Finite Group Databasebeta

← #18078855

Subgroups — #18078855

Order 4864.

452 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14572293C211yesmaximal, characteristic
2#14563734C211yesmaximal, characteristic
3#14562155C211yesmaximal, characteristic
4#14561999C211yesmaximal, characteristic
5#14561512C211yesmaximal, characteristic
6#14561482C211yesmaximal, characteristic
7C2×C19×#485C211yesmaximal, characteristic
8#11926605—22no—
9#11926601—21no—
10#11926597—21no—
11#11926571—21no—
12#11926508C2211yescharacteristic
13#11926508C2211yescharacteristic
14C2×C22⋊(C19⋊C8)C2211yescharacteristic
15#11926500—21no—
16C4×C22⋊Dic19C2211yescharacteristic
17#11926303—21no—
18#11926303—21no—
19#11926281—22no—
20#11926270—21no—
21#11926270—21no—
22C2×C19×C22⋊Q8C2211yescharacteristic
23C2×C19×#117C2211yescharacteristic
24C19×#485—21no—
25C19×#485—21no—
26C19×#485—21no—
27C19×#485—21no—
28C2×C19×#107C411yescharacteristic, complemented
29C2×C19×#106C411yescharacteristic, complemented
30C2×C19×#103C411yescharacteristic, complemented
31C2×C19×#103C411yescharacteristic, complemented
32C2×C19×C22⋊C8C2211yescharacteristic
33C22×Q8×C19C2×C411yescharacteristic
34C23×C4×C19C2311yescharacteristic
35C22×C8×C19C2×C411yescharacteristic
36C22×C8×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×#117D411yescharacteristic
44C19×#117D411yescharacteristic
45C19×#117D411yescharacteristic
46C19×#117D411yescharacteristic
47C2×C4⋊C4×C19—21no—
48C2×C4⋊C4×C19C2×C411yescharacteristic
49C2×C4⋊C4×C19C2×C411yescharacteristic
50C2×C4⋊C4×C19C2×C411yescharacteristic
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—
57C2×#64520—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)D412yes—
75C22⋊(C19⋊C8)D411yescharacteristic
76C22⋊(C19⋊C8)D411yescharacteristic
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—
99C2×C8×C19—21no—
100C2×C8×C19—21no—
101C2×C8×C19—41no—
102C2×C8×C19—41no—
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—22no—
124C22⋊Dic19—41no—
125C4×Dic19—41no—
126C4×Dic19—41no—
127#64520—41no—
128#64520—41no—
129#64520—41no—
130#64520—41no—
131C2×C19⋊C8—21no—
132C2×C19⋊C8—22no—
133C2×C19⋊C8—21no—
134C2×C19⋊C8—41no—
135C2×C19⋊C8—41no—
136C2×C19⋊C8—41no—
137#9240—191nomaximal, Sylow
138C23×C19—21no—
139C23×C19—21no—
140C23×C19—41no—
141C23×C19—41no—
142C23×C19C4×D411yescharacteristic
143C23×C19#12111yescharacteristic
144C23×C19#12311yescharacteristic
145Q8×C19—41no—
146Q8×C19—41no—
147Q8×C19—81no—
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—21no—
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×C19—41no—
165C2×C4×C19—41no—
166C2×C4×C19—41no—
167C2×C4×C19—81no—
168C2×C4×C19—81no—
169C2×C4×C19C2×C22⋊C411yescharacteristic
170C2×C4×C19C4×D411yescharacteristic
171C2×C4×C19#12011yescharacteristic
172C2×C4×C19#12111yescharacteristic
173C2×Dic19—42no—
174C2×Dic19—81no—
175C2×Dic19—81no—
176C8×C19—41no—
177C8×C19—41no—
178C19⋊C8—41no—
179C19⋊C8—41no—
180C19⋊C8—42no—
181C19⋊C8—81no—
182C2×#485D1911yescharacteristic
183#2924—191no—
184#1826—191no—
185#1508—191no—
186#1472—191no—
187#1293—191no—
188#1282—191no—
189C22×C19—21no—
190C22×C19—21no—
191C22×C19—21no—
192C22×C19—21no—
193C22×C19—21no—
194C22×C19—21no—
195C22×C19—21no—
196C22×C19—21no—
197C22×C19—81no—
198C22×C19—81no—
199C22×C19#38611yescharacteristic
200C22×C19#44311yescharacteristic
201C22×C19#44411yescharacteristic
202C4×C19—21no—
203C4×C19—21no—
204C4×C19—21no—
205C4×C19—41no—
206C4×C19—41no—
207C4×C19—41no—
208C4×C19—41no—
209C4×C19—81no—
210C4×C19—81no—
211C4×C19#41011yescharacteristic
212C4×C19#41011yescharacteristic
213Dic19—82no—
214C2×C22⋊Q8C2×D1911yescharacteristic
215C2×#117C2×D1911yescharacteristic
216#485—21no—
217#485—21no—
218#485—21no—
219#485—21no—
220#433—382no—
221#432—381no—
222#431—381no—
223C2×#107Dic1911yescharacteristic, complemented
224C2×#106Dic1911yescharacteristic, complemented
225#424—381no—
226C2×#103Dic1911yescharacteristic, complemented
227C2×#103Dic1911yescharacteristic, complemented
228#407—191no—
229#407—191no—
230C2×C22⋊C8—191no—
231C2×C22⋊C8C2×D1911yescharacteristic
232#405—381no—
233C4×C22⋊C4—191no—
234#339—381no—
235#339—381no—
236#328—382no—
237#324—381no—
238#324—381no—
239C2×C19—21no—
240C2×C19—21no—
241C2×C19—41no—
242C2×C19—41no—
243C2×C19#187611yescharacteristic
244C2×C19#189911yescharacteristic
245C2×C19#190211yescharacteristic
246C22×Q8C2×Dic1911yescharacteristic
247C23×C4C22×D1911yescharacteristic
248C2×M16—381no—
249C2×M16—381no—
250C22×C8—381no—
251C22×C8C2×Dic1911yescharacteristic
252C22×C8C2×Dic1911yescharacteristic
253C22⋊Q8—21no—
254C22⋊Q8—21no—
255C22⋊Q8—21no—
256C22⋊Q8—21no—
257#117—21no—
258#117—21no—
259#117C22⋊D1911yescharacteristic
260#117C22⋊D1911yescharacteristic
261#117C22⋊D1911yescharacteristic
262#117C22⋊D1911yescharacteristic
263C2×C4⋊C4—21no—
264C2×C4⋊C4C2×Dic1911yescharacteristic
265C2×C4⋊C4C2×Dic1911yescharacteristic
266C2×C4⋊C4C2×Dic1911yescharacteristic
267C2×C22⋊C4—21no—
268C2×C22⋊C4—21no—
269C2×C22⋊C4—381no—
270C2×C42—21no—
271C2×C42—381no—
272#107—21no—
273#107—21no—
274#106—21no—
275#106—21no—
276C4⋊C8—382no—
277C4⋊C8—382no—
278#103—21no—
279#103—21no—
280#103—21no—
281#103—21no—
282C22⋊C8—21no—
283C22⋊C8—21no—
284C22⋊C8—191no—
285C22⋊C8—191no—
286C22⋊C8—192no—
287C22⋊C8—381no—
288C22⋊C8—381no—
289C22⋊C8—381no—
290C22⋊C8—381no—
291#97—382no—
292C4×C8—382no—
293#95—381no—
294C19#924011yescharacteristic, complemented, Sylow
295C24#6454311yescharacteristic
296C2×Q8—21no—
297C2×Q8—21no—
298C2×Q8—41no—
299C2×Q8—41no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—41no—
305C22×C4—41no—
306C22×C4—761no—
307C22×C4D4×D1911yescharacteristic
308C22×C4D4×D1911yescharacteristic
309C22×C4#6454311yescharacteristic
310C22×C4C22×Dic1911yescharacteristic
311C22×C4C2×C22⋊D1911yescharacteristic
312C22×C4C2×C22⋊D1911yescharacteristic
313M16—761no—
314M16—761no—
315M16—761no—
316M16—761no—
317C2×C8—21no—
318C2×C8—21no—
319C2×C8—41no—
320C2×C8—41no—
321C2×C8—381no—
322C2×C8—382no—
323C2×C8—381no—
324C2×C8—761no—
325C2×C8—761no—
326C2×C8—761no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—21no—
330C4⋊C4—21no—
331C4⋊C4—41no—
332C4⋊C4—41no—
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—382no—
344C22⋊C4—761no—
345C42—21no—
346C42—21no—
347C42—21no—
348C42—21no—
349C42—761no—
350C42—761no—
351C23—21no—
352C23—21no—
353C23—41no—
354C23—41no—
355C23D4×Dic1911yescharacteristic
356C23#1059738111yescharacteristic
357C23#1059738511yescharacteristic
358Q8—41no—
359Q8—41no—
360Q8—81no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—81no—
381C2×C4—81no—
382C2×C4—762no—
383C2×C4—1521no—
384C2×C4—1521no—
385C2×C4D4×Dic1911yescharacteristic
386C2×C4#1059738311yescharacteristic
387C2×C4#1059738511yescharacteristic
388C2×C4C2×C22⋊Dic1911yescharacteristic
389C8—41no—
390C8—41no—
391C8—761no—
392C8—761no—
393C8—762no—
394C8—1521no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—21no—
401C22—21no—
402C22—21no—
403C22—81no—
404C22—81no—
405C22#1192642411yescharacteristic
406C22#1192666111yescharacteristic
407C22#1192666611yescharacteristic
408C4—21no—
409C4—21no—
410C4—21no—
411C4—41no—
412C4—41no—
413C4—41no—
414C4—41no—
415C4—81no—
416C4—81no—
417C4—1522no—
418C4#1192651811yescharacteristic
419C4#1192651811yescharacteristic
420C2—21no—
421C2—21no—
422C2—41no—
423C2—41no—
424C2#1456396411yescharacteristic
425C2#1456409411yescharacteristic
426C2#1456411011yescharacteristic
subgroupG/H
centerC22#11926424
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC2×C19×#485C2
socleC22×C19#386
prime radicalC24×C19#41
cosocleC23×C4×C19C23
hypercenterC2×#485D19
hypocenterC19#9240
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#485

Complements

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

NH ≅ G/Ntype
28. C2×C19×#107C4semidirect
29. C2×C19×#106C4semidirect
30. C2×C19×#103C4semidirect
31. C2×C19×#103C4semidirect
223. C2×#107Dic19semidirect
224. C2×#106Dic19semidirect
226. C2×#103Dic19semidirect
227. C2×#103Dic19semidirect
294. C19#9240semidirect

Maximal subgroups

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

subgroupindex
#145722932
#145637342
#145621552
#145619992
#145615122
#145614822
C2×C19×#4852
#924019