Finite Group Databasebeta

← #34056252

Subgroups — #34056252

Order 19072.

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×#18011940C211yesmaximal, characteristic, complemented
2C2×#18011930C211yesmaximal, characteristic, complemented
3#23750283C211yesmaximal, characteristic, complemented
4#23750279C211yesmaximal, characteristic, complemented
5#23750020C211yesmaximal, characteristic, complemented
6#23749870C211yesmaximal, characteristic, complemented
7#23749865C211yesmaximal, characteristic, complemented
8#23749836C211yesmaximal, characteristic, complemented
9#23749788C211yesmaximal, characteristic, complemented
10#23749784C211yesmaximal, characteristic, complemented
11#23749782C211yesmaximal, characteristic, complemented
12#23749767C211yesmaximal, characteristic, complemented
13#23749725C211yesmaximal, characteristic, complemented
14#23749695C211yesmaximal, characteristic, complemented
15#463×C149C211yesmaximal, characteristic, complemented
16C2×#14558735C2211yescharacteristic
17C2×#14558735C2211yescharacteristic
18C2×#14558735C2211yescharacteristic
19C2×Q8×D149C2211yescharacteristic
20#18011940—24no—
21#18011930—24no—
22C2×Dic596C2211yescharacteristic
23C2×Dic596C2211yescharacteristic
24C2×#14558726C2211yescharacteristic
25C2×#14558726C2211yescharacteristic
26C2×#14558724C2211yescharacteristic
27C2×#14558724C2211yescharacteristic
28C2×#14558724C2211yescharacteristic
29C2×#14558719C2211yescharacteristic
30C2×C8×D149C2211yescharacteristic
31#18011911C2211yescharacteristic
32#18011897—21no—
33#18011895—21no—
34#18011895—21no—
35#18011891C2211yescharacteristic
36#18011891C2211yescharacteristic
37#18011888—21no—
38#18011887C2211yescharacteristic
39#18011885—21no—
40#18011884—21no—
41#18011882C2211yescharacteristic
42C4×Dic298C2211yescharacteristic
43C4×D596C2211yescharacteristic
44#18011871—21no—
45C2×C4⋊Dic149—21no—
46#18011844C2211yescharacteristic
47#18011836C2211yescharacteristic
48#18011836C2211yescharacteristic
49#18011834C2211yescharacteristic
50#18011832C2211yescharacteristic
51#18011823C2211yescharacteristic
52#18011823C2211yescharacteristic
53#18011822C2211yescharacteristic
54C2×SD16×C149C2211yescharacteristic
55C2×D8×C149C2211yescharacteristic
56#124×C149C2211yescharacteristic
57C4×D4×C149C2211yescharacteristic
58C4⋊C8×C149C2211yescharacteristic
59#103×C149C2211yescharacteristic
60#102×C149C2211yescharacteristic
61#14558735—22no—
62#14558735—22no—
63#14558735—22no—
64#14558735—41no—
65#14558735—41no—
66#14558735—41no—
67C2×Dic298—21no—
68C2×Dic298C2311yescharacteristic
69C2×Dic298C2311yescharacteristic
70C2×Dic298C2311yescharacteristic
71Q8×D149—22no—
72Q8×D149—41no—
73C2×D596D411yescharacteristic
74C2×C22⋊D149—21no—
75C2×C22⋊D149—21no—
76C2×C22⋊D149—21no—
77C2×C22⋊D149—21no—
78C22×Dic149—21no—
79C22×Dic149—21no—
80C22×Dic149—21no—
81C2×C4×D149—21no—
82C2×C4×D149C2311yescharacteristic
83C2×C4×D149C2311yescharacteristic
84Dic596—22no—
85Dic596—22no—
86#14558726—22no—
87#14558726—41no—
88#14558724—22no—
89#14558724—41no—
90#14558724D414yescomplemented
91#14558719—22no—
92C2×#11924746C2311yescharacteristic
93C2×#11924746C2311yescharacteristic
94C8×D149—22no—
95C4⋊Dic149—21no—
96C4⋊Dic149—21no—
97C4⋊Dic149—21no—
98C4⋊Dic149—21no—
99C4⋊Dic149D411yescharacteristic
100C4⋊Dic149C2311yescharacteristic
101#14558715—21no—
102#14558715—21no—
103C22⋊Dic149—21no—
104#14558713—21no—
105#14558713—21no—
106#14558713—21no—
107#14558713D411yescharacteristic
108#14558713D411yescharacteristic
109C4×Dic149—21no—
110C2×Q8×C149C2311yescharacteristic
111C2×D4×C149C2311yescharacteristic
112C2×D4×C149C2311yescharacteristic
113C22×C4×C149—21no—
114SD16×C149—22no—
115D8×C149—22no—
116C2×C8×C149C2311yescharacteristic
117C2×C8×C149C2311yescharacteristic
118C4⋊C4×C149C2311yescharacteristic
119C22⋊C4×C149—21no—
120C22⋊C4×C149—21no—
121C22⋊C4×C149—21no—
122C42×C149C2311yescharacteristic
123C22×D149C2×D411yescharacteristic
124C22×D149C2×D411yescharacteristic
125Dic298—21no—
126Dic298—21no—
127Dic298—21no—
128Dic298—21no—
129Dic298—21no—
130Dic298—42no—
131Dic298C2×D412yes—
132D596—41no—
133C22⋊D149—42no—
134C22⋊D149—42no—
135C22⋊D149—42no—
136C22⋊D149—42no—
137C2×Dic149—21no—
138C2×Dic149—21no—
139C2×Dic149—21no—
140C2×Dic149—21no—
141C2×Dic149—42no—
142C2×Dic149—42no—
143C2×Dic149—42no—
144C2×Dic149C2×D411yescharacteristic
145C2×Dic149C2×D411yescharacteristic
146C4×D149—21no—
147C4×D149—21no—
148C4×D149—21no—
149C4×D149—21no—
150C4×D149—42no—
151#11924746—21no—
152#11924746C2×D412yes—
153C23×C149—21no—
154C23×C149—21no—
155Q8×C149—21no—
156Q8×C149—21no—
157D4×C149—21no—
158D4×C149—21no—
159D4×C149—21no—
160D4×C149C2×D412yes—
161C2×C4×C149—21no—
162C2×C4×C149—21no—
163C2×C4×C149—42no—
164C2×C4×C149C2×D411yescharacteristic
165C2×C4×C149C2×D411yescharacteristic
166C2×C4×C149C2411yescharacteristic
167C8×C149—21no—
168C8×C149—21no—
169C22×C149—22no—
170C22×C149—41no—
171C22×C149—41no—
172C22×C149—41no—
173C22×C149—41no—
174C22×C149—41no—
175C22×C149C22×D411yescharacteristic
176C2×D149—21no—
177C2×D149—21no—
178C2×D149—21no—
179C2×D149—21no—
180C2×D149—21no—
181C2×D149—21no—
182C4×C149—21no—
183C4×C149—21no—
184C4×C149—41no—
185C4×C149—41no—
186C4×C149C22×D411yescharacteristic
187C4×C149H(5,𝔽2)11yescharacteristic
188Dic149—21no—
189Dic149—21no—
190Dic149—22no—
191Dic149—41no—
192Dic149—41no—
193Dic149—41no—
194C2×C149—42no—
195C2×C149—81no—
196C2×C149D4211yescharacteristic
197C2×C149#57511yescharacteristic
198C2×C149#57811yescharacteristic
199D149—41no—
200D149—41no—
201C149#326911yescharacteristic, complemented, Sylow
202#3269—1491nomaximal, Sylow
203C2×#137—1491no—
204C2×#135—1491no—
205#548—1491no—
206#547—1491no—
207#497—1491no—
208#468—1491no—
209#467—1491no—
210#463D14911yescharacteristic, complemented
211#462—1491no—
212#452—1491no—
213#452—1491no—
214#451—1491no—
215#449—1491no—
216#440—1491no—
217#435—1491no—
218C2×#41—1491no—
219C2×#41—1491no—
220C2×#41—1491no—
221C22×Q8—1491no—
222#137—2984no—
223#135—2984no—
224C2×Q16—1491no—
225C2×Q16—1491no—
226C2×Q16—1491no—
227C2×Q16—1491no—
228C2×SD16—1491no—
229C2×SD16—1491no—
230C2×SD16—1491no—
231C2×SD16C2×D14911yescharacteristic
232C2×D8C2×D14911yescharacteristic
233C2×M16—1491no—
234C22×C8—1491no—
235C4⋊Q8—1491no—
236#124—2981no—
237#124C2×D14911yescharacteristic
238#123—2981no—
239#123—2981no—
240C22⋊Q8—2981no—
241C22⋊Q8—1491no—
242C22⋊Q8—1491no—
243C22⋊Q8—1491no—
244#121—2981no—
245#121—2981no—
246#121—1491no—
247C4×Q8—1491no—
248C4×D4—2981no—
249C4×D4—1491no—
250C4×D4C2×D14911yescharacteristic
251C2×C4⋊C4—2981no—
252#107—1491no—
253C4⋊C8C2×D14911yescharacteristic
254#103—1491no—
255#103—1491no—
256#103—1491no—
257#103C2×D14911yescharacteristic
258#102—1491no—
259#102C2×D14911yescharacteristic
260C22⋊C8—1491no—
261C22⋊C8—1491no—
262#97—1491no—
263#41—2982no—
264#41—2982no—
265#41—2982no—
266#41—5961no—
267#41—5961no—
268#41—5961no—
269C2×Q8—2981no—
270C2×Q8—2982no—
271C2×Q8—5961no—
272C2×Q8—1491no—
273C2×Q8—1491no—
274C2×Q8—1491no—
275C2×Q8C22×D14911yescharacteristic
276C2×D4—2981no—
277C2×D4—2981no—
278C2×D4—2981no—
279C2×D4—2981no—
280C2×D4—1491no—
281C2×D4C22×D14911yescharacteristic
282C2×D4C22×D14911yescharacteristic
283C22×C4—21no—
284C22×C4—2981no—
285C22×C4—2981no—
286C22×C4—2981no—
287C22×C4—2981no—
288C22×C4—1491no—
289C22×C4—1491no—
290Q16—2982no—
291Q16—2982no—
292Q16—2982no—
293Q16—5961no—
294SD16—22no—
295SD16—2982no—
296SD16—5961no—
297SD16—1494no—
298D8—22no—
299M16—2982no—
300C2×C8—2982no—
301C2×C8—1491no—
302C2×C8—1491no—
303C2×C8C22×D14911yescharacteristic
304C2×C8C22×D14911yescharacteristic
305C4⋊C4—2981no—
306C4⋊C4—2981no—
307C4⋊C4—2981no—
308C4⋊C4—2981no—
309C4⋊C4—2981no—
310C4⋊C4—2981no—
311C4⋊C4—1491no—
312C4⋊C4—1491no—
313C4⋊C4C22×D14911yescharacteristic
314C22⋊C4—21no—
315C22⋊C4—21no—
316C22⋊C4—21no—
317C22⋊C4—2981no—
318C22⋊C4—2981no—
319C22⋊C4—2981no—
320C22⋊C4—2981no—
321C22⋊C4—1491no—
322C22⋊C4—1491no—
323C42—2981no—
324C42C22×D14911yescharacteristic
325C23—21no—
326C23—21no—
327C23—1491no—
328C23—1491no—
329Q8—21no—
330Q8—21no—
331Q8—2981no—
332Q8—2981no—
333Q8—2981no—
334Q8—2981no—
335Q8—2981no—
336Q8—5962no—
337Q8—1492no—
338D4—21no—
339D4—21no—
340D4—21no—
341D4—5961no—
342D4—5962no—
343D4—5962no—
344D4—5962no—
345D4—5962no—
346D4D4×D14912yes—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—42no—
350C2×C4—2981no—
351C2×C4—2981no—
352C2×C4—2981no—
353C2×C4—2981no—
354C2×C4—2981no—
355C2×C4—2981no—
356C2×C4—2981no—
357C2×C4—2981no—
358C2×C4—5962no—
359C2×C4—5962no—
360C2×C4—5962no—
361C2×C4—5962no—
362C2×C4—1491no—
363C2×C4—1491no—
364C2×C4D4×D14911yescharacteristic
365C2×C4D4×D14911yescharacteristic
366C2×C4C23×D14911yescharacteristic
367C8—21no—
368C8—21no—
369C8—2981no—
370C8—1492no—
371C22—22no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—2981no—
378C22—2981no—
379C22—2981no—
380C22—2981no—
381C22—2981no—
382C22—2981no—
383C22C2×D4×D14911yescharacteristic
384C4—21no—
385C4—21no—
386C4—41no—
387C4—41no—
388C4—2981no—
389C4—2981no—
390C4—2982no—
391C4—5961no—
392C4—5961no—
393C4—5961no—
394C4C2×D4×D14911yescharacteristic
395C4#1801195711yescharacteristic
396C2—42no—
397C2—81no—
398C2—5961no—
399C2—5961no—
400C2#2375025911yescharacteristic
401C2#2375042111yescharacteristic
402C2#2375043911yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#463×C149C2
socleC22×C149C22×D4
hypercenter#463D149
hypocenterC149#3269
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. C2×#18011940C2semidirect
2. C2×#18011930C2semidirect
3. #23750283C2semidirect
4. #23750279C2semidirect
5. #23750020C2semidirect
6. #23749870C2semidirect
7. #23749865C2semidirect
8. #23749836C2semidirect
9. #23749788C2semidirect
10. #23749784C2semidirect
11. #23749782C2semidirect
12. #23749767C2semidirect
13. #23749725C2semidirect
14. #23749695C2semidirect
15. #463×C149C2semidirect
90. #14558724D4semidirect
201. C149#3269semidirect
210. #463D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180119402
C2×#180119302
#237502832
#237502792
#237500202
#237498702
#237498652
#237498362
#237497882
#237497842
#237497822
#237497672
#237497252
#237496952
#463×C1492
#3269149