Finite Group Databasebeta

← #18078879

Subgroups — #18078879

Order 4864.

464 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11926766C211yesmaximal, characteristic
2#14572724C211yesmaximal, characteristic, complemented
3#14562232C211yesmaximal, characteristic
4#14561988C211yesmaximal, characteristic
5#14561504C211yesmaximal, characteristic, complemented
6#14561486C211yesmaximal, characteristic, complemented
7C19×#1491C211yesmaximal, characteristic, complemented
8C22×#64528C411yescharacteristic
9C22×#64527C411yescharacteristic
10C2×#10597321C2211yescharacteristic
11#11926766—21no—
12#11926766—21no—
13#11926766—21no—
14#11926766—21no—
15#11926675—22no—
16#11926675—21no—
17Q8×C19⋊C8—21no—
18#11926601—21no—
19#11926601C2211yescharacteristic
20#11926597—21no—
21#11926597C2211yescharacteristic
22C2×C4⋊(C19⋊C8)C2211yescharacteristic
23C2×#10597267C411yescharacteristic
24C2×#10597266C411yescharacteristic
25#11926283—22no—
26#11926267—21no—
27#11926267—21no—
28C2×C4×Q8×C19C2211yescharacteristic
29C19×#432C2211yescharacteristic
30C4×M16×C19C2211yescharacteristic
31C19×Q8⋊C8—21no—
32C19×Q8⋊C8—21no—
33C22×Q8×C19C2×C411yescharacteristic
34C22×D76C2×C411yescharacteristic
35C22×Dic38C2×C411yescharacteristic
36C2×M16×C19—21no—
37C4×Q8×C19—21no—
38C4×Q8×C19—21no—
39C4×Q8×C19D411yescharacteristic
40C4×Q8×C19D411yescharacteristic
41C4×Q8×C19D411yescharacteristic
42C4×Q8×C19D411yescharacteristic
43C2×C4⋊C4×C19—21no—
44C2×C4⋊C4×C19C2×C411yescharacteristic
45C2×C42×C19—21no—
46C2×C42×C19C2311yescharacteristic
47C2×#64528—21no—
48C2×#64528—21no—
49C2×#64528—42no—
50C2×#64527—21no—
51C2×#64527—21no—
52C2×#64527—42no—
53C2×(C2×D19)⋊C4—21no—
54C2×(C2×D19)⋊C4—21no—
55C22×C19⋊C8C2×C411yescharacteristic
56C22×C19⋊C8C2×C411yescharacteristic
57#10597321—21no—
58#10597321—21no—
59#10597321—21no—
60#10597321—21no—
61C19×C4⋊C8—21no—
62C19×C22⋊C8—21no—
63C19×#97—21no—
64C19×#97—21no—
65C4×C8×C19—21no—
66C22⋊(C19⋊C8)—21no—
67C22⋊(C19⋊C8)D411yescharacteristic
68C22⋊(C19⋊C8)D411yescharacteristic
69#10597267—21no—
70#10597267—21no—
71#10597266—21no—
72#10597266—21no—
73C4⋊(C19⋊C8)—22no—
74C4⋊(C19⋊C8)—22no—
75C4⋊(C19⋊C8)—21no—
76C4⋊(C19⋊C8)—21no—
77C4⋊(C19⋊C8)—21no—
78C4⋊(C19⋊C8)—21no—
79#10597260—22no—
80#10597260D412yes—
81C4×C19⋊C8—22no—
82C4×C19⋊C8—21no—
83C23×D19—21no—
84C2×Q8×C19—21no—
85C2×Q8×C19—22no—
86C2×Q8×C19—41no—
87C2×Q8×C19C22⋊C411yescharacteristic
88C2×Q8×C19C22⋊C411yescharacteristic
89C22×C4×C19—21no—
90C22×C4×C19—21no—
91C22×C4×C19C22×C411yescharacteristic
92C22×C4×C19C2×D411yescharacteristic
93C22×C4×C19#4111yescharacteristic
94C22×Dic19—21no—
95C2×D76—21no—
96C2×D76—21no—
97C2×D76—41no—
98C2×D76—41no—
99C2×Dic38—21no—
100C2×Dic38—21no—
101C2×Dic38—41no—
102C2×Dic38—41no—
103M16×C19—22no—
104M16×C19—41no—
105C2×C8×C19—41no—
106C2×C8×C19—41no—
107C4⋊C4×C19—21no—
108C4⋊C4×C19—21no—
109C4⋊C4×C19—21no—
110C4⋊C4×C19—21no—
111C4⋊C4×C19—21no—
112C4⋊C4×C19C22⋊C411yescharacteristic
113C4⋊C4×C19C22⋊C411yescharacteristic
114C42×C19—21no—
115C42×C19—21no—
116C42×C19—21no—
117C42×C19—21no—
118C42×C19C2×D411yescharacteristic
119C42×C19C2×D411yescharacteristic
120C42×C19C2×D411yescharacteristic
121C42×C19#4111yescharacteristic
122#64528—42no—
123#64528—42no—
124#64527—42no—
125#64527—42no—
126(C2×D19)⋊C4—41no—
127(C2×D19)⋊C4—41no—
128(C2×D19)⋊C4—41no—
129(C2×D19)⋊C4—41no—
130C2×C19⋊C8—21no—
131C2×C19⋊C8—21no—
132C2×C19⋊C8—21no—
133C2×C19⋊C8—21no—
134C2×C19⋊C8—22no—
135C2×C19⋊C8—41no—
136C2×C19⋊C8—41no—
137#9244—191nomaximal, Sylow
138C23×C19C4×D411yescharacteristic
139C22×D19—41no—
140C22×D19—41no—
141C22×D19—41no—
142C22×D19—81no—
143C22×D19—81no—
144Q8×C19—21no—
145Q8×C19—21no—
146Q8×C19—21no—
147Q8×C19—42no—
148Q8×C19#10012yes—
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—41no—
158C2×C4×C19—42no—
159C2×C4×C19—41no—
160C2×C4×C19—41no—
161C2×C4×C19C2×C22⋊C411yescharacteristic
162C2×C4×C19C4×D411yescharacteristic
163C2×C4×C19#12011yescharacteristic
164C2×C4×C19#12111yescharacteristic
165C2×C4×C19#12111yescharacteristic
166C2×C4×C19#12311yescharacteristic
167C2×Dic19—41no—
168C2×Dic19—81no—
169D76—41no—
170D76—41no—
171D76—81no—
172Dic38—41no—
173Dic38—41no—
174Dic38—81no—
175C8×C19—42no—
176C8×C19—81no—
177C19⋊C8—41no—
178C19⋊C8—41no—
179C19⋊C8—42no—
180C19⋊C8—41no—
181C19⋊C8—41no—
182C2×#464—191no—
183#2984—191no—
184#1527—191no—
185#1491D1911yescharacteristic, complemented
186#1469—191no—
187#1290—191no—
188#1283—191no—
189C22×C19—21no—
190C22×C19—21no—
191C22×C19#38611yescharacteristic
192C22×C19#44311yescharacteristic
193C22×C19#44411yescharacteristic
194C2×D19—81no—
195C2×D19—81no—
196C2×D19—81no—
197C2×D19—161no—
198C2×D19—161no—
199C4×C19—21no—
200C4×C19—21no—
201C4×C19—21no—
202C4×C19—22no—
203C4×C19—21no—
204C4×C19—21no—
205C4×C19—41no—
206C4×C19—41no—
207C4×C19—41no—
208C4×C19C2×#10011yescharacteristic
209C4×C19#41311yescharacteristic
210Dic19—81no—
211C22×Q16—191no—
212C22×SD16—191no—
213C2×#124—191no—
214C2×C4×Q8C2×D1911yescharacteristic
215#464—381no—
216#464—381no—
217#464—381no—
218#464—381no—
219#446—382no—
220#446—381no—
221C8×Q8—381no—
222#432—191no—
223#432—381no—
224#432C2×D1911yescharacteristic
225#431—191no—
226#431—381no—
227C2×C4⋊C8—191no—
228C2×#103—191no—
229C2×#102—191no—
230C4×M16C2×D1911yescharacteristic
231#329—382no—
232Q8⋊C8—21no—
233Q8⋊C8—21no—
234#323—381no—
235#323—381no—
236C2×C19—21no—
237C2×C19—21no—
238C2×C19#187611yescharacteristic
239C2×C19#190011yescharacteristic
240C2×C19#190511yescharacteristic
241D19—161no—
242C22×Q8—191no—
243C22×Q8C4×D1911yescharacteristic
244C22×D4—191no—
245C2×Q16—381no—
246C2×Q16—381no—
247C2×Q16—762no—
248C2×SD16—381no—
249C2×SD16—381no—
250C2×SD16—762no—
251C2×M16—21no—
252C22×C8—191no—
253C22×C8—191no—
254#124—381no—
255#124—381no—
256#124—381no—
257#124—381no—
258C4×Q8—21no—
259C4×Q8—21no—
260C4×Q8D7611yescharacteristic
261C4×Q8D7611yescharacteristic
262C4×Q8C22⋊D1911yescharacteristic
263C4×Q8C22⋊D1911yescharacteristic
264C2×C4⋊C4—21no—
265C2×C4⋊C4C4×D1911yescharacteristic
266C2×C22⋊C4—381no—
267C2×C22⋊C4—381no—
268C2×C42—21no—
269C2×C42C22×D1911yescharacteristic
270C4⋊C8—21no—
271C4⋊C8—382no—
272C4⋊C8—382no—
273C4⋊C8—381no—
274C4⋊C8—381no—
275C4⋊C8—381no—
276C4⋊C8—381no—
277#103—381no—
278#103—381no—
279#102—381no—
280#102—381no—
281C22⋊C8—21no—
282C22⋊C8—191no—
283C22⋊C8—191no—
284C22⋊C8—381no—
285#97—21no—
286#97—21no—
287#97—192no—
288#97—382no—
289C4×C8—21no—
290C4×C8—382no—
291C4×C8—381no—
292C19#924411yescharacteristic, complemented, Sylow
293C24—381no—
294C2×Q8—21no—
295C2×Q8—22no—
296C2×Q8—41no—
297C2×Q8—381no—
298C2×Q8—381no—
299C2×Q8—761no—
300C2×Q8—761no—
301C2×Q8(C2×D19)⋊C411yescharacteristic
302C2×Q8(C2×D19)⋊C411yescharacteristic
303C2×D4—381no—
304C2×D4—381no—
305C2×D4—761no—
306C2×D4—761no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—381no—
310C22×C4C2×C4×D1911yescharacteristic
311C22×C4D4×D1911yescharacteristic
312C22×C4#6454311yescharacteristic
313Q16—762no—
314Q16—762no—
315SD16—762no—
316SD16—762no—
317M16—22no—
318M16—41no—
319C2×C8—41no—
320C2×C8—41no—
321C2×C8—381no—
322C2×C8—382no—
323C2×C8—381no—
324C2×C8—381no—
325C2×C8—381no—
326C2×C8—761no—
327C2×C8—761no—
328C4⋊C4—21no—
329C4⋊C4—21no—
330C4⋊C4—21no—
331C4⋊C4—21no—
332C4⋊C4—21no—
333C4⋊C4(C2×D19)⋊C411yescharacteristic
334C4⋊C4(C2×D19)⋊C411yescharacteristic
335C22⋊C4—761no—
336C22⋊C4—761no—
337C22⋊C4—761no—
338C22⋊C4—761no—
339C42—21no—
340C42—21no—
341C42—21no—
342C42—21no—
343C42C2×D7611yescharacteristic
344C42D4×D1911yescharacteristic
345C42#6454311yescharacteristic
346C42C2×C22⋊D1911yescharacteristic
347C23—761no—
348C23—761no—
349C23—761no—
350C23—1521no—
351C23—1521no—
352C23(C22⋊D19)⋊C411yescharacteristic
353Q8—21no—
354Q8—21no—
355Q8—21no—
356Q8—42no—
357Q8—761no—
358Q8—761no—
359Q8—1521no—
360Q8#1059728012yes—
361D4—761no—
362D4—761no—
363D4—1521no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—41no—
373C2×C4—42no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—761no—
377C2×C4—1521no—
378C2×C4(C22⋊D19)⋊C411yescharacteristic
379C2×C4#1059732811yescharacteristic
380C2×C4#1059733211yescharacteristic
381C2×C4C2×(C2×D19)⋊C411yescharacteristic
382C2×C4#1059738511yescharacteristic
383C2×C4#1059738511yescharacteristic
384C8—42no—
385C8—81no—
386C8—761no—
387C8—762no—
388C8—761no—
389C8—761no—
390C8—761no—
391C22—21no—
392C22—21no—
393C22—3041no—
394C22—3041no—
395C22—1521no—
396C22—1521no—
397C22—1521no—
398C22#1192642111yescharacteristic
399C22#1192665811yescharacteristic
400C22#1192666311yescharacteristic
401C4—21no—
402C4—22no—
403C4—21no—
404C4—21no—
405C4—21no—
406C4—21no—
407C4—41no—
408C4—41no—
409C4—41no—
410C4—1521no—
411C4C2×#1059728011yescharacteristic
412C4#1192652611yescharacteristic
413C2—21no—
414C2—21no—
415C2—3041no—
416C2#1456396011yescharacteristic
417C2#1456409611yescharacteristic
418C2#1456412711yescharacteristic
subgroupG/H
centerC22#11926421
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1491C2
socleC22×C19#386
prime radicalC22×D76C2×C4
cosocleC2×C42×C19C23
hypercenter#1491D19
hypocenterC19#9244
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1491

Complements

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

NH ≅ G/Ntype
2. #14572724C2semidirect
5. #14561504C2semidirect
6. #14561486C2semidirect
7. C19×#1491C2semidirect
185. #1491D19semidirect
292. C19#9244semidirect

Maximal subgroups

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

subgroupindex
C2×#119267662
#145727242
#145622322
#145619882
#145615042
#145614862
C19×#14912
#924419