Finite Group Databasebeta

← #18077566

Subgroups — #18077566

Order 4864.

812 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 812 conjugacy classes of subgroups — too many to draw. Only its 143 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
1C2×#11926480C211yesmaximal, characteristic
2#14566249C211yesmaximal, characteristic
3#14563726C212yesmaximal, complemented
4#14561515C212yesmaximal, complemented
5C2×C19×#323C211yesmaximal, characteristic
6C22×C4⋊Dic19C2211yescharacteristic
7C22×Dic19⋊C4—21no—
8C22×C22⋊Dic19—21no—
9C22×C22⋊Dic19—21no—
10#11926480—22no—
11#11926480C414yescomplemented
12#11926419—24no—
13#11926404—21no—
14#11926404C2212yes—
15C2×C19⋊#95C2211yescharacteristic
16#11926307—24no—
17C22×C22⋊C4×C19C2211yescharacteristic
18C2×C19×C22⋊C8C2212yes—
19C19×#323—22no—
20C25×C19D411yescharacteristic
21C23×C4×C19D411yescharacteristic
22C23×C4×C19C2311yescharacteristic
23C23×Dic19—21no—
24C23×Dic19—21no—
25C23×Dic19—22no—
26C22×C8×C19—22no—
27C2×C22⋊C4×C19—22no—
28C2×C22⋊C4×C19—22no—
29C2×C22⋊C4×C19C2×C412yes—
30C2×C22⋊C4×C19D412yes—
31C2×C22⋊Dic19—22no—
32C2×C22⋊Dic19—24no—
33C2×C22⋊Dic19—22no—
34C2×C22⋊Dic19—44no—
35C2×C22⋊Dic19—42no—
36C2×C22⋊Dic19—42no—
37C2×C4⋊Dic19—22no—
38C2×C4⋊Dic19—22no—
39C2×C4⋊Dic19—21no—
40C2×C4⋊Dic19—22no—
41C2×C4⋊Dic19C2×C412yescomplemented
42C2×C4⋊Dic19D414yes—
43C2×Dic19⋊C4—24no—
44C2×Dic19⋊C4—44no—
45C19×C22⋊C8—22no—
46C19×C22⋊C8—22no—
47C19⋊#95—22no—
48C19⋊#95—21no—
49C19⋊#95—22no—
50C19⋊#95C2×C412yescomplemented
51C24×C19—21no—
52C24×C19—21no—
53C24×C19—21no—
54C24×C19—21no—
55C24×C19—42no—
56C24×C19—42no—
57C24×C19C22⋊C412yes—
58C24×C19SD1612yes—
59C24×C19Q1612yes—
60C24×C19C2×D411yescharacteristic
61C22×C4×C19—21no—
62C22×C4×C19—21no—
63C22×C4×C19—42no—
64C22×C4×C19—42no—
65C22×C4×C19C22⋊C412yes—
66C22×C4×C19C22×C411yescharacteristic
67C22×C4×C19C2×D412yes—
68C22×C4×C19C2×D411yescharacteristic
69C22×C4×C19#4112yes—
70C22×Dic19—24no—
71C22×Dic19—22no—
72C22×Dic19—22no—
73C22×Dic19—24no—
74C22×Dic19—42no—
75C22×Dic19—41no—
76C22×Dic19—41no—
77C22×Dic19—42no—
78C22×Dic19—44no—
79C22×Dic19—42no—
80C22×Dic19—41no—
81C22×Dic19—41no—
82C22×Dic19—82no—
83C22×Dic19—82no—
84C2×C8×C19—44no—
85C2×C8×C19—42no—
86C22⋊C4×C19—24no—
87C22⋊C4×C19—24no—
88C22⋊Dic19—48no—
89C22⋊Dic19—44no—
90C22⋊Dic19—42no—
91C22⋊Dic19—42no—
92C4⋊Dic19—24no—
93C4⋊Dic19—42no—
94C4⋊Dic19—44no—
95C4⋊Dic19—82no—
96Dic19⋊C4—48no—
97#9021—191nomaximal, Sylow
98C23×C19—22no—
99C23×C19—22no—
100C23×C19—22no—
101C23×C19—22no—
102C23×C19—22no—
103C23×C19—22no—
104C23×C19—22no—
105C23×C19—22no—
106C23×C19—42no—
107C23×C19—42no—
108C23×C19—44no—
109C23×C19—44no—
110C23×C19—42no—
111C23×C19—42no—
112C23×C19—82no—
113C23×C19—82no—
114C23×C19—81no—
115C23×C19—81no—
116C23×C19#10314yes—
117C23×C19C2×C22⋊C411yescharacteristic
118C23×C19#12011yescharacteristic
119C23×C19#12311yescharacteristic
120C23×C19C2×SD1611yescharacteristic
121C23×C19C2×Q1611yescharacteristic
122C23×C19AGL(1,ℤ/8)11yescharacteristic
123C23×C19#13711yescharacteristic
124C2×C4×C19—24no—
125C2×C4×C19—22no—
126C2×C4×C19—41no—
127C2×C4×C19—41no—
128C2×C4×C19—42no—
129C2×C4×C19—42no—
130C2×C4×C19—42no—
131C2×C4×C19—81no—
132C2×C4×C19C4×D412yes—
133C2×C4×C19#12112yes—
134C2×Dic19—24no—
135C2×Dic19—44no—
136C2×Dic19—44no—
137C2×Dic19—42no—
138C2×Dic19—42no—
139C2×Dic19—42no—
140C2×Dic19—42no—
141C2×Dic19—42no—
142C2×Dic19—44no—
143C2×Dic19—44no—
144C2×Dic19—44no—
145C2×Dic19—82no—
146C2×Dic19—88no—
147C2×Dic19—82no—
148C8×C19—82no—
149C2×#399—191no—
150#2315—191no—
151#1824—192no—
152C2×#323D1911yescharacteristic
153#1294—192no—
154C22×C19—22no—
155C22×C19—22no—
156C22×C19—22no—
157C22×C19—22no—
158C22×C19—21no—
159C22×C19—21no—
160C22×C19—21no—
161C22×C19—21no—
162C22×C19—24no—
163C22×C19—44no—
164C22×C19—44no—
165C22×C19—44no—
166C22×C19—42no—
167C22×C19—42no—
168C22×C19—82no—
169C22×C19—82no—
170C22×C19—82no—
171C22×C19#38611yescharacteristic
172C22×C19C2×#10311yescharacteristic
173C22×C19#41711yescharacteristic
174C22×C19#45011yescharacteristic
175C22×C19#45111yescharacteristic
176C22×C19#45312yes—
177C22×C19#45812yes—
178C22×C19#48311yescharacteristic
179C22×C19#48411yescharacteristic
180C4×C19—22no—
181C4×C19—22no—
182C4×C19—42no—
183Dic19—44no—
184Dic19—84no—
185Dic19—82no—
186C22×C4⋊C4—191no—
187C22×C4⋊C4—381no—
188C22×C22⋊C4—381no—
189C22×C22⋊C4—381no—
190C22×C22⋊C4C2×D1911yescharacteristic
191C2×C22⋊C8C2×D1912yes—
192#399—194no—
193#399—382no—
194#385—384no—
195#380—192no—
196#380—381no—
197C2×#95—191no—
198#340—384no—
199#323—22no—
200C2×C19—21no—
201C2×C19—21no—
202C2×C19—21no—
203C2×C19—21no—
204C2×C19—44no—
205C2×C19#161312yes—
206C2×C19#161412yes—
207C2×C19#187211yescharacteristic
208C2×C19#188711yescharacteristic
209C2×C19#189011yescharacteristic
210C25D7611yescharacteristic
211C23×C4—381no—
212C23×C4—381no—
213C23×C4—382no—
214C23×C4D7611yescharacteristic
215C23×C4C22×D1911yescharacteristic
216C22×C8—22no—
217C2×C4⋊C4—192no—
218C2×C4⋊C4—194no—
219C2×C4⋊C4—382no—
220C2×C4⋊C4—382no—
221C2×C4⋊C4—384no—
222C2×C4⋊C4—381no—
223C2×C4⋊C4—382no—
224C2×C4⋊C4—764no—
225C2×C22⋊C4—22no—
226C2×C22⋊C4—22no—
227C2×C22⋊C4—382no—
228C2×C22⋊C4—384no—
229C2×C22⋊C4—382no—
230C2×C22⋊C4—764no—
231C2×C22⋊C4—762no—
232C2×C22⋊C4—762no—
233C2×C22⋊C4C4×D1912yes—
234C2×C22⋊C4C22⋊D1912yes—
235C22⋊C8—22no—
236C22⋊C8—22no—
237#95—192no—
238#95—382no—
239#95—382no—
240#95—381no—
241C19#902111yescharacteristic, complemented, Sylow
242C24—21no—
243C24—21no—
244C24—21no—
245C24—21no—
246C24—42no—
247C24—42no—
248C24#6451612yes—
249C24Dic7612yes—
250C24(C2×D19)⋊C412yes—
251C24C2×D7611yescharacteristic
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—42no—
255C22×C4—42no—
256C22×C4—384no—
257C22×C4—382no—
258C22×C4—384no—
259C22×C4—382no—
260C22×C4—762no—
261C22×C4—761no—
262C22×C4—761no—
263C22×C4—762no—
264C22×C4—764no—
265C22×C4—762no—
266C22×C4—761no—
267C22×C4—761no—
268C22×C4—1522no—
269C22×C4—1522no—
270C22×C4(C2×D19)⋊C412yes—
271C22×C4C2×C4×D1911yescharacteristic
272C22×C4D4×D1912yes—
273C22×C4#6454312yes—
274C22×C4C2×C22⋊D1911yescharacteristic
275C2×C8—44no—
276C2×C8—42no—
277C4⋊C4—384no—
278C4⋊C4—764no—
279C4⋊C4—768no—
280C4⋊C4—762no—
281C4⋊C4—1522no—
282C22⋊C4—24no—
283C22⋊C4—24no—
284C22⋊C4—768no—
285C22⋊C4—764no—
286C22⋊C4—762no—
287C22⋊C4—762no—
288C23—22no—
289C23—22no—
290C23—22no—
291C23—22no—
292C23—22no—
293C23—22no—
294C23—22no—
295C23—22no—
296C23—42no—
297C23—44no—
298C23—44no—
299C23—42no—
300C23—42no—
301C23—42no—
302C23—82no—
303C23—82no—
304C23—81no—
305C23—81no—
306C23#1059727314yes—
307C23#1059732811yescharacteristic
308C23#1059733211yescharacteristic
309C23C2×#6451611yescharacteristic
310C23C2×Dic7611yescharacteristic
311C23#1059735411yescharacteristic
312C23#1059735511yescharacteristic
313C23C2×(C2×D19)⋊C411yescharacteristic
314C2×C4—24no—
315C2×C4—22no—
316C2×C4—41no—
317C2×C4—42no—
318C2×C4—41no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—81no—
322C2×C4—384no—
323C2×C4—764no—
324C2×C4—764no—
325C2×C4—762no—
326C2×C4—762no—
327C2×C4—762no—
328C2×C4—762no—
329C2×C4—762no—
330C2×C4—764no—
331C2×C4—764no—
332C2×C4—764no—
333C2×C4—1522no—
334C2×C4—1528no—
335C2×C4—1522no—
336C2×C4(C22⋊D19)⋊C412yes—
337C2×C4#1059738512yes—
338C8—82no—
339C22—22no—
340C22—22no—
341C22—22no—
342C22—22no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—24no—
348C22—44no—
349C22—44no—
350C22—44no—
351C22—42no—
352C22—42no—
353C22—82no—
354C22—82no—
355C22—82no—
356C22#1192642111yescharacteristic
357C22C2×#1059727311yescharacteristic
358C22#1192654611yescharacteristic
359C22#1192669711yescharacteristic
360C22#1192670211yescharacteristic
361C22#1192671412yes—
362C22#1192673512yes—
363C22#1192687511yescharacteristic
364C22#1192688011yescharacteristic
365C4—22no—
366C4—22no—
367C4—42no—
368C4—764no—
369C4—1524no—
370C4—1522no—
371C2—21no—
372C2—21no—
373C2—21no—
374C2—21no—
375C2—44no—
376C2#1456265712yes—
377C2#1456266212yes—
378C2#1456394011yescharacteristic
379C2#1456403111yescharacteristic
380C2#1456404611yescharacteristic
subgroupG/H
centerC23#10597328
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC2×C19×#323C2
socleC23×C19#120
prime radicalC25×C19D4
cosocleC23×C4×C19C23
hypercenterC2×#323D19
hypocenterC19#9021
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#323

Complements

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

NH ≅ G/Ntype
3. #14563726C2semidirect
4. #14561515C2semidirect
11. #11926480C4semidirect
41. C2×C4⋊Dic19C2×C4semidirect
50. C19⋊#95C2×C4semidirect
241. C19#9021semidirect

Maximal subgroups

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

subgroupindex
C2×#119264802
#145662492
#145637262
#145615152
C2×C19×#3232
#902119