Finite Group Databasebeta

← #18085474

Subgroups — #18085474

Order 4864.

914 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 914 conjugacy classes of subgroups — too many to draw. Only its 89 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#14574456C211yesmaximal, characteristic, complemented
2#14567282C211yesmaximal, characteristic
3#14563556C211yesmaximal, characteristic
4#14562155C211yesmaximal, characteristic, complemented
5#14562154C211yesmaximal, characteristic, complemented
6#14561521C211yesmaximal, characteristic, complemented
7C19×#2435C211yesmaximal, characteristic
8C2×#10597382—21no—
9C2×#10597370C2211yescharacteristic
10#11926874—21no—
11#11926872—21no—
12#11926800—22no—
13#11926700—21no—
14#11926699—21no—
15C2×#10597290—22no—
16#11926508C2211yescharacteristic
17#11926508C2211yescharacteristic
18#11926458—22no—
19#11926447—21no—
20#11926400—22no—
21C4×C22⋊Dic19C2211yescharacteristic
22#11926281—22no—
23#11926280—22no—
24C23×D4×C19C2211yescharacteristic
25C2×C19×#124—21no—
26C2×C19×C22⋊Q8C2211yescharacteristic
27C19×#394—22no—
28C19×#390—21no—
29C19×#379—22no—
30C4×C22⋊C4×C19C2211yescharacteristic
31C25×C19D412yes—
32C22×Q8×C19D411yescharacteristic
33C22×D4×C19—21no—
34C22×D4×C19—21no—
35C22×D4×C19—21no—
36C22×D4×C19—21no—
37C22×D4×C19—21no—
38C22×D4×C19—21no—
39C22×D4×C19—44no—
40C23×C4×C19C2311yescharacteristic
41C22×Dic38D411yescharacteristic
42C19×#124—44no—
43C19×C22⋊Q8—21no—
44C19×C22⋊Q8—21no—
45C19×C22⋊Q8—21no—
46C19×C22⋊Q8—21no—
47C2×C4⋊C4×C19—21no—
48C2×C4⋊C4×C19D411yescharacteristic
49C2×C22⋊C4×C19—24no—
50C2×C22⋊C4×C19—21no—
51C2×C22⋊C4×C19—21no—
52C2×C22⋊C4×C19—24no—
53C2×C42×C19—21no—
54C2×C22⋊Dic19—24no—
55C2×C22⋊Dic19—21no—
56C2×C22⋊Dic19—21no—
57C2×C22⋊Dic19—24no—
58C2×#64528—22no—
59#10597382—44no—
60C2×C4⋊Dic19D411yescharacteristic
61#10597370—21no—
62#10597370—21no—
63#10597370—21no—
64#10597370—21no—
65C2×Dic19⋊C4—21no—
66C2×C4×Dic19—21no—
67C2×#64520—21no—
68C2×#64520D412yes—
69C19×#95D412yes—
70#10597292—22no—
71#10597290—44no—
72C19⋊#95D412yes—
73C22⋊(C19⋊C8)—21no—
74C22⋊(C19⋊C8)—21no—
75C22⋊(C19⋊C8)—21no—
76C22⋊(C19⋊C8)—21no—
77#10597267—22no—
78#10597265—22no—
79C24×C19—22no—
80C24×C19—22no—
81C24×C19—22no—
82C24×C19—44no—
83C24×C19—44no—
84C24×C19—44no—
85C24×C19C2×D411yescharacteristic
86C2×Q8×C19—21no—
87C2×Q8×C19—21no—
88C2×Q8×C19—42no—
89C2×D4×C19—24no—
90C2×D4×C19—24no—
91C2×D4×C19—24no—
92C2×D4×C19—42no—
93C2×D4×C19—42no—
94C2×D4×C19—42no—
95C2×D4×C19—44no—
96C2×D4×C19—44no—
97C2×D4×C19—44no—
98C2×D4×C19—41no—
99C2×D4×C19—41no—
100C2×D4×C19—41no—
101C2×D4×C19—41no—
102C22×C4×C19—22no—
103C22×C4×C19—21no—
104C22×C4×C19—21no—
105C22×C4×C19—42no—
106C22×C4×C19C2×D411yescharacteristic
107C22×C4×C19C2×D411yescharacteristic
108C22×C4×C19C2×D411yescharacteristic
109C22×C4×C19C2×D411yescharacteristic
110C22×C4×C19C2×D411yescharacteristic
111C22×C4×C19#4111yescharacteristic
112C22×Dic19—21no—
113C22×Dic19—22no—
114C22×Dic19—21no—
115C2×Dic38—21no—
116C2×Dic38—21no—
117C2×Dic38—42no—
118C4⋊C4×C19—21no—
119C4⋊C4×C19—21no—
120C4⋊C4×C19—41no—
121C4⋊C4×C19—41no—
122C22⋊C4×C19—42no—
123C22⋊C4×C19—48no—
124C22⋊C4×C19—41no—
125C22⋊C4×C19—41no—
126C22⋊C4×C19—84no—
127C42×C19—42no—
128C22⋊Dic19—48no—
129C22⋊Dic19—42no—
130C22⋊Dic19—41no—
131C22⋊Dic19—41no—
132C22⋊Dic19—84no—
133#64528—82no—
134C4⋊Dic19—21no—
135C4⋊Dic19—21no—
136Dic19⋊C4—41no—
137Dic19⋊C4—41no—
138C4×Dic19—42no—
139#64520—42no—
140#64520—42no—
141C2×C19⋊C8—22no—
142C2×C19⋊C8—41no—
143#10333—191nomaximal, Sylow
144C23×C19—22no—
145C23×C19—22no—
146C23×C19—24no—
147C23×C19—24no—
148C23×C19—24no—
149C23×C19—41no—
150C23×C19—42no—
151C23×C19—42no—
152C23×C19—42no—
153C23×C19—44no—
154C23×C19—44no—
155C23×C19—42no—
156C23×C19—44no—
157C23×C19—44no—
158C23×C19—82no—
159C23×C19—82no—
160C23×C19—816no—
161C23×C19#12011yescharacteristic
162C23×C19#12011yescharacteristic
163C23×C19#12111yescharacteristic
164Q8×C19—42no—
165Q8×C19—81no—
166D4×C19—44no—
167D4×C19—44no—
168D4×C19—44no—
169D4×C19—44no—
170C2×C4×C19—22no—
171C2×C4×C19—22no—
172C2×C4×C19—22no—
173C2×C4×C19—41no—
174C2×C4×C19—41no—
175C2×C4×C19—41no—
176C2×C4×C19—42no—
177C2×C4×C19—42no—
178C2×C4×C19—42no—
179C2×C4×C19—41no—
180C2×C4×C19—41no—
181C2×C4×C19—42no—
182C2×C4×C19—42no—
183C2×C4×C19#12011yescharacteristic
184C2×C4×C19#12111yescharacteristic
185C2×C4×C19#12111yescharacteristic
186C2×C4×C19#12711yescharacteristic
187C2×Dic19—42no—
188C2×Dic19—42no—
189C2×Dic19—42no—
190C2×Dic19—41no—
191C2×Dic19—41no—
192C2×Dic19—42no—
193C2×Dic19—42no—
194Dic38—42no—
195Dic38—81no—
196C19⋊C8—42no—
197C19⋊C8—81no—
198#3195—191no—
199#2435—191no—
200#2435D1911yescharacteristic
201#1783—191no—
202#1508—191no—
203#1508—191no—
204#1297—191no—
205C22×C19—21no—
206C22×C19—21no—
207C22×C19—21no—
208C22×C19—21no—
209C22×C19—21no—
210C22×C19—21no—
211C22×C19—21no—
212C22×C19—44no—
213C22×C19—48no—
214C22×C19—48no—
215C22×C19—44no—
216C22×C19—84no—
217C22×C19—84no—
218C22×C19—84no—
219C22×C19—84no—
220C22×C19—82no—
221C22×C19—82no—
222C22×C19#39211yescharacteristic
223C22×C19#45512yes—
224C22×C19#45512yes—
225C4×C19—21no—
226C4×C19—21no—
227C4×C19—21no—
228C4×C19—82no—
229C4×C19—81no—
230C4×C19—81no—
231C4×C19B(4,𝔽2)12yes—
232Dic19—82no—
233Dic19—81no—
234Dic19—81no—
235C23×D4C2×D1911yescharacteristic
236C2×#124—21no—
237C2×#124—381no—
238C2×C22⋊Q8—191no—
239C2×C22⋊Q8C2×D1911yescharacteristic
240#483—381no—
241#483—381no—
242#470—382no—
243#451—381no—
244#451—381no—
245C2×#100—382no—
246#407—191no—
247#407—191no—
248#394—22no—
249#394—382no—
250#390—21no—
251#390—381no—
252#379—22no—
253#379—382no—
254C4×C22⋊C4—191no—
255C4×C22⋊C4C2×D1911yescharacteristic
256#328—382no—
257#328—382no—
258C2×C19—22no—
259C2×C19—22no—
260C2×C19—41no—
261C2×C19—84no—
262C2×C19#200411yescharacteristic
263C2×C19#200411yescharacteristic
264C2×C19#202111yescharacteristic
265C25C22⋊D1912yes—
266C22×Q8—191no—
267C22×Q8C22⋊D1911yescharacteristic
268C22×D4—21no—
269C22×D4—21no—
270C22×D4—21no—
271C22×D4—21no—
272C22×D4—21no—
273C22×D4—21no—
274C22×D4—44no—
275C23×C4C22×D1911yescharacteristic
276C2×Q16—382no—
277C2×M16—192no—
278C2×M16—381no—
279#124—44no—
280#124—764no—
281C22⋊Q8—21no—
282C22⋊Q8—21no—
283C22⋊Q8—21no—
284C22⋊Q8—21no—
285C22⋊Q8—381no—
286C22⋊Q8—381no—
287C22⋊Q8—381no—
288C22⋊Q8—381no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—191no—
291C2×C4⋊C4—381no—
292C2×C4⋊C4C22⋊D1911yescharacteristic
293C2×C22⋊C4—24no—
294C2×C22⋊C4—21no—
295C2×C22⋊C4—21no—
296C2×C22⋊C4—24no—
297C2×C22⋊C4—384no—
298C2×C22⋊C4—381no—
299C2×C22⋊C4—381no—
300C2×C22⋊C4—384no—
301C2×C42—21no—
302C2×C42—381no—
303#106—382no—
304#103—382no—
305#103—382no—
306#100—764no—
307C22⋊C8—381no—
308C22⋊C8—381no—
309C22⋊C8—381no—
310C22⋊C8—381no—
311#95—192no—
312#95C22⋊D1912yes—
313C19#1033311yescharacteristic, complemented, Sylow
314C24—22no—
315C24—22no—
316C24—22no—
317C24—44no—
318C24—44no—
319C24—44no—
320C24C2×C22⋊D1911yescharacteristic
321C2×Q8—21no—
322C2×Q8—21no—
323C2×Q8—42no—
324C2×Q8—381no—
325C2×Q8—381no—
326C2×Q8—762no—
327C2×D4—24no—
328C2×D4—24no—
329C2×D4—24no—
330C2×D4—42no—
331C2×D4—42no—
332C2×D4—42no—
333C2×D4—44no—
334C2×D4—44no—
335C2×D4—44no—
336C2×D4—41no—
337C2×D4—41no—
338C2×D4—41no—
339C2×D4—41no—
340C22×C4—22no—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—42no—
344C22×C4—382no—
345C22×C4—381no—
346C22×C4—381no—
347C22×C4D4×D1911yescharacteristic
348C22×C4D4×D1911yescharacteristic
349C22×C4D4×D1911yescharacteristic
350C22×C4#6454311yescharacteristic
351C22×C4C2×C22⋊D1911yescharacteristic
352C22×C4C2×C22⋊D1911yescharacteristic
353Q16—1522no—
354M16—762no—
355M16—762no—
356C2×C8—382no—
357C2×C8—761no—
358C4⋊C4—21no—
359C4⋊C4—21no—
360C4⋊C4—41no—
361C4⋊C4—41no—
362C4⋊C4—381no—
363C4⋊C4—381no—
364C4⋊C4—761no—
365C4⋊C4—761no—
366C22⋊C4—42no—
367C22⋊C4—48no—
368C22⋊C4—41no—
369C22⋊C4—41no—
370C22⋊C4—84no—
371C22⋊C4—762no—
372C22⋊C4—768no—
373C22⋊C4—761no—
374C22⋊C4—761no—
375C22⋊C4—1524no—
376C42—42no—
377C42—762no—
378C23—22no—
379C23—22no—
380C23—24no—
381C23—24no—
382C23—24no—
383C23—41no—
384C23—42no—
385C23—42no—
386C23—42no—
387C23—44no—
388C23—44no—
389C23—42no—
390C23—44no—
391C23—44no—
392C23—82no—
393C23—82no—
394C23—816no—
395C23#1059738311yescharacteristic
396C23#1059738511yescharacteristic
397C23#1059739911yescharacteristic
398Q8—42no—
399Q8—81no—
400Q8—762no—
401Q8—1521no—
402D4—44no—
403D4—44no—
404D4—44no—
405D4—44no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—762no—
420C2×C4—762no—
421C2×C4—762no—
422C2×C4—761no—
423C2×C4—761no—
424C2×C4—762no—
425C2×C4—762no—
426C2×C4#1059738311yescharacteristic
427C2×C4#1059738411yescharacteristic
428C2×C4#1059738511yescharacteristic
429C2×C4#1059738611yescharacteristic
430C8—762no—
431C8—1521no—
432C22—21no—
433C22—21no—
434C22—21no—
435C22—21no—
436C22—21no—
437C22—21no—
438C22—21no—
439C22—44no—
440C22—48no—
441C22—48no—
442C22—44no—
443C22—84no—
444C22—84no—
445C22—84no—
446C22—84no—
447C22—82no—
448C22—82no—
449C22#1192645211yescharacteristic
450C22#1192672112yes—
451C22#1192672212yes—
452C4—21no—
453C4—21no—
454C4—21no—
455C4—82no—
456C4—81no—
457C4—81no—
458C4—1522no—
459C4—1521no—
460C4—1521no—
461C4#1192673012yes—
462C2—22no—
463C2—22no—
464C2—41no—
465C2—84no—
466C2#1456466211yescharacteristic
467C2#1456466411yescharacteristic
468C2#1456475811yescharacteristic
subgroupG/H
centerC22#11926452
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC19×#2435C2
socleC22×C19#392
prime radicalC23×D4×C19C22
hypercenter#2435D19
hypocenterC19#10333
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2435

Complements

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

NH ≅ G/Ntype
1. #14574456C2semidirect
4. #14562155C2semidirect
5. #14562154C2semidirect
6. #14561521C2semidirect
313. C19#10333semidirect

Maximal subgroups

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

subgroupindex
#145744562
#145672822
#145635562
#145621552
#145621542
#145615212
C19×#24352
#1033319