Finite Group Databasebeta

← #14571716

Subgroups — #14571716

Order 2432.

472 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#11926485C211yesmaximal, characteristic, complemented
2#11926473C211yesmaximal, characteristic, complemented
3#11926470C211yesmaximal, characteristic, complemented
4#11926462C211yesmaximal, characteristic, complemented
5#11926462C211yesmaximal, characteristic, complemented
6#11926461C211yesmaximal, characteristic, complemented
7#11926461C211yesmaximal, characteristic, complemented
8#11926457C211yesmaximal, characteristic, complemented
9#11926457C211yesmaximal, characteristic, complemented
10#11926457C211yesmaximal, characteristic, complemented
11#11926454C211yesmaximal, characteristic
12#11926422C211yesmaximal, characteristic, complemented
13#11926422C211yesmaximal, characteristic, complemented
14#11926415C211yesmaximal, characteristic, complemented
15C19×#400C211yesmaximal, characteristic, complemented
16C22×D76C2211yescharacteristic
17C22×D76C2211yescharacteristic
18C22×D76C2211yescharacteristic
19C22×C4×D19C2211yescharacteristic
20C22×Dic38C2211yescharacteristic
21C2×C4⋊C4×C19C2211yescharacteristic
22C2×C4⋊C4×C19C2211yescharacteristic
23C2×(C2×D19)⋊C4C2211yescharacteristic
24C2×(C2×D19)⋊C4C2211yescharacteristic
25C2×(C2×D19)⋊C4C2211yescharacteristic
26C2×(C2×D19)⋊C4C2211yescharacteristic
27C2×(C2×D19)⋊C4C2211yescharacteristic
28C2×(C2×D19)⋊C4C2211yescharacteristic
29C2×(C2×D19)⋊C4C2211yescharacteristic
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×Dic19⋊C4C2211yescharacteristic
38C2×Dic19⋊C4C2211yescharacteristic
39C19×#95C2211yescharacteristic
40C19×#95C2211yescharacteristic
41C19×#95C2211yescharacteristic
42C19×#95C2211yescharacteristic
43C19×#95C2211yescharacteristic
44C19⋊#95C2211yescharacteristic
45C19⋊#95C2211yescharacteristic
46C19⋊#95C2211yescharacteristic
47C19⋊#95C2211yescharacteristic
48C19⋊#95C2211yescharacteristic
49C19⋊#95C2211yescharacteristic
50C19⋊#95C2211yescharacteristic
51C23×D19C2311yescharacteristic
52C23×D19C2311yescharacteristic
53C23×D19C2311yescharacteristic
54C22×C4×C19C2311yescharacteristic
55C22×C4×C19C2311yescharacteristic
56C22×C4×C19C2311yescharacteristic
57C22×C4×C19C2311yescharacteristic
58C22×C4×C19C2311yescharacteristic
59C22×C4×C19C2311yescharacteristic
60C22×C4×C19C2311yescharacteristic
61C22×Dic19C2311yescharacteristic
62C22×Dic19C2311yescharacteristic
63C22×Dic19C2311yescharacteristic
64C22×Dic19C2311yescharacteristic
65C22×Dic19C2311yescharacteristic
66C2×D76—22no—
67C2×D76—22no—
68C2×D76—41no—
69C2×D76—41no—
70C2×D76—41no—
71C2×D76—41no—
72C2×D76—41no—
73C2×D76—41no—
74C2×D76—41no—
75C2×C4×D19—41no—
76C2×C4×D19—41no—
77C2×C4×D19—41no—
78C2×Dic38—41no—
79C2×Dic38—41no—
80C2×Dic38—41no—
81C4⋊C4×C19—41no—
82C4⋊C4×C19—41no—
83(C2×D19)⋊C4—22no—
84(C2×D19)⋊C4—41no—
85(C2×D19)⋊C4—41no—
86(C2×D19)⋊C4—41no—
87(C2×D19)⋊C4—41no—
88(C2×D19)⋊C4—41no—
89(C2×D19)⋊C4—41no—
90(C2×D19)⋊C4—41no—
91(C2×D19)⋊C4—41no—
92(C2×D19)⋊C4—41no—
93(C2×D19)⋊C4—41no—
94(C2×D19)⋊C4—41no—
95(C2×D19)⋊C4—41no—
96(C2×D19)⋊C4—41no—
97Dic19⋊C4—41no—
98Dic19⋊C4—41no—
99C23×C19C2411yescharacteristic
100C22×D19—21no—
101C22×D19—21no—
102C22×D19—21no—
103C22×D19—21no—
104C22×D19—21no—
105C22×D19—21no—
106C22×D19—21no—
107C22×D19—21no—
108C22×D19—21no—
109C22×D19—21no—
110C22×D19—21no—
111C22×D19—21no—
112C22×D19—21no—
113C22×D19—21no—
114C22×D19—21no—
115C22×D19—21no—
116C22×D19—21no—
117C22×D19—21no—
118C22×D19—21no—
119C22×D19—21no—
120C22×D19#4112yes—
121C2×C4×C19—21no—
122C2×C4×C19—21no—
123C2×C4×C19—21no—
124C2×C4×C19—21no—
125C2×C4×C19—21no—
126C2×C4×C19—21no—
127C2×C4×C19—21no—
128C2×C4×C19—21no—
129C2×C4×C19—21no—
130C2×C4×C19—21no—
131C2×C4×C19—21no—
132C2×C4×C19—21no—
133C2×C4×C19—21no—
134C2×C4×C19—21no—
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×Dic19—21no—
143C2×Dic19—21no—
144C2×Dic19—21no—
145C2×Dic19—21no—
146C2×Dic19—21no—
147C2×Dic19—21no—
148C2×Dic19—21no—
149C2×Dic19—21no—
150C2×Dic19—21no—
151C2×Dic19—21no—
152C2×Dic19—21no—
153C2×Dic19—21no—
154C2×Dic19—21no—
155C2×Dic19—21no—
156C2×Dic19—21no—
157D76—44no—
158D76—44no—
159D76—44no—
160C4×D19—44no—
161Dic38—44no—
162#2824—191nomaximal, Sylow
163C22×C19C2×#4111yescharacteristic
164C22×C19H(5,𝔽2)11yescharacteristic
165C22×C19H(5,𝔽2)11yescharacteristic
166C22×C19H(5,𝔽2)11yescharacteristic
167C22×C19H(5,𝔽2)11yescharacteristic
168C22×C19H(5,𝔽2)11yescharacteristic
169C22×C192−1+411yescharacteristic
170C2×D19—22no—
171C2×D19—22no—
172C2×D19—22no—
173C2×D19—41no—
174C2×D19—41no—
175C2×D19—41no—
176C2×D19—41no—
177C2×D19—41no—
178C2×D19—41no—
179C2×D19—41no—
180C2×D19—41no—
181C2×D19—41no—
182C2×D19—41no—
183C2×D19—41no—
184C2×D19—41no—
185C2×D19—41no—
186C2×D19—41no—
187C2×D19—41no—
188C2×D19—41no—
189C2×D19—41no—
190C2×D19—41no—
191C4×C19—41no—
192C4×C19—41no—
193C4×C19—41no—
194C4×C19—41no—
195C4×C19—41no—
196C4×C19—41no—
197C4×C19—41no—
198Dic19—41no—
199Dic19—41no—
200Dic19—41no—
201Dic19—41no—
202Dic19—41no—
203#400—191no—
204#400D1911yescharacteristic, complemented
205#397—191no—
206#397—191no—
207#394—191no—
208#394—191no—
209#394—191no—
210#394—191no—
211#393—191no—
212#393—191no—
213#393—191no—
214#392—191no—
215#386—191no—
216#386—191no—
217#385—191no—
218C2×C19#53811yescharacteristic
219C2×C19#53811yescharacteristic
220C2×C19#53911yescharacteristic
221C2×C19#56011yescharacteristic
222C2×C19H(3,𝔽4)11yescharacteristic
223C2×C19#56211yescharacteristic
224C2×C19#56211yescharacteristic
225D19—42no—
226D19—81no—
227D19—81no—
228C22×Q8—191no—
229C22×D4—191no—
230C22×D4—191no—
231C22×D4—191no—
232C23×C4—191no—
233C2×C4⋊C4—191no—
234C2×C4⋊C4—191no—
235C2×C4⋊C4C2×D1911yescharacteristic
236C2×C4⋊C4C2×D1911yescharacteristic
237C2×C22⋊C4—191no—
238C2×C22⋊C4—191no—
239C2×C22⋊C4—191no—
240C2×C22⋊C4—191no—
241C2×C22⋊C4—191no—
242C2×C22⋊C4—191no—
243C2×C22⋊C4—191no—
244C2×C22⋊C4—191no—
245C2×C22⋊C4—191no—
246C2×C22⋊C4—191no—
247C2×C22⋊C4—191no—
248C2×C22⋊C4—191no—
249C2×C22⋊C4—191no—
250C2×C22⋊C4—191no—
251#95—191no—
252#95—191no—
253#95—191no—
254#95—191no—
255#95—191no—
256#95—191no—
257#95—191no—
258#95C2×D1911yescharacteristic
259#95C2×D1911yescharacteristic
260#95C2×D1911yescharacteristic
261#95C2×D1911yescharacteristic
262#95C2×D1911yescharacteristic
263C19#282411yescharacteristic, complemented, Sylow
264C24—191no—
265C24—191no—
266C24—191no—
267C2×Q8—761no—
268C2×Q8—761no—
269C2×Q8—761no—
270C2×D4—382no—
271C2×D4—382no—
272C2×D4—761no—
273C2×D4—761no—
274C2×D4—761no—
275C2×D4—761no—
276C2×D4—761no—
277C2×D4—761no—
278C2×D4—761no—
279C22×C4—191no—
280C22×C4—191no—
281C22×C4—191no—
282C22×C4—191no—
283C22×C4—191no—
284C22×C4—761no—
285C22×C4—761no—
286C22×C4—761no—
287C22×C4C22×D1911yescharacteristic
288C22×C4C22×D1911yescharacteristic
289C22×C4C22×D1911yescharacteristic
290C22×C4C22×D1911yescharacteristic
291C22×C4C22×D1911yescharacteristic
292C22×C4C22×D1911yescharacteristic
293C22×C4C22×D1911yescharacteristic
294C4⋊C4—41no—
295C4⋊C4—41no—
296C4⋊C4—761no—
297C4⋊C4—761no—
298C22⋊C4—382no—
299C22⋊C4—761no—
300C22⋊C4—761no—
301C22⋊C4—761no—
302C22⋊C4—761no—
303C22⋊C4—761no—
304C22⋊C4—761no—
305C22⋊C4—761no—
306C22⋊C4—761no—
307C22⋊C4—761no—
308C22⋊C4—761no—
309C22⋊C4—761no—
310C22⋊C4—761no—
311C22⋊C4—761no—
312C23—192no—
313C23—381no—
314C23—381no—
315C23—381no—
316C23—381no—
317C23—381no—
318C23—381no—
319C23—381no—
320C23—381no—
321C23—381no—
322C23—381no—
323C23—381no—
324C23—381no—
325C23—381no—
326C23—381no—
327C23—381no—
328C23—381no—
329C23—381no—
330C23—381no—
331C23—381no—
332C23—381no—
333C23C23×D1911yescharacteristic
334Q8—764no—
335D4—764no—
336D4—764no—
337D4—764no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—381no—
360C2×C4—381no—
361C2×C4—381no—
362C2×C4—381no—
363C2×C4—381no—
364C2×C4—381no—
365C2×C4—381no—
366C2×C4—381no—
367C2×C4—381no—
368C2×C4—381no—
369C2×C4—381no—
370C2×C4—381no—
371C2×C4—381no—
372C2×C4—381no—
373C2×C4—381no—
374C2×C4—764no—
375C22—382no—
376C22—382no—
377C22—382no—
378C22—761no—
379C22—761no—
380C22—761no—
381C22—761no—
382C22—761no—
383C22—761no—
384C22—761no—
385C22—761no—
386C22—761no—
387C22—761no—
388C22—761no—
389C22—761no—
390C22—761no—
391C22—761no—
392C22—761no—
393C22—761no—
394C22—761no—
395C22—761no—
396C22#1059743011yescharacteristic
397C22#1059743311yescharacteristic
398C22#41×D1911yescharacteristic
399C22#1059743511yescharacteristic
400C22#1059743511yescharacteristic
401C22#1059743511yescharacteristic
402C22#1059743511yescharacteristic
403C4—41no—
404C4—41no—
405C4—41no—
406C4—41no—
407C4—41no—
408C4—41no—
409C4—41no—
410C4—761no—
411C4—761no—
412C4—761no—
413C4—761no—
414C4—761no—
415C2—762no—
416C2—1521no—
417C2—1521no—
418C2#1192713011yescharacteristic
419C2#1192713311yescharacteristic
420C2#1192714211yescharacteristic
421C2#1192728511yescharacteristic
422C2#1192728611yescharacteristic
423C2#1192729011yescharacteristic
424C2#1192729211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#400C2
prime radical#11926454C2
hypercenter#400D19
hypocenterC19#2824
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
1. #11926485C2semidirect
2. #11926473C2semidirect
3. #11926470C2semidirect
4. #11926462C2semidirect
5. #11926462C2semidirect
6. #11926461C2semidirect
7. #11926461C2semidirect
8. #11926457C2semidirect
9. #11926457C2semidirect
10. #11926457C2semidirect
12. #11926422C2semidirect
13. #11926422C2semidirect
14. #11926415C2semidirect
15. C19×#400C2semidirect
204. #400D19semidirect
263. C19#2824semidirect

Maximal subgroups

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

subgroupindex
#119264852
#119264732
#119264702
#119264622
#119264612
#119264572
#119264542
#119264222
#119264152
C19×#4002
#282419