Finite Group Databasebeta

← #18077773

Subgroups — #18077773

Order 4864.

500 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14574194C211yesmaximal, characteristic
2#14572378C211yesmaximal, characteristic
3#14564578C211yesmaximal, characteristic, complemented
4#14562129C211yesmaximal, characteristic
5#14562037C211yesmaximal, characteristic, complemented
6#14561472C211yesmaximal, characteristic, complemented
7C19×#1279C211yesmaximal, characteristic, complemented
8C2×#10597347—21no—
9#11927101C2211yescharacteristic
10#11927094C2211yescharacteristic
11#11926942C411yescharacteristic, complemented
12#11926917C411yescharacteristic, complemented
13#11926895C411yescharacteristic, complemented
14#11926891C411yescharacteristic, complemented
15#11926773—22no—
16C4×#64516—22no—
17#11926621—21no—
18#11926614—22no—
19#11926609—21no—
20#11926597C2211yescharacteristic
21#11926510—21no—
22C4×#64520C2211yescharacteristic
23#11926304—21no—
24#11926304—21no—
25#11926277—22no—
26#11926274—21no—
27#11926274—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#10597376D412yes—
39#10597372—21no—
40#10597370—21no—
41#10597370—21no—
42C2×#64520D411yescharacteristic
43C2×#64520D411yescharacteristic
44C2×#64516—22no—
45#10597347—42no—
46#10597347—42no—
47C2×#64515—22no—
48C2×C8×D19—22no—
49#10597321—21no—
50#10597320C2×C411yescharacteristic
51C4×D76—21no—
52C4×D76D412yes—
53#10597316—21no—
54#10597315C2×C411yescharacteristic
55#10597315C2×C411yescharacteristic
56#10597315C2×C411yescharacteristic
57C4×Dic38—21no—
58C4×Dic38—21no—
59C19×C4⋊C8—21no—
60C19×C4⋊C8D411yescharacteristic
61C19×C4⋊C8D411yescharacteristic
62C4×C8×C19—21no—
63C4×C8×C19C2×C411yescharacteristic
64C4×C8×C19C2×C411yescharacteristic
65C19×#95—21no—
66C22⋊(C19⋊C8)—21no—
67#10597278—22no—
68(C2×D19)⋊C8—22no—
69(C2×D19)⋊C8—22no—
70#10597274—22no—
71#10597273—22no—
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—22no—
81#64541—41no—
82#64541—41no—
83#64541—41no—
84#64541—41no—
85C2×D76—21no—
86C2×D76—21no—
87C2×D76C22⋊C412yes—
88C2×C4×D19—22no—
89C2×Dic38—21no—
90C2×Dic38—21no—
91C2×Dic38—21no—
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—41no—
108(C2×D19)⋊C4—22no—
109(C2×D19)⋊C4—22no—
110C4⋊Dic19—21no—
111C4⋊Dic19—21no—
112C4⋊Dic19—21no—
113C4⋊Dic19—21no—
114C4⋊Dic19—21no—
115C4⋊Dic19C22⋊C412yes—
116Dic19⋊C4—41no—
117Dic19⋊C4—41no—
118C4×Dic19—41no—
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#64515—44no—
128C8×D19—44no—
129#9055—191nomaximal, Sylow
130C23×C19#12111yescharacteristic
131C22×D19—22no—
132C2×C4×C19—21no—
133C2×C4×C19—21no—
134C2×C4×C19—41no—
135C2×C4×C19—42no—
136C2×C4×C19—81no—
137C2×C4×C19—81no—
138C2×C4×C19C2×C22⋊C411yescharacteristic
139C2×C4×C19C4×D411yescharacteristic
140C2×C4×C19C4×D411yescharacteristic
141C2×C4×C19#12011yescharacteristic
142C2×C4×C19#12111yescharacteristic
143C2×C4×C19#12311yescharacteristic
144C2×C4×C19C2×SD1611yescharacteristic
145C2×C4×C19#13511yescharacteristic
146C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
147C2×C4×C19#13711yescharacteristic
148C22⋊D19—42no—
149C22⋊D19—42no—
150C2×Dic19—22no—
151C2×Dic19—41no—
152C2×Dic19—41no—
153D76—42no—
154D76—41no—
155D76—41no—
156D76—41no—
157D76—41no—
158C4×D19—42no—
159C4×D19—42no—
160Dic38—41no—
161Dic38—41no—
162Dic38—42no—
163Dic38—41no—
164Dic38—41no—
165C8×C19—22no—
166C8×C19—41no—
167C8×C19—41no—
168C8×C19—41no—
169C19⋊C8—22no—
170C19⋊C8—41no—
171C19⋊C8—81no—
172#3167—191no—
173#2935—191no—
174#1986—191no—
175#1502—191no—
176#1481—191no—
177#1279D1911yescharacteristic, complemented
178#1278—191no—
179C22×C19—21no—
180C22×C19—21no—
181C22×C19#38611yescharacteristic
182C22×C19#46111yescharacteristic
183C22×C19#46311yescharacteristic
184C2×D19—42no—
185C2×D19—42no—
186C2×D19—42no—
187C4×C19—21no—
188C4×C19—21no—
189C4×C19—21no—
190C4×C19—82no—
191C4×C19C4×SD1611yescharacteristic
192C4×C19#44011yescharacteristic
193C4×C19#44311yescharacteristic
194C4×C19#44411yescharacteristic
195C4×C19#45011yescharacteristic
196C4×C19#45211yescharacteristic
197Dic19—42no—
198Dic19—81no—
199Dic19—81no—
200C2×#131—381no—
201#533—191no—
202#532—191no—
203#498—191no—
204#492—191no—
205#487—191no—
206#486—191no—
207#465—382no—
208C4×SD16—382no—
209#436—381no—
210#435—382no—
211C8×D4—381no—
212#431—191no—
213C2×C4⋊C8C2×D1911yescharacteristic
214#408—381no—
215C4×M16—191no—
216C2×C4×C8C2×D1911yescharacteristic
217C4×C4⋊C4C2×D1911yescharacteristic
218#339—381no—
219#339—381no—
220#327—382no—
221Q8⋊C8—381no—
222Q8⋊C8—381no—
223C2×C19—21no—
224C2×C19—21no—
225C2×C19#187611yescharacteristic
226C2×C19#187711yescharacteristic
227C2×C19#188411yescharacteristic
228D19—82no—
229C2×#41—381no—
230C2×SD16—382no—
231#131—762no—
232#131—762no—
233C2×M16—191no—
234C2×M16—191no—
235C2×M16—382no—
236C22×C8—21no—
237C22×C8—21no—
238C22×C8—382no—
239C4⋊Q8—191no—
240C4⋊Q8—191no—
241C4⋊Q8—191no—
242#127—191no—
243#125—381no—
244#124—381no—
245C22⋊Q8—381no—
246C22⋊Q8—381no—
247#121—192no—
248#121—381no—
249C4×Q8—381no—
250C4×Q8—381no—
251C4×D4—192no—
252C4×D4—381no—
253#117—381no—
254C2×C4⋊C4—21no—
255C2×C42—21no—
256C2×C42C22×D1911yescharacteristic
257#106—382no—
258C4⋊C8—21no—
259C4⋊C8—381no—
260C4⋊C8D7611yescharacteristic
261C4⋊C8D7611yescharacteristic
262#103—382no—
263#102—382no—
264C22⋊C8—382no—
265C22⋊C8—382no—
266C22⋊C8—381no—
267#97—381no—
268C4×C8—21no—
269C4×C8—381no—
270C4×C8—381no—
271C4×C8C4×D1911yescharacteristic
272C4×C8C4×D1911yescharacteristic
273#95—21no—
274C19#905511yescharacteristic, complemented, Sylow
275#41—761no—
276#41—761no—
277#41—761no—
278#41—761no—
279C2×Q8—381no—
280C2×Q8—381no—
281C2×Q8—381no—
282C2×D4—192no—
283C2×D4—382no—
284C2×D4—381no—
285C2×D4—381no—
286C22×C4—41no—
287C22×C4—382no—
288C22×C4#6454111yescharacteristic
289C22×C4D4×D1911yescharacteristic
290C22×C4D4×D1911yescharacteristic
291SD16—764no—
292M16—192no—
293M16—381no—
294M16—381no—
295M16—381no—
296M16—764no—
297C2×C8—21no—
298C2×C8—21no—
299C2×C8—21no—
300C2×C8—21no—
301C2×C8—42no—
302C2×C8—41no—
303C2×C8—41no—
304C2×C8—381no—
305C2×C8—381no—
306C2×C8—764no—
307C2×C8—761no—
308C4⋊C4—22no—
309C4⋊C4—41no—
310C4⋊C4—192no—
311C4⋊C4—381no—
312C4⋊C4—381no—
313C4⋊C4—381no—
314C4⋊C4—381no—
315C4⋊C4—381no—
316C4⋊C4—761no—
317C4⋊C4—761no—
318C22⋊C4—382no—
319C22⋊C4—382no—
320C22⋊C4—761no—
321C42—41no—
322C42—41no—
323C42—761no—
324C42C2×C4×D1911yescharacteristic
325C42C2×D7611yescharacteristic
326C42D4×D1911yescharacteristic
327C42#6454511yescharacteristic
328C23—382no—
329C23#1059733011yescharacteristic
330Q8—762no—
331Q8—761no—
332Q8—761no—
333Q8—761no—
334Q8—761no—
335D4—762no—
336D4—762no—
337D4—762no—
338D4—761no—
339D4—761no—
340D4—761no—
341D4—761no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—41no—
345C2×C4—42no—
346C2×C4—81no—
347C2×C4—81no—
348C2×C4—382no—
349C2×C4—762no—
350C2×C4—762no—
351C2×C4—761no—
352C2×C4—761no—
353C2×C4C4×D7611yescharacteristic
354C2×C4C22⋊C4×D1911yescharacteristic
355C2×C4#1059732811yescharacteristic
356C2×C4#1059733911yescharacteristic
357C2×C4#1059734011yescharacteristic
358C2×C4#1059734111yescharacteristic
359C2×C4#1059735711yescharacteristic
360C2×C4SD16×D1911yescharacteristic
361C2×C4#1059736211yescharacteristic
362C2×C4#1059736411yescharacteristic
363C8—22no—
364C8—41no—
365C8—41no—
366C8—41no—
367C8—382no—
368C8—761no—
369C8—1521no—
370C22—21no—
371C22—21no—
372C22—762no—
373C22—762no—
374C22—762no—
375C22#1192642211yescharacteristic
376C22#1192674811yescharacteristic
377C22#1192675811yescharacteristic
378C4—21no—
379C4—21no—
380C4—21no—
381C4—82no—
382C4—762no—
383C4—1521no—
384C4—1521no—
385C4#1192663111yescharacteristic
386C4#1192664311yescharacteristic
387C4#1192666211yescharacteristic
388C4#1192666711yescharacteristic
389C4#1192669611yescharacteristic
390C4#1192670911yescharacteristic
391C2—21no—
392C2—21no—
393C2—1522no—
394C2#1456396111yescharacteristic
395C2#1456397011yescharacteristic
396C2#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#9055
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
3. #14564578C2semidirect
5. #14562037C2semidirect
6. #14561472C2semidirect
7. C19×#1279C2semidirect
11. #11926942C4semidirect
12. #11926917C4semidirect
13. #11926895C4semidirect
14. #11926891C4semidirect
122. #64520SD16semidirect
177. #1279D19semidirect
274. C19#9055semidirect

Maximal subgroups

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

subgroupindex
#145741942
#145723782
#145645782
#145621292
#145620372
#145614722
C19×#12792
#905519