Finite Group Databasebeta

← #18075185

Subgroups — #18075185

Order 4864.

1102 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 1102 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#14563715C211yesmaximal, characteristic, complemented
3#14561964C212yesmaximal, complemented
4#14561961C212yesmaximal
5C19×#1821C211yesmaximal, characteristic, complemented
6C23×Dic38C411yescharacteristic
7C23×C4×D19C411yescharacteristic
8C2×#10597342—24no—
9C2×#10597342—24no—
10C2×#10597342—22no—
11C2×#10597342—22no—
12C22×Dic19⋊C4C411yescharacteristic
13C22×Dic19⋊C4C2211yescharacteristic
14C22×(C2×D19)⋊C4C411yescharacteristic
15C22×(C2×D19)⋊C4C2211yescharacteristic
16#11926508C2212yes—
17#11926313—22no—
18#11926269—24no—
19#11926267—24no—
20C22×C4⋊C4×C19C2211yescharacteristic
21C19×#407C2212yes—
22C19×#343—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—22no—
35C22×Dic38—22no—
36C22×Dic38—22no—
37C22×Dic38—44no—
38C2×M16×C19—22no—
39C2×C4⋊C4×C19—22no—
40C2×C4⋊C4×C19—22no—
41C2×C4⋊C4×C19D412yes—
42C2×C4⋊C4×C19D412yes—
43C2×(C2×D19)⋊C4—22no—
44C2×(C2×D19)⋊C4—22no—
45C2×(C2×D19)⋊C4—21no—
46C2×(C2×D19)⋊C4—22no—
47C2×(C2×D19)⋊C4—21no—
48C2×(C2×D19)⋊C4—22no—
49C2×(C2×D19)⋊C4D414yes—
50C2×Dic19⋊C4—22no—
51C2×Dic19⋊C4—21no—
52C2×Dic19⋊C4—22no—
53C2×Dic19⋊C4—21no—
54C2×Dic19⋊C4—22no—
55C2×Dic19⋊C4—22no—
56C2×Dic19⋊C4D414yes—
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—
64C24×C19C22×C411yescharacteristic
65C23×D19—21no—
66C23×D19—21no—
67C23×D19—24no—
68C23×D19—42no—
69C23×D19—42no—
70C23×D19C22⋊C412yes—
71C22×C4×C19—21no—
72C22×C4×C19—21no—
73C22×C4×C19—21no—
74C22×C4×C19—21no—
75C22×C4×C19—42no—
76C22×C4×C19—42no—
77C22×C4×C19—42no—
78C22×C4×C19C22⋊C412yes—
79C22×C4×C19C22⋊C412yes—
80C22×C4×C19C2×D411yescharacteristic
81C22×C4×C19C2×D412yes—
82C22×C4×C19C2×D412yes—
83C22×C4×C19C2×D411yescharacteristic
84C22×Dic19—21no—
85C22×Dic19—21no—
86C22×Dic19—24no—
87C22×Dic19—21no—
88C22×Dic19—21no—
89C22×Dic19—21no—
90C22×Dic19—21no—
91C22×Dic19—42no—
92C22×Dic19—42no—
93C22×Dic19C22⋊C412yes—
94C22×Dic19C22⋊C412yes—
95C22×Dic19C22⋊C412yes—
96C2×C4×D19—28no—
97C2×C4×D19—48no—
98C2×C4×D19—48no—
99C2×C4×D19—44no—
100C2×C4×D19—44no—
101C2×Dic38—28no—
102C2×Dic38—48no—
103C2×Dic38—48no—
104C2×Dic38—44no—
105C2×Dic38—44no—
106M16×C19—44no—
107C2×C8×C19—42no—
108C4⋊C4×C19—24no—
109C4⋊C4×C19—24no—
110(C2×D19)⋊C4—28no—
111(C2×D19)⋊C4—24no—
112(C2×D19)⋊C4—24no—
113Dic19⋊C4—28no—
114Dic19⋊C4—24no—
115Dic19⋊C4—24no—
116#64520—44no—
117C2×C19⋊C8—42no—
118#8555—191nomaximal, Sylow
119C23×C19—22no—
120C23×C19—22no—
121C23×C19—22no—
122C23×C19C2×C22⋊C411yescharacteristic
123C23×C19C2×C22⋊C411yescharacteristic
124C23×C19C2×C22⋊C411yescharacteristic
125C22×D19—24no—
126C22×D19—24no—
127C22×D19—22no—
128C22×D19—22no—
129C22×D19—42no—
130C22×D19—416no—
131C22×D19—42no—
132C22×D19—42no—
133C22×D19—42no—
134C22×D19—42no—
135C22×D19—42no—
136C22×D19#10114yes—
137C2×C4×C19—22no—
138C2×C4×C19—22no—
139C2×C4×C19—22no—
140C2×C4×C19—22no—
141C2×C4×C19—42no—
142C2×C4×C19—42no—
143C2×C4×C19—42no—
144C2×C4×C19—42no—
145C2×C4×C19—42no—
146C2×C4×C19—42no—
147C2×C4×C19—42no—
148C2×C4×C19—42no—
149C2×C4×C19#12012yes—
150C2×C4×C19#12012yes—
151C2×Dic19—24no—
152C2×Dic19—24no—
153C2×Dic19—22no—
154C2×Dic19—22no—
155C2×Dic19—22no—
156C2×Dic19—22no—
157C2×Dic19—42no—
158C2×Dic19—42no—
159C2×Dic19—42no—
160C2×Dic19—42no—
161C2×Dic19—42no—
162C2×Dic19—42no—
163C2×Dic19#10014yes—
164C4×D19—416no—
165Dic38—416no—
166C8×C19—82no—
167C19⋊C8—82no—
168C22×C22⋊Q8—191no—
169#1821—191no—
170#1821D1911yescharacteristic, complemented
171#1463—192no—
172#1462—192no—
173C22×C19—28no—
174C22×C19—21no—
175C22×C19—21no—
176C22×C19—21no—
177C22×C19—21no—
178C22×C19—21no—
179C22×C19—21no—
180C22×C19#37911yescharacteristic
181C22×C19#41012yes—
182C22×C19C2×#10012yes—
183C22×C19C2×#10112yes—
184C2×D19—24no—
185C2×D19—48no—
186C2×D19—48no—
187C2×D19—44no—
188C2×D19—42no—
189C2×D19—42no—
190C2×D19—44no—
191C4×C19—22no—
192C4×C19—22no—
193C4×C19—42no—
194C4×C19—42no—
195Dic19—24no—
196Dic19—42no—
197Dic19—42no—
198C23×Q8—191no—
199C24×C4—191no—
200C2×C22⋊Q8—384no—
201C2×C22⋊Q8—384no—
202C2×C22⋊Q8—382no—
203C2×C22⋊Q8—382no—
204C22×C4⋊C4—191no—
205C22×C4⋊C4—191no—
206C22×C4⋊C4C2×D1911yescharacteristic
207C22×C22⋊C4—191no—
208C22×C22⋊C4—191no—
209#407—192no—
210#407C2×D1912yes—
211#343—22no—
212#343—382no—
213#324—384no—
214#323—384no—
215C2×C19—22no—
216C2×C19—22no—
217C2×C19—22no—
218C2×C19#178211yescharacteristic
219C2×C19#178311yescharacteristic
220C2×C19#178411yescharacteristic
221D19—44no—
222C25—191no—
223C22×Q8—382no—
224C22×Q8—382no—
225C22×Q8—382no—
226C22×Q8—764no—
227C23×C4—191no—
228C23×C4—191no—
229C23×C4—191no—
230C23×C4—382no—
231C23×C4—382no—
232C23×C4—382no—
233C23×C4—764no—
234C23×C4C4×D1911yescharacteristic
235C23×C4C4×D1911yescharacteristic
236C23×C4C22×D1911yescharacteristic
237C2×M16—22no—
238C2×M16—382no—
239C22⋊Q8—3816no—
240C22⋊Q8—3816no—
241C2×C4⋊C4—22no—
242C2×C4⋊C4—22no—
243C2×C4⋊C4—194no—
244C2×C4⋊C4—382no—
245C2×C4⋊C4—382no—
246C2×C4⋊C4—382no—
247C2×C4⋊C4—381no—
248C2×C4⋊C4—382no—
249C2×C4⋊C4—381no—
250C2×C4⋊C4D7612yes—
251C2×C4⋊C4C22⋊D1912yes—
252C2×C22⋊C4—194no—
253C2×C22⋊C4—382no—
254C2×C22⋊C4—382no—
255C2×C22⋊C4—382no—
256C2×C22⋊C4—381no—
257C2×C22⋊C4—382no—
258C2×C22⋊C4—381no—
259C22⋊C8—22no—
260C22⋊C8—22no—
261C22⋊C8—382no—
262C22⋊C8—382no—
263C19#855511yescharacteristic, complemented, Sylow
264C24—192no—
265C24—384no—
266C24—381no—
267C24—381no—
268C24—762no—
269C24—762no—
270C24C2×C4×D1911yescharacteristic
271C2×Q8—388no—
272C2×Q8—764no—
273C2×Q8—768no—
274C2×Q8—764no—
275C2×Q8—768no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—42no—
281C22×C4—42no—
282C22×C4—42no—
283C22×C4—192no—
284C22×C4—192no—
285C22×C4—192no—
286C22×C4—388no—
287C22×C4—384no—
288C22×C4—381no—
289C22×C4—381no—
290C22×C4—381no—
291C22×C4—381no—
292C22×C4—381no—
293C22×C4—381no—
294C22×C4—764no—
295C22×C4—768no—
296C22×C4—764no—
297C22×C4—768no—
298C22×C4—762no—
299C22×C4—762no—
300C22×C4(C2×D19)⋊C412yes—
301C22×C4(C2×D19)⋊C412yes—
302C22×C4C2×D7611yescharacteristic
303C22×C4D4×D1912yes—
304C22×C4D4×D1912yes—
305C22×C4C2×C22⋊D1911yescharacteristic
306M16—44no—
307M16—764no—
308C2×C8—42no—
309C2×C8—762no—
310C4⋊C4—24no—
311C4⋊C4—24no—
312C4⋊C4—388no—
313C4⋊C4—384no—
314C4⋊C4—384no—
315C22⋊C4—388no—
316C22⋊C4—384no—
317C22⋊C4—384no—
318C23—22no—
319C23—22no—
320C23—22no—
321C23—194no—
322C23—384no—
323C23—384no—
324C23—382no—
325C23—382no—
326C23—762no—
327C23—762no—
328C23—762no—
329C23—7616no—
330C23—762no—
331C23—762no—
332C23—762no—
333C23C22⋊C4×D1911yescharacteristic
334C23C22⋊C4×D1911yescharacteristic
335C23C2×(C2×D19)⋊C411yescharacteristic
336Q8—7616no—
337C2×C4—22no—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—22no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—194no—
350C2×C4—384no—
351C2×C4—384no—
352C2×C4—382no—
353C2×C4—382no—
354C2×C4—382no—
355C2×C4—382no—
356C2×C4—7616no—
357C2×C4—762no—
358C2×C4—762no—
359C2×C4—762no—
360C2×C4—762no—
361C2×C4—762no—
362C2×C4—762no—
363C2×C4#1059732812yes—
364C2×C4#1059738312yes—
365C8—82no—
366C8—1522no—
367C22—28no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—384no—
375C22—764no—
376C22—768no—
377C22—768no—
378C22—764no—
379C22—762no—
380C22—762no—
381C22#1192639911yescharacteristic
382C22#1192651712yes—
383C22#100×D1912yes—
384C22#101×D1912yes—
385C4—22no—
386C4—22no—
387C4—42no—
388C4—42no—
389C4—384no—
390C4—762no—
391C4—762no—
392C2—22no—
393C2—22no—
394C2—22no—
395C2—764no—
396C2#1456355211yescharacteristic
397C2#1456355411yescharacteristic
398C2#1456355711yescharacteristic
subgroupG/H
centerC22#11926399
commutatorC24×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1821C2
socleC22×C19#379
prime radicalC24×D19C2×C4
cosocleC23×C4×C19C23
hypercenter#1821D19
hypocenterC19#8555
LCSG ▷ C24×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1821

Complements

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

NH ≅ G/Ntype
2. #14563715C2semidirect
3. #14561964C2semidirect
5. C19×#1821C2semidirect
170. #1821D19semidirect
263. C19#8555semidirect

Maximal subgroups

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

subgroupindex
C22×#105973422
#145637152
#145619642
#145619612
C19×#18212
#855519