaximal, characteristic
7C19×#1276C211yesmaximal, characteristic
8#11927101C2211yescharacteristic
9C2×C4×Dic38—21no—
10C2×C4×Dic38C2211yescharacteristic
11#11926880—21no—
12#11926840C412yescomplemented
13#11926755C412yescomplemented
14#11926702—21no—
15C4×Dic76—22no—
16#11926568C2211yescharacteristic
17C4×Dic19⋊C4—22no—
18C4×Dic19⋊C4—21no—
19C4×C4⋊Dic19—21no—
20C4×C4⋊Dic19C2211yescharacteristic
21C42×Dic19—21no—
22#11926304—21no—
23#11926304—21no—
24#11926282—22no—
25#11926276—22no—
26C19×#431C2211yescharacteristic
27C19×#431C2211yescharacteristic
28C43×C19C2211yescharacteristic
29C22×Dic38D411yescharacteristic
30C2×C42×C19—21no—
31C2×C42×C19—21no—
32C2×C42×C19D411yescharacteristic
33C2×C42×C19D411yescharacteristic
34C2×C42×C19C2311yescharacteristic
35#10597372—21no—
36C2×C4⋊Dic19—21no—
37C2×C4⋊Dic19D411yescharacteristic
38#10597370—21no—
39#10597370—21no—
40C2×Dic19⋊C4—22no—
41C2×Dic19⋊C4—21no—
42C2×C4×Dic19—22no—
43C2×C4×Dic19—21no—
44C2×C4×Dic19—22no—
45C2×C4×Dic19—21no—
46C2×#64520—21no—
47C2×Dic76—22no—
48#10597316—21no—
49#10597315C2×C411yescharacteristic
50#10597315C2×C411yescharacteristic
51C4×Dic38—28no—
52C4×Dic38—21no—
53C4×Dic38—21no—
54C4×Dic38—21no—
55C4×Dic38—21no—
56C4×Dic38C2×C412yes—
57C4×Dic38D412yes—
58C19×C4⋊C8—21no—
59C19×C4⋊C8C2×C412yes—
60C19×C22⋊C8—21no—
61C19×C22⋊C8—21no—
62C4×C8×C19—21no—
63C4×C8×C19—21no—
64C19⋊#95—22no—
65C19⋊#95D412yes—
66#10597275—22no—
67#10597273—22no—
68#10597273—22no—
69C4⋊(C19⋊C8)—21no—
70C4⋊(C19⋊C8)—21no—
71C22×C4×C19—21no—
72C22×C4×C19—21no—
73C22×C4×C19C2×D411yescharacteristic
74C22×C4×C19C2×D411yescharacteristic
75C22×C4×C19C2×D411yescharacteristic
76C22×Dic19—21no—
77C22×Dic19—21no—
78C22×Dic19—22no—
79C2×Dic38—21no—
80C2×Dic38—24no—
81C2×Dic38—21no—
82C2×Dic38—21no—
83C2×Dic38C22⋊C412yes—
84C2×C8×C19—22no—
85C2×C8×C19—41no—
86C42×C19—24no—
87C42×C19—21no—
88C42×C19—21no—
89C42×C19—21no—
90C42×C19—42no—
91C42×C19Q1612yescomplemented
92C42×C19C22×C411yescharacteristic
93C42×C19C2×D411yescharacteristic
94C42×C19#4111yescharacteristic
95C42×C19#4111yescharacteristic
96C22⋊Dic19—41no—
97C4⋊Dic19—24no—
98C4⋊Dic19—21no—
99C4⋊Dic19—21no—
100C4⋊Dic19—21no—
101C4⋊Dic19—21no—
102C4⋊Dic19—21no—
103C4⋊Dic19C22⋊C412yes—
104Dic19⋊C4—28no—
105Dic19⋊C4—22no—
106Dic19⋊C4—22no—
107Dic19⋊C4—41no—
108Dic19⋊C4—41no—
109C4×Dic19—28no—
110C4×Dic19—22no—
111C4×Dic19—22no—
112C4×Dic19—44no—
113C4×Dic19—41no—
114C4×Dic19—41no—
115C4×Dic19—41no—
116#64520—41no—
117#64520—41no—
118C2×C19⋊C8—41no—
119Dic76—44no—
120#9232—191nomaximal, Sylow
121C23×C19#12011yescharacteristic
122C2×C4×C19—22no—
123C2×C4×C19—22no—
124C2×C4×C19—22no—
125C2×C4×C19—22no—
126C2×C4×C19—22no—
127C2×C4×C19—41no—
128C2×C4×C19—41no—
129C2×C4×C19—41no—
130C2×C4×C19C2×C22⋊C411yescharacteristic
131C2×C4×C19C4×D411yescharacteristic
132C2×C4×C19C4×D411yescharacteristic
133C2×C4×C19#12111yescharacteristic
134C2×C4×C19#12111yescharacteristic
135C2×C4×C19#12311yescharacteristic
136C2×C4×C19C2×Q1611yescharacteristic
137C2×C4×C19#13511yescharacteristic
138C2×C4×C19#13711yescharacteristic
139C2×C4×C19#13711yescharacteristic
140C2×Dic19—24no—
141C2×Dic19—22no—
142C2×Dic19—24no—
143C2×Dic19—22no—
144C2×Dic19—42no—
145C2×Dic19—42no—
146C2×Dic19—42no—
147C2×Dic19—41no—
148C2×Dic19—41no—
149Dic38—24no—
150Dic38—22no—
151Dic38—42no—
152Dic38—81no—
153Dic38#10414yes—
154C8×C19—42no—
155C8×C19—81no—
156C19⋊C8—81no—
157#3104—191no—
158C42×Q8—191no—
159#1994—191no—
160#1503—191no—
161#1487—191no—
162#1303—191no—
163#1276D1911yescharacteristic
164C22×C19—21no—
165C22×C19—21no—
166C22×C19#38611yescharacteristic
167C22×C19#45111yescharacteristic
168C22×C19#45211yescharacteristic
169C4×C19—24no—
170C4×C19—21no—
171C4×C19—21no—
172C4×C19—21no—
173C4×C19—42no—
174C4×C19C2×#10412yes—
175C4×C19C4×Q1611yescharacteristic
176C4×C19#44111yescharacteristic
177C4×C19#46211yescharacteristic
178C4×C19#46411yescharacteristic
179Dic19—24no—
180Dic19—44no—
181Dic19—42no—
182Dic19—81no—
183Dic19—81no—
184#533—191no—
185C2×C4×Q8—191no—
186C2×C4×Q8—381no—
187#484—381no—
188#477—192no—
189#462—192no—
190#451—381no—
191C4×Q16—382no—
192#431C2×D1911yescharacteristic
193#431C2×D1911yescharacteristic
194#423—191no—
195C4×C4⋊C4—191no—
196C4×C4⋊C4—382no—
197C4×C4⋊C4—381no—
198C4×C4⋊C4—381no—
199C43—381no—
200C43C2×D1911yescharacteristic
201#339—381no—
202#339—381no—
203#328—382no—
204Q8⋊C8—382no—
205C2×C19—21no—
206C2×C19—21no—
207C2×C19#187811yescharacteristic
208C2×C19#189611yescharacteristic
209C2×C19#190611yescharacteristic
210C22×Q8—191no—
211C2×Q16—382no—
212C2×M16—381no—
213C4⋊Q8—191no—
214C4⋊Q8—191no—
215#125—381no—
216C22⋊Q8—381no—
217C22⋊Q8—381no—
218C4×Q8—192no—
219C4×Q8—192no—
220C4×Q8—388no—
221C4×Q8—381no—
222C4×Q8—381no—
223C4×Q8—381no—
224C4×Q8—381no—
225#117—381no—
226C2×C4⋊C4—191no—
227C2×C4⋊C4—382no—
228C2×C4⋊C4—381no—
229C2×C4⋊C4—381no—
230C2×C42—21no—
231C2×C42—21no—
232C2×C42—382no—
233C2×C42—381no—
234C2×C42—382no—
235C2×C42—381no—
236C2×C42D7611yescharacteristic
237C2×C42D7611yescharacteristic
238C2×C42C22×D1911yescharacteristic
239#107—382no—
240C4⋊C8—21no—
241C4⋊C8—381no—
242C4⋊C8—381no—
243C4⋊C8C4×D1912yes—
244#103—382no—
245#103—382no—
246C22⋊C8—21no—
247C22⋊C8—21no—
248C4×C8—21no—
249C4×C8—21no—
250#95—192no—
251#95—382no—
252C19#923211yescharacteristic, complemented, Sylow
253C2×Q8—192no—
254C2×Q8—384no—
255C2×Q8—381no—
256C2×Q8—381no—
257C2×Q8—381no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—381no—
261C22×C4—382no—
262C22×C4—381no—
263C22×C4C2×D7611yescharacteristic
264C22×C4D4×D1911yescharacteristic
265C22×C4D4×D1911yescharacteristic
266Q16—764no—
267M16—761no—
268M16—761no—
269C2×C8—22no—
270C2×C8—41no—
271C2×C8—761no—
272C4⋊C4—192no—
273C4⋊C4—388no—
274C4⋊C4—384no—
275C4⋊C4—382no—
276C4⋊C4—382no—
277C4⋊C4—381no—
278C4⋊C4—381no—
279C4⋊C4—381no—
280C4⋊C4—381no—
281C4⋊C4—381no—
282C4⋊C4—761no—
283C4⋊C4—761no—
284C22⋊C4—761no—
285C42—24no—
286C42—21no—
287C42—21no—
288C42—21no—
289C42—42no—
290C42—388no—
291C42—382no—
292C42—382no—
293C42—764no—
294C42—761no—
295C42—761no—
296C42—761no—
297C42Dic7612yescomplemented
298C42C2×C4×D1911yescharacteristic
299C42#6454111yescharacteristic
300C42D4×D1911yescharacteristic
301C42#6454511yescharacteristic
302C23#1059732811yescharacteristic
303Q8—194no—
304Q8—384no—
305Q8—382no—
306Q8—762no—
307Q8—1521no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—384no—
317C2×C4—382no—
318C2×C4—384no—
319C2×C4—382no—
320C2×C4—762no—
321C2×C4—762no—
322C2×C4—762no—
323C2×C4—761no—
324C2×C4—761no—
325C2×C4C4×D7611yescharacteristic
326C2×C4C22⋊C4×D1911yescharacteristic
327C2×C4#1059733011yescharacteristic
328C2×C4#1059733911yescharacteristic
329C2×C4#1059734011yescharacteristic
330C2×C4#1059734111yescharacteristic
331C2×C4#1059735011yescharacteristic
332C2×C4C2×Dic7611yescharacteristic
333C2×C4#1059735511yescharacteristic
334C2×C4#1059735511yescharacteristic
335C8—42no—
336C8—81no—
337C8—1521no—
338C22—21no—
339C22—21no—
340C22#1192642211yescharacteristic
341C22#1192670211yescharacteristic
342C22#1192670811yescharacteristic
343C4—24no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—42no—
348C4—384no—
349C4—764no—
350C4—762no—
351C4—1521no—
352C4—1521no—
353C4#104×D1912yes—
354C4C4×Dic7611yescharacteristic
355C4#1192665211yescharacteristic
356C4#1192675511yescharacteristic
357C4#1192676711yescharacteristic
358C2—21no—
359C2—21no—
360C2#1456397511yescharacteristic
361C2#1456407711yescharacteristic
362C2#1456413511yescharacteristic
subgroupG/H
centerC2×C4#10597341
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1276C2
socleC22×C19#386
prime radicalC23×C19#120
cosocleC2×C42×C19C23
hypercenter#1276D19
hypocenterC19#9232
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1276

Complements

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

NH ≅ G/Ntype
12. #11926840C4semidirect
13. #11926755C4semidirect
91. C42×C19Q16semidirect
252. C19#9232semidirect
297. C42Dic76semidirect

Maximal subgroups

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

subgroupindex
#145736752
C42×Dic382
#145646122
#145621352
#145620652
#145615372
C19×#12762
#923219