Finite Group Databasebeta

← #18080259

Subgroups — #18080259

Order 4864.

904 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 904 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14566213C211yesmaximal, characteristic
2#14563556C211yesmaximal, characteristic
3#14562168C212yesmaximal, complemented
4#14561488C212yesmaximal, complemented
5C19×#2435C211yesmaximal, characteristic
6C22×C22⋊Dic19—21no—
7C2×#10597290—22no—
8#11926508C2212yes—
9#11926424—24no—
10#11926407C2212yes—
11#11926400—21no—
12#11926281—24no—
13C23×D4×C19C2211yescharacteristic
14C2×C19×#124C412yescomplemented
15C2×C19×C22⋊Q8C2211yescharacteristic
16C19×#394—22no—
17C19×#390C412yescomplemented
18C19×#379—21no—
19C19×#379—21no—
20C4×C22⋊C4×C19C2211yescharacteristic
21C25×C19D411yescharacteristic
22C25×C19D411yescharacteristic
23C22×Q8×C19C2×C411yescharacteristic, complemented
24C22×D4×C19—22no—
25C22×D4×C19—22no—
26C22×D4×C19—44no—
27C22×D4×C19C2×C412yes—
28C22×D4×C19D412yes—
29C23×C4×C19C2311yescharacteristic
30C23×Dic19—22no—
31C19×#124—44no—
32C19×C22⋊Q8—22no—
33C19×C22⋊Q8—22no—
34C2×C4⋊C4×C19—21no—
35C2×C4⋊C4×C19C2×C411yescharacteristic, complemented
36C2×C22⋊C4×C19—22no—
37C2×C22⋊C4×C19—22no—
38C2×C22⋊C4×C19—21no—
39C2×C22⋊C4×C19—21no—
40C2×C22⋊C4×C19—22no—
41C2×C22⋊C4×C19—22no—
42C2×C42×C19C2×C412yescomplemented
43C2×C22⋊Dic19—22no—
44C2×C22⋊Dic19—22no—
45C2×C22⋊Dic19—22no—
46C2×C22⋊Dic19—22no—
47C2×C22⋊Dic19—44no—
48C2×#64520—22no—
49C19×#95—21no—
50#10597290—44no—
51C19⋊#95—22no—
52C19⋊#95D414yes—
53C22⋊(C19⋊C8)—22no—
54C22⋊(C19⋊C8)—22no—
55C24×C19—21no—
56C24×C19—24no—
57C24×C19—21no—
58C24×C19—21no—
59C24×C19—21no—
60C24×C19—42no—
61C24×C19—42no—
62C24×C19—42no—
63C24×C19—81no—
64C24×C19—81no—
65C24×C19C22⋊C412yes—
66C24×C19C22⋊C412yes—
67C24×C19C2×D411yescharacteristic
68C2×Q8×C19—22no—
69C2×Q8×C19—42no—
70C2×D4×C19—24no—
71C2×D4×C19—24no—
72C2×D4×C19—24no—
73C2×D4×C19—24no—
74C2×D4×C19—42no—
75C2×D4×C19—42no—
76C2×D4×C19—44no—
77C2×D4×C19—44no—
78C2×D4×C19—48no—
79C22×C4×C19—22no—
80C22×C4×C19—21no—
81C22×C4×C19—21no—
82C22×C4×C19—42no—
83C22×C4×C19C22×C411yescharacteristic
84C22×C4×C19C2×D412yes—
85C22×C4×C19C2×D411yescharacteristic
86C22×C4×C19#4112yes—
87C22×Dic19—24no—
88C22×Dic19—44no—
89C22×Dic19—82no—
90C22×Dic19—82no—
91C4⋊C4×C19—22no—
92C4⋊C4×C19—42no—
93C22⋊C4×C19—42no—
94C22⋊C4×C19—44no—
95C22⋊C4×C19—44no—
96C22⋊C4×C19—41no—
97C22⋊C4×C19—41no—
98C22⋊C4×C19—82no—
99C22⋊C4×C19—82no—
100C42×C19—42no—
101C22⋊Dic19—44no—
102C22⋊Dic19—44no—
103C22⋊Dic19—82no—
104C22⋊Dic19—82no—
105#64520—44no—
106C2×C19⋊C8—42no—
107#9459—191nomaximal, Sylow
108C23×C19—22no—
109C23×C19—22no—
110C23×C19—24no—
111C23×C19—22no—
112C23×C19—22no—
113C23×C19—22no—
114C23×C19—22no—
115C23×C19—22no—
116C23×C19—22no—
117C23×C19—22no—
118C23×C19—41no—
119C23×C19—42no—
120C23×C19—42no—
121C23×C19—42no—
122C23×C19—42no—
123C23×C19—42no—
124C23×C19—42no—
125C23×C19—42no—
126C23×C19—42no—
127C23×C19—42no—
128C23×C19—42no—
129C23×C19—81no—
130C23×C19—81no—
131C23×C19—81no—
132C23×C19—81no—
133C23×C19—88no—
134C23×C19—88no—
135C23×C19#9914yes—
136C23×C19C2×C22⋊C411yescharacteristic
137C23×C19#12011yescharacteristic
138C23×C19#12311yescharacteristic
139Q8×C19—82no—
140D4×C19—48no—
141D4×C19—48no—
142C2×C4×C19—22no—
143C2×C4×C19—22no—
144C2×C4×C19—42no—
145C2×C4×C19—42no—
146C2×C4×C19—42no—
147C2×C4×C19—42no—
148C2×C4×C19—42no—
149C2×C4×C19—41no—
150C2×C4×C19—41no—
151C2×C4×C19—42no—
152C2×C4×C19—42no—
153C2×C4×C19C4×D412yes—
154C2×C4×C19#12112yes—
155C2×Dic19—44no—
156C2×Dic19—44no—
157C2×Dic19—44no—
158C2×Dic19—88no—
159C19⋊C8—82no—
160#2435D1911yescharacteristic
161#2308—191no—
162#1783—191no—
163#1511—192no—
164#1284—192no—
165C22×C19—21no—
166C22×C19—21no—
167C22×C19—21no—
168C22×C19—21no—
169C22×C19—21no—
170C22×C19—21no—
171C22×C19—24no—
172C22×C19—21no—
173C22×C19—44no—
174C22×C19—44no—
175C22×C19—44no—
176C22×C19—44no—
177C22×C19—44no—
178C22×C19—42no—
179C22×C19—42no—
180C22×C19—42no—
181C22×C19—42no—
182C22×C19—42no—
183C22×C19—82no—
184C22×C19—82no—
185C22×C19—84no—
186C22×C19—84no—
187C22×C19—84no—
188C22×C19#38611yescharacteristic
189C22×C19C2×#9912yes—
190C22×C19#45512yes—
191C4×C19—22no—
192C4×C19—22no—
193C4×C19—82no—
194C4×C19—81no—
195C4×C19—81no—
196Dic19—84no—
197C23×D4C2×D1911yescharacteristic
198C2×#124Dic1912yescomplemented
199C2×C22⋊Q8C2×D1911yescharacteristic
200C22×C22⋊C4—381no—
201C2×#100—382no—
202#407—192no—
203#394—22no—
204#390Dic1912yescomplemented
205#386—384no—
206#381—192no—
207#379—21no—
208#379—21no—
209#379—381no—
210C4×C22⋊C4C2×D1911yescharacteristic
211#328—384no—
212C2×C19—22no—
213C2×C19—22no—
214C2×C19—41no—
215C2×C19—44no—
216C2×C19—82no—
217C2×C19#188511yescharacteristic
218C2×C19#189811yescharacteristic
219C2×C19#191111yescharacteristic
220C25C22⋊D1911yescharacteristic
221C25C22⋊D1911yescharacteristic
222C22×Q8C2×Dic1911yescharacteristic, complemented
223C22×D4—22no—
224C22×D4—22no—
225C22×D4—44no—
226C22×D4C2×Dic1912yes—
227C22×D4C22⋊D1912yes—
228C23×C4—382no—
229C23×C4C22×D1911yescharacteristic
230C2×M16—382no—
231#124—44no—
232C22⋊Q8—22no—
233C22⋊Q8—22no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4C2×Dic1911yescharacteristic, complemented
236C2×C22⋊C4—22no—
237C2×C22⋊C4—22no—
238C2×C22⋊C4—21no—
239C2×C22⋊C4—21no—
240C2×C22⋊C4—22no—
241C2×C22⋊C4—22no—
242C2×C22⋊C4—382no—
243C2×C22⋊C4—382no—
244C2×C22⋊C4—382no—
245C2×C22⋊C4—382no—
246C2×C22⋊C4—764no—
247C2×C42C2×Dic1912yescomplemented
248#100—764no—
249C22⋊C8—382no—
250C22⋊C8—382no—
251#95—21no—
252#95—194no—
253#95—382no—
254C19#945911yescharacteristic, complemented, Sylow
255C24—21no—
256C24—21no—
257C24—24no—
258C24—21no—
259C24—21no—
260C24—42no—
261C24—42no—
262C24—42no—
263C24—81no—
264C24—81no—
265C24C22⋊Dic1912yes—
266C24C22⋊Dic1912yes—
267C24C2×C22⋊D1911yescharacteristic
268C2×Q8—22no—
269C2×Q8—42no—
270C2×D4—24no—
271C2×D4—24no—
272C2×D4—24no—
273C2×D4—24no—
274C2×D4—42no—
275C2×D4—42no—
276C2×D4—44no—
277C2×D4—44no—
278C2×D4—48no—
279C22×C4—22no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—42no—
283C22×C4—384no—
284C22×C4—764no—
285C22×C4—1522no—
286C22×C4—1522no—
287C22×C4D4×D1912yes—
288C22×C4#6454312yes—
289C22×C4C22×Dic1911yescharacteristic
290C22×C4C2×C22⋊D1911yescharacteristic
291M16—764no—
292C2×C8—762no—
293C4⋊C4—22no—
294C4⋊C4—42no—
295C22⋊C4—42no—
296C22⋊C4—44no—
297C22⋊C4—41no—
298C22⋊C4—41no—
299C22⋊C4—44no—
300C22⋊C4—82no—
301C22⋊C4—82no—
302C22⋊C4—764no—
303C22⋊C4—764no—
304C22⋊C4—1522no—
305C22⋊C4—1522no—
306C42—42no—
307C23—22no—
308C23—22no—
309C23—24no—
310C23—22no—
311C23—22no—
312C23—22no—
313C23—22no—
314C23—22no—
315C23—22no—
316C23—22no—
317C23—41no—
318C23—42no—
319C23—42no—
320C23—42no—
321C23—42no—
322C23—42no—
323C23—42no—
324C23—42no—
325C23—42no—
326C23—42no—
327C23—42no—
328C23—81no—
329C23—81no—
330C23—81no—
331C23—81no—
332C23—88no—
333C23—88no—
334C23#1059729114yes—
335C23#1059738111yescharacteristic
336C23#1059738311yescharacteristic
337C23C2×C22⋊Dic1911yescharacteristic
338Q8—82no—
339D4—48no—
340D4—48no—
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—764no—
353C2×C4—764no—
354C2×C4—764no—
355C2×C4—1528no—
356C2×C4D4×Dic1912yes—
357C2×C4#1059738512yes—
358C8—1522no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—24no—
367C22—44no—
368C22—44no—
369C22—44no—
370C22—44no—
371C22—44no—
372C22—42no—
373C22—42no—
374C22—42no—
375C22—42no—
376C22—42no—
377C22—82no—
378C22—82no—
379C22—84no—
380C22—84no—
381C22—84no—
382C22#1192642411yescharacteristic
383C22C2×#1059729112yes—
384C22#1192672112yes—
385C4—22no—
386C4—22no—
387C4—82no—
388C4—81no—
389C4—81no—
390C4—1524no—
391C2—22no—
392C2—22no—
393C2—41no—
394C2—44no—
395C2—82no—
396C2#1456402411yescharacteristic
397C2#1456408911yescharacteristic
398C2#1456416811yescharacteristic
subgroupG/H
centerC22#11926424
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#2435C2
socleC22×C19#386
prime radicalC23×D4×C19C22
cosocleC23×C4×C19C23
hypercenter#2435D19
hypocenterC19#9459
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2435

Complements

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

NH ≅ G/Ntype
3. #14562168C2semidirect
4. #14561488C2semidirect
14. C2×C19×#124C4semidirect
17. C19×#390C4semidirect
23. C22×Q8×C19C2×C4semidirect
35. C2×C4⋊C4×C19C2×C4semidirect
42. C2×C42×C19C2×C4semidirect
198. C2×#124Dic19semidirect
204. #390Dic19semidirect
222. C22×Q8C2×Dic19semidirect
235. C2×C4⋊C4C2×Dic19semidirect
247. C2×C42C2×Dic19semidirect
254. C19#9459semidirect

Maximal subgroups

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

subgroupindex
#145662132
#145635562
#145621682
#145614882
C19×#24352
#945919