Finite Group Databasebeta

← #18072097

Subgroups — #18072097

Order 4864.

710 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11926600C211yesmaximal, characteristic
2C2×C4×C8×D19C211yesmaximal, characteristic
3#14566031C211yesmaximal, characteristic
4#14561476C211yesmaximal, characteristic, complemented
5#14561475C211yesmaximal, characteristic, complemented
6#14561474C211yesmaximal, characteristic, complemented
7C19×#1279C211yesmaximal, characteristic, complemented
8C22×C8×D19—21no—
9C2×C42×D19C2211yescharacteristic
10#11926600—22no—
11#11926600C414yescomplemented
12C2×C4⋊(C19⋊C8)C2211yescharacteristic
13C2×(C2×D19)⋊C8—21no—
14C2×#10597272—21no—
15C2×C4×C19⋊C8C2211yescharacteristic
16C2×C8×Dic19—21no—
17C4×C8×D19—22no—
18C4×C8×D19C414yescomplemented
19#11926411—21no—
20#11926409C412yes—
21#11926406—21no—
22#11926401C412yes—
23C4×C4⋊Dic19C2211yescharacteristic
24C4×(C2×D19)⋊C4—21no—
25#11926390—21no—
26C2×C19×C4⋊C8C2211yescharacteristic
27C2×C4×C8×C19C2211yescharacteristic
28C4×C4⋊C4×C19C2211yescharacteristic
29C22×C4×D19C2×C411yescharacteristic
30C22×C4×D19D411yescharacteristic
31C22×C4×D19D411yescharacteristic
32C22×C8×C19—21no—
33C22×C8×C19—21no—
34C2×C4⋊C4×C19C2×C412yes—
35C2×C42×C19—21no—
36C2×C42×C19C2311yescharacteristic
37C2×(C2×D19)⋊C4—22no—
38C2×C4⋊Dic19C2×C412yes—
39C2×C4×Dic19—21no—
40C2×C4×Dic19C2×C411yescharacteristic
41C2×C4×Dic19D411yescharacteristic
42C2×C4×Dic19D411yescharacteristic
43C22×C19⋊C8—21no—
44C22×C19⋊C8—21no—
45C2×C8×D19—28no—
46C2×C8×D19—24no—
47C42×D19C2×C412yes—
48C42×D19C2×C412yes—
49C42×D19D412yes—
50C42×D19Q812yes—
51C19×C4⋊C8—21no—
52C19×C4⋊C8C2×C412yes—
53C4×C8×C19—21no—
54C4×C8×C19C2×C412yes—
55C19×#95—21no—
56C19⋊#95—21no—
57C19⋊#95—22no—
58C19⋊#95—22no—
59C19⋊#95—22no—
60(C2×D19)⋊C8—24no—
61#10597272—24no—
62C8×Dic19—24no—
63C4⋊(C19⋊C8)—21no—
64C4⋊(C19⋊C8)C2×C412yes—
65C4×C19⋊C8—21no—
66C4×C19⋊C8C2×C412yes—
67C23×D19C22⋊C411yescharacteristic
68C22×C4×C19—22no—
69C22×C4×C19C22×C411yescharacteristic
70C22×C4×C19C2×D411yescharacteristic
71C22×C4×C19C2×D411yescharacteristic
72C22×Dic19—22no—
73C22×Dic19C22⋊C411yescharacteristic
74C22×Dic19C22⋊C411yescharacteristic
75C22×Dic19C22⋊C411yescharacteristic
76C2×C4×D19—24no—
77C2×C4×D19—22no—
78C2×C4×D19—22no—
79C2×C4×D19—21no—
80C2×C4×D19—21no—
81C2×C4×D19—21no—
82C2×C4×D19—21no—
83C2×C4×D19C4212yes—
84C2×C4×D19C22⋊C412yes—
85C2×C4×D19C22⋊C412yes—
86C2×C4×D19C4⋊C412yes—
87C2×C4×D19C4⋊C412yes—
88C2×C4×D19C4⋊C412yes—
89C2×C8×C19—24no—
90C2×C8×C19—22no—
91C2×C8×C19—22no—
92C2×C8×C19—41no—
93C2×C8×C19—41no—
94C4⋊C4×C19—22no—
95C4⋊C4×C19—22no—
96C42×C19—41no—
97C42×C19—41no—
98C42×C19C22×C411yescharacteristic
99C42×C19C22×C411yescharacteristic
100C42×C19C2×D411yescharacteristic
101C42×C19C2×Q811yescharacteristic
102(C2×D19)⋊C4—44no—
103C4⋊Dic19—22no—
104C4⋊Dic19—22no—
105C4×Dic19—41no—
106C4×Dic19—41no—
107C4×Dic19C4212yes—
108C4×Dic19C22⋊C412yes—
109C4×Dic19C22⋊C412yes—
110C4×Dic19C4⋊C412yes—
111C4×Dic19C4⋊C412yes—
112C4×Dic19C4⋊C412yes—
113C2×C19⋊C8—24no—
114C2×C19⋊C8—22no—
115C2×C19⋊C8—22no—
116C2×C19⋊C8—41no—
117C2×C19⋊C8—41no—
118C8×D19—216no—
119#7898—191nomaximal, Sylow
120C23×C19C2×C22⋊C411yescharacteristic
121C22×D19—22no—
122C22×D19—21no—
123C22×D19—21no—
124C22×D19#9512yes—
125C22×D19#10414yes—
126C2×C4×C19—22no—
127C2×C4×C19—42no—
128C2×C4×C19—42no—
129C2×C4×C19—42no—
130C2×C4×C19C2×C4211yescharacteristic
131C2×C4×C19C2×C22⋊C411yescharacteristic
132C2×C4×C19C2×C22⋊C411yescharacteristic
133C2×C4×C19C2×C4⋊C411yescharacteristic
134C2×C4×C19C2×C4⋊C411yescharacteristic
135C2×C4×C19C2×C4⋊C411yescharacteristic
136C2×C4×C19#13112yes—
137C2×C4×C19#13112yes—
138C2×C4×C19#13511yescharacteristic
139C2×C4×C19#13511yescharacteristic
140C2×C4×C19#13511yescharacteristic
141C2×C4×C19#13511yescharacteristic
142C2×Dic19—22no—
143C2×Dic19—21no—
144C2×Dic19—21no—
145C2×Dic19—22no—
146C2×Dic19—42no—
147C2×Dic19—42no—
148C2×Dic19—42no—
149C2×Dic19#9512yes—
150C2×Dic19#9512yes—
151C2×Dic19#9512yes—
152C4×D19—24no—
153C4×D19—24no—
154C4×D19—22no—
155C4×D19—22no—
156C4×D19—22no—
157C4×D19—22no—
158C4×D19—24no—
159C4×D19—22no—
160C4×D19—22no—
161C8×C19—24no—
162C8×C19—42no—
163C19⋊C8—24no—
164C19⋊C8—42no—
165C2×#432—191no—
166C22×C4×C8—191no—
167#2283—191no—
168#1279—191no—
169#1279—191no—
170#1279—191no—
171#1279D1911yescharacteristic, complemented
172C22×C19C2×#9511yescharacteristic
173C22×C19#40812yes—
174C22×C19#41611yescharacteristic
175C22×C19#41611yescharacteristic
176C22×C19C2×#10412yes—
177C2×D19—22no—
178C2×D19—22no—
179C2×D19—24no—
180C2×D19—24no—
181C2×D19#33914yes—
182C4×C19—21no—
183C4×C19—21no—
184C4×C19—82no—
185C4×C19#40511yescharacteristic
186C4×C19#40511yescharacteristic
187C4×C19#41611yescharacteristic
188C4×C19#41611yescharacteristic
189C4×C19#42412yes—
190C4×C19#42711yescharacteristic
191C4×C19#42711yescharacteristic
192Dic19—22no—
193Dic19—22no—
194Dic19—22no—
195Dic19—82no—
196C23×C8—381no—
197C22×C42—191no—
198#432—194no—
199#432—382no—
200C2×C4⋊C8—191no—
201C2×C4⋊C8C2×D1911yescharacteristic
202C2×C22⋊C8—381no—
203C2×#97—381no—
204C2×C4×C8—191no—
205C2×C4×C8—194no—
206C2×C4×C8—382no—
207C2×C4×C8—381no—
208C2×C4×C8C2×D1911yescharacteristic
209#383—381no—
210#382—192no—
211#381—381no—
212#380—192no—
213C4×C4⋊C4—191no—
214C4×C4⋊C4C2×D1911yescharacteristic
215C4×C22⋊C4—381no—
216#376—381no—
217C2×C19#149412yes—
218C2×C19#149412yes—
219C2×C19#172911yescharacteristic
220C2×C19C2×#33911yescharacteristic
221C2×C19#173511yescharacteristic
222D19—24no—
223C23×C4—191no—
224C23×C4—191no—
225C23×C4—191no—
226C22×C8—21no—
227C22×C8—21no—
228C22×C8—384no—
229C22×C8—388no—
230C22×C8—381no—
231C22×C8—381no—
232C2×C4⋊C4—192no—
233C2×C4⋊C4C4×D1912yes—
234C2×C22⋊C4—382no—
235C2×C42—21no—
236C2×C42—191no—
237C2×C42—191no—
238C2×C42—191no—
239C2×C42—192no—
240C2×C42—192no—
241C2×C42—192no—
242C2×C42—192no—
243C2×C42—381no—
244C2×C42C22×D1911yescharacteristic
245C4⋊C8—21no—
246C4⋊C8—192no—
247C4⋊C8—381no—
248C4⋊C8C4×D1912yes—
249C22⋊C8—384no—
250#97—384no—
251C4×C8—21no—
252C4×C8—192no—
253C4×C8—384no—
254C4×C8—381no—
255C4×C8C4×D1912yes—
256#95—21no—
257#95—382no—
258#95—382no—
259#95—382no—
260#95—381no—
261C19#789811yescharacteristic, complemented, Sylow
262C24—191no—
263C22×C4—22no—
264C22×C4—191no—
265C22×C4—191no—
266C22×C4—191no—
267C22×C4—192no—
268C22×C4—192no—
269C22×C4—192no—
270C22×C4—192no—
271C22×C4—192no—
272C22×C4—192no—
273C22×C4—384no—
274C22×C4—382no—
275C22×C4—382no—
276C22×C4—381no—
277C22×C4—381no—
278C22×C4—381no—
279C22×C4—381no—
280C22×C4—382no—
281C22×C4C2×C4×D1911yescharacteristic
282C22×C4D4×D1911yescharacteristic
283C22×C4D4×D1911yescharacteristic
284C2×C8—24no—
285C2×C8—22no—
286C2×C8—22no—
287C2×C8—41no—
288C2×C8—41no—
289C2×C8—3816no—
290C2×C8—384no—
291C2×C8—382no—
292C2×C8—382no—
293C2×C8—761no—
294C2×C8—761no—
295C4⋊C4—22no—
296C4⋊C4—22no—
297C4⋊C4—382no—
298C4⋊C4—382no—
299C22⋊C4—764no—
300C42—41no—
301C42—41no—
302C42—192no—
303C42—192no—
304C42—192no—
305C42—192no—
306C42—192no—
307C42—192no—
308C42—761no—
309C42—761no—
310C42C2×C4×D1911yescharacteristic
311C42C2×C4×D1911yescharacteristic
312C42D4×D1911yescharacteristic
313C42Q8×D1911yescharacteristic
314C23—194no—
315C23—192no—
316C23—381no—
317C23—381no—
318C23—382no—
319C23C22⋊C4×D1911yescharacteristic
320C2×C4—22no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—192no—
325C2×C4—192no—
326C2×C4—192no—
327C2×C4—384no—
328C2×C4—384no—
329C2×C4—381no—
330C2×C4—381no—
331C2×C4—382no—
332C2×C4—382no—
333C2×C4—382no—
334C2×C4—382no—
335C2×C4—384no—
336C2×C4—382no—
337C2×C4—382no—
338C2×C4—382no—
339C2×C4—382no—
340C2×C4—762no—
341C2×C4—762no—
342C2×C4—762no—
343C2×C4C42×D1911yescharacteristic
344C2×C4C22⋊C4×D1911yescharacteristic
345C2×C4C22⋊C4×D1911yescharacteristic
346C2×C4C4⋊C4×D1911yescharacteristic
347C2×C4C4⋊C4×D1911yescharacteristic
348C2×C4C4⋊C4×D1911yescharacteristic
349C2×C4#1059734712yes—
350C2×C4#1059735312yes—
351C2×C4#1059735811yescharacteristic
352C2×C4#1059736211yescharacteristic
353C2×C4#1059736211yescharacteristic
354C2×C4#1059736511yescharacteristic
355C8—24no—
356C8—42no—
357C8—384no—
358C8—762no—
359C22—194no—
360C22—382no—
361C22—382no—
362C22—384no—
363C22—384no—
364C22#95×D1911yescharacteristic
365C22#1192650912yes—
366C22#1192653711yescharacteristic
367C22#1192653911yescharacteristic
368C22#104×D1912yes—
369C4—21no—
370C4—21no—
371C4—82no—
372C4—382no—
373C4—382no—
374C4—382no—
375C4—1522no—
376C4#1192649811yescharacteristic
377C4#1192650111yescharacteristic
378C4#1192653711yescharacteristic
379C4#1192653911yescharacteristic
380C4#1192656912yes—
381C4#1192657911yescharacteristic
382C4#1192658111yescharacteristic
383C2—384no—
384C2#1456209212yes—
385C2#1456209412yes—
386C2#1456333011yescharacteristic
387C2D19×#33911yescharacteristic
388C2#1456335011yescharacteristic
subgroupG/H
centerC22×C4D4×D19
commutatorC2×C4×C19C2×C42
FrattiniC2×C42C22×D19
FittingC19×#1279C2
socleC23×C19C2×C22⋊C4
prime radicalC23×D19C22⋊C4
cosocleC2×C42×C19C23
hypercenter#1279D19
hypocenterC19#7898
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
4. #14561476C2semidirect
5. #14561475C2semidirect
6. #14561474C2semidirect
7. C19×#1279C2semidirect
11. #11926600C4semidirect
18. C4×C8×D19C4semidirect
171. #1279D19semidirect
261. C19#7898semidirect

Maximal subgroups

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

subgroupindex
C2×#119266002
C2×C4×C8×D192
#145660312
#145614762
#145614752
#145614742
C19×#12792
#789819