Finite Group Databasebeta

← #18080280

Subgroups — #18080280

Order 4864.

610 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 610 conjugacy classes of subgroups — too many to draw. Only its 93 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#14568107C211yesmaximal, characteristic
2#14566236C211yesmaximal, characteristic, complemented
3#14563713C211yesmaximal, characteristic, complemented
4#14562164C211yesmaximal, characteristic
5#14561489C211yesmaximal, characteristic, complemented
6#14561487C211yesmaximal, characteristic, complemented
7C19×#1510C211yesmaximal, characteristic
8C2×#10597381—21no—
9C2×#10597381—21no—
10C22×C4⋊Dic19C2211yescharacteristic
11#11926508C2211yescharacteristic
12#11926480—22no—
13#11926447C412yescomplemented
14#11926429—22no—
15#11926427—22no—
16#11926413C412yescomplemented
17#11926407C2211yescharacteristic
18#11926402—21no—
19C22⋊C4×Dic19—21no—
20C4×C22⋊Dic19C2211yescharacteristic
21#11926312—22no—
22#11926278—22no—
23C2×C19×#121C2211yescharacteristic
24C19×#407C2211yescharacteristic
25C19×#381C2211yescharacteristic
26C19×#327—22no—
27C22×D4×C19—21no—
28C22×D4×C19C2×C411yescharacteristic
29C23×C4×C19C2311yescharacteristic
30C23×Dic19D411yescharacteristic
31C23×Dic19D411yescharacteristic
32C2×M16×C19—21no—
33C19×#121—21no—
34C19×#121—21no—
35C19×#121—21no—
36C19×#121—21no—
37C2×C4⋊C4×C19C2×C411yescharacteristic
38C2×C22⋊C4×C19—21no—
39C2×C22⋊C4×C19—21no—
40C2×C22⋊Dic19—21no—
41C2×C22⋊Dic19—21no—
42C2×C22⋊Dic19—22no—
43C2×C22⋊Dic19—22no—
44#10597381—44no—
45#10597381—44no—
46C2×C4⋊Dic19—21no—
47C2×C4⋊Dic19—21no—
48C2×C4⋊Dic19—21no—
49C2×C4⋊Dic19—21no—
50C2×C4⋊Dic19C2×C412yes—
51C2×C4⋊Dic19D412yes—
52C2×Dic19⋊C4—22no—
53C2×Dic19⋊C4—22no—
54C2×Dic19⋊C4—22no—
55C2×C4×Dic19—22no—
56C2×C4×Dic19C2×C412yes—
57C2×#64520—21no—
58C19×C22⋊C8—21no—
59C19×C22⋊C8—21no—
60C19×#95—21no—
61C19×#95D412yes—
62C19⋊#95—22no—
63C19⋊#95—22no—
64C19⋊#95—21no—
65C19⋊#95—21no—
66C19⋊#95D412yes—
67C22⋊(C19⋊C8)—21no—
68C22⋊(C19⋊C8)—21no—
69C24×C19—21no—
70C24×C19C2×D411yescharacteristic
71C2×D4×C19—21no—
72C2×D4×C19—21no—
73C2×D4×C19—42no—
74C2×D4×C19—42no—
75C2×D4×C19—42no—
76C2×D4×C19—41no—
77C2×D4×C19—41no—
78C22×C4×C19—21no—
79C22×C4×C19—22no—
80C22×C4×C19—42no—
81C22×C4×C19C22×C411yescharacteristic
82C22×C4×C19C2×D411yescharacteristic
83C22×C4×C19C2×D411yescharacteristic
84C22×C4×C19C2×D411yescharacteristic
85C22×C4×C19#4111yescharacteristic
86C22×C4×C19#4111yescharacteristic
87C22×Dic19—22no—
88C22×Dic19—21no—
89C22×Dic19—21no—
90C22×Dic19—21no—
91C22×Dic19—21no—
92C22×Dic19—22no—
93C22×Dic19—42no—
94C22×Dic19—42no—
95C22×Dic19C22⋊C412yes—
96C22×Dic19C22⋊C412yes—
97M16×C19—42no—
98C2×C8×C19—41no—
99C4⋊C4×C19—21no—
100C4⋊C4×C19—21no—
101C22⋊C4×C19—42no—
102C22⋊C4×C19—41no—
103C22⋊C4×C19—41no—
104C22⋊Dic19—24no—
105C22⋊Dic19—44no—
106C22⋊Dic19—44no—
107C22⋊Dic19—42no—
108C4⋊Dic19—22no—
109C4⋊Dic19—22no—
110C4⋊Dic19—22no—
111C4⋊Dic19—22no—
112Dic19⋊C4—44no—
113Dic19⋊C4—44no—
114Dic19⋊C4—82no—
115C4×Dic19—42no—
116C4×Dic19—82no—
117#64520—42no—
118C2×C19⋊C8—41no—
119#9464—191nomaximal, Sylow
120C23×C19—22no—
121C23×C19—22no—
122C23×C19—41no—
123C23×C19—41no—
124C23×C19—41no—
125C23×C19—42no—
126C23×C19—41no—
127C23×C19—42no—
128C23×C19C2×C22⋊C411yescharacteristic
129C23×C19#12011yescharacteristic
130C23×C19#12311yescharacteristic
131D4×C19—81no—
132D4×C19—81no—
133D4×C19—82no—
134D4×C19—82no—
135C2×C4×C19—22no—
136C2×C4×C19—22no—
137C2×C4×C19—41no—
138C2×C4×C19—41no—
139C2×C4×C19—41no—
140C2×C4×C19—41no—
141C2×C4×C19—41no—
142C2×C4×C19—41no—
143C2×C4×C19—42no—
144C2×C4×C19—42no—
145C2×C4×C19—41no—
146C2×C4×C19—42no—
147C2×C4×C19C4×D411yescharacteristic
148C2×C4×C19C4×D411yescharacteristic
149C2×C4×C19#12111yescharacteristic
150C2×C4×C19#12111yescharacteristic
151C2×Dic19—24no—
152C2×Dic19—22no—
153C2×Dic19—22no—
154C2×Dic19—42no—
155C2×Dic19—42no—
156C2×Dic19—42no—
157C2×Dic19—42no—
158C2×Dic19—42no—
159C2×Dic19—42no—
160C2×Dic19—42no—
161C2×Dic19—42no—
162C2×Dic19—42no—
163C2×Dic19—81no—
164C2×Dic19—81no—
165C8×C19—81no—
166C19⋊C8—81no—
167#2501—191no—
168#2313—191no—
169#1821—191no—
170#1510—191no—
171#1510D1911yescharacteristic
172#1284—191no—
173#1284—191no—
174C22×C19—21no—
175C22×C19—21no—
176C22×C19—21no—
177C22×C19—21no—
178C22×C19—21no—
179C22×C19—21no—
180C22×C19—21no—
181C22×C19—44no—
182C22×C19—82no—
183C22×C19—82no—
184C22×C19—81no—
185C22×C19—81no—
186C22×C19—81no—
187C22×C19#38611yescharacteristic
188C22×C19#41012yes—
189C22×C19#45312yes—
190C4×C19—21no—
191C4×C19—21no—
192C4×C19—21no—
193C4×C19—21no—
194C4×C19—82no—
195C4×C19—81no—
196Dic19—44no—
197Dic19—42no—
198Dic19—42no—
199Dic19—82no—
200C2×#123—381no—
201C2×#123—381no—
202C2×#121C2×D1911yescharacteristic
203C22×C4⋊C4—191no—
204#407—191no—
205#407C2×D1911yescharacteristic
206#399—382no—
207#390—192no—
208#387—382no—
209#387—382no—
210#384—192no—
211#381—191no—
212#381C2×D1911yescharacteristic
213#380—381no—
214C4×C22⋊C4—191no—
215C4×C22⋊C4—381no—
216#343—382no—
217#327—22no—
218#327—382no—
219C2×C19—22no—
220C2×C19—22no—
221C2×C19—41no—
222C2×C19—161no—
223C2×C19#188711yescharacteristic
224C2×C19#189911yescharacteristic
225C2×C19#191211yescharacteristic
226C22×D4—21no—
227C22×D4C4×D1911yescharacteristic
228C23×C4—191no—
229C23×C4—191no—
230C23×C4C22×D1911yescharacteristic
231C2×M16—21no—
232C2×M16—381no—
233#123—764no—
234#123—764no—
235#121—21no—
236#121—21no—
237#121—21no—
238#121—21no—
239C2×C4⋊C4—192no—
240C2×C4⋊C4—192no—
241C2×C4⋊C4—381no—
242C2×C4⋊C4—381no—
243C2×C4⋊C4—381no—
244C2×C4⋊C4—381no—
245C2×C4⋊C4—382no—
246C2×C4⋊C4—382no—
247C2×C4⋊C4—382no—
248C2×C4⋊C4C4×D1911yescharacteristic
249C2×C22⋊C4—21no—
250C2×C22⋊C4—21no—
251C2×C22⋊C4—381no—
252C2×C22⋊C4—382no—
253C2×C22⋊C4—382no—
254C2×C22⋊C4—381no—
255C2×C42—192no—
256C2×C42—382no—
257C22⋊C8—21no—
258C22⋊C8—21no—
259C22⋊C8—381no—
260C22⋊C8—381no—
261#95—21no—
262#95—192no—
263#95—382no—
264#95—382no—
265#95—381no—
266#95—381no—
267#95C22⋊D1912yes—
268C19#946411yescharacteristic, complemented, Sylow
269C24—21no—
270C24D4×D1911yescharacteristic
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—42no—
274C2×D4—42no—
275C2×D4—42no—
276C2×D4—41no—
277C2×D4—41no—
278C22×C4—22no—
279C22×C4—21no—
280C22×C4—42no—
281C22×C4—192no—
282C22×C4—192no—
283C22×C4—381no—
284C22×C4—381no—
285C22×C4—382no—
286C22×C4—381no—
287C22×C4—381no—
288C22×C4—382no—
289C22×C4—762no—
290C22×C4—762no—
291C22×C4C2×C4×D1911yescharacteristic
292C22×C4#6454111yescharacteristic
293C22×C4D4×D1911yescharacteristic
294C22×C4D4×D1911yescharacteristic
295C22×C4#6454311yescharacteristic
296C22×C4C2×C22⋊D1911yescharacteristic
297M16—42no—
298M16—762no—
299C2×C8—41no—
300C2×C8—761no—
301C4⋊C4—21no—
302C4⋊C4—21no—
303C4⋊C4—382no—
304C4⋊C4—382no—
305C4⋊C4—382no—
306C4⋊C4—382no—
307C4⋊C4—764no—
308C4⋊C4—764no—
309C4⋊C4—1522no—
310C22⋊C4—42no—
311C22⋊C4—41no—
312C22⋊C4—41no—
313C22⋊C4—384no—
314C22⋊C4—764no—
315C22⋊C4—764no—
316C22⋊C4—762no—
317C42—762no—
318C42—1522no—
319C23—22no—
320C23—22no—
321C23—41no—
322C23—41no—
323C23—41no—
324C23—42no—
325C23—41no—
326C23—42no—
327C23C22⋊C4×D1911yescharacteristic
328C23#1059732911yescharacteristic
329C23#1059738311yescharacteristic
330D4—81no—
331D4—81no—
332D4—82no—
333D4—82no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—42no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—42no—
344C2×C4—41no—
345C2×C4—42no—
346C2×C4—384no—
347C2×C4—382no—
348C2×C4—382no—
349C2×C4—762no—
350C2×C4—762no—
351C2×C4—762no—
352C2×C4—762no—
353C2×C4—762no—
354C2×C4—762no—
355C2×C4—762no—
356C2×C4—762no—
357C2×C4—762no—
358C2×C4—1521no—
359C2×C4—1521no—
360C2×C4(C22⋊D19)⋊C411yescharacteristic
361C2×C4#1059733011yescharacteristic
362C2×C4C4×C22⋊D1911yescharacteristic
363C2×C4#1059738411yescharacteristic
364C8—81no—
365C8—1521no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—44no—
374C22—82no—
375C22—82no—
376C22—81no—
377C22—81no—
378C22—81no—
379C22#1192642011yescharacteristic
380C22#1192651612yes—
381C22#1192671012yes—
382C4—21no—
383C4—21no—
384C4—21no—
385C4—21no—
386C4—82no—
387C4—81no—
388C4—764no—
389C4—762no—
390C4—762no—
391C4—1522no—
392C2—22no—
393C2—22no—
394C2—41no—
395C2—161no—
396C2#1456403011yescharacteristic
397C2#1456409011yescharacteristic
398C2#1456416911yescharacteristic
subgroupG/H
centerC22#11926420
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1510C2
socleC22×C19#386
prime radicalC2×C19×#121C22
cosocleC23×C4×C19C23
hypercenter#1510D19
hypocenterC19#9464
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1510

Complements

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

NH ≅ G/Ntype
2. #14566236C2semidirect
3. #14563713C2semidirect
5. #14561489C2semidirect
6. #14561487C2semidirect
13. #11926447C4semidirect
16. #11926413C4semidirect
268. C19#9464semidirect

Maximal subgroups

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

subgroupindex
#145681072
#145662362
#145637132
#145621642
#145614892
#145614872
C19×#15102
#946419