Finite Group Databasebeta

← #14575216

Subgroups — #14575216

Order 2432.

488 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10597397C211yesmaximal, characteristic, complemented
2C2×#10597396C211yesmaximal, characteristic, complemented
3#11927203C211yesmaximal, characteristic, complemented
4#11926931C211yesmaximal, characteristic, complemented
5#11926795C211yesmaximal, characteristic, complemented
6#11926771C211yesmaximal, characteristic, complemented
7#11926766C211yesmaximal, characteristic, complemented
8#11926741C211yesmaximal, characteristic, complemented
9#11926706C211yesmaximal, characteristic, complemented
10#11926689C211yesmaximal, characteristic, complemented
11#11926687C211yesmaximal, characteristic, complemented
12#11926682C211yesmaximal, characteristic, complemented
13#11926649C211yesmaximal, characteristic, complemented
14#11926616C211yesmaximal, characteristic, complemented
15C19×#550C211yesmaximal, characteristic, complemented
16C2×#41×C19C2211yescharacteristic
17C2×#41×C19C2211yescharacteristic
18C2×#64541C2211yescharacteristic
19C22×Dic38C2211yescharacteristic
20C19×#127—21no—
21C19×#127C2211yescharacteristic
22C19×#121—21no—
23C19×#121—21no—
24C19×#121C2211yescharacteristic
25C19×#121C2211yescharacteristic
26C4×Q8×C19C2211yescharacteristic
27C4×D4×C19—21no—
28C4×D4×C19C2211yescharacteristic
29#10597397—24no—
30#10597396—24no—
31C2×#64528C2211yescharacteristic
32C2×#64528C2211yescharacteristic
33C2×#64527C2211yescharacteristic
34#10597385—21no—
35C2×#64526C2211yescharacteristic
36C2×#64526C2211yescharacteristic
37C2×#64526C2211yescharacteristic
38C2×#64526C2211yescharacteristic
39C2×#64525C2211yescharacteristic
40C2×#64525C2211yescharacteristic
41#10597376C2211yescharacteristic
42#10597370C2211yescharacteristic
43C2×#64520C2211yescharacteristic
44C22×C19⋊C8C2211yescharacteristic
45#10597342—21no—
46#10597331—21no—
47(C22⋊D19)⋊C4—21no—
48#10597321C2211yescharacteristic
49C4×Dic38C2211yescharacteristic
50#10597292C2211yescharacteristic
51#10597289C2211yescharacteristic
52#10597289C2211yescharacteristic
53C22⋊(C19⋊C8)C2211yescharacteristic
54C22⋊(C19⋊C8)C2211yescharacteristic
55#10597267C2211yescharacteristic
56#10597267C2211yescharacteristic
57#10597266C2211yescharacteristic
58#10597265C2211yescharacteristic
59C4⋊(C19⋊C8)C2211yescharacteristic
60#10597260C2211yescharacteristic
61#41×C19—22no—
62#41×C19—22no—
63#41×C19—41no—
64#41×C19—41no—
65C2×Q8×C19C2311yescharacteristic
66C2×D4×C19—21no—
67C2×D4×C19—21no—
68C2×D4×C19—21no—
69C2×D4×C19—21no—
70C2×D4×C19—21no—
71C2×D4×C19—21no—
72C2×D4×C19D411yescharacteristic
73C2×D4×C19C2311yescharacteristic
74C2×D4×C19C2311yescharacteristic
75C22×C4×C19—21no—
76C22×C4×C19—21no—
77C22×C4×C19C2311yescharacteristic
78C22×C4×C19C2311yescharacteristic
79C2×C22⋊D19—21no—
80C2×C22⋊D19—21no—
81C22×Dic19—21no—
82#64541—22no—
83#64541—41no—
84C2×D76C2311yescharacteristic
85C2×C4×D19—21no—
86C2×Dic38—22no—
87C2×Dic38—21no—
88C2×Dic38—41no—
89C2×Dic38C2311yescharacteristic
90C2×Dic38C2311yescharacteristic
91C4⋊C4×C19—21no—
92C4⋊C4×C19D411yescharacteristic
93C4⋊C4×C19C2311yescharacteristic
94C22⋊C4×C19—21no—
95C22⋊C4×C19—21no—
96C22⋊C4×C19D411yescharacteristic
97C22⋊C4×C19D411yescharacteristic
98C42×C19—21no—
99C42×C19C2311yescharacteristic
100C22⋊Dic19—21no—
101#64528—22no—
102#64528D414yescomplemented
103#64527—22no—
104#64526—22no—
105#64526—22no—
106#64526—22no—
107#64526—41no—
108#64525—22no—
109#64525—41no—
110(C2×D19)⋊C4—21no—
111(C2×D19)⋊C4—21no—
112(C2×D19)⋊C4—21no—
113C4⋊Dic19C2311yescharacteristic
114Dic19⋊C4—21no—
115Dic19⋊C4—21no—
116C4×Dic19—21no—
117#64520—22no—
118C2×C19⋊C8—22no—
119C2×C19⋊C8C2311yescharacteristic
120C2×C19⋊C8C2311yescharacteristic
121C2×C19⋊C8C2311yescharacteristic
122C2×C19⋊C8C2311yescharacteristic
123C23×C19—21no—
124C23×C19—21no—
125C23×C19C2×D411yescharacteristic
126C23×C19C2×D411yescharacteristic
127C22×D19—21no—
128Q8×C19—21no—
129Q8×C19C2×D412yes—
130D4×C19—21no—
131D4×C19—21no—
132D4×C19—21no—
133D4×C19—21no—
134D4×C19—41no—
135D4×C19—42no—
136D4×C19—42no—
137D4×C19—42no—
138D4×C19—81no—
139D4×C19—81no—
140D4×C19—81no—
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—42no—
148C2×C4×C19—42no—
149C2×C4×C19C2×D411yescharacteristic
150C2×C4×C19C2×D411yescharacteristic
151C2×C4×C19C2×D411yescharacteristic
152C2×C4×C19C2×D411yescharacteristic
153C2×C4×C19C2411yescharacteristic
154C22⋊D19—42no—
155C22⋊D19—42no—
156C2×Dic19—21no—
157C2×Dic19—21no—
158C2×Dic19—21no—
159C2×Dic19—42no—
160D76—21no—
161D76—21no—
162C4×D19—42no—
163Dic38—21no—
164Dic38—21no—
165Dic38—21no—
166Dic38—42no—
167Dic38C2×D412yes—
168C19⋊C8—21no—
169C19⋊C8—21no—
170C19⋊C8—21no—
171C19⋊C8C2×D412yes—
172#3271—191nomaximal, Sylow
173C22×C19—21no—
174C22×C19—21no—
175C22×C19—21no—
176C22×C19—21no—
177C22×C19—21no—
178C22×C19—21no—
179C22×C19—41no—
180C22×C19—41no—
181C22×C19—41no—
182C22×C19—41no—
183C22×C19—41no—
184C22×C19—41no—
185C22×C19C22×D411yescharacteristic
186C2×D19—41no—
187C2×D19—41no—
188C2×D19—41no—
189C4×C19—21no—
190C4×C19—21no—
191C4×C19—22no—
192C4×C19—21no—
193C4×C19—21no—
194C4×C19—41no—
195C4×C19C22×D411yescharacteristic
196C4×C19H(5,𝔽2)11yescharacteristic
197Dic19—22no—
198Dic19—41no—
199Dic19—41no—
200C2×#137—191no—
201C2×#135—191no—
202#550D1911yescharacteristic, complemented
203#548—191no—
204#496—191no—
205#469—191no—
206#465—191no—
207#464—191no—
208#460—191no—
209#452—191no—
210#449—191no—
211#449—191no—
212#448—191no—
213#441—191no—
214#435—191no—
215C2×C19—41no—
216C2×C19—41no—
217C2×C19—81no—
218C2×C19—81no—
219C2×C19D4211yescharacteristic
220C2×C19#57511yescharacteristic
221C2×C19#57711yescharacteristic
222D19—81no—
223C2×#41—191no—
224C2×#41C2×D1911yescharacteristic
225C2×#41C2×D1911yescharacteristic
226C22×Q8—191no—
227#137—384no—
228#135—384no—
229C2×Q16—191no—
230C2×Q16—191no—
231C2×SD16—191no—
232C2×SD16—191no—
233C2×SD16—191no—
234C2×SD16—191no—
235C2×SD16—191no—
236C2×D8—191no—
237C2×D8—191no—
238C2×M16—191no—
239C22×C8—191no—
240#127—21no—
241#127C2×D1911yescharacteristic
242#124—191no—
243#124—381no—
244C22⋊Q8—191no—
245C22⋊Q8—381no—
246#121—21no—
247#121—21no—
248#121—191no—
249#121—381no—
250#121C2×D1911yescharacteristic
251#121C2×D1911yescharacteristic
252C4×Q8—191no—
253C4×Q8C2×D1911yescharacteristic
254C4×D4—21no—
255C4×D4—381no—
256C4×D4C2×D1911yescharacteristic
257#106—191no—
258C4⋊C8—191no—
259#103—191no—
260#103—191no—
261#103—191no—
262#102—191no—
263#102—191no—
264#102—191no—
265C22⋊C8—191no—
266C22⋊C8—191no—
267#97—191no—
268C19#327111yescharacteristic, complemented, Sylow
269#41—22no—
270#41—22no—
271#41—41no—
272#41—41no—
273#41—382no—
274#41—761no—
275C2×Q8—191no—
276C2×Q8—191no—
277C2×Q8—382no—
278C2×Q8—381no—
279C2×Q8—761no—
280C2×Q8C22×D1911yescharacteristic
281C2×D4—21no—
282C2×D4—21no—
283C2×D4—21no—
284C2×D4—21no—
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—191no—
288C2×D4—381no—
289C2×D4—381no—
290C2×D4C22⋊D1911yescharacteristic
291C2×D4C22×D1911yescharacteristic
292C2×D4C22×D1911yescharacteristic
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—381no—
296C22×C4—381no—
297C22×C4C22×D1911yescharacteristic
298C22×C4C22×D1911yescharacteristic
299Q16—194no—
300Q16—382no—
301SD16—382no—
302SD16—382no—
303SD16—382no—
304SD16—382no—
305SD16—761no—
306D8—382no—
307D8—761no—
308M16—382no—
309C2×C8—191no—
310C2×C8—191no—
311C2×C8—191no—
312C2×C8—191no—
313C2×C8—382no—
314C4⋊C4—21no—
315C4⋊C4—191no—
316C4⋊C4—381no—
317C4⋊C4—381no—
318C4⋊C4C22⋊D1911yescharacteristic
319C4⋊C4C22×D1911yescharacteristic
320C22⋊C4—21no—
321C22⋊C4—21no—
322C22⋊C4—381no—
323C22⋊C4—381no—
324C22⋊C4—381no—
325C22⋊C4—381no—
326C22⋊C4C22⋊D1911yescharacteristic
327C22⋊C4C22⋊D1911yescharacteristic
328C42—21no—
329C42—381no—
330C42C22×D1911yescharacteristic
331C23—21no—
332C23—21no—
333C23—381no—
334C23C2×C22⋊D1911yescharacteristic
335C23C2×C22⋊D1911yescharacteristic
336Q8—21no—
337Q8—192no—
338Q8—381no—
339Q8—381no—
340Q8—381no—
341Q8—762no—
342Q8D4×D1912yes—
343D4—21no—
344D4—21no—
345D4—21no—
346D4—21no—
347D4—41no—
348D4—42no—
349D4—42no—
350D4—42no—
351D4—81no—
352D4—81no—
353D4—81no—
354D4—381no—
355D4—381no—
356D4—762no—
357D4—762no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—381no—
367C2×C4—381no—
368C2×C4—381no—
369C2×C4—762no—
370C2×C4—762no—
371C2×C4C2×C22⋊D1911yescharacteristic
372C2×C4C2×C22⋊D1911yescharacteristic
373C2×C4C2×C22⋊D1911yescharacteristic
374C2×C4C2×C22⋊D1911yescharacteristic
375C2×C4C23×D1911yescharacteristic
376C8—192no—
377C8—381no—
378C8—381no—
379C8—381no—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22—761no—
393C22—761no—
394C22—761no—
395C22C22×C22⋊D1911yescharacteristic
396C4—21no—
397C4—21no—
398C4—21no—
399C4—21no—
400C4—22no—
401C4—41no—
402C4—382no—
403C4—761no—
404C4—761no—
405C4C2×D4×D1911yescharacteristic
406C4#1059743011yescharacteristic
407C2—41no—
408C2—41no—
409C2—81no—
410C2—81no—
411C2—1521no—
412C2D4×C22⋊D1911yescharacteristic
413C2#1192734211yescharacteristic
414C2#1192735511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#550C2
socleC22×C19C22×D4
hypercenter#550D19
hypocenterC19#3271
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C4×D4 ◁ #550

Complements

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

NH ≅ G/Ntype
1. C2×#10597397C2semidirect
2. C2×#10597396C2semidirect
3. #11927203C2semidirect
4. #11926931C2semidirect
5. #11926795C2semidirect
6. #11926771C2semidirect
7. #11926766C2semidirect
8. #11926741C2semidirect
9. #11926706C2semidirect
10. #11926689C2semidirect
11. #11926687C2semidirect
12. #11926682C2semidirect
13. #11926649C2semidirect
14. #11926616C2semidirect
15. C19×#550C2semidirect
102. #64528D4semidirect
202. #550D19semidirect
268. C19#3271semidirect

Maximal subgroups

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

subgroupindex
C2×#105973972
C2×#105973962
#119272032
#119269312
#119267952
#119267712
#119267662
#119267412
#119267062
#119266892
#119266872
#119266822
#119266492
#119266162
C19×#5502
#327119