Finite Group Databasebeta

← #18077766

Subgroups — #18077766

Order 4864.

470 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14574194C211yesmaximal, characteristic
2#14572578C211yesmaximal, characteristic, complemented
3#14564553C211yesmaximal, characteristic
4#14562133C211yesmaximal, characteristic, complemented
5#14562033C211yesmaximal, characteristic
6#14561472C211yesmaximal, characteristic, complemented
7C19×#1279C211yesmaximal, characteristic, complemented
8#11927101C2211yescharacteristic
9#11927094C2211yescharacteristic
10#11926942C411yescharacteristic, complemented
11#11926917C411yescharacteristic, complemented
12#11926895C411yescharacteristic, complemented
13#11926891C411yescharacteristic, complemented
14#11926773—22no—
15#11926673—22no—
16#11926671—21no—
17#11926668—21no—
18C4×#64516—22no—
19#11926597C2211yescharacteristic
20#11926570—21no—
21C2×#10597262—21no—
22C2×#10597262—21no—
23#11926499—21no—
24C4×#64520C2211yescharacteristic
25#11926280—22no—
26#11926271—21no—
27#11926271—21no—
28C2×C19×C4⋊C8C2211yescharacteristic
29C2×C4×C8×C19C2211yescharacteristic
30C4×C4⋊C4×C19C2211yescharacteristic
31C2×#64541—21no—
32C22×C8×C19—21no—
33C22×C8×C19—21no—
34C2×C4⋊C4×C19—21no—
35C2×C42×C19—21no—
36C2×C42×C19C2311yescharacteristic
37#10597376—21no—
38#10597376—21no—
39#10597372—21no—
40#10597370—21no—
41#10597370D412yes—
42C2×#64520D411yescharacteristic
43C2×#64520D411yescharacteristic
44C2×#64516—22no—
45#10597321—21no—
46#10597320C2×C411yescharacteristic
47C4×D76—21no—
48C4×D76—21no—
49#10597316—21no—
50#10597315C2×C411yescharacteristic
51#10597315C2×C411yescharacteristic
52#10597315C2×C411yescharacteristic
53C4×Dic38—21no—
54C4×Dic38D412yes—
55C19×C4⋊C8—21no—
56C19×C4⋊C8D411yescharacteristic
57C19×C4⋊C8D411yescharacteristic
58C4×C8×C19—21no—
59C4×C8×C19C2×C411yescharacteristic
60C4×C8×C19C2×C411yescharacteristic
61C19×#95—21no—
62C22⋊(C19⋊C8)—21no—
63#10597278—22no—
64#10597274—22no—
65#10597273—22no—
66#10597272—22no—
67Dic19⋊C8—22no—
68Dic19⋊C8—22no—
69C8×Dic19—22no—
70#10597262—42no—
71#10597262—42no—
72C4⋊(C19⋊C8)—21no—
73#10597260—21no—
74C4×C19⋊C8—21no—
75C4×C19⋊C8—21no—
76C22×C4×C19—41no—
77C22×C4×C19C2×D411yescharacteristic
78C22×C4×C19C2×D411yescharacteristic
79C22×C4×C19#4111yescharacteristic
80C2×C22⋊D19—41no—
81#64541—41no—
82#64541—41no—
83#64541—41no—
84#64541—41no—
85C2×D76—21no—
86C2×D76—21no—
87C2×D76—21no—
88C2×C4×D19—41no—
89C2×Dic38—21no—
90C2×Dic38—21no—
91C2×Dic38C22⋊C412yes—
92C2×C8×C19—21no—
93C2×C8×C19—21no—
94C2×C8×C19—21no—
95C2×C8×C19—21no—
96C2×C8×C19—42no—
97C2×C8×C19—41no—
98C2×C8×C19—41no—
99C4⋊C4×C19—22no—
100C4⋊C4×C19—41no—
101C42×C19—41no—
102C42×C19—41no—
103C42×C19C22×C411yescharacteristic
104C42×C19C2×D411yescharacteristic
105C42×C19C2×D411yescharacteristic
106C42×C19#4111yescharacteristic
107C22⋊Dic19—22no—
108(C2×D19)⋊C4—41no—
109(C2×D19)⋊C4—41no—
110C4⋊Dic19—21no—
111C4⋊Dic19—21no—
112C4⋊Dic19—21no—
113C4⋊Dic19—21no—
114C4⋊Dic19—21no—
115C4⋊Dic19C22⋊C412yes—
116Dic19⋊C4—22no—
117Dic19⋊C4—22no—
118C4×Dic19—22no—
119#64520—21no—
120#64520—21no—
121#64520—21no—
122#64520SD1612yescomplemented
123C2×C19⋊C8—21no—
124C2×C19⋊C8—21no—
125C2×C19⋊C8—41no—
126#64516—44no—
127#9054—191nomaximal, Sylow
128C23×C19#12111yescharacteristic
129C22×D19—41no—
130C2×C4×C19—21no—
131C2×C4×C19—21no—
132C2×C4×C19—41no—
133C2×C4×C19—42no—
134C2×C4×C19—81no—
135C2×C4×C19—81no—
136C2×C4×C19C2×C22⋊C411yescharacteristic
137C2×C4×C19C4×D411yescharacteristic
138C2×C4×C19C4×D411yescharacteristic
139C2×C4×C19#12011yescharacteristic
140C2×C4×C19#12111yescharacteristic
141C2×C4×C19#12311yescharacteristic
142C2×C4×C19C2×SD1611yescharacteristic
143C2×C4×C19#13511yescharacteristic
144C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
145C2×C4×C19#13711yescharacteristic
146C22⋊D19—81no—
147C22⋊D19—81no—
148C2×Dic19—22no—
149C2×Dic19—22no—
150C2×Dic19—41no—
151D76—42no—
152D76—41no—
153D76—41no—
154D76—41no—
155D76—41no—
156C4×D19—81no—
157C4×D19—81no—
158Dic38—41no—
159Dic38—41no—
160Dic38—42no—
161Dic38—41no—
162Dic38—41no—
163C8×C19—22no—
164C8×C19—41no—
165C8×C19—41no—
166C8×C19—41no—
167C19⋊C8—22no—
168C19⋊C8—41no—
169C19⋊C8—81no—
170#3167—191no—
171#2962—191no—
172#1980—191no—
173#1503—191no—
174#1480—191no—
175#1279D1911yescharacteristic, complemented
176#1278—191no—
177C22×C19—21no—
178C22×C19—21no—
179C22×C19#38611yescharacteristic
180C22×C19#46011yescharacteristic
181C22×C19#46411yescharacteristic
182C2×D19—81no—
183C2×D19—81no—
184C2×D19—81no—
185C4×C19—21no—
186C4×C19—21no—
187C4×C19—21no—
188C4×C19—82no—
189C4×C19C4×SD1611yescharacteristic
190C4×C19#44011yescharacteristic
191C4×C19#44311yescharacteristic
192C4×C19#44411yescharacteristic
193C4×C19#44811yescharacteristic
194C4×C19#44911yescharacteristic
195Dic19—42no—
196Dic19—42no—
197Dic19—81no—
198#533—191no—
199#532—191no—
200#498—191no—
201#492—191no—
202#487—191no—
203#486—191no—
204#465—382no—
205#446—382no—
206#446—381no—
207C8×Q8—381no—
208C4×SD16—382no—
209#431—191no—
210#424—381no—
211C2×C4⋊C8C2×D1911yescharacteristic
212C2×#104—381no—
213C2×#104—381no—
214#405—381no—
215C4×M16—191no—
216C2×C4×C8C2×D1911yescharacteristic
217C4×C4⋊C4C2×D1911yescharacteristic
218#328—382no—
219D4⋊C8—381no—
220D4⋊C8—381no—
221C2×C19—21no—
222C2×C19—21no—
223C2×C19#187611yescharacteristic
224C2×C19#188011yescharacteristic
225C2×C19#188411yescharacteristic
226D19—161no—
227C2×#41—381no—
228C2×SD16—382no—
229C2×M16—191no—
230C2×M16—191no—
231C22×C8—21no—
232C22×C8—21no—
233C4⋊Q8—191no—
234C4⋊Q8—191no—
235C4⋊Q8—191no—
236#127—191no—
237#125—381no—
238#124—381no—
239C22⋊Q8—192no—
240C22⋊Q8—381no—
241#121—381no—
242#121—381no—
243C4×Q8—192no—
244C4×Q8—381no—
245C4×D4—381no—
246C4×D4—381no—
247#117—381no—
248C2×C4⋊C4—21no—
249C2×C42—21no—
250C2×C42C22×D1911yescharacteristic
251#106—382no—
252C4⋊C8—21no—
253C4⋊C8—382no—
254C4⋊C8—382no—
255C4⋊C8—381no—
256C4⋊C8D7611yescharacteristic
257C4⋊C8D7611yescharacteristic
258#104—762no—
259#104—762no—
260#103—382no—
261#102—382no—
262C22⋊C8—381no—
263#97—382no—
264#97—381no—
265C4×C8—21no—
266C4×C8—382no—
267C4×C8—381no—
268C4×C8—381no—
269C4×C8C4×D1911yescharacteristic
270C4×C8C4×D1911yescharacteristic
271#95—21no—
272C19#905411yescharacteristic, complemented, Sylow
273#41—761no—
274#41—761no—
275#41—761no—
276#41—761no—
277C2×Q8—192no—
278C2×Q8—381no—
279C2×Q8—381no—
280C2×D4—381no—
281C2×D4—381no—
282C2×D4—381no—
283C2×D4—761no—
284C22×C4—41no—
285C22×C4—761no—
286C22×C4#6454111yescharacteristic
287C22×C4D4×D1911yescharacteristic
288C22×C4D4×D1911yescharacteristic
289SD16—764no—
290M16—192no—
291M16—381no—
292M16—381no—
293M16—381no—
294C2×C8—21no—
295C2×C8—21no—
296C2×C8—21no—
297C2×C8—21no—
298C2×C8—42no—
299C2×C8—41no—
300C2×C8—41no—
301C2×C8—381no—
302C2×C8—381no—
303C2×C8—761no—
304C4⋊C4—22no—
305C4⋊C4—41no—
306C4⋊C4—192no—
307C4⋊C4—381no—
308C4⋊C4—381no—
309C4⋊C4—381no—
310C4⋊C4—382no—
311C4⋊C4—382no—
312C4⋊C4—381no—
313C4⋊C4—381no—
314C22⋊C4—382no—
315C22⋊C4—761no—
316C22⋊C4—761no—
317C42—41no—
318C42—41no—
319C42—382no—
320C42C2×C4×D1911yescharacteristic
321C42C2×D7611yescharacteristic
322C42D4×D1911yescharacteristic
323C42#6454511yescharacteristic
324C23—761no—
325C23#1059733011yescharacteristic
326Q8—762no—
327Q8—761no—
328Q8—761no—
329Q8—761no—
330Q8—761no—
331D4—762no—
332D4—761no—
333D4—761no—
334D4—761no—
335D4—761no—
336D4—1521no—
337D4—1521no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—41no—
341C2×C4—42no—
342C2×C4—81no—
343C2×C4—81no—
344C2×C4—382no—
345C2×C4—382no—
346C2×C4—761no—
347C2×C4—1521no—
348C2×C4—1521no—
349C2×C4C4×D7611yescharacteristic
350C2×C4C22⋊C4×D1911yescharacteristic
351C2×C4#1059732811yescharacteristic
352C2×C4#1059733911yescharacteristic
353C2×C4#1059734011yescharacteristic
354C2×C4#1059734111yescharacteristic
355C2×C4#1059735711yescharacteristic
356C2×C4SD16×D1911yescharacteristic
357C2×C4#1059736211yescharacteristic
358C2×C4#1059736411yescharacteristic
359C8—22no—
360C8—41no—
361C8—41no—
362C8—41no—
363C8—382no—
364C8—761no—
365C8—1521no—
366C22—21no—
367C22—21no—
368C22—1521no—
369C22—1521no—
370C22—1521no—
371C22#1192642211yescharacteristic
372C22#1192674311yescharacteristic
373C22#1192676911yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—82no—
378C4—762no—
379C4—762no—
380C4—1521no—
381C4#1192663111yescharacteristic
382C4#1192664311yescharacteristic
383C4#1192666211yescharacteristic
384C4#1192666711yescharacteristic
385C4#1192668411yescharacteristic
386C4#1192669011yescharacteristic
387C2—21no—
388C2—21no—
389C2—3041no—
390C2#1456396111yescharacteristic
391C2#1456399111yescharacteristic
392C2#1456401711yescharacteristic
subgroupG/H
centerC2×C4#10597328
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1279C2
socleC22×C19#386
prime radical#11927094C22
cosocleC2×C42×C19C23
hypercenter#1279D19
hypocenterC19#9054
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
2. #14572578C2semidirect
4. #14562133C2semidirect
6. #14561472C2semidirect
7. C19×#1279C2semidirect
10. #11926942C4semidirect
11. #11926917C4semidirect
12. #11926895C4semidirect
13. #11926891C4semidirect
122. #64520SD16semidirect
175. #1279D19semidirect
272. C19#9054semidirect

Maximal subgroups

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

subgroupindex
#145741942
#145725782
#145645532
#145621332
#145620332
#145614722
C19×#12792
#905419