Finite Group Databasebeta

← #18076650

Subgroups — #18076650

Order 4864.

464 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14563938C211yesmaximal, characteristic
2#14563839C211yesmaximal, characteristic, complemented
3#14563817C211yesmaximal, characteristic, complemented
4#14562126C211yesmaximal, characteristic
5#14561520C211yesmaximal, characteristic, complemented
6#14561482C211yesmaximal, characteristic, complemented
7C19×#2976C211yesmaximal, characteristic
8C22×#64520C2211yescharacteristic
9C2×#10597279—21no—
10C2×Dic19⋊C8—21no—
11C2×#10597294—21no—
12C2×C22⋊(C19⋊C8)C2211yescharacteristic
13C4×C22⋊Dic19C2211yescharacteristic
14C4×C22⋊Dic19C2211yescharacteristic
15#11926308—21no—
16#11926303—21no—
17#11926298—21no—
18#11926281C411yescharacteristic, complemented
19#11926281C411yescharacteristic, complemented
20#11926278C411yescharacteristic, complemented
21#11926278C411yescharacteristic, complemented
22C19×#525C2211yescharacteristic
23C19×#436—21no—
24C19×#435—21no—
25C19×#435—21no—
26C8×D4×C19—21no—
27C19×#433—21no—
28C19×#408—21no—
29C19×#407C2211yescharacteristic
30C2×C19×C22⋊C8C2211yescharacteristic
31C2×#41×C19D411yescharacteristic
32C23×C4×C19C2311yescharacteristic
33C2×M16×C19—21no—
34C2×M16×C19D411yescharacteristic
35C2×M16×C19D411yescharacteristic
36C22×C8×C19—21no—
37C22×C8×C19D411yescharacteristic
38C22×C8×C19D411yescharacteristic
39C19×#123—21no—
40C19×C22⋊Q8C2×C411yescharacteristic
41C19×C22⋊Q8Q811yescharacteristic
42C19×#121C2×C411yescharacteristic
43C19×#121Q811yescharacteristic
44C19×#120—21no—
45C4×D4×C19—21no—
46C4×D4×C19—21no—
47C19×#117D411yescharacteristic
48C2×C22⋊Dic19—21no—
49C2×C22⋊Dic19—21no—
50C2×C4×Dic19—21no—
51C2×C4×Dic19—21no—
52C2×#64520—21no—
53C2×#64520—21no—
54C2×#64520—42no—
55C22×C19⋊C8—21no—
56C22×C19⋊C8—21no—
57C19×C4⋊C8—21no—
58C19×C4⋊C8—21no—
59C19×C22⋊C8—21no—
60C19×C22⋊C8—21no—
61C19×C22⋊C8—21no—
62C19×C22⋊C8—21no—
63C19×C22⋊C8—21no—
64C19×C22⋊C8—21no—
65C19×#97—21no—
66C4×C8×C19—21no—
67#10597294—42no—
68C19⋊#95—21no—
69C19⋊#95C2×C411yescharacteristic
70C19⋊#95C2×C411yescharacteristic
71C22⋊(C19⋊C8)—21no—
72C22⋊(C19⋊C8)C2×C411yescharacteristic
73C22⋊(C19⋊C8)C2×C411yescharacteristic
74#10597279—42no—
75Dic19⋊C8—42no—
76C24×C19#4111yescharacteristic
77#41×C19—41no—
78#41×C19—41no—
79C2×Q8×C19C4⋊C411yescharacteristic
80C2×D4×C19—21no—
81C2×D4×C19—21no—
82C2×D4×C19—21no—
83C2×D4×C19C4⋊C411yescharacteristic
84C22×C4×C19—21no—
85C22×C4×C19—41no—
86C22×C4×C19—41no—
87C22×C4×C19C22×C411yescharacteristic
88C22×C4×C19C2×D411yescharacteristic
89C22×C4×C19C2×D411yescharacteristic
90C22×C4×C19C2×D411yescharacteristic
91C22×C4×C19C2×Q811yescharacteristic
92C22×C4×C19#4111yescharacteristic
93C22×Dic19—21no—
94C22×Dic19—21no—
95C22×Dic19—41no—
96M16×C19—41no—
97M16×C19—41no—
98M16×C19—81no—
99C2×C8×C19—21no—
100C2×C8×C19—21no—
101C2×C8×C19—21no—
102C2×C8×C19—21no—
103C2×C8×C19—41no—
104C2×C8×C19—41no—
105C2×C8×C19—81no—
106C4⋊C4×C19—21no—
107C4⋊C4×C19—21no—
108C4⋊C4×C19C4⋊C411yescharacteristic
109C4⋊C4×C19C4⋊C411yescharacteristic
110C22⋊C4×C19—21no—
111C22⋊C4×C19—21no—
112C22⋊C4×C19—21no—
113C22⋊C4×C19—21no—
114C22⋊C4×C19—21no—
115C42×C19—21no—
116C22⋊Dic19—22no—
117C22⋊Dic19—42no—
118C22⋊Dic19—41no—
119C4×Dic19—41no—
120C4×Dic19—41no—
121C4×Dic19—41no—
122C4×Dic19—41no—
123#64520—22no—
124#64520—22no—
125#64520—41no—
126#64520—41no—
127C2×C19⋊C8—22no—
128C2×C19⋊C8—21no—
129C2×C19⋊C8—21no—
130C2×C19⋊C8—41no—
131C2×C19⋊C8—41no—
132C2×C19⋊C8—41no—
133C2×C19⋊C8—41no—
134#8875—191nomaximal, Sylow
135C23×C19—21no—
136C23×C19—21no—
137C23×C19—21no—
138C23×C19—41no—
139C23×C19—41no—
140C23×C19C4×D411yescharacteristic
141C23×C19C22⋊Q811yescharacteristic
142C23×C19#12311yescharacteristic
143Q8×C19—41no—
144D4×C19—41no—
145D4×C19—41no—
146D4×C19—41no—
147D4×C19—81no—
148D4×C19—81no—
149C2×C4×C19—21no—
150C2×C4×C19—21no—
151C2×C4×C19—21no—
152C2×C4×C19—21no—
153C2×C4×C19—21no—
154C2×C4×C19—21no—
155C2×C4×C19—21no—
156C2×C4×C19—21no—
157C2×C4×C19—21no—
158C2×C4×C19—41no—
159C2×C4×C19—41no—
160C2×C4×C19—41no—
161C2×C4×C19—41no—
162C2×C4×C19—41no—
163C2×C4×C19C2×C4⋊C411yescharacteristic
164C2×C4×C19C4×D411yescharacteristic
165C2×C4×C19#12011yescharacteristic
166C2×C4×C19C22⋊Q811yescharacteristic
167C2×Dic19—22no—
168C2×Dic19—41no—
169C2×Dic19—41no—
170C2×Dic19—41no—
171C2×Dic19—42no—
172C2×Dic19—41no—
173C2×Dic19—41no—
174C2×Dic19—81no—
175C2×Dic19—81no—
176C8×C19—41no—
177C8×C19—41no—
178C8×C19—41no—
179C8×C19—41no—
180C19⋊C8—41no—
181C19⋊C8—41no—
182C19⋊C8—42no—
183#2976D1911yescharacteristic
184#1871—191no—
185#1855—191no—
186#1851—191no—
187#1501—191no—
188#1297—191no—
189#1282—191no—
190C22×C19—21no—
191C22×C19—21no—
192C22×C19—21no—
193C22×C19—21no—
194C22×C19—21no—
195C22×C19—21no—
196C22×C19—21no—
197C22×C19—21no—
198C22×C19—41no—
199C22×C19—41no—
200C22×C19—41no—
201C22×C19—81no—
202C22×C19—81no—
203C22×C19#38511yescharacteristic
204C22×C19#44311yescharacteristic
205C22×C19#44411yescharacteristic
206C4×C19—21no—
207C4×C19—21no—
208C4×C19—21no—
209C4×C19—41no—
210C4×C19—41no—
211C4×C19—41no—
212C4×C19B(4,𝔽2)11yescharacteristic
213C4×C19#45811yescharacteristic
214Dic19—42no—
215Dic19—81no—
216Dic19—82no—
217C22×M16—191no—
218#525C2×D1911yescharacteristic
219#436—21no—
220#435—21no—
221#435—21no—
222C8×D4—21no—
223#433—21no—
224C2×#108—381no—
225C2×C4⋊C8—381no—
226C2×#104—381no—
227#408—21no—
228#407C2×D1911yescharacteristic
229C2×C22⋊C8—191no—
230C2×C22⋊C8C2×D1911yescharacteristic
231C4×C22⋊C4—191no—
232C4×C22⋊C4—191no—
233#341—381no—
234#339—381no—
235#336—381no—
236#328—191no—
237#328—191no—
238#327—191no—
239#327—191no—
240C2×C19—21no—
241C2×C19—21no—
242C2×C19—41no—
243C2×C19—41no—
244C2×C19—81no—
245C2×C19#186111yescharacteristic
246C2×C19#186611yescharacteristic
247C2×C19#186711yescharacteristic
248C2×#41C22⋊D1911yescharacteristic
249C23×C4C22×D1911yescharacteristic
250C2×M16—21no—
251C2×M16—381no—
252C2×M16—381no—
253C2×M16—762no—
254C2×M16C22⋊D1911yescharacteristic
255C2×M16C22⋊D1911yescharacteristic
256C22×C8—21no—
257C22×C8—381no—
258C22×C8—381no—
259C22×C8C22⋊D1911yescharacteristic
260C22×C8C22⋊D1911yescharacteristic
261#123—21no—
262C22⋊Q8Dic3811yescharacteristic
263C22⋊Q8C4×D1911yescharacteristic
264#121Dic3811yescharacteristic
265#121C4×D1911yescharacteristic
266#120—21no—
267C4×D4—21no—
268C4×D4—21no—
269#117C22⋊D1911yescharacteristic
270C2×C22⋊C4—381no—
271C2×C22⋊C4—381no—
272C2×C42—381no—
273C2×C42—381no—
274#108—762no—
275C4⋊C8—21no—
276C4⋊C8—21no—
277C4⋊C8—762no—
278#104—762no—
279C22⋊C8—21no—
280C22⋊C8—21no—
281C22⋊C8—21no—
282C22⋊C8—21no—
283C22⋊C8—21no—
284C22⋊C8—21no—
285C22⋊C8—191no—
286C22⋊C8—191no—
287C22⋊C8—381no—
288#97—21no—
289C4×C8—21no—
290#95—191no—
291#95—191no—
292#95—381no—
293C19#887511yescharacteristic, complemented, Sylow
294C24#6454111yescharacteristic
295#41—41no—
296#41—41no—
297C2×Q8Dic19⋊C411yescharacteristic
298C2×D4—21no—
299C2×D4—21no—
300C2×D4—21no—
301C2×D4Dic19⋊C411yescharacteristic
302C22×C4—21no—
303C22×C4—41no—
304C22×C4—41no—
305C22×C4—381no—
306C22×C4—381no—
307C22×C4—761no—
308C22×C4C2×Dic3811yescharacteristic
309C22×C4C2×C4×D1911yescharacteristic
310C22×C4#6454111yescharacteristic
311C22×C4C2×C22⋊D1911yescharacteristic
312C22×C4C2×C22⋊D1911yescharacteristic
313C22×C4C2×C22⋊D1911yescharacteristic
314M16—41no—
315M16—41no—
316M16—81no—
317M16—382no—
318M16—382no—
319M16—761no—
320M16—761no—
321C2×C8—21no—
322C2×C8—21no—
323C2×C8—21no—
324C2×C8—21no—
325C2×C8—41no—
326C2×C8—41no—
327C2×C8—81no—
328C2×C8—382no—
329C2×C8—381no—
330C2×C8—381no—
331C2×C8—761no—
332C2×C8—761no—
333C2×C8—761no—
334C2×C8—761no—
335C4⋊C4—21no—
336C4⋊C4—21no—
337C4⋊C4Dic19⋊C411yescharacteristic
338C4⋊C4Dic19⋊C411yescharacteristic
339C22⋊C4—21no—
340C22⋊C4—21no—
341C22⋊C4—21no—
342C22⋊C4—21no—
343C22⋊C4—21no—
344C22⋊C4—382no—
345C22⋊C4—762no—
346C22⋊C4—761no—
347C42—21no—
348C42—761no—
349C42—761no—
350C42—761no—
351C42—761no—
352C23—21no—
353C23—21no—
354C23—21no—
355C23—41no—
356C23—41no—
357C23#1059737011yescharacteristic
358C23C4×C22⋊D1911yescharacteristic
359C23#1059737511yescharacteristic
360Q8—41no—
361D4—41no—
362D4—41no—
363D4—41no—
364D4—81no—
365D4—81no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—382no—
381C2×C4—761no—
382C2×C4—761no—
383C2×C4—761no—
384C2×C4—762no—
385C2×C4—761no—
386C2×C4—761no—
387C2×C4—1521no—
388C2×C4—1521no—
389C2×C4C2×Dic19⋊C411yescharacteristic
390C2×C4#1059737011yescharacteristic
391C2×C4C4×C22⋊D1911yescharacteristic
392C2×C4#1059739911yescharacteristic
393C8—41no—
394C8—41no—
395C8—41no—
396C8—41no—
397C8—761no—
398C8—761no—
399C8—762no—
400C22—21no—
401C22—21no—
402C22—21no—
403C22—21no—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—21no—
408C22—41no—
409C22—41no—
410C22—41no—
411C22—81no—
412C22—81no—
413C22#1192641711yescharacteristic
414C22#1192665911yescharacteristic
415C22#1192666411yescharacteristic
416C4—21no—
417C4—21no—
418C4—21no—
419C4—41no—
420C4—41no—
421C4—41no—
422C4—762no—
423C4—1521no—
424C4—1522no—
425C4#1192673111yescharacteristic
426C4#1192673411yescharacteristic
427C2—21no—
428C2—21no—
429C2—41no—
430C2—41no—
431C2—81no—
432C2#1456387511yescharacteristic
433C2#1456391011yescharacteristic
434C2#1456391611yescharacteristic
subgroupG/H
centerC2×C4#10597399
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#2976C2
socleC22×C19#385
prime radicalC19×#525C22
cosocleC23×C4×C19C23
hypercenter#2976D19
hypocenterC19#8875
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #2976

Complements

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

NH ≅ G/Ntype
2. #14563839C2semidirect
3. #14563817C2semidirect
5. #14561520C2semidirect
6. #14561482C2semidirect
18. #11926281C4semidirect
19. #11926281C4semidirect
20. #11926278C4semidirect
21. #11926278C4semidirect
293. C19#8875semidirect

Maximal subgroups

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

subgroupindex
#145639382
#145638392
#145638172
#145621262
#145615202
#145614822
C19×#29762
#887519