Finite Group Databasebeta

← #18077768

Subgroups — #18077768

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#14572582C211yesmaximal, characteristic, complemented
3#14564554C211yesmaximal, characteristic
4#14562135C211yesmaximal, characteristic, complemented
5#14562035C211yesmaximal, characteristic
6#14561475C211yesmaximal, characteristic, complemented
7C19×#1278C211yesmaximal, characteristic, complemented
8#11927101C2211yescharacteristic
9#11927094C2211yescharacteristic
10#11926942C411yescharacteristic, complemented
11#11926917C411yescharacteristic, complemented
12#11926895C411yescharacteristic, complemented
13#11926891C411yescharacteristic, complemented
14#11926773—22no—
15#11926674—21no—
16#11926672—22no—
17C8×Dic38—21no—
18C4×#64516—22no—
19#11926572—21no—
20C2×C4⋊(C19⋊C8)C2211yescharacteristic
21C2×#10597282—21no—
22C2×#10597282—21no—
23#11926502—21no—
24C4×C4⋊Dic19C2211yescharacteristic
25#11926282—22no—
26#11926273—21no—
27#11926273—21no—
28C19×#431C2211yescharacteristic
29C4×M16×C19C2211yescharacteristic
30C2×C4×C8×C19C2211yescharacteristic
31C2×#64541—21no—
32C2×M16×C19D411yescharacteristic
33C2×M16×C19D411yescharacteristic
34C22×C8×C19—21no—
35C2×C42×C19C2311yescharacteristic
36#10597376—21no—
37#10597376—21no—
38#10597372—21no—
39C2×C4⋊Dic19—21no—
40#10597370—21no—
41#10597370D412yes—
42C2×C4×Dic19—21no—
43C22×C19⋊C8—21no—
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×C22⋊C8—21no—
57C19×#97—21no—
58C4×C8×C19—21no—
59C4×C8×C19—21no—
60C4×C8×C19—21no—
61C4×C8×C19C2×C411yescharacteristic
62C4×C8×C19C2×C411yescharacteristic
63C19⋊#95—21no—
64#10597282—42no—
65#10597282—42no—
66#10597278—22no—
67#10597274—22no—
68#10597273—22no—
69#10597272—22no—
70Dic19⋊C8—22no—
71Dic19⋊C8—22no—
72C8×Dic19—22no—
73C4⋊(C19⋊C8)—21no—
74C4⋊(C19⋊C8)D411yescharacteristic
75C4⋊(C19⋊C8)D411yescharacteristic
76C22×C4×C19C2×D411yescharacteristic
77C22×C4×C19C2×D411yescharacteristic
78C22×C4×C19#4111yescharacteristic
79C2×C22⋊D19—41no—
80C22×Dic19—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—
92M16×C19—21no—
93M16×C19—21no—
94M16×C19—21no—
95M16×C19SD1612yescomplemented
96C2×C8×C19—21no—
97C2×C8×C19—21no—
98C2×C8×C19—21no—
99C2×C8×C19—21no—
100C2×C8×C19—42no—
101C2×C8×C19—41no—
102C42×C19C22×C411yescharacteristic
103C42×C19C2×D411yescharacteristic
104C42×C19C2×D411yescharacteristic
105C42×C19#4111yescharacteristic
106C22⋊Dic19—22no—
107(C2×D19)⋊C4—41no—
108(C2×D19)⋊C4—41no—
109C4⋊Dic19—21no—
110C4⋊Dic19—21no—
111C4⋊Dic19—21no—
112C4⋊Dic19—22no—
113C4⋊Dic19—21no—
114C4⋊Dic19—21no—
115C4⋊Dic19—41no—
116C4⋊Dic19C22⋊C412yes—
117Dic19⋊C4—22no—
118Dic19⋊C4—22no—
119C4×Dic19—22no—
120C4×Dic19—41no—
121C4×Dic19—41no—
122C2×C19⋊C8—21no—
123C2×C19⋊C8—21no—
124C2×C19⋊C8—41no—
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×C19C2×C22⋊C411yescharacteristic
134C2×C4×C19C4×D411yescharacteristic
135C2×C4×C19C4×D411yescharacteristic
136C2×C4×C19#12011yescharacteristic
137C2×C4×C19#12111yescharacteristic
138C2×C4×C19#12311yescharacteristic
139C2×C4×C19C2×SD1611yescharacteristic
140C2×C4×C19#13511yescharacteristic
141C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
142C2×C4×C19#13711yescharacteristic
143C22⋊D19—81no—
144C22⋊D19—81no—
145C2×Dic19—22no—
146C2×Dic19—22no—
147C2×Dic19—42no—
148C2×Dic19—41no—
149C2×Dic19—81no—
150C2×Dic19—81no—
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—22no—
165C8×C19—41no—
166C8×C19—41no—
167C8×C19—81no—
168C19⋊C8—41no—
169C19⋊C8—41no—
170#3167—191no—
171#2962—191no—
172#1980—191no—
173#1503—191no—
174#1480—191no—
175#1279—191no—
176#1278D1911yescharacteristic, complemented
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×C19C4×SD1611yescharacteristic
189C4×C19#44011yescharacteristic
190C4×C19#44311yescharacteristic
191C4×C19#44411yescharacteristic
192C4×C19#44811yescharacteristic
193C4×C19#44911yescharacteristic
194Dic19—42no—
195Dic19—42no—
196Dic19—82no—
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—381no—
206#446—382no—
207C8×Q8—381no—
208C4×SD16—382no—
209#431C2×D1911yescharacteristic
210#424—381no—
211C2×C4⋊C8—191no—
212C2×#104—381no—
213C2×#104—381no—
214#405—381no—
215C4×M16C2×D1911yescharacteristic
216C2×C4×C8C2×D1911yescharacteristic
217C4×C4⋊C4—191no—
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×M16D7611yescharacteristic
230C2×M16D7611yescharacteristic
231C22×C8—21no—
232C22×C8—381no—
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—381no—
249C2×C42—381no—
250C2×C42C22×D1911yescharacteristic
251#106—382no—
252C4⋊C8—21no—
253C4⋊C8—191no—
254C4⋊C8—191no—
255C4⋊C8—382no—
256C4⋊C8—382no—
257C4⋊C8—381no—
258#104—762no—
259#104—762no—
260#103—382no—
261#102—382no—
262C22⋊C8—21no—
263#97—21no—
264#97—382no—
265C4×C8—21no—
266C4×C8—21no—
267C4×C8—21no—
268C4×C8—382no—
269C4×C8C4×D1911yescharacteristic
270C4×C8C4×D1911yescharacteristic
271#95—381no—
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—761no—
285C22×C4—761no—
286C22×C4C2×D7611yescharacteristic
287C22×C4D4×D1911yescharacteristic
288C22×C4#6454511yescharacteristic
289SD16—764no—
290M16—21no—
291M16—21no—
292M16—21no—
293M16#6451612yescomplemented
294C2×C8—21no—
295C2×C8—21no—
296C2×C8—21no—
297C2×C8—21no—
298C2×C8—42no—
299C2×C8—41no—
300C2×C8—381no—
301C2×C8—381no—
302C2×C8—761no—
303C2×C8—761no—
304C4⋊C4—192no—
305C4⋊C4—382no—
306C4⋊C4—381no—
307C4⋊C4—381no—
308C4⋊C4—382no—
309C4⋊C4—381no—
310C4⋊C4—382no—
311C4⋊C4—381no—
312C4⋊C4—381no—
313C4⋊C4—761no—
314C22⋊C4—382no—
315C22⋊C4—761no—
316C22⋊C4—761no—
317C42—382no—
318C42—761no—
319C42—761no—
320C42C2×C4×D1911yescharacteristic
321C42#6454111yescharacteristic
322C42D4×D1911yescharacteristic
323C42D4×D1911yescharacteristic
324C23—761no—
325C23#1059734111yescharacteristic
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—382no—
342C2×C4—382no—
343C2×C4—762no—
344C2×C4—761no—
345C2×C4—1521no—
346C2×C4—1521no—
347C2×C4—1521no—
348C2×C4—1521no—
349C2×C4C4×D7611yescharacteristic
350C2×C4C22⋊C4×D1911yescharacteristic
351C2×C4#1059732811yescharacteristic
352C2×C4#1059733011yescharacteristic
353C2×C4#1059733911yescharacteristic
354C2×C4#1059734011yescharacteristic
355C2×C4C2×#6451611yescharacteristic
356C2×C4#1059735011yescharacteristic
357C2×C4#1059735411yescharacteristic
358C2×C4#1059735511yescharacteristic
359C8—22no—
360C8—22no—
361C8—41no—
362C8—41no—
363C8—81no—
364C8—761no—
365C8—761no—
366C22—21no—
367C22—21no—
368C22—1521no—
369C22—1521no—
370C22—1521no—
371C22#1192642211yescharacteristic
372C22#1192674511yescharacteristic
373C22#1192676711yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—762no—
378C4—762no—
379C4—1522no—
380C4—1521no—
381C4C4×#6451611yescharacteristic
382C4#1192664611yescharacteristic
383C4#1192666011yescharacteristic
384C4#1192666511yescharacteristic
385C4#1192668511yescharacteristic
386C4#1192669111yescharacteristic
387C2—21no—
388C2—21no—
389C2—3041no—
390C2#1456396311yescharacteristic
391C2#1456398911yescharacteristic
392C2#1456401711yescharacteristic
subgroupG/H
centerC2×C4#10597328
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1278C2
socleC22×C19#386
prime radical#11927094C22
cosocleC2×C42×C19C23
hypercenter#1278D19
hypocenterC19#9054
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1278

Complements

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

NH ≅ G/Ntype
2. #14572582C2semidirect
4. #14562135C2semidirect
6. #14561475C2semidirect
7. C19×#1278C2semidirect
10. #11926942C4semidirect
11. #11926917C4semidirect
12. #11926895C4semidirect
13. #11926891C4semidirect
95. M16×C19SD16semidirect
176. #1278D19semidirect
272. C19#9054semidirect
293. M16#64516semidirect

Maximal subgroups

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

subgroupindex
#145741942
#145725822
#145645542
#145621352
#145620352
#145614752
C19×#12782
#905419