Finite Group Databasebeta

← #18075375

Subgroups — #18075375

Order 4864.

598 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C8×D19C211yesmaximal, characteristic
2#14563612C212yesmaximal
3C2×#11926297C211yesmaximal, characteristic, complemented
4#14561469C212yesmaximal, complemented
5C2×C19×#335C211yesmaximal, characteristic, complemented
6C22×C8×D19C411yescharacteristic
7C22×C8×D19C411yescharacteristic
8C2×C42×D19C2211yescharacteristic
9C2×C4⋊(C19⋊C8)C2212yes—
10C2×(C2×D19)⋊C8—22no—
11C2×C4×C19⋊C8C2211yescharacteristic
12C2×C8×Dic19C411yescharacteristic
13C2×C8×Dic19C411yescharacteristic
14C4×C8×D19—22no—
15C4×C8×D19—22no—
16#11926298—22no—
17#11926297—22no—
18C2×C19×C4⋊C8C2212yes—
19C2×C4×C8×C19C2211yescharacteristic
20C19×#335—22no—
21C22×C4×D19C2×C411yescharacteristic
22C22×C4×D19D411yescharacteristic
23C22×C4×D19Q811yescharacteristic
24C22×C8×C19—22no—
25C22×C8×C19C2×C411yescharacteristic
26C22×C8×C19C2×C411yescharacteristic
27C2×C42×C19C2311yescharacteristic
28C2×C4×Dic19C2×C411yescharacteristic
29C2×C4×Dic19D411yescharacteristic
30C2×C4×Dic19Q811yescharacteristic
31C22×C19⋊C8—22no—
32C22×C19⋊C8C2×C411yescharacteristic
33C22×C19⋊C8C2×C411yescharacteristic
34C2×C8×D19—22no—
35C2×C8×D19—22no—
36C2×C8×D19—22no—
37C2×C8×D19—22no—
38C2×C8×D19—22no—
39C2×C8×D19C814yescomplemented
40C42×D19—21no—
41C42×D19—21no—
42C42×D19—21no—
43C42×D19—21no—
44C19×C4⋊C8—22no—
45C19×C4⋊C8—22no—
46C4×C8×C19D412yes—
47C4×C8×C19D412yes—
48(C2×D19)⋊C8—44no—
49C8×Dic19—22no—
50C8×Dic19—22no—
51C4⋊(C19⋊C8)—22no—
52C4⋊(C19⋊C8)—22no—
53C4×C19⋊C8—21no—
54C4×C19⋊C8—21no—
55C23×D19C4⋊C411yescharacteristic
56C22×C4×C19C22×C411yescharacteristic
57C22×C4×C19C2×D411yescharacteristic
58C22×C4×C19C2×Q811yescharacteristic
59C22×Dic19C4⋊C411yescharacteristic
60C22×Dic19C4⋊C411yescharacteristic
61C22×Dic19C4⋊C411yescharacteristic
62C2×C4×D19—22no—
63C2×C4×D19—21no—
64C2×C4×D19—21no—
65C2×C4×D19—21no—
66C2×C4×D19—21no—
67C2×C4×D19—21no—
68C2×C4×D19—21no—
69C2×C4×D19—21no—
70C2×C4×D19—21no—
71C2×C4×D19—21no—
72C2×C4×D19—21no—
73C2×C4×D19—22no—
74C2×C4×D19C2×C812yes—
75C2×C4×D19M1612yes—
76C2×C4×D19D812yes—
77C2×C4×D19Q1612yes—
78C2×C8×C19—21no—
79C2×C8×C19—21no—
80C2×C8×C19—42no—
81C2×C8×C19—42no—
82C2×C8×C19—42no—
83C2×C8×C19C22⋊C412yes—
84C2×C8×C19C22⋊C412yes—
85C2×C8×C19C2×C812yes—
86C2×C8×C19M1612yes—
87C42×C19C2×D411yescharacteristic
88C42×C19C2×D411yescharacteristic
89C42×C19#4111yescharacteristic
90C42×C19#4111yescharacteristic
91C4×Dic19—21no—
92C4×Dic19—21no—
93C4×Dic19—21no—
94C4×Dic19—21no—
95C4×Dic19—21no—
96C4×Dic19—21no—
97C2×C19⋊C8—21no—
98C2×C19⋊C8—21no—
99C2×C19⋊C8—21no—
100C2×C19⋊C8—21no—
101C2×C19⋊C8—42no—
102C2×C19⋊C8—42no—
103C2×C19⋊C8—42no—
104C2×C19⋊C8C2×C812yes—
105C2×C19⋊C8M1612yes—
106C8×D19—28no—
107C8×D19—28no—
108#8596—191nomaximal, Sylow
109C23×C19C2×C4⋊C411yescharacteristic
110C22×D19—21no—
111C22×D19—21no—
112C22×D19—21no—
113C22×D19—21no—
114C22×D19C4⋊C812yes—
115C22×D19#10712yes—
116C22×D19#10812yes—
117C2×C4×C19—21no—
118C2×C4×C19—21no—
119C2×C4×C19C2×C22⋊C411yescharacteristic
120C2×C4×C19#11711yescharacteristic
121C2×C4×C19#12111yescharacteristic
122C2×C4×C19#12111yescharacteristic
123C2×C4×C19C22⋊Q811yescharacteristic
124C2×C4×C19C22⋊Q811yescharacteristic
125C2×C4×C19C22×C811yescharacteristic
126C2×C4×C19C2×M1611yescharacteristic
127C2×C4×C19C2×M1611yescharacteristic
128C2×C4×C19C2×M1611yescharacteristic
129C2×C4×C19C2×D811yescharacteristic
130C2×C4×C19C2×Q1611yescharacteristic
131C2×C4×C19#13511yescharacteristic
132C2×C4×C19#13511yescharacteristic
133C2×Dic19—21no—
134C2×Dic19—21no—
135C2×Dic19—21no—
136C2×Dic19—21no—
137C2×Dic19—21no—
138C2×Dic19—21no—
139C2×Dic19C4⋊C812yes—
140C2×Dic19#10712yes—
141C2×Dic19#10812yes—
142C4×D19—24no—
143C4×D19—24no—
144C4×D19—22no—
145C4×D19—22no—
146C4×D19—22no—
147C4×D19—22no—
148C4×D19—22no—
149C4×D19—22no—
150C4×D19—22no—
151C4×D19—22no—
152C8×C19—22no—
153C8×C19—82no—
154C8×C19C22⋊C814yescomplemented
155C19⋊C8—22no—
156C19⋊C8—22no—
157C19⋊C8—82no—
158C22×C4×C8—191no—
159#1797—192no—
160C2×#335—191no—
161C2×#335D1911yescharacteristic, complemented
162#1277—192no—
163C22×C19#38011yescharacteristic
164C22×C19C2×C4⋊C811yescharacteristic
165C22×C19#42311yescharacteristic
166C22×C19C2×#10711yescharacteristic
167C22×C19#42711yescharacteristic
168C22×C19C2×#10811yescharacteristic
169C22×C19C2×#10811yescharacteristic
170C2×D19—22no—
171C2×D19—22no—
172C2×D19—22no—
173C2×D19—22no—
174C2×D19—22no—
175C2×D19—22no—
176C2×D19#33514yescomplemented
177C4×C19—21no—
178C4×C19—21no—
179C4×C19C2×C22⋊C811yescharacteristic
180C4×C19#40711yescharacteristic
181C4×C19#43111yescharacteristic
182C4×C19#43211yescharacteristic
183C4×C19#46611yescharacteristic
184C4×C19#46611yescharacteristic
185C4×C19#46711yescharacteristic
186C4×C19#46711yescharacteristic
187Dic19—22no—
188Dic19—22no—
189Dic19—22no—
190C23×C8—191no—
191C23×C8—191no—
192C22×C42—191no—
193C2×C4⋊C8—192no—
194C2×C4⋊C8C2×D1912yes—
195C2×C22⋊C8—382no—
196C2×C4×C8—191no—
197C2×C4×C8—191no—
198C2×C4×C8—191no—
199C2×C4×C8—382no—
200C2×C4×C8—382no—
201C2×C4×C8C2×D1911yescharacteristic
202#336—382no—
203#335—22no—
204#335—382no—
205C2×C19C2×#33511yescharacteristic
206C2×C19#156411yescharacteristic
207C2×C19#156711yescharacteristic
208C2×C19#156811yescharacteristic
209C2×C19#179711yescharacteristic
210C2×C19#180811yescharacteristic
211C2×C19#181011yescharacteristic
212D19—24no—
213C23×C4—191no—
214C23×C4—191no—
215C23×C4—191no—
216C22×C8—22no—
217C22×C8—191no—
218C22×C8—191no—
219C22×C8—194no—
220C22×C8—382no—
221C22×C8—382no—
222C22×C8—382no—
223C22×C8—382no—
224C22×C8—382no—
225C22×C8—382no—
226C22×C8C4×D1911yescharacteristic
227C22×C8C4×D1911yescharacteristic
228C2×C42—191no—
229C2×C42—191no—
230C2×C42—191no—
231C2×C42—381no—
232C2×C42—381no—
233C2×C42—381no—
234C2×C42—381no—
235C2×C42C22×D1911yescharacteristic
236C4⋊C8—22no—
237C4⋊C8—22no—
238C4⋊C8—382no—
239C4⋊C8—382no—
240C22⋊C8—764no—
241C4×C8—382no—
242C4×C8—382no—
243C4×C8—381no—
244C4×C8—381no—
245C4×C8D7612yes—
246C4×C8C22⋊D1912yes—
247C19#859611yescharacteristic, complemented, Sylow
248C24—191no—
249C22×C4—191no—
250C22×C4—191no—
251C22×C4—191no—
252C22×C4—192no—
253C22×C4—192no—
254C22×C4—192no—
255C22×C4—192no—
256C22×C4—382no—
257C22×C4—382no—
258C22×C4—381no—
259C22×C4—381no—
260C22×C4—381no—
261C22×C4—381no—
262C22×C4—381no—
263C22×C4—381no—
264C22×C4—381no—
265C22×C4—381no—
266C22×C4—381no—
267C22×C4—381no—
268C22×C4C2×C4×D1911yescharacteristic
269C22×C4D4×D1911yescharacteristic
270C22×C4Q8×D1911yescharacteristic
271C2×C8—21no—
272C2×C8—21no—
273C2×C8—42no—
274C2×C8—42no—
275C2×C8—42no—
276C2×C8—192no—
277C2×C8—192no—
278C2×C8—388no—
279C2×C8—381no—
280C2×C8—381no—
281C2×C8—381no—
282C2×C8—381no—
283C2×C8—388no—
284C2×C8—762no—
285C2×C8—762no—
286C2×C8—762no—
287C2×C8C8×D1912yes—
288C2×C8#6451512yes—
289C2×C8(C2×D19)⋊C412yes—
290C2×C8(C2×D19)⋊C412yes—
291C42—381no—
292C42—381no—
293C42—381no—
294C42—381no—
295C42—381no—
296C42—381no—
297C42C2×D7611yescharacteristic
298C42#6454311yescharacteristic
299C42#6454511yescharacteristic
300C42C2×C22⋊D1911yescharacteristic
301C23—192no—
302C23—192no—
303C23—192no—
304C23—381no—
305C23—381no—
306C23—381no—
307C23—381no—
308C23C4⋊C4×D1911yescharacteristic
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—192no—
312C2×C4—192no—
313C2×C4—192no—
314C2×C4—384no—
315C2×C4—384no—
316C2×C4—381no—
317C2×C4—381no—
318C2×C4—381no—
319C2×C4—381no—
320C2×C4—381no—
321C2×C4—381no—
322C2×C4—382no—
323C2×C4—382no—
324C2×C4—382no—
325C2×C4—382no—
326C2×C4—382no—
327C2×C4—382no—
328C2×C4—382no—
329C2×C4—382no—
330C2×C4#1059733811yescharacteristic
331C2×C4#1059734111yescharacteristic
332C2×C4#1059734311yescharacteristic
333C2×C4C2×C8×D1911yescharacteristic
334C2×C4C2×#6451511yescharacteristic
335C2×C4M16×D1911yescharacteristic
336C2×C4M16×D1911yescharacteristic
337C2×C4D8×D1911yescharacteristic
338C2×C4#1059735811yescharacteristic
339C2×C4Q16×D1911yescharacteristic
340C2×C4#1059736511yescharacteristic
341C2×C4C2×(C2×D19)⋊C411yescharacteristic
342C2×C4#1059738411yescharacteristic
343C2×C4#1059739211yescharacteristic
344C8—22no—
345C8—82no—
346C8—382no—
347C8—382no—
348C8—1522no—
349C8(C2×D19)⋊C814yescomplemented
350C22—194no—
351C22—382no—
352C22—382no—
353C22—382no—
354C22—382no—
355C22—382no—
356C22—382no—
357C22#1192640111yescharacteristic
358C22C4⋊C8×D1911yescharacteristic
359C22#1192656611yescharacteristic
360C22#107×D1911yescharacteristic
361C22#1192658111yescharacteristic
362C22#108×D1911yescharacteristic
363C22#108×D1911yescharacteristic
364C4—21no—
365C4—21no—
366C4—382no—
367C4—382no—
368C4—382no—
369C4C2×(C2×D19)⋊C811yescharacteristic
370C4#1192650711yescharacteristic
371C4#1192659611yescharacteristic
372C4#1192660011yescharacteristic
373C4#1192677711yescharacteristic
374C4#1192678111yescharacteristic
375C4#1192678211yescharacteristic
376C4#1192678611yescharacteristic
377C2—384no—
378C2D19×#33511yescharacteristic
379C2#1456238211yescharacteristic
380C2#1456239211yescharacteristic
381C2#1456239711yescharacteristic
382C2#1456361211yescharacteristic
383C2#1456366111yescharacteristic
384C2#1456367011yescharacteristic
subgroupG/H
centerC22×C4D4×D19
commutatorC2×C4×C19C22×C8
FrattiniC2×C42C22×D19
FittingC2×C19×#335C2
socleC23×C19C2×C4⋊C4
prime radicalC23×D19C4⋊C4
cosocleC2×C42×C19C23
hypercenterC2×#335D19
hypocenterC19#8596
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×#335

Complements

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

NH ≅ G/Ntype
3. C2×#11926297C2semidirect
4. #14561469C2semidirect
5. C2×C19×#335C2semidirect
39. C2×C8×D19C8semidirect
154. C8×C19C22⋊C8semidirect
161. C2×#335D19semidirect
176. C2×D19#335semidirect
247. C19#8596semidirect
349. C8(C2×D19)⋊C8semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C8×D192
#145636122
C2×#119262972
#145614692
C2×C19×#3352
#859619