Finite Group Databasebeta

← #18072101

Subgroups — #18072101

Order 4864.

638 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11926595C211yesmaximal, characteristic
2C2×#11926566C211yesmaximal, characteristic
3#14566031C211yesmaximal, characteristic
4#14561476C211yesmaximal, characteristic, complemented
5#14561475C211yesmaximal, characteristic, complemented
6#14561474C211yesmaximal, characteristic, complemented
7C19×#1279C211yesmaximal, characteristic, complemented
8C22×#64515—21no—
9C2×C42×D19C2211yescharacteristic
10#11926595—22no—
11#11926595C414yescomplemented
12#11926566—22no—
13#11926566C414yescomplemented
14C2×C4⋊(C19⋊C8)C2211yescharacteristic
15C2×Dic19⋊C8—21no—
16C2×Dic19⋊C8—21no—
17C2×(C2×D19)⋊C8—21no—
18C2×C4×C19⋊C8C2211yescharacteristic
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×#64515—24no—
46C2×#64515—42no—
47C2×#64515—42no—
48C42×D19C2×C412yes—
49C42×D19C2×C412yes—
50C42×D19D412yes—
51C42×D19Q812yes—
52C19×C4⋊C8—21no—
53C19×C4⋊C8C2×C412yes—
54C4×C8×C19—21no—
55C4×C8×C19C2×C412yes—
56C19×#95—21no—
57C19⋊#95—21no—
58C19⋊#95—22no—
59C19⋊#95—22no—
60C19⋊#95—22no—
61(C2×D19)⋊C8—24no—
62Dic19⋊C8—24no—
63Dic19⋊C8—24no—
64C4⋊(C19⋊C8)—21no—
65C4⋊(C19⋊C8)C2×C412yes—
66C4×C19⋊C8—21no—
67C4×C19⋊C8C2×C412yes—
68C23×D19C22⋊C411yescharacteristic
69C22×C4×C19—22no—
70C22×C4×C19C22×C411yescharacteristic
71C22×C4×C19C2×D411yescharacteristic
72C22×C4×C19C2×D411yescharacteristic
73C22×Dic19—22no—
74C22×Dic19C22⋊C411yescharacteristic
75C22×Dic19C22⋊C411yescharacteristic
76C22×Dic19C22⋊C411yescharacteristic
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×D19—42no—
84C2×C4×D19C4212yes—
85C2×C4×D19C22⋊C412yes—
86C2×C4×D19C22⋊C412yes—
87C2×C4×D19C4⋊C412yes—
88C2×C4×D19C4⋊C412yes—
89C2×C4×D19C4⋊C412yes—
90C2×C8×C19—22no—
91C2×C8×C19—22no—
92C2×C8×C19—42no—
93C2×C8×C19—41no—
94C2×C8×C19—41no—
95C4⋊C4×C19—22no—
96C4⋊C4×C19—22no—
97C42×C19—41no—
98C42×C19—41no—
99C42×C19C22×C411yescharacteristic
100C42×C19C22×C411yescharacteristic
101C42×C19C2×D411yescharacteristic
102C42×C19C2×Q811yescharacteristic
103(C2×D19)⋊C4—44no—
104C4⋊Dic19—22no—
105C4⋊Dic19—22no—
106C4×Dic19—41no—
107C4×Dic19—41no—
108C4×Dic19C4212yes—
109C4×Dic19C22⋊C412yes—
110C4×Dic19C22⋊C412yes—
111C4×Dic19C4⋊C412yes—
112C4×Dic19C4⋊C412yes—
113C4×Dic19C4⋊C412yes—
114C2×C19⋊C8—22no—
115C2×C19⋊C8—22no—
116C2×C19⋊C8—42no—
117C2×C19⋊C8—41no—
118C2×C19⋊C8—41no—
119#64515—48no—
120#7899—191nomaximal, Sylow
121C23×C19C2×C22⋊C411yescharacteristic
122C22×D19—22no—
123C22×D19—21no—
124C22×D19—21no—
125C22×D19—22no—
126C22×D19#9512yes—
127C2×C4×C19—22no—
128C2×C4×C19—42no—
129C2×C4×C19—42no—
130C2×C4×C19—42no—
131C2×C4×C19C2×C4211yescharacteristic
132C2×C4×C19C2×C22⋊C411yescharacteristic
133C2×C4×C19C2×C22⋊C411yescharacteristic
134C2×C4×C19C2×C4⋊C411yescharacteristic
135C2×C4×C19C2×C4⋊C411yescharacteristic
136C2×C4×C19C2×C4⋊C411yescharacteristic
137C2×C4×C19#13112yes—
138C2×C4×C19#13112yes—
139C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
140C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
141C2×C4×C19#13711yescharacteristic
142C2×C4×C19#13711yescharacteristic
143C2×Dic19—22no—
144C2×Dic19—21no—
145C2×Dic19—21no—
146C2×Dic19—22no—
147C2×Dic19—42no—
148C2×Dic19—42no—
149C2×Dic19—42no—
150C2×Dic19#9512yes—
151C2×Dic19#9512yes—
152C2×Dic19#9512yes—
153C4×D19—22no—
154C4×D19—22no—
155C4×D19—22no—
156C4×D19—22no—
157C4×D19—24no—
158C4×D19—22no—
159C4×D19—22no—
160C4×D19—42no—
161C4×D19—42no—
162C8×C19—42no—
163C8×C19—42no—
164C19⋊C8—42no—
165C19⋊C8—42no—
166C2×#431—191no—
167C2×#423—191no—
168#2283—191no—
169#1279—191no—
170#1279—191no—
171#1279—191no—
172#1279D1911yescharacteristic, complemented
173C22×C19C2×#9511yescharacteristic
174C22×C19#40812yes—
175C22×C19#41711yescharacteristic
176C22×C19#41711yescharacteristic
177C22×C19#42112yes—
178C2×D19—22no—
179C2×D19—22no—
180C2×D19—22no—
181C2×D19—42no—
182C2×D19—42no—
183C4×C19—21no—
184C4×C19—21no—
185C4×C19—82no—
186C4×C19#40511yescharacteristic
187C4×C19#40511yescharacteristic
188C4×C19#41811yescharacteristic
189C4×C19#41911yescharacteristic
190C4×C19#42412yes—
191C4×C19#42811yescharacteristic
192C4×C19#42811yescharacteristic
193Dic19—22no—
194Dic19—22no—
195Dic19—22no—
196Dic19—82no—
197C22×M16—381no—
198C22×C42—191no—
199#431—194no—
200#431—382no—
201#423—194no—
202#423—382no—
203C2×C4⋊C8—191no—
204C2×C4⋊C8—381no—
205C2×C4⋊C8—381no—
206C2×C4⋊C8C2×D1911yescharacteristic
207C2×C22⋊C8—381no—
208C2×C4×C8—191no—
209C2×C4×C8C2×D1911yescharacteristic
210#383—381no—
211#382—192no—
212#381—381no—
213#380—192no—
214C4×C4⋊C4—191no—
215C4×C4⋊C4C2×D1911yescharacteristic
216C4×C22⋊C4—381no—
217#376—381no—
218C2×C19#149512yes—
219C2×C19#149512yes—
220C2×C19#172911yescharacteristic
221C2×C19#173311yescharacteristic
222C2×C19#173611yescharacteristic
223D19—42no—
224C23×C4—191no—
225C23×C4—191no—
226C23×C4—191no—
227C2×M16—384no—
228C2×M16—762no—
229C2×M16—762no—
230C22×C8—21no—
231C22×C8—21no—
232C22×C8—381no—
233C22×C8—381no—
234C2×C4⋊C4—192no—
235C2×C4⋊C4C4×D1912yes—
236C2×C22⋊C4—382no—
237C2×C42—21no—
238C2×C42—191no—
239C2×C42—191no—
240C2×C42—191no—
241C2×C42—192no—
242C2×C42—192no—
243C2×C42—192no—
244C2×C42—192no—
245C2×C42—381no—
246C2×C42C22×D1911yescharacteristic
247C4⋊C8—21no—
248C4⋊C8—192no—
249C4⋊C8—384no—
250C4⋊C8—384no—
251C4⋊C8—381no—
252C4⋊C8C4×D1912yes—
253C22⋊C8—384no—
254C4×C8—21no—
255C4×C8—192no—
256C4×C8—381no—
257C4×C8C4×D1912yes—
258#95—21no—
259#95—382no—
260#95—382no—
261#95—382no—
262#95—381no—
263C19#789911yescharacteristic, complemented, Sylow
264C24—191no—
265C22×C4—22no—
266C22×C4—191no—
267C22×C4—191no—
268C22×C4—191no—
269C22×C4—192no—
270C22×C4—192no—
271C22×C4—192no—
272C22×C4—192no—
273C22×C4—192no—
274C22×C4—192no—
275C22×C4—382no—
276C22×C4—382no—
277C22×C4—381no—
278C22×C4—381no—
279C22×C4—381no—
280C22×C4—381no—
281C22×C4—382no—
282C22×C4—762no—
283C22×C4C2×C4×D1911yescharacteristic
284C22×C4D4×D1911yescharacteristic
285C22×C4D4×D1911yescharacteristic
286M16—768no—
287C2×C8—22no—
288C2×C8—22no—
289C2×C8—42no—
290C2×C8—41no—
291C2×C8—41no—
292C2×C8—382no—
293C2×C8—382no—
294C2×C8—762no—
295C2×C8—761no—
296C2×C8—761no—
297C4⋊C4—22no—
298C4⋊C4—22no—
299C4⋊C4—382no—
300C4⋊C4—382no—
301C22⋊C4—764no—
302C42—41no—
303C42—41no—
304C42—192no—
305C42—192no—
306C42—192no—
307C42—192no—
308C42—192no—
309C42—192no—
310C42—761no—
311C42—761no—
312C42C2×C4×D1911yescharacteristic
313C42C2×C4×D1911yescharacteristic
314C42D4×D1911yescharacteristic
315C42Q8×D1911yescharacteristic
316C23—192no—
317C23—381no—
318C23—381no—
319C23—382no—
320C23—382no—
321C23C22⋊C4×D1911yescharacteristic
322C2×C4—22no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—192no—
327C2×C4—192no—
328C2×C4—192no—
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×C4—762no—
344C2×C4—762no—
345C2×C4C42×D1911yescharacteristic
346C2×C4C22⋊C4×D1911yescharacteristic
347C2×C4C22⋊C4×D1911yescharacteristic
348C2×C4C4⋊C4×D1911yescharacteristic
349C2×C4C4⋊C4×D1911yescharacteristic
350C2×C4C4⋊C4×D1911yescharacteristic
351C2×C4#1059734712yes—
352C2×C4#1059735312yes—
353C2×C4#1059735711yescharacteristic
354C2×C4#1059736011yescharacteristic
355C2×C4#1059736111yescharacteristic
356C2×C4#1059736411yescharacteristic
357C8—42no—
358C8—42no—
359C8—762no—
360C8—762no—
361C22—382no—
362C22—382no—
363C22—382no—
364C22—762no—
365C22—762no—
366C22#95×D1911yescharacteristic
367C22#1192650912yes—
368C22#1192654211yescharacteristic
369C22#1192654411yescharacteristic
370C22#1192655912yes—
371C4—21no—
372C4—21no—
373C4—82no—
374C4—382no—
375C4—382no—
376C4—382no—
377C4—1522no—
378C4#1192649811yescharacteristic
379C4#1192650111yescharacteristic
380C4#1192654711yescharacteristic
381C4#1192655111yescharacteristic
382C4#1192656912yes—
383C4#1192658311yescharacteristic
384C4#1192658511yescharacteristic
385C2—762no—
386C2#1456209712yes—
387C2#1456209912yes—
388C2#1456333011yescharacteristic
389C2#1456334311yescharacteristic
390C2#1456335311yescharacteristic
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#7899
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. #11926595C4semidirect
13. #11926566C4semidirect
172. #1279D19semidirect
263. C19#7899semidirect

Maximal subgroups

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

subgroupindex
C2×#119265952
C2×#119265662
#145660312
#145614762
#145614752
#145614742
C19×#12792
#789919