Finite Group Databasebeta

← #34056241

Subgroups — #34056241

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×#18011943C211yesmaximal, characteristic, complemented
2C2×#18011934C211yesmaximal, characteristic, complemented
3#23750287C211yesmaximal, characteristic, complemented
4#23750278C211yesmaximal, characteristic, complemented
5#23750017C211yesmaximal, characteristic, complemented
6#23749874C211yesmaximal, characteristic, complemented
7#23749865C211yesmaximal, characteristic, complemented
8#23749841C211yesmaximal, characteristic, complemented
9#23749790C211yesmaximal, characteristic, complemented
10#23749786C211yesmaximal, characteristic, complemented
11#23749779C211yesmaximal, characteristic, complemented
12#23749773C211yesmaximal, characteristic, complemented
13#23749723C211yesmaximal, characteristic, complemented
14#23749695C211yesmaximal, characteristic, complemented
15#462×C149C211yesmaximal, characteristic, complemented
16C2×#14558737C2211yescharacteristic
17C2×#14558737C2211yescharacteristic
18C2×#14558737C2211yescharacteristic
19C2×Q8×D149C2211yescharacteristic
20#18011943—24no—
21#18011934—24no—
22C2×#14558726C2211yescharacteristic
23C2×#14558726C2211yescharacteristic
24C2×#14558725C2211yescharacteristic
25C2×#14558723C2211yescharacteristic
26C2×#14558723C2211yescharacteristic
27C2×#14558723C2211yescharacteristic
28C2×D1192C2211yescharacteristic
29C2×#14558719C2211yescharacteristic
30C2×C8×D149C2211yescharacteristic
31#18011899—21no—
32#18011899C2211yescharacteristic
33#18011896—21no—
34#18011896—21no—
35#18011891—21no—
36#18011891C2211yescharacteristic
37#18011887C2211yescharacteristic
38#18011887C2211yescharacteristic
39#18011886—21no—
40#18011886—21no—
41#18011886C2211yescharacteristic
42C4×D596—21no—
43C4×D596C2211yescharacteristic
44C4×D596C2211yescharacteristic
45C4⋊C4×D149—21no—
46#18011844C2211yescharacteristic
47#18011836C2211yescharacteristic
48#18011835C2211yescharacteristic
49#18011833C2211yescharacteristic
50#18011831C2211yescharacteristic
51#18011823C2211yescharacteristic
52#18011823C2211yescharacteristic
53#18011822C2211yescharacteristic
54C2×Q16×C149C2211yescharacteristic
55C2×Q16×C149C2211yescharacteristic
56C4⋊Q8×C149C2211yescharacteristic
57C4×Q8×C149C2211yescharacteristic
58C4⋊C8×C149C2211yescharacteristic
59#103×C149C2211yescharacteristic
60#103×C149C2211yescharacteristic
61#14558737—22no—
62#14558737—22no—
63#14558737—22no—
64#14558737—41no—
65#14558737—41no—
66#14558737—41no—
67C2×Dic298—21no—
68C2×Dic298C2311yescharacteristic
69Q8×D149—22no—
70Q8×D149—41no—
71C2×D596—21no—
72C2×D596—21no—
73C2×D596—21no—
74C2×D596—21no—
75C2×D596D411yescharacteristic
76C2×D596C2311yescharacteristic
77C2×D596C2311yescharacteristic
78C2×C4×D149—21no—
79C2×C4×D149—21no—
80C2×C4×D149—21no—
81C2×C4×D149—21no—
82C2×C4×D149—21no—
83C2×C4×D149C2311yescharacteristic
84C2×C4×D149C2311yescharacteristic
85#14558726—22no—
86#14558726—41no—
87#14558725—22no—
88#14558723—22no—
89#14558723—41no—
90#14558723D414yescomplemented
91D1192—22no—
92#14558719—22no—
93C2×#11924746C2311yescharacteristic
94C2×#11924746C2311yescharacteristic
95C8×D149—22no—
96C4⋊Dic149—21no—
97C4⋊Dic149D411yescharacteristic
98C4⋊Dic149C2311yescharacteristic
99#14558715—21no—
100#14558715—21no—
101#14558713—21no—
102#14558713—21no—
103#14558713—21no—
104#14558713—21no—
105#14558713—21no—
106#14558713—21no—
107#14558713—21no—
108#14558713D411yescharacteristic
109#14558713D411yescharacteristic
110C2×Q8×C149C2311yescharacteristic
111C2×Q8×C149C2311yescharacteristic
112C2×Q8×C149C2311yescharacteristic
113Q16×C149—22no—
114Q16×C149—22no—
115C2×C8×C149C2311yescharacteristic
116C2×C8×C149C2311yescharacteristic
117C4⋊C4×C149—21no—
118C4⋊C4×C149—21no—
119C4⋊C4×C149—21no—
120C4⋊C4×C149C2311yescharacteristic
121C42×C149—21no—
122C42×C149C2311yescharacteristic
123C22×D149—21no—
124C22×D149—21no—
125C22×D149C2×D411yescharacteristic
126C22×D149C2×D411yescharacteristic
127Dic298—21no—
128Dic298—21no—
129Dic298—42no—
130D596—21no—
131D596—21no—
132D596—21no—
133D596—41no—
134D596—42no—
135D596—42no—
136D596—42no—
137D596—42no—
138D596C2×D412yes—
139C2×Dic149—21no—
140C2×Dic149—21no—
141C2×Dic149C2×D411yescharacteristic
142C2×Dic149C2×D411yescharacteristic
143C4×D149—21no—
144C4×D149—21no—
145C4×D149—21no—
146C4×D149—21no—
147C4×D149—42no—
148C4×D149—42no—
149C4×D149—42no—
150C4×D149—42no—
151C4×D149—42no—
152#11924746—21no—
153#11924746C2×D412yes—
154Q8×C149—21no—
155Q8×C149—21no—
156Q8×C149—21no—
157Q8×C149—21no—
158Q8×C149—21no—
159Q8×C149C2×D412yes—
160C2×C4×C149—21no—
161C2×C4×C149—21no—
162C2×C4×C149—21no—
163C2×C4×C149—21no—
164C2×C4×C149C2×D411yescharacteristic
165C2×C4×C149C2×D411yescharacteristic
166C2×C4×C149C2411yescharacteristic
167C8×C149—21no—
168C8×C149—21no—
169C22×C149C22×D411yescharacteristic
170C2×D149—21no—
171C2×D149—21no—
172C2×D149—22no—
173C2×D149—21no—
174C2×D149—21no—
175C2×D149—21no—
176C2×D149—21no—
177C2×D149—41no—
178C2×D149—41no—
179C2×D149—41no—
180C2×D149—41no—
181C2×D149—41no—
182C4×C149—22no—
183C4×C149—21no—
184C4×C149—21no—
185C4×C149—41no—
186C4×C149—41no—
187C4×C149—41no—
188C4×C149C22×D411yescharacteristic
189C4×C149H(5,𝔽2)11yescharacteristic
190Dic149—21no—
191Dic149—21no—
192Dic149—41no—
193Dic149—41no—
194C2×C149D4211yescharacteristic
195C2×C149#57511yescharacteristic
196C2×C149#57811yescharacteristic
197D149—41no—
198D149—41no—
199D149—42no—
200D149—81no—
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#463—1491no—
211#462D14911yescharacteristic, complemented
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×Q16C2×D14911yescharacteristic
227C2×Q16C2×D14911yescharacteristic
228C2×SD16—1491no—
229C2×SD16—1491no—
230C2×SD16—1491no—
231C2×SD16—1491no—
232C2×D8—1491no—
233C2×M16—1491no—
234C22×C8—1491no—
235C4⋊Q8C2×D14911yescharacteristic
236#124—2981no—
237#124—1491no—
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×Q8C2×D14911yescharacteristic
248C4×D4—2981no—
249C4×D4—1491no—
250C4×D4—1491no—
251C2×C4⋊C4—2981no—
252#107—1491no—
253C4⋊C8C2×D14911yescharacteristic
254#103—1491no—
255#103—1491no—
256#103C2×D14911yescharacteristic
257#103C2×D14911yescharacteristic
258#102—1491no—
259#102—1491no—
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×Q8C22×D14911yescharacteristic
274C2×Q8C22×D14911yescharacteristic
275C2×Q8C22×D14911yescharacteristic
276C2×D4—2981no—
277C2×D4—2981no—
278C2×D4—2981no—
279C2×D4—2981no—
280C2×D4—1491no—
281C2×D4—1491no—
282C2×D4—1491no—
283C22×C4—2981no—
284C22×C4—2981no—
285C22×C4—2981no—
286C22×C4—2981no—
287C22×C4—2981no—
288C22×C4—1491no—
289C22×C4—1491no—
290Q16—22no—
291Q16—22no—
292Q16—2982no—
293Q16—5961no—
294SD16—2982no—
295SD16—2982no—
296SD16—5961no—
297SD16—1494no—
298D8—2982no—
299M16—2982no—
300C2×C8—2982no—
301C2×C8—1491no—
302C2×C8—1491no—
303C2×C8C22×D14911yescharacteristic
304C2×C8C22×D14911yescharacteristic
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—21no—
308C4⋊C4—2981no—
309C4⋊C4—2981no—
310C4⋊C4—2981no—
311C4⋊C4—1491no—
312C4⋊C4—1491no—
313C4⋊C4C22×D14911yescharacteristic
314C22⋊C4—2981no—
315C22⋊C4—2981no—
316C22⋊C4—2981no—
317C22⋊C4—2981no—
318C22⋊C4—2981no—
319C22⋊C4—2981no—
320C22⋊C4—2981no—
321C22⋊C4—1491no—
322C22⋊C4—1491no—
323C42—21no—
324C42C22×D14911yescharacteristic
325C23—2981no—
326C23—2981no—
327C23—1491no—
328C23—1491no—
329Q8—21no—
330Q8—21no—
331Q8—21no—
332Q8—21no—
333Q8—21no—
334Q8—2981no—
335Q8—2981no—
336Q8—5962no—
337Q8D4×D14912yes—
338D4—2981no—
339D4—2981no—
340D4—2981no—
341D4—5961no—
342D4—5962no—
343D4—5962no—
344D4—5962no—
345D4—5962no—
346D4—1492no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—2981no—
352C2×C4—2981no—
353C2×C4—2981no—
354C2×C4—2981no—
355C2×C4—2981no—
356C2×C4—2981no—
357C2×C4—5962no—
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—2981no—
372C22—2981no—
373C22—2981no—
374C22—2981no—
375C22—2981no—
376C22—2981no—
377C22—2982no—
378C22—5961no—
379C22—5961no—
380C22—5961no—
381C22—5961no—
382C22—5961no—
383C22C2×D4×D14911yescharacteristic
384C4—21no—
385C4—21no—
386C4—22no—
387C4—41no—
388C4—41no—
389C4—41no—
390C4—2981no—
391C4—2981no—
392C4—5961no—
393C4—5961no—
394C4C2×D4×D14911yescharacteristic
395C4#1801195711yescharacteristic
396C2—5961no—
397C2—5961no—
398C2—5962no—
399C2—11921no—
400C2#2375025911yescharacteristic
401C2#2375042411yescharacteristic
402C2#2375043811yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#462×C149C2
socleC22×C149C22×D4
hypercenter#462D149
hypocenterC149#3269
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
1. C2×#18011943C2semidirect
2. C2×#18011934C2semidirect
3. #23750287C2semidirect
4. #23750278C2semidirect
5. #23750017C2semidirect
6. #23749874C2semidirect
7. #23749865C2semidirect
8. #23749841C2semidirect
9. #23749790C2semidirect
10. #23749786C2semidirect
11. #23749779C2semidirect
12. #23749773C2semidirect
13. #23749723C2semidirect
14. #23749695C2semidirect
15. #462×C149C2semidirect
90. #14558723D4semidirect
201. C149#3269semidirect
211. #462D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180119432
C2×#180119342
#237502872
#237502782
#237500172
#237498742
#237498652
#237498412
#237497902
#237497862
#237497792
#237497732
#237497232
#237496952
#462×C1492
#3269149