Finite Group Databasebeta

← #18071589

Subgroups — #18071589

Order 4864.

516 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 91 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#14565163C211yesmaximal, characteristic, complemented
2#14565106C211yesmaximal, characteristic, complemented
3#14565038C211yesmaximal, characteristic, complemented
4#14561458C211yesmaximal, characteristic, complemented
5#14561456C211yesmaximal, characteristic, complemented
6#14561456C211yesmaximal, characteristic, complemented
7C19×#2682C211yesmaximal, characteristic
8C2×#10597264—21no—
9C2×#10597264—21no—
10C2×#10597289—21no—
11C2×#10597289—21no—
12#11926414C2211yescharacteristic
13#11926306—21no—
14#11926306—21no—
15#11926299C2211yescharacteristic
16#11926299C2211yescharacteristic
17#11926299C2211yescharacteristic
18C2×C19×#123—21no—
19C2×C19×#121—21no—
20C19×#396—21no—
21C19×#394—21no—
22C19×#392—21no—
23C19×#390C2211yescharacteristic
24C19×#390C2211yescharacteristic
25C19×#389C2211yescharacteristic
26C19×#385—21no—
27C22×D4×C19—21no—
28C22×D4×C19—21no—
29C22×D4×C19D411yescharacteristic
30C22×D4×C19D411yescharacteristic
31C23×C4×C19—21no—
32C19×#123—42no—
33C19×#123—42no—
34C19×#121—42no—
35C19×#121—42no—
36C2×C4⋊C4×C19—21no—
37C2×C4⋊C4×C19—21no—
38C2×C4⋊C4×C19D411yescharacteristic
39C2×C4⋊C4×C19D411yescharacteristic
40C2×C4⋊C4×C19D411yescharacteristic
41C2×C4⋊C4×C19D411yescharacteristic
42C2×C22⋊C4×C19—21no—
43C2×C22⋊C4×C19—21no—
44C2×C22⋊C4×C19—21no—
45C2×C22⋊C4×C19—21no—
46C2×C22⋊C4×C19—21no—
47C2×C22⋊C4×C19—21no—
48C2×C22⋊C4×C19—21no—
49C2×C42×C19C2311yescharacteristic
50C2×C4⋊Dic19—21no—
51C2×C4⋊Dic19—21no—
52C2×C4⋊Dic19—21no—
53C22×C19⋊C8—21no—
54C22×C19⋊C8—21no—
55C22×C19⋊C8—21no—
56C19×#95—21no—
57C19×#95—21no—
58#10597289—42no—
59#10597289—42no—
60#10597264—42no—
61#10597264—42no—
62C24×C19—21no—
63C24×C19—21no—
64C2×D4×C19—21no—
65C2×D4×C19—21no—
66C2×D4×C19—21no—
67C2×D4×C19—41no—
68C2×D4×C19—41no—
69C2×D4×C19—41no—
70C2×D4×C19—41no—
71C2×D4×C19—42no—
72C2×D4×C19—42no—
73C2×D4×C19—42no—
74C2×D4×C19—81no—
75C2×D4×C19—81no—
76C2×D4×C19—81no—
77C2×D4×C19D812yes—
78C22×C4×C19—21no—
79C22×C4×C19—21no—
80C22×C4×C19—21no—
81C22×C4×C19—21no—
82C22×C4×C19—42no—
83C22×C4×C19—42no—
84C22×C4×C19—81no—
85C22×C4×C19C2×D411yescharacteristic
86C22×C4×C19C2×D411yescharacteristic
87C22×C4×C19C2×D411yescharacteristic
88C22×Dic19—41no—
89C4⋊C4×C19—21no—
90C4⋊C4×C19—41no—
91C4⋊C4×C19—41no—
92C4⋊C4×C19—41no—
93C4⋊C4×C19—42no—
94C4⋊C4×C19—41no—
95C4⋊C4×C19—41no—
96C4⋊C4×C19D812yes—
97C22⋊C4×C19—42no—
98C22⋊C4×C19—42no—
99C22⋊C4×C19—41no—
100C22⋊C4×C19—41no—
101C22⋊C4×C19—41no—
102C22⋊C4×C19—41no—
103C22⋊C4×C19—41no—
104C22⋊C4×C19—41no—
105C22⋊C4×C19—41no—
106C22⋊C4×C19—41no—
107C22⋊C4×C19—81no—
108C42×C19—41no—
109C4⋊Dic19—41no—
110C4⋊Dic19—41no—
111C4⋊Dic19—41no—
112C4⋊Dic19—41no—
113C4⋊Dic19—41no—
114C4⋊Dic19—41no—
115C2×C19⋊C8—22no—
116C2×C19⋊C8—22no—
117C2×C19⋊C8—41no—
118C2×C19⋊C8—41no—
119C2×C19⋊C8—41no—
120C2×C19⋊C8—41no—
121C2×C19⋊C8—41no—
122C2×C19⋊C8—41no—
123C2×C19⋊C8—41no—
124#7790—191nomaximal, Sylow
125C23×C19—22no—
126C23×C19—41no—
127C23×C19—41no—
128C23×C19—41no—
129C23×C19—41no—
130C23×C19—41no—
131C23×C19—41no—
132C23×C19—41no—
133C23×C19—41no—
134C23×C19—41no—
135C23×C19—41no—
136C23×C19—41no—
137C23×C19—41no—
138C23×C19—41no—
139C23×C19#12011yescharacteristic
140D4×C19—42no—
141D4×C19—42no—
142D4×C19—81no—
143D4×C19—81no—
144D4×C19—84no—
145D4×C19—84no—
146C2×C4×C19—21no—
147C2×C4×C19—21no—
148C2×C4×C19—21no—
149C2×C4×C19—21no—
150C2×C4×C19—21no—
151C2×C4×C19—21no—
152C2×C4×C19—22no—
153C2×C4×C19—41no—
154C2×C4×C19—41no—
155C2×C4×C19—41no—
156C2×C4×C19—41no—
157C2×C4×C19—41no—
158C2×C4×C19—41no—
159C2×C4×C19—41no—
160C2×C4×C19—41no—
161C2×C4×C19—41no—
162C2×C4×C19—41no—
163C2×C4×C19—41no—
164C2×C4×C19—84no—
165C2×C4×C19C2×D811yescharacteristic
166C2×C4×C19C2×D811yescharacteristic
167C2×C4×C19#13511yescharacteristic
168C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
169C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
170C2×C4×C19#13711yescharacteristic
171C2×Dic19—81no—
172C2×Dic19—81no—
173C2×Dic19—81no—
174C19⋊C8—42no—
175C19⋊C8—42no—
176C19⋊C8—81no—
177#2682D1911yescharacteristic
178#2093—191no—
179#2083—191no—
180#2071—191no—
181#1271—191no—
182#1270—191no—
183#1270—191no—
184C22×C19—42no—
185C22×C19—42no—
186C22×C19—42no—
187C22×C19—81no—
188C22×C19—81no—
189C22×C19—81no—
190C22×C19—81no—
191C22×C19—81no—
192C22×C19—81no—
193C22×C19—81no—
194C22×C19—81no—
195C22×C19—81no—
196C22×C19—81no—
197C22×C19—81no—
198C22×C19#44711yescharacteristic
199C22×C19#44711yescharacteristic
200C22×C19#45211yescharacteristic
201C22×C19#45311yescharacteristic
202C22×C19#45511yescharacteristic
203C22×C19#45611yescharacteristic
204C22×C19#45811yescharacteristic
205C4×C19—21no—
206C4×C19—21no—
207C4×C19—21no—
208C4×C19—21no—
209C4×C19—21no—
210C4×C19—21no—
211C4×C19—42no—
212C4×C19—81no—
213C4×C19—81no—
214C4×C19—81no—
215Dic19—161no—
216C2×#123—21no—
217C2×#121—21no—
218C2×#107—381no—
219C2×#107—381no—
220C2×#102—381no—
221C2×#102—381no—
222#396—21no—
223#394—21no—
224#392—21no—
225#390C2×D1911yescharacteristic
226#390C2×D1911yescharacteristic
227#389C2×D1911yescharacteristic
228#385—21no—
229#384—191no—
230#340—381no—
231#340—381no—
232#336—191no—
233#336—191no—
234#336—191no—
235C2×C19—82no—
236C2×C19—161no—
237C2×C19#160711yescharacteristic
238C2×C19#161011yescharacteristic
239C2×C19#161811yescharacteristic
240C2×C19#161911yescharacteristic
241C2×C19#164111yescharacteristic
242C2×C19#164711yescharacteristic
243C2×C19#166111yescharacteristic
244C22×D4—21no—
245C22×D4—21no—
246C22×D4C22⋊D1911yescharacteristic
247C22×D4C22⋊D1911yescharacteristic
248C23×C4—21no—
249C22×C8—381no—
250C22×C8—381no—
251C22×C8—381no—
252#123—42no—
253#123—42no—
254#121—42no—
255#121—42no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—381no—
259C2×C4⋊C4—381no—
260C2×C4⋊C4—381no—
261C2×C4⋊C4C22⋊D1911yescharacteristic
262C2×C4⋊C4C22⋊D1911yescharacteristic
263C2×C4⋊C4C22⋊D1911yescharacteristic
264C2×C4⋊C4C22⋊D1911yescharacteristic
265C2×C22⋊C4—21no—
266C2×C22⋊C4—21no—
267C2×C22⋊C4—21no—
268C2×C22⋊C4—21no—
269C2×C22⋊C4—21no—
270C2×C22⋊C4—21no—
271C2×C22⋊C4—21no—
272C2×C42C22×D1911yescharacteristic
273#107—762no—
274#107—762no—
275#102—762no—
276#102—762no—
277#95—21no—
278#95—21no—
279C19#779011yescharacteristic, complemented, Sylow
280C24—21no—
281C24—21no—
282C2×D4—21no—
283C2×D4—21no—
284C2×D4—21no—
285C2×D4—41no—
286C2×D4—41no—
287C2×D4—41no—
288C2×D4—41no—
289C2×D4—42no—
290C2×D4—42no—
291C2×D4—42no—
292C2×D4—81no—
293C2×D4—81no—
294C2×D4—81no—
295C2×D4#6452512yes—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—42no—
301C22×C4—42no—
302C22×C4—81no—
303C22×C4—761no—
304C22×C4C2×C22⋊D1911yescharacteristic
305C22×C4C2×C22⋊D1911yescharacteristic
306C22×C4C2×C22⋊D1911yescharacteristic
307C2×C8—382no—
308C2×C8—382no—
309C2×C8—761no—
310C2×C8—761no—
311C2×C8—761no—
312C2×C8—761no—
313C2×C8—761no—
314C2×C8—761no—
315C2×C8—761no—
316C4⋊C4—21no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—42no—
321C4⋊C4—41no—
322C4⋊C4—41no—
323C4⋊C4—761no—
324C4⋊C4—761no—
325C4⋊C4—761no—
326C4⋊C4—761no—
327C4⋊C4—761no—
328C4⋊C4—761no—
329C4⋊C4#6452512yes—
330C22⋊C4—42no—
331C22⋊C4—42no—
332C22⋊C4—41no—
333C22⋊C4—41no—
334C22⋊C4—41no—
335C22⋊C4—41no—
336C22⋊C4—41no—
337C22⋊C4—41no—
338C22⋊C4—41no—
339C22⋊C4—41no—
340C22⋊C4—81no—
341C42—41no—
342C23—22no—
343C23—41no—
344C23—41no—
345C23—41no—
346C23—41no—
347C23—41no—
348C23—41no—
349C23—41no—
350C23—41no—
351C23—41no—
352C23—41no—
353C23—41no—
354C23—41no—
355C23—41no—
356C23#1059739911yescharacteristic
357D4—42no—
358D4—42no—
359D4—81no—
360D4—81no—
361D4—84no—
362D4—84no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—22no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—84no—
382C2×C4—1521no—
383C2×C4—1521no—
384C2×C4—1521no—
385C2×C4C2×#6452511yescharacteristic
386C2×C4C2×#6452511yescharacteristic
387C2×C4#1059737811yescharacteristic
388C2×C4#1059737811yescharacteristic
389C2×C4#1059739611yescharacteristic
390C2×C4#1059739711yescharacteristic
391C8—762no—
392C8—762no—
393C8—1521no—
394C22—42no—
395C22—42no—
396C22—42no—
397C22—81no—
398C22—81no—
399C22—81no—
400C22—81no—
401C22—81no—
402C22—81no—
403C22—81no—
404C22—81no—
405C22—81no—
406C22—81no—
407C22—81no—
408C22#1192667811yescharacteristic
409C22#1192667811yescharacteristic
410C22#1192670611yescharacteristic
411C22#1192671211yescharacteristic
412C22#1192672211yescharacteristic
413C22#1192672711yescharacteristic
414C22#1192673411yescharacteristic
415C4—21no—
416C4—21no—
417C4—21no—
418C4—21no—
419C4—21no—
420C4—21no—
421C4—42no—
422C4—81no—
423C4—81no—
424C4—81no—
425C4—3041no—
426C2—82no—
427C2—161no—
428C2#1456262111yescharacteristic
429C2#1456263811yescharacteristic
430C2#1456268311yescharacteristic
431C2#1456268911yescharacteristic
432C2#1456282811yescharacteristic
433C2#1456287011yescharacteristic
434C2#1456295211yescharacteristic
subgroupG/H
centerC23#10597399
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
Fitting, prime radicalC19×#2682C2
socleC23×C19#120
hypercenter#2682D19
hypocenterC19#7790
LCSG ▷ C2×C42×C19 ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2682

Complements

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

NH ≅ G/Ntype
1. #14565163C2semidirect
2. #14565106C2semidirect
3. #14565038C2semidirect
4. #14561458C2semidirect
5. #14561456C2semidirect
6. #14561456C2semidirect
279. C19#7790semidirect

Maximal subgroups

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

subgroupindex
#145651632
#145651062
#145650382
#145614582
#145614562
C19×#26822
#779019