Finite Group Databasebeta

← #18077267

Subgroups — #18077267

Order 4864.

476 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14572767C211yesmaximal, characteristic
2#14564613C211yesmaximal, characteristic, complemented
3C4×#10597294C211yesmaximal, characteristic
4#14562056C211yesmaximal, characteristic, complemented
5#14561526C211yesmaximal, characteristic, complemented
6#14561467C211yesmaximal, characteristic, complemented
7C19×#3107C211yesmaximal, characteristic
8Q8×C19⋊C8—21no—
9#11926622—22no—
10#11926622—21no—
11#11926597—21no—
12#11926597C2211yescharacteristic
13#11926568—21no—
14#11926568C2211yescharacteristic
15C2×#10597294—21no—
16C4×#64520C2211yescharacteristic
17C42×Dic19C2211yescharacteristic
18#11926303—22no—
19#11926303—21no—
20Q8⋊(C19⋊C8)—21no—
21Q8⋊(C19⋊C8)—21no—
22C19×#533C2211yescharacteristic
23C4×#41×C19C2211yescharacteristic
24C19×#485—21no—
25C19×#475C411yescharacteristic, complemented
26C19×#474C411yescharacteristic, complemented
27C19×#462C411yescharacteristic, complemented
28C19×#461C411yescharacteristic, complemented
29C19×#452—21no—
30C4×Q16×C19—21no—
31C4×SD16×C19—21no—
32C19×#431C2211yescharacteristic
33C2×#41×C19D411yescharacteristic
34C2×Q16×C19—21no—
35C2×SD16×C19—21no—
36C19×C4⋊Q8C2×C411yescharacteristic
37C19×C4⋊Q8C2×C411yescharacteristic
38C19×#125—21no—
39C19×C22⋊Q8—21no—
40C19×C22⋊Q8—21no—
41C4×Q8×C19—21no—
42C4×Q8×C19—21no—
43C4×Q8×C19C2×C411yescharacteristic
44C4×Q8×C19D411yescharacteristic
45C4×D4×C19—21no—
46C4×D4×C19—21no—
47C4×D4×C19C2×C411yescharacteristic
48C4×D4×C19D411yescharacteristic
49C19×#117—21no—
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×#103—21no—
66C19×#103—21no—
67C19×#102—21no—
68C19×C22⋊C8—21no—
69C4×C8×C19—21no—
70#10597294—24no—
71C22⋊(C19⋊C8)—22no—
72C22⋊(C19⋊C8)—21no—
73C4⋊(C19⋊C8)—22no—
74C4⋊(C19⋊C8)—21no—
75C4⋊(C19⋊C8)—21no—
76C4⋊(C19⋊C8)D411yescharacteristic
77C4⋊(C19⋊C8)D411yescharacteristic
78#10597260—21no—
79C4×C19⋊C8—22no—
80C4×C19⋊C8—21no—
81C4×C19⋊C8—21no—
82#41×C19—22no—
83#41×C19—41no—
84C2×Q8×C19—21no—
85C2×Q8×C19—21no—
86C2×Q8×C19C22⋊C411yescharacteristic
87C2×D4×C19—21no—
88C2×D4×C19C22⋊C411yescharacteristic
89C22×C4×C19—21no—
90C22×C4×C19—21no—
91C22×C4×C19—21no—
92C22×C4×C19C2×D411yescharacteristic
93C22×C4×C19C2×D411yescharacteristic
94C22×C4×C19#4111yescharacteristic
95C22×Dic19—41no—
96Q16×C19—42no—
97SD16×C19—42no—
98C2×C8×C19—21no—
99C2×C8×C19—21no—
100C4⋊C4×C19—21no—
101C4⋊C4×C19—21no—
102C4⋊C4×C19—21no—
103C4⋊C4×C19—21no—
104C4⋊C4×C19—21no—
105C4⋊C4×C19—21no—
106C4⋊C4×C19—41no—
107C4⋊C4×C19—41no—
108C4⋊C4×C19C22⋊C411yescharacteristic
109C4⋊C4×C19C22⋊C411yescharacteristic
110C22⋊C4×C19—21no—
111C22⋊C4×C19—21no—
112C22⋊C4×C19—21no—
113C22⋊C4×C19—41no—
114C42×C19—21no—
115C42×C19—21no—
116C42×C19—21no—
117C42×C19—41no—
118C42×C19C22×C411yescharacteristic
119C42×C19C2×D411yescharacteristic
120C42×C19C2×D411yescharacteristic
121C42×C19#4111yescharacteristic
122C4×Dic19—22no—
123C4×Dic19—22no—
124C4×Dic19—22no—
125C4×Dic19—41no—
126C4×Dic19—41no—
127C4×Dic19—41no—
128#64520—22no—
129#64520—41no—
130#64520—42no—
131#64520—82no—
132C2×C19⋊C8—21no—
133C2×C19⋊C8—22no—
134C2×C19⋊C8—21no—
135C2×C19⋊C8—41no—
136#8972—191nomaximal, Sylow
137C23×C19—21no—
138C23×C19#12111yescharacteristic
139Q8×C19—21no—
140Q8×C19—41no—
141Q8×C19—41no—
142Q8×C19—41no—
143Q8×C19—41no—
144Q8×C19#10412yes—
145D4×C19—21no—
146D4×C19—21no—
147D4×C19—42no—
148C2×C4×C19—21no—
149C2×C4×C19—21no—
150C2×C4×C19—21no—
151C2×C4×C19—21no—
152C2×C4×C19—21no—
153C2×C4×C19—21no—
154C2×C4×C19—21no—
155C2×C4×C19—21no—
156C2×C4×C19—21no—
157C2×C4×C19—42no—
158C2×C4×C19—41no—
159C2×C4×C19—41no—
160C2×C4×C19—41no—
161C2×C4×C19—41no—
162C2×C4×C19—41no—
163C2×C4×C19—41no—
164C2×C4×C19C2×C22⋊C411yescharacteristic
165C2×C4×C19C4×D411yescharacteristic
166C2×C4×C19C4×D411yescharacteristic
167C2×C4×C19#12011yescharacteristic
168C2×C4×C19#12111yescharacteristic
169C2×C4×C19#12311yescharacteristic
170C2×Dic19—42no—
171C2×Dic19—42no—
172C2×Dic19—42no—
173C8×C19—41no—
174C8×C19—41no—
175C19⋊C8—42no—
176C19⋊C8—42no—
177C19⋊C8—41no—
178C19⋊C8—41no—
179#3107D1911yescharacteristic
180#2991—191no—
181#1994—191no—
182C4×#104—191no—
183#1485—191no—
184#1299—191no—
185#1276—191no—
186C22×C19—21no—
187C22×C19—21no—
188C22×C19—21no—
189C22×C19—41no—
190C22×C19—41no—
191C22×C19—41no—
192C22×C19#38611yescharacteristic
193C4×C19—21no—
194C4×C19—22no—
195C4×C19—21no—
196C4×C19—21no—
197C4×C19—41no—
198C4×C19—41no—
199C4×C19—81no—
200C4×C19—81no—
201C4×C19C2×#10411yescharacteristic
202C4×C19#42111yescharacteristic
203C4×C19#44311yescharacteristic
204C4×C19#44411yescharacteristic
205C4×C19#45511yescharacteristic
206C4×C19#45611yescharacteristic
207Dic19—44no—
208#533C2×D1911yescharacteristic
209C4×#41C2×D1911yescharacteristic
210#485—21no—
211#475Dic1911yescharacteristic, complemented
212#474Dic1911yescharacteristic, complemented
213#462Dic1911yescharacteristic, complemented
214#461Dic1911yescharacteristic, complemented
215#452—21no—
216C8×Q8—381no—
217C4×Q16—21no—
218C4×SD16—21no—
219#436—382no—
220#436—381no—
221#431—191no—
222#431—381no—
223#431C2×D1911yescharacteristic
224#423—191no—
225#423—381no—
226C2×#104—381no—
227C4×M16—191no—
228C43—191no—
229#339—382no—
230#339—381no—
231Q8⋊C8—381no—
232Q8⋊C8—381no—
233C2×C19—41no—
234C2×C19—81no—
235C2×C19#187111yescharacteristic
236C2×C19#187611yescharacteristic
237C2×C19#188211yescharacteristic
238C2×#41C22⋊D1911yescharacteristic
239C2×Q16—21no—
240C2×SD16—21no—
241C2×M16—192no—
242C2×M16—382no—
243C2×M16—381no—
244C4⋊Q8C2×Dic1911yescharacteristic
245C4⋊Q8C2×Dic1911yescharacteristic
246#125—21no—
247C22⋊Q8—21no—
248C22⋊Q8—21no—
249C4×Q8—21no—
250C4×Q8—21no—
251C4×Q8C2×Dic1911yescharacteristic
252C4×Q8C22⋊D1911yescharacteristic
253C4×D4—21no—
254C4×D4—21no—
255C4×D4C2×Dic1911yescharacteristic
256C4×D4C22⋊D1911yescharacteristic
257#117—21no—
258#117—21no—
259#117C22⋊D1911yescharacteristic
260C2×C42—21no—
261C2×C42—381no—
262C2×C42—381no—
263C2×C42—381no—
264C2×C42C22×D1911yescharacteristic
265#107—21no—
266#106—21no—
267C4⋊C8—191no—
268C4⋊C8—191no—
269C4⋊C8—382no—
270C4⋊C8—381no—
271C4⋊C8—381no—
272C4⋊C8C2×Dic1911yescharacteristic
273C4⋊C8C2×Dic1911yescharacteristic
274#104—384no—
275#103—21no—
276#103—21no—
277#103—21no—
278#102—21no—
279C22⋊C8—21no—
280C22⋊C8—382no—
281C22⋊C8—381no—
282#97—381no—
283C4×C8—21no—
284C4×C8—382no—
285C4×C8—381no—
286C4×C8—381no—
287C19#897211yescharacteristic, complemented, Sylow
288#41—22no—
289#41—41no—
290C2×Q8—21no—
291C2×Q8—21no—
292C2×Q8C22⋊Dic1911yescharacteristic
293C2×D4—21no—
294C2×D4C22⋊Dic1911yescharacteristic
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—761no—
299C22×C4D4×D1911yescharacteristic
300C22×C4#6454311yescharacteristic
301C22×C4C2×C22⋊D1911yescharacteristic
302Q16—42no—
303SD16—42no—
304M16—382no—
305M16—761no—
306M16—762no—
307M16—1522no—
308C2×C8—21no—
309C2×C8—21no—
310C2×C8—381no—
311C2×C8—381no—
312C2×C8—382no—
313C2×C8—761no—
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—21no—
318C4⋊C4—21no—
319C4⋊C4—21no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4C22⋊Dic1911yescharacteristic
323C4⋊C4C22⋊Dic1911yescharacteristic
324C22⋊C4—21no—
325C22⋊C4—21no—
326C22⋊C4—21no—
327C22⋊C4—41no—
328C42—21no—
329C42—21no—
330C42—21no—
331C42—41no—
332C42—382no—
333C42—382no—
334C42—382no—
335C42—761no—
336C42—761no—
337C42—761no—
338C42D4×D1911yescharacteristic
339C42#6454311yescharacteristic
340C42C22×Dic1911yescharacteristic
341C42C2×C22⋊D1911yescharacteristic
342C23—21no—
343C23#1059738511yescharacteristic
344Q8—21no—
345Q8—41no—
346Q8—41no—
347Q8—41no—
348Q8—41no—
349Q8#1059729412yes—
350D4—21no—
351D4—21no—
352D4—42no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—42no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—762no—
370C2×C4—762no—
371C2×C4—762no—
372C2×C4D4×Dic1911yescharacteristic
373C2×C4D4×Dic1911yescharacteristic
374C2×C4#1059738111yescharacteristic
375C2×C4#1059738311yescharacteristic
376C2×C4#1059738511yescharacteristic
377C2×C4C2×C22⋊Dic1911yescharacteristic
378C8—41no—
379C8—41no—
380C8—762no—
381C8—762no—
382C8—761no—
383C8—761no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22#1192642411yescharacteristic
391C4—21no—
392C4—22no—
393C4—21no—
394C4—21no—
395C4—41no—
396C4—41no—
397C4—81no—
398C4—81no—
399C4—764no—
400C4C2×#1059729411yescharacteristic
401C4#1192656111yescharacteristic
402C4#1192666111yescharacteristic
403C4#1192666611yescharacteristic
404C4#1192672011yescharacteristic
405C4#1192672511yescharacteristic
406C2—41no—
407C2—81no—
408C2#1456393811yescharacteristic
409C2#1456396411yescharacteristic
410C2#1456400611yescharacteristic
subgroupG/H
centerC2×C4#10597383
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#3107C2
socleC22×C19#386
prime radicalC2×#41×C19D4
cosocleC2×C42×C19C23
hypercenter#3107D19
hypocenterC19#8972
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3107

Complements

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

NH ≅ G/Ntype
2. #14564613C2semidirect
4. #14562056C2semidirect
5. #14561526C2semidirect
6. #14561467C2semidirect
25. C19×#475C4semidirect
26. C19×#474C4semidirect
27. C19×#462C4semidirect
28. C19×#461C4semidirect
211. #475Dic19semidirect
212. #474Dic19semidirect
213. #462Dic19semidirect
214. #461Dic19semidirect
287. C19#8972semidirect

Maximal subgroups

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

subgroupindex
#145727672
#145646132
C4×#105972942
#145620562
#145615262
#145614672
C19×#31072
#897219