Finite Group Databasebeta

← #18086387

Subgroups — #18086387

Order 4864.

474 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11926835C211yesmaximal, characteristic
2#14564596C211yesmaximal, characteristic, complemented
3#14564429C211yesmaximal, characteristic
4#14563636C211yesmaximal, characteristic
5C2×#11926292C211yesmaximal, characteristic, complemented
6#14561519C211yesmaximal, characteristic, complemented
7C2×C19×#334C211yesmaximal, characteristic, complemented
8C2×#10597315C2211yescharacteristic
9C2×C4×D76C2211yescharacteristic
10#11926835—22no—
11#11926835—22no—
12C2×#10597274—21no—
13C2×C4⋊(C19⋊C8)C2211yescharacteristic
14C2×#10597278—21no—
15C2×#10597278—21no—
16C2×(C2×D19)⋊C8—21no—
17C2×(C2×D19)⋊C8—21no—
18#11926414C2211yescharacteristic
19#11926307—21no—
20#11926307—21no—
21#11926307—21no—
22#11926292—22no—
23C2×C19×C4⋊C8C2211yescharacteristic
24C2×C19×C4⋊C8C2211yescharacteristic
25C2×C4×C8×C19C2211yescharacteristic
26C19×#334—22no—
27C22×D76D411yescharacteristic
28C22×C4×D19—21no—
29C22×Dic38—21no—
30C22×C8×C19—21no—
31C22×C8×C19—21no—
32C22×C8×C19D411yescharacteristic
33C22×C8×C19D411yescharacteristic
34C2×C42×C19C2311yescharacteristic
35C2×(C2×D19)⋊C4—21no—
36C2×C4⋊Dic19—21no—
37C2×C4⋊Dic19—21no—
38C2×C4⋊Dic19—21no—
39C2×C4⋊Dic19—21no—
40C2×C4⋊Dic19—21no—
41C2×C4⋊Dic19D411yescharacteristic
42C22×C19⋊C8—21no—
43C4×D76—21no—
44C4×D76—21no—
45C4×D76—21no—
46C4×D76—21no—
47#10597315—21no—
48#10597315—21no—
49#10597315—21no—
50#10597315D412yes—
51C19×C4⋊C8—21no—
52C19×C4⋊C8—21no—
53C19×C4⋊C8—21no—
54C19×C4⋊C8D412yes—
55C4×C8×C19—21no—
56C4×C8×C19—21no—
57#10597278—24no—
58#10597278—42no—
59(C2×D19)⋊C8—42no—
60(C2×D19)⋊C8—42no—
61#10597274—24no—
62C4⋊(C19⋊C8)—21no—
63C4⋊(C19⋊C8)—21no—
64C23×D19—21no—
65C22×C4×C19C2×D411yescharacteristic
66C22×C4×C19C2×D411yescharacteristic
67C22×C4×C19#4111yescharacteristic
68C22×Dic19—21no—
69C22×Dic19—41no—
70C22×Dic19—41no—
71C2×D76—21no—
72C2×D76—21no—
73C2×D76—21no—
74C2×D76—21no—
75C2×D76—21no—
76C2×D76SD1612yes—
77C2×C4×D19—41no—
78C2×C4×D19—41no—
79C2×C4×D19—41no—
80C2×C4×D19—41no—
81C2×C4×D19—41no—
82C2×C4×D19—41no—
83C2×Dic38—22no—
84C2×Dic38—41no—
85C2×Dic38—81no—
86C2×Dic38—81no—
87C2×C8×C19—21no—
88C2×C8×C19—21no—
89C2×C8×C19—22no—
90C2×C8×C19—21no—
91C2×C8×C19—21no—
92C2×C8×C19—21no—
93C2×C8×C19—41no—
94C2×C8×C19—41no—
95C2×C8×C19—41no—
96C2×C8×C19—41no—
97C2×C8×C19—41no—
98C2×C8×C19SD1612yes—
99C42×C19C2×D411yescharacteristic
100C42×C19C2×D411yescharacteristic
101C42×C19#4111yescharacteristic
102C42×C19#4111yescharacteristic
103(C2×D19)⋊C4—41no—
104(C2×D19)⋊C4—41no—
105C4⋊Dic19—21no—
106C4⋊Dic19—22no—
107C4⋊Dic19—22no—
108C4⋊Dic19—21no—
109C4⋊Dic19—41no—
110C4⋊Dic19—41no—
111C4⋊Dic19—41no—
112C4⋊Dic19—41no—
113C4⋊Dic19—41no—
114C4⋊Dic19—41no—
115C4⋊Dic19—81no—
116C2×C19⋊C8—41no—
117C2×C19⋊C8—41no—
118C2×C19⋊C8—41no—
119#10480—191nomaximal, Sylow
120C23×C19#12111yescharacteristic
121C22×D19—22no—
122C22×D19—41no—
123C22×D19—41no—
124C22×D19—41no—
125C22×D19—41no—
126C22×D19—41no—
127C22×D19—41no—
128C2×C4×C19—21no—
129C2×C4×C19—21no—
130C2×C4×C19#12011yescharacteristic
131C2×C4×C19#12111yescharacteristic
132C2×C4×C19#12111yescharacteristic
133C2×C4×C19#12311yescharacteristic
134C2×C4×C19#12311yescharacteristic
135C2×C4×C19#12411yescharacteristic
136C2×C4×C19C2×SD1611yescharacteristic
137C2×C4×C19C2×SD1611yescharacteristic
138C2×C4×C19#13511yescharacteristic
139C2×C4×C19#13511yescharacteristic
140C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
141C2×C4×C19#13711yescharacteristic
142C2×C4×C19#13711yescharacteristic
143C2×C4×C19#13711yescharacteristic
144C2×Dic19—42no—
145C2×Dic19—41no—
146C2×Dic19—41no—
147C2×Dic19—41no—
148C2×Dic19—81no—
149C2×Dic19—81no—
150C2×Dic19—81no—
151C2×Dic19—81no—
152C2×Dic19—81no—
153D76—22no—
154D76—22no—
155D76—41no—
156D76—41no—
157C4×D19—81no—
158C4×D19—81no—
159C4×D19—81no—
160C4×D19—81no—
161Dic38—82no—
162Dic38—82no—
163C8×C19—22no—
164C8×C19—42no—
165C8×C19—41no—
166C8×C19—81no—
167C19⋊C8—81no—
168C2×#476—191no—
169#1990—191no—
170#1954—191no—
171#1802—191no—
172C2×#334D1911yescharacteristic, complemented
173C2×#333—191no—
174#1296—191no—
175C22×C19#39411yescharacteristic
176C22×C19#46111yescharacteristic
177C22×C19#46311yescharacteristic
178C22×C19#46511yescharacteristic
179C22×C19#47011yescharacteristic
180C22×C19#47111yescharacteristic
181C22×C19#47211yescharacteristic
182C2×D19—42no—
183C2×D19—42no—
184C2×D19—42no—
185C2×D19—81no—
186C2×D19—81no—
187C2×D19—81no—
188C2×D19—81no—
189C4×C19—21no—
190C4×C19—21no—
191C4×C19#44811yescharacteristic
192C4×C19#45211yescharacteristic
193C4×C19#46011yescharacteristic
194C4×C19#46411yescharacteristic
195C4×C19#46511yescharacteristic
196C4×C19#46811yescharacteristic
197C4×C19#48311yescharacteristic
198C4×C19#48511yescharacteristic
199Dic19—82no—
200Dic19—81no—
201Dic19—161no—
202C2×C4⋊Q8—191no—
203C2×C4×D4—191no—
204#476—382no—
205#476—382no—
206C2×#106—381no—
207C2×C4⋊C8—191no—
208C2×C4⋊C8C2×D1911yescharacteristic
209C2×C4⋊C8C2×D1911yescharacteristic
210C2×#102—381no—
211C2×#102—381no—
212C2×C22⋊C8—381no—
213C2×C22⋊C8—381no—
214C2×C4×C8C2×D1911yescharacteristic
215#384—191no—
216#340—381no—
217#340—381no—
218#340—381no—
219#334—22no—
220#333—382no—
221C2×C19#167111yescharacteristic
222C2×C19#167711yescharacteristic
223C2×C19#169511yescharacteristic
224C2×C19#170311yescharacteristic
225C2×C19#203511yescharacteristic
226C2×C19#205111yescharacteristic
227C2×C19#205511yescharacteristic
228D19—82no—
229C22×Q8—381no—
230C22×D4—191no—
231C23×C4—381no—
232C22×C8—21no—
233C22×C8—21no—
234C22×C8—381no—
235C22×C8D7611yescharacteristic
236C22×C8D7611yescharacteristic
237C4⋊Q8—192no—
238C4⋊Q8—381no—
239C4⋊Q8—381no—
240C4⋊Q8—381no—
241C4×D4—381no—
242C4×D4—381no—
243C4×D4—381no—
244C4×D4—381no—
245C2×C4⋊C4—191no—
246C2×C4⋊C4—381no—
247C2×C4⋊C4—381no—
248C2×C4⋊C4—381no—
249C2×C4⋊C4—381no—
250C2×C4⋊C4—381no—
251C2×C22⋊C4—381no—
252C2×C42C22×D1911yescharacteristic
253#106—384no—
254C4⋊C8—21no—
255C4⋊C8—21no—
256C4⋊C8—21no—
257C4⋊C8—381no—
258C4⋊C8—381no—
259C4⋊C8C22⋊D1912yes—
260#102—384no—
261#102—762no—
262C22⋊C8—762no—
263C22⋊C8—762no—
264C4×C8—21no—
265C4×C8—21no—
266C19#1048011yescharacteristic, complemented, Sylow
267C24—381no—
268C2×Q8—382no—
269C2×Q8—761no—
270C2×Q8—1521no—
271C2×Q8—1521no—
272C2×D4—192no—
273C2×D4—381no—
274C2×D4—381no—
275C2×D4—381no—
276C2×D4—381no—
277C2×D4—381no—
278C22×C4—381no—
279C22×C4—761no—
280C22×C4—761no—
281C22×C4—761no—
282C22×C4—761no—
283C22×C4—761no—
284C22×C4—761no—
285C22×C4—761no—
286C22×C4—761no—
287C22×C4C2×D7611yescharacteristic
288C22×C4D4×D1911yescharacteristic
289C22×C4#6454511yescharacteristic
290C2×C8—21no—
291C2×C8—21no—
292C2×C8—21no—
293C2×C8—22no—
294C2×C8—21no—
295C2×C8—21no—
296C2×C8—41no—
297C2×C8—41no—
298C2×C8—41no—
299C2×C8—41no—
300C2×C8—41no—
301C2×C8—761no—
302C2×C8—761no—
303C2×C8—761no—
304C2×C8#6451612yes—
305C4⋊C4—382no—
306C4⋊C4—381no—
307C4⋊C4—381no—
308C4⋊C4—382no—
309C4⋊C4—761no—
310C4⋊C4—761no—
311C4⋊C4—761no—
312C4⋊C4—761no—
313C4⋊C4—761no—
314C4⋊C4—761no—
315C4⋊C4—1521no—
316C22⋊C4—761no—
317C22⋊C4—761no—
318C42#6454111yescharacteristic
319C42D4×D1911yescharacteristic
320C42#6454511yescharacteristic
321C42C2×C22⋊D1911yescharacteristic
322C23—382no—
323C23—761no—
324C23—761no—
325C23—761no—
326C23—761no—
327C23—761no—
328C23—761no—
329C23#1059734111yescharacteristic
330Q8—1522no—
331Q8—1522no—
332D4—382no—
333D4—382no—
334D4—761no—
335D4—761no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—761no—
339C2×C4—762no—
340C2×C4—761no—
341C2×C4—761no—
342C2×C4—1521no—
343C2×C4—1521no—
344C2×C4—1521no—
345C2×C4—1521no—
346C2×C4—1521no—
347C2×C4—1521no—
348C2×C4—1521no—
349C2×C4—1521no—
350C2×C4—1521no—
351C2×C4#1059734011yescharacteristic
352C2×C4#1059734011yescharacteristic
353C2×C4#1059734111yescharacteristic
354C2×C4C2×#6451611yescharacteristic
355C2×C4#1059735011yescharacteristic
356C2×C4#1059735411yescharacteristic
357C2×C4#1059735511yescharacteristic
358C2×C4SD16×D1911yescharacteristic
359C2×C4#1059736111yescharacteristic
360C2×C4#1059736111yescharacteristic
361C2×C4#1059736211yescharacteristic
362C2×C4#1059737611yescharacteristic
363C2×C4#1059738311yescharacteristic
364C2×C4#1059739311yescharacteristic
365C8—22no—
366C8—41no—
367C8—42no—
368C8—81no—
369C8—1521no—
370C22—762no—
371C22—762no—
372C22—762no—
373C22—1521no—
374C22—1521no—
375C22—1521no—
376C22—1521no—
377C22#1192646111yescharacteristic
378C22#1192675011yescharacteristic
379C22#1192676011yescharacteristic
380C22#1192677411yescharacteristic
381C22#1192680311yescharacteristic
382C22#1192680811yescharacteristic
383C22#1192681511yescharacteristic
384C4—21no—
385C4—21no—
386C4—3041no—
387C4—1522no—
388C4—1521no—
389C4#1192668111yescharacteristic
390C4#1192670311yescharacteristic
391C4#1192674511yescharacteristic
392C4#1192676711yescharacteristic
393C4#1192677311yescharacteristic
394C4#1192679011yescharacteristic
395C4#1192687611yescharacteristic
396C4#1192688811yescharacteristic
397C2—1522no—
398C2#1456301111yescharacteristic
399C2#1456304511yescharacteristic
400C2#1456315911yescharacteristic
401C2#1456321111yescharacteristic
402C2#1456483311yescharacteristic
403C2#1456492911yescharacteristic
404C2#1456495311yescharacteristic
subgroupG/H
centerC23#10597341
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC2×C19×#334C2
socleC23×C19#121
prime radicalC22×D76D4
hypercenterC2×#334D19
hypocenterC19#10480
LCSG ▷ C2×C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#334

Complements

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

NH ≅ G/Ntype
2. #14564596C2semidirect
5. C2×#11926292C2semidirect
6. #14561519C2semidirect
7. C2×C19×#334C2semidirect
172. C2×#334D19semidirect
266. C19#10480semidirect

Maximal subgroups

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

subgroupindex
C2×#119268352
#145645962
#145644292
#145636362
C2×#119262922
#145615192
C2×C19×#3342
#1048019