Finite Group Databasebeta

← #18071513

Subgroups — #18071513

Order 4864.

454 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 79 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#14571617C211yesmaximal, characteristic
2#14564960C211yesmaximal, characteristic, complemented
3#14564718C211yesmaximal, characteristic
4#14561461C211yesmaximal, characteristic, complemented
5#14561457C211yesmaximal, characteristic, complemented
6#14561455C211yesmaximal, characteristic
7C19×#2024C211yesmaximal, characteristic, complemented
8C22×#64527—21no—
9C2×#10597264—21no—
10C2×#10597292—21no—
11#11926471—21no—
12#11926462—21no—
13#11926455—21no—
14#11926446C2211yescharacteristic
15#11926442C2211yescharacteristic
16#11926436—21no—
17#11926434—21no—
18#11926431—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×C8×C19—21no—
31C19×C4⋊Q8—42no—
32C2×C4⋊C4×C19—21no—
33C2×C4⋊C4×C19—21no—
34C2×C4⋊C4×C19D411yescharacteristic
35C2×C42×C19C2311yescharacteristic
36C2×#64527—42no—
37C2×#64527—42no—
38C2×#64527—42no—
39C2×(C2×D19)⋊C4—21no—
40C2×(C2×D19)⋊C4—21no—
41C2×(C2×D19)⋊C4—21no—
42C2×(C2×D19)⋊C4—21no—
43C2×(C2×D19)⋊C4—21no—
44C2×(C2×D19)⋊C4—21no—
45C2×C4⋊Dic19D411yescharacteristic
46C2×C4⋊Dic19D411yescharacteristic
47C2×C4⋊Dic19D411yescharacteristic
48C2×Dic19⋊C4—21no—
49C2×C4×Dic19—21no—
50C22×C19⋊C8—21no—
51C22×C19⋊C8—21no—
52C19×#103—42no—
53C19×#95—21no—
54C19×#95—21no—
55#10597292—42no—
56C19⋊#95—21no—
57C19⋊#95—21no—
58C19⋊#95—21no—
59C19⋊#95—21no—
60#10597264—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—21no—
83C2×D76—41no—
84C2×D76—41no—
85C2×C8×C19—41no—
86C2×C8×C19—41no—
87C2×C8×C19—41no—
88C4⋊C4×C19—22no—
89C4⋊C4×C19—22no—
90C4⋊C4×C19—41no—
91C4⋊C4×C19—41no—
92C4⋊C4×C19—41no—
93C42×C19—41no—
94#64527—48no—
95(C2×D19)⋊C4—41no—
96(C2×D19)⋊C4—41no—
97(C2×D19)⋊C4—41no—
98(C2×D19)⋊C4—41no—
99(C2×D19)⋊C4—81no—
100(C2×D19)⋊C4—81no—
101(C2×D19)⋊C4—81no—
102(C2×D19)⋊C4—81no—
103C4⋊Dic19—21no—
104C4⋊Dic19—21no—
105C4⋊Dic19—41no—
106C4⋊Dic19—41no—
107Dic19⋊C4—41no—
108Dic19⋊C4—41no—
109C4×Dic19—81no—
110C2×C19⋊C8—22no—
111C2×C19⋊C8—22no—
112C2×C19⋊C8—41no—
113C2×C19⋊C8—41no—
114C2×C19⋊C8—41no—
115C2×C19⋊C8—41no—
116#7779—191nomaximal, Sylow
117C23×C19#12011yescharacteristic
118C22×D19—41no—
119C22×D19—41no—
120C22×D19—41no—
121C22×D19—41no—
122C22×D19—41no—
123C22×D19—41no—
124C22×D19—41no—
125Q8×C19—42no—
126Q8×C19—42no—
127Q8×C19—42no—
128Q8×C19—81no—
129Q8×C19—81no—
130Q8×C19—81no—
131C2×C4×C19—21no—
132C2×C4×C19—21no—
133C2×C4×C19—21no—
134C2×C4×C19—21no—
135C2×C4×C19—21no—
136C2×C4×C19—21no—
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—42no—
144C2×C4×C19—81no—
145C2×C4×C19—81no—
146C2×C4×C19#13511yescharacteristic
147C2×C4×C19#13511yescharacteristic
148C2×C4×C19#13511yescharacteristic
149C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
150C2×C4×C19#13711yescharacteristic
151C2×C4×C19#13711yescharacteristic
152C2×Dic19—41no—
153C2×Dic19—41no—
154C2×Dic19—41no—
155C2×Dic19—41no—
156C2×Dic19—41no—
157C2×Dic19—41no—
158C2×Dic19—41no—
159C2×Dic19—41no—
160C2×Dic19—41no—
161D76—42no—
162D76—81no—
163C8×C19—81no—
164C19⋊C8—42no—
165C19⋊C8—42no—
166#2808—191no—
167#2057—191no—
168#2024D1911yescharacteristic, complemented
169#2013—191no—
170#1272—191no—
171#1271—191no—
172#1270—191no—
173C22×C19#44911yescharacteristic
174C22×C19#45211yescharacteristic
175C22×C19#45211yescharacteristic
176C22×C19#45311yescharacteristic
177C22×C19#45511yescharacteristic
178C22×C19#45611yescharacteristic
179C22×C19B(4,𝔽2)11yescharacteristic
180C2×D19—81no—
181C2×D19—81no—
182C2×D19—81no—
183C2×D19—81no—
184C2×D19—81no—
185C2×D19—81no—
186C2×D19—81no—
187C4×C19—21no—
188C4×C19—21no—
189C4×C19—21no—
190C4×C19—21no—
191C4×C19—21no—
192C4×C19—21no—
193C4×C19—82no—
194C4×C19—81no—
195C4×C19—81no—
196Dic19—81no—
197Dic19—81no—
198Dic19—81no—
199C22×SD16—381no—
200C2×C4⋊Q8C2×D1911yescharacteristic
201C2×#107—381no—
202C2×#103—21no—
203C2×#103—381no—
204#397—381no—
205#394—381no—
206#393—381no—
207#391C2×D1911yescharacteristic
208#390—191no—
209#389—191no—
210#388—381no—
211#388—381no—
212#387—381no—
213#340—21no—
214#340—381no—
215#336—191no—
216#336—191no—
217#336C2×D1911yescharacteristic
218C2×C19#160011yescharacteristic
219C2×C19#160311yescharacteristic
220C2×C19#160611yescharacteristic
221C2×C19#163011yescharacteristic
222C2×C19#164611yescharacteristic
223C2×C19#165011yescharacteristic
224C2×C19#166111yescharacteristic
225D19—161no—
226C22×Q8—21no—
227C22×Q8C22⋊D1911yescharacteristic
228C22×D4—191no—
229C2×SD16—762no—
230C2×SD16—762no—
231C2×SD16—762no—
232C22×C8—21no—
233C22×C8—381no—
234C22×C8—381no—
235C4⋊Q8—42no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—191no—
239C2×C4⋊C4—191no—
240C2×C4⋊C4—191no—
241C2×C4⋊C4—381no—
242C2×C4⋊C4C22⋊D1911yescharacteristic
243C2×C22⋊C4—381no—
244C2×C22⋊C4—381no—
245C2×C22⋊C4—381no—
246C2×C22⋊C4—381no—
247C2×C22⋊C4—381no—
248C2×C22⋊C4—381no—
249C2×C42—381no—
250C2×C42C22×D1911yescharacteristic
251#107—762no—
252#103—42no—
253#103—762no—
254#95—21no—
255#95—21no—
256#95—381no—
257#95—381no—
258#95—381no—
259#95—381no—
260C19#777911yescharacteristic, complemented, Sylow
261C24—381no—
262C2×Q8—22no—
263C2×Q8—21no—
264C2×Q8—21no—
265C2×Q8—41no—
266C2×Q8—41no—
267C2×Q8—41no—
268C2×Q8—41no—
269C2×Q8—41no—
270C2×Q8—41no—
271C2×Q8—41no—
272C2×D4—381no—
273C2×D4—381no—
274C2×D4—761no—
275C2×D4—761no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—41no—
279C22×C4—381no—
280C22×C4—381no—
281C22×C4—381no—
282C22×C4D4×D1911yescharacteristic
283C22×C4D4×D1911yescharacteristic
284C22×C4C2×C22⋊D1911yescharacteristic
285SD16—768no—
286C2×C8—41no—
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—381no—
301C4⋊C4—381no—
302C4⋊C4—761no—
303C4⋊C4—761no—
304C4⋊C4—761no—
305C4⋊C4—761no—
306C22⋊C4—761no—
307C22⋊C4—761no—
308C22⋊C4—761no—
309C22⋊C4—761no—
310C22⋊C4—1521no—
311C22⋊C4—1521no—
312C22⋊C4—1521no—
313C22⋊C4—1521no—
314C42—41no—
315C42—1521no—
316C23—761no—
317C23—761no—
318C23—761no—
319C23—761no—
320C23—761no—
321C23—761no—
322C23—761no—
323C23#1059738311yescharacteristic
324Q8—42no—
325Q8—42no—
326Q8—42no—
327Q8—81no—
328Q8—81no—
329Q8—81no—
330D4—762no—
331D4—1521no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—42no—
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#1059736011yescharacteristic
357C2×C4#1059736211yescharacteristic
358C2×C4#1059736411yescharacteristic
359C2×C4#1059736511yescharacteristic
360C2×C4#1059738811yescharacteristic
361C2×C4#1059739611yescharacteristic
362C8—81no—
363C8—762no—
364C8—762no—
365C22—1521no—
366C22—1521no—
367C22—1521no—
368C22—1521no—
369C22—1521no—
370C22—1521no—
371C22—1521no—
372C22#1192668811yescharacteristic
373C22#1192670411yescharacteristic
374C22#1192670511yescharacteristic
375C22#1192671011yescharacteristic
376C22#1192672111yescharacteristic
377C22#1192672511yescharacteristic
378C22#1192673011yescharacteristic
379C4—21no—
380C4—21no—
381C4—21no—
382C4—21no—
383C4—21no—
384C4—21no—
385C4—82no—
386C4—81no—
387C4—81no—
388C4—1521no—
389C4—1521no—
390C4—1521no—
391C2—3041no—
392C2#1456258011yescharacteristic
393C2#1456259711yescharacteristic
394C2#1456261311yescharacteristic
395C2#1456275511yescharacteristic
396C2#1456286011yescharacteristic
397C2#1456289011yescharacteristic
398C2#1456295111yescharacteristic
subgroupG/H
centerC23#10597383
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#2024C2
socleC23×C19#120
prime radicalC22×D76D4
hypercenter#2024D19
hypocenterC19#7779
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
2. #14564960C2semidirect
4. #14561461C2semidirect
5. #14561457C2semidirect
7. C19×#2024C2semidirect
168. #2024D19semidirect
260. C19#7779semidirect

Maximal subgroups

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

subgroupindex
#145716172
#145649602
#145647182
#145614612
#145614572
#145614552
C19×#20242
#777919