Finite Group Databasebeta

← #34056497

Subgroups — #34056497

Order 19072.

494 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
1#23750275C211yesmaximal, characteristic, complemented
2D4×C22⋊D149C211yesmaximal, characteristic, complemented
3#23749970C211yesmaximal, characteristic, complemented
4#23749939C211yesmaximal, characteristic, complemented
5#23749937C211yesmaximal, characteristic, complemented
6#23749903C211yesmaximal, characteristic, complemented
7#23749859C211yesmaximal, characteristic, complemented
8#23749858C211yesmaximal, characteristic, complemented
9#23749818C211yesmaximal, characteristic, complemented
10#23749757C211yesmaximal, characteristic, complemented
11D8×Dic149C211yesmaximal, characteristic, complemented
12#23749688C211yesmaximal, characteristic, complemented
13C2×#18011832C211yesmaximal, characteristic, complemented
14#102×D149C211yesmaximal, characteristic, complemented
15#447×C149C211yesmaximal, characteristic, complemented
16C2×#14558735—21no—
17C22×C22⋊D149—21no—
18C2×D4×D149C2211yescharacteristic
19C2×#14558721C2211yescharacteristic, complemented
20C22×#11924746C2211yescharacteristic, complemented
21C2×C8×D149C2211yescharacteristic, complemented
22#18011910C2211yescharacteristic, complemented
23#18011907C2211yescharacteristic
24#18011893—21no—
25#18011892—21no—
26#18011888—21no—
27#18011885C2211yescharacteristic
28#18011883—21no—
29#18011882C2211yescharacteristic
30#18011882C2211yescharacteristic, complemented
31#18011880—21no—
32#18011879—21no—
33D4×Dic149C2211yescharacteristic
34D4×Dic149C2211yescharacteristic, complemented
35C4×C22⋊D149C2211yescharacteristic
36C2×C4⋊Dic149C2211yescharacteristic, complemented
37C4⋊C4×D149C2211yescharacteristic, complemented
38#18011845C2211yescharacteristic, complemented
39#18011845C2211yescharacteristic, complemented
40#18011844C2211yescharacteristic, complemented
41#18011840C2211yescharacteristic, complemented
42#18011833C2211yescharacteristic, complemented
43#18011833C2211yescharacteristic, complemented
44#18011832C2211yescharacteristic
45#18011832C2211yescharacteristic
46#18011832C2211yescharacteristic, complemented
47#18011832C2211yescharacteristic, complemented
48#18011832C2211yescharacteristic, complemented
49#18011831C2211yescharacteristic, complemented
50#18011823C2211yescharacteristic, complemented
51C8×Dic149C2211yescharacteristic, complemented
52C22×D4×C149C2211yescharacteristic
53C2×D8×C149C2211yescharacteristic
54C2×D8×C149C2211yescharacteristic, complemented
55#121×C149C2211yescharacteristic, complemented
56#102×C149C2211yescharacteristic
57#102×C149C2211yescharacteristic, complemented
58C22⋊C8×C149C2211yescharacteristic, complemented
59C23×D149—21no—
60#14558735—44no—
61C2×Dic298—21no—
62C2×D596C2311yescharacteristic
63C2×C22⋊D149—21no—
64C2×C22⋊D149—21no—
65C2×C22⋊D149—21no—
66C2×C22⋊D149—21no—
67C2×C22⋊D149—21no—
68C2×C22⋊D149—21no—
69C2×C22⋊D149—44no—
70C2×C22⋊D149D411yescharacteristic
71D4×D149—22no—
72D4×D149—41no—
73C22×Dic149—21no—
74C22×Dic149—21no—
75C22×Dic149—21no—
76C2×C4×D149—21no—
77C2×C4×D149C2311yescharacteristic
78#14558721—41no—
79C2×#11924746—41no—
80C2×#11924746C2311yescharacteristic
81C2×#11924746C2311yescharacteristic
82C8×D149—41no—
83C4⋊Dic149—21no—
84C4⋊Dic149C2311yescharacteristic
85C4⋊Dic149C2311yescharacteristic
86C4⋊Dic149C2311yescharacteristic
87#14558715—21no—
88#14558715—21no—
89#14558715D411yescharacteristic
90C22⋊Dic149—21no—
91C22⋊Dic149—21no—
92C22⋊Dic149—21no—
93C22⋊Dic149—21no—
94C22⋊Dic149D411yescharacteristic
95#14558713—21no—
96#14558713D411yescharacteristic
97C4×Dic149C2311yescharacteristic
98C24×C149—21no—
99C2×D4×C149—22no—
100C2×D4×C149—21no—
101C2×D4×C149—21no—
102C2×D4×C149—41no—
103C2×D4×C149C2311yescharacteristic
104C2×D4×C149C2311yescharacteristic
105C2×D4×C149C2311yescharacteristic
106C22×C4×C149C2311yescharacteristic
107D8×C149—22no—
108D8×C149—41no—
109C2×C8×C149C2311yescharacteristic
110C2×C8×C149C2311yescharacteristic
111C4⋊C4×C149C2311yescharacteristic
112C22⋊C4×C149—21no—
113C22×D149—21no—
114C22×D149—42no—
115C22×D149—42no—
116C22×D149—81no—
117C22×D149C2×D411yescharacteristic
118Dic298—42no—
119D596—21no—
120D596—21no—
121C22⋊D149—42no—
122C22⋊D149—42no—
123C22⋊D149—42no—
124C22⋊D149—42no—
125C22⋊D149—42no—
126C22⋊D149—81no—
127C22⋊D149D814yescomplemented
128C2×Dic149—21no—
129C2×Dic149—21no—
130C2×Dic149—21no—
131C2×Dic149—42no—
132C2×Dic149—42no—
133C2×Dic149—42no—
134C2×Dic149C2×D411yescharacteristic
135C2×Dic149C2×D411yescharacteristic
136C2×Dic149C2×D411yescharacteristic
137C4×D149—21no—
138C4×D149—21no—
139C4×D149—42no—
140#11924746—21no—
141#11924746—21no—
142C23×C149—21no—
143C23×C149—21no—
144C23×C149—21no—
145C23×C149—42no—
146C23×C149—42no—
147C23×C149—81no—
148C23×C149C2×D411yescharacteristic
149D4×C149—21no—
150D4×C149—21no—
151D4×C149—21no—
152D4×C149—21no—
153D4×C149—21no—
154D4×C149—42no—
155D4×C149—42no—
156D4×C149#4112yescomplemented
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—22no—
167C22×C149—41no—
168C22×C149—41no—
169C22×C149—41no—
170C22×C149—41no—
171C22×C149—41no—
172C22×C149—41no—
173C22×C149—41no—
174C22×C149—41no—
175C22×C149—84no—
176C22×C149C2×D812yes—
177C22×C149C22×D411yescharacteristic
178C2×D149—21no—
179C2×D149—21no—
180C2×D149—41no—
181C2×D149—41no—
182C2×D149—41no—
183C2×D149—84no—
184C2×D149C2×D812yes—
185C4×C149—21no—
186C4×C149—41no—
187C4×C149C2×#4111yescharacteristic
188C4×C149H(5,𝔽2)11yescharacteristic
189Dic149—21no—
190Dic149—21no—
191Dic149—41no—
192Dic149—41no—
193Dic149—41no—
194Dic149C2×D812yes—
195C2×C149—22no—
196C2×C149—42no—
197C2×C149—81no—
198C2×C149—81no—
199C2×C149#54611yescharacteristic
200C2×C149C22×D811yescharacteristic
201C2×C149#57711yescharacteristic
202D149—22no—
203D149—81no—
204C149#329411yescharacteristic, complemented, Sylow
205#3294—1491nomaximal, Sylow
206#547—1491no—
207D42—1491no—
208#486—1491no—
209#480—1491no—
210#480—1491no—
211#474—1491no—
212#466—1491no—
213#466—1491no—
214#459—1491no—
215#447—1491no—
216#447D14911yescharacteristic, complemented
217C4×D8—1491no—
218C8×D4—1491no—
219C2×#102—1491no—
220C2×#102—1491no—
221C2×#41—2981no—
222C22×D4—2981no—
223C22×D4—1491no—
224C22×D4C2×D14911yescharacteristic
225C2×D8—1491no—
226C2×D8C2×D14911yescharacteristic
227C2×D8C2×D14911yescharacteristic, complemented
228C22×C8—1491no—
229C22×C8—1491no—
230C4⋊Q8—1491no—
231#127—1491no—
232#123—2981no—
233#123—2981no—
234C22⋊Q8—2981no—
235#121—2981no—
236#121—1491no—
237#121—1491no—
238#121—1491no—
239#121C2×D14911yescharacteristic, complemented
240#120—2981no—
241#120—2981no—
242C4×D4—1491no—
243C4×D4—1491no—
244C4×D4—1491no—
245C2×C4⋊C4—1491no—
246C2×C4⋊C4—1491no—
247#107—1491no—
248#107—1491no—
249#107—1491no—
250C4⋊C8—1491no—
251#102—1491no—
252#102—1491no—
253#102—1491no—
254#102—1491no—
255#102—1491no—
256#102—1491no—
257#102—1491no—
258#102—1491no—
259#102C2×D14911yescharacteristic
260#102C2×D14911yescharacteristic, complemented
261C22⋊C8—1491no—
262C22⋊C8C2×D14911yescharacteristic, complemented
263C4×C8—1491no—
264C24—21no—
265C24—2981no—
266#41—5964no—
267C2×Q8—2981no—
268C2×D4—22no—
269C2×D4—21no—
270C2×D4—21no—
271C2×D4—41no—
272C2×D4—2982no—
273C2×D4—2981no—
274C2×D4—2981no—
275C2×D4—2981no—
276C2×D4—2981no—
277C2×D4—2981no—
278C2×D4—2981no—
279C2×D4—5961no—
280C2×D4—5964no—
281C2×D4—1491no—
282C2×D4—1491no—
283C2×D4C22×D14911yescharacteristic
284C2×D4C22×D14911yescharacteristic
285C2×D4C22×D14911yescharacteristic
286C22×C4—2981no—
287C22×C4—2981no—
288C22×C4—2981no—
289C22×C4—2981no—
290C22×C4—1491no—
291C22×C4C22×D14911yescharacteristic
292D8—22no—
293D8—41no—
294D8—5961no—
295C2×C8—5961no—
296C2×C8—5961no—
297C2×C8—1491no—
298C2×C8—1491no—
299C2×C8C22×D14911yescharacteristic
300C2×C8C22×D14911yescharacteristic
301C4⋊C4—2981no—
302C4⋊C4—2981no—
303C4⋊C4—2981no—
304C4⋊C4—1491no—
305C4⋊C4—1491no—
306C4⋊C4—1491no—
307C4⋊C4—1491no—
308C4⋊C4C22×D14911yescharacteristic
309C22⋊C4—21no—
310C22⋊C4—2981no—
311C22⋊C4—2981no—
312C22⋊C4—2981no—
313C22⋊C4—2981no—
314C22⋊C4—2981no—
315C22⋊C4—1491no—
316C22⋊C4—1491no—
317C42—1491no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23—42no—
322C23—42no—
323C23—81no—
324C23—2981no—
325C23—5962no—
326C23—5962no—
327C23—1491no—
328C23—11921no—
329C23D4×D14911yescharacteristic
330Q8—5962no—
331D4—21no—
332D4—21no—
333D4—21no—
334D4—21no—
335D4—21no—
336D4—42no—
337D4—42no—
338D4—2981no—
339D4—2981no—
340D4—5962no—
341D4—5962no—
342D4—5962no—
343D4—5962no—
344D4—5962no—
345D4—1494no—
346D4—11921no—
347D4#1455873512yescomplemented
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—5962no—
357C2×C4—5962no—
358C2×C4—5962no—
359C2×C4—5962no—
360C2×C4—1491no—
361C2×C4—1491no—
362C2×C4—1491no—
363C2×C4D4×D14911yescharacteristic
364C2×C4C23×D14911yescharacteristic
365C8—21no—
366C8—21no—
367C8—2981no—
368C8—2981no—
369C22—21no—
370C22—21no—
371C22—22no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—84no—
381C22—2981no—
382C22—2981no—
383C22—5961no—
384C22—5961no—
385C22—5961no—
386C22—1492no—
387C22—11924no—
388C22D8×D14912yes—
389C22C2×D4×D14911yescharacteristic
390C4—21no—
391C4—41no—
392C4—2981no—
393C4—2981no—
394C4—5961no—
395C4—5961no—
396C4—5961no—
397C4—1492no—
398C4C2×#1455873511yescharacteristic
399C4#1801195611yescharacteristic
400C2—22no—
401C2—42no—
402C2—81no—
403C2—81no—
404C2—2982no—
405C2—11921no—
406C2#2375026211yescharacteristic
407C2C2×D8×D14911yescharacteristic
408C2#2375043511yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#447×C149C2
socleC22×C149C22×D4
hypercenter#447D149
hypocenterC149#3294
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #23750275C2semidirect
2. D4×C22⋊D149C2semidirect
3. #23749970C2semidirect
4. #23749939C2semidirect
5. #23749937C2semidirect
6. #23749903C2semidirect
7. #23749859C2semidirect
8. #23749858C2semidirect
9. #23749818C2semidirect
10. #23749757C2semidirect
11. D8×Dic149C2semidirect
12. #23749688C2semidirect
13. C2×#18011832C2semidirect
14. #102×D149C2semidirect
15. #447×C149C2semidirect
19. C2×#14558721C22semidirect
20. C22×#11924746C22semidirect
21. C2×C8×D149C22semidirect
22. #18011910C22semidirect
30. #18011882C22semidirect
34. D4×Dic149C22semidirect
36. C2×C4⋊Dic149C22semidirect
37. C4⋊C4×D149C22semidirect
38. #18011845C22semidirect
39. #18011845C22semidirect
40. #18011844C22semidirect
41. #18011840C22semidirect
42. #18011833C22semidirect
43. #18011833C22semidirect
46. #18011832C22semidirect
47. #18011832C22semidirect
48. #18011832C22semidirect
49. #18011831C22semidirect
50. #18011823C22semidirect
51. C8×Dic149C22semidirect
54. C2×D8×C149C22semidirect
55. #121×C149C22semidirect
57. #102×C149C22semidirect
58. C22⋊C8×C149C22semidirect
127. C22⋊D149D8semidirect
156. D4×C149#41semidirect
204. C149#3294semidirect
216. #447D149semidirect
227. C2×D8C2×D149semidirect
239. #121C2×D149semidirect
260. #102C2×D149semidirect
262. C22⋊C8C2×D149semidirect
347. D4#14558735semidirect

Maximal subgroups

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

subgroupindex
#237502752
D4×C22⋊D1492
#237499702
#237499392
#237499372
#237499032
#237498592
#237498582
#237498182
#237497572
D8×Dic1492
#237496882
C2×#180118322
#102×D1492
#447×C1492
#3294149