Finite Group Databasebeta

← #34055547

Subgroups — #34055547

Order 19072.

422 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750205C211yesmaximal, characteristic, complemented
2#23750192C211yesmaximal, characteristic, complemented
3#23749963C211yesmaximal, characteristic, complemented
4#23749950C211yesmaximal, characteristic, complemented
5#23749942C211yesmaximal, characteristic, complemented
6#23749937C211yesmaximal, characteristic, complemented
7#23749877C211yesmaximal, characteristic, complemented
8#23749868C211yesmaximal, characteristic, complemented
9#23749860C211yesmaximal, characteristic, complemented
10#23749851C211yesmaximal, characteristic, complemented
11#23749769C211yesmaximal, characteristic, complemented
12#23749769C211yesmaximal, characteristic, complemented
13#23749759C211yesmaximal, characteristic, complemented
14#23749590C211yesmaximal, characteristic, complemented
15#450×C149C211yesmaximal, characteristic, complemented
16C2×#14558737C2211yescharacteristic, complemented
17C2×#14558736C2211yescharacteristic
18C2×#14558721C2211yescharacteristic
19C2×#14558721C2211yescharacteristic
20C2×#14558719C2211yescharacteristic, complemented
21C2×C8×D149C2211yescharacteristic, complemented
22#18011907—21no—
23#18011898—21no—
24#18011889—21no—
25#18011887C2211yescharacteristic, complemented
26#18011886—21no—
27#18011886C2211yescharacteristic, complemented
28#18011885C2211yescharacteristic
29#18011884—21no—
30#18011884—21no—
31#18011882C2211yescharacteristic
32#18011882C2211yescharacteristic
33#18011882C2211yescharacteristic
34#18011882C2211yescharacteristic
35#18011880—21no—
36#18011880—21no—
37#18011870C2211yescharacteristic
38C4⋊C4×D149C2211yescharacteristic, complemented
39#18011845C2211yescharacteristic, complemented
40#18011844C2211yescharacteristic, complemented
41#18011843C2211yescharacteristic, complemented
42#18011842C2211yescharacteristic, complemented
43#18011835C2211yescharacteristic, complemented
44#18011835C2211yescharacteristic, complemented
45#18011833C2211yescharacteristic, complemented
46#18011833C2211yescharacteristic, complemented
47#18011832C2211yescharacteristic
48#18011832C2211yescharacteristic
49C22⋊#11924746C2211yescharacteristic
50#18011823C2211yescharacteristic, complemented
51#18011823C2211yescharacteristic, complemented
52C22×D4×C149C2211yescharacteristic
53C2×SD16×C149C2211yescharacteristic
54C2×SD16×C149C2211yescharacteristic
55C22⋊Q8×C149C2211yescharacteristic
56#102×C149C2211yescharacteristic
57#102×C149C2211yescharacteristic
58C22⋊C8×C149C2211yescharacteristic
59#14558737—41no—
60#14558737—41no—
61#14558736—41no—
62#14558736—41no—
63C2×Dic298D411yescharacteristic
64C2×D596—21no—
65C2×D596—21no—
66C2×D596D411yescharacteristic
67C2×D596C2311yescharacteristic
68C2×C22⋊D149—21no—
69C2×C22⋊D149—21no—
70C2×C22⋊D149—21no—
71C2×C22⋊D149—21no—
72C2×C22⋊D149—21no—
73C2×C22⋊D149D411yescharacteristic
74C2×C22⋊D149D411yescharacteristic
75C2×C4×D149—21no—
76C2×C4×D149—21no—
77C2×C4×D149C2311yescharacteristic
78C2×C4×D149C2311yescharacteristic
79#14558721—41no—
80#14558721—41no—
81#14558719—41no—
82C2×#11924746C2311yescharacteristic
83C2×#11924746C2311yescharacteristic
84C8×D149—41no—
85C4⋊Dic149C2311yescharacteristic
86C4⋊Dic149C2311yescharacteristic
87C4⋊Dic149C2311yescharacteristic
88#14558715—21no—
89#14558715—21no—
90C22⋊Dic149—21no—
91C22⋊Dic149—21no—
92C22⋊Dic149—21no—
93C22⋊Dic149—21no—
94C22⋊Dic149—21no—
95#14558713—21no—
96#14558713—21no—
97#14558713—21no—
98C4×Dic149—21no—
99C24×C149—21no—
100C2×Q8×C149C2311yescharacteristic
101C2×D4×C149—21no—
102C2×D4×C149—41no—
103C2×D4×C149—41no—
104C2×D4×C149C2311yescharacteristic
105C2×D4×C149C2311yescharacteristic
106C22×C4×C149C2311yescharacteristic
107SD16×C149—41no—
108SD16×C149—41no—
109C2×C8×C149C2311yescharacteristic
110C2×C8×C149C2311yescharacteristic
111C4⋊C4×C149—21no—
112C4⋊C4×C149C2311yescharacteristic
113C22⋊C4×C149—21no—
114C22×D149—21no—
115C22×D149C2×D411yescharacteristic
116C22×D149C2×D411yescharacteristic
117Dic298—41no—
118D596—21no—
119D596—21no—
120D596—41no—
121D596—42no—
122D596—81no—
123C22⋊D149—41no—
124C22⋊D149—41no—
125C22⋊D149—81no—
126C22⋊D149—81no—
127C22⋊D149—81no—
128C22⋊D149—81no—
129C22⋊D149—81no—
130C2×Dic149—21no—
131C2×Dic149—21no—
132C2×Dic149—21no—
133C2×Dic149C2×D411yescharacteristic
134C2×Dic149C2×D411yescharacteristic
135C4×D149—21no—
136C4×D149—21no—
137C4×D149—21no—
138C4×D149—21no—
139C4×D149—42no—
140C4×D149—81no—
141#11924746—21no—
142#11924746—21no—
143C23×C149—21no—
144C23×C149—21no—
145C23×C149—42no—
146C23×C149—81no—
147C23×C149—81no—
148C23×C149C2×D411yescharacteristic
149Q8×C149—21no—
150Q8×C149—21no—
151D4×C149—21no—
152D4×C149—21no—
153D4×C149—21no—
154D4×C149—21no—
155D4×C149—42no—
156C2×C4×C149—21no—
157C2×C4×C149—21no—
158C2×C4×C149—21no—
159C2×C4×C149—21no—
160C2×C4×C149C2×D411yescharacteristic
161C2×C4×C149C2411yescharacteristic
162C8×C149—21no—
163C8×C149—21no—
164C22×C149—21no—
165C22×C149—21no—
166C22×C149—21no—
167C22×C149—41no—
168C22×C149—41no—
169C22×C149—41no—
170C22×C149—41no—
171C22×C149—41no—
172C22×C149—41no—
173C22×C149—84no—
174C22×C149C22×D411yescharacteristic
175C2×D149—21no—
176C2×D149—21no—
177C2×D149—21no—
178C2×D149—21no—
179C2×D149—21no—
180C2×D149—21no—
181C2×D149—41no—
182C2×D149—41no—
183C2×D149—41no—
184C4×C149—21no—
185C4×C149—41no—
186C4×C149—41no—
187C4×C149H(5,𝔽2)11yescharacteristic
188C4×C149H(5,𝔽2)11yescharacteristic
189Dic149—21no—
190Dic149—21no—
191Dic149—41no—
192Dic149—41no—
193Dic149—41no—
194C2×C149—41no—
195C2×C149—81no—
196C2×C149—81no—
197C2×C149#53411yescharacteristic
198C2×C149#57611yescharacteristic
199C2×C149#57711yescharacteristic
200D149—41no—
201D149—41no—
202D149—81no—
203C149#319811yescharacteristic, complemented, Sylow
204#3198—1491nomaximal, Sylow
205#537—1491no—
206#535—1491no—
207#485—1491no—
208#482—1491no—
209#481—1491no—
210#480—1491no—
211#469—1491no—
212#468—1491no—
213#466—1491no—
214#465—1491no—
215#450D14911yescharacteristic, complemented
216#449—1491no—
217#449—1491no—
218#447—1491no—
219#408—1491no—
220C2×#41—1491no—
221C2×#41—1491no—
222C22×D4C2×D14911yescharacteristic
223C2×SD16C2×D14911yescharacteristic
224C2×SD16C2×D14911yescharacteristic
225C2×D8—1491no—
226C2×D8—1491no—
227C2×M16—1491no—
228C22×C8—1491no—
229#127—2981no—
230#124—2981no—
231C22⋊Q8—2981no—
232C22⋊Q8—1491no—
233C22⋊Q8C2×D14911yescharacteristic
234#121—2981no—
235#121—2981no—
236#121—2981no—
237#121—1491no—
238#121—1491no—
239#121—1491no—
240#121—1491no—
241#121—1491no—
242#121—1491no—
243#120—2981no—
244#120—2981no—
245#117—1491no—
246C2×C4⋊C4—1491no—
247#107—1491no—
248#107—1491no—
249#106—1491no—
250#106—1491no—
251#103—1491no—
252#103—1491no—
253#102—1491no—
254#102—1491no—
255#102—1491no—
256#102—1491no—
257#102C2×D14911yescharacteristic
258#102C2×D14911yescharacteristic
259C22⋊C8—1491no—
260C22⋊C8—1491no—
261C22⋊C8—1491no—
262C22⋊C8C2×D14911yescharacteristic
263C24—21no—
264#41—5961no—
265#41—5961no—
266#41—5961no—
267#41—5961no—
268C2×Q8—1491no—
269C2×Q8C22×D14911yescharacteristic
270C2×D4—21no—
271C2×D4—41no—
272C2×D4—41no—
273C2×D4—2981no—
274C2×D4—2981no—
275C2×D4—2981no—
276C2×D4—2981no—
277C2×D4—2981no—
278C2×D4—2981no—
279C2×D4—2981no—
280C2×D4—1491no—
281C2×D4—1491no—
282C2×D4—1491no—
283C2×D4—1491no—
284C2×D4C22×D14911yescharacteristic
285C2×D4C22×D14911yescharacteristic
286C22×C4—2981no—
287C22×C4—2981no—
288C22×C4—1491no—
289C22×C4—1491no—
290C22×C4C22×D14911yescharacteristic
291SD16—41no—
292SD16—41no—
293D8—5961no—
294D8—5961no—
295M16—5961no—
296C2×C8—5961no—
297C2×C8—1491no—
298C2×C8—1491no—
299C2×C8C22×D14911yescharacteristic
300C2×C8C22×D14911yescharacteristic
301C4⋊C4—21no—
302C4⋊C4—2981no—
303C4⋊C4—2981no—
304C4⋊C4—1491no—
305C4⋊C4—1491no—
306C4⋊C4—1491no—
307C4⋊C4C22×D14911yescharacteristic
308C22⋊C4—21no—
309C22⋊C4—2981no—
310C22⋊C4—2981no—
311C22⋊C4—2981no—
312C22⋊C4—2981no—
313C22⋊C4—2981no—
314C22⋊C4—2981no—
315C22⋊C4—2981no—
316C22⋊C4—2981no—
317C42—2981no—
318C23—21no—
319C23—21no—
320C23—42no—
321C23—81no—
322C23—81no—
323C23—2981no—
324C23—1491no—
325C23—1491no—
326C23D4×D14911yescharacteristic
327Q8—21no—
328Q8—21no—
329Q8—5961no—
330D4—21no—
331D4—21no—
332D4—21no—
333D4—21no—
334D4—42no—
335D4—2981no—
336D4—2981no—
337D4—5961no—
338D4—5962no—
339D4—5961no—
340D4—5961no—
341D4—11921no—
342D4—11921no—
343D4—11921no—
344D4—11921no—
345D4—11921no—
346D4—11921no—
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—2981no—
358C2×C4—5962no—
359C2×C4—1491no—
360C2×C4—1491no—
361C2×C4—11921no—
362C2×C4D4×D14911yescharacteristic
363C2×C4C23×D14911yescharacteristic
364C8—21no—
365C8—21no—
366C8—2981no—
367C8—2981no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—84no—
378C22—2981no—
379C22—2981no—
380C22—2981no—
381C22—2981no—
382C22—2981no—
383C22—2981no—
384C22—5961no—
385C22—5961no—
386C22—5961no—
387C22C2×D4×D14911yescharacteristic
388C4—21no—
389C4—41no—
390C4—41no—
391C4—2981no—
392C4—2981no—
393C4—5961no—
394C4—5961no—
395C4—5961no—
396C4#1801195611yescharacteristic
397C4#1801195611yescharacteristic
398C2—41no—
399C2—81no—
400C2—81no—
401C2—5961no—
402C2—5961no—
403C2—11921no—
404C2#2375018511yescharacteristic
405C2#2375042911yescharacteristic
406C2#2375043111yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#450×C149C2
socleC22×C149C22×D4
hypercenter#450D149
hypocenterC149#3198
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #23750205C2semidirect
2. #23750192C2semidirect
3. #23749963C2semidirect
4. #23749950C2semidirect
5. #23749942C2semidirect
6. #23749937C2semidirect
7. #23749877C2semidirect
8. #23749868C2semidirect
9. #23749860C2semidirect
10. #23749851C2semidirect
11. #23749769C2semidirect
12. #23749769C2semidirect
13. #23749759C2semidirect
14. #23749590C2semidirect
15. #450×C149C2semidirect
16. C2×#14558737C22semidirect
20. C2×#14558719C22semidirect
21. C2×C8×D149C22semidirect
25. #18011887C22semidirect
27. #18011886C22semidirect
38. C4⋊C4×D149C22semidirect
39. #18011845C22semidirect
40. #18011844C22semidirect
41. #18011843C22semidirect
42. #18011842C22semidirect
43. #18011835C22semidirect
44. #18011835C22semidirect
45. #18011833C22semidirect
46. #18011833C22semidirect
50. #18011823C22semidirect
51. #18011823C22semidirect
203. C149#3198semidirect
215. #450D149semidirect

Maximal subgroups

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

subgroupindex
#237502052
#237501922
#237499632
#237499502
#237499422
#237499372
#237498772
#237498682
#237498602
#237498512
#237497692
#237497592
#237495902
#450×C1492
#3198149