Finite Group Databasebeta

← #18075167

Subgroups — #18075167

Order 4864.

1134 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 1134 conjugacy classes of subgroups — too many to draw. Only its 127 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
1C22×#10597392C211yesmaximal, characteristic
2#14563559C211yesmaximal, characteristic, complemented
3#14561964C212yesmaximal, complemented
4#14561961C212yesmaximal
5C19×#1784C211yesmaximal, characteristic, complemented
6C23×C4×D19C411yescharacteristic
7C2×#10597392—24no—
8C2×#10597392—24no—
9C2×#10597392—22no—
10C2×#10597392—22no—
11C22×C4⋊Dic19C411yescharacteristic
12C22×Dic19⋊C4C411yescharacteristic
13C22×Dic19⋊C4C2211yescharacteristic
14C22×(C2×D19)⋊C4C411yescharacteristic
15C22×(C2×D19)⋊C4C2211yescharacteristic
16C2×#10597293—22no—
17#11926508C2212yes—
18#11926269—24no—
19#11926267—24no—
20C23×Q8×C19C2211yescharacteristic
21C2×C19×#101—22no—
22C19×#407C2212yes—
23C24×D19C2×C411yescharacteristic
24C22×Q8×C19—22no—
25C22×Q8×C19—22no—
26C22×Q8×C19—44no—
27C22×Q8×C19D412yes—
28C22×Q8×C19D412yes—
29C23×C4×C19C2×C411yescharacteristic
30C23×C4×C19C2×C411yescharacteristic
31C23×C4×C19C2311yescharacteristic
32C23×Dic19C2×C411yescharacteristic
33C23×Dic19C2×C411yescharacteristic
34C23×Dic19C2×C411yescharacteristic
35C22×C4×D19—22no—
36C22×C4×D19—22no—
37C22×C4×D19—22no—
38C22×C4×D19—44no—
39C2×M16×C19—22no—
40#10597392—216no—
41#10597392—216no—
42C2×(C2×D19)⋊C4—22no—
43C2×(C2×D19)⋊C4—22no—
44C2×(C2×D19)⋊C4—21no—
45C2×(C2×D19)⋊C4—22no—
46C2×(C2×D19)⋊C4—21no—
47C2×(C2×D19)⋊C4—22no—
48C2×(C2×D19)⋊C4D414yes—
49C2×C4⋊Dic19—22no—
50C2×C4⋊Dic19—22no—
51C2×C4⋊Dic19—22no—
52C2×Dic19⋊C4—22no—
53C2×Dic19⋊C4—21no—
54C2×Dic19⋊C4—22no—
55C2×Dic19⋊C4—21no—
56C2×Dic19⋊C4—22no—
57C2×Dic19⋊C4—22no—
58C2×Dic19⋊C4D414yes—
59C2×#64520—22no—
60C19×#101—44no—
61C19×C22⋊C8—22no—
62C19×C22⋊C8—22no—
63#10597293—44no—
64C22⋊(C19⋊C8)—22no—
65C22⋊(C19⋊C8)—22no—
66C24×C19C22×C411yescharacteristic
67C23×D19—21no—
68C23×D19—21no—
69C23×D19—24no—
70C23×D19—42no—
71C23×D19—42no—
72C23×D19C22⋊C412yes—
73C2×Q8×C19—24no—
74C2×Q8×C19—24no—
75C2×Q8×C19—24no—
76C2×Q8×C19—24no—
77C2×Q8×C19—42no—
78C2×Q8×C19—42no—
79C2×Q8×C19—48no—
80C2×Q8×C19—48no—
81C22×C4×C19—21no—
82C22×C4×C19—21no—
83C22×C4×C19—24no—
84C22×C4×C19—21no—
85C22×C4×C19—21no—
86C22×C4×C19—42no—
87C22×C4×C19—42no—
88C22×C4×C19C22⋊C412yes—
89C22×C4×C19C22⋊C412yes—
90C22×C4×C19C2×D411yescharacteristic
91C22×C4×C19C2×D412yes—
92C22×C4×C19C2×D412yes—
93C22×C4×C19C2×D411yescharacteristic
94C22×Dic19—21no—
95C22×Dic19—21no—
96C22×Dic19—21no—
97C22×Dic19—21no—
98C22×Dic19—21no—
99C22×Dic19—21no—
100C22×Dic19—42no—
101C22×Dic19—42no—
102C22×Dic19—42no—
103C22×Dic19C22⋊C412yes—
104C22×Dic19C22⋊C412yes—
105C22×Dic19C22⋊C412yes—
106C2×C4×D19—28no—
107C2×C4×D19—48no—
108C2×C4×D19—44no—
109C2×C4×D19—48no—
110C2×C4×D19—44no—
111M16×C19—44no—
112C2×C8×C19—42no—
113(C2×D19)⋊C4—28no—
114(C2×D19)⋊C4—24no—
115(C2×D19)⋊C4—24no—
116C4⋊Dic19—28no—
117Dic19⋊C4—28no—
118Dic19⋊C4—24no—
119Dic19⋊C4—24no—
120#64520—44no—
121C2×C19⋊C8—42no—
122#8550—191nomaximal, Sylow
123C23×C19—22no—
124C23×C19—22no—
125C23×C19—22no—
126C23×C19C2×C22⋊C411yescharacteristic
127C23×C19C2×C22⋊C411yescharacteristic
128C23×C19C2×C22⋊C411yescharacteristic
129C22×D19—24no—
130C22×D19—24no—
131C22×D19—22no—
132C22×D19—22no—
133C22×D19—42no—
134C22×D19—416no—
135C22×D19—42no—
136C22×D19—42no—
137C22×D19—42no—
138C22×D19—42no—
139C22×D19—42no—
140C22×D19#10114yescomplemented
141Q8×C19—48no—
142Q8×C19—48no—
143C2×C4×C19—24no—
144C2×C4×C19—24no—
145C2×C4×C19—22no—
146C2×C4×C19—22no—
147C2×C4×C19—22no—
148C2×C4×C19—22no—
149C2×C4×C19—22no—
150C2×C4×C19—22no—
151C2×C4×C19—22no—
152C2×C4×C19—42no—
153C2×C4×C19—42no—
154C2×C4×C19—42no—
155C2×C4×C19—42no—
156C2×C4×C19#9914yes—
157C2×C4×C19#12012yes—
158C2×C4×C19#12012yes—
159C2×Dic19—22no—
160C2×Dic19—22no—
161C2×Dic19—22no—
162C2×Dic19—24no—
163C2×Dic19—42no—
164C2×Dic19—42no—
165C2×Dic19—42no—
166C2×Dic19—42no—
167C2×Dic19—42no—
168C2×Dic19—42no—
169C2×Dic19—42no—
170C2×Dic19—42no—
171C4×D19—416no—
172C8×C19—82no—
173C19⋊C8—82no—
174C22×C22⋊Q8—191no—
175#1784—191no—
176#1784D1911yescharacteristic, complemented
177#1463—192no—
178#1462—192no—
179C22×C19—28no—
180C22×C19—21no—
181C22×C19—21no—
182C22×C19—21no—
183C22×C19—21no—
184C22×C19—21no—
185C22×C19—21no—
186C22×C19#37911yescharacteristic
187C22×C19C2×#9912yes—
188C22×C19C2×#10112yes—
189C22×C19#41312yes—
190C2×D19—24no—
191C2×D19—48no—
192C2×D19—44no—
193C2×D19—48no—
194C2×D19—42no—
195C2×D19—42no—
196C2×D19—44no—
197C4×C19—22no—
198C4×C19—22no—
199C4×C19—24no—
200C4×C19—42no—
201Dic19—42no—
202Dic19—42no—
203Dic19—42no—
204C23×Q8C2×D1911yescharacteristic
205C24×C4—191no—
206C2×C22⋊Q8—384no—
207C2×C22⋊Q8—384no—
208C2×C22⋊Q8—382no—
209C2×C22⋊Q8—382no—
210C22×C4⋊C4—191no—
211C22×C4⋊C4—191no—
212C22×C4⋊C4—191no—
213C22×C22⋊C4—191no—
214C22×C22⋊C4—191no—
215C2×#101—22no—
216C2×#101—382no—
217#407—192no—
218#407C2×D1912yes—
219#324—384no—
220#323—384no—
221C2×C19—22no—
222C2×C19—22no—
223C2×C19—22no—
224C2×C19#178111yescharacteristic
225C2×C19#178411yescharacteristic
226C2×C19#178511yescharacteristic
227D19—44no—
228C25—191no—
229C22×Q8—22no—
230C22×Q8—22no—
231C22×Q8—44no—
232C22×Q8D7612yes—
233C22×Q8C22⋊D1912yes—
234C23×C4—191no—
235C23×C4—191no—
236C23×C4—191no—
237C23×C4—382no—
238C23×C4—382no—
239C23×C4—382no—
240C23×C4—764no—
241C23×C4C4×D1911yescharacteristic
242C23×C4C4×D1911yescharacteristic
243C23×C4C22×D1911yescharacteristic
244C2×M16—22no—
245C2×M16—382no—
246C22⋊Q8—3816no—
247C22⋊Q8—3816no—
248C2×C4⋊C4—194no—
249C2×C4⋊C4—382no—
250C2×C4⋊C4—382no—
251C2×C4⋊C4—382no—
252C2×C4⋊C4—382no—
253C2×C4⋊C4—382no—
254C2×C4⋊C4—382no—
255C2×C4⋊C4—381no—
256C2×C4⋊C4—382no—
257C2×C4⋊C4—381no—
258C2×C22⋊C4—194no—
259C2×C22⋊C4—382no—
260C2×C22⋊C4—382no—
261C2×C22⋊C4—382no—
262C2×C22⋊C4—381no—
263C2×C22⋊C4—382no—
264C2×C22⋊C4—381no—
265#101—44no—
266#101—764no—
267C22⋊C8—22no—
268C22⋊C8—22no—
269C22⋊C8—382no—
270C22⋊C8—382no—
271C19#855011yescharacteristic, complemented, Sylow
272C24—192no—
273C24—384no—
274C24—381no—
275C24—381no—
276C24—762no—
277C24—762no—
278C24C2×C4×D1911yescharacteristic
279C2×Q8—24no—
280C2×Q8—24no—
281C2×Q8—24no—
282C2×Q8—24no—
283C2×Q8—42no—
284C2×Q8—42no—
285C2×Q8—48no—
286C2×Q8—48no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—24no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—42no—
293C22×C4—42no—
294C22×C4—192no—
295C22×C4—192no—
296C22×C4—192no—
297C22×C4—388no—
298C22×C4—381no—
299C22×C4—381no—
300C22×C4—381no—
301C22×C4—381no—
302C22×C4—381no—
303C22×C4—381no—
304C22×C4—768no—
305C22×C4—768no—
306C22×C4—764no—
307C22×C4—762no—
308C22×C4—764no—
309C22×C4—762no—
310C22×C4—762no—
311C22×C4(C2×D19)⋊C412yes—
312C22×C4(C2×D19)⋊C412yes—
313C22×C4C2×D7611yescharacteristic
314C22×C4D4×D1912yes—
315C22×C4D4×D1912yes—
316C22×C4C2×C22⋊D1911yescharacteristic
317M16—44no—
318M16—764no—
319C2×C8—42no—
320C2×C8—762no—
321C4⋊C4—388no—
322C4⋊C4—388no—
323C4⋊C4—384no—
324C4⋊C4—384no—
325C22⋊C4—388no—
326C22⋊C4—384no—
327C22⋊C4—384no—
328C23—22no—
329C23—22no—
330C23—22no—
331C23—194no—
332C23—384no—
333C23—384no—
334C23—382no—
335C23—382no—
336C23—762no—
337C23—762no—
338C23—762no—
339C23—7616no—
340C23—762no—
341C23—762no—
342C23—762no—
343C23C22⋊C4×D1911yescharacteristic
344C23C22⋊C4×D1911yescharacteristic
345C23C2×(C2×D19)⋊C411yescharacteristic
346Q8—48no—
347Q8—48no—
348C2×C4—24no—
349C2×C4—24no—
350C2×C4—22no—
351C2×C4—22no—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—22no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—42no—
361C2×C4—382no—
362C2×C4—382no—
363C2×C4—382no—
364C2×C4—384no—
365C2×C4—7616no—
366C2×C4—762no—
367C2×C4—762no—
368C2×C4—762no—
369C2×C4—762no—
370C2×C4—762no—
371C2×C4—762no—
372C2×C4—762no—
373C2×C4—762no—
374C2×C4#1059726314yes—
375C2×C4#1059732812yes—
376C2×C4#1059738312yes—
377C8—82no—
378C8—1522no—
379C22—28no—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—384no—
387C22—764no—
388C22—768no—
389C22—764no—
390C22—768no—
391C22—762no—
392C22—762no—
393C22#1192639911yescharacteristic
394C22C2×#1059726312yes—
395C22#101×D1912yes—
396C22#1192652712yes—
397C4—22no—
398C4—22no—
399C4—24no—
400C4—42no—
401C4—762no—
402C4—762no—
403C4—762no—
404C2—22no—
405C2—22no—
406C2—22no—
407C2—764no—
408C2#1456354911yescharacteristic
409C2#1456355711yescharacteristic
410C2#1456356211yescharacteristic
subgroupG/H
centerC22#11926399
commutatorC24×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1784C2
socleC22×C19#379
prime radicalC24×D19C2×C4
cosocleC23×C4×C19C23
hypercenter#1784D19
hypocenterC19#8550
LCSG ▷ C24×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1784

Complements

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

NH ≅ G/Ntype
2. #14563559C2semidirect
3. #14561964C2semidirect
5. C19×#1784C2semidirect
140. C22×D19#101semidirect
176. #1784D19semidirect
271. C19#8550semidirect

Maximal subgroups

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

subgroupindex
C22×#105973922
#145635592
#145619642
#145619612
C19×#17842
#855019