Finite Group Databasebeta

← #14575191

Subgroups — #14575191

Order 2432.

478 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10597388C211yesmaximal, characteristic, complemented
2C2×#10597396C211yesmaximal, characteristic, complemented
3#11927199C211yesmaximal, characteristic, complemented
4#11926939C211yesmaximal, characteristic, complemented
5#11926788C211yesmaximal, characteristic, complemented
6#11926783C211yesmaximal, characteristic, complemented
7#11926756C211yesmaximal, characteristic, complemented
8#11926754C211yesmaximal, characteristic, complemented
9#11926706C211yesmaximal, characteristic, complemented
10#11926704C211yesmaximal, characteristic, complemented
11#11926700C211yesmaximal, characteristic, complemented
12#11926687C211yesmaximal, characteristic, complemented
13#11926642C211yesmaximal, characteristic, complemented
14#11926616C211yesmaximal, characteristic, complemented
15C19×#548C211yesmaximal, characteristic, complemented
16C2×#41×C19C2211yescharacteristic
17C22×Q8×C19C2211yescharacteristic
18C2×#64541C2211yescharacteristic
19C2×#64541C2211yescharacteristic
20C19×#124—21no—
21C19×#124C2211yescharacteristic
22C19×C22⋊Q8—21no—
23C19×C22⋊Q8C2211yescharacteristic
24C19×#121—21no—
25C19×#121C2211yescharacteristic
26C4×Q8×C19C2211yescharacteristic
27C4×D4×C19—21no—
28C4×D4×C19C2211yescharacteristic
29#10597396—24no—
30C2×#64528C2211yescharacteristic
31C2×#64528C2211yescharacteristic
32C2×#64528C2211yescharacteristic
33C2×#64528C2211yescharacteristic
34#10597388—24no—
35C2×#64527C2211yescharacteristic
36C2×#64527C2211yescharacteristic
37#10597384—21no—
38C2×#64526C2211yescharacteristic
39C2×#64526C2211yescharacteristic
40C2×#64525C2211yescharacteristic
41#10597370C2211yescharacteristic
42#10597370C2211yescharacteristic
43C2×#64520C2211yescharacteristic
44C22×C19⋊C8C2211yescharacteristic
45C4⋊C4×D19—21no—
46#10597329—21no—
47#10597329—21no—
48C4×D76C2211yescharacteristic
49#10597315C2211yescharacteristic
50#10597292C2211yescharacteristic
51#10597292C2211yescharacteristic
52#10597289C2211yescharacteristic
53C22⋊(C19⋊C8)C2211yescharacteristic
54C22⋊(C19⋊C8)C2211yescharacteristic
55#10597267C2211yescharacteristic
56#10597267C2211yescharacteristic
57#10597266C2211yescharacteristic
58#10597264C2211yescharacteristic
59C4⋊(C19⋊C8)C2211yescharacteristic
60#10597260C2211yescharacteristic
61#41×C19—22no—
62#41×C19—41no—
63C2×Q8×C19—21no—
64C2×Q8×C19—22no—
65C2×Q8×C19—41no—
66C2×Q8×C19C2311yescharacteristic
67C2×Q8×C19C2311yescharacteristic
68C2×D4×C19—21no—
69C2×D4×C19—21no—
70C2×D4×C19D411yescharacteristic
71C2×D4×C19C2311yescharacteristic
72C22×C4×C19—21no—
73C22×C4×C19—21no—
74C22×C4×C19C2311yescharacteristic
75C22×C4×C19C2311yescharacteristic
76C2×C22⋊D19—21no—
77C2×C22⋊D19—21no—
78#64541—22no—
79#64541—22no—
80#64541—41no—
81#64541—41no—
82C2×D76C2311yescharacteristic
83C2×C4×D19—21no—
84C2×C4×D19—21no—
85C2×C4×D19—21no—
86C2×Dic38C2311yescharacteristic
87C2×Dic38C2311yescharacteristic
88C4⋊C4×C19—21no—
89C4⋊C4×C19—21no—
90C4⋊C4×C19D411yescharacteristic
91C4⋊C4×C19C2311yescharacteristic
92C22⋊C4×C19—21no—
93C22⋊C4×C19—21no—
94C22⋊C4×C19—21no—
95C22⋊C4×C19—21no—
96C22⋊C4×C19D411yescharacteristic
97C22⋊C4×C19D411yescharacteristic
98C42×C19—21no—
99C42×C19C2311yescharacteristic
100C22⋊Dic19—21no—
101C22⋊Dic19—21no—
102#64528—22no—
103#64528—22no—
104#64528—22no—
105#64528—41no—
106#64527—22no—
107#64527D414yescomplemented
108#64526—22no—
109#64526—41no—
110#64525—22no—
111(C2×D19)⋊C4—21no—
112C4⋊Dic19—21no—
113C4⋊Dic19—21no—
114C4⋊Dic19C2311yescharacteristic
115Dic19⋊C4—21no—
116Dic19⋊C4—21no—
117#64520—22no—
118C2×C19⋊C8—22no—
119C2×C19⋊C8C2311yescharacteristic
120C2×C19⋊C8C2311yescharacteristic
121C2×C19⋊C8C2311yescharacteristic
122C2×C19⋊C8C2311yescharacteristic
123C23×C19—21no—
124C23×C19C2×D411yescharacteristic
125C23×C19C2×D411yescharacteristic
126C22×D19—21no—
127Q8×C19—21no—
128Q8×C19—21no—
129Q8×C19—21no—
130Q8×C19—42no—
131Q8×C19C2×D412yes—
132D4×C19—21no—
133D4×C19—21no—
134D4×C19—41no—
135D4×C19—42no—
136D4×C19—42no—
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—42no—
145C2×C4×C19—42no—
146C2×C4×C19C2×D411yescharacteristic
147C2×C4×C19C2×D411yescharacteristic
148C2×C4×C19C2×D411yescharacteristic
149C2×C4×C19C2×D411yescharacteristic
150C2×C4×C19C2411yescharacteristic
151C22⋊D19—42no—
152C22⋊D19—42no—
153C2×Dic19—21no—
154C2×Dic19—21no—
155C2×Dic19—21no—
156D76—21no—
157D76C2×D412yes—
158C4×D19—42no—
159C4×D19—42no—
160C4×D19—42no—
161Dic38—21no—
162Dic38—21no—
163Dic38—21no—
164Dic38—21no—
165C19⋊C8—21no—
166C19⋊C8—21no—
167C19⋊C8—21no—
168C19⋊C8C2×D412yes—
169#3269—191nomaximal, Sylow
170C22×C19—21no—
171C22×C19—21no—
172C22×C19—21no—
173C22×C19—21no—
174C22×C19—21no—
175C22×C19—21no—
176C22×C19—41no—
177C22×C19—41no—
178C22×C19—41no—
179C22×C19C22×D411yescharacteristic
180C2×D19—22no—
181C2×D19—41no—
182C2×D19—41no—
183C4×C19—21no—
184C4×C19—21no—
185C4×C19—22no—
186C4×C19—21no—
187C4×C19—21no—
188C4×C19—41no—
189C4×C19—41no—
190C4×C19C22×D411yescharacteristic
191C4×C19H(5,𝔽2)11yescharacteristic
192Dic19—41no—
193Dic19—41no—
194Dic19—41no—
195C2×#137—191no—
196C2×#135—191no—
197#548D1911yescharacteristic, complemented
198#547—191no—
199#497—191no—
200#468—191no—
201#467—191no—
202#463—191no—
203#462—191no—
204#452—191no—
205#452—191no—
206#451—191no—
207#449—191no—
208#440—191no—
209#435—191no—
210C2×C19—41no—
211C2×C19—41no—
212C2×C19—81no—
213C2×C19D4211yescharacteristic
214C2×C19#57511yescharacteristic
215C2×C19#57811yescharacteristic
216D19—42no—
217C2×#41—191no—
218C2×#41—191no—
219C2×#41C2×D1911yescharacteristic
220C22×Q8C2×D1911yescharacteristic
221#137—384no—
222#135—384no—
223C2×Q16—191no—
224C2×Q16—191no—
225C2×Q16—191no—
226C2×Q16—191no—
227C2×SD16—191no—
228C2×SD16—191no—
229C2×SD16—191no—
230C2×SD16—191no—
231C2×D8—191no—
232C2×M16—191no—
233C22×C8—191no—
234C4⋊Q8—191no—
235#124—21no—
236#124C2×D1911yescharacteristic
237#123—381no—
238#123—381no—
239C22⋊Q8—21no—
240C22⋊Q8—191no—
241C22⋊Q8—191no—
242C22⋊Q8C2×D1911yescharacteristic
243#121—21no—
244#121—381no—
245#121C2×D1911yescharacteristic
246C4×Q8C2×D1911yescharacteristic
247C4×D4—21no—
248C4×D4—191no—
249C4×D4C2×D1911yescharacteristic
250C2×C4⋊C4—381no—
251#107—191no—
252C4⋊C8—191no—
253#103—191no—
254#103—191no—
255#103—191no—
256#103—191no—
257#102—191no—
258#102—191no—
259C22⋊C8—191no—
260C22⋊C8—191no—
261#97—191no—
262C19#326911yescharacteristic, complemented, Sylow
263#41—22no—
264#41—41no—
265#41—382no—
266#41—382no—
267#41—761no—
268#41—761no—
269C2×Q8—21no—
270C2×Q8—22no—
271C2×Q8—41no—
272C2×Q8—191no—
273C2×Q8—191no—
274C2×Q8C22×D1911yescharacteristic
275C2×Q8C22×D1911yescharacteristic
276C2×D4—21no—
277C2×D4—21no—
278C2×D4—191no—
279C2×D4—381no—
280C2×D4—381no—
281C2×D4C22⋊D1911yescharacteristic
282C2×D4C22×D1911yescharacteristic
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—381no—
286C22×C4—381no—
287C22×C4—381no—
288C22×C4C22×D1911yescharacteristic
289C22×C4C22×D1911yescharacteristic
290Q16—382no—
291Q16—382no—
292Q16—382no—
293Q16—761no—
294SD16—194no—
295SD16—382no—
296SD16—382no—
297SD16—761no—
298D8—382no—
299M16—382no—
300C2×C8—191no—
301C2×C8—191no—
302C2×C8—191no—
303C2×C8—191no—
304C2×C8—382no—
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—191no—
308C4⋊C4—381no—
309C4⋊C4—381no—
310C4⋊C4—381no—
311C4⋊C4—381no—
312C4⋊C4C22⋊D1911yescharacteristic
313C4⋊C4C22×D1911yescharacteristic
314C22⋊C4—21no—
315C22⋊C4—21no—
316C22⋊C4—21no—
317C22⋊C4—21no—
318C22⋊C4—381no—
319C22⋊C4—381no—
320C22⋊C4—381no—
321C22⋊C4C22⋊D1911yescharacteristic
322C22⋊C4C22⋊D1911yescharacteristic
323C42—21no—
324C42C22×D1911yescharacteristic
325C23—21no—
326C23—381no—
327C23C2×C22⋊D1911yescharacteristic
328C23C2×C22⋊D1911yescharacteristic
329Q8—21no—
330Q8—21no—
331Q8—21no—
332Q8—42no—
333Q8—381no—
334Q8—381no—
335Q8—381no—
336Q8—381no—
337Q8D4×D1912yes—
338D4—21no—
339D4—21no—
340D4—41no—
341D4—42no—
342D4—42no—
343D4—192no—
344D4—381no—
345D4—762no—
346D4—762no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—42no—
355C2×C4—42no—
356C2×C4—381no—
357C2×C4—381no—
358C2×C4—381no—
359C2×C4—762no—
360C2×C4—762no—
361C2×C4—762no—
362C2×C4C2×C22⋊D1911yescharacteristic
363C2×C4C2×C22⋊D1911yescharacteristic
364C2×C4C2×C22⋊D1911yescharacteristic
365C2×C4C2×C22⋊D1911yescharacteristic
366C2×C4C23×D1911yescharacteristic
367C8—192no—
368C8—381no—
369C8—381no—
370C8—381no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—382no—
381C22—761no—
382C22—761no—
383C22C22×C22⋊D1911yescharacteristic
384C4—21no—
385C4—21no—
386C4—21no—
387C4—21no—
388C4—22no—
389C4—41no—
390C4—41no—
391C4—761no—
392C4—761no—
393C4—761no—
394C4C2×D4×D1911yescharacteristic
395C4#1059743011yescharacteristic
396C2—41no—
397C2—41no—
398C2—81no—
399C2—762no—
400C2D4×C22⋊D1911yescharacteristic
401C2#1192734211yescharacteristic
402C2#1192735911yescharacteristic
subgroupG/H
centerC22C22×C22⋊D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#548C2
socleC22×C19C22×D4
hypercenter#548D19
hypocenterC19#3269
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C4×D4 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C2×#10597388C2semidirect
2. C2×#10597396C2semidirect
3. #11927199C2semidirect
4. #11926939C2semidirect
5. #11926788C2semidirect
6. #11926783C2semidirect
7. #11926756C2semidirect
8. #11926754C2semidirect
9. #11926706C2semidirect
10. #11926704C2semidirect
11. #11926700C2semidirect
12. #11926687C2semidirect
13. #11926642C2semidirect
14. #11926616C2semidirect
15. C19×#548C2semidirect
107. #64527D4semidirect
197. #548D19semidirect
262. C19#3269semidirect

Maximal subgroups

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

subgroupindex
C2×#105973882
C2×#105973962
#119271992
#119269392
#119267882
#119267832
#119267562
#119267542
#119267062
#119267042
#119267002
#119266872
#119266422
#119266162
C19×#5482
#326919