Finite Group Databasebeta

← #18075513

Subgroups — #18075513

Order 4864.

456 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14572329C211yesmaximal, characteristic
2#14563673C211yesmaximal, characteristic, complemented
3#14562176C212yesmaximal
4#14561541C212yesmaximal, complemented
5C19×#1808C211yesmaximal, characteristic, complemented
6C2×#10597347C411yescharacteristic, complemented
7#11927055C2211yescharacteristic
8#11926615—21no—
9#11926615—21no—
10C8×C22⋊D19—21no—
11C8×C22⋊D19—21no—
12C2×#10597276—21no—
13#11926570C411yescharacteristic, complemented
14#11926510C411yescharacteristic, complemented
15#11926508C2212yes—
16#11926508C2211yescharacteristic
17#11926499C411yescharacteristic, complemented
18#11926309—21no—
19#11926280—22no—
20#11926277—22no—
21C23×C8×C19C2211yescharacteristic
22C2×C19×#107—21no—
23C19×#380C2212yes—
24C19×#340—21no—
25C23×C4×C19C2311yescharacteristic
26C2×#64541C2×C411yescharacteristic
27C22×C8×C19—42no—
28C22×C8×C19C2×C411yescharacteristic
29C22×C8×C19C2×C411yescharacteristic
30C22×C8×C19D411yescharacteristic
31C22×C8×C19D411yescharacteristic
32C22×C8×C19D411yescharacteristic
33C22×C8×C19D411yescharacteristic
34C2×C4⋊C4×C19—22no—
35C2×C22⋊C4×C19—22no—
36#10597399—21no—
37#10597376D411yescharacteristic
38#10597376Q811yescharacteristic
39#10597375—21no—
40C4×C22⋊D19—21no—
41C4×C22⋊D19—21no—
42#10597372C2×C411yescharacteristic
43#10597370D411yescharacteristic
44#10597370Q811yescharacteristic
45C2×#64520—22no—
46C2×#64520C2×C411yescharacteristic
47C2×#64520C2×C411yescharacteristic
48#10597347—42no—
49C2×#64515—21no—
50C2×C8×D19—21no—
51C19×#107—42no—
52C19×#95—22no—
53C22⋊(C19⋊C8)—21no—
54C22⋊(C19⋊C8)—21no—
55C22⋊(C19⋊C8)—22no—
56C22⋊(C19⋊C8)—22no—
57(C2×D19)⋊C8—21no—
58(C2×D19)⋊C8—21no—
59#10597276—42no—
60#10597272—21no—
61Dic19⋊C8—21no—
62Dic19⋊C8—21no—
63C8×Dic19—21no—
64C24×C19#4111yescharacteristic
65C22×C4×C19—41no—
66C22×C4×C19—41no—
67C22×C4×C19—42no—
68C22×C4×C19C22×C411yescharacteristic
69C22×C4×C19C2×D411yescharacteristic
70C22×C4×C19C2×D411yescharacteristic
71C22×C4×C19C2×D411yescharacteristic
72C22×C4×C19C2×Q811yescharacteristic
73C22×C4×C19#4111yescharacteristic
74C2×C22⋊D19—21no—
75C2×C22⋊D19—21no—
76C2×C22⋊D19—21no—
77#64541—41no—
78#64541—41no—
79C2×D76C4⋊C411yescharacteristic
80C2×C4×D19—21no—
81C2×Dic38C4⋊C411yescharacteristic
82C2×C8×C19—22no—
83C2×C8×C19—22no—
84C2×C8×C19—22no—
85C2×C8×C19—41no—
86C2×C8×C19—41no—
87C2×C8×C19—41no—
88C2×C8×C19C22⋊C411yescharacteristic
89C2×C8×C19C22⋊C411yescharacteristic
90C2×C8×C19C22⋊C411yescharacteristic
91C2×C8×C19C22⋊C411yescharacteristic
92C4⋊C4×C19—42no—
93C4⋊C4×C19—42no—
94C22⋊C4×C19—82no—
95C22⋊Dic19—21no—
96C22⋊Dic19—21no—
97C22⋊Dic19—21no—
98(C2×D19)⋊C4—21no—
99(C2×D19)⋊C4—21no—
100C4⋊Dic19C4⋊C411yescharacteristic
101C4⋊Dic19C4⋊C411yescharacteristic
102Dic19⋊C4—21no—
103Dic19⋊C4—21no—
104C4×Dic19—21no—
105#64520—41no—
106#64520—41no—
107#64520—42no—
108#64520—42no—
109C2×C19⋊C8—21no—
110C2×C19⋊C8—21no—
111C2×C19⋊C8—42no—
112#64515—42no—
113C8×D19—42no—
114#8627—191nomaximal, Sylow
115C23×C19—21no—
116C23×C19—21no—
117C23×C19—41no—
118C23×C19—41no—
119C23×C19#11711yescharacteristic
120C23×C19#12111yescharacteristic
121C23×C19C22⋊Q811yescharacteristic
122C22×D19—21no—
123C2×C4×C19—21no—
124C2×C4×C19—21no—
125C2×C4×C19—21no—
126C2×C4×C19—21no—
127C2×C4×C19—21no—
128C2×C4×C19—21no—
129C2×C4×C19—41no—
130C2×C4×C19—41no—
131C2×C4×C19—41no—
132C2×C4×C19—82no—
133C2×C4×C19—82no—
134C2×C4×C19—82no—
135C2×C4×C19C2×C22⋊C411yescharacteristic
136C2×C4×C19C2×C4⋊C411yescharacteristic
137C2×C4×C19#12111yescharacteristic
138C2×C4×C19C22⋊Q811yescharacteristic
139C22⋊D19—42no—
140C22⋊D19—42no—
141C22⋊D19—41no—
142C22⋊D19—41no—
143C2×Dic19—21no—
144C2×Dic19—21no—
145C2×Dic19—21no—
146D76—41no—
147C4×D19—41no—
148C4×D19—41no—
149Dic38—41no—
150C8×C19—21no—
151C8×C19—21no—
152C8×C19—21no—
153C8×C19#9912yes—
154C19⋊C8—41no—
155C19⋊C8—41no—
156C19⋊C8—82no—
157#2929—191no—
158#1810—191no—
159#1808D1911yescharacteristic, complemented
160#1513—192no—
161#1305—192no—
162C22×C19—21no—
163C22×C19—21no—
164C22×C19—21no—
165C22×C19—21no—
166C22×C19—21no—
167C22×C19—21no—
168C22×C19—21no—
169C22×C19—21no—
170C22×C19—42no—
171C22×C19—42no—
172C22×C19#38011yescharacteristic
173C22×C19#47211yescharacteristic
174C22×C19#47311yescharacteristic
175C2×D19—41no—
176C2×D19—41no—
177C2×D19—41no—
178C4×C19—21no—
179C4×C19—21no—
180C4×C19—21no—
181C4×C19—162no—
182C4×C19C2×#9911yescharacteristic
183C4×C19#41011yescharacteristic
184Dic19—41no—
185Dic19—41no—
186Dic19—41no—
187C2×#131—191no—
188C23×C8C2×D1911yescharacteristic
189#525—191no—
190#435—381no—
191#435—381no—
192C8×D4—381no—
193C8×D4—381no—
194C2×#108—381no—
195C2×#107—21no—
196#424—191no—
197#408—191no—
198#407—191no—
199#407—192no—
200#405—191no—
201#380C2×D1912yes—
202#341—381no—
203#340—21no—
204#328—382no—
205#327—382no—
206C2×C19—21no—
207C2×C19—21no—
208C2×C19—41no—
209C2×C19—41no—
210C2×C19#179911yescharacteristic
211C2×C19#181411yescharacteristic
212C2×C19#181611yescharacteristic
213D19—81no—
214C2×#41—191no—
215C23×C4C22×D1911yescharacteristic
216#131—762no—
217C2×M16—191no—
218C2×M16—191no—
219C2×M16—381no—
220C2×M16—382no—
221C22×C8—42no—
222C22×C8—381no—
223C22×C8C4×D1911yescharacteristic
224C22×C8C4×D1911yescharacteristic
225C22×C8D7611yescharacteristic
226C22×C8D7611yescharacteristic
227C22×C8C22⋊D1911yescharacteristic
228C22×C8C22⋊D1911yescharacteristic
229#123—381no—
230C22⋊Q8—191no—
231C22⋊Q8—191no—
232#121—191no—
233#121—191no—
234#120—381no—
235C4×D4—381no—
236C4×D4—381no—
237#117—191no—
238C2×C4⋊C4—22no—
239C2×C22⋊C4—22no—
240#108—762no—
241#107—42no—
242C4⋊C8—381no—
243C4⋊C8—381no—
244C22⋊C8—381no—
245C22⋊C8—381no—
246C22⋊C8—381no—
247C22⋊C8—381no—
248C22⋊C8—382no—
249C22⋊C8—382no—
250#97—381no—
251C4×C8—381no—
252#95—22no—
253C19#862711yescharacteristic, complemented, Sylow
254C24#6454311yescharacteristic
255#41—761no—
256#41—761no—
257C2×Q8—191no—
258C2×D4—191no—
259C2×D4—381no—
260C2×D4—381no—
261C2×D4—381no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4—42no—
265C22×C4—381no—
266C22×C4C2×C4×D1911yescharacteristic
267C22×C4C2×D7611yescharacteristic
268C22×C4D4×D1911yescharacteristic
269C22×C4Q8×D1911yescharacteristic
270C22×C4#6454511yescharacteristic
271C22×C4C2×C22⋊D1911yescharacteristic
272M16—762no—
273M16—761no—
274M16—761no—
275M16—762no—
276M16—762no—
277C2×C8—22no—
278C2×C8—22no—
279C2×C8—22no—
280C2×C8—41no—
281C2×C8—41no—
282C2×C8—41no—
283C2×C8—381no—
284C2×C8—381no—
285C2×C8—762no—
286C2×C8—762no—
287C2×C8(C2×D19)⋊C411yescharacteristic
288C2×C8(C2×D19)⋊C411yescharacteristic
289C2×C8(C2×D19)⋊C411yescharacteristic
290C2×C8(C2×D19)⋊C411yescharacteristic
291C4⋊C4—42no—
292C4⋊C4—42no—
293C4⋊C4—191no—
294C4⋊C4—191no—
295C4⋊C4—381no—
296C4⋊C4—381no—
297C22⋊C4—82no—
298C22⋊C4—381no—
299C22⋊C4—381no—
300C22⋊C4—381no—
301C22⋊C4—381no—
302C22⋊C4—381no—
303C42—381no—
304C23—21no—
305C23—21no—
306C23—41no—
307C23—41no—
308C23—381no—
309C23#1059733811yescharacteristic
310C23#1059734311yescharacteristic
311C23#1059738411yescharacteristic
312Q8—761no—
313D4—761no—
314D4—762no—
315D4—762no—
316D4—761no—
317D4—761no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—82no—
328C2×C4—82no—
329C2×C4—82no—
330C2×C4—381no—
331C2×C4—381no—
332C2×C4—381no—
333C2×C4—761no—
334C2×C4—761no—
335C2×C4C4⋊C4×D1911yescharacteristic
336C2×C4#1059734111yescharacteristic
337C2×C4C2×(C2×D19)⋊C411yescharacteristic
338C2×C4#1059739211yescharacteristic
339C8—21no—
340C8—21no—
341C8—21no—
342C8—761no—
343C8—761no—
344C8—1522no—
345C8#1059726312yes—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—42no—
355C22—42no—
356C22—761no—
357C22—761no—
358C22—761no—
359C22#1192640111yescharacteristic
360C22#1192681111yescharacteristic
361C22#1192681611yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—162no—
366C4—761no—
367C4—761no—
368C4—761no—
369C4C2×#1059726311yescharacteristic
370C4#1192651711yescharacteristic
371C2—21no—
372C2—21no—
373C2—41no—
374C2—41no—
375C2—1521no—
376C2#1456362011yescharacteristic
377C2#1456368611yescharacteristic
378C2#1456370011yescharacteristic
subgroupG/H
centerC22#11926401
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1808C2
socleC22×C19#380
prime radical#11927055C22
cosocleC23×C4×C19C23
hypercenter#1808D19
hypocenterC19#8627
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1808

Complements

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

NH ≅ G/Ntype
2. #14563673C2semidirect
4. #14561541C2semidirect
5. C19×#1808C2semidirect
6. C2×#10597347C4semidirect
13. #11926570C4semidirect
14. #11926510C4semidirect
17. #11926499C4semidirect
159. #1808D19semidirect
253. C19#8627semidirect

Maximal subgroups

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

subgroupindex
#145723292
#145636732
#145621762
#145615412
C19×#18082
#862719