Finite Group Databasebeta

← #34055555

Subgroups — #34055555

Order 19072.

442 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750194C211yesmaximal, characteristic, complemented
2#23750191C211yesmaximal, characteristic, complemented
3#23749952C211yesmaximal, characteristic, complemented
4#23749951C211yesmaximal, characteristic, complemented
5#23749949C211yesmaximal, characteristic, complemented
6#23749879C211yesmaximal, characteristic, complemented
7#23749877C211yesmaximal, characteristic, complemented
8#23749862C211yesmaximal, characteristic, complemented
9#23749860C211yesmaximal, characteristic, complemented
10#23749761C211yesmaximal, characteristic, complemented
11#23749760C211yesmaximal, characteristic, complemented
12#23749760C211yesmaximal, characteristic, complemented
13#23749758C211yesmaximal, characteristic, complemented
14#23749590C211yesmaximal, characteristic, complemented
15#482×C149C211yesmaximal, characteristic, complemented
16C2×#14558736C2211yescharacteristic
17C22×D596C2211yescharacteristic, complemented
18C2×D4×D149C2211yescharacteristic, complemented
19C2×D1192C2211yescharacteristic
20C2×D1192C2211yescharacteristic
21C2×#14558721C2211yescharacteristic
22C2×#14558721C2211yescharacteristic
23C2×#14558719C2211yescharacteristic, complemented
24C2×C8×D149C2211yescharacteristic, complemented
25#18011908—21no—
26#18011907—21no—
27#18011899—21no—
28#18011897—21no—
29#18011886C2211yescharacteristic
30#18011886C2211yescharacteristic
31#18011886C2211yescharacteristic, complemented
32#18011886C2211yescharacteristic, complemented
33#18011886C2211yescharacteristic, complemented
34#18011885C2211yescharacteristic
35#18011882C2211yescharacteristic, complemented
36#18011881—21no—
37#18011881—21no—
38#18011881—21no—
39#18011879—21no—
40#18011869C2211yescharacteristic, complemented
41#18011844C2211yescharacteristic, complemented
42#18011842C2211yescharacteristic, complemented
43#18011833C2211yescharacteristic, complemented
44#18011833C2211yescharacteristic, complemented
45#18011831C2211yescharacteristic, complemented
46#18011831C2211yescharacteristic, complemented
47#18011831C2211yescharacteristic, complemented
48#18011831C2211yescharacteristic, complemented
49C22⋊#11924746C2211yescharacteristic, complemented
50#18011823C2211yescharacteristic, complemented
51#18011823C2211yescharacteristic, complemented
52#121×C149C2211yescharacteristic
53#117×C149C2211yescharacteristic, complemented
54#107×C149C2211yescharacteristic, complemented
55#106×C149C2211yescharacteristic, complemented
56#102×C149C2211yescharacteristic, complemented
57#102×C149C2211yescharacteristic, complemented
58C22⋊C8×C149C2211yescharacteristic, complemented
59C23×D149—21no—
60C23×D149—21no—
61#14558736—41no—
62#14558736—41no—
63C2×Dic298D411yescharacteristic
64C2×D596—21no—
65C2×D596—21no—
66C2×D596—21no—
67C2×D596—21no—
68C2×D596—21no—
69C2×D596—21no—
70C2×D596—41no—
71C2×D596—41no—
72C2×D596D411yescharacteristic
73C2×D596C2311yescharacteristic
74C2×D596C2311yescharacteristic
75C2×D596C2311yescharacteristic
76C2×C22⋊D149—21no—
77C2×C22⋊D149—21no—
78C2×C22⋊D149—21no—
79C2×C22⋊D149D411yescharacteristic
80C2×C22⋊D149D411yescharacteristic
81D4×D149—41no—
82D4×D149—41no—
83C2×C4×D149C2311yescharacteristic
84C2×C4×D149C2311yescharacteristic
85D1192—41no—
86D1192—41no—
87#14558721—41no—
88#14558721—41no—
89#14558719—41no—
90C2×#11924746C2311yescharacteristic
91C2×#11924746C2311yescharacteristic
92C8×D149—41no—
93C4⋊Dic149C2311yescharacteristic
94C22⋊Dic149—21no—
95#14558713—21no—
96#14558713—21no—
97#14558713—21no—
98#14558713—21no—
99#14558713—21no—
100#14558713—21no—
101#14558713—21no—
102C4×Dic149—21no—
103C2×D4×C149—21no—
104C2×D4×C149C2311yescharacteristic
105C22×C4×C149C2311yescharacteristic
106C2×C8×C149C2311yescharacteristic
107C2×C8×C149C2311yescharacteristic
108C4⋊C4×C149C2311yescharacteristic
109C4⋊C4×C149C2311yescharacteristic
110C4⋊C4×C149C2311yescharacteristic
111C22⋊C4×C149—21no—
112C22⋊C4×C149—21no—
113C42×C149—21no—
114C22×D149—21no—
115C22×D149—21no—
116C22×D149—21no—
117C22×D149—42no—
118C22×D149—42no—
119C22×D149—81no—
120C22×D149—81no—
121C22×D149—81no—
122C22×D149—81no—
123C22×D149C2×D411yescharacteristic
124C22×D149C2×D411yescharacteristic
125Dic298—41no—
126D596—21no—
127D596—21no—
128D596—21no—
129D596—21no—
130D596—21no—
131D596—21no—
132D596—41no—
133D596—42no—
134D596—81no—
135D596—81no—
136D596—81no—
137D596—81no—
138D596—81no—
139C22⋊D149—41no—
140C22⋊D149—41no—
141C22⋊D149—42no—
142C22⋊D149—81no—
143C22⋊D149—81no—
144C2×Dic149—21no—
145C2×Dic149C2×D411yescharacteristic
146C2×Dic149C2×D411yescharacteristic
147C4×D149—21no—
148C4×D149—21no—
149C4×D149—21no—
150C4×D149—21no—
151#11924746—21no—
152#11924746—21no—
153C23×C149—21no—
154C23×C149C2×D411yescharacteristic
155D4×C149—21no—
156D4×C149—21no—
157D4×C149—81no—
158C2×C4×C149—21no—
159C2×C4×C149—21no—
160C2×C4×C149—21no—
161C2×C4×C149—21no—
162C2×C4×C149—21no—
163C2×C4×C149C2×D411yescharacteristic
164C2×C4×C149C2411yescharacteristic
165C8×C149—21no—
166C8×C149—21no—
167C22×C149—21no—
168C22×C149—21no—
169C22×C149—21no—
170C22×C149—41no—
171C22×C149—41no—
172C22×C149—41no—
173C22×C149C22×D411yescharacteristic
174C2×D149—21no—
175C2×D149—21no—
176C2×D149—21no—
177C2×D149—21no—
178C2×D149—21no—
179C2×D149—21no—
180C2×D149—41no—
181C2×D149—41no—
182C2×D149—41no—
183C2×D149—41no—
184C2×D149—41no—
185C2×D149—41no—
186C2×D149—41no—
187C2×D149—41no—
188C2×D149—41no—
189C2×D149—84no—
190C2×D149—84no—
191C4×C149—21no—
192C4×C149—41no—
193C4×C149—41no—
194C4×C149—41no—
195C4×C149H(5,𝔽2)11yescharacteristic
196C4×C149H(5,𝔽2)11yescharacteristic
197Dic149—21no—
198Dic149—21no—
199Dic149—41no—
200C2×C149—41no—
201C2×C149—81no—
202C2×C149#53411yescharacteristic
203C2×C149#57611yescharacteristic
204C2×C149#57611yescharacteristic
205D149—41no—
206D149—41no—
207D149—81no—
208D149—81no—
209D149—81no—
210C149#319911yescharacteristic, complemented, Sylow
211#3199—1491nomaximal, Sylow
212#535—1491no—
213#535—1491no—
214#482—1491no—
215#482—1491no—
216#482—1491no—
217#482D14911yescharacteristic, complemented
218#469—1491no—
219#469—1491no—
220#466—1491no—
221#466—1491no—
222#447—1491no—
223#447—1491no—
224#447—1491no—
225#447—1491no—
226#408—1491no—
227C2×#41—1491no—
228C22×D4—1491no—
229C22×D4—1491no—
230C2×D8—1491no—
231C2×D8—1491no—
232C2×D8—1491no—
233C2×D8—1491no—
234C2×M16—1491no—
235C22×C8—1491no—
236#127—2981no—
237#127—2981no—
238#124—2981no—
239#124—2981no—
240#121—1491no—
241#121—1491no—
242#121—1491no—
243#121—1491no—
244#121—1491no—
245#121—1491no—
246#121—1491no—
247#121C2×D14911yescharacteristic
248#120—2981no—
249#120—2981no—
250#120—2981no—
251#120—2981no—
252#117—1491no—
253#117C2×D14911yescharacteristic, complemented
254#107—1491no—
255#107C2×D14911yescharacteristic, complemented
256#106—1491no—
257#106C2×D14911yescharacteristic, complemented
258#102—1491no—
259#102—1491no—
260#102—1491no—
261#102—1491no—
262#102—1491no—
263#102—1491no—
264#102C2×D14911yescharacteristic, complemented
265#102C2×D14911yescharacteristic, complemented
266C22⋊C8—1491no—
267C22⋊C8—1491no—
268C22⋊C8—1491no—
269C22⋊C8C2×D14911yescharacteristic, complemented
270C24—2981no—
271C24—2981no—
272#41—5961no—
273#41—5961no—
274C2×Q8—1491no—
275C2×D4—21no—
276C2×D4—2981no—
277C2×D4—2981no—
278C2×D4—2981no—
279C2×D4—2981no—
280C2×D4—2981no—
281C2×D4—2981no—
282C2×D4—2981no—
283C2×D4—2981no—
284C2×D4—2981no—
285C2×D4—5961no—
286C2×D4—5961no—
287C2×D4—5961no—
288C2×D4—5961no—
289C2×D4—1491no—
290C2×D4—1491no—
291C2×D4—1491no—
292C2×D4—1491no—
293C2×D4—1491no—
294C2×D4—1491no—
295C2×D4C22×D14911yescharacteristic
296C22×C4—1491no—
297C22×C4—1491no—
298C22×C4C22×D14911yescharacteristic
299D8—5961no—
300D8—5961no—
301D8—5961no—
302D8—5961no—
303M16—5961no—
304C2×C8—5961no—
305C2×C8—1491no—
306C2×C8—1491no—
307C2×C8C22×D14911yescharacteristic
308C2×C8C22×D14911yescharacteristic
309C4⋊C4—1491no—
310C4⋊C4C22×D14911yescharacteristic
311C4⋊C4C22×D14911yescharacteristic
312C4⋊C4C22×D14911yescharacteristic
313C22⋊C4—21no—
314C22⋊C4—21no—
315C22⋊C4—2981no—
316C22⋊C4—2981no—
317C22⋊C4—2981no—
318C22⋊C4—2981no—
319C22⋊C4—2981no—
320C22⋊C4—2981no—
321C22⋊C4—2981no—
322C22⋊C4—2981no—
323C42—21no—
324C42—2981no—
325C23—21no—
326C23—2981no—
327C23—2981no—
328C23—2981no—
329C23—5962no—
330C23—5962no—
331C23—1491no—
332C23—1491no—
333C23—11921no—
334C23—11921no—
335C23—11921no—
336C23—11921no—
337C23D4×D14911yescharacteristic
338Q8—5961no—
339D4—21no—
340D4—21no—
341D4—81no—
342D4—2981no—
343D4—2981no—
344D4—2981no—
345D4—2981no—
346D4—2981no—
347D4—2981no—
348D4—5961no—
349D4—5962no—
350D4—5961no—
351D4—5961no—
352D4—5962no—
353D4—11921no—
354D4—11921no—
355D4—11921no—
356D4—11921no—
357D4—11921no—
358D4—11921no—
359D4—11921no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—2981no—
366C2×C4—2981no—
367C2×C4—2981no—
368C2×C4—2981no—
369C2×C4—2981no—
370C2×C4—1491no—
371C2×C4—1491no—
372C2×C4D4×D14911yescharacteristic
373C2×C4C23×D14911yescharacteristic
374C8—21no—
375C8—21no—
376C8—2981no—
377C8—2981no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—2981no—
385C22—2981no—
386C22—2981no—
387C22—2981no—
388C22—2981no—
389C22—2981no—
390C22—5961no—
391C22—5961no—
392C22—5961no—
393C22—5961no—
394C22—5961no—
395C22—5961no—
396C22—5961no—
397C22—5961no—
398C22—5961no—
399C22—11924no—
400C22—11924no—
401C22C2×D4×D14911yescharacteristic
402C4—21no—
403C4—41no—
404C4—41no—
405C4—41no—
406C4—2981no—
407C4—2981no—
408C4—5961no—
409C4#1801195711yescharacteristic
410C4#1801195711yescharacteristic
411C2—41no—
412C2—81no—
413C2—5961no—
414C2—5961no—
415C2—11921no—
416C2—11921no—
417C2—11921no—
418C2#2375018611yescharacteristic
419C2#2375042711yescharacteristic
420C2#2375042911yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#482×C149C2
socleC22×C149C22×D4
hypercenter#482D149
hypocenterC149#3199
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #23750194C2semidirect
2. #23750191C2semidirect
3. #23749952C2semidirect
4. #23749951C2semidirect
5. #23749949C2semidirect
6. #23749879C2semidirect
7. #23749877C2semidirect
8. #23749862C2semidirect
9. #23749860C2semidirect
10. #23749761C2semidirect
11. #23749760C2semidirect
12. #23749760C2semidirect
13. #23749758C2semidirect
14. #23749590C2semidirect
15. #482×C149C2semidirect
17. C22×D596C22semidirect
18. C2×D4×D149C22semidirect
23. C2×#14558719C22semidirect
24. C2×C8×D149C22semidirect
31. #18011886C22semidirect
32. #18011886C22semidirect
33. #18011886C22semidirect
35. #18011882C22semidirect
40. #18011869C22semidirect
41. #18011844C22semidirect
42. #18011842C22semidirect
43. #18011833C22semidirect
44. #18011833C22semidirect
45. #18011831C22semidirect
46. #18011831C22semidirect
47. #18011831C22semidirect
48. #18011831C22semidirect
49. C22⋊#11924746C22semidirect
50. #18011823C22semidirect
51. #18011823C22semidirect
53. #117×C149C22semidirect
54. #107×C149C22semidirect
55. #106×C149C22semidirect
56. #102×C149C22semidirect
57. #102×C149C22semidirect
58. C22⋊C8×C149C22semidirect
210. C149#3199semidirect
217. #482D149semidirect
253. #117C2×D149semidirect
255. #107C2×D149semidirect
257. #106C2×D149semidirect
264. #102C2×D149semidirect
265. #102C2×D149semidirect
269. C22⋊C8C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237501942
#237501912
#237499522
#237499512
#237499492
#237498792
#237498772
#237498622
#237498602
#237497612
#237497602
#237497582
#237495902
#482×C1492
#3199149