Finite Group Databasebeta

← #18085087

Subgroups — #18085087

Order 4864.

646 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11926891C211yesmaximal, characteristic, complemented
2C2×#11926834C211yesmaximal, characteristic, complemented
3C2×#11926739C211yesmaximal, characteristic
4C2×#11926292C211yesmaximal, characteristic, complemented
5C2×#11926287C211yesmaximal, characteristic, complemented
6#14561470C211yesmaximal, characteristic, complemented
7C19×#1954C211yesmaximal, characteristic, complemented
8C22×#64525—21no—
9C2×#10597315C2211yescharacteristic
10C2×#10597320C2211yescharacteristic
11#11926891—22no—
12#11926891—22no—
13#11926834—22no—
14#11926834—22no—
15#11926739—22no—
16#11926739—22no—
17C2×#10597265—21no—
18C2×C4⋊(C19⋊C8)C2211yescharacteristic
19C2×C4⋊(C19⋊C8)C2211yescharacteristic
20C2×#10597278—22no—
21C2×#10597289—21no—
22C2×#10597266—21no—
23#11926292—22no—
24#11926287—22no—
25C2×C4×D4×C19C2211yescharacteristic
26C2×C19×C4⋊C8C2211yescharacteristic
27C2×C19×C22⋊C8—22no—
28C2×C4×C8×C19C2211yescharacteristic
29C22×D4×C19D411yescharacteristic
30C23×C4×C19—21no—
31C22×D76—21no—
32C22×D76—21no—
33C22×D76—21no—
34C22×Dic38—21no—
35C22×C8×C19—21no—
36C22×C8×C19D412yes—
37C4×D4×C19—21no—
38C4×D4×C19—21no—
39C4×D4×C19—21no—
40C4×D4×C19—21no—
41C2×C4⋊C4×C19D411yescharacteristic
42C2×C22⋊C4×C19—21no—
43C2×C42×C19C2311yescharacteristic
44C2×#64525—24no—
45C2×#64525—42no—
46C2×#64525—42no—
47C2×C4⋊Dic19—21no—
48C2×C4⋊Dic19—21no—
49C22×C19⋊C8—21no—
50C22×C19⋊C8—21no—
51#10597320—21no—
52#10597320—21no—
53#10597320—21no—
54#10597320D412yes—
55#10597315—21no—
56#10597315—21no—
57#10597315—21no—
58#10597315D412yes—
59C19×C4⋊C8—21no—
60C19×C4⋊C8—21no—
61C19×C22⋊C8—44no—
62C4×C8×C19—21no—
63C4×C8×C19—21no—
64#10597289—24no—
65#10597278—28no—
66#10597266—24no—
67#10597265—24no—
68C4⋊(C19⋊C8)—21no—
69C4⋊(C19⋊C8)—21no—
70C4⋊(C19⋊C8)D412yes—
71C4⋊(C19⋊C8)D412yes—
72C24×C19—21no—
73C23×D19—41no—
74C2×D4×C19—21no—
75C2×D4×C19—21no—
76C2×D4×C19—21no—
77C2×D4×C19—21no—
78C2×D4×C19—21no—
79C2×D4×C19SD1612yes—
80C22×C4×C19—21no—
81C22×C4×C19—41no—
82C22×C4×C19—41no—
83C22×C4×C19—42no—
84C22×C4×C19—42no—
85C22×C4×C19C2×D411yescharacteristic
86C22×C4×C19C2×D411yescharacteristic
87C22×C4×C19#4111yescharacteristic
88C22×Dic19—41no—
89C2×D76—22no—
90C2×D76—22no—
91C2×D76—22no—
92C2×D76—41no—
93C2×D76—42no—
94C2×D76—41no—
95C2×D76—41no—
96C2×D76—42no—
97C2×D76—41no—
98C2×D76—41no—
99C2×D76—41no—
100C2×D76—41no—
101C2×D76—82no—
102C2×Dic38—22no—
103C2×Dic38—41no—
104C2×Dic38—82no—
105C2×C8×C19—22no—
106C2×C8×C19—22no—
107C2×C8×C19—22no—
108C2×C8×C19—41no—
109C2×C8×C19—42no—
110C4⋊C4×C19—21no—
111C4⋊C4×C19—21no—
112C22⋊C4×C19—41no—
113C22⋊C4×C19—41no—
114C42×C19C2×D411yescharacteristic
115C42×C19C2×D411yescharacteristic
116C42×C19C2×D411yescharacteristic
117C42×C19C2×D411yescharacteristic
118#64525—48no—
119C4⋊Dic19—22no—
120C4⋊Dic19—22no—
121C4⋊Dic19—41no—
122C4⋊Dic19—41no—
123C2×C19⋊C8—22no—
124C2×C19⋊C8—22no—
125C2×C19⋊C8—41no—
126C2×C19⋊C8—41no—
127C2×C19⋊C8—41no—
128C2×C19⋊C8—41no—
129#10267—191nomaximal, Sylow
130C23×C19—22no—
131C23×C19—41no—
132C23×C19—42no—
133C23×C19—41no—
134C23×C19—42no—
135C23×C19#12111yescharacteristic
136C22×D19—42no—
137C22×D19—82no—
138C22×D19—81no—
139C22×D19—81no—
140C22×D19—82no—
141D4×C19—22no—
142D4×C19—22no—
143D4×C19—41no—
144D4×C19—41no—
145C2×C4×C19—22no—
146C2×C4×C19—41no—
147C2×C4×C19—42no—
148C2×C4×C19—82no—
149C2×C4×C19—81no—
150C2×C4×C19—81no—
151C2×C4×C19#12011yescharacteristic
152C2×C4×C19#12011yescharacteristic
153C2×C4×C19#12011yescharacteristic
154C2×C4×C19#12111yescharacteristic
155C2×C4×C19#12111yescharacteristic
156C2×C4×C19#12711yescharacteristic
157C2×C4×C19C2×SD1611yescharacteristic
158C2×C4×C19#13512yes—
159C2×C4×C19#13511yescharacteristic
160C2×C4×C19AGL(1,ℤ/8)12yes—
161C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
162C2×C4×C19#13711yescharacteristic
163C2×Dic19—42no—
164C2×Dic19—82no—
165D76—44no—
166D76—42no—
167D76—42no—
168D76—82no—
169D76—82no—
170D76—81no—
171D76—81no—
172D76—81no—
173D76—81no—
174Dic38—82no—
175Dic38—82no—
176C8×C19—42no—
177C8×C19—81no—
178C19⋊C8—42no—
179C19⋊C8—42no—
180C2×#486—191no—
181C2×#476—191no—
182C2×#459—191no—
183#1954D1911yescharacteristic, complemented
184C2×#333—191no—
185C2×#331—191no—
186#1277—191no—
187C22×C19—44no—
188C22×C19—42no—
189C22×C19—82no—
190C22×C19—81no—
191C22×C19—81no—
192C22×C19#39211yescharacteristic
193C22×C19#46312yes—
194C22×C19#46511yescharacteristic
195C22×C19#46811yescharacteristic
196C22×C19#47212yes—
197C2×D19—82no—
198C2×D19—82no—
199C2×D19—82no—
200C2×D19—162no—
201C2×D19—162no—
202C4×C19—21no—
203C4×C19—21no—
204C4×C19—81no—
205C4×C19#44811yescharacteristic
206C4×C19#44912yes—
207C4×C19#44911yescharacteristic
208C4×C19#45011yescharacteristic
209C4×C19#45211yescharacteristic
210C4×C19#49511yescharacteristic
211C4×C19#49611yescharacteristic
212Dic19—82no—
213C22×D8—381no—
214C2×C4⋊Q8—191no—
215C2×#127—191no—
216C2×C4×D4C2×D1911yescharacteristic
217#486—382no—
218#486—382no—
219#476—382no—
220#476—382no—
221#459—382no—
222#459—382no—
223C2×#106—381no—
224C2×C4⋊C8—191no—
225C2×C4⋊C8—191no—
226C2×C4⋊C8C2×D1911yescharacteristic
227C2×#102—381no—
228C2×#102—382no—
229C2×#102—381no—
230C2×C22⋊C8—22no—
231C2×C4×C8C2×D1911yescharacteristic
232#333—382no—
233#331—382no—
234C2×C19—82no—
235C2×C19#167712yes—
236C2×C19#169712yes—
237C2×C19#200011yescharacteristic
238C2×C19#201211yescharacteristic
239C2×C19#201811yescharacteristic
240D19—162no—
241C22×Q8—381no—
242C22×D4—381no—
243C22×D4—381no—
244C22×D4—381no—
245C22×D4D7611yescharacteristic
246C23×C4—21no—
247C2×D8—384no—
248C2×D8—762no—
249C2×D8—762no—
250C22×C8—21no—
251C22×C8—381no—
252C22×C8—381no—
253C22×C8C22⋊D1912yes—
254C4⋊Q8—192no—
255C4⋊Q8—381no—
256C4⋊Q8—381no—
257C4⋊Q8—381no—
258#127—192no—
259#127—381no—
260#127—381no—
261#127—381no—
262C4×D4—21no—
263C4×D4—21no—
264C4×D4—21no—
265C4×D4—21no—
266C2×C4⋊C4—381no—
267C2×C4⋊C4—381no—
268C2×C4⋊C4D7611yescharacteristic
269C2×C22⋊C4—21no—
270C2×C42C22×D1911yescharacteristic
271#106—384no—
272C4⋊C8—21no—
273C4⋊C8—21no—
274C4⋊C8—192no—
275C4⋊C8—192no—
276C4⋊C8—381no—
277C4⋊C8—381no—
278#102—384no—
279#102—388no—
280#102—384no—
281C22⋊C8—44no—
282C4×C8—21no—
283C4×C8—21no—
284C19#1026711yescharacteristic, complemented, Sylow
285C24—21no—
286C24—761no—
287C2×Q8—382no—
288C2×Q8—761no—
289C2×Q8—1522no—
290C2×D4—21no—
291C2×D4—21no—
292C2×D4—21no—
293C2×D4—21no—
294C2×D4—21no—
295C2×D4—382no—
296C2×D4—382no—
297C2×D4—382no—
298C2×D4—762no—
299C2×D4—761no—
300C2×D4—762no—
301C2×D4—761no—
302C2×D4—761no—
303C2×D4—761no—
304C2×D4—761no—
305C2×D4—761no—
306C2×D4—761no—
307C2×D4—1522no—
308C2×D4#6451612yes—
309C22×C4—21no—
310C22×C4—42no—
311C22×C4—41no—
312C22×C4—41no—
313C22×C4—42no—
314C22×C4—761no—
315C22×C4C2×D7611yescharacteristic
316C22×C4#6454111yescharacteristic
317C22×C4C2×C22⋊D1911yescharacteristic
318D8—768no—
319C2×C8—22no—
320C2×C8—22no—
321C2×C8—22no—
322C2×C8—42no—
323C2×C8—41no—
324C2×C8—382no—
325C2×C8—382no—
326C2×C8—761no—
327C2×C8—761no—
328C2×C8—761no—
329C2×C8—761no—
330C4⋊C4—21no—
331C4⋊C4—21no—
332C4⋊C4—382no—
333C4⋊C4—382no—
334C4⋊C4—761no—
335C4⋊C4—761no—
336C22⋊C4—41no—
337C22⋊C4—41no—
338C42D4×D1911yescharacteristic
339C42D4×D1911yescharacteristic
340C42D4×D1911yescharacteristic
341C42D4×D1911yescharacteristic
342C23—22no—
343C23—41no—
344C23—42no—
345C23—41no—
346C23—42no—
347C23—762no—
348C23—1521no—
349C23—1522no—
350C23—1522no—
351C23—1521no—
352C23#1059737611yescharacteristic
353Q8—1522no—
354Q8—1522no—
355D4—22no—
356D4—22no—
357D4—41no—
358D4—41no—
359D4—764no—
360D4—762no—
361D4—762no—
362D4—1522no—
363D4—1522no—
364D4—1521no—
365D4—1521no—
366D4—1521no—
367D4—1521no—
368C2×C4—22no—
369C2×C4—41no—
370C2×C4—42no—
371C2×C4—81no—
372C2×C4—81no—
373C2×C4—82no—
374C2×C4—762no—
375C2×C4—1522no—
376C2×C4#1059732811yescharacteristic
377C2×C4#1059732811yescharacteristic
378C2×C4#1059733011yescharacteristic
379C2×C4#1059733011yescharacteristic
380C2×C4C2×#6451611yescharacteristic
381C2×C4#1059735011yescharacteristic
382C2×C4#1059735411yescharacteristic
383C2×C4#1059735511yescharacteristic
384C2×C4#1059737812yes—
385C2×C4#1059738311yescharacteristic
386C2×C4#1059738611yescharacteristic
387C2×C4#1059739612yes—
388C8—42no—
389C8—81no—
390C8—762no—
391C8—762no—
392C22—42no—
393C22—44no—
394C22—82no—
395C22—81no—
396C22—81no—
397C22—3042no—
398C22—3042no—
399C22—1522no—
400C22—1522no—
401C22—1522no—
402C22#1192645311yescharacteristic
403C22#1192675912yes—
404C22#1192677311yescharacteristic
405C22#1192679011yescharacteristic
406C22#1192681412yes—
407C4—21no—
408C4—21no—
409C4—81no—
410C4—1522no—
411C4#1192668511yescharacteristic
412C4#1192668712yes—
413C4#1192669111yescharacteristic
414C4#1192669711yescharacteristic
415C4#1192670811yescharacteristic
416C4#1192692611yescharacteristic
417C4#1192693111yescharacteristic
418C2—82no—
419C2—3042no—
420C2#1456304412yes—
421C2#1456316812yes—
422C2#1456464011yescharacteristic
423C2#1456471111yescharacteristic
424C2#1456474411yescharacteristic
subgroupG/H
centerC23#10597376
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#1954C2
socleC23×C19#121
prime radicalC2×#11926739C2
hypercenter#1954D19
hypocenterC19#10267
LCSG ▷ C2×C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1954

Complements

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

NH ≅ G/Ntype
1. C2×#11926891C2semidirect
2. C2×#11926834C2semidirect
4. C2×#11926292C2semidirect
5. C2×#11926287C2semidirect
6. #14561470C2semidirect
7. C19×#1954C2semidirect
183. #1954D19semidirect
284. C19#10267semidirect

Maximal subgroups

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

subgroupindex
C2×#119268912
C2×#119268342
C2×#119267392
C2×#119262922
C2×#119262872
#145614702
C19×#19542
#1026719