Finite Group Databasebeta

← #18075047

Subgroups — #18075047

Order 4864.

754 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 754 conjugacy classes of subgroups — too many to draw. Only its 107 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
1C2×#11927165C211yesmaximal, characteristic
2#14563712C211yesmaximal, characteristic, complemented
3#14562169C212yesmaximal, complemented
4#14562165C212yesmaximal
5C19×#1822C211yesmaximal, characteristic, complemented
6#11927165—24no—
7#11927165—24no—
8C2×#10597315C411yescharacteristic, complemented
9C2×#10597344—21no—
10C2×#10597321C411yescharacteristic, complemented
11C2×#10597331—21no—
12C2×#10597329—21no—
13C2×#10597370C2211yescharacteristic
14C2×#10597342—21no—
15C2×#10597376C2211yescharacteristic
16C2×C4×Dic38C411yescharacteristic, complemented
17C2×C4×D76C411yescharacteristic, complemented
18#11926407C2212yes—
19#11926311—21no—
20#11926311—21no—
21#11926282—24no—
22#11926279—24no—
23C2×C19×#117C2211yescharacteristic
24C19×#407C2212yes—
25C19×#343—21no—
26C19×#343—21no—
27C23×C4×C19C2311yescharacteristic
28C22×C22⋊D19—21no—
29C22×D76C2×C411yescharacteristic
30C22×C4×D19—21no—
31C22×Dic38—21no—
32C22×Dic38C2×C411yescharacteristic
33C2×M16×C19—22no—
34C19×#117—22no—
35C19×#117—22no—
36C2×C4⋊C4×C19D411yescharacteristic
37C2×C4⋊C4×C19D411yescharacteristic
38C2×C22⋊C4×C19D411yescharacteristic
39C2×C22⋊C4×C19D411yescharacteristic
40C2×C42×C19C2×C411yescharacteristic
41C2×C42×C19C2×C411yescharacteristic
42C2×C22⋊Dic19—21no—
43C2×C22⋊Dic19—22no—
44#10597376—22no—
45#10597376D414yes—
46C2×(C2×D19)⋊C4—21no—
47C2×(C2×D19)⋊C4—21no—
48C2×(C2×D19)⋊C4—21no—
49C2×(C2×D19)⋊C4—21no—
50C2×C4⋊Dic19—21no—
51C2×C4⋊Dic19C2×C411yescharacteristic
52C2×C4⋊Dic19C2×C411yescharacteristic
53#10597370—22no—
54#10597370D414yes—
55C2×Dic19⋊C4—21no—
56C2×Dic19⋊C4—21no—
57C2×C4×Dic19—21no—
58#10597344—28no—
59#10597342—28no—
60#10597331—28no—
61#10597329—28no—
62#10597321—22no—
63#10597321—22no—
64C4×D76—22no—
65C4×D76—22no—
66#10597315—22no—
67#10597315—22no—
68C4×Dic38—22no—
69C4×Dic38—22no—
70C19×C22⋊C8—22no—
71C19×C22⋊C8—22no—
72C19⋊#95—22no—
73C19⋊#95—22no—
74C24×C19C2×D411yescharacteristic
75C23×D19—21no—
76C22×C4×C19—42no—
77C22×C4×C19C22⋊C411yescharacteristic
78C22×C4×C19C22⋊C411yescharacteristic
79C22×C4×C19C22⋊C411yescharacteristic
80C22×C4×C19C22⋊C411yescharacteristic
81C22×C4×C19C22×C411yescharacteristic
82C22×C4×C19C2×D412yes—
83C22×C4×C19C2×D412yes—
84C22×C4×C19C2×D411yescharacteristic
85C2×C22⋊D19—24no—
86C2×C22⋊D19—82no—
87C22×Dic19—21no—
88C22×Dic19—21no—
89C22×Dic19—21no—
90C22×Dic19—42no—
91C2×D76—21no—
92C2×D76—42no—
93C2×D76C22⋊C412yes—
94C2×C4×D19—24no—
95C2×C4×D19—82no—
96C2×Dic38—21no—
97C2×Dic38—24no—
98C2×Dic38—42no—
99C2×Dic38—82no—
100C2×Dic38C22⋊C412yes—
101M16×C19—44no—
102C2×C8×C19—42no—
103C4⋊C4×C19—22no—
104C4⋊C4×C19—22no—
105C22⋊C4×C19—22no—
106C22⋊C4×C19—22no—
107C42×C19—21no—
108C42×C19—21no—
109C42×C19—21no—
110C42×C19—21no—
111C22⋊Dic19—24no—
112C22⋊Dic19—44no—
113(C2×D19)⋊C4—24no—
114(C2×D19)⋊C4—24no—
115(C2×D19)⋊C4—24no—
116(C2×D19)⋊C4—24no—
117C4⋊Dic19—24no—
118C4⋊Dic19—21no—
119C4⋊Dic19—21no—
120C4⋊Dic19C22⋊C412yes—
121C4⋊Dic19C22⋊C412yes—
122Dic19⋊C4—24no—
123Dic19⋊C4—24no—
124C4×Dic19—24no—
125#8519—191nomaximal, Sylow
126C23×C19—22no—
127C23×C19—41no—
128C23×C19—41no—
129C23×C19C2×C22⋊C411yescharacteristic
130C23×C19#12012yes—
131C22×D19—22no—
132C22×D19—42no—
133C22×D19—42no—
134C22×D19—42no—
135C2×C4×C19—22no—
136C2×C4×C19—22no—
137C2×C4×C19—21no—
138C2×C4×C19—21no—
139C2×C4×C19—21no—
140C2×C4×C19—21no—
141C2×C4×C19—42no—
142C2×C4×C19—42no—
143C2×C4×C19—41no—
144C2×C4×C19—41no—
145C2×C4×C19—41no—
146C2×C4×C19—41no—
147C2×C4×C19C2×C22⋊C411yescharacteristic
148C2×C4×C19C2×C22⋊C411yescharacteristic
149C2×C4×C19#12012yes—
150C22⋊D19—84no—
151C2×Dic19—22no—
152C2×Dic19—22no—
153C2×Dic19—22no—
154C2×Dic19—42no—
155C2×Dic19—42no—
156C2×Dic19—42no—
157C2×Dic19—82no—
158C2×Dic19—82no—
159C2×Dic19—82no—
160D76—42no—
161D76—42no—
162C4×D19—84no—
163Dic38—42no—
164Dic38—42no—
165Dic38—84no—
166C8×C19—82no—
167C2×#542—191no—
168#1822D1911yescharacteristic, complemented
169#1820—191no—
170#1511—192no—
171#1510—192no—
172C22×C19—21no—
173C22×C19—21no—
174C22×C19—22no—
175C22×C19—22no—
176C22×C19—22no—
177C22×C19—82no—
178C22×C19#37911yescharacteristic
179C22×C19#41012yes—
180C2×D19—42no—
181C2×D19—42no—
182C2×D19—42no—
183C2×D19—84no—
184C4×C19—22no—
185C4×C19—21no—
186C4×C19—21no—
187C4×C19—41no—
188C4×C19—41no—
189C4×C19—41no—
190C4×C19—41no—
191Dic19—42no—
192Dic19—42no—
193Dic19—42no—
194Dic19—162no—
195#542—384no—
196#542—384no—
197C2×C4⋊Q8—191no—
198C2×#126—381no—
199C2×#124—191no—
200C2×#124—381no—
201C2×#123—381no—
202C2×C22⋊Q8—191no—
203C2×C22⋊Q8—381no—
204C2×#121—191no—
205C2×C4×Q8—191no—
206C2×C4×D4—191no—
207C2×#117C2×D1911yescharacteristic
208#407C2×D1912yes—
209#381—192no—
210#343—21no—
211#343—21no—
212#342—381no—
213#342—381no—
214#328—384no—
215#327—384no—
216C2×C19—22no—
217C2×C19—42no—
218C2×C19#178211yescharacteristic
219C2×C19#179511yescharacteristic
220C2×C19#179611yescharacteristic
221D19—82no—
222C22×Q8—191no—
223C22×Q8—381no—
224C22×D4—191no—
225C22×D4—381no—
226C23×C4—381no—
227C23×C4C22×D1911yescharacteristic
228C2×M16—22no—
229C4⋊Q8—382no—
230C4⋊Q8—382no—
231#126—388no—
232#124—382no—
233#124—382no—
234#124—388no—
235#123—388no—
236C22⋊Q8—194no—
237C22⋊Q8—388no—
238C22⋊Q8—382no—
239#121—194no—
240#121—382no—
241C4×Q8—382no—
242C4×Q8—382no—
243C4×D4—382no—
244C4×D4—382no—
245#117—22no—
246#117—22no—
247C2×C4⋊C4—191no—
248C2×C4⋊C4—191no—
249C2×C4⋊C4—381no—
250C2×C4⋊C4—381no—
251C2×C4⋊C4—381no—
252C2×C4⋊C4C22⋊D1911yescharacteristic
253C2×C4⋊C4C22⋊D1911yescharacteristic
254C2×C22⋊C4—381no—
255C2×C22⋊C4—381no—
256C2×C22⋊C4—381no—
257C2×C22⋊C4—381no—
258C2×C22⋊C4—381no—
259C2×C22⋊C4—382no—
260C2×C22⋊C4D7611yescharacteristic
261C2×C22⋊C4D7611yescharacteristic
262C2×C42—381no—
263C2×C42C4×D1911yescharacteristic
264C2×C42C4×D1911yescharacteristic
265C22⋊C8—22no—
266C22⋊C8—22no—
267#95—382no—
268#95—382no—
269C19#851911yescharacteristic, complemented, Sylow
270C24—381no—
271C24C2×D7611yescharacteristic
272C2×Q8—192no—
273C2×Q8—384no—
274C2×Q8—381no—
275C2×Q8—762no—
276C2×Q8—1522no—
277C2×D4—192no—
278C2×D4—384no—
279C2×D4—381no—
280C2×D4—762no—
281C2×D4—1522no—
282C22×C4—42no—
283C22×C4—384no—
284C22×C4—381no—
285C22×C4—381no—
286C22×C4—381no—
287C22×C4—762no—
288C22×C4—1522no—
289C22×C4(C2×D19)⋊C411yescharacteristic
290C22×C4(C2×D19)⋊C411yescharacteristic
291C22×C4(C2×D19)⋊C411yescharacteristic
292C22×C4(C2×D19)⋊C411yescharacteristic
293C22×C4C2×C4×D1911yescharacteristic
294C22×C4D4×D1912yes—
295C22×C4D4×D1912yes—
296C22×C4C2×C22⋊D1911yescharacteristic
297M16—44no—
298C2×C8—42no—
299C4⋊C4—22no—
300C4⋊C4—22no—
301C4⋊C4—192no—
302C4⋊C4—192no—
303C4⋊C4—384no—
304C4⋊C4—384no—
305C4⋊C4—384no—
306C4⋊C4—381no—
307C4⋊C4—381no—
308C22⋊C4—22no—
309C22⋊C4—22no—
310C22⋊C4—384no—
311C22⋊C4—384no—
312C22⋊C4—384no—
313C22⋊C4—384no—
314C22⋊C4—384no—
315C22⋊C4—764no—
316C42—21no—
317C42—21no—
318C42—21no—
319C42—21no—
320C42—384no—
321C23—22no—
322C23—41no—
323C23—41no—
324C23—382no—
325C23—762no—
326C23—762no—
327C23—762no—
328C23#1059732812yes—
329C23C2×(C2×D19)⋊C411yescharacteristic
330Q8—762no—
331Q8—762no—
332Q8—1524no—
333D4—762no—
334D4—762no—
335D4—1524no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—382no—
349C2×C4—382no—
350C2×C4—382no—
351C2×C4—762no—
352C2×C4—762no—
353C2×C4—762no—
354C2×C4—1524no—
355C2×C4—1522no—
356C2×C4—1522no—
357C2×C4—1522no—
358C2×C4C22⋊C4×D1911yescharacteristic
359C2×C4C22⋊C4×D1911yescharacteristic
360C2×C4#1059738312yes—
361C8—82no—
362C22—21no—
363C22—21no—
364C22—22no—
365C22—22no—
366C22—22no—
367C22—82no—
368C22—762no—
369C22—762no—
370C22—762no—
371C22—1524no—
372C22#1192639911yescharacteristic
373C22#1192651712yes—
374C4—22no—
375C4—21no—
376C4—21no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—41no—
381C4—3042no—
382C4—762no—
383C4—762no—
384C4—762no—
385C2—22no—
386C2—42no—
387C2—1522no—
388C2#1456355211yescharacteristic
389C2#1456360611yescharacteristic
390C2#1456361111yescharacteristic
subgroupG/H
centerC22#11926399
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1822C2
socleC22×C19#379
prime radicalC2×#10597376C22
cosocleC23×C4×C19C23
hypercenter#1822D19
hypocenterC19#8519
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1822

Complements

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

NH ≅ G/Ntype
2. #14563712C2semidirect
3. #14562169C2semidirect
5. C19×#1822C2semidirect
8. C2×#10597315C4semidirect
10. C2×#10597321C4semidirect
16. C2×C4×Dic38C4semidirect
17. C2×C4×D76C4semidirect
168. #1822D19semidirect
269. C19#8519semidirect

Maximal subgroups

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

subgroupindex
C2×#119271652
#145637122
#145621692
#145621652
C19×#18222
#851919