Finite Group Databasebeta

← #18078520

Subgroups — #18078520

Order 4864.

560 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 560 conjugacy classes of subgroups — too many to draw. Only its 99 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#14572664C211yesmaximal, characteristic, complemented
2#14569487C211yesmaximal, characteristic
3#14562232C212yesmaximal, complemented
4#14561500C212yesmaximal, complemented
5C4×C19×#100C211yesmaximal, characteristic, complemented
6C2×#10597321C2211yescharacteristic
7#11926616—24no—
8#11926601C2212yes—
9#11926508—21no—
10C2×C22⋊(C19⋊C8)—21no—
11#11926470—21no—
12#11926456C411yescharacteristic
13#11926456C411yescharacteristic
14#11926453C411yescharacteristic
15#11926453C411yescharacteristic
16#11926452—21no—
17#11926423—21no—
18#11926423—21no—
19#11926412C2211yescharacteristic
20#11926283—24no—
21C2×C4×D4×C19C2211yescharacteristic
22C2×C19×#100—21no—
23C4×M16×C19C2212yes—
24C19×#343—21no—
25C22×D4×C19D411yescharacteristic
26C23×C4×C19D411yescharacteristic
27C23×C4×C19D411yescharacteristic
28C22×C22⋊D19—21no—
29C22×C22⋊D19—21no—
30C22×D76C2×C411yescharacteristic
31C22×Dic38C2×C411yescharacteristic
32C2×M16×C19—22no—
33C4×D4×C19—22no—
34C4×D4×C19—22no—
35C2×C4⋊C4×C19D411yescharacteristic
36C2×C22⋊C4×C19C2×C411yescharacteristic
37C2×C22⋊C4×C19C2×C411yescharacteristic
38C2×C42×C19C2311yescharacteristic
39C2×C22⋊Dic19—21no—
40C2×C22⋊Dic19—21no—
41C2×(C2×D19)⋊C4—21no—
42C2×(C2×D19)⋊C4—21no—
43C2×(C2×D19)⋊C4—21no—
44C2×(C2×D19)⋊C4—21no—
45C2×#64520—22no—
46C22×C19⋊C8—22no—
47#10597321—22no—
48#10597321—22no—
49C19×#100—24no—
50C19×#97—22no—
51C4×C8×C19—22no—
52C19⋊#95—21no—
53C19⋊#95—21no—
54C19⋊#95—21no—
55C19⋊#95—21no—
56C19⋊#95C2×C411yescharacteristic
57C19⋊#95C2×C411yescharacteristic
58C22⋊(C19⋊C8)—22no—
59C22⋊(C19⋊C8)—22no—
60C22⋊(C19⋊C8)—22no—
61C4⋊(C19⋊C8)—22no—
62#10597260D414yescomplemented
63C24×C19C22⋊C411yescharacteristic
64C24×C19C22⋊C411yescharacteristic
65C23×D19—21no—
66C2×D4×C19—22no—
67C2×D4×C19—22no—
68C2×D4×C19—41no—
69C22×C4×C19—21no—
70C22×C4×C19—21no—
71C22×C4×C19—21no—
72C22×C4×C19—21no—
73C22×C4×C19—81no—
74C22×C4×C19—81no—
75C22×C4×C19C22⋊C411yescharacteristic
76C22×C4×C19C22⋊C411yescharacteristic
77C22×C4×C19C22×C411yescharacteristic
78C22×C4×C19C2×D411yescharacteristic
79C22×C4×C19C2×D411yescharacteristic
80C2×C22⋊D19—42no—
81C2×C22⋊D19—42no—
82C2×C22⋊D19—81no—
83C2×C22⋊D19—81no—
84C2×C22⋊D19—81no—
85C2×C22⋊D19—81no—
86C22×Dic19—21no—
87C22×Dic19—21no—
88C22×Dic19—21no—
89C2×D76—22no—
90C2×D76—81no—
91C2×Dic38—22no—
92C2×Dic38—81no—
93M16×C19—24no—
94M16×C19—42no—
95C2×C8×C19—42no—
96C4⋊C4×C19—22no—
97C22⋊C4×C19—22no—
98C22⋊C4×C19—22no—
99C42×C19C2×D412yes—
100C42×C19#4112yes—
101C22⋊Dic19—81no—
102C22⋊Dic19—81no—
103(C2×D19)⋊C4—41no—
104(C2×D19)⋊C4—42no—
105(C2×D19)⋊C4—41no—
106(C2×D19)⋊C4—81no—
107(C2×D19)⋊C4—81no—
108#64520—82no—
109C2×C19⋊C8—24no—
110C2×C19⋊C8—82no—
111#9187—191nomaximal, Sylow
112C23×C19—21no—
113C23×C19—21no—
114C23×C19—21no—
115C23×C19—21no—
116C23×C19—21no—
117C23×C19—41no—
118C23×C19—41no—
119C23×C19—41no—
120C23×C19—41no—
121C23×C19#10412yes—
122C23×C19C2×C22⋊C411yescharacteristic
123C22×D19—41no—
124C22×D19—41no—
125C22×D19—41no—
126C22×D19—41no—
127C22×D19—41no—
128C22×D19—41no—
129C22×D19—41no—
130D4×C19—44no—
131C2×C4×C19—21no—
132C2×C4×C19—21no—
133C2×C4×C19—21no—
134C2×C4×C19—21no—
135C2×C4×C19—41no—
136C2×C4×C19—41no—
137C2×C4×C19—42no—
138C2×C4×C19—42no—
139C2×C4×C19—41no—
140C2×C4×C19—41no—
141C2×C4×C19—81no—
142C2×C4×C19—81no—
143C2×C4×C19C4×D412yes—
144C2×C4×C19#12011yescharacteristic
145C2×C4×C19#12112yes—
146C2×C4×C19#12311yescharacteristic
147C22⋊D19—84no—
148C22⋊D19—84no—
149C2×Dic19—41no—
150C2×Dic19—41no—
151C2×Dic19—41no—
152C2×Dic19—41no—
153C2×Dic19—41no—
154C2×Dic19—41no—
155C2×Dic19—41no—
156C2×Dic19—41no—
157C2×Dic19—41no—
158D76—82no—
159Dic38—82no—
160C8×C19—44no—
161C19⋊C8—44no—
162#2973—191no—
163#2631—191no—
164C4×#100D1911yescharacteristic, complemented
165#1527—192no—
166#1288—192no—
167C22×C19—21no—
168C22×C19—21no—
169C22×C19—22no—
170C22×C19—42no—
171C22×C19—42no—
172C22×C19—41no—
173C22×C19—41no—
174C22×C19—41no—
175C22×C19—41no—
176C22×C19—41no—
177C22×C19—81no—
178C22×C19—81no—
179C22×C19#38611yescharacteristic
180C22×C19C2×#10411yescharacteristic
181C22×C19#42111yescharacteristic
182C2×D19—81no—
183C2×D19—81no—
184C2×D19—81no—
185C2×D19—81no—
186C2×D19—81no—
187C2×D19—81no—
188C2×D19—81no—
189C4×C19—22no—
190C4×C19—21no—
191C4×C19—21no—
192C4×C19—22no—
193C4×C19—41no—
194C4×C19—41no—
195Dic19—81no—
196Dic19—81no—
197Dic19—81no—
198C2×#124—191no—
199C2×C4×D4C2×D1911yescharacteristic
200#435—384no—
201#432—192no—
202C2×#100—21no—
203#407—381no—
204C2×C22⋊C8—381no—
205C4×M16C2×D1912yes—
206#397—381no—
207#393—191no—
208#393—191no—
209#392—191no—
210#392—191no—
211#392—381no—
212#386—381no—
213#386—381no—
214#383—191no—
215#343—21no—
216#329—384no—
217C2×C19—21no—
218C2×C19—21no—
219C2×C19—42no—
220C2×C19—81no—
221C2×C19#187111yescharacteristic
222C2×C19#191111yescharacteristic
223C2×C19#191411yescharacteristic
224D19—161no—
225C22×Q8—191no—
226C22×D4—191no—
227C22×D4—381no—
228C22×D4—381no—
229C22×D4C22⋊D1911yescharacteristic
230C23×C4D7611yescharacteristic
231C23×C4D7611yescharacteristic
232C2×M16—22no—
233C2×M16—382no—
234C22×C8—382no—
235#124—382no—
236#124—382no—
237C4×D4—22no—
238C4×D4—22no—
239C2×C4⋊C4C22⋊D1911yescharacteristic
240C2×C22⋊C4—381no—
241C2×C22⋊C4—381no—
242C2×C22⋊C4—381no—
243C2×C22⋊C4—381no—
244C2×C22⋊C4—381no—
245C2×C22⋊C4—381no—
246C2×C22⋊C4C4×D1911yescharacteristic
247C2×C22⋊C4C4×D1911yescharacteristic
248C2×C42C22×D1911yescharacteristic
249C4⋊C8—382no—
250#100—24no—
251C22⋊C8—382no—
252C22⋊C8—382no—
253C22⋊C8—382no—
254#97—22no—
255#97—194no—
256C4×C8—22no—
257#95—191no—
258#95—191no—
259#95—381no—
260#95—381no—
261#95—381no—
262#95—381no—
263C19#918711yescharacteristic, complemented, Sylow
264C24—381no—
265C24(C2×D19)⋊C411yescharacteristic
266C24(C2×D19)⋊C411yescharacteristic
267C2×Q8—382no—
268C2×Q8—1521no—
269C2×D4—22no—
270C2×D4—22no—
271C2×D4—41no—
272C2×D4—382no—
273C2×D4—762no—
274C2×D4—762no—
275C2×D4—1521no—
276C2×D4—1521no—
277C2×D4—1521no—
278C2×D4—1521no—
279C2×D4—1521no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—81no—
285C22×C4—81no—
286C22×C4—381no—
287C22×C4—381no—
288C22×C4—381no—
289C22×C4(C2×D19)⋊C411yescharacteristic
290C22×C4(C2×D19)⋊C411yescharacteristic
291C22×C4C2×C4×D1911yescharacteristic
292C22×C4C2×D7611yescharacteristic
293C22×C4C2×C22⋊D1911yescharacteristic
294M16—24no—
295M16—42no—
296M16—1522no—
297C2×C8—42no—
298C2×C8—384no—
299C2×C8—1522no—
300C4⋊C4—22no—
301C22⋊C4—22no—
302C22⋊C4—22no—
303C22⋊C4—762no—
304C22⋊C4—761no—
305C22⋊C4—761no—
306C22⋊C4—1521no—
307C22⋊C4—1521no—
308C22⋊C4—1521no—
309C22⋊C4—1521no—
310C42D4×D1912yes—
311C42#6454312yes—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23—761no—
322C23—761no—
323C23—761no—
324C23—761no—
325C23—761no—
326C23—761no—
327C23—761no—
328C23#1059726212yes—
329C23C2×(C2×D19)⋊C411yescharacteristic
330Q8—1522no—
331D4—44no—
332D4—1522no—
333D4—1524no—
334D4—1524no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—81no—
346C2×C4—81no—
347C2×C4—761no—
348C2×C4—761no—
349C2×C4—761no—
350C2×C4—761no—
351C2×C4—761no—
352C2×C4—761no—
353C2×C4—761no—
354C2×C4—761no—
355C2×C4—761no—
356C2×C4(C22⋊D19)⋊C412yes—
357C2×C4#1059732811yescharacteristic
358C2×C4#1059733211yescharacteristic
359C2×C4#1059738512yes—
360C8—44no—
361C8—764no—
362C22—21no—
363C22—21no—
364C22—22no—
365C22—42no—
366C22—42no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—81no—
373C22—81no—
374C22—1521no—
375C22—1521no—
376C22—1521no—
377C22—1521no—
378C22—1521no—
379C22—1521no—
380C22—1521no—
381C22#1192642111yescharacteristic
382C22C2×#1059726211yescharacteristic
383C22#1192656211yescharacteristic
384C4—21no—
385C4—21no—
386C4—22no—
387C4—22no—
388C4—41no—
389C4—41no—
390C4—1521no—
391C4—1521no—
392C4—1521no—
393C2—21no—
394C2—21no—
395C2—42no—
396C2—81no—
397C2—3041no—
398C2#1456393511yescharacteristic
399C2#1456416511yescharacteristic
400C2#1456418011yescharacteristic
subgroupG/H
centerC22#11926421
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC4×C19×#100C2
socleC22×C19#386
prime radical#14569487C2
cosocleC2×C42×C19C23
hypercenterC4×#100D19
hypocenterC19#9187
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×#100

Complements

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

NH ≅ G/Ntype
1. #14572664C2semidirect
3. #14562232C2semidirect
4. #14561500C2semidirect
5. C4×C19×#100C2semidirect
62. #10597260D4semidirect
164. C4×#100D19semidirect
263. C19#9187semidirect

Maximal subgroups

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

subgroupindex
#145726642
#145694872
#145622322
#145615002
C4×C19×#1002
#918719