Finite Group Databasebeta

← #18077265

Subgroups — #18077265

Order 4864.

476 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14573706C211yesmaximal, characteristic
2#14564611C211yesmaximal, characteristic, complemented
3C4×#10597294C211yesmaximal, characteristic
4#14562055C211yesmaximal, characteristic, complemented
5#14561524C211yesmaximal, characteristic, complemented
6#14561467C211yesmaximal, characteristic, complemented
7C19×#2991C211yesmaximal, characteristic
8#11927101C2211yescharacteristic
9#11926885—21no—
10#11926829C411yescharacteristic, complemented
11#11926824C411yescharacteristic, complemented
12#11926754C411yescharacteristic, complemented
13#11926749C411yescharacteristic, complemented
14#11926706—21no—
15C4×#64528—21no—
16C4×#64526—21no—
17#11926597C2211yescharacteristic
18C2×#10597294—21no—
19C4×#64520C2211yescharacteristic
20C42×Dic19C2211yescharacteristic
21#11926305—22no—
22#11926303—21no—
23#11926274—21no—
24#11926274—21no—
25C4×#41×C19C2211yescharacteristic
26C8×Q8×C19—21no—
27C19×#436—22no—
28C19×#436—21no—
29C19×#431—21no—
30C19×#431C2211yescharacteristic
31C19×#423—21no—
32C19×#423C2211yescharacteristic
33C2×#41×C19D411yescharacteristic
34C2×M16×C19—22no—
35C2×M16×C19D412yes—
36C4×Q8×C19C2×C411yescharacteristic
37C4×Q8×C19D411yescharacteristic
38C4×D4×C19—21no—
39C4×D4×C19—21no—
40C4×D4×C19C2×C411yescharacteristic
41C4×D4×C19D411yescharacteristic
42C19×#117—21no—
43C19×#117D411yescharacteristic
44C2×C42×C19—21no—
45C2×C42×C19C2311yescharacteristic
46C2×#64528—21no—
47C2×#64526—21no—
48#10597372—21no—
49#10597370—21no—
50#10597370—21no—
51C2×C4×Dic19—21no—
52C2×C4×Dic19—21no—
53C2×C4×Dic19—21no—
54C2×#64520—21no—
55#10597316—21no—
56#10597315C2×C411yescharacteristic
57#10597315C2×C411yescharacteristic
58C4×Dic38—21no—
59C4×Dic38—21no—
60C19×C4⋊C8—22no—
61C19×C4⋊C8—21no—
62C19×C4⋊C8—21no—
63C19×C4⋊C8D411yescharacteristic
64C19×C4⋊C8D411yescharacteristic
65C19×C22⋊C8—22no—
66C19×C22⋊C8—21no—
67C4×C8×C19—22no—
68C4×C8×C19—21no—
69#10597294—24no—
70#10597292—21no—
71#10597289—21no—
72C22⋊(C19⋊C8)—21no—
73#10597267—21no—
74#10597267—21no—
75#10597265—21no—
76#10597264—21no—
77C4⋊(C19⋊C8)C2×C411yescharacteristic
78C4⋊(C19⋊C8)C2×C411yescharacteristic
79#10597260—21no—
80C4×C19⋊C8—21no—
81C4×C19⋊C8—21no—
82#41×C19—22no—
83#41×C19—41no—
84C2×Q8×C19C22⋊C411yescharacteristic
85C2×D4×C19—21no—
86C2×D4×C19C22⋊C411yescharacteristic
87C22×C4×C19—21no—
88C22×C4×C19—21no—
89C22×C4×C19—21no—
90C22×C4×C19C2×D411yescharacteristic
91C22×C4×C19C2×D411yescharacteristic
92C22×C4×C19#4111yescharacteristic
93C22×Dic19—41no—
94C2×Dic38—21no—
95C2×Dic38—21no—
96M16×C19—42no—
97M16×C19—82no—
98C2×C8×C19—21no—
99C2×C8×C19—22no—
100C2×C8×C19—21no—
101C4⋊C4×C19—21no—
102C4⋊C4×C19—21no—
103C4⋊C4×C19C22⋊C411yescharacteristic
104C4⋊C4×C19C22⋊C411yescharacteristic
105C22⋊C4×C19—21no—
106C22⋊C4×C19—21no—
107C22⋊C4×C19—21no—
108C42×C19—21no—
109C42×C19—21no—
110C42×C19—21no—
111C42×C19C22×C411yescharacteristic
112C42×C19C2×D411yescharacteristic
113C42×C19C2×D411yescharacteristic
114C42×C19#4111yescharacteristic
115C22⋊Dic19—41no—
116#64528—42no—
117#64526—42no—
118C4⋊Dic19—21no—
119C4⋊Dic19—21no—
120C4⋊Dic19—21no—
121C4⋊Dic19—21no—
122Dic19⋊C4—41no—
123Dic19⋊C4—41no—
124C4×Dic19—22no—
125C4×Dic19—22no—
126C4×Dic19—22no—
127C4×Dic19—41no—
128C4×Dic19—41no—
129C4×Dic19—41no—
130C4×Dic19—41no—
131#64520—22no—
132#64520—41no—
133C2×C19⋊C8—21no—
134C2×C19⋊C8—21no—
135C2×C19⋊C8—41no—
136#8972—191nomaximal, Sylow
137C23×C19—21no—
138C23×C19#12111yescharacteristic
139Q8×C19—21no—
140Q8×C19#10412yes—
141D4×C19—21no—
142D4×C19—21no—
143D4×C19—42no—
144C2×C4×C19—21no—
145C2×C4×C19—21no—
146C2×C4×C19—21no—
147C2×C4×C19—21no—
148C2×C4×C19—21no—
149C2×C4×C19—21no—
150C2×C4×C19—21no—
151C2×C4×C19—21no—
152C2×C4×C19—21no—
153C2×C4×C19—42no—
154C2×C4×C19—41no—
155C2×C4×C19—41no—
156C2×C4×C19—41no—
157C2×C4×C19—41no—
158C2×C4×C19C2×C22⋊C411yescharacteristic
159C2×C4×C19C4×D411yescharacteristic
160C2×C4×C19C4×D411yescharacteristic
161C2×C4×C19#12011yescharacteristic
162C2×C4×C19#12111yescharacteristic
163C2×C4×C19#12311yescharacteristic
164C2×Dic19—42no—
165C2×Dic19—42no—
166C2×Dic19—42no—
167C2×Dic19—41no—
168C2×Dic19—41no—
169Dic38—41no—
170Dic38—41no—
171Dic38—41no—
172Dic38—41no—
173C8×C19—42no—
174C8×C19—41no—
175C8×C19—41no—
176C19⋊C8—42no—
177C19⋊C8—41no—
178C19⋊C8—41no—
179#3107—191no—
180#2991D1911yescharacteristic
181#1994—191no—
182C4×#104—191no—
183#1485—191no—
184#1299—191no—
185#1276—191no—
186C22×C19—21no—
187C22×C19—21no—
188C22×C19—21no—
189C22×C19—41no—
190C22×C19—41no—
191C22×C19—41no—
192C22×C19#38611yescharacteristic
193C4×C19—21no—
194C4×C19—22no—
195C4×C19—21no—
196C4×C19—21no—
197C4×C19—41no—
198C4×C19—41no—
199C4×C19C2×#10411yescharacteristic
200C4×C19#42111yescharacteristic
201C4×C19#44311yescharacteristic
202C4×C19#44411yescharacteristic
203C4×C19#45511yescharacteristic
204C4×C19#45611yescharacteristic
205Dic19—44no—
206Dic19—81no—
207Dic19—81no—
208#533—191no—
209C4×#41C2×D1911yescharacteristic
210#485—381no—
211#475—191no—
212#474—191no—
213#462—191no—
214#461—191no—
215#452—381no—
216C8×Q8—21no—
217C4×Q16—381no—
218C4×SD16—381no—
219#436—22no—
220#436—21no—
221#431—21no—
222#431—191no—
223#431C2×D1911yescharacteristic
224#423—21no—
225#423C2×D1911yescharacteristic
226C2×#104—381no—
227C4×M16—191no—
228C43—191no—
229#339—382no—
230#339—381no—
231Q8⋊C8—381no—
232Q8⋊C8—381no—
233C2×C19—41no—
234C2×C19—81no—
235C2×C19#187111yescharacteristic
236C2×C19#187611yescharacteristic
237C2×C19#188211yescharacteristic
238C2×#41D7611yescharacteristic
239C2×Q16—381no—
240C2×SD16—381no—
241C2×M16—22no—
242C2×M16—381no—
243C2×M16C22⋊D1912yes—
244C4⋊Q8—191no—
245C4⋊Q8—191no—
246#125—381no—
247C22⋊Q8—381no—
248C22⋊Q8—381no—
249C4×Q8—381no—
250C4×Q8—381no—
251C4×Q8C4×D1911yescharacteristic
252C4×Q8C22⋊D1911yescharacteristic
253C4×D4—21no—
254C4×D4—21no—
255C4×D4C4×D1911yescharacteristic
256C4×D4C22⋊D1911yescharacteristic
257#117—21no—
258#117—381no—
259#117D7611yescharacteristic
260C2×C42—21no—
261C2×C42—381no—
262C2×C42—381no—
263C2×C42—381no—
264C2×C42C22×D1911yescharacteristic
265#107—381no—
266#106—381no—
267C4⋊C8—22no—
268C4⋊C8—21no—
269C4⋊C8—21no—
270C4⋊C8—191no—
271C4⋊C8—191no—
272C4⋊C8C22⋊D1911yescharacteristic
273C4⋊C8C22⋊D1911yescharacteristic
274#104—384no—
275#103—381no—
276#103—381no—
277#103—381no—
278#102—381no—
279C22⋊C8—22no—
280C22⋊C8—21no—
281C22⋊C8—381no—
282#97—381no—
283C4×C8—22no—
284C4×C8—21no—
285C4×C8—381no—
286C4×C8—381no—
287C19#897211yescharacteristic, complemented, Sylow
288#41—22no—
289#41—41no—
290C2×Q8—381no—
291C2×Q8—381no—
292C2×Q8(C2×D19)⋊C411yescharacteristic
293C2×D4—21no—
294C2×D4(C2×D19)⋊C411yescharacteristic
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—761no—
299C22×C4C2×D7611yescharacteristic
300C22×C4#6454111yescharacteristic
301C22×C4C2×C22⋊D1911yescharacteristic
302Q16—762no—
303SD16—762no—
304M16—42no—
305M16—82no—
306M16—382no—
307M16—761no—
308C2×C8—21no—
309C2×C8—22no—
310C2×C8—21no—
311C2×C8—381no—
312C2×C8—381no—
313C2×C8—761no—
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4—381no—
317C4⋊C4—381no—
318C4⋊C4—381no—
319C4⋊C4—381no—
320C4⋊C4—761no—
321C4⋊C4—761no—
322C4⋊C4(C2×D19)⋊C411yescharacteristic
323C4⋊C4(C2×D19)⋊C411yescharacteristic
324C22⋊C4—21no—
325C22⋊C4—21no—
326C22⋊C4—21no—
327C22⋊C4—761no—
328C42—21no—
329C42—21no—
330C42—21no—
331C42—382no—
332C42—382no—
333C42—382no—
334C42—761no—
335C42—761no—
336C42—761no—
337C42—761no—
338C42C2×C4×D1911yescharacteristic
339C42#6454111yescharacteristic
340C42C2×C22⋊D1911yescharacteristic
341C42C2×C22⋊D1911yescharacteristic
342C23—21no—
343C23#1059737611yescharacteristic
344Q8—21no—
345Q8—761no—
346Q8—761no—
347Q8—761no—
348Q8—761no—
349Q8#1059728212yes—
350D4—21no—
351D4—21no—
352D4—42no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—42no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—762no—
368C2×C4—762no—
369C2×C4—762no—
370C2×C4—761no—
371C2×C4—761no—
372C2×C4C2×(C2×D19)⋊C411yescharacteristic
373C2×C4C4×C22⋊D1911yescharacteristic
374C2×C4C4×C22⋊D1911yescharacteristic
375C2×C4#1059737511yescharacteristic
376C2×C4#1059737611yescharacteristic
377C2×C4#1059739911yescharacteristic
378C8—42no—
379C8—41no—
380C8—41no—
381C8—762no—
382C8—761no—
383C8—761no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22#1192642311yescharacteristic
391C4—21no—
392C4—22no—
393C4—21no—
394C4—21no—
395C4—41no—
396C4—41no—
397C4—764no—
398C4—1521no—
399C4—1521no—
400C4C2×#1059728211yescharacteristic
401C4#1192656011yescharacteristic
402C4#1192665911yescharacteristic
403C4#1192666411yescharacteristic
404C4#1192672211yescharacteristic
405C4#1192672711yescharacteristic
406C2—41no—
407C2—81no—
408C2#1456393711yescharacteristic
409C2#1456396211yescharacteristic
410C2#1456400411yescharacteristic
subgroupG/H
centerC2×C4#10597399
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#2991C2
socleC22×C19#386
prime radicalC2×#41×C19D4
cosocleC2×C42×C19C23
hypercenter#2991D19
hypocenterC19#8972
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2991

Complements

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

NH ≅ G/Ntype
2. #14564611C2semidirect
4. #14562055C2semidirect
5. #14561524C2semidirect
6. #14561467C2semidirect
10. #11926829C4semidirect
11. #11926824C4semidirect
12. #11926754C4semidirect
13. #11926749C4semidirect
287. C19#8972semidirect

Maximal subgroups

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

subgroupindex
#145737062
#145646112
C4×#105972942
#145620552
#145615242
#145614672
C19×#29912
#897219