Finite Group Databasebeta

← #18075063

Subgroups — #18075063

Order 4864.

720 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 720 conjugacy classes of subgroups — too many to draw. Only its 131 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#14562352C212yesmaximal, complemented
2#14562259C212yesmaximal, complemented
3#14561969C211yesmaximal, characteristic, complemented
4#14561969C211yesmaximal, characteristic, complemented
5C2×C19×#542C211yesmaximal, characteristic
6#11926601C2212yes—
7#11926601C2212yes—
8#11926290—24no—
9#11926284—24no—
10#11926270—21no—
11#11926270—21no—
12#11926268—21no—
13#11926268—21no—
14C19×#542—24no—
15C19×#542—24no—
16C2×C19×C4⋊Q8C2211yescharacteristic
17C2×C19×#126—21no—
18C2×C19×#124—21no—
19C2×C19×#124C2211yescharacteristic
20C2×C19×#123—21no—
21C2×C19×C22⋊Q8—21no—
22C2×C19×C22⋊Q8C411yescharacteristic
23C2×C19×#121C411yescharacteristic
24C2×C4×Q8×C19C411yescharacteristic
25C2×C4×D4×C19C411yescharacteristic
26C2×C19×#117C2211yescharacteristic
27C22×Q8×C19—21no—
28C22×Q8×C19C2×C411yescharacteristic
29C22×D4×C19—21no—
30C22×D4×C19C2×C411yescharacteristic
31C23×C4×C19—21no—
32C23×C4×C19C2×C411yescharacteristic
33C19×C4⋊Q8—22no—
34C19×C4⋊Q8D414yes—
35C19×#126—28no—
36C19×#124—28no—
37C19×#124—22no—
38C19×#124D414yes—
39C19×#123—28no—
40C19×C22⋊Q8—28no—
41C19×C22⋊Q8—22no—
42C19×C22⋊Q8—22no—
43C19×#121—22no—
44C19×#121—22no—
45C4×Q8×C19—22no—
46C4×Q8×C19—22no—
47C4×D4×C19—22no—
48C4×D4×C19—22no—
49C19×#117—22no—
50C19×#117—22no—
51C2×C4⋊C4×C19—21no—
52C2×C4⋊C4×C19—21no—
53C2×C4⋊C4×C19—21no—
54C2×C4⋊C4×C19C2×C411yescharacteristic
55C2×C4⋊C4×C19C2×C411yescharacteristic
56C2×C4⋊C4×C19D411yescharacteristic
57C2×C4⋊C4×C19D411yescharacteristic
58C2×C22⋊C4×C19—21no—
59C2×C22⋊C4×C19—21no—
60C2×C22⋊C4×C19—21no—
61C2×C22⋊C4×C19—21no—
62C2×C22⋊C4×C19—21no—
63C2×C22⋊C4×C19D411yescharacteristic
64C2×C22⋊C4×C19D411yescharacteristic
65C2×C42×C19—21no—
66C2×C42×C19C2×C411yescharacteristic
67C2×C42×C19C2311yescharacteristic
68C22⋊(C19⋊C8)—22no—
69C22⋊(C19⋊C8)—22no—
70C4⋊(C19⋊C8)—22no—
71C4⋊(C19⋊C8)—22no—
72#10597260—22no—
73#10597260—22no—
74C24×C19—21no—
75C24×C19C22⋊C411yescharacteristic
76C2×Q8×C19—21no—
77C2×Q8×C19—24no—
78C2×Q8×C19—42no—
79C2×Q8×C19—82no—
80C2×Q8×C19C22⋊C412yes—
81C2×D4×C19—24no—
82C2×D4×C19—21no—
83C2×D4×C19—42no—
84C2×D4×C19—82no—
85C2×D4×C19C22⋊C412yes—
86C22×C4×C19—21no—
87C22×C4×C19—21no—
88C22×C4×C19—21no—
89C22×C4×C19—24no—
90C22×C4×C19—21no—
91C22×C4×C19—21no—
92C22×C4×C19—42no—
93C22×C4×C19—82no—
94C22×C4×C19C22⋊C411yescharacteristic
95C22×C4×C19C22⋊C411yescharacteristic
96C22×C4×C19C22⋊C411yescharacteristic
97C22×C4×C19C22×C411yescharacteristic
98C22×C4×C19C2×D411yescharacteristic
99C22×C4×C19C2×D411yescharacteristic
100C4⋊C4×C19—24no—
101C4⋊C4×C19—24no—
102C4⋊C4×C19—21no—
103C4⋊C4×C19—21no—
104C4⋊C4×C19—24no—
105C4⋊C4×C19—22no—
106C4⋊C4×C19—22no—
107C4⋊C4×C19C22⋊C412yes—
108C4⋊C4×C19C22⋊C412yes—
109C22⋊C4×C19—24no—
110C22⋊C4×C19—24no—
111C22⋊C4×C19—24no—
112C22⋊C4×C19—24no—
113C22⋊C4×C19—24no—
114C22⋊C4×C19—22no—
115C22⋊C4×C19—22no—
116C42×C19—24no—
117C42×C19—21no—
118C42×C19—21no—
119C42×C19C2×D412yes—
120C42×C19C2×D412yes—
121C2×C19⋊C8—42no—
122C2×C19⋊C8—42no—
123#8523—191nomaximal, Sylow
124C23×C19—21no—
125C23×C19—22no—
126C23×C19—22no—
127C23×C19—42no—
128C23×C19—42no—
129C23×C19—41no—
130C23×C19—41no—
131C23×C19—42no—
132C23×C19C2×C22⋊C411yescharacteristic
133Q8×C19—42no—
134Q8×C19—42no—
135Q8×C19—84no—
136D4×C19—42no—
137D4×C19—42no—
138D4×C19—84no—
139C2×C4×C19—22no—
140C2×C4×C19—21no—
141C2×C4×C19—22no—
142C2×C4×C19—21no—
143C2×C4×C19—22no—
144C2×C4×C19—21no—
145C2×C4×C19—22no—
146C2×C4×C19—22no—
147C2×C4×C19—41no—
148C2×C4×C19—41no—
149C2×C4×C19—42no—
150C2×C4×C19—42no—
151C2×C4×C19—42no—
152C2×C4×C19—42no—
153C2×C4×C19—42no—
154C2×C4×C19—41no—
155C2×C4×C19—41no—
156C2×C4×C19—84no—
157C2×C4×C19C2×C22⋊C411yescharacteristic
158C2×C4×C19C2×C22⋊C411yescharacteristic
159C2×C4×C19#12012yes—
160C2×C4×C19#12012yes—
161C19⋊C8—82no—
162C19⋊C8—82no—
163C2×#542D1911yescharacteristic
164#1556—192no—
165#1533—192no—
166#1464—191no—
167#1464—191no—
168C22×C19—21no—
169C22×C19—21no—
170C22×C19—42no—
171C22×C19—41no—
172C22×C19—41no—
173C22×C19—42no—
174C22×C19—41no—
175C22×C19—42no—
176C22×C19—82no—
177C22×C19—84no—
178C22×C19#37911yescharacteristic
179C22×C19#41312yes—
180C4×C19—22no—
181C4×C19—22no—
182C4×C19—21no—
183C4×C19—21no—
184C4×C19—42no—
185C4×C19—42no—
186C4×C19—41no—
187C4×C19—41no—
188C4×C19—41no—
189C4×C19—42no—
190#542—24no—
191#542—24no—
192C2×C4⋊Q8C2×D1911yescharacteristic
193C2×#126—21no—
194C2×#124—21no—
195C2×#124C2×D1911yescharacteristic
196C2×#123—21no—
197C2×C22⋊Q8—21no—
198C2×C22⋊Q8Dic1911yescharacteristic
199C2×#121Dic1911yescharacteristic
200C2×C4×Q8Dic1911yescharacteristic
201C2×C4×D4Dic1911yescharacteristic
202C2×#117C2×D1911yescharacteristic
203#432—192no—
204#432—192no—
205#332—384no—
206#329—384no—
207#324—381no—
208#324—381no—
209#323—381no—
210#323—381no—
211C2×C19—22no—
212C2×C19—81no—
213C2×C19—82no—
214C2×C19#178511yescharacteristic
215C2×C19#179511yescharacteristic
216C2×C19#179611yescharacteristic
217C22×Q8—21no—
218C22×Q8C2×Dic1911yescharacteristic
219C22×D4—21no—
220C22×D4C2×Dic1911yescharacteristic
221C23×C4—21no—
222C23×C4C2×Dic1911yescharacteristic
223C4⋊Q8—22no—
224C4⋊Q8C22⋊D1914yes—
225#126—28no—
226#124—28no—
227#124—22no—
228#124C22⋊D1914yes—
229#123—28no—
230C22⋊Q8—28no—
231C22⋊Q8—22no—
232C22⋊Q8—22no—
233#121—22no—
234#121—22no—
235C4×Q8—22no—
236C4×Q8—22no—
237C4×D4—22no—
238C4×D4—22no—
239#117—22no—
240#117—22no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4C2×Dic1911yescharacteristic
245C2×C4⋊C4C2×Dic1911yescharacteristic
246C2×C4⋊C4C22⋊D1911yescharacteristic
247C2×C4⋊C4C22⋊D1911yescharacteristic
248C2×C22⋊C4—21no—
249C2×C22⋊C4—21no—
250C2×C22⋊C4—21no—
251C2×C22⋊C4—21no—
252C2×C22⋊C4—21no—
253C2×C22⋊C4C22⋊D1911yescharacteristic
254C2×C22⋊C4C22⋊D1911yescharacteristic
255C2×C42—21no—
256C2×C42C2×Dic1911yescharacteristic
257C2×C42C22×D1911yescharacteristic
258C4⋊C8—382no—
259C4⋊C8—382no—
260C22⋊C8—382no—
261C22⋊C8—382no—
262#97—382no—
263#97—382no—
264C19#852311yescharacteristic, complemented, Sylow
265C24—21no—
266C24C22⋊Dic1911yescharacteristic
267C2×Q8—21no—
268C2×Q8—24no—
269C2×Q8—42no—
270C2×Q8—82no—
271C2×Q8C22⋊Dic1912yes—
272C2×D4—24no—
273C2×D4—21no—
274C2×D4—42no—
275C2×D4—82no—
276C2×D4C22⋊Dic1912yes—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—24no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—42no—
284C22×C4—82no—
285C22×C4C22⋊Dic1911yescharacteristic
286C22×C4C22⋊Dic1911yescharacteristic
287C22×C4C22⋊Dic1911yescharacteristic
288C22×C4C22×Dic1911yescharacteristic
289C22×C4C2×C22⋊D1911yescharacteristic
290C22×C4C2×C22⋊D1911yescharacteristic
291C2×C8—762no—
292C2×C8—762no—
293C4⋊C4—24no—
294C4⋊C4—24no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—24no—
298C4⋊C4—22no—
299C4⋊C4—22no—
300C4⋊C4C22⋊Dic1912yes—
301C4⋊C4C22⋊Dic1912yes—
302C22⋊C4—24no—
303C22⋊C4—24no—
304C22⋊C4—24no—
305C22⋊C4—24no—
306C22⋊C4—24no—
307C22⋊C4—22no—
308C22⋊C4—22no—
309C42—24no—
310C42—21no—
311C42—21no—
312C42C2×C22⋊D1912yes—
313C42C2×C22⋊D1912yes—
314C23—21no—
315C23—22no—
316C23—22no—
317C23—42no—
318C23—42no—
319C23—41no—
320C23—41no—
321C23—42no—
322C23C2×C22⋊Dic1911yescharacteristic
323Q8—42no—
324Q8—42no—
325Q8—84no—
326D4—42no—
327D4—42no—
328D4—84no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—21no—
332C2×C4—22no—
333C2×C4—21no—
334C2×C4—22no—
335C2×C4—21no—
336C2×C4—22no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—84no—
347C2×C4C2×C22⋊Dic1911yescharacteristic
348C2×C4C2×C22⋊Dic1911yescharacteristic
349C2×C4#1059739912yes—
350C2×C4#1059739912yes—
351C8—1522no—
352C8—1522no—
353C22—21no—
354C22—21no—
355C22—42no—
356C22—41no—
357C22—42no—
358C22—41no—
359C22—41no—
360C22—42no—
361C22—82no—
362C22—84no—
363C22#1192640011yescharacteristic
364C22#1192652812yes—
365C4—22no—
366C4—22no—
367C4—21no—
368C4—21no—
369C4—42no—
370C4—42no—
371C4—41no—
372C4—41no—
373C4—41no—
374C4—42no—
375C2—22no—
376C2—82no—
377C2—81no—
378C2#1456356311yescharacteristic
379C2#1456360511yescharacteristic
380C2#1456361011yescharacteristic
subgroupG/H
centerC22#11926400
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC2×C19×#542C2
socleC22×C19#379
prime radicalC2×C19×#121C4
cosocleC2×C42×C19C23
hypercenterC2×#542D19
hypocenterC19#8523
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. #14562352C2semidirect
2. #14562259C2semidirect
3. #14561969C2semidirect
4. #14561969C2semidirect
264. C19#8523semidirect

Maximal subgroups

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

subgroupindex
#145623522
#145622592
#145619692
C2×C19×#5422
#852319