Finite Group Databasebeta

← #18079737

Subgroups — #18079737

Order 4864.

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

normal subgroups only

This group has 542 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
1#14566528C211yesmaximal, characteristic, complemented
2#14564472C211yesmaximal, characteristic
3#14563734C211yesmaximal, characteristic, complemented
4#14562151C211yesmaximal, characteristic
5#14561540C211yesmaximal, characteristic, complemented
6#14561520C211yesmaximal, characteristic, complemented
7C19×#3094C211yesmaximal, characteristic
8C2×#10597291—22no—
9#11926508C2211yescharacteristic
10#11926443—21no—
11#11926437—22no—
12#11926412—21no—
13#11926404C2211yescharacteristic
14C4⋊C4×Dic19—21no—
15C4×C4⋊Dic19—21no—
16C4×C22⋊Dic19C2211yescharacteristic
17C4×C22⋊Dic19C2211yescharacteristic
18#11926303—22no—
19#11926278—21no—
20#11926278—21no—
21C2×C19×#121C2211yescharacteristic
22C2×C19×#117C2211yescharacteristic
23C19×#482—22no—
24C19×#481—21no—
25C19×#480—21no—
26C19×#428C412yescomplemented
27C19×#418C412yescomplemented
28C19×#407C2211yescharacteristic
29C22×D4×C19—21no—
30C22×D4×C19C2×C411yescharacteristic
31C23×C4×C19C2311yescharacteristic
32C2×M16×C19C2×C412yes—
33C19×#121—21no—
34C19×#121—21no—
35C19×#121—21no—
36C19×#121—21no—
37C19×#117—21no—
38C19×#117—21no—
39C19×#117C2×C412yes—
40C19×#117D412yes—
41C2×C4⋊C4×C19C2×C411yescharacteristic
42C2×C4⋊C4×C19D411yescharacteristic
43C2×C4⋊C4×C19D411yescharacteristic
44C2×C22⋊C4×C19—21no—
45C2×C22⋊C4×C19—21no—
46C2×C42×C19—21no—
47C2×C22⋊Dic19—21no—
48C2×C22⋊Dic19—21no—
49C2×C22⋊Dic19D412yes—
50C2×C4⋊Dic19—22no—
51C2×C4⋊Dic19—21no—
52C2×C4×Dic19—21no—
53C2×C4×Dic19—21no—
54C2×C4×Dic19—22no—
55C2×#64520—21no—
56C19×#107—22no—
57C19×#106—22no—
58C19×#102—22no—
59C19×#102—22no—
60C19×C22⋊C8—21no—
61C19×C22⋊C8—21no—
62#10597291—44no—
63C19⋊#95—22no—
64C19⋊#95—22no—
65C19⋊#95—21no—
66C19⋊#95—21no—
67C19⋊#95D411yescharacteristic
68C19⋊#95D411yescharacteristic
69C22⋊(C19⋊C8)—21no—
70C22⋊(C19⋊C8)—21no—
71C24×C19—21no—
72C24×C19C2×D411yescharacteristic
73C2×D4×C19—21no—
74C2×D4×C19—21no—
75C2×D4×C19—42no—
76C2×D4×C19—42no—
77C2×D4×C19—42no—
78C2×D4×C19—41no—
79C2×D4×C19—41no—
80C22×C4×C19—21no—
81C22×C4×C19—21no—
82C22×C4×C19—21no—
83C22×C4×C19—42no—
84C22×C4×C19C22×C411yescharacteristic
85C22×C4×C19C2×D411yescharacteristic
86C22×C4×C19C2×D411yescharacteristic
87C22×C4×C19C2×D411yescharacteristic
88C22×C4×C19#4111yescharacteristic
89C22×C4×C19#4111yescharacteristic
90C22×Dic19—21no—
91C22×Dic19—21no—
92C22×Dic19—22no—
93C22×Dic19—41no—
94M16×C19—42no—
95C2×C8×C19—22no—
96C4⋊C4×C19—21no—
97C4⋊C4×C19—21no—
98C4⋊C4×C19—21no—
99C4⋊C4×C19—21no—
100C4⋊C4×C19C22⋊C412yes—
101C4⋊C4×C19C22⋊C412yes—
102C22⋊C4×C19—22no—
103C22⋊C4×C19—22no—
104C22⋊C4×C19—41no—
105C22⋊C4×C19—41no—
106C42×C19—22no—
107C42×C19—22no—
108C22⋊Dic19—22no—
109C22⋊Dic19—42no—
110C22⋊Dic19—41no—
111C22⋊Dic19—42no—
112C4⋊Dic19—44no—
113C4⋊Dic19—42no—
114C4×Dic19—42no—
115C4×Dic19—42no—
116C4×Dic19—82no—
117#64520—42no—
118C2×C19⋊C8—41no—
119#9366—191nomaximal, Sylow
120C23×C19—21no—
121C23×C19—21no—
122C23×C19—41no—
123C23×C19—41no—
124C23×C19—42no—
125C23×C19—41no—
126C23×C19—81no—
127C23×C19—81no—
128C23×C19C4×D411yescharacteristic
129C23×C19#12011yescharacteristic
130C23×C19#12111yescharacteristic
131D4×C19—42no—
132D4×C19—81no—
133D4×C19—82no—
134D4×C19—81no—
135D4×C19—81no—
136C2×C4×C19—22no—
137C2×C4×C19—22no—
138C2×C4×C19—22no—
139C2×C4×C19—22no—
140C2×C4×C19—22no—
141C2×C4×C19—41no—
142C2×C4×C19—41no—
143C2×C4×C19—41no—
144C2×C4×C19—42no—
145C2×C4×C19—41no—
146C2×C4×C19—41no—
147C2×C4×C19—42no—
148C2×C4×C19—41no—
149C2×C4×C19C2×C22⋊C411yescharacteristic
150C2×C4×C19C4×D411yescharacteristic
151C2×C4×C19#12111yescharacteristic
152C2×C4×C19#12311yescharacteristic
153C2×Dic19—22no—
154C2×Dic19—41no—
155C2×Dic19—41no—
156C2×Dic19—41no—
157C2×Dic19—42no—
158C2×Dic19—42no—
159C2×Dic19—42no—
160C2×Dic19—41no—
161C2×Dic19—42no—
162C2×Dic19—41no—
163C2×Dic19—81no—
164C2×Dic19—81no—
165C8×C19—42no—
166C19⋊C8—81no—
167#3094D1911yescharacteristic
168#2347—191no—
169#1964—191no—
170#1826—191no—
171#1507—191no—
172#1305—191no—
173#1297—191no—
174C22×C19—21no—
175C22×C19—21no—
176C22×C19—21no—
177C22×C19—21no—
178C22×C19—21no—
179C22×C19—21no—
180C22×C19—21no—
181C22×C19—21no—
182C22×C19—81no—
183C22×C19—81no—
184C22×C19—81no—
185C22×C19—81no—
186C22×C19—81no—
187C22×C19—162no—
188C22×C19#38611yescharacteristic
189C22×C19#45311yescharacteristic
190C22×C19#45411yescharacteristic
191C4×C19—21no—
192C4×C19—21no—
193C4×C19—21no—
194C4×C19—42no—
195C4×C19—42no—
196C4×C19—81no—
197C4×C19#41012yes—
198Dic19—42no—
199Dic19—82no—
200Dic19—81no—
201Dic19—82no—
202C2×#121C2×D1911yescharacteristic
203C2×#117C2×D1911yescharacteristic
204#482—22no—
205#481—21no—
206#480—21no—
207#428Dic1912yescomplemented
208#418Dic1912yescomplemented
209C2×#99—382no—
210#407—191no—
211#407C2×D1911yescharacteristic
212#389—381no—
213#388—382no—
214#383—381no—
215#380—191no—
216C4×C4⋊C4—381no—
217C4×C4⋊C4—381no—
218C4×C22⋊C4—191no—
219C4×C22⋊C4—191no—
220#339—382no—
221#327—381no—
222#327—381no—
223C2×C19—21no—
224C2×C19—21no—
225C2×C19—41no—
226C2×C19—41no—
227C2×C19—161no—
228C2×C19#188311yescharacteristic
229C2×C19#189911yescharacteristic
230C2×C19#190611yescharacteristic
231C22×D4—21no—
232C22×D4C2×Dic1911yescharacteristic
233C23×C4C22×D1911yescharacteristic
234C2×M16—381no—
235C2×M16C2×Dic1912yes—
236#121—21no—
237#121—21no—
238#121—21no—
239#121—21no—
240#117—21no—
241#117—21no—
242#117C2×Dic1912yes—
243#117C22⋊D1912yes—
244C2×C4⋊C4—382no—
245C2×C4⋊C4—381no—
246C2×C4⋊C4C2×Dic1911yescharacteristic
247C2×C4⋊C4C22⋊D1911yescharacteristic
248C2×C4⋊C4C22⋊D1911yescharacteristic
249C2×C22⋊C4—21no—
250C2×C22⋊C4—21no—
251C2×C22⋊C4—192no—
252C2×C22⋊C4—381no—
253C2×C22⋊C4—381no—
254C2×C42—21no—
255C2×C42—381no—
256C2×C42—381no—
257C2×C42—382no—
258#107—22no—
259#106—22no—
260#102—22no—
261#102—22no—
262#99—764no—
263C22⋊C8—21no—
264C22⋊C8—21no—
265C22⋊C8—381no—
266C22⋊C8—381no—
267#95—191no—
268#95—191no—
269#95—382no—
270#95—382no—
271#95—381no—
272#95—381no—
273C19#936611yescharacteristic, complemented, Sylow
274C24—21no—
275C24D4×D1911yescharacteristic
276C2×D4—21no—
277C2×D4—21no—
278C2×D4—42no—
279C2×D4—42no—
280C2×D4—42no—
281C2×D4—41no—
282C2×D4—41no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—42no—
287C22×C4—381no—
288C22×C4—381no—
289C22×C4—382no—
290C22×C4—761no—
291C22×C4D4×D1911yescharacteristic
292C22×C4#6454311yescharacteristic
293C22×C4#6454311yescharacteristic
294C22×C4C22×Dic1911yescharacteristic
295C22×C4C2×C22⋊D1911yescharacteristic
296C22×C4C2×C22⋊D1911yescharacteristic
297M16—42no—
298M16—762no—
299C2×C8—22no—
300C2×C8—761no—
301C4⋊C4—21no—
302C4⋊C4—21no—
303C4⋊C4—21no—
304C4⋊C4—21no—
305C4⋊C4—762no—
306C4⋊C4—764no—
307C4⋊C4C22⋊Dic1912yes—
308C4⋊C4C22⋊Dic1912yes—
309C22⋊C4—22no—
310C22⋊C4—22no—
311C22⋊C4—41no—
312C22⋊C4—41no—
313C22⋊C4—382no—
314C22⋊C4—762no—
315C22⋊C4—761no—
316C22⋊C4—762no—
317C42—22no—
318C42—22no—
319C42—762no—
320C42—762no—
321C42—1522no—
322C23—21no—
323C23—21no—
324C23—41no—
325C23—41no—
326C23—42no—
327C23—41no—
328C23—81no—
329C23—81no—
330C23D4×Dic1911yescharacteristic
331C23#1059738311yescharacteristic
332C23#1059738511yescharacteristic
333D4—42no—
334D4—81no—
335D4—82no—
336D4—81no—
337D4—81no—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—22no—
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—42no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—42no—
350C2×C4—41no—
351C2×C4—382no—
352C2×C4—761no—
353C2×C4—761no—
354C2×C4—761no—
355C2×C4—762no—
356C2×C4—761no—
357C2×C4—762no—
358C2×C4—762no—
359C2×C4—762no—
360C2×C4—761no—
361C2×C4—1521no—
362C2×C4—1521no—
363C2×C4D4×Dic1911yescharacteristic
364C2×C4#1059738111yescharacteristic
365C2×C4#1059738511yescharacteristic
366C2×C4C2×C22⋊Dic1911yescharacteristic
367C8—42no—
368C8—1521no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—81no—
378C22—81no—
379C22—81no—
380C22—81no—
381C22—81no—
382C22—162no—
383C22#1192642411yescharacteristic
384C22#1192671011yescharacteristic
385C22#1192671511yescharacteristic
386C4—21no—
387C4—21no—
388C4—21no—
389C4—42no—
390C4—42no—
391C4—81no—
392C4—762no—
393C4—1522no—
394C4—1521no—
395C4—1522no—
396C4#1192651812yes—
397C2—21no—
398C2—21no—
399C2—41no—
400C2—41no—
401C2—161no—
402C2#1456401311yescharacteristic
403C2#1456409411yescharacteristic
404C2#1456413811yescharacteristic
subgroupG/H
centerC22#11926424
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#3094C2
socleC22×C19#386
prime radicalC2×C19×#121C22
cosocleC23×C4×C19C23
hypercenter#3094D19
hypocenterC19#9366
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3094

Complements

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

NH ≅ G/Ntype
1. #14566528C2semidirect
3. #14563734C2semidirect
5. #14561540C2semidirect
6. #14561520C2semidirect
26. C19×#428C4semidirect
27. C19×#418C4semidirect
207. #428Dic19semidirect
208. #418Dic19semidirect
273. C19#9366semidirect

Maximal subgroups

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

subgroupindex
#145665282
#145644722
#145637342
#145621512
#145615402
#145615202
C19×#30942
#936619