Finite Group Databasebeta

← #18075751

Subgroups — #18075751

Order 4864.

434 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14572347C211yesmaximal, characteristic
2#14563797C211yesmaximal, characteristic, complemented
3#14562381C211yesmaximal, characteristic, complemented
4#14562195C211yesmaximal, characteristic
5#14561494C211yesmaximal, characteristic, complemented
6#14561493C211yesmaximal, characteristic, complemented
7C19×#1517C211yesmaximal, characteristic
8C2×#10597394—21no—
9#11926622—21no—
10#11926622C412yescomplemented
11D4×C19⋊C8—21no—
12D4×C19⋊C8C412yescomplemented
13#11926597C2211yescharacteristic
14C2×#10597264—21no—
15C2×#10597265—21no—
16#11926568C2211yescharacteristic
17#11926511—21no—
18C2×C4×C19⋊C8C2211yescharacteristic
19#11926410C2211yescharacteristic
20#11926296—21no—
21#11926294—21no—
22#11926278—22no—
23C19×#532C2211yescharacteristic
24C19×#431C2211yescharacteristic
25C19×#382C2211yescharacteristic
26C19×#327—22no—
27C2×#41×C19—21no—
28C19×C4⋊Q8Q811yescharacteristic
29C19×#127Q811yescharacteristic
30C19×#124—21no—
31C19×#121—21no—
32C19×#121D412yes—
33C4×D4×C19—21no—
34C4×D4×C19C2×C412yes—
35C2×C4⋊C4×C19—21no—
36C2×C42×C19C2311yescharacteristic
37#10597394—42no—
38#10597394—42no—
39C2×C4⋊Dic19—21no—
40C2×#64520—21no—
41C2×#64520—22no—
42C22×C19⋊C8—22no—
43C22×C19⋊C8D411yescharacteristic
44C22×C19⋊C8D411yescharacteristic
45C19×C4⋊C8—21no—
46C19×C22⋊C8—21no—
47C4×C8×C19—21no—
48C19×#95—21no—
49C19×#95—21no—
50C19⋊#95—21no—
51C19⋊#95—21no—
52C22⋊(C19⋊C8)—22no—
53C22⋊(C19⋊C8)—22no—
54C22⋊(C19⋊C8)—21no—
55#10597265—42no—
56#10597264—42no—
57C4⋊(C19⋊C8)—21no—
58C4⋊(C19⋊C8)—21no—
59C4⋊(C19⋊C8)C2×C412yes—
60C4×C19⋊C8—21no—
61C4×C19⋊C8C2×C411yescharacteristic
62C4×C19⋊C8C2×C411yescharacteristic
63C4×C19⋊C8D411yescharacteristic
64C4×C19⋊C8D411yescharacteristic
65#41×C19—41no—
66#41×C19—41no—
67#41×C19—41no—
68#41×C19—41no—
69C2×Q8×C19—21no—
70C2×D4×C19—22no—
71C2×D4×C19—21no—
72C2×D4×C19—21no—
73C2×D4×C19C4⋊C412yes—
74C22×C4×C19—22no—
75C22×C4×C19—41no—
76C22×C4×C19C2×D411yescharacteristic
77C22×C4×C19C2×D411yescharacteristic
78C22×C4×C19#4111yescharacteristic
79C22×Dic19—41no—
80C2×C8×C19—41no—
81C4⋊C4×C19—21no—
82C4⋊C4×C19—41no—
83C4⋊C4×C19—41no—
84C4⋊C4×C19C4⋊C412yes—
85C22⋊C4×C19—22no—
86C22⋊C4×C19—22no—
87C42×C19C22×C411yescharacteristic
88C42×C19C2×D411yescharacteristic
89C42×C19C2×Q811yescharacteristic
90C42×C19#4111yescharacteristic
91C4⋊Dic19—41no—
92C4⋊Dic19—41no—
93#64520—41no—
94#64520—41no—
95#64520—44no—
96C2×C19⋊C8—21no—
97C2×C19⋊C8—21no—
98C2×C19⋊C8—22no—
99C2×C19⋊C8—44no—
100C2×C19⋊C8—41no—
101C2×C19⋊C8C22⋊C411yescharacteristic
102C2×C19⋊C8C22⋊C411yescharacteristic
103C2×C19⋊C8C22⋊C411yescharacteristic
104C2×C19⋊C8C22⋊C411yescharacteristic
105C2×C19⋊C8D812yes—
106C2×C19⋊C8SD1612yes—
107#8676—191nomaximal, Sylow
108C23×C19—22no—
109C23×C19#12111yescharacteristic
110Q8×C19—41no—
111Q8×C19—41no—
112D4×C19—42no—
113D4×C19—42no—
114D4×C19—42no—
115D4×C19—42no—
116D4×C19—41no—
117D4×C19—41no—
118C2×C4×C19—22no—
119C2×C4×C19—41no—
120C2×C4×C19—41no—
121C2×C4×C19—42no—
122C2×C4×C19—42no—
123C2×C4×C19—81no—
124C2×C4×C19—81no—
125C2×C4×C19—81no—
126C2×C4×C19C2×C22⋊C411yescharacteristic
127C2×C4×C19C2×C4⋊C411yescharacteristic
128C2×C4×C19#11711yescharacteristic
129C2×C4×C19#12111yescharacteristic
130C2×C4×C19C22⋊Q811yescharacteristic
131C2×C4×C19C22⋊Q811yescharacteristic
132C2×C4×C19C2×D811yescharacteristic
133C2×C4×C19C2×SD1611yescharacteristic
134C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
135C2×C4×C19#13711yescharacteristic
136C2×Dic19—81no—
137C2×Dic19—81no—
138C2×Dic19—81no—
139C8×C19—81no—
140C19⋊C8—21no—
141C19⋊C8—21no—
142C19⋊C8—42no—
143C19⋊C8—81no—
144C19⋊C8#10212yes—
145C19⋊C8#10212yes—
146#2931—191no—
147#1846—191no—
148#1564—191no—
149#1517—191no—
150#1517D1911yescharacteristic
151#1286—191no—
152#1286—191no—
153C22×C19—21no—
154C22×C19—21no—
155C22×C19—42no—
156C22×C19—42no—
157C22×C19—42no—
158C22×C19#38011yescharacteristic
159C22×C19#45911yescharacteristic
160C22×C19#46111yescharacteristic
161C4×C19—21no—
162C4×C19—21no—
163C4×C19—21no—
164C4×C19—21no—
165C4×C19—42no—
166C4×C19—161no—
167C4×C19C2×#10211yescharacteristic
168C4×C19#41711yescharacteristic
169C4×C19#47411yescharacteristic
170C4×C19#47611yescharacteristic
171Dic19—161no—
172C2×#131—381no—
173#532C2×D1911yescharacteristic
174#436—192no—
175#436—381no—
176C8×D4—192no—
177C8×D4—381no—
178#431—191no—
179#431C2×D1911yescharacteristic
180C2×#107—381no—
181C2×#106—381no—
182#423—191no—
183#408—381no—
184C2×C4×C8—191no—
185#382—191no—
186#382C2×D1911yescharacteristic
187#335—381no—
188#334—381no—
189#327—22no—
190#327—382no—
191C2×C19—21no—
192C2×C19—21no—
193C2×C19—82no—
194C2×C19#180211yescharacteristic
195C2×C19#181211yescharacteristic
196C2×C19#181411yescharacteristic
197C2×#41—21no—
198#131—762no—
199#131—762no—
200C2×M16—382no—
201C2×M16—381no—
202C22×C8—191no—
203C22×C8—191no—
204C22×C8—382no—
205C4⋊Q8Dic3811yescharacteristic
206#127Dic3811yescharacteristic
207#124—21no—
208#121—21no—
209#121C22⋊D1912yes—
210C4×D4—21no—
211C4×D4C4×D1912yes—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—381no—
214C2×C42C22×D1911yescharacteristic
215#107—762no—
216#106—762no—
217C4⋊C8—21no—
218C4⋊C8—192no—
219C4⋊C8—381no—
220C4⋊C8—381no—
221C22⋊C8—21no—
222C22⋊C8—382no—
223C22⋊C8—382no—
224C22⋊C8—381no—
225C4×C8—21no—
226C4×C8—191no—
227C4×C8—191no—
228C4×C8—191no—
229C4×C8—191no—
230C4×C8—381no—
231#95—21no—
232#95—21no—
233#95—381no—
234#95—381no—
235C19#867611yescharacteristic, complemented, Sylow
236#41—41no—
237#41—41no—
238#41—41no—
239#41—41no—
240C2×Q8—21no—
241C2×D4—22no—
242C2×D4—21no—
243C2×D4—21no—
244C2×D4Dic19⋊C412yes—
245C22×C4—22no—
246C22×C4—41no—
247C22×C4—761no—
248C22×C4D4×D1911yescharacteristic
249C22×C4#6454311yescharacteristic
250C22×C4C2×C22⋊D1911yescharacteristic
251M16—764no—
252M16—761no—
253M16—761no—
254C2×C8—41no—
255C2×C8—191no—
256C2×C8—191no—
257C2×C8—192no—
258C2×C8—192no—
259C2×C8—191no—
260C2×C8—191no—
261C2×C8—381no—
262C2×C8—381no—
263C2×C8—382no—
264C2×C8—764no—
265C2×C8—761no—
266C4⋊C4—21no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—761no—
270C4⋊C4—761no—
271C4⋊C4Dic19⋊C412yes—
272C22⋊C4—22no—
273C22⋊C4—22no—
274C42C2×Dic3811yescharacteristic
275C42C2×C4×D1911yescharacteristic
276C42D4×D1911yescharacteristic
277C42#6454311yescharacteristic
278C23—22no—
279C23#1059738511yescharacteristic
280Q8—41no—
281Q8—41no—
282D4—42no—
283D4—42no—
284D4—42no—
285D4—42no—
286D4—41no—
287D4—41no—
288C2×C4—22no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—81no—
294C2×C4—81no—
295C2×C4—81no—
296C2×C4—1521no—
297C2×C4—1521no—
298C2×C4—1521no—
299C2×C4#1059732311yescharacteristic
300C2×C4#1059732411yescharacteristic
301C2×C4#1059732411yescharacteristic
302C2×C4C22⋊C4×D1911yescharacteristic
303C2×C4D8×D1911yescharacteristic
304C2×C4#1059735711yescharacteristic
305C2×C4SD16×D1911yescharacteristic
306C2×C4#1059736111yescharacteristic
307C2×C4C2×Dic19⋊C411yescharacteristic
308C2×C4#1059738511yescharacteristic
309C8—81no—
310C8—192no—
311C8—192no—
312C8—381no—
313C8—381no—
314C8—762no—
315C8—1521no—
316C22—21no—
317C22—21no—
318C22—42no—
319C22—42no—
320C22—42no—
321C22#1192640211yescharacteristic
322C22#1192673711yescharacteristic
323C22#1192674711yescharacteristic
324C4—21no—
325C4—21no—
326C4—21no—
327C4—21no—
328C4—42no—
329C4—161no—
330C4—3041no—
331C4#102×D1911yescharacteristic
332C4#1192654211yescharacteristic
333C4#1192682211yescharacteristic
334C4#1192683211yescharacteristic
335C2—21no—
336C2—21no—
337C2—82no—
338C2#1456363311yescharacteristic
339C2#1456367911yescharacteristic
340C2#1456368711yescharacteristic
subgroupG/H
centerC22#11926402
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1517C2
socleC22×C19#380
prime radicalC19×#532C22
cosocleC2×C42×C19C23
hypercenter#1517D19
hypocenterC19#8676
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1517

Complements

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

NH ≅ G/Ntype
2. #14563797C2semidirect
3. #14562381C2semidirect
5. #14561494C2semidirect
6. #14561493C2semidirect
10. #11926622C4semidirect
12. D4×C19⋊C8C4semidirect
235. C19#8676semidirect

Maximal subgroups

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

subgroupindex
#145723472
#145637972
#145623812
#145621952
#145614942
#145614932
C19×#15172
#867619