Finite Group Databasebeta

← #34056263

Subgroups — #34056263

Order 19072.

472 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18011943C211yesmaximal, characteristic, complemented
2C2×Q16×D149C211yesmaximal, characteristic, complemented
3Q8×D596C211yesmaximal, characteristic, complemented
4#23750287C211yesmaximal, characteristic
5#23750019C211yesmaximal, characteristic, complemented
6#23749884C211yesmaximal, characteristic, complemented
7#23749855C211yesmaximal, characteristic, complemented
8#23749847C211yesmaximal, characteristic, complemented
9#23749835C211yesmaximal, characteristic, complemented
10#23749790C211yesmaximal, characteristic, complemented
11#23749782C211yesmaximal, characteristic, complemented
12#23749782C211yesmaximal, characteristic, complemented
13#23749765C211yesmaximal, characteristic, complemented
14#23749698C211yesmaximal, characteristic, complemented
15#441×C149C211yesmaximal, characteristic, complemented
16C2×#14558737C2211yescharacteristic
17C2×Q8×D149C2211yescharacteristic
18C2×Q8×D149C2211yescharacteristic
19C2×Q8×D149C2211yescharacteristic
20#18011943—24no—
21C2×Dic596C2211yescharacteristic
22C2×Dic596C2211yescharacteristic
23C2×#14558726C2211yescharacteristic
24C2×#14558726C2211yescharacteristic
25C2×#14558726C2211yescharacteristic
26Q16×D149—24no—
27C2×#14558725C2211yescharacteristic
28C2×#14558725C2211yescharacteristic
29C2×#14558723C2211yescharacteristic
30C2×#14558719C2211yescharacteristic
31C2×C8×D149C2211yescharacteristic
32#18011911—21no—
33#18011911C2211yescharacteristic
34#18011899—21no—
35#18011899C2211yescharacteristic
36#18011891—21no—
37#18011891—21no—
38#18011891—21no—
39#18011891C2211yescharacteristic
40#18011891C2211yescharacteristic
41#18011891C2211yescharacteristic
42#18011886—21no—
43#18011886C2211yescharacteristic
44C4×D596—21no—
45C4×D596—21no—
46C4×D596C2211yescharacteristic
47C4⋊#11924746C2211yescharacteristic
48#18011834C2211yescharacteristic
49#18011834C2211yescharacteristic
50#18011834C2211yescharacteristic
51#18011831C2211yescharacteristic
52#18011823C2211yescharacteristic
53#18011823C2211yescharacteristic
54C2×Q16×C149C2211yescharacteristic
55C4×Q8×C149C2211yescharacteristic
56C4×Q8×C149C2211yescharacteristic
57#106×C149C2211yescharacteristic
58#103×C149C2211yescharacteristic
59#103×C149C2211yescharacteristic
60#97×C149C2211yescharacteristic
61#14558737—22no—
62#14558737—41no—
63C2×Dic298—21no—
64C2×Dic298—21no—
65C2×Dic298—21no—
66C2×Dic298C2311yescharacteristic
67C2×Dic298C2311yescharacteristic
68C2×Dic298C2311yescharacteristic
69Q8×D149—22no—
70Q8×D149—22no—
71Q8×D149—22no—
72Q8×D149—41no—
73Q8×D149—41no—
74Q8×D149—41no—
75C2×D596—21no—
76C2×D596—21no—
77C2×D596D411yescharacteristic
78C2×D596C2311yescharacteristic
79C2×C4×D149—21no—
80C2×C4×D149—21no—
81C2×C4×D149—21no—
82C2×C4×D149—21no—
83C2×C4×D149C2311yescharacteristic
84C2×C4×D149C2311yescharacteristic
85Dic596—22no—
86Dic596—41no—
87#14558726—22no—
88#14558726—22no—
89#14558726—22no—
90#14558725—22no—
91#14558725—41no—
92#14558723—22no—
93#14558719—22no—
94C2×#11924746C2311yescharacteristic
95C2×#11924746C2311yescharacteristic
96C8×D149—22no—
97C4⋊Dic149—21no—
98C4⋊Dic149—21no—
99C4⋊Dic149—21no—
100C4⋊Dic149—21no—
101C4⋊Dic149—21no—
102C4⋊Dic149D411yescharacteristic
103#14558713—21no—
104#14558713—21no—
105#14558713—21no—
106#14558713—21no—
107#14558713—21no—
108#14558713—21no—
109#14558713D411yescharacteristic
110#14558713D411yescharacteristic
111C2×Q8×C149C2311yescharacteristic
112C2×Q8×C149C2311yescharacteristic
113Q16×C149D414yescomplemented
114C2×C8×C149C2311yescharacteristic
115C2×C8×C149C2311yescharacteristic
116C4⋊C4×C149—21no—
117C4⋊C4×C149—21no—
118C4⋊C4×C149C2311yescharacteristic
119C4⋊C4×C149C2311yescharacteristic
120C42×C149—21no—
121C42×C149—21no—
122C42×C149C2311yescharacteristic
123C22×D149—21no—
124C22×D149C2×D411yescharacteristic
125C22×D149C2×D411yescharacteristic
126Dic298—21no—
127Dic298—21no—
128Dic298—21no—
129Dic298—21no—
130Dic298—21no—
131Dic298—21no—
132Dic298—42no—
133Dic298—42no—
134Dic298—42no—
135D596—22no—
136D596—21no—
137D596—21no—
138D596—42no—
139D596—42no—
140C2×Dic149—21no—
141C2×Dic149—21no—
142C2×Dic149—21no—
143C2×Dic149C2×D411yescharacteristic
144C2×Dic149C2×D411yescharacteristic
145C4×D149—21no—
146C4×D149—21no—
147C4×D149—21no—
148C4×D149—21no—
149C4×D149—42no—
150C4×D149—42no—
151C4×D149—42no—
152C4×D149—42no—
153#11924746—21no—
154#11924746—21no—
155Q8×C149—21no—
156Q8×C149—21no—
157Q8×C149C2×D412yes—
158Q8×C149C2×D412yes—
159C2×C4×C149—21no—
160C2×C4×C149—21no—
161C2×C4×C149—21no—
162C2×C4×C149—21no—
163C2×C4×C149C2×D411yescharacteristic
164C2×C4×C149C2×D411yescharacteristic
165C2×C4×C149C2411yescharacteristic
166C8×C149—21no—
167C8×C149C2×D412yes—
168C22×C149C22×D411yescharacteristic
169C2×D149—21no—
170C2×D149—21no—
171C2×D149—21no—
172C2×D149—21no—
173C2×D149—21no—
174C2×D149—41no—
175C2×D149—41no—
176C2×D149—41no—
177C2×D149#13712yescomplemented
178C4×C149—22no—
179C4×C149—22no—
180C4×C149—21no—
181C4×C149—21no—
182C4×C149—41no—
183C4×C149—41no—
184C4×C149C22×D411yescharacteristic
185C4×C149H(5,𝔽2)11yescharacteristic
186Dic149—21no—
187Dic149—21no—
188Dic149—41no—
189Dic149—41no—
190Dic149—41no—
191C2×C149D4211yescharacteristic
192C2×C149C2×#13711yescharacteristic
193C2×C149#57811yescharacteristic
194D149—22no—
195D149—41no—
196D149—81no—
197C149#327011yescharacteristic, complemented, Sylow
198#3270—1491nomaximal, Sylow
199C2×#137—1491no—
200C22×Q16—1491no—
201D4×Q8—1491no—
202#548—1491no—
203#497—1491no—
204#470—1491no—
205#465—1491no—
206#464—1491no—
207#462—1491no—
208#452—1491no—
209#451—1491no—
210#451—1491no—
211#448—1491no—
212#441D14911yescharacteristic, complemented
213#435—1491no—
214C2×#41—1491no—
215C22×Q8—1491no—
216C22×Q8—1491no—
217C22×Q8—1491no—
218#137—2984no—
219C2×Q16—2984no—
220C2×Q16—1491no—
221C2×Q16—1491no—
222C2×Q16—1491no—
223C2×Q16—1491no—
224C2×Q16—1491no—
225C2×Q16C2×D14911yescharacteristic
226C2×SD16—1491no—
227C2×SD16—1491no—
228C2×SD16—1491no—
229C2×M16—1491no—
230C22×C8—1491no—
231C4⋊Q8—2981no—
232C4⋊Q8—1491no—
233#124—2981no—
234#124—1491no—
235C22⋊Q8—2981no—
236C22⋊Q8—2981no—
237C22⋊Q8—2981no—
238C22⋊Q8—1491no—
239C22⋊Q8—1491no—
240C22⋊Q8—1491no—
241#121—2981no—
242#121—1491no—
243C4×Q8C2×D14911yescharacteristic
244C4×Q8C2×D14911yescharacteristic
245C4×D4—2981no—
246C4×D4—2981no—
247C4×D4—1491no—
248#106C2×D14911yescharacteristic
249C4⋊C8—1491no—
250#103—1491no—
251#103—1491no—
252#103—1491no—
253#103C2×D14911yescharacteristic
254#103C2×D14911yescharacteristic
255#102—1491no—
256C22⋊C8—1491no—
257C22⋊C8—1491no—
258#97C2×D14911yescharacteristic
259#41—2982no—
260#41—5961no—
261C2×Q8—2981no—
262C2×Q8—2981no—
263C2×Q8—2981no—
264C2×Q8—2982no—
265C2×Q8—2982no—
266C2×Q8—2982no—
267C2×Q8—5961no—
268C2×Q8—5961no—
269C2×Q8—5961no—
270C2×Q8—1491no—
271C2×Q8—1491no—
272C2×Q8—1491no—
273C2×Q8C22×D14911yescharacteristic
274C2×Q8C22×D14911yescharacteristic
275C2×D4—2981no—
276C2×D4—2981no—
277C2×D4—1491no—
278C2×D4—1491no—
279C22×C4—2981no—
280C22×C4—2981no—
281C22×C4—2981no—
282C22×C4—2981no—
283C22×C4—1491no—
284C22×C4—1491no—
285Q16—2982no—
286Q16—2982no—
287Q16—2982no—
288Q16—2982no—
289Q16—5961no—
290Q16D59614yescomplemented
291SD16—2982no—
292SD16—2982no—
293SD16—5961no—
294M16—2982no—
295C2×C8—2982no—
296C2×C8—1491no—
297C2×C8—1491no—
298C2×C8C22×D14911yescharacteristic
299C2×C8C22×D14911yescharacteristic
300C4⋊C4—21no—
301C4⋊C4—21no—
302C4⋊C4—2981no—
303C4⋊C4—2981no—
304C4⋊C4—2981no—
305C4⋊C4—2981no—
306C4⋊C4—2981no—
307C4⋊C4—1491no—
308C4⋊C4C22×D14911yescharacteristic
309C4⋊C4C22×D14911yescharacteristic
310C22⋊C4—2981no—
311C22⋊C4—2981no—
312C22⋊C4—2981no—
313C22⋊C4—2981no—
314C22⋊C4—2981no—
315C22⋊C4—2981no—
316C22⋊C4—1491no—
317C22⋊C4—1491no—
318C42—21no—
319C42—21no—
320C42C22×D14911yescharacteristic
321C23—2981no—
322C23—1491no—
323C23—1491no—
324Q8—21no—
325Q8—21no—
326Q8—2981no—
327Q8—2981no—
328Q8—2981no—
329Q8—2981no—
330Q8—2981no—
331Q8—2981no—
332Q8—5962no—
333Q8—5962no—
334Q8—5962no—
335Q8C2×D59612yes—
336Q8C2×D59612yes—
337D4—2982no—
338D4—2981no—
339D4—2981no—
340D4—5962no—
341D4—5962no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—2981no—
347C2×C4—2981no—
348C2×C4—2981no—
349C2×C4—2981no—
350C2×C4—2981no—
351C2×C4—2981no—
352C2×C4—2981no—
353C2×C4—5962no—
354C2×C4—5962no—
355C2×C4—5962no—
356C2×C4—5962no—
357C2×C4—1491no—
358C2×C4—1491no—
359C2×C4D4×D14911yescharacteristic
360C2×C4D4×D14911yescharacteristic
361C2×C4C23×D14911yescharacteristic
362C8—21no—
363C8—2981no—
364C8—2981no—
365C8C2×D59612yes—
366C22—2981no—
367C22—2981no—
368C22—2981no—
369C22—2981no—
370C22—2981no—
371C22—5961no—
372C22—5961no—
373C22—5961no—
374C22—1492no—
375C22C2×D4×D14911yescharacteristic
376C4—21no—
377C4—21no—
378C4—22no—
379C4—22no—
380C4—41no—
381C4—41no—
382C4—2981no—
383C4—2981no—
384C4—5961no—
385C4—5961no—
386C4—5961no—
387C4C22×D59611yescharacteristic
388C4#1801195711yescharacteristic
389C2—2982no—
390C2—5961no—
391C2—11921no—
392C2D4×D59611yescharacteristic
393C2#137×D14911yescharacteristic
394C2#2375044111yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#441×C149C2
socleC22×C149C22×D4
prime radical#23750287C2
hypercenter#441D149
hypocenterC149#3270
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #441

Complements

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

NH ≅ G/Ntype
1. C2×#18011943C2semidirect
2. C2×Q16×D149C2semidirect
3. Q8×D596C2semidirect
5. #23750019C2semidirect
6. #23749884C2semidirect
7. #23749855C2semidirect
8. #23749847C2semidirect
9. #23749835C2semidirect
10. #23749790C2semidirect
11. #23749782C2semidirect
12. #23749782C2semidirect
13. #23749765C2semidirect
14. #23749698C2semidirect
15. #441×C149C2semidirect
113. Q16×C149D4semidirect
177. C2×D149#137semidirect
197. C149#3270semidirect
212. #441D149semidirect
290. Q16D596semidirect

Maximal subgroups

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

subgroupindex
C2×#180119432
C2×Q16×D1492
Q8×D5962
#237502872
#237500192
#237498842
#237498552
#237498472
#237498352
#237497902
#237497822
#237497652
#237496982
#441×C1492
#3270149