Finite Group Databasebeta

← #18079040

Subgroups — #18079040

Order 4864.

492 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14574557C211yesmaximal, characteristic
2#14572379C211yesmaximal, characteristic
3#14564623C211yesmaximal, characteristic, complemented
4C2×#11926292C211yesmaximal, characteristic, complemented
5#14561530C211yesmaximal, characteristic, complemented
6#14561485C211yesmaximal, characteristic, complemented
7C19×#1547C211yesmaximal, characteristic
8C2×#10597394—21no—
9C2×#10597315C2211yescharacteristic
10#11926916—21no—
11#11926896—21no—
12#11926749—22no—
13#11926682C414yes—
14#11926622—21no—
15#11926616—22no—
16D4×C19⋊C8—21no—
17#11926597C2211yescharacteristic
18C2×C4⋊(C19⋊C8)C2211yescharacteristic
19#11926511—21no—
20C4×#64520C2211yescharacteristic
21#11926312—21no—
22#11926312—21no—
23#11926292—21no—
24#11926292—21no—
25C19×#532C2211yescharacteristic
26C19×#423C2211yescharacteristic
27C2×C19×C4⋊C8C2211yescharacteristic
28C19×#332—21no—
29C19×#331—21no—
30C2×#41×C19—21no—
31C22×Dic38C2×C412yes—
32C2×M16×C19—21no—
33C22×C8×C19—21no—
34C19×C4⋊Q8D411yescharacteristic
35C19×#127D411yescharacteristic
36C19×#124—21no—
37C19×#121—21no—
38C19×#121C2×C412yes—
39C4×D4×C19—21no—
40C4×D4×C19D412yes—
41C2×C42×C19C2311yescharacteristic
42#10597394—42no—
43#10597394—42no—
44C2×#64526—24no—
45C2×C4⋊Dic19—21no—
46C2×C4⋊Dic19—21no—
47C2×#64520—22no—
48C2×#64520D411yescharacteristic
49C2×#64520D411yescharacteristic
50C22×C19⋊C8—22no—
51C22×C19⋊C8—21no—
52#10597315—21no—
53#10597315—21no—
54#10597315—21no—
55#10597315—21no—
56C19×C4⋊C8—21no—
57C19×C4⋊C8—21no—
58C19×C4⋊C8—21no—
59C19×C4⋊C8—21no—
60C22⋊(C19⋊C8)—22no—
61C22⋊(C19⋊C8)—22no—
62C22⋊(C19⋊C8)C2×C412yes—
63#10597267—24no—
64C4⋊(C19⋊C8)—21no—
65C4⋊(C19⋊C8)—21no—
66C4⋊(C19⋊C8)D411yescharacteristic
67C4⋊(C19⋊C8)D411yescharacteristic
68#10597260—21no—
69C4×C19⋊C8—21no—
70C4×C19⋊C8—21no—
71#41×C19—41no—
72#41×C19—41no—
73#41×C19—41no—
74#41×C19—41no—
75C2×Q8×C19—21no—
76C2×D4×C19—22no—
77C2×D4×C19—21no—
78C2×D4×C19—21no—
79C2×D4×C19C22⋊C412yes—
80C22×C4×C19—22no—
81C22×C4×C19C22×C411yescharacteristic
82C22×C4×C19C2×D411yescharacteristic
83C22×C4×C19#4111yescharacteristic
84C22×Dic19—22no—
85C2×Dic38—22no—
86C2×Dic38—22no—
87C2×Dic38—82no—
88M16×C19—41no—
89M16×C19—41no—
90C2×C8×C19—41no—
91C2×C8×C19—41no—
92C2×C8×C19—81no—
93C4⋊C4×C19—21no—
94C4⋊C4×C19C22⋊C412yes—
95C22⋊C4×C19—22no—
96C22⋊C4×C19—22no—
97C42×C19C2×D411yescharacteristic
98C42×C19C2×D411yescharacteristic
99C42×C19C2×D411yescharacteristic
100C42×C19#4111yescharacteristic
101#64526—84no—
102C4⋊Dic19—41no—
103C4⋊Dic19—41no—
104C4⋊Dic19—41no—
105C4⋊Dic19—41no—
106#64520—21no—
107#64520—21no—
108#64520—21no—
109#64520—44no—
110#64520SD1612yescomplemented
111C2×C19⋊C8—21no—
112C2×C19⋊C8—22no—
113C2×C19⋊C8—21no—
114C2×C19⋊C8—21no—
115C2×C19⋊C8—21no—
116C2×C19⋊C8—44no—
117C2×C19⋊C8—41no—
118C2×C19⋊C8—41no—
119#9267—191nomaximal, Sylow
120C23×C19—22no—
121C23×C19C4×D411yescharacteristic
122Q8×C19—41no—
123Q8×C19—41no—
124D4×C19—42no—
125D4×C19—42no—
126D4×C19—42no—
127D4×C19—41no—
128D4×C19—41no—
129D4×C19—41no—
130D4×C19—41no—
131C2×C4×C19—21no—
132C2×C4×C19—21no—
133C2×C4×C19—22no—
134C2×C4×C19—41no—
135C2×C4×C19—42no—
136C2×C4×C19—42no—
137C2×C4×C19C2×C22⋊C411yescharacteristic
138C2×C4×C19C4×D411yescharacteristic
139C2×C4×C19#12011yescharacteristic
140C2×C4×C19#12111yescharacteristic
141C2×C4×C19#12111yescharacteristic
142C2×C4×C19#12311yescharacteristic
143C2×C4×C19C2×SD1611yescharacteristic
144C2×C4×C19#13511yescharacteristic
145C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
146C2×C4×C19#13711yescharacteristic
147C2×Dic19—42no—
148C2×Dic19—82no—
149Dic38—44no—
150Dic38—82no—
151C8×C19—81no—
152C8×C19—81no—
153C19⋊C8—22no—
154C19⋊C8—42no—
155C19⋊C8—41no—
156C19⋊C8—41no—
157C19⋊C8—41no—
158#3206—191no—
159#2935—191no—
160#1997—191no—
161#1547D1911yescharacteristic
162C2×#333—191no—
163#1301—191no—
164#1283—191no—
165C22×C19—21no—
166C22×C19—21no—
167C22×C19—42no—
168C22×C19—42no—
169C22×C19—42no—
170C22×C19#38611yescharacteristic
171C22×C19C4×SD1611yescharacteristic
172C22×C19#44011yescharacteristic
173C4×C19—21no—
174C4×C19—21no—
175C4×C19—21no—
176C4×C19—42no—
177C4×C19#45011yescharacteristic
178C4×C19#45211yescharacteristic
179C4×C19#46111yescharacteristic
180C4×C19#46311yescharacteristic
181C4×C19#47111yescharacteristic
182C4×C19#47311yescharacteristic
183Dic19—82no—
184C2×#131—381no—
185#532C2×D1911yescharacteristic
186C2×C4⋊Q8—191no—
187#492—381no—
188#487—381no—
189#461—382no—
190#448—194no—
191#436—381no—
192#435—382no—
193C8×D4—381no—
194#431—191no—
195#423C2×D1911yescharacteristic
196C2×C4⋊C8—191no—
197C2×C4⋊C8C2×D1911yescharacteristic
198#408—381no—
199C4×M16—191no—
200#343—381no—
201#343—381no—
202#333—381no—
203#333—381no—
204#332—21no—
205#331—21no—
206C2×C19—21no—
207C2×C19—21no—
208C2×C19—82no—
209C2×C19#187711yescharacteristic
210C2×C19#190811yescharacteristic
211C2×C19#191411yescharacteristic
212C2×#41—21no—
213C22×Q8—192no—
214C2×SD16—384no—
215#131—762no—
216#131—762no—
217C2×M16—21no—
218C2×M16—191no—
219C2×M16—191no—
220C2×M16—382no—
221C22×C8—21no—
222C22×C8—382no—
223C22×C8—381no—
224C4⋊Q8—381no—
225C4⋊Q8—381no—
226C4⋊Q8—381no—
227C4⋊Q8—381no—
228C4⋊Q8C22⋊D1911yescharacteristic
229#127C22⋊D1911yescharacteristic
230#124—21no—
231#121—21no—
232#121C4×D1912yes—
233C4×D4—21no—
234C4×D4D7612yes—
235C2×C4⋊C4—381no—
236C2×C4⋊C4—381no—
237C2×C42C22×D1911yescharacteristic
238C4⋊C8—21no—
239C4⋊C8—21no—
240C4⋊C8—21no—
241C4⋊C8—21no—
242C4⋊C8—191no—
243C4⋊C8—191no—
244C4⋊C8—381no—
245C4⋊C8—381no—
246#103—384no—
247C22⋊C8—192no—
248C22⋊C8—382no—
249C22⋊C8—382no—
250#97—381no—
251C4×C8—381no—
252C4×C8—381no—
253C19#926711yescharacteristic, complemented, Sylow
254#41—41no—
255#41—41no—
256#41—41no—
257#41—41no—
258C2×Q8—21no—
259C2×Q8—382no—
260C2×Q8—382no—
261C2×Q8—1522no—
262C2×D4—22no—
263C2×D4—21no—
264C2×D4—21no—
265C2×D4(C2×D19)⋊C412yes—
266C22×C4—22no—
267C22×C4—382no—
268C22×C4C2×C4×D1911yescharacteristic
269C22×C4D4×D1911yescharacteristic
270C22×C4#6454311yescharacteristic
271SD16—1524no—
272M16—41no—
273M16—41no—
274M16—192no—
275M16—381no—
276M16—381no—
277M16—381no—
278M16—764no—
279C2×C8—41no—
280C2×C8—41no—
281C2×C8—81no—
282C2×C8—381no—
283C2×C8—381no—
284C2×C8—381no—
285C2×C8—381no—
286C2×C8—382no—
287C2×C8—764no—
288C2×C8—761no—
289C2×C8—761no—
290C4⋊C4—21no—
291C4⋊C4—761no—
292C4⋊C4—761no—
293C4⋊C4—761no—
294C4⋊C4—761no—
295C4⋊C4(C2×D19)⋊C412yes—
296C22⋊C4—22no—
297C22⋊C4—22no—
298C42C2×D7611yescharacteristic
299C42D4×D1911yescharacteristic
300C42#6454311yescharacteristic
301C42C2×C22⋊D1911yescharacteristic
302C23—22no—
303C23(C22⋊D19)⋊C411yescharacteristic
304Q8—41no—
305Q8—41no—
306Q8—764no—
307Q8—1522no—
308D4—42no—
309D4—42no—
310D4—42no—
311D4—41no—
312D4—41no—
313D4—41no—
314D4—41no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—22no—
318C2×C4—41no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—762no—
322C2×C4—1522no—
323C2×C4(C22⋊D19)⋊C411yescharacteristic
324C2×C4#1059732811yescharacteristic
325C2×C4#1059733211yescharacteristic
326C2×C4#1059735711yescharacteristic
327C2×C4#1059735811yescharacteristic
328C2×C4SD16×D1911yescharacteristic
329C2×C4#1059736111yescharacteristic
330C2×C4C2×(C2×D19)⋊C411yescharacteristic
331C2×C4#1059738511yescharacteristic
332C2×C4#1059738511yescharacteristic
333C8—81no—
334C8—81no—
335C8—382no—
336C8—762no—
337C8—761no—
338C8—761no—
339C8—761no—
340C22—21no—
341C22—21no—
342C22—42no—
343C22—42no—
344C22—42no—
345C22#1192642111yescharacteristic
346C22#1192663511yescharacteristic
347C22#1192664111yescharacteristic
348C4—21no—
349C4—21no—
350C4—21no—
351C4—42no—
352C4—1522no—
353C4#1192669611yescharacteristic
354C4#1192670711yescharacteristic
355C4#1192674711yescharacteristic
356C4#1192675711yescharacteristic
357C4#1192680511yescharacteristic
358C4#1192681711yescharacteristic
359C2—21no—
360C2—21no—
361C2—82no—
362C2#1456396711yescharacteristic
363C2#1456414811yescharacteristic
364C2#1456418011yescharacteristic
subgroupG/H
centerC22#11926421
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1547C2
socleC22×C19#386
prime radicalC19×#532C22
cosocleC2×C42×C19C23
hypercenter#1547D19
hypocenterC19#9267
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1547

Complements

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

NH ≅ G/Ntype
3. #14564623C2semidirect
4. C2×#11926292C2semidirect
5. #14561530C2semidirect
6. #14561485C2semidirect
110. #64520SD16semidirect
253. C19#9267semidirect

Maximal subgroups

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

subgroupindex
#145745572
#145723792
#145646232
C2×#119262922
#145615302
#145614852
C19×#15472
#926719