Finite Group Databasebeta

← #34054227

Subgroups — #34054227

Order 19072.

504 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
1C2×#18011938C211yesmaximal, characteristic, complemented
2C2×#18011932C211yesmaximal, characteristic, complemented
3#23750188C211yesmaximal, characteristic, complemented
4#23750107C211yesmaximal, characteristic, complemented
5#23749847C211yesmaximal, characteristic, complemented
6#23749845C211yesmaximal, characteristic, complemented
7#23749841C211yesmaximal, characteristic, complemented
8#23749839C211yesmaximal, characteristic, complemented
9#23749823C211yesmaximal, characteristic, complemented
10#23749819C211yesmaximal, characteristic, complemented
11#23749817C211yesmaximal, characteristic, complemented
12#23749650C211yesmaximal, characteristic, complemented
13#23749623C211yesmaximal, characteristic, complemented
14#102×D149C211yesmaximal, characteristic, complemented
15#460×C149C211yesmaximal, characteristic, complemented
16C2×#14558737C2211yescharacteristic
17C2×#14558735C2211yescharacteristic
18C2×D4×D149C2211yescharacteristic
19#18011938—24no—
20#18011932—24no—
21C2×#14558726C2211yescharacteristic, complemented
22C2×#14558725C2211yescharacteristic, complemented
23C2×#14558723C2211yescharacteristic
24C2×D1192C2211yescharacteristic
25C2×#14558721C2211yescharacteristic
26C2×#14558721C2211yescharacteristic, complemented
27C2×#14558719C2211yescharacteristic
28C2×C8×D149C2211yescharacteristic
29#18011907C2211yescharacteristic
30#18011899C2211yescharacteristic
31#18011898C2211yescharacteristic
32#18011883—21no—
33#18011883—21no—
34#18011879—21no—
35#18011879—21no—
36Q8×Dic149C2211yescharacteristic, complemented
37C4×D596—21no—
38C4×D596C2211yescharacteristic, complemented
39#18011873—21no—
40#18011873C2211yescharacteristic, complemented
41#18011868—21no—
42#18011868C2211yescharacteristic
43C4⋊C4×D149—21no—
44C4⋊C4×D149C2211yescharacteristic
45C4⋊#11924746C2211yescharacteristic, complemented
46#18011840C2211yescharacteristic, complemented
47#18011840C2211yescharacteristic, complemented
48#18011836C2211yescharacteristic, complemented
49#18011834C2211yescharacteristic, complemented
50#18011833C2211yescharacteristic
51#18011832C2211yescharacteristic
52#18011832C2211yescharacteristic, complemented
53#18011831C2211yescharacteristic
54C2×SD16×C149C2211yescharacteristic
55C2×SD16×C149C2211yescharacteristic, complemented
56#127×C149C2211yescharacteristic
57C4×Q8×C149C2211yescharacteristic, complemented
58C4⋊C8×C149C2211yescharacteristic, complemented
59#102×C149C2211yescharacteristic
60#102×C149C2211yescharacteristic, complemented
61C23×D149—21no—
62#14558737—22no—
63#14558737D414yescomplemented
64#14558735—22no—
65#14558735—22no—
66C2×Dic298C2311yescharacteristic
67C2×D596—21no—
68C2×D596C2311yescharacteristic
69C2×D596C2311yescharacteristic
70C2×C22⋊D149—21no—
71C2×C22⋊D149—21no—
72C2×C22⋊D149—21no—
73C2×C22⋊D149—21no—
74D4×D149—22no—
75D4×D149—22no—
76C22×Dic149—21no—
77C2×C4×D149—21no—
78C2×C4×D149—21no—
79C2×C4×D149—21no—
80C2×C4×D149—21no—
81C2×C4×D149C2311yescharacteristic
82#14558726—22no—
83#14558725—22no—
84#14558723—22no—
85D1192—22no—
86#14558721—22no—
87#14558721—22no—
88#14558719—22no—
89C2×#11924746C2311yescharacteristic
90C2×#11924746C2311yescharacteristic
91C8×D149—22no—
92C4⋊Dic149—21no—
93C4⋊Dic149C2311yescharacteristic
94#14558715—21no—
95#14558715D411yescharacteristic
96#14558715D411yescharacteristic
97C22⋊Dic149—21no—
98C22⋊Dic149—21no—
99#14558713—21no—
100#14558713—21no—
101#14558713—21no—
102#14558713—21no—
103#14558713D411yescharacteristic
104#14558713D411yescharacteristic
105C4×Dic149—21no—
106C4×Dic149C2311yescharacteristic
107C2×Q8×C149C2311yescharacteristic
108C2×D4×C149—21no—
109C2×D4×C149—21no—
110C2×D4×C149C2311yescharacteristic
111C2×D4×C149C2311yescharacteristic
112SD16×C149—22no—
113SD16×C149—22no—
114C2×C8×C149C2311yescharacteristic
115C2×C8×C149C2311yescharacteristic
116C4⋊C4×C149—21no—
117C4⋊C4×C149C2311yescharacteristic
118C42×C149—21no—
119C42×C149C2311yescharacteristic
120C22×D149—21no—
121C22×D149—21no—
122C22×D149—42no—
123C22×D149—81no—
124C22×D149—81no—
125C22×D149C2×D411yescharacteristic
126Dic298—21no—
127Dic298—21no—
128D596—24no—
129D596—21no—
130D596—21no—
131D596—21no—
132D596C2×D412yes—
133C22⋊D149—42no—
134C22⋊D149—42no—
135C22⋊D149—81no—
136C22⋊D149—81no—
137C2×Dic149—21no—
138C2×Dic149—21no—
139C2×Dic149—42no—
140C2×Dic149C2×D411yescharacteristic
141C2×Dic149C2×D411yescharacteristic
142C2×Dic149C2×D411yescharacteristic
143C4×D149—24no—
144C4×D149—81no—
145C4×D149—81no—
146C4×D149—81no—
147C4×D149C2×D412yes—
148C4×D149#4112yes—
149#11924746—21no—
150#11924746—21no—
151C23×C149—21no—
152C23×C149—21no—
153Q8×C149—21no—
154Q8×C149C2×D412yes—
155D4×C149—21no—
156D4×C149—21no—
157D4×C149—21no—
158D4×C149—21no—
159D4×C149—81no—
160D4×C149—81no—
161C2×C4×C149—21no—
162C2×C4×C149—21no—
163C2×C4×C149C2×D411yescharacteristic
164C2×C4×C149C2×D411yescharacteristic
165C2×C4×C149C2411yescharacteristic
166C8×C149—21no—
167C8×C149—21no—
168C22×C149—41no—
169C22×C149—41no—
170C22×C149—41no—
171C22×C149—41no—
172C22×C149—41no—
173C22×C149—41no—
174C22×C149C22×D411yescharacteristic
175C2×D149—21no—
176C2×D149—21no—
177C2×D149—22no—
178C2×D149—41no—
179C2×D149—41no—
180C2×D149—41no—
181C2×D149—41no—
182C2×D149—41no—
183C2×D149—84no—
184C2×D149#12112yes—
185C4×C149—22no—
186C4×C149—21no—
187C4×C149—21no—
188C4×C149—41no—
189C4×C149C22×D411yescharacteristic
190C4×C149C2×#4111yescharacteristic
191Dic149—21no—
192Dic149—21no—
193Dic149—41no—
194Dic149—41no—
195Dic149#12112yes—
196C2×C149—81no—
197C2×C149—81no—
198C2×C149C2×#12111yescharacteristic
199C2×C149#57611yescharacteristic
200C2×C149#57711yescharacteristic
201D149—22no—
202D149—42no—
203D149—81no—
204C149#304511yescharacteristic, complemented, Sylow
205#3045—1491nomaximal, Sylow
206C2×AGL(1,ℤ/8)—1491no—
207C2×#135—1491no—
208#535—1491no—
209#520—1491no—
210#464—1491no—
211#464—1491no—
212#463—1491no—
213#463—1491no—
214#460—1491no—
215#460D14911yescharacteristic, complemented
216#459—1491no—
217#459—1491no—
218#424—1491no—
219#417—1491no—
220C2×#102—1491no—
221C2×#41—1491no—
222C2×#41—1491no—
223C22×D4—1491no—
224AGL(1,ℤ/8)—2984no—
225#135—2984no—
226C2×Q16—1491no—
227C2×SD16—1491no—
228C2×SD16—1491no—
229C2×SD16C2×D14911yescharacteristic
230C2×SD16C2×D14911yescharacteristic, complemented
231C2×D8—1491no—
232C2×D8—1491no—
233C2×D8—1491no—
234C2×M16—1491no—
235C22×C8—1491no—
236#127—1491no—
237#127C2×D14911yescharacteristic
238#124—1491no—
239#124—1491no—
240#121—2981no—
241#121—2981no—
242#120—2981no—
243#120—2981no—
244C4×Q8—1491no—
245C4×Q8C2×D14911yescharacteristic, complemented
246C4×D4—2981no—
247C4×D4—2981no—
248C4×D4—1491no—
249C4×D4—1491no—
250#117—2981no—
251#117—1491no—
252C2×C4⋊C4—2981no—
253C2×C4⋊C4—1491no—
254C4⋊C8—1491no—
255C4⋊C8—1491no—
256C4⋊C8—1491no—
257C4⋊C8C2×D14911yescharacteristic, complemented
258#103—1491no—
259#103—1491no—
260#102—1491no—
261#102—1491no—
262#102—1491no—
263#102—1491no—
264#102C2×D14911yescharacteristic
265#102C2×D14911yescharacteristic, complemented
266C24—2981no—
267#41—2982no—
268#41—2982no—
269#41—2982no—
270#41—1494no—
271C2×Q8—1491no—
272C2×Q8C22×D14911yescharacteristic
273C2×D4—21no—
274C2×D4—21no—
275C2×D4—2981no—
276C2×D4—2981no—
277C2×D4—2982no—
278C2×D4—2982no—
279C2×D4—2981no—
280C2×D4—2981no—
281C2×D4—2981no—
282C2×D4—1491no—
283C2×D4—1491no—
284C2×D4C22×D14911yescharacteristic
285C2×D4C22×D14911yescharacteristic
286C22×C4—2981no—
287C22×C4—2981no—
288C22×C4—2981no—
289C22×C4—2981no—
290C22×C4—2981no—
291C22×C4—1491no—
292Q16—2982no—
293SD16—22no—
294SD16—22no—
295SD16—2982no—
296SD16—2982no—
297D8—2982no—
298D8—2982no—
299D8—2982no—
300M16—2982no—
301C2×C8—2982no—
302C2×C8—1491no—
303C2×C8—1491no—
304C2×C8C22×D14911yescharacteristic
305C2×C8C22×D14911yescharacteristic
306C4⋊C4—21no—
307C4⋊C4—2981no—
308C4⋊C4—2981no—
309C4⋊C4—1491no—
310C4⋊C4—1491no—
311C4⋊C4—1491no—
312C4⋊C4C22×D14911yescharacteristic
313C22⋊C4—2981no—
314C22⋊C4—2981no—
315C22⋊C4—2981no—
316C22⋊C4—2981no—
317C22⋊C4—2981no—
318C22⋊C4—2981no—
319C22⋊C4—1491no—
320C22⋊C4—1491no—
321C42—21no—
322C42—2981no—
323C42—1491no—
324C42C22×D14911yescharacteristic
325C23—21no—
326C23—21no—
327C23—2981no—
328C23—2981no—
329C23—5962no—
330C23—1491no—
331C23—11921no—
332C23—11921no—
333Q8—21no—
334Q8—2981no—
335Q8—2981no—
336Q8D4×D14912yes—
337D4—21no—
338D4—21no—
339D4—21no—
340D4—21no—
341D4—81no—
342D4—81no—
343D4—2984no—
344D4—2981no—
345D4—2981no—
346D4—2981no—
347D4—5962no—
348D4—5962no—
349D4—1492no—
350D4—11921no—
351D4—11921no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—2984no—
355C2×C4—2981no—
356C2×C4—2981no—
357C2×C4—5962no—
358C2×C4—1491no—
359C2×C4—1491no—
360C2×C4—1491no—
361C2×C4—1492no—
362C2×C4—1492no—
363C2×C4—11921no—
364C2×C4—11921no—
365C2×C4—11921no—
366C2×C4D4×D14911yescharacteristic
367C2×C4D4×D14911yescharacteristic
368C2×C4C23×D14911yescharacteristic
369C8—21no—
370C8—21no—
371C8—2981no—
372C8—2981no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—2981no—
380C22—2981no—
381C22—2982no—
382C22—5961no—
383C22—5961no—
384C22—5961no—
385C22—5961no—
386C22—5961no—
387C22—1492no—
388C22—11924no—
389C22C2×D4×D14911yescharacteristic
390C4—21no—
391C4—21no—
392C4—22no—
393C4—41no—
394C4—2981no—
395C4—2981no—
396C4—5961no—
397C4—5961no—
398C4—1492no—
399C4C2×D4×D14911yescharacteristic
400C4#41×D14911yescharacteristic
401C2—81no—
402C2—81no—
403C2—2982no—
404C2—5962no—
405C2—11921no—
406C2#121×D14911yescharacteristic
407C2#2375042911yescharacteristic
408C2#2375043111yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#460×C149C2
socleC22×C149C22×D4
hypercenter#460D149
hypocenterC149#3045
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. C2×#18011938C2semidirect
2. C2×#18011932C2semidirect
3. #23750188C2semidirect
4. #23750107C2semidirect
5. #23749847C2semidirect
6. #23749845C2semidirect
7. #23749841C2semidirect
8. #23749839C2semidirect
9. #23749823C2semidirect
10. #23749819C2semidirect
11. #23749817C2semidirect
12. #23749650C2semidirect
13. #23749623C2semidirect
14. #102×D149C2semidirect
15. #460×C149C2semidirect
21. C2×#14558726C22semidirect
22. C2×#14558725C22semidirect
26. C2×#14558721C22semidirect
36. Q8×Dic149C22semidirect
38. C4×D596C22semidirect
40. #18011873C22semidirect
45. C4⋊#11924746C22semidirect
46. #18011840C22semidirect
47. #18011840C22semidirect
48. #18011836C22semidirect
49. #18011834C22semidirect
52. #18011832C22semidirect
55. C2×SD16×C149C22semidirect
57. C4×Q8×C149C22semidirect
58. C4⋊C8×C149C22semidirect
60. #102×C149C22semidirect
63. #14558737D4semidirect
204. C149#3045semidirect
215. #460D149semidirect
230. C2×SD16C2×D149semidirect
245. C4×Q8C2×D149semidirect
257. C4⋊C8C2×D149semidirect
265. #102C2×D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180119382
C2×#180119322
#237501882
#237501072
#237498472
#237498452
#237498412
#237498392
#237498232
#237498192
#237498172
#237496502
#237496232
#102×D1492
#460×C1492
#3045149