Finite Group Databasebeta

← #18071528

Subgroups — #18071528

Order 4864.

536 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 87 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#14564776C211yesmaximal, characteristic, complemented
2#14564771C211yesmaximal, characteristic, complemented
3#14564717C211yesmaximal, characteristic, complemented
4#14561461C211yesmaximal, characteristic, complemented
5#14561456C211yesmaximal, characteristic, complemented
6#14561456C211yesmaximal, characteristic, complemented
7C19×#2733C211yesmaximal, characteristic
8C22×#64526—21no—
9C2×#10597315C2211yescharacteristic
10C2×#10597292—21no—
11C2×#10597267—21no—
12C2×#10597289—21no—
13#11926306—21no—
14#11926306—21no—
15#11926299C2211yescharacteristic
16#11926299C2211yescharacteristic
17#11926299C2211yescharacteristic
18C2×C19×#124—21no—
19C19×#394—21no—
20C19×#392—21no—
21C19×#392—21no—
22C19×#391C2211yescharacteristic
23C19×#390C2211yescharacteristic
24C19×#390C2211yescharacteristic
25C19×#388—21no—
26C19×#388—21no—
27C22×Q8×C19D411yescharacteristic
28C22×D4×C19—21no—
29C22×D4×C19—21no—
30C22×D4×C19D411yescharacteristic
31C22×D4×C19D411yescharacteristic
32C22×Dic38—21no—
33C19×#124—42no—
34C19×#124—42no—
35C2×C4⋊C4×C19D411yescharacteristic
36C2×C4⋊C4×C19D411yescharacteristic
37C2×C4⋊C4×C19D411yescharacteristic
38C2×C22⋊C4×C19—21no—
39C2×C22⋊C4×C19—21no—
40C2×C22⋊C4×C19—21no—
41C2×C22⋊C4×C19—21no—
42C2×C22⋊C4×C19—21no—
43C2×C22⋊C4×C19—21no—
44C2×C22⋊C4×C19—21no—
45C2×C22⋊C4×C19—21no—
46C2×C42×C19—21no—
47C2×C42×C19C2311yescharacteristic
48C2×#64526—42no—
49C2×#64526—42no—
50C2×#64526—42no—
51C2×C4⋊Dic19—21no—
52C2×C4⋊Dic19—21no—
53C22×C19⋊C8—21no—
54C22×C19⋊C8—21no—
55C22×C19⋊C8—21no—
56#10597315—42no—
57C19×#95—21no—
58C19×#95—21no—
59C19×#95—21no—
60#10597292—42no—
61#10597289—42no—
62#10597267—42no—
63C24×C19—21no—
64C24×C19—21no—
65C2×Q8×C19—21no—
66C2×Q8×C19—41no—
67C2×Q8×C19—41no—
68C2×Q8×C19SD1612yescomplemented
69C2×D4×C19—21no—
70C2×D4×C19—21no—
71C2×D4×C19—21no—
72C2×D4×C19—21no—
73C2×D4×C19—41no—
74C2×D4×C19—41no—
75C2×D4×C19—41no—
76C2×D4×C19—41no—
77C2×D4×C19—42no—
78C2×D4×C19—81no—
79C2×D4×C19—81no—
80C2×D4×C19—81no—
81C2×D4×C19—81no—
82C2×D4×C19—81no—
83C22×C4×C19—21no—
84C22×C4×C19—21no—
85C22×C4×C19—21no—
86C22×C4×C19—21no—
87C22×C4×C19C2×D411yescharacteristic
88C22×C4×C19C2×D411yescharacteristic
89C22×C4×C19C2×D411yescharacteristic
90C22×Dic19—41no—
91C2×Dic38—22no—
92C2×Dic38—41no—
93C2×Dic38—41no—
94C2×Dic38—41no—
95C2×Dic38—41no—
96C2×Dic38—41no—
97C4⋊C4×C19—41no—
98C4⋊C4×C19—41no—
99C4⋊C4×C19—41no—
100C22⋊C4×C19—42no—
101C22⋊C4×C19—42no—
102C22⋊C4×C19—41no—
103C22⋊C4×C19—41no—
104C22⋊C4×C19—41no—
105C22⋊C4×C19—41no—
106C22⋊C4×C19—41no—
107C22⋊C4×C19—41no—
108C22⋊C4×C19—41no—
109C22⋊C4×C19—41no—
110C22⋊C4×C19—81no—
111C22⋊C4×C19—81no—
112C42×C19—41no—
113C42×C19—42no—
114#64526—48no—
115C4⋊Dic19—22no—
116C4⋊Dic19—22no—
117C4⋊Dic19—41no—
118C4⋊Dic19—41no—
119C2×C19⋊C8—22no—
120C2×C19⋊C8—41no—
121C2×C19⋊C8—41no—
122C2×C19⋊C8—41no—
123C2×C19⋊C8—41no—
124C2×C19⋊C8—41no—
125C2×C19⋊C8—41no—
126C2×C19⋊C8—41no—
127C2×C19⋊C8—41no—
128#7781—191nomaximal, Sylow
129C23×C19—41no—
130C23×C19—41no—
131C23×C19—41no—
132C23×C19—41no—
133C23×C19—41no—
134C23×C19—41no—
135C23×C19—41no—
136C23×C19—41no—
137C23×C19—41no—
138C23×C19—41no—
139C23×C19—41no—
140C23×C19—41no—
141C23×C19—41no—
142C23×C19—41no—
143C23×C19#12011yescharacteristic
144Q8×C19—42no—
145Q8×C19—81no—
146D4×C19—42no—
147D4×C19—42no—
148D4×C19—81no—
149D4×C19—81no—
150D4×C19—84no—
151D4×C19—84no—
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—22no—
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×SD1611yescharacteristic
171C2×C4×C19#13511yescharacteristic
172C2×C4×C19#13511yescharacteristic
173C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
174C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
175C2×C4×C19#13711yescharacteristic
176C2×Dic19—42no—
177C2×Dic19—81no—
178C2×Dic19—81no—
179Dic38—42no—
180Dic38—42no—
181Dic38—81no—
182Dic38—81no—
183C19⋊C8—42no—
184C19⋊C8—81no—
185C19⋊C8—81no—
186#2733D1911yescharacteristic
187#2024—191no—
188#2023—191no—
189#2013—191no—
190#1272—191no—
191#1270—191no—
192#1270—191no—
193C22×C19—81no—
194C22×C19—81no—
195C22×C19—81no—
196C22×C19—81no—
197C22×C19—81no—
198C22×C19—81no—
199C22×C19—81no—
200C22×C19—81no—
201C22×C19—81no—
202C22×C19—81no—
203C22×C19—81no—
204C22×C19—81no—
205C22×C19—81no—
206C22×C19—81no—
207C22×C19#44911yescharacteristic
208C22×C19#45011yescharacteristic
209C22×C19#45211yescharacteristic
210C22×C19#45311yescharacteristic
211C22×C19#45511yescharacteristic
212C22×C19#45511yescharacteristic
213C22×C19B(4,𝔽2)11yescharacteristic
214C4×C19—21no—
215C4×C19—21no—
216C4×C19—21no—
217C4×C19—21no—
218C4×C19—21no—
219C4×C19—21no—
220C4×C19—42no—
221C4×C19—81no—
222C4×C19—81no—
223C4×C19—81no—
224Dic19—82no—
225C22×SD16—381no—
226C2×C4⋊Q8—191no—
227C2×#124—21no—
228C2×#103—381no—
229C2×#103—381no—
230C2×#102—381no—
231#394—21no—
232#392—21no—
233#392—21no—
234#391C2×D1911yescharacteristic
235#390C2×D1911yescharacteristic
236#390C2×D1911yescharacteristic
237#388—21no—
238#388—21no—
239#340—381no—
240#340—381no—
241#336—191no—
242#336—191no—
243#336—191no—
244C2×C19—161no—
245C2×C19—161no—
246C2×C19#160011yescharacteristic
247C2×C19#160111yescharacteristic
248C2×C19#160611yescharacteristic
249C2×C19#163111yescharacteristic
250C2×C19#164211yescharacteristic
251C2×C19#164611yescharacteristic
252C2×C19#165911yescharacteristic
253C22×Q8—381no—
254C22×Q8C22⋊D1911yescharacteristic
255C22×D4—21no—
256C22×D4—21no—
257C22×D4C22⋊D1911yescharacteristic
258C22×D4C22⋊D1911yescharacteristic
259C2×SD16—762no—
260C2×SD16—762no—
261C2×SD16—762no—
262C22×C8—381no—
263C22×C8—381no—
264C22×C8—381no—
265C4⋊Q8—762no—
266#124—42no—
267#124—42no—
268C2×C4⋊C4—381no—
269C2×C4⋊C4—381no—
270C2×C4⋊C4C22⋊D1911yescharacteristic
271C2×C4⋊C4C22⋊D1911yescharacteristic
272C2×C4⋊C4C22⋊D1911yescharacteristic
273C2×C22⋊C4—21no—
274C2×C22⋊C4—21no—
275C2×C22⋊C4—21no—
276C2×C22⋊C4—21no—
277C2×C22⋊C4—21no—
278C2×C22⋊C4—21no—
279C2×C22⋊C4—21no—
280C2×C22⋊C4—21no—
281C2×C42—21no—
282C2×C42C22×D1911yescharacteristic
283#103—762no—
284#103—762no—
285#102—762no—
286#95—21no—
287#95—21no—
288#95—21no—
289C19#778111yescharacteristic, complemented, Sylow
290C24—21no—
291C24—21no—
292C2×Q8—21no—
293C2×Q8—41no—
294C2×Q8—41no—
295C2×Q8—382no—
296C2×Q8—761no—
297C2×Q8—761no—
298C2×Q8—761no—
299C2×Q8—761no—
300C2×Q8—761no—
301C2×Q8#6452612yescomplemented
302C2×D4—21no—
303C2×D4—21no—
304C2×D4—21no—
305C2×D4—21no—
306C2×D4—41no—
307C2×D4—41no—
308C2×D4—41no—
309C2×D4—41no—
310C2×D4—42no—
311C2×D4—81no—
312C2×D4—81no—
313C2×D4—81no—
314C2×D4—81no—
315C2×D4—81no—
316C22×C4—21no—
317C22×C4—21no—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—761no—
321C22×C4C2×C22⋊D1911yescharacteristic
322C22×C4C2×C22⋊D1911yescharacteristic
323C22×C4C2×C22⋊D1911yescharacteristic
324SD16—768no—
325C2×C8—382no—
326C2×C8—761no—
327C2×C8—761no—
328C2×C8—761no—
329C2×C8—761no—
330C2×C8—761no—
331C2×C8—761no—
332C2×C8—761no—
333C2×C8—761no—
334C4⋊C4—41no—
335C4⋊C4—41no—
336C4⋊C4—41no—
337C4⋊C4—382no—
338C4⋊C4—382no—
339C4⋊C4—761no—
340C4⋊C4—761no—
341C22⋊C4—42no—
342C22⋊C4—42no—
343C22⋊C4—41no—
344C22⋊C4—41no—
345C22⋊C4—41no—
346C22⋊C4—41no—
347C22⋊C4—41no—
348C22⋊C4—41no—
349C22⋊C4—41no—
350C22⋊C4—41no—
351C22⋊C4—81no—
352C22⋊C4—81no—
353C42—41no—
354C42—42no—
355C23—41no—
356C23—41no—
357C23—41no—
358C23—41no—
359C23—41no—
360C23—41no—
361C23—41no—
362C23—41no—
363C23—41no—
364C23—41no—
365C23—41no—
366C23—41no—
367C23—41no—
368C23—41no—
369C23#1059739911yescharacteristic
370Q8—42no—
371Q8—81no—
372Q8—762no—
373Q8—762no—
374Q8—1521no—
375Q8—1521no—
376D4—42no—
377D4—42no—
378D4—81no—
379D4—81no—
380D4—84no—
381D4—84no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—22no—
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—41no—
399C2×C4—41no—
400C2×C4—762no—
401C2×C4—1521no—
402C2×C4—1521no—
403C2×C4#1059737811yescharacteristic
404C2×C4C2×#6452611yescharacteristic
405C2×C4#1059739511yescharacteristic
406C2×C4#1059739611yescharacteristic
407C2×C4#1059739611yescharacteristic
408C2×C4#1059739711yescharacteristic
409C8—762no—
410C8—1521no—
411C8—1521no—
412C22—81no—
413C22—81no—
414C22—81no—
415C22—81no—
416C22—81no—
417C22—81no—
418C22—81no—
419C22—81no—
420C22—81no—
421C22—81no—
422C22—81no—
423C22—81no—
424C22—81no—
425C22—81no—
426C22#1192668911yescharacteristic
427C22#1192669511yescharacteristic
428C22#1192670611yescharacteristic
429C22#1192671211yescharacteristic
430C22#1192672211yescharacteristic
431C22#1192672211yescharacteristic
432C22#1192673111yescharacteristic
433C4—21no—
434C4—21no—
435C4—21no—
436C4—21no—
437C4—21no—
438C4—21no—
439C4—42no—
440C4—81no—
441C4—81no—
442C4—81no—
443C4—1522no—
444C2—161no—
445C2—161no—
446C2#1456258111yescharacteristic
447C2#1456258711yescharacteristic
448C2#1456261511yescharacteristic
449C2#1456276211yescharacteristic
450C2#1456283511yescharacteristic
451C2#1456286311yescharacteristic
452C2#1456294111yescharacteristic
subgroupG/H
centerC23#10597399
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
Fitting, prime radicalC19×#2733C2
socleC23×C19#120
hypercenter#2733D19
hypocenterC19#7781
LCSG ▷ C2×C42×C19 ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2733

Complements

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

NH ≅ G/Ntype
1. #14564776C2semidirect
2. #14564771C2semidirect
3. #14564717C2semidirect
4. #14561461C2semidirect
5. #14561456C2semidirect
6. #14561456C2semidirect
68. C2×Q8×C19SD16semidirect
289. C19#7781semidirect
301. C2×Q8#64526semidirect

Maximal subgroups

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

subgroupindex
#145647762
#145647712
#145647172
#145614612
#145614562
C19×#27332
#778119