Finite Group Databasebeta

← #18075123

Subgroups — #18075123

Order 4864.

794 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 794 conjugacy classes of subgroups — too many to draw. Only its 143 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#14564104C212yesmaximal, complemented
2#14563933C211yesmaximal, characteristic
3#14561999C212yesmaximal, complemented
4#14561973C211yesmaximal, characteristic
5C19×#3501C211yesmaximal, characteristic
6C22×#64520C2211yescharacteristic
7C2×#10597293—22no—
8#11926508C2212yes—
9C2×C22⋊(C19⋊C8)—21no—
10C2×C22⋊(C19⋊C8)C2211yescharacteristic
11#11926313—22no—
12#11926299—21no—
13#11926270—21no—
14#11926270—24no—
15#11926268—21no—
16C19×#554—22no—
17C19×#554—24no—
18D4×Q8×C19—22no—
19C19×#544—21no—
20C19×#543—21no—
21C19×#543C412yes—
22C19×#533—21no—
23C2×C19×C22⋊Q8—21no—
24C2×C19×C22⋊Q8C2212yes—
25C19×#518C412yes—
26C2×C4×D4×C19C2211yescharacteristic
27C22×Q8×C19—21no—
28C22×Q8×C19D412yes—
29C22×D4×C19C2×C411yescharacteristic
30C23×C4×C19D411yescharacteristic
31C23×C4×C19C2311yescharacteristic
32C19×C4⋊Q8—21no—
33C19×C4⋊Q8—21no—
34C19×C4⋊Q8—24no—
35C19×#125—22no—
36C19×#125—24no—
37C19×C22⋊Q8—22no—
38C19×C22⋊Q8—22no—
39C19×C22⋊Q8—24no—
40C19×C22⋊Q8—24no—
41C19×C22⋊Q8—22no—
42C19×C22⋊Q8—22no—
43C19×C22⋊Q8—24no—
44C19×C22⋊Q8—24no—
45C19×C22⋊Q8—22no—
46C19×C22⋊Q8—22no—
47C19×C22⋊Q8—22no—
48C19×C22⋊Q8—22no—
49C4×Q8×C19—22no—
50C4×Q8×C19—22no—
51C4×D4×C19—24no—
52C4×D4×C19—24no—
53C4×D4×C19—22no—
54C4×D4×C19—22no—
55C19×#117—22no—
56C2×C4⋊C4×C19—21no—
57C2×C4⋊C4×C19—22no—
58C2×C4⋊C4×C19D412yes—
59C2×C4⋊C4×C19D411yescharacteristic
60C2×C4⋊C4×C19D414yes—
61C2×C22⋊C4×C19—22no—
62C2×C22⋊C4×C19C2×C411yescharacteristic
63C2×C22⋊C4×C19C2×C414yes—
64C2×C22⋊C4×C19D411yescharacteristic
65C2×C42×C19D411yescharacteristic
66C2×#64520—22no—
67C2×#64520—22no—
68C2×#64520—42no—
69C22×C19⋊C8—21no—
70C22×C19⋊C8—21no—
71#10597293—44no—
72C22⋊(C19⋊C8)—22no—
73C22⋊(C19⋊C8)—22no—
74C22⋊(C19⋊C8)—22no—
75C22⋊(C19⋊C8)—42no—
76C24×C19C22⋊C411yescharacteristic
77C24×C19C22×C411yescharacteristic
78C2×Q8×C19—22no—
79C2×Q8×C19—22no—
80C2×Q8×C19—22no—
81C2×Q8×C19—22no—
82C2×Q8×C19—42no—
83C2×Q8×C19—42no—
84C2×Q8×C19—81no—
85C2×Q8×C19—81no—
86C2×D4×C19—22no—
87C2×D4×C19—22no—
88C2×D4×C19—22no—
89C22×C4×C19—22no—
90C22×C4×C19—22no—
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×C19C22⋊C414yes—
100C22×C4×C19C22⋊C414yes—
101C22×C4×C19C22⋊C411yescharacteristic
102C22×C4×C19C2×D411yescharacteristic
103C22×C4×C19C2×D412yes—
104C22×C4×C19C2×D411yescharacteristic
105C22×C4×C19C2×D412yes—
106C4⋊C4×C19—22no—
107C4⋊C4×C19—24no—
108C4⋊C4×C19—22no—
109C4⋊C4×C19—22no—
110C4⋊C4×C19—24no—
111C4⋊C4×C19—22no—
112C4⋊C4×C19—24no—
113C4⋊C4×C19—22no—
114C4⋊C4×C19—22no—
115C4⋊C4×C19—22no—
116C4⋊C4×C19—24no—
117C22⋊C4×C19—24no—
118C22⋊C4×C19—24no—
119C22⋊C4×C19—22no—
120C22⋊C4×C19—24no—
121C22⋊C4×C19—22no—
122C42×C19—24no—
123C42×C19—21no—
124C42×C19—21no—
125#64520—24no—
126#64520—42no—
127#64520—42no—
128#64520—42no—
129C2×C19⋊C8—22no—
130C2×C19⋊C8—41no—
131C2×C19⋊C8—41no—
132C2×C19⋊C8—41no—
133C2×C19⋊C8—41no—
134C2×C19⋊C8—41no—
135C2×C19⋊C8—42no—
136#8537—191nomaximal, Sylow
137C23×C19—21no—
138C23×C19—21no—
139C23×C19—21no—
140C23×C19—21no—
141C23×C19—41no—
142C23×C19—41no—
143C23×C19—41no—
144C23×C19—41no—
145C23×C19#10112yescomplemented
146C23×C19C2×C22⋊C412yes—
147C23×C19C2×C22⋊C411yescharacteristic
148Q8×C19—42no—
149Q8×C19—42no—
150Q8×C19—82no—
151Q8×C19—82no—
152Q8×C19—82no—
153D4×C19—28no—
154C2×C4×C19—21no—
155C2×C4×C19—21no—
156C2×C4×C19—21no—
157C2×C4×C19—22no—
158C2×C4×C19—21no—
159C2×C4×C19—22no—
160C2×C4×C19—21no—
161C2×C4×C19—24no—
162C2×C4×C19—24no—
163C2×C4×C19—21no—
164C2×C4×C19—42no—
165C2×C4×C19—41no—
166C2×C4×C19—41no—
167C2×C4×C19—41no—
168C2×C4×C19—41no—
169C2×C4×C19—44no—
170C2×C4×C19—41no—
171C2×C4×C19—44no—
172C2×C4×C19—81no—
173C2×C4×C19—82no—
174C2×C4×C19—82no—
175C2×C4×C19#10112yescomplemented
176C2×C4×C19#12011yescharacteristic
177C2×C4×C19#12012yes—
178C2×C4×C19#12011yescharacteristic
179C19⋊C8—42no—
180C19⋊C8—81no—
181C19⋊C8—82no—
182#3501D1911yescharacteristic
183#1901—192no—
184#1870—191no—
185#1472—192no—
186#1465—191no—
187C22×C19—21no—
188C22×C19—21no—
189C22×C19—22no—
190C22×C19—22no—
191C22×C19—22no—
192C22×C19—22no—
193C22×C19—42no—
194C22×C19—41no—
195C22×C19—41no—
196C22×C19—81no—
197C22×C19—81no—
198C22×C19—81no—
199C22×C19#37911yescharacteristic
200C22×C19C2×#10111yescharacteristic
201C22×C19C2×#10111yescharacteristic
202C4×C19—22no—
203C4×C19—21no—
204C4×C19—22no—
205C4×C19—41no—
206C4×C19—44no—
207C4×C19—44no—
208C4×C19—41no—
209C4×C19B(4,𝔽2)11yescharacteristic
210C4×C19#45811yescharacteristic
211C22×M16—191no—
212#554—24no—
213#554—22no—
214D4×Q8—22no—
215#544—21no—
216#543—21no—
217#543Dic1912yes—
218#533—21no—
219C2×C22⋊Q8—21no—
220C2×C22⋊Q8C2×D1912yes—
221#518Dic1912yes—
222C2×C4×D4C2×D1911yescharacteristic
223C2×#101—382no—
224#407—192no—
225C2×C22⋊C8—191no—
226C2×C22⋊C8—381no—
227#343—382no—
228#336—381no—
229#324—381no—
230#324—384no—
231#323—381no—
232C2×C19—21no—
233C2×C19—21no—
234C2×C19—42no—
235C2×C19—42no—
236C2×C19#178411yescharacteristic
237C2×C19#179011yescharacteristic
238C2×C19#179111yescharacteristic
239C22×Q8—21no—
240C22×Q8C22⋊D1912yes—
241C22×D4C2×Dic1911yescharacteristic
242C23×C4C22⋊D1911yescharacteristic
243C23×C4C22×D1911yescharacteristic
244C2×M16—382no—
245C2×M16—382no—
246C2×M16—762no—
247C22×C8—381no—
248C22×C8—381no—
249C4⋊Q8—21no—
250C4⋊Q8—21no—
251C4⋊Q8—24no—
252#125—22no—
253#125—24no—
254C22⋊Q8—22no—
255C22⋊Q8—22no—
256C22⋊Q8—24no—
257C22⋊Q8—24no—
258C22⋊Q8—22no—
259C22⋊Q8—22no—
260C22⋊Q8—24no—
261C22⋊Q8—24no—
262C22⋊Q8—22no—
263C22⋊Q8—22no—
264C22⋊Q8—22no—
265C22⋊Q8—22no—
266C4×Q8—22no—
267C4×Q8—22no—
268C4×D4—24no—
269C4×D4—24no—
270C4×D4—22no—
271C4×D4—22no—
272#117—22no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—22no—
275C2×C4⋊C4C22⋊D1911yescharacteristic
276C2×C4⋊C4C22⋊D1914yes—
277C2×C4⋊C4C22⋊D1912yes—
278C2×C22⋊C4—22no—
279C2×C22⋊C4C2×Dic1911yescharacteristic
280C2×C22⋊C4C2×Dic1914yes—
281C2×C22⋊C4C22⋊D1911yescharacteristic
282C2×C42C22⋊D1911yescharacteristic
283#101—764no—
284C22⋊C8—382no—
285C22⋊C8—382no—
286C22⋊C8—382no—
287C22⋊C8—762no—
288C19#853711yescharacteristic, complemented, Sylow
289C24C22⋊Dic1911yescharacteristic
290C24C22×Dic1911yescharacteristic
291C2×Q8—22no—
292C2×Q8—22no—
293C2×Q8—22no—
294C2×Q8—22no—
295C2×Q8—42no—
296C2×Q8—42no—
297C2×Q8—81no—
298C2×Q8—81no—
299C2×D4—22no—
300C2×D4—22no—
301C2×D4—22no—
302C22×C4—22no—
303C22×C4—22no—
304C22×C4—21no—
305C22×C4—21no—
306C22×C4—41no—
307C22×C4—41no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4C22⋊Dic1911yescharacteristic
311C22×C4C22⋊Dic1911yescharacteristic
312C22×C4C22⋊Dic1914yes—
313C22×C4C22⋊Dic1914yes—
314C22×C4C22⋊Dic1911yescharacteristic
315C22×C4C2×C22⋊D1911yescharacteristic
316C22×C4C2×C22⋊D1912yes—
317C22×C4C2×C22⋊D1911yescharacteristic
318C22×C4C2×C22⋊D1912yes—
319M16—384no—
320M16—762no—
321M16—762no—
322M16—762no—
323C2×C8—382no—
324C2×C8—761no—
325C2×C8—761no—
326C2×C8—761no—
327C2×C8—761no—
328C2×C8—761no—
329C2×C8—762no—
330C4⋊C4—22no—
331C4⋊C4—24no—
332C4⋊C4—22no—
333C4⋊C4—22no—
334C4⋊C4—24no—
335C4⋊C4—22no—
336C4⋊C4—24no—
337C4⋊C4—22no—
338C4⋊C4—22no—
339C4⋊C4—22no—
340C4⋊C4—24no—
341C22⋊C4—24no—
342C22⋊C4—24no—
343C22⋊C4—22no—
344C22⋊C4—24no—
345C22⋊C4—22no—
346C42—24no—
347C42—21no—
348C42—21no—
349C23—21no—
350C23—21no—
351C23—21no—
352C23—21no—
353C23—41no—
354C23—41no—
355C23—41no—
356C23—41no—
357C23#1059729312yescomplemented
358C23C2×C22⋊Dic1912yes—
359C23C2×C22⋊Dic1911yescharacteristic
360Q8—42no—
361Q8—42no—
362Q8—82no—
363Q8—82no—
364Q8—82no—
365D4—28no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—22no—
370C2×C4—21no—
371C2×C4—22no—
372C2×C4—21no—
373C2×C4—24no—
374C2×C4—24no—
375C2×C4—21no—
376C2×C4—42no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—44no—
382C2×C4—44no—
383C2×C4—41no—
384C2×C4—81no—
385C2×C4—82no—
386C2×C4—82no—
387C2×C4#1059729312yescomplemented
388C2×C4#1059739911yescharacteristic
389C2×C4#1059739912yes—
390C2×C4#1059739911yescharacteristic
391C8—762no—
392C8—1521no—
393C8—1522no—
394C22—21no—
395C22—21no—
396C22—22no—
397C22—22no—
398C22—22no—
399C22—22no—
400C22—42no—
401C22—41no—
402C22—41no—
403C22—81no—
404C22—81no—
405C22—81no—
406C22#1192640011yescharacteristic
407C22C2×#1059729311yescharacteristic
408C22C2×#1059729311yescharacteristic
409C4—22no—
410C4—21no—
411C4—22no—
412C4—44no—
413C4—41no—
414C4—41no—
415C4—44no—
416C4#1192673111yescharacteristic
417C4#1192673411yescharacteristic
418C2—21no—
419C2—21no—
420C2—42no—
421C2—42no—
422C2#1456355911yescharacteristic
423C2#1456358311yescharacteristic
424C2#1456358611yescharacteristic
subgroupG/H
centerC22#11926400
commutatorC24×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#3501C2
socleC22×C19#379
prime radicalC22×D4×C19C2×C4
cosocleC23×C4×C19C23
hypercenter#3501D19
hypocenterC19#8537
LCSG ▷ C24×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3501

Complements

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

NH ≅ G/Ntype
1. #14564104C2semidirect
3. #14561999C2semidirect
145. C23×C19#101semidirect
175. C2×C4×C19#101semidirect
288. C19#8537semidirect
357. C23#10597293semidirect
387. C2×C4#10597293semidirect

Maximal subgroups

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

subgroupindex
#145641042
#145639332
#145619992
#145619732
C19×#35012
#853719