Finite Group Databasebeta

← #18078867

Subgroups — #18078867

Order 4864.

478 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11926868C211yesmaximal, characteristic
2#14563734C211yesmaximal, characteristic, complemented
3#14562152C211yesmaximal, characteristic
4#14561994C211yesmaximal, characteristic
5#14561511C211yesmaximal, characteristic, complemented
6#14561481C211yesmaximal, characteristic, complemented
7C19×#2924C211yesmaximal, characteristic, complemented
8C2×#10597376C2211yescharacteristic
9#11926868—21no—
10#11926868—21no—
11#11926868—21no—
12#11926868—21no—
13C2×#10597264C411yescharacteristic, complemented
14C2×#10597265C411yescharacteristic, complemented
15C2×#10597266C411yescharacteristic, complemented
16C2×#10597266C411yescharacteristic, complemented
17#11926508C2211yescharacteristic
18C2×C22⋊(C19⋊C8)C2211yescharacteristic
19C4×C22⋊Dic19C2211yescharacteristic
20#11926303—21no—
21#11926303—21no—
22#11926279—22no—
23#11926267—21no—
24#11926267—21no—
25C2×C19×#117C2211yescharacteristic
26C19×#433—22no—
27C19×#432—21no—
28C19×#431—21no—
29C19×#424—21no—
30C19×#407C2211yescharacteristic
31C2×C19×C22⋊C8C2211yescharacteristic
32C19×#405—21no—
33C23×C4×C19C2311yescharacteristic
34C22×C22⋊D19—21no—
35C22×D76C2×C411yescharacteristic
36C2×M16×C19—21no—
37C22×C8×C19—21no—
38C19×#117—21no—
39C19×#117—21no—
40C19×#117D411yescharacteristic
41C19×#117D411yescharacteristic
42C19×#117D411yescharacteristic
43C19×#117D411yescharacteristic
44C2×C4⋊C4×C19C2×C411yescharacteristic
45C2×C4⋊C4×C19C2×C411yescharacteristic
46C2×C22⋊C4×C19—21no—
47C2×C42×C19—21no—
48C2×C22⋊Dic19—21no—
49#10597376—21no—
50#10597376—21no—
51#10597376—21no—
52#10597376—21no—
53C2×(C2×D19)⋊C4—21no—
54C2×C4⋊Dic19C2×C411yescharacteristic
55C2×C4×Dic19—21no—
56C2×#64520—21no—
57C22×C19⋊C8C2×C411yescharacteristic
58C22×C19⋊C8C2×C411yescharacteristic
59C19×C4⋊C8—22no—
60C19×C4⋊C8—22no—
61C19×C22⋊C8—21no—
62C19×C22⋊C8—21no—
63C19×C22⋊C8D412yes—
64C19×C22⋊C8D411yescharacteristic
65C19×C22⋊C8D411yescharacteristic
66C19×#97—22no—
67C4×C8×C19—22no—
68C19⋊#95—21no—
69C22⋊(C19⋊C8)—21no—
70C22⋊(C19⋊C8)—21no—
71C22⋊(C19⋊C8)—21no—
72C22⋊(C19⋊C8)—21no—
73#10597266—21no—
74#10597266—21no—
75#10597266—21no—
76#10597266—21no—
77#10597265—21no—
78#10597265—21no—
79#10597264—21no—
80#10597264—21no—
81C24×C19#4111yescharacteristic
82C23×D19—21no—
83C22×C4×C19—21no—
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×D411yescharacteristic
92C22×C4×C19#4111yescharacteristic
93C2×C22⋊D19—41no—
94C2×C22⋊D19—41no—
95C2×C22⋊D19—82no—
96C22×Dic19—21no—
97C22×Dic19—41no—
98C2×D76—21no—
99C2×D76—21no—
100C2×D76—41no—
101C2×D76—41no—
102M16×C19—41no—
103M16×C19—41no—
104C2×C8×C19—21no—
105C2×C8×C19—21no—
106C2×C8×C19—22no—
107C2×C8×C19—41no—
108C2×C8×C19—41no—
109C4⋊C4×C19—21no—
110C4⋊C4×C19—21no—
111C4⋊C4×C19C22⋊C411yescharacteristic
112C4⋊C4×C19C22⋊C411yescharacteristic
113C4⋊C4×C19C22⋊C411yescharacteristic
114C4⋊C4×C19C22⋊C411yescharacteristic
115C22⋊C4×C19—21no—
116C22⋊C4×C19—21no—
117C22⋊C4×C19—21no—
118C22⋊C4×C19—21no—
119C42×C19—21no—
120C42×C19—21no—
121C42×C19—21no—
122C42×C19—21no—
123C22⋊Dic19—22no—
124C22⋊Dic19—41no—
125(C2×D19)⋊C4—41no—
126(C2×D19)⋊C4—41no—
127C4⋊Dic19—21no—
128C4⋊Dic19—21no—
129C4×Dic19—41no—
130C4×Dic19—41no—
131#64520—41no—
132#64520—41no—
133C2×C19⋊C8—21no—
134C2×C19⋊C8—21no—
135C2×C19⋊C8—41no—
136C2×C19⋊C8—41no—
137C2×C19⋊C8—41no—
138#9242—191nomaximal, Sylow
139C23×C19—21no—
140C23×C19—21no—
141C23×C19—41no—
142C23×C19—41no—
143C23×C19C4×D411yescharacteristic
144C23×C19#12111yescharacteristic
145C23×C19#12311yescharacteristic
146C22×D19—41no—
147C22×D19—41no—
148C22×D19—41no—
149C22×D19—81no—
150C22×D19—81no—
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—21no—
159C2×C4×C19—21no—
160C2×C4×C19—21no—
161C2×C4×C19—41no—
162C2×C4×C19—41no—
163C2×C4×C19—41no—
164C2×C4×C19—41no—
165C2×C4×C19—41no—
166C2×C4×C19—81no—
167C2×C4×C19C2×C22⋊C411yescharacteristic
168C2×C4×C19C4×D411yescharacteristic
169C2×C4×C19#12011yescharacteristic
170C2×C4×C19#12111yescharacteristic
171C22⋊D19—82no—
172C22⋊D19—82no—
173C2×Dic19—42no—
174C2×Dic19—41no—
175C2×Dic19—81no—
176C2×Dic19—81no—
177C2×Dic19—81no—
178D76—41no—
179D76—41no—
180D76—81no—
181C8×C19—41no—
182C8×C19—41no—
183C8×C19—42no—
184C19⋊C8—41no—
185C19⋊C8—41no—
186C19⋊C8—81no—
187C2×#482—191no—
188#2924D1911yescharacteristic, complemented
189#1826—191no—
190#1507—191no—
191#1471—191no—
192#1293—191no—
193#1282—191no—
194C22×C19—21no—
195C22×C19—21no—
196C22×C19—21no—
197C22×C19—21no—
198C22×C19—21no—
199C22×C19—21no—
200C22×C19—21no—
201C22×C19—21no—
202C22×C19—81no—
203C22×C19—81no—
204C22×C19#38611yescharacteristic
205C22×C19#44311yescharacteristic
206C22×C19#44411yescharacteristic
207C2×D19—81no—
208C2×D19—81no—
209C2×D19—81no—
210C2×D19—161no—
211C2×D19—161no—
212C4×C19—21no—
213C4×C19—21no—
214C4×C19—21no—
215C4×C19—41no—
216C4×C19—41no—
217C4×C19—41no—
218C4×C19—41no—
219C4×C19#41011yescharacteristic
220C4×C19#41011yescharacteristic
221Dic19—82no—
222Dic19—81no—
223C2×#121—191no—
224C2×#117C2×D1911yescharacteristic
225#482—381no—
226#482—381no—
227#482—381no—
228#482—381no—
229#433—22no—
230#432—21no—
231#431—21no—
232C2×#107—191no—
233C2×#106—191no—
234#424—21no—
235C2×#102—191no—
236C2×#102—191no—
237#407—191no—
238#407C2×D1911yescharacteristic
239C2×C22⋊C8—191no—
240C2×C22⋊C8C2×D1911yescharacteristic
241#405—21no—
242C4×C22⋊C4—191no—
243#339—381no—
244#339—381no—
245#327—382no—
246#323—381no—
247#323—381no—
248C2×C19—21no—
249C2×C19—21no—
250C2×C19—41no—
251C2×C19—41no—
252C2×C19#187611yescharacteristic
253C2×C19#189911yescharacteristic
254C2×C19#190311yescharacteristic
255D19—161no—
256C22×D4—191no—
257C22×D4—381no—
258C23×C4C22×D1911yescharacteristic
259C2×M16—21no—
260C2×M16—381no—
261C22×C8—21no—
262C22×C8—191no—
263C22×C8—191no—
264#121—381no—
265#121—381no—
266#121—381no—
267#121—381no—
268#117—21no—
269#117—21no—
270#117D7611yescharacteristic
271#117D7611yescharacteristic
272#117C22⋊D1911yescharacteristic
273#117C22⋊D1911yescharacteristic
274C2×C4⋊C4—191no—
275C2×C4⋊C4C4×D1911yescharacteristic
276C2×C4⋊C4C4×D1911yescharacteristic
277C2×C22⋊C4—21no—
278C2×C22⋊C4—381no—
279C2×C22⋊C4—381no—
280C2×C42—21no—
281C2×C42—381no—
282#107—381no—
283#107—381no—
284#106—381no—
285#106—381no—
286C4⋊C8—22no—
287C4⋊C8—22no—
288#102—381no—
289#102—381no—
290#102—381no—
291#102—381no—
292C22⋊C8—21no—
293C22⋊C8—21no—
294C22⋊C8—381no—
295C22⋊C8—381no—
296C22⋊C8—381no—
297C22⋊C8—381no—
298C22⋊C8C22⋊D1911yescharacteristic
299C22⋊C8C22⋊D1911yescharacteristic
300C22⋊C8C22⋊D1912yes—
301#97—22no—
302C4×C8—22no—
303#95—381no—
304C19#924211yescharacteristic, complemented, Sylow
305C24—381no—
306C24#6454111yescharacteristic
307C2×D4—381no—
308C2×D4—381no—
309C2×D4—761no—
310C2×D4—761no—
311C2×D4—761no—
312C2×D4—761no—
313C2×D4—1522no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—41no—
317C22×C4—41no—
318C22×C4—381no—
319C22×C4—761no—
320C22×C4C2×C4×D1911yescharacteristic
321C22×C4C2×D7611yescharacteristic
322C22×C4#6454111yescharacteristic
323C22×C4C2×C22⋊D1911yescharacteristic
324C22×C4C2×C22⋊D1911yescharacteristic
325C22×C4C2×C22⋊D1911yescharacteristic
326M16—41no—
327M16—41no—
328M16—761no—
329M16—761no—
330C2×C8—21no—
331C2×C8—22no—
332C2×C8—21no—
333C2×C8—41no—
334C2×C8—41no—
335C2×C8—381no—
336C2×C8—381no—
337C2×C8—761no—
338C2×C8—761no—
339C2×C8—761no—
340C4⋊C4—21no—
341C4⋊C4—21no—
342C4⋊C4—381no—
343C4⋊C4—381no—
344C4⋊C4(C2×D19)⋊C411yescharacteristic
345C4⋊C4(C2×D19)⋊C411yescharacteristic
346C4⋊C4(C2×D19)⋊C411yescharacteristic
347C4⋊C4(C2×D19)⋊C411yescharacteristic
348C22⋊C4—21no—
349C22⋊C4—21no—
350C22⋊C4—21no—
351C22⋊C4—21no—
352C22⋊C4—382no—
353C22⋊C4—761no—
354C22⋊C4—761no—
355C22⋊C4—761no—
356C42—21no—
357C42—21no—
358C42—21no—
359C42—21no—
360C42—761no—
361C42—761no—
362C23—21no—
363C23—21no—
364C23—41no—
365C23—41no—
366C23—761no—
367C23—761no—
368C23—761no—
369C23—1521no—
370C23—1521no—
371C23C4×C22⋊D1911yescharacteristic
372C23#1059737511yescharacteristic
373C23#1059737611yescharacteristic
374D4—761no—
375D4—761no—
376D4—1521no—
377D4—1522no—
378D4—1522no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—81no—
395C2×C4—762no—
396C2×C4—761no—
397C2×C4—1521no—
398C2×C4—1521no—
399C2×C4—1521no—
400C2×C4C2×(C2×D19)⋊C411yescharacteristic
401C2×C4C4×C22⋊D1911yescharacteristic
402C2×C4#1059737611yescharacteristic
403C2×C4#1059739911yescharacteristic
404C8—41no—
405C8—41no—
406C8—42no—
407C8—761no—
408C8—761no—
409C8—1521no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—21no—
414C22—21no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—81no—
419C22—81no—
420C22—3041no—
421C22—3041no—
422C22—1521no—
423C22—1521no—
424C22—1521no—
425C22#1192642311yescharacteristic
426C22#1192665911yescharacteristic
427C22#1192666411yescharacteristic
428C4—21no—
429C4—21no—
430C4—21no—
431C4—41no—
432C4—41no—
433C4—41no—
434C4—41no—
435C4—1522no—
436C4—1521no—
437C4#1192651711yescharacteristic
438C4#1192651711yescharacteristic
439C2—21no—
440C2—21no—
441C2—41no—
442C2—41no—
443C2—3041no—
444C2#1456396211yescharacteristic
445C2#1456409311yescharacteristic
446C2#1456411511yescharacteristic
subgroupG/H
centerC22#11926423
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#2924C2
socleC22×C19#386
prime radicalC2×#10597376C22
cosocleC23×C4×C19C23
hypercenter#2924D19
hypocenterC19#9242
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2924

Complements

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

NH ≅ G/Ntype
2. #14563734C2semidirect
5. #14561511C2semidirect
6. #14561481C2semidirect
7. C19×#2924C2semidirect
13. C2×#10597264C4semidirect
14. C2×#10597265C4semidirect
15. C2×#10597266C4semidirect
16. C2×#10597266C4semidirect
188. #2924D19semidirect
304. C19#9242semidirect

Maximal subgroups

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

subgroupindex
C2×#119268682
#145637342
#145621522
#145619942
#145615112
#145614812
C19×#29242
#924219