Finite Group Databasebeta

← #18078436

Subgroups — #18078436

Order 4864.

516 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14573111C211yesmaximal, characteristic
2#14572303C211yesmaximal, characteristic, complemented
3C2×#11926288C211yesmaximal, characteristic, complemented
4#14562023C211yesmaximal, characteristic, complemented
5#14561531C211yesmaximal, characteristic, complemented
6#14561509C211yesmaximal, characteristic, complemented
7C19×#1545C211yesmaximal, characteristic, complemented
8C2×#10597378—21no—
9C4×#64541C2211yescharacteristic
10#11926741—21no—
11#11926741C412yes—
12#11926736—21no—
13#11926736C412yes—
14#11926604—22no—
15#11926600—21no—
16#11926596—21no—
17#11926568C2211yescharacteristic
18C2×C4⋊(C19⋊C8)C2211yescharacteristic
19C2×C4⋊(C19⋊C8)C2211yescharacteristic
20#11926549—21no—
21#11926512—21no—
22#11926502—21no—
23#11926288—21no—
24#11926288—21no—
25#11926276—21no—
26#11926273—21no—
27C2×C19×#127C2211yescharacteristic
28C19×#431C2211yescharacteristic
29C19×#423C2211yescharacteristic
30C19×#331—22no—
31C22×D4×C19—21no—
32C22×D4×C19—21no—
33C22×D4×C19—21no—
34C2×#64541D411yescharacteristic
35C2×M16×C19—21no—
36C19×#127—21no—
37C19×#127—21no—
38C19×#127—21no—
39C19×#127C2×C412yes—
40C2×C42×C19C2311yescharacteristic
41C2×#64526—22no—
42#10597378—42no—
43#10597378—42no—
44C2×#64525—22no—
45C4×C22⋊D19—21no—
46C4×C22⋊D19—21no—
47#10597372D411yescharacteristic
48C2×#64520—21no—
49C22×C19⋊C8—21no—
50C22×C19⋊C8—21no—
51C4×D76C2×C411yescharacteristic
52C4×D76D411yescharacteristic
53#10597318—21no—
54C42×D19—21no—
55C4×Dic38C2×C411yescharacteristic
56C4×Dic38D411yescharacteristic
57C19×C4⋊C8—21no—
58C19×C4⋊C8—21no—
59C19×C4⋊C8D412yes—
60C19×C22⋊C8—21no—
61C4×C8×C19—21no—
62#10597289—22no—
63#10597289—22no—
64(C2×D19)⋊C8—22no—
65(C2×D19)⋊C8—22no—
66#10597272—22no—
67C8×Dic19—22no—
68C4⋊(C19⋊C8)—21no—
69C4⋊(C19⋊C8)—21no—
70C4⋊(C19⋊C8)—21no—
71C4⋊(C19⋊C8)—21no—
72C4⋊(C19⋊C8)C2×C412yes—
73C4⋊(C19⋊C8)D411yescharacteristic
74C4⋊(C19⋊C8)D411yescharacteristic
75C24×C19—41no—
76C2×D4×C19—22no—
77C2×D4×C19—22no—
78C2×D4×C19—22no—
79C2×D4×C19—41no—
80C2×D4×C19—41no—
81C2×D4×C19—41no—
82C2×D4×C19—41no—
83C2×D4×C19—41no—
84C2×D4×C19—41no—
85C2×D4×C19—41no—
86C2×D4×C19—81no—
87C2×D4×C19—81no—
88C2×D4×C19—82no—
89C22×C4×C19C2×D411yescharacteristic
90C22×C4×C19#4111yescharacteristic
91C22×C4×C19#4111yescharacteristic
92C2×C22⋊D19—21no—
93#64541—21no—
94#64541—21no—
95#64541—21no—
96#64541—21no—
97C2×D76C22⋊C411yescharacteristic
98C2×C4×D19—21no—
99C2×C4×D19—21no—
100C2×C4×D19—21no—
101C2×Dic38C22⋊C411yescharacteristic
102M16×C19—41no—
103M16×C19—41no—
104C2×C8×C19—22no—
105C2×C8×C19—41no—
106C42×C19C22×C411yescharacteristic
107C42×C19C2×D411yescharacteristic
108C42×C19C2×D411yescharacteristic
109C42×C19C2×D411yescharacteristic
110C22⋊Dic19—21no—
111#64526—44no—
112#64525—44no—
113(C2×D19)⋊C4—21no—
114(C2×D19)⋊C4—21no—
115C4⋊Dic19C22⋊C411yescharacteristic
116C4⋊Dic19C22⋊C411yescharacteristic
117Dic19⋊C4—21no—
118Dic19⋊C4—21no—
119C4×Dic19—21no—
120C4×Dic19—21no—
121C4×Dic19—21no—
122#64520—41no—
123#64520—41no—
124C2×C19⋊C8—22no—
125C2×C19⋊C8—21no—
126C2×C19⋊C8—21no—
127C2×C19⋊C8—41no—
128C2×C19⋊C8—41no—
129C2×C19⋊C8—41no—
130C2×C19⋊C8—81no—
131#9174—191nomaximal, Sylow
132C23×C19—42no—
133C23×C19—82no—
134C23×C19—82no—
135C23×C19—81no—
136C23×C19—81no—
137C23×C19#12311yescharacteristic
138C22×D19—21no—
139D4×C19—42no—
140D4×C19—42no—
141D4×C19—82no—
142D4×C19—82no—
143D4×C19—82no—
144D4×C19—81no—
145D4×C19—81no—
146D4×C19—81no—
147D4×C19—81no—
148C2×C4×C19—21no—
149C2×C4×C19—21no—
150C2×C4×C19—41no—
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
157C2×C4×C19#13511yescharacteristic
158C2×C4×C19#13511yescharacteristic
159C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
160C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
161C22⋊D19—41no—
162C22⋊D19—41no—
163C2×Dic19—21no—
164C2×Dic19—21no—
165C2×Dic19—21no—
166D76—21no—
167D76—21no—
168C4×D19—41no—
169C4×D19—41no—
170C4×D19—41no—
171C4×D19—41no—
172C4×D19—81no—
173Dic38—21no—
174Dic38—21no—
175C8×C19—42no—
176C8×C19—81no—
177C19⋊C8—42no—
178C19⋊C8—41no—
179C19⋊C8—41no—
180C19⋊C8—81no—
181#3038—191no—
182#2925—191no—
183#1545D1911yescharacteristic, complemented
184C2×#331—191no—
185#1477—191no—
186#1301—191no—
187#1292—191no—
188C22×C19—21no—
189C22×C19—21no—
190C22×C19—82no—
191C22×C19—82no—
192C22×C19—82no—
193C22×C19—162no—
194C22×C19—162no—
195C22×C19#38611yescharacteristic
196C22×C19#48211yescharacteristic
197C22×C19#48211yescharacteristic
198C2×D19—41no—
199C2×D19—41no—
200C2×D19—41no—
201C4×C19—21no—
202C4×C19—21no—
203C4×C19—21no—
204C4×C19#41611yescharacteristic
205C4×C19#41811yescharacteristic
206C4×C19#44911yescharacteristic
207C4×C19#44911yescharacteristic
208C4×C19#47111yescharacteristic
209C4×C19#47211yescharacteristic
210Dic19—41no—
211Dic19—41no—
212Dic19—41no—
213C2×AGL(1,ℤ/8)—381no—
214C2×#127C2×D1911yescharacteristic
215C4×#41—191no—
216#460—192no—
217#460—381no—
218#459—192no—
219#459—381no—
220#433—382no—
221#432—381no—
222#431—381no—
223#431C2×D1911yescharacteristic
224#423—191no—
225#423C2×D1911yescharacteristic
226C2×C4⋊C8—191no—
227C2×C4⋊C8—191no—
228#418—381no—
229#408—381no—
230#405—381no—
231#331—22no—
232#331—381no—
233#331—381no—
234Q8⋊C8—381no—
235D4⋊C8—381no—
236C2×C19—21no—
237C2×C19—21no—
238C2×C19—162no—
239C2×C19#187511yescharacteristic
240C2×C19#190311yescharacteristic
241C2×C19#190711yescharacteristic
242D19—81no—
243C2×#41—191no—
244C22×D4—21no—
245C22×D4—21no—
246C22×D4—21no—
247AGL(1,ℤ/8)—762no—
248AGL(1,ℤ/8)—762no—
249C2×SD16—382no—
250C2×D8—382no—
251C2×M16—21no—
252C2×M16—381no—
253C22×C8—381no—
254C22×C8—381no—
255#127—21no—
256#127—21no—
257#127—21no—
258#127C4×D1912yes—
259C4×Q8—191no—
260C4×Q8—191no—
261C4×D4—191no—
262C4×D4—191no—
263C4×D4—381no—
264C4×D4—381no—
265#117—191no—
266#117—381no—
267C2×C42—381no—
268C2×C42C22×D1911yescharacteristic
269C4⋊C8—21no—
270C4⋊C8—21no—
271C4⋊C8—192no—
272C4⋊C8—191no—
273C4⋊C8—191no—
274C4⋊C8—381no—
275C4⋊C8—381no—
276C4⋊C8—381no—
277C4⋊C8—381no—
278C4⋊C8C22⋊D1912yes—
279#102—382no—
280#102—382no—
281C22⋊C8—21no—
282C22⋊C8—382no—
283C22⋊C8—382no—
284#97—382no—
285C4×C8—21no—
286C4×C8—382no—
287C19#917411yescharacteristic, complemented, Sylow
288C24—41no—
289#41—381no—
290#41—381no—
291#41—381no—
292#41—381no—
293C2×Q8—191no—
294C2×D4—22no—
295C2×D4—22no—
296C2×D4—22no—
297C2×D4—41no—
298C2×D4—41no—
299C2×D4—41no—
300C2×D4—41no—
301C2×D4—41no—
302C2×D4—41no—
303C2×D4—41no—
304C2×D4—81no—
305C2×D4—81no—
306C2×D4—82no—
307C2×D4—191no—
308C2×D4—381no—
309C22×C4—381no—
310C22×C4—381no—
311C22×C4—381no—
312C22×C4#6454111yescharacteristic
313C22×C4D4×D1911yescharacteristic
314C22×C4#6454311yescharacteristic
315SD16—764no—
316D8—764no—
317M16—41no—
318M16—41no—
319M16—761no—
320M16—761no—
321C2×C8—22no—
322C2×C8—41no—
323C2×C8—381no—
324C2×C8—381no—
325C2×C8—382no—
326C2×C8—761no—
327C2×C8—761no—
328C2×C8—761no—
329C2×C8—1521no—
330C4⋊C4—191no—
331C4⋊C4—191no—
332C4⋊C4—381no—
333C4⋊C4—381no—
334C22⋊C4—381no—
335C22⋊C4—381no—
336C22⋊C4—381no—
337C42—381no—
338C42—381no—
339C42—381no—
340C42C2×C4×D1911yescharacteristic
341C42D4×D1911yescharacteristic
342C42D4×D1911yescharacteristic
343C42C2×C22⋊D1911yescharacteristic
344C23—42no—
345C23—82no—
346C23—82no—
347C23—81no—
348C23—81no—
349C23—381no—
350C23#1059732911yescharacteristic
351Q8—381no—
352Q8—381no—
353D4—42no—
354D4—42no—
355D4—82no—
356D4—82no—
357D4—82no—
358D4—81no—
359D4—81no—
360D4—81no—
361D4—81no—
362D4—381no—
363D4—381no—
364D4—761no—
365D4—761no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—41no—
369C2×C4—381no—
370C2×C4—381no—
371C2×C4—381no—
372C2×C4—761no—
373C2×C4—761no—
374C2×C4—761no—
375C2×C4—761no—
376C2×C4—1521no—
377C2×C4C22⋊C4×D1911yescharacteristic
378C2×C4(C22⋊D19)⋊C411yescharacteristic
379C2×C4#1059733011yescharacteristic
380C2×C4#1059735711yescharacteristic
381C2×C4#1059735811yescharacteristic
382C2×C4#1059736011yescharacteristic
383C2×C4#1059736211yescharacteristic
384C2×C4C4×C22⋊D1911yescharacteristic
385C2×C4#1059738311yescharacteristic
386C2×C4#1059738411yescharacteristic
387C8—42no—
388C8—81no—
389C8—762no—
390C8—761no—
391C8—761no—
392C8—1521no—
393C22—21no—
394C22—21no—
395C22—82no—
396C22—82no—
397C22—82no—
398C22—162no—
399C22—162no—
400C22—761no—
401C22—761no—
402C22—761no—
403C22#1192642011yescharacteristic
404C22#1192686611yescharacteristic
405C22#1192686711yescharacteristic
406C4—21no—
407C4—21no—
408C4—21no—
409C4—761no—
410C4—761no—
411C4—761no—
412C4#1192653711yescharacteristic
413C4#1192654711yescharacteristic
414C4#1192668611yescharacteristic
415C4#1192668811yescharacteristic
416C4#1192680611yescharacteristic
417C4#1192681311yescharacteristic
418C2—21no—
419C2—21no—
420C2—162no—
421C2—1521no—
422C2#1456395411yescharacteristic
423C2#1456411211yescharacteristic
424C2#1456414011yescharacteristic
subgroupG/H
centerC22#11926420
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1545C2
socleC22×C19#386
prime radical#14573111C2
cosocleC2×C42×C19C23
hypercenter#1545D19
hypocenterC19#9174
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1545

Complements

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

NH ≅ G/Ntype
2. #14572303C2semidirect
3. C2×#11926288C2semidirect
4. #14562023C2semidirect
5. #14561531C2semidirect
6. #14561509C2semidirect
7. C19×#1545C2semidirect
183. #1545D19semidirect
287. C19#9174semidirect

Maximal subgroups

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

subgroupindex
#145731112
#145723032
C2×#119262882
#145620232
#145615312
#145615092
C19×#15452
#917419