Finite Group Databasebeta

← #18071220

Subgroups — #18071220

Order 4864.

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

normal subgroups only

This group has 520 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#14571936C211yesmaximal, characteristic
2#14563703C211yesmaximal, characteristic, complemented
3#14561460C212yesmaximal, complemented
4#14561455C212yesmaximal, complemented
5C19×#1797C211yesmaximal, characteristic, complemented
6C2×#10597321C411yescharacteristic
7C2×#10597370C411yescharacteristic
8C2×#10597376C411yescharacteristic
9C2×C22⋊(C19⋊C8)—21no—
10#11926450C2211yescharacteristic
11#11926446C2211yescharacteristic
12#11926435—21no—
13#11926435—21no—
14#11926423—21no—
15#11926423—21no—
16#11926410C411yescharacteristic
17#11926299—21no—
18#11926299C2212yes—
19C22×C42×C19C2211yescharacteristic
20C2×C19×C4⋊C8—21no—
21C2×C19×C22⋊C8—21no—
22C19×#336C2212yes—
23C23×C4×C19C2×C411yescharacteristic
24C23×C4×C19D411yescharacteristic
25C23×C4×C19D411yescharacteristic
26C22×C22⋊D19—21no—
27C22×D76C2×C411yescharacteristic
28C22×Dic38C2×C411yescharacteristic
29C22×C8×C19—22no—
30C2×C42×C19—42no—
31C2×C42×C19C2×C411yescharacteristic
32C2×C42×C19D411yescharacteristic
33C2×C42×C19D411yescharacteristic
34C2×C42×C19C2311yescharacteristic
35C2×C22⋊Dic19—21no—
36#10597376—42no—
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
44#10597370—42no—
45C2×Dic19⋊C4—21no—
46C22×C19⋊C8—22no—
47#10597321—42no—
48C19×C4⋊C8—42no—
49C19×C22⋊C8—42no—
50C19⋊#95—21no—
51C19⋊#95—21no—
52C19⋊#95—21no—
53C19⋊#95—21no—
54C22⋊(C19⋊C8)—42no—
55C24×C19C22⋊C411yescharacteristic
56C23×D19—21no—
57C22×C4×C19—22no—
58C22×C4×C19—22no—
59C22×C4×C19—22no—
60C22×C4×C19—22no—
61C22×C4×C19—21no—
62C22×C4×C19—21no—
63C22×C4×C19—41no—
64C22×C4×C19—41no—
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×Dic38—22no—
83C2×Dic38—41no—
84C2×Dic38—41no—
85C2×C8×C19—42no—
86C2×C8×C19—42no—
87C2×C8×C19—42no—
88C42×C19—22no—
89C42×C19—22no—
90C42×C19—41no—
91C42×C19—41no—
92C22⋊Dic19—42no—
93(C2×D19)⋊C4—42no—
94(C2×D19)⋊C4—42no—
95(C2×D19)⋊C4—42no—
96(C2×D19)⋊C4—42no—
97(C2×D19)⋊C4—41no—
98(C2×D19)⋊C4—41no—
99C4⋊Dic19—41no—
100C4⋊Dic19—41no—
101Dic19⋊C4—42no—
102C2×C19⋊C8—42no—
103C2×C19⋊C8—42no—
104C2×C19⋊C8—42no—
105#7730—191nomaximal, Sylow
106C23×C19—21no—
107C23×C19—21no—
108C23×C19—21no—
109C23×C19—21no—
110C23×C19—21no—
111C23×C19—21no—
112C23×C19#10012yes—
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—21no—
122C2×C4×C19—21no—
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—44no—
136C2×C4×C19—44no—
137C2×C4×C19—42no—
138C2×C4×C19—42no—
139C2×C4×C19#9912yes—
140C2×C4×C19#13112yes—
141C2×C4×C19#13512yes—
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—
155Dic38—82no—
156C8×C19—82no—
157C19⋊C8—82no—
158#2850—191no—
159#1817—191no—
160#1797D1911yescharacteristic, complemented
161#1272—192no—
162#1270—192no—
163C22×C19—22no—
164C22×C19—22no—
165C22×C19—22no—
166C22×C19—41no—
167C22×C19—41no—
168C22×C19—41no—
169C22×C19—41no—
170C22×C19#40811yescharacteristic
171C22×C19C2×#9911yescharacteristic
172C22×C19C2×#10011yescharacteristic
173C22×C19#41611yescharacteristic
174C22×C19#41711yescharacteristic
175C22×C19#42111yescharacteristic
176C22×C19#42111yescharacteristic
177C2×D19—81no—
178C2×D19—81no—
179C2×D19—81no—
180C2×D19—81no—
181C2×D19—81no—
182C2×D19—81no—
183C2×D19—81no—
184C4×C19—22no—
185C4×C19—21no—
186C4×C19—21no—
187C4×C19—22no—
188C4×C19—22no—
189C4×C19—41no—
190C4×C19—41no—
191Dic19—81no—
192Dic19—81no—
193Dic19—81no—
194C2×#124—191no—
195C2×C22⋊Q8—191no—
196C2×#121—191no—
197C22×C42C2×D1911yescharacteristic
198C2×C4⋊C8—21no—
199C2×C22⋊C8—21no—
200C2×C22⋊C8—381no—
201#391—191no—
202#390—191no—
203#388—381no—
204#388—381no—
205#386—381no—
206#386—381no—
207#382—191no—
208#336—192no—
209#336—381no—
210#336C2×D1912yes—
211C2×C19—42no—
212C2×C19#147111yescharacteristic
213C2×C19#148211yescharacteristic
214C2×C19#149511yescharacteristic
215C2×C19#151311yescharacteristic
216C2×C19#151611yescharacteristic
217C2×C19#153311yescharacteristic
218C2×C19#155111yescharacteristic
219D19—161no—
220C22×Q8—191no—
221C22×D4—191no—
222C22×D4—381no—
223C23×C4C4×D1911yescharacteristic
224C23×C4D7611yescharacteristic
225C23×C4C22⋊D1911yescharacteristic
226C22×C8—22no—
227C22×C8—382no—
228#124—762no—
229C22⋊Q8—762no—
230#121—762no—
231C2×C4⋊C4—191no—
232C2×C4⋊C4—191no—
233C2×C4⋊C4—381no—
234C2×C22⋊C4—381no—
235C2×C22⋊C4—381no—
236C2×C22⋊C4—381no—
237C2×C22⋊C4—381no—
238C2×C22⋊C4—381no—
239C2×C22⋊C4—381no—
240C2×C42—42no—
241C2×C42C4×D1911yescharacteristic
242C2×C42D7611yescharacteristic
243C2×C42C22⋊D1911yescharacteristic
244C2×C42C22×D1911yescharacteristic
245C4⋊C8—42no—
246C22⋊C8—42no—
247C22⋊C8—762no—
248#95—381no—
249#95—381no—
250#95—381no—
251#95—381no—
252C19#773011yescharacteristic, complemented, Sylow
253C24—381no—
254C24(C2×D19)⋊C411yescharacteristic
255C2×Q8—382no—
256C2×Q8—761no—
257C2×Q8—761no—
258C2×D4—382no—
259C2×D4—761no—
260C2×D4—761no—
261C2×D4—762no—
262C2×D4—762no—
263C2×D4—762no—
264C22×C4—22no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—22no—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—41no—
271C22×C4—41no—
272C22×C4—41no—
273C22×C4—41no—
274C22×C4—381no—
275C22×C4—381no—
276C22×C4—381no—
277C22×C4(C2×D19)⋊C411yescharacteristic
278C22×C4(C2×D19)⋊C411yescharacteristic
279C22×C4(C2×D19)⋊C411yescharacteristic
280C22×C4C2×C4×D1911yescharacteristic
281C22×C4C2×D7611yescharacteristic
282C22×C4C2×C22⋊D1911yescharacteristic
283C2×C8—42no—
284C2×C8—42no—
285C2×C8—42no—
286C2×C8—762no—
287C2×C8—762no—
288C2×C8—762no—
289C4⋊C4—761no—
290C4⋊C4—761no—
291C4⋊C4—762no—
292C22⋊C4—762no—
293C22⋊C4—762no—
294C22⋊C4—762no—
295C22⋊C4—761no—
296C22⋊C4—761no—
297C22⋊C4—762no—
298C22⋊C4—762no—
299C42—22no—
300C42—22no—
301C42—41no—
302C42—41no—
303C23—21no—
304C23—21no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23—761no—
310C23—761no—
311C23—761no—
312C23—761no—
313C23—761no—
314C23—761no—
315C23—761no—
316C23#1059728012yes—
317C23C2×(C2×D19)⋊C411yescharacteristic
318Q8—1522no—
319D4—1522no—
320D4—1524no—
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—42no—
338C2×C4—42no—
339C2×C4—761no—
340C2×C4—761no—
341C2×C4—761no—
342C2×C4—761no—
343C2×C4—761no—
344C2×C4—761no—
345C2×C4—761no—
346C2×C4—761no—
347C2×C4—761no—
348C2×C4#1059726312yes—
349C2×C4#1059735012yes—
350C2×C4#1059735312yes—
351C2×C4#1059737811yescharacteristic
352C2×C4#1059738811yescharacteristic
353C8—82no—
354C8—1522no—
355C22—22no—
356C22—22no—
357C22—22no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—1521no—
363C22—1521no—
364C22—1521no—
365C22—1521no—
366C22—1521no—
367C22—1521no—
368C22—1521no—
369C22#1192651211yescharacteristic
370C22C2×#1059726311yescharacteristic
371C22C2×#1059728011yescharacteristic
372C22#1192654111yescharacteristic
373C22#1192654311yescharacteristic
374C22#1192656011yescharacteristic
375C22#1192656211yescharacteristic
376C4—21no—
377C4—21no—
378C4—22no—
379C4—22no—
380C4—22no—
381C4—41no—
382C4—41no—
383C4—1521no—
384C4—1521no—
385C4—1521no—
386C2—42no—
387C2—3041no—
388C2#1456199611yescharacteristic
389C2#1456204411yescharacteristic
390C2#1456209811yescharacteristic
391C2#1456217611yescharacteristic
392C2#1456219211yescharacteristic
393C2#1456225811yescharacteristic
394C2#1456232811yescharacteristic
subgroupG/H
centerC23C2×(C2×D19)⋊C4
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1797C2
socleC23×C19C2×C22⋊C4
prime radicalC2×#10597376C4
cosocleC2×C42×C19C23
hypercenter#1797D19
hypocenterC19#7730
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1797

Complements

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

NH ≅ G/Ntype
2. #14563703C2semidirect
3. #14561460C2semidirect
4. #14561455C2semidirect
5. C19×#1797C2semidirect
160. #1797D19semidirect
252. C19#7730semidirect

Maximal subgroups

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

subgroupindex
#145719362
#145637032
#145614602
#145614552
C19×#17972
#773019