Finite Group Databasebeta

← #18085705

Subgroups — #18085705

Order 4864.

422 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 93 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#14564620C211yesmaximal, characteristic
2#14562206C211yesmaximal, characteristic
3C2×#11926280C211yesmaximal, characteristic
4#14561514C211yesmaximal, characteristic
5#14561502C211yesmaximal, characteristic
6#14561483C211yesmaximal, characteristic
7C19×#2569C211yesmaximal, characteristic
8C2×#10597370C2211yescharacteristic
9C2×C22⋊(C19⋊C8)C2211yescharacteristic
10C2×C22⋊(C19⋊C8)C2211yescharacteristic
11#11926404C2211yescharacteristic
12#11926310—21no—
13#11926310—21no—
14#11926280—21no—
15#11926280—21no—
16#11926280—21no—
17#11926280—21no—
18C19×#400—21no—
19C19×#398—21no—
20C19×#387—21no—
21C19×#387—21no—
22C19×#385—21no—
23C19×#380—21no—
24C19×#380C2211yescharacteristic
25C4×C22⋊C4×C19C2211yescharacteristic
26C2×C19×#95C2211yescharacteristic
27C23×C4×C19—21no—
28C23×C4×C19C2311yescharacteristic
29C22×Dic38Q811yescharacteristic
30C2×C4⋊C4×C19—21no—
31C2×C4⋊C4×C19—21no—
32C2×C4⋊C4×C19—21no—
33C2×C4⋊C4×C19—21no—
34C2×C4⋊C4×C19—21no—
35C2×C22⋊C4×C19—21no—
36C2×C22⋊C4×C19D411yescharacteristic
37C2×C22⋊C4×C19D411yescharacteristic
38C2×C42×C19—21no—
39C2×C22⋊Dic19—21no—
40C2×C22⋊Dic19—21no—
41C2×C4⋊Dic19—21no—
42C2×C4⋊Dic19Q811yescharacteristic
43#10597370—21no—
44#10597370—21no—
45#10597370—21no—
46#10597370—21no—
47C2×Dic19⋊C4—21no—
48C22×C19⋊C8—21no—
49C22×C19⋊C8—21no—
50C19×#95—21no—
51C19×#95—21no—
52C19×#95—21no—
53C19×#95—21no—
54C19×#95—21no—
55C19×#95—21no—
56C19×#95D411yescharacteristic
57C19×#95D411yescharacteristic
58C19×#95D411yescharacteristic
59C19×#95D411yescharacteristic
60C19⋊#95—21no—
61C22⋊(C19⋊C8)—21no—
62C22⋊(C19⋊C8)—21no—
63C22⋊(C19⋊C8)—21no—
64C22⋊(C19⋊C8)—21no—
65C24×C19C2×D411yescharacteristic
66C22×C4×C19—21no—
67C22×C4×C19—21no—
68C22×C4×C19—21no—
69C22×C4×C19—21no—
70C22×C4×C19—21no—
71C22×C4×C19—21no—
72C22×C4×C19—42no—
73C22×C4×C19—41no—
74C22×C4×C19—41no—
75C22×C4×C19—81no—
76C22×C4×C19—81no—
77C22×C4×C19C2×D411yescharacteristic
78C22×C4×C19C2×D411yescharacteristic
79C22×C4×C19C2×Q811yescharacteristic
80C22×C4×C19#4111yescharacteristic
81C22×C4×C19#4111yescharacteristic
82C22×C4×C19#4111yescharacteristic
83C22×Dic19—21no—
84C22×Dic19—21no—
85C22×Dic19—41no—
86C2×Dic38—21no—
87C2×Dic38—21no—
88C2×Dic38—81no—
89C4⋊C4×C19—42no—
90C4⋊C4×C19—42no—
91C4⋊C4×C19—81no—
92C4⋊C4×C19—81no—
93C4⋊C4×C19—81no—
94C22⋊C4×C19—21no—
95C22⋊C4×C19—21no—
96C22⋊C4×C19—21no—
97C22⋊C4×C19—21no—
98C22⋊C4×C19—41no—
99C22⋊C4×C19—41no—
100C42×C19—81no—
101C22⋊Dic19—41no—
102C22⋊Dic19—41no—
103C22⋊Dic19—41no—
104C22⋊Dic19—41no—
105C4⋊Dic19—21no—
106C4⋊Dic19—21no—
107C4⋊Dic19—81no—
108Dic19⋊C4—41no—
109Dic19⋊C4—41no—
110C2×C19⋊C8—41no—
111C2×C19⋊C8—41no—
112C2×C19⋊C8—81no—
113C2×C19⋊C8—81no—
114#10377—191nomaximal, Sylow
115C23×C19—41no—
116C23×C19—41no—
117C23×C19#12011yescharacteristic
118C23×C19C22⋊Q811yescharacteristic
119C23×C19#12411yescharacteristic
120C23×C19#13511yescharacteristic
121C23×C19#13511yescharacteristic
122C23×C19#13711yescharacteristic
123C23×C19#13711yescharacteristic
124C2×C4×C19—22no—
125C2×C4×C19—41no—
126C2×C4×C19—41no—
127C2×C4×C19—41no—
128C2×C4×C19—41no—
129C2×C4×C19—41no—
130C2×C4×C19—41no—
131C2×C4×C19—41no—
132C2×C4×C19—41no—
133C2×C4×C19—41no—
134C2×C4×C19—41no—
135C2×C4×C19—41no—
136C2×C4×C19—41no—
137C2×C4×C19—41no—
138C2×C4×C19—41no—
139C2×C4×C19—41no—
140C2×C4×C19—41no—
141C2×C4×C19—41no—
142C2×C4×C19—41no—
143C2×C4×C19—41no—
144C2×C4×C19—41no—
145C2×C4×C19—41no—
146C2×C4×C19—41no—
147C2×C4×C19—41no—
148C2×C4×C19—82no—
149C2×C4×C19—82no—
150C2×C4×C19C22⋊Q811yescharacteristic
151C2×C4×C19C22⋊Q811yescharacteristic
152C2×C4×C19#12411yescharacteristic
153C2×C4×C19#12411yescharacteristic
154C2×Dic19—41no—
155C2×Dic19—41no—
156C2×Dic19—81no—
157C2×Dic19—81no—
158C2×Dic19—81no—
159C2×Dic19—81no—
160C2×Dic19—81no—
161Dic38—81no—
162Dic38—81no—
163C19⋊C8—81no—
164C19⋊C8—81no—
165#2569D1911yescharacteristic
166#1996—191no—
167#1520—191no—
168C2×#328—191no—
169#1294—191no—
170#1289—191no—
171#1282—191no—
172C22×C19—21no—
173C22×C19—21no—
174C22×C19—21no—
175C22×C19—21no—
176C22×C19—21no—
177C22×C19—21no—
178C22×C19—41no—
179C22×C19—41no—
180C22×C19—41no—
181C22×C19—41no—
182C22×C19#39311yescharacteristic
183C22×C19#45211yescharacteristic
184C22×C19#45211yescharacteristic
185C22×C19#47911yescharacteristic
186C22×C19#47911yescharacteristic
187C22×C19#48811yescharacteristic
188C22×C19#49111yescharacteristic
189C4×C19—21no—
190C4×C19—21no—
191C4×C19—21no—
192C4×C19—21no—
193C4×C19—42no—
194C4×C19—81no—
195C4×C19—81no—
196C4×C19—81no—
197C4×C19—81no—
198C4×C19—81no—
199Dic19—81no—
200Dic19—81no—
201Dic19—161no—
202C2×C22⋊Q8—191no—
203C2×C22⋊C8—191no—
204C2×C22⋊C8—191no—
205#400—21no—
206#398—21no—
207#387—21no—
208#387—21no—
209#385—21no—
210#380—21no—
211#380—191no—
212#380C2×D1911yescharacteristic
213C4×C22⋊C4C2×D1911yescharacteristic
214C2×#95C2×D1911yescharacteristic
215#342—381no—
216#342—381no—
217#328—381no—
218#328—381no—
219#328—381no—
220#328—381no—
221C2×C19—21no—
222C2×C19—21no—
223C2×C19—21no—
224C2×C19—21no—
225C2×C19—21no—
226C2×C19—21no—
227C2×C19#202611yescharacteristic
228C2×C19#203111yescharacteristic
229C2×C19#203211yescharacteristic
230C22×Q8—191no—
231C23×C4—21no—
232C23×C4C22×D1911yescharacteristic
233C22×C8—381no—
234C22×C8—381no—
235C22⋊Q8—381no—
236C22⋊Q8—381no—
237C22⋊Q8—381no—
238C22⋊Q8—381no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—191no—
245C2×C4⋊C4—381no—
246C2×C4⋊C4—381no—
247C2×C22⋊C4—21no—
248C2×C22⋊C4—381no—
249C2×C22⋊C4—381no—
250C2×C22⋊C4C22⋊D1911yescharacteristic
251C2×C22⋊C4C22⋊D1911yescharacteristic
252C2×C42—21no—
253C22⋊C8—381no—
254C22⋊C8—381no—
255C22⋊C8—381no—
256C22⋊C8—381no—
257#95—21no—
258#95—21no—
259#95—21no—
260#95—21no—
261#95—21no—
262#95—21no—
263#95—381no—
264#95C22⋊D1911yescharacteristic
265#95C22⋊D1911yescharacteristic
266#95C22⋊D1911yescharacteristic
267#95C22⋊D1911yescharacteristic
268C19#1037711yescharacteristic, complemented, Sylow
269C24C2×C22⋊D1911yescharacteristic
270C2×Q8—381no—
271C2×Q8—381no—
272C2×Q8—1521no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—42no—
280C22×C4—41no—
281C22×C4—41no—
282C22×C4—81no—
283C22×C4—81no—
284C22×C4—381no—
285C22×C4—381no—
286C22×C4—761no—
287C22×C4Q8×D1911yescharacteristic
288C22×C4#6454511yescharacteristic
289C22×C4#6454511yescharacteristic
290C22×C4#6454511yescharacteristic
291C22×C4C2×C22⋊D1911yescharacteristic
292C22×C4C2×C22⋊D1911yescharacteristic
293C2×C8—761no—
294C2×C8—761no—
295C2×C8—1521no—
296C2×C8—1521no—
297C4⋊C4—42no—
298C4⋊C4—42no—
299C4⋊C4—81no—
300C4⋊C4—81no—
301C4⋊C4—81no—
302C4⋊C4—381no—
303C4⋊C4—381no—
304C4⋊C4—761no—
305C4⋊C4—761no—
306C4⋊C4—1521no—
307C22⋊C4—21no—
308C22⋊C4—21no—
309C22⋊C4—21no—
310C22⋊C4—21no—
311C22⋊C4—41no—
312C22⋊C4—41no—
313C22⋊C4—761no—
314C22⋊C4—761no—
315C22⋊C4—761no—
316C22⋊C4—761no—
317C42—81no—
318C23—41no—
319C23—41no—
320C23#1059739211yescharacteristic
321C23#1059739311yescharacteristic
322C23#1059739611yescharacteristic
323C23#1059739611yescharacteristic
324C23#1059739711yescharacteristic
325C23#1059739711yescharacteristic
326C23#1059739911yescharacteristic
327Q8—1521no—
328Q8—1521no—
329C2×C4—22no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—82no—
354C2×C4—82no—
355C2×C4—761no—
356C2×C4—761no—
357C2×C4—1521no—
358C2×C4—1521no—
359C2×C4—1521no—
360C2×C4—1521no—
361C2×C4—1521no—
362C2×C4#1059739211yescharacteristic
363C2×C4#1059739211yescharacteristic
364C2×C4#1059739311yescharacteristic
365C2×C4#1059739311yescharacteristic
366C8—1521no—
367C8—1521no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22#1192645511yescharacteristic
379C22#1192670611yescharacteristic
380C22#1192670611yescharacteristic
381C22#1192684811yescharacteristic
382C22#1192684811yescharacteristic
383C22#1192690111yescharacteristic
384C22#1192691411yescharacteristic
385C4—21no—
386C4—21no—
387C4—21no—
388C4—21no—
389C4—42no—
390C4—81no—
391C4—81no—
392C4—81no—
393C4—81no—
394C4—81no—
395C4—3041no—
396C4—1521no—
397C4—1521no—
398C2—21no—
399C2—21no—
400C2—21no—
401C2—21no—
402C2—21no—
403C2—21no—
404C2#1456478311yescharacteristic
405C2#1456480411yescharacteristic
406C2#1456481111yescharacteristic
subgroupG/H
centerC22#11926455
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC19×#2569C2
socleC22×C19#393
prime radicalC24×C19C2×D4
hypercenter#2569D19
hypocenterC19#10377
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2569

Complements

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

NH ≅ G/Ntype
268. C19#10377semidirect

Maximal subgroups

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

subgroupindex
#145646202
#145622062
C2×#119262802
#145615142
#145615022
#145614832
C19×#25692
#1037719