Finite Group Databasebeta

← #14578044

Subgroups — #14578044

Order 2432.

1002 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11927297C212yesmaximal, complemented
2#11927293C212yesmaximal, complemented
3#11927278C212yesmaximal, complemented
4#11927274C212yesmaximal, complemented
5#11927265C212yesmaximal, complemented
6#11927262C212yesmaximal, complemented
7Q8×C22⋊D19C212yesmaximal, complemented
8#11927207C212yesmaximal, complemented
9#11927162C214yesmaximal, complemented
10#11927158C214yesmaximal, complemented
11#11927117C212yesmaximal, complemented
12#11927115C211yesmaximal, characteristic, complemented
13#11927096C212yesmaximal, complemented
14#11927090C211yesmaximal, characteristic
15C19×#536C211yesmaximal, characteristic, complemented
16C2×#41×C19C2211yescharacteristic
17C22×Q8×C19C2211yescharacteristic
18C2×Q8×D19C2212yes—
19C2×#64541C2211yescharacteristic
20C22×Dic38C2211yescharacteristic
21C19×C4⋊Q8C2212yes—
22C19×#124C2212yes—
23C19×#123C2212yes—
24C19×#123C2212yes—
25C19×C22⋊Q8C2212yes—
26C19×C22⋊Q8C2212yes—
27C19×#117C2211yescharacteristic
28#10597393C2211yescharacteristic
29#10597392C2212yes—
30#10597392C2214yes—
31Q8×Dic19C2212yes—
32#10597390C2211yescharacteristic
33#10597390C2212yes—
34#10597390C2212yes—
35#10597390C2214yes—
36#10597386C2211yescharacteristic
37#10597385C2212yes—
38#10597385C2212yes—
39#10597382C2211yescharacteristic
40#10597382C2212yes—
41#10597381C2212yes—
42#10597381C2212yes—
43C4×C22⋊D19C2212yes—
44C4×C22⋊D19C2212yes—
45C4×C22⋊D19C2214yes—
46#10597372C2211yescharacteristic
47#10597370C2214yes—
48#10597370C2212yes—
49#10597370C2212yes—
50C2×C4×Dic19C2211yescharacteristic
51#10597344C2214yes—
52#10597343C2212yes—
53#10597342C2214yes—
54#10597340C2214yes—
55#10597338C2212yes—
56#10597335C2214yes—
57#10597334C2214yes—
58#10597334C2212yes—
59#10597334C2214yes—
60#10597333C2212yes—
61#10597333C2214yes—
62#10597333C2214yes—
63#10597331C2214yes—
64#10597331C2214yes—
65#10597331C2214yes—
66#10597329C2214yes—
67(C22⋊D19)⋊C4C2214yes—
68#10597325C2214yes—
69#10597325C2214yes—
70#10597324C2214yes—
71#10597324C2214yes—
72#10597323C2214yes—
73#10597322C2214yes—
74C4×Dic38C2214yes—
75#41×C19—42no—
76C2×Q8×C19—42no—
77C2×Q8×C19C2312yes—
78C2×Q8×C19C2311yescharacteristic
79C2×Q8×C19C2312yes—
80C2×D4×C19C2311yescharacteristic
81C2×D4×C19C2311yescharacteristic
82C2×D4×C19C2311yescharacteristic
83C22×C4×C19C2311yescharacteristic
84C22×C4×C19C2311yescharacteristic
85C22×C4×C19C2311yescharacteristic
86C22×C4×C19C2312yes—
87C2×C22⋊D19C2312yes—
88C2×C22⋊D19C2312yes—
89C2×C22⋊D19C2312yes—
90C22×Dic19C2312yes—
91C22×Dic19C2312yes—
92Q8×D19—44no—
93#64541—42no—
94C2×D76C2311yescharacteristic
95C2×C4×D19C2312yes—
96C2×C4×D19C2314yes—
97C2×Dic38—42no—
98C2×Dic38C2312yes—
99C2×Dic38C2314yes—
100C2×Dic38C2312yes—
101C2×Dic38C2311yescharacteristic
102C2×Dic38C2314yes—
103C4⋊C4×C19C2312yes—
104C4⋊C4×C19C2314yes—
105C4⋊C4×C19C2314yes—
106C22⋊C4×C19C2312yes—
107C22⋊C4×C19C2314yes—
108C22⋊C4×C19C2314yes—
109C42×C19C2312yes—
110C22⋊Dic19C2312yes—
111C22⋊Dic19C2314yes—
112C22⋊Dic19C2314yes—
113C22⋊Dic19C2312yes—
114C22⋊Dic19C2312yes—
115(C2×D19)⋊C4C2312yes—
116(C2×D19)⋊C4C2312yes—
117(C2×D19)⋊C4C2314yes—
118(C2×D19)⋊C4C2314yes—
119(C2×D19)⋊C4C2314yes—
120C4⋊Dic19C2314yes—
121C4⋊Dic19C2312yes—
122C4⋊Dic19C2314yes—
123Dic19⋊C4C2314yes—
124Dic19⋊C4C2314yes—
125Dic19⋊C4C2312yes—
126Dic19⋊C4C2312yes—
127Dic19⋊C4C2314yes—
128Dic19⋊C4C2314yes—
129Dic19⋊C4C2314yes—
130Dic19⋊C4C2314yes—
131Dic19⋊C4C2314yes—
132C4×Dic19C2312yes—
133C4×Dic19C2311yescharacteristic
134C4×Dic19C2311yescharacteristic
135C4×Dic19C2314yes—
136C4×Dic19C2312yes—
137C4×Dic19C2314yes—
138C4×Dic19C2314yes—
139C23×C19C2411yescharacteristic
140C23×C19C2411yescharacteristic
141C23×C19C2411yescharacteristic
142C22×D19C2412yes—
143Q8×C19—24no—
144Q8×C19—42no—
145Q8×C19—41no—
146D4×C19—41no—
147D4×C19—41no—
148D4×C19—41no—
149C2×C4×C19—22no—
150C2×C4×C19—22no—
151C2×C4×C19—22no—
152C2×C4×C19—42no—
153C2×C4×C19C2411yescharacteristic
154C2×C4×C19C2414yes—
155C2×C4×C19C2411yescharacteristic
156C2×C4×C19C2414yes—
157C2×C4×C19C2411yescharacteristic
158C2×C4×C19C2411yescharacteristic
159C22⋊D19—24no—
160C22⋊D19—24no—
161C22⋊D19—42no—
162C2×Dic19—24no—
163C2×Dic19—42no—
164C2×Dic19C2414yes—
165C2×Dic19C2412yes—
166C2×Dic19C2412yes—
167C2×Dic19C2414yes—
168C2×Dic19C2412yes—
169D76—41no—
170C4×D19—24no—
171C4×D19—44no—
172Dic38—24no—
173Dic38—28no—
174Dic38—42no—
175Dic38—41no—
176Dic38—44no—
177#3550—191nomaximal, Sylow
178C22×C19—21no—
179C22×C19—21no—
180C22×C19—21no—
181C22×C19—22no—
182C22×C19—22no—
183C22×C19—22no—
184C22×C19C2511yescharacteristic
185C2×D19—22no—
186C2×D19—22no—
187C2×D19—22no—
188C4×C19—21no—
189C4×C19—24no—
190C4×C19—21no—
191C4×C19—21no—
192C4×C19—24no—
193C4×C19H(5,𝔽2)12yes—
194Dic19—24no—
195Dic19—22no—
196Dic19—24no—
197Dic19—22no—
198Dic192−1+414yes—
199#563—192no—
200#563—192no—
201#559—192no—
202Q82—192no—
203#556—192no—
204#556—192no—
205D4×Q8—192no—
206D4×Q8—192no—
207#542—194no—
208#542—194no—
209#536—191no—
210#536—192no—
211#536D1911yescharacteristic, complemented
212#533—192no—
213#532—191no—
214C2×C19—41no—
215C2×C19—41no—
216C2×C19—41no—
217C2×C19C2×H(5,𝔽2)11yescharacteristic
218C2×C19C2×2−1+412yes—
219D19—42no—
220C2×#41—191no—
221C2×#41C2×D1911yescharacteristic
222C22×Q8—192no—
223C22×Q8—191no—
224C22×Q8C2×D1911yescharacteristic
225C4⋊Q8—191no—
226C4⋊Q8—192no—
227C4⋊Q8—192no—
228C4⋊Q8—194no—
229C4⋊Q8—192no—
230C4⋊Q8—194no—
231C4⋊Q8—194no—
232C4⋊Q8C2×D1912yes—
233#127—191no—
234#126—194no—
235#126—194no—
236#126—194no—
237#126—194no—
238#125—194no—
239#124—191no—
240#124—191no—
241#124—192no—
242#124—194no—
243#124—194no—
244#124—194no—
245#124C2×D1912yes—
246#123—192no—
247#123—192no—
248#123—194no—
249#123—194no—
250#123C2×D1912yes—
251#123C2×D1912yes—
252C22⋊Q8—192no—
253C22⋊Q8—194no—
254C22⋊Q8—192no—
255C22⋊Q8—192no—
256C22⋊Q8—194no—
257C22⋊Q8—192no—
258C22⋊Q8—194no—
259C22⋊Q8—194no—
260C22⋊Q8—194no—
261C22⋊Q8C2×D1912yes—
262C22⋊Q8C2×D1912yes—
263#121—192no—
264#121—192no—
265C4×Q8—192no—
266C4×Q8—192no—
267C4×Q8—194no—
268C4×Q8—194no—
269C4×Q8—194no—
270C4×D4—192no—
271C4×D4—192no—
272C4×D4—194no—
273C4×D4—194no—
274#117—191no—
275#117—192no—
276#117—194no—
277#117C2×D1911yescharacteristic
278C2×C42—191no—
279C19#355011yescharacteristic, complemented, Sylow
280#41—42no—
281#41—762no—
282C2×Q8—42no—
283C2×Q8—194no—
284C2×Q8—192no—
285C2×Q8—194no—
286C2×Q8—192no—
287C2×Q8—191no—
288C2×Q8—762no—
289C2×Q8—764no—
290C2×Q8C22×D1912yes—
291C2×Q8C22×D1912yes—
292C2×Q8C22×D1911yescharacteristic
293C2×D4—192no—
294C2×D4—192no—
295C2×D4—192no—
296C2×D4—191no—
297C2×D4C22×D1911yescharacteristic
298C2×D4C22×D1911yescharacteristic
299C2×D4C22×D1911yescharacteristic
300C22×C4—192no—
301C22×C4—192no—
302C22×C4—192no—
303C22×C4—194no—
304C22×C4C22×D1911yescharacteristic
305C22×C4C22×D1911yescharacteristic
306C22×C4C22×D1911yescharacteristic
307C22×C4C22×D1912yes—
308C4⋊C4—194no—
309C4⋊C4—194no—
310C4⋊C4—194no—
311C4⋊C4—192no—
312C4⋊C4—192no—
313C4⋊C4—194no—
314C4⋊C4—194no—
315C4⋊C4—194no—
316C4⋊C4—194no—
317C4⋊C4—192no—
318C4⋊C4—194no—
319C4⋊C4—194no—
320C4⋊C4C22×D1912yes—
321C4⋊C4C22×D1914yes—
322C4⋊C4C22×D1914yes—
323C22⋊C4—194no—
324C22⋊C4—192no—
325C22⋊C4—192no—
326C22⋊C4—192no—
327C22⋊C4—194no—
328C22⋊C4—194no—
329C22⋊C4—192no—
330C22⋊C4—192no—
331C22⋊C4—194no—
332C22⋊C4—194no—
333C22⋊C4C22×D1914yes—
334C22⋊C4C22×D1912yes—
335C22⋊C4C22×D1914yes—
336C42—192no—
337C42—191no—
338C42—191no—
339C42—194no—
340C42—194no—
341C42—192no—
342C42—194no—
343C42C22×D1912yes—
344C23—192no—
345C23C23×D1911yescharacteristic
346C23C23×D1911yescharacteristic
347C23C23×D1911yescharacteristic
348Q8—24no—
349Q8—42no—
350Q8—41no—
351Q8—388no—
352Q8—384no—
353Q8—762no—
354Q8—764no—
355Q8—761no—
356D4—41no—
357D4—41no—
358D4—41no—
359D4—384no—
360D4—384no—
361D4—761no—
362D4—762no—
363C2×C4—22no—
364C2×C4—22no—
365C2×C4—22no—
366C2×C4—42no—
367C2×C4—192no—
368C2×C4—194no—
369C2×C4—192no—
370C2×C4—192no—
371C2×C4—194no—
372C2×C4—384no—
373C2×C4—384no—
374C2×C4—764no—
375C2×C4—762no—
376C2×C4C23×D1914yes—
377C2×C4C23×D1911yescharacteristic
378C2×C4C23×D1911yescharacteristic
379C2×C4C23×D1914yes—
380C2×C4C23×D1911yescharacteristic
381C2×C4C23×D1911yescharacteristic
382C22—21no—
383C22—21no—
384C22—21no—
385C22—22no—
386C22—22no—
387C22—22no—
388C22—382no—
389C22—382no—
390C22—382no—
391C22C24×D1911yescharacteristic
392C4—21no—
393C4—21no—
394C4—21no—
395C4—24no—
396C4—24no—
397C4—194no—
398C4—382no—
399C4—384no—
400C4—382no—
401C4—384no—
402C4#1059743012yes—
403C2—41no—
404C2—41no—
405C2—41no—
406C2—762no—
407C2C2×#1059743011yescharacteristic
408C22−1+4×D1912yes—
subgroupG/H
center, FrattiniC22C24×D19
commutator, socle, cosocleC22×C19C25
FittingC19×#536C2
prime radical#11927090C2
hypercenter#536D19
hypocenterC19#3550
LCSG ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ #536

Complements

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

NH ≅ G/Ntype
1. #11927297C2semidirect
2. #11927293C2semidirect
3. #11927278C2semidirect
4. #11927274C2semidirect
5. #11927265C2semidirect
6. #11927262C2semidirect
7. Q8×C22⋊D19C2semidirect
8. #11927207C2semidirect
9. #11927162C2semidirect
10. #11927158C2semidirect
11. #11927117C2semidirect
12. #11927115C2semidirect
13. #11927096C2semidirect
15. C19×#536C2semidirect
211. #536D19semidirect
279. C19#3550semidirect

Maximal subgroups

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

subgroupindex
#119272972
#119272932
#119272782
#119272742
#119272652
#119272622
Q8×C22⋊D192
#119272072
#119271622
#119271582
#119271172
#119271152
#119270962
#119270902
C19×#5362
#355019