Finite Group Databasebeta

← #18071518

Subgroups — #18071518

Order 4864.

478 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 81 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#14570594C211yesmaximal, characteristic
2#14564965C211yesmaximal, characteristic, complemented
3#14564960C211yesmaximal, characteristic, complemented
4#14561459C211yesmaximal, characteristic, complemented
5#14561457C211yesmaximal, characteristic, complemented
6#14561456C211yesmaximal, characteristic
7C19×#2013C211yesmaximal, characteristic
8C2×#10597325—21no—
9C2×#10597264—21no—
10C2×#10597265—21no—
11#11926480—21no—
12#11926467—21no—
13#11926458—21no—
14#11926442C2211yescharacteristic
15#11926442C2211yescharacteristic
16#11926439—21no—
17#11926437—21no—
18#11926306—21no—
19#11926306—21no—
20#11926299C2211yescharacteristic
21#11926299C2211yescharacteristic
22C22×SD16×C19—21no—
23C2×C19×C4⋊Q8C2211yescharacteristic
24C2×C19×#103—21no—
25C19×#390C2211yescharacteristic
26C19×#336C2211yescharacteristic
27C22×Q8×C19—21no—
28C22×D4×C19D411yescharacteristic
29C2×SD16×C19—42no—
30C2×SD16×C19—42no—
31C2×SD16×C19—42no—
32C22×C8×C19—21no—
33C19×C4⋊Q8—42no—
34C2×C4⋊C4×C19—21no—
35C2×C4⋊C4×C19—21no—
36C2×C4⋊C4×C19D411yescharacteristic
37C2×C22⋊C4×C19—21no—
38C2×C22⋊C4×C19—21no—
39C2×C42×C19C2311yescharacteristic
40C2×C22⋊Dic19—21no—
41C2×C22⋊Dic19—21no—
42C2×C22⋊Dic19—21no—
43C2×C22⋊Dic19—21no—
44C2×C4⋊Dic19D411yescharacteristic
45C2×C4⋊Dic19D411yescharacteristic
46C2×C4⋊Dic19D411yescharacteristic
47C2×C4⋊Dic19D411yescharacteristic
48C2×Dic19⋊C4—21no—
49C2×Dic19⋊C4—21no—
50C2×Dic19⋊C4—21no—
51C2×Dic19⋊C4—21no—
52C2×C4×Dic19—21no—
53C22×C19⋊C8—21no—
54C22×C19⋊C8—21no—
55#10597325—42no—
56#10597325—42no—
57C19×#103—42no—
58C19⋊#95—21no—
59C19⋊#95—21no—
60C19⋊#95—21no—
61#10597265—42no—
62#10597264—42no—
63C24×C19—21no—
64C2×Q8×C19—22no—
65C2×Q8×C19—41no—
66C2×Q8×C19—41no—
67C2×Q8×C19—41no—
68C2×Q8×C19—41no—
69C2×Q8×C19—41no—
70C2×D4×C19—21no—
71C2×D4×C19—21no—
72C2×D4×C19—41no—
73C2×D4×C19—41no—
74C22×C4×C19—21no—
75C22×C4×C19—41no—
76C22×C4×C19C2×D411yescharacteristic
77C22×C4×C19C2×D411yescharacteristic
78C22×C4×C19C2×D411yescharacteristic
79C22×Dic19—21no—
80C22×Dic19—21no—
81C22×Dic19—21no—
82C22×Dic19—21no—
83SD16×C19—48no—
84C2×C8×C19—22no—
85C2×C8×C19—41no—
86C2×C8×C19—41no—
87C4⋊C4×C19—22no—
88C4⋊C4×C19—22no—
89C4⋊C4×C19—41no—
90C4⋊C4×C19—41no—
91C4⋊C4×C19—41no—
92C22⋊C4×C19—41no—
93C22⋊C4×C19—41no—
94C22⋊C4×C19—41no—
95C22⋊C4×C19—41no—
96C42×C19—41no—
97C22⋊Dic19—42no—
98C22⋊Dic19—42no—
99C22⋊Dic19—81no—
100C22⋊Dic19—81no—
101C4⋊Dic19—21no—
102C4⋊Dic19—21no—
103C4⋊Dic19—21no—
104C4⋊Dic19—41no—
105C4⋊Dic19—41no—
106C4⋊Dic19SD1612yescomplemented
107Dic19⋊C4—42no—
108Dic19⋊C4—41no—
109Dic19⋊C4—41no—
110Dic19⋊C4—41no—
111Dic19⋊C4—41no—
112Dic19⋊C4—81no—
113C4×Dic19—42no—
114C2×C19⋊C8—22no—
115C2×C19⋊C8—22no—
116C2×C19⋊C8—41no—
117C2×C19⋊C8—41no—
118C2×C19⋊C8—41no—
119C2×C19⋊C8—41no—
120#7780—191nomaximal, Sylow
121C23×C19—41no—
122C23×C19—41no—
123C23×C19—41no—
124C23×C19—41no—
125C23×C19—41no—
126C23×C19—41no—
127C23×C19—41no—
128C23×C19#12011yescharacteristic
129Q8×C19—42no—
130Q8×C19—42no—
131Q8×C19—81no—
132Q8×C19—81no—
133D4×C19—42no—
134D4×C19—81no—
135C2×C4×C19—21no—
136C2×C4×C19—21no—
137C2×C4×C19—21no—
138C2×C4×C19—21no—
139C2×C4×C19—21no—
140C2×C4×C19—21no—
141C2×C4×C19—41no—
142C2×C4×C19—41no—
143C2×C4×C19—41no—
144C2×C4×C19—42no—
145C2×C4×C19—81no—
146C2×C4×C19—81no—
147C2×C4×C19C2×SD1611yescharacteristic
148C2×C4×C19#13511yescharacteristic
149C2×C4×C19#13511yescharacteristic
150C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
151C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
152C2×C4×C19#13711yescharacteristic
153C2×Dic19—22no—
154C2×Dic19—41no—
155C2×Dic19—41no—
156C2×Dic19—41no—
157C2×Dic19—41no—
158C2×Dic19—41no—
159C2×Dic19—41no—
160C2×Dic19—41no—
161C2×Dic19—41no—
162C2×Dic19—41no—
163C2×Dic19—41no—
164C2×Dic19—41no—
165C8×C19—42no—
166C19⋊C8—42no—
167C19⋊C8—42no—
168#2727—191no—
169#2058—191no—
170#2057—191no—
171#2013D1911yescharacteristic
172#1271—191no—
173#1271—191no—
174#1270—191no—
175C22×C19—81no—
176C22×C19—81no—
177C22×C19—81no—
178C22×C19—81no—
179C22×C19—81no—
180C22×C19—81no—
181C22×C19—81no—
182C22×C19#44911yescharacteristic
183C22×C19#45011yescharacteristic
184C22×C19#45211yescharacteristic
185C22×C19#45311yescharacteristic
186C22×C19#45611yescharacteristic
187C22×C19#45611yescharacteristic
188C22×C19B(4,𝔽2)11yescharacteristic
189C4×C19—21no—
190C4×C19—21no—
191C4×C19—21no—
192C4×C19—21no—
193C4×C19—21no—
194C4×C19—21no—
195C4×C19—82no—
196C4×C19—81no—
197Dic19—42no—
198Dic19—81no—
199Dic19—81no—
200Dic19—81no—
201C22×SD16—21no—
202C2×C4⋊Q8C2×D1911yescharacteristic
203C2×#126—381no—
204C2×#107—381no—
205C2×#106—381no—
206C2×#103—21no—
207#399—381no—
208#396—381no—
209#394—381no—
210#390C2×D1911yescharacteristic
211#389—191no—
212#389—191no—
213#389—381no—
214#388—381no—
215#340—381no—
216#340—381no—
217#336—191no—
218#336—191no—
219#336C2×D1911yescharacteristic
220C2×C19—161no—
221C2×C19#160011yescharacteristic
222C2×C19#160311yescharacteristic
223C2×C19#160411yescharacteristic
224C2×C19#163111yescharacteristic
225C2×C19#165011yescharacteristic
226C2×C19#165411yescharacteristic
227C2×C19#166011yescharacteristic
228C22×Q8—21no—
229C22×D4C22⋊D1911yescharacteristic
230C2×SD16—42no—
231C2×SD16—42no—
232C2×SD16—42no—
233C22×C8—21no—
234C22×C8—381no—
235C22×C8—381no—
236C4⋊Q8—42no—
237#126—762no—
238#126—762no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—191no—
242C2×C4⋊C4—191no—
243C2×C4⋊C4—191no—
244C2×C4⋊C4—191no—
245C2×C4⋊C4—381no—
246C2×C4⋊C4—381no—
247C2×C4⋊C4—381no—
248C2×C4⋊C4—381no—
249C2×C4⋊C4C22⋊D1911yescharacteristic
250C2×C22⋊C4—21no—
251C2×C22⋊C4—21no—
252C2×C22⋊C4—381no—
253C2×C22⋊C4—381no—
254C2×C22⋊C4—381no—
255C2×C22⋊C4—381no—
256C2×C42—381no—
257C2×C42C22×D1911yescharacteristic
258#107—762no—
259#106—762no—
260#103—42no—
261#95—381no—
262#95—381no—
263#95—381no—
264C19#778011yescharacteristic, complemented, Sylow
265C24—21no—
266C2×Q8—22no—
267C2×Q8—41no—
268C2×Q8—41no—
269C2×Q8—41no—
270C2×Q8—41no—
271C2×Q8—41no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—41no—
275C2×D4—41no—
276C22×C4—21no—
277C22×C4—41no—
278C22×C4—381no—
279C22×C4—381no—
280C22×C4—381no—
281C22×C4—381no—
282C22×C4D4×D1911yescharacteristic
283C22×C4D4×D1911yescharacteristic
284C22×C4C2×C22⋊D1911yescharacteristic
285SD16—48no—
286C2×C8—22no—
287C2×C8—41no—
288C2×C8—41no—
289C2×C8—382no—
290C2×C8—382no—
291C2×C8—761no—
292C2×C8—761no—
293C2×C8—761no—
294C2×C8—761no—
295C4⋊C4—22no—
296C4⋊C4—22no—
297C4⋊C4—41no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C4⋊C4—192no—
301C4⋊C4—381no—
302C4⋊C4—381no—
303C4⋊C4—381no—
304C4⋊C4—761no—
305C4⋊C4—761no—
306C4⋊C4—762no—
307C4⋊C4—761no—
308C4⋊C4—761no—
309C4⋊C4—761no—
310C4⋊C4—761no—
311C4⋊C4—1521no—
312C22⋊C4—41no—
313C22⋊C4—41no—
314C22⋊C4—41no—
315C22⋊C4—41no—
316C22⋊C4—762no—
317C22⋊C4—762no—
318C22⋊C4—1521no—
319C22⋊C4—1521no—
320C42—41no—
321C42—762no—
322C23—41no—
323C23—41no—
324C23—41no—
325C23—41no—
326C23—41no—
327C23—41no—
328C23—41no—
329C23#1059738311yescharacteristic
330Q8—42no—
331Q8—42no—
332Q8—81no—
333Q8—81no—
334D4—42no—
335D4—81no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—42no—
346C2×C4—81no—
347C2×C4—81no—
348C2×C4—382no—
349C2×C4—761no—
350C2×C4—761no—
351C2×C4—761no—
352C2×C4—761no—
353C2×C4—761no—
354C2×C4—761no—
355C2×C4—761no—
356C2×C4—761no—
357C2×C4—761no—
358C2×C4—761no—
359C2×C4—761no—
360C2×C4SD16×D1911yescharacteristic
361C2×C4#1059736011yescharacteristic
362C2×C4#1059736111yescharacteristic
363C2×C4#1059736211yescharacteristic
364C2×C4#1059737811yescharacteristic
365C2×C4#1059739611yescharacteristic
366C8—42no—
367C8—762no—
368C8—762no—
369C22—81no—
370C22—81no—
371C22—81no—
372C22—81no—
373C22—81no—
374C22—81no—
375C22—81no—
376C22#1192668711yescharacteristic
377C22#1192669311yescharacteristic
378C22#1192670311yescharacteristic
379C22#1192671111yescharacteristic
380C22#1192672511yescharacteristic
381C22#1192672511yescharacteristic
382C22#1192673011yescharacteristic
383C4—21no—
384C4—21no—
385C4—21no—
386C4—21no—
387C4—21no—
388C4—21no—
389C4—82no—
390C4—81no—
391C4—762no—
392C4—1521no—
393C4—1521no—
394C4—1521no—
395C2—161no—
396C2#1456257911yescharacteristic
397C2#1456259511yescharacteristic
398C2#1456260211yescharacteristic
399C2#1456275911yescharacteristic
400C2#1456288911yescharacteristic
401C2#1456291711yescharacteristic
402C2#1456294411yescharacteristic
subgroupG/H
centerC23#10597383
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#2013C2
socleC23×C19#120
prime radicalC22×D4×C19D4
hypercenter#2013D19
hypocenterC19#7780
LCSG ▷ C2×C42×C19 ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2013

Complements

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

NH ≅ G/Ntype
2. #14564965C2semidirect
3. #14564960C2semidirect
4. #14561459C2semidirect
5. #14561457C2semidirect
106. C4⋊Dic19SD16semidirect
264. C19#7780semidirect

Maximal subgroups

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

subgroupindex
#145705942
#145649652
#145649602
#145614592
#145614572
#145614562
C19×#20132
#778019