Finite Group Databasebeta

← #18077600

Subgroups — #18077600

Order 4864.

696 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11926470C211yesmaximal, characteristic
2#14566232C211yesmaximal, characteristic
3#14563721C211yesmaximal, characteristic, complemented
4C2×#11926267C211yesmaximal, characteristic
5#14561515C211yesmaximal, characteristic, complemented
6#14561513C211yesmaximal, characteristic, complemented
7C19×#1823C211yesmaximal, characteristic, complemented
8C22×(C2×D19)⋊C4—21no—
9C22×(C2×D19)⋊C4C2211yescharacteristic
10C2×C22⋊(C19⋊C8)C2211yescharacteristic
11#11926470—22no—
12#11926470C414yescomplemented
13#11926436—22no—
14#11926434—22no—
15#11926404C2211yescharacteristic
16#11926399—21no—
17C22⋊C4×Dic19—21no—
18C2×C19⋊#95—21no—
19C2×C19⋊#95C2211yescharacteristic
20#11926306—22no—
21#11926267—22no—
22C22×C4⋊C4×C19C2211yescharacteristic
23C2×C19×C22⋊C8C2211yescharacteristic
24C19×#380C2211yescharacteristic
25C19×#340—22no—
26C24×D19D411yescharacteristic
27C23×C4×C19—21no—
28C23×C4×C19C2311yescharacteristic
29C23×Dic19—21no—
30C23×Dic19D411yescharacteristic
31C22×C8×C19—21no—
32C2×C4⋊C4×C19—21no—
33C2×C4⋊C4×C19—21no—
34C2×C4⋊C4×C19—21no—
35C2×C4⋊C4×C19—21no—
36C2×C4⋊C4×C19—21no—
37C2×C4⋊C4×C19C2×C412yes—
38C2×C4⋊C4×C19D412yes—
39C2×C22⋊C4×C19—21no—
40C2×C22⋊Dic19—21no—
41C2×(C2×D19)⋊C4—21no—
42C2×(C2×D19)⋊C4—21no—
43C2×(C2×D19)⋊C4—21no—
44C2×(C2×D19)⋊C4—21no—
45C2×(C2×D19)⋊C4—24no—
46C2×(C2×D19)⋊C4—22no—
47C2×(C2×D19)⋊C4—22no—
48C2×(C2×D19)⋊C4—42no—
49C2×(C2×D19)⋊C4—42no—
50C2×(C2×D19)⋊C4C2×C412yes—
51C2×(C2×D19)⋊C4D412yes—
52C2×C4⋊Dic19D412yes—
53C2×C4×Dic19—22no—
54C22×C19⋊C8—21no—
55C19×C22⋊C8—21no—
56C19×C22⋊C8—21no—
57C19×#95—21no—
58C19⋊#95—22no—
59C19⋊#95—21no—
60C19⋊#95—21no—
61C19⋊#95—24no—
62C19⋊#95C2×C412yes—
63C22⋊(C19⋊C8)—21no—
64C22⋊(C19⋊C8)—21no—
65C24×C19C2×D411yescharacteristic
66C23×D19—21no—
67C23×D19—21no—
68C23×D19—21no—
69C23×D19—21no—
70C23×D19—21no—
71C23×D19—21no—
72C23×D19—42no—
73C23×D19—42no—
74C23×D19C22⋊C412yes—
75C22×C4×C19—22no—
76C22×C4×C19—22no—
77C22×C4×C19—42no—
78C22×C4×C19—41no—
79C22×C4×C19—41no—
80C22×C4×C19—41no—
81C22×C4×C19—41no—
82C22×C4×C19—41no—
83C22×C4×C19—41no—
84C22×C4×C19C22×C411yescharacteristic
85C22×C4×C19C2×D411yescharacteristic
86C22×C4×C19C2×D411yescharacteristic
87C22×C4×C19C2×D411yescharacteristic
88C22×C4×C19#4111yescharacteristic
89C22×C4×C19#4111yescharacteristic
90C22×Dic19—21no—
91C22×Dic19—21no—
92C22×Dic19—22no—
93C22×Dic19—22no—
94C22×Dic19—42no—
95C22×Dic19—42no—
96C22×Dic19—42no—
97C22×Dic19—41no—
98C22×Dic19—41no—
99C22×Dic19C22⋊C412yes—
100C2×C8×C19—42no—
101C2×C8×C19—41no—
102C4⋊C4×C19—22no—
103C4⋊C4×C19—22no—
104C4⋊C4×C19—42no—
105C4⋊C4×C19—41no—
106C4⋊C4×C19—41no—
107C22⋊C4×C19—41no—
108C22⋊C4×C19—41no—
109C22⋊Dic19—41no—
110C22⋊Dic19—41no—
111(C2×D19)⋊C4—22no—
112(C2×D19)⋊C4—22no—
113(C2×D19)⋊C4—22no—
114(C2×D19)⋊C4—22no—
115(C2×D19)⋊C4—48no—
116(C2×D19)⋊C4—82no—
117(C2×D19)⋊C4—82no—
118C4⋊Dic19—42no—
119C4×Dic19—82no—
120C2×C19⋊C8—42no—
121C2×C19⋊C8—41no—
122#9028—191nomaximal, Sylow
123C23×C19—22no—
124C23×C19—22no—
125C23×C19C2×C22⋊C411yescharacteristic
126C23×C19#12011yescharacteristic
127C23×C19#12311yescharacteristic
128C23×C19#13511yescharacteristic
129C23×C19#13511yescharacteristic
130C23×C19AGL(1,ℤ/8)11yescharacteristic
131C23×C19AGL(1,ℤ/8)11yescharacteristic
132C22×D19—22no—
133C22×D19—22no—
134C22×D19—22no—
135C22×D19—42no—
136C22×D19—42no—
137C22×D19—44no—
138C22×D19—44no—
139C22×D19—41no—
140C22×D19—41no—
141C22×D19—42no—
142C22×D19—42no—
143C22×D19—41no—
144C22×D19—41no—
145C22×D19—81no—
146C22×D19—81no—
147C22×D19—82no—
148C22×D19—82no—
149C2×C4×C19—22no—
150C2×C4×C19—22no—
151C2×C4×C19—41no—
152C2×C4×C19—41no—
153C2×C4×C19—41no—
154C2×C4×C19—41no—
155C2×C4×C19—42no—
156C2×C4×C19—42no—
157C2×C4×C19—42no—
158C2×C4×C19—42no—
159C2×C4×C19—42no—
160C2×C4×C19—42no—
161C2×C4×C19—81no—
162C2×C4×C19—81no—
163C2×C4×C19—81no—
164C2×C4×C19—81no—
165C2×C4×C19C4×D411yescharacteristic
166C2×C4×C19C4×D411yescharacteristic
167C2×C4×C19#12111yescharacteristic
168C2×C4×C19#12111yescharacteristic
169C2×Dic19—22no—
170C2×Dic19—42no—
171C2×Dic19—42no—
172C2×Dic19—42no—
173C2×Dic19—42no—
174C2×Dic19—42no—
175C2×Dic19—42no—
176C2×Dic19—42no—
177C2×Dic19—42no—
178C2×Dic19—81no—
179C2×Dic19—82no—
180C2×Dic19—82no—
181C8×C19—81no—
182C19⋊C8—81no—
183C2×#397—191no—
184#2312—191no—
185#1823—191no—
186#1823D1911yescharacteristic, complemented
187C2×#323—191no—
188#1294—191no—
189#1294—191no—
190C22×C19—22no—
191C22×C19—22no—
192C22×C19—22no—
193C22×C19—22no—
194C22×C19—21no—
195C22×C19—21no—
196C22×C19—21no—
197C22×C19—21no—
198C22×C19#38611yescharacteristic
199C22×C19#41611yescharacteristic
200C22×C19#41811yescharacteristic
201C22×C19#44911yescharacteristic
202C22×C19#44911yescharacteristic
203C22×C19#45512yes—
204C22×C19#45812yes—
205C22×C19#48211yescharacteristic
206C22×C19#48211yescharacteristic
207C2×D19—44no—
208C2×D19—42no—
209C2×D19—42no—
210C2×D19—42no—
211C2×D19—82no—
212C2×D19—82no—
213C2×D19—82no—
214C2×D19—82no—
215C2×D19—82no—
216C4×C19—21no—
217C4×C19—21no—
218C4×C19—21no—
219C4×C19—21no—
220C4×C19—82no—
221C4×C19—82no—
222Dic19—42no—
223Dic19—82no—
224Dic19—82no—
225C22×C4⋊C4C2×D1911yescharacteristic
226C22×C22⋊C4—191no—
227C22×C22⋊C4—381no—
228C2×C22⋊C8—191no—
229C2×C22⋊C8C2×D1911yescharacteristic
230#397—194no—
231#397—382no—
232#388—382no—
233#388—382no—
234#380—191no—
235#380C2×D1911yescharacteristic
236#379—381no—
237C4×C22⋊C4—381no—
238C2×#95—191no—
239C2×#95—381no—
240#340—22no—
241#340—382no—
242#323—382no—
243C2×C19—21no—
244C2×C19—21no—
245C2×C19—21no—
246C2×C19—21no—
247C2×C19#161212yes—
248C2×C19#161212yes—
249C2×C19#187511yescharacteristic
250C2×C19#188511yescharacteristic
251C2×C19#189011yescharacteristic
252D19—82no—
253C25—191no—
254C23×C4—21no—
255C23×C4—191no—
256C23×C4—381no—
257C23×C4C22×D1911yescharacteristic
258C22×C8—21no—
259C22×C8—381no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—192no—
266C2×C4⋊C4C4×D1912yes—
267C2×C4⋊C4C22⋊D1912yes—
268C2×C22⋊C4—21no—
269C2×C22⋊C4—192no—
270C2×C22⋊C4—192no—
271C2×C22⋊C4—381no—
272C2×C22⋊C4—381no—
273C2×C22⋊C4—381no—
274C2×C22⋊C4—381no—
275C2×C22⋊C4—384no—
276C2×C22⋊C4—381no—
277C2×C22⋊C4—382no—
278C2×C22⋊C4—382no—
279C2×C22⋊C4—762no—
280C2×C22⋊C4—762no—
281C2×C42—382no—
282C22⋊C8—21no—
283C22⋊C8—21no—
284C22⋊C8—381no—
285C22⋊C8—381no—
286#95—21no—
287#95—192no—
288#95—384no—
289#95—382no—
290#95—381no—
291#95—381no—
292C19#902811yescharacteristic, complemented, Sylow
293C24—192no—
294C24—381no—
295C24—381no—
296C24—381no—
297C24—381no—
298C24—381no—
299C24—381no—
300C24—762no—
301C24—762no—
302C24D4×D1911yescharacteristic
303C22×C4—22no—
304C22×C4—22no—
305C22×C4—42no—
306C22×C4—41no—
307C22×C4—41no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—41no—
312C22×C4—192no—
313C22×C4—381no—
314C22×C4—381no—
315C22×C4—382no—
316C22×C4—382no—
317C22×C4—762no—
318C22×C4—762no—
319C22×C4—762no—
320C22×C4—761no—
321C22×C4—761no—
322C22×C4C2×C4×D1911yescharacteristic
323C22×C4#6454111yescharacteristic
324C22×C4D4×D1911yescharacteristic
325C22×C4D4×D1911yescharacteristic
326C22×C4#6454311yescharacteristic
327C22×C4C2×C22⋊D1911yescharacteristic
328C2×C8—42no—
329C2×C8—41no—
330C2×C8—762no—
331C2×C8—761no—
332C4⋊C4—22no—
333C4⋊C4—22no—
334C4⋊C4—42no—
335C4⋊C4—41no—
336C4⋊C4—41no—
337C4⋊C4—762no—
338C22⋊C4—41no—
339C22⋊C4—41no—
340C22⋊C4—382no—
341C22⋊C4—382no—
342C22⋊C4—382no—
343C22⋊C4—382no—
344C22⋊C4—768no—
345C22⋊C4—761no—
346C22⋊C4—761no—
347C22⋊C4—1522no—
348C22⋊C4—1522no—
349C42—1522no—
350C23—22no—
351C23—22no—
352C23—382no—
353C23—382no—
354C23—382no—
355C23—762no—
356C23—762no—
357C23—764no—
358C23—764no—
359C23—761no—
360C23—761no—
361C23—761no—
362C23—761no—
363C23—762no—
364C23—762no—
365C23—1521no—
366C23—1521no—
367C23—1522no—
368C23—1522no—
369C23C22⋊C4×D1911yescharacteristic
370C23#1059732911yescharacteristic
371C23#1059735711yescharacteristic
372C23#1059735811yescharacteristic
373C23#1059736011yescharacteristic
374C23#1059736211yescharacteristic
375C23#1059738311yescharacteristic
376C2×C4—22no—
377C2×C4—22no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—81no—
389C2×C4—81no—
390C2×C4—81no—
391C2×C4—81no—
392C2×C4—382no—
393C2×C4—762no—
394C2×C4—762no—
395C2×C4—762no—
396C2×C4—762no—
397C2×C4—762no—
398C2×C4—762no—
399C2×C4—762no—
400C2×C4—762no—
401C2×C4—1521no—
402C2×C4—1522no—
403C2×C4—1522no—
404C2×C4(C22⋊D19)⋊C411yescharacteristic
405C2×C4#1059733011yescharacteristic
406C2×C4C4×C22⋊D1911yescharacteristic
407C2×C4#1059738411yescharacteristic
408C8—81no—
409C8—1521no—
410C22—22no—
411C22—22no—
412C22—22no—
413C22—22no—
414C22—21no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—764no—
419C22—762no—
420C22—762no—
421C22—762no—
422C22—1522no—
423C22—1522no—
424C22—1522no—
425C22—1522no—
426C22—1522no—
427C22#1192642011yescharacteristic
428C22#1192653711yescharacteristic
429C22#1192654711yescharacteristic
430C22#1192668611yescharacteristic
431C22#1192668811yescharacteristic
432C22#1192672012yes—
433C22#1192673312yes—
434C22#1192686611yescharacteristic
435C22#1192686711yescharacteristic
436C4—21no—
437C4—21no—
438C4—21no—
439C4—21no—
440C4—82no—
441C4—82no—
442C4—762no—
443C4—1522no—
444C4—1522no—
445C2—21no—
446C2—21no—
447C2—21no—
448C2—21no—
449C2—1522no—
450C2#1456264612yes—
451C2#1456264812yes—
452C2#1456395411yescharacteristic
453C2#1456402011yescharacteristic
454C2#1456404511yescharacteristic
subgroupG/H
centerC23#10597383
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1823C2
socleC23×C19#120
prime radicalC24×D19D4
cosocleC23×C4×C19C23
hypercenter#1823D19
hypocenterC19#9028
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1823

Complements

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

NH ≅ G/Ntype
3. #14563721C2semidirect
5. #14561515C2semidirect
6. #14561513C2semidirect
7. C19×#1823C2semidirect
12. #11926470C4semidirect
186. #1823D19semidirect
292. C19#9028semidirect

Maximal subgroups

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

subgroupindex
C2×#119264702
#145662322
#145637212
C2×#119262672
#145615152
#145615132
C19×#18232
#902819