Finite Group Databasebeta

← #18080934

Subgroups — #18080934

Order 4864.

386 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14564595C211yesmaximal, characteristic
2#14564557C211yesmaximal, characteristic
3#14564396C211yesmaximal, characteristic
4#14563505C211yesmaximal, characteristic
5C2×#11926289C211yesmaximal, characteristic
6#14561469C211yesmaximal, characteristic
7C19×#1296C211yesmaximal, characteristic
8C2×#10597315C2211yescharacteristic
9C2×#10597265—21no—
10C2×C4⋊(C19⋊C8)C2211yescharacteristic
11C2×#10597273—21no—
12C2×#10597273—21no—
13C2×#10597272—21no—
14C2×C4×C19⋊C8C2211yescharacteristic
15C4×C4⋊Dic19C2211yescharacteristic
16#11926306—21no—
17#11926306—21no—
18#11926306—21no—
19#11926298—21no—
20#11926289C414yescomplemented
21C2×C19×C4⋊C8C2211yescharacteristic
22C2×C19×C4⋊C8C2211yescharacteristic
23C19×#384C2211yescharacteristic
24C22×Dic38—21no—
25C22×C8×C19—21no—
26C22×C8×C19—21no—
27C2×C4⋊C4×C19—21no—
28C2×C4⋊C4×C19—21no—
29C2×C4⋊C4×C19—21no—
30C2×C42×C19C2311yescharacteristic
31C2×C4⋊Dic19—21no—
32C2×C4⋊Dic19—21no—
33C2×C4⋊Dic19D411yescharacteristic
34C2×C4⋊Dic19D411yescharacteristic
35C2×C4×Dic19—21no—
36C22×C19⋊C8—21no—
37C22×C19⋊C8D411yescharacteristic
38C22×C19⋊C8D411yescharacteristic
39#10597315—21no—
40#10597315—21no—
41#10597315—21no—
42#10597315C2×C412yes—
43C19×C4⋊C8—21no—
44C19×C4⋊C8—21no—
45C19×C4⋊C8—21no—
46C19×C4⋊C8C2×C412yes—
47C19⋊#95—21no—
48#10597273—42no—
49#10597273—42no—
50#10597272—42no—
51#10597265—42no—
52C4⋊(C19⋊C8)—21no—
53C4⋊(C19⋊C8)C2×C412yes—
54C4×C19⋊C8—21no—
55C4×C19⋊C8—21no—
56C22×C4×C19—41no—
57C22×C4×C19C2×D411yescharacteristic
58C22×C4×C19C2×D411yescharacteristic
59C22×C4×C19#4111yescharacteristic
60C22×Dic19—21no—
61C22×Dic19—21no—
62C22×Dic19—41no—
63C2×Dic38—22no—
64C2×Dic38—41no—
65C2×Dic38—41no—
66C2×Dic38—41no—
67C2×Dic38—41no—
68C2×Dic38—41no—
69C2×C8×C19—22no—
70C2×C8×C19—41no—
71C2×C8×C19—41no—
72C2×C8×C19—41no—
73C2×C8×C19—41no—
74C2×C8×C19—41no—
75C4⋊C4×C19—41no—
76C4⋊C4×C19—41no—
77C4⋊C4×C19—41no—
78C4⋊C4×C19—41no—
79C4⋊C4×C19—81no—
80C42×C19C22×C411yescharacteristic
81C42×C19#4111yescharacteristic
82C42×C19#4111yescharacteristic
83C42×C19#4111yescharacteristic
84C4⋊Dic19—22no—
85C4⋊Dic19—22no—
86C4⋊Dic19—21no—
87C4⋊Dic19—21no—
88C4⋊Dic19—21no—
89C4⋊Dic19—21no—
90C4⋊Dic19—41no—
91C4⋊Dic19—41no—
92C4×Dic19—41no—
93C4×Dic19—41no—
94C2×C19⋊C8—21no—
95C2×C19⋊C8—21no—
96C2×C19⋊C8—22no—
97C2×C19⋊C8—21no—
98C2×C19⋊C8—21no—
99C2×C19⋊C8—21no—
100C2×C19⋊C8—41no—
101C2×C19⋊C8—41no—
102C2×C19⋊C8SD1612yes—
103#9573—191nomaximal, Sylow
104C23×C19#12111yescharacteristic
105C2×C4×C19—21no—
106C2×C4×C19—21no—
107C2×C4×C19—81no—
108C2×C4×C19—81no—
109C2×C4×C19—81no—
110C2×C4×C19#11711yescharacteristic
111C2×C4×C19C4×D411yescharacteristic
112C2×C4×C19C4×D411yescharacteristic
113C2×C4×C19#12311yescharacteristic
114C2×C4×C19#12411yescharacteristic
115C2×C4×C19#12611yescharacteristic
116C2×C4×C19C2×SD1611yescharacteristic
117C2×C4×C19#13511yescharacteristic
118C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
119C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
120C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
121C2×C4×C19#13711yescharacteristic
122C2×C4×C19#13711yescharacteristic
123C2×C4×C19#13711yescharacteristic
124C2×Dic19—42no—
125C2×Dic19—41no—
126C2×Dic19—41no—
127C2×Dic19—41no—
128C2×Dic19—41no—
129C2×Dic19—41no—
130C2×Dic19—41no—
131C2×Dic19—81no—
132C2×Dic19—81no—
133Dic38—42no—
134Dic38—42no—
135Dic38—81no—
136Dic38—81no—
137C8×C19—42no—
138C8×C19—81no—
139C19⋊C8—22no—
140C19⋊C8—42no—
141C19⋊C8—41no—
142#1990—191no—
143#1981—191no—
144#1948—191no—
145#1770—191no—
146C2×#332—191no—
147#1296D1911yescharacteristic
148#1277—191no—
149C22×C19#38811yescharacteristic
150C22×C19#46111yescharacteristic
151C22×C19#46411yescharacteristic
152C22×C19#46811yescharacteristic
153C22×C19#46911yescharacteristic
154C22×C19#47111yescharacteristic
155C22×C19#47311yescharacteristic
156C4×C19—21no—
157C4×C19—21no—
158C4×C19—161no—
159C4×C19C4×SD1611yescharacteristic
160C4×C19#44011yescharacteristic
161C4×C19#44111yescharacteristic
162C4×C19#44211yescharacteristic
163C4×C19#48311yescharacteristic
164C4×C19#48511yescharacteristic
165C4×C19#48911yescharacteristic
166C4×C19#49011yescharacteristic
167Dic19—82no—
168Dic19—81no—
169Dic19—81no—
170C2×C4⋊Q8—191no—
171C2×#106—381no—
172C2×C4⋊C8—191no—
173C2×C4⋊C8C2×D1911yescharacteristic
174C2×C4⋊C8C2×D1911yescharacteristic
175C2×#103—381no—
176C2×#103—381no—
177C2×#97—381no—
178C2×C4×C8—191no—
179#384C2×D1911yescharacteristic
180C4×C4⋊C4—191no—
181#340—381no—
182#340—381no—
183#340—381no—
184#336—381no—
185#332—194no—
186C2×C19#169111yescharacteristic
187C2×C19#169311yescharacteristic
188C2×C19#170011yescharacteristic
189C2×C19#170211yescharacteristic
190C2×C19#192711yescharacteristic
191C2×C19#193011yescharacteristic
192C2×C19#193611yescharacteristic
193C22×Q8—381no—
194C22×C8—21no—
195C22×C8—21no—
196C22×C8—191no—
197C22×C8—191no—
198C22×C8—381no—
199C4⋊Q8—192no—
200C4⋊Q8—381no—
201C4⋊Q8—381no—
202C4⋊Q8—381no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—191no—
207C2×C4⋊C4—191no—
208C2×C4⋊C4—381no—
209C2×C4⋊C4—381no—
210C2×C42—381no—
211C2×C42C22×D1911yescharacteristic
212#106—762no—
213C4⋊C8—21no—
214C4⋊C8—21no—
215C4⋊C8—21no—
216C4⋊C8—192no—
217C4⋊C8—381no—
218C4⋊C8C4×D1912yes—
219#103—762no—
220#103—762no—
221#97—762no—
222C4×C8—381no—
223C4×C8—381no—
224#95—381no—
225C19#957311yescharacteristic, complemented, Sylow
226C2×Q8—382no—
227C2×Q8—761no—
228C2×Q8—761no—
229C2×Q8—761no—
230C2×Q8—761no—
231C2×Q8—761no—
232C22×C4—41no—
233C22×C4—381no—
234C22×C4—381no—
235C22×C4—761no—
236C22×C4#6454111yescharacteristic
237C22×C4D4×D1911yescharacteristic
238C22×C4D4×D1911yescharacteristic
239C2×C8—22no—
240C2×C8—41no—
241C2×C8—41no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—41no—
245C2×C8—192no—
246C2×C8—381no—
247C2×C8—381no—
248C2×C8—382no—
249C2×C8—381no—
250C2×C8—381no—
251C2×C8—381no—
252C2×C8—761no—
253C2×C8—761no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—81no—
259C4⋊C4—382no—
260C4⋊C4—382no—
261C4⋊C4—381no—
262C4⋊C4—381no—
263C4⋊C4—381no—
264C4⋊C4—381no—
265C4⋊C4—761no—
266C4⋊C4—761no—
267C42—761no—
268C42—761no—
269C42C2×C4×D1911yescharacteristic
270C42#6454111yescharacteristic
271C42#6454311yescharacteristic
272C42#6454511yescharacteristic
273C23#1059733011yescharacteristic
274Q8—762no—
275Q8—762no—
276Q8—1521no—
277Q8—1521no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—81no—
281C2×C4—81no—
282C2×C4—81no—
283C2×C4—761no—
284C2×C4—761no—
285C2×C4—761no—
286C2×C4—761no—
287C2×C4—762no—
288C2×C4—761no—
289C2×C4—761no—
290C2×C4—1521no—
291C2×C4—1521no—
292C2×C4#1059731811yescharacteristic
293C2×C4(C22⋊D19)⋊C411yescharacteristic
294C2×C4#1059733111yescharacteristic
295C2×C4#1059733911yescharacteristic
296C2×C4#1059734011yescharacteristic
297C2×C4#1059734411yescharacteristic
298C2×C4#1059735711yescharacteristic
299C2×C4#1059735811yescharacteristic
300C2×C4SD16×D1911yescharacteristic
301C2×C4#1059736011yescharacteristic
302C2×C4#1059736011yescharacteristic
303C2×C4#1059736111yescharacteristic
304C2×C4#1059736411yescharacteristic
305C2×C4#1059736411yescharacteristic
306C8—42no—
307C8—81no—
308C8—382no—
309C8—761no—
310C8—762no—
311C22#1192643311yescharacteristic
312C22#1192674811yescharacteristic
313C22#1192676511yescharacteristic
314C22#1192679311yescharacteristic
315C22#1192679611yescharacteristic
316C22#1192680611yescharacteristic
317C22#1192681811yescharacteristic
318C4—21no—
319C4—21no—
320C4—161no—
321C4—1521no—
322C4—1521no—
323C4—1522no—
324C4#1192663511yescharacteristic
325C4#1192664311yescharacteristic
326C4#1192664811yescharacteristic
327C4#1192665511yescharacteristic
328C4#1192687611yescharacteristic
329C4#1192688711yescharacteristic
330C4#1192690511yescharacteristic
331C4#1192690711yescharacteristic
332C2#1456313711yescharacteristic
333C2#1456314711yescharacteristic
334C2#1456318811yescharacteristic
335C2#1456320211yescharacteristic
336C2#1456426711yescharacteristic
337C2#1456428811yescharacteristic
338C2#1456433011yescharacteristic
subgroupG/H
centerC23#10597330
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1296C2
socle, prime radicalC23×C19#121
cosocleC2×C42×C19C23
hypercenter#1296D19
hypocenterC19#9573
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
20. #11926289C4semidirect
225. C19#9573semidirect

Maximal subgroups

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

subgroupindex
#145645952
#145645572
#145643962
#145635052
C2×#119262892
#145614692
C19×#12962
#957319