Finite Group Databasebeta

← #18071053

Subgroups — #18071053

Order 4864.

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

normal subgroups only

This group has 556 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#14571966C211yesmaximal, characteristic
2#14563329C211yesmaximal, characteristic, complemented
3#14561459C212yesmaximal, complemented
4#14561455C212yesmaximal, complemented
5C19×#1817C211yesmaximal, characteristic, complemented
6C22×#64520—21no—
7C2×#10597375—21no—
8C2×#10597376C411yescharacteristic
9#11926446C411yescharacteristic
10#11926446C2211yescharacteristic
11#11926442C411yescharacteristic
12#11926442C2211yescharacteristic
13#11926435—21no—
14#11926435—21no—
15#11926423—21no—
16#11926404C411yescharacteristic
17#11926299—21no—
18#11926299C2212yes—
19C22×C42×C19C2211yescharacteristic
20C2×C19×C22⋊C8—21no—
21C19×#336—21no—
22C19×#336C2212yes—
23C23×C4×C19C2×C411yescharacteristic
24C23×C4×C19D411yescharacteristic
25C23×C4×C19D411yescharacteristic
26C22×C22⋊D19—21no—
27C22×D76C2×C411yescharacteristic
28C22×C8×C19—22no—
29C2×C42×C19—42no—
30C2×C42×C19C2×C411yescharacteristic
31C2×C42×C19D411yescharacteristic
32C2×C42×C19D411yescharacteristic
33C2×C42×C19C2311yescharacteristic
34C2×C22⋊Dic19—21no—
35#10597376—42no—
36#10597375—44no—
37C2×(C2×D19)⋊C4—21no—
38C2×(C2×D19)⋊C4—21no—
39C2×(C2×D19)⋊C4—21no—
40C2×(C2×D19)⋊C4—21no—
41C2×(C2×D19)⋊C4—21no—
42C2×C4⋊Dic19C2×C411yescharacteristic
43C2×C4⋊Dic19C2×C411yescharacteristic
44C2×C4⋊Dic19C2×C411yescharacteristic
45C2×Dic19⋊C4—21no—
46C2×Dic19⋊C4—21no—
47C2×#64520—24no—
48C2×#64520—42no—
49C2×#64520—42no—
50C22×C19⋊C8—22no—
51C19×C22⋊C8—42no—
52C19⋊#95—21no—
53C19⋊#95—21no—
54C19⋊#95—21no—
55C24×C19C22⋊C411yescharacteristic
56C23×D19—21no—
57C22×C4×C19—22no—
58C22×C4×C19—22no—
59C22×C4×C19—21no—
60C22×C4×C19—21no—
61C22×C4×C19—22no—
62C22×C4×C19—22no—
63C22×C4×C19—22no—
64C22×C4×C19—22no—
65C22×C4×C19—41no—
66C22×C4×C19—41no—
67C22×C4×C19C22⋊C411yescharacteristic
68C22×C4×C19C22⋊C411yescharacteristic
69C22×C4×C19C22⋊C411yescharacteristic
70C22×C4×C19C22×C411yescharacteristic
71C22×C4×C19C2×D411yescharacteristic
72C22×C4×C19C2×D411yescharacteristic
73C2×C22⋊D19—42no—
74C2×C22⋊D19—42no—
75C2×C22⋊D19—42no—
76C22×Dic19—21no—
77C22×Dic19—21no—
78C22×Dic19—21no—
79C2×D76—22no—
80C2×D76—41no—
81C2×D76—41no—
82C2×C8×C19—42no—
83C2×C8×C19—42no—
84C2×C8×C19—42no—
85C42×C19—41no—
86C42×C19—41no—
87C42×C19—41no—
88C42×C19—41no—
89C22⋊Dic19—42no—
90(C2×D19)⋊C4—42no—
91(C2×D19)⋊C4—42no—
92(C2×D19)⋊C4—42no—
93(C2×D19)⋊C4—41no—
94(C2×D19)⋊C4—42no—
95(C2×D19)⋊C4—41no—
96C4⋊Dic19—22no—
97C4⋊Dic19—41no—
98C4⋊Dic19—41no—
99Dic19⋊C4—42no—
100Dic19⋊C4—42no—
101#64520—48no—
102C2×C19⋊C8—24no—
103C2×C19⋊C8—42no—
104C2×C19⋊C8—42no—
105#7694—191nomaximal, Sylow
106C23×C19—21no—
107C23×C19—21no—
108C23×C19—21no—
109C23×C19—21no—
110C23×C19—21no—
111C23×C19—21no—
112C23×C19#9912yes—
113C23×C19C2×C22⋊C411yescharacteristic
114C22×D19—41no—
115C22×D19—41no—
116C22×D19—41no—
117C22×D19—41no—
118C22×D19—41no—
119C22×D19—41no—
120C22×D19—41no—
121C2×C4×C19—24no—
122C2×C4×C19—24no—
123C2×C4×C19—21no—
124C2×C4×C19—21no—
125C2×C4×C19—21no—
126C2×C4×C19—21no—
127C2×C4×C19—21no—
128C2×C4×C19—21no—
129C2×C4×C19—21no—
130C2×C4×C19—21no—
131C2×C4×C19—21no—
132C2×C4×C19—21no—
133C2×C4×C19—21no—
134C2×C4×C19—21no—
135C2×C4×C19—21no—
136C2×C4×C19—21no—
137C2×C4×C19—44no—
138C2×C4×C19—44no—
139C2×C4×C19#10412yes—
140C2×C4×C19#13112yes—
141C2×C4×C19AGL(1,ℤ/8)12yes—
142C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
143C2×C4×C19#13711yescharacteristic
144C22⋊D19—84no—
145C2×Dic19—41no—
146C2×Dic19—41no—
147C2×Dic19—41no—
148C2×Dic19—41no—
149C2×Dic19—41no—
150C2×Dic19—41no—
151C2×Dic19—41no—
152C2×Dic19—41no—
153C2×Dic19—41no—
154D76—82no—
155C8×C19—82no—
156C19⋊C8—44no—
157#2854—191no—
158#1817D1911yescharacteristic, complemented
159#1728—191no—
160#1271—192no—
161#1270—192no—
162C22×C19—22no—
163C22×C19—22no—
164C22×C19—22no—
165C22×C19—41no—
166C22×C19—41no—
167C22×C19—41no—
168C22×C19—41no—
169C22×C19#40811yescharacteristic
170C22×C19C2×#9911yescharacteristic
171C22×C19#41311yescharacteristic
172C22×C19#41711yescharacteristic
173C22×C19#41811yescharacteristic
174C22×C19C2×#10411yescharacteristic
175C22×C19#42111yescharacteristic
176C2×D19—81no—
177C2×D19—81no—
178C2×D19—81no—
179C2×D19—81no—
180C2×D19—81no—
181C2×D19—81no—
182C2×D19—81no—
183C4×C19—22no—
184C4×C19—21no—
185C4×C19—22no—
186C4×C19—21no—
187C4×C19—22no—
188C4×C19—41no—
189C4×C19—41no—
190Dic19—81no—
191Dic19—81no—
192Dic19—81no—
193C22×M16—381no—
194C2×#123—381no—
195C2×#121—191no—
196C22×C42C2×D1911yescharacteristic
197C2×C22⋊C8—21no—
198#390—191no—
199#390—191no—
200#389—191no—
201#389—191no—
202#388—381no—
203#388—381no—
204#386—381no—
205#380—191no—
206#336—21no—
207#336—192no—
208#336—381no—
209#336C2×D1912yes—
210C2×C19—42no—
211C2×C19#146811yescharacteristic
212C2×C19#148411yescharacteristic
213C2×C19#149511yescharacteristic
214C2×C19#150411yescharacteristic
215C2×C19#151011yescharacteristic
216C2×C19#152911yescharacteristic
217C2×C19#155711yescharacteristic
218D19—161no—
219C22×D4—191no—
220C22×D4—381no—
221C23×C4C4×D1911yescharacteristic
222C23×C4D7611yescharacteristic
223C23×C4C22⋊D1911yescharacteristic
224C2×M16—384no—
225C2×M16—762no—
226C2×M16—762no—
227C22×C8—22no—
228C22×C8—382no—
229#123—764no—
230#121—762no—
231C2×C4⋊C4—191no—
232C2×C4⋊C4—191no—
233C2×C4⋊C4—191no—
234C2×C4⋊C4—381no—
235C2×C4⋊C4—381no—
236C2×C22⋊C4—381no—
237C2×C22⋊C4—381no—
238C2×C22⋊C4—381no—
239C2×C22⋊C4—381no—
240C2×C22⋊C4—381no—
241C2×C22⋊C4—381no—
242C2×C42—42no—
243C2×C42C4×D1911yescharacteristic
244C2×C42D7611yescharacteristic
245C2×C42C22⋊D1911yescharacteristic
246C2×C42C22×D1911yescharacteristic
247C22⋊C8—42no—
248#95—381no—
249#95—381no—
250#95—381no—
251C19#769411yescharacteristic, complemented, Sylow
252C24—381no—
253C24(C2×D19)⋊C411yescharacteristic
254C2×D4—382no—
255C2×D4—761no—
256C2×D4—761no—
257C2×D4—762no—
258C2×D4—762no—
259C2×D4—762no—
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—22no—
265C22×C4—22no—
266C22×C4—22no—
267C22×C4—22no—
268C22×C4—41no—
269C22×C4—41no—
270C22×C4—381no—
271C22×C4—381no—
272C22×C4—381no—
273C22×C4(C2×D19)⋊C411yescharacteristic
274C22×C4(C2×D19)⋊C411yescharacteristic
275C22×C4(C2×D19)⋊C411yescharacteristic
276C22×C4C2×C4×D1911yescharacteristic
277C22×C4C2×D7611yescharacteristic
278C22×C4C2×C22⋊D1911yescharacteristic
279M16—768no—
280C2×C8—42no—
281C2×C8—42no—
282C2×C8—42no—
283C2×C8—384no—
284C2×C8—762no—
285C2×C8—762no—
286C4⋊C4—382no—
287C4⋊C4—761no—
288C4⋊C4—761no—
289C4⋊C4—762no—
290C4⋊C4—762no—
291C22⋊C4—762no—
292C22⋊C4—762no—
293C22⋊C4—762no—
294C22⋊C4—762no—
295C22⋊C4—762no—
296C22⋊C4—761no—
297C22⋊C4—761no—
298C42—41no—
299C42—41no—
300C42—41no—
301C42—41no—
302C23—21no—
303C23—21no—
304C23—21no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23—761no—
309C23—761no—
310C23—761no—
311C23—761no—
312C23—761no—
313C23—761no—
314C23—761no—
315C23#1059726312yes—
316C23C2×(C2×D19)⋊C411yescharacteristic
317D4—1522no—
318D4—1524no—
319C2×C4—24no—
320C2×C4—24no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—44no—
336C2×C4—44no—
337C2×C4—761no—
338C2×C4—761no—
339C2×C4—761no—
340C2×C4—761no—
341C2×C4—761no—
342C2×C4—761no—
343C2×C4—761no—
344C2×C4—761no—
345C2×C4—761no—
346C2×C4#1059728212yes—
347C2×C4#1059734712yes—
348C2×C4#1059735411yescharacteristic
349C2×C4#1059735511yescharacteristic
350C2×C4#1059739512yes—
351C8—82no—
352C8—764no—
353C22—22no—
354C22—22no—
355C22—22no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—1521no—
361C22—1521no—
362C22—1521no—
363C22—1521no—
364C22—1521no—
365C22—1521no—
366C22—1521no—
367C22#1192651011yescharacteristic
368C22C2×#1059726311yescharacteristic
369C22#1192652611yescharacteristic
370C22#1192654611yescharacteristic
371C22#1192654811yescharacteristic
372C22C2×#1059728211yescharacteristic
373C22#1192656211yescharacteristic
374C4—21no—
375C4—22no—
376C4—21no—
377C4—22no—
378C4—22no—
379C4—41no—
380C4—41no—
381C4—1521no—
382C4—1521no—
383C4—1521no—
384C2—42no—
385C2—3041no—
386C2#1456198111yescharacteristic
387C2#1456205111yescharacteristic
388C2#1456210111yescharacteristic
389C2#1456214011yescharacteristic
390C2#1456216311yescharacteristic
391C2#1456224311yescharacteristic
392C2#1456235811yescharacteristic
subgroupG/H
centerC23C2×(C2×D19)⋊C4
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1817C2
socleC23×C19C2×C22⋊C4
prime radicalC2×#10597376C4
cosocleC2×C42×C19C23
hypercenter#1817D19
hypocenterC19#7694
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1817

Complements

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

NH ≅ G/Ntype
2. #14563329C2semidirect
3. #14561459C2semidirect
4. #14561455C2semidirect
5. C19×#1817C2semidirect
158. #1817D19semidirect
251. C19#7694semidirect

Maximal subgroups

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

subgroupindex
#145719662
#145633292
#145614592
#145614552
C19×#18172
#769419