Finite Group Databasebeta

← #18073462

Subgroups — #18073462

Order 4864.

528 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
1C4×#10597321C211yesmaximal, characteristic
2#14563384C211yesmaximal, characteristic, complemented
3C2×#11926283C212yesmaximal
4#14561517C212yesmaximal, complemented
5C19×#1745C211yesmaximal, characteristic, complemented
6C2×#10597321C2211yescharacteristic
7C2×C4×Dic38C411yescharacteristic
8C2×C4×D76C411yescharacteristic
9C2×#10597260C2212yes—
10#11926450C411yescharacteristic
11#11926446C411yescharacteristic
12#11926435—21no—
13#11926435—21no—
14#11926410C2211yescharacteristic
15C4×(C2×D19)⋊C4—21no—
16C4×(C2×D19)⋊C4—21no—
17#11926299—21no—
18#11926299—21no—
19#11926283C418yescomplemented
20C2×C19×#97C2212yes—
21C43×C19C2211yescharacteristic
22C19×#336—21no—
23C19×#336—21no—
24C22×D76C2×C411yescharacteristic
25C22×C4×D19—21no—
26C22×Dic38C2×C411yescharacteristic
27C22×C8×C19—22no—
28C2×C42×C19C2×C411yescharacteristic
29C2×C42×C19C2×C411yescharacteristic
30C2×C42×C19D411yescharacteristic
31C2×C42×C19D411yescharacteristic
32C2×C42×C19D411yescharacteristic
33C2×C42×C19D411yescharacteristic
34C2×C42×C19C2311yescharacteristic
35C2×(C2×D19)⋊C4—21no—
36C2×(C2×D19)⋊C4—21no—
37C2×(C2×D19)⋊C4—21no—
38C2×(C2×D19)⋊C4—21no—
39C2×(C2×D19)⋊C4—21no—
40C2×C4⋊Dic19C2×C411yescharacteristic
41C2×C4⋊Dic19C2×C411yescharacteristic
42C2×Dic19⋊C4—21no—
43C2×C4×Dic19—21no—
44C22×C19⋊C8—22no—
45#10597321—22no—
46#10597321C2×C414yes—
47C4×D76—42no—
48C4×Dic38—42no—
49C19×#97—22no—
50C19×#97C2×C414yescomplemented
51C19⋊#95—21no—
52C19⋊#95—21no—
53C19⋊#95—21no—
54C19⋊#95—21no—
55#10597260—22no—
56#10597260C2×C414yescomplemented
57C23×D19—21no—
58C22×C4×C19C22⋊C411yescharacteristic
59C22×C4×C19C22⋊C411yescharacteristic
60C22×C4×C19C22⋊C411yescharacteristic
61C22×C4×C19C22⋊C411yescharacteristic
62C22×C4×C19C22×C411yescharacteristic
63C22×C4×C19C2×D411yescharacteristic
64C22×C4×C19C2×D411yescharacteristic
65C22×Dic19—21no—
66C22×Dic19—21no—
67C22×Dic19—21no—
68C2×D76—21no—
69C2×D76—41no—
70C2×D76—41no—
71C2×D76C4212yes—
72C2×C4×D19—42no—
73C2×C4×D19—42no—
74C2×C4×D19—42no—
75C2×Dic38—21no—
76C2×Dic38—41no—
77C2×Dic38—41no—
78C2×Dic38C4212yes—
79C2×C8×C19—24no—
80C2×C8×C19—42no—
81C2×C8×C19—42no—
82C42×C19—22no—
83C42×C19—41no—
84C42×C19—41no—
85C42×C19—41no—
86C42×C19—41no—
87C42×C19—41no—
88C42×C19C22×C412yes—
89C42×C19#4112yes—
90(C2×D19)⋊C4—24no—
91(C2×D19)⋊C4—24no—
92(C2×D19)⋊C4—42no—
93(C2×D19)⋊C4—42no—
94(C2×D19)⋊C4—42no—
95C4⋊Dic19—41no—
96C4⋊Dic19—41no—
97Dic19⋊C4—42no—
98C4×Dic19—42no—
99C2×C19⋊C8—24no—
100C2×C19⋊C8—42no—
101C2×C19⋊C8—42no—
102#8224—191nomaximal, Sylow
103C23×C19C2×C22⋊C411yescharacteristic
104C22×D19—22no—
105C22×D19—41no—
106C22×D19—41no—
107C22×D19—41no—
108C22×D19—41no—
109C22×D19—41no—
110C22×D19—41no—
111C2×C4×C19—21no—
112C2×C4×C19—21no—
113C2×C4×C19—21no—
114C2×C4×C19—21no—
115C2×C4×C19—21no—
116C2×C4×C19—21no—
117C2×C4×C19—21no—
118C2×C4×C19—21no—
119C2×C4×C19—21no—
120C2×C4×C19—21no—
121C2×C4×C19—21no—
122C2×C4×C19—21no—
123C2×C4×C19—21no—
124C2×C4×C19—21no—
125C2×C4×C19—21no—
126C2×C4×C19—21no—
127C2×C4×C19—21no—
128C2×C4×C19#10012yes—
129C2×C4×C19C2×C4211yescharacteristic
130C2×C4×C19#11711yescharacteristic
131C2×C4×C19C4×D412yes—
132C2×C4×C19C4×D412yes—
133C2×Dic19—22no—
134C2×Dic19—41no—
135C2×Dic19—41no—
136C2×Dic19—41no—
137C2×Dic19—41no—
138C2×Dic19—41no—
139C2×Dic19—41no—
140C2×Dic19—41no—
141C2×Dic19—41no—
142D76—42no—
143D76—42no—
144C4×D19—84no—
145Dic38—42no—
146Dic38—42no—
147C8×C19—44no—
148C19⋊C8—44no—
149C4×#124—191no—
150#1745—191no—
151#1745D1911yescharacteristic, complemented
152C2×#329—192no—
153#1295—192no—
154C22×C19C4×C22⋊C411yescharacteristic
155C22×C19C2×#10011yescharacteristic
156C22×C19#41311yescharacteristic
157C22×C19#42111yescharacteristic
158C22×C19#42111yescharacteristic
159C22×C19#42111yescharacteristic
160C22×C19#42111yescharacteristic
161C2×D19—42no—
162C2×D19—42no—
163C2×D19—42no—
164C2×D19—81no—
165C2×D19—81no—
166C2×D19—81no—
167C2×D19—81no—
168C4×C19—21no—
169C4×C19—21no—
170C4×C19—22no—
171C4×C19—22no—
172C4×C19—22no—
173C4×C19—41no—
174C4×C19—41no—
175C4×C19—41no—
176Dic19—42no—
177Dic19—81no—
178Dic19—81no—
179C2×#124—191no—
180C2×C4×Q8—191no—
181C2×C4×D4—191no—
182C2×#97—192no—
183C2×#97C2×D1912yes—
184#391—191no—
185#390—191no—
186#388—381no—
187#388—381no—
188#382—191no—
189C4×C22⋊C4—381no—
190C4×C22⋊C4—381no—
191C43C2×D1911yescharacteristic
192#336—21no—
193#336—21no—
194#336—381no—
195#336—381no—
196#329—198no—
197C2×C19#153311yescharacteristic
198C2×C19#153511yescharacteristic
199C2×C19#153511yescharacteristic
200C2×C19#153611yescharacteristic
201C2×C19C4×#10011yescharacteristic
202C2×C19#175911yescharacteristic
203C2×C19#175911yescharacteristic
204D19—82no—
205C22×Q8—191no—
206C22×D4—191no—
207C23×C4—381no—
208C22×C8—22no—
209C22×C8—382no—
210#124—194no—
211#124—382no—
212C4×Q8—762no—
213C4×D4—762no—
214C2×C4⋊C4—191no—
215C2×C4⋊C4—191no—
216C2×C4⋊C4—381no—
217C2×C22⋊C4—381no—
218C2×C22⋊C4—381no—
219C2×C22⋊C4—381no—
220C2×C22⋊C4—381no—
221C2×C22⋊C4—381no—
222C2×C42—381no—
223C2×C42C4×D1911yescharacteristic
224C2×C42C4×D1911yescharacteristic
225C2×C42D7611yescharacteristic
226C2×C42D7611yescharacteristic
227C2×C42C22⋊D1911yescharacteristic
228C2×C42C22⋊D1911yescharacteristic
229C2×C42C22×D1911yescharacteristic
230#97—22no—
231#97—194no—
232#97—382no—
233#97C4×D1914yescomplemented
234#95—381no—
235#95—381no—
236#95—381no—
237#95—381no—
238C19#822411yescharacteristic, complemented, Sylow
239C24—381no—
240C2×Q8—192no—
241C2×Q8—381no—
242C2×Q8—761no—
243C2×Q8—761no—
244C2×D4—192no—
245C2×D4—381no—
246C2×D4—761no—
247C2×D4—761no—
248C22×C4—381no—
249C22×C4—381no—
250C22×C4—381no—
251C22×C4—762no—
252C22×C4—762no—
253C22×C4—762no—
254C22×C4(C2×D19)⋊C411yescharacteristic
255C22×C4(C2×D19)⋊C411yescharacteristic
256C22×C4(C2×D19)⋊C411yescharacteristic
257C22×C4(C2×D19)⋊C411yescharacteristic
258C22×C4C2×C4×D1911yescharacteristic
259C22×C4C2×D7611yescharacteristic
260C22×C4C2×C22⋊D1911yescharacteristic
261C2×C8—24no—
262C2×C8—42no—
263C2×C8—42no—
264C2×C8—384no—
265C2×C8—762no—
266C2×C8—762no—
267C4⋊C4—761no—
268C4⋊C4—761no—
269C4⋊C4—762no—
270C22⋊C4—384no—
271C22⋊C4—384no—
272C22⋊C4—762no—
273C22⋊C4—762no—
274C22⋊C4—762no—
275C42—22no—
276C42—41no—
277C42—41no—
278C42—41no—
279C42—41no—
280C42—41no—
281C42—762no—
282C42C2×C4×D1912yes—
283C42#6454112yes—
284C23—382no—
285C23—761no—
286C23—761no—
287C23—761no—
288C23—761no—
289C23—761no—
290C23—761no—
291C23C2×(C2×D19)⋊C411yescharacteristic
292Q8—762no—
293Q8—762no—
294D4—762no—
295D4—762no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—382no—
314C2×C4—761no—
315C2×C4—761no—
316C2×C4—761no—
317C2×C4—761no—
318C2×C4—761no—
319C2×C4—761no—
320C2×C4—761no—
321C2×C4—761no—
322C2×C4—1524no—
323C2×C4#1059728012yes—
324C2×C4C42×D1911yescharacteristic
325C2×C4#1059731811yescharacteristic
326C2×C4C4×D7612yes—
327C2×C4C4×C22⋊D1912yes—
328C8—44no—
329C8—764no—
330C22—762no—
331C22—762no—
332C22—762no—
333C22—1521no—
334C22—1521no—
335C22—1521no—
336C22—1521no—
337C22C4×(C2×D19)⋊C411yescharacteristic
338C22C2×#1059728011yescharacteristic
339C22#1192652611yescharacteristic
340C22#1192656011yescharacteristic
341C22#1192656011yescharacteristic
342C22#1192656211yescharacteristic
343C22#1192656211yescharacteristic
344C4—21no—
345C4—21no—
346C4—22no—
347C4—22no—
348C4—22no—
349C4—41no—
350C4—41no—
351C4—41no—
352C4—762no—
353C4—1521no—
354C4—1521no—
355C2—1522no—
356C2#1456225811yescharacteristic
357C2#1456226411yescharacteristic
358C2#1456226711yescharacteristic
359C2#1456226911yescharacteristic
360C2C4×#1059728011yescharacteristic
361C2#1456344611yescharacteristic
362C2#1456344811yescharacteristic
subgroupG/H
centerC23C2×(C2×D19)⋊C4
commutatorC2×C4×C19C2×C42
FrattiniC2×C42C22×D19
FittingC19×#1745C2
socleC23×C19C2×C22⋊C4
prime radicalC22×D76C2×C4
cosocleC2×C42×C19C23
hypercenter#1745D19
hypocenterC19#8224
LCSG ▷ C2×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C43 ◁ #1745

Complements

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

NH ≅ G/Ntype
2. #14563384C2semidirect
4. #14561517C2semidirect
5. C19×#1745C2semidirect
19. #11926283C4semidirect
50. C19×#97C2×C4semidirect
56. #10597260C2×C4semidirect
151. #1745D19semidirect
233. #97C4×D19semidirect
238. C19#8224semidirect

Maximal subgroups

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

subgroupindex
C4×#105973212
#145633842
C2×#119262832
#145615172
C19×#17452
#822419