Finite Group Databasebeta

← #18085323

Subgroups — #18085323

Order 4864.

754 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11926920C211yesmaximal, characteristic
2C2×#11926891C211yesmaximal, characteristic, complemented
3C2×#11926890C211yesmaximal, characteristic, complemented
4#14564440C211yesmaximal, characteristic, complemented
5#14564436C211yesmaximal, characteristic, complemented
6C19⋊#1273C211yesmaximal, characteristic, complemented
7C19×#1957C211yesmaximal, characteristic, complemented
8C22×#64525—22no—
9C2×#10597315C2211yescharacteristic
10C2×#10597320C2211yescharacteristic
11#11926920—22no—
12#11926920—22no—
13#11926891—22no—
14#11926891—22no—
15#11926890—22no—
16#11926890—22no—
17C2×#10597267—22no—
18C2×#10597278—22no—
19C2×#10597289—22no—
20C2×#10597266—22no—
21C2×C4×C19⋊C8C2211yescharacteristic
22C2×C4×C19⋊C8C2211yescharacteristic
23C2×C19×#127C2211yescharacteristic
24C2×C19×#102—22no—
25C2×C4×C8×C19C2211yescharacteristic
26C19×#384C2211yescharacteristic
27C22×D4×C19—21no—
28C22×D4×C19—21no—
29C22×D4×C19—21no—
30C22×D76—21no—
31C22×D76—21no—
32C22×D76—21no—
33C22×Dic38—21no—
34C22×C8×C19D412yes—
35C19×#127—21no—
36C19×#127—21no—
37C19×#127—21no—
38C19×#127D412yes—
39C2×C4⋊C4×C19—21no—
40C2×C4⋊C4×C19—21no—
41C2×C4⋊C4×C19—21no—
42C2×C42×C19C2311yescharacteristic
43C2×#64525—28no—
44C2×#64525—44no—
45C2×#64525—44no—
46C2×C4⋊Dic19—21no—
47C2×C4⋊Dic19—21no—
48C22×C19⋊C8D412yes—
49C22×C19⋊C8D412yes—
50#10597320—21no—
51#10597320—21no—
52#10597320—21no—
53#10597320D412yes—
54#10597315—21no—
55#10597315—21no—
56#10597315—21no—
57#10597315D412yes—
58C19×#102—44no—
59C4×C8×C19—21no—
60C4×C8×C19—21no—
61#10597289—28no—
62#10597278—28no—
63#10597267—44no—
64#10597266—44no—
65C4×C19⋊C8—21no—
66C4×C19⋊C8—21no—
67C4×C19⋊C8—21no—
68C4×C19⋊C8—21no—
69C24×C19—41no—
70C23×D19—41no—
71C2×D4×C19—22no—
72C2×D4×C19—22no—
73C2×D4×C19—22no—
74C2×D4×C19—41no—
75C2×D4×C19—41no—
76C2×D4×C19—41no—
77C2×D4×C19—42no—
78C2×D4×C19—42no—
79C2×D4×C19—42no—
80C2×D4×C19—42no—
81C2×D4×C19—42no—
82C2×D4×C19—42no—
83C22×C4×C19—41no—
84C22×C4×C19C2×D411yescharacteristic
85C22×C4×C19C2×D411yescharacteristic
86C22×C4×C19C2×D411yescharacteristic
87C22×Dic19—41no—
88C2×D76—22no—
89C2×D76—22no—
90C2×D76—22no—
91C2×D76—42no—
92C2×D76—42no—
93C2×D76—42no—
94C2×D76—42no—
95C2×D76—42no—
96C2×D76—42no—
97C2×D76—41no—
98C2×D76—41no—
99C2×D76—41no—
100C2×Dic38—22no—
101C2×Dic38—42no—
102C2×Dic38—42no—
103C2×Dic38—41no—
104C2×C8×C19—22no—
105C2×C8×C19—22no—
106C2×C8×C19—22no—
107C4⋊C4×C19—42no—
108C4⋊C4×C19—42no—
109C4⋊C4×C19—42no—
110C42×C19C2×D411yescharacteristic
111C42×C19C2×D411yescharacteristic
112C42×C19C2×D411yescharacteristic
113C42×C19#4111yescharacteristic
114#64525—416no—
115C4⋊Dic19—22no—
116C4⋊Dic19—22no—
117C4⋊Dic19—41no—
118C4⋊Dic19—41no—
119C2×C19⋊C8—22no—
120C2×C19⋊C8—22no—
121C2×C19⋊C8—22no—
122C2×C19⋊C8—22no—
123C2×C19⋊C8—22no—
124C2×C19⋊C8D814yes—
125#10307—191nomaximal, Sylow
126C23×C19—42no—
127C23×C19—81no—
128C23×C19—81no—
129C23×C19—81no—
130C23×C19—81no—
131C23×C19—81no—
132C23×C19—81no—
133C23×C19#12711yescharacteristic
134C22×D19—42no—
135C22×D19—81no—
136C22×D19—81no—
137C22×D19—81no—
138C22×D19—81no—
139C22×D19—81no—
140C22×D19—81no—
141D4×C19—44no—
142D4×C19—44no—
143D4×C19—44no—
144D4×C19—82no—
145D4×C19—82no—
146D4×C19—82no—
147C2×C4×C19—81no—
148C2×C4×C19—81no—
149C2×C4×C19—81no—
150C2×C4×C19#12011yescharacteristic
151C2×C4×C19#12011yescharacteristic
152C2×C4×C19#12011yescharacteristic
153C2×C4×C19#12111yescharacteristic
154C2×C4×C19#12111yescharacteristic
155C2×C4×C19#12111yescharacteristic
156C2×C4×C19C2×D812yes—
157C2×C4×C19#13512yes—
158C2×C4×C19#13512yes—
159C2×C4×C19AGL(1,ℤ/8)12yes—
160C2×C4×C19AGL(1,ℤ/8)12yes—
161C2×C4×C19AGL(1,ℤ/8)12yes—
162C2×Dic19—42no—
163C2×Dic19—81no—
164C2×Dic19—81no—
165D76—44no—
166D76—44no—
167D76—44no—
168D76—82no—
169D76—82no—
170D76—82no—
171Dic38—44no—
172Dic38—82no—
173C8×C19—42no—
174C19⋊C8—24no—
175C19⋊C8—42no—
176C2×#493—191no—
177C2×#486—191no—
178C2×#486—191no—
179#1957—191no—
180#1957D1911yescharacteristic, complemented
181#1956—191no—
182#1273—191no—
183C22×C19—82no—
184C22×C19—82no—
185C22×C19—82no—
186C22×C19—161no—
187C22×C19—161no—
188C22×C19—161no—
189C22×C19—161no—
190C22×C19#39211yescharacteristic
191C22×C19#49311yescharacteristic
192C22×C19#49511yescharacteristic
193C22×C19#49511yescharacteristic
194C22×C19#49611yescharacteristic
195C22×C19#49611yescharacteristic
196C22×C19#49611yescharacteristic
197C2×D19—82no—
198C2×D19—82no—
199C2×D19—82no—
200C2×D19—161no—
201C2×D19—161no—
202C2×D19—161no—
203C2×D19—161no—
204C4×C19—161no—
205C4×C19#44712yes—
206C4×C19#44912yes—
207C4×C19#44912yes—
208C4×C19#45912yes—
209C4×C19#46312yes—
210C4×C19#46312yes—
211Dic19—82no—
212C22×D8—382no—
213C2×C4⋊Q8—191no—
214C2×#127—191no—
215C2×#127C2×D1911yescharacteristic
216#493—382no—
217#493—382no—
218#486—382no—
219#486—382no—
220#486—382no—
221#486—382no—
222C2×#103—382no—
223C2×#102—22no—
224C2×#102—382no—
225C2×#102—382no—
226C2×#102—382no—
227C2×C4×C8—191no—
228C2×C4×C8—191no—
229C2×C4×C8C2×D1911yescharacteristic
230#384C2×D1911yescharacteristic
231C2×C19—162no—
232C2×C19#170911yescharacteristic
233C2×C19#171711yescharacteristic
234C2×C19#171711yescharacteristic
235C2×C19#172111yescharacteristic
236C2×C19#201111yescharacteristic
237C2×C19#201211yescharacteristic
238C2×C19#201211yescharacteristic
239D19—162no—
240C22×Q8—381no—
241C22×D4—21no—
242C22×D4—21no—
243C22×D4—21no—
244C22×D4—381no—
245C22×D4—381no—
246C22×D4—381no—
247C2×D8—388no—
248C2×D8—764no—
249C2×D8—764no—
250C22×C8—192no—
251C22×C8—192no—
252C22×C8C22⋊D1912yes—
253C4⋊Q8—192no—
254C4⋊Q8—381no—
255C4⋊Q8—381no—
256C4⋊Q8—381no—
257#127—21no—
258#127—21no—
259#127—21no—
260#127—192no—
261#127—381no—
262#127—381no—
263#127—381no—
264#127D7612yes—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—381no—
269C2×C4⋊C4—381no—
270C2×C42C22×D1911yescharacteristic
271#103—764no—
272#102—44no—
273#102—388no—
274#102—388no—
275#102—764no—
276C4×C8—21no—
277C4×C8—21no—
278C4×C8—381no—
279C4×C8—381no—
280C4×C8—381no—
281C4×C8—381no—
282C19#1030711yescharacteristic, complemented, Sylow
283C24—41no—
284C24—761no—
285C2×Q8—382no—
286C2×Q8—761no—
287C2×Q8—762no—
288C2×Q8—762no—
289C2×D4—22no—
290C2×D4—22no—
291C2×D4—22no—
292C2×D4—42no—
293C2×D4—41no—
294C2×D4—42no—
295C2×D4—41no—
296C2×D4—41no—
297C2×D4—42no—
298C2×D4—42no—
299C2×D4—42no—
300C2×D4—42no—
301C2×D4—382no—
302C2×D4—382no—
303C2×D4—382no—
304C2×D4—761no—
305C2×D4—762no—
306C2×D4—762no—
307C2×D4—761no—
308C2×D4—761no—
309C2×D4—762no—
310C2×D4—762no—
311C2×D4—762no—
312C2×D4—762no—
313C22×C4—41no—
314C22×C4—761no—
315C22×C4D4×D1911yescharacteristic
316C22×C4D4×D1911yescharacteristic
317C22×C4C2×C22⋊D1911yescharacteristic
318D8—7616no—
319C2×C8—22no—
320C2×C8—22no—
321C2×C8—22no—
322C2×C8—194no—
323C2×C8—382no—
324C2×C8—382no—
325C2×C8—382no—
326C2×C8—382no—
327C2×C8—382no—
328C4⋊C4—42no—
329C4⋊C4—42no—
330C4⋊C4—42no—
331C4⋊C4—382no—
332C4⋊C4—382no—
333C4⋊C4—761no—
334C4⋊C4—761no—
335C42C2×D7611yescharacteristic
336C42#6454111yescharacteristic
337C42D4×D1911yescharacteristic
338C42D4×D1911yescharacteristic
339C23—42no—
340C23—81no—
341C23—81no—
342C23—81no—
343C23—81no—
344C23—81no—
345C23—81no—
346C23—762no—
347C23—1521no—
348C23—1521no—
349C23—1521no—
350C23—1521no—
351C23—1521no—
352C23—1521no—
353C23#1059738611yescharacteristic
354Q8—764no—
355Q8—1522no—
356D4—44no—
357D4—44no—
358D4—44no—
359D4—82no—
360D4—82no—
361D4—82no—
362D4—764no—
363D4—764no—
364D4—764no—
365D4—1522no—
366D4—1522no—
367D4—1522no—
368C2×C4—81no—
369C2×C4—81no—
370C2×C4—81no—
371C2×C4—762no—
372C2×C4—1521no—
373C2×C4—1521no—
374C2×C4#1059732811yescharacteristic
375C2×C4#1059732811yescharacteristic
376C2×C4#1059733011yescharacteristic
377C2×C4#1059733011yescharacteristic
378C2×C4D8×D1912yes—
379C2×C4#1059735712yes—
380C2×C4#1059736012yes—
381C2×C4#1059736212yes—
382C2×C4#1059737611yescharacteristic
383C2×C4#1059737812yes—
384C2×C4#1059738311yescharacteristic
385C2×C4#1059739612yes—
386C8—42no—
387C8—384no—
388C8—762no—
389C22—82no—
390C22—82no—
391C22—82no—
392C22—161no—
393C22—161no—
394C22—161no—
395C22—161no—
396C22—3041no—
397C22—3041no—
398C22—3041no—
399C22—3041no—
400C22—1522no—
401C22—1522no—
402C22—1522no—
403C22#1192645311yescharacteristic
404C22#1192691911yescharacteristic
405C22#1192692511yescharacteristic
406C22#1192692611yescharacteristic
407C22#1192693011yescharacteristic
408C22#1192693111yescharacteristic
409C22#1192693211yescharacteristic
410C4—161no—
411C4—1522no—
412C4#1192667912yes—
413C4#1192668712yes—
414C4#1192669012yes—
415C4#1192673812yes—
416C4#1192675812yes—
417C4#1192675912yes—
418C2—162no—
419C2—3042no—
420C2#1456323911yescharacteristic
421C2#1456327211yescharacteristic
422C2#1456327511yescharacteristic
423C2#1456330011yescharacteristic
424C2#1456470711yescharacteristic
425C2#1456471111yescharacteristic
426C2#1456471411yescharacteristic
subgroupG/H
centerC23#10597386
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#1957C2
socleC23×C19#127
prime radicalC2×#11926920C2
hypercenter#1957D19
hypocenterC19#10307
LCSG ▷ C2×C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1957

Complements

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

NH ≅ G/Ntype
2. C2×#11926891C2semidirect
3. C2×#11926890C2semidirect
4. #14564440C2semidirect
5. #14564436C2semidirect
6. C19⋊#1273C2semidirect
7. C19×#1957C2semidirect
180. #1957D19semidirect
282. C19#10307semidirect

Maximal subgroups

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

subgroupindex
C2×#119269202
C2×#119268912
C2×#119268902
#145644402
#145644362
C19⋊#12732
C19×#19572
#1030719