Finite Group Databasebeta

← #18079053

Subgroups — #18079053

Order 4864.

480 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14574763C211yesmaximal, characteristic
2#14572378C211yesmaximal, characteristic
3#14564625C211yesmaximal, characteristic, complemented
4#14562310C211yesmaximal, characteristic
5#14561532C211yesmaximal, characteristic, complemented
6#14561485C211yesmaximal, characteristic, complemented
7C2×C19×#332C211yesmaximal, characteristic, complemented
8C2×#10597347—21no—
9#11927094C2211yescharacteristic
10#11926940—21no—
11#11926892—21no—
12#11926862C414yes—
13#11926831—22no—
14#11926621—21no—
15#11926614—22no—
16#11926609—21no—
17#11926597C2211yescharacteristic
18#11926568C2211yescharacteristic
19#11926510—21no—
20C4×#64520C2211yescharacteristic
21#11926313—21no—
22#11926313—21no—
23#11926289—21no—
24#11926287—21no—
25C2×C19×C4⋊Q8C2211yescharacteristic
26C2×C19×C4⋊C8C2211yescharacteristic
27C2×C19×C4⋊C8C2211yescharacteristic
28C19×#332—21no—
29C19×#332—21no—
30C22×Q8×C19—21no—
31C2×#64541—21no—
32C22×C8×C19—21no—
33C22×C8×C19—21no—
34C19×C4⋊Q8—21no—
35C19×C4⋊Q8—21no—
36C19×C4⋊Q8—21no—
37C19×C4⋊Q8—21no—
38C2×C4⋊C4×C19—21no—
39C2×C4⋊C4×C19C2×C412yes—
40C2×C42×C19C2311yescharacteristic
41#10597376—21no—
42#10597376C2×C412yes—
43C2×#64520—21no—
44C2×#64520D411yescharacteristic
45C2×#64520D411yescharacteristic
46#10597347—42no—
47#10597347—42no—
48C2×#64515—22no—
49C2×C8×D19—22no—
50#10597321—21no—
51#10597320D411yescharacteristic
52C4×D76—21no—
53C4×D76D412yes—
54#10597315D411yescharacteristic
55C19×C4⋊C8—21no—
56C19×C4⋊C8—21no—
57C19×C4⋊C8—21no—
58C19×C4⋊C8D411yescharacteristic
59C19×C4⋊C8D411yescharacteristic
60C22⋊(C19⋊C8)C2×C412yes—
61(C2×D19)⋊C8—22no—
62(C2×D19)⋊C8—22no—
63#10597266—24no—
64#10597265—24no—
65C4⋊(C19⋊C8)—21no—
66C4⋊(C19⋊C8)—21no—
67C4⋊(C19⋊C8)—21no—
68#10597260—21no—
69C4×C19⋊C8—21no—
70C4×C19⋊C8—21no—
71C2×Q8×C19—41no—
72C2×Q8×C19—41no—
73C2×Q8×C19—81no—
74C2×Q8×C19—81no—
75C22×C4×C19—22no—
76C22×C4×C19C22×C411yescharacteristic
77C22×C4×C19C2×D411yescharacteristic
78C22×C4×C19#4111yescharacteristic
79C2×C22⋊D19—22no—
80#64541—41no—
81#64541—41no—
82#64541—41no—
83#64541—41no—
84C2×D76—21no—
85C2×D76—21no—
86C2×D76C22⋊C412yes—
87C2×C4×D19—22no—
88C2×Dic38—21no—
89C2×C8×C19—21no—
90C2×C8×C19—21no—
91C2×C8×C19—41no—
92C2×C8×C19—41no—
93C2×C8×C19—41no—
94C2×C8×C19—81no—
95C4⋊C4×C19—22no—
96C4⋊C4×C19—22no—
97C4⋊C4×C19—41no—
98C4⋊C4×C19—41no—
99C42×C19C2×D411yescharacteristic
100C42×C19C2×D411yescharacteristic
101C42×C19C2×D411yescharacteristic
102C42×C19#4111yescharacteristic
103(C2×D19)⋊C4—22no—
104(C2×D19)⋊C4—22no—
105C4⋊Dic19—21no—
106C4⋊Dic19C22⋊C412yes—
107#64520—21no—
108#64520—21no—
109#64520—21no—
110#64520—41no—
111#64520—41no—
112#64520SD1612yes—
113C2×C19⋊C8—21no—
114C2×C19⋊C8—22no—
115C2×C19⋊C8—21no—
116C2×C19⋊C8—41no—
117#64515—44no—
118C8×D19—44no—
119#9269—191nomaximal, Sylow
120C23×C19C4×D411yescharacteristic
121C22×D19—22no—
122Q8×C19—82no—
123Q8×C19—81no—
124Q8×C19—81no—
125C2×C4×C19—21no—
126C2×C4×C19—21no—
127C2×C4×C19—41no—
128C2×C4×C19—42no—
129C2×C4×C19—82no—
130C2×C4×C19C2×C22⋊C411yescharacteristic
131C2×C4×C19C4×D411yescharacteristic
132C2×C4×C19#12011yescharacteristic
133C2×C4×C19#12111yescharacteristic
134C2×C4×C19#12111yescharacteristic
135C2×C4×C19#12311yescharacteristic
136C2×C4×C19C2×SD1611yescharacteristic
137C2×C4×C19#13511yescharacteristic
138C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
139C2×C4×C19#13711yescharacteristic
140C22⋊D19—42no—
141C22⋊D19—42no—
142C2×Dic19—22no—
143D76—42no—
144D76—41no—
145D76—41no—
146D76—41no—
147D76—41no—
148C4×D19—42no—
149C4×D19—42no—
150Dic38—41no—
151Dic38—41no—
152C8×C19—41no—
153C8×C19—41no—
154C8×C19—81no—
155C19⋊C8—22no—
156C19⋊C8—42no—
157C19⋊C8—41no—
158C19⋊C8—81no—
159#3227—191no—
160#2935—191no—
161#1997—191no—
162#1547—191no—
163C2×#332D1911yescharacteristic, complemented
164#1301—191no—
165#1283—191no—
166C22×C19—21no—
167C22×C19—21no—
168C22×C19#38611yescharacteristic
169C22×C19C4×SD1611yescharacteristic
170C22×C19#44011yescharacteristic
171C2×D19—42no—
172C2×D19—42no—
173C2×D19—42no—
174C4×C19—21no—
175C4×C19—21no—
176C4×C19—21no—
177C4×C19—82no—
178C4×C19#45011yescharacteristic
179C4×C19#45211yescharacteristic
180C4×C19#46111yescharacteristic
181C4×C19#46311yescharacteristic
182C4×C19#47111yescharacteristic
183C4×C19#47211yescharacteristic
184Dic19—42no—
185C2×#131—381no—
186#532—191no—
187C2×C4⋊Q8C2×D1911yescharacteristic
188#498—381no—
189#486—381no—
190#481—194no—
191#476—382no—
192#436—381no—
193#435—382no—
194C8×D4—381no—
195#431—191no—
196#423—191no—
197C2×C4⋊C8C2×D1911yescharacteristic
198C2×C4⋊C8C2×D1911yescharacteristic
199#408—381no—
200C4×M16—191no—
201#343—381no—
202#343—381no—
203#332—21no—
204#332—21no—
205#332—381no—
206#331—381no—
207C2×C19—21no—
208C2×C19—21no—
209C2×C19#187711yescharacteristic
210C2×C19#190711yescharacteristic
211C2×C19#191511yescharacteristic
212D19—82no—
213C2×#41—381no—
214C22×Q8—21no—
215#131—762no—
216#131—762no—
217C2×M16—191no—
218C2×M16—191no—
219C2×M16—382no—
220C2×M16—381no—
221C22×C8—21no—
222C22×C8—21no—
223C22×C8—382no—
224C4⋊Q8—21no—
225C4⋊Q8—21no—
226C4⋊Q8—21no—
227C4⋊Q8—21no—
228C4⋊Q8—191no—
229#127—191no—
230#124—381no—
231#121—192no—
232#121—381no—
233C4×D4—192no—
234C4×D4—381no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4C4×D1912yes—
237C2×C42C22×D1911yescharacteristic
238#106—384no—
239C4⋊C8—21no—
240C4⋊C8—21no—
241C4⋊C8—21no—
242C4⋊C8—381no—
243C4⋊C8—381no—
244C4⋊C8—381no—
245C4⋊C8C22⋊D1911yescharacteristic
246C4⋊C8C22⋊D1911yescharacteristic
247#102—384no—
248C22⋊C8—192no—
249C22⋊C8—382no—
250C22⋊C8—382no—
251#97—381no—
252C4×C8—381no—
253C4×C8—381no—
254C19#926911yescharacteristic, complemented, Sylow
255#41—761no—
256#41—761no—
257#41—761no—
258#41—761no—
259C2×Q8—41no—
260C2×Q8—41no—
261C2×Q8—81no—
262C2×Q8—81no—
263C2×Q8—381no—
264C2×D4—192no—
265C2×D4—382no—
266C2×D4—381no—
267C2×D4—381no—
268C22×C4—22no—
269C22×C4—382no—
270C22×C4C2×C4×D1911yescharacteristic
271C22×C4D4×D1911yescharacteristic
272C22×C4#6454311yescharacteristic
273M16—192no—
274M16—381no—
275M16—381no—
276M16—381no—
277M16—764no—
278M16—761no—
279M16—761no—
280C2×C8—21no—
281C2×C8—21no—
282C2×C8—41no—
283C2×C8—41no—
284C2×C8—41no—
285C2×C8—81no—
286C2×C8—381no—
287C2×C8—381no—
288C2×C8—382no—
289C2×C8—764no—
290C2×C8—761no—
291C4⋊C4—22no—
292C4⋊C4—22no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4—192no—
296C4⋊C4—381no—
297C22⋊C4—382no—
298C22⋊C4—382no—
299C42#6454111yescharacteristic
300C42D4×D1911yescharacteristic
301C42D4×D1911yescharacteristic
302C42C2×C22⋊D1911yescharacteristic
303C23—382no—
304C23(C22⋊D19)⋊C411yescharacteristic
305Q8—82no—
306Q8—81no—
307Q8—81no—
308Q8—761no—
309Q8—761no—
310D4—762no—
311D4—762no—
312D4—762no—
313D4—761no—
314D4—761no—
315D4—761no—
316D4—761no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—41no—
320C2×C4—42no—
321C2×C4—82no—
322C2×C4—382no—
323C2×C4—762no—
324C2×C4—762no—
325C2×C4C22⋊C4×D1911yescharacteristic
326C2×C4#1059732911yescharacteristic
327C2×C4#1059733011yescharacteristic
328C2×C4SD16×D1911yescharacteristic
329C2×C4#1059736011yescharacteristic
330C2×C4#1059736411yescharacteristic
331C2×C4#1059736511yescharacteristic
332C2×C4C4×C22⋊D1911yescharacteristic
333C2×C4#1059738311yescharacteristic
334C2×C4#1059738411yescharacteristic
335C8—41no—
336C8—41no—
337C8—81no—
338C8—382no—
339C8—762no—
340C8—761no—
341C8—1521no—
342C22—21no—
343C22—21no—
344C22—762no—
345C22—762no—
346C22—762no—
347C22#1192642011yescharacteristic
348C22#1192662911yescharacteristic
349C22#1192664711yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—82no—
354C4—762no—
355C4#1192669311yescharacteristic
356C4#1192670511yescharacteristic
357C4#1192674811yescharacteristic
358C4#1192676211yescharacteristic
359C4#1192680411yescharacteristic
360C4#1192681111yescharacteristic
361C2—21no—
362C2—21no—
363C2—1522no—
364C2#1456396611yescharacteristic
365C2#1456414611yescharacteristic
366C2#1456418411yescharacteristic
subgroupG/H
centerC22#11926420
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC2×C19×#332C2
socleC22×C19#386
prime radical#11927094C22
cosocleC2×C42×C19C23
hypercenterC2×#332D19
hypocenterC19#9269
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
3. #14564625C2semidirect
5. #14561532C2semidirect
6. #14561485C2semidirect
7. C2×C19×#332C2semidirect
163. C2×#332D19semidirect
254. C19#9269semidirect

Maximal subgroups

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

subgroupindex
#145747632
#145723782
#145646252
#145623102
#145615322
#145614852
C2×C19×#3322
#926919