Finite Group Databasebeta

← #18081915

Subgroups — #18081915

Order 4864.

502 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14574061C211yesmaximal, characteristic
2#14563797C211yesmaximal, characteristic, complemented
3#14562196C211yesmaximal, characteristic, complemented
4#14562195C211yesmaximal, characteristic, complemented
5#14562194C211yesmaximal, characteristic, complemented
6#14561919C211yesmaximal, 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×#10597264—21no—
19C2×#10597265—21no—
20C2×C4×C19⋊C8C2211yescharacteristic
21#11926410C2211yescharacteristic
22#11926279—22no—
23#11926278—22no—
24#11926277—22no—
25#11926266—21no—
26C8×C19⋊C8—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—
72#10597265—42no—
73#10597264—42no—
74C4⋊(C19⋊C8)—21no—
75C4×C19⋊C8—21no—
76C4×C19⋊C8C2×C411yescharacteristic
77C4×C19⋊C8C2×C411yescharacteristic
78C4×C19⋊C8D411yescharacteristic
79C4×C19⋊C8D411yescharacteristic
80#41×C19—41no—
81#41×C19—41no—
82#41×C19—41no—
83#41×C19—41no—
84C2×Q8×C19—21no—
85C2×D4×C19—21no—
86C2×D4×C19—21no—
87C2×D4×C19—21no—
88C2×D4×C19—41no—
89C22×C4×C19—41no—
90C22×C4×C19—41no—
91C22×C4×C19C2×D411yescharacteristic
92C22×C4×C19C2×D411yescharacteristic
93C22×C4×C19C2×D411yescharacteristic
94C2×C22⋊D19—41no—
95C22×Dic19—41no—
96#64541—41no—
97#64541—41no—
98#64541—41no—
99#64541—41no—
100C2×D76—21no—
101C2×D76—21no—
102C2×D76—21no—
103C2×C4×D19—41no—
104C2×Dic38—21no—
105C2×C8×C19—22no—
106C4⋊C4×C19—21no—
107C4⋊C4×C19—21no—
108C4⋊C4×C19—41no—
109C4⋊C4×C19—41no—
110C22⋊C4×C19—41no—
111C22⋊C4×C19—41no—
112C42×C19C22×C411yescharacteristic
113C42×C19C2×D411yescharacteristic
114C42×C19#4111yescharacteristic
115C42×C19#4111yescharacteristic
116#64528—42no—
117#64528—42no—
118#64527—42no—
119#64527—42no—
120#64526—42no—
121#64526—42no—
122#64525—42no—
123#64525—42no—
124(C2×D19)⋊C4—41no—
125(C2×D19)⋊C4—41no—
126C4⋊Dic19—21no—
127C4⋊Dic19—21no—
128C4⋊Dic19—41no—
129C4⋊Dic19—41no—
130C2×C19⋊C8—22no—
131C2×C19⋊C8C22⋊C411yescharacteristic
132C2×C19⋊C8C22⋊C411yescharacteristic
133C2×C19⋊C8C22⋊C411yescharacteristic
134C2×C19⋊C8C22⋊C411yescharacteristic
135C2×C19⋊C8D812yes—
136C2×C19⋊C8D812yes—
137C2×C19⋊C8SD1612yes—
138C2×C19⋊C8SD1612yes—
139#9756—191nomaximal, Sylow
140C23×C19—41no—
141C23×C19#12711yescharacteristic
142C22×D19—41no—
143Q8×C19—41no—
144Q8×C19—41no—
145D4×C19—41no—
146D4×C19—41no—
147D4×C19—81no—
148D4×C19—81no—
149D4×C19—81no—
150D4×C19—81no—
151C2×C4×C19—41no—
152C2×C4×C19—41no—
153C2×C4×C19—41no—
154C2×C4×C19—81no—
155C2×C4×C19—81no—
156C2×C4×C19—81no—
157C2×C4×C19—81no—
158C2×C4×C19—81no—
159C2×C4×C19C2×C22⋊C411yescharacteristic
160C2×C4×C19C4×D411yescharacteristic
161C2×C4×C19C4×D411yescharacteristic
162C2×C4×C19#12111yescharacteristic
163C2×C4×C19#12111yescharacteristic
164C2×C4×C19#12411yescharacteristic
165C2×C4×C19C2×D811yescharacteristic
166C2×C4×C19C2×D811yescharacteristic
167C2×C4×C19C2×SD1611yescharacteristic
168C2×C4×C19C2×SD1611yescharacteristic
169C22⋊D19—81no—
170C22⋊D19—81no—
171C2×Dic19—41no—
172C2×Dic19—81no—
173C2×Dic19—81no—
174C2×Dic19—81no—
175D76—41no—
176D76—41no—
177D76—81no—
178D76—81no—
179C4×D19—81no—
180C4×D19—81no—
181Dic38—41no—
182Dic38—41no—
183C8×C19—42no—
184C19⋊C8—42no—
185C19⋊C8#10212yes—
186C19⋊C8#10212yes—
187C19⋊C8#10212yes—
188C19⋊C8#10212yes—
189#3147—191no—
190#1846—191no—
191#1517—191no—
192#1517—191no—
193#1517—191no—
194#1517D1911yescharacteristic, complemented
195#1450—191no—
196C22×C19—21no—
197C22×C19—21no—
198C22×C19—81no—
199C22×C19—81no—
200C22×C19—81no—
201C22×C19#39011yescharacteristic
202C22×C19#49211yescharacteristic
203C22×C19#49311yescharacteristic
204C2×D19—81no—
205C2×D19—81no—
206C2×D19—81no—
207C4×C19—21no—
208C4×C19—21no—
209C4×C19—21no—
210C4×C19—21no—
211C4×C19—81no—
212C4×C19—161no—
213C4×C19C2×#10211yescharacteristic
214C4×C19C2×#10211yescharacteristic
215C4×C19#48611yescharacteristic
216C4×C19#48611yescharacteristic
217Dic19—81no—
218Dic19—161no—
219C2×#135—381no—
220C2×#135—381no—
221#532—191no—
222#532C2×D1911yescharacteristic
223#495—381no—
224#495—381no—
225#494—191no—
226#493—191no—
227#492—191no—
228#492—191no—
229#431—191no—
230#431C2×D1911yescharacteristic
231C2×#107—381no—
232C2×#106—381no—
233C2×C4×C8—191no—
234#382—191no—
235#382C2×D1911yescharacteristic
236#327—22no—
237#327—382no—
238#327—382no—
239#327—382no—
240#322—381no—
241C82—381no—
242C2×C19—21no—
243C2×C19—21no—
244C2×C19—161no—
245C2×C19#195711yescharacteristic
246C2×C19#197611yescharacteristic
247C2×C19#197611yescharacteristic
248D19—161no—
249C2×#41—21no—
250C2×#41—381no—
251#135—762no—
252#135—762no—
253#135—762no—
254#135—762no—
255C2×Q16—381no—
256C2×Q16—381no—
257C2×SD16—381no—
258C2×SD16—381no—
259C2×SD16—381no—
260C2×SD16—381no—
261C2×D8—381no—
262C2×D8—381no—
263C22×C8—191no—
264C22×C8—191no—
265C4⋊Q8—191no—
266C4⋊Q8C4×D1911yescharacteristic
267#127—191no—
268#127C4×D1911yescharacteristic
269#124—21no—
270#124—381no—
271#121—21no—
272#121—21no—
273#121—381no—
274#121—381no—
275C4×D4—21no—
276C4×D4—21no—
277C4×D4—381no—
278C4×D4—381no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—381no—
281C2×C42C22×D1911yescharacteristic
282#107—762no—
283#106—762no—
284C4⋊C8—21no—
285C4⋊C8—381no—
286C22⋊C8—192no—
287C22⋊C8C22⋊D1912yes—
288C4×C8—21no—
289C4×C8—191no—
290C4×C8—191no—
291C4×C8—191no—
292C4×C8—191no—
293C4×C8—381no—
294#95—21no—
295#95—21no—
296#95—381no—
297#95—381no—
298C19#975611yescharacteristic, complemented, Sylow
299#41—41no—
300#41—41no—
301#41—41no—
302#41—41no—
303#41—761no—
304#41—761no—
305#41—761no—
306#41—761no—
307C2×Q8—21no—
308C2×Q8—381no—
309C2×D4—21no—
310C2×D4—21no—
311C2×D4—21no—
312C2×D4—41no—
313C2×D4—381no—
314C2×D4—381no—
315C2×D4—381no—
316C2×D4—761no—
317C22×C4—41no—
318C22×C4—41no—
319C22×C4—761no—
320C22×C4—761no—
321C22×C4D4×D1911yescharacteristic
322C22×C4D4×D1911yescharacteristic
323C22×C4C2×C22⋊D1911yescharacteristic
324Q16—762no—
325Q16—762no—
326SD16—762no—
327SD16—762no—
328SD16—762no—
329SD16—762no—
330D8—762no—
331D8—762no—
332C2×C8—22no—
333C2×C8—191no—
334C2×C8—191no—
335C2×C8—191no—
336C2×C8—191no—
337C2×C8—192no—
338C2×C8—192no—
339C2×C8—192no—
340C2×C8—192no—
341C2×C8—382no—
342C4⋊C4—21no—
343C4⋊C4—21no—
344C4⋊C4—41no—
345C4⋊C4—41no—
346C4⋊C4—381no—
347C4⋊C4—381no—
348C4⋊C4—761no—
349C4⋊C4—761no—
350C22⋊C4—41no—
351C22⋊C4—41no—
352C22⋊C4—761no—
353C22⋊C4—761no—
354C42C2×C4×D1911yescharacteristic
355C42#6454111yescharacteristic
356C42D4×D1911yescharacteristic
357C42#6454311yescharacteristic
358C23—41no—
359C23—761no—
360C23#1059738611yescharacteristic
361Q8—41no—
362Q8—41no—
363Q8—761no—
364Q8—761no—
365D4—41no—
366D4—41no—
367D4—81no—
368D4—81no—
369D4—81no—
370D4—81no—
371D4—761no—
372D4—761no—
373D4—1521no—
374D4—1521no—
375D4—1521no—
376D4—1521no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—81no—
381C2×C4—81no—
382C2×C4—81no—
383C2×C4—81no—
384C2×C4—81no—
385C2×C4—761no—
386C2×C4—1521no—
387C2×C4—1521no—
388C2×C4—1521no—
389C2×C4—1521no—
390C2×C4—1521no—
391C2×C4C22⋊C4×D1911yescharacteristic
392C2×C4(C22⋊D19)⋊C411yescharacteristic
393C2×C4#1059733011yescharacteristic
394C2×C4#1059733111yescharacteristic
395C2×C4D8×D1911yescharacteristic
396C2×C4D8×D1911yescharacteristic
397C2×C4SD16×D1911yescharacteristic
398C2×C4SD16×D1911yescharacteristic
399C2×C4C4×C22⋊D1911yescharacteristic
400C2×C4#1059738511yescharacteristic
401C8—42no—
402C8—192no—
403C8—192no—
404C8—192no—
405C8—192no—
406C8—762no—
407C22—21no—
408C22—21no—
409C22—81no—
410C22—81no—
411C22—81no—
412C22—1521no—
413C22—1521no—
414C22—1521no—
415C22#1192644411yescharacteristic
416C22#1192691511yescharacteristic
417C22#1192691911yescharacteristic
418C4—21no—
419C4—21no—
420C4—21no—
421C4—21no—
422C4—81no—
423C4—161no—
424C4—3041no—
425C4—1521no—
426C4#102×D1911yescharacteristic
427C4#102×D1911yescharacteristic
428C4#1192688911yescharacteristic
429C4#1192688911yescharacteristic
430C2—21no—
431C2—21no—
432C2—161no—
433C2—3041no—
434C2#1456443911yescharacteristic
435C2#1456453011yescharacteristic
436C2#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#9756
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. #14562196C2semidirect
4. #14562195C2semidirect
5. #14562194C2semidirect
6. #14561919C2semidirect
7. C19×#1517C2semidirect
13. #11926923C4semidirect
14. #11926920C4semidirect
15. #11926918C4semidirect
16. #11926916C4semidirect
194. #1517D19semidirect
298. C19#9756semidirect

Maximal subgroups

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

subgroupindex
#145740612
#145637972
#145621962
#145621952
#145621942
#145619192
C19×#15172
#975619