Finite Group Databasebeta

← #18079182

Subgroups — #18079182

Order 4864.

478 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14574760C211yesmaximal, characteristic
2#14564608C211yesmaximal, characteristic, complemented
3#14562317C211yesmaximal, characteristic, complemented
4#14562195C211yesmaximal, characteristic
5#14561495C211yesmaximal, characteristic, complemented
6#14561466C211yesmaximal, characteristic, complemented
7C19×#2932C211yesmaximal, characteristic
8C2×#10597315C2211yescharacteristic
9#11926940C412yescomplemented
10#11926890C412yescomplemented
11#11926860—22no—
12#11926834—22no—
13#11926597C2211yescharacteristic
14#11926597C2211yescharacteristic
15#11926410C2211yescharacteristic
16#11926307—21no—
17#11926307—21no—
18#11926292—22no—
19#11926278—22no—
20C2×C19×#131—21no—
21C19×#532C2211yescharacteristic
22C19×#435—22no—
23C19×#435—22no—
24C19×#423C2211yescharacteristic
25C19×#408—21no—
26C2×C19×#97C2211yescharacteristic
27C2×#41×C19—21no—
28C22×Dic38—21no—
29C19×#131—42no—
30C19×#131—42no—
31C2×M16×C19—22no—
32C2×M16×C19—21no—
33C22×C8×C19—22no—
34C22×C8×C19D411yescharacteristic
35C22×C8×C19D411yescharacteristic
36C19×C4⋊Q8C2×C411yescharacteristic
37C19×#127C2×C411yescharacteristic
38C19×#124—21no—
39C19×#121—21no—
40C19×#121D412yes—
41C4×D4×C19—21no—
42C4×D4×C19D412yes—
43C2×C42×C19C2311yescharacteristic
44C2×C4⋊Dic19—21no—
45C2×C4⋊Dic19—21no—
46C2×C4⋊Dic19—21no—
47#10597315—21no—
48#10597315—21no—
49#10597315—21no—
50#10597315C2×C412yes—
51C19×C4⋊C8—21no—
52C19×C4⋊C8D412yes—
53C19×C22⋊C8—24no—
54C19×#97—21no—
55C19×#97—21no—
56#10597289—24no—
57C19⋊#95—21no—
58C19⋊#95—21no—
59C22⋊(C19⋊C8)—21no—
60C22⋊(C19⋊C8)—21no—
61#10597265—24no—
62C4⋊(C19⋊C8)—21no—
63C4⋊(C19⋊C8)—21no—
64C4×C19⋊C8—21no—
65C4×C19⋊C8C2×C412yes—
66#41×C19—41no—
67#41×C19—41no—
68#41×C19—41no—
69#41×C19—41no—
70C2×Q8×C19—21no—
71C2×D4×C19—22no—
72C2×D4×C19—21no—
73C2×D4×C19—21no—
74C2×D4×C19C22⋊C412yes—
75C22×C4×C19—22no—
76C22×C4×C19C2×D411yescharacteristic
77C22×C4×C19C2×D411yescharacteristic
78C22×C4×C19#4111yescharacteristic
79C22×Dic19—41no—
80C22×Dic19—41no—
81C2×Dic38—22no—
82C2×Dic38—41no—
83C2×Dic38—82no—
84M16×C19—44no—
85M16×C19—41no—
86M16×C19—41no—
87C2×C8×C19—21no—
88C2×C8×C19—21no—
89C2×C8×C19—22no—
90C2×C8×C19—21no—
91C2×C8×C19—21no—
92C2×C8×C19—21no—
93C2×C8×C19—44no—
94C2×C8×C19SD1612yes—
95C4⋊C4×C19—21no—
96C4⋊C4×C19C22⋊C412yes—
97C22⋊C4×C19—22no—
98C22⋊C4×C19—22no—
99C42×C19C22×C411yescharacteristic
100C42×C19C2×D411yescharacteristic
101C42×C19C2×D411yescharacteristic
102C42×C19#4111yescharacteristic
103C4⋊Dic19—22no—
104C4⋊Dic19—22no—
105C4⋊Dic19—41no—
106C4⋊Dic19—41no—
107C4⋊Dic19—41no—
108C4⋊Dic19—41no—
109C2×C19⋊C8—22no—
110C2×C19⋊C8—41no—
111#9287—191nomaximal, Sylow
112C23×C19—22no—
113C23×C19#12111yescharacteristic
114Q8×C19—41no—
115Q8×C19—41no—
116D4×C19—42no—
117D4×C19—42no—
118D4×C19—42no—
119D4×C19—41no—
120D4×C19—41no—
121D4×C19—81no—
122C2×C4×C19—22no—
123C2×C4×C19—41no—
124C2×C4×C19—41no—
125C2×C4×C19—42no—
126C2×C4×C19—42no—
127C2×C4×C19C2×C22⋊C411yescharacteristic
128C2×C4×C19C4×D411yescharacteristic
129C2×C4×C19C4×D411yescharacteristic
130C2×C4×C19#12011yescharacteristic
131C2×C4×C19#12111yescharacteristic
132C2×C4×C19#12311yescharacteristic
133C2×C4×C19C2×SD1611yescharacteristic
134C2×C4×C19#13511yescharacteristic
135C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
136C2×C4×C19#13711yescharacteristic
137C2×Dic19—42no—
138C2×Dic19—82no—
139C2×Dic19—81no—
140C2×Dic19—81no—
141C2×Dic19—81no—
142Dic38—82no—
143Dic38—82no—
144C8×C19—22no—
145C8×C19—42no—
146C8×C19—41no—
147C19⋊C8—42no—
148C19⋊C8—81no—
149#3227—191no—
150#2932D1911yescharacteristic
151#1993—191no—
152#1548—191no—
153#1517—191no—
154#1286—191no—
155#1275—191no—
156C22×C19—21no—
157C22×C19—21no—
158C22×C19—42no—
159C22×C19—42no—
160C22×C19—42no—
161C22×C19#38611yescharacteristic
162C22×C19#46111yescharacteristic
163C22×C19#46311yescharacteristic
164C4×C19—21no—
165C4×C19—21no—
166C4×C19—21no—
167C4×C19—21no—
168C4×C19—42no—
169C4×C19C4×SD1611yescharacteristic
170C4×C19#44011yescharacteristic
171C4×C19#45011yescharacteristic
172C4×C19#45211yescharacteristic
173Dic19—82no—
174Dic19—161no—
175C2×#131—21no—
176#532C2×D1911yescharacteristic
177C2×C4⋊Q8—191no—
178#498—192no—
179#486—192no—
180#481—382no—
181#476—382no—
182#435—22no—
183#435—22no—
184#431—191no—
185#431—191no—
186#423C2×D1911yescharacteristic
187#408—21no—
188C2×#97C2×D1911yescharacteristic
189#382—191no—
190#340—381no—
191#340—381no—
192#333—382no—
193#327—382no—
194C2×C19—21no—
195C2×C19—21no—
196C2×C19—82no—
197C2×C19#187711yescharacteristic
198C2×C19#190311yescharacteristic
199C2×C19#190911yescharacteristic
200C2×#41—21no—
201C22×Q8—381no—
202#131—42no—
203#131—42no—
204C2×M16—22no—
205C2×M16—21no—
206C22×C8—22no—
207C22×C8C22⋊D1911yescharacteristic
208C22×C8C22⋊D1911yescharacteristic
209C4⋊Q8—192no—
210C4⋊Q8—381no—
211C4⋊Q8—381no—
212C4⋊Q8—381no—
213C4⋊Q8C4×D1911yescharacteristic
214#127C4×D1911yescharacteristic
215#124—21no—
216#121—21no—
217#121D7612yes—
218C4×D4—21no—
219C4×D4C22⋊D1912yes—
220C2×C4⋊C4—381no—
221C2×C4⋊C4—381no—
222C2×C4⋊C4—381no—
223C2×C42C22×D1911yescharacteristic
224#106—384no—
225C4⋊C8—21no—
226C4⋊C8—381no—
227C4⋊C8—381no—
228C4⋊C8C22⋊D1912yes—
229#102—384no—
230C22⋊C8—24no—
231C22⋊C8—381no—
232C22⋊C8—381no—
233#97—21no—
234#97—21no—
235C4×C8—192no—
236C4×C8—381no—
237#95—381no—
238#95—381no—
239C19#928711yescharacteristic, complemented, Sylow
240#41—41no—
241#41—41no—
242#41—41no—
243#41—41no—
244C2×Q8—21no—
245C2×Q8—382no—
246C2×Q8—761no—
247C2×Q8—1522no—
248C2×D4—22no—
249C2×D4—21no—
250C2×D4—21no—
251C2×D4(C2×D19)⋊C412yes—
252C22×C4—22no—
253C22×C4—761no—
254C22×C4—761no—
255C22×C4C2×D7611yescharacteristic
256C22×C4#6454111yescharacteristic
257C22×C4C2×C22⋊D1911yescharacteristic
258M16—44no—
259M16—41no—
260M16—41no—
261C2×C8—21no—
262C2×C8—21no—
263C2×C8—21no—
264C2×C8—21no—
265C2×C8—21no—
266C2×C8—22no—
267C2×C8—44no—
268C2×C8—382no—
269C2×C8—761no—
270C2×C8#6452612yes—
271C4⋊C4—21no—
272C4⋊C4—382no—
273C4⋊C4—382no—
274C4⋊C4—761no—
275C4⋊C4—761no—
276C4⋊C4—761no—
277C4⋊C4—761no—
278C4⋊C4(C2×D19)⋊C412yes—
279C22⋊C4—22no—
280C22⋊C4—22no—
281C42C2×C4×D1911yescharacteristic
282C42#6454111yescharacteristic
283C42C2×C22⋊D1911yescharacteristic
284C42C2×C22⋊D1911yescharacteristic
285C23—22no—
286C23#1059737611yescharacteristic
287Q8—41no—
288Q8—41no—
289Q8—1522no—
290Q8—1522no—
291D4—42no—
292D4—42no—
293D4—42no—
294D4—41no—
295D4—41no—
296D4—81no—
297C2×C4—22no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—42no—
301C2×C4—42no—
302C2×C4—762no—
303C2×C4—1521no—
304C2×C4—1521no—
305C2×C4—1521no—
306C2×C4—1522no—
307C2×C4C2×(C2×D19)⋊C411yescharacteristic
308C2×C4C4×C22⋊D1911yescharacteristic
309C2×C4C4×C22⋊D1911yescharacteristic
310C2×C4#1059737511yescharacteristic
311C2×C4#1059737611yescharacteristic
312C2×C4#1059737811yescharacteristic
313C2×C4C2×#6452611yescharacteristic
314C2×C4#1059739611yescharacteristic
315C2×C4#1059739711yescharacteristic
316C2×C4#1059739911yescharacteristic
317C8—22no—
318C8—42no—
319C8—41no—
320C8—762no—
321C8—1521no—
322C22—21no—
323C22—21no—
324C22—42no—
325C22—42no—
326C22—42no—
327C22#1192642311yescharacteristic
328C22#1192674911yescharacteristic
329C22#1192675911yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—42no—
335C4—3041no—
336C4—1522no—
337C4C4×#6452611yescharacteristic
338C4#1192664411yescharacteristic
339C4#1192669511yescharacteristic
340C4#1192670611yescharacteristic
341C2—21no—
342C2—21no—
343C2—82no—
344C2#1456396911yescharacteristic
345C2#1456411511yescharacteristic
346C2#1456415711yescharacteristic
subgroupG/H
centerC22#11926423
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#2932C2
socleC22×C19#386
prime radicalC19×#532C22
cosocleC2×C42×C19C23
hypercenter#2932D19
hypocenterC19#9287
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2932

Complements

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

NH ≅ G/Ntype
2. #14564608C2semidirect
3. #14562317C2semidirect
5. #14561495C2semidirect
6. #14561466C2semidirect
9. #11926940C4semidirect
10. #11926890C4semidirect
239. C19#9287semidirect

Maximal subgroups

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

subgroupindex
#145747602
#145646082
#145623172
#145621952
#145614952
#145614662
C19×#29322
#928719