Finite Group Databasebeta

← #18079597

Subgroups — #18079597

Order 4864.

444 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14572293C211yesmaximal, characteristic
2#14563730C211yesmaximal, characteristic
3#14562207C211yesmaximal, characteristic
4#14561999C211yesmaximal, characteristic
5#14561540C211yesmaximal, characteristic
6#14561522C211yesmaximal, characteristic
7C19×#3095C211yesmaximal, characteristic
8#11926605—22no—
9#11926601—21no—
10#11926597—21no—
11#11926571—21no—
12#11926508C2211yescharacteristic
13C2×C22⋊(C19⋊C8)C2211yescharacteristic
14C2×C22⋊(C19⋊C8)C2211yescharacteristic
15#11926500—21no—
16#11926404C2211yescharacteristic
17#11926306—21no—
18#11926306—21no—
19#11926281—21no—
20#11926281—21no—
21#11926270—22no—
22C2×C19×C22⋊Q8C2211yescharacteristic
23C2×C19×#117C2211yescharacteristic
24C19×#485—21no—
25C19×#485—21no—
26C19×#484—21no—
27C19×#483—21no—
28C19×#428C411yescharacteristic, complemented
29C19×#428C411yescharacteristic, complemented
30C19×#419C411yescharacteristic, complemented
31C19×#419C411yescharacteristic, complemented
32C19×#407C2211yescharacteristic
33C22×Q8×C19C2×C411yescharacteristic
34C23×C4×C19C2311yescharacteristic
35C2×M16×C19C2×C411yescharacteristic
36C2×M16×C19C2×C411yescharacteristic
37C19×C22⋊Q8—21no—
38C19×C22⋊Q8—21no—
39C19×C22⋊Q8—21no—
40C19×C22⋊Q8—21no—
41C19×#117—21no—
42C19×#117—21no—
43C19×#117C2×C411yescharacteristic
44C19×#117C2×C411yescharacteristic
45C19×#117D411yescharacteristic
46C19×#117D411yescharacteristic
47C2×C4⋊C4×C19—21no—
48C2×C4⋊C4×C19C2×C411yescharacteristic
49C2×C4⋊C4×C19D411yescharacteristic
50C2×C4⋊C4×C19D411yescharacteristic
51C2×C22⋊C4×C19—21no—
52C2×C22⋊C4×C19—21no—
53C2×C42×C19—21no—
54C2×C22⋊Dic19—21no—
55C2×C4⋊Dic19—21no—
56C2×#64520—21no—
57C22×C19⋊C8—21no—
58C22×C19⋊C8—21no—
59C19×#107—21no—
60C19×#107—21no—
61C19×#106—21no—
62C19×#106—21no—
63C19×#103—21no—
64C19×#103—21no—
65C19×#103—21no—
66C19×#103—21no—
67C19×C22⋊C8—21no—
68C19×C22⋊C8—21no—
69C19⋊#95—21no—
70C22⋊(C19⋊C8)—21no—
71C22⋊(C19⋊C8)—21no—
72C22⋊(C19⋊C8)—21no—
73C22⋊(C19⋊C8)—21no—
74C22⋊(C19⋊C8)D411yescharacteristic
75C22⋊(C19⋊C8)D411yescharacteristic
76C22⋊(C19⋊C8)D412yes—
77C4⋊(C19⋊C8)—22no—
78C4⋊(C19⋊C8)—22no—
79#10597260—22no—
80C4×C19⋊C8—22no—
81C24×C19#4111yescharacteristic
82C2×Q8×C19—21no—
83C2×Q8×C19—21no—
84C2×Q8×C19—41no—
85C2×Q8×C19—41no—
86C22×C4×C19—21no—
87C22×C4×C19—21no—
88C22×C4×C19—21no—
89C22×C4×C19—21no—
90C22×C4×C19—41no—
91C22×C4×C19—41no—
92C22×C4×C19C22×C411yescharacteristic
93C22×C4×C19C2×D411yescharacteristic
94C22×C4×C19C2×D411yescharacteristic
95C22×C4×C19C2×D411yescharacteristic
96C22×C4×C19C2×D411yescharacteristic
97C22×C4×C19#4111yescharacteristic
98C22×Dic19—41no—
99M16×C19—41no—
100M16×C19—41no—
101C2×C8×C19—21no—
102C2×C8×C19—21no—
103C4⋊C4×C19—21no—
104C4⋊C4×C19—21no—
105C4⋊C4×C19—21no—
106C4⋊C4×C19—21no—
107C4⋊C4×C19—41no—
108C4⋊C4×C19—41no—
109C4⋊C4×C19C22⋊C411yescharacteristic
110C4⋊C4×C19C22⋊C411yescharacteristic
111C4⋊C4×C19C22⋊C411yescharacteristic
112C4⋊C4×C19C22⋊C411yescharacteristic
113C22⋊C4×C19—21no—
114C22⋊C4×C19—21no—
115C22⋊C4×C19—21no—
116C22⋊C4×C19—21no—
117C22⋊C4×C19—41no—
118C22⋊C4×C19—41no—
119C42×C19—21no—
120C42×C19—21no—
121C42×C19—21no—
122C42×C19—21no—
123C22⋊Dic19—81no—
124C4⋊Dic19—41no—
125C4⋊Dic19—41no—
126#64520—41no—
127#64520—41no—
128C2×C19⋊C8—21no—
129C2×C19⋊C8—22no—
130C2×C19⋊C8—21no—
131C2×C19⋊C8—41no—
132C2×C19⋊C8—41no—
133C2×C19⋊C8—41no—
134C2×C19⋊C8—41no—
135C2×C19⋊C8—41no—
136#9346—191nomaximal, Sylow
137C23×C19—21no—
138C23×C19—21no—
139C23×C19—41no—
140C23×C19—41no—
141C23×C19C4×D411yescharacteristic
142C23×C19#12111yescharacteristic
143C23×C19#12311yescharacteristic
144Q8×C19—41no—
145Q8×C19—41no—
146Q8×C19—81no—
147C2×C4×C19—21no—
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—41no—
158C2×C4×C19—41no—
159C2×C4×C19—41no—
160C2×C4×C19—41no—
161C2×C4×C19—41no—
162C2×C4×C19—42no—
163C2×C4×C19—41no—
164C2×C4×C19—41no—
165C2×C4×C19—81no—
166C2×C4×C19—81no—
167C2×C4×C19C2×C22⋊C411yescharacteristic
168C2×C4×C19C4×D411yescharacteristic
169C2×C4×C19#12011yescharacteristic
170C2×C4×C19#12111yescharacteristic
171C2×Dic19—81no—
172C2×Dic19—81no—
173C2×Dic19—81no—
174C8×C19—41no—
175C8×C19—41no—
176C19⋊C8—41no—
177C19⋊C8—41no—
178C19⋊C8—42no—
179C19⋊C8—81no—
180#3095D1911yescharacteristic
181#2924—191no—
182#1825—191no—
183#1520—191no—
184#1472—191no—
185#1305—191no—
186#1298—191no—
187C22×C19—21no—
188C22×C19—21no—
189C22×C19—21no—
190C22×C19—21no—
191C22×C19—21no—
192C22×C19—21no—
193C22×C19—21no—
194C22×C19—21no—
195C22×C19—81no—
196C22×C19—81no—
197C22×C19#38611yescharacteristic
198C22×C19#47111yescharacteristic
199C22×C19#47311yescharacteristic
200C4×C19—21no—
201C4×C19—21no—
202C4×C19—21no—
203C4×C19—41no—
204C4×C19—41no—
205C4×C19—41no—
206C4×C19—41no—
207C4×C19—81no—
208C4×C19—81no—
209C4×C19#41011yescharacteristic
210C4×C19#41011yescharacteristic
211Dic19—161no—
212C2×C22⋊Q8C2×D1911yescharacteristic
213C2×#117C2×D1911yescharacteristic
214#485—21no—
215#485—21no—
216#484—21no—
217#483—21no—
218#433—382no—
219#432—381no—
220#431—381no—
221#428Dic1911yescharacteristic, complemented
222#428Dic1911yescharacteristic, complemented
223#424—381no—
224#419Dic1911yescharacteristic, complemented
225#419Dic1911yescharacteristic, complemented
226#407—191no—
227#407C2×D1911yescharacteristic
228C2×C22⋊C8—191no—
229C2×C22⋊C8—191no—
230#405—381no—
231#380—191no—
232#340—381no—
233#340—381no—
234#328—381no—
235#328—381no—
236#324—382no—
237C2×C19—21no—
238C2×C19—21no—
239C2×C19—41no—
240C2×C19—41no—
241C2×C19#188111yescharacteristic
242C2×C19#189911yescharacteristic
243C2×C19#190811yescharacteristic
244C22×Q8C2×Dic1911yescharacteristic
245C23×C4C22×D1911yescharacteristic
246C2×M16—381no—
247C2×M16C2×Dic1911yescharacteristic
248C2×M16C2×Dic1911yescharacteristic
249C22×C8—381no—
250C22×C8—381no—
251C22⋊Q8—21no—
252C22⋊Q8—21no—
253C22⋊Q8—21no—
254C22⋊Q8—21no—
255#117—21no—
256#117—21no—
257#117C2×Dic1911yescharacteristic
258#117C2×Dic1911yescharacteristic
259#117C22⋊D1911yescharacteristic
260#117C22⋊D1911yescharacteristic
261C2×C4⋊C4—21no—
262C2×C4⋊C4—381no—
263C2×C4⋊C4C2×Dic1911yescharacteristic
264C2×C4⋊C4C22⋊D1911yescharacteristic
265C2×C4⋊C4C22⋊D1911yescharacteristic
266C2×C22⋊C4—21no—
267C2×C22⋊C4—21no—
268C2×C22⋊C4—381no—
269C2×C42—21no—
270#107—21no—
271#107—21no—
272#106—21no—
273#106—21no—
274C4⋊C8—382no—
275C4⋊C8—382no—
276#103—21no—
277#103—21no—
278#103—21no—
279#103—21no—
280C22⋊C8—21no—
281C22⋊C8—21no—
282C22⋊C8—192no—
283C22⋊C8—191no—
284C22⋊C8—191no—
285C22⋊C8—381no—
286C22⋊C8—381no—
287C22⋊C8—381no—
288C22⋊C8—381no—
289#97—382no—
290C4×C8—382no—
291#95—381no—
292C19#934611yescharacteristic, complemented, Sylow
293C24#6454311yescharacteristic
294C2×Q8—21no—
295C2×Q8—21no—
296C2×Q8—41no—
297C2×Q8—41no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—41no—
303C22×C4—41no—
304C22×C4—761no—
305C22×C4D4×D1911yescharacteristic
306C22×C4D4×D1911yescharacteristic
307C22×C4#6454311yescharacteristic
308C22×C4C22×Dic1911yescharacteristic
309C22×C4C2×C22⋊D1911yescharacteristic
310C22×C4C2×C22⋊D1911yescharacteristic
311M16—41no—
312M16—41no—
313M16—761no—
314M16—761no—
315C2×C8—21no—
316C2×C8—21no—
317C2×C8—381no—
318C2×C8—382no—
319C2×C8—381no—
320C2×C8—761no—
321C2×C8—761no—
322C2×C8—761no—
323C2×C8—761no—
324C2×C8—761no—
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—41no—
330C4⋊C4—41no—
331C4⋊C4—761no—
332C4⋊C4—761no—
333C4⋊C4C22⋊Dic1911yescharacteristic
334C4⋊C4C22⋊Dic1911yescharacteristic
335C4⋊C4C22⋊Dic1911yescharacteristic
336C4⋊C4C22⋊Dic1911yescharacteristic
337C22⋊C4—21no—
338C22⋊C4—21no—
339C22⋊C4—21no—
340C22⋊C4—21no—
341C22⋊C4—41no—
342C22⋊C4—41no—
343C22⋊C4—1521no—
344C42—21no—
345C42—21no—
346C42—21no—
347C42—21no—
348C23—21no—
349C23—21no—
350C23—41no—
351C23—41no—
352C23D4×Dic1911yescharacteristic
353C23#1059738111yescharacteristic
354C23#1059738511yescharacteristic
355Q8—41no—
356Q8—41no—
357Q8—81no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—42no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—81no—
377C2×C4—81no—
378C2×C4—1521no—
379C2×C4—1521no—
380C2×C4—1521no—
381C2×C4D4×Dic1911yescharacteristic
382C2×C4#1059738311yescharacteristic
383C2×C4#1059738511yescharacteristic
384C2×C4C2×C22⋊Dic1911yescharacteristic
385C8—41no—
386C8—41no—
387C8—761no—
388C8—761no—
389C8—762no—
390C8—1521no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—81no—
400C22—81no—
401C22#1192642411yescharacteristic
402C22#1192680911yescharacteristic
403C22#1192681711yescharacteristic
404C4—21no—
405C4—21no—
406C4—21no—
407C4—41no—
408C4—41no—
409C4—41no—
410C4—41no—
411C4—81no—
412C4—81no—
413C4—3041no—
414C4#1192651811yescharacteristic
415C4#1192651811yescharacteristic
416C2—21no—
417C2—21no—
418C2—41no—
419C2—41no—
420C2#1456399911yescharacteristic
421C2#1456409411yescharacteristic
422C2#1456415211yescharacteristic
subgroupG/H
centerC22#11926424
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#3095C2
socleC22×C19#386
prime radicalC24×C19#41
cosocleC23×C4×C19C23
hypercenter#3095D19
hypocenterC19#9346
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3095

Complements

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

NH ≅ G/Ntype
28. C19×#428C4semidirect
29. C19×#428C4semidirect
30. C19×#419C4semidirect
31. C19×#419C4semidirect
221. #428Dic19semidirect
222. #428Dic19semidirect
224. #419Dic19semidirect
225. #419Dic19semidirect
292. C19#9346semidirect

Maximal subgroups

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

subgroupindex
#145722932
#145637302
#145622072
#145619992
#145615402
#145615222
C19×#30952
#934619