Finite Group Databasebeta

← #14571721

Subgroups — #14571721

Order 2432.

522 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C19⋊#401C211yesmaximal, characteristic, complemented
2#11926473C211yesmaximal, characteristic, complemented
3#11926472C211yesmaximal, characteristic, complemented
4#11926471C211yesmaximal, characteristic, complemented
5#11926467C211yesmaximal, characteristic, complemented
6#11926462C211yesmaximal, characteristic, complemented
7#11926460C211yesmaximal, characteristic, complemented
8#11926459C211yesmaximal, characteristic, complemented
9#11926453C211yesmaximal, characteristic, complemented
10#11926453C211yesmaximal, characteristic, complemented
11#11926452C211yesmaximal, characteristic, complemented
12#11926452C211yesmaximal, characteristic, complemented
13#11926423C211yesmaximal, characteristic, complemented
14#11926423C211yesmaximal, characteristic, complemented
15C19×#386C211yesmaximal, characteristic, complemented
16C22×D4×C19C2211yescharacteristic
17C23×C4×C19C2211yescharacteristic
18C22×C22⋊D19C2211yescharacteristic
19C22×C22⋊D19C2211yescharacteristic
20C22×C22⋊D19C2211yescharacteristic
21C22×C22⋊D19C2211yescharacteristic
22C22×D76C2211yescharacteristic
23C2×C22⋊C4×C19C2211yescharacteristic
24C2×C22⋊C4×C19C2211yescharacteristic
25C2×C22⋊C4×C19C2211yescharacteristic
26C2×C22⋊Dic19C2211yescharacteristic
27C2×C22⋊Dic19C2211yescharacteristic
28C2×C22⋊Dic19C2211yescharacteristic
29C2×C22⋊Dic19C2211yescharacteristic
30C2×(C2×D19)⋊C4C2211yescharacteristic
31C2×(C2×D19)⋊C4C2211yescharacteristic
32C2×(C2×D19)⋊C4C2211yescharacteristic
33C2×(C2×D19)⋊C4C2211yescharacteristic
34C2×(C2×D19)⋊C4C2211yescharacteristic
35C2×(C2×D19)⋊C4C2211yescharacteristic
36C2×(C2×D19)⋊C4C2211yescharacteristic
37C2×(C2×D19)⋊C4C2211yescharacteristic
38C2×C4⋊Dic19C2211yescharacteristic
39C2×Dic19⋊C4C2211yescharacteristic
40C2×Dic19⋊C4C2211yescharacteristic
41C19×#95C2211yescharacteristic
42C19×#95C2211yescharacteristic
43C19⋊#95C2211yescharacteristic
44C19⋊#95C2211yescharacteristic
45C19⋊#95C2211yescharacteristic
46C19⋊#95C2211yescharacteristic
47C19⋊#95C2211yescharacteristic
48C19⋊#95C2211yescharacteristic
49C19⋊#95C2211yescharacteristic
50C19⋊#95C2211yescharacteristic
51C24×C19C2311yescharacteristic
52C24×C19C2311yescharacteristic
53C23×D19C2311yescharacteristic
54C23×D19C2311yescharacteristic
55C2×D4×C19—22no—
56C2×D4×C19—41no—
57C2×D4×C19—41no—
58C22×C4×C19—41no—
59C22×C4×C19—41no—
60C22×C4×C19—41no—
61C22×C4×C19C2311yescharacteristic
62C22×C4×C19C2311yescharacteristic
63C22×C4×C19C2311yescharacteristic
64C22×C4×C19C2311yescharacteristic
65C22×C4×C19C2311yescharacteristic
66C2×C22⋊D19—22no—
67C2×C22⋊D19—22no—
68C2×C22⋊D19—41no—
69C2×C22⋊D19—41no—
70C2×C22⋊D19—41no—
71C2×C22⋊D19—41no—
72C2×C22⋊D19—41no—
73C2×C22⋊D19—41no—
74C2×C22⋊D19—41no—
75C2×C22⋊D19—41no—
76C2×C22⋊D19—41no—
77C2×C22⋊D19—41no—
78C22×Dic19C2311yescharacteristic
79C22×Dic19C2311yescharacteristic
80C22×Dic19C2311yescharacteristic
81C22×Dic19C2311yescharacteristic
82C22×Dic19C2311yescharacteristic
83C22×Dic19C2311yescharacteristic
84C2×D76—41no—
85C2×D76—41no—
86C2×D76—41no—
87C22⋊C4×C19—41no—
88C22⋊C4×C19—41no—
89C22⋊C4×C19—41no—
90C22⋊Dic19—41no—
91C22⋊Dic19—41no—
92C22⋊Dic19—41no—
93C22⋊Dic19—41no—
94(C2×D19)⋊C4—41no—
95(C2×D19)⋊C4—41no—
96(C2×D19)⋊C4—41no—
97(C2×D19)⋊C4—41no—
98(C2×D19)⋊C4—41no—
99(C2×D19)⋊C4—41no—
100(C2×D19)⋊C4—41no—
101(C2×D19)⋊C4—41no—
102C4⋊Dic19—41no—
103Dic19⋊C4—41no—
104Dic19⋊C4—41no—
105C23×C19—21no—
106C23×C19—21no—
107C23×C19—21no—
108C23×C19—21no—
109C23×C19—21no—
110C23×C19—21no—
111C23×C19—21no—
112C23×C19—21no—
113C23×C19—21no—
114C23×C19—21no—
115C23×C19—21no—
116C23×C19—21no—
117C23×C19—21no—
118C23×C19#4112yes—
119C23×C19C2411yescharacteristic
120C22×D19—21no—
121C22×D19—21no—
122C22×D19—21no—
123C22×D19—21no—
124C22×D19—21no—
125C22×D19—21no—
126C22×D19—21no—
127C22×D19—21no—
128C22×D19—21no—
129C22×D19—21no—
130C22×D19—21no—
131C22×D19—21no—
132C22×D19—21no—
133C22×D19—21no—
134D4×C19—44no—
135C2×C4×C19—21no—
136C2×C4×C19—21no—
137C2×C4×C19—21no—
138C2×C4×C19—21no—
139C2×C4×C19—21no—
140C2×C4×C19—21no—
141C2×C4×C19—21no—
142C2×C4×C19—21no—
143C2×C4×C19—21no—
144C2×C4×C19—21no—
145C2×C4×C19—21no—
146C2×C4×C19—21no—
147C2×C4×C19—21no—
148C2×C4×C19—21no—
149C2×C4×C19—21no—
150C2×C4×C19—44no—
151C22⋊D19—44no—
152C22⋊D19—44no—
153C22⋊D19—44no—
154C22⋊D19—44no—
155C2×Dic19—21no—
156C2×Dic19—21no—
157C2×Dic19—21no—
158C2×Dic19—21no—
159C2×Dic19—21no—
160C2×Dic19—21no—
161C2×Dic19—21no—
162C2×Dic19—21no—
163C2×Dic19—21no—
164C2×Dic19—21no—
165C2×Dic19—21no—
166C2×Dic19—21no—
167C2×Dic19—21no—
168C2×Dic19—21no—
169C2×Dic19—21no—
170C2×Dic19—21no—
171C2×Dic19—21no—
172C2×Dic19—21no—
173D76—44no—
174#2825—191nomaximal, Sylow
175C22×C19—22no—
176C22×C19—22no—
177C22×C19—22no—
178C22×C19—41no—
179C22×C19—41no—
180C22×C19—41no—
181C22×C19—41no—
182C22×C19—41no—
183C22×C19—41no—
184C22×C19—41no—
185C22×C19—41no—
186C22×C19—41no—
187C22×C19—41no—
188C22×C19—41no—
189C22×C19C2×#4111yescharacteristic
190C22×C19H(5,𝔽2)11yescharacteristic
191C22×C19H(5,𝔽2)11yescharacteristic
192C22×C19H(5,𝔽2)11yescharacteristic
193C22×C19H(5,𝔽2)11yescharacteristic
194C22×C19H(5,𝔽2)11yescharacteristic
195C22×C19H(5,𝔽2)11yescharacteristic
196C2×D19—41no—
197C2×D19—41no—
198C2×D19—41no—
199C2×D19—41no—
200C2×D19—41no—
201C2×D19—41no—
202C2×D19—41no—
203C2×D19—41no—
204C2×D19—41no—
205C2×D19—41no—
206C2×D19—41no—
207C2×D19—41no—
208C2×D19—41no—
209C2×D19—41no—
210C4×C19—41no—
211C4×C19—41no—
212C4×C19—41no—
213C4×C19—41no—
214C4×C19—41no—
215Dic19—41no—
216Dic19—41no—
217Dic19—41no—
218Dic19—41no—
219Dic19—41no—
220Dic19—41no—
221#401—191no—
222#397—191no—
223#397—191no—
224#397—191no—
225#396—191no—
226#394—191no—
227#394—191no—
228#394—191no—
229#392—191no—
230#392—191no—
231#392—191no—
232#392—191no—
233#386—191no—
234#386—191no—
235#386D1911yescharacteristic, complemented
236C2×C19—42no—
237C2×C19—81no—
238C2×C19#53811yescharacteristic
239C2×C19#53811yescharacteristic
240C2×C19#53811yescharacteristic
241C2×C19#56011yescharacteristic
242C2×C19#56011yescharacteristic
243C2×C19#56011yescharacteristic
244C2×C19#56011yescharacteristic
245D19—81no—
246D19—81no—
247C22×D4—191no—
248C22×D4—191no—
249C22×D4—191no—
250C22×D4—191no—
251C22×D4—191no—
252C22×D4C2×D1911yescharacteristic
253C23×C4C2×D1911yescharacteristic
254C2×C4⋊C4—191no—
255C2×C4⋊C4—191no—
256C2×C4⋊C4—191no—
257C2×C22⋊C4—191no—
258C2×C22⋊C4—191no—
259C2×C22⋊C4—191no—
260C2×C22⋊C4—191no—
261C2×C22⋊C4—191no—
262C2×C22⋊C4—191no—
263C2×C22⋊C4—191no—
264C2×C22⋊C4—191no—
265C2×C22⋊C4—191no—
266C2×C22⋊C4—191no—
267C2×C22⋊C4—191no—
268C2×C22⋊C4—191no—
269C2×C22⋊C4C2×D1911yescharacteristic
270C2×C22⋊C4C2×D1911yescharacteristic
271C2×C22⋊C4C2×D1911yescharacteristic
272#95—191no—
273#95—191no—
274#95—191no—
275#95—191no—
276#95—191no—
277#95—191no—
278#95—191no—
279#95—191no—
280#95C2×D1911yescharacteristic
281#95C2×D1911yescharacteristic
282C19#282511yescharacteristic, complemented, Sylow
283C24—191no—
284C24—191no—
285C24C22×D1911yescharacteristic
286C24C22×D1911yescharacteristic
287C2×D4—22no—
288C2×D4—41no—
289C2×D4—41no—
290C2×D4—382no—
291C2×D4—382no—
292C2×D4—761no—
293C2×D4—761no—
294C2×D4—761no—
295C2×D4—761no—
296C2×D4—761no—
297C2×D4—761no—
298C2×D4—761no—
299C2×D4—761no—
300C2×D4—761no—
301C2×D4—761no—
302C2×D4—761no—
303C2×D4—761no—
304C2×D4—761no—
305C22×C4—41no—
306C22×C4—41no—
307C22×C4—41no—
308C22×C4—191no—
309C22×C4—191no—
310C22×C4—191no—
311C22×C4—191no—
312C22×C4—191no—
313C22×C4—191no—
314C22×C4C22×D1911yescharacteristic
315C22×C4C22×D1911yescharacteristic
316C22×C4C22×D1911yescharacteristic
317C22×C4C22×D1911yescharacteristic
318C22×C4C22×D1911yescharacteristic
319C4⋊C4—761no—
320C4⋊C4—761no—
321C4⋊C4—761no—
322C22⋊C4—41no—
323C22⋊C4—41no—
324C22⋊C4—41no—
325C22⋊C4—761no—
326C22⋊C4—761no—
327C22⋊C4—761no—
328C22⋊C4—761no—
329C22⋊C4—761no—
330C22⋊C4—761no—
331C22⋊C4—761no—
332C22⋊C4—761no—
333C22⋊C4—761no—
334C22⋊C4—761no—
335C22⋊C4—761no—
336C22⋊C4—761no—
337C23—21no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—21no—
345C23—21no—
346C23—21no—
347C23—21no—
348C23—21no—
349C23—21no—
350C23—381no—
351C23—381no—
352C23—381no—
353C23—381no—
354C23—381no—
355C23—381no—
356C23—381no—
357C23—381no—
358C23—381no—
359C23—381no—
360C23—381no—
361C23—381no—
362C23—381no—
363C23—381no—
364C23#6454112yes—
365C23C23×D1911yescharacteristic
366D4—44no—
367D4—764no—
368D4—764no—
369D4—764no—
370D4—764no—
371D4—764no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—44no—
388C2×C4—381no—
389C2×C4—381no—
390C2×C4—381no—
391C2×C4—381no—
392C2×C4—381no—
393C2×C4—381no—
394C2×C4—381no—
395C2×C4—381no—
396C2×C4—381no—
397C2×C4—381no—
398C2×C4—381no—
399C2×C4—381no—
400C2×C4—381no—
401C2×C4—381no—
402C2×C4—381no—
403C2×C4—381no—
404C2×C4—381no—
405C2×C4—381no—
406C22—22no—
407C22—22no—
408C22—22no—
409C22—41no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—41no—
415C22—41no—
416C22—41no—
417C22—41no—
418C22—41no—
419C22—41no—
420C22—761no—
421C22—761no—
422C22—761no—
423C22—761no—
424C22—761no—
425C22—761no—
426C22—761no—
427C22—761no—
428C22—761no—
429C22—761no—
430C22—761no—
431C22—761no—
432C22—761no—
433C22—761no—
434C22C2×#6454111yescharacteristic
435C22#1059743011yescharacteristic
436C22#1059743011yescharacteristic
437C22#1059743011yescharacteristic
438C22#1059743011yescharacteristic
439C22#1059743511yescharacteristic
440C22#1059743511yescharacteristic
441C4—41no—
442C4—41no—
443C4—41no—
444C4—41no—
445C4—41no—
446C4—761no—
447C4—761no—
448C4—761no—
449C4—761no—
450C4—761no—
451C4—761no—
452C2—42no—
453C2—81no—
454C2—1521no—
455C2—1521no—
456C2#1192712711yescharacteristic
457C2#1192712711yescharacteristic
458C2#1192713211yescharacteristic
459C2#1192728211yescharacteristic
460C2#1192728211yescharacteristic
461C2#1192728311yescharacteristic
462C2#1192728411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#386C2
hypercenter#386D19
hypocenterC19#2825
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
1. C19⋊#401C2semidirect
2. #11926473C2semidirect
3. #11926472C2semidirect
4. #11926471C2semidirect
5. #11926467C2semidirect
6. #11926462C2semidirect
7. #11926460C2semidirect
8. #11926459C2semidirect
9. #11926453C2semidirect
10. #11926453C2semidirect
11. #11926452C2semidirect
12. #11926452C2semidirect
13. #11926423C2semidirect
14. #11926423C2semidirect
15. C19×#386C2semidirect
235. #386D19semidirect
282. C19#2825semidirect

Maximal subgroups

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

subgroupindex
C19⋊#4012
#119264732
#119264722
#119264712
#119264672
#119264622
#119264602
#119264592
#119264532
#119264522
#119264232
C19×#3862
#282519