Finite Group Databasebeta

← #18072801

Subgroups — #18072801

Order 4864.

524 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14572263C211yesmaximal, characteristic
2C2×#11926599C211yesmaximal, characteristic
3D19×#432C211yesmaximal, characteristic
4#14561535C211yesmaximal, characteristic, complemented
5#14561534C211yesmaximal, characteristic, complemented
6#14561533C211yesmaximal, characteristic, complemented
7C19×#1302C211yesmaximal, characteristic, complemented
8C2×C42×D19C2211yescharacteristic
9#11926601C2211yescharacteristic
10#11926600—21no—
11#11926600C412yes—
12#11926599—21no—
13#11926599—21no—
14#11926599—21no—
15#11926599C412yes—
16#11926599C412yes—
17#11926598—21no—
18#11926598C412yes—
19#11926597C2211yescharacteristic
20#11926595—21no—
21#11926566—21no—
22C2×Dic19⋊C8—21no—
23C4⋊C8×D19C412yes—
24#11926506C412yes—
25C2×(C2×D19)⋊C8—21no—
26C22⋊C8×D19—21no—
27C4×#64515—21no—
28C2×#10597260C2211yescharacteristic
29#97×D19—21no—
30C19×#432C2211yescharacteristic
31C19×#431C2211yescharacteristic
32C2×C19×#97C2211yescharacteristic
33C22×C4×D19C2×C411yescharacteristic
34C22×C4×D19D411yescharacteristic
35C22×C4×D19Q811yescharacteristic
36C22×C8×C19—21no—
37C2×C42×C19C2311yescharacteristic
38C2×C4×Dic19C2×C411yescharacteristic
39C2×C4×Dic19D411yescharacteristic
40C2×C4×Dic19Q811yescharacteristic
41C22×C19⋊C8—21no—
42C2×#64515—22no—
43C2×C8×D19—22no—
44C42×D19C2×C411yescharacteristic
45C42×D19C2×C411yescharacteristic
46C42×D19C2×C411yescharacteristic
47C42×D19C2×C411yescharacteristic
48C42×D19D411yescharacteristic
49C42×D19D411yescharacteristic
50C42×D19D411yescharacteristic
51C42×D19D411yescharacteristic
52C19×C4⋊C8—21no—
53C19×C4⋊C8C2×C412yes—
54C19×C22⋊C8—21no—
55C19×C22⋊C8C2×C412yes—
56C19×#97—21no—
57C19×#97—21no—
58C19×#97C2×C412yes—
59C4×C8×C19—21no—
60C22⋊(C19⋊C8)—21no—
61C22⋊(C19⋊C8)C2×C412yes—
62(C2×D19)⋊C8—22no—
63(C2×D19)⋊C8—22no—
64(C2×D19)⋊C8—22no—
65(C2×D19)⋊C8—22no—
66#10597272—22no—
67#10597272—22no—
68Dic19⋊C8—22no—
69Dic19⋊C8—22no—
70Dic19⋊C8—22no—
71Dic19⋊C8—22no—
72C4⋊(C19⋊C8)—21no—
73C4⋊(C19⋊C8)C2×C412yes—
74#10597260—21no—
75#10597260—21no—
76#10597260C2×C412yes—
77C4×C19⋊C8—21no—
78C23×D19C4⋊C411yescharacteristic
79C22×C4×C19C22×C411yescharacteristic
80C22×C4×C19C2×D411yescharacteristic
81C22×C4×C19C2×Q811yescharacteristic
82C22×Dic19C4⋊C411yescharacteristic
83C22×Dic19C4⋊C411yescharacteristic
84C22×Dic19C4⋊C411yescharacteristic
85C2×C4×D19—42no—
86C2×C4×D19—42no—
87C2×C4×D19—42no—
88C2×C4×D19C4211yescharacteristic
89C2×C4×D19C4211yescharacteristic
90C2×C4×D19C22⋊C411yescharacteristic
91C2×C4×D19C22⋊C411yescharacteristic
92C2×C4×D19C22⋊C411yescharacteristic
93C2×C4×D19C22⋊C411yescharacteristic
94C2×C4×D19C22⋊C411yescharacteristic
95C2×C4×D19C22⋊C411yescharacteristic
96C2×C4×D19C4⋊C411yescharacteristic
97C2×C4×D19C4⋊C411yescharacteristic
98C2×C4×D19C4⋊C411yescharacteristic
99C2×C4×D19C4⋊C411yescharacteristic
100C2×C8×C19—22no—
101C2×C8×C19—22no—
102C2×C8×C19—22no—
103C2×C8×C19—42no—
104C42×C19C22×C411yescharacteristic
105C42×C19C22×C411yescharacteristic
106C42×C19C2×D411yescharacteristic
107C42×C19C2×D411yescharacteristic
108C4×Dic19C4211yescharacteristic
109C4×Dic19C4211yescharacteristic
110C4×Dic19C22⋊C411yescharacteristic
111C4×Dic19C22⋊C411yescharacteristic
112C4×Dic19C22⋊C411yescharacteristic
113C4×Dic19C22⋊C411yescharacteristic
114C4×Dic19C22⋊C411yescharacteristic
115C4×Dic19C22⋊C411yescharacteristic
116C4×Dic19C4⋊C411yescharacteristic
117C4×Dic19C4⋊C411yescharacteristic
118C4×Dic19C4⋊C411yescharacteristic
119C4×Dic19C4⋊C411yescharacteristic
120C2×C19⋊C8—22no—
121C2×C19⋊C8—22no—
122C2×C19⋊C8—22no—
123C2×C19⋊C8—42no—
124#64515—44no—
125C8×D19—44no—
126#8085—191nomaximal, Sylow
127C23×C19C2×C4⋊C411yescharacteristic
128C22×D19—22no—
129C22×D19—22no—
130C22×D19—41no—
131C22×D19#9511yescharacteristic
132C22×D19#9511yescharacteristic
133C2×C4×C19—22no—
134C2×C4×C19—22no—
135C2×C4×C19—41no—
136C2×C4×C19C2×C4211yescharacteristic
137C2×C4×C19C2×C22⋊C411yescharacteristic
138C2×C4×C19C2×C22⋊C411yescharacteristic
139C2×C4×C19C2×C22⋊C411yescharacteristic
140C2×C4×C19C2×C4⋊C411yescharacteristic
141C2×C4×C19C2×C4⋊C411yescharacteristic
142C2×Dic19—22no—
143C2×Dic19—41no—
144C2×Dic19—41no—
145C2×Dic19#9511yescharacteristic
146C2×Dic19#9511yescharacteristic
147C2×Dic19#9511yescharacteristic
148C2×Dic19#9511yescharacteristic
149C2×Dic19#9511yescharacteristic
150C2×Dic19#9511yescharacteristic
151C4×D19—22no—
152C4×D19—22no—
153C4×D19—22no—
154C4×D19—22no—
155C4×D19—41no—
156C4×D19—41no—
157C4×D19—41no—
158C4×D19—41no—
159C4×D19—41no—
160C4×D19—41no—
161C4×D19—41no—
162C4×D19—41no—
163C8×C19—42no—
164C8×C19—42no—
165C8×C19—42no—
166C19⋊C8—42no—
167C19⋊C8—42no—
168C19⋊C8—42no—
169#2920—191no—
170C2×#432—191no—
171C2×#432—191no—
172#1302—191no—
173#1302—191no—
174#1302—191no—
175#1302D1911yescharacteristic, complemented
176C22×C19—21no—
177C22×C19—21no—
178C22×C19C2×#9511yescharacteristic
179C22×C19#43012yes—
180C2×D19—21no—
181C2×D19—21no—
182C2×D19—21no—
183C2×D19—21no—
184C2×D19—21no—
185C2×D19—44no—
186C2×D19#34412yes—
187C4×C19—21no—
188C4×C19—21no—
189C4×C19—21no—
190C4×C19—21no—
191C4×C19—21no—
192C4×C19#42112yes—
193Dic19—21no—
194Dic19—21no—
195Dic19—21no—
196Dic19—21no—
197Dic19—21no—
198Dic19—21no—
199C22×C42—191no—
200#432—192no—
201#432—192no—
202#432—192no—
203#432—191no—
204#432—192no—
205#432—381no—
206#432—381no—
207#432—381no—
208#432—381no—
209#432—381no—
210#432C2×D1911yescharacteristic
211#431—191no—
212#431—381no—
213#431C2×D1911yescharacteristic
214#423—381no—
215C2×C4⋊C8—192no—
216C2×C4⋊C8—381no—
217#407—192no—
218C2×C22⋊C8—381no—
219C2×C22⋊C8—381no—
220C4×M16—381no—
221C2×#97—191no—
222C2×#97—381no—
223C2×#97C2×D1911yescharacteristic
224C2×C19—22no—
225C2×C19#173311yescharacteristic
226C2×C19#173811yescharacteristic
227C2×C19C2×#34411yescharacteristic
228D19—22no—
229D19—41no—
230C23×C4—191no—
231C23×C4—191no—
232C23×C4—191no—
233C2×M16—382no—
234C22×C8—21no—
235C22×C8—382no—
236C22×C8—381no—
237C2×C42—191no—
238C2×C42—191no—
239C2×C42—191no—
240C2×C42—191no—
241C2×C42—191no—
242C2×C42—191no—
243C2×C42—191no—
244C2×C42—191no—
245C2×C42—191no—
246C2×C42—191no—
247C2×C42—191no—
248C2×C42C22×D1911yescharacteristic
249C4⋊C8—21no—
250C4⋊C8—192no—
251C4⋊C8—382no—
252C4⋊C8—382no—
253C4⋊C8—382no—
254C4⋊C8—382no—
255C4⋊C8—381no—
256C4⋊C8C4×D1912yes—
257C22⋊C8—21no—
258C22⋊C8—192no—
259C22⋊C8—382no—
260C22⋊C8—382no—
261C22⋊C8—382no—
262C22⋊C8—382no—
263C22⋊C8—381no—
264C22⋊C8C4×D1912yes—
265#97—21no—
266#97—21no—
267#97—192no—
268#97—382no—
269#97—382no—
270#97—381no—
271#97—381no—
272#97C4×D1912yes—
273C4×C8—21no—
274C4×C8—381no—
275C19#808511yescharacteristic, complemented, Sylow
276C24—191no—
277C22×C4—191no—
278C22×C4—191no—
279C22×C4—191no—
280C22×C4—191no—
281C22×C4—191no—
282C22×C4—191no—
283C22×C4—191no—
284C22×C4—191no—
285C22×C4—191no—
286C22×C4—191no—
287C22×C4—191no—
288C22×C4—191no—
289C22×C4—191no—
290C22×C4—191no—
291C22×C4—191no—
292C22×C4—762no—
293C22×C4—762no—
294C22×C4—762no—
295C22×C4C2×C4×D1911yescharacteristic
296C22×C4D4×D1911yescharacteristic
297C22×C4Q8×D1911yescharacteristic
298M16—764no—
299C2×C8—22no—
300C2×C8—22no—
301C2×C8—22no—
302C2×C8—42no—
303C2×C8—382no—
304C2×C8—382no—
305C2×C8—382no—
306C2×C8—764no—
307C2×C8—762no—
308C42—191no—
309C42—191no—
310C42—191no—
311C42—191no—
312C42—191no—
313C42—191no—
314C42—191no—
315C42—191no—
316C42—191no—
317C42—191no—
318C42—191no—
319C42—191no—
320C42C2×C4×D1911yescharacteristic
321C42C2×C4×D1911yescharacteristic
322C42D4×D1911yescharacteristic
323C42D4×D1911yescharacteristic
324C23—191no—
325C23—191no—
326C23—382no—
327C23—382no—
328C23—761no—
329C23C4⋊C4×D1911yescharacteristic
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—41no—
333C2×C4—191no—
334C2×C4—191no—
335C2×C4—191no—
336C2×C4—191no—
337C2×C4—191no—
338C2×C4—191no—
339C2×C4—382no—
340C2×C4—382no—
341C2×C4—382no—
342C2×C4—382no—
343C2×C4—382no—
344C2×C4—761no—
345C2×C4—761no—
346C2×C4—761no—
347C2×C4—761no—
348C2×C4—761no—
349C2×C4—761no—
350C2×C4—761no—
351C2×C4—761no—
352C2×C4—761no—
353C2×C4—761no—
354C2×C4C42×D1911yescharacteristic
355C2×C4C22⋊C4×D1911yescharacteristic
356C2×C4C22⋊C4×D1911yescharacteristic
357C2×C4C22⋊C4×D1911yescharacteristic
358C2×C4C4⋊C4×D1911yescharacteristic
359C2×C4C4⋊C4×D1911yescharacteristic
360C8—42no—
361C8—42no—
362C8—42no—
363C8—762no—
364C8—762no—
365C8—762no—
366C22—21no—
367C22—21no—
368C22—192no—
369C22—381no—
370C22—381no—
371C22—381no—
372C22—381no—
373C22—381no—
374C22—764no—
375C22#95×D1911yescharacteristic
376C22#1192659112yes—
377C4—21no—
378C4—21no—
379C4—21no—
380C4—21no—
381C4—21no—
382C4—381no—
383C4—381no—
384C4—381no—
385C4—381no—
386C4—381no—
387C4—381no—
388C4#1192655912yes—
389C2—22no—
390C2—382no—
391C2—761no—
392C2#1456334311yescharacteristic
393C2#1456336011yescharacteristic
394C2D19×#34411yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D19
commutatorC2×C4×C19C2×C42
FrattiniC2×C42C22×D19
FittingC19×#1302C2
socleC22×C19C2×#95
prime radicalC23×D19C4⋊C4
cosocleC2×C42×C19C23
hypercenter#1302D19
hypocenterC19#8085
LCSG ▷ C2×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1302

Complements

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

NH ≅ G/Ntype
4. #14561535C2semidirect
5. #14561534C2semidirect
6. #14561533C2semidirect
7. C19×#1302C2semidirect
175. #1302D19semidirect
275. C19#8085semidirect

Maximal subgroups

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

subgroupindex
#145722632
C2×#119265992
D19×#4322
#145615352
#145615342
#145615332
C19×#13022
#808519