Finite Group Databasebeta

← #18080176

Subgroups — #18080176

Order 4864.

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

normal subgroups only

This group has 712 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#14567259C211yesmaximal, characteristic
3#14562167C212yesmaximal, complemented
4#14561487C212yesmaximal, complemented
5C19×#1782C211yesmaximal, characteristic
6C22×#64520—21no—
7C2×#10597390C411yescharacteristic, complemented
8C2×#10597382C411yescharacteristic, complemented
9C2×#10597370C2211yescharacteristic
10#11926511—24no—
11#11926508—21no—
12#11926508C2212yes—
13#11926458—21no—
14#11926458—21no—
15#11926451C411yescharacteristic, complemented
16#11926447C411yescharacteristic, complemented
17#11926417—21no—
18#11926417—21no—
19C4×C22⋊Dic19C2211yescharacteristic
20#11926280—24no—
21C22×#41×C19C2211yescharacteristic
22C2×C19×#99—21no—
23C2×C19×#99—21no—
24C19×#381C2212yes—
25C2×#41×C19—22no—
26C2×#41×C19—22no—
27C2×#41×C19—42no—
28C2×#41×C19—42no—
29C22×Q8×C19C2×C411yescharacteristic
30C22×D4×C19C2×C411yescharacteristic
31C22×D4×C19D411yescharacteristic
32C22×D4×C19D411yescharacteristic
33C23×C4×C19D411yescharacteristic
34C23×C4×C19D411yescharacteristic
35C23×C4×C19C2311yescharacteristic
36C22×Dic38C2×C411yescharacteristic
37C2×C22⋊C4×C19—22no—
38C2×C22⋊Dic19—21no—
39C2×C22⋊Dic19—21no—
40C2×C22⋊Dic19—21no—
41C2×C22⋊Dic19—21no—
42C2×C22⋊Dic19—21no—
43C2×C22⋊Dic19—21no—
44#10597390—42no—
45#10597382—42no—
46C2×C4⋊Dic19C2×C411yescharacteristic
47#10597370—22no—
48#10597370—22no—
49C2×Dic19⋊C4—21no—
50C2×Dic19⋊C4—21no—
51C2×Dic19⋊C4—21no—
52C2×C4×Dic19C2×C411yescharacteristic
53C2×C4×Dic19C2×C411yescharacteristic
54C2×#64520—22no—
55C2×#64520—22no—
56C2×#64520—42no—
57C2×#64520—42no—
58C22×C19⋊C8—22no—
59C19×#99—42no—
60C19×#99—42no—
61C19×#95—22no—
62C19×#95—22no—
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×C19C2×D411yescharacteristic
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×C19—42no—
98C22×C4×C19C22⋊C411yescharacteristic
99C22×C4×C19C22⋊C411yescharacteristic
100C22×C4×C19C22×C411yescharacteristic
101C22×C4×C19C2×D411yescharacteristic
102C22×C4×C19C2×D412yes—
103C22×C4×C19#4112yes—
104C22×Dic19—21no—
105C22×Dic19—21no—
106C22×Dic19—21no—
107C22×Dic19—21no—
108C2×Dic38—22no—
109C2×Dic38—41no—
110C2×Dic38—41no—
111C22⋊C4×C19—42no—
112C22⋊C4×C19—42no—
113C22⋊Dic19—42no—
114C22⋊Dic19—42no—
115C22⋊Dic19—42no—
116C22⋊Dic19—42no—
117C22⋊Dic19—42no—
118C22⋊Dic19—42no—
119C4⋊Dic19—22no—
120Dic19⋊C4—42no—
121Dic19⋊C4—42no—
122Dic19⋊C4—41no—
123Dic19⋊C4—41no—
124C4×Dic19—41no—
125C4×Dic19—41no—
126#64520—44no—
127#64520—42no—
128#64520—42no—
129C2×C19⋊C8—24no—
130C2×C19⋊C8—44no—
131#9443—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×C19#12112yes—
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—82no—
169C2×C4×C19—82no—
170C2×C4×C19—82no—
171C2×C4×C19#9912yes—
172C2×C4×C19C4×D412yes—
173C2×C4×C19#12011yescharacteristic
174C2×C4×C19#12311yescharacteristic
175C2×Dic19—22no—
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—41no—
187Dic38—82no—
188C19⋊C8—44no—
189#2879—191no—
190#2432—191no—
191#1782D1911yescharacteristic
192#1511—192no—
193#1284—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—41no—
203C22×C19—41no—
204C22×C19—41no—
205C22×C19—41no—
206C22×C19—41no—
207C22×C19—81no—
208C22×C19—81no—
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—
219C4×C19—162no—
220Dic19—42no—
221Dic19—81no—
222Dic19—81no—
223Dic19—81no—
224C22×#41C2×D1911yescharacteristic
225C22×M16—381no—
226C2×C4⋊Q8—191no—
227C2×#124—191no—
228C2×C22⋊Q8—191no—
229C2×#99—21no—
230C2×#99—21no—
231#408—384no—
232#407—192no—
233#407—381no—
234#394—381no—
235#394—381no—
236#391—191no—
237#390—191no—
238#385—381no—
239#385—381no—
240#381C2×D1912yes—
241C4×C22⋊C4—191no—
242#328—384no—
243C2×C19—21no—
244C2×C19—21no—
245C2×C19—42no—
246C2×C19—42no—
247C2×C19—81no—
248C2×C19#188411yescharacteristic
249C2×C19#189811yescharacteristic
250C2×C19#190911yescharacteristic
251C2×#41—22no—
252C2×#41—22no—
253C2×#41—42no—
254C2×#41—42no—
255C22×Q8—191no—
256C22×Q8C4×D1911yescharacteristic
257C22×D4C4×D1911yescharacteristic
258C22×D4C22⋊D1911yescharacteristic
259C22×D4C22⋊D1911yescharacteristic
260C23×C4D7611yescharacteristic
261C23×C4D7611yescharacteristic
262C23×C4C22×D1911yescharacteristic
263C2×M16—382no—
264C2×M16—382no—
265C2×M16—762no—
266C2×M16—762no—
267C22×C8—382no—
268C4⋊Q8—762no—
269#124—762no—
270C22⋊Q8—382no—
271C22⋊Q8—382no—
272C2×C4⋊C4—191no—
273C2×C4⋊C4—381no—
274C2×C4⋊C4—381no—
275C2×C4⋊C4—381no—
276C2×C22⋊C4—22no—
277C2×C22⋊C4—381no—
278C2×C22⋊C4—381no—
279C2×C22⋊C4—381no—
280C2×C22⋊C4—381no—
281C2×C22⋊C4—381no—
282C2×C22⋊C4—381no—
283C2×C42—191no—
284C2×C42—191no—
285#99—42no—
286#99—42no—
287C22⋊C8—194no—
288C22⋊C8—384no—
289C22⋊C8—382no—
290#95—22no—
291#95—22no—
292#95—381no—
293#95—381no—
294#95—381no—
295C19#944311yescharacteristic, complemented, Sylow
296C24(C2×D19)⋊C411yescharacteristic
297C24(C2×D19)⋊C411yescharacteristic
298C24C2×C22⋊D1911yescharacteristic
299#41—44no—
300#41—44no—
301#41—48no—
302C2×Q8—22no—
303C2×Q8—22no—
304C2×Q8—41no—
305C2×Q8—382no—
306C2×Q8—761no—
307C2×Q8—761no—
308C2×D4—22no—
309C2×D4—22no—
310C2×D4—22no—
311C2×D4—22no—
312C2×D4—22no—
313C2×D4—22no—
314C2×D4—41no—
315C2×D4—41no—
316C2×D4—41no—
317C22×C4—22no—
318C22×C4—22no—
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—21no—
323C22×C4—41no—
324C22×C4—41no—
325C22×C4—41no—
326C22×C4—41no—
327C22×C4—42no—
328C22×C4—381no—
329C22×C4—381no—
330C22×C4—381no—
331C22×C4—381no—
332C22×C4(C2×D19)⋊C411yescharacteristic
333C22×C4(C2×D19)⋊C411yescharacteristic
334C22×C4C2×C4×D1911yescharacteristic
335C22×C4C2×D7611yescharacteristic
336C22×C4D4×D1912yes—
337C22×C4#6454312yes—
338M16—764no—
339M16—762no—
340M16—762no—
341C2×C8—384no—
342C2×C8—764no—
343C4⋊C4—382no—
344C4⋊C4—762no—
345C4⋊C4—762no—
346C4⋊C4—761no—
347C4⋊C4—761no—
348C22⋊C4—42no—
349C22⋊C4—42no—
350C22⋊C4—762no—
351C22⋊C4—762no—
352C22⋊C4—762no—
353C22⋊C4—762no—
354C22⋊C4—762no—
355C22⋊C4—762no—
356C42—761no—
357C42—761no—
358C23—21no—
359C23—21no—
360C23—21no—
361C23—21no—
362C23—21no—
363C23—21no—
364C23—21no—
365C23—41no—
366C23—41no—
367C23—41no—
368C23—41no—
369C23—41no—
370C23—41no—
371C23#1059726312yes—
372C23C2×(C2×D19)⋊C411yescharacteristic
373C23#1059738512yes—
374Q8—44no—
375Q8—1522no—
376D4—44no—
377D4—44no—
378D4—44no—
379C2×C4—22no—
380C2×C4—22no—
381C2×C4—24no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4—82no—
396C2×C4—82no—
397C2×C4—82no—
398C2×C4—382no—
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—761no—
408C2×C4—761no—
409C2×C4—761no—
410C2×C4#1059726312yes—
411C2×C4(C22⋊D19)⋊C412yes—
412C2×C4#1059732811yescharacteristic
413C2×C4#1059733211yescharacteristic
414C8—764no—
415C22—21no—
416C22—21no—
417C22—22no—
418C22—22no—
419C22—22no—
420C22—22no—
421C22—42no—
422C22—42no—
423C22—41no—
424C22—41no—
425C22—41no—
426C22—41no—
427C22—41no—
428C22—81no—
429C22—81no—
430C22—81no—
431C22—81no—
432C22#1192642111yescharacteristic
433C22C2×#1059726311yescharacteristic
434C22C2×#1059726311yescharacteristic
435C4—21no—
436C4—21no—
437C4—22no—
438C4—22no—
439C4—41no—
440C4—162no—
441C4—762no—
442C4—1521no—
443C4—1521no—
444C4—1521no—
445C2—21no—
446C2—21no—
447C2—42no—
448C2—42no—
449C2—81no—
450C2#1456401611yescharacteristic
451C2#1456408611yescharacteristic
452C2#1456415511yescharacteristic
subgroupG/H
centerC22#11926421
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1782C2
socleC22×C19#386
prime radicalC22×#41×C19C22
cosocleC23×C4×C19C23
hypercenter#1782D19
hypocenterC19#9443
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1782

Complements

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

NH ≅ G/Ntype
3. #14562167C2semidirect
4. #14561487C2semidirect
7. C2×#10597390C4semidirect
8. C2×#10597382C4semidirect
15. #11926451C4semidirect
16. #11926447C4semidirect
295. C19#9443semidirect

Maximal subgroups

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

subgroupindex
#145720802
#145672592
#145621672
#145614872
C19×#17822
#944319