Finite Group Databasebeta

← #18075169

Subgroups — #18075169

Order 4864.

1134 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 1134 conjugacy classes of subgroups — too many to draw. Only its 123 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×#10597342C211yesmaximal, characteristic
2#14563558C212yesmaximal, complemented
3#14561965C211yesmaximal, characteristic, complemented
4#14561961C212yesmaximal
5C19×#1463C211yesmaximal, characteristic, complemented
6C23×Dic38C2211yescharacteristic
7C23×C4×D19C411yescharacteristic
8C2×#10597342—24no—
9C2×#10597342—24no—
10C2×#10597342—22no—
11C2×#10597342—22no—
12C22×Dic19⋊C4C411yescharacteristic
13C22×Dic19⋊C4C411yescharacteristic
14C22×(C2×D19)⋊C4C411yescharacteristic
15C22×(C2×D19)⋊C4C2211yescharacteristic
16C2×#10597281—24no—
17#11926508C2212yes—
18#11926270—22no—
19#11926267—24no—
20C22×C4⋊C4×C19C2211yescharacteristic
21C19×#407C2212yes—
22C19×#324—22no—
23C24×D19C2×C411yescharacteristic
24C23×C4×C19C2×C411yescharacteristic
25C23×C4×C19C2×C411yescharacteristic
26C23×C4×C19C2311yescharacteristic
27C23×Dic19C2×C411yescharacteristic
28C23×Dic19C2×C411yescharacteristic
29C23×Dic19C2×C411yescharacteristic
30C22×C4×D19—22no—
31C22×C4×D19—22no—
32C22×C4×D19—22no—
33C22×C4×D19—44no—
34C22×Dic38—21no—
35C22×Dic38—22no—
36C22×Dic38—21no—
37C22×Dic38—44no—
38C22×Dic38D414yes—
39C2×M16×C19—22no—
40C2×C4⋊C4×C19—22no—
41C2×C4⋊C4×C19—22no—
42C2×C4⋊C4×C19D412yes—
43C2×C4⋊C4×C19D412yes—
44C2×(C2×D19)⋊C4—22no—
45C2×(C2×D19)⋊C4—22no—
46C2×(C2×D19)⋊C4—21no—
47C2×(C2×D19)⋊C4—22no—
48C2×(C2×D19)⋊C4—21no—
49C2×(C2×D19)⋊C4—22no—
50C2×(C2×D19)⋊C4D414yes—
51C2×Dic19⋊C4—22no—
52C2×Dic19⋊C4—22no—
53C2×Dic19⋊C4—22no—
54C2×Dic19⋊C4—22no—
55C2×Dic19⋊C4—22no—
56C2×Dic19⋊C4—22no—
57C2×#64520—22no—
58#10597342—216no—
59#10597342—216no—
60C19×C22⋊C8—22no—
61C19×C22⋊C8—22no—
62C22⋊(C19⋊C8)—22no—
63C22⋊(C19⋊C8)—22no—
64#10597281—48no—
65C24×C19C22×C411yescharacteristic
66C23×D19—21no—
67C23×D19—21no—
68C23×D19—24no—
69C23×D19—42no—
70C23×D19—42no—
71C23×D19C22⋊C412yes—
72C22×C4×C19—21no—
73C22×C4×C19—21no—
74C22×C4×C19—21no—
75C22×C4×C19—21no—
76C22×C4×C19—42no—
77C22×C4×C19—42no—
78C22×C4×C19—42no—
79C22×C4×C19C22⋊C412yes—
80C22×C4×C19C22⋊C412yes—
81C22×C4×C19C2×D411yescharacteristic
82C22×C4×C19C2×D412yes—
83C22×C4×C19C2×D412yes—
84C22×C4×C19C2×D411yescharacteristic
85C22×Dic19—21no—
86C22×Dic19—21no—
87C22×Dic19—24no—
88C22×Dic19—21no—
89C22×Dic19—21no—
90C22×Dic19—21no—
91C22×Dic19—21no—
92C22×Dic19—42no—
93C22×Dic19—42no—
94C22×Dic19C22⋊C412yes—
95C22×Dic19C22⋊C412yes—
96C22×Dic19C22⋊C412yes—
97C2×C4×D19—28no—
98C2×C4×D19—48no—
99C2×C4×D19—48no—
100C2×C4×D19—44no—
101C2×C4×D19—44no—
102C2×Dic38—24no—
103C2×Dic38—24no—
104C2×Dic38—28no—
105C2×Dic38—44no—
106C2×Dic38—44no—
107C2×Dic38—48no—
108C2×Dic38—44no—
109M16×C19—44no—
110C2×C8×C19—42no—
111C4⋊C4×C19—24no—
112C4⋊C4×C19—24no—
113(C2×D19)⋊C4—28no—
114(C2×D19)⋊C4—24no—
115(C2×D19)⋊C4—24no—
116Dic19⋊C4—28no—
117Dic19⋊C4—28no—
118#64520—44no—
119C2×C19⋊C8—42no—
120#8550—191nomaximal, Sylow
121C23×C19—22no—
122C23×C19—22no—
123C23×C19—22no—
124C23×C19C2×C22⋊C411yescharacteristic
125C23×C19C2×C22⋊C411yescharacteristic
126C23×C19C2×C22⋊C411yescharacteristic
127C22×D19—24no—
128C22×D19—24no—
129C22×D19—22no—
130C22×D19—22no—
131C22×D19—42no—
132C22×D19—416no—
133C22×D19—42no—
134C22×D19—42no—
135C22×D19—42no—
136C22×D19—42no—
137C22×D19—42no—
138C22×D19#10114yescomplemented
139C2×C4×C19—24no—
140C2×C4×C19—22no—
141C2×C4×C19—22no—
142C2×C4×C19—24no—
143C2×C4×C19—41no—
144C2×C4×C19—42no—
145C2×C4×C19—41no—
146C2×C4×C19—42no—
147C2×C4×C19—42no—
148C2×C4×C19—42no—
149C2×C4×C19—42no—
150C2×C4×C19—42no—
151C2×C4×C19#12012yes—
152C2×C4×C19#12012yes—
153C2×Dic19—24no—
154C2×Dic19—24no—
155C2×Dic19—22no—
156C2×Dic19—22no—
157C2×Dic19—22no—
158C2×Dic19—22no—
159C2×Dic19—24no—
160C2×Dic19—42no—
161C2×Dic19—42no—
162C2×Dic19—42no—
163C2×Dic19—42no—
164C2×Dic19—42no—
165C2×Dic19#9914yes—
166C4×D19—416no—
167Dic38—48no—
168Dic38—48no—
169C8×C19—82no—
170C19⋊C8—82no—
171C22×C22⋊Q8—191no—
172#1784—192no—
173#1463—191no—
174#1463D1911yescharacteristic, complemented
175#1462—192no—
176C22×C19—28no—
177C22×C19—21no—
178C22×C19—21no—
179C22×C19—21no—
180C22×C19—21no—
181C22×C19—21no—
182C22×C19—21no—
183C22×C19#37911yescharacteristic
184C22×C19C2×#9912yes—
185C22×C19C2×#10112yes—
186C22×C19#41312yes—
187C2×D19—24no—
188C2×D19—48no—
189C2×D19—44no—
190C2×D19—48no—
191C2×D19—42no—
192C2×D19—42no—
193C2×D19—44no—
194C4×C19—22no—
195C4×C19—22no—
196C4×C19—42no—
197C4×C19—42no—
198Dic19—24no—
199Dic19—42no—
200Dic19—42no—
201C23×Q8—191no—
202C24×C4—191no—
203C2×C22⋊Q8—384no—
204C2×C22⋊Q8—384no—
205C2×C22⋊Q8—382no—
206C2×C22⋊Q8—382no—
207C22×C4⋊C4—191no—
208C22×C4⋊C4—191no—
209C22×C4⋊C4C2×D1911yescharacteristic
210C22×C22⋊C4—191no—
211C22×C22⋊C4—191no—
212C2×#101—384no—
213#407—192no—
214#407C2×D1912yes—
215#324—22no—
216#324—382no—
217#323—384no—
218C2×C19—22no—
219C2×C19—22no—
220C2×C19—22no—
221C2×C19#178111yescharacteristic
222C2×C19#178411yescharacteristic
223C2×C19#178511yescharacteristic
224D19—44no—
225C25—191no—
226C22×Q8—194no—
227C22×Q8—381no—
228C22×Q8—382no—
229C22×Q8—381no—
230C22×Q8—764no—
231C23×C4—191no—
232C23×C4—191no—
233C23×C4—191no—
234C23×C4—382no—
235C23×C4—382no—
236C23×C4—382no—
237C23×C4—764no—
238C23×C4C4×D1911yescharacteristic
239C23×C4C4×D1911yescharacteristic
240C23×C4C22×D1911yescharacteristic
241C2×M16—22no—
242C2×M16—382no—
243C22⋊Q8—3816no—
244C22⋊Q8—3816no—
245C2×C4⋊C4—22no—
246C2×C4⋊C4—22no—
247C2×C4⋊C4—382no—
248C2×C4⋊C4—382no—
249C2×C4⋊C4—382no—
250C2×C4⋊C4—382no—
251C2×C4⋊C4—382no—
252C2×C4⋊C4—382no—
253C2×C4⋊C4D7612yes—
254C2×C4⋊C4C22⋊D1912yes—
255C2×C22⋊C4—194no—
256C2×C22⋊C4—382no—
257C2×C22⋊C4—382no—
258C2×C22⋊C4—382no—
259C2×C22⋊C4—381no—
260C2×C22⋊C4—382no—
261C2×C22⋊C4—381no—
262#101—768no—
263C22⋊C8—22no—
264C22⋊C8—22no—
265C22⋊C8—382no—
266C22⋊C8—382no—
267C19#855011yescharacteristic, complemented, Sylow
268C24—192no—
269C24—384no—
270C24—381no—
271C24—381no—
272C24—762no—
273C24—762no—
274C24C2×C4×D1911yescharacteristic
275C2×Q8—388no—
276C2×Q8—384no—
277C2×Q8—384no—
278C2×Q8—764no—
279C2×Q8—764no—
280C2×Q8—768no—
281C2×Q8—764no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—42no—
287C22×C4—42no—
288C22×C4—42no—
289C22×C4—192no—
290C22×C4—192no—
291C22×C4—192no—
292C22×C4—388no—
293C22×C4—384no—
294C22×C4—381no—
295C22×C4—381no—
296C22×C4—381no—
297C22×C4—381no—
298C22×C4—381no—
299C22×C4—381no—
300C22×C4—764no—
301C22×C4—768no—
302C22×C4—764no—
303C22×C4—768no—
304C22×C4—762no—
305C22×C4—762no—
306C22×C4(C2×D19)⋊C412yes—
307C22×C4(C2×D19)⋊C412yes—
308C22×C4C2×D7611yescharacteristic
309C22×C4D4×D1912yes—
310C22×C4D4×D1912yes—
311C22×C4C2×C22⋊D1911yescharacteristic
312M16—44no—
313M16—764no—
314C2×C8—42no—
315C2×C8—762no—
316C4⋊C4—24no—
317C4⋊C4—24no—
318C4⋊C4—388no—
319C4⋊C4—388no—
320C22⋊C4—388no—
321C22⋊C4—384no—
322C22⋊C4—384no—
323C23—22no—
324C23—22no—
325C23—22no—
326C23—194no—
327C23—384no—
328C23—384no—
329C23—382no—
330C23—382no—
331C23—762no—
332C23—762no—
333C23—762no—
334C23—7616no—
335C23—762no—
336C23—762no—
337C23—762no—
338C23C22⋊C4×D1911yescharacteristic
339C23C22⋊C4×D1911yescharacteristic
340C23C2×(C2×D19)⋊C411yescharacteristic
341Q8—768no—
342Q8—768no—
343C2×C4—24no—
344C2×C4—22no—
345C2×C4—22no—
346C2×C4—24no—
347C2×C4—41no—
348C2×C4—42no—
349C2×C4—41no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—42no—
355C2×C4—194no—
356C2×C4—384no—
357C2×C4—384no—
358C2×C4—382no—
359C2×C4—382no—
360C2×C4—382no—
361C2×C4—382no—
362C2×C4—384no—
363C2×C4—7616no—
364C2×C4—762no—
365C2×C4—762no—
366C2×C4—762no—
367C2×C4—762no—
368C2×C4—762no—
369C2×C4#1059732812yes—
370C2×C4#1059738312yes—
371C8—82no—
372C8—1522no—
373C22—28no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—384no—
381C22—764no—
382C22—768no—
383C22—764no—
384C22—768no—
385C22—762no—
386C22—762no—
387C22#1192639911yescharacteristic
388C22#99×D1912yes—
389C22#101×D1912yes—
390C22#1192652612yes—
391C4—22no—
392C4—22no—
393C4—42no—
394C4—42no—
395C4—384no—
396C4—762no—
397C4—762no—
398C2—22no—
399C2—22no—
400C2—22no—
401C2—764no—
402C2#1456354811yescharacteristic
403C2#1456355711yescharacteristic
404C2#1456356111yescharacteristic
subgroupG/H
centerC22#11926399
commutatorC24×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1463C2
socleC22×C19#379
prime radicalC24×D19C2×C4
cosocleC23×C4×C19C23
hypercenter#1463D19
hypocenterC19#8550
LCSG ▷ C24×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1463

Complements

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

NH ≅ G/Ntype
2. #14563558C2semidirect
3. #14561965C2semidirect
5. C19×#1463C2semidirect
138. C22×D19#101semidirect
174. #1463D19semidirect
267. C19#8550semidirect

Maximal subgroups

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

subgroupindex
C22×#105973422
#145635582
#145619652
#145619612
C19×#14632
#855019