Finite Group Databasebeta

← #18071412

Subgroups — #18071412

Order 4864.

504 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 87 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#14570007C211yesmaximal, characteristic
2#14564964C211yesmaximal, characteristic, complemented
3#14564882C211yesmaximal, characteristic, complemented
4#14564771C211yesmaximal, characteristic
5#14561459C211yesmaximal, characteristic, complemented
6#14561459C211yesmaximal, characteristic, complemented
7C19×#1270C211yesmaximal, characteristic
8C2×#10597315C2211yescharacteristic
9C2×#10597324—21no—
10C2×#10597324—21no—
11C2×#10597275—21no—
12C2×#10597273—21no—
13C2×#10597273—21no—
14C2×#10597289—21no—
15#11926467—21no—
16#11926467—21no—
17#11926464—21no—
18#11926442C2211yescharacteristic
19#11926442C2211yescharacteristic
20#11926424—21no—
21#11926307—21no—
22#11926306—21no—
23#11926299C2211yescharacteristic
24C19×#390C2211yescharacteristic
25C19×#336C2211yescharacteristic
26C19×#336C2211yescharacteristic
27C22×D4×C19D411yescharacteristic
28C23×Dic19—21no—
29C22×Dic38—21no—
30C22×Dic38—21no—
31C22×C8×C19—21no—
32C22×C8×C19—21no—
33C2×C4⋊C4×C19D411yescharacteristic
34C2×C22⋊C4×C19—21no—
35C2×C22⋊C4×C19—21no—
36C2×C42×C19C2311yescharacteristic
37C2×C22⋊Dic19—21no—
38C2×C22⋊Dic19—21no—
39C2×C22⋊Dic19—21no—
40C2×C4⋊Dic19—21no—
41C2×C4⋊Dic19—21no—
42C2×C4⋊Dic19D411yescharacteristic
43C2×C4⋊Dic19D411yescharacteristic
44C2×C4⋊Dic19D411yescharacteristic
45C2×C4⋊Dic19D411yescharacteristic
46C2×Dic19⋊C4—21no—
47C2×Dic19⋊C4—21no—
48C2×Dic19⋊C4—21no—
49C2×Dic19⋊C4—21no—
50C22×C19⋊C8—21no—
51#10597324—42no—
52#10597324—42no—
53#10597324—42no—
54#10597324—42no—
55#10597315—42no—
56#10597289—42no—
57C19⋊#95—21no—
58C19⋊#95—21no—
59C19⋊#95—21no—
60#10597275—42no—
61#10597273—42no—
62#10597273—42no—
63C24×C19—21no—
64C2×D4×C19—21no—
65C2×D4×C19—41no—
66C2×D4×C19—41no—
67C2×D4×C19Q1612yes—
68C22×C4×C19—21no—
69C22×C4×C19C2×D411yescharacteristic
70C22×C4×C19C2×D411yescharacteristic
71C22×C4×C19C2×D411yescharacteristic
72C22×Dic19—21no—
73C22×Dic19—21no—
74C22×Dic19—21no—
75C22×Dic19—21no—
76C22×Dic19—42no—
77C22×Dic19—42no—
78C22×Dic19—41no—
79C22×Dic19—81no—
80C2×Dic38—22no—
81C2×Dic38—41no—
82C2×Dic38—41no—
83C2×Dic38—41no—
84C2×Dic38—41no—
85C2×Dic38—42no—
86C2×Dic38—42no—
87C2×Dic38—41no—
88C2×Dic38—81no—
89C2×C8×C19—22no—
90C2×C8×C19—41no—
91C2×C8×C19—41no—
92C2×C8×C19—41no—
93C2×C8×C19—41no—
94C2×C8×C19—41no—
95C4⋊C4×C19—41no—
96C22⋊C4×C19—41no—
97C22⋊C4×C19—41no—
98C22⋊C4×C19—41no—
99C22⋊C4×C19—41no—
100C42×C19—41no—
101C22⋊Dic19—42no—
102C22⋊Dic19—42no—
103C22⋊Dic19—81no—
104C4⋊Dic19—21no—
105C4⋊Dic19—21no—
106C4⋊Dic19—22no—
107C4⋊Dic19—22no—
108C4⋊Dic19—41no—
109C4⋊Dic19—41no—
110C4⋊Dic19—41no—
111C4⋊Dic19—41no—
112C4⋊Dic19D812yes—
113C4⋊Dic19SD1612yes—
114Dic19⋊C4—42no—
115Dic19⋊C4—42no—
116Dic19⋊C4—41no—
117Dic19⋊C4—41no—
118Dic19⋊C4—41no—
119Dic19⋊C4—41no—
120C2×C19⋊C8—41no—
121C2×C19⋊C8—41no—
122C2×C19⋊C8—41no—
123#7764—191nomaximal, Sylow
124C23×C19—22no—
125C23×C19—41no—
126C23×C19—41no—
127C23×C19—41no—
128C23×C19—41no—
129C23×C19—41no—
130C23×C19—41no—
131C23×C19#12011yescharacteristic
132D4×C19—42no—
133D4×C19—81no—
134C2×C4×C19—21no—
135C2×C4×C19—21no—
136C2×C4×C19—21no—
137C2×C4×C19—21no—
138C2×C4×C19—21no—
139C2×C4×C19—21no—
140C2×C4×C19—41no—
141C2×C4×C19—41no—
142C2×C4×C19—41no—
143C2×C4×C19C2×D811yescharacteristic
144C2×C4×C19C2×SD1611yescharacteristic
145C2×C4×C19C2×Q1611yescharacteristic
146C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
147C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
148C2×C4×C19#13711yescharacteristic
149C2×Dic19—22no—
150C2×Dic19—22no—
151C2×Dic19—41no—
152C2×Dic19—41no—
153C2×Dic19—41no—
154C2×Dic19—41no—
155C2×Dic19—41no—
156C2×Dic19—41no—
157C2×Dic19—41no—
158C2×Dic19—41no—
159C2×Dic19—42no—
160C2×Dic19—41no—
161C2×Dic19—41no—
162C2×Dic19—84no—
163C2×Dic19—81no—
164C2×Dic19—81no—
165Dic38—42no—
166Dic38—42no—
167Dic38—84no—
168Dic38—81no—
169Dic38—81no—
170C8×C19—42no—
171C8×C19—81no—
172C19⋊C8—81no—
173#2683—191no—
174#2057—191no—
175#2043—191no—
176#2023—191no—
177#1271—191no—
178#1271—191no—
179#1270D1911yescharacteristic
180C22×C19—42no—
181C22×C19—42no—
182C22×C19—42no—
183C22×C19—81no—
184C22×C19—81no—
185C22×C19—81no—
186C22×C19—81no—
187C22×C19#44711yescharacteristic
188C22×C19#45011yescharacteristic
189C22×C19#45111yescharacteristic
190C22×C19#45411yescharacteristic
191C22×C19#45511yescharacteristic
192C22×C19#45611yescharacteristic
193C22×C19B(4,𝔽2)11yescharacteristic
194C4×C19—21no—
195C4×C19—21no—
196C4×C19—21no—
197C4×C19—21no—
198C4×C19—21no—
199C4×C19—21no—
200C4×C19—81no—
201Dic19—42no—
202Dic19—42no—
203Dic19—82no—
204Dic19—81no—
205Dic19—81no—
206C2×C4⋊Q8—191no—
207C2×C22⋊Q8—381no—
208C2×C22⋊Q8—381no—
209C2×#107—381no—
210C2×#103—381no—
211C2×#103—381no—
212C2×#102—381no—
213#396—381no—
214#396—381no—
215#395—381no—
216#390C2×D1911yescharacteristic
217#389—191no—
218#389—191no—
219#386—381no—
220#340—381no—
221#340—381no—
222#336—191no—
223#336C2×D1911yescharacteristic
224#336C2×D1911yescharacteristic
225C2×C19—82no—
226C2×C19#159811yescharacteristic
227C2×C19#160211yescharacteristic
228C2×C19#160411yescharacteristic
229C2×C19#163711yescharacteristic
230C2×C19#163911yescharacteristic
231C2×C19#164911yescharacteristic
232C2×C19#166411yescharacteristic
233C22×Q8—381no—
234C22×Q8—381no—
235C22×D4D7611yescharacteristic
236C23×C4—381no—
237C22×C8—21no—
238C22×C8—21no—
239C22×C8—381no—
240C4⋊Q8—762no—
241C22⋊Q8—762no—
242C22⋊Q8—762no—
243C22⋊Q8—762no—
244C22⋊Q8—762no—
245C2×C4⋊C4—191no—
246C2×C4⋊C4—191no—
247C2×C4⋊C4—191no—
248C2×C4⋊C4—191no—
249C2×C4⋊C4—381no—
250C2×C4⋊C4—381no—
251C2×C4⋊C4—381no—
252C2×C4⋊C4—381no—
253C2×C4⋊C4—381no—
254C2×C4⋊C4—381no—
255C2×C4⋊C4D7611yescharacteristic
256C2×C22⋊C4—21no—
257C2×C22⋊C4—21no—
258C2×C22⋊C4—381no—
259C2×C22⋊C4—381no—
260C2×C22⋊C4—381no—
261C2×C42C22×D1911yescharacteristic
262#107—762no—
263#103—762no—
264#103—762no—
265#102—762no—
266#95—381no—
267#95—381no—
268#95—381no—
269C19#776411yescharacteristic, complemented, Sylow
270C24—21no—
271C2×Q8—382no—
272C2×Q8—761no—
273C2×Q8—761no—
274C2×Q8—761no—
275C2×Q8—762no—
276C2×Q8—762no—
277C2×Q8—761no—
278C2×Q8—761no—
279C2×Q8—1521no—
280C2×D4—21no—
281C2×D4—41no—
282C2×D4—41no—
283C2×D4Dic7612yes—
284C22×C4—21no—
285C22×C4—381no—
286C22×C4—381no—
287C22×C4—381no—
288C22×C4—381no—
289C22×C4—762no—
290C22×C4—762no—
291C22×C4—761no—
292C22×C4—1521no—
293C22×C4C2×D7611yescharacteristic
294C22×C4D4×D1911yescharacteristic
295C22×C4D4×D1911yescharacteristic
296C2×C8—22no—
297C2×C8—41no—
298C2×C8—41no—
299C2×C8—41no—
300C2×C8—41no—
301C2×C8—41no—
302C2×C8—761no—
303C2×C8—761no—
304C2×C8—761no—
305C4⋊C4—41no—
306C4⋊C4—192no—
307C4⋊C4—192no—
308C4⋊C4—382no—
309C4⋊C4—382no—
310C4⋊C4—381no—
311C4⋊C4—381no—
312C4⋊C4—761no—
313C4⋊C4—761no—
314C4⋊C4—761no—
315C4⋊C4—761no—
316C4⋊C4—762no—
317C4⋊C4—762no—
318C4⋊C4—761no—
319C4⋊C4—761no—
320C4⋊C4—761no—
321C4⋊C4—761no—
322C22⋊C4—41no—
323C22⋊C4—41no—
324C22⋊C4—41no—
325C22⋊C4—41no—
326C22⋊C4—762no—
327C22⋊C4—762no—
328C22⋊C4—1521no—
329C42—41no—
330C23—22no—
331C23—41no—
332C23—41no—
333C23—41no—
334C23—41no—
335C23—41no—
336C23—41no—
337C23#1059732811yescharacteristic
338Q8—762no—
339Q8—762no—
340Q8—1521no—
341Q8—1521no—
342Q8—1524no—
343D4—42no—
344D4—81no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—382no—
355C2×C4—382no—
356C2×C4—761no—
357C2×C4—761no—
358C2×C4—761no—
359C2×C4—761no—
360C2×C4—761no—
361C2×C4—761no—
362C2×C4—761no—
363C2×C4—761no—
364C2×C4—761no—
365C2×C4—761no—
366C2×C4—762no—
367C2×C4—1524no—
368C2×C4—1521no—
369C2×C4—1521no—
370C2×C4C2×Dic7611yescharacteristic
371C2×C4#1059735511yescharacteristic
372C2×C4D8×D1911yescharacteristic
373C2×C4#1059735711yescharacteristic
374C2×C4SD16×D1911yescharacteristic
375C2×C4#1059736011yescharacteristic
376C8—42no—
377C8—81no—
378C8—1521no—
379C22—42no—
380C22—42no—
381C22—42no—
382C22—81no—
383C22—81no—
384C22—81no—
385C22—81no—
386C22#1192667911yescharacteristic
387C22#1192669611yescharacteristic
388C22#1192670211yescharacteristic
389C22#1192671811yescharacteristic
390C22#1192672411yescharacteristic
391C22#1192672811yescharacteristic
392C22#1192673211yescharacteristic
393C4—21no—
394C4—21no—
395C4—21no—
396C4—21no—
397C4—21no—
398C4—21no—
399C4—81no—
400C4—762no—
401C4—762no—
402C4—1521no—
403C4—1522no—
404C4—1521no—
405C2—82no—
406C2#1456257111yescharacteristic
407C2#1456259411yescharacteristic
408C2#1456260511yescharacteristic
409C2#1456280311yescharacteristic
410C2#1456281511yescharacteristic
411C2#1456288711yescharacteristic
412C2#1456297211yescharacteristic
subgroupG/H
centerC23#10597328
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#1270C2
socleC23×C19#120
prime radicalC22×D4×C19D4
hypercenter#1270D19
hypocenterC19#7764
LCSG ▷ C2×C42×C19 ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1270

Complements

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

NH ≅ G/Ntype
2. #14564964C2semidirect
3. #14564882C2semidirect
5. #14561459C2semidirect
6. #14561459C2semidirect
269. C19#7764semidirect

Maximal subgroups

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

subgroupindex
#145700072
#145649642
#145648822
#145647712
#145614592
C19×#12702
#776419