Finite Group Databasebeta

← #18081933

Subgroups — #18081933

Order 4864.

478 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14574061C211yesmaximal, characteristic
2#14563765C211yesmaximal, characteristic, complemented
3#14562196C211yesmaximal, characteristic, complemented
4#14562195C211yesmaximal, characteristic, complemented
5#14562194C211yesmaximal, characteristic, complemented
6#14561928C211yesmaximal, characteristic, complemented
7C19×#1517C211yesmaximal, characteristic, complemented
8C2×#10597396—21no—
9C2×#10597396—21no—
10#11927094C2211yescharacteristic
11#11926926—21no—
12#11926926—21no—
13#11926923C411yescharacteristic, complemented
14#11926920C411yescharacteristic, complemented
15#11926918C411yescharacteristic, complemented
16#11926916C411yescharacteristic, complemented
17#11926597C2211yescharacteristic
18C2×C4×C19⋊C8C2211yescharacteristic
19#11926410C2211yescharacteristic
20#11926306—21no—
21#11926306—21no—
22#11926279—22no—
23#11926278—22no—
24#11926277—22no—
25#11926266—21no—
26#11926265—21no—
27C19×#532C2211yescharacteristic
28C19×#431C2211yescharacteristic
29C19×#382C2211yescharacteristic
30C19×#327—22no—
31C2×#41×C19—21no—
32C2×#64541—21no—
33C19×C4⋊Q8C2×C411yescharacteristic
34C19×#127C2×C411yescharacteristic
35C19×#124—21no—
36C19×#121—21no—
37C19×#121—21no—
38C4×D4×C19—21no—
39C4×D4×C19—21no—
40C2×C4⋊C4×C19—21no—
41C2×C42×C19C2311yescharacteristic
42#10597396—42no—
43#10597396—42no—
44#10597396—42no—
45#10597396—42no—
46C2×#64528—21no—
47C2×#64528—21no—
48C2×#64527—21no—
49C2×#64527—21no—
50C2×#64526—21no—
51C2×#64526—21no—
52C2×#64525—21no—
53C2×#64525—21no—
54#10597376—21no—
55#10597376—21no—
56C2×C4⋊Dic19—21no—
57C22×C19⋊C8D411yescharacteristic
58C22×C19⋊C8D411yescharacteristic
59#10597321—21no—
60#10597320C2×C411yescharacteristic
61C4×D76—21no—
62C4×D76—21no—
63#10597315C2×C411yescharacteristic
64C19×C4⋊C8—21no—
65C19×C22⋊C8D412yes—
66C4×C8×C19—21no—
67C19×#95—21no—
68C19×#95—21no—
69C19⋊#95—21no—
70C19⋊#95—21no—
71C22⋊(C19⋊C8)D412yes—
72C4⋊(C19⋊C8)—21no—
73C4×C19⋊C8—21no—
74C4×C19⋊C8C2×C411yescharacteristic
75C4×C19⋊C8C2×C411yescharacteristic
76C4×C19⋊C8D411yescharacteristic
77C4×C19⋊C8D411yescharacteristic
78#41×C19—41no—
79#41×C19—41no—
80#41×C19—41no—
81#41×C19—41no—
82C2×Q8×C19—21no—
83C2×D4×C19—21no—
84C2×D4×C19—21no—
85C2×D4×C19—21no—
86C2×D4×C19—41no—
87C22×C4×C19—41no—
88C22×C4×C19—41no—
89C22×C4×C19C2×D411yescharacteristic
90C22×C4×C19C2×D411yescharacteristic
91C22×C4×C19C2×D411yescharacteristic
92C2×C22⋊D19—41no—
93C22×Dic19—41no—
94#64541—41no—
95#64541—41no—
96#64541—41no—
97#64541—41no—
98C2×D76—21no—
99C2×D76—21no—
100C2×D76—21no—
101C2×C4×D19—41no—
102C2×Dic38—21no—
103C2×C8×C19—22no—
104C4⋊C4×C19—21no—
105C4⋊C4×C19—21no—
106C4⋊C4×C19—41no—
107C4⋊C4×C19—41no—
108C22⋊C4×C19—41no—
109C22⋊C4×C19—41no—
110C42×C19C22×C411yescharacteristic
111C42×C19C2×D411yescharacteristic
112C42×C19#4111yescharacteristic
113C42×C19#4111yescharacteristic
114#64528—42no—
115#64528—42no—
116#64527—42no—
117#64527—42no—
118#64526—42no—
119#64526—42no—
120#64525—42no—
121#64525—42no—
122(C2×D19)⋊C4—41no—
123(C2×D19)⋊C4—41no—
124C4⋊Dic19—21no—
125C4⋊Dic19—21no—
126C4⋊Dic19—41no—
127C4⋊Dic19—41no—
128C2×C19⋊C8—21no—
129C2×C19⋊C8—21no—
130C2×C19⋊C8—21no—
131C2×C19⋊C8—21no—
132C2×C19⋊C8—22no—
133C2×C19⋊C8C22⋊C411yescharacteristic
134C2×C19⋊C8C22⋊C411yescharacteristic
135C2×C19⋊C8C22⋊C411yescharacteristic
136C2×C19⋊C8C22⋊C411yescharacteristic
137#9760—191nomaximal, Sylow
138C23×C19—41no—
139C23×C19#12711yescharacteristic
140C22×D19—41no—
141Q8×C19—41no—
142Q8×C19—41no—
143D4×C19—41no—
144D4×C19—41no—
145D4×C19—81no—
146D4×C19—81no—
147D4×C19—81no—
148D4×C19—81no—
149C2×C4×C19—41no—
150C2×C4×C19—41no—
151C2×C4×C19—41no—
152C2×C4×C19—81no—
153C2×C4×C19—81no—
154C2×C4×C19—81no—
155C2×C4×C19—81no—
156C2×C4×C19—81no—
157C2×C4×C19C2×C22⋊C411yescharacteristic
158C2×C4×C19C4×D411yescharacteristic
159C2×C4×C19C4×D411yescharacteristic
160C2×C4×C19#12111yescharacteristic
161C2×C4×C19#12111yescharacteristic
162C2×C4×C19#12411yescharacteristic
163C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
164C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
165C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
166C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
167C22⋊D19—81no—
168C22⋊D19—81no—
169C2×Dic19—41no—
170C2×Dic19—81no—
171C2×Dic19—81no—
172C2×Dic19—81no—
173D76—41no—
174D76—41no—
175D76—81no—
176D76—81no—
177C4×D19—81no—
178C4×D19—81no—
179Dic38—41no—
180Dic38—41no—
181C8×C19—42no—
182C19⋊C8—21no—
183C19⋊C8—21no—
184C19⋊C8—21no—
185C19⋊C8—21no—
186C19⋊C8—42no—
187#3147—191no—
188#1835—191no—
189#1517—191no—
190#1517—191no—
191#1517—191no—
192#1517D1911yescharacteristic, complemented
193#1452—191no—
194C22×C19—21no—
195C22×C19—21no—
196C22×C19—81no—
197C22×C19—81no—
198C22×C19—81no—
199C22×C19#39011yescharacteristic
200C22×C19#49611yescharacteristic
201C22×C19#49611yescharacteristic
202C2×D19—81no—
203C2×D19—81no—
204C2×D19—81no—
205C4×C19—21no—
206C4×C19—21no—
207C4×C19—21no—
208C4×C19—21no—
209C4×C19—81no—
210C4×C19—161no—
211C4×C19#41811yescharacteristic
212C4×C19#41811yescharacteristic
213C4×C19#49011yescharacteristic
214C4×C19#49011yescharacteristic
215Dic19—81no—
216Dic19—161no—
217C2×#135—381no—
218C2×#135—381no—
219#532—191no—
220#532C2×D1911yescharacteristic
221#495—381no—
222#495—381no—
223#494—191no—
224#493—191no—
225#492—191no—
226#492—191no—
227#431—191no—
228#431C2×D1911yescharacteristic
229C2×C4×C8—191no—
230#382—191no—
231#382C2×D1911yescharacteristic
232#340—381no—
233#340—381no—
234#327—22no—
235#327—382no—
236#327—382no—
237#327—382no—
238#322—381no—
239#322—381no—
240C2×C19—21no—
241C2×C19—21no—
242C2×C19—161no—
243C2×C19#196111yescharacteristic
244C2×C19#197611yescharacteristic
245C2×C19#197611yescharacteristic
246D19—161no—
247C2×#41—21no—
248C2×#41—381no—
249#135—762no—
250#135—762no—
251#135—762no—
252#135—762no—
253C2×Q16—381no—
254C2×Q16—381no—
255C2×SD16—381no—
256C2×SD16—381no—
257C2×SD16—381no—
258C2×SD16—381no—
259C2×D8—381no—
260C2×D8—381no—
261C22×C8—191no—
262C22×C8—191no—
263C4⋊Q8—191no—
264C4⋊Q8C4×D1911yescharacteristic
265#127—191no—
266#127C4×D1911yescharacteristic
267#124—21no—
268#124—381no—
269#121—21no—
270#121—21no—
271#121—381no—
272#121—381no—
273C4×D4—21no—
274C4×D4—21no—
275C4×D4—381no—
276C4×D4—381no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—381no—
279C2×C42C22×D1911yescharacteristic
280C4⋊C8—21no—
281C4⋊C8—381no—
282C22⋊C8—192no—
283C22⋊C8C22⋊D1912yes—
284C4×C8—21no—
285C4×C8—191no—
286C4×C8—191no—
287C4×C8—191no—
288C4×C8—191no—
289C4×C8—381no—
290#95—21no—
291#95—21no—
292#95—381no—
293#95—381no—
294C19#976011yescharacteristic, complemented, Sylow
295#41—41no—
296#41—41no—
297#41—41no—
298#41—41no—
299#41—761no—
300#41—761no—
301#41—761no—
302#41—761no—
303C2×Q8—21no—
304C2×Q8—381no—
305C2×D4—21no—
306C2×D4—21no—
307C2×D4—21no—
308C2×D4—41no—
309C2×D4—381no—
310C2×D4—381no—
311C2×D4—381no—
312C2×D4—761no—
313C22×C4—41no—
314C22×C4—41no—
315C22×C4—761no—
316C22×C4—761no—
317C22×C4D4×D1911yescharacteristic
318C22×C4D4×D1911yescharacteristic
319C22×C4C2×C22⋊D1911yescharacteristic
320Q16—762no—
321Q16—762no—
322SD16—762no—
323SD16—762no—
324SD16—762no—
325SD16—762no—
326D8—762no—
327D8—762no—
328C2×C8—22no—
329C2×C8—191no—
330C2×C8—191no—
331C2×C8—191no—
332C2×C8—191no—
333C2×C8—381no—
334C2×C8—381no—
335C2×C8—381no—
336C2×C8—381no—
337C2×C8—382no—
338C4⋊C4—21no—
339C4⋊C4—21no—
340C4⋊C4—41no—
341C4⋊C4—41no—
342C4⋊C4—381no—
343C4⋊C4—381no—
344C4⋊C4—761no—
345C4⋊C4—761no—
346C22⋊C4—41no—
347C22⋊C4—41no—
348C22⋊C4—761no—
349C22⋊C4—761no—
350C42C2×C4×D1911yescharacteristic
351C42#6454111yescharacteristic
352C42D4×D1911yescharacteristic
353C42#6454311yescharacteristic
354C23—41no—
355C23—761no—
356C23#1059738611yescharacteristic
357Q8—41no—
358Q8—41no—
359Q8—761no—
360Q8—761no—
361D4—41no—
362D4—41no—
363D4—81no—
364D4—81no—
365D4—81no—
366D4—81no—
367D4—761no—
368D4—761no—
369D4—1521no—
370D4—1521no—
371D4—1521no—
372D4—1521no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—81no—
377C2×C4—81no—
378C2×C4—81no—
379C2×C4—81no—
380C2×C4—81no—
381C2×C4—761no—
382C2×C4—1521no—
383C2×C4—1521no—
384C2×C4—1521no—
385C2×C4—1521no—
386C2×C4—1521no—
387C2×C4C22⋊C4×D1911yescharacteristic
388C2×C4(C22⋊D19)⋊C411yescharacteristic
389C2×C4#1059733011yescharacteristic
390C2×C4#1059733111yescharacteristic
391C2×C4#1059735711yescharacteristic
392C2×C4#1059735711yescharacteristic
393C2×C4#1059736011yescharacteristic
394C2×C4#1059736011yescharacteristic
395C2×C4C4×C22⋊D1911yescharacteristic
396C2×C4#1059738511yescharacteristic
397C8—42no—
398C8—381no—
399C8—381no—
400C8—381no—
401C8—381no—
402C8—762no—
403C22—21no—
404C22—21no—
405C22—81no—
406C22—81no—
407C22—81no—
408C22—1521no—
409C22—1521no—
410C22—1521no—
411C22#1192644411yescharacteristic
412C22#1192693011yescharacteristic
413C22#1192693211yescharacteristic
414C4—21no—
415C4—21no—
416C4—21no—
417C4—21no—
418C4—81no—
419C4—161no—
420C4—3041no—
421C4—1521no—
422C4#1192654711yescharacteristic
423C4#1192654711yescharacteristic
424C4#1192690711yescharacteristic
425C4#1192690711yescharacteristic
426C2—21no—
427C2—21no—
428C2—161no—
429C2—3041no—
430C2#1456445711yescharacteristic
431C2#1456453011yescharacteristic
432C2#1456453211yescharacteristic
subgroupG/H
centerC22#11926444
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1517C2
socleC22×C19#390
prime radical#14574061C2
cosocleC2×C42×C19C23
hypercenter#1517D19
hypocenterC19#9760
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. #14563765C2semidirect
3. #14562196C2semidirect
4. #14562195C2semidirect
5. #14562194C2semidirect
6. #14561928C2semidirect
7. C19×#1517C2semidirect
13. #11926923C4semidirect
14. #11926920C4semidirect
15. #11926918C4semidirect
16. #11926916C4semidirect
192. #1517D19semidirect
294. C19#9760semidirect

Maximal subgroups

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

subgroupindex
#145740612
#145637652
#145621962
#145621952
#145621942
#145619282
C19×#15172
#976019