Finite Group Databasebeta

← #18072709

Subgroups — #18072709

Order 4864.

520 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14572267C211yesmaximal, characteristic
2#14572266C211yesmaximal, characteristic
3#14572263C211yesmaximal, characteristic
4#14561526C211yesmaximal, characteristic, complemented
5#14561525C211yesmaximal, characteristic, complemented
6#14561524C211yesmaximal, characteristic, complemented
7C19×#1299C211yesmaximal, characteristic, complemented
8C2×C42×D19C2211yescharacteristic
9#11926600—21no—
10#11926600—21no—
11#11926600C412yes—
12#11926599C412yes—
13#11926599C412yes—
14#11926598—21no—
15#11926597C2211yescharacteristic
16#11926596—21no—
17#11926596—21no—
18#11926595—21no—
19#11926595—21no—
20#11926595—21no—
21#11926568C2211yescharacteristic
22#11926567—21no—
23#11926566C412yes—
24#11926507—21no—
25#11926507C412yes—
26#11926506—21no—
27C4×#64520C2211yescharacteristic
28M16×Dic19C412yes—
29C4×#64515—21no—
30C19×#431C2211yescharacteristic
31C19×#423C2211yescharacteristic
32C4×M16×C19C2211yescharacteristic
33C22×C4×D19C2×C411yescharacteristic
34C22×C4×D19D411yescharacteristic
35C22×C4×D19Q811yescharacteristic
36C2×M16×C19—21no—
37C2×M16×C19C2×C412yes—
38C2×C42×C19C2311yescharacteristic
39C2×C4×Dic19C2×C411yescharacteristic
40C2×C4×Dic19D411yescharacteristic
41C2×C4×Dic19Q811yescharacteristic
42C2×#64520—21no—
43C2×#64520C2×C412yes—
44C2×#64515—22no—
45C42×D19C2×C411yescharacteristic
46C42×D19C2×C411yescharacteristic
47C42×D19C2×C411yescharacteristic
48C42×D19C2×C411yescharacteristic
49C42×D19D411yescharacteristic
50C42×D19D411yescharacteristic
51C42×D19D411yescharacteristic
52C42×D19D411yescharacteristic
53C19×C4⋊C8—21no—
54C19×C4⋊C8—21no—
55C19×C4⋊C8C2×C412yes—
56C19×C22⋊C8—21no—
57C19×#97C2×C412yes—
58C4×C8×C19—21no—
59C4×C8×C19—21no—
60C22⋊(C19⋊C8)—21no—
61(C2×D19)⋊C8—22no—
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—
71C8×Dic19—22no—
72C4⋊(C19⋊C8)—21no—
73C4⋊(C19⋊C8)—21no—
74C4⋊(C19⋊C8)C2×C412yes—
75#10597260C2×C412yes—
76C4×C19⋊C8—21no—
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—41no—
86C2×C4×D19—41no—
87C2×C4×D19—42no—
88C2×C4×D19—42no—
89C2×C4×D19C4211yescharacteristic
90C2×C4×D19C4211yescharacteristic
91C2×C4×D19C22⋊C411yescharacteristic
92C2×C4×D19C22⋊C411yescharacteristic
93C2×C4×D19C22⋊C411yescharacteristic
94C2×C4×D19C22⋊C411yescharacteristic
95C2×C4×D19C22⋊C411yescharacteristic
96C2×C4×D19C22⋊C411yescharacteristic
97C2×C4×D19C4⋊C411yescharacteristic
98C2×C4×D19C4⋊C411yescharacteristic
99C2×C4×D19C4⋊C411yescharacteristic
100C2×C4×D19C4⋊C411yescharacteristic
101M16×C19—42no—
102M16×C19—42no—
103C2×C8×C19—22no—
104C2×C8×C19—22no—
105C2×C8×C19—22no—
106C42×C19C22×C411yescharacteristic
107C42×C19C22×C411yescharacteristic
108C42×C19C2×D411yescharacteristic
109C42×C19C2×D411yescharacteristic
110C4×Dic19C4211yescharacteristic
111C4×Dic19C4211yescharacteristic
112C4×Dic19C22⋊C411yescharacteristic
113C4×Dic19C22⋊C411yescharacteristic
114C4×Dic19C22⋊C411yescharacteristic
115C4×Dic19C22⋊C411yescharacteristic
116C4×Dic19C22⋊C411yescharacteristic
117C4×Dic19C22⋊C411yescharacteristic
118C4×Dic19C4⋊C411yescharacteristic
119C4×Dic19C4⋊C411yescharacteristic
120C4×Dic19C4⋊C411yescharacteristic
121C4×Dic19C4⋊C411yescharacteristic
122#64520—42no—
123#64520—42no—
124C2×C19⋊C8—22no—
125C2×C19⋊C8—22no—
126C2×C19⋊C8—22no—
127#64515—44no—
128#8062—191nomaximal, Sylow
129C23×C19C2×C4⋊C411yescharacteristic
130C22×D19—41no—
131C22×D19—41no—
132C22×D19—41no—
133C22×D19#9511yescharacteristic
134C22×D19#9511yescharacteristic
135C2×C4×C19—21no—
136C2×C4×C19—21no—
137C2×C4×C19—22no—
138C2×C4×C19—22no—
139C2×C4×C19C2×C4211yescharacteristic
140C2×C4×C19C2×C22⋊C411yescharacteristic
141C2×C4×C19C2×C22⋊C411yescharacteristic
142C2×C4×C19C2×C22⋊C411yescharacteristic
143C2×C4×C19C2×C4⋊C411yescharacteristic
144C2×C4×C19C2×C4⋊C411yescharacteristic
145C2×Dic19—41no—
146C2×Dic19—41no—
147C2×Dic19—41no—
148C2×Dic19#9511yescharacteristic
149C2×Dic19#9511yescharacteristic
150C2×Dic19#9511yescharacteristic
151C2×Dic19#9511yescharacteristic
152C2×Dic19#9511yescharacteristic
153C2×Dic19#9511yescharacteristic
154C4×D19—21no—
155C4×D19—21no—
156C4×D19—21no—
157C4×D19—21no—
158C4×D19—22no—
159C4×D19—22no—
160C4×D19—22no—
161C4×D19—22no—
162C4×D19—41no—
163C4×D19—41no—
164C4×D19—41no—
165C4×D19—41no—
166C4×D19—41no—
167C4×D19—41no—
168C8×C19—42no—
169C8×C19—42no—
170C8×C19—42no—
171C19⋊C8—42no—
172C19⋊C8—42no—
173C19⋊C8—42no—
174#2920—191no—
175#2920—191no—
176#2920—191no—
177#1299—191no—
178#1299—191no—
179#1299—191no—
180#1299D1911yescharacteristic, complemented
181C22×C19—21no—
182C22×C19—21no—
183C22×C19—21no—
184C22×C19C2×#9511yescharacteristic
185C2×D19—21no—
186C2×D19—21no—
187C2×D19—21no—
188C2×D19—21no—
189C2×D19—21no—
190C2×D19—21no—
191C2×D19—44no—
192C4×C19—21no—
193C4×C19—21no—
194C4×C19—21no—
195C4×C19#41311yescharacteristic
196C4×C19#41311yescharacteristic
197C4×C19#42112yes—
198C4×C19#43012yes—
199Dic19—21no—
200Dic19—21no—
201Dic19—21no—
202Dic19—21no—
203Dic19—21no—
204Dic19—21no—
205C22×C42—191no—
206#432—192no—
207#432—192no—
208#432—192no—
209#432—381no—
210#432—381no—
211#432—381no—
212#431—191no—
213#431—381no—
214#431—381no—
215#431—381no—
216#431—381no—
217#431—381no—
218#431C2×D1911yescharacteristic
219#423—192no—
220#423—191no—
221#423—381no—
222#423C2×D1911yescharacteristic
223#407—192no—
224#407—381no—
225#407—381no—
226C4×M16—191no—
227C4×M16—192no—
228C4×M16—381no—
229C4×M16C2×D1911yescharacteristic
230C2×C19—41no—
231C2×C19#173311yescharacteristic
232C2×C19#173811yescharacteristic
233C2×C19#174211yescharacteristic
234D19—41no—
235D19—41no—
236C23×C4—191no—
237C23×C4—191no—
238C23×C4—191no—
239C2×M16—21no—
240C2×M16—192no—
241C2×M16—382no—
242C2×M16—381no—
243C2×M16C4×D1912yes—
244C2×C42—191no—
245C2×C42—191no—
246C2×C42—191no—
247C2×C42—191no—
248C2×C42—191no—
249C2×C42—191no—
250C2×C42—191no—
251C2×C42—191no—
252C2×C42—191no—
253C2×C42—191no—
254C2×C42—191no—
255C2×C42C22×D1911yescharacteristic
256C4⋊C8—21no—
257C4⋊C8—21no—
258C4⋊C8—192no—
259C4⋊C8—382no—
260C4⋊C8—382no—
261C4⋊C8—382no—
262C4⋊C8—381no—
263C4⋊C8—381no—
264C4⋊C8C4×D1912yes—
265C22⋊C8—21no—
266C22⋊C8—382no—
267C22⋊C8—382no—
268C22⋊C8—382no—
269C22⋊C8—382no—
270C22⋊C8—382no—
271C22⋊C8—381no—
272#97—192no—
273#97—382no—
274#97—382no—
275#97C4×D1912yes—
276C4×C8—21no—
277C4×C8—21no—
278C4×C8—382no—
279C4×C8—381no—
280C4×C8—381no—
281C19#806211yescharacteristic, complemented, Sylow
282C24—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—191no—
293C22×C4—191no—
294C22×C4—191no—
295C22×C4—191no—
296C22×C4—191no—
297C22×C4—191no—
298C22×C4—762no—
299C22×C4—762no—
300C22×C4—761no—
301C22×C4—761no—
302C22×C4C2×C4×D1911yescharacteristic
303C22×C4D4×D1911yescharacteristic
304C22×C4Q8×D1911yescharacteristic
305M16—42no—
306M16—42no—
307M16—764no—
308M16—762no—
309M16—762no—
310C2×C8—22no—
311C2×C8—22no—
312C2×C8—22no—
313C2×C8—382no—
314C2×C8—382no—
315C2×C8—382no—
316C42—191no—
317C42—191no—
318C42—191no—
319C42—191no—
320C42—191no—
321C42—191no—
322C42—191no—
323C42—191no—
324C42—191no—
325C42—191no—
326C42—191no—
327C42—191no—
328C42C2×C4×D1911yescharacteristic
329C42C2×C4×D1911yescharacteristic
330C42D4×D1911yescharacteristic
331C42D4×D1911yescharacteristic
332C23—191no—
333C23—191no—
334C23—761no—
335C23—761no—
336C23—761no—
337C23C4⋊C4×D1911yescharacteristic
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—191no—
343C2×C4—191no—
344C2×C4—191no—
345C2×C4—191no—
346C2×C4—191no—
347C2×C4—191no—
348C2×C4—382no—
349C2×C4—382no—
350C2×C4—382no—
351C2×C4—382no—
352C2×C4—381no—
353C2×C4—381no—
354C2×C4—381no—
355C2×C4—381no—
356C2×C4—761no—
357C2×C4—761no—
358C2×C4—761no—
359C2×C4—761no—
360C2×C4—761no—
361C2×C4—761no—
362C2×C4—761no—
363C2×C4—761no—
364C2×C4—761no—
365C2×C4C42×D1911yescharacteristic
366C2×C4C22⋊C4×D1911yescharacteristic
367C2×C4C22⋊C4×D1911yescharacteristic
368C2×C4C22⋊C4×D1911yescharacteristic
369C2×C4C4⋊C4×D1911yescharacteristic
370C2×C4C4⋊C4×D1911yescharacteristic
371C8—42no—
372C8—42no—
373C8—42no—
374C8—762no—
375C8—762no—
376C8—762no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—381no—
381C22—381no—
382C22—381no—
383C22—381no—
384C22—381no—
385C22—381no—
386C22—764no—
387C22#95×D1911yescharacteristic
388C4—21no—
389C4—21no—
390C4—21no—
391C4—381no—
392C4—381no—
393C4—381no—
394C4—381no—
395C4—381no—
396C4—381no—
397C4#1192652511yescharacteristic
398C4#1192652711yescharacteristic
399C4#1192655912yes—
400C4#1192659112yes—
401C2—41no—
402C2—761no—
403C2—761no—
404C2#1456334311yescharacteristic
405C2#1456336011yescharacteristic
406C2#1456337211yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D19
commutatorC2×C4×C19C2×C42
FrattiniC2×C42C22×D19
FittingC19×#1299C2
socleC22×C19C2×#95
prime radicalC23×D19C4⋊C4
cosocleC2×C42×C19C23
hypercenter#1299D19
hypocenterC19#8062
LCSG ▷ C2×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1299

Complements

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

NH ≅ G/Ntype
4. #14561526C2semidirect
5. #14561525C2semidirect
6. #14561524C2semidirect
7. C19×#1299C2semidirect
180. #1299D19semidirect
281. C19#8062semidirect

Maximal subgroups

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

subgroupindex
#145722672
#145722662
#145722632
#145615262
#145615252
#145615242
C19×#12992
#806219