Finite Group Databasebeta

← #18089024

Subgroups — #18089024

Order 4864.

978 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
1C22×#10597293C212yesmaximal
2C2×C4×#64520C211yesmaximal, characteristic
3C2×#11926313C212yesmaximal
4#14563329C211yesmaximal, characteristic
5C2×C19×#391C211yesmaximal, characteristic
6C22×#64520C2212yes—
7C22×#64520C2212yes—
8C2×#10597293—24no—
9C2×#10597293—24no—
10C2×#10597293C418yescomplemented
11C4×#64520—24no—
12C2×#10597260—21no—
13C2×C4×C19⋊C8—21no—
14#11926313—24no—
15#11926299—22no—
16C23×Q8×C19C2211yescharacteristic
17C22×C4⋊C4×C19C2211yescharacteristic
18C22×C42×C19C2211yescharacteristic
19C19×#391—22no—
20C19×#391—21no—
21C19×#391—21no—
22C2×C19×#95C414yes—
23C22×Q8×C19—21no—
24C22×Q8×C19—21no—
25C22×Q8×C19—22no—
26C22×Q8×C19—22no—
27C22×Q8×C19—22no—
28C22×Q8×C19—22no—
29C22×Q8×C19—22no—
30C22×Q8×C19C2×C414yes—
31C23×C4×C19C2×C412yes—
32C23×C4×C19C2×C412yes—
33C23×C4×C19C2×C412yes—
34C23×C4×C19C2311yescharacteristic
35C2×C4⋊C4×C19—22no—
36C2×C4⋊C4×C19—21no—
37C2×C4⋊C4×C19—21no—
38C2×C4⋊C4×C19—22no—
39C2×C42×C19—22no—
40C2×C42×C19—22no—
41C2×C42×C19D412yes—
42C2×C42×C19D411yescharacteristic
43C2×C42×C19D411yescharacteristic
44C2×#64520—22no—
45C2×#64520—22no—
46C2×#64520—22no—
47C2×#64520—22no—
48C2×#64520—22no—
49C2×#64520—22no—
50C2×#64520—22no—
51C2×#64520—22no—
52C2×#64520C2×C414yes—
53C2×#64520C2×C414yes—
54C2×#64520D414yes—
55C2×#64520D414yes—
56C22×C19⋊C8—22no—
57C22×C19⋊C8—22no—
58C19×#95—24no—
59C19×#95—24no—
60#10597293—216no—
61#10597260—24no—
62C4×C19⋊C8—24no—
63C24×C19C22×C411yescharacteristic
64C2×Q8×C19—24no—
65C2×Q8×C19—24no—
66C2×Q8×C19—24no—
67C2×Q8×C19—24no—
68C2×Q8×C19—24no—
69C2×Q8×C19—24no—
70C2×Q8×C19—41no—
71C2×Q8×C19—42no—
72C2×Q8×C19—42no—
73C2×Q8×C19—42no—
74C2×Q8×C19—41no—
75C2×Q8×C19—42no—
76C2×Q8×C19—41no—
77C2×Q8×C19—42no—
78C2×Q8×C19—42no—
79C2×Q8×C19—41no—
80C22×C4×C19—22no—
81C22×C4×C19—22no—
82C22×C4×C19—24no—
83C22×C4×C19—24no—
84C22×C4×C19—24no—
85C22×C4×C19—24no—
86C22×C4×C19—22no—
87C22×C4×C19—24no—
88C22×C4×C19—42no—
89C22×C4×C19—44no—
90C22×C4×C19C4214yes—
91C22×C4×C19C22⋊C412yes—
92C22×C4×C19C22⋊C412yes—
93C22×C4×C19C22×C412yes—
94C22×C4×C19C2×D412yes—
95C22×C4×C19C2×D412yes—
96C22×C4×C19C2×D411yescharacteristic
97C22×C4×C19C2×D411yescharacteristic
98C22×C4×C19#4112yes—
99C22×C4×C19#4112yes—
100C22×C4×C19#4112yes—
101C4⋊C4×C19—42no—
102C4⋊C4×C19—41no—
103C4⋊C4×C19—41no—
104C42×C19—21no—
105C42×C19—21no—
106C42×C19—24no—
107C42×C19—21no—
108C42×C19—21no—
109#64520—24no—
110#64520—24no—
111#64520—24no—
112#64520—24no—
113#64520—24no—
114#64520—42no—
115#64520—42no—
116#64520C22⋊C418yes—
117C2×C19⋊C8—24no—
118C2×C19⋊C8—24no—
119C2×C19⋊C8—24no—
120C2×C19⋊C8—24no—
121C2×C19⋊C8—42no—
122C2×C19⋊C8—42no—
123#10963—191nomaximal, Sylow
124C23×C19—22no—
125C23×C19—22no—
126C23×C19C2×C4211yescharacteristic
127C23×C19C2×C22⋊C411yescharacteristic
128C23×C19#11711yescharacteristic
129C23×C19C4×D412yes—
130C23×C19C4×D412yes—
131Q8×C19—44no—
132Q8×C19—44no—
133Q8×C19—44no—
134Q8×C19—44no—
135C2×C4×C19—22no—
136C2×C4×C19—22no—
137C2×C4×C19—24no—
138C2×C4×C19—28no—
139C2×C4×C19—22no—
140C2×C4×C19—22no—
141C2×C4×C19—22no—
142C2×C4×C19—48no—
143C2×C4×C19—42no—
144C2×C4×C19—44no—
145C2×C4×C19—42no—
146C2×C4×C19—42no—
147C2×C4×C19—44no—
148C2×C4×C19—84no—
149C2×C4×C19#10114yescomplemented
150C2×C4×C19C2×C22⋊C412yes—
151C2×C4×C19#11712yes—
152C2×C4×C19C4×D412yes—
153C2×C4×C19C4×D412yes—
154C2×C4×C19C4×D412yes—
155C2×C4×C19C4×D412yes—
156C2×C4×C19#12011yescharacteristic
157C2×C4×C19#12112yes—
158C2×C4×C19#12112yes—
159C2×C4×C19#12112yes—
160C2×C4×C19#12311yescharacteristic
161C2×C4×C19#12312yes—
162C2×C4×C19#12411yescharacteristic
163C2×C4×C19#12412yes—
164C2×C4×C19#12612yes—
165C2×C4×C19#12711yescharacteristic
166C19⋊C8—28no—
167C19⋊C8—44no—
168C22×#101—192no—
169C2×C4×M16—191no—
170C2×#391D1911yescharacteristic
171C2×#343—192no—
172#1728—191no—
173C22×C19—24no—
174C22×C19—22no—
175C22×C19—22no—
176C22×C19—22no—
177C22×C19—22no—
178C22×C19C4×C22⋊C411yescharacteristic
179C22×C19C4×C22⋊C412yes—
180C22×C19#38611yescharacteristic
181C22×C19#38812yes—
182C22×C19#39011yescharacteristic
183C22×C19C2×#10112yes—
184C22×C19#41312yes—
185C4×C19—24no—
186C4×C19—42no—
187C4×C19—44no—
188C4×C19—82no—
189C4×C19#38612yes—
190C4×C19#38812yes—
191C4×C19#38812yes—
192C4×C19#39012yes—
193C23×Q8C2×D1911yescharacteristic
194C22×M16—192no—
195C22×M16—192no—
196C22×C4⋊C4C2×D1911yescharacteristic
197C22×C42C2×D1911yescharacteristic
198C2×#101—198no—
199C2×#101—384no—
200C2×#101—384no—
201C4×M16—384no—
202C2×#97—381no—
203C2×C4×C8—381no—
204#391—22no—
205#391—21no—
206#391—21no—
207C2×#95Dic1914yes—
208#343—384no—
209#336—382no—
210C2×C19—22no—
211C2×C19—22no—
212C2×C19#143711yescharacteristic
213C2×C19C4×#10112yes—
214C2×C19#190112yes—
215C2×C19#196611yescharacteristic
216C2×C19#196711yescharacteristic
217C22×Q8—22no—
218C22×Q8—22no—
219C22×Q8—22no—
220C22×Q8—22no—
221C22×Q8—22no—
222C22×Q8—21no—
223C22×Q8—21no—
224C22×Q8C4×D1914yes—
225C23×C4C2×Dic1912yes—
226C23×C4C2×Dic1912yes—
227C23×C4C2×Dic1912yes—
228C23×C4C22×D1911yescharacteristic
229C2×M16—194no—
230C2×M16—194no—
231C2×M16—194no—
232C2×M16—194no—
233C2×M16—382no—
234C2×M16—382no—
235C2×M16—382no—
236C2×M16—382no—
237C2×M16—382no—
238C2×M16—382no—
239C2×M16—382no—
240C2×M16—382no—
241C22×C8—382no—
242C22×C8—382no—
243C2×C4⋊C4—22no—
244C2×C4⋊C4—22no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C42—22no—
248C2×C42—22no—
249C2×C42C22⋊D1912yes—
250C2×C42C22⋊D1911yescharacteristic
251C2×C42C22⋊D1911yescharacteristic
252#101—3816no—
253#97—384no—
254C4×C8—384no—
255#95—24no—
256#95—24no—
257C19#1096311yescharacteristic, complemented, Sylow
258C24C22×Dic1911yescharacteristic
259C2×Q8—24no—
260C2×Q8—24no—
261C2×Q8—24no—
262C2×Q8—24no—
263C2×Q8—24no—
264C2×Q8—24no—
265C2×Q8—41no—
266C2×Q8—41no—
267C2×Q8—41no—
268C2×Q8—42no—
269C2×Q8—42no—
270C2×Q8—41no—
271C2×Q8—42no—
272C2×Q8—42no—
273C2×Q8—42no—
274C2×Q8—42no—
275C22×C4—24no—
276C22×C4—24no—
277C22×C4—24no—
278C22×C4—22no—
279C22×C4—22no—
280C22×C4—24no—
281C22×C4—22no—
282C22×C4—24no—
283C22×C4—42no—
284C22×C4—44no—
285C22×C4C4×Dic1914yes—
286C22×C4C22⋊Dic1912yes—
287C22×C4C22⋊Dic1912yes—
288C22×C4C2×C4×D1912yes—
289C22×C4#6454112yes—
290C22×C4D4×D1912yes—
291C22×C4D4×D1912yes—
292C22×C4#6454312yes—
293C22×C4#6454312yes—
294C22×C4C2×C22⋊D1911yescharacteristic
295C22×C4C2×C22⋊D1911yescharacteristic
296M16—198no—
297M16—384no—
298M16—384no—
299M16—384no—
300M16—384no—
301M16—384no—
302M16—762no—
303M16—762no—
304C2×C8—384no—
305C2×C8—384no—
306C2×C8—384no—
307C2×C8—384no—
308C2×C8—762no—
309C2×C8—762no—
310C4⋊C4—41no—
311C4⋊C4—42no—
312C4⋊C4—41no—
313C42—21no—
314C42—21no—
315C42—21no—
316C42—21no—
317C42—24no—
318C23—22no—
319C23—22no—
320C23C2×C4×Dic1911yescharacteristic
321C23#1059737211yescharacteristic
322C23D4×Dic1912yes—
323C23D4×Dic1912yes—
324C23C2×C22⋊Dic1911yescharacteristic
325Q8—44no—
326Q8—44no—
327Q8—44no—
328Q8—44no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—24no—
333C2×C4—28no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—48no—
337C2×C4—42no—
338C2×C4—44no—
339C2×C4—42no—
340C2×C4—44no—
341C2×C4—42no—
342C2×C4—84no—
343C2×C4#1059729314yescomplemented
344C2×C4#1059732312yes—
345C2×C4#1059732512yes—
346C2×C4C22⋊C4×D1912yes—
347C2×C4(C22⋊D19)⋊C412yes—
348C2×C4(C22⋊D19)⋊C412yes—
349C2×C4#1059732912yes—
350C2×C4#1059733012yes—
351C2×C4#1059733112yes—
352C2×C4C4×C22⋊D1912yes—
353C2×C4C4×C22⋊D1912yes—
354C2×C4#1059738111yescharacteristic
355C2×C4#1059738211yescharacteristic
356C2×C4#1059738311yescharacteristic
357C2×C4#1059738412yes—
358C2×C4#1059738512yes—
359C2×C4#1059738611yescharacteristic
360C8—388no—
361C8—764no—
362C22—24no—
363C22—22no—
364C22—22no—
365C22—22no—
366C22—22no—
367C22C4×C22⋊Dic1911yescharacteristic
368C22C22⋊C4×Dic1912yes—
369C22#1192642411yescharacteristic
370C22#1192643712yes—
371C22#1192644711yescharacteristic
372C22C2×#1059729312yes—
373C22#1192652812yes—
374C4—24no—
375C4—42no—
376C4—44no—
377C4—82no—
378C4#1192642012yes—
379C4#1192643212yes—
380C4#1192643812yes—
381C4#1192644412yes—
382C2—22no—
383C2—22no—
384C2#1456187211yescharacteristic
385C2C4×#1059729312yes—
386C2#1456410412yes—
387C2#1456448011yescharacteristic
388C2#1456448511yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic19
commutatorC23×C19C2×C42
FrattiniC23×C4C22×D19
FittingC2×C19×#391C2
socleC23×C19C2×C22⋊C4
prime radicalC24×C19C22×C4
cosocleC23×C4×C19C23
hypercenterC2×#391D19
hypocenterC19#10963
LCSG ▷ C23×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
10. C2×#10597293C4semidirect
149. C2×C4×C19#101semidirect
257. C19#10963semidirect
343. C2×C4#10597293semidirect

Maximal subgroups

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

subgroupindex
C22×#105972932
C2×C4×#645202
C2×#119263132
#145633292
C2×C19×#3912
#1096319