Finite Group Databasebeta

← #18078633

Subgroups — #18078633

Order 4864.

456 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14573417C211yesmaximal, characteristic
2#14572596C211yesmaximal, characteristic
3#14563656C211yesmaximal, characteristic
4#14562090C211yesmaximal, characteristic, complemented
5#14561531C211yesmaximal, characteristic, complemented
6#14561476C211yesmaximal, characteristic, complemented
7C19×#1503C211yesmaximal, characteristic, complemented
8C4×#64541C2211yescharacteristic
9#11926848—21no—
10#11926841—21no—
11#11926836C411yescharacteristic, complemented
12#11926831C411yescharacteristic, complemented
13#11926826C411yescharacteristic, complemented
14#11926821C411yescharacteristic, complemented
15#11926671—21no—
16#11926621—21no—
17#11926612—22no—
18#11926595—21no—
19#11926580—21no—
20#11926568C2211yescharacteristic
21C2×C4⋊(C19⋊C8)C2211yescharacteristic
22C2×#10597262—21no—
23#11926538—21no—
24C4×#64515—21no—
25C2×C4×C19⋊C8C2211yescharacteristic
26#11926304—21no—
27Q8⋊(C19⋊C8)—21no—
28Q8⋊(C19⋊C8)—21no—
29C19×#533C2211yescharacteristic
30C19×#431C2211yescharacteristic
31C4×C4⋊C4×C19C2211yescharacteristic
32C19×#328—22no—
33C2×#64541D411yescharacteristic
34C19×C4⋊Q8C2×C411yescharacteristic
35C19×C4⋊Q8C2×C411yescharacteristic
36C19×#125—21no—
37C19×C22⋊Q8—21no—
38C19×C22⋊Q8—21no—
39C4×Q8×C19—21no—
40C4×Q8×C19—21no—
41C19×#117—21no—
42C2×C4⋊C4×C19—21no—
43C2×C42×C19—21no—
44C2×C42×C19C2311yescharacteristic
45C4×C22⋊D19—21no—
46C4×C22⋊D19—21no—
47#10597372D411yescharacteristic
48C2×#64520—21no—
49C22×C19⋊C8—21no—
50C22×C19⋊C8—21no—
51C2×#64515—22no—
52C4×D76C2×C411yescharacteristic
53C4×D76D411yescharacteristic
54#10597318—21no—
55C42×D19—21no—
56C4×Dic38C2×C411yescharacteristic
57C4×Dic38D411yescharacteristic
58C19×C4⋊C8—21no—
59C19×C22⋊C8D412yes—
60C4×C8×C19—21no—
61C19×#95—21no—
62(C2×D19)⋊C8—22no—
63#10597272—22no—
64Dic19⋊C8—22no—
65#10597267—21no—
66#10597267—21no—
67#10597266—21no—
68#10597266—21no—
69#10597265—21no—
70#10597265—21no—
71#10597264—21no—
72#10597264—21no—
73#10597262—42no—
74C4⋊(C19⋊C8)—21no—
75C4⋊(C19⋊C8)—21no—
76C4⋊(C19⋊C8)—21no—
77C4⋊(C19⋊C8)C2×C411yescharacteristic
78C4⋊(C19⋊C8)C2×C411yescharacteristic
79C4×C19⋊C8—21no—
80C4×C19⋊C8D411yescharacteristic
81C4×C19⋊C8D411yescharacteristic
82C2×Q8×C19—21no—
83C2×Q8×C19—21no—
84C22×C4×C19—41no—
85C22×C4×C19C2×D411yescharacteristic
86C22×C4×C19C2×D411yescharacteristic
87C22×C4×C19#4111yescharacteristic
88C2×C22⋊D19—21no—
89#64541—21no—
90#64541—21no—
91#64541—21no—
92#64541—21no—
93C2×D76C22⋊C411yescharacteristic
94C2×C4×D19—21no—
95C2×C4×D19—21no—
96C2×C4×D19—21no—
97C2×Dic38C22⋊C411yescharacteristic
98C2×C8×C19—22no—
99C4⋊C4×C19—22no—
100C4⋊C4×C19—21no—
101C4⋊C4×C19—21no—
102C4⋊C4×C19—21no—
103C4⋊C4×C19—21no—
104C4⋊C4×C19—41no—
105C4⋊C4×C19—41no—
106C4⋊C4×C19—41no—
107C22⋊C4×C19—41no—
108C42×C19—41no—
109C42×C19—41no—
110C42×C19—41no—
111C42×C19C22×C411yescharacteristic
112C42×C19C2×D411yescharacteristic
113C42×C19C2×D411yescharacteristic
114C42×C19#4111yescharacteristic
115C22⋊Dic19—21no—
116(C2×D19)⋊C4—21no—
117(C2×D19)⋊C4—21no—
118C4⋊Dic19C22⋊C411yescharacteristic
119C4⋊Dic19C22⋊C411yescharacteristic
120Dic19⋊C4—21no—
121Dic19⋊C4—21no—
122C4×Dic19—21no—
123C4×Dic19—21no—
124C4×Dic19—21no—
125#64520—41no—
126#64520—41no—
127C2×C19⋊C8—21no—
128C2×C19⋊C8—21no—
129C2×C19⋊C8—21no—
130C2×C19⋊C8—21no—
131C2×C19⋊C8—42no—
132C2×C19⋊C8—41no—
133C2×C19⋊C8—41no—
134C2×C19⋊C8—41no—
135#64515—44no—
136#9209—191nomaximal, Sylow
137C23×C19#12111yescharacteristic
138C22×D19—21no—
139Q8×C19—41no—
140Q8×C19—41no—
141Q8×C19—81no—
142C2×C4×C19—21no—
143C2×C4×C19—21no—
144C2×C4×C19—41no—
145C2×C4×C19—42no—
146C2×C4×C19—41no—
147C2×C4×C19—41no—
148C2×C4×C19—81no—
149C2×C4×C19—81no—
150C2×C4×C19C2×C22⋊C411yescharacteristic
151C2×C4×C19C4×D411yescharacteristic
152C2×C4×C19C4×D411yescharacteristic
153C2×C4×C19#12011yescharacteristic
154C2×C4×C19#12111yescharacteristic
155C2×C4×C19#12311yescharacteristic
156C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
157C2×C4×C19#13711yescharacteristic
158C2×C4×C19#13711yescharacteristic
159C2×C4×C19#13711yescharacteristic
160C22⋊D19—41no—
161C22⋊D19—41no—
162C2×Dic19—21no—
163C2×Dic19—21no—
164C2×Dic19—21no—
165D76—21no—
166D76—21no—
167C4×D19—42no—
168C4×D19—41no—
169C4×D19—41no—
170C4×D19—41no—
171C4×D19—41no—
172Dic38—21no—
173Dic38—21no—
174C8×C19—42no—
175C19⋊C8—22no—
176C19⋊C8—41no—
177C19⋊C8—41no—
178C19⋊C8—41no—
179C19⋊C8—81no—
180#3076—191no—
181#2965—191no—
182#1806—191no—
183#1503D1911yescharacteristic, complemented
184#1493—191no—
185#1301—191no—
186#1279—191no—
187C22×C19—21no—
188C22×C19—21no—
189C22×C19#38611yescharacteristic
190C22×C19#46811yescharacteristic
191C22×C19#47011yescharacteristic
192C2×D19—41no—
193C2×D19—41no—
194C2×D19—41no—
195C4×C19—21no—
196C4×C19—21no—
197C4×C19—21no—
198C4×C19—82no—
199C4×C19—81no—
200C4×C19—81no—
201C4×C19#41711yescharacteristic
202C4×C19#41911yescharacteristic
203C4×C19#44311yescharacteristic
204C4×C19#44411yescharacteristic
205C4×C19#46811yescharacteristic
206C4×C19#47011yescharacteristic
207Dic19—41no—
208Dic19—41no—
209Dic19—41no—
210#533C2×D1911yescharacteristic
211C4×#41—191no—
212#479—381no—
213#478—381no—
214#477—191no—
215#476—191no—
216#475—191no—
217#474—191no—
218#446—381no—
219#436—381no—
220#435—382no—
221#431—381no—
222#431C2×D1911yescharacteristic
223#427—381no—
224#423—191no—
225C2×C4⋊C8—191no—
226C2×#104—381no—
227#416—381no—
228C4×M16—381no—
229C2×C4×C8—191no—
230C4×C4⋊C4C2×D1911yescharacteristic
231#339—381no—
232#328—22no—
233Q8⋊C8—381no—
234Q8⋊C8—381no—
235C2×C19—21no—
236C2×C19—21no—
237C2×C19#187611yescharacteristic
238C2×C19#189411yescharacteristic
239C2×C19#190611yescharacteristic
240D19—81no—
241C2×#41—191no—
242C2×M16—382no—
243C2×M16—381no—
244C22×C8—381no—
245C22×C8—381no—
246C4⋊Q8C4×D1911yescharacteristic
247C4⋊Q8C4×D1911yescharacteristic
248#125—21no—
249C22⋊Q8—21no—
250C22⋊Q8—21no—
251C4×Q8—21no—
252C4×Q8—21no—
253C4×Q8—191no—
254C4×Q8—191no—
255C4×D4—191no—
256C4×D4—191no—
257C4×D4—381no—
258C4×D4—381no—
259#117—21no—
260#117—191no—
261#117—381no—
262C2×C4⋊C4—21no—
263C2×C42—21no—
264C2×C42—381no—
265C2×C42C22×D1911yescharacteristic
266#107—381no—
267#107—381no—
268#106—381no—
269#106—381no—
270C4⋊C8—21no—
271C4⋊C8—191no—
272C4⋊C8—191no—
273C4⋊C8—382no—
274C4⋊C8—381no—
275C4⋊C8—381no—
276C4⋊C8—381no—
277#104—762no—
278#103—381no—
279#103—381no—
280#102—381no—
281#102—381no—
282C22⋊C8—382no—
283C22⋊C8C22⋊D1912yes—
284#97—382no—
285C4×C8—21no—
286C4×C8—191no—
287C4×C8—191no—
288C4×C8—381no—
289#95—21no—
290C19#920911yescharacteristic, complemented, Sylow
291#41—381no—
292#41—381no—
293#41—381no—
294#41—381no—
295C2×Q8—21no—
296C2×Q8—21no—
297C2×Q8—191no—
298C2×D4—191no—
299C2×D4—381no—
300C22×C4—41no—
301C22×C4—381no—
302C22×C4—381no—
303C22×C4—381no—
304C22×C4D4×D1911yescharacteristic
305C22×C4#6454311yescharacteristic
306C22×C4C2×C22⋊D1911yescharacteristic
307M16—764no—
308M16—761no—
309M16—761no—
310C2×C8—22no—
311C2×C8—381no—
312C2×C8—381no—
313C2×C8—381no—
314C2×C8—381no—
315C2×C8—762no—
316C2×C8—761no—
317C2×C8—761no—
318C2×C8—761no—
319C4⋊C4—22no—
320C4⋊C4—21no—
321C4⋊C4—21no—
322C4⋊C4—21no—
323C4⋊C4—21no—
324C4⋊C4—41no—
325C4⋊C4—41no—
326C4⋊C4—41no—
327C4⋊C4—191no—
328C4⋊C4—191no—
329C4⋊C4—381no—
330C4⋊C4—381no—
331C22⋊C4—41no—
332C22⋊C4—381no—
333C22⋊C4—381no—
334C22⋊C4—381no—
335C42—41no—
336C42—41no—
337C42—41no—
338C42—381no—
339C42—381no—
340C42—381no—
341C42C2×C4×D1911yescharacteristic
342C42#6454111yescharacteristic
343C42D4×D1911yescharacteristic
344C42D4×D1911yescharacteristic
345C23—381no—
346C23#1059738411yescharacteristic
347Q8—41no—
348Q8—41no—
349Q8—81no—
350Q8—381no—
351Q8—381no—
352D4—381no—
353D4—381no—
354D4—761no—
355D4—761no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—41no—
359C2×C4—42no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—81no—
363C2×C4—81no—
364C2×C4—381no—
365C2×C4—381no—
366C2×C4—381no—
367C2×C4—762no—
368C2×C4—761no—
369C2×C4—761no—
370C2×C4—761no—
371C2×C4—761no—
372C2×C4C22⋊C4×D1911yescharacteristic
373C2×C4(C22⋊D19)⋊C411yescharacteristic
374C2×C4#1059732911yescharacteristic
375C2×C4#1059733011yescharacteristic
376C2×C4#1059736011yescharacteristic
377C2×C4#1059736111yescharacteristic
378C2×C4#1059736411yescharacteristic
379C2×C4#1059736411yescharacteristic
380C2×C4C4×C22⋊D1911yescharacteristic
381C2×C4#1059738311yescharacteristic
382C8—42no—
383C8—382no—
384C8—761no—
385C8—761no—
386C8—761no—
387C8—1521no—
388C22—21no—
389C22—21no—
390C22—761no—
391C22—761no—
392C22—761no—
393C22#1192642011yescharacteristic
394C22#1192678711yescharacteristic
395C22#1192679911yescharacteristic
396C4—21no—
397C4—21no—
398C4—21no—
399C4—82no—
400C4—81no—
401C4—81no—
402C4—761no—
403C4—761no—
404C4—761no—
405C4#1192654411yescharacteristic
406C4#1192655111yescharacteristic
407C4#1192665811yescharacteristic
408C4#1192666311yescharacteristic
409C4#1192679311yescharacteristic
410C4#1192680111yescharacteristic
411C2—21no—
412C2—21no—
413C2—1521no—
414C2#1456395911yescharacteristic
415C2#1456406511yescharacteristic
416C2#1456413311yescharacteristic
subgroupG/H
centerC2×C4#10597330
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1503C2
socleC22×C19#386
prime radicalC2×#64541D4
cosocleC2×C42×C19C23
hypercenter#1503D19
hypocenterC19#9209
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
4. #14562090C2semidirect
5. #14561531C2semidirect
6. #14561476C2semidirect
7. C19×#1503C2semidirect
11. #11926836C4semidirect
12. #11926831C4semidirect
13. #11926826C4semidirect
14. #11926821C4semidirect
183. #1503D19semidirect
290. C19#9209semidirect

Maximal subgroups

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

subgroupindex
#145734172
#145725962
#145636562
#145620902
#145615312
#145614762
C19×#15032
#920919