Finite Group Databasebeta

← #18073867

Subgroups — #18073867

Order 4864.

1502 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊C4×D19C211yesmaximal, characteristic
2#14563544C212yesmaximal
3C2×#11926270C211yesmaximal, characteristic, complemented
4C2×#11926269C212yesmaximal, complemented
5C2×C19×#324C211yesmaximal, characteristic, complemented
6C23×C4×D19C411yescharacteristic
7C23×C4×D19C411yescharacteristic
8C23×C4×D19C2211yescharacteristic
9C22×C4⋊Dic19C411yescharacteristic
10C22×Dic19⋊C4C411yescharacteristic
11C22×Dic19⋊C4C2211yescharacteristic
12C2×C4⋊C4×D19—24no—
13C2×C4⋊C4×D19—24no—
14C2×C4⋊C4×D19—22no—
15C2×C4⋊C4×D19—22no—
16C2×C22⋊(C19⋊C8)C2212yes—
17C2×(C2×D19)⋊C8—24no—
18#11926270—22no—
19#11926269—24no—
20C22×C4⋊C4×C19C2211yescharacteristic
21C2×C19×C22⋊C8C2212yes—
22C19×#324—22no—
23C24×D19C2×C411yescharacteristic
24C23×C4×C19C2×C411yescharacteristic
25C23×C4×C19C2×C411yescharacteristic
26C23×C4×C19C2311yescharacteristic
27C23×Dic19C2×C411yescharacteristic
28C23×Dic19C2×C411yescharacteristic
29C23×Dic19C2×C411yescharacteristic
30C22×C4×D19—22no—
31C22×C4×D19—22no—
32C22×C4×D19—22no—
33C22×C4×D19—22no—
34C22×C4×D19—22no—
35C22×C4×D19—22no—
36C22×C4×D19—22no—
37C22×C4×D19—22no—
38C22×C4×D19—21no—
39C22×C4×D19—22no—
40C22×C4×D19—21no—
41C22×C4×D19—22no—
42C22×C4×D19—44no—
43C22×C4×D19—44no—
44C22×C4×D19C814yescomplemented
45C22×C4×D19D414yes—
46C22×C8×C19—22no—
47C2×C4⋊C4×C19—22no—
48C2×C4⋊C4×C19—22no—
49C2×C4⋊C4×C19D412yes—
50C2×C4⋊C4×C19D412yes—
51C2×C4⋊Dic19—22no—
52C2×C4⋊Dic19—22no—
53C2×C4⋊Dic19—22no—
54C2×Dic19⋊C4—22no—
55C2×Dic19⋊C4—21no—
56C2×Dic19⋊C4—22no—
57C2×Dic19⋊C4—21no—
58C2×Dic19⋊C4—22no—
59C2×Dic19⋊C4—22no—
60C2×Dic19⋊C4D414yes—
61C22×C19⋊C8—22no—
62C4⋊C4×D19—216no—
63C4⋊C4×D19—216no—
64C19×C22⋊C8—22no—
65C19×C22⋊C8—22no—
66C22⋊(C19⋊C8)—22no—
67C22⋊(C19⋊C8)—22no—
68(C2×D19)⋊C8—48no—
69C24×C19C22×C411yescharacteristic
70C23×D19—21no—
71C23×D19—21no—
72C23×D19—21no—
73C23×D19—21no—
74C23×D19—24no—
75C23×D19—24no—
76C23×D19C22⋊C412yes—
77C23×D19C2×C812yes—
78C23×D19M1612yes—
79C22×C4×C19—21no—
80C22×C4×C19—21no—
81C22×C4×C19—21no—
82C22×C4×C19—21no—
83C22×C4×C19—21no—
84C22×C4×C19—21no—
85C22×C4×C19—42no—
86C22×C4×C19—42no—
87C22×C4×C19C22⋊C412yes—
88C22×C4×C19C22⋊C412yes—
89C22×C4×C19C2×C812yes—
90C22×C4×C19M1612yes—
91C22×C4×C19C2×D411yescharacteristic
92C22×C4×C19C2×D412yes—
93C22×C4×C19C2×D412yes—
94C22×C4×C19C2×D411yescharacteristic
95C22×Dic19—21no—
96C22×Dic19—21no—
97C22×Dic19—21no—
98C22×Dic19—21no—
99C22×Dic19—21no—
100C22×Dic19—21no—
101C22×Dic19—21no—
102C22×Dic19—21no—
103C22×Dic19—42no—
104C22×Dic19—42no—
105C22×Dic19C22⋊C412yes—
106C22×Dic19C22⋊C412yes—
107C22×Dic19C22⋊C412yes—
108C22×Dic19C2×C812yes—
109C22×Dic19M1612yes—
110C2×C4×D19—28no—
111C2×C4×D19—28no—
112C2×C4×D19—28no—
113C2×C4×D19—28no—
114C2×C4×D19—28no—
115C2×C4×D19—28no—
116C2×C4×D19—28no—
117C2×C4×D19—28no—
118C2×C4×D19—28no—
119C2×C4×D19—24no—
120C2×C4×D19—24no—
121C2×C4×D19—44no—
122C2×C4×D19—44no—
123C2×C4×D19—48no—
124C2×C4×D19—44no—
125C2×C4×D19—48no—
126C2×C4×D19—44no—
127C2×C4×D19—48no—
128C2×C4×D19—44no—
129C2×C8×C19—44no—
130C2×C8×C19—42no—
131C4⋊C4×C19—24no—
132C4⋊C4×C19—24no—
133C4⋊Dic19—28no—
134Dic19⋊C4—28no—
135Dic19⋊C4—24no—
136Dic19⋊C4—24no—
137C2×C19⋊C8—44no—
138C2×C19⋊C8—42no—
139#8299—191nomaximal, Sylow
140C23×C19—22no—
141C23×C19—22no—
142C23×C19C2×C22⋊C411yescharacteristic
143C23×C19C2×C22⋊C411yescharacteristic
144C23×C19C2×C22⋊C411yescharacteristic
145C23×C19C22×C811yescharacteristic
146C23×C19C2×M1611yescharacteristic
147C23×C19C2×M1611yescharacteristic
148C23×C19C2×M1611yescharacteristic
149C22×D19—24no—
150C22×D19—24no—
151C22×D19—28no—
152C22×D19—28no—
153C22×D19—24no—
154C22×D19—24no—
155C22×D19—22no—
156C22×D19—22no—
157C22×D19—22no—
158C22×D19—22no—
159C22×D19—22no—
160C22×D19—22no—
161C22×D19—22no—
162C22×D19—22no—
163C22×D19—28no—
164C22×D19—28no—
165C22×D19C22⋊C814yes—
166C22×D19#9914yes—
167C22×D19#10114yes—
168C2×C4×C19—22no—
169C2×C4×C19—22no—
170C2×C4×C19—22no—
171C2×C4×C19—22no—
172C2×C4×C19—22no—
173C2×C4×C19—22no—
174C2×C4×C19—24no—
175C2×C4×C19—22no—
176C2×C4×C19—41no—
177C2×C4×C19—42no—
178C2×C4×C19—41no—
179C2×C4×C19—42no—
180C2×C4×C19—42no—
181C2×C4×C19—42no—
182C2×C4×C19C22⋊C814yescomplemented
183C2×C4×C19#12012yes—
184C2×C4×C19#12012yes—
185C2×Dic19—22no—
186C2×Dic19—22no—
187C2×Dic19—22no—
188C2×Dic19—22no—
189C2×Dic19—22no—
190C2×Dic19—22no—
191C2×Dic19—22no—
192C2×Dic19—22no—
193C2×Dic19—24no—
194C2×Dic19—42no—
195C2×Dic19—42no—
196C2×Dic19—42no—
197C2×Dic19—42no—
198C2×Dic19—42no—
199C2×Dic19C22⋊C814yescomplemented
200C4×D19—232no—
201C4×D19—48no—
202C4×D19—48no—
203C4×D19—416no—
204C8×C19—82no—
205C19⋊C8—82no—
206C23×C4⋊C4—191no—
207#1779—192no—
208C2×#324—192no—
209C2×#324—191no—
210C2×#324D1911yescharacteristic, complemented
211C22×C19—22no—
212C22×C19—22no—
213C22×C19—22no—
214C22×C19—22no—
215C22×C19—21no—
216C22×C19—21no—
217C22×C19—21no—
218C22×C19—21no—
219C22×C19#37911yescharacteristic
220C22×C19C2×C22⋊C811yescharacteristic
221C22×C19C2×C22⋊C811yescharacteristic
222C22×C19C2×C22⋊C811yescharacteristic
223C22×C19#40711yescharacteristic
224C22×C19#40711yescharacteristic
225C22×C19#40711yescharacteristic
226C22×C19C2×#9912yes—
227C22×C19C2×#10112yes—
228C2×D19—28no—
229C2×D19—28no—
230C2×D19—28no—
231C2×D19—28no—
232C2×D19—24no—
233C2×D19—24no—
234C2×D19—24no—
235C2×D19—24no—
236C2×D19—24no—
237C2×D19—24no—
238C2×D19#32418yescomplemented
239C4×C19—24no—
240C4×C19—22no—
241C4×C19—22no—
242C4×C19—42no—
243Dic19—24no—
244Dic19—42no—
245Dic19—42no—
246C24×C4—191no—
247C24×C4—191no—
248C24×C4—191no—
249C22×C4⋊C4—191no—
250C22×C4⋊C4—191no—
251C22×C4⋊C4—191no—
252C22×C4⋊C4—384no—
253C22×C4⋊C4—384no—
254C22×C4⋊C4—382no—
255C22×C4⋊C4—382no—
256C22×C4⋊C4C2×D1911yescharacteristic
257C2×C22⋊C8—192no—
258C2×C22⋊C8—384no—
259C2×C22⋊C8C2×D1912yes—
260#324—22no—
261#324—384no—
262#324—382no—
263C2×C19—21no—
264C2×C19—21no—
265C2×C19—21no—
266C2×C19—21no—
267C2×C19C2×#32412yes—
268C2×C19#146312yes—
269C2×C19#177911yescharacteristic
270C2×C19#178111yescharacteristic
271C2×C19#178411yescharacteristic
272D19—28no—
273C25—191no—
274C23×C4—191no—
275C23×C4—191no—
276C23×C4—191no—
277C23×C4—194no—
278C23×C4—194no—
279C23×C4—382no—
280C23×C4—382no—
281C23×C4—382no—
282C23×C4—382no—
283C23×C4—382no—
284C23×C4—382no—
285C23×C4—382no—
286C23×C4—382no—
287C23×C4—382no—
288C23×C4—381no—
289C23×C4—382no—
290C23×C4—381no—
291C23×C4—764no—
292C23×C4—764no—
293C23×C4C4×D1911yescharacteristic
294C23×C4C4×D1911yescharacteristic
295C23×C4C22×D1911yescharacteristic
296C22×C8—22no—
297C22×C8—382no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—194no—
301C2×C4⋊C4—3816no—
302C2×C4⋊C4—3816no—
303C2×C4⋊C4—382no—
304C2×C4⋊C4—382no—
305C2×C4⋊C4—382no—
306C2×C4⋊C4—382no—
307C2×C4⋊C4—382no—
308C2×C4⋊C4—382no—
309C2×C4⋊C4—381no—
310C2×C4⋊C4—382no—
311C2×C4⋊C4—381no—
312C2×C4⋊C4D7612yes—
313C2×C4⋊C4C22⋊D1912yes—
314C22⋊C8—22no—
315C22⋊C8—22no—
316C22⋊C8—382no—
317C22⋊C8—382no—
318C22⋊C8—768no—
319C19#829911yescharacteristic, complemented, Sylow
320C24—192no—
321C24—192no—
322C24—192no—
323C24—384no—
324C24—384no—
325C24—381no—
326C24—381no—
327C24—381no—
328C24—381no—
329C24C2×C4×D1911yescharacteristic
330C22×C4—21no—
331C22×C4—21no—
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—42no—
337C22×C4—42no—
338C22×C4—192no—
339C22×C4—192no—
340C22×C4—192no—
341C22×C4—192no—
342C22×C4—192no—
343C22×C4—388no—
344C22×C4—388no—
345C22×C4—388no—
346C22×C4—388no—
347C22×C4—388no—
348C22×C4—388no—
349C22×C4—388no—
350C22×C4—388no—
351C22×C4—381no—
352C22×C4—381no—
353C22×C4—381no—
354C22×C4—381no—
355C22×C4—388no—
356C22×C4—381no—
357C22×C4—381no—
358C22×C4—381no—
359C22×C4—381no—
360C22×C4—384no—
361C22×C4—384no—
362C22×C4—764no—
363C22×C4—764no—
364C22×C4—764no—
365C22×C4—768no—
366C22×C4—764no—
367C22×C4—768no—
368C22×C4—764no—
369C22×C4—768no—
370C22×C4—762no—
371C22×C4—762no—
372C22×C4C8×D1912yes—
373C22×C4#6451512yes—
374C22×C4(C2×D19)⋊C412yes—
375C22×C4(C2×D19)⋊C412yes—
376C22×C4C2×D7611yescharacteristic
377C22×C4D4×D1912yes—
378C22×C4D4×D1912yes—
379C22×C4C2×C22⋊D1911yescharacteristic
380C2×C8—44no—
381C2×C8—42no—
382C2×C8—764no—
383C2×C8—762no—
384C4⋊C4—24no—
385C4⋊C4—24no—
386C4⋊C4—388no—
387C4⋊C4—388no—
388C4⋊C4—384no—
389C4⋊C4—384no—
390C23—22no—
391C23—22no—
392C23—194no—
393C23—194no—
394C23—194no—
395C23—388no—
396C23—388no—
397C23—384no—
398C23—384no—
399C23—388no—
400C23—388no—
401C23—384no—
402C23—384no—
403C23—382no—
404C23—382no—
405C23—382no—
406C23—382no—
407C23—382no—
408C23—382no—
409C23—382no—
410C23—382no—
411C23C22⋊C4×D1911yescharacteristic
412C23C22⋊C4×D1911yescharacteristic
413C23C2×C8×D1911yescharacteristic
414C23C2×#6451511yescharacteristic
415C23M16×D1911yescharacteristic
416C23M16×D1911yescharacteristic
417C23C2×(C2×D19)⋊C411yescharacteristic
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—24no—
425C2×C4—22no—
426C2×C4—41no—
427C2×C4—42no—
428C2×C4—41no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—194no—
433C2×C4—3832no—
434C2×C4—382no—
435C2×C4—382no—
436C2×C4—382no—
437C2×C4—382no—
438C2×C4—382no—
439C2×C4—382no—
440C2×C4—382no—
441C2×C4—382no—
442C2×C4—384no—
443C2×C4—768no—
444C2×C4—768no—
445C2×C4—7616no—
446C2×C4—762no—
447C2×C4—762no—
448C2×C4—762no—
449C2×C4—762no—
450C2×C4—762no—
451C2×C4(C2×D19)⋊C814yescomplemented
452C2×C4#1059732812yes—
453C2×C4#1059738312yes—
454C8—82no—
455C8—1522no—
456C22—22no—
457C22—22no—
458C22—22no—
459C22—22no—
460C22—21no—
461C22—21no—
462C22—21no—
463C22—21no—
464C22—198no—
465C22—388no—
466C22—388no—
467C22—388no—
468C22—388no—
469C22—384no—
470C22—384no—
471C22—384no—
472C22—384no—
473C22—384no—
474C22—384no—
475C22#1192639911yescharacteristic
476C22C22⋊C8×D1911yescharacteristic
477C22C22⋊C8×D1911yescharacteristic
478C22C2×(C2×D19)⋊C811yescharacteristic
479C22#1192650611yescharacteristic
480C22#1192650611yescharacteristic
481C22#1192650711yescharacteristic
482C22#99×D1912yes—
483C22#101×D1912yes—
484C4—24no—
485C4—22no—
486C4—22no—
487C4—42no—
488C4—384no—
489C4—762no—
490C4—762no—
491C2—21no—
492C2—21no—
493C2—21no—
494C2—21no—
495C2—388no—
496C2D19×#32412yes—
497C2#1456196312yes—
498C2#1456354411yescharacteristic
499C2#1456354811yescharacteristic
500C2#1456355711yescharacteristic
subgroupG/H
centerC23C22⋊C4×D19
commutatorC23×C19C22×C8
FrattiniC23×C4C22×D19
FittingC2×C19×#324C2
socleC23×C19C2×C22⋊C4
prime radicalC24×D19C2×C4
cosocleC23×C4×C19C23
hypercenterC2×#324D19
hypocenterC19#8299
LCSG ▷ C23×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
3. C2×#11926270C2semidirect
4. C2×#11926269C2semidirect
5. C2×C19×#324C2semidirect
44. C22×C4×D19C8semidirect
182. C2×C4×C19C22⋊C8semidirect
199. C2×Dic19C22⋊C8semidirect
210. C2×#324D19semidirect
238. C2×D19#324semidirect
319. C19#8299semidirect
451. C2×C4(C2×D19)⋊C8semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊C4×D192
#145635442
C2×#119262702
C2×#119262692
C2×C19×#3242
#829919