Finite Group Databasebeta

← #18082770

Subgroups — #18082770

Order 4864.

716 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
1C2×#11926857C211yesmaximal, characteristic
2#14569377C211yesmaximal, characteristic
3#14563721C211yesmaximal, characteristic, complemented
4C2×#11926277C211yesmaximal, characteristic
5C2×#11926270C211yesmaximal, characteristic, complemented
6#14561514C211yesmaximal, characteristic, complemented
7C2×C19×#398C211yesmaximal, characteristic, complemented
8C2×#10597375—21no—
9C2×#10597376C2211yescharacteristic
10#11926857—22no—
11#11926857—22no—
12C2×#10597264—21no—
13C2×#10597266—21no—
14C2×C22⋊(C19⋊C8)C2211yescharacteristic
15C2×C22⋊(C19⋊C8)C2211yescharacteristic
16#11926474—21no—
17#11926466—22no—
18#11926461—21no—
19#11926423—21no—
20#11926404C2211yescharacteristic
21#11926306—22no—
22#11926277—22no—
23#11926270—22no—
24C22×C4⋊C4×C19—21no—
25C22×C4⋊C4×C19C2211yescharacteristic
26C22×C4⋊C4×C19C2211yescharacteristic
27C19×#398—22no—
28C19×#398—22no—
29C2×C19×#95—21no—
30C2×C19×#95C2211yescharacteristic
31C23×C4×C19—21no—
32C23×C4×C19—21no—
33C23×C4×C19D411yescharacteristic
34C23×C4×C19D411yescharacteristic
35C23×C4×C19C2311yescharacteristic
36C22×C22⋊D19—21no—
37C22×D76D411yescharacteristic
38C2×C4⋊C4×C19—21no—
39C2×C4⋊C4×C19—21no—
40C2×C4⋊C4×C19—21no—
41C2×C4⋊C4×C19—21no—
42C2×C4⋊C4×C19—24no—
43C2×C4⋊C4×C19—21no—
44C2×C4⋊C4×C19—21no—
45C2×C4⋊C4×C19—21no—
46C2×C4⋊C4×C19—21no—
47C2×C4⋊C4×C19—21no—
48C2×C4⋊C4×C19—21no—
49C2×C4⋊C4×C19—21no—
50C2×C4⋊C4×C19—42no—
51C2×C4⋊C4×C19—42no—
52C2×C4⋊C4×C19D412yes—
53C2×C22⋊Dic19—21no—
54#10597376—21no—
55#10597376—21no—
56#10597376—21no—
57#10597376—21no—
58#10597375—42no—
59#10597375—42no—
60C2×(C2×D19)⋊C4—22no—
61C2×(C2×D19)⋊C4—21no—
62C2×(C2×D19)⋊C4—22no—
63C2×C4⋊Dic19D411yescharacteristic
64C2×C4⋊Dic19D412yes—
65C2×Dic19⋊C4—22no—
66C22×C19⋊C8—21no—
67C22×C19⋊C8—21no—
68C19×#95—24no—
69C19×#95—21no—
70C19×#95D412yes—
71C19⋊#95—22no—
72C19⋊#95—21no—
73C22⋊(C19⋊C8)—21no—
74C22⋊(C19⋊C8)—21no—
75C22⋊(C19⋊C8)—21no—
76C22⋊(C19⋊C8)D412yes—
77#10597266—24no—
78#10597264—24no—
79C24×C19C2×D411yescharacteristic
80C23×D19—21no—
81C22×C4×C19—24no—
82C22×C4×C19—21no—
83C22×C4×C19—22no—
84C22×C4×C19—21no—
85C22×C4×C19—21no—
86C22×C4×C19—21no—
87C22×C4×C19—21no—
88C22×C4×C19—21no—
89C22×C4×C19—22no—
90C22×C4×C19—21no—
91C22×C4×C19—21no—
92C22×C4×C19—21no—
93C22×C4×C19—42no—
94C22×C4×C19—42no—
95C22×C4×C19—41no—
96C22×C4×C19—41no—
97C22×C4×C19—42no—
98C22×C4×C19—41no—
99C22×C4×C19—41no—
100C22×C4×C19—41no—
101C22×C4×C19—41no—
102C22×C4×C19—41no—
103C22×C4×C19—41no—
104C22×C4×C19D812yes—
105C22×C4×C19C2×D411yescharacteristic
106C22×C4×C19C2×D411yescharacteristic
107C22×C4×C19C2×D411yescharacteristic
108C22×C4×C19C2×D411yescharacteristic
109C22×C4×C19C2×D411yescharacteristic
110C22×C4×C19#4111yescharacteristic
111C2×C22⋊D19—41no—
112C2×C22⋊D19—41no—
113C2×C22⋊D19—41no—
114C2×C22⋊D19—41no—
115C2×C22⋊D19—41no—
116C2×C22⋊D19—41no—
117C22×Dic19—22no—
118C22×Dic19—21no—
119C2×D76—21no—
120C2×D76—21no—
121C2×D76—42no—
122C4⋊C4×C19—22no—
123C4⋊C4×C19—22no—
124C4⋊C4×C19—48no—
125C4⋊C4×C19—41no—
126C4⋊C4×C19—41no—
127C4⋊C4×C19—41no—
128C4⋊C4×C19—41no—
129C4⋊C4×C19—41no—
130C4⋊C4×C19—41no—
131C22⋊Dic19—41no—
132C22⋊Dic19—41no—
133(C2×D19)⋊C4—44no—
134(C2×D19)⋊C4—41no—
135(C2×D19)⋊C4—41no—
136(C2×D19)⋊C4—82no—
137C4⋊Dic19—21no—
138C4⋊Dic19—21no—
139C4⋊Dic19—42no—
140Dic19⋊C4—44no—
141C2×C19⋊C8—22no—
142C2×C19⋊C8—42no—
143C2×C19⋊C8—42no—
144C2×C19⋊C8—41no—
145#9919—191nomaximal, Sylow
146C23×C19—22no—
147C23×C19—22no—
148C23×C19#12011yescharacteristic
149C23×C19#12011yescharacteristic
150C23×C19#12111yescharacteristic
151C23×C19C2×D811yescharacteristic
152C23×C19#13511yescharacteristic
153C23×C19AGL(1,ℤ/8)11yescharacteristic
154C23×C19AGL(1,ℤ/8)11yescharacteristic
155C22×D19—41no—
156C22×D19—41no—
157C22×D19—41no—
158C22×D19—42no—
159C22×D19—42no—
160C2×C4×C19—22no—
161C2×C4×C19—22no—
162C2×C4×C19—24no—
163C2×C4×C19—22no—
164C2×C4×C19—22no—
165C2×C4×C19—22no—
166C2×C4×C19—41no—
167C2×C4×C19—41no—
168C2×C4×C19—41no—
169C2×C4×C19—41no—
170C2×C4×C19—44no—
171C2×C4×C19—44no—
172C2×C4×C19—42no—
173C2×C4×C19—41no—
174C2×C4×C19—42no—
175C2×C4×C19—41no—
176C2×C4×C19—41no—
177C2×C4×C19—41no—
178C2×C4×C19—42no—
179C2×C4×C19—42no—
180C2×C4×C19—41no—
181C2×C4×C19—42no—
182C2×C4×C19—42no—
183C2×C4×C19—42no—
184C2×C4×C19—81no—
185C2×C4×C19—81no—
186C2×C4×C19—81no—
187C2×C4×C19—81no—
188C2×C4×C19—81no—
189C2×C4×C19#12011yescharacteristic
190C2×C4×C19#12111yescharacteristic
191C2×C4×C19#12111yescharacteristic
192C2×C4×C19#12711yescharacteristic
193C22⋊D19—81no—
194C22⋊D19—81no—
195C22⋊D19—81no—
196C22⋊D19—81no—
197C2×Dic19—41no—
198C2×Dic19—41no—
199C2×Dic19—42no—
200C2×Dic19—41no—
201C2×Dic19—42no—
202C2×Dic19—42no—
203D76—42no—
204D76—81no—
205C19⋊C8—42no—
206C19⋊C8—81no—
207C2×#480—191no—
208#2618—191no—
209C2×#398D1911yescharacteristic, complemented
210#1823—191no—
211C2×#327—191no—
212C2×#324—191no—
213#1294—191no—
214C22×C19—22no—
215C22×C19—22no—
216C22×C19—22no—
217C22×C19—22no—
218C22×C19—21no—
219C22×C19—21no—
220C22×C19—21no—
221C22×C19—21no—
222C22×C19#39211yescharacteristic
223C22×C19#44711yescharacteristic
224C22×C19#44711yescharacteristic
225C22×C19#44911yescharacteristic
226C22×C19#44911yescharacteristic
227C22×C19#45612yes—
228C22×C19#45812yes—
229C22×C19#46611yescharacteristic
230C22×C19#46911yescharacteristic
231C2×D19—82no—
232C2×D19—82no—
233C2×D19—81no—
234C2×D19—81no—
235C2×D19—81no—
236C4×C19—21no—
237C4×C19—21no—
238C4×C19—21no—
239C4×C19—21no—
240C4×C19—44no—
241C4×C19—42no—
242C4×C19—82no—
243C4×C19—81no—
244Dic19—82no—
245Dic19—81no—
246C2×#123—381no—
247C2×#121—191no—
248C22×C4⋊C4—21no—
249C22×C4⋊C4C2×D1911yescharacteristic
250C22×C4⋊C4C2×D1911yescharacteristic
251#480—382no—
252#480—382no—
253C2×#107—381no—
254C2×#102—381no—
255C2×C22⋊C8—191no—
256C2×C22⋊C8—191no—
257#398—22no—
258#398—22no—
259#398—381no—
260#396—382no—
261#394—381no—
262#386—381no—
263#380—191no—
264C2×#95—21no—
265C2×#95C2×D1911yescharacteristic
266#340—382no—
267#327—382no—
268#324—382no—
269C2×C19—21no—
270C2×C19—21no—
271C2×C19—21no—
272C2×C19—21no—
273C2×C19#160912yes—
274C2×C19#161012yes—
275C2×C19#199911yescharacteristic
276C2×C19#200511yescharacteristic
277C2×C19#202211yescharacteristic
278D19—161no—
279C22×D4—191no—
280C22×D4—381no—
281C23×C4—21no—
282C23×C4—21no—
283C23×C4C22⋊D1911yescharacteristic
284C23×C4C22⋊D1911yescharacteristic
285C23×C4C22×D1911yescharacteristic
286C22×C8—381no—
287C22×C8—381no—
288#123—762no—
289#123—762no—
290#121—381no—
291#121—381no—
292#121—381no—
293#121—381no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—42no—
307C2×C4⋊C4—42no—
308C2×C4⋊C4—191no—
309C2×C4⋊C4—192no—
310C2×C4⋊C4—382no—
311C2×C4⋊C4C22⋊D1912yes—
312C2×C22⋊C4—382no—
313C2×C22⋊C4—381no—
314C2×C22⋊C4—381no—
315C2×C22⋊C4—382no—
316#107—384no—
317#102—384no—
318C22⋊C8—192no—
319C22⋊C8—381no—
320C22⋊C8—381no—
321C22⋊C8—381no—
322#95—24no—
323#95—21no—
324#95—382no—
325#95—381no—
326#95C22⋊D1912yes—
327C19#991911yescharacteristic, complemented, Sylow
328C24—381no—
329C24C2×C22⋊D1911yescharacteristic
330C2×D4—381no—
331C2×D4—381no—
332C2×D4—762no—
333C2×D4—761no—
334C2×D4—761no—
335C2×D4—761no—
336C2×D4—761no—
337C2×D4—761no—
338C2×D4—761no—
339C22×C4—24no—
340C22×C4—21no—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—22no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—21no—
349C22×C4—22no—
350C22×C4—21no—
351C22×C4—42no—
352C22×C4—42no—
353C22×C4—41no—
354C22×C4—41no—
355C22×C4—42no—
356C22×C4—41no—
357C22×C4—41no—
358C22×C4—41no—
359C22×C4—41no—
360C22×C4—41no—
361C22×C4—41no—
362C22×C4—382no—
363C22×C4—381no—
364C22×C4#6452512yes—
365C22×C4D4×D1911yescharacteristic
366C22×C4D4×D1911yescharacteristic
367C22×C4D4×D1911yescharacteristic
368C22×C4#6454311yescharacteristic
369C22×C4C2×C22⋊D1911yescharacteristic
370C22×C4C2×C22⋊D1911yescharacteristic
371C2×C8—382no—
372C2×C8—762no—
373C2×C8—762no—
374C2×C8—761no—
375C4⋊C4—22no—
376C4⋊C4—22no—
377C4⋊C4—48no—
378C4⋊C4—41no—
379C4⋊C4—41no—
380C4⋊C4—41no—
381C4⋊C4—41no—
382C4⋊C4—41no—
383C4⋊C4—41no—
384C4⋊C4—381no—
385C4⋊C4—381no—
386C4⋊C4—762no—
387C4⋊C4—764no—
388C22⋊C4—764no—
389C22⋊C4—761no—
390C22⋊C4—761no—
391C22⋊C4—761no—
392C22⋊C4—761no—
393C22⋊C4—1522no—
394C23—22no—
395C23—22no—
396C23—761no—
397C23—761no—
398C23—761no—
399C23—762no—
400C23—762no—
401C23C2×#6452511yescharacteristic
402C23#1059737811yescharacteristic
403C23#1059738311yescharacteristic
404C23#1059738511yescharacteristic
405C23#1059739511yescharacteristic
406C23#1059739611yescharacteristic
407C23#1059739911yescharacteristic
408D4—762no—
409D4—1521no—
410D4—1521no—
411D4—1521no—
412D4—1521no—
413D4—1521no—
414C2×C4—22no—
415C2×C4—22no—
416C2×C4—24no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—44no—
425C2×C4—44no—
426C2×C4—42no—
427C2×C4—41no—
428C2×C4—42no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—41no—
437C2×C4—42no—
438C2×C4—81no—
439C2×C4—81no—
440C2×C4—81no—
441C2×C4—81no—
442C2×C4—81no—
443C2×C4—762no—
444C2×C4—761no—
445C2×C4—761no—
446C2×C4—761no—
447C2×C4—762no—
448C2×C4—762no—
449C2×C4#1059738311yescharacteristic
450C2×C4#1059738411yescharacteristic
451C2×C4#1059738511yescharacteristic
452C2×C4#1059738611yescharacteristic
453C8—762no—
454C8—1521no—
455C22—21no—
456C22—21no—
457C22—22no—
458C22—22no—
459C22—22no—
460C22—22no—
461C22—21no—
462C22—21no—
463C22—1521no—
464C22—1521no—
465C22—1522no—
466C22—1522no—
467C22—1521no—
468C22#1192645211yescharacteristic
469C22#1192667711yescharacteristic
470C22#1192667811yescharacteristic
471C22#1192668711yescharacteristic
472C22#1192668911yescharacteristic
473C22#1192672612yes—
474C22#1192673312yes—
475C22#1192677811yescharacteristic
476C22#1192679511yescharacteristic
477C4—21no—
478C4—21no—
479C4—21no—
480C4—21no—
481C4—44no—
482C4—42no—
483C4—82no—
484C4—81no—
485C4—1521no—
486C4—1522no—
487C2—21no—
488C2—21no—
489C2—21no—
490C2—21no—
491C2—3041no—
492C2#1456263012yes—
493C2#1456263712yes—
494C2#1456463111yescharacteristic
495C2#1456467111yescharacteristic
496C2#1456476311yescharacteristic
subgroupG/H
centerC23#10597383
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC2×C19×#398C2
socleC23×C19#120
prime radicalC2×#10597376C22
hypercenterC2×#398D19
hypocenterC19#9919
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
3. #14563721C2semidirect
5. C2×#11926270C2semidirect
6. #14561514C2semidirect
7. C2×C19×#398C2semidirect
209. C2×#398D19semidirect
327. C19#9919semidirect

Maximal subgroups

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

subgroupindex
C2×#119268572
#145693772
#145637212
C2×#119262772
C2×#119262702
#145615142
C2×C19×#3982
#991919