Finite Group Databasebeta

← #18078235

Subgroups — #18078235

Order 4864.

612 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11926568C211yesmaximal, characteristic
2#14563615C211yesmaximal, characteristic
3C2×#11926290C212yesmaximal, complemented
4#14561518C212yesmaximal, complemented
5C19×#2857C211yesmaximal, characteristic
6C22×#64520—21no—
7#11926568—24no—
8C2×C4⋊(C19⋊C8)—21no—
9C2×C4⋊(C19⋊C8)C2212yes—
10C2×C4⋊(C19⋊C8)C2212yes—
11C2×C22⋊(C19⋊C8)—21no—
12#11926299—21no—
13#11926290—24no—
14C2×C19×C4⋊Q8C2211yescharacteristic
15C2×C19×C22⋊Q8—21no—
16C22×C42×C19C2211yescharacteristic
17C19×#391—21no—
18C19×#389—21no—
19C19×#389C412yes—
20C19×#384C2211yescharacteristic
21C19×#380—21no—
22C19×#380C412yes—
23C22×Q8×C19—21no—
24C23×C4×C19C2×C411yescharacteristic
25C23×C4×C19D411yescharacteristic
26C23×C4×C19D411yescharacteristic
27C19×C4⋊Q8—22no—
28C19×C4⋊Q8—22no—
29C19×C22⋊Q8—42no—
30C19×C22⋊Q8—42no—
31C2×C4⋊C4×C19—22no—
32C2×C4⋊C4×C19—21no—
33C2×C4⋊C4×C19—21no—
34C2×C4⋊C4×C19—21no—
35C2×C4⋊C4×C19C2×C412yes—
36C2×C4⋊C4×C19C2×C412yes—
37C2×C22⋊C4×C19—22no—
38C2×C42×C19—22no—
39C2×C42×C19—22no—
40C2×C42×C19C2×C411yescharacteristic
41C2×C42×C19D411yescharacteristic
42C2×C42×C19D411yescharacteristic
43C2×C42×C19C2311yescharacteristic
44C2×#64520—24no—
45C2×#64520—42no—
46C2×#64520—42no—
47C22×C19⋊C8—22no—
48C22×C19⋊C8—22no—
49C19×#95—22no—
50C19×#95—22no—
51C22⋊(C19⋊C8)—42no—
52C4⋊(C19⋊C8)—24no—
53C4⋊(C19⋊C8)—22no—
54C4⋊(C19⋊C8)—22no—
55C4⋊(C19⋊C8)—22no—
56C4⋊(C19⋊C8)D414yes—
57C24×C19C22⋊C411yescharacteristic
58C2×Q8×C19—41no—
59C2×Q8×C19—41no—
60C2×Q8×C19—41no—
61C2×Q8×C19—41no—
62C2×Q8×C19—41no—
63C2×Q8×C19—41no—
64C22×C4×C19—21no—
65C22×C4×C19—21no—
66C22×C4×C19—21no—
67C22×C4×C19—21no—
68C22×C4×C19—22no—
69C22×C4×C19—22no—
70C22×C4×C19—22no—
71C22×C4×C19—21no—
72C22×C4×C19—22no—
73C22×C4×C19—21no—
74C22×C4×C19—22no—
75C22×C4×C19—22no—
76C22×C4×C19—41no—
77C22×C4×C19C22⋊C411yescharacteristic
78C22×C4×C19C22⋊C411yescharacteristic
79C22×C4×C19C22⋊C411yescharacteristic
80C22×C4×C19D812yes—
81C22×C4×C19SD1612yes—
82C22×C4×C19C22×C411yescharacteristic
83C22×C4×C19C2×D411yescharacteristic
84C22×C4×C19C2×D411yescharacteristic
85C4⋊C4×C19—24no—
86C4⋊C4×C19—42no—
87C4⋊C4×C19—44no—
88C4⋊C4×C19—42no—
89C4⋊C4×C19—41no—
90C4⋊C4×C19—41no—
91C4⋊C4×C19—41no—
92C4⋊C4×C19—41no—
93C22⋊C4×C19—44no—
94C42×C19—22no—
95C42×C19—21no—
96C42×C19—22no—
97C42×C19—21no—
98C42×C19C2×D412yes—
99C42×C19#4112yes—
100#64520—48no—
101C2×C19⋊C8—24no—
102C2×C19⋊C8—42no—
103C2×C19⋊C8—42no—
104C2×C19⋊C8—42no—
105C2×C19⋊C8—42no—
106C2×C19⋊C8—42no—
107#9139—191nomaximal, Sylow
108C23×C19—21no—
109C23×C19—21no—
110C23×C19—21no—
111C23×C19—21no—
112C23×C19—21no—
113C23×C19—21no—
114C23×C19#10212yes—
115C23×C19C2×C22⋊C411yescharacteristic
116Q8×C19—81no—
117Q8×C19—81no—
118Q8×C19—81no—
119Q8×C19—81no—
120C2×C4×C19—21no—
121C2×C4×C19—21no—
122C2×C4×C19—21no—
123C2×C4×C19—21no—
124C2×C4×C19—21no—
125C2×C4×C19—21no—
126C2×C4×C19—22no—
127C2×C4×C19—22no—
128C2×C4×C19—22no—
129C2×C4×C19—22no—
130C2×C4×C19—21no—
131C2×C4×C19—21no—
132C2×C4×C19—21no—
133C2×C4×C19—44no—
134C2×C4×C19—42no—
135C2×C4×C19—42no—
136C2×C4×C19—42no—
137C2×C4×C19—42no—
138C2×C4×C19—42no—
139C2×C4×C19—42no—
140C2×C4×C19—42no—
141C2×C4×C19—42no—
142C2×C4×C19#10112yes—
143C2×C4×C19#10212yes—
144C2×C4×C19C4×D412yes—
145C2×C4×C19#12011yescharacteristic
146C2×C4×C19#12112yes—
147C2×C4×C19#12311yescharacteristic
148C2×C4×C19C2×D811yescharacteristic
149C2×C4×C19C2×SD1611yescharacteristic
150C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
151C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
152C2×C4×C19#13712yes—
153C2×C4×C19#13711yescharacteristic
154C2×C4×C19#13711yescharacteristic
155C19⋊C8—44no—
156C19⋊C8—82no—
157C2×#423—191no—
158#2857D1911yescharacteristic
159#1797—191no—
160C2×#332—192no—
161#1296—192no—
162C22×C19—22no—
163C22×C19—22no—
164C22×C19—22no—
165C22×C19—41no—
166C22×C19—41no—
167C22×C19—41no—
168C22×C19—41no—
169C22×C19#38611yescharacteristic
170C22×C19C2×#10111yescharacteristic
171C22×C19#41311yescharacteristic
172C22×C19C2×#10211yescharacteristic
173C22×C19#41711yescharacteristic
174C22×C19#41711yescharacteristic
175C22×C19#41911yescharacteristic
176C4×C19—22no—
177C4×C19—22no—
178C4×C19—22no—
179C4×C19—41no—
180C4×C19—82no—
181C4×C19—82no—
182C4×C19#44711yescharacteristic
183C4×C19#44811yescharacteristic
184C4×C19#46812yes—
185C4×C19#47012yes—
186C4×C19#48011yescharacteristic
187C4×C19#48111yescharacteristic
188C22×M16—381no—
189C2×C4⋊Q8C2×D1911yescharacteristic
190C2×C22⋊Q8—21no—
191C22×C42C2×D1911yescharacteristic
192#423—384no—
193C2×C4⋊C8—192no—
194C2×C4⋊C8—192no—
195C2×C4⋊C8—381no—
196C2×C22⋊C8—381no—
197#391—21no—
198#389—21no—
199#389Dic1912yes—
200#384C2×D1911yescharacteristic
201#380—21no—
202#380Dic1912yes—
203#336—381no—
204#332—384no—
205C2×C19—42no—
206C2×C19#154611yescharacteristic
207C2×C19#154711yescharacteristic
208C2×C19#155911yescharacteristic
209C2×C19#156111yescharacteristic
210C2×C19#187411yescharacteristic
211C2×C19#189411yescharacteristic
212C2×C19#190111yescharacteristic
213C22×Q8—21no—
214C23×C4C2×Dic1911yescharacteristic
215C23×C4C22⋊D1911yescharacteristic
216C23×C4C22⋊D1911yescharacteristic
217C2×M16—384no—
218C2×M16—762no—
219C2×M16—762no—
220C22×C8—382no—
221C22×C8—382no—
222C4⋊Q8—22no—
223C4⋊Q8—22no—
224C22⋊Q8—42no—
225C22⋊Q8—42no—
226C2×C4⋊C4—22no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4C2×Dic1912yes—
231C2×C4⋊C4C2×Dic1912yes—
232C2×C22⋊C4—22no—
233C2×C42—22no—
234C2×C42—22no—
235C2×C42C2×Dic1911yescharacteristic
236C2×C42C22⋊D1911yescharacteristic
237C2×C42C22⋊D1911yescharacteristic
238C2×C42C22×D1911yescharacteristic
239C4⋊C8—194no—
240C4⋊C8—384no—
241C4⋊C8—382no—
242C4⋊C8—382no—
243C4⋊C8—382no—
244C22⋊C8—762no—
245#95—22no—
246#95—22no—
247C19#913911yescharacteristic, complemented, Sylow
248C24C22⋊Dic1911yescharacteristic
249C2×Q8—41no—
250C2×Q8—41no—
251C2×Q8—41no—
252C2×Q8—41no—
253C2×Q8—41no—
254C2×Q8—41no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—22no—
265C22×C4—22no—
266C22×C4—22no—
267C22×C4—41no—
268C22×C4#6452512yes—
269C22×C4#6452612yes—
270C22×C4C22⋊Dic1911yescharacteristic
271C22×C4C22⋊Dic1911yescharacteristic
272C22×C4C22⋊Dic1911yescharacteristic
273C22×C4C22×Dic1911yescharacteristic
274C22×C4C2×C22⋊D1911yescharacteristic
275C22×C4C2×C22⋊D1911yescharacteristic
276M16—768no—
277C2×C8—384no—
278C2×C8—762no—
279C2×C8—762no—
280C2×C8—762no—
281C2×C8—762no—
282C2×C8—762no—
283C4⋊C4—24no—
284C4⋊C4—42no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4—42no—
288C4⋊C4—41no—
289C4⋊C4—41no—
290C4⋊C4—44no—
291C22⋊C4—44no—
292C42—22no—
293C42—21no—
294C42—21no—
295C42—22no—
296C42D4×D1912yes—
297C42#6454312yes—
298C23—21no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23#1059728912yes—
305C23C2×C22⋊Dic1911yescharacteristic
306Q8—81no—
307Q8—81no—
308Q8—81no—
309Q8—81no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—44no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4#1059728912yes—
333C2×C4#1059729312yes—
334C2×C4C2×#6452511yescharacteristic
335C2×C4C2×#6452611yescharacteristic
336C2×C4D4×Dic1912yes—
337C2×C4#1059738111yescharacteristic
338C2×C4#1059738311yescharacteristic
339C2×C4#1059738512yes—
340C2×C4#1059738812yes—
341C2×C4#1059739511yescharacteristic
342C2×C4#1059739511yescharacteristic
343C2×C4#1059739711yescharacteristic
344C2×C4#1059739711yescharacteristic
345C8—764no—
346C8—1522no—
347C22—22no—
348C22—22no—
349C22—22no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22#1192642411yescharacteristic
355C22C2×#1059729311yescharacteristic
356C22#1192652811yescharacteristic
357C22C2×#1059728911yescharacteristic
358C22#1192654511yescharacteristic
359C22#1192654511yescharacteristic
360C22#1192655311yescharacteristic
361C4—22no—
362C4—22no—
363C4—22no—
364C4—41no—
365C4—82no—
366C4—82no—
367C4#1192667711yescharacteristic
368C4#1192668211yescharacteristic
369C4#1192679212yes—
370C4#1192680012yes—
371C4#1192685511yescharacteristic
372C4#1192686011yescharacteristic
373C2—42no—
374C2#1456230711yescharacteristic
375C2#1456231211yescharacteristic
376C2#1456236511yescharacteristic
377C2#1456237311yescharacteristic
378C2#1456395311yescharacteristic
379C2#1456406911yescharacteristic
380C2#1456410411yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic19
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#2857C2
socleC23×C19C2×C22⋊C4
prime radicalC24×C19C22⋊C4
cosocleC2×C42×C19C23
hypercenter#2857D19
hypocenterC19#9139
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2857

Complements

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

NH ≅ G/Ntype
3. C2×#11926290C2semidirect
4. #14561518C2semidirect
247. C19#9139semidirect

Maximal subgroups

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

subgroupindex
C2×#119265682
#145636152
C2×#119262902
#145615182
C19×#28572
#913919