Finite Group Databasebeta

← #18071534

Subgroups — #18071534

Order 4864.

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

normal subgroups only

This group has 480 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#14571579C211yesmaximal, characteristic
2#14564768C211yesmaximal, characteristic
3#14564735C211yesmaximal, characteristic, complemented
4#14561461C211yesmaximal, characteristic, complemented
5#14561460C211yesmaximal, characteristic, complemented
6#14561455C211yesmaximal, characteristic
7C19×#2024C211yesmaximal, characteristic, complemented
8C22×#64528—21no—
9C2×#10597292—21no—
10C2×#10597266—21no—
11#11926486—21no—
12#11926457—21no—
13#11926455—21no—
14#11926450C2211yescharacteristic
15#11926446C2211yescharacteristic
16#11926422—21no—
17#11926418—21no—
18#11926415—21no—
19#11926306—21no—
20#11926299C2211yescharacteristic
21#11926299C2211yescharacteristic
22C2×C19×C4⋊Q8C2211yescharacteristic
23C2×C19×#103—21no—
24C19×#391C2211yescharacteristic
25C19×#340—21no—
26C19×#336C2211yescharacteristic
27C22×Q8×C19—21no—
28C22×Q8×C19D411yescharacteristic
29C22×D76D411yescharacteristic
30C22×C4×D19—21no—
31C22×Dic38D411yescharacteristic
32C22×C8×C19—21no—
33C19×C4⋊Q8—42no—
34C2×C4⋊C4×C19—21no—
35C2×C4⋊C4×C19—21no—
36C2×C4⋊C4×C19D411yescharacteristic
37C2×C42×C19C2311yescharacteristic
38C2×#64528—42no—
39C2×#64528—42no—
40C2×#64528—42no—
41C2×(C2×D19)⋊C4—21no—
42C2×(C2×D19)⋊C4—21no—
43C2×(C2×D19)⋊C4—21no—
44C2×(C2×D19)⋊C4—21no—
45C2×(C2×D19)⋊C4—21no—
46C2×C4⋊Dic19D411yescharacteristic
47C2×C4⋊Dic19D411yescharacteristic
48C2×Dic19⋊C4—21no—
49C22×C19⋊C8—21no—
50C22×C19⋊C8—21no—
51C19×#103—42no—
52C19×#95—21no—
53C19×#95—21no—
54#10597292—42no—
55C19⋊#95—21no—
56C19⋊#95—21no—
57C19⋊#95—21no—
58C19⋊#95—21no—
59C19⋊#95—21no—
60#10597266—42no—
61C23×D19—21no—
62C2×Q8×C19—22no—
63C2×Q8×C19—21no—
64C2×Q8×C19—21no—
65C2×Q8×C19—41no—
66C2×Q8×C19—41no—
67C2×Q8×C19—41no—
68C2×Q8×C19—41no—
69C2×Q8×C19—41no—
70C2×Q8×C19—41no—
71C2×Q8×C19—41no—
72C22×C4×C19—21no—
73C22×C4×C19—21no—
74C22×C4×C19—41no—
75C22×C4×C19C2×D411yescharacteristic
76C22×C4×C19C2×D411yescharacteristic
77C22×C4×C19C2×D411yescharacteristic
78C22×Dic19—21no—
79C22×Dic19—21no—
80C22×Dic19—21no—
81C2×D76—21no—
82C2×D76—41no—
83C2×D76—41no—
84C2×D76Q1612yescomplemented
85C2×C4×D19—81no—
86C2×C4×D19—81no—
87C2×C4×D19—81no—
88C2×Dic38—21no—
89C2×Dic38—21no—
90C2×Dic38—41no—
91C2×Dic38—41no—
92C2×C8×C19—41no—
93C2×C8×C19—41no—
94C2×C8×C19—41no—
95C4⋊C4×C19—22no—
96C4⋊C4×C19—22no—
97C4⋊C4×C19—41no—
98C4⋊C4×C19—41no—
99C4⋊C4×C19—41no—
100C42×C19—41no—
101#64528—48no—
102(C2×D19)⋊C4—41no—
103(C2×D19)⋊C4—41no—
104(C2×D19)⋊C4—41no—
105(C2×D19)⋊C4—41no—
106(C2×D19)⋊C4—81no—
107(C2×D19)⋊C4—81no—
108(C2×D19)⋊C4—81no—
109C4⋊Dic19—41no—
110C4⋊Dic19—41no—
111Dic19⋊C4—81no—
112C2×C19⋊C8—22no—
113C2×C19⋊C8—41no—
114C2×C19⋊C8—41no—
115C2×C19⋊C8—41no—
116C2×C19⋊C8—41no—
117C2×C19⋊C8—41no—
118#7782—191nomaximal, Sylow
119C23×C19#12011yescharacteristic
120C22×D19—22no—
121C22×D19—41no—
122C22×D19—41no—
123C22×D19—41no—
124C22×D19—41no—
125C22×D19—41no—
126C22×D19—41no—
127Q8×C19—42no—
128Q8×C19—42no—
129Q8×C19—42no—
130Q8×C19—81no—
131Q8×C19—81no—
132Q8×C19—81no—
133C2×C4×C19—21no—
134C2×C4×C19—21no—
135C2×C4×C19—21no—
136C2×C4×C19—21no—
137C2×C4×C19—21no—
138C2×C4×C19—21no—
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—42no—
146C2×C4×C19—81no—
147C2×C4×C19—81no—
148C2×C4×C19C2×Q1611yescharacteristic
149C2×C4×C19#13511yescharacteristic
150C2×C4×C19#13511yescharacteristic
151C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
152C2×C4×C19#13711yescharacteristic
153C2×C4×C19#13711yescharacteristic
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—
163D76—42no—
164D76—81no—
165C4×D19—84no—
166Dic38—42no—
167Dic38—81no—
168C8×C19—81no—
169C19⋊C8—42no—
170C19⋊C8—81no—
171#2804—191no—
172#2024D1911yescharacteristic, complemented
173#2023—191no—
174#2016—191no—
175#1272—191no—
176#1272—191no—
177#1270—191no—
178C22×C19#44911yescharacteristic
179C22×C19#45111yescharacteristic
180C22×C19#45211yescharacteristic
181C22×C19#45311yescharacteristic
182C22×C19#45511yescharacteristic
183C22×C19#45511yescharacteristic
184C22×C19B(4,𝔽2)11yescharacteristic
185C2×D19—42no—
186C2×D19—42no—
187C2×D19—42no—
188C2×D19—81no—
189C2×D19—81no—
190C2×D19—81no—
191C2×D19—81no—
192C4×C19—21no—
193C4×C19—21no—
194C4×C19—21no—
195C4×C19—21no—
196C4×C19—21no—
197C4×C19—21no—
198C4×C19—82no—
199C4×C19—81no—
200C4×C19—81no—
201Dic19—81no—
202Dic19—81no—
203Dic19—81no—
204C22×Q16—381no—
205C2×C4⋊Q8C2×D1911yescharacteristic
206C2×#103—21no—
207C2×#103—381no—
208C2×#102—381no—
209#400—381no—
210#393—381no—
211#393—381no—
212#391—191no—
213#391C2×D1911yescharacteristic
214#390—191no—
215#386—381no—
216#385—381no—
217#385—381no—
218#340—21no—
219#340—381no—
220#336—191no—
221#336—191no—
222#336C2×D1911yescharacteristic
223C2×C19#160011yescharacteristic
224C2×C19#160211yescharacteristic
225C2×C19#160611yescharacteristic
226C2×C19#163211yescharacteristic
227C2×C19#164011yescharacteristic
228C2×C19#164411yescharacteristic
229C2×C19#165911yescharacteristic
230D19—82no—
231C22×Q8—21no—
232C22×Q8—191no—
233C22×Q8C22⋊D1911yescharacteristic
234C22×D4—191no—
235C23×C4—381no—
236C2×Q16—762no—
237C2×Q16—762no—
238C2×Q16—762no—
239C22×C8—21no—
240C22×C8—381no—
241C22×C8—381no—
242C4⋊Q8—42no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—191no—
246C2×C4⋊C4—191no—
247C2×C4⋊C4—381no—
248C2×C4⋊C4C22⋊D1911yescharacteristic
249C2×C22⋊C4—381no—
250C2×C22⋊C4—381no—
251C2×C22⋊C4—381no—
252C2×C22⋊C4—381no—
253C2×C22⋊C4—381no—
254C2×C42C22×D1911yescharacteristic
255#103—42no—
256#103—762no—
257#102—762no—
258#95—21no—
259#95—21no—
260#95—381no—
261#95—381no—
262#95—381no—
263#95—381no—
264#95—381no—
265C19#778211yescharacteristic, complemented, Sylow
266C24—381no—
267C2×Q8—22no—
268C2×Q8—21no—
269C2×Q8—21no—
270C2×Q8—41no—
271C2×Q8—41no—
272C2×Q8—41no—
273C2×Q8—41no—
274C2×Q8—41no—
275C2×Q8—41no—
276C2×Q8—41no—
277C2×Q8—381no—
278C2×Q8—381no—
279C2×Q8—761no—
280C2×Q8—761no—
281C2×D4—192no—
282C2×D4—381no—
283C2×D4—761no—
284C2×D4—761no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—41no—
288C22×C4—381no—
289C22×C4—381no—
290C22×C4—381no—
291C22×C4—1521no—
292C22×C4—1521no—
293C22×C4—1521no—
294C22×C4D4×D1911yescharacteristic
295C22×C4D4×D1911yescharacteristic
296C22×C4C2×C22⋊D1911yescharacteristic
297Q16—768no—
298C2×C8—41no—
299C2×C8—41no—
300C2×C8—41no—
301C2×C8—382no—
302C2×C8—761no—
303C2×C8—761no—
304C2×C8—761no—
305C2×C8—761no—
306C2×C8—761no—
307C4⋊C4—22no—
308C4⋊C4—22no—
309C4⋊C4—41no—
310C4⋊C4—41no—
311C4⋊C4—41no—
312C4⋊C4—761no—
313C4⋊C4—761no—
314C4⋊C4—1521no—
315C22⋊C4—761no—
316C22⋊C4—761no—
317C22⋊C4—761no—
318C22⋊C4—761no—
319C22⋊C4—1521no—
320C22⋊C4—1521no—
321C22⋊C4—1521no—
322C42—41no—
323C23—382no—
324C23—761no—
325C23—761no—
326C23—761no—
327C23—761no—
328C23—761no—
329C23—761no—
330C23#1059738311yescharacteristic
331Q8—42no—
332Q8—42no—
333Q8—42no—
334Q8—81no—
335Q8—81no—
336Q8—81no—
337Q8—762no—
338Q8—1521no—
339D4—762no—
340D4—1521no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—42no—
354C2×C4—81no—
355C2×C4—81no—
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—1524no—
366C2×C4#1059736011yescharacteristic
367C2×C4#1059736211yescharacteristic
368C2×C4Q16×D1911yescharacteristic
369C2×C4#1059736411yescharacteristic
370C2×C4#1059738811yescharacteristic
371C2×C4#1059739611yescharacteristic
372C8—81no—
373C8—762no—
374C8—1521no—
375C22—762no—
376C22—762no—
377C22—762no—
378C22—1521no—
379C22—1521no—
380C22—1521no—
381C22—1521no—
382C22#1192668811yescharacteristic
383C22#1192669811yescharacteristic
384C22#1192670411yescharacteristic
385C22#1192671011yescharacteristic
386C22#1192672011yescharacteristic
387C22#1192672111yescharacteristic
388C22#1192673011yescharacteristic
389C4—21no—
390C4—21no—
391C4—21no—
392C4—21no—
393C4—21no—
394C4—21no—
395C4—82no—
396C4—81no—
397C4—81no—
398C4—1521no—
399C4—1521no—
400C4—1521no—
401C2—1522no—
402C2#1456258011yescharacteristic
403C2#1456259011yescharacteristic
404C2#1456261311yescharacteristic
405C2#1456276811yescharacteristic
406C2#1456282011yescharacteristic
407C2#1456284611yescharacteristic
408C2#1456294011yescharacteristic
subgroupG/H
centerC23#10597383
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#2024C2
socleC23×C19#120
prime radicalC22×D76D4
hypercenter#2024D19
hypocenterC19#7782
LCSG ▷ C2×C42×C19 ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2024

Complements

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

NH ≅ G/Ntype
3. #14564735C2semidirect
4. #14561461C2semidirect
5. #14561460C2semidirect
7. C19×#2024C2semidirect
84. C2×D76Q16semidirect
172. #2024D19semidirect
265. C19#7782semidirect

Maximal subgroups

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

subgroupindex
#145715792
#145647682
#145647352
#145614612
#145614602
#145614552
C19×#20242
#778219