Finite Group Databasebeta

← #18077430

Subgroups — #18077430

Order 4864.

484 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14573084C211yesmaximal, characteristic
2#14572303C211yesmaximal, characteristic, complemented
3#14562034C211yesmaximal, characteristic, complemented
4#14562018C211yesmaximal, characteristic, complemented
5#14561530C211yesmaximal, characteristic, complemented
6#14561470C211yesmaximal, characteristic, complemented
7C19×#1492C211yesmaximal, characteristic, complemented
8C2×#10597396—21no—
9C4×#64541C2211yescharacteristic
10#11926763—21no—
11#11926756—21no—
12#11926751C411yescharacteristic
13#11926746C411yescharacteristic
14#11926741C411yescharacteristic
15#11926736C411yescharacteristic
16#11926604—22no—
17#11926600—21no—
18#11926597C2211yescharacteristic
19#11926596—21no—
20C2×C4⋊(C19⋊C8)C2211yescharacteristic
21C2×C4⋊(C19⋊C8)C2211yescharacteristic
22#11926540—21no—
23#11926512—21no—
24#11926502—21no—
25#11926276—21no—
26#11926273—21no—
27D4⋊(C19⋊C8)—21no—
28D4⋊(C19⋊C8)—21no—
29C19×#532C2211yescharacteristic
30C19×#423C2211yescharacteristic
31C2×C4×C8×C19C2211yescharacteristic
32C19×D4⋊C8—22no—
33C2×#41×C19—21no—
34C2×#64541D411yescharacteristic
35C2×M16×C19—21no—
36C22×C8×C19—21no—
37C19×C4⋊Q8C2×C411yescharacteristic
38C19×#127C2×C411yescharacteristic
39C19×#124—21no—
40C19×#121—21no—
41C19×#121—21no—
42C4×D4×C19—21no—
43C4×D4×C19—21no—
44C2×C42×C19C2311yescharacteristic
45#10597396—42no—
46#10597396—42no—
47C2×#64528—21no—
48C2×#64527—21no—
49C2×#64526—21no—
50C2×#64525—21no—
51C4×C22⋊D19—21no—
52C4×C22⋊D19—21no—
53#10597372D411yescharacteristic
54C22×C19⋊C8—21no—
55C22×C19⋊C8—21no—
56C4×D76C2×C411yescharacteristic
57C4×D76D411yescharacteristic
58#10597318—21no—
59C42×D19—21no—
60C4×Dic38C2×C411yescharacteristic
61C4×Dic38D411yescharacteristic
62C19×C4⋊C8—21no—
63C19×C4⋊C8D412yes—
64C4×C8×C19—21no—
65C4×C8×C19—21no—
66#10597292—21no—
67#10597292—21no—
68#10597289—21no—
69#10597289—21no—
70C22⋊(C19⋊C8)—21no—
71(C2×D19)⋊C8—22no—
72(C2×D19)⋊C8—22no—
73#10597272—22no—
74C8×Dic19—22no—
75C4⋊(C19⋊C8)—21no—
76C4⋊(C19⋊C8)—21no—
77C4⋊(C19⋊C8)—21no—
78C4⋊(C19⋊C8)C2×C411yescharacteristic
79C4⋊(C19⋊C8)C2×C411yescharacteristic
80C4⋊(C19⋊C8)D411yescharacteristic
81C4⋊(C19⋊C8)D411yescharacteristic
82C4×C19⋊C8—21no—
83#41×C19—41no—
84#41×C19—41no—
85#41×C19—41no—
86#41×C19—41no—
87C2×Q8×C19—21no—
88C2×D4×C19—21no—
89C2×D4×C19—21no—
90C2×D4×C19—21no—
91C2×D4×C19—41no—
92C22×C4×C19—41no—
93C22×C4×C19C2×D411yescharacteristic
94C22×C4×C19#4111yescharacteristic
95C22×C4×C19#4111yescharacteristic
96C2×C22⋊D19—21no—
97#64541—21no—
98#64541—21no—
99#64541—21no—
100#64541—21no—
101C2×D76C22⋊C411yescharacteristic
102C2×C4×D19—21no—
103C2×C4×D19—21no—
104C2×C4×D19—21no—
105C2×Dic38C22⋊C411yescharacteristic
106M16×C19—41no—
107M16×C19—41no—
108C2×C8×C19—22no—
109C2×C8×C19—22no—
110C2×C8×C19—41no—
111C2×C8×C19—41no—
112C4⋊C4×C19—21no—
113C4⋊C4×C19—21no—
114C22⋊C4×C19—41no—
115C22⋊C4×C19—41no—
116C42×C19C22×C411yescharacteristic
117C42×C19C2×D411yescharacteristic
118C42×C19C2×D411yescharacteristic
119C42×C19C2×D411yescharacteristic
120C22⋊Dic19—21no—
121#64528—42no—
122#64527—42no—
123#64526—42no—
124#64525—42no—
125(C2×D19)⋊C4—21no—
126(C2×D19)⋊C4—21no—
127C4⋊Dic19C22⋊C411yescharacteristic
128C4⋊Dic19C22⋊C411yescharacteristic
129Dic19⋊C4—21no—
130Dic19⋊C4—21no—
131C4×Dic19—21no—
132C4×Dic19—21no—
133C4×Dic19—21no—
134C2×C19⋊C8—21no—
135C2×C19⋊C8—21no—
136C2×C19⋊C8—21no—
137C2×C19⋊C8—21no—
138C2×C19⋊C8—41no—
139C2×C19⋊C8—41no—
140C2×C19⋊C8—41no—
141C2×C19⋊C8—41no—
142C2×C19⋊C8—41no—
143#8996—191nomaximal, Sylow
144C23×C19—41no—
145C23×C19#12311yescharacteristic
146C22×D19—21no—
147Q8×C19—41no—
148Q8×C19—41no—
149D4×C19—42no—
150D4×C19—41no—
151D4×C19—41no—
152D4×C19—41no—
153D4×C19—41no—
154D4×C19—81no—
155D4×C19—81no—
156C2×C4×C19—21no—
157C2×C4×C19—21no—
158C2×C4×C19—41no—
159C2×C4×C19—41no—
160C2×C4×C19—81no—
161C2×C4×C19—81no—
162C2×C4×C19C2×C22⋊C411yescharacteristic
163C2×C4×C19C4×D411yescharacteristic
164C2×C4×C19C4×D411yescharacteristic
165C2×C4×C19#12011yescharacteristic
166C2×C4×C19#12111yescharacteristic
167C2×C4×C19#12111yescharacteristic
168C2×C4×C19#13511yescharacteristic
169C2×C4×C19#13511yescharacteristic
170C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
171C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
172C22⋊D19—41no—
173C22⋊D19—41no—
174C2×Dic19—21no—
175C2×Dic19—21no—
176C2×Dic19—21no—
177D76—21no—
178D76—21no—
179C4×D19—41no—
180C4×D19—41no—
181C4×D19—41no—
182C4×D19—41no—
183C4×D19—81no—
184Dic38—21no—
185Dic38—21no—
186C8×C19—42no—
187C8×C19—42no—
188C19⋊C8—41no—
189C19⋊C8—41no—
190C19⋊C8—41no—
191C19⋊C8—41no—
192C19⋊C8—81no—
193#3035—191no—
194#2925—191no—
195#1492D1911yescharacteristic, complemented
196#1480—191no—
197#1476—191no—
198#1301—191no—
199#1277—191no—
200C22×C19—21no—
201C22×C19—21no—
202C22×C19—81no—
203C22×C19—81no—
204C22×C19—81no—
205C22×C19#38611yescharacteristic
206C22×C19#48211yescharacteristic
207C22×C19#48211yescharacteristic
208C2×D19—41no—
209C2×D19—41no—
210C2×D19—41no—
211C4×C19—21no—
212C4×C19—21no—
213C4×C19—21no—
214C4×C19—81no—
215C4×C19#41611yescharacteristic
216C4×C19#41811yescharacteristic
217C4×C19#44311yescharacteristic
218C4×C19#44411yescharacteristic
219C4×C19#44911yescharacteristic
220C4×C19#44911yescharacteristic
221Dic19—41no—
222Dic19—41no—
223Dic19—41no—
224C2×#135—381no—
225#532C2×D1911yescharacteristic
226C4×#41—191no—
227#464—381no—
228#463—381no—
229#462—191no—
230#461—191no—
231#460—191no—
232#459—191no—
233#433—382no—
234#432—381no—
235#431—191no—
236#431—381no—
237#423C2×D1911yescharacteristic
238C2×C4⋊C8—191no—
239C2×C4⋊C8—191no—
240#416—381no—
241#408—381no—
242#405—381no—
243C2×C4×C8C2×D1911yescharacteristic
244Q8⋊C8—381no—
245D4⋊C8—22no—
246D4⋊C8—381no—
247D4⋊C8—381no—
248D4⋊C8—381no—
249C2×C19—21no—
250C2×C19—21no—
251C2×C19—161no—
252C2×C19#187511yescharacteristic
253C2×C19#187611yescharacteristic
254C2×C19#188111yescharacteristic
255D19—81no—
256C2×#41—21no—
257C2×#41—191no—
258#135—762no—
259#135—762no—
260C2×Q16—381no—
261C2×SD16—381no—
262C2×SD16—381no—
263C2×D8—381no—
264C2×M16—21no—
265C22×C8—21no—
266C22×C8—381no—
267C22×C8—381no—
268C4⋊Q8C4×D1911yescharacteristic
269#127C4×D1911yescharacteristic
270#124—21no—
271#121—21no—
272#121—21no—
273C4×Q8—191no—
274C4×Q8—191no—
275C4×D4—21no—
276C4×D4—21no—
277C4×D4—191no—
278C4×D4—191no—
279C4×D4—381no—
280C4×D4—381no—
281#117—191no—
282#117—381no—
283C2×C42—381no—
284C2×C42C22×D1911yescharacteristic
285C4⋊C8—21no—
286C4⋊C8—191no—
287C4⋊C8—191no—
288C4⋊C8—191no—
289C4⋊C8—191no—
290C4⋊C8—381no—
291C4⋊C8—381no—
292C4⋊C8—381no—
293C4⋊C8C22⋊D1912yes—
294#103—381no—
295#103—381no—
296#102—381no—
297#102—381no—
298C22⋊C8—382no—
299C22⋊C8—382no—
300C22⋊C8—381no—
301#97—382no—
302C4×C8—21no—
303C4×C8—21no—
304C4×C8—382no—
305C4×C8—381no—
306C19#899611yescharacteristic, complemented, Sylow
307#41—41no—
308#41—41no—
309#41—41no—
310#41—41no—
311#41—381no—
312#41—381no—
313#41—381no—
314#41—381no—
315C2×Q8—21no—
316C2×Q8—191no—
317C2×D4—21no—
318C2×D4—21no—
319C2×D4—21no—
320C2×D4—41no—
321C2×D4—191no—
322C2×D4—381no—
323C22×C4—41no—
324C22×C4—381no—
325C22×C4—381no—
326C22×C4—381no—
327C22×C4#6454111yescharacteristic
328C22×C4D4×D1911yescharacteristic
329C22×C4#6454311yescharacteristic
330Q16—762no—
331SD16—762no—
332SD16—762no—
333D8—762no—
334M16—41no—
335M16—41no—
336C2×C8—22no—
337C2×C8—22no—
338C2×C8—41no—
339C2×C8—41no—
340C2×C8—381no—
341C2×C8—381no—
342C2×C8—381no—
343C2×C8—381no—
344C2×C8—761no—
345C2×C8—761no—
346C2×C8—761no—
347C2×C8—761no—
348C2×C8—761no—
349C4⋊C4—21no—
350C4⋊C4—21no—
351C4⋊C4—191no—
352C4⋊C4—191no—
353C4⋊C4—381no—
354C4⋊C4—381no—
355C22⋊C4—41no—
356C22⋊C4—41no—
357C22⋊C4—381no—
358C22⋊C4—381no—
359C22⋊C4—381no—
360C42—381no—
361C42—381no—
362C42—381no—
363C42C2×C4×D1911yescharacteristic
364C42D4×D1911yescharacteristic
365C42D4×D1911yescharacteristic
366C42C2×C22⋊D1911yescharacteristic
367C23—41no—
368C23—381no—
369C23#1059732911yescharacteristic
370Q8—41no—
371Q8—41no—
372Q8—381no—
373Q8—381no—
374D4—42no—
375D4—41no—
376D4—41no—
377D4—41no—
378D4—41no—
379D4—81no—
380D4—81no—
381D4—381no—
382D4—381no—
383D4—761no—
384D4—761no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—81no—
390C2×C4—81no—
391C2×C4—381no—
392C2×C4—381no—
393C2×C4—381no—
394C2×C4—761no—
395C2×C4—761no—
396C2×C4—761no—
397C2×C4—761no—
398C2×C4—1521no—
399C2×C4C22⋊C4×D1911yescharacteristic
400C2×C4(C22⋊D19)⋊C411yescharacteristic
401C2×C4#1059733011yescharacteristic
402C2×C4#1059735711yescharacteristic
403C2×C4#1059735811yescharacteristic
404C2×C4#1059736011yescharacteristic
405C2×C4#1059736211yescharacteristic
406C2×C4C4×C22⋊D1911yescharacteristic
407C2×C4#1059738311yescharacteristic
408C2×C4#1059738411yescharacteristic
409C8—42no—
410C8—42no—
411C8—761no—
412C8—761no—
413C8—761no—
414C8—761no—
415C8—1521no—
416C22—21no—
417C22—21no—
418C22—81no—
419C22—81no—
420C22—81no—
421C22—761no—
422C22—761no—
423C22—761no—
424C22#1192642011yescharacteristic
425C22#1192686611yescharacteristic
426C22#1192686711yescharacteristic
427C4—21no—
428C4—21no—
429C4—21no—
430C4—81no—
431C4—761no—
432C4—761no—
433C4—761no—
434C4#1192653711yescharacteristic
435C4#1192654711yescharacteristic
436C4#1192665811yescharacteristic
437C4#1192666311yescharacteristic
438C4#1192668611yescharacteristic
439C4#1192668811yescharacteristic
440C2—21no—
441C2—21no—
442C2—161no—
443C2—1521no—
444C2#1456395411yescharacteristic
445C2#1456395911yescharacteristic
446C2#1456400011yescharacteristic
subgroupG/H
centerC2×C4#10597383
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1492C2
socleC22×C19#386
prime radical#14573084C2
cosocleC2×C42×C19C23
hypercenter#1492D19
hypocenterC19#8996
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1492

Complements

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

NH ≅ G/Ntype
2. #14572303C2semidirect
3. #14562034C2semidirect
4. #14562018C2semidirect
5. #14561530C2semidirect
6. #14561470C2semidirect
7. C19×#1492C2semidirect
195. #1492D19semidirect
306. C19#8996semidirect

Maximal subgroups

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

subgroupindex
#145730842
#145723032
#145620342
#145620182
#145615302
#145614702
C19×#14922
#899619