Finite Group Databasebeta

← #18078664

Subgroups — #18078664

Order 4864.

450 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14573695C211yesmaximal, characteristic
2#14562226C211yesmaximal, characteristic, complemented
3#14562087C211yesmaximal, characteristic, complemented
4#14562074C211yesmaximal, characteristic, complemented
5#14561525C211yesmaximal, characteristic, complemented
6#14561472C211yesmaximal, characteristic, complemented
7C19×#2922C211yesmaximal, characteristic, complemented
8#11927094C2211yescharacteristic
9#11926868—21no—
10#11926839C411yescharacteristic
11#11926834C411yescharacteristic
12#11926744C411yescharacteristic
13#11926739C411yescharacteristic
14#11926689—21no—
15C4×#64527—21no—
16C4×#64525—21no—
17#11926597C2211yescharacteristic
18#11926568C2211yescharacteristic
19C4×#64520C2211yescharacteristic
20#11926283—22no—
21Q8⋊(C19⋊C8)—21no—
22#11926273—22no—
23D4⋊(C19⋊C8)—21no—
24C4×#41×C19C2211yescharacteristic
25C19×#433—22no—
26C19×#431—22no—
27C19×#424—21no—
28C19×#408—21no—
29C4×M16×C19C2211yescharacteristic
30C2×C4×C8×C19C2211yescharacteristic
31C2×#41×C19D411yescharacteristic
32C2×#64541—21no—
33C2×M16×C19—21no—
34C22×C8×C19—21no—
35C4×Q8×C19C2×C411yescharacteristic
36C4×Q8×C19D411yescharacteristic
37C4×D4×C19—21no—
38C4×D4×C19—21no—
39C4×D4×C19C2×C411yescharacteristic
40C4×D4×C19D411yescharacteristic
41C19×#117—21no—
42C19×#117D411yescharacteristic
43C2×C42×C19—21no—
44C2×C42×C19C2311yescharacteristic
45C2×#64527—21no—
46C2×#64525—21no—
47#10597376—21no—
48#10597376—21no—
49C2×#64520—21no—
50C2×#64520—21no—
51#10597321—21no—
52#10597320C2×C411yescharacteristic
53C4×D76—21no—
54C4×D76—21no—
55#10597315C2×C411yescharacteristic
56C19×C4⋊C8—24no—
57C19×C22⋊C8—24no—
58C19×#97D412yes—
59C4×C8×C19—21no—
60C4×C8×C19—21no—
61C4×C8×C19D412yes—
62#10597292—21no—
63#10597289—21no—
64C22⋊(C19⋊C8)—21no—
65#10597266—21no—
66#10597266—21no—
67#10597265—21no—
68#10597264—21no—
69C4⋊(C19⋊C8)—21no—
70C4⋊(C19⋊C8)—21no—
71C4⋊(C19⋊C8)C2×C411yescharacteristic
72C4⋊(C19⋊C8)C2×C411yescharacteristic
73#10597260—21no—
74C4×C19⋊C8—21no—
75C4×C19⋊C8—21no—
76#41×C19—41no—
77#41×C19—41no—
78C2×Q8×C19C22⋊C411yescharacteristic
79C2×D4×C19—21no—
80C2×D4×C19C22⋊C411yescharacteristic
81C22×C4×C19—21no—
82C22×C4×C19—21no—
83C22×C4×C19—21no—
84C22×C4×C19C2×D411yescharacteristic
85C22×C4×C19#4111yescharacteristic
86C22×C4×C19#4111yescharacteristic
87C2×C22⋊D19—41no—
88#64541—81no—
89#64541—81no—
90C2×D76—21no—
91C2×D76—21no—
92C2×D76—21no—
93C2×C4×D19—41no—
94C2×Dic38—21no—
95M16×C19—41no—
96M16×C19—41no—
97C2×C8×C19—22no—
98C2×C8×C19—22no—
99C2×C8×C19—41no—
100C2×C8×C19—41no—
101C4⋊C4×C19—21no—
102C4⋊C4×C19—21no—
103C4⋊C4×C19C22⋊C411yescharacteristic
104C4⋊C4×C19C22⋊C411yescharacteristic
105C22⋊C4×C19—21no—
106C22⋊C4×C19—21no—
107C22⋊C4×C19—21no—
108C42×C19—21no—
109C42×C19—21no—
110C42×C19—21no—
111C42×C19C22×C411yescharacteristic
112C42×C19C2×D411yescharacteristic
113C42×C19C2×D411yescharacteristic
114C42×C19C2×D411yescharacteristic
115#64527—42no—
116#64525—42no—
117(C2×D19)⋊C4—41no—
118(C2×D19)⋊C4—41no—
119C4⋊Dic19—21no—
120C4⋊Dic19—21no—
121#64520—22no—
122#64520—41no—
123#64520—81no—
124C2×C19⋊C8—21no—
125C2×C19⋊C8—21no—
126C2×C19⋊C8—41no—
127C2×C19⋊C8—41no—
128#9213—191nomaximal, Sylow
129C23×C19—21no—
130C23×C19#12311yescharacteristic
131C22×D19—41no—
132Q8×C19—21no—
133Q8×C19—21no—
134D4×C19—21no—
135D4×C19—21no—
136D4×C19—42no—
137C2×C4×C19—21no—
138C2×C4×C19—21no—
139C2×C4×C19—21no—
140C2×C4×C19—21no—
141C2×C4×C19—21no—
142C2×C4×C19—21no—
143C2×C4×C19—21no—
144C2×C4×C19—21no—
145C2×C4×C19—21no—
146C2×C4×C19—42no—
147C2×C4×C19—41no—
148C2×C4×C19—41no—
149C2×C4×C19—41no—
150C2×C4×C19—41no—
151C2×C4×C19C2×C22⋊C411yescharacteristic
152C2×C4×C19C4×D411yescharacteristic
153C2×C4×C19C4×D411yescharacteristic
154C2×C4×C19#12011yescharacteristic
155C2×C4×C19#12111yescharacteristic
156C2×C4×C19#12111yescharacteristic
157C22⋊D19—82no—
158C2×Dic19—41no—
159D76—41no—
160D76—41no—
161D76—41no—
162D76—41no—
163D76—81no—
164C4×D19—81no—
165C4×D19—81no—
166Dic38—81no—
167C8×C19—42no—
168C8×C19—42no—
169C19⋊C8—42no—
170C19⋊C8—41no—
171C19⋊C8—41no—
172C19⋊C8—81no—
173#3106—191no—
174#2922D1911yescharacteristic, complemented
175#1525—191no—
176#1492—191no—
177#1489—191no—
178#1299—191no—
179#1278—191no—
180C22×C19—21no—
181C22×C19—21no—
182C22×C19—21no—
183C22×C19—41no—
184C22×C19—41no—
185C22×C19—41no—
186C22×C19#38611yescharacteristic
187C2×D19—81no—
188C2×D19—81no—
189C2×D19—81no—
190C4×C19—21no—
191C4×C19—21no—
192C4×C19—21no—
193C4×C19—41no—
194C4×C19—41no—
195C4×C19—41no—
196C4×C19#42111yescharacteristic
197C4×C19#42111yescharacteristic
198C4×C19#44311yescharacteristic
199C4×C19#44411yescharacteristic
200C4×C19#47111yescharacteristic
201C4×C19#47211yescharacteristic
202Dic19—81no—
203#532—191no—
204C4×#41C2×D1911yescharacteristic
205#482—381no—
206#477—191no—
207#476—191no—
208#460—191no—
209#459—191no—
210#449—381no—
211C4×SD16—381no—
212C4×D8—381no—
213#433—22no—
214#431—22no—
215#431—191no—
216#424—21no—
217#423—191no—
218#408—21no—
219C4×M16—191no—
220C4×M16C2×D1911yescharacteristic
221C2×C4×C8C2×D1911yescharacteristic
222#329—382no—
223Q8⋊C8—381no—
224D4⋊C8—381no—
225D4⋊C8—382no—
226C2×C19—41no—
227C2×C19—81no—
228C2×C19#187611yescharacteristic
229C2×C19#189711yescharacteristic
230C2×C19#190711yescharacteristic
231D19—161no—
232C2×#41—381no—
233C2×#41C22⋊D1911yescharacteristic
234C2×SD16—381no—
235C2×D8—381no—
236C2×M16—21no—
237C2×M16—381no—
238C2×M16—381no—
239C22×C8—21no—
240C4⋊Q8—191no—
241#127—191no—
242#124—381no—
243#121—381no—
244#121—381no—
245C4×Q8C4×D1911yescharacteristic
246C4×Q8D7611yescharacteristic
247C4×D4—21no—
248C4×D4—21no—
249C4×D4—381no—
250C4×D4—381no—
251C4×D4C4×D1911yescharacteristic
252C4×D4D7611yescharacteristic
253#117—21no—
254#117C22⋊D1911yescharacteristic
255C2×C42—21no—
256C2×C42C22×D1911yescharacteristic
257#107—381no—
258#106—381no—
259C4⋊C8—24no—
260C4⋊C8—191no—
261C4⋊C8—191no—
262C4⋊C8—381no—
263C4⋊C8—381no—
264#103—381no—
265#102—381no—
266#102—381no—
267#102—381no—
268C22⋊C8—24no—
269C22⋊C8—381no—
270#97—381no—
271#97C22⋊D1912yes—
272C4×C8—21no—
273C4×C8—21no—
274C4×C8—381no—
275C4×C8—381no—
276C4×C8C22⋊D1912yes—
277C19#921311yescharacteristic, complemented, Sylow
278#41—41no—
279#41—41no—
280#41—1521no—
281#41—1521no—
282C2×Q8—381no—
283C2×Q8(C2×D19)⋊C411yescharacteristic
284C2×D4—21no—
285C2×D4—381no—
286C2×D4—381no—
287C2×D4—381no—
288C2×D4—761no—
289C2×D4(C2×D19)⋊C411yescharacteristic
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—761no—
294C22×C4#6454111yescharacteristic
295C22×C4#6454111yescharacteristic
296C22×C4C2×C22⋊D1911yescharacteristic
297SD16—762no—
298D8—762no—
299M16—41no—
300M16—41no—
301M16—382no—
302M16—761no—
303M16—1521no—
304C2×C8—22no—
305C2×C8—22no—
306C2×C8—41no—
307C2×C8—41no—
308C2×C8—381no—
309C2×C8—381no—
310C2×C8—761no—
311C2×C8—761no—
312C4⋊C4—21no—
313C4⋊C4—21no—
314C4⋊C4—381no—
315C4⋊C4—381no—
316C4⋊C4(C2×D19)⋊C411yescharacteristic
317C4⋊C4(C2×D19)⋊C411yescharacteristic
318C22⋊C4—21no—
319C22⋊C4—21no—
320C22⋊C4—21no—
321C22⋊C4—761no—
322C22⋊C4—761no—
323C42—21no—
324C42—21no—
325C42—21no—
326C42C2×C4×D1911yescharacteristic
327C42C2×D7611yescharacteristic
328C42C2×C22⋊D1911yescharacteristic
329C42C2×C22⋊D1911yescharacteristic
330C23—21no—
331C23—761no—
332C23#1059737511yescharacteristic
333Q8—21no—
334Q8—21no—
335Q8—1521no—
336D4—21no—
337D4—21no—
338D4—42no—
339D4—761no—
340D4—761no—
341D4—761no—
342D4—761no—
343D4—1521no—
344D4—1522no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—42no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—761no—
360C2×C4—1521no—
361C2×C4—1521no—
362C2×C4C2×(C2×D19)⋊C411yescharacteristic
363C2×C4C4×C22⋊D1911yescharacteristic
364C2×C4C4×C22⋊D1911yescharacteristic
365C2×C4#1059737611yescharacteristic
366C2×C4#1059737611yescharacteristic
367C2×C4#1059739911yescharacteristic
368C8—42no—
369C8—42no—
370C8—762no—
371C8—761no—
372C8—761no—
373C8—1521no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—1521no—
381C22—1521no—
382C22—1521no—
383C22#1192642311yescharacteristic
384C4—21no—
385C4—21no—
386C4—21no—
387C4—41no—
388C4—41no—
389C4—41no—
390C4—1521no—
391C4#1192656211yescharacteristic
392C4#1192656211yescharacteristic
393C4#1192665911yescharacteristic
394C4#1192666411yescharacteristic
395C4#1192680711yescharacteristic
396C4#1192681411yescharacteristic
397C2—41no—
398C2—81no—
399C2—3041no—
400C2#1456396211yescharacteristic
401C2#1456408311yescharacteristic
402C2#1456414311yescharacteristic
subgroupG/H
centerC2×C4#10597376
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#2922C2
socleC22×C19#386
prime radical#14573695C2
cosocleC2×C42×C19C23
hypercenter#2922D19
hypocenterC19#9213
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2922

Complements

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

NH ≅ G/Ntype
2. #14562226C2semidirect
3. #14562087C2semidirect
4. #14562074C2semidirect
5. #14561525C2semidirect
6. #14561472C2semidirect
7. C19×#2922C2semidirect
174. #2922D19semidirect
277. C19#9213semidirect

Maximal subgroups

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

subgroupindex
#145736952
#145622262
#145620872
#145620742
#145615252
#145614722
C19×#29222
#921319