Finite Group Databasebeta

← #18071633

Subgroups — #18071633

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#14570660C211yesmaximal, characteristic
2#14565162C211yesmaximal, characteristic, complemented
3#14565045C211yesmaximal, characteristic, complemented
4#14565038C211yesmaximal, characteristic, complemented
5#14561460C211yesmaximal, characteristic, complemented
6#14561455C211yesmaximal, characteristic, complemented
7C19×#1270C211yesmaximal, characteristic, complemented
8C2×#10597331—21no—
9C2×#10597275—21no—
10C2×#10597273—21no—
11C2×#10597278—21no—
12C2×#10597289—21no—
13#11926460—21no—
14#11926453—21no—
15#11926452—21no—
16#11926450C2211yescharacteristic
17#11926446C2211yescharacteristic
18#11926437—21no—
19#11926434—21no—
20#11926414C2211yescharacteristic
21#11926307—21no—
22#11926306—21no—
23#11926299C2211yescharacteristic
24C19×#390C2211yescharacteristic
25C19×#336C2211yescharacteristic
26C19×#336C2211yescharacteristic
27C22×D4×C19D411yescharacteristic
28C22×C22⋊D19—21no—
29C22×C22⋊D19—21no—
30C22×D76D411yescharacteristic
31C22×Dic38D411yescharacteristic
32C22×C8×C19—21no—
33C22×C8×C19—21no—
34C2×C4⋊C4×C19D411yescharacteristic
35C2×C22⋊C4×C19—21no—
36C2×C22⋊C4×C19—21no—
37C2×C42×C19C2311yescharacteristic
38C2×C22⋊Dic19—21no—
39C2×C22⋊Dic19—21no—
40C2×(C2×D19)⋊C4—21no—
41C2×(C2×D19)⋊C4—21no—
42C2×(C2×D19)⋊C4—21no—
43C2×(C2×D19)⋊C4—21no—
44C2×C4⋊Dic19—21no—
45C2×C4⋊Dic19—21no—
46C2×C4⋊Dic19—21no—
47C2×C4⋊Dic19D411yescharacteristic
48C2×C4⋊Dic19D411yescharacteristic
49C2×C4×Dic19—21no—
50C22×C19⋊C8—21no—
51#10597331—42no—
52#10597331—42no—
53#10597289—42no—
54C19⋊#95—21no—
55C19⋊#95—21no—
56C19⋊#95—21no—
57#10597278—42no—
58#10597275—42no—
59#10597273—42no—
60C24×C19—21no—
61C23×D19—21no—
62C2×D4×C19—21no—
63C2×D4×C19—21no—
64C2×D4×C19—41no—
65C2×D4×C19—41no—
66C22×C4×C19—21no—
67C22×C4×C19C2×D411yescharacteristic
68C22×C4×C19C2×D411yescharacteristic
69C22×C4×C19C2×D411yescharacteristic
70C2×C22⋊D19—42no—
71C2×C22⋊D19—81no—
72C2×C22⋊D19—81no—
73C2×C22⋊D19—81no—
74C2×C22⋊D19—81no—
75C2×C22⋊D19—81no—
76C22×Dic19—21no—
77C22×Dic19—21no—
78C22×Dic19—21no—
79C22×Dic19—41no—
80C2×D76—21no—
81C2×D76—21no—
82C2×D76—41no—
83C2×D76—41no—
84C2×Dic38—21no—
85C2×Dic38—41no—
86C2×Dic38—41no—
87C2×Dic38D812yes—
88C2×C8×C19—22no—
89C2×C8×C19—41no—
90C2×C8×C19—41no—
91C2×C8×C19—41no—
92C2×C8×C19—41no—
93C2×C8×C19—41no—
94C4⋊C4×C19—41no—
95C22⋊C4×C19—41no—
96C22⋊C4×C19—41no—
97C22⋊C4×C19—41no—
98C22⋊C4×C19—41no—
99C42×C19—41no—
100C22⋊Dic19—42no—
101C22⋊Dic19—81no—
102(C2×D19)⋊C4—42no—
103(C2×D19)⋊C4—41no—
104(C2×D19)⋊C4—41no—
105(C2×D19)⋊C4—41no—
106(C2×D19)⋊C4—41no—
107(C2×D19)⋊C4—81no—
108C4⋊Dic19—41no—
109C4⋊Dic19—41no—
110C4⋊Dic19—41no—
111C4⋊Dic19—41no—
112C4⋊Dic19—41no—
113C4⋊Dic19—41no—
114C4⋊Dic19—41no—
115C4⋊Dic19—41no—
116C4×Dic19—42no—
117C2×C19⋊C8—41no—
118C2×C19⋊C8—41no—
119C2×C19⋊C8—41no—
120#7796—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
129C22×D19—41no—
130C22×D19—41no—
131C22×D19—41no—
132C22×D19—41no—
133C22×D19—41no—
134C22×D19—41no—
135C22×D19—41no—
136D4×C19—42no—
137D4×C19—81no—
138C2×C4×C19—21no—
139C2×C4×C19—21no—
140C2×C4×C19—21no—
141C2×C4×C19—21no—
142C2×C4×C19—21no—
143C2×C4×C19—21no—
144C2×C4×C19—41no—
145C2×C4×C19—41no—
146C2×C4×C19—41no—
147C2×C4×C19C2×D811yescharacteristic
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
153C22⋊D19—84no—
154C22⋊D19—84no—
155C2×Dic19—22no—
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—81no—
165C2×Dic19—81no—
166C2×Dic19—81no—
167D76—42no—
168D76—81no—
169Dic38—42no—
170Dic38—81no—
171C8×C19—42no—
172C8×C19—81no—
173C19⋊C8—81no—
174#2733—191no—
175#2093—191no—
176#2072—191no—
177#2071—191no—
178#1272—191no—
179#1270—191no—
180#1270D1911yescharacteristic, complemented
181C22×C19—81no—
182C22×C19—81no—
183C22×C19—81no—
184C22×C19—81no—
185C22×C19—81no—
186C22×C19—81no—
187C22×C19—81no—
188C22×C19#44711yescharacteristic
189C22×C19#44911yescharacteristic
190C22×C19#45211yescharacteristic
191C22×C19#45311yescharacteristic
192C22×C19#45511yescharacteristic
193C22×C19#45511yescharacteristic
194C22×C19#45811yescharacteristic
195C2×D19—81no—
196C2×D19—81no—
197C2×D19—81no—
198C2×D19—81no—
199C2×D19—81no—
200C2×D19—81no—
201C2×D19—81no—
202C4×C19—21no—
203C4×C19—21no—
204C4×C19—21no—
205C4×C19—21no—
206C4×C19—21no—
207C4×C19—21no—
208C4×C19—81no—
209Dic19—42no—
210Dic19—81no—
211Dic19—81no—
212Dic19—161no—
213C2×#124—381no—
214C2×#107—381no—
215C2×#103—381no—
216C2×#102—381no—
217C2×#102—381no—
218#394—381no—
219#392—381no—
220#392—381no—
221#391—191no—
222#390—191no—
223#390C2×D1911yescharacteristic
224#388—381no—
225#388—381no—
226#384—191no—
227#340—381no—
228#340—381no—
229#336—191no—
230#336C2×D1911yescharacteristic
231#336C2×D1911yescharacteristic
232C2×C19—161no—
233C2×C19#160711yescharacteristic
234C2×C19#161211yescharacteristic
235C2×C19#161811yescharacteristic
236C2×C19#162111yescharacteristic
237C2×C19#164111yescharacteristic
238C2×C19#164611yescharacteristic
239C2×C19#165911yescharacteristic
240D19—161no—
241C22×Q8—191no—
242C22×D4—191no—
243C22×D4—381no—
244C22×D4—381no—
245C22×D4D7611yescharacteristic
246C22×C8—21no—
247C22×C8—21no—
248C22×C8—381no—
249#124—762no—
250#124—762no—
251C2×C4⋊C4—191no—
252C2×C4⋊C4—191no—
253C2×C4⋊C4—381no—
254C2×C4⋊C4—381no—
255C2×C4⋊C4—381no—
256C2×C4⋊C4D7611yescharacteristic
257C2×C22⋊C4—21no—
258C2×C22⋊C4—21no—
259C2×C22⋊C4—381no—
260C2×C22⋊C4—381no—
261C2×C22⋊C4—381no—
262C2×C22⋊C4—381no—
263C2×C22⋊C4—381no—
264C2×C22⋊C4—381no—
265C2×C42—381no—
266C2×C42C22×D1911yescharacteristic
267#107—762no—
268#103—762no—
269#102—762no—
270#102—762no—
271#95—381no—
272#95—381no—
273#95—381no—
274C19#779611yescharacteristic, complemented, Sylow
275C24—21no—
276C24—381no—
277C2×Q8—192no—
278C2×Q8—381no—
279C2×Q8—761no—
280C2×Q8—761no—
281C2×D4—21no—
282C2×D4—21no—
283C2×D4—41no—
284C2×D4—41no—
285C2×D4—381no—
286C2×D4—381no—
287C2×D4—761no—
288C2×D4—761no—
289C2×D4—762no—
290C2×D4—1521no—
291C2×D4—1521no—
292C2×D4—1521no—
293C2×D4—1521no—
294C2×D4—1521no—
295C22×C4—21no—
296C22×C4—381no—
297C22×C4—381no—
298C22×C4—381no—
299C22×C4—761no—
300C22×C4C2×D7611yescharacteristic
301C22×C4D4×D1911yescharacteristic
302C22×C4D4×D1911yescharacteristic
303C2×C8—22no—
304C2×C8—41no—
305C2×C8—41no—
306C2×C8—41no—
307C2×C8—41no—
308C2×C8—41no—
309C2×C8—761no—
310C2×C8—761no—
311C2×C8—761no—
312C4⋊C4—41no—
313C4⋊C4—761no—
314C4⋊C4—761no—
315C4⋊C4—761no—
316C4⋊C4—761no—
317C4⋊C4—761no—
318C4⋊C4—761no—
319C4⋊C4—761no—
320C4⋊C4—761no—
321C22⋊C4—41no—
322C22⋊C4—41no—
323C22⋊C4—41no—
324C22⋊C4—41no—
325C22⋊C4—762no—
326C22⋊C4—762no—
327C22⋊C4—761no—
328C22⋊C4—761no—
329C22⋊C4—761no—
330C22⋊C4—761no—
331C22⋊C4—1521no—
332C22⋊C4—1521no—
333C42—41no—
334C42—762no—
335C23—41no—
336C23—41no—
337C23—41no—
338C23—41no—
339C23—41no—
340C23—41no—
341C23—41no—
342C23—761no—
343C23—761no—
344C23—761no—
345C23—761no—
346C23—761no—
347C23—761no—
348C23—761no—
349C23#1059732811yescharacteristic
350Q8—762no—
351Q8—1521no—
352D4—42no—
353D4—81no—
354D4—762no—
355D4—1521no—
356D4—1524no—
357D4—1524no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—382no—
368C2×C4—761no—
369C2×C4—761no—
370C2×C4—761no—
371C2×C4—761no—
372C2×C4—761no—
373C2×C4—761no—
374C2×C4—761no—
375C2×C4—761no—
376C2×C4—1521no—
377C2×C4—1521no—
378C2×C4—1521no—
379C2×C4#1059735011yescharacteristic
380C2×C4#1059735411yescharacteristic
381C2×C4D8×D1911yescharacteristic
382C2×C4#1059735811yescharacteristic
383C2×C4#1059736011yescharacteristic
384C2×C4#1059736111yescharacteristic
385C8—42no—
386C8—81no—
387C8—1521no—
388C22—81no—
389C22—81no—
390C22—81no—
391C22—81no—
392C22—81no—
393C22—81no—
394C22—81no—
395C22—1521no—
396C22—1521no—
397C22—1521no—
398C22—1521no—
399C22—1521no—
400C22—1521no—
401C22—1521no—
402C22#1192667911yescharacteristic
403C22#1192669111yescharacteristic
404C22#1192670711yescharacteristic
405C22#1192671311yescharacteristic
406C22#1192672311yescharacteristic
407C22#1192672411yescharacteristic
408C22#1192673511yescharacteristic
409C4—21no—
410C4—21no—
411C4—21no—
412C4—21no—
413C4—21no—
414C4—21no—
415C4—81no—
416C4—3041no—
417C4—762no—
418C4—1521no—
419C4—1521no—
420C2—161no—
421C2—3041no—
422C2#1456262211yescharacteristic
423C2#1456265111yescharacteristic
424C2#1456268411yescharacteristic
425C2#1456270311yescharacteristic
426C2#1456282911yescharacteristic
427C2#1456286511yescharacteristic
428C2#1456294311yescharacteristic
subgroupG/H
centerC23#10597328
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#1270C2
socleC23×C19#120
prime radical#14570660C2
hypercenter#1270D19
hypocenterC19#7796
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. #14565162C2semidirect
3. #14565045C2semidirect
4. #14565038C2semidirect
5. #14561460C2semidirect
6. #14561455C2semidirect
7. C19×#1270C2semidirect
180. #1270D19semidirect
274. C19#7796semidirect

Maximal subgroups

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

subgroupindex
#145706602
#145651622
#145650452
#145650382
#145614602
#145614552
C19×#12702
#779619