Finite Group Databasebeta

← #18080526

Subgroups — #18080526

Order 4864.

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

normal subgroups only

This group has 716 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#14572080C211yesmaximal, characteristic
2#14566966C211yesmaximal, characteristic
3#14561964C212yesmaximal, complemented
4#14561544C212yesmaximal, complemented
5C19×#1785C211yesmaximal, characteristic
6C22×#64520—21no—
7C2×#10597381C411yescharacteristic
8C2×#10597381C411yescharacteristic
9C22×Dic19⋊C4C2211yescharacteristic
10#11926511—24no—
11#11926508—21no—
12#11926508C2212yes—
13#11926463—21no—
14#11926458—21no—
15#11926424C411yescharacteristic
16#11926424C411yescharacteristic
17#11926417—21no—
18#11926417—21no—
19#11926407C2211yescharacteristic
20#11926269—24no—
21C22×#41×C19C2211yescharacteristic
22C2×C19×#101—21no—
23C2×C19×#100—21no—
24C19×#407C2212yes—
25C2×#41×C19—22no—
26C2×#41×C19—22no—
27C2×#41×C19—42no—
28C2×#41×C19—42no—
29C22×Q8×C19D411yescharacteristic
30C22×D4×C19C2×C411yescharacteristic
31C22×D4×C19C2×C411yescharacteristic
32C22×D4×C19D411yescharacteristic
33C23×C4×C19D411yescharacteristic
34C23×C4×C19D411yescharacteristic
35C23×C4×C19C2311yescharacteristic
36C23×Dic19C2×C411yescharacteristic
37C23×Dic19C2×C411yescharacteristic
38C2×M16×C19—22no—
39C2×C22⋊Dic19—21no—
40C2×C22⋊Dic19—21no—
41C2×C22⋊Dic19—21no—
42C2×C22⋊Dic19—21no—
43C2×C22⋊Dic19C2×C411yescharacteristic
44C2×C22⋊Dic19C2×C411yescharacteristic
45#10597381—42no—
46#10597381—42no—
47C2×Dic19⋊C4—21no—
48C2×Dic19⋊C4—21no—
49C2×Dic19⋊C4—21no—
50C2×Dic19⋊C4—21no—
51C2×Dic19⋊C4—22no—
52C2×Dic19⋊C4—22no—
53C2×#64520—22no—
54C2×#64520—22no—
55C2×#64520—42no—
56C2×#64520—42no—
57C22×C19⋊C8—22no—
58C19×#101—42no—
59C19×#100—42no—
60C19×C22⋊C8—22no—
61C19×C22⋊C8—22no—
62C19⋊#95—21no—
63C19⋊#95—21no—
64C19⋊#95—21no—
65C19⋊#95—21no—
66C22⋊(C19⋊C8)—24no—
67C22⋊(C19⋊C8)—22no—
68C22⋊(C19⋊C8)D414yes—
69C24×C19C22⋊C411yescharacteristic
70C24×C19C22⋊C411yescharacteristic
71C24×C19C22×C411yescharacteristic
72#41×C19—44no—
73#41×C19—44no—
74#41×C19—48no—
75C2×Q8×C19—22no—
76C2×Q8×C19—22no—
77C2×Q8×C19—41no—
78C2×D4×C19—22no—
79C2×D4×C19—22no—
80C2×D4×C19—22no—
81C2×D4×C19—22no—
82C2×D4×C19—22no—
83C2×D4×C19—22no—
84C2×D4×C19—41no—
85C2×D4×C19—41no—
86C2×D4×C19—41no—
87C22×C4×C19—22no—
88C22×C4×C19—22no—
89C22×C4×C19—21no—
90C22×C4×C19—21no—
91C22×C4×C19—21no—
92C22×C4×C19—21no—
93C22×C4×C19—41no—
94C22×C4×C19—41no—
95C22×C4×C19—41no—
96C22×C4×C19—41no—
97C22×C4×C19C22⋊C411yescharacteristic
98C22×C4×C19C22⋊C411yescharacteristic
99C22×C4×C19C2×D411yescharacteristic
100C22×C4×C19C2×D412yes—
101C22×C4×C19C2×D411yescharacteristic
102C22×C4×C19#4112yes—
103C22×Dic19—21no—
104C22×Dic19—22no—
105C22×Dic19—21no—
106C22×Dic19—21no—
107C22×Dic19—21no—
108C22×Dic19—22no—
109C22×Dic19—42no—
110C22×Dic19—41no—
111C22×Dic19—41no—
112M16×C19—42no—
113M16×C19—42no—
114C2×C8×C19—42no—
115C22⋊Dic19—42no—
116C22⋊Dic19—42no—
117C22⋊Dic19—42no—
118C22⋊Dic19—42no—
119C22⋊Dic19—41no—
120C22⋊Dic19—41no—
121Dic19⋊C4—42no—
122Dic19⋊C4—42no—
123Dic19⋊C4—41no—
124Dic19⋊C4—42no—
125Dic19⋊C4—41no—
126#64520—44no—
127#64520—42no—
128#64520—42no—
129C2×C19⋊C8—24no—
130C2×C19⋊C8—44no—
131#9513—191nomaximal, Sylow
132C23×C19—21no—
133C23×C19—21no—
134C23×C19—21no—
135C23×C19—21no—
136C23×C19—21no—
137C23×C19—21no—
138C23×C19—21no—
139C23×C19—41no—
140C23×C19—41no—
141C23×C19—41no—
142C23×C19—41no—
143C23×C19—41no—
144C23×C19—41no—
145C23×C19#9912yes—
146C23×C19C2×C22⋊C411yescharacteristic
147C23×C19C4×D412yes—
148Q8×C19—44no—
149D4×C19—44no—
150D4×C19—44no—
151D4×C19—44no—
152C2×C4×C19—22no—
153C2×C4×C19—22no—
154C2×C4×C19—24no—
155C2×C4×C19—21no—
156C2×C4×C19—21no—
157C2×C4×C19—21no—
158C2×C4×C19—21no—
159C2×C4×C19—21no—
160C2×C4×C19—21no—
161C2×C4×C19—21no—
162C2×C4×C19—21no—
163C2×C4×C19—21no—
164C2×C4×C19—42no—
165C2×C4×C19—42no—
166C2×C4×C19—42no—
167C2×C4×C19—42no—
168C2×C4×C19#9912yes—
169C2×C4×C19#12011yescharacteristic
170C2×C4×C19#12112yes—
171C2×C4×C19#12311yescharacteristic
172C2×Dic19—22no—
173C2×Dic19—24no—
174C2×Dic19—41no—
175C2×Dic19—42no—
176C2×Dic19—41no—
177C2×Dic19—41no—
178C2×Dic19—41no—
179C2×Dic19—41no—
180C2×Dic19—41no—
181C2×Dic19—41no—
182C2×Dic19—41no—
183C2×Dic19—41no—
184C2×Dic19—41no—
185C2×Dic19—41no—
186C2×Dic19—82no—
187C8×C19—82no—
188C19⋊C8—44no—
189#2879—191no—
190#2406—191no—
191#1785D1911yescharacteristic
192#1463—192no—
193#1306—192no—
194C22×C19—21no—
195C22×C19—21no—
196C22×C19—22no—
197C22×C19—22no—
198C22×C19—22no—
199C22×C19—22no—
200C22×C19—42no—
201C22×C19—42no—
202C22×C19—42no—
203C22×C19—42no—
204C22×C19—41no—
205C22×C19—41no—
206C22×C19—41no—
207C22×C19—41no—
208C22×C19—41no—
209C22×C19—81no—
210C22×C19—81no—
211C22×C19#38611yescharacteristic
212C22×C19C2×#9911yescharacteristic
213C22×C19C2×#9911yescharacteristic
214C4×C19—21no—
215C4×C19—22no—
216C4×C19—21no—
217C4×C19—22no—
218C4×C19—41no—
219Dic19—42no—
220Dic19—81no—
221Dic19—81no—
222Dic19—81no—
223C22×#41C2×D1911yescharacteristic
224C22×M16—381no—
225C2×#123—191no—
226C2×#123—191no—
227C22×C4⋊C4—191no—
228C2×#101—21no—
229C2×#100—21no—
230#408—384no—
231#407—192no—
232#407—381no—
233#407C2×D1912yes—
234#395—381no—
235#394—381no—
236#386—191no—
237#386—191no—
238#385—381no—
239#385—381no—
240#381—191no—
241#324—384no—
242C2×C19—21no—
243C2×C19—21no—
244C2×C19—42no—
245C2×C19—42no—
246C2×C19—81no—
247C2×C19#189111yescharacteristic
248C2×C19#189811yescharacteristic
249C2×C19#191511yescharacteristic
250C2×#41—22no—
251C2×#41—22no—
252C2×#41—42no—
253C2×#41—42no—
254C22×Q8C22⋊D1911yescharacteristic
255C22×D4C4×D1911yescharacteristic
256C22×D4C4×D1911yescharacteristic
257C22×D4C22⋊D1911yescharacteristic
258C23×C4—191no—
259C23×C4—191no—
260C23×C4D7611yescharacteristic
261C23×C4D7611yescharacteristic
262C23×C4C22×D1911yescharacteristic
263C2×M16—22no—
264C2×M16—382no—
265C2×M16—382no—
266C2×M16—762no—
267C2×M16—762no—
268C22×C8—382no—
269#123—762no—
270#123—762no—
271C2×C4⋊C4—381no—
272C2×C4⋊C4—381no—
273C2×C4⋊C4—381no—
274C2×C4⋊C4—382no—
275C2×C4⋊C4—382no—
276C2×C4⋊C4—381no—
277C2×C22⋊C4—191no—
278C2×C22⋊C4—191no—
279C2×C22⋊C4—381no—
280C2×C22⋊C4—381no—
281C2×C22⋊C4—381no—
282C2×C22⋊C4—381no—
283#101—42no—
284#100—42no—
285C22⋊C8—22no—
286C22⋊C8—22no—
287C22⋊C8—194no—
288C22⋊C8—384no—
289C22⋊C8—382no—
290#95—381no—
291#95—381no—
292#95—381no—
293#95—381no—
294C19#951311yescharacteristic, complemented, Sylow
295C24(C2×D19)⋊C411yescharacteristic
296C24(C2×D19)⋊C411yescharacteristic
297C24C2×C4×D1911yescharacteristic
298#41—44no—
299#41—44no—
300#41—48no—
301C2×Q8—22no—
302C2×Q8—22no—
303C2×Q8—41no—
304C2×D4—22no—
305C2×D4—22no—
306C2×D4—22no—
307C2×D4—22no—
308C2×D4—22no—
309C2×D4—22no—
310C2×D4—41no—
311C2×D4—41no—
312C2×D4—41no—
313C22×C4—22no—
314C22×C4—22no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—21no—
318C22×C4—21no—
319C22×C4—41no—
320C22×C4—41no—
321C22×C4—41no—
322C22×C4—41no—
323C22×C4—382no—
324C22×C4—381no—
325C22×C4—381no—
326C22×C4—381no—
327C22×C4—381no—
328C22×C4—382no—
329C22×C4—762no—
330C22×C4—761no—
331C22×C4—761no—
332C22×C4(C2×D19)⋊C411yescharacteristic
333C22×C4(C2×D19)⋊C411yescharacteristic
334C22×C4C2×D7611yescharacteristic
335C22×C4D4×D1912yes—
336C22×C4#6454312yes—
337C22×C4C2×C22⋊D1911yescharacteristic
338M16—42no—
339M16—42no—
340M16—764no—
341M16—762no—
342M16—762no—
343C2×C8—42no—
344C2×C8—384no—
345C2×C8—764no—
346C4⋊C4—762no—
347C4⋊C4—762no—
348C4⋊C4—762no—
349C4⋊C4—761no—
350C4⋊C4—761no—
351C22⋊C4—762no—
352C22⋊C4—762no—
353C22⋊C4—762no—
354C22⋊C4—762no—
355C22⋊C4—761no—
356C22⋊C4—761no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23—21no—
361C23—21no—
362C23—21no—
363C23—21no—
364C23—41no—
365C23—41no—
366C23—41no—
367C23—41no—
368C23—41no—
369C23—41no—
370C23#1059726312yes—
371C23(C22⋊D19)⋊C412yes—
372C23C2×(C2×D19)⋊C411yescharacteristic
373Q8—44no—
374D4—44no—
375D4—44no—
376D4—44no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—24no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—382no—
394C2×C4—384no—
395C2×C4—761no—
396C2×C4—762no—
397C2×C4—761no—
398C2×C4—761no—
399C2×C4—761no—
400C2×C4—761no—
401C2×C4—761no—
402C2×C4—761no—
403C2×C4—761no—
404C2×C4—761no—
405C2×C4—761no—
406C2×C4—761no—
407C2×C4—1522no—
408C2×C4#1059726312yes—
409C2×C4#1059732811yescharacteristic
410C2×C4#1059733211yescharacteristic
411C2×C4#1059738512yes—
412C8—82no—
413C8—764no—
414C22—21no—
415C22—21no—
416C22—22no—
417C22—22no—
418C22—22no—
419C22—22no—
420C22—42no—
421C22—42no—
422C22—42no—
423C22—42no—
424C22—41no—
425C22—41no—
426C22—41no—
427C22—41no—
428C22—41no—
429C22—81no—
430C22—81no—
431C22#1192642111yescharacteristic
432C22C2×#1059726311yescharacteristic
433C22C2×#1059726311yescharacteristic
434C4—22no—
435C4—21no—
436C4—21no—
437C4—22no—
438C4—41no—
439C4—762no—
440C4—1521no—
441C4—1521no—
442C4—1521no—
443C2—21no—
444C2—21no—
445C2—42no—
446C2—42no—
447C2—81no—
448C2#1456405111yescharacteristic
449C2#1456408611yescharacteristic
450C2#1456418511yescharacteristic
subgroupG/H
centerC22#11926421
commutatorC24×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1785C2
socleC22×C19#386
prime radicalC22×#41×C19C22
cosocleC23×C4×C19C23
hypercenter#1785D19
hypocenterC19#9513
LCSG ▷ C24×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1785

Complements

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

NH ≅ G/Ntype
3. #14561964C2semidirect
4. #14561544C2semidirect
294. C19#9513semidirect

Maximal subgroups

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

subgroupindex
#145720802
#145669662
#145619642
#145615442
C19×#17852
#951319