Finite Group Databasebeta

← #18081904

Subgroups — #18081904

Order 4864.

416 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14573960C211yesmaximal, characteristic
2#14563504C211yesmaximal, characteristic, complemented
3#14562381C211yesmaximal, characteristic, complemented
4#14562129C211yesmaximal, characteristic
5#14562038C211yesmaximal, characteristic, complemented
6#14562035C211yesmaximal, characteristic
7C19×#1503C211yesmaximal, characteristic, complemented
8#11927094C2211yescharacteristic
9#11926901—21no—
10#11926901—21no—
11#11926896C411yescharacteristic, complemented
12#11926896C411yescharacteristic, complemented
13#11926892C411yescharacteristic, complemented
14#11926892C411yescharacteristic, complemented
15#11926597C2211yescharacteristic
16C2×C4⋊(C19⋊C8)C2211yescharacteristic
17#11926538—21no—
18#11926538—21no—
19C2×#10597260—21no—
20C2×C4×C19⋊C8C2211yescharacteristic
21#11926299—21no—
22#11926296—21no—
23#11926294—21no—
24#11926277—22no—
25Q8⋊(C19⋊C8)—22no—
26#11926273—22no—
27C19×#533C2211yescharacteristic
28C19×#431C2211yescharacteristic
29C4×C4⋊C4×C19C2211yescharacteristic
30C19×#328—22no—
31C2×#64541—21no—
32C19×C4⋊Q8C2×C411yescharacteristic
33C19×C4⋊Q8C2×C411yescharacteristic
34C19×#125—21no—
35C19×C22⋊Q8—21no—
36C19×C22⋊Q8—21no—
37C4×Q8×C19—21no—
38C4×Q8×C19—21no—
39C19×#117—21no—
40C2×C4⋊C4×C19—21no—
41C2×C42×C19—21no—
42C2×C42×C19C2311yescharacteristic
43#10597376—21no—
44#10597376—21no—
45C22×C19⋊C8—21no—
46C22×C19⋊C8D411yescharacteristic
47C22×C19⋊C8D411yescharacteristic
48#10597321—21no—
49#10597320C2×C411yescharacteristic
50C4×D76—21no—
51C4×D76—21no—
52#10597315C2×C411yescharacteristic
53C19×C4⋊C8—21no—
54C19×C22⋊C8—21no—
55C4×C8×C19—21no—
56C19×#95D412yes—
57C22⋊(C19⋊C8)—21no—
58#10597267—21no—
59#10597267—21no—
60#10597267—21no—
61#10597267—21no—
62#10597266—21no—
63#10597266—21no—
64#10597266—21no—
65#10597266—21no—
66C4⋊(C19⋊C8)—21no—
67C4⋊(C19⋊C8)—21no—
68C4⋊(C19⋊C8)D412yes—
69#10597260—42no—
70C4×C19⋊C8—21no—
71C4×C19⋊C8C2×C411yescharacteristic
72C4×C19⋊C8C2×C411yescharacteristic
73C4×C19⋊C8D411yescharacteristic
74C4×C19⋊C8D411yescharacteristic
75C2×Q8×C19—21no—
76C2×Q8×C19—21no—
77C22×C4×C19—22no—
78C22×C4×C19C2×D411yescharacteristic
79C22×C4×C19C2×D411yescharacteristic
80C22×C4×C19#4111yescharacteristic
81C2×C22⋊D19—41no—
82#64541—41no—
83#64541—41no—
84#64541—41no—
85#64541—41no—
86C2×D76—21no—
87C2×D76—21no—
88C2×D76—21no—
89C2×C4×D19—41no—
90C2×Dic38—21no—
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×C19C2×D411yescharacteristic
106C42×C19#4111yescharacteristic
107(C2×D19)⋊C4—41no—
108(C2×D19)⋊C4—41no—
109C4⋊Dic19—21no—
110C4⋊Dic19—21no—
111C2×C19⋊C8—21no—
112C2×C19⋊C8—21no—
113C2×C19⋊C8—21no—
114C2×C19⋊C8—21no—
115C2×C19⋊C8—22no—
116C2×C19⋊C8—41no—
117C2×C19⋊C8—41no—
118C2×C19⋊C8—41no—
119C2×C19⋊C8C22⋊C411yescharacteristic
120C2×C19⋊C8C22⋊C411yescharacteristic
121C2×C19⋊C8C22⋊C411yescharacteristic
122C2×C19⋊C8C22⋊C411yescharacteristic
123#9754—191nomaximal, Sylow
124C23×C19#12111yescharacteristic
125C22×D19—41no—
126Q8×C19—42no—
127Q8×C19—81no—
128C2×C4×C19—22no—
129C2×C4×C19—41no—
130C2×C4×C19—42no—
131C2×C4×C19—42no—
132C2×C4×C19—41no—
133C2×C4×C19—41no—
134C2×C4×C19—42no—
135C2×C4×C19C2×C22⋊C411yescharacteristic
136C2×C4×C19C4×D411yescharacteristic
137C2×C4×C19C4×D411yescharacteristic
138C2×C4×C19#12111yescharacteristic
139C2×C4×C19#12411yescharacteristic
140C2×C4×C19#12711yescharacteristic
141C2×C4×C19#13511yescharacteristic
142C2×C4×C19#13511yescharacteristic
143C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
144C2×C4×C19#13711yescharacteristic
145C22⋊D19—81no—
146C22⋊D19—81no—
147C2×Dic19—41no—
148D76—41no—
149D76—41no—
150D76—42no—
151D76—81no—
152C4×D19—81no—
153C4×D19—81no—
154Dic38—41no—
155Dic38—41no—
156C8×C19—81no—
157C19⋊C8—21no—
158C19⋊C8—21no—
159C19⋊C8—21no—
160C19⋊C8—21no—
161C19⋊C8—42no—
162C19⋊C8—81no—
163#3131—191no—
164#1770—191no—
165#1564—191no—
166#1503D1911yescharacteristic, complemented
167#1502—191no—
168#1481—191no—
169#1480—191no—
170C22×C19—21no—
171C22×C19—21no—
172C22×C19#39011yescharacteristic
173C22×C19#46311yescharacteristic
174C22×C19#46411yescharacteristic
175C2×D19—81no—
176C2×D19—81no—
177C2×D19—81no—
178C4×C19—21no—
179C4×C19—21no—
180C4×C19—21no—
181C4×C19—82no—
182C4×C19—81no—
183C4×C19—81no—
184C4×C19#41611yescharacteristic
185C4×C19#41711yescharacteristic
186C4×C19#44412yes—
187C4×C19#46311yescharacteristic
188C4×C19#46411yescharacteristic
189Dic19—81no—
190#533C2×D1911yescharacteristic
191#532—191no—
192#488—381no—
193#488—381no—
194#487—191no—
195#487—191no—
196#486—191no—
197#486—191no—
198#431—191no—
199#431C2×D1911yescharacteristic
200C2×C4⋊C8—191no—
201#416—381no—
202#416—381no—
203C2×#97—381no—
204C2×C4×C8—191no—
205C4×C4⋊C4C2×D1911yescharacteristic
206#336—381no—
207#335—381no—
208#334—381no—
209#328—22no—
210#327—382no—
211Q8⋊C8—382no—
212D4⋊C8—382no—
213C2×C19—21no—
214C2×C19—21no—
215C2×C19#197511yescharacteristic
216C2×C19#197611yescharacteristic
217C2×C19#198311yescharacteristic
218D19—161no—
219C2×#41—381no—
220C22×C8—191no—
221C22×C8—191no—
222C22×C8—381no—
223C4⋊Q8—191no—
224C4⋊Q8C4×D1911yescharacteristic
225C4⋊Q8C4×D1911yescharacteristic
226#127—191no—
227#125—21no—
228#124—381no—
229C22⋊Q8—21no—
230C22⋊Q8—21no—
231#121—381no—
232#121—381no—
233C4×Q8—21no—
234C4×Q8—21no—
235C4×D4—381no—
236C4×D4—381no—
237#117—21no—
238C2×C4⋊C4—21no—
239C2×C42—21no—
240C2×C42C22×D1911yescharacteristic
241C4⋊C8—21no—
242C4⋊C8—192no—
243C4⋊C8—381no—
244C4⋊C8—381no—
245#103—381no—
246#103—381no—
247#103—381no—
248#103—381no—
249#102—381no—
250#102—381no—
251#102—381no—
252#102—381no—
253C22⋊C8—21no—
254C22⋊C8—381no—
255#97—762no—
256C4×C8—21no—
257C4×C8—191no—
258C4×C8—191no—
259C4×C8—191no—
260C4×C8—191no—
261C4×C8—381no—
262#95C22⋊D1912yes—
263C19#975411yescharacteristic, complemented, Sylow
264#41—761no—
265#41—761no—
266#41—761no—
267#41—761no—
268C2×Q8—21no—
269C2×Q8—21no—
270C2×Q8—381no—
271C2×D4—381no—
272C2×D4—381no—
273C2×D4—381no—
274C2×D4—761no—
275C22×C4—22no—
276C22×C4—761no—
277C22×C4D4×D1911yescharacteristic
278C22×C4#6454311yescharacteristic
279C22×C4C2×C22⋊D1911yescharacteristic
280C2×C8—41no—
281C2×C8—191no—
282C2×C8—191no—
283C2×C8—191no—
284C2×C8—191no—
285C2×C8—381no—
286C2×C8—381no—
287C2×C8—381no—
288C2×C8—381no—
289C2×C8—382no—
290C2×C8—761no—
291C2×C8—761no—
292C2×C8—761no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—42no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C4⋊C4—381no—
301C4⋊C4—381no—
302C22⋊C4—41no—
303C22⋊C4—761no—
304C22⋊C4—761no—
305C42—41no—
306C42—41no—
307C42—41no—
308C42C2×C4×D1911yescharacteristic
309C42#6454111yescharacteristic
310C42D4×D1911yescharacteristic
311C42D4×D1911yescharacteristic
312C23—761no—
313C23#1059738511yescharacteristic
314Q8—42no—
315Q8—81no—
316Q8—761no—
317Q8—761no—
318D4—761no—
319D4—761no—
320D4—762no—
321D4—1521no—
322D4—1521no—
323D4—1521no—
324C2×C4—22no—
325C2×C4—41no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—42no—
331C2×C4—761no—
332C2×C4—1521no—
333C2×C4—1521no—
334C2×C4C22⋊C4×D1911yescharacteristic
335C2×C4(C22⋊D19)⋊C411yescharacteristic
336C2×C4#1059733011yescharacteristic
337C2×C4#1059733111yescharacteristic
338C2×C4#1059736011yescharacteristic
339C2×C4#1059736211yescharacteristic
340C2×C4#1059736411yescharacteristic
341C2×C4#1059736511yescharacteristic
342C2×C4C4×C22⋊D1911yescharacteristic
343C2×C4#1059738611yescharacteristic
344C8—81no—
345C8—381no—
346C8—381no—
347C8—381no—
348C8—381no—
349C8—762no—
350C8—1521no—
351C22—21no—
352C22—21no—
353C22—1521no—
354C22—1521no—
355C22—1521no—
356C22#1192644411yescharacteristic
357C22#1192676111yescharacteristic
358C22#1192676811yescharacteristic
359C4—21no—
360C4—21no—
361C4—21no—
362C4—82no—
363C4—81no—
364C4—81no—
365C4—1521no—
366C4#1192653911yescharacteristic
367C4#1192654411yescharacteristic
368C4#1192666312yes—
369C4#1192676211yescharacteristic
370C4#1192676911yescharacteristic
371C2—21no—
372C2—21no—
373C2—3041no—
374C2#1456452511yescharacteristic
375C2#1456453011yescharacteristic
376C2#1456456411yescharacteristic
subgroupG/H
centerC2×C4#10597330
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1503C2
socleC22×C19#390
prime radical#11927094C22
cosocleC2×C42×C19C23
hypercenter#1503D19
hypocenterC19#9754
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
2. #14563504C2semidirect
3. #14562381C2semidirect
5. #14562038C2semidirect
7. C19×#1503C2semidirect
11. #11926896C4semidirect
12. #11926896C4semidirect
13. #11926892C4semidirect
14. #11926892C4semidirect
166. #1503D19semidirect
263. C19#9754semidirect

Maximal subgroups

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

subgroupindex
#145739602
#145635042
#145623812
#145621292
#145620382
#145620352
C19×#15032
#975419