Finite Group Databasebeta

← #18079366

Subgroups — #18079366

Order 4864.

428 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14572286C211yesmaximal, characteristic, complemented
2#14562246C211yesmaximal, characteristic, complemented
3#14562069C211yesmaximal, characteristic, complemented
4#14562052C211yesmaximal, characteristic, complemented
5#14561533C211yesmaximal, characteristic, complemented
6#14561506C211yesmaximal, characteristic, complemented
7C19×#3115C211yesmaximal, characteristic
8#11926605—22no—
9#11926601—22no—
10#11926601C2211yescharacteristic
11#11926597C2211yescharacteristic
12#11926571—21no—
13#11926511—21no—
14C4×#64520C2211yescharacteristic
15C2×#10597260C2211yescharacteristic
16#11926284—22no—
17Q8⋊(C19⋊C8)—21no—
18D4⋊(C19⋊C8)—22no—
19D4⋊(C19⋊C8)—21no—
20C19×#532C2211yescharacteristic
21C4×#41×C19C2211yescharacteristic
22C19×#482—21no—
23C19×#475C411yescharacteristic
24C19×#474C411yescharacteristic
25C19×#460C411yescharacteristic
26C19×#459C411yescharacteristic
27C19×#449—21no—
28C19×#442—21no—
29C19×#440—21no—
30C19×#432C2211yescharacteristic
31C2×#41×C19—21no—
32C2×#41×C19D411yescharacteristic
33C2×SD16×C19—21no—
34C2×D8×C19—21no—
35C19×C4⋊Q8C2×C411yescharacteristic
36C19×#127C2×C411yescharacteristic
37C19×#124—21no—
38C19×#121—21no—
39C19×#121—21no—
40C4×Q8×C19C2×C411yescharacteristic
41C4×Q8×C19D411yescharacteristic
42C4×D4×C19—21no—
43C4×D4×C19—21no—
44C4×D4×C19—21no—
45C4×D4×C19—21no—
46C4×D4×C19C2×C411yescharacteristic
47C4×D4×C19D411yescharacteristic
48C19×#117—21no—
49C19×#117D411yescharacteristic
50C2×C42×C19—21no—
51C2×C42×C19C2311yescharacteristic
52C2×#64520—21no—
53C22×C19⋊C8—21no—
54C19×#107—21no—
55C19×#106—21no—
56C19×C4⋊C8C2×C411yescharacteristic
57C19×C4⋊C8C2×C411yescharacteristic
58C19×#103—21no—
59C19×#102—21no—
60C19×#102—21no—
61C19×#102—21no—
62C19×C22⋊C8—21no—
63C19×#97—21no—
64C22⋊(C19⋊C8)—24no—
65C22⋊(C19⋊C8)—21no—
66C22⋊(C19⋊C8)—21no—
67C4⋊(C19⋊C8)—24no—
68C4⋊(C19⋊C8)—21no—
69C4⋊(C19⋊C8)—21no—
70#10597260—21no—
71#10597260—21no—
72#10597260—21no—
73#10597260D412yes—
74C4×C19⋊C8—21no—
75C4×C19⋊C8D412yes—
76#41×C19—41no—
77#41×C19—41no—
78#41×C19—82no—
79C2×Q8×C19—21no—
80C2×Q8×C19C22⋊C411yescharacteristic
81C2×D4×C19—21no—
82C2×D4×C19—21no—
83C2×D4×C19—21no—
84C2×D4×C19—21no—
85C2×D4×C19—41no—
86C2×D4×C19C22⋊C411yescharacteristic
87C22×C4×C19—21no—
88C22×C4×C19—21no—
89C22×C4×C19—21no—
90C22×C4×C19—41no—
91C22×C4×C19C2×D411yescharacteristic
92C22×C4×C19#4111yescharacteristic
93C22×C4×C19#4111yescharacteristic
94SD16×C19—42no—
95D8×C19—42no—
96C2×C8×C19—21no—
97C2×C8×C19—21no—
98C4⋊C4×C19—21no—
99C4⋊C4×C19—21no—
100C4⋊C4×C19—21no—
101C4⋊C4×C19—21no—
102C4⋊C4×C19C22⋊C411yescharacteristic
103C4⋊C4×C19C22⋊C411yescharacteristic
104C22⋊C4×C19—21no—
105C22⋊C4×C19—21no—
106C22⋊C4×C19—21no—
107C22⋊C4×C19—41no—
108C22⋊C4×C19—41no—
109C42×C19—21no—
110C42×C19—21no—
111C42×C19—21no—
112C42×C19C22×C411yescharacteristic
113C42×C19C2×D411yescharacteristic
114C42×C19C2×D411yescharacteristic
115C42×C19C2×D411yescharacteristic
116#64520—41no—
117#64520—41no—
118C2×C19⋊C8—22no—
119C2×C19⋊C8—22no—
120C2×C19⋊C8—41no—
121C2×C19⋊C8—41no—
122C2×C19⋊C8—41no—
123C2×C19⋊C8—41no—
124#9313—191nomaximal, Sylow
125C23×C19—21no—
126C23×C19—41no—
127C23×C19#12311yescharacteristic
128Q8×C19—21no—
129Q8×C19—21no—
130Q8×C19—81no—
131D4×C19—21no—
132D4×C19—21no—
133D4×C19—42no—
134D4×C19—42no—
135D4×C19—41no—
136D4×C19—41no—
137D4×C19—81no—
138D4×C19—82no—
139C2×C4×C19—21no—
140C2×C4×C19—21no—
141C2×C4×C19—21no—
142C2×C4×C19—21no—
143C2×C4×C19—21no—
144C2×C4×C19—41no—
145C2×C4×C19—41no—
146C2×C4×C19—42no—
147C2×C4×C19—41no—
148C2×C4×C19—81no—
149C2×C4×C19—81no—
150C2×C4×C19—82no—
151C2×C4×C19C2×C22⋊C411yescharacteristic
152C2×C4×C19C4×D411yescharacteristic
153C2×C4×C19C4×D411yescharacteristic
154C2×C4×C19#12011yescharacteristic
155C2×C4×C19#12111yescharacteristic
156C2×C4×C19#12111yescharacteristic
157C8×C19—41no—
158C8×C19—41no—
159C19⋊C8—42no—
160C19⋊C8—42no—
161C19⋊C8—81no—
162C19⋊C8—81no—
163#3115D1911yescharacteristic
164#2923—191no—
165#1530—191no—
166#1488—191no—
167#1484—191no—
168#1302—191no—
169#1291—191no—
170C22×C19—21no—
171C22×C19—21no—
172C22×C19—21no—
173C22×C19—41no—
174C22×C19—41no—
175C22×C19—41no—
176C22×C19—81no—
177C22×C19—81no—
178C22×C19—81no—
179C22×C19#38611yescharacteristic
180C4×C19—21no—
181C4×C19—21no—
182C4×C19—21no—
183C4×C19—21no—
184C4×C19—21no—
185C4×C19—41no—
186C4×C19—41no—
187C4×C19—41no—
188C4×C19—81no—
189C4×C19#42111yescharacteristic
190C4×C19#42111yescharacteristic
191#532C2×D1911yescharacteristic
192C4×#41C2×D1911yescharacteristic
193#482—21no—
194#475Dic1911yescharacteristic
195#474Dic1911yescharacteristic
196#460Dic1911yescharacteristic
197#459Dic1911yescharacteristic
198#449—21no—
199#442—21no—
200#440—21no—
201#433—382no—
202#432—191no—
203#432—382no—
204#432C2×D1911yescharacteristic
205#431—191no—
206#424—381no—
207#408—381no—
208C4×M16—191no—
209C2×#97—191no—
210#329—382no—
211Q8⋊C8—381no—
212D4⋊C8—382no—
213D4⋊C8—381no—
214C2×C19—41no—
215C2×C19—81no—
216C2×C19—161no—
217C2×C19#188111yescharacteristic
218C2×C19#189711yescharacteristic
219C2×C19#190311yescharacteristic
220C2×#41—21no—
221C2×#41C22⋊D1911yescharacteristic
222C2×SD16—21no—
223C2×D8—21no—
224C2×M16—381no—
225C22×C8—381no—
226C4⋊Q8C2×Dic1911yescharacteristic
227#127C2×Dic1911yescharacteristic
228#124—21no—
229#121—21no—
230#121—21no—
231C4×Q8C2×Dic1911yescharacteristic
232C4×Q8C22⋊D1911yescharacteristic
233C4×D4—21no—
234C4×D4—21no—
235C4×D4—21no—
236C4×D4—21no—
237C4×D4C2×Dic1911yescharacteristic
238C4×D4C22⋊D1911yescharacteristic
239#117—21no—
240#117C22⋊D1911yescharacteristic
241C2×C42—21no—
242C2×C42C22×D1911yescharacteristic
243#107—21no—
244#106—21no—
245C4⋊C8—384no—
246C4⋊C8—381no—
247C4⋊C8—381no—
248C4⋊C8C2×Dic1911yescharacteristic
249C4⋊C8C2×Dic1911yescharacteristic
250#103—21no—
251#102—21no—
252#102—21no—
253#102—21no—
254C22⋊C8—21no—
255C22⋊C8—384no—
256C22⋊C8—381no—
257C22⋊C8—381no—
258#97—21no—
259#97—192no—
260#97—381no—
261#97—381no—
262#97—381no—
263C4×C8—192no—
264C4×C8—381no—
265C19#931311yescharacteristic, complemented, Sylow
266#41—41no—
267#41—41no—
268#41—82no—
269C2×Q8—21no—
270C2×Q8C22⋊Dic1911yescharacteristic
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—21no—
275C2×D4—41no—
276C2×D4C22⋊Dic1911yescharacteristic
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—41no—
281C22×C4#6454311yescharacteristic
282C22×C4#6454311yescharacteristic
283C22×C4C2×C22⋊D1911yescharacteristic
284SD16—42no—
285D8—42no—
286M16—761no—
287M16—761no—
288C2×C8—21no—
289C2×C8—21no—
290C2×C8—382no—
291C2×C8—382no—
292C2×C8—761no—
293C2×C8—761no—
294C2×C8—761no—
295C2×C8—761no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4C22⋊Dic1911yescharacteristic
301C4⋊C4C22⋊Dic1911yescharacteristic
302C22⋊C4—21no—
303C22⋊C4—21no—
304C22⋊C4—21no—
305C22⋊C4—41no—
306C22⋊C4—41no—
307C42—21no—
308C42—21no—
309C42—21no—
310C42D4×D1911yescharacteristic
311C42D4×D1911yescharacteristic
312C42C22×Dic1911yescharacteristic
313C42C2×C22⋊D1911yescharacteristic
314C23—21no—
315C23—41no—
316C23#1059738111yescharacteristic
317Q8—21no—
318Q8—21no—
319Q8—81no—
320D4—21no—
321D4—21no—
322D4—42no—
323D4—42no—
324D4—41no—
325D4—41no—
326D4—81no—
327D4—82no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—42no—
336C2×C4—41no—
337C2×C4—81no—
338C2×C4—81no—
339C2×C4—82no—
340C2×C4D4×Dic1911yescharacteristic
341C2×C4D4×Dic1911yescharacteristic
342C2×C4#1059738311yescharacteristic
343C2×C4#1059738511yescharacteristic
344C2×C4#1059738511yescharacteristic
345C2×C4C2×C22⋊Dic1911yescharacteristic
346C8—41no—
347C8—41no—
348C8—762no—
349C8—762no—
350C8—1521no—
351C8—1521no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—81no—
359C22—81no—
360C22—81no—
361C22#1192642411yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—21no—
366C4—21no—
367C4—41no—
368C4—41no—
369C4—41no—
370C4—81no—
371C4#1192656111yescharacteristic
372C4#1192656111yescharacteristic
373C2—41no—
374C2—81no—
375C2—161no—
376C2#1456399911yescharacteristic
377C2#1456408411yescharacteristic
378C2#1456411711yescharacteristic
subgroupG/H
centerC22#11926424
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
Fitting, prime radicalC19×#3115C2
socleC22×C19#386
cosocleC2×C42×C19C23
hypercenter#3115D19
hypocenterC19#9313
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3115

Complements

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

NH ≅ G/Ntype
1. #14572286C2semidirect
2. #14562246C2semidirect
3. #14562069C2semidirect
4. #14562052C2semidirect
5. #14561533C2semidirect
6. #14561506C2semidirect
265. C19#9313semidirect

Maximal subgroups

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

subgroupindex
#145722862
#145622462
#145620692
#145620522
#145615332
#145615062
C19×#31152
#931319