Finite Group Databasebeta

← #18080310

Subgroups — #18080310

Order 4864.

598 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14572657C211yesmaximal, characteristic
2#14567937C211yesmaximal, characteristic
3#14563721C211yesmaximal, characteristic, complemented
4#14563620C211yesmaximal, characteristic
5#14561503C211yesmaximal, characteristic, complemented
6#14561502C211yesmaximal, characteristic, complemented
7C19×#1823C211yesmaximal, characteristic, complemented
8C2×#10597375—21no—
9C2×C4×C22⋊D19C2211yescharacteristic
10C8×C22⋊D19—22no—
11(C22⋊D19)⋊C8—22no—
12#11926594—21no—
13C2×#10597263—21no—
14C2×C22⋊(C19⋊C8)C2211yescharacteristic
15C22⋊C8×D19—21no—
16#11926475C412yescomplemented
17#11926470C412yescomplemented
18#11926440—21no—
19#11926407—21no—
20#11926404C2211yescharacteristic
21#11926404C2211yescharacteristic
22#11926401—21no—
23#11926310—21no—
24#11926306—22no—
25C22×C4⋊C4×C19C2211yescharacteristic
26C2×C19×C22⋊C8C2211yescharacteristic
27C19×#380C2211yescharacteristic
28C19×#340—22no—
29C23×C4×C19—21no—
30C23×C4×C19C2311yescharacteristic
31C22×C22⋊D19D411yescharacteristic
32C22×C4×D19D411yescharacteristic
33C22×C8×C19D412yes—
34C2×C4⋊C4×C19—21no—
35C2×C4⋊C4×C19—21no—
36C2×C4⋊C4×C19—21no—
37C2×C4⋊C4×C19—21no—
38C2×C4⋊C4×C19—21no—
39C2×C4⋊C4×C19—21no—
40C2×C4⋊C4×C19C2×C412yes—
41C2×C22⋊C4×C19—21no—
42C2×C22⋊Dic19—21no—
43C2×C22⋊Dic19—21no—
44C2×C22⋊Dic19D411yescharacteristic
45#10597375—42no—
46#10597375—42no—
47C4×C22⋊D19—21no—
48C4×C22⋊D19—21no—
49C4×C22⋊D19—21no—
50C4×C22⋊D19—21no—
51C2×(C2×D19)⋊C4—22no—
52C2×(C2×D19)⋊C4C2×C411yescharacteristic
53C2×C4⋊Dic19—21no—
54C2×C4⋊Dic19—21no—
55C2×Dic19⋊C4—22no—
56C2×Dic19⋊C4C2×C411yescharacteristic
57C2×C4×Dic19D411yescharacteristic
58C22×C19⋊C8D412yes—
59C2×C8×D19—22no—
60C19×C22⋊C8—21no—
61C19×C22⋊C8—21no—
62C19×#95—21no—
63C19⋊#95—22no—
64C19⋊#95—22no—
65C19⋊#95—21no—
66C19⋊#95C2×C412yes—
67C22⋊(C19⋊C8)—21no—
68C22⋊(C19⋊C8)—21no—
69(C2×D19)⋊C8—22no—
70Dic19⋊C8—22no—
71C8×Dic19—22no—
72#10597263—42no—
73C24×C19C2×D411yescharacteristic
74C23×D19C22⋊C411yescharacteristic
75C22×C4×C19—22no—
76C22×C4×C19—42no—
77C22×C4×C19—41no—
78C22×C4×C19—41no—
79C22×C4×C19—41no—
80C22×C4×C19—41no—
81C22×C4×C19—41no—
82C22×C4×C19—41no—
83C22×C4×C19—41no—
84C22×C4×C19C22×C411yescharacteristic
85C22×C4×C19C2×D411yescharacteristic
86C22×C4×C19C2×D411yescharacteristic
87C22×C4×C19C2×D411yescharacteristic
88C22×C4×C19#4111yescharacteristic
89C22×C4×C19#4111yescharacteristic
90C2×C22⋊D19—21no—
91C2×C22⋊D19—21no—
92C2×C22⋊D19—21no—
93C2×C22⋊D19—21no—
94C2×C22⋊D19D812yes—
95C2×C22⋊D19SD1612yes—
96C22×Dic19—22no—
97C22×Dic19—41no—
98C22×Dic19C22⋊C411yescharacteristic
99C22×Dic19C22⋊C411yescharacteristic
100C22×Dic19C22⋊C411yescharacteristic
101C2×C4×D19—21no—
102C2×C4×D19—21no—
103C2×C4×D19—42no—
104C2×C8×C19—22no—
105C2×C8×C19—42no—
106C4⋊C4×C19—22no—
107C4⋊C4×C19—22no—
108C4⋊C4×C19—42no—
109C4⋊C4×C19—41no—
110C4⋊C4×C19—41no—
111C22⋊C4×C19—41no—
112C22⋊C4×C19—41no—
113C22⋊Dic19—21no—
114C22⋊Dic19—21no—
115C22⋊Dic19—41no—
116C22⋊Dic19—41no—
117C22⋊Dic19—41no—
118C22⋊Dic19—41no—
119(C2×D19)⋊C4—21no—
120(C2×D19)⋊C4—21no—
121(C2×D19)⋊C4—44no—
122C4⋊Dic19—42no—
123C4⋊Dic19—42no—
124Dic19⋊C4—21no—
125Dic19⋊C4—21no—
126Dic19⋊C4—44no—
127C4×Dic19—21no—
128C4×Dic19—21no—
129C2×C19⋊C8—22no—
130C2×C19⋊C8—42no—
131C8×D19—82no—
132#9470—191nomaximal, Sylow
133C23×C19—41no—
134C23×C19—41no—
135C23×C19C2×C22⋊C411yescharacteristic
136C23×C19#12111yescharacteristic
137C23×C19#12111yescharacteristic
138C23×C19C2×D811yescharacteristic
139C23×C19C2×SD1611yescharacteristic
140C23×C19#13511yescharacteristic
141C23×C19#13511yescharacteristic
142C22×D19—21no—
143C22×D19—21no—
144C22×D19—41no—
145C22×D19—41no—
146C22×D19#10212yes—
147C2×C4×C19—22no—
148C2×C4×C19—22no—
149C2×C4×C19—22no—
150C2×C4×C19—41no—
151C2×C4×C19—41no—
152C2×C4×C19—41no—
153C2×C4×C19—42no—
154C2×C4×C19—42no—
155C2×C4×C19—42no—
156C2×C4×C19—81no—
157C2×C4×C19—81no—
158C2×C4×C19—81no—
159C2×C4×C19—81no—
160C2×C4×C19—81no—
161C2×C4×C19—81no—
162C2×C4×C19—81no—
163C2×C4×C19C4×D411yescharacteristic
164C2×C4×C19C4×D411yescharacteristic
165C2×C4×C19#12011yescharacteristic
166C2×C4×C19#12311yescharacteristic
167C22⋊D19—22no—
168C22⋊D19—22no—
169C22⋊D19—22no—
170C22⋊D19—22no—
171C2×Dic19—21no—
172C2×Dic19—21no—
173C2×Dic19—21no—
174C2×Dic19—21no—
175C2×Dic19—41no—
176C2×Dic19—41no—
177C2×Dic19—42no—
178C2×Dic19—42no—
179C2×Dic19—42no—
180C2×Dic19—81no—
181C2×Dic19—81no—
182C2×Dic19—81no—
183C2×Dic19#10212yes—
184C4×D19—42no—
185C4×D19—81no—
186C8×C19—42no—
187C19⋊C8—42no—
188#2972—191no—
189#2486—191no—
190#1823—191no—
191#1823D1911yescharacteristic, complemented
192#1799—191no—
193#1289—191no—
194#1289—191no—
195C22×C19—21no—
196C22×C19—21no—
197C22×C19—21no—
198C22×C19—21no—
199C22×C19—21no—
200C22×C19—21no—
201C22×C19—41no—
202C22×C19—41no—
203C22×C19—41no—
204C22×C19—41no—
205C22×C19#38611yescharacteristic
206C22×C19C2×#10211yescharacteristic
207C22×C19#41611yescharacteristic
208C22×C19#46511yescharacteristic
209C22×C19#46511yescharacteristic
210C22×C19#46611yescharacteristic
211C22×C19#46611yescharacteristic
212C2×D19—22no—
213C2×D19—41no—
214C2×D19—41no—
215C2×D19—42no—
216C2×D19—81no—
217C4×C19—21no—
218C4×C19—21no—
219C4×C19—21no—
220C4×C19—82no—
221C4×C19—161no—
222C4×C19#45812yes—
223Dic19—22no—
224Dic19—41no—
225Dic19—41no—
226Dic19—82no—
227Dic19—161no—
228C2×#123—381no—
229C2×C4×D4—191no—
230C22×C4⋊C4C2×D1911yescharacteristic
231C8×D4—382no—
232C8×D4—382no—
233#431—381no—
234C2×#99—381no—
235C2×C22⋊C8—191no—
236C2×C22⋊C8—381no—
237C2×C22⋊C8C2×D1911yescharacteristic
238#398—192no—
239#397—192no—
240#389—381no—
241#381—381no—
242#380—191no—
243#380—191no—
244#380—381no—
245#380C2×D1911yescharacteristic
246#342—381no—
247#340—22no—
248#340—382no—
249C2×C19—21no—
250C2×C19—21no—
251C2×C19—21no—
252C2×C19—21no—
253C2×C19—21no—
254C2×C19—21no—
255C2×C19#189011yescharacteristic
256C2×C19#189311yescharacteristic
257C2×C19#190911yescharacteristic
258D19—42no—
259C22×D4—191no—
260C23×C4—21no—
261C23×C4—191no—
262C23×C4C22×D1911yescharacteristic
263C22×C8—192no—
264C22×C8—382no—
265C22×C8C22⋊D1912yes—
266#123—762no—
267#123—762no—
268C4×D4—381no—
269C4×D4—381no—
270C4×D4—381no—
271C4×D4—381no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—191no—
279C2×C4⋊C4—382no—
280C2×C4⋊C4—381no—
281C2×C4⋊C4—381no—
282C2×C4⋊C4C4×D1912yes—
283C2×C22⋊C4—21no—
284C2×C22⋊C4—191no—
285C2×C22⋊C4—191no—
286C2×C22⋊C4—382no—
287C2×C22⋊C4—381no—
288C2×C22⋊C4—381no—
289C2×C42—191no—
290C4⋊C8—382no—
291#99—762no—
292C22⋊C8—21no—
293C22⋊C8—21no—
294C22⋊C8—382no—
295C22⋊C8—381no—
296C22⋊C8—381no—
297C4×C8—382no—
298#95—21no—
299#95—192no—
300#95—382no—
301#95—382no—
302#95—381no—
303C19#947011yescharacteristic, complemented, Sylow
304C24—191no—
305C24D4×D1911yescharacteristic
306C2×D4—192no—
307C2×D4—192no—
308C2×D4—381no—
309C2×D4—381no—
310C2×D4—381no—
311C2×D4—381no—
312C22×C4—22no—
313C22×C4—42no—
314C22×C4—41no—
315C22×C4—41no—
316C22×C4—41no—
317C22×C4—41no—
318C22×C4—41no—
319C22×C4—41no—
320C22×C4—41no—
321C22×C4—191no—
322C22×C4—191no—
323C22×C4—191no—
324C22×C4—381no—
325C22×C4—381no—
326C22×C4—382no—
327C22×C4—762no—
328C22×C4—761no—
329C22×C4C2×C4×D1911yescharacteristic
330C22×C4#6454111yescharacteristic
331C22×C4D4×D1911yescharacteristic
332C22×C4D4×D1911yescharacteristic
333C22×C4#6454311yescharacteristic
334C22×C4C2×C22⋊D1911yescharacteristic
335C2×C8—22no—
336C2×C8—42no—
337C2×C8—382no—
338C2×C8—762no—
339C2×C8—1522no—
340C4⋊C4—22no—
341C4⋊C4—22no—
342C4⋊C4—42no—
343C4⋊C4—41no—
344C4⋊C4—41no—
345C4⋊C4—381no—
346C4⋊C4—381no—
347C4⋊C4—762no—
348C4⋊C4—762no—
349C4⋊C4—764no—
350C22⋊C4—41no—
351C22⋊C4—41no—
352C22⋊C4—381no—
353C22⋊C4—381no—
354C22⋊C4—381no—
355C22⋊C4—381no—
356C22⋊C4—764no—
357C22⋊C4—761no—
358C22⋊C4—761no—
359C22⋊C4—761no—
360C22⋊C4—761no—
361C42—381no—
362C42—381no—
363C23—41no—
364C23—41no—
365C23—192no—
366C23—381no—
367C23—381no—
368C23—761no—
369C23—761no—
370C23C22⋊C4×D1911yescharacteristic
371C23#1059733011yescharacteristic
372C23D8×D1911yescharacteristic
373C23#1059735811yescharacteristic
374C23SD16×D1911yescharacteristic
375C23#1059736211yescharacteristic
376C23#1059738411yescharacteristic
377D4—382no—
378D4—382no—
379D4—382no—
380D4—382no—
381C2×C4—22no—
382C2×C4—22no—
383C2×C4—22no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—81no—
391C2×C4—81no—
392C2×C4—81no—
393C2×C4—81no—
394C2×C4—81no—
395C2×C4—81no—
396C2×C4—81no—
397C2×C4—192no—
398C2×C4—381no—
399C2×C4—381no—
400C2×C4—381no—
401C2×C4—381no—
402C2×C4—762no—
403C2×C4—761no—
404C2×C4—761no—
405C2×C4—762no—
406C2×C4—762no—
407C2×C4—762no—
408C2×C4—1521no—
409C2×C4—1521no—
410C2×C4—1521no—
411C2×C4—1521no—
412C2×C4(C22⋊D19)⋊C411yescharacteristic
413C2×C4#1059732911yescharacteristic
414C2×C4C4×C22⋊D1911yescharacteristic
415C2×C4#1059738311yescharacteristic
416C8—42no—
417C8—762no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—21no—
423C22—21no—
424C22—41no—
425C22—41no—
426C22—41no—
427C22—41no—
428C22—382no—
429C22—762no—
430C22—761no—
431C22—761no—
432C22—1521no—
433C22#1192642011yescharacteristic
434C22#102×D1911yescharacteristic
435C22#1192653711yescharacteristic
436C22#1192677011yescharacteristic
437C22#1192677211yescharacteristic
438C22#1192677711yescharacteristic
439C22#1192677911yescharacteristic
440C4—21no—
441C4—21no—
442C4—21no—
443C4—82no—
444C4—161no—
445C4—382no—
446C4—3041no—
447C4—761no—
448C4—761no—
449C4—1522no—
450C4#1192673312yes—
451C2—21no—
452C2—21no—
453C2—21no—
454C2—21no—
455C2—21no—
456C2—21no—
457C2—762no—
458C2#1456404511yescharacteristic
459C2#1456406011yescharacteristic
460C2#1456415411yescharacteristic
subgroupG/H
centerC22#11926420
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1823C2
socleC22×C19#386
prime radicalC22×C22⋊D19D4
cosocleC23×C4×C19C23
hypercenter#1823D19
hypocenterC19#9470
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1823

Complements

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

NH ≅ G/Ntype
3. #14563721C2semidirect
5. #14561503C2semidirect
6. #14561502C2semidirect
7. C19×#1823C2semidirect
16. #11926475C4semidirect
17. #11926470C4semidirect
191. #1823D19semidirect
303. C19#9470semidirect

Maximal subgroups

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

subgroupindex
#145726572
#145679372
#145637212
#145636202
#145615032
#145615022
C19×#18232
#947019