Finite Group Databasebeta

← #18083305

Subgroups — #18083305

Order 4864.

568 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 568 conjugacy classes of subgroups — too many to draw. Only its 97 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#14573643C211yesmaximal, characteristic
2#14573442C211yesmaximal, characteristic, complemented
3#14568544C211yesmaximal, characteristic
4#14562200C211yesmaximal, characteristic, complemented
5#14562029C211yesmaximal, characteristic, complemented
6#14561495C211yesmaximal, characteristic, complemented
7C19×#1486C211yesmaximal, characteristic
8#11927101C2211yescharacteristic
9C2×#10597370—21no—
10C2×C4×Dic38C2211yescharacteristic
11#11926874—21no—
12#11926852—22no—
13#11926840—21no—
14#11926834—21no—
15#11926830—21no—
16#11926749—21no—
17#11926695—21no—
18C4×#64526—22no—
19#11926597C2211yescharacteristic
20#11926586—21no—
21#11926554—21no—
22#11926475—21no—
23#11926458—21no—
24#11926432—22no—
25#11926410C2211yescharacteristic
26#11926404—21no—
27#11926282—22no—
28#11926274—22no—
29C2×C4×D4×C19C2211yescharacteristic
30C19×#431C2211yescharacteristic
31C19×#423C2211yescharacteristic
32C19×D4⋊C8—22no—
33C22×D4×C19D411yescharacteristic
34C23×C4×C19—21no—
35C22×Dic38D411yescharacteristic
36C2×M16×C19—21no—
37C4×D4×C19—21no—
38C4×D4×C19—21no—
39C4×D4×C19—21no—
40C4×D4×C19—21no—
41C2×C4⋊C4×C19D411yescharacteristic
42C2×C22⋊C4×C19—21no—
43C2×C42×C19C2311yescharacteristic
44C2×C22⋊Dic19—22no—
45C2×C22⋊Dic19—22no—
46C2×#64526—22no—
47#10597372—21no—
48C2×C4⋊Dic19—21no—
49C2×C4⋊Dic19D411yescharacteristic
50#10597370—21no—
51#10597370—21no—
52#10597370—42no—
53#10597370—42no—
54C2×Dic19⋊C4—22no—
55C2×Dic19⋊C4—21no—
56C2×C4×Dic19—21no—
57#10597316—21no—
58#10597315D411yescharacteristic
59#10597315D411yescharacteristic
60C4×Dic38—21no—
61C4×Dic38—21no—
62C4×Dic38—21no—
63C4×Dic38—21no—
64C4×Dic38—21no—
65C4×Dic38—21no—
66C19×C4⋊C8—21no—
67C19×C4⋊C8—21no—
68C19×C4⋊C8D412yes—
69C19×C22⋊C8—21no—
70C4×C8×C19—21no—
71#10597289—22no—
72C19⋊#95—22no—
73C19⋊#95—21no—
74C19⋊#95D412yes—
75C22⋊(C19⋊C8)—21no—
76#10597275—22no—
77#10597274—22no—
78#10597273—22no—
79#10597273—22no—
80#10597267—22no—
81#10597265—22no—
82C4⋊(C19⋊C8)—21no—
83C4×C19⋊C8D412yes—
84C24×C19—21no—
85C2×D4×C19—21no—
86C2×D4×C19—21no—
87C2×D4×C19—42no—
88C22×C4×C19—21no—
89C22×C4×C19—41no—
90C22×C4×C19—41no—
91C22×C4×C19—41no—
92C22×C4×C19—41no—
93C22×C4×C19—41no—
94C22×C4×C19—41no—
95C22×C4×C19C2×D411yescharacteristic
96C22×C4×C19C2×D411yescharacteristic
97C22×C4×C19C2×D411yescharacteristic
98C22×Dic19—21no—
99C22×Dic19—22no—
100C22×Dic19—21no—
101C2×Dic38—21no—
102C2×Dic38—21no—
103C2×Dic38—21no—
104C2×Dic38—21no—
105C2×Dic38—21no—
106C2×Dic38—21no—
107C2×Dic38—21no—
108C2×Dic38SD1612yescomplemented
109M16×C19—41no—
110M16×C19—41no—
111C2×C8×C19—22no—
112C2×C8×C19—41no—
113C4⋊C4×C19—21no—
114C4⋊C4×C19—21no—
115C22⋊C4×C19—41no—
116C22⋊C4×C19—41no—
117C42×C19C2×D411yescharacteristic
118C42×C19C2×D411yescharacteristic
119C42×C19C2×D411yescharacteristic
120C42×C19#4111yescharacteristic
121C22⋊Dic19—44no—
122C22⋊Dic19—44no—
123C22⋊Dic19—41no—
124#64526—44no—
125C4⋊Dic19—21no—
126C4⋊Dic19—21no—
127C4⋊Dic19—21no—
128C4⋊Dic19—21no—
129C4⋊Dic19—21no—
130C4⋊Dic19—21no—
131C4⋊Dic19—41no—
132C4⋊Dic19—41no—
133Dic19⋊C4—44no—
134Dic19⋊C4—41no—
135Dic19⋊C4—41no—
136Dic19⋊C4—41no—
137Dic19⋊C4—41no—
138C4×Dic19—41no—
139C4×Dic19—41no—
140C4×Dic19—41no—
141C2×C19⋊C8—22no—
142#10001—191nomaximal, Sylow
143C23×C19—22no—
144C23×C19—41no—
145C23×C19—41no—
146C23×C19—41no—
147C23×C19—41no—
148C23×C19—41no—
149C23×C19—41no—
150C23×C19#12011yescharacteristic
151D4×C19—22no—
152D4×C19—22no—
153D4×C19—41no—
154D4×C19—41no—
155C2×C4×C19—41no—
156C2×C4×C19—41no—
157C2×C4×C19—41no—
158C2×C4×C19—41no—
159C2×C4×C19—41no—
160C2×C4×C19—81no—
161C2×C4×C19—81no—
162C2×C4×C19—81no—
163C2×C4×C19—81no—
164C2×C4×C19#12011yescharacteristic
165C2×C4×C19#12011yescharacteristic
166C2×C4×C19#12111yescharacteristic
167C2×C4×C19#12111yescharacteristic
168C2×C4×C19#12111yescharacteristic
169C2×C4×C19#12711yescharacteristic
170C2×C4×C19C2×SD1611yescharacteristic
171C2×C4×C19#13511yescharacteristic
172C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
173C2×C4×C19#13711yescharacteristic
174C2×Dic19—22no—
175C2×Dic19—41no—
176C2×Dic19—41no—
177C2×Dic19—42no—
178C2×Dic19—42no—
179C2×Dic19—42no—
180C2×Dic19—41no—
181C2×Dic19—41no—
182C2×Dic19—41no—
183C2×Dic19—42no—
184Dic38—22no—
185Dic38—22no—
186Dic38—41no—
187Dic38—41no—
188Dic38—42no—
189Dic38—81no—
190C8×C19—42no—
191C8×C19—81no—
192C19⋊C8—42no—
193#3101—191no—
194#3078—191no—
195#2536—191no—
196#1518—191no—
197#1486D1911yescharacteristic
198#1479—191no—
199#1286—191no—
200C22×C19—21no—
201C22×C19—21no—
202C22×C19—42no—
203C22×C19—42no—
204C22×C19—42no—
205C22×C19—81no—
206C22×C19—81no—
207C22×C19—81no—
208C22×C19—81no—
209C22×C19#39211yescharacteristic
210C22×C19#45011yescharacteristic
211C22×C19#45211yescharacteristic
212C4×C19—21no—
213C4×C19—21no—
214C4×C19—21no—
215C4×C19—21no—
216C4×C19—81no—
217C4×C19#44811yescharacteristic
218C4×C19#44911yescharacteristic
219C4×C19#46511yescharacteristic
220C4×C19#46811yescharacteristic
221Dic19—42no—
222Dic19—82no—
223Dic19—81no—
224Dic19—81no—
225Dic19—81no—
226#533—191no—
227C2×C22⋊Q8—381no—
228C2×C4×Q8—191no—
229C2×C4×D4C2×D1911yescharacteristic
230#483—381no—
231#479—382no—
232#477—381no—
233#476—381no—
234#475—381no—
235#461—381no—
236#450—381no—
237C4×SD16—382no—
238#431—191no—
239#431C2×D1911yescharacteristic
240#428—381no—
241#423C2×D1911yescharacteristic
242#419—381no—
243#398—381no—
244#394—381no—
245#388—382no—
246#382—191no—
247#380—381no—
248#328—382no—
249Q8⋊C8—382no—
250D4⋊C8—22no—
251C2×C19—21no—
252C2×C19—21no—
253C2×C19—82no—
254C2×C19#200011yescharacteristic
255C2×C19#200911yescharacteristic
256C2×C19#201011yescharacteristic
257C22×Q8—191no—
258C22×D4D7611yescharacteristic
259C23×C4—21no—
260C2×SD16—382no—
261C2×M16—21no—
262C4⋊Q8—191no—
263C4⋊Q8—191no—
264#125—381no—
265C22⋊Q8—381no—
266C22⋊Q8—381no—
267C22⋊Q8—762no—
268C22⋊Q8—762no—
269C4×Q8—381no—
270C4×Q8—381no—
271C4×Q8—381no—
272C4×Q8—381no—
273C4×Q8—381no—
274C4×Q8—381no—
275C4×D4—21no—
276C4×D4—21no—
277C4×D4—21no—
278C4×D4—21no—
279#117—381no—
280C2×C4⋊C4—191no—
281C2×C4⋊C4—382no—
282C2×C4⋊C4—381no—
283C2×C4⋊C4—381no—
284C2×C4⋊C4D7611yescharacteristic
285C2×C22⋊C4—21no—
286C2×C22⋊C4—382no—
287C2×C22⋊C4—382no—
288C2×C42—381no—
289C2×C42C22×D1911yescharacteristic
290#107—382no—
291#106—382no—
292#106—382no—
293C4⋊C8—21no—
294C4⋊C8—21no—
295C4⋊C8—381no—
296C4⋊C8C22⋊D1912yes—
297#103—382no—
298#103—382no—
299#103—382no—
300#102—382no—
301C22⋊C8—21no—
302C22⋊C8—381no—
303C4×C8—21no—
304C4×C8—192no—
305#95—192no—
306#95—382no—
307#95—381no—
308C19#1000111yescharacteristic, complemented, Sylow
309C24—21no—
310C2×Q8—192no—
311C2×Q8—381no—
312C2×Q8—381no—
313C2×Q8—381no—
314C2×Q8—381no—
315C2×Q8—381no—
316C2×Q8—381no—
317C2×Q8—381no—
318C2×D4—21no—
319C2×D4—21no—
320C2×D4—42no—
321C22×C4—21no—
322C22×C4—41no—
323C22×C4—41no—
324C22×C4—41no—
325C22×C4—41no—
326C22×C4—41no—
327C22×C4—41no—
328C22×C4—381no—
329C22×C4—382no—
330C22×C4—381no—
331C22×C4C2×D7611yescharacteristic
332C22×C4D4×D1911yescharacteristic
333C22×C4D4×D1911yescharacteristic
334SD16—764no—
335M16—41no—
336M16—41no—
337C2×C8—22no—
338C2×C8—41no—
339C2×C8—382no—
340C4⋊C4—21no—
341C4⋊C4—21no—
342C4⋊C4—381no—
343C4⋊C4—381no—
344C4⋊C4—381no—
345C4⋊C4—381no—
346C4⋊C4—381no—
347C4⋊C4—381no—
348C4⋊C4—764no—
349C4⋊C4—761no—
350C4⋊C4—761no—
351C4⋊C4—761no—
352C4⋊C4—761no—
353C4⋊C4—761no—
354C4⋊C4—761no—
355C22⋊C4—41no—
356C22⋊C4—41no—
357C22⋊C4—764no—
358C22⋊C4—764no—
359C22⋊C4—761no—
360C42—761no—
361C42—761no—
362C42—761no—
363C42#6454111yescharacteristic
364C42D4×D1911yescharacteristic
365C42D4×D1911yescharacteristic
366C42C2×C22⋊D1911yescharacteristic
367C23—22no—
368C23—41no—
369C23—41no—
370C23—41no—
371C23—41no—
372C23—41no—
373C23—41no—
374C23#1059732811yescharacteristic
375Q8—382no—
376Q8—382no—
377Q8—762no—
378Q8—761no—
379Q8—761no—
380Q8—1521no—
381D4—22no—
382D4—22no—
383D4—41no—
384D4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—81no—
391C2×C4—81no—
392C2×C4—81no—
393C2×C4—81no—
394C2×C4—382no—
395C2×C4—761no—
396C2×C4—761no—
397C2×C4—762no—
398C2×C4—762no—
399C2×C4—762no—
400C2×C4—762no—
401C2×C4—761no—
402C2×C4—761no—
403C2×C4—761no—
404C2×C4#1059732811yescharacteristic
405C2×C4#1059733011yescharacteristic
406C2×C4#1059733011yescharacteristic
407C2×C4#1059735711yescharacteristic
408C2×C4#1059735811yescharacteristic
409C2×C4SD16×D1911yescharacteristic
410C2×C4#1059736111yescharacteristic
411C2×C4#1059737611yescharacteristic
412C2×C4#1059738311yescharacteristic
413C2×C4#1059738611yescharacteristic
414C8—42no—
415C8—81no—
416C8—762no—
417C22—21no—
418C22—21no—
419C22—42no—
420C22—42no—
421C22—42no—
422C22—81no—
423C22—81no—
424C22—81no—
425C22—81no—
426C22#1192645311yescharacteristic
427C22#1192669611yescharacteristic
428C22#1192670711yescharacteristic
429C4—21no—
430C4—21no—
431C4—21no—
432C4—21no—
433C4—81no—
434C4—762no—
435C4—1522no—
436C4—1521no—
437C4—1521no—
438C4—1521no—
439C4#1192668111yescharacteristic
440C4#1192668611yescharacteristic
441C4#1192677211yescharacteristic
442C4#1192678911yescharacteristic
443C2—21no—
444C2—21no—
445C2—82no—
446C2#1456463911yescharacteristic
447C2#1456469611yescharacteristic
448C2#1456470211yescharacteristic
subgroupG/H
centerC22#11926453
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#1486C2
socleC22×C19#392
prime radicalC22×D4×C19D4
hypercenter#1486D19
hypocenterC19#10001
LCSG ▷ C2×C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1486

Complements

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

NH ≅ G/Ntype
2. #14573442C2semidirect
4. #14562200C2semidirect
5. #14562029C2semidirect
6. #14561495C2semidirect
108. C2×Dic38SD16semidirect
308. C19#10001semidirect

Maximal subgroups

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

subgroupindex
#145736432
#145734422
#145685442
#145622002
#145620292
#145614952
C19×#14862
#1000119