Finite Group Databasebeta

← #18072013

Subgroups — #18072013

Order 4864.

674 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11926595C211yesmaximal, characteristic
2C2×#11926566C211yesmaximal, characteristic
3C2×C4⋊C8×D19C211yesmaximal, characteristic
4#14561470C211yesmaximal, characteristic, complemented
5#14561469C211yesmaximal, characteristic, complemented
6#14561469C211yesmaximal, characteristic, complemented
7C19×#1277C211yesmaximal, characteristic, complemented
8C22×#64515—21no—
9C22×C8×D19—21no—
10C2×C42×D19C2211yescharacteristic
11#11926595—22no—
12#11926595—22no—
13#11926566—22no—
14#11926566C414yes—
15C2×C4⋊(C19⋊C8)C2211yescharacteristic
16C2×C4⋊(C19⋊C8)C2211yescharacteristic
17C2×Dic19⋊C8—21no—
18C2×Dic19⋊C8—21no—
19C2×Dic19⋊C8C412yes—
20C4⋊C8×D19—22no—
21C4⋊C8×D19C414yes—
22C2×(C2×D19)⋊C8C412yes—
23C2×C4×C19⋊C8C2211yescharacteristic
24C2×C19×C4⋊C8C2211yescharacteristic
25C2×C19×C4⋊C8C2211yescharacteristic
26C2×C4×C8×C19C2211yescharacteristic
27C22×C4×D19C2×C411yescharacteristic
28C22×C4×D19D411yescharacteristic
29C22×C4×D19Q811yescharacteristic
30C22×C8×C19—21no—
31C22×C8×C19—21no—
32C22×C8×C19C2×C412yes—
33C2×C42×C19C2311yescharacteristic
34C2×C4×Dic19C2×C411yescharacteristic
35C2×C4×Dic19D411yescharacteristic
36C2×C4×Dic19Q811yescharacteristic
37C22×C19⋊C8—21no—
38C22×C19⋊C8—21no—
39C22×C19⋊C8C2×C412yes—
40C2×#64515—24no—
41C2×#64515—42no—
42C2×#64515—42no—
43C2×C8×D19—24no—
44C2×C8×D19—42no—
45C2×C8×D19—42no—
46C42×D19C2×C412yes—
47C42×D19C2×C412yes—
48C42×D19D412yes—
49C42×D19D412yes—
50C19×C4⋊C8—21no—
51C19×C4⋊C8—21no—
52C19×C4⋊C8C2×C412yes—
53C19×C4⋊C8C2×C412yes—
54C4×C8×C19—21no—
55C4×C8×C19—21no—
56(C2×D19)⋊C8—24no—
57Dic19⋊C8—24no—
58Dic19⋊C8—24no—
59Dic19⋊C8—24no—
60C4⋊(C19⋊C8)—21no—
61C4⋊(C19⋊C8)—21no—
62C4⋊(C19⋊C8)C2×C412yes—
63C4⋊(C19⋊C8)C2×C412yes—
64C4×C19⋊C8—21no—
65C4×C19⋊C8—21no—
66C23×D19C4⋊C411yescharacteristic
67C22×C4×C19C22×C411yescharacteristic
68C22×C4×C19C2×D411yescharacteristic
69C22×C4×C19C2×Q811yescharacteristic
70C22×Dic19C4⋊C411yescharacteristic
71C22×Dic19C4⋊C411yescharacteristic
72C22×Dic19C4⋊C411yescharacteristic
73C2×C4×D19—22no—
74C2×C4×D19—22no—
75C2×C4×D19—42no—
76C2×C4×D19C4212yes—
77C2×C4×D19C22⋊C412yes—
78C2×C4×D19C22⋊C412yes—
79C2×C4×D19C22⋊C412yes—
80C2×C4×D19C4⋊C412yes—
81C2×C4×D19C4⋊C412yes—
82C2×C4×D19D812yes—
83C2×C4×D19SD1612yes—
84C2×C4×D19SD1612yes—
85C2×C4×D19Q1612yes—
86C2×C8×C19—22no—
87C2×C8×C19—22no—
88C2×C8×C19—22no—
89C2×C8×C19—22no—
90C2×C8×C19—22no—
91C2×C8×C19—41no—
92C2×C8×C19—41no—
93C2×C8×C19—41no—
94C2×C8×C19—41no—
95C42×C19C22×C411yescharacteristic
96C42×C19C22×C411yescharacteristic
97C42×C19C2×D411yescharacteristic
98C42×C19C2×D411yescharacteristic
99C4×Dic19C4212yes—
100C4×Dic19C22⋊C412yes—
101C4×Dic19C22⋊C412yes—
102C4×Dic19C22⋊C412yes—
103C4×Dic19C4⋊C412yes—
104C4×Dic19C4⋊C412yes—
105C2×C19⋊C8—22no—
106C2×C19⋊C8—22no—
107C2×C19⋊C8—22no—
108C2×C19⋊C8—22no—
109C2×C19⋊C8—22no—
110C2×C19⋊C8—41no—
111C2×C19⋊C8—41no—
112C2×C19⋊C8—41no—
113C2×C19⋊C8—41no—
114#64515—48no—
115C8×D19—48no—
116#7877—191nomaximal, Sylow
117C23×C19C2×C4⋊C411yescharacteristic
118C22×D19—22no—
119C22×D19—22no—
120C22×D19#9512yes—
121C22×D19#10612yes—
122C22×D19#10712yes—
123C2×C4×C19—22no—
124C2×C4×C19C2×C4211yescharacteristic
125C2×C4×C19C2×C22⋊C411yescharacteristic
126C2×C4×C19C2×C22⋊C411yescharacteristic
127C2×C4×C19C2×C22⋊C411yescharacteristic
128C2×C4×C19C2×C4⋊C411yescharacteristic
129C2×C4×C19C2×C4⋊C411yescharacteristic
130C2×C4×C19#13112yes—
131C2×C4×C19#13112yes—
132C2×C4×C19C2×D811yescharacteristic
133C2×C4×C19C2×SD1611yescharacteristic
134C2×C4×C19C2×SD1611yescharacteristic
135C2×C4×C19C2×Q1611yescharacteristic
136C2×Dic19—22no—
137C2×Dic19—22no—
138C2×Dic19#9512yes—
139C2×Dic19#9512yes—
140C2×Dic19#9512yes—
141C2×Dic19#10612yes—
142C2×Dic19#10712yes—
143C4×D19—22no—
144C4×D19—22no—
145C4×D19—24no—
146C4×D19—42no—
147C4×D19—42no—
148C4×D19#10214yes—
149C4×D19#10214yes—
150C4×D19#10314yes—
151C4×D19#10314yes—
152C8×C19—42no—
153C8×C19—42no—
154C8×C19—42no—
155C19⋊C8—42no—
156C19⋊C8—42no—
157C19⋊C8—42no—
158C2×#431—191no—
159C2×#423—191no—
160C22×C4⋊C8—191no—
161#1277—191no—
162#1277—191no—
163#1277—191no—
164#1277D1911yescharacteristic, complemented
165C22×C19C2×#9511yescharacteristic
166C22×C19#42412yes—
167C22×C19C2×#10611yescharacteristic
168C22×C19C2×#10711yescharacteristic
169C22×C19#43012yes—
170C2×D19—24no—
171C2×D19—24no—
172C2×D19—22no—
173C2×D19—22no—
174C2×D19#34014yes—
175C4×C19—21no—
176C4×C19—21no—
177C4×C19#40511yescharacteristic
178C4×C19#40511yescharacteristic
179C4×C19#40812yes—
180C4×C19C2×#10211yescharacteristic
181C4×C19C2×#10211yescharacteristic
182C4×C19C2×#10311yescharacteristic
183C4×C19C2×#10311yescharacteristic
184Dic19—22no—
185Dic19—22no—
186Dic19#34014yes—
187C22×M16—381no—
188C23×C8—381no—
189C22×C42—191no—
190#431—382no—
191#431—382no—
192#423—194no—
193#423—382no—
194C2×C4⋊C8—191no—
195C2×C4⋊C8—191no—
196C2×C4⋊C8—194no—
197C2×C4⋊C8—192no—
198C2×C4⋊C8—382no—
199C2×C4⋊C8—381no—
200C2×C4⋊C8—381no—
201C2×C4⋊C8C2×D1911yescharacteristic
202C2×C4⋊C8C2×D1911yescharacteristic
203C2×C22⋊C8—192no—
204C2×C4×C8—191no—
205C2×C4×C8C2×D1911yescharacteristic
206C2×C19#157012yes—
207C2×C19#157112yes—
208C2×C19#172911yescharacteristic
209C2×C19C2×#34011yescharacteristic
210C2×C19#173811yescharacteristic
211D19—24no—
212C23×C4—191no—
213C23×C4—191no—
214C23×C4—191no—
215C2×M16—384no—
216C2×M16—762no—
217C2×M16—762no—
218C22×C8—21no—
219C22×C8—21no—
220C22×C8—192no—
221C22×C8—384no—
222C22×C8—381no—
223C22×C8—381no—
224C22×C8—762no—
225C22×C8—762no—
226C22×C8C4×D1912yes—
227C2×C42—191no—
228C2×C42—191no—
229C2×C42—191no—
230C2×C42—192no—
231C2×C42—192no—
232C2×C42—192no—
233C2×C42—192no—
234C2×C42C22×D1911yescharacteristic
235C4⋊C8—21no—
236C4⋊C8—21no—
237C4⋊C8—192no—
238C4⋊C8—192no—
239C4⋊C8—384no—
240C4⋊C8—384no—
241C4⋊C8—384no—
242C4⋊C8—381no—
243C4⋊C8—381no—
244C4⋊C8C4×D1912yes—
245C4⋊C8C4×D1912yes—
246C22⋊C8—384no—
247C4×C8—21no—
248C4×C8—21no—
249C4×C8—381no—
250C4×C8—381no—
251C19#787711yescharacteristic, complemented, Sylow
252C24—191no—
253C22×C4—191no—
254C22×C4—192no—
255C22×C4—192no—
256C22×C4—192no—
257C22×C4—192no—
258C22×C4—192no—
259C22×C4—192no—
260C22×C4—191no—
261C22×C4—191no—
262C22×C4—192no—
263C22×C4—192no—
264C22×C4—192no—
265C22×C4—192no—
266C22×C4—382no—
267C22×C4—382no—
268C22×C4—762no—
269C22×C4C2×C4×D1911yescharacteristic
270C22×C4D4×D1911yescharacteristic
271C22×C4Q8×D1911yescharacteristic
272M16—768no—
273C2×C8—22no—
274C2×C8—22no—
275C2×C8—22no—
276C2×C8—22no—
277C2×C8—22no—
278C2×C8—41no—
279C2×C8—41no—
280C2×C8—41no—
281C2×C8—41no—
282C2×C8—382no—
283C2×C8—382no—
284C2×C8—382no—
285C2×C8—382no—
286C2×C8—382no—
287C2×C8—768no—
288C2×C8—761no—
289C2×C8—761no—
290C2×C8—761no—
291C2×C8—761no—
292C42—192no—
293C42—192no—
294C42—192no—
295C42—192no—
296C42—192no—
297C42—192no—
298C42C2×C4×D1911yescharacteristic
299C42C2×C4×D1911yescharacteristic
300C42D4×D1911yescharacteristic
301C42D4×D1911yescharacteristic
302C23—192no—
303C23—192no—
304C23—192no—
305C23—382no—
306C23—382no—
307C23C4⋊C4×D1911yescharacteristic
308C2×C4—22no—
309C2×C4—192no—
310C2×C4—192no—
311C2×C4—192no—
312C2×C4—194no—
313C2×C4—194no—
314C2×C4—194no—
315C2×C4—194no—
316C2×C4—192no—
317C2×C4—192no—
318C2×C4—382no—
319C2×C4—382no—
320C2×C4—382no—
321C2×C4—382no—
322C2×C4—384no—
323C2×C4—762no—
324C2×C4—762no—
325C2×C4C42×D1911yescharacteristic
326C2×C4C22⋊C4×D1911yescharacteristic
327C2×C4C22⋊C4×D1911yescharacteristic
328C2×C4C22⋊C4×D1911yescharacteristic
329C2×C4C4⋊C4×D1911yescharacteristic
330C2×C4C4⋊C4×D1911yescharacteristic
331C2×C4#1059734712yes—
332C2×C4#1059735312yes—
333C2×C4D8×D1911yescharacteristic
334C2×C4SD16×D1911yescharacteristic
335C2×C4SD16×D1911yescharacteristic
336C2×C4Q16×D1911yescharacteristic
337C8—42no—
338C8—42no—
339C8—42no—
340C8—762no—
341C8—762no—
342C8—762no—
343C22—194no—
344C22—382no—
345C22—382no—
346C22—384no—
347C22—384no—
348C22#95×D1911yescharacteristic
349C22#1192656912yes—
350C22#106×D1911yescharacteristic
351C22#107×D1911yescharacteristic
352C22#1192659112yes—
353C4—21no—
354C4—21no—
355C4—194no—
356C4—382no—
357C4—382no—
358C4#1192649811yescharacteristic
359C4#1192650111yescharacteristic
360C4#1192650912yes—
361C4#102×D1911yescharacteristic
362C4#102×D1911yescharacteristic
363C4#103×D1911yescharacteristic
364C4#103×D1911yescharacteristic
365C2—384no—
366C2#1456240412yes—
367C2#1456240812yes—
368C2#1456333011yescharacteristic
369C2D19×#34011yescharacteristic
370C2#1456336011yescharacteristic
subgroupG/H
centerC22×C4D4×D19
commutatorC2×C4×C19C2×C42
FrattiniC2×C42C22×D19
FittingC19×#1277C2
socleC23×C19C2×C4⋊C4
prime radicalC23×D19C4⋊C4
cosocleC2×C42×C19C23
hypercenter#1277D19
hypocenterC19#7877
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ #1277

Complements

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

NH ≅ G/Ntype
4. #14561470C2semidirect
5. #14561469C2semidirect
6. #14561469C2semidirect
7. C19×#1277C2semidirect
164. #1277D19semidirect
251. C19#7877semidirect

Maximal subgroups

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

subgroupindex
C2×#119265952
C2×#119265662
C2×C4⋊C8×D192
#145614702
#145614692
C19×#12772
#787719