Finite Group Databasebeta

← #18079030

Subgroups — #18079030

Order 4864.

438 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14572631C211yesmaximal, characteristic, complemented
2#14562255C211yesmaximal, characteristic, complemented
3C2×#11926284C211yesmaximal, characteristic, complemented
4#14561987C211yesmaximal, characteristic, complemented
5#14561535C211yesmaximal, characteristic, complemented
6#14561479C211yesmaximal, characteristic, complemented
7C19×#3211C211yesmaximal, characteristic
8#11926675—21no—
9#11926616—21no—
10#11926616—21no—
11D4×C19⋊C8—21no—
12#11926605—21no—
13#11926601C2211yescharacteristic
14#11926597C2211yescharacteristic
15#11926500—21no—
16C2×#10597260C2211yescharacteristic
17C2×#10597260C2211yescharacteristic
18#11926286—21no—
19#11926284—21no—
20#11926284—21no—
21#11926284—21no—
22#11926268—21no—
23#11926268—21no—
24C19×#529C2211yescharacteristic
25C2×C19×#124C2211yescharacteristic
26C19×#495—21no—
27C19×#488—21no—
28C19×#464—21no—
29C19×#463—21no—
30C19×#451C411yescharacteristic
31C19×#450C411yescharacteristic
32C19×#448C411yescharacteristic
33C19×#447C411yescharacteristic
34C19×#431C2211yescharacteristic
35C22×Q8×C19C2×C411yescharacteristic
36C22×D4×C19C2×C411yescharacteristic
37C2×Q16×C19—21no—
38C2×SD16×C19—21no—
39C2×SD16×C19—21no—
40C2×D8×C19—21no—
41C19×#126—21no—
42C19×#125D411yescharacteristic
43C19×#124—21no—
44C19×#124—21no—
45C19×#124—21no—
46C19×#124—21no—
47C19×#124D411yescharacteristic
48C19×#123—21no—
49C19×C22⋊Q8C2×C411yescharacteristic
50C19×#121C2×C411yescharacteristic
51C4×Q8×C19D411yescharacteristic
52C4×D4×C19—21no—
53C4×D4×C19D411yescharacteristic
54C19×#117—21no—
55C2×C22⋊C4×C19—21no—
56C2×C22⋊C4×C19—21no—
57C2×C42×C19C2311yescharacteristic
58C2×#64520—21no—
59C22×C19⋊C8—21no—
60C22×C19⋊C8—21no—
61C22×C19⋊C8—21no—
62C19×C4⋊C8—21no—
63C19×#103—21no—
64C19×#103—21no—
65C19×#102—21no—
66C19×#102—21no—
67C19×C22⋊C8C2×C411yescharacteristic
68C19×C22⋊C8C2×C411yescharacteristic
69C4×C8×C19—21no—
70C22⋊(C19⋊C8)—21no—
71C22⋊(C19⋊C8)—21no—
72C22⋊(C19⋊C8)—21no—
73C22⋊(C19⋊C8)D411yescharacteristic
74C22⋊(C19⋊C8)D411yescharacteristic
75C4⋊(C19⋊C8)—21no—
76C4⋊(C19⋊C8)—21no—
77C4⋊(C19⋊C8)—21no—
78C4⋊(C19⋊C8)—21no—
79#10597260—21no—
80#10597260—21no—
81#10597260—21no—
82#10597260—21no—
83#10597260—21no—
84#10597260D411yescharacteristic
85#10597260D411yescharacteristic
86C4×C19⋊C8—21no—
87C4×C19⋊C8—21no—
88C24×C19—21no—
89C2×Q8×C19—21no—
90C2×Q8×C19—21no—
91C2×Q8×C19—81no—
92C2×Q8×C19C22⋊C411yescharacteristic
93C2×D4×C19—21no—
94C2×D4×C19—21no—
95C2×D4×C19—21no—
96C2×D4×C19—81no—
97C2×D4×C19C22⋊C411yescharacteristic
98C22×C4×C19—21no—
99C22×C4×C19—21no—
100C22×C4×C19C22×C411yescharacteristic
101C22×C4×C19C2×D411yescharacteristic
102C22×C4×C19#4111yescharacteristic
103Q16×C19—81no—
104SD16×C19—81no—
105SD16×C19—81no—
106D8×C19—81no—
107C2×C8×C19—21no—
108C2×C8×C19—21no—
109C4⋊C4×C19—21no—
110C4⋊C4×C19—21no—
111C4⋊C4×C19—21no—
112C4⋊C4×C19—21no—
113C4⋊C4×C19C22⋊C411yescharacteristic
114C4⋊C4×C19C22⋊C411yescharacteristic
115C22⋊C4×C19—21no—
116C22⋊C4×C19—21no—
117C22⋊C4×C19—21no—
118C22⋊C4×C19—21no—
119C22⋊C4×C19—21no—
120C22⋊C4×C19—41no—
121C22⋊C4×C19—41no—
122C22⋊C4×C19—41no—
123C22⋊C4×C19—41no—
124C42×C19—21no—
125C42×C19C2×D411yescharacteristic
126C42×C19C2×D411yescharacteristic
127C42×C19C2×D411yescharacteristic
128C42×C19#4111yescharacteristic
129#64520—42no—
130C2×C19⋊C8—21no—
131C2×C19⋊C8—22no—
132C2×C19⋊C8—21no—
133C2×C19⋊C8—21no—
134C2×C19⋊C8—21no—
135C2×C19⋊C8—42no—
136C2×C19⋊C8—42no—
137C2×C19⋊C8—41no—
138C2×C19⋊C8—41no—
139C2×C19⋊C8—41no—
140#9265—191nomaximal, Sylow
141C23×C19—21no—
142C23×C19—41no—
143C23×C19—41no—
144C23×C19—41no—
145C23×C19—81no—
146C23×C19—81no—
147C23×C19C4×D411yescharacteristic
148Q8×C19—41no—
149Q8×C19—41no—
150Q8×C19—41no—
151Q8×C19—81no—
152D4×C19—41no—
153D4×C19—41no—
154D4×C19—41no—
155D4×C19—41no—
156D4×C19—41no—
157D4×C19—81no—
158C2×C4×C19—21no—
159C2×C4×C19—21no—
160C2×C4×C19—21no—
161C2×C4×C19—21no—
162C2×C4×C19—21no—
163C2×C4×C19—41no—
164C2×C4×C19—41no—
165C2×C4×C19—41no—
166C2×C4×C19—41no—
167C2×C4×C19—41no—
168C2×C4×C19—81no—
169C2×C4×C19C2×C22⋊C411yescharacteristic
170C2×C4×C19C4×D411yescharacteristic
171C2×C4×C19#12011yescharacteristic
172C2×C4×C19#12111yescharacteristic
173C2×C4×C19#12111yescharacteristic
174C2×C4×C19#12311yescharacteristic
175C8×C19—41no—
176C8×C19—41no—
177C19⋊C8—22no—
178C19⋊C8—42no—
179C19⋊C8—41no—
180C19⋊C8—41no—
181C19⋊C8—41no—
182C19⋊C8—81no—
183#3211D1911yescharacteristic
184#2968—191no—
185#1532—191no—
186C2×#329—191no—
187#1469—191no—
188#1302—191no—
189#1281—191no—
190C22×C19—21no—
191C22×C19—21no—
192C22×C19—41no—
193C22×C19—41no—
194C22×C19—41no—
195C22×C19—81no—
196C22×C19—81no—
197C22×C19—81no—
198C22×C19—161no—
199C22×C19—161no—
200C22×C19#38611yescharacteristic
201C22×C19#44311yescharacteristic
202C22×C19#44411yescharacteristic
203C4×C19—21no—
204C4×C19—21no—
205C4×C19—21no—
206C4×C19—21no—
207C4×C19—21no—
208C4×C19—21no—
209C4×C19—41no—
210C4×C19—41no—
211C4×C19—41no—
212C4×C19—81no—
213#529C2×D1911yescharacteristic
214C2×#124C2×D1911yescharacteristic
215#495—21no—
216#488—21no—
217#464—21no—
218#463—21no—
219#451Dic1911yescharacteristic
220#450Dic1911yescharacteristic
221#448Dic1911yescharacteristic
222#447Dic1911yescharacteristic
223#446—381no—
224#435—381no—
225#435—381no—
226C8×D4—381no—
227#433—381no—
228#432—191no—
229#431—191no—
230#431C2×D1911yescharacteristic
231#405—381no—
232C2×#97—191no—
233C2×#97—191no—
234#330—381no—
235#329—381no—
236#329—381no—
237#329—381no—
238#323—381no—
239#323—381no—
240C2×C19—21no—
241C2×C19—21no—
242C2×C19—81no—
243C2×C19—161no—
244C2×C19#187611yescharacteristic
245C2×C19#190611yescharacteristic
246C2×C19#191411yescharacteristic
247C22×Q8C2×Dic1911yescharacteristic
248C22×D4C2×Dic1911yescharacteristic
249C2×Q16—21no—
250C2×SD16—21no—
251C2×SD16—21no—
252C2×D8—21no—
253C2×M16—381no—
254C22×C8—381no—
255C22×C8—381no—
256C22×C8—381no—
257#126—21no—
258#125C22⋊D1911yescharacteristic
259#124—21no—
260#124—21no—
261#124—21no—
262#124—21no—
263#124C22⋊D1911yescharacteristic
264#123—21no—
265C22⋊Q8C2×Dic1911yescharacteristic
266#121C2×Dic1911yescharacteristic
267C4×Q8C22⋊D1911yescharacteristic
268C4×D4—21no—
269C4×D4C22⋊D1911yescharacteristic
270#117—21no—
271C2×C22⋊C4—21no—
272C2×C22⋊C4—21no—
273C2×C42C22×D1911yescharacteristic
274C4⋊C8—21no—
275C4⋊C8—381no—
276C4⋊C8—381no—
277C4⋊C8—381no—
278C4⋊C8—381no—
279#103—21no—
280#103—21no—
281#102—21no—
282#102—21no—
283C22⋊C8—191no—
284C22⋊C8—191no—
285C22⋊C8—381no—
286C22⋊C8—381no—
287C22⋊C8—381no—
288C22⋊C8C2×Dic1911yescharacteristic
289C22⋊C8C2×Dic1911yescharacteristic
290#97—191no—
291#97—191no—
292#97—381no—
293#97—381no—
294#97—381no—
295#97—381no—
296#97—381no—
297C4×C8—21no—
298C4×C8—381no—
299C4×C8—381no—
300C19#926511yescharacteristic, complemented, Sylow
301C24—21no—
302C2×Q8—21no—
303C2×Q8—21no—
304C2×Q8—81no—
305C2×Q8C22⋊Dic1911yescharacteristic
306C2×D4—21no—
307C2×D4—21no—
308C2×D4—21no—
309C2×D4—81no—
310C2×D4C22⋊Dic1911yescharacteristic
311C22×C4—21no—
312C22×C4—21no—
313C22×C4D4×D1911yescharacteristic
314C22×C4#6454311yescharacteristic
315C22×C4C22×Dic1911yescharacteristic
316Q16—81no—
317SD16—81no—
318SD16—81no—
319D8—81no—
320M16—762no—
321C2×C8—21no—
322C2×C8—21no—
323C2×C8—381no—
324C2×C8—382no—
325C2×C8—381no—
326C2×C8—381no—
327C2×C8—381no—
328C2×C8—762no—
329C2×C8—762no—
330C2×C8—761no—
331C2×C8—761no—
332C2×C8—761no—
333C4⋊C4—21no—
334C4⋊C4—21no—
335C4⋊C4—21no—
336C4⋊C4—21no—
337C4⋊C4C22⋊Dic1911yescharacteristic
338C4⋊C4C22⋊Dic1911yescharacteristic
339C22⋊C4—21no—
340C22⋊C4—21no—
341C22⋊C4—21no—
342C22⋊C4—21no—
343C22⋊C4—21no—
344C22⋊C4—41no—
345C22⋊C4—41no—
346C22⋊C4—41no—
347C22⋊C4—41no—
348C42—21no—
349C42D4×D1911yescharacteristic
350C42#6454311yescharacteristic
351C42C2×C22⋊D1911yescharacteristic
352C42C2×C22⋊D1911yescharacteristic
353C23—21no—
354C23—41no—
355C23—41no—
356C23—41no—
357C23—81no—
358C23—81no—
359C23D4×Dic1911yescharacteristic
360Q8—41no—
361Q8—41no—
362Q8—41no—
363Q8—81no—
364D4—41no—
365D4—41no—
366D4—41no—
367D4—41no—
368D4—41no—
369D4—81no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—81no—
381C2×C4D4×Dic1911yescharacteristic
382C2×C4#1059738111yescharacteristic
383C2×C4#1059738311yescharacteristic
384C2×C4#1059738511yescharacteristic
385C2×C4#1059738511yescharacteristic
386C2×C4C2×C22⋊Dic1911yescharacteristic
387C8—41no—
388C8—41no—
389C8—382no—
390C8—761no—
391C8—761no—
392C8—762no—
393C8—761no—
394C8—1521no—
395C22—21no—
396C22—21no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—81no—
401C22—81no—
402C22—81no—
403C22—161no—
404C22—161no—
405C22#1192642411yescharacteristic
406C22#1192666111yescharacteristic
407C22#1192666611yescharacteristic
408C4—21no—
409C4—21no—
410C4—21no—
411C4—21no—
412C4—21no—
413C4—21no—
414C4—41no—
415C4—41no—
416C4—41no—
417C4—81no—
418C2—21no—
419C2—21no—
420C2—81no—
421C2—161no—
422C2#1456396411yescharacteristic
423C2#1456413811yescharacteristic
424C2#1456418311yescharacteristic
subgroupG/H
centerC22#11926424
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#3211C2
socleC22×C19#386
prime radicalC19×#447C4
cosocleC2×C42×C19C23
hypercenter#3211D19
hypocenterC19#9265
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3211

Complements

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

NH ≅ G/Ntype
1. #14572631C2semidirect
2. #14562255C2semidirect
3. C2×#11926284C2semidirect
4. #14561987C2semidirect
5. #14561535C2semidirect
6. #14561479C2semidirect
300. C19#9265semidirect

Maximal subgroups

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

subgroupindex
#145726312
#145622552
C2×#119262842
#145619872
#145615352
#145614792
C19×#32112
#926519