Finite Group Databasebeta

← #34054233

Subgroups — #34054233

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×#18011934C211yesmaximal, characteristic, complemented
3#23750193C211yesmaximal, characteristic, complemented
4#23750107C211yesmaximal, characteristic, complemented
5#23749849C211yesmaximal, characteristic, complemented
6#23749843C211yesmaximal, characteristic, complemented
7#23749837C211yesmaximal, characteristic, complemented
8#23749825C211yesmaximal, characteristic, complemented
9#23749823C211yesmaximal, characteristic, complemented
10#23749821C211yesmaximal, characteristic, complemented
11#23749819C211yesmaximal, characteristic, complemented
12#23749650C211yesmaximal, characteristic, complemented
13#23749625C211yesmaximal, characteristic, complemented
14#102×D149C211yesmaximal, characteristic, complemented
15#464×C149C211yesmaximal, characteristic, complemented
16C2×#14558737C2211yescharacteristic
17C2×#14558737C2211yescharacteristic
18C2×D4×D149C2211yescharacteristic
19#18011938—24no—
20#18011934—24no—
21C2×#14558723C2211yescharacteristic
22C2×#14558723C2211yescharacteristic, complemented
23C2×#14558723C2211yescharacteristic, complemented
24C2×D1192C2211yescharacteristic
25C2×D1192C2211yescharacteristic, complemented
26C2×#14558721C2211yescharacteristic
27C2×#14558719C2211yescharacteristic
28C2×C8×D149C2211yescharacteristic
29#18011908C2211yescharacteristic
30#18011907C2211yescharacteristic
31#18011900C2211yescharacteristic
32#18011884—21no—
33#18011884—21no—
34#18011881—21no—
35#18011881—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#18011835C2211yescharacteristic, complemented
49#18011833C2211yescharacteristic
50#18011833C2211yescharacteristic, complemented
51#18011832C2211yescharacteristic
52#18011831C2211yescharacteristic
53#18011831C2211yescharacteristic, complemented
54C2×Q16×C149C2211yescharacteristic, complemented
55C2×SD16×C149C2211yescharacteristic
56#124×C149C2211yescharacteristic
57C4×Q8×C149C2211yescharacteristic, complemented
58C4⋊C8×C149C2211yescharacteristic, complemented
59#103×C149C2211yescharacteristic, complemented
60#102×C149C2211yescharacteristic
61C23×D149—21no—
62#14558737—22no—
63#14558737—22no—
64#14558737—22no—
65#14558737D414yescomplemented
66C2×D596—21no—
67C2×D596—21no—
68C2×D596—21no—
69C2×D596—21no—
70C2×D596C2311yescharacteristic
71C2×D596C2311yescharacteristic
72C2×D596C2311yescharacteristic
73C2×C22⋊D149—21no—
74C2×C22⋊D149—21no—
75C2×C22⋊D149—21no—
76D4×D149—22no—
77D4×D149—22no—
78C2×C4×D149—21no—
79C2×C4×D149—21no—
80C2×C4×D149—21no—
81C2×C4×D149—21no—
82C2×C4×D149—21no—
83C2×C4×D149C2311yescharacteristic
84#14558723—22no—
85#14558723—22no—
86#14558723—22no—
87D1192—22no—
88D1192—22no—
89#14558721—22no—
90#14558719—22no—
91C2×#11924746C2311yescharacteristic
92C2×#11924746C2311yescharacteristic
93C8×D149—22no—
94C4⋊Dic149—21no—
95C4⋊Dic149C2311yescharacteristic
96#14558715—21no—
97#14558715D411yescharacteristic
98#14558715D411yescharacteristic
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×Q8×C149C2311yescharacteristic
109C2×D4×C149C2311yescharacteristic
110Q16×C149—22no—
111SD16×C149—22no—
112C2×C8×C149C2311yescharacteristic
113C2×C8×C149C2311yescharacteristic
114C4⋊C4×C149—21no—
115C4⋊C4×C149C2311yescharacteristic
116C22⋊C4×C149—21no—
117C22⋊C4×C149—21no—
118C42×C149—21no—
119C42×C149C2311yescharacteristic
120C22×D149—21no—
121C22×D149—21no—
122C22×D149—21no—
123C22×D149—42no—
124C22×D149—81no—
125C22×D149—81no—
126C22×D149C2×D411yescharacteristic
127D596—24no—
128D596—21no—
129D596—21no—
130D596—21no—
131D596—21no—
132D596—21no—
133D596—42no—
134D596—81no—
135D596—81no—
136D596C2×D412yes—
137C22⋊D149—42no—
138C22⋊D149—81no—
139C22⋊D149—81no—
140C2×Dic149—21no—
141C2×Dic149C2×D411yescharacteristic
142C2×Dic149C2×D411yescharacteristic
143C2×Dic149C2×D411yescharacteristic
144C4×D149—24no—
145C4×D149—42no—
146C4×D149—81no—
147C4×D149—81no—
148C4×D149—81no—
149C4×D149C2×D412yes—
150C4×D149#4112yes—
151#11924746—21no—
152#11924746—21no—
153C23×C149—21no—
154Q8×C149—21no—
155Q8×C149—21no—
156Q8×C149—21no—
157Q8×C149C2×D412yes—
158D4×C149—21no—
159D4×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×C149—21no—
168C22×C149—41no—
169C22×C149—41no—
170C22×C149—41no—
171C22×C149C22×D411yescharacteristic
172C2×D149—21no—
173C2×D149—21no—
174C2×D149—22no—
175C2×D149—41no—
176C2×D149—41no—
177C2×D149—41no—
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×C149—41no—
190C4×C149C22×D411yescharacteristic
191C4×C149C2×#4111yescharacteristic
192Dic149—21no—
193Dic149—21no—
194Dic149—41no—
195Dic149#12112yes—
196C2×C149—81no—
197C2×C149C2×#12111yescharacteristic
198C2×C149#57611yescharacteristic
199C2×C149#57711yescharacteristic
200D149—22no—
201D149—42no—
202D149—81no—
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#464D14911yescharacteristic, complemented
212#463—1491no—
213#463—1491no—
214#460—1491no—
215#460—1491no—
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×Q16C2×D14911yescharacteristic, complemented
227C2×SD16—1491no—
228C2×SD16—1491no—
229C2×SD16—1491no—
230C2×SD16C2×D14911yescharacteristic
231C2×D8—1491no—
232C2×D8—1491no—
233C2×D8—1491no—
234C2×M16—1491no—
235C22×C8—1491no—
236#127—1491no—
237#127—1491no—
238#124—1491no—
239#124C2×D14911yescharacteristic
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#103C2×D14911yescharacteristic, complemented
260#102—1491no—
261#102—1491no—
262#102—1491no—
263#102—1491no—
264#102—1491no—
265#102C2×D14911yescharacteristic
266C24—2981no—
267#41—2982no—
268#41—2982no—
269#41—2982no—
270#41—1494no—
271C2×Q8C22×D14911yescharacteristic
272C2×Q8C22×D14911yescharacteristic
273C2×D4—2981no—
274C2×D4—2981no—
275C2×D4—2982no—
276C2×D4—2982no—
277C2×D4—2981no—
278C2×D4—2981no—
279C2×D4—2981no—
280C2×D4—2981no—
281C2×D4—2981no—
282C2×D4—1491no—
283C2×D4—1491no—
284C2×D4—1491no—
285C2×D4C22×D14911yescharacteristic
286C22×C4—2981no—
287C22×C4—2981no—
288C22×C4—2981no—
289C22×C4—2981no—
290C22×C4—2981no—
291C22×C4—1491no—
292Q16—22no—
293SD16—22no—
294SD16—2982no—
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—21no—
314C22⋊C4—21no—
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—2981no—
327C23—2981no—
328C23—2981no—
329C23—5962no—
330C23—1491no—
331C23—11921no—
332C23—11921no—
333Q8—21no—
334Q8—21no—
335Q8—21no—
336Q8D4×D14912yes—
337D4—21no—
338D4—21no—
339D4—2984no—
340D4—2981no—
341D4—2981no—
342D4—2981no—
343D4—2981no—
344D4—2981no—
345D4—5962no—
346D4—5962no—
347D4—1492no—
348D4—11921no—
349D4—11921no—
350D4—11921no—
351D4—11921no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—2984no—
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—2981no—
377C22—2981no—
378C22—2982no—
379C22—5961no—
380C22—5961no—
381C22—5961no—
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—41no—
395C4—2981no—
396C4—2981no—
397C4—5961no—
398C4—1492no—
399C4C2×D4×D14911yescharacteristic
400C4#41×D14911yescharacteristic
401C2—81no—
402C2—2982no—
403C2—5962no—
404C2—11921no—
405C2—11921no—
406C2#121×D14911yescharacteristic
407C2#2375042711yescharacteristic
408C2#2375043411yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#464×C149C2
socleC22×C149C22×D4
hypercenter#464D149
hypocenterC149#3045
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. C2×#18011938C2semidirect
2. C2×#18011934C2semidirect
3. #23750193C2semidirect
4. #23750107C2semidirect
5. #23749849C2semidirect
6. #23749843C2semidirect
7. #23749837C2semidirect
8. #23749825C2semidirect
9. #23749823C2semidirect
10. #23749821C2semidirect
11. #23749819C2semidirect
12. #23749650C2semidirect
13. #23749625C2semidirect
14. #102×D149C2semidirect
15. #464×C149C2semidirect
22. C2×#14558723C22semidirect
23. C2×#14558723C22semidirect
25. C2×D1192C22semidirect
36. Q8×Dic149C22semidirect
38. C4×D596C22semidirect
40. #18011873C22semidirect
45. C4⋊#11924746C22semidirect
46. #18011840C22semidirect
47. #18011840C22semidirect
48. #18011835C22semidirect
50. #18011833C22semidirect
53. #18011831C22semidirect
54. C2×Q16×C149C22semidirect
57. C4×Q8×C149C22semidirect
58. C4⋊C8×C149C22semidirect
59. #103×C149C22semidirect
65. #14558737D4semidirect
204. C149#3045semidirect
211. #464D149semidirect
226. C2×Q16C2×D149semidirect
245. C4×Q8C2×D149semidirect
257. C4⋊C8C2×D149semidirect
259. #103C2×D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180119382
C2×#180119342
#237501932
#237501072
#237498492
#237498432
#237498372
#237498252
#237498232
#237498212
#237498192
#237496502
#237496252
#102×D1492
#464×C1492
#3045149