Finite Group Databasebeta

← #18077253

Subgroups — #18077253

Order 4864.

514 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#14572767C211yesmaximal, characteristic, complemented
2#14564464C211yesmaximal, characteristic, complemented
3C4×#10597294C211yesmaximal, characteristic, complemented
4#14562052C211yesmaximal, characteristic, complemented
5#14561526C211yesmaximal, characteristic, complemented
6#14561467C211yesmaximal, characteristic, complemented
7C19×#3106C211yesmaximal, characteristic
8Q8×C19⋊C8—21no—
9#11926622—22no—
10#11926622—21no—
11#11926597—21no—
12#11926597C2211yescharacteristic
13#11926568—21no—
14#11926568C2211yescharacteristic
15C2×#10597294—22no—
16C2×#10597294—21no—
17C4×#64520C2211yescharacteristic
18C42×Dic19C2211yescharacteristic
19#11926303—21no—
20D4⋊(C19⋊C8)—21no—
21D4⋊(C19⋊C8)—21no—
22C19×#532C2211yescharacteristic
23C4×#41×C19C2211yescharacteristic
24C19×#482—21no—
25C19×#477C411yescharacteristic, complemented
26C19×#476C411yescharacteristic, complemented
27C19×#460C411yescharacteristic, complemented
28C19×#459C411yescharacteristic, complemented
29C19×#449—21no—
30C4×SD16×C19—21no—
31C4×D8×C19—21no—
32C19×#431C2211yescharacteristic
33C2×#41×C19—21no—
34C2×#41×C19D411yescharacteristic
35C2×SD16×C19—21no—
36C2×D8×C19—21no—
37C19×C4⋊Q8C2×C411yescharacteristic
38C19×#127C2×C411yescharacteristic
39C19×#124—21no—
40C19×#121—21no—
41C19×#121—21no—
42C4×Q8×C19C2×C411yescharacteristic
43C4×Q8×C19D411yescharacteristic
44C4×D4×C19—21no—
45C4×D4×C19—21no—
46C4×D4×C19—21no—
47C4×D4×C19—21no—
48C4×D4×C19C2×C411yescharacteristic
49C4×D4×C19D411yescharacteristic
50C19×#117—21no—
51C19×#117D411yescharacteristic
52C2×C42×C19—21no—
53C2×C42×C19C2311yescharacteristic
54C2×C4×Dic19—21no—
55C2×C4×Dic19—21no—
56C2×C4×Dic19—21no—
57C2×#64520—22no—
58C2×#64520—21no—
59C2×#64520D412yes—
60C19×#107—21no—
61C19×#106—21no—
62C19×C4⋊C8C2×C411yescharacteristic
63C19×C4⋊C8C2×C411yescharacteristic
64C19×#103—21no—
65C19×#102—21no—
66C19×#102—21no—
67C19×#102—21no—
68C19×C22⋊C8—21no—
69C4×C8×C19—21no—
70#10597294—24no—
71#10597294—44no—
72C22⋊(C19⋊C8)—22no—
73C22⋊(C19⋊C8)—21no—
74C4⋊(C19⋊C8)—22no—
75C4⋊(C19⋊C8)—21no—
76C4⋊(C19⋊C8)—21no—
77C4⋊(C19⋊C8)D411yescharacteristic
78C4⋊(C19⋊C8)D411yescharacteristic
79#10597260—21no—
80C4×C19⋊C8—22no—
81C4×C19⋊C8—21no—
82C4×C19⋊C8—21no—
83#41×C19—22no—
84#41×C19—41no—
85#41×C19—42no—
86#41×C19—42no—
87C2×Q8×C19—21no—
88C2×Q8×C19C22⋊C411yescharacteristic
89C2×D4×C19—21no—
90C2×D4×C19—21no—
91C2×D4×C19—21no—
92C2×D4×C19—21no—
93C2×D4×C19—41no—
94C2×D4×C19C22⋊C411yescharacteristic
95C22×C4×C19—21no—
96C22×C4×C19—21no—
97C22×C4×C19—21no—
98C22×C4×C19—41no—
99C22×C4×C19C2×D411yescharacteristic
100C22×C4×C19C2×D411yescharacteristic
101C22×C4×C19#4111yescharacteristic
102C22×Dic19—41no—
103SD16×C19—42no—
104D8×C19—42no—
105C2×C8×C19—21no—
106C2×C8×C19—21no—
107C4⋊C4×C19—21no—
108C4⋊C4×C19—21no—
109C4⋊C4×C19—21no—
110C4⋊C4×C19—21no—
111C4⋊C4×C19C22⋊C411yescharacteristic
112C4⋊C4×C19C22⋊C411yescharacteristic
113C22⋊C4×C19—21no—
114C22⋊C4×C19—21no—
115C22⋊C4×C19—21no—
116C22⋊C4×C19—41no—
117C22⋊C4×C19—41no—
118C42×C19—21no—
119C42×C19—21no—
120C42×C19—21no—
121C42×C19C22×C411yescharacteristic
122C42×C19C2×D411yescharacteristic
123C42×C19C2×D411yescharacteristic
124C42×C19#4111yescharacteristic
125C4×Dic19—22no—
126C4×Dic19—22no—
127C4×Dic19—22no—
128C4×Dic19—41no—
129C4×Dic19—41no—
130C4×Dic19—41no—
131#64520—22no—
132#64520—41no—
133#64520—42no—
134#64520—82no—
135C2×C19⋊C8—21no—
136C2×C19⋊C8—22no—
137C2×C19⋊C8—21no—
138C2×C19⋊C8—41no—
139#8970—191nomaximal, Sylow
140C23×C19—21no—
141C23×C19—41no—
142C23×C19#12111yescharacteristic
143Q8×C19—21no—
144Q8×C19—42no—
145Q8×C19#10412yescomplemented
146D4×C19—21no—
147D4×C19—21no—
148D4×C19—42no—
149D4×C19—42no—
150D4×C19—41no—
151D4×C19—41no—
152D4×C19—41no—
153D4×C19—41no—
154D4×C19—82no—
155C2×C4×C19—21no—
156C2×C4×C19—21no—
157C2×C4×C19—21no—
158C2×C4×C19—21no—
159C2×C4×C19—21no—
160C2×C4×C19—21no—
161C2×C4×C19—21no—
162C2×C4×C19—21no—
163C2×C4×C19—21no—
164C2×C4×C19—42no—
165C2×C4×C19—41no—
166C2×C4×C19—41no—
167C2×C4×C19—41no—
168C2×C4×C19—41no—
169C2×C4×C19—41no—
170C2×C4×C19—81no—
171C2×C4×C19—81no—
172C2×C4×C19C2×C22⋊C411yescharacteristic
173C2×C4×C19C4×D411yescharacteristic
174C2×C4×C19C4×D411yescharacteristic
175C2×C4×C19#12011yescharacteristic
176C2×C4×C19#12111yescharacteristic
177C2×C4×C19#12311yescharacteristic
178C2×Dic19—42no—
179C2×Dic19—42no—
180C2×Dic19—42no—
181C8×C19—41no—
182C8×C19—41no—
183C19⋊C8—42no—
184C19⋊C8—42no—
185C19⋊C8—41no—
186C19⋊C8—41no—
187#3106D1911yescharacteristic
188#2991—191no—
189#1962—191no—
190C4×#104—191no—
191#1484—191no—
192#1299—191no—
193#1276—191no—
194C22×C19—21no—
195C22×C19—21no—
196C22×C19—21no—
197C22×C19—41no—
198C22×C19—41no—
199C22×C19—41no—
200C22×C19—81no—
201C22×C19—81no—
202C22×C19—81no—
203C22×C19#38611yescharacteristic
204C4×C19—21no—
205C4×C19—22no—
206C4×C19—21no—
207C4×C19—21no—
208C4×C19—41no—
209C4×C19—41no—
210C4×C19—81no—
211C4×C19C2×#10411yescharacteristic
212C4×C19#42111yescharacteristic
213C4×C19#44311yescharacteristic
214C4×C19#44411yescharacteristic
215C4×C19#45311yescharacteristic
216C4×C19#45411yescharacteristic
217Dic19—44no—
218#532C2×D1911yescharacteristic
219C4×#41C2×D1911yescharacteristic
220#482—21no—
221#477Dic1911yescharacteristic, complemented
222#476Dic1911yescharacteristic, complemented
223#460Dic1911yescharacteristic, complemented
224#459Dic1911yescharacteristic, complemented
225#449—21no—
226C8×Q8—381no—
227C4×SD16—21no—
228C4×D8—21no—
229#436—382no—
230#436—381no—
231#431—191no—
232#431—381no—
233#431C2×D1911yescharacteristic
234#423—191no—
235#423—381no—
236C2×#104—381no—
237C2×#104—382no—
238C4×M16—191no—
239C43—191no—
240#339—381no—
241D4⋊C8—381no—
242D4⋊C8—381no—
243C2×C19—41no—
244C2×C19—81no—
245C2×C19—161no—
246C2×C19#187111yescharacteristic
247C2×C19#187611yescharacteristic
248C2×C19#188311yescharacteristic
249C2×#41—21no—
250C2×#41C22⋊D1911yescharacteristic
251C2×SD16—21no—
252C2×D8—21no—
253C2×M16—192no—
254C2×M16—382no—
255C2×M16—381no—
256C4⋊Q8C2×Dic1911yescharacteristic
257#127C2×Dic1911yescharacteristic
258#124—21no—
259#121—21no—
260#121—21no—
261C4×Q8C2×Dic1911yescharacteristic
262C4×Q8C22⋊D1911yescharacteristic
263C4×D4—21no—
264C4×D4—21no—
265C4×D4—21no—
266C4×D4—21no—
267C4×D4C2×Dic1911yescharacteristic
268C4×D4C22⋊D1911yescharacteristic
269#117—21no—
270#117C22⋊D1911yescharacteristic
271C2×C42—21no—
272C2×C42—381no—
273C2×C42—381no—
274C2×C42—381no—
275C2×C42C22×D1911yescharacteristic
276#107—21no—
277#106—21no—
278C4⋊C8—191no—
279C4⋊C8—191no—
280C4⋊C8—382no—
281C4⋊C8—381no—
282C4⋊C8—381no—
283C4⋊C8C2×Dic1911yescharacteristic
284C4⋊C8C2×Dic1911yescharacteristic
285#104—384no—
286#104—764no—
287#103—21no—
288#102—21no—
289#102—21no—
290#102—21no—
291C22⋊C8—21no—
292C22⋊C8—382no—
293C22⋊C8—381no—
294#97—381no—
295C4×C8—21no—
296C4×C8—382no—
297C4×C8—381no—
298C4×C8—381no—
299C19#897011yescharacteristic, complemented, Sylow
300#41—22no—
301#41—41no—
302#41—42no—
303#41—42no—
304C2×Q8—21no—
305C2×Q8C22⋊Dic1911yescharacteristic
306C2×D4—21no—
307C2×D4—21no—
308C2×D4—21no—
309C2×D4—21no—
310C2×D4—41no—
311C2×D4C22⋊Dic1911yescharacteristic
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—41no—
316C22×C4—761no—
317C22×C4D4×D1911yescharacteristic
318C22×C4#6454311yescharacteristic
319C22×C4C2×C22⋊D1911yescharacteristic
320SD16—42no—
321D8—42no—
322M16—382no—
323M16—761no—
324M16—762no—
325M16—1522no—
326C2×C8—21no—
327C2×C8—21no—
328C2×C8—381no—
329C2×C8—381no—
330C2×C8—382no—
331C2×C8—761no—
332C4⋊C4—21no—
333C4⋊C4—21no—
334C4⋊C4—21no—
335C4⋊C4—21no—
336C4⋊C4C22⋊Dic1911yescharacteristic
337C4⋊C4C22⋊Dic1911yescharacteristic
338C22⋊C4—21no—
339C22⋊C4—21no—
340C22⋊C4—21no—
341C22⋊C4—41no—
342C22⋊C4—41no—
343C42—21no—
344C42—21no—
345C42—21no—
346C42—382no—
347C42—382no—
348C42—382no—
349C42—761no—
350C42—761no—
351C42—761no—
352C42D4×D1911yescharacteristic
353C42#6454311yescharacteristic
354C42C22×Dic1911yescharacteristic
355C42C2×C22⋊D1911yescharacteristic
356C23—21no—
357C23—41no—
358C23#1059738511yescharacteristic
359Q8—21no—
360Q8—42no—
361Q8#1059729412yescomplemented
362D4—21no—
363D4—21no—
364D4—42no—
365D4—42no—
366D4—41no—
367D4—41no—
368D4—41no—
369D4—41no—
370D4—82no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—42no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—81no—
387C2×C4—81no—
388C2×C4—762no—
389C2×C4—762no—
390C2×C4—762no—
391C2×C4D4×Dic1911yescharacteristic
392C2×C4D4×Dic1911yescharacteristic
393C2×C4#1059738111yescharacteristic
394C2×C4#1059738311yescharacteristic
395C2×C4#1059738511yescharacteristic
396C2×C4C2×C22⋊Dic1911yescharacteristic
397C8—41no—
398C8—41no—
399C8—762no—
400C8—762no—
401C8—761no—
402C8—761no—
403C22—21no—
404C22—21no—
405C22—21no—
406C22—41no—
407C22—41no—
408C22—41no—
409C22—81no—
410C22—81no—
411C22—81no—
412C22#1192642411yescharacteristic
413C4—21no—
414C4—22no—
415C4—21no—
416C4—21no—
417C4—41no—
418C4—41no—
419C4—81no—
420C4—764no—
421C4C2×#1059729411yescharacteristic
422C4#1192656111yescharacteristic
423C4#1192666111yescharacteristic
424C4#1192666611yescharacteristic
425C4#1192671011yescharacteristic
426C4#1192671511yescharacteristic
427C2—41no—
428C2—81no—
429C2—161no—
430C2#1456393811yescharacteristic
431C2#1456396411yescharacteristic
432C2#1456401311yescharacteristic
subgroupG/H
centerC2×C4#10597383
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
Fitting, prime radicalC19×#3106C2
socleC22×C19#386
cosocleC2×C42×C19C23
hypercenter#3106D19
hypocenterC19#8970
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3106

Complements

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

NH ≅ G/Ntype
1. #14572767C2semidirect
2. #14564464C2semidirect
3. C4×#10597294C2semidirect
4. #14562052C2semidirect
5. #14561526C2semidirect
6. #14561467C2semidirect
25. C19×#477C4semidirect
26. C19×#476C4semidirect
27. C19×#460C4semidirect
28. C19×#459C4semidirect
145. Q8×C19#104semidirect
221. #477Dic19semidirect
222. #476Dic19semidirect
223. #460Dic19semidirect
224. #459Dic19semidirect
299. C19#8970semidirect
361. Q8#10597294semidirect

Maximal subgroups

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

subgroupindex
#145727672
#145644642
C4×#105972942
#145620522
#145615262
#145614672
C19×#31062
#897019