Finite Group Databasebeta

← #18079583

Subgroups — #18079583

Order 4864.

520 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 103 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14566801C211yesmaximal, characteristic, complemented
2#14564472C211yesmaximal, characteristic
3#14562164C211yesmaximal, characteristic
4#14562155C211yesmaximal, characteristic, complemented
5#14561542C211yesmaximal, characteristic, complemented
6#14561489C211yesmaximal, characteristic, complemented
7C19×#3193C211yesmaximal, characteristic
8C2×#10597291—21no—
9C2×#10597291—21no—
10#11926508C2211yescharacteristic
11#11926451—21no—
12#11926443—21no—
13#11926437—21no—
14#11926437—21no—
15#11926430—21no—
16#11926430—21no—
17#11926407C2211yescharacteristic
18#11926404C2211yescharacteristic
19C4×C22⋊Dic19C2211yescharacteristic
20#11926281—22no—
21#11926278—21no—
22#11926278—21no—
23C2×C19×C22⋊Q8C2211yescharacteristic
24C2×C19×#121C2211yescharacteristic
25C19×#484C412yescomplemented
26C19×#480—21no—
27C19×#468—22no—
28C19×#450C412yescomplemented
29C19×#448—21no—
30C19×#407C2211yescharacteristic
31C22×Q8×C19D411yescharacteristic
32C22×D4×C19—21no—
33C22×D4×C19C2×C411yescharacteristic
34C23×C4×C19C2311yescharacteristic
35C2×SD16×C19—22no—
36C2×M16×C19—21no—
37C19×C22⋊Q8—21no—
38C19×C22⋊Q8—21no—
39C19×C22⋊Q8C2×C412yes—
40C19×C22⋊Q8D412yes—
41C19×#121—21no—
42C19×#121—21no—
43C19×#121—21no—
44C19×#121—21no—
45C2×C4⋊C4×C19—21no—
46C2×C4⋊C4×C19C2×C411yescharacteristic
47C2×C4⋊C4×C19D411yescharacteristic
48C2×C22⋊C4×C19—21no—
49C2×C22⋊C4×C19—21no—
50C2×C22⋊Dic19—21no—
51C2×C22⋊Dic19—21no—
52C2×C22⋊Dic19D411yescharacteristic
53C2×C22⋊Dic19D411yescharacteristic
54C2×C4⋊Dic19—21no—
55C2×C4⋊Dic19—21no—
56C2×C4⋊Dic19—21no—
57C2×C4×Dic19—21no—
58C2×C4×Dic19—21no—
59C2×C4×Dic19—21no—
60C2×#64520—21no—
61C19×#107—22no—
62C19×#103—22no—
63C19×#102—22no—
64C19×C22⋊C8—21no—
65C19×C22⋊C8C2×C412yes—
66#10597291—42no—
67#10597291—42no—
68C19⋊#95—21no—
69C19⋊#95—21no—
70C19⋊#95—21no—
71C19⋊#95—21no—
72C19⋊#95—21no—
73C19⋊#95—21no—
74C19⋊#95—21no—
75C19⋊#95D411yescharacteristic
76C19⋊#95D411yescharacteristic
77C22⋊(C19⋊C8)—21no—
78C22⋊(C19⋊C8)—21no—
79C24×C19—21no—
80C24×C19C2×D411yescharacteristic
81C2×Q8×C19—21no—
82C2×Q8×C19—81no—
83C2×Q8×C19C22⋊C412yes—
84C2×D4×C19—21no—
85C2×D4×C19—21no—
86C2×D4×C19—41no—
87C2×D4×C19—41no—
88C2×D4×C19—41no—
89C2×D4×C19—41no—
90C2×D4×C19—41no—
91C2×D4×C19—41no—
92C2×D4×C19—81no—
93C22×C4×C19—21no—
94C22×C4×C19—21no—
95C22×C4×C19—21no—
96C22×C4×C19—81no—
97C22×C4×C19C22×C411yescharacteristic
98C22×C4×C19C2×D411yescharacteristic
99C22×C4×C19C2×D411yescharacteristic
100C22×C4×C19C2×D411yescharacteristic
101C22×C4×C19#4111yescharacteristic
102C22×C4×C19#4111yescharacteristic
103C22×Dic19—21no—
104C22×Dic19—21no—
105C22×Dic19—21no—
106C22×Dic19—21no—
107C22×Dic19—41no—
108SD16×C19—82no—
109M16×C19—81no—
110C2×C8×C19—22no—
111C4⋊C4×C19—22no—
112C4⋊C4×C19—22no—
113C4⋊C4×C19—21no—
114C4⋊C4×C19—21no—
115C4⋊C4×C19—21no—
116C4⋊C4×C19C22⋊C412yes—
117C22⋊C4×C19—22no—
118C22⋊C4×C19—22no—
119C22⋊C4×C19—41no—
120C22⋊C4×C19—41no—
121C22⋊Dic19—22no—
122C22⋊Dic19—41no—
123C22⋊Dic19—41no—
124C22⋊Dic19—41no—
125C22⋊Dic19—81no—
126C4⋊Dic19—81no—
127C4⋊Dic19—81no—
128C4⋊Dic19—81no—
129C4×Dic19—81no—
130C4×Dic19—81no—
131C4×Dic19—81no—
132#64520—81no—
133C2×C19⋊C8—41no—
134#9344—191nomaximal, Sylow
135C23×C19—21no—
136C23×C19—21no—
137C23×C19—41no—
138C23×C19—41no—
139C23×C19—41no—
140C23×C19—41no—
141C23×C19—41no—
142C23×C19—81no—
143C23×C19—81no—
144C23×C19C4×D411yescharacteristic
145C23×C19#12011yescharacteristic
146C23×C19#12111yescharacteristic
147Q8×C19—42no—
148Q8×C19—81no—
149D4×C19—42no—
150D4×C19—81no—
151D4×C19—81no—
152D4×C19—81no—
153D4×C19—81no—
154D4×C19—81no—
155C2×C4×C19—22no—
156C2×C4×C19—22no—
157C2×C4×C19—41no—
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—41no—
168C2×C4×C19—41no—
169C2×C4×C19—41no—
170C2×C4×C19C2×C22⋊C411yescharacteristic
171C2×C4×C19C4×D411yescharacteristic
172C2×C4×C19#12111yescharacteristic
173C2×C4×C19#12311yescharacteristic
174C2×Dic19—41no—
175C2×Dic19—41no—
176C2×Dic19—41no—
177C2×Dic19—41no—
178C2×Dic19—42no—
179C2×Dic19—41no—
180C2×Dic19—41no—
181C2×Dic19—41no—
182C2×Dic19—41no—
183C2×Dic19—41no—
184C2×Dic19—41no—
185C2×Dic19—41no—
186C2×Dic19—41no—
187C2×Dic19—81no—
188C2×Dic19—81no—
189C8×C19—42no—
190C19⋊C8—81no—
191#3193D1911yescharacteristic
192#2378—191no—
193#1964—191no—
194#1510—191no—
195#1508—191no—
196#1305—191no—
197#1284—191no—
198C22×C19—21no—
199C22×C19—21no—
200C22×C19—21no—
201C22×C19—21no—
202C22×C19—21no—
203C22×C19—21no—
204C22×C19—21no—
205C22×C19—21no—
206C22×C19—81no—
207C22×C19—81no—
208C22×C19—81no—
209C22×C19—81no—
210C22×C19—81no—
211C22×C19—161no—
212C22×C19—161no—
213C22×C19#38611yescharacteristic
214C22×C19#45311yescharacteristic
215C22×C19#45411yescharacteristic
216C4×C19—21no—
217C4×C19—21no—
218C4×C19—21no—
219C4×C19—21no—
220C4×C19—42no—
221C4×C19—42no—
222C4×C19—81no—
223Dic19—81no—
224Dic19—81no—
225Dic19—81no—
226Dic19—81no—
227Dic19—82no—
228C2×C22⋊Q8C2×D1911yescharacteristic
229C2×#121C2×D1911yescharacteristic
230#484Dic1912yescomplemented
231#480—21no—
232#468—22no—
233#450Dic1912yescomplemented
234#448—21no—
235C2×#99—381no—
236C2×#99—381no—
237#407—191no—
238#407C2×D1911yescharacteristic
239#391—381no—
240#389—381no—
241#388—381no—
242#388—381no—
243#387—381no—
244#387—381no—
245#381—191no—
246#380—191no—
247C4×C22⋊C4—191no—
248#328—382no—
249#327—381no—
250#327—381no—
251C2×C19—21no—
252C2×C19—21no—
253C2×C19—41no—
254C2×C19—41no—
255C2×C19—161no—
256C2×C19#188311yescharacteristic
257C2×C19#190511yescharacteristic
258C2×C19#191311yescharacteristic
259C22×Q8C22⋊D1911yescharacteristic
260C22×D4—21no—
261C22×D4C2×Dic1911yescharacteristic
262C23×C4C22×D1911yescharacteristic
263C2×SD16—22no—
264C2×M16—21no—
265C2×M16—381no—
266C22⋊Q8—21no—
267C22⋊Q8—21no—
268C22⋊Q8C2×Dic1912yes—
269C22⋊Q8C22⋊D1912yes—
270#121—21no—
271#121—21no—
272#121—21no—
273#121—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—381no—
276C2×C4⋊C4—381no—
277C2×C4⋊C4—381no—
278C2×C4⋊C4C2×Dic1911yescharacteristic
279C2×C4⋊C4C22⋊D1911yescharacteristic
280C2×C22⋊C4—21no—
281C2×C22⋊C4—21no—
282C2×C22⋊C4—191no—
283C2×C22⋊C4—191no—
284C2×C22⋊C4—381no—
285C2×C22⋊C4—381no—
286C2×C42—381no—
287C2×C42—381no—
288C2×C42—381no—
289#107—22no—
290#103—22no—
291#102—22no—
292#99—762no—
293#99—762no—
294C22⋊C8—21no—
295C22⋊C8—381no—
296C22⋊C8—381no—
297C22⋊C8C2×Dic1912yes—
298#95—191no—
299#95—191no—
300#95—381no—
301#95—381no—
302#95—381no—
303#95—381no—
304#95—381no—
305#95—381no—
306#95—381no—
307C19#934411yescharacteristic, complemented, Sylow
308C24—21no—
309C24D4×D1911yescharacteristic
310C2×Q8—21no—
311C2×Q8—81no—
312C2×Q8C22⋊Dic1912yes—
313C2×D4—21no—
314C2×D4—21no—
315C2×D4—41no—
316C2×D4—41no—
317C2×D4—41no—
318C2×D4—41no—
319C2×D4—41no—
320C2×D4—41no—
321C2×D4—81no—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—81no—
326C22×C4—381no—
327C22×C4—381no—
328C22×C4—381no—
329C22×C4—381no—
330C22×C4—761no—
331C22×C4D4×D1911yescharacteristic
332C22×C4#6454311yescharacteristic
333C22×C4#6454311yescharacteristic
334C22×C4C22×Dic1911yescharacteristic
335C22×C4C2×C22⋊D1911yescharacteristic
336C22×C4C2×C22⋊D1911yescharacteristic
337SD16—82no—
338M16—81no—
339M16—1521no—
340C2×C8—22no—
341C2×C8—761no—
342C4⋊C4—22no—
343C4⋊C4—21no—
344C4⋊C4—22no—
345C4⋊C4—21no—
346C4⋊C4—21no—
347C4⋊C4—1521no—
348C4⋊C4—1521no—
349C4⋊C4—1521no—
350C4⋊C4C22⋊Dic1912yes—
351C22⋊C4—22no—
352C22⋊C4—22no—
353C22⋊C4—41no—
354C22⋊C4—41no—
355C22⋊C4—382no—
356C22⋊C4—761no—
357C22⋊C4—761no—
358C22⋊C4—761no—
359C22⋊C4—1521no—
360C42—1521no—
361C42—1521no—
362C42—1521no—
363C23—21no—
364C23—21no—
365C23—41no—
366C23—41no—
367C23—41no—
368C23—41no—
369C23—41no—
370C23—81no—
371C23—81no—
372C23D4×Dic1911yescharacteristic
373C23#1059738311yescharacteristic
374C23#1059738511yescharacteristic
375Q8—42no—
376Q8—81no—
377D4—42no—
378D4—81no—
379D4—81no—
380D4—81no—
381D4—81no—
382D4—81no—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—761no—
399C2×C4—761no—
400C2×C4—762no—
401C2×C4—761no—
402C2×C4—761no—
403C2×C4—761no—
404C2×C4—761no—
405C2×C4—761no—
406C2×C4—761no—
407C2×C4—761no—
408C2×C4—761no—
409C2×C4—761no—
410C2×C4—761no—
411C2×C4—1521no—
412C2×C4—1521no—
413C2×C4D4×Dic1911yescharacteristic
414C2×C4#1059738111yescharacteristic
415C2×C4#1059738511yescharacteristic
416C2×C4C2×C22⋊Dic1911yescharacteristic
417C8—42no—
418C8—1521no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—21no—
423C22—21no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—81no—
428C22—81no—
429C22—81no—
430C22—81no—
431C22—81no—
432C22—161no—
433C22—161no—
434C22#1192642411yescharacteristic
435C22#1192671011yescharacteristic
436C22#1192671511yescharacteristic
437C4—21no—
438C4—21no—
439C4—21no—
440C4—21no—
441C4—42no—
442C4—42no—
443C4—81no—
444C4—1521no—
445C4—1521no—
446C4—1521no—
447C4—1521no—
448C4—1522no—
449C2—21no—
450C2—21no—
451C2—41no—
452C2—41no—
453C2—161no—
454C2#1456401311yescharacteristic
455C2#1456413111yescharacteristic
456C2#1456417811yescharacteristic
subgroupG/H
centerC22#11926424
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#3193C2
socleC22×C19#386
prime radicalC2×C19×#121C22
cosocleC23×C4×C19C23
hypercenter#3193D19
hypocenterC19#9344
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3193

Complements

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

NH ≅ G/Ntype
1. #14566801C2semidirect
4. #14562155C2semidirect
5. #14561542C2semidirect
6. #14561489C2semidirect
25. C19×#484C4semidirect
28. C19×#450C4semidirect
230. #484Dic19semidirect
233. #450Dic19semidirect
307. C19#9344semidirect

Maximal subgroups

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

subgroupindex
#145668012
#145644722
#145621642
#145621552
#145615422
#145614892
C19×#31932
#934419