Finite Group Databasebeta

← #18078086

Subgroups — #18078086

Order 4864.

560 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14572661C211yesmaximal, characteristic
2#14566304C211yesmaximal, characteristic
3#14561951C211yesmaximal, characteristic
4C2×#11926270C211yesmaximal, characteristic, complemented
5#14561482C211yesmaximal, characteristic, complemented
6#14561481C211yesmaximal, characteristic, complemented
7C2×C19×#324C211yesmaximal, characteristic, complemented
8C2×#10597375C411yescharacteristic
9C2×C4×C22⋊D19C2211yescharacteristic
10#11926615—22no—
11#11926612—22no—
12#11926598—21no—
13#11926506—21no—
14C2×C22⋊(C19⋊C8)C2211yescharacteristic
15C2×C22⋊(C19⋊C8)C2211yescharacteristic
16#11926439—21no—
17#11926434—21no—
18#11926425—21no—
19#11926423C411yescharacteristic
20#11926417C411yescharacteristic
21#11926415—21no—
22#11926407C411yescharacteristic
23C4×C22⋊Dic19C2211yescharacteristic
24#11926270—22no—
25#11926269—21no—
26#11926267—21no—
27C22×C4⋊C4×C19C2211yescharacteristic
28C2×C19×C22⋊C8C2211yescharacteristic
29C2×C19×C22⋊C8C2211yescharacteristic
30C19×#324—22no—
31C23×C4×C19C2×C411yescharacteristic
32C23×C4×C19C2×C411yescharacteristic
33C23×C4×C19C2311yescharacteristic
34C22×C22⋊D19C2×C411yescharacteristic
35C22×C4×D19D411yescharacteristic
36C22×C8×C19—21no—
37C22×C8×C19—21no—
38C2×C4⋊C4×C19—21no—
39C2×C4⋊C4×C19—21no—
40C2×C4⋊C4×C19—21no—
41C2×C4⋊C4×C19—21no—
42C2×C4⋊C4×C19—21no—
43C2×C4⋊C4×C19—21no—
44C2×C22⋊Dic19C2×C411yescharacteristic
45C2×C22⋊Dic19C2×C411yescharacteristic
46C2×C22⋊Dic19C2×C411yescharacteristic
47#10597375—22no—
48#10597375—22no—
49C4×C22⋊D19—21no—
50C4×C22⋊D19—21no—
51C4×C22⋊D19—21no—
52C4×C22⋊D19—21no—
53C2×(C2×D19)⋊C4—21no—
54C2×(C2×D19)⋊C4—21no—
55C2×(C2×D19)⋊C4D411yescharacteristic
56C2×Dic19⋊C4—21no—
57C2×Dic19⋊C4—21no—
58C2×Dic19⋊C4D411yescharacteristic
59C2×C4×Dic19—21no—
60C2×C4×Dic19D411yescharacteristic
61C22×C19⋊C8—21no—
62C22×C19⋊C8—21no—
63C2×#64515—22no—
64C19×C22⋊C8—21no—
65C19×C22⋊C8—21no—
66C19×C22⋊C8—21no—
67C19×C22⋊C8D412yes—
68C19⋊#95—21no—
69C19⋊#95—21no—
70C19⋊#95—21no—
71C19⋊#95—21no—
72C19⋊#95—21no—
73C22⋊(C19⋊C8)—21no—
74C22⋊(C19⋊C8)—21no—
75C22⋊(C19⋊C8)—21no—
76C22⋊(C19⋊C8)D412yes—
77(C2×D19)⋊C8—22no—
78#10597272—22no—
79Dic19⋊C8—22no—
80C24×C19C22×C411yescharacteristic
81C23×D19C22⋊C411yescharacteristic
82C22×C4×C19—21no—
83C22×C4×C19—21no—
84C22×C4×C19—21no—
85C22×C4×C19—21no—
86C22×C4×C19—21no—
87C22×C4×C19—21no—
88C22×C4×C19—21no—
89C22×C4×C19—21no—
90C22×C4×C19—21no—
91C22×C4×C19—81no—
92C22×C4×C19—81no—
93C22×C4×C19M1612yescomplemented
94C22×C4×C19C2×D411yescharacteristic
95C22×C4×C19C2×D411yescharacteristic
96C22×C4×C19C2×D411yescharacteristic
97C22×C4×C19C2×D411yescharacteristic
98C22×C4×C19#4111yescharacteristic
99C22×C4×C19#4111yescharacteristic
100C2×C22⋊D19—21no—
101C2×C22⋊D19—21no—
102C2×C22⋊D19—21no—
103C2×C22⋊D19—21no—
104C2×C22⋊D19—21no—
105C2×C22⋊D19—21no—
106C22×Dic19—21no—
107C22×Dic19—21no—
108C22×Dic19C22⋊C411yescharacteristic
109C22×Dic19C22⋊C411yescharacteristic
110C22×Dic19C22⋊C411yescharacteristic
111C2×C4×D19—21no—
112C2×C4×D19—21no—
113C2×C4×D19—81no—
114C2×C8×C19—22no—
115C2×C8×C19—41no—
116C2×C8×C19—81no—
117C2×C8×C19—81no—
118C4⋊C4×C19—41no—
119C4⋊C4×C19—41no—
120C4⋊C4×C19—41no—
121C4⋊C4×C19—41no—
122C22⋊Dic19—21no—
123C22⋊Dic19—21no—
124C22⋊Dic19—21no—
125C22⋊Dic19—21no—
126C22⋊Dic19—21no—
127C22⋊Dic19M1612yescomplemented
128(C2×D19)⋊C4—24no—
129(C2×D19)⋊C4—21no—
130(C2×D19)⋊C4—21no—
131(C2×D19)⋊C4—81no—
132Dic19⋊C4—24no—
133Dic19⋊C4—21no—
134Dic19⋊C4—21no—
135Dic19⋊C4—81no—
136C4×Dic19—21no—
137C4×Dic19—21no—
138C4×Dic19—81no—
139C2×C19⋊C8—22no—
140C2×C19⋊C8—41no—
141C2×C19⋊C8—81no—
142C2×C19⋊C8—81no—
143#64515—82no—
144#9110—191nomaximal, Sylow
145C23×C19—41no—
146C23×C19—41no—
147C23×C19C2×C22⋊C411yescharacteristic
148C23×C19C4×D411yescharacteristic
149C23×C19C4×D411yescharacteristic
150C23×C19C2×M1611yescharacteristic
151C23×C19C2×M1611yescharacteristic
152C23×C19#13111yescharacteristic
153C23×C19#13111yescharacteristic
154C22×D19—21no—
155C22×D19—21no—
156C22×D19—21no—
157C22×D19—41no—
158C22×D19—41no—
159C2×C4×C19—22no—
160C2×C4×C19—22no—
161C2×C4×C19—22no—
162C2×C4×C19—41no—
163C2×C4×C19—41no—
164C2×C4×C19—41no—
165C2×C4×C19—41no—
166C2×C4×C19—41no—
167C2×C4×C19—41no—
168C2×C4×C19—41no—
169C2×C4×C19—41no—
170C2×C4×C19—41no—
171C2×C4×C19—41no—
172C2×C4×C19—41no—
173C2×C4×C19—41no—
174C2×C4×C19—41no—
175C2×C4×C19—81no—
176C2×C4×C19—81no—
177C2×C4×C19#12011yescharacteristic
178C2×C4×C19#12111yescharacteristic
179C2×C4×C19#12111yescharacteristic
180C2×C4×C19#12311yescharacteristic
181C22⋊D19—41no—
182C22⋊D19—41no—
183C22⋊D19—41no—
184C22⋊D19—41no—
185C2×Dic19—21no—
186C2×Dic19—21no—
187C2×Dic19—21no—
188C2×Dic19—21no—
189C2×Dic19—22no—
190C2×Dic19—21no—
191C2×Dic19—41no—
192C2×Dic19—41no—
193C2×Dic19—41no—
194C2×Dic19—41no—
195C2×Dic19—41no—
196C2×Dic19—41no—
197C2×Dic19—41no—
198C4×D19—42no—
199C4×D19—81no—
200C8×C19—42no—
201C8×C19—81no—
202C19⋊C8—42no—
203C19⋊C8—81no—
204#2973—191no—
205#2322—191no—
206#1459—191no—
207C2×#324—191no—
208C2×#324D1911yescharacteristic, complemented
209#1282—191no—
210#1282—191no—
211C22×C19—21no—
212C22×C19—21no—
213C22×C19—21no—
214C22×C19—21no—
215C22×C19—21no—
216C22×C19—21no—
217C22×C19—41no—
218C22×C19—41no—
219C22×C19—41no—
220C22×C19—41no—
221C22×C19#38611yescharacteristic
222C22×C19#40711yescharacteristic
223C22×C19#40811yescharacteristic
224C22×C19#43511yescharacteristic
225C22×C19#43511yescharacteristic
226C22×C19#43611yescharacteristic
227C22×C19#43611yescharacteristic
228C2×D19—42no—
229C2×D19—41no—
230C2×D19—41no—
231C2×D19—41no—
232C2×D19—81no—
233C4×C19—21no—
234C4×C19—21no—
235C4×C19—21no—
236C4×C19—21no—
237C4×C19—42no—
238C4×C19—81no—
239Dic19—42no—
240Dic19—41no—
241Dic19—41no—
242Dic19—41no—
243Dic19—81no—
244C2×#123—191no—
245C2×C4×D4—191no—
246C22×C4⋊C4C2×D1911yescharacteristic
247#435—382no—
248#435—382no—
249#432—381no—
250#407—381no—
251C2×C22⋊C8—191no—
252C2×C22⋊C8—191no—
253C2×C22⋊C8C2×D1911yescharacteristic
254C2×C22⋊C8C2×D1911yescharacteristic
255#389—381no—
256#388—381no—
257#387—381no—
258#386—191no—
259#385—191no—
260#385—381no—
261#381—191no—
262C4×C22⋊C4—191no—
263#324—22no—
264#324—381no—
265#324—382no—
266#323—381no—
267C2×C19—21no—
268C2×C19—21no—
269C2×C19—21no—
270C2×C19—21no—
271C2×C19—21no—
272C2×C19—21no—
273C2×C19#187011yescharacteristic
274C2×C19#191311yescharacteristic
275C2×C19#191511yescharacteristic
276D19—81no—
277C22×D4—191no—
278C23×C4—191no—
279C23×C4C4×D1911yescharacteristic
280C23×C4C4×D1911yescharacteristic
281C23×C4C22×D1911yescharacteristic
282C2×M16—382no—
283C22×C8—21no—
284C22×C8—21no—
285C22×C8—381no—
286C22×C8—381no—
287#123—382no—
288#123—382no—
289C4×D4—381no—
290C4×D4—381no—
291C4×D4—381no—
292C4×D4—381no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—191no—
300C2×C4⋊C4—381no—
301C2×C4⋊C4—381no—
302C2×C22⋊C4—191no—
303C2×C22⋊C4—191no—
304C2×C22⋊C4—191no—
305C2×C22⋊C4—191no—
306C2×C22⋊C4—381no—
307C2×C22⋊C4—381no—
308C2×C42—191no—
309C2×C42—381no—
310C4⋊C8—382no—
311C22⋊C8—21no—
312C22⋊C8—21no—
313C22⋊C8—21no—
314C22⋊C8—192no—
315C22⋊C8—382no—
316C22⋊C8—381no—
317C22⋊C8—381no—
318C22⋊C8—381no—
319C22⋊C8C22⋊D1912yes—
320#97—382no—
321#95—381no—
322#95—381no—
323#95—381no—
324#95—381no—
325#95—381no—
326C19#911011yescharacteristic, complemented, Sylow
327C24—191no—
328C24C2×C4×D1911yescharacteristic
329C2×D4—381no—
330C2×D4—381no—
331C2×D4—381no—
332C2×D4—381no—
333C2×D4—381no—
334C2×D4—381no—
335C22×C4—21no—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—21no—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—81no—
345C22×C4—81no—
346C22×C4—191no—
347C22×C4—191no—
348C22×C4—191no—
349C22×C4—381no—
350C22×C4—381no—
351C22×C4—381no—
352C22×C4—381no—
353C22×C4—1521no—
354C22×C4#6451512yescomplemented
355C22×C4#6454111yescharacteristic
356C22×C4D4×D1911yescharacteristic
357C22×C4D4×D1911yescharacteristic
358C22×C4D4×D1911yescharacteristic
359C22×C4#6454311yescharacteristic
360C22×C4C2×C22⋊D1911yescharacteristic
361M16—1522no—
362C2×C8—22no—
363C2×C8—41no—
364C2×C8—81no—
365C2×C8—81no—
366C2×C8—382no—
367C2×C8—761no—
368C2×C8—1521no—
369C2×C8—1521no—
370C4⋊C4—41no—
371C4⋊C4—41no—
372C4⋊C4—41no—
373C4⋊C4—41no—
374C4⋊C4—384no—
375C4⋊C4—381no—
376C4⋊C4—381no—
377C4⋊C4—1521no—
378C22⋊C4—192no—
379C22⋊C4—384no—
380C22⋊C4—381no—
381C22⋊C4—381no—
382C22⋊C4—381no—
383C22⋊C4—381no—
384C22⋊C4—381no—
385C22⋊C4—381no—
386C22⋊C4—381no—
387C22⋊C4—1521no—
388C42—381no—
389C42—381no—
390C42—1521no—
391C23—41no—
392C23—41no—
393C23—381no—
394C23—381no—
395C23—381no—
396C23—761no—
397C23—761no—
398C23C22⋊C4×D1911yescharacteristic
399C23(C22⋊D19)⋊C411yescharacteristic
400C23C2×#6451511yescharacteristic
401C23#1059734711yescharacteristic
402C23M16×D1911yescharacteristic
403C23#1059735311yescharacteristic
404C23C4×C22⋊D1911yescharacteristic
405D4—761no—
406D4—761no—
407D4—761no—
408D4—761no—
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—81no—
426C2×C4—81no—
427C2×C4—381no—
428C2×C4—381no—
429C2×C4—381no—
430C2×C4—382no—
431C2×C4—381no—
432C2×C4—381no—
433C2×C4—762no—
434C2×C4—761no—
435C2×C4—761no—
436C2×C4—761no—
437C2×C4—761no—
438C2×C4—761no—
439C2×C4—761no—
440C2×C4—761no—
441C2×C4—1521no—
442C2×C4#1059732911yescharacteristic
443C2×C4#1059733011yescharacteristic
444C2×C4#1059738311yescharacteristic
445C2×C4#1059738411yescharacteristic
446C8—42no—
447C8—81no—
448C8—762no—
449C8—1521no—
450C22—21no—
451C22—21no—
452C22—21no—
453C22—21no—
454C22—21no—
455C22—21no—
456C22—41no—
457C22—41no—
458C22—41no—
459C22—41no—
460C22—762no—
461C22—761no—
462C22—761no—
463C22—761no—
464C22—1521no—
465C22#1192642011yescharacteristic
466C22#1192650611yescharacteristic
467C22#1192650911yescharacteristic
468C22#1192661211yescharacteristic
469C22#1192661511yescharacteristic
470C22#1192661911yescharacteristic
471C22#1192662011yescharacteristic
472C4—21no—
473C4—21no—
474C4—21no—
475C4—21no—
476C4—42no—
477C4—81no—
478C4—762no—
479C4—761no—
480C4—761no—
481C4—761no—
482C4—1521no—
483C2—21no—
484C2—21no—
485C2—21no—
486C2—21no—
487C2—21no—
488C2—21no—
489C2—1521no—
490C2#1456392911yescharacteristic
491C2#1456417411yescharacteristic
492C2#1456418411yescharacteristic
subgroupG/H
centerC22#11926420
commutatorC24×C19C22×C4
FrattiniC23×C4C22×D19
FittingC2×C19×#324C2
socleC22×C19#386
prime radicalC22×C22⋊D19C2×C4
cosocleC23×C4×C19C23
hypercenterC2×#324D19
hypocenterC19#9110
LCSG ▷ C24×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
4. C2×#11926270C2semidirect
5. #14561482C2semidirect
6. #14561481C2semidirect
7. C2×C19×#324C2semidirect
93. C22×C4×C19M16semidirect
127. C22⋊Dic19M16semidirect
208. C2×#324D19semidirect
326. C19#9110semidirect
354. C22×C4#64515semidirect

Maximal subgroups

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

subgroupindex
#145726612
#145663042
#145619512
C2×#119262702
#145614822
#145614812
C2×C19×#3242
#911019