Finite Group Databasebeta

← #18090731

Subgroups — #18090731

Order 4864.

814 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10597274C211yesmaximal, characteristic
2C2×#11926307C212yesmaximal
3C2×#11926307C211yesmaximal, characteristic
4#14561865C212yesmaximal
5C2×C19×#336C211yesmaximal, characteristic
6C22×C4⋊Dic19C2212yes—
7C22×C4⋊Dic19C2212yes—
8C2×#10597274—24no—
9C2×#10597274—22no—
10C2×C19⋊#95—22no—
11C2×C19⋊#95—22no—
12#11926307—24no—
13#11926307C414yescomplemented
14C23×C8×C19C2211yescharacteristic
15C23×C8×C19C2211yescharacteristic
16C22×C42×C19C2211yescharacteristic
17C19×#336—22no—
18C23×C4×C19D412yes—
19C23×C4×C19C2311yescharacteristic
20C23×Dic19—22no—
21C23×Dic19—22no—
22C22×C8×C19—22no—
23C22×C8×C19—22no—
24C22×C8×C19—22no—
25C22×C8×C19—21no—
26C22×C8×C19—21no—
27C22×C8×C19—22no—
28C22×C8×C19C2×C412yes—
29C22×C8×C19D412yes—
30C22×C8×C19Q812yes—
31C22×C8×C19Q812yes—
32C2×C42×C19—21no—
33C2×C42×C19—22no—
34C2×C42×C19—22no—
35C2×C42×C19—21no—
36C2×C4⋊Dic19—22no—
37C2×C4⋊Dic19—22no—
38C2×C4⋊Dic19—22no—
39C2×C4⋊Dic19—22no—
40C2×C4⋊Dic19—22no—
41C2×C4⋊Dic19—22no—
42C2×C4⋊Dic19—22no—
43C2×C4⋊Dic19—22no—
44C2×C4⋊Dic19—22no—
45C2×C4⋊Dic19—22no—
46C2×C4⋊Dic19C2×C414yes—
47C2×C4⋊Dic19D414yes—
48C19⋊#95—44no—
49C19⋊#95—44no—
50#10597274—28no—
51C24×C19C2×D411yescharacteristic
52C22×C4×C19—22no—
53C22×C4×C19—22no—
54C22×C4×C19—22no—
55C22×C4×C19—22no—
56C22×C4×C19—22no—
57C22×C4×C19—22no—
58C22×C4×C19SD1614yes—
59C22×C4×C19C22×C411yescharacteristic
60C22×C4×C19C2×D412yes—
61C22×C4×C19C2×D411yescharacteristic
62C22×C4×C19C2×Q811yescharacteristic
63C22×C4×C19C2×Q811yescharacteristic
64C22×C4×C19#4111yescharacteristic
65C22×C4×C19#4111yescharacteristic
66C22×C4×C19#4112yes—
67C22×C4×C19#4112yes—
68C22×C4×C19#4112yes—
69C22×Dic19—24no—
70C22×Dic19—24no—
71C22×Dic19—42no—
72C22×Dic19—42no—
73C22×Dic19—42no—
74C22×Dic19—42no—
75C22×Dic19—42no—
76C22×Dic19—42no—
77C22×Dic19—42no—
78C22×Dic19—42no—
79C22×Dic19—42no—
80C22×Dic19—42no—
81C22×Dic19—42no—
82C22×Dic19—42no—
83C2×C8×C19—24no—
84C2×C8×C19—22no—
85C2×C8×C19—24no—
86C2×C8×C19—22no—
87C2×C8×C19—24no—
88C2×C8×C19—22no—
89C2×C8×C19—41no—
90C2×C8×C19—41no—
91C2×C8×C19—42no—
92C2×C8×C19C4⋊C414yes—
93C42×C19—41no—
94C42×C19—41no—
95C42×C19—42no—
96C4⋊Dic19—24no—
97C4⋊Dic19—24no—
98C4⋊Dic19—24no—
99C4⋊Dic19—24no—
100C4⋊Dic19—42no—
101C4⋊Dic19—42no—
102C4⋊Dic19—42no—
103C4⋊Dic19—42no—
104#11257—191nomaximal, Sylow
105C23×C19C4×D411yescharacteristic
106C23×C19#12111yescharacteristic
107C23×C19#12112yes—
108C23×C19#12312yes—
109C23×C19C4⋊Q811yescharacteristic
110C23×C19C2×SD1612yes—
111C23×C19#13512yes—
112C23×C19AGL(1,ℤ/8)12yes—
113C23×C19#13712yes—
114C2×C4×C19—24no—
115C2×C4×C19—24no—
116C2×C4×C19—24no—
117C2×C4×C19—42no—
118C2×C4×C19—42no—
119C2×C4×C19—42no—
120C2×C4×C19—42no—
121C2×C4×C19C2×C4⋊C411yescharacteristic
122C2×C4×C19#11712yes—
123C2×C4×C19C4×D412yes—
124C2×C4×C19C4×Q811yescharacteristic
125C2×C4×C19#12011yescharacteristic
126C2×C4×C19C22⋊Q812yes—
127C2×C4×C19C22⋊Q812yes—
128C2×C4×C19C22⋊Q811yescharacteristic
129C2×C4×C19#12311yescharacteristic
130C2×C4×C19#12312yes—
131C2×C4×C19#12411yescharacteristic
132C2×C4×C19#12411yescharacteristic
133C2×C4×C19#12412yes—
134C2×C4×C19#12511yescharacteristic
135C2×C4×C19#12512yes—
136C2×C4×C19#12512yes—
137C2×C4×C19#12612yes—
138C2×C4×C19#12612yes—
139C2×Dic19—44no—
140C2×Dic19—44no—
141C2×Dic19—44no—
142C2×Dic19—44no—
143C2×Dic19—44no—
144C2×Dic19—44no—
145C2×Dic19—82no—
146C2×Dic19—82no—
147C2×Dic19—82no—
148C2×Dic19—82no—
149C2×Dic19—82no—
150C2×Dic19—82no—
151C2×Dic19—82no—
152C2×Dic19—82no—
153C8×C19—24no—
154C8×C19—42no—
155C22×#106—191no—
156C2×#340—191no—
157C2×#340—192no—
158C2×#336D1911yescharacteristic
159C4⋊#95—192no—
160C22×C19#38812yes—
161C22×C19#38911yescharacteristic
162C22×C19#39411yescharacteristic
163C22×C19#39711yescharacteristic
164C22×C19#39812yes—
165C22×C19C4×SD1612yes—
166C22×C19#44111yescharacteristic
167C22×C19#44211yescharacteristic
168C22×C19#46012yes—
169C22×C19#46112yes—
170C22×C19#46312yes—
171C22×C19#46412yes—
172C22×C19#46512yes—
173C22×C19#46812yes—
174C22×C19#48112yes—
175C22×C19#48212yes—
176C22×C19#48312yes—
177C22×C19#48512yes—
178C22×C19#49811yescharacteristic
179C22×C19#49911yescharacteristic
180C22×C19#50112yes—
181C4×C19—44no—
182C4×C19#38211yescharacteristic
183C4×C19#38511yescharacteristic
184C4×C19#38712yes—
185C4×C19#39311yescharacteristic
186C4×C19#40011yescharacteristic
187C4×C19#40012yes—
188Dic19—84no—
189Dic19—84no—
190C23×C8C2×D1911yescharacteristic
191C23×C8C2×D1911yescharacteristic
192C22×C4⋊C4—192no—
193C22×C4⋊C4—192no—
194C22×C42C2×D1911yescharacteristic
195C2×#106—384no—
196C2×#106—382no—
197C2×#95—382no—
198C2×#95—382no—
199#340—194no—
200#340—384no—
201#336—22no—
202C2×C19#144211yescharacteristic
203C2×C19#192612yes—
204C2×C19#192712yes—
205C2×C19#194111yescharacteristic
206C2×C19#194311yescharacteristic
207C2×C19#205512yes—
208C2×C19#207712yes—
209C2×C19#208412yes—
210C2×C19#208512yes—
211C23×C4—382no—
212C23×C4—382no—
213C23×C4D7612yes—
214C23×C4C22×D1911yescharacteristic
215C22×C8—22no—
216C22×C8—22no—
217C22×C8—21no—
218C22×C8—22no—
219C22×C8—22no—
220C22×C8—21no—
221C22×C8Dic3812yes—
222C22×C8Dic3812yes—
223C22×C8C4×D1912yes—
224C22×C8C22⋊D1912yes—
225C2×C4⋊C4—194no—
226C2×C4⋊C4—194no—
227C2×C4⋊C4—382no—
228C2×C4⋊C4—382no—
229C2×C4⋊C4—382no—
230C2×C4⋊C4—382no—
231C2×C4⋊C4—382no—
232C2×C4⋊C4—382no—
233C2×C4⋊C4—382no—
234C2×C4⋊C4—382no—
235C2×C4⋊C4—382no—
236C2×C4⋊C4—382no—
237C2×C42—21no—
238C2×C42—22no—
239C2×C42—22no—
240C2×C42—21no—
241#106—388no—
242#95—764no—
243#95—764no—
244C19#1125711yescharacteristic, complemented, Sylow
245C24C2×D7611yescharacteristic
246C22×C4—22no—
247C22×C4—22no—
248C22×C4—22no—
249C22×C4—22no—
250C22×C4—22no—
251C22×C4—22no—
252C22×C4—384no—
253C22×C4—384no—
254C22×C4—762no—
255C22×C4—762no—
256C22×C4—762no—
257C22×C4—762no—
258C22×C4—762no—
259C22×C4—762no—
260C22×C4—762no—
261C22×C4—762no—
262C22×C4—762no—
263C22×C4—762no—
264C22×C4—762no—
265C22×C4—762no—
266C22×C4#6451614yes—
267C22×C4C2×Dic3811yescharacteristic
268C22×C4C2×Dic3811yescharacteristic
269C22×C4C2×C4×D1911yescharacteristic
270C22×C4#6454111yescharacteristic
271C22×C4#6454111yescharacteristic
272C22×C4D4×D1912yes—
273C22×C4#6454312yes—
274C22×C4#6454312yes—
275C22×C4#6454512yes—
276C22×C4C2×C22⋊D1911yescharacteristic
277C2×C8—22no—
278C2×C8—22no—
279C2×C8—24no—
280C2×C8—24no—
281C2×C8—24no—
282C2×C8—22no—
283C2×C8—41no—
284C2×C8—41no—
285C2×C8—42no—
286C2×C8Dic19⋊C414yes—
287C4⋊C4—384no—
288C4⋊C4—384no—
289C4⋊C4—384no—
290C4⋊C4—384no—
291C4⋊C4—762no—
292C4⋊C4—762no—
293C4⋊C4—762no—
294C4⋊C4—762no—
295C42—41no—
296C42—41no—
297C42—42no—
298C23#1059731511yescharacteristic
299C23C4×D7611yescharacteristic
300C23#1059733212yes—
301C23#1059734112yes—
302C23C2×#6451612yes—
303C23#1059735012yes—
304C23#1059735412yes—
305C23#1059735512yes—
306C23#1059737611yescharacteristic
307C2×C4—24no—
308C2×C4—24no—
309C2×C4—24no—
310C2×C4—42no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—764no—
315C2×C4—764no—
316C2×C4—764no—
317C2×C4—764no—
318C2×C4—764no—
319C2×C4—764no—
320C2×C4—1522no—
321C2×C4—1522no—
322C2×C4—1522no—
323C2×C4—1522no—
324C2×C4—1522no—
325C2×C4—1522no—
326C2×C4—1522no—
327C2×C4—1522no—
328C2×C4C4×Dic3811yescharacteristic
329C2×C4#1059731611yescharacteristic
330C2×C4#1059732412yes—
331C2×C4#1059732412yes—
332C2×C4#1059732512yes—
333C2×C4(C22⋊D19)⋊C412yes—
334C2×C4#1059733112yes—
335C2×C4#1059733612yes—
336C2×C4#1059733612yes—
337C2×C4#1059733812yes—
338C2×C4#1059734012yes—
339C2×C4#1059734412yes—
340C2×C4C2×Dic19⋊C411yescharacteristic
341C2×C4#1059737011yescharacteristic
342C2×C4#1059738111yescharacteristic
343C2×C4#1059738211yescharacteristic
344C2×C4#1059738311yescharacteristic
345C2×C4#1059739311yescharacteristic
346C8—24no—
347C8—42no—
348C22#1192643612yes—
349C22#1192644211yescharacteristic
350C22#1192646111yescharacteristic
351C22#1192646911yescharacteristic
352C22#1192647612yes—
353C22C4×#6451612yes—
354C22#1192665211yescharacteristic
355C22#1192665711yescharacteristic
356C22#1192674512yes—
357C22#1192675012yes—
358C22#1192676012yes—
359C22#1192676712yes—
360C22#1192677312yes—
361C22#1192679012yes—
362C22#1192686312yes—
363C22#1192686912yes—
364C22#1192687512yes—
365C22#1192688612yes—
366C22#1192694211yescharacteristic
367C22#1192694611yescharacteristic
368C22#1192695312yes—
369C4—44no—
370C4—1524no—
371C4—1524no—
372C4#1192640911yescharacteristic
373C4#1192641611yescharacteristic
374C4#1192643112yes—
375C4#1192645611yescharacteristic
376C4#1192648311yescharacteristic
377C4#1192648612yes—
378C2#1456189111yescharacteristic
379C2#1456426312yes—
380C2#1456427012yes—
381C2#1456436311yescharacteristic
382C2#1456437311yescharacteristic
383C2#1456495312yes—
384C2#1456506812yes—
385C2#1456511312yes—
386C2#1456511812yes—
subgroupG/H
centerC24C2×D76
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC2×C19×#336C2
socle, prime radicalC24×C19C2×D4
cosocleC23×C4×C19C23
hypercenterC2×#336D19
hypocenterC19#11257
LCSG ▷ C22×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C24 ◁ C22×C42 ◁ C2×#336

Complements

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

NH ≅ G/Ntype
13. #11926307C4semidirect
244. C19#11257semidirect

Maximal subgroups

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

subgroupindex
C22×#105972742
C2×#119263072
#145618652
C2×C19×#3362
#1125719