Finite Group Databasebeta

← #18074859

Subgroups — #18074859

Order 4864.

686 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14564629C211yesmaximal, characteristic, complemented
2#14562357C211yesmaximal, characteristic, complemented
3#14562242C211yesmaximal, characteristic, complemented
4#14562100C211yesmaximal, characteristic, complemented
5#14562052C211yesmaximal, characteristic, complemented
6#14561991C211yesmaximal, characteristic, complemented
7C19×#3559C211yesmaximal, characteristic
8#11926601C2211yescharacteristic
9#11926597C2211yescharacteristic
10#11926568C2211yescharacteristic
11C4×#64520C2211yescharacteristic
12#11926313—21no—
13#11926313—21no—
14#11926290—21no—
15#11926288—21no—
16#11926286—21no—
17#11926284—21no—
18Q8⋊(C19⋊C8)—21no—
19D4⋊(C19⋊C8)—22no—
20D4⋊(C19⋊C8)—21no—
21#11926270—22no—
22C19×#563—21no—
23C19×#562—21no—
24C19×#554—21no—
25C19×#553—21no—
26C19×#553—21no—
27C19×#547—22no—
28C19×#547—21no—
29C19×#544—21no—
30C19×#540—21no—
31C19×#539—22no—
32C19×#539C412yes—
33C19×#537C412yes—
34C19×#532C2211yescharacteristic
35C19×#529C2211yescharacteristic
36C2×C19×#125C2211yescharacteristic
37C2×#41×C19—22no—
38C2×#41×C19—21no—
39C19×C4⋊Q8—21no—
40C19×C4⋊Q8—22no—
41C19×C4⋊Q8D411yescharacteristic
42C19×#127D411yescharacteristic
43C19×#126—22no—
44C19×#126—22no—
45C19×#126—21no—
46C19×#125—21no—
47C19×#125—22no—
48C19×#125—21no—
49C19×#125—21no—
50C19×#125—21no—
51C19×#125—21no—
52C19×#125D411yescharacteristic
53C19×#124—21no—
54C19×#124D411yescharacteristic
55C19×#123—22no—
56C19×#123—22no—
57C19×#123—22no—
58C19×#123—22no—
59C19×#123—22no—
60C19×#123—22no—
61C19×#123—21no—
62C19×C22⋊Q8—22no—
63C19×C22⋊Q8—22no—
64C19×C22⋊Q8—22no—
65C19×C22⋊Q8—22no—
66C19×C22⋊Q8—22no—
67C19×C22⋊Q8—22no—
68C19×C22⋊Q8C2×C411yescharacteristic
69C19×#121—21no—
70C19×#121—22no—
71C19×#121—21no—
72C19×#121—22no—
73C19×#121—22no—
74C19×#121—22no—
75C19×#121—21no—
76C19×#121C2×C411yescharacteristic
77C19×#121C2×C412yes—
78C4×Q8×C19D411yescharacteristic
79C4×D4×C19—22no—
80C4×D4×C19—21no—
81C4×D4×C19—21no—
82C4×D4×C19—22no—
83C4×D4×C19—21no—
84C4×D4×C19—21no—
85C4×D4×C19D411yescharacteristic
86C4×D4×C19D412yes—
87C19×#117—21no—
88C19×#117—21no—
89C2×C4⋊C4×C19—22no—
90C2×C4⋊C4×C19—21no—
91C2×C4⋊C4×C19C2×C412yes—
92C2×C4⋊C4×C19D411yescharacteristic
93C2×C4⋊C4×C19D411yescharacteristic
94C2×C4⋊C4×C19D412yes—
95C2×C42×C19C2311yescharacteristic
96C2×#64520—21no—
97C2×#64520—21no—
98C22⋊(C19⋊C8)—21no—
99C22⋊(C19⋊C8)—21no—
100C4⋊(C19⋊C8)—21no—
101C4⋊(C19⋊C8)—21no—
102C4⋊(C19⋊C8)—21no—
103C4⋊(C19⋊C8)—21no—
104#10597260—21no—
105#10597260—21no—
106C4×C19⋊C8—21no—
107C4×C19⋊C8—21no—
108#41×C19—82no—
109#41×C19—84no—
110C2×Q8×C19—22no—
111C2×Q8×C19—21no—
112C2×Q8×C19C22⋊C411yescharacteristic
113C2×D4×C19—22no—
114C2×D4×C19—21no—
115C2×D4×C19—22no—
116C2×D4×C19—22no—
117C2×D4×C19—21no—
118C2×D4×C19—21no—
119C2×D4×C19C22⋊C411yescharacteristic
120C2×D4×C19C22⋊C412yes—
121C22×C4×C19—22no—
122C22×C4×C19—22no—
123C22×C4×C19—22no—
124C22×C4×C19—21no—
125C22×C4×C19—22no—
126C22×C4×C19C22⋊C412yes—
127C22×C4×C19C22⋊C412yes—
128C22×C4×C19C22×C411yescharacteristic
129C22×C4×C19C2×D411yescharacteristic
130C22×C4×C19C2×D411yescharacteristic
131C4⋊C4×C19—22no—
132C4⋊C4×C19—22no—
133C4⋊C4×C19—22no—
134C4⋊C4×C19—22no—
135C4⋊C4×C19—22no—
136C4⋊C4×C19—22no—
137C4⋊C4×C19—21no—
138C4⋊C4×C19—21no—
139C4⋊C4×C19—21no—
140C4⋊C4×C19—22no—
141C4⋊C4×C19—21no—
142C4⋊C4×C19—21no—
143C4⋊C4×C19—22no—
144C4⋊C4×C19—21no—
145C4⋊C4×C19—21no—
146C4⋊C4×C19—21no—
147C4⋊C4×C19—21no—
148C4⋊C4×C19C22⋊C412yes—
149C4⋊C4×C19C22⋊C411yescharacteristic
150C4⋊C4×C19C22⋊C411yescharacteristic
151C22⋊C4×C19—22no—
152C22⋊C4×C19—22no—
153C22⋊C4×C19—22no—
154C22⋊C4×C19—22no—
155C22⋊C4×C19—22no—
156C22⋊C4×C19—21no—
157C22⋊C4×C19—21no—
158C22⋊C4×C19—22no—
159C22⋊C4×C19—21no—
160C22⋊C4×C19—21no—
161C22⋊C4×C19—21no—
162C22⋊C4×C19—22no—
163C42×C19—22no—
164C42×C19—21no—
165C42×C19C2×D411yescharacteristic
166C42×C19C2×D411yescharacteristic
167C42×C19C2×D411yescharacteristic
168C42×C19C2×D411yescharacteristic
169#64520—22no—
170#64520—41no—
171#64520—42no—
172C2×C19⋊C8—41no—
173C2×C19⋊C8—41no—
174C2×C19⋊C8—41no—
175C2×C19⋊C8—41no—
176#8486—191nomaximal, Sylow
177C23×C19—21no—
178C23×C19—22no—
179C23×C19C2×C22⋊C411yescharacteristic
180Q8×C19—41no—
181Q8×C19—81no—
182Q8×C19—82no—
183D4×C19—42no—
184D4×C19—41no—
185D4×C19—44no—
186D4×C19—42no—
187D4×C19—41no—
188D4×C19—41no—
189D4×C19—81no—
190D4×C19—82no—
191D4×C19—82no—
192C2×C4×C19—21no—
193C2×C4×C19—21no—
194C2×C4×C19—21no—
195C2×C4×C19—21no—
196C2×C4×C19—22no—
197C2×C4×C19—22no—
198C2×C4×C19—21no—
199C2×C4×C19—22no—
200C2×C4×C19—41no—
201C2×C4×C19—41no—
202C2×C4×C19—41no—
203C2×C4×C19—41no—
204C2×C4×C19—42no—
205C2×C4×C19—42no—
206C2×C4×C19—82no—
207C2×C4×C19—82no—
208C2×C4×C19—82no—
209C2×C4×C19—82no—
210C2×C4×C19C2×C22⋊C411yescharacteristic
211C2×C4×C19C2×C22⋊C411yescharacteristic
212C2×C4×C19#12011yescharacteristic
213C2×C4×C19#12011yescharacteristic
214C2×C4×C19#12011yescharacteristic
215C2×C4×C19#12011yescharacteristic
216C19⋊C8—42no—
217C19⋊C8—81no—
218C19⋊C8—81no—
219C19⋊C8—81no—
220#3559D1911yescharacteristic
221#1998—191no—
222#1557—191no—
223#1529—191no—
224#1495—191no—
225#1484—191no—
226#1470—191no—
227C22×C19—21no—
228C22×C19—21no—
229C22×C19—21no—
230C22×C19—41no—
231C22×C19—42no—
232C22×C19—42no—
233C22×C19—41no—
234C22×C19—42no—
235C22×C19—41no—
236C22×C19#37911yescharacteristic
237C4×C19—21no—
238C4×C19—21no—
239C4×C19—21no—
240C4×C19—21no—
241C4×C19—21no—
242C4×C19—41no—
243C4×C19—42no—
244C4×C19—42no—
245C4×C19—41no—
246C4×C19—42no—
247C4×C19—41no—
248C4×C19#45411yescharacteristic
249C4×C19#45611yescharacteristic
250#563—21no—
251#562—21no—
252#554—21no—
253#553—21no—
254#553—21no—
255#547—22no—
256#547—21no—
257#544—21no—
258#540—21no—
259#539—22no—
260#539Dic1912yes—
261#537Dic1912yes—
262#532C2×D1911yescharacteristic
263#529C2×D1911yescharacteristic
264C2×#125C2×D1911yescharacteristic
265#432—191no—
266#431—191no—
267#423—191no—
268C4×M16—191no—
269#343—381no—
270#343—381no—
271#332—381no—
272#331—381no—
273#330—381no—
274#329—381no—
275Q8⋊C8—381no—
276D4⋊C8—382no—
277D4⋊C8—381no—
278#324—382no—
279C2×C19—41no—
280C2×C19—81no—
281C2×C19—82no—
282C2×C19#179111yescharacteristic
283C2×C19#179311yescharacteristic
284C2×C19#179511yescharacteristic
285C2×#41—22no—
286C2×#41—21no—
287C2×M16—381no—
288C2×M16—381no—
289C4⋊Q8—21no—
290C4⋊Q8—22no—
291C4⋊Q8C22⋊D1911yescharacteristic
292#127C22⋊D1911yescharacteristic
293#126—22no—
294#126—22no—
295#126—21no—
296#125—21no—
297#125—22no—
298#125—21no—
299#125—21no—
300#125—21no—
301#125—21no—
302#125C22⋊D1911yescharacteristic
303#124—21no—
304#124C22⋊D1911yescharacteristic
305#123—22no—
306#123—22no—
307#123—22no—
308#123—22no—
309#123—22no—
310#123—22no—
311#123—21no—
312C22⋊Q8—22no—
313C22⋊Q8—22no—
314C22⋊Q8—22no—
315C22⋊Q8—22no—
316C22⋊Q8—22no—
317C22⋊Q8—22no—
318C22⋊Q8C2×Dic1911yescharacteristic
319#121—21no—
320#121—22no—
321#121—21no—
322#121—22no—
323#121—22no—
324#121—22no—
325#121—21no—
326#121C2×Dic1911yescharacteristic
327#121C2×Dic1912yes—
328C4×Q8C22⋊D1911yescharacteristic
329C4×D4—22no—
330C4×D4—21no—
331C4×D4—21no—
332C4×D4—22no—
333C4×D4—21no—
334C4×D4—21no—
335C4×D4C22⋊D1911yescharacteristic
336C4×D4C22⋊D1912yes—
337#117—21no—
338#117—21no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4C2×Dic1912yes—
342C2×C4⋊C4C22⋊D1912yes—
343C2×C4⋊C4C22⋊D1911yescharacteristic
344C2×C4⋊C4C22⋊D1911yescharacteristic
345C2×C42C22×D1911yescharacteristic
346C4⋊C8—381no—
347C4⋊C8—381no—
348C4⋊C8—381no—
349C4⋊C8—381no—
350C22⋊C8—381no—
351C22⋊C8—381no—
352#97—381no—
353#97—381no—
354C4×C8—381no—
355C4×C8—381no—
356C19#848611yescharacteristic, complemented, Sylow
357#41—82no—
358#41—84no—
359C2×Q8—22no—
360C2×Q8—21no—
361C2×Q8C22⋊Dic1911yescharacteristic
362C2×D4—22no—
363C2×D4—21no—
364C2×D4—22no—
365C2×D4—22no—
366C2×D4—21no—
367C2×D4—21no—
368C2×D4C22⋊Dic1911yescharacteristic
369C2×D4C22⋊Dic1912yes—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—21no—
374C22×C4—22no—
375C22×C4C22⋊Dic1912yes—
376C22×C4C22⋊Dic1912yes—
377C22×C4C22×Dic1911yescharacteristic
378C22×C4C2×C22⋊D1911yescharacteristic
379C22×C4C2×C22⋊D1911yescharacteristic
380M16—382no—
381M16—761no—
382M16—762no—
383C2×C8—761no—
384C2×C8—761no—
385C2×C8—761no—
386C2×C8—761no—
387C4⋊C4—22no—
388C4⋊C4—22no—
389C4⋊C4—22no—
390C4⋊C4—22no—
391C4⋊C4—22no—
392C4⋊C4—22no—
393C4⋊C4—21no—
394C4⋊C4—21no—
395C4⋊C4—21no—
396C4⋊C4—22no—
397C4⋊C4—21no—
398C4⋊C4—21no—
399C4⋊C4—22no—
400C4⋊C4—21no—
401C4⋊C4—21no—
402C4⋊C4—21no—
403C4⋊C4—21no—
404C4⋊C4C22⋊Dic1912yes—
405C4⋊C4C22⋊Dic1911yescharacteristic
406C4⋊C4C22⋊Dic1911yescharacteristic
407C22⋊C4—22no—
408C22⋊C4—22no—
409C22⋊C4—22no—
410C22⋊C4—22no—
411C22⋊C4—22no—
412C22⋊C4—21no—
413C22⋊C4—21no—
414C22⋊C4—22no—
415C22⋊C4—21no—
416C22⋊C4—21no—
417C22⋊C4—21no—
418C22⋊C4—22no—
419C42—22no—
420C42—21no—
421C42C2×C22⋊D1911yescharacteristic
422C42C2×C22⋊D1911yescharacteristic
423C42C2×C22⋊D1911yescharacteristic
424C42C2×C22⋊D1911yescharacteristic
425C23—22no—
426C23—21no—
427C23C2×C22⋊Dic1911yescharacteristic
428Q8—41no—
429Q8—81no—
430Q8—82no—
431D4—42no—
432D4—41no—
433D4—44no—
434D4—42no—
435D4—41no—
436D4—41no—
437D4—81no—
438D4—82no—
439D4—82no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—21no—
447C2×C4—22no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—82no—
455C2×C4—82no—
456C2×C4—82no—
457C2×C4—82no—
458C2×C4C2×C22⋊Dic1911yescharacteristic
459C2×C4C2×C22⋊Dic1911yescharacteristic
460C2×C4#1059739911yescharacteristic
461C2×C4#1059739911yescharacteristic
462C2×C4#1059739911yescharacteristic
463C2×C4#1059739911yescharacteristic
464C8—762no—
465C8—1521no—
466C8—1521no—
467C8—1521no—
468C22—21no—
469C22—21no—
470C22—21no—
471C22—42no—
472C22—41no—
473C22—41no—
474C22—42no—
475C22—42no—
476C22—41no—
477C22#1192640011yescharacteristic
478C4—21no—
479C4—21no—
480C4—21no—
481C4—21no—
482C4—21no—
483C4—42no—
484C4—41no—
485C4—41no—
486C4—42no—
487C4—42no—
488C4—41no—
489C4#1192671711yescharacteristic
490C4#1192672711yescharacteristic
491C2—41no—
492C2—82no—
493C2—81no—
494C2#1456358611yescharacteristic
495C2#1456359411yescharacteristic
496C2#1456360511yescharacteristic
subgroupG/H
centerC22#11926400
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
Fitting, prime radicalC19×#3559C2
socleC22×C19#379
cosocleC2×C42×C19C23
hypercenter#3559D19
hypocenterC19#8486
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3559

Complements

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

NH ≅ G/Ntype
1. #14564629C2semidirect
2. #14562357C2semidirect
3. #14562242C2semidirect
4. #14562100C2semidirect
5. #14562052C2semidirect
6. #14561991C2semidirect
356. C19#8486semidirect

Maximal subgroups

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

subgroupindex
#145646292
#145623572
#145622422
#145621002
#145620522
#145619912
C19×#35592
#848619