Finite Group Databasebeta

← #18076439

Subgroups — #18076439

Order 4864.

440 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14572753C211yesmaximal, characteristic
2#14563786C211yesmaximal, characteristic, complemented
3C4×#10597282C211yesmaximal, characteristic
4#14562387C211yesmaximal, characteristic, complemented
5#14562023C211yesmaximal, characteristic
6#14561467C211yesmaximal, characteristic, complemented
7C19×#1283C211yesmaximal, characteristic, complemented
8C4×#64541C2211yescharacteristic
9#11926671—21no—
10#11926621—21no—
11#11926615—22no—
12#11926600—21no—
13#11926597C2211yescharacteristic
14#11926566—21no—
15C2×C4⋊(C19⋊C8)C2211yescharacteristic
16C2×Dic19⋊C8—22no—
17C2×#10597282C411yescharacteristic
18C2×#10597282C411yescharacteristic
19C42×Dic19C2211yescharacteristic
20#11926305C411yescharacteristic
21#11926305C411yescharacteristic
22#11926297—21no—
23#11926295—21no—
24#11926276—21no—
25#11926273—21no—
26C19×#431C2211yescharacteristic
27C2×C19×C4⋊C8C2211yescharacteristic
28C4×M16×C19C2211yescharacteristic
29C2×#64541C2×C411yescharacteristic
30C2×M16×C19C2×C411yescharacteristic
31C2×M16×C19C2×C411yescharacteristic
32C22×C8×C19D412yes—
33C2×C42×C19C2311yescharacteristic
34C4×C22⋊D19—21no—
35C4×C22⋊D19—21no—
36#10597372C2×C411yescharacteristic
37C2×C4×Dic19—21no—
38C2×C4×Dic19—21no—
39C2×C4×Dic19C2×C411yescharacteristic
40C2×C4×Dic19C2×C411yescharacteristic
41C22×C19⋊C8—21no—
42C2×#64515—22no—
43C4×D76D411yescharacteristic
44C4×D76Q811yescharacteristic
45#10597318—21no—
46C42×D19—21no—
47C4×Dic38D411yescharacteristic
48C4×Dic38Q811yescharacteristic
49C19×C4⋊C8—21no—
50C19×C4⋊C8—21no—
51C19×C4⋊C8—21no—
52C19×C22⋊C8—21no—
53C19×#97—21no—
54C4×C8×C19—21no—
55C4×C8×C19—21no—
56C22⋊(C19⋊C8)—21no—
57#10597282—22no—
58#10597282—22no—
59(C2×D19)⋊C8—22no—
60#10597272—22no—
61Dic19⋊C8—22no—
62Dic19⋊C8—44no—
63C4⋊(C19⋊C8)—21no—
64C4⋊(C19⋊C8)—21no—
65C4⋊(C19⋊C8)D411yescharacteristic
66C4⋊(C19⋊C8)D411yescharacteristic
67C4×C19⋊C8—21no—
68C22×C4×C19C22×C411yescharacteristic
69C22×C4×C19C2×D411yescharacteristic
70C22×C4×C19#4111yescharacteristic
71C2×C22⋊D19—21no—
72C22×Dic19—21no—
73C22×Dic19—21no—
74#64541—21no—
75#64541—21no—
76#64541—21no—
77#64541—21no—
78C2×D76C4⋊C411yescharacteristic
79C2×C4×D19—21no—
80C2×C4×D19—21no—
81C2×C4×D19—21no—
82C2×Dic38C4⋊C411yescharacteristic
83M16×C19—21no—
84M16×C19—21no—
85M16×C19—21no—
86M16×C19M1612yescomplemented
87C2×C8×C19—21no—
88C2×C8×C19—21no—
89C2×C8×C19—22no—
90C2×C8×C19—42no—
91C2×C8×C19—41no—
92C42×C19C2×D411yescharacteristic
93C42×C19C2×D411yescharacteristic
94C42×C19C2×Q811yescharacteristic
95C42×C19#4111yescharacteristic
96C22⋊Dic19—21no—
97(C2×D19)⋊C4—21no—
98(C2×D19)⋊C4—21no—
99C4⋊Dic19C4⋊C411yescharacteristic
100C4⋊Dic19C4⋊C411yescharacteristic
101Dic19⋊C4—21no—
102Dic19⋊C4—21no—
103C4×Dic19—22no—
104C4×Dic19—22no—
105C4×Dic19—21no—
106C4×Dic19—21no—
107C4×Dic19—21no—
108C4×Dic19—21no—
109C4×Dic19—21no—
110C4×Dic19—21no—
111C4×Dic19—42no—
112C4×Dic19M1612yescomplemented
113C2×C19⋊C8—21no—
114C2×C19⋊C8—21no—
115C2×C19⋊C8—42no—
116C2×C19⋊C8—41no—
117#64515—82no—
118#8841—191nomaximal, Sylow
119C23×C19C4×D411yescharacteristic
120C22×D19—21no—
121C2×C4×C19—21no—
122C2×C4×C19—21no—
123C2×C4×C19—41no—
124C2×C4×C19C2×C4⋊C411yescharacteristic
125C2×C4×C19C4×D411yescharacteristic
126C2×C4×C19#12011yescharacteristic
127C2×C4×C19C22⋊Q811yescharacteristic
128C2×C4×C19C22⋊Q811yescharacteristic
129C2×C4×C19#12311yescharacteristic
130C2×C4×C19C2×M1611yescharacteristic
131C2×C4×C19C2×M1611yescharacteristic
132C2×C4×C19#13111yescharacteristic
133C2×C4×C19#13111yescharacteristic
134C22⋊D19—41no—
135C22⋊D19—41no—
136C2×Dic19—22no—
137C2×Dic19—22no—
138C2×Dic19—22no—
139C2×Dic19—22no—
140C2×Dic19—21no—
141C2×Dic19—21no—
142C2×Dic19—21no—
143C2×Dic19—41no—
144C2×Dic19—41no—
145D76—21no—
146D76—21no—
147C4×D19—41no—
148C4×D19—41no—
149C4×D19—41no—
150C4×D19—41no—
151C4×D19—81no—
152Dic38—21no—
153Dic38—21no—
154C8×C19—22no—
155C8×C19—41no—
156C8×C19—42no—
157C8×C19—81no—
158C19⋊C8—41no—
159C19⋊C8—41no—
160C19⋊C8—81no—
161#2989—191no—
162#1842—191no—
163C4×#104—191no—
164#1565—191no—
165#1477—191no—
166#1283D1911yescharacteristic, complemented
167#1276—191no—
168C22×C19—21no—
169C22×C19—21no—
170C22×C19#38511yescharacteristic
171C22×C19#43511yescharacteristic
172C22×C19#43611yescharacteristic
173C2×D19—41no—
174C2×D19—41no—
175C2×D19—41no—
176C4×C19—21no—
177C4×C19—21no—
178C4×C19—21no—
179C4×C19#42311yescharacteristic
180C4×C19#42411yescharacteristic
181C4×C19#43511yescharacteristic
182C4×C19#43611yescharacteristic
183C4×C19#45311yescharacteristic
184C4×C19#45611yescharacteristic
185Dic19—24no—
186Dic19—42no—
187Dic19—41no—
188Dic19—41no—
189Dic19—41no—
190C4×#41—191no—
191#446—381no—
192#436—381no—
193#435—382no—
194#432—381no—
195#431—191no—
196#431C2×D1911yescharacteristic
197#423—381no—
198C2×C4⋊C8—191no—
199C2×C4⋊C8—382no—
200C2×C4⋊C8C2×D1911yescharacteristic
201C2×#104—191no—
202C2×#104—191no—
203C4×M16C2×D1911yescharacteristic
204C43—191no—
205#339—191no—
206#339—191no—
207#335—381no—
208#334—381no—
209Q8⋊C8—381no—
210D4⋊C8—381no—
211C2×C19—21no—
212C2×C19—21no—
213C2×C19#185111yescharacteristic
214C2×C19#185911yescharacteristic
215C2×C19#186111yescharacteristic
216D19—81no—
217C2×#41—191no—
218C2×M16—382no—
219C2×M16C4×D1911yescharacteristic
220C2×M16C4×D1911yescharacteristic
221C22×C8—381no—
222C22×C8D7612yes—
223C4×Q8—191no—
224C4×Q8—191no—
225C4×D4—191no—
226C4×D4—191no—
227C4×D4—381no—
228C4×D4—381no—
229#117—191no—
230#117—381no—
231C2×C42—191no—
232C2×C42—191no—
233C2×C42—381no—
234C2×C42—381no—
235C2×C42—381no—
236C2×C42C22×D1911yescharacteristic
237C4⋊C8—21no—
238C4⋊C8—21no—
239C4⋊C8—21no—
240C4⋊C8—191no—
241C4⋊C8—191no—
242C4⋊C8—382no—
243C4⋊C8—381no—
244C4⋊C8—381no—
245C4⋊C8—764no—
246#104—382no—
247#104—382no—
248C22⋊C8—21no—
249C22⋊C8—382no—
250C22⋊C8—381no—
251#97—21no—
252#97—382no—
253C4×C8—21no—
254C4×C8—21no—
255C4×C8—381no—
256C19#884111yescharacteristic, complemented, Sylow
257#41—381no—
258#41—381no—
259#41—381no—
260#41—381no—
261C2×Q8—191no—
262C2×D4—191no—
263C2×D4—381no—
264C22×C4—381no—
265C22×C4—381no—
266C22×C4—381no—
267C22×C4—381no—
268C22×C4—381no—
269C22×C4C2×C4×D1911yescharacteristic
270C22×C4C2×D7611yescharacteristic
271C22×C4#6454111yescharacteristic
272M16—21no—
273M16—21no—
274M16—21no—
275M16—1522no—
276M16#6451512yescomplemented
277C2×C8—21no—
278C2×C8—21no—
279C2×C8—22no—
280C2×C8—42no—
281C2×C8—41no—
282C2×C8—381no—
283C2×C8—381no—
284C2×C8—762no—
285C2×C8—761no—
286C4⋊C4—191no—
287C4⋊C4—191no—
288C4⋊C4—381no—
289C4⋊C4—381no—
290C22⋊C4—381no—
291C22⋊C4—381no—
292C22⋊C4—381no—
293C42—192no—
294C42—382no—
295C42—382no—
296C42—381no—
297C42—381no—
298C42—381no—
299C42—381no—
300C42—381no—
301C42—381no—
302C42—762no—
303C42D4×D1911yescharacteristic
304C42D4×D1911yescharacteristic
305C42#6454311yescharacteristic
306C42Q8×D1911yescharacteristic
307C23—381no—
308C23C4×D7611yescharacteristic
309Q8—381no—
310Q8—381no—
311D4—381no—
312D4—381no—
313D4—761no—
314D4—761no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—41no—
318C2×C4—382no—
319C2×C4—382no—
320C2×C4—382no—
321C2×C4—382no—
322C2×C4—381no—
323C2×C4—381no—
324C2×C4—381no—
325C2×C4—761no—
326C2×C4—761no—
327C2×C4—761no—
328C2×C4—761no—
329C2×C4—761no—
330C2×C4—761no—
331C2×C4—1521no—
332C2×C4(C22⋊D19)⋊C411yescharacteristic
333C2×C4#1059732811yescharacteristic
334C2×C4#1059732911yescharacteristic
335C2×C4C4⋊C4×D1911yescharacteristic
336C2×C4#1059734211yescharacteristic
337C2×C4#1059734311yescharacteristic
338C2×C4C2×#6451511yescharacteristic
339C2×C4#1059734711yescharacteristic
340C2×C4M16×D1911yescharacteristic
341C2×C4#1059735311yescharacteristic
342C8—22no—
343C8—41no—
344C8—42no—
345C8—81no—
346C8—761no—
347C8—761no—
348C8—1521no—
349C22—21no—
350C22—21no—
351C22—761no—
352C22—761no—
353C22—761no—
354C22#1192641811yescharacteristic
355C22#1192661711yescharacteristic
356C22#1192662311yescharacteristic
357C4—21no—
358C4—21no—
359C4—21no—
360C4—384no—
361C4—762no—
362C4—761no—
363C4—761no—
364C4—761no—
365C4#1192656611yescharacteristic
366C4#1192656911yescharacteristic
367C4#1192661211yescharacteristic
368C4#1192661911yescharacteristic
369C4#1192671411yescharacteristic
370C4#1192672911yescharacteristic
371C2—21no—
372C2—21no—
373C2—1521no—
374C2#1456381911yescharacteristic
375C2#1456386411yescharacteristic
376C2#1456387811yescharacteristic
subgroupG/H
centerC2×C4#10597328
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1283C2
socleC22×C19#385
prime radicalC2×#64541C2×C4
cosocleC2×C42×C19C23
hypercenter#1283D19
hypocenterC19#8841
LCSG ▷ C22×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1283

Complements

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

NH ≅ G/Ntype
2. #14563786C2semidirect
4. #14562387C2semidirect
6. #14561467C2semidirect
7. C19×#1283C2semidirect
86. M16×C19M16semidirect
112. C4×Dic19M16semidirect
166. #1283D19semidirect
256. C19#8841semidirect
276. M16#64515semidirect

Maximal subgroups

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

subgroupindex
#145727532
#145637862
C4×#105972822
#145623872
#145620232
#145614672
C19×#12832
#884119